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Digital simulation of a crushing plant Hatch, Christopher 1977

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DIGITAL SIMULATION OF A CRUSHING PLANT by C h r i s t o p h e r Ha tch , B . A . S c . U n i v e r s i t y o f B r i t i s h Columbia , Canada, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Mineral Engineering We accept t h i s t h e s i s as conforming to the r equ i r ed s tandard . THE UNIVERSITY OF BRITISH COLUMBIA (c} Christopher Hatch, 1977 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Depa rtment The University of Brit ish Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date - i i -ABSTRACT To improve upon the unders tanding and e f f i c i e n c y o f the c r u s h i n g / i s c reen ing p roces s , the Brenda Mines L i m i t e d secondary c rush ing p l a n t was s imu la t ed . The p l a n t c o n s i s t s o f two stages o f c r u s h i n g , w i t h a s i n g l e stage o f s c r een ing employed i n c l o s e d c i r c u i t w i th the l a t t e r c rush ing s tage . A c q u i s i t i o n o f p l a n t data was c a r r i e d out accord ing to f u l l o r mod i f i ed f a c t o r i a l designs intended to cover normal ope ra t ing ranges. The un i t s sampled i n c l u d e a Symons Nordberg 7 - foot s tandard cone c r u s h e r , a Symons Nordberg 7 - foot shor t -head cone c rusher and two A l l i s - C h a l m e r s 8 f t . x 2 0 f t . double deck v i r b r a t i n g sc reens . Sampling was c a r r i e d out under c o n d i t i o n s as c l o s e to steady s t a t e as was p o s s i b l e . A l l samples were screened a t the p l a n t us ing a s t anda r i zed procedure. Raw data ob ta ined around the screens was l a t e r adjus ted by means o f a l e a s t squares technique tha t assumes a l l measured values are i n e r r o r . The models developed to desc r ibe both c rush ing opera t ions are m o d i f i c a t i o n s o f those used a t Mt. I sa Mines L i m i t e d . The model para-meters were e m p i r i c a l l y f i t t e d to the observed da ta . Both models gave s a t i s f a c t o r y performance. The model proposed f o r the v i b r a t i n g screens was de r i ved from smal l p a r t i c l e s t a t i s t i c s . I t i s continuous over a l l s i z e ranges and was judged to perform s a t i s f a c t o r i l y . Models f o r the shor t -head crushers and the screens can be e x t r a p o l a t e d approximate ly twenty percent beyond t h e i r f i t t e d data ranges. The f i t t e d models were combined to enable a s t e a d y - s t a t e s i m u l a t i o n o f the complete secondary c ru sh ing p l a n t . A study o f the s i m u l a t i o n was performed i n accordance w i th a f u l l f a c t o r i a l design modi f i ed to i n c l u d e in te rmedia te ranges. Opera t ing v a r i a b l e s whose values were generated dur ing the s i m u l a t i o n remained w i t h i n t h e i r f i t t e d ranges, w i th the excep t ion o f the shor t -head c rusher feedra te . P re -l i m i n a r y a n a l y s i s o f the s i m u l a t i o n output shows t ha t the r e s u l t s conform to expected and observed p l a n t behav io r . Fur the r a n a l y s i s w i t h respec t to shor t -head c rusher power draw i n d i c a t e s t ha t i t may be p o s s i b l e to inc rease p l a n t c a p a c i t y under some c o n d i t i o n s . The economic advantage o f a d i g i t a l s i m u l a t i o n i s demonstrated by the f a c t t ha t the average cos t f o r one computer run i s approximate ly twenty cen t s . - i v -TABLE OF CONTENTS Page ABSTRACT i i LIST OF FIGURES v i i i LIST OF TABLES x i i LIST OF SYMBOLS x i v ACKNOWLEDGEMENTS x i x CHAPTER I :: INTRODUCTION 1.1 Statement o f Ob jec t ives 1 1.2 L i t e r a t u r e Survey 3 (a) Summary o f Comminution D i s t r i b u t i o n Funct ions 4 1.3 The Cone Crusher Model 6 1.4 The V i b r a t i n g Screen Model 7 CHAPTER I I DATA ACQUISITION 2.1 D e s c r i p t i o n o f Crushing P l a n t (a) In t roduc t ion 10 (b) The Primary Crusher 10 (c) The Secondary Crusher 12 (d) The Secondary Screens 12 (e) The T e r t i a r y Crushers 13 (f) General 14 2.2 Procedures f o r A c q u i s i t i o n o f Raw Data (a) In t roduc t ion 15 (b) Secondary Crusher Sampling 29 (c) T e r t i a r y Crusher Sampling 32 (d) Secondary Screen Sampling 36 (e) Primary Fines Sampling 41 2 .3 Sample Screening 42 CHAPTER I I I DATA ADJUSTMENT 3.1 The Secondary and T e r t i a r y Crushers 44 3.2 The Secondary Screens 44 - V -Page CHAPTER IV MODEL DEVELOPMENT 4.1 Summary o f Development Procedures 49 4.2 The Secondary Crusher Model 51 (a) The Breakage M a t r i x , B 51 (b) The C l a s s i f i c a t i o n M a t r i x , C 56 (c) The Crusher Curren t 57 (d) Model Accuracy and Range 58 4 .3 The T e r t i a r y Crusher Model 62 (a) The Breakage M a t r i x , B 62 (b) The C l a s s i f i c a t i o n M a t r i x , C 63 (c) The Crusher Curren t 64 (d) Model Accuracy and Range 64 4.4 The Secondary Screen Model 69 (a) Model D e s c r i p t i o n 70 (b) Model Behavior 72 (c) Model Accuracy and Range 75 4 .5 The Pr imary Fines Model 76 (a) Model D e s c r i p t i o n 80 (b) Model Accuracy 82 CHAPTER V SIMULATION OF THE CRUSHING PLANT 5.1 The S i m u l a t i o n Programs 84 5.2 Methodology Employed to Study the S imu la t i on Program PGM2 86 CHAPTER VI DISCUSSION 6.1 A n a l y s i s o f S i m u l a t i o n Output (a) General 91 (b) P l a n t Feedrate 96 (c) P l a n t Feed S i ze D i s t r i b u t i o n 98 (d) Secondary Crusher Gap 98 (e) Secondary Screen Opening 101 ( f ) T e r t i a r y Crusher Gap 103 (g) E f f e c t s o f V a r i a b l e s on Responses 107 (h) T e r t i a r y Crusher Curren t 110 6.2 P o t e n t i a l A p p l i c a t i o n s f o r the S imu la t i on Programs 116 - v i -Page. SUMMARY AND CONCLUSIONS 119 RECOMMENDATIONS FOR FURTHER WORK 121 BIBLIOGRAPHY 123 APPENDICES A. Major Equipment S p e c i f i c a t i o n s f o r Secondary Crush ing P l a n t (a) Secondary and T e r t i a r y Crushers 127 (b) Primary and Secondary V i b r a t i n g Screens 131 Measured (Raw) Data (a) S i z e D i s t r i b u t i o n s f o r Secondary Crusher Samples 135 (b) S i z e D i s t r i b u t i o n s f o r T e r t i a r y Crusher Samples 137 (c) S i z e D i s t r i b u t i o n s f o r Secondary Screens Samples 139 (d) S i z e D i s t r i b u t i o n s f o r Primary Screens Unders ize Samples 142 (e) Flowrate Record f o r Primary Screens Unders ize Stream 143 C. Adjustment o f Secondary Screen Data (a) L i s t i n g o f the Program SCREEN, a Program 147 Developed f o r Adjustment o f Raw Screen Data (b) Adjus ted Data f o r the Secondary Screens 152 D. L i s t i n g o f Computer Programs (a) ALLREDD, a Program f o r M u l t i - v a r i a b l e 169 L i n e a r Regression A n a l y s i s (b) TRANS4, a Support Program f o r ALLREDD 173 to Permit Data Transformat ion E. Summary o f the Secondary Crusher Model (a) L i s t i n g o f the Model F i t t i n g Program TURKEY 175 (b) L i s t i n g o f the Secondary Crusher Mode l , SECRUSH 180 (c) Output from SECRUSH - Model P r e d i c t i o n s f o r 183 Observed Data - v i i -Page F. Summary o f the T e r t i a r y Crusher Model (a) L i s t i n g o f the Model F i t t i n g Program TURKEY 189 (b) L i s t i n g o f the T e r t i a r y Crusher Model , TERCR 194 (c) Output from TERCR - Model P r e d i c t i o n s f o r 197 Observed Data G. D e r i v a t i o n o f a Screen E f f i c i e n c y Equat ion 203 H. Summary o f Secondary Screen Model (a) L i s t i n g o f the Model F i t t i n g Program SCRN5 212 (b) L i s t i n g o f the Secondary Screen Mode l , SCRN3 217 (c) Output from SCRN3 - Model P r e d i c t i o n s f o r 220 Observed Data I . Summary.of the Primary Fines Model (a) L i s t i n g o f the Model F i t t i n g Program TURKEY 232 (b) L i s t i n g o f the Primary Fines Mode l , PF 236 (c) Output from PF - Model P r e d i c t i o n s f o r 238 Observed Data J . Secondary Crushing P l a n t S imu la t i on Programs (a) L i s t i n g o f the S i m i l a t i o n Program M2 ( i ) Main Program M2 243 ( i i ) Subprogram SCMS (Secondary Crusher) 247 ( i i i ) Subprogram TCMS ( T e r t i a r y Crusher) 249 ( i v ) Subprogram PRNT1 ( P r i n t o u t ) 251 (v) Subprogram PRNT2 ( P r i n t o u t ) 253 (b) Sample Outputs from Program M2 (2) 255 (c) L i s t i n g o f the S i m u l a t i o n Program PGM2 263 (d) Sample Outputs from Program PGM2 (2) 268 K. Output from S i m u l a t i o n S tud ies (a) F u l l F a c t o r i a l Design Study 272 (b) Intermediate Ranges Study 302 L . Computation o f E f f e c t s o f S imu la t i on V a r i a b l e s 329 on Responses - v i i i -LIST OF FIGURES Figure Page 1 Schematic Representa t ion o f a Cone Crusher 6 2 Geometric Cons ide ra t ions f o r D e r i v a t i o n o f Screening P r o b a b i l i t y 7 3 E f f i c i e n c y Curve f o r Whiten Screen Model 9 4 G e n e r a l i z e d Crushing P l a n t Flowsheet 11 5 M o d i f i c a t i o n s to Secondary and T e r t i a r y Crusher Mantles 14 (a) Standard Crushers (b) Short -head Crushers 6 F a c t o r i a l Design Used f o r Sampling Schedules 18 7 General Views o f the Brenda Crush ing P l a n t (a) P h y s i c a l Loca t ions o f Crushing P l a n t Components 19 (b) I n t e r i o r View o f the S e c o n d a r y / T e r t i a r y Crusher B u i l d i n g 20 (c) I n t e r i o r View o f the Secondary Screens B u i l d i n g 21 (d) D e t a i l e d View o f the I n t e r i o r o f a Secondary Screen 21 (e) The Secondary Crushing P l a n t Con t ro l Room 22 8 L o c a t i o n o f Sample Po in t s (a) Secondary Crushing P l a n t Flowsheet Showing Sample Loca t ions 24 (b) Sample P o i n t f o r Secondary Crusher Feed 25 (c) Sample P o i n t f o r Secondary Crusher P roduc t , Secondary Screen Feed and T e r t i a r y Crusher Product 25 (d) Sample P o i n t f o r T e r t i a r y - C r u s h e r Feed 26 (e) Sample P o i n t s f o r Secondary Screen Overs ize and Unders ize Products 27 ( f ) Sample P o i n t f o r Pr imary Screens Unders ize Product (Pr imary F ines) 27 (g) Sample Screening S t a t i o n 28 - i x -Figure 9 Exper imenta l Design f o r Secondary Crushers 10 Exper imental Design f o r T e r t i a r y Crushers 11 Segregat ion Trends w i t h i n Screen Surge Bin 12 Combined Exper imental Design f o r Secondary Screens 13 Schematic Diagram f o r Mass Balance o f a Secondary Screen 14 Computational Procedure f o r Pr imary Breakage Component, B l 15 Computational Procedure f o r Secondary Breakage Component, B2 16 R e l a t i v e C o n t r i b u t i o n s o f Breakage Funct ion Components, B l and B2 17 C l a s s i f i c a t i o n Func t ion c(x) 18 (a) Performance o f Secondary Crusher Mode l , Best P r e d i c t i o n (b) Performance o f Secondary Crusher Mode l , Worst P r e d i c t i o n 19 Behavior o f T e r t i a r y Crusher Model Parameters (a) Parameter a (b) Parameter 3 (c) Parameter k l (d) Parameter k2 20 (a) Performance o f T e r t i a r y Crusher Mode l , Best P r e d i c t i o n (b) Performance o f T e r t i a r y Crusher Mode l , Worst P r e d i c t i o n 21 Behavior o f A l t e r n a t i v e k2 R e l a t i o n 22 (a) Behav io r o f Screen E f f i c i e n c y as a Funct ion o f Parameter x 5 0 (a=2.0 cm 3) (b) Behav ior o f Screen E f f i c i e n c y as a Funct ion o f Parameter a ( x 5 0 = 1 . 9 2 cm) - x -Fi gure Page 23 (a) Performance of Secondary Screen Mode l , Best P r e d i c t i o n 77 (b) Performance o f Secondary Screen Mode l , Worst P r e d i c t i o n 78 (c) Performance o f Secondary Screen Mode l , Second Worst P r e d i c t i o n 79 24 Behavior o f Pr imary Fines Model Parameters 81 (a) Parameters b 0 and b1 (b) Parameter b 2 25 S imu la t i on Flow Diagram 85 26 The Inf luence o f P l a n t Feedrate on S i m u l a t i o n Responses 97 27 The Inf luence o f Percent + 1 Inch i n P l a n t Feed on S i m u l a t i o n Responses 99 28 The Inf luence o f Secondary Crusher Gap on S imu la t i on Responses 100 29 The Inf luence o f Secondary Screen Opening on S imu la t i on Responses 102 30 The Inf luence o f T e r t i a r y Crusher Gap on S imu la t i on Responses 104 31 (a) Behav ior o f R a t i o A as a Funct ion o f T e r t i a r y Crusher Gap 106 (b) Behav ior o f R a t i o A as a Funct ion o f P a r t i c l e S i ze 106 32 Behav ior o f T e r t i a r y Crusher Curren t Draw as a Funct ion o f Feedrate f o r Constant Crusher Gap 111 33 Ind ica t ed Capac i ty Increases f o r T e r t i a r y Crushers 1-13 34 The Inf luence o f S imu la t i on V a r i a b l e s on T e r t i a r y Crusher Curren t Draw and Feedrate 115 - x i -Figure Page A l Design S p e c i f i c a t i o n s f o r Symons Nordberg Cone Crushers 128 A2 Design S p e c i f i c a t i o n s f o r A l l i s - C h a l m e r s R i p l - F l o 132 I n c l i n e d V i b r a t i n g Screens Gl Schematic Representa t ion o f a V i b r a t i n g Screen 205 G2 Comparison o f Observed and P r e d i c t e d Screen Response 209 - x i i -LIST OF TABLES Table Page 1 Thermal Over load S e t t i n g s f o r Crushers 15 2 Represen ta t ive Un i t s Sampled 17 3 Summary o f Opera t ing Data ; Secondary Crusher Sampling Phase 32 4 Summary o f Opera t ing D a t a ; . . T e r t i a r y Crusher Sampling Phase 36 5 Summary o f Opera t ing Data; Secondary Screen Sampling Phase 41 6 Screening Procedures f o r Secondary Crushing P l a n t Samples 43 7 Gene ra l i z ed Table o f Data Obtained Around a Screen 46 8 Primary Fines Sampling Schedule 82 9 Opera t ing Ranges o f V a r i a b l e s S tud ied wi th Program PGM2 87 10 Coded Two-Level F u l l F a c t o r i a l Design M a t r i x Used f o r Secondary Crushing P l a n t S i m u l a t i o n Study 88 11 Coded Two-Level Intermediate Range Design M a t r i x Used f o r Secondary Crushing P l a n t S i m u l a t i o n Study 90 12 Summary o f Two-Level F u l l F a c t o r i a l Design S i m u l a t i o n Study 92 13 Summary o f Two-Level Intermediate Range Design S i m u l a t i o n Study 93 14 Summary o f E f f e c t s o f V a r i a b l e s on Responses 108 15 Ind ica t ed Capac i ty Increases f o r T e r t i a r y Crushers 112 - x i i i -Table Page A l A d d i t i o n a l S p e c i f i c a t i o n s f o r Secondary and 127 T e r t i a r y Crushers A2 Design S p e c i f i c a t i o n s f o r Symons Nordberg 129 Cone Crushers A3 Opera t ing S p e c i f i c a t i o n s f o r Symons Nordberg 130 Cone Crushers A4 A d d i t i o n a l S p e c i f i c a t i o n s f o r Pr imary and 131 Secondary V i b r a t i n g Screens Bl Flowrate Record f o r Primary Screens Undersize 143 Stream; August , 1975 B2 Flowrate Record f o r Pr imary Screens Undersize 144 Stream; September, 1975 B3 Flowrate Record f o r Pr imary Screens Unders ize 145 Stream;. October , 1975 - x i v -LIST OF SYMBOLS Symbol A. GENERAL TERMINOLOGY U n i t i , j = counter v a r i a b l e s n = number o f screen s i z e f r a c t i o n s n-1 = number o f screen s i z e s x = screen s i z e ( lower l i m i t o f s i z e f r a c t i o n ) G = crusher c l o s e s ide s e t t i n g or gap T = u n i t feedrate S = percent + 1 inch ma te r i a l i n u n i t feed stream. <}> = secondary screen opening Yc = cumulat ive weight f r a c t i o n pass ing screen RSS = r e s i d u a l sum o f squares between two vectors dimensi on less d imens ionless dimension l e s s cen t imete r cen t imeter tons /hour weight percent cen t imeter d imensionless d imensionless B. THE WHITEN SCREEN MODEL m = number o f random passes a p a r t i c l e makes at openings w h i l e pass ing over a screen deck 1 = length o f screen a = screen opening (square mesh) w = wid th o f screen ki2 = an e f f i c i e n c y cons tant k 2 = a l o a d i n g constant V = vo lume t r i c feedrate b = screen c l o t h wi re diameter s = p a r t i c l e s i z e d imens ionless f ee t inch f ee t d imens ionless d imens ionless ton/hour inch inch - xv -Symbol C. DATA ADJUSTMENT PROCEDURE FOR SECONDARY SCREENS F = measured screen feedrate 0 = measured screen o v e r s i z e product f lowra te U = measured screen unders ize product f lowra te f.j = measured weight f r a c t i o n r e t a i n e d on s i z e i f o r screen feed o.j = measured weight f r a c t i o n r e t a i n e d on s i z e i f o r screen o v e r s i z e product u.j = measured weight f r a c t i o n r e t a i n e d on s i z e i f o r screen unders ize product = a symbol used i n conjunct ion w i t h any o f the above screen v a r i a b l e s to denote an adjusted or p r e d i c t e d val ue = a symbol used i n conjunct ion w i t h any o f the above screen v a r i a b l e s to denote a program search v a r i a b l e S f . = s tandard d e v i a t i o n o f i t h s i z e f r a c t i o n o f measured screen feed So^ = s tandard d e v i a t i o n o f i t h s i z e f r a c t i o n o f measured screen o v e r s i z e product Su . = s tandard d e v i a t i o n o f i t h s i z e f r a c t i o n o f measured screen unders ize product Y. = o rd ina te value f o r i t h s i z e f r a c t i o n o f adjusted screen e f f i c i e n c y curve = weight f r a c t i o n o f screen feed s i z e range i r e p o r t i n g to o v e r s i z e product U n i t ton /hour ton /hour ton /hour d imens ionless d imens ion less d imens ion less d imens ionless d imens ionless d imens ion less d imens ion less d imens ionless d imens ionless - x v i -Symbol U n i t D. THE SIMULATION MODELS (a) The Crusher Model F = c rusher feed vec tor X = vec to r d e s c r i b i n g instantaneous crusher contents P = c rusher product vec to r B = t o t a l breakage ma t r ix B l = pr imary breakage component m a t r i x B2 = secondary breakage component m a t r i x C = c l a s s i f i c a t i o n ma t r ix CX = p r o p o r t i o n o f c rusher contents to be broken BCX = p r o p o r t i o n o f c rusher contents a c t u a l l y broken x = geometr ic mean s i z e o f l a r g e s t p a r t i c l e e n t e r i n g c rusher (de f ined as the geometric mean s i z e o f the sma l l e s t screen f r a c t i o n pass ing 100 percent i n 1/2 screen r a t i o ) x . = lower s i z e l i m i t o f p a r t i c l e s i z e f r a c t i o n i Ypn- = value o f pr imary breakage d i s t r i -bu t ion func t ion f o r p a r t i c l e s i z e x i Ys . = value o f secondary breakage d i s t r i -bu t ion func t ion f o r p a r t i c l e s i z e x i a = l i n e a r combination c o e f f i c i e n t (model parameter) y = model constant 3 = model parameter weight percent weight percent weight percent d imens ion less d imens ion less d imens ion less d imens ionless weight percent weight percent cen t imete r cen t imete r d imens ion less d imens ion less d imens ion less d imens ion less d imens ionless - XVI1 -Symbol U n i t a i c (x n . ) C ^ ) F ( x i ) Kl K2 C = model constant = i t h element o f secondary breakage ma t r i x = i t h element o f primary breakage ma t r i x = c l a s s i f i c a t i o n p r o b a b i l i t y f u n c t i o n = i t h element o f c l a s s i f i c a t i o n ma t r i x d iagonal = in te rmedia te c a l c u l a t i o n v e c t o r = model parameter = model parameter = p r e d i c t e d crusher cu r ren t cen t ime te r d imens ion less d imens ion less d imens ion less d imens ion less d imens ion less cen t ime te r cen t imete r amperes The Screen Model x 5 0 a Ci m a 0 a i = e q u i v a l e n t screen opening f o r composite screen = geometric mean s i z e o f p a r t i c l e s i z e range i = weigh t f r a c t i o n o f feed r e p o r t i n g to o v e r s i z e product = model parameter ( p a r t i c l e s i z e a t which 50 percent o f feed r epor t s to ove r s i ze product) = model parameter = a u x i l l i a r y func t ion to account f o r s h o r t - c i r c u i t i n g o f under-s i z e m a t e r i a l i n t o o v e r s i z e product = moisture content o f feed = proposed model parameter = proposed model parameter cen t imete r cen t ime te r d imens ion less cen t ime te r cub i c cen t imete r d imens ion less weight percent d imens ion less d imens ion less - x v m -Symbol Uni t The Pr imary Fines Model Yc.j = cumula t ive weight percent pass ing screen s i z e i we igh t percent b ° = model parameter d imens ion less bi = model parameter d imens ionless b 2 = model parameter d imens ion less - x i x -ACKNOWLEDGEMENTS The author wishes to extend h i s g r a t i t u d e and a p p r e c i a t i o n to the s u p e r v i s o r o f t h i s r e s e a r c h , P ro fes so r A. L . M u l a r , whose guidance and encouragement was i n v a l u a b l e throughout . Thanks are a l s o extended to var ious f a c u l t y members and graduate s tudents o f the Department o f Mine ra l E n g i n e e r i n g , i n p a r t i c u l a r to Mr. H. F. So lbe rg f o r s t i m u l a t i n g conversa t ions concern ing mode l l i ng techniques and to Mrs . S. M a i r o f the Department o f Computer Science f o r many hours o f c o n s u l t a t i o n regarding the BASIC language a t U . B . C . The author a l s o wishes t o express h i s g r a t i t u d e t o the o p e r a t i n g personnel a t the Brenda Mines L t d . concen t r a to r , and e s p e c i a l l y t o thank both Mr. J . A u s t i n , M i l l M e t a l l u r g i s t and Mr. E. F l e i s c h a c k e r , Crusher Foreman, f o r t h e i r pa t ience and support throughout the data a c q u i s i t i o n program. The f i n a n c i a l support o f both the N a t i o n a l Research Counc i l o f Canada and the Canada Center f o r M i n e r a l s and Energy Technology i s g r e a t l y app rec i a t ed . Without t h e i r suppor t , t h i s study would no t have been p o s s i b l e . The author wishes p e r s o n a l l y to acknowledge the g e n e r o s i t y o f the K i t s a u l t Community Club f o r t h e i r f i n a n c i a l support i n the form o f a s c h o l a r s h i p . - 1 -CHAPTER 1 INTRODUCTION 1.1 Statement o f Ob jec t i ve s The comminution process i s one o f the most impor tant compon-ents o f the minera l p roces s ing i n d u s t r y , and c e r t a i n l y the most c o s t l y . In conven t iona l m i l l i n g o p e r a t i o n s , comminution i s c a r r i e d out i n two s tages : coarse s i z e r educ t ion through c rush ing and f i n e r educ t ion through g r i n d i n g . I t i s g e n e r a l l y accepted tha t the cos t o f s i z e reduc t ion inc reases w i th decreas ing p a r t i c l e s i z e , so tha t g r i n d i n g i s i n e v i t a b l y the more c o s t l y o f the two o p e r a t i o n s . T h e r e f o r e , i t i s ev iden t t ha t improvement i n c rush ing e f f i c i e n c y should produce the most s i g n i f i c a n t gains f o r the t o t a l ope ra t i on i n terms o f de-creased ope ra t ing cos ts and inc reased c o n t r o l o f subsequent (downstream) ope ra t i ons . Ex tens ive o n - l i n e s tud i e s o f an ope ra t i ng process f o r o p t i m i z a t i o n purposes are u s u a l l y very c o s t l y w i t h r e spec t to l o s t p roduc t ion and p l a n t e f f i c i e n c y . Consequent ly , o f f - l i n e s t u d i e s conducted us ing a d i g i t a l s i m u l a t i o n o f f e r an a t t r a c t i v e a l t e r n a t i v e . In t h i s approach, i n d i v i d u a l process un i t s are model led ma thema t i ca l l y . The models may be used f o r a general s i m u l a t i o n to permi t s tudy and o p t i m i z a t i o n o f a process wi thou t any o f the problems a s s o c i a t e d wi th i n - p l a n t t e s t i n g and at a minimal cos t . - 2 -Th i s p r o j e c t i s concerned wi th the a p p l i c a t i o n o f o f f - l i n e computer s i m u l a t i o n methods t o an ope ra t ing c ru sh ing p l a n t . The o b j e c t i v e s o f the p r o j e c t were t h r e e f o l d : (a) to ob ta in ope ra t i ng models f o r each o f the three u n i t opera t ions s t u d i e d : secondary c r u s h i n g , t e r t i a r y c rush ing and secondary s c r e e n i n g . (b) to combine the models developed f o r i n d i v i d u a l u n i t s i n a general program capable o f s i m u l a t i n g the s teady s t a t e ope ra t ion o f the e n t i r e c rush ing p l a n t . (c) to t e s t the s i m u l a t i o n program over normal o p e r a t i n g ranges and to perform p r e l i m i n a r y analyses o f c r u s h i n g p l a n t performance w i t h respec t to a l l o f the major manipu la tab le and non-manipula table (but measurable) o p e r a t i n g v a r i a b l e s . Once a general p l a n t s i m u l a t i o n has been o b t a i n e d , there are numerous s t u d i e s t ha t may be performed. Severa l p o s s i b i l i t i e s a re : (a) e v a l u a t i o n o f equipment wear on p l a n t performance and product q u a l i t y . (b) o p t i m i z a t i o n o f p l a n t ope ra t ing v a r i a b l e s w i t h respec t t o p l a n t c a p a c i t y o r f i n a l product q u a l i t y . (c) e v a l u a t i o n o f a l t e r n a t i v e c i r c u i t c o n f i g u r a t i o n s . (d) proposal and /or e v a l u a t i o n o f p l a n t c o n t r o l s t r a t e g i e s . (e) a d e t a i l e d study o f p l a n t behaviour l e a d i n g t o a comprehensive o p e r a t i n g manual. - 3 -1.2 L i t e r a t u r e Survey The h i s t o r y o f d i g i t a l s i m u l a t i o n i n the area o f comminution (Pi) has been documented . I n i t i a l work on c i r c u i t design and c o n t r o l o f ope ra t ing g r i n d i n g c i r c u i t s was s u c c e s s f u l l y undertaken by Lynch Ik 5) (12) et a l v . More r e c e n t l y , Whiten e t a l v ' ' have s imu la t ed an ope ra t ing c rush ing p l a n t us ing models developed f o r cone c rushers and v i b r a t i n g sc reens . Th i s i s the most comprehensive e f f o r t towards c rush ing p l a n t s i m u l a t i o n to date and forms the b a s i s f o r the s t u d i e s (3) conducted dur ing t h i s p r o j e c t . Gurun v 1 has c l a imed development o f a success fu l "program" f o r s i m u l a t i n g c rush ing p l a n t s , but too l i t t l e in fo rmat ion has been pub l i shed to enable s a t i s f a c t o r y e v a l u a t i o n o f the system. A cons ide rab le volume o f l i t e r a t u r e has been generated con-ce rn ing the subjec ts o f c rush ing and s c r e e n i n g . A good summary o f the p r i n c i p l e s i n v o l v e d i n both c rush ing and sc r een ing i s a v a i l a b l e (2M (25) (11) i n textbooks by T a g g a r v ' and Gaudin v . In a d d i t i o n , M a r s h a l l v has prepared a c r i t i q u e o f e x i s t i n g c rush ing l a w s , w h i l e Suzuki and ldndkaKX ' have attempted to r e l a t e c ru sh ing e f f i c i e n c y to ope ra t i ng c o n d i t i o n s . F e r r a r a and P r e t i ^ 2 ^ have undertaken a d e t a i l e d s tudy o f sc reen ing k i n e t i c s and have de r ived two equat ions useful f o r screen design and a n a l y s i s o f exper imenta l s c reen ing r e s u l t s . The A l l i s C h a l m e r s p u b l i c a t i o n on commercial sc reen ing has been found to be a good general reference f o r p r a c t i c a l sc reen ing a p p l i c a t i o n s . - 4 -P r e s e n t a t i o n o f a comprehensive survey o f p u b l i s h e d l i t e r a t u r e concerning mathematical m o d e l l i n g , r eg re s s ion analyses and computer methods i s not f e a s i b l e f o r the purpose o f t h i s t h e s i s . E x c e l l e n t textbooks d e s c r i b i n g the f i e l d s o f process a n a l y s i s by mathematical techniques are a v a i l a b l e by Mular and B u l l v (mode l l i ng techniques) and by H i m m e l b l a u ^ 1 0 ^ ( s t a t i s t i c a l t e chn iques ) . The f i e l d o f r e g r e s s i o n a n a l y s i s has been very thoroughly covered i n the t e x t by Draper and Smi th v . The reader i s r e f e r r e d to papers by Ne lde r and Mead v , M u l a r ^ , and Mula r and B u l l ^ f o r d e s c r i p t i o n s o f the b a s i c computer methods employed i n t h i s s tudy . (a) Summary o f Comminution D i s t r i b u t i o n Funct ions There have been a number o f mathematical func t ions developed to desc r ibe the d i s t r i b u t i o n o f p a r t i c l e s due t o breakage phenomena. One o f the most useful func t ions f o r d e s c r i b i n g the s i z e d i s t r i b u t i o n o f broken coal and r e l a t i v e l y f i n e l y crushed ore i s the Rosin-Rommler v " equat ion Yc = 1 - e x p ( - ( | ) b ) (1) T h i s func t ion has a s t a t i s t i c a l ba s i s g iven by F i s h e r and T i p p e t ^ 1 ^ i n 1928. Severa l v a r i a t i o n s o f t h i s equat ion have s ince been proposed. (23) In 1951, W e i b u l r ' r epor ted a more general form Yc = 1 - exp ( - ( x ^ ) b ) (2) In 1956, B r o a d b e n t ^ 1 ^ used a m o d i f i c a t i o n by E p s t e i n ^ 2 0 ^ w i t h the form Yc = 1 - e x p ( - ( ^ b ) (3) a__ 1 - exp (-1) - 5 -Another f u n c t i o n which has widespread a p p l i c a t i o n i s the G a u d i n - S c h u h m a n n ^ 1 5 ' - ^ equat ion Yc = ( £ ) C (4) Th i s func t ion i s u s u a l l y a p p l i c a b l e t o par t o f the data on ly and d e t e r i o r a t e s f o r the coarse s i z e s i n v o l v e d i n c r u s h i n g . However, the equat ion i s employed e x t e n s i v e l y i n the minera l p r o c e s s i n g f i e l d . A d i s t r i b u t i o n sometimes c i t e d , but not i n f requent use i s the R o l l e r ^ 2 ^ f u n c t i o n Yc = aTx e x p ( - | ) (5) A d i s t r i b u t i o n func t ion w i th a t h e o r e t i c a l b a s i s was d e r i v e d by Gaudin and M e l o y ^ 1 3 , 1 ^ i n 1962. The f u n c t i o n desc r ibes s i z e d i s t r i b u t i o n s c rea ted by the mechanism o f s i n g l e f r a c t u r e and i s expressed as Yc = 1 - (1 - | ) b (6) ( 21 22) A more general m o d i f i c a t i o n o f t h i s e q u a t i o n , by Bergs t ronr ' ,was used dur ing t h i s p r o j e c t i n the form Yc = 1 - ( 1 - ( £ ) C ) b (7) - 6 -1.3 The Cone Crusher Model (1 32) The cone c rusher model developed by Whiten e t a l served as a s t a r t i n g p o i n t f o r the crusher models developed i n t h i s s tudy. The Whiten model i s shown s c h e m a t i c a l l y i n F igure 1. The model i s b u i l t around the two opera t ions o f p a r t i c l e breakage and c l a s s i f i c a t i o n . B i s a lower t r i a n g u l a r mat r ix which descr ibes p a r t i c l e breakage and C i s a d iagonal ma t r ix which descr ibes the p r o b a b i l i t y o f p a r t i c l e breakage. F represents the new crusher feed v e c t o r , P represents the c rusher product v e c t o r and X represents the c rusher contents v e c t o r a t any given i n s t a n t . F igure 1 Schematic Representa t ion o f a Cone Crusher To ob ta in the mat r ix form o f the model , mass balances are taken around nodes 1 and 2 i n F igure 1 as f o l l o w s : (1) X = F + BCX ( 8 ) (2) X = CX + P (g) - 7 -S o l v i n g f o r P gives the ma t r ix equa t ion : P = [T - C] [T - BC]" 1 ?" (10) which represents the f i n a l i z e d form of the cone c rusher model. 1.4 The V i b r a t i n g Screen Model The model developed by Whiten to s imula te v i b r a t i n g screens i s based on the p r o b a b i l i t y cons ide r a t i ons o f a s p h e r i c a l p a r t i c l e ( 25) pass ing thorugh a square ape r tu re , f i r s t proposed by Gaudin v i n 1938. i 11 . . . 1 I 1 - I *" » a - s b V ) Q * Figure 2 Geometric Cons ide ra t ions f o r D e r i v a t i o n o f Screening P r o b a b i l i t y R e f e r r i n g to Figure 2 , the area o f the b a s i c s e p a r a t i n g u n i t o f the screen i s (a+b) 2 . A p a r t i c l e o f s i z e ' s 1 must f a l l i n t o an area ( a - s ) 2 to pass through the screen wi thout touch ing the w i r e s . The p r o b a b i l i t y o f t h i s o c c u r r i n g on a s i n g l e , random pass w i l l be: PO) = [(IS) 2] 2 (n) - 8 -and f o r 'm' random t r i a l s : P(m) = [ ( f ^ - ) 2 ] " 1 (12) This r a t i o represents the lower l i m i t o f p r o b a b i l i t y o f passage, as passage can a l so occur when a p a r t i c l e i s d e f l e c t e d through the hole a f t e r s t r i k i n g a w i r e . The e f f i c i e n c y curve f o r the screen can be represented i n terms o f the p r o b a b i l i t y o f a p a r t i c l e not pass ing the screen ( i . e . o f e n t e r i n g the o v e r s i z e product) expressed by the equa t ion : E(s) = [1 - ( § = f ) 2 f (13) Whiten found t ha t the number o f t r i a l s , ' m ' , t ha t a p a r t i c l e performs i n pass ing over the screen can be expressed by the e q u a t i o n : m = k i 2 l f (14) where: f = ] ( ] 5 ) 1 = screen length a = screen aperture w = screen width k i = e f f i c i e n c y constant k 2 = l oad ing constant V = vo lume t r i c feed ra te The load f a c t o r "f" w i l l be u n i t y f o r low feed ra tes and w i l l tend towards zero f o r very l a rge feed r a t e s . To use t h i s model , an average o f the e f f i c i e n c y curve i s r equ i r ed over each screen s i z e f r a c t i o n to overcome problems a s s o c i a t e d w i th the steep g rad i en t o f the curve . The f o l l o w i n g technique was a p p l i e d : Average E(s) = s { S 2 E(s)ds (16) s 2 - S i - 9 -Th i s equat ion represents a weighted average over a screen i n t e r v a l . J l , 3 i ) which i s eva lua ted us ing computer approximation methods Particle Size , s ( cm ) Figure 3 E f f i c i e n c y Curve f o r Whiten Screen Model A p l o t o f the e f f i c i e n c y curve(13) f o r t h i s model i s presented i n F igure 3. Any theory o f v i b r a t i n g screens should p r e d i c t t h a t a l l p a r t i c l e s l a r g e r than the screen opening w i l l r epo r t to the coarse product . However, t h i s i s not i n d i c a t e d by the e f f i c i e n c y curve o f F igure 3. I t i s ev iden t t ha t i n order to use t h i s cu rve , the model must be d i s c o n t i n u -ous and, i n f a c t , t h i s i s observed. Whitens screen model can be d i v i d e d i n t o four separate zones as f o l l o w s : (a) a l l complete s i z e f r a c t i o n s coa r se r than the screen opening (b) the s i z e f r a c t i o n c o n t a i n i n g the screen opening. T h i s can be subd i v i ded i n t o : ( i ) a p o r t i o n coarse r than the screen opening ( i i ) a p o r t i o n f i n e r than the screen opening (c) those complete s i z e f r a c t i o n s f i n e r than the screen opening , but coa r se r than a sub-mesh f r a c t i o n (d) the sub-mesh f r a c t i o n (-420y) Whiten s t a t e s t ha t t h i s model p rovides an adequate d e s c r i p t i o n o f screen b e h a v i o r , except i n the sub-mesh ranges. - 10 -CHAPTER I I DATA ACQUISITION 2.1 D e s c r i p t i o n o f Crush ing P l a n t (a) I n t r o d u c t i o n Exper imental data f o r t h i s p r o j e c t were ob ta ined from the secondary c rush ing p l a n t a t the Brenda Mines L t d . concen t r a to r near Peachland, B . C . Th i s opera t ion recovers separate c h a l c o p y r i t e and molybdenite concentra tes through convent iona l m i l l i n g o f a low grade porphyry type ore . M i n i n g i s by the open p i t method and d a i l y p l a n t c a p a c i t y averages 30,000 tpd . (b) The Primary Crusher The t o t a l Brenda c rush ing p l an t c o n s i s t s o f three stages o f s i z e r e d u c t i o n . The p l a n t f lowsheet i s dep ic t ed i n F igure 4. The pr imary c rusher i s a 60 i n . x 89 i n . gyra tory c rusher d r iven by a 700 Hp motor and i s capable o f reduc ing run-of-mine ore to -7 i n c h s i z e a t the ra te o f 3,000 t p h . The crushed product f a l l s onto two 78 i n c h apron feeders and i s d i scharged onto two conveyors , each feeding an 8 f t . x 20 f t . double deck v i b r a t i n g sc reen . The unders ize product from the sc reens , at - 3 /4 i n c h , i s conveyed to the m i l l f i n e ore b i n s , w h i l e the coarse product i s conveyed to a 45,000 ton l i v e s t o c k p i l e . The secondary c rush ing p l a n t , c o n s i s t i n g o f two stages o f c ru sh ing and one o f s c r e e n i n g , i s o u t l i n e d i n F igure 4 . T h i s t h e s i s i s concerned p r i m a r i l y w i t h t h i s s e c t i o n o f the o v e r a l l p l a n t . LEGEND 1 Pr imary Crusher (1) 2 Primary Screens (2) 3 Coarse Ore Stockpile 4 Secondary Crushers (2) 5 Surge Bin 6 Secondary Screens (5) 7 Surge Bin 8 Tertiary Crushers (4) Figure 4 G e n e r a l i z e d Crush ing P l a n t Flowsheet - 12 -(c) The Secondary Crusher The secondary c rush ing c i r c u i t c o n s i s t s o f two Symons Nordberg 7 foot s tandard heavy duty cone crushers ope ra t i ng i n p a r a l l e l open c i r c u i t . Feed i s r ec la imed d i r e c t l y from the coarse ore s t o c k p i l e by two 48 - inch conveyors , each i n c o r p o r a t i n g four v a r i a b l e c o n t r o l v i b r a t i n g feeders . Th i s m a t e r i a l i s then passed to two 5 4 - i n c h t r a n s f e r b e l t s and i n t o the c rushe r s . The feed enters an i n v e r t e d c o n i c a l chute and impinges on a d i s t r i b u t i o n p l a t e b o l t e d to the mantle to a s s i s t i n un i form d i s t r i b u t i o n around the c rush ing chamber. The chamber i t s e l f c o n s i s t s o f a coarse type concave and mantle w i th a nominal c l o s e s i d e s e t t i n g o f 1-1/4 inch and a throw o f 3-5/8 i n c h . The counte rshaf t s are d i r e c t l y d r iven by s i n g l e , 350 Hp synchronous motors. The crushed product passes through a s loped d ischarge compartment and onto a 72 - inch conveyor . Th i s conveyor then d ischarges onto a 6 0 - i n c h conveyor which empties i n t o a 1600 ton surge b i n ahead o f the secondary sc reens . (d) The Secondary Screens The secondary sc reen ing c i r c u i t c o n s i s t s o f f i v e A l l i s Chalmers double deck v i b r a t i n g screens ope ra t ing i n p a r a l l e l . The upper deck o f each screen c o n s i s t s o f p a r a l l e l segments o f 32 i n . x 48 i n . punched p l a t e , w i th s l o t dimensions o f 1-1/16 i n . x 3 i n . The feed end o f each upper deck has been blanked o f f wi th rubber mat t ing to e l i m i n a t e excess ive wear no rmal ly encountered when feed p a r t i c l e s f a l l onto the sc reen . As a r e s u l t , the e f f e c t i v e sc reen ing area i s reduced by approximate ly 10 pe rcen t . The lower deck c o n s i s t s o f f i v e panels o f woven wire c l o t h w i t h s l o t s 3-1/2 inch long by va r ious w id th s . For the - 13 -purpose o f t h i s t h e s i s , the width o f the lower deck s l o t w i l l be r e f e r r e d to as the screen opening. Th i s i s a major v a r i a b l e i n s c r e e n i n g . Each screen i s s loped at 20° from the h o r i z o n t a l and i s d r i v e n by two 25 Hp motors l i n k e d through a d i r e c t b e l t d r i v e . Screen feed i s withdrawn from the base o f the surge b in by f i v e v a r i a b l e c o n t r o l v i b r a t i n g feeders emptying d i r e c t l y onto the upper deck o f the r e s p e c t i v e sc reen . The unders ize product f a l l s i n t o a s loped compartment which d i r e c t s i t onto a sho r t 48- inch t r a n s f e r b e l t , where i t i s conveyed through two longe r b e l t s to the f i n e ore b i n s . The unders ize product i s blended w i t h the primary screen unders ize product (pr imary f i n e s ) a t the t r a n s f e r p o i n t between the two longer conveyors . The o v e r s i z e product f a l l s i n t o a s loped p l a t e and then onto a s h o r t , 6 0 - i n c h conveyor p a r a l l e l i n g the unders ize d i scha rge . A f t e r t r a n s f e r t o a l o n g e r , 48 - inch b e l t , the o v e r s i z e i s t r anspo r t ed to a second 1600 ton surge b in ahead o f the t e r t i a r y c rushe r s . (e) The T e r t i a r y Crushers The t e r t i a r y c rush ing c i r c u i t c o n s i s t s o f four Symons Nordberg 7 foot heavy duty shor t -head cone crushers ope ra t i ng i n p a r a l l e l and i n c l o sed c i r c u i t w i t h the secondary sc reens . With the excep t ion o f the c rush ing chamber c o n f i g u r a t i o n , these machines are v i r t u a l l y i d e n t i c a l to the secondary c rushe r s . Feed i s r ec la imed from the c rusher surge b in by four v a r i a b l e c o n t r o l v i b r a t i n g feeders , each supp ly ing a s h o r t , 54 - inch t r a n s f e r b e l t emptying d i r e c t l y i n t o i t s r e spec t i ve c rushe r . As w i th the secondary c r u s h e r s , feed enters an i n v e r t e d c o n i c a l chute and impinges on a d i s t r i b u t i o n p l a t e b o l t e d to the mantle. The c rush ing chamber c o n s i s t s o f a coarse concave and medium mantle, w i th a nominal - 14 -c lo se s ide s e t t i n g o f .27 inches and a throw o f 3-5/8 i nches . The counter shaf t s are d i r e c t l y d r iven by 300 Hp motors. Crushed product passes through a s loped discharge chamber onto the same 72- inch conveyor as the secondary crusher product and i s t r anspor t ed to the surge b in ahead o f the sc reens . ( f ) General The ope ra t ing personnel a t the Brenda p l a n t have subsequently modi f i ed the shape o f the c rush ing chambers i n both the secondary and t e r t i a r y c rushers . These m o d i f i c a t i o n s a f f e c t the mantles on ly and c o n s i s t o f b u i l d i n g up the lower c o n i c a l s e c t i o n s o f each mantle . The m o d i f i c a t i o n s to the secondary c rusher mantles are s u b s t a n t i a l l y d i f f e r -ent to those f o r the t e r t i a r y c rushers . These m o d i f i c a t i o n s , d e p i c t e d i n Figure 5 , are b e l i e v e d to achieve a b e t t e r c rush ing a c t i o n and h ighe r c a p a c i t y . (a) Standard Crusher (b) Short-head Crusher Figure 5 M o d i f i c a t i o n s to Crusher Mantles i - 15 -A l l secondary and t e r t i a r y crushers have a thermal ove r load p r o t e c t i o n fea ture which w i l l shut down a given c rusher when the motor winding temperature exceeds a manually determined s e t p o i n t v a l u e . T h i s feature p ro t ec t s the c rusher motors from sus ta ined o v e r l o a d i n g , but may be a hindrance i n o the r a spec t s , as the motor wind ing temperatures may cont inue to r i s e a f t e r a surge i n feedra te has a l ready passed. The present thermal ove r load s e t p o i n t s , i n terms o f cu r r en t draw, are presented i n Table I. TABLE 1 Thermal Over load Se t t i ngs f o r Crushers Crusher Number Crushing Ci r c u i t Crusher Type Sus ta ined F u l l - L o a d (amperes) Thermal Over load Curren t (amperes) Power Draw (Horsepower) Vol tage ( V o l t s ) 1 Secondary Standard 48 67.5 350 4160 2 • Secondary Standard 48 74.3 350 4160 3 - 6 T e r t i a r y Shor t -head 42 60.4 300 4160 More d e t a i l e d d e s c r i p t i o n s o f the major process u n i t s sampled are presented i n Appendix A. 2 .2 Procedures f o r A c q u i s i t i o n - o f Raw Data (a) I n t r o d u c t i o n Only the secondary c rush ing p l a n t was sampled. I t would be d e s i r a b l e to s imula te the primary c rush ing p l a n t , c o n s i s t i n g o f the primary c rusher and the two pr imary sc reens , but the d i f f i c u l t y o f sampling and sc reen ing the pr imary c rusher feed (ROM ore) are p r o h i b i t i v e . Furthermore, - 16 -the i n t e r m i t t e n t nature o f the primary c rush ing p l a n t ope ra t ion would present cons ide rab l e d i f f i c u l t y t o model development, as i t would depend upon mining methods and s c h e d u l i n g , which are beyond the c o n t r o l o f the m i l l i n g department. The presence o f the coarse ore s t o c k p i l e ensures continuous and c o n t r o l l a b l e ope ra t ion throughout the secondary c rush ing p l a n t . The u n i t opera t ions sampled i n the secondary c rush ing p l a n t were secondary c r u s h i n g , t e r t i a r y c rush ing and secondary s c r een ing . In sampling each o p e r a t i o n , the assumption was made tha t a l l u n i t s w i t h i n the s p e c i f i e d opera t ion behave i n a s i m i l a r manner to the u n i t sampled. This assumption was made w i t h the knowledge tha t a l l u n i t s w i t h i n each opera t ion were p h y s i c a l l y " s i m i l a r " . O b v i o u s l y , u n i t s w i t h i n a s p e c i f i e d opera t ion ( i . e . secondary crushing) w i l l behave d i f f e r e n t l y when se t d i f f e r e n t l y , but t h i s case i s i r r e l e v a n t to the assumption, as these d i f f e r e n c e s are d e l i b e r a t e l y and a r t i f i c a l l y induced. However, d i f f e r ences i n wear ra tes and pa t te rns w i l l cause behav ioura l d i f f e r e n c e s , thus d e v i a t i o n from the assumption. At p resen t , wear phenomena are beyond opera tor c o n t r o l , al though study o f these phenomena may o f f e r an i d e a l a p p l i c a t i o n f o r a t o t a l s i m u l a t i o n program. Another f a c t o r which may cause d e v i a t i o n from the above assump-t i o n i s p a r t i c l e s i z e segregat ion w i t h i n the surge b i n s . At p re sen t , there i s no method o f q u a n t i f y i n g t h i s e f f e c t . 1 However, i t i s known t ha t screens fed from the outermost feeders produce product s i z e d i s t r i -bu t ions which d i f f e r s l i g h t l y from the c e n t r a l l y fed screen.. I t i s j i o t known whether t h i s e f f e c t i s due t o d i f f e r e n c e s i n feed s i z e d i s t r i b u t i o n s o r i n screen behav io r . Current o p i n i o n favours the former case . As 1 This observation applies to the Brenda surge bins only. - 17 -sampling and m o d e l l i n g o f each u n i t i s u n r e a l i s t i c , the " . s i m i l a r i t y " assumption was made. Table 2 i n d i c a t e s the un i t s chosen f o r r ep re sen ta t ion o f each o p e r a t i o n . TABLE 2 Represen ta t ive U n i t s Sampled U n i t Opera t ion Uni t Sampled Comments Secondary Crushing T e r t i a r y Crushing Secondary Screen ing #1 Standard #2 Short-head #2 and 4 Screens Feed s l i g h t l y f i n e r , e a s i e r sampling Min imized b in segrega t ion Chosen as most r ep re sen t a t i ve o f "average" screen feed. Samples o f the primary screens unders ize product ( to be r e f e r r e d to as "pr imary f i n e s " ) were taken over a p e r i o d o f seven days. As mentioned e a r l i e r , segrega t ion e f f e c t s were known to occur w i t h i n both surge b i n s . However, no attempts were made to sample o r s imula te t h i s behav iour , p r i m a r i l y because o f d i f f i c u l t y i n o b t a i n i n g r e l i a b l e samples. The sampling schedule f o r each u n i t opera t ion was cons t ruc ted accord ing to a f u l l f a c t o r i a l design i n v o l v i n g two f ac to r s ( c o n t r o l l a b l e process v a r i a b l e s ) . For both c rush ing o p e r a t i o n s , the f ac to r s were c rusher c l o s e s ide s e t t i n g (gap) and f eed ra t e , and f o r sc reen ing the f ac to r s were screen opening and feed r a t e . With two f a c t o r s , the design, i n v o l v e s four runs , scheduled accord ing to the pa t te rn o u t l i n e d i n F igure 6. A d d i t i o n a l runs were scheduled to cover the c e n t e r p o i n t area f o r each sampling schedule . In each case , the measured dependent v a r i a b l e was the product s i z e d i s t r i b u t i o n . - 18 -F igure 6 F a c t o r i a l Design Used f o r Sampling Schedules To e s t a b l i s h an i n s i g h t i n t o the d i f f i c u l t i e s o f sampling a c rush ing p l a n t , i t i s useful to d i scuss the p h y s i c a l l ayou t o f the Brenda p l a n t a t t h i s p o i n t . T h i s i s shown p h o t o g r a p h i c a l l y i n F igures 7(a) to ( e ) . The t o t a l c rush ing p l a n t i s housed i n three separate b u i l d i n g s and in t e rconnec ted through a network o f enc losed conveyors . The c rush ing p l a n t i s separate from the main concen t ra to r . The f i r s t b u i l d i n g houses the pr imary c rusher and s c r eens , the second houses the secondary screens and a f f i l i a t e d dust c o l l e c t i o n systems.and the t h i r d b u i l d i n g houses the combined secondary and t e r t i a r y crushers w i t h t h e i r dust c o n t r o l systems. Between the sc reen ing and c rush ing b u i l d i n g s l i e s the t r a n s f e r tower , where mix ing o f the screen unders ize and pr imary f ines streams takes place dur ing t r a n s p o r t to the f ine ore b ins a t tached to the mi l 1. - 19 -Primary Crusher Figure 7(a) P h y s i c a l Loca t ions o f Crushing P l a n t Components Figure 7(b) I n t e r i o r View o f the S e c o n d a r y / T e r t i a r y Crusher B u i l d i n g - 21 -Figure 7(d) D e t a i l e d View o f the I n t e r i o r o f a Secondary Screen - 22 -Figure 7(e) The Secondary Crushing P l a n t Con t ro l Room - 23 -The pr imary c rush ing c i r c u i t f a l l s under the j u r i s d i c t i o n o f the mining department a n d . i s c o n t r o l l e d from i t s own b u i l d i n g . The e n t i r e secondary c r u s h i n g p l a n t i s manually c o n t r o l l e d from a s i n g l e c o n t r o l room l o c a t e d i n the c rush ing b u i l d i n g . A more d e t a i l e d schematic o f the c rush ing p l a n t showing sample p o i n t l o c a t i o n s i s g iven i n F igure 8 ( a ) . Photographs o f sample po in t s and work areas are shown i n F igures 8(b); through 8(h) r e s p e c t i v e l y . P r i o r to i n i t i a t i n g the sampling program, a sample sc reen ing s t a t i o n (F igure 8(g)) was l oca t ed i n the g r i n d i n g bay o f the main con-c e n t r a t o r . I t was imposs ib le t o s i t u a t e a sc reen ing s t a t i o n w i t h i n the secondary c rush ing p l a n t b u i l d i n g s because o f Brenda maintenance p o l i c y . The c rush ing p l an t s support t h e i r own maintenance f o r c e , separa-te from the main concen t r a to r , and main ta in t h e i r own i n v e n t o r y . Th i s force i s h e a v i l y o r i e n t e d towards p reven t ive main tenance 1 , so t ha t a l l a v a i l a b l e space w i t h i n the c r u s h i n g / s c r e e n i n g b u i l d i n g s i s occupied by e i t h e r par t s i nven to ry o r workshops. The g r i n d i n g bay was chosen f o r the sc reen ing s t a t i o n as i t o f f e r ed the on ly l o c a t i o n w i t h s u f f i c i e n t room tha t would not i n t e r f e r e w i t h normal p l a n t o p e r a t i o n . Th i s meant tha t a l l samples taken throughout the secondary c rush ing p l a n t had to be t r anspor t ed to and s t o r e d i n the g r i n d i n g bay. These sc reen ing f a c i l i t i e s were shared f o r a shor t p e r i o d w i t h Brenda research personnel execu t ing a sampling program around one o f the rod m i l l s . Few he lpers were a v a i l a b l e to a s s i s t the author du r ing the course o f the data a c q u i s i t i o n program and n e a r l y a l l sampl ing was done alone and by hand. 1 I t i s current operating pract ice to shut down the ent i re secondary crushing plant for a minimum of four hours on dayshif t , Monday through Friday, to carry out maintenance repairs and inspect ions. LEGEND Screens ) EEL mr Screens 10 f i -l l f2 a. Coarse Ore S t o c k p i l e b. Secondary Crushers c. Secondary Screen Surge Bin d. Secondary Screens e. T e r t i a r y Crusher Surge B i n f. T e r t i a r y Crushers Nos .4 ,6 -20 r e f e r to conveyors referenced i n t e x t A. Secondary Crusher Feed B. Secondary and T e r t i a r y Crusher Products ,Secondary Screen Feed C. Secondary Screen Overs ize Product D. T e r t i a r y Crusher Feed E . Secondary Screen Unders ize Product to Fine Ore Bins F igure 8(a) Secondary Crush ing P l a n t Flowsheet Showing Sample L o c a t i o n s - 25 -Figure 8(c) Sample P o i n t f o r Secondary Crusher Product ,Secondary Screen Feed and T e r t i a r y Crusher Product Figure 8(d) Sample P o i n t f o r T e r t i a r y Crusher Feed - 27 -Figure 8(e) Sample Po in t s f o r Secondary Screen Over s i ze and Undersize Products Figure 8 ( f ) Sample P o i n t f o r Primary Screens Unders ize Product (Pr imary Fines) - 28 -Figure 8(g) Sample Screening S t a t i o n - 29 -(b) Secondary Crusher Sampling The c rusher s e l e c t e d f o r sampling was number 1 s tandard . The feed to t h i s c rusher i s b e l i e v e d to be s l i g h t l y f i n e r 1 than the feed to the second machine, a f a c t t ha t would a i d i n sc reen ing o f the upper s i z e ranges. A M e r r i c k weightometer i s l o c a t e d on each o f the two crusher feed b e l t s drawing from the coarse ore s t o c k p i l e , but at the time o f s ampl ing , the conveyor b e l t i n g t o number 2 s tandard had j u s t been r e p l a c e d , and i t s weightometer not y e t c a l i b r a t e d . The sample po in t s f o r the number 1 s tandard are shown i n F igure 8 ( a ) , (b) and ( c ) . The sample p o i n t f o r the c rusher feed was on number 6 conveyor l o c a t e d i n the access shaf t to the r ec lamat ion tunnels under the coarse ore s t o c k p i l e . The c rusher product was sampled on number 14 conveyor on the t h i r d f l o o r o f the t r a n s f e r tower. Both crushers d i scharge onto number 13 conveyor which i n tu rn d ischarges onto number 14 b e l t , but as number 13 conveyor i s enc losed and i n a c c e s s i b l e over i t s e n t i r e l e n g t h , sampling from t h i s b e l t was i m p o s s i b l e . The assump-t i o n was made tha t the c rusher was ope ra t i ng a t steady s t a t e when sampled and tha t the time l a g between the feed and product sample po in t s had n e g l i g i b l e e f f e c t . Th i s time l a g , i n a c t u a l i t y , was o f the order o f 90 seconds. The sampl ing procedure adopted f o r the secondary crushers i s t a b u l a t e d as f o l l o w s : (1) the secondary screen b i n was drawn down s u f f i c i e n t l y to r e c e i v e approximate ly 20 minutes o f d i scharge from number 1 s tandard c rusher . .1 Due to segregation effects on the coarse ore s tockp i l e . - 30 -(2) the e n t i r e secondary c rush ing p l a n t was shut down. ( I t i s convenient i f s teps 1 and 2 can be scheduled to c o i n c i d e w i t h the m i l l f i n e ore b ins be ing f u l l ) . (3) the c l o s e s i d e s e t t i n g o f number 1 s tandard was adjusted and recorded . (4) number 1 s tandard was s t a r t e d and feed run through u n t i l opera t ion was s t a b i l i z e d a t the d e s i r e d feedra te . (5) number 1 s tandard was h e l d a t t h i s feedra te f o r approximate ly 10 minutes to ensure steady s t a t e o p e r a t i o n . Adjustments were made as r e q u i r e d . (6) du r ing t h i s p e r i o d , cu r r en t draw was measured over a p e r i o d o f approximate ly 4-5 minutes f o r number 1 s tandard motor. (7) a f t e r 10 minutes , the feed and d ischarge b e l t s were shut down s imu l t aneous ly and locked out . (Note: the p rev ious t ime l a g assumption) . (8) tonnage and time measurements were recorded f o r feedrate c a l c u l a t i o n . (9) a 10-foot s e c t i o n o f product was taken from number 14 b e l t and s t o r e d i n a covered 4 5 - g a l l o n b a r r e l i n the t r a n s f e r tower. (Note: a t t h i s p o i n t the secondary c rush ing p l a n t may be r e s t a r t e d , minus number 1 s tandard c r u s h e r ) . (10) a 20 - foo t s e c t i o n o f feed was taken from number 6 b e l t and s to red i n two covered 4 5 - g a l l o n drums i n the access sha f t . (11) a f t e r every second t e s t , the s to red samples were removed to the g r i n d i n g bay f o r s c r een ing . In a l l , there were e i g h t t e s t s conducted around the secondary c rushe r s . F igure 9 dep i c t s the comparison between the scheduled design and sampl ing schedule ob ta ined . There were no p a r t i c u l a r d i f f i c u l t i e s i n p r e p a r i n g , o p e r a t i n g o r sampling the number 1.s tandard c rushe r . D i sc repanc i e s between scheduled and observed design po in t s are b e l i e v e d . t o be due t o . e i t h e r the cons ide rab le shor t term f l u c t u a t i o n s in c rusher feedrate o r the d i f f e r e n t ope ra t i ng p e r s o n a l i t i e s o f d i f f e r e n t ope ra to r s . 31 The c rusher gaps were adjusted us ing the 4 p o i n t l ead weight technique . B e t t e r p r e c i s i o n cou ld have been o b t a i n e d , but on ly at the expense o f t ime , w h i c h , i n terms o f p l a n t shutdown, i s a very expensive commodity. The s h o r t term f l u c t u a t i o n s i n feedrate are a t t r i b u t e d to the ext remely coarse nature o f the feed and are beyond c o n t r o l o f the present o p e r a t i o n . 4.0H E u CL o 0 3.5H 03 3.0-1 sz to Z5 2.5H 5 5 0 % © -6 1 A - D e s i g n Point ©-Observed Point i i i i i i i i i i i i i 600 650 700 T I ' l l T - 1 1 I I 1 I 750 800 850 Crusher Feedrate (tph) Figure 9 Exper imental Design f o r Secondary Crushers Measured values o f gap, f e e d r a t e , percent of .+ .1 inch i n feed and cu r r en t draw obta ined around the secondary crusher f o r the e i g h t runs performed are summarized i n Table 3. The percent o f + 1 inch 1 This procedure involves attaching a c y l i n d r i c a l lead weight, with a diameter several times that of the estimated gap, to a wire cord. While the crusher i s running, hut empty, the weight, i s quickly lowered between the: mantle and concave, u n t i l no more crushing action i s f e l t . The weight i s withdrawn and the thinnest pa r t of the f lat tened disc i s a measure of the crusher gap at that point . This procedure i s repeated at four equidistant points to locate the minimum gap. - 32 -m a t e r i a l i n the feed i s an u n c o n t r o l l a b l e v a r i a b l e and i s used as a measure o f the coarseness o f the feed s i z e d i s t r i b u t i o n . T h i s v a r i a b l e i s determined g r a p h i c a l l y from the measured s i z e d i s t r i b u t i o n s o f a l l un i t feeds. A complete s i z e a n a l y s i s o f each sample taken around the secondary crushers i s presented i n Appendix B ( a ) . TABLE 3 Summary o f Opera t ing Data  Secondary Crusher Sampling Phase INDEPEf\ DENT DEPENDENT Run Close Side S e t t i n g Feedrate % + 1 inch Curren t Draw Number ( inch ) (cm) ( tph) i n Feed (amperes) 1 1.275 3.239 701.1 81.9 20.0 2 1.215 3.086 727.3 93.7 23.5 3 1.240 3.150 724.8 82.0 22.0 4 1.475 3.747 635.3 85.9 18.0 5 1.490 3.785 789.4 75.1 19.0 6 1.000 2.540 782.3 82.8 32.0 7 1.260 3.200 741.2 87.6 21.0 8 1.000 2.540 627.7 87.0 22.0 (c) T e r t i a r y Crusher Sampling In comparison w i t h the secondary c ru she r s , sampling around the t e r t i a r y crushers was cons ide r ab ly more d i f f i c u l t . The surge b in ahead o f the t e r t i a r y crushers pe rmi t t ed t h e i r ope ra t ion f o r s u b s t a n t i a l per iods under non-steady s t a t e c o n d i t i o n s . Weightometers were not mounted on the t e r t i a r y c rusher feed b e l t s , so measurement o f feedrate was obta ined i n d i r e c t l y . I t was - 33 -observed tha t when the surge b in was empty, the conveyor t r a n s p o r t i n g screen o v e r s i z e (number 16 b e l t ) d i scharged almost d i r e c t l y i n t o the feeder f o r number 2 shor t -head c rushe r . For t h i s reason , the number 2 c rusher was chosen to represent the t e r t i a r y c i r c u i t . F o r t u n a t e l y , a M e r r i c k weightometer was l o c a t e d on number 16 b e l t , so tha t f l owra te s o n t h a t b e l t cou ld be ob ta ined . Sampling runs were conducted w i t h the surge b i n empty and w i t h number 16 b e l t d i s c h a r g i n g i n t o number 2 feeder . Des i r ed feedra tes to.number 2 shor t -head were e s t a b l i s h e d by means o f t h i s weightometer . The sample p o i n t chosen f o r c rusher feed was on the number 2 shor t -head feed b e l t (number 11 b e l t ) d i r e c t l y p r i o r to d ischarge i n t o the c ru she r . T h i s n e c e s s i t a t e d removal o f the conveyor cover p l a t e . The product was sampled on number 14 b e l t i n the t r a n s f e r tower , a t the same l o c a t i o n as the secondary c rusher product . The l o c a t i o n o f the t e r t i a r y c rusher sample po in t s i s i n d i c a t e d on F igures 8 ( a ) , (c) and ( d ) , pages 24 to 26 . The f o l l o w i n g sampl ing procedure was adopted f o r the number 2 shor t -head c rushe r : (1) the secondary screen b in was f i l l e d to supply feed f o r the du ra t i on o f the t e s t . (2) the t e r t i a r y surge b in was emptied u n t i l feeder th roa t s were v i s i b l e . The b in was a l so checked f o r dead s to rage . (3) the e n t i r e secondary c rush ing p l a n t was shut down. (4) the c lo se s ide s e t t i n g o f number.2 shor t -head c rusher was adjusted and recorded. (5) number 2 shor t -head c rusher was s t a r t e d . Severa l screens were s t a r t e d s h o r t l y af terwards to supply f eed . to number 16 b e l t . - 34 -(6) number 16 b e l t weightometer tonnage readings were r e l a y e d to the ope ra to r (no i n t e g r a t i o n i n c o n t r o l room)., who adjusted the screen feeders u n t i l the d e s i r e d f lowra te ach ieved . Number 16 b e l t was mainta ined a t t h i s ra te as c l o s e l y as p o s s i b l e f o r approximate ly TO minutes . Adjustments were made as r e q u i r e d . (7) dur ing the t e s t p e r i o d , cu r r en t and power draws were monitored and r eco rded , as were tonnage/t ime readings f o r the weightometer. (8) numbers 11 , 14 and 16 b e l t s were shut down s imul taneous ly and locked out . (9) a measured length o f product was taken from number 14 b e l t and s to red i n a c l o sed drum i n the t r a n s f e r tower. The c rush ing p l a n t cou ld be s t a r t e d a t t h i s p o i n t , l e s s number 2 shor t -head . (10) a measured length o f feed was taken from number 11 b e l t and s to red i n a c l o sed drum by the c rusher . (11) the t e r t i a r y surge b i n was inspec ted f o r accumulat ion ( c o n d i t i o n s p e r m i t t i n g ) . (12) the samples were removed to the m i l l g r i n d i n g bay as soon as p o s s i b l e . There were ten runs conducted around, the number 2 shor t -head c rusher . A comparison o f the scheduled and .obse rved . f ac to r l e v e l s i s presented i n Figure 10. I t i s ev iden t t ha t the observed sampling schedule was unable to f o l l o w c l o s e l y the design schedule and tha t the observed data po in t s are not a p p l i c a b l e to a f u l l 2 n f a c t o r i a l de s ign . The c rusher gap, adjusted by the l ead weight technique appears to be w e l l c o n t r o l l e d and r e l i a b l e . However, c o n t r o l o f the feedrate was not good. S e v e r a l - p o s s i b l e , reasons f o r t h i s are as f o l l o w s : (a) f o r a f i x e d f eed ra t e , changes i n feed s i z e d i s t r i b u t i o n s to ; the secondary screens w i l l cause changes i n o v e r s i z e product f lowra te and thus changes i n c rusher f eedra te . These changes can occur q u i t e r a p i d l y on a smal l s c a l e , r e s u l t i n g i n high f requencies o f shor t term f l u c t u a t i o n s in . c rusher f eedra te . (b) accumulat ion i n the t e r t i a r y surge b i n w i l l r e s u l t i n a c rusher feedrate l e s s than i n d i c a t e d by the weightometer on number 16 b e l t . - 35 -(c) occurrence o f a "free feed ing" c o n d i t i o n , where dead s torage o r accumulated m a t e r i a l l i n i n g the feeder t h roa t s p o r a d i c a l l y s l i d e s i n t o the feeder . Th i s r e s u l t s i n h ighe r than i n d i c a t e d feedrates and s u b s t a n t i a l non-s tead s t a t e behaviour . T h i s i s b e l i e v e d to be the major f a c t o r c o n t r i b u t i n g to d e v i a t i o n from the designs schedule . (d) s eve ra l operators were suspected o f i n a t t e n t i o n and a l l o w i n g c o n t r o l s to s l i p w h i l e readings were being .taken ou t s ide the c o n t r o l room. E u 1.0 : 4V •9H c -7i -£= -i/l .6-6 . 5 ^ .4 -0-0 © O 0 - 4 A-Design Point ©-Observed Point —r—i—l—| 1-150 200 ->—1 I—r-250 t — i — I — r -300 - i—|—i—r-350 f 1 — i r — , • — , 400 450 Crusher Feedrate ( tph) Figure 10 Exper imental Design f o r T e r t i a r y Crushers Because feedrate measurements obta ined from the number 16 b e l t weightometer were judged to be i n e r r o r , the crusher feedrates were back c a l c u l a t e d from the measured sample we igh t s , lengths and b e l t speeds r e s p e c t i v e l y . This was done f o r both feed and product samples, w i t h the c a l c u l a t e d feedrates be ing averaged to y i e l d a f i n a l value f o r each run. Th i s averaged feedrate was used f o r a l l subsequent work p e r t a i n i n g to the t e r t i a r y c rushers . - 36 -Table 4 summarizes ope ra t ing data f o r the t e r t i a r y crusher sampling phase. The feedrate values measured from the weightometer on number 16 b e l t are presented f o r comparison. TABLE 4 Summary o f Opera t ing Data T e r t i a r y Crusher Sampling Phase INDEPENDENT DEPENDENT Run Close Side S e t t i n g Feedrates %+l inch Current Number ( inch) (cm) #16 b e l t C a l c . Avg. i n feed (amps) (TPH) (TPH) 9 .290 .737 • 249.6 299.1 60.0 37 10' .265 .673 211.0 272.9 67.5 36 11 .300 .762 252.0 346.6 75.5 38 12 .260 .660 299.9 244.9 65.0 37 13 .425 1.080 388.1 328.0 70.0 40 14 .400 1.016 180.0 220.9 68.0 27 15 .195 .495 205.4 239.9 72.0 35 16 .250 .521 345.2 349.2 49.0 43 16A .375 .953 339.8 421.0 69.0 39 16B .300 .762 189.1 344.7 81.5 40 Complete s i z e analyses o f a l l samples taken f o r the t e r t i a r y crushers are presented i n Appendix B ( b ) . (d) Secondary Screen Sampling I t i s known tha t p a r t i c l e s i z e segrega t ion e f f e c t s occur w i t h i n the secondary screen surge b i n . Al though these e f fec t s -have not been a c c u r a t e l y q u a n t i f i e d , the segrega t ion trends which have been observed are dep i c t ed i n F igure 11. In an attempt to minimize these e f f e c t s , - 37 -screens number 2 and 4 were chosen as r ep re sen t a t i ve o f secondary screen behaviour . I t i s f e l t t ha t the feed s i z e d i s t r i b u t i o n s to these screens most c l o s e l y represents both the s i z e d i s t r i b u t i o n of feed to the b i n and the most probable "average" feed d i s t r i b u t i o n to a l l o f the sc reens . h s i 1 4 | 13 i 1 21 11 i — 1 Coarsest Fine Finest Fine Coarsest Figure 11 Segregat ion Trends w i t h i n Screen Surge Bin Sampling o f the secondary screens was undertaken i n two phases. During the f i r s t phase (August , 1975) , both the primary and secondary c rush ing p lan t s were undergoing ex tens ive maintenance programs. Con-sequen t ly , no changes i n lower deck screen panels were a v a i l a b l e and sampling had to be c a r r i e d out on the screens as they were. A l l screens had composite lower decks , so the most "uniform" o f numbers 2 and 4 screens was se l ec ted , f o r sampl ing . T h i s was the number 2 s c r een , wi th a lower deck c o n s i s t i n g o f two feed end panels o f 5/8 i n . x 3-1/2 i n . s l o t t e d openings and three d ischarge end panels o f 1/2 i n . x " 3-1/2 i n . openings. - 38 -During the second phase o f sampling (December, 1975), two screens were made a v a i l a b l e f o r t e s t i n g , both w i th uniform openings i n the lower deck. The number 2 screen conta ined only 1/2 i n . x 3-1/2 i n . openings , w h i l e the number 4 screen conta ined on ly 5/8 i n . x 3-1/2 i n . openings. The same sampling procedures were used f o r each phase. F ive samples were taken dur ing the f i r s t phase. With screen feedrate. being the on ly manipulable v a r i a b l e , . t h e sample schedule was s i m p l e . Sampling c o n s i s t e d o f three c e n t e r p o i n t repeat runs , a h igh feedrate run and a low feedrate run . Dur ing the second phase, two manipulable v a r i a b l e s were a v a i l a b l e , so a modi f ied 2 n f a c t o r i a l design was cons t ruc t ed . S i x t e s t s were run : three a t the l a r g e r screen s i z e and three a t the s m a l l e r . The combined sample s c h e d u l e 1 f o r both phases i s depic ted, i n F igure 12. 1.25 1.30 1.35 1.40 1.45 Screen Opening 1.50 1.55 (cm) 1.60 1.65 Figure 12 Combined Exper imenta l Design f o r Secondary Screens 1 Calcula t ion of the equivalent screen opening for the composite screen i s presented i n Chapter h, Section - 39 -The presence o f the screen surge b i n , d i s c h a r g i n g d i r e c t l y onto each screen,.made sampling o f screen feed v i r t u a l l y i m p o s s i b l e , both w i t h respec t to measuring feedra te and to p h y s i c a l l y o b t a i n i n g a sample f o r a n a l y s i s . However, the "percent maximum feedra te" cou ld be a c c u r a t e l y measured and c o n t r o l l e d 1 ' f o r each o f the feeders drawing from the b in (wi thout knowledge o f the ac tua l va lue) thus enab l ing screen feedrate to be h e l d cons tant on- a r e l a t i v e s c a l e . Knowing t h a t segrega-t i o n occurs w i t h i n the b i n , approximations o f the t rue feed to the t e s t screens were made by sampling the feed t o the b i n . These samples were taken on number 14 conveyor i n the t r a n s f e r tower a t the same l o c a t i o n where the c rusher product samples were t aken . Sampling o f the screen o v e r s i z e and unders ize product streams presented no problems. Easy access to each stream was obta ined i n the t r a n s f e r tower , where both o v e r s i z e (number 16) and unders ize (number 18) conveyors are open and running p a r a l l e l . Loca t ions o f the sample po in t s are presented i n F i g s . 8(a) and 8 ( e ) , pages 24 and 2 7 . An attempt was made to minimize the e f f e c t s o f surge b in res idence time and b e l t l a g to ensure t ha t feed ma te r i a l sampled on number 14 b e l t would correspond to the product m a t e r i a l sampled on numbers 16 and 18 b e l t s . Th i s was accomplished through the use o f pa in t ed rock t r a c e r s . The sampl ing procedure adopted f o r the secondary screens i s o u t l i n e d as fol1ows: 1 Control of screen feedrate i s achieved through.control l ing current to the v ib ra t ing feeder discharging onto the desired un i t . - 40 -(1) s t a r t by ope ra t ing the secondary c rush ing p l an t under normal c o n d i t i o n s and s l o w l y f i l l i n g the screen surge b in u n t i l the high l e v e l alarm comes on. Shut down the e n t i r e c rush ing p l a n t , en su r ing number 14 b e l t i s f u l l y loaded . (2) take the feed sample from number 14 b e l t and s tore i n a covered drum. (3) spray about 20 fee t o f f eed -ma te r i a l j u s t ahead o f the sample cut w i th b r i g h t , f l u o r e s c e n t p a i n t . (4) s t a r t e n t i r e c rush ing p l a n t as q u i c k l y as p o s s i b l e . A l l screens and c rushers -a re to be running under normal ope ra t ing c o n d i t i o n s . (5) set feeders f o r t e s t screen to d e s i r e d percentage o f maximum feedra te . (6) watch f o r t r a c e r s on number 16 b e l t ( o v e r s i z e ) . When de t ec t ed , shut down a l l but the t e s t s c reen . (7) a l l o w time f o r o ther screens to c l e a r . (8) w a i t u n t i l t r a c e r s appear on number 16 b e l t aga in . When v i s i b l e , shut down numbers 16 and 18 b e l t s s i m u l t a n e o u s l y , us ing t r i p chords . (9) sample numbers 16 and 18 b e l t s and s to re the samples i n covered drums. Record res idence time o f t r a c e r s . Opera t ing data f o r both o f the screen sampling phases are pre -sented i n Table 5. Screen feedrates can be determined by assuming s teady-s t a t e around a screen and summing ,the o v e r s i z e and unders ize product f l o w r a t e s . - 41 -TABLE 5 Summary o f Opera t ing Data  Secondary Screen Sampling Phases INDEPENDENT ...Run Sample Screen Opening Feedrate % + 1 inch Number Phase inches cm. % max. s tph i n feed 17 1 • 16/27 • 1.50 40 . 356.8 47.29 18 1 16.27 1.50 40 353.4 33.65 19 1 16/27 1.50 40 345.4 43.26 20 1 16/27 1.50 60 563.7 34.81 21 1 16/27 1.50 20 157.8 . 22.86 25 2 1/2 1.27 TOO 1044.5 43.14 26 2 1/2 1.27 66 562.8 17.94 27 2 1/2 1.27 33 279.2 31.05 28 2 5/8 1.59 100 1004.2 29.40 29 2 5/8 1.59 66 498.7 36.90 30 2 5/8 1.59 33 265.3 34.12 Complete s i z e analyses o f a l l samples taken f o r the secondary screens i s presented i n Appendix B ( c ) . (e) Primary Fines Sampling Sampling o f the pr imary f i ne s stream was s t r a i g h t f o r w a r d . The f low o f t h i s stream i s d i s c r e t e and depends upon mining methods and ore haulage ra tes a t the mine. Flowrate a t any given t ime cannot be r e l i a b l y measured, because there are f requen t , long per iods when ore does not f l o w . However, the t o t a l d a i l y tonnage o f primary f i ne s has been recorded f o r a consecu t ive p e r i o d o f 96 days and i s presented i n Appendix B ( e ) . Samples o f the primary f i ne s stream were taken over a p e r i o d o f seven days. These samples were taken from number 19 conveyor - 42 -at the t r a n s f e r p o i n t where the primary f i ne s b lend wi th the secondary screens unders ize product . The sample procedure c o n s i s t e d o f pass ing two l a rge sample buckets through the d ischarge stream tha t f a l l s from conveyor head p u l l e y . The samples were taken as c lo se to the same time o f day (10:00 .A.M.) as was p o s s i b l e , w i t h i n the c o n s t r a i n t s o f mine haulage. On the second day, the mine was down dur ing the day s h i f t , so no sample was t aken . . In a l l , s i x samples were t aken , and t h e i r s i z e analyses are presented i n Appendix B ( d ) . 2.3 Sample Screening A f t e r the samples were t r a n s p o r t e d . t o the sc reen ing s t a t i o n i n the g r i n d i n g bay, they were s i z e d on a G i l son s c r een ing machine. The sc reen ing s t a t i o n (F igure 8 ( g ) , page28') was j o i n t l y shared w i t h the Brenda research personnel dur ing the e a r l y stages o f the p r o j e c t . A screen r a t i o of 1/2 (Canadian T y l e r S ieves) was d e s i r e d . However, f o r the + 1/2 inch s i z e f r a c t i o n s , G i l s o n screens i n the 1/2 r a t i o s e r i e s were u n a v a i l a b l e and a l t e r n a t e screens were used. The appropr i a t e 1/2 r a t i o screen s i z e s were l a t e r obta ined by e x t r a p o l a t i o n from l o g a r i t h m i c p l o t s o f the a c t u a l l y measured d i s t r i b u t i o n s . The screen s i z e s chosen f o r a n a l y s i s , and the method o f s c r e e n i n g , are l i s t e d i n Table 6. - 43 -TABLE 6 Screening Procedure f o r Secondary Crushing P l a n t Samples Intended 1/2 r a t i o Screen S i z e s ( i n y) Ac tua l Screen S izes used. ( U n i t s v a r i a b l e ) Screening Method 10 i n . - By hand, us ing s p e c i a l l y f a b r i c a t e d , 870,400u 8 i n . square mesh templates . 435,200y 6 i n . - P a r t i c l e s i n d i v i d u a l l y s i z e d . 217,600y 108,800y 4 i n . - By G i l son s c r e e n , s h o v e l l i n g from 54,400y 3 i n . sample drum u n t i l e n t i r e sampled 27,200y 1-1/2 i n . screened. S i z e f r a c t i o n s h e l d i n 13,600y 3/4 i n . p l a s t i c p a i l s u n t i l f u l l ; p a i l s 6,800y 1/4 i n . weighed on T o l e d o1 w e i g h s c a l e ; -1 /4 i n . f r a c t i o n r e t a i n e d , o ther f r a c t i o n s di scarded . - Using G i l son square mesh screens 3,400y 6 mesh - By rotap machine us ing s tandard T y l e r l , 7 0 0 y 10 mesh 1/2 r a t i o (square mesh) s i e v e sc reens . 850y 20 mesh - Samples r i f f l e d to approx. 5-10 l b s . 425y 35 mesh then d r i e d . Fur the r r i f f l e d to 212y 65 mesh approx. 350-400 gm., then dry screened. 106y 150 mesh D u p l i c a t e samples s to red f o r future 53y 270 mesh re fe rence . 37y 400 mesh - Suspect approx. 1 to 1-1/2% moisture content p r i o r to d r y i n g . pan pan 1 Toledo weighscale;. range from 0 to 75 l b . i n 2 oz. graduations. Scale ca l ib ra ted both before and after screening program and found to be accurate to wi th in 2-1/2 oz. at maximum def lec t ion . - 44 -CHAPTER I I I DATA ADJUSTMENT 3.1 The Secondary and T e r t i a r y Crushers No adjustment was made on data ob ta ined around the secondary c rushers . As p r e v i o u s l y d e s c r i b e d , the t e r t i a r y c rusher feedrates were found by averaging the f lowra tes c a l c u l a t e d from feed and product we igh t s . No f u r t h e r adjustments o f t e r t i a r y c rusher data were attempted. A d j u s t -ment o f the open c i r c u i t s i z e d i s t r i b u t i o n data from e i t h e r c rusher i s not p o s s i b l e . 3.2 The Secondary Screens I t was mentioned e a r l i e r t ha t d i r e c t sampling o f the v i b r a t i n g screen feed was i m p o s s i b l e . Consequent ly , a sample o f t h i s f lowstream was approximated by another sample taken from the feed to the screen surge b i n . However, due to p a r t i c l e segrega t ion e f f e c t s known to occur w i t h i n the b i n , the r e l i a b i l i t y o f the approximated feed sample i s unknown. Although d i r e c t sampling o f both o v e r s i z e and unders ize product streams was e a s i l y accompl ished , both o f these samples are a l so sub jec t to ex-per imental e r r o r . To minimize the above exper imental e r r o r , a data adjustment procedure was d e v i s e d . Th i s procedure i s analogous to one used f o r a (30v g r i n d i n g c i r c u i t by M u l a r , L a r s e n , Bradburn and F l i n t o f f v . The procedure assumes tha t a l l measured data are i n e r r o r and f inds adjusted data po in t s which minimize a l e a s t squares c r i t e r i o n , expressed as: - 45 Q = ? i [ — S ~ ] 1 = 1 (17) where M-j i s the i t h measured data p o i n t , S-j i s the s tandard d e v i a t i o n a s s o c i a t e d w i th the i t h measured data p o i n t and M | i s computed us ing the minimum number o f search v a r i a b l e s which permit c a l c u l a t i o n o f a l l data p o i n t s . Th i s s e t o f search v a r i a b l e s must s a t i s f y the steady s t a t e c o n d i t i o n s dep ic t ed i n F igure 13. As an example , i f one cons iders the g e n e r a l i z e d data l i s t e d i n Table 7, the f o l l o w i n g must be v a l i d at steady s t a t e : F = 0 + U i = 1 to n (18) fi = (0 /F) OJ. + ( U / F ) U i where F , 0 , U , f | , o-j and u-j have been measured around the sc reen . Note tha t one o f the v a r i a b l e s f.n-, o.j o r un- i s unnecessary f o r complet ion o f a mass balance c a l c u l a t i o n . Furthermore, one o f the f lowra tes F , 0 o r U can a l s o be cons idered to be redundant. F,f: (No. 14 Belt)' (No.18 Belt) O.O, (No. 16 Belt) Figure 13 Schematic Diagram f o r Mass Balance of a Secondary Screen - 46 -TABLE 7 Gene ra l i z ed Table o f Data Obtained Around Screen S i z e i Weight Percent Reta ined on S i z e Feed Overs ize Undersize 1 2 3 4 n ' I 0, U. F lowrates 0 U A f t e r ca re fu l c o n s i d e r a t i o n , the absolute values o f the f o l l o w i n g were def ined as search v a r i a b l e s : 0 , U , Oj and u-j , f o r i = 1 to n - 1. The symbols ~ and " r e s p e c t i v e l y denote a search v a r i a b l e and an adjusted data p o i n t . Adjus ted d a t a . p o i n t s can be computed from search v a r i a b l e s as f o l l o w s : 6 = 6 U = 0 F = 6 + U Uj. f i °h "n = pi = Ui = (1-u . ) c i , + ( ^ ) u i ; i = 1 to n - 1 6+U 0+U (19) . n-1 ~ 1-E 0,-i = l 1 - 47 -The adjusted data po in t s may be determined by f i n d i n g the combination o f search v a r i a b l e s which minimizes the f o l l o w i n g o b j e c t i v e f u n c t i o n : O . F . = " ( ! i ^ i ) 2 + S ( u J - H ) 2 + nT. ( f i i f i ) 2 i= l So-j i = l Sui i = l S-fj + (0 - 6) 2 + (U - U ) 2 (20) where S o j , Su^ and Sfj are the s tandard d e v i a t i o n s a s soc i a t ed w i t h the i t h s i z e f r a c t i o n o f the measured o v e r s i z e , unders ize and feed streams (6 29) r e s p e c t i v e l y . A m o d i f i c a t i o n o f the s implex d i r e c t search method^ ' ' was employed to f i n d the se t o f search v a r i a b l e s t ha t would minimize equat ion (20 ) . Tes ts numbers 17, 18 and 19 are repeat runs where ope ra t i ng v a r i a b l e s were se t to the same l e v e l s . From these r epea t s , es t imates o f s tandard d e v i a t i o n can be determined f o r each s i z e f r a c t i o n o f the measured feed and product s i z e d i s t r i b u t i o n s . These es t imates o f So-,- , Su-j and Sfj; are then in t roduced i n t o the o b j e c t i v e func t ion to enable the search program to minimize w i t h respec t to the s t a t i s t i c a l p r e c i s i o n inheren t to the sampling o f t h i s p a r t i c u l a r o p e r a t i o n . The computer program c rea ted to perform the screen data ad jus t -ment i s c a l l e d SCREEN and i s w r i t t e n i n the BASIC language 1 . A l i s t i n g o f t h i s program i s presented i n Appendix C ( a ) . The output from SCREEN represents the f i n a l , f u l l y adjusted screen data used i n development o f the screen model. 1 A l l computer programs used during th i s project are wri t ten i n U.B .C . BASIC, with.the exception of p l o t t i n g programswhich are wr i t ten i n FORTRAN .IV,.WATFIY d i a l e c t , i n order to u t i l i z e the U.B .C . p l o t t i n g • machines. - 48 -Incorpora ted w i t h i n SCREEN i s a shor t subrout ine used to c a l c u l a t e o rd ina t e values f o r the corresponding screen e f f i c i e n c y curve . For the purpose o f t h i s t h e s i s , the screen e f f i c i e n c y curve i s de f ined as the p l o t o f the weight f r a c t i o n o f feed i n s i z e range i r e p o r t i n g to the o v e r s i z e product versus the l o g a r i t h m o f the geometric mean o f p a r t i c l e s i z e range i . The o rd ina t e o f the e f f i c i e n c y curve i s computed as f o l l o w s : Y i = ° L ° i = l to n-1: (21) f^O+U) The adjusted screen da t a , complete w i t h e f f i c i e n c y curve o r d i n -a t e s , i s presented i n Appendix C ( b ) . - 49 -CHAPTER IV MODEL DEVELOPMENT 4.1 Summary o f Development Procedures A l l four models were developed accord ing to the same b a s i c s t r a t e g y . Th i s s t r a t egy c o n s i s t s o f four stages and i s summarized as f ol1ows: (a) propose a model form (b) determine constants tha t enable the model to f i t observed data (c) q u a n t i t a t i v e l y r e l a t e constants i n f i t t e d models to measured ope ra t i ng v a r i a b l e s . (d) es t imate how w e l l model performs and modify as necessary u n t i l s a t i s f a c t o r y performance i s achieved The c rusher models proposed are based on a model t e s t ed by W h i t e n ^ i n 1972. Important d i f f e r e n c e s a r i s e i n the c a l c u l a t i o n o f the breakage mat r ix B~, i n the e m p i r i c a l r e l a t i o n s developed to p r e d i c t model parameters and i n the crusher cu r r en t e q u a t i o n . The model adapted to the t e r t i a r y crushers d i f f e r s app rec i ab ly from t h a t developed the secondar i e s . The d i scon t inuous nature o f Whi ten ' s screen model was found to be awkward, so an a l t e r n a t i v e model was proposed to desc r ibe the secondary screens . The primary f i n e s model was developed e m p i r i c a l l y . Once models were e s t a b l i s h e d , d i r e c t s e a r c h e s 1 were made f o r the values o f a l l unknown model parameters t ha t would enable a "best f i t " o f the proposed model to the observed da ta . Th i s was done f o r each data s e t . These "optimum" parameters were then analysed both g r a p h i c a l l y and us ing s imple hand c a l c u l a t o r r eg re s s ion analyses t o determine i f any i These were modified Simplex type di rec t searches. The program de-veloped for parameter searches i s ca l l ed BRCRUSH and i s wr i t ten i n BASIC. I t i s a modification of the program SCREEN. - 50 -r e l a t i o n s h i p s e x i s t e d between parameters. Th i s u s u a l l y enabled some parameters t o be f i x e d as t rue constants and others to be expressed i n terms o f the remaining parameters , thus reducing the number o f parameters t o be r e l a t e d to ope ra t ing v a r i a b l e s . D i r e c t searches were again c a r r i e d out to f i n d "optimum" values f o r the new se t o f parameters. With the "optimum" values f o r the new se t o f parameters , a complete r eg re s s ion a n a l y s i s was performed to determine r e l a t i o n s h i p s w i th ope ra t i ng v a r i a b l e s . A BASIC language computer program c a l l e d ALLREDD was used to perform the m u l t i - v a r i a b l e r eg re s s ion ana lyses . A complete l i s t i n g o f the program ALLREDD and a da ta t r ans fo rmat ion program, c a l l e d TRANS 4 , i s i n c l u d e d i n Appendix D. Us ing ALLREDD, equat ions r e l a t i n g the model parameters t o observed ope ra t ing v a r i a b l e s were developed. A f t e r an approximate model form had been found, a "s imul taneous" Simplex search was conducted f o r values o f constants i n the model t ha t would minimize the o b j e c t i v e f u n c t i o n d i r e c t i n g the sea rch . Th i s search was conducted s imu l t aneous ly on a l l v a l i d data se t s p e r t i n e n t t o the model under development. The computer program w r i t t e n to perform t h i s search i s c a l l e d TURKEY and uses the s implex d i r e c t . s e a r c h method p r e v i o u s l y r e f e r r enced . T h i s program was a l t e r e d to i nco rpora t e the model under development and the va r ious m o d i f i c a t i o n s are presented i n the appro-p r i a t e appendices. Output from t h i s program c o n s t i t u t e d a model. However, not a l l model forms were s a t i s f a c t o r y and the above process was u s u a l l y repeated f o r seve ra l forms before an acceptable model was e s t a b l i s h e d . A l l computer programs us ing the Simplex search method ( i n c l u d i n g SCREEN) employ a f i t t i n g technique i n the o b j e c t i v e f u n c t i o n based on - 51 -m i n i m i z a t i o n o f the r e s i d u a l sum o f squares between observed and p r e d i c t e d data p o i n t s . The sum o f squares are c a l c u l a t e d us ing the product s i z e d i s t r i b u t i o n s expressed i n weight f r a c t i o n r e t a i n e d on s i z e r a the r than s i z e f r a c t i o n mass f l ows . The i n d i v i d u a l s i z e f r a c t i o n s may o r may not be weighted dur ing e v a l u a t i o n o f the o b j e c t i v e f u n c t i o n , depending upon the a v a i l a b i l i t y o f repeat da ta . 4.2 The Secondary Crusher Model The bas i s f o r the cone c rusher model i s the assumption tha t p a r t i c l e s e n t e r i n g the c rusher s p l i t i n t o . p o r t i o n s t ha t e i t h e r leave the crusher unharmed or are broken. Those p a r t i c l e s which are broken then have the same choice o f e i t h e r be ing broken again or l e a v i n g the c rusher . Consequent ly , the c rush ing phenomenon can be d i v i d e d i n t o two b a s i c ope ra t i ons : t ha t o f p a r t i c l e breakage and t ha t o f p a r t i c l e c l a s s i f i c a t i o n . As shown i n F igure 1, page 6 , the c rusher model can be expressed by a s i n g l e breakage zone, represented by B", and a p r o b a b i l i t y o f e n t e r i n g tha t zone, represented by C. From mass balances aroundnodes 1 and 2 (see F igure 1, page 6 ) , the product vec to r i s p r e d i c t e d from the e q u a t i o n : P = [T - C] [T - B C ~ ] ~ T (.10) which represents the f i n a l i z e d ma t r ix form o f the model. Note t ha t the ma t r ix [ I - BZ] must always be n o n - s i n g u l a r (determinant f 0 ) , as a u n i t element on the d iagonal o f B" C] i m p l i e s both no breakage and no d ischarge o f t ha t s i z e f r a c t i o n . (a) The Breakage M a t r i x , B" Whiten d i v i d e d the breakage ma t r i x i n t o two components, each i - 52 -presumably d e s c r i b i n g a d i f f e r e n t type o f c rush ing a c t i o n . Both compon-ents are lower t r i a n g u l a r . The f i r s t component, B l , desc r ibed the mechanism o f pr imary breakage by g i v i n g the product d i s t r i b u t i o n r e l a t i v e to the s i z e of the l a r g e s t o r i g i n a l feed p a r t i c l e . Th i s component forms an (n-1) by (n-1) s tep m a t r i x . w h i c h was normal i zed w i t h respec t to the l a r g e s t o r i g i n a l feed p a r t i c l e . Consequent ly , the e n t i r e ma t r ix can-be computed once the elements o f the f i r s t column are known. Th i s i s done by d i s p l a c i n g the f i r s t column over one column and down one row f o r success ive s i z e f r a c t i o n s , wi th zeros occupying empty l o c a t i o n s i n the a r r ay . Th i s procedure i s shown d i a g r a m a t i c a l l y i n F igure 14. 0 0 b b. b b n - 2 b n - 3 n n n-1 f i r s t column known Figure 14 Computational Procedure f o r Primary Breakage. Component, BT - 53 -The elements o f the f i r s t column o f the B l ma t r ix are computed from the modi f i ed Gaudin-Meloy pr imary breakage e q u a t i o n 1 : Y p = 1 - (1 - (•*!)?)* (7) where y and 3 were determined to be cons tant f o r the secondary crushers w i th y = 2 .0 and 3 = 6 . 0 . These elements are computed as f o l l o w s : b i = Y p ( i ) - Y p( i+1) 1 = 1 t 0 n _ 1 Y p ( o ) = 1.0 (23) f o r the i t h row, f i r s t column. The second component o f the breakage m a t r i x , B2~, was assumed to be independent o f the o r i g i n a l p a r t i c l e s i z e and consequent ly , not n o r m a l i z a b l e . However, t h i s ma t r ix can be e m p i r i c a l l y c a l c u l a t e d once the elements o f the f i r s t row are known. Th i s i s achieved by d i s p l a c i n g the f i r s t column sideways to form an (n-1) by (n-1) m a t r i x , then adding the ma te r i a l p r e d i c t e d above the s i z e being broken to tha t s i z e . The computat ional procedure i s shown i n F igure 15. The elements o f the f i r s t column o f the B2" mat r ix are c a l c u l a t e d from , t n e Rosin-RammTer d i s t r i b u t i o n f u n c t i o n : Y s = 1 - exp ( - ( | L ) V ) (24) where S" and v are model constants found to have the values o f 2 .0 cm and 0.664 r e s p e c t i v e l y . The method o f computing B2~ elements i s : a i = Y - s ( i ) " Y s ( i + 1 ) 1 = 1 t 0 n-" 1 (25)' 1 This breakage equation d i f fe rs from that used by Whiten. He used a modificat ion of the Rosin-Rammler equation proposed by BroadbentU^' (equation ( 3 ) , page h ) . From prel iminary analyses, t h i s equation did not appear to be sa t i s fac tory for our data. - 54 -B2 (1 ,1) = a l a l a l • a i a 2 a 2 a 2 a 2 a 3 -> a 3 a 3 a 3 a 3 a 4 • • • a n V a n a • • n • •a n B2= a l ° 1 0 — i .0 a 2 a-|+a2 n 0 a 3 a 3 a l + a 2 + a 3 0 a 4 a 4 a 4 n n m i V ' - + a n f i r s t column known Figure 15 Computation Procedure f o r Secondary Breakage Component, B2 However, i f the d i s t r i b u t i o n func t ion i s r e w r i t t e n as: ys = exp [ - ( i i ) v ] (26) S" where y s i s the cumulat ive f r a c t i o n coa r se r than s i z e x- j , then the computation becomes: a i = y ; s ( i + l ) - V s ( i ) i = 1 to n-1 (27) where y s ( o ) = 0 Equat ion (27) was found to s i m p l i f y computations i n the search programs BRCRUSH and TURKEY. - 55 -To ob ta in the t o t a l breakage m a t r i x , the two components are summed i n l i n e a r combination accord ing t o : B = a BT + (1-a) B2 (28) where « , the l i n e a r combination c o e f f i c i e n t , was found to be r e l a t e d to the crusher gap and feedrate by the equa t ion : a = -0.91489 + 0.21729 G+ 0.000626T + 0.0056345 (29) The r e l a t i v e c o n t r i b u t i o n s o f the two breakage components are presented g r a p h i c a l l y i n Figure 16. A t y p i c a l secondary c rusher product s i z e d i s t r i b u t i o n i s i n c l u d e d f o r comparison. Figure 16 R e l a t i v e C o n t r i b u t i o n s o f Breakage Func t ion Components, Bl and B2 - 56 -(b) The C l a s s i f i c a t i o n M a t r i x , C The d iagonal elements o f the c l a s s i f i c a t i o n ma t r ix (C) are ob ta ined from a d i s c r e t e func t ion o f p a r t i c l e s i z e based on the f o l l o w i n g assumptions: (1) p a r t i c l e s above a c e r t a i n s i z e K2 are always broken, o r : c(x.j) = 1.0 x i > K2 (30) (2) p a r t i c l e s below a c e r t a i n s i z e Kl are not b roken , but pass through the c ru she r , so t h a t : c(x-j) = 0 x-j < Kl (31) (3) p a r t i c l e s between these s i z e s are broken acco rd ing to a p a r a b o l i c p r o b a b i l i t y r e l a t i o n s h i p expressed by: c(x ) = l - ( ^ J < 2 ) 2 1 K l - K2 Kl < x . < K2 The c l a s s i f i c a t i o n func t ion c(x-j) i s dep ic t ed i n F igure 17. 11 x u _Q O _Q O £_ Q_ K1 K2 Particle Size , x (32) F igure 17 C l a s s i f i c a t i o n F u n c t i o n , c(x) - 57 -The diagonal elements o f the C mat r ix are c a l c u l a t e d as the mean values o f c(x) over the s i z e range i n ques t ion accord ing t o : C(x) = XJ c (x)dx (33) X 2 - X l A f t e r i n t e g r a t i o n and s u b s t i t u t i o n o f boundary c o n d i t i o n s , the f o l l o w i n g may be used to c a l c u l a t e the C elements: ( i ) F ( x i ) + Kl - 1/3(K1 - K2) Kl > x.,-( i i ) F ( X i ) = x.. - V 3 ( x ; i - K 2 ) K 1 ^ K 2 ( K l - K 2 P ( 3 4 ) ( i i i ) F(x ; 1-) = x i K2 < X i ( 1 V ) C ( l ) " x ^ - x i + 1 1 = 1 * o " - l The two parameters , Kl and K2 , are p r e d i c t e d from the equa t ions : K l = 44.5875 - 33.5157 G+ 5.677T.G 2 + 0.1221 S (35) and K2 = -22.8812 + 23.7981 G - 3.7319 ; G 2 - 0.02798S (36) (c) The Crusher Current . The secondary c rusher cu r r en t draw can be p r e d i c t e d from the c rusher gap and feedrate by the equa t ion : C = 20.6182 - 7.323393 G+ 0.0345158T (37) Th i s r e l a t i o n i s s imple and agrees w i t h what i s expected f o r the i n f l u e n c e o f gap and feedrate on cu r r en t draw. I t was observed tha t a change i n feed s i z e d i s t r i b u t i o n had n e g l i g i b l e e f f e c t upon the measured cu r r en t over the ranges s t u d i e d . Equat ion (3 7) i s subs tan-t i a l l y d i f f e r e n t from tha t proposed by W h i t e n ^ . - 58 -(d) Model Accuracy and Range The computer program used f o r f i t t i n g the secondary c rusher model (TURKEY) i s presented i n Appendix E . The program f i n d s model parameters t ha t minimize the sum o f the square o f the d i f f e r e n c e s . (RSS) between measured and p r e d i c t e d product s i z e d i s t r i b u t i o n s . A l s o presented i n Appendix E i s the computer program f o r the f i t t e d model , c a l l e d SECRUSH, w i t h p r e d i c t i o n s f o r a l l t e s t runs. I t i s not p o s s i b l e to t e s t f o r l ack o f f i t o f the model because o f the absence o f repeat runs. Thus, i t i s not p o s s i b l e t o determine the r e l a t i v e c o n t r i b u t i o n s o f the RSS components due to l ack o f f i t and to random e r r o r . The obvious method f o r e v a l u a t i o n o f the secondary c rusher model i s by a p p r a i s a l o f the RSS c a l c u l a t e d f o r each run. A mean RSS o f 1 3 . 5 , w i t h a s tandard d e v i a t i o n o f 1 6 . 3 , was observed. Crusher cu r ren t p r e d i c t i o n s are w i t h i n the observed measurement p r e c i s i o n o f + 3 amperes. The secondary c rusher model i s judged to be s a t i s f a c t o r y f o r s i m u l a t i o n purposes , al though i t i s f e l t tha t improvements may be p o s s i b l e i n the c l a s s i f i c a t i o n mat r ix s e c t i o n . The g r a p h i c a l performance o f the model i s dep ic t ed i n F igures 18(a) and ( b ) , r ep resen t ing the best and the wors t model p r e d i c t i o n s . The secondary c rusher model d i f f e r s from Whitens model i n the f o l l o w i n g ways: (a) use o f a d i f f e r e n t equat ion to desc r ibe primary breakage (b) use o f d i f f e r e n t r e l a t i o n s f o r p r e d i c t i n g model parameters (c) use o f a d i f f e r e n t r e l a t i o n f o r p r e d i c t i n g c rusher cu r r en t draw There i s no doubt t ha t e r r o r has been in t roduced du r ing sampl ing o f the secondary c rushe r s . Both the extremely la rge p a r t i c l e s i z e s - 59 -Figure 18(a) Performance o f Secondary Crusher Mode l , Best P r e d i c t i o n - 60 -Figure 18(b) Performance o f Secondary Crusher Mode l , Worst P r e d i c t i o n - 61 -i n v o l v e d and the h igh frequency o f shor t term f l u c t u a t i o n s i n feedrate made accurate sampling very d i f f i c u l t . Furthermore, due to the d i f f i c u l t y o f sampling,and i n t e r f e r e n c e wi th p l a n t o p e r a t i o n , only a smal l number o f samples were ob ta ined . For these reasons , the accuracy o f the cone c rusher model should not be expected to equal t h a t o f a rod o r b a l l m i l l model , unless a much l a r g e r sample popu la t ion has been a c q u i r e d . There i s cons ide rab le danger i n e x t r a p o l a t i o n o f an e m p i r i c a l model beyond the data range over which the model was f i t t e d . However, i t i s useful to know how a model w i l l behave when ope ra t i ng v a r i a b l e s are se t beyond the f i t t e d data range. T h i s knowledge becomes e s s e n t i a l i n a mul t i -model s i m u l a t i o n , where the s i m u l a t i o n has the a b i l i t y to generate values f o r ope ra t ing v a r i a b l e s which may span w e l l beyond the f i t t e d data ranges w h i l e approaching a convergence. S tudies were conducted on the secondary c rusher model to see how w e l l i t would e x t r a p o l a t e beyond i t s f i t t e d data ranges. I t was found t ha t a l l combinations o f ope ra t ing v a r i a b l e s cou ld be e x t r a p o l a t e d twenty percent below the lower l i m i t s o f the f i t t e d data ranges w i th no apparent problems. However, t h i s was not t rue f o r e x t r a p o l a t i o n above the upper l i m i t s , where se r ious problems, such as p r e d i c t i n g negat ive values where p o s i t i v e ones are manditory,were observed to occur . Since parameters were observed to be func t ions o f two o r more ope ra t ing v a r i a -b l e s , the parameters are i n t e r a c t i v e and s imple e x t r a p o l a t i o n i s d i f f i -c u l t . However, i t has been p o s s i b l e to make the f o l l o w i n g i n d i v i d u a l parameter e x t r a p o l a t i o n s under the c o n d i t i o n s s t a t e d : - 62 -(a) feedrate to + .20%, i f the gap and % + 1 inch do not exceed the upper l i m i t o f the sampled data range. (b) gap to + 7%, i f the feedrate and % + 1 inch do not exceed the upper l i m i t o f the observed data range. The e x t r a p o l a t i o n range increases as T and S decrease. (c) % + 1 inch to + 5.5%, i f the gap and feedrate . do not exceed the upper l i m i t o f the observed data range. I t was not p o s s i b l e to e x t r a p o l a t e combinat ions o f two o r more ope ra t i ng v a r i a b l e s beyond +2%. 4 .3 The T e r t i a r y Crusher Model The model proposed f o r the t e r t i a r y crushers i s very s i m i l a r to t ha t repor ted f o r the secondary c rushe r s . The d i f f e r ence l i e s i n the equat ions developed to p r e d i c t the model parameters as func t ions o f the o p e r a t i n g v a r i a b l e s . I t was a l s o found t ha t an a d d i t i o n a l para-meter r equ i r ed p r e d i c t i o n . The'..matrix form o f the model, remains ex-pressed i n terms o f the c rusher feed by the equa t ion : ( a ) . The Breakage M a t r i x , B The breakage phenomenon i s s t i l l e x p l a i n e d by a t o t a l breakage mat r ix comprised o f two components-, both o f which are lower t r i a n g u l a r . The breakage component mat r ices are c a l c u l a t e d as p r e v i o u s l y d e s c r i b e d . However, an important d i f f e r ence a r i s e s i n the use o f the modi f i ed Gaudin-Meloy d i s t r i b u t i o n f u n c t i o n to desc r ibe primary breakage. Th i s func t ion i s expressed as : I t was found tha t the parameter e, determined to be constant f o r the P = [ I - C] [ I - B C ] _ 1 F (10) Y p ( i ) = 1 " *1 - ( (7) - 63 -secondary c r u s h e r s , e x h i b i t e d too much v a r i a t i o n to be he ld constant f o r the t e r t i a r y c rushe r s . I t was a l s o found t h a t 3 was s t r o n g l y r e -l a t e d to the l i n e a r combinat ion c o e f f i c i e n t a. In a d d i t i o n , the para-meter Y) al though s t i l l cons tan t , i s l a r g e r by a f a c t o r o f two. The parameters i n v o l v e d i n the Gaudin-Meloy pr imary breakage equat ion are expressed as : Y = 4 .0 (38) and 3 = 27.4583 + 43.97832 EXP (-2599.762 ai&'.766 3) (39) The secondary breakage equat ion expressed by the Rosin-Rammler d i s t r i b u t i o n f u n c t i o n : Y s ( 1 ) = 1 - exp ( - ( | r ) v ) (2.4) remains unchanged. The values o f the parameters a re : S" = 2 .0 ,cm. and v = 0.664. The l i n e a r combination c o e f f i c i e n t , a , can be p r e d i c t e d from the c rushe r feedrate by the equa t ion : a = 0.1133812 + 1.178078 x 1 0 - H + (- 0 , 5 1 8 0 7 6 : ) (40) l+3 .632176x l0~ l t (T-299 .381) 2 (b) The C l a s s i f i c a t i o n M a t r i x , C~ The c l a s s i f i c a t i o n mat r ix i s a l s o def ined and c a l c u l a t e d as desc r ibed f o r the secondary crusher.mode1. The d i f f e r ence between the c l a s s i f i c a t i o n mat r ices l i e s w i t h the equat ions tha t p r e d i c t the para-meters K l and K2. For the t e r t i a r y c r u s h e r s , these parameters can be p r e d i c t e d from the feed s i z e and c rusher gap by the equa t ions : Kl = -1.793265 + 0.05284647 S (41 ) - 64 -and K2 = 6.331619 - 0.8040997 G _ { 1.042385 -j 1 7.966.98 ( 4 2 ) 1 + 2.996623(G-0.7135176) 2 I t should be noted tha t the model i s very s e n s i t i v e to round-o f f e r r o r i n the parameter equat ion cons tan t s . Attempts were made to round-o f f a l l equa t ion constants w i th very s i g n i f i c a n t l o s s o f model accuracy . The behaviours o f the fou r model parameters are dep i c t ed g r a p h i c a l l y i n Figure 19. (c) The Crusher Curren t The t e r t i a r y c rusher cu r ren t i s p r e d i c t e d from the crusher gap and feedrate by the equa t ion : C = 27.55756 - 9.608871 G+ .0.0554204 T (43) Th i s r e l a t i o n has the same form as t ha t developed f o r the secondary c rusher m o d e l . . As b e f o r e , the feed s i z e d i s t r i b u t i o n was observed to have a n e g l i g i b l e e f f e c t upon the c rusher cu r ren t draw. Th i s express ion i s again cons ide r ab ly d i f f e r e n t from, the one used by Whiten f o r p r e d i c -t i o n o f the c rusher c u r r e n t . (d) Model Accuracy and Range The computer program used to f i t the t e r t i a r y c rusher model (TURKEY) i s presented i n Appendix F. As w i t h the secondary c rusher v e r s i o n , the o b j e c t i v e f u n c t i o n f o r t h i s program u t i l i z e s the sum o f the squares o f the d i f f e r ences between measured, and p r e d i c t e d product s i z e d i s t r i b u t i o n s (RSS). A l s o presented i n Appendix F i s the program f o r the f i t t e d model , c a l l e d . T E R C R , w i th p r e d i c t i o n s f o r a l l f i t t e d - 65 -(a) Parameter a (b) Parameter 3 (c) Parameter K l (d) Parameter K2 Figure 19 Behav ior o f T e r t i a r y Crusher Model Parameters - 66 -t e s t runs. As no repeat runs were a v a i l a b l e , a l ack o f f i t t e s t cannot be performed. Dur ing development o f the t e r t i a r y c rusher model , two data se ts were noted to behave i n a c o n s i s t e n t l y d i f f e r e n t manner from the o the r s . These data sets represent t e s t s numbered 14 and 16B. I t i s suspected tha t the c rusher gap was read i n c o r r e c t l y w h i l e p repa r ing f o r t e s t no . 16B and t ha t the t rue .gap i s somewhat l a r g e r than was recorded. Data from t e s t no . 16B seems to conf i rm t h i s o b s e r v a t i o n , as.more p l a u s i b l e behaviour was observed when a gap s i z e o f .85 cm. was used i n place o f the recorded .762 cm. No obvious reason can be d i sce rned f o r severe d e v i a t i o n s noted from t e s t n o . 14. Due to these s u b s t a n t i a l l y dev ian t behav iou r s , data sets numbered 14 and.16B were de le t ed f o r development o f the f i n a l model . As a r e s u l t o f the bad data s e t s , cons ide rab le d i f f i c u l t y was exper ienced i n development o f the parameter p r e d i c t i n g r e l a t i o n s . Severa l se ts o f a l t e r n a t i v e r e l a t i o n s were developed, t e s t ed and e v e n t u a l l y d i s -carded . The f i n a l model enables s a t i s f a c t o r y p r e d i c t i o n o f the r e l i a b l e data s e t s , w i t h a mean RSS o f 25.7 and a s tandard d e v i a t i o n o f 2 4 . 6 . The g r a p h i c a l performance o f the model i s i l l u s t r a t e d i n F igures 20(a) and 2 0 ( b ) , d e p i c t i n g p r e d i c t i o n s f o r the best and wors t runs r e s p e c t i v e l y . Severa l o f the a l t e r n a t i v e model forms developed gave b e t t e r p r e d i c t i n g performance over the data range to which they were f i t t e d . However, these forms were cons ide r ab ly more complex than the present form and caused s e r i o u s problems when e x t r a p o l a t e d beyond t h e i r f i t t e d data range. The present model can be s u c c e s s f u l l y e x t r a p o l a t e d a t l e a s t Figure 20(a) Performance o f T e r t i a r y Crusher Model , Best P r e d i c t i o n Figure 20(b) Performance o f T e r t i a r y Crusher Mode l , Worst P r e d i c t i o n , - 69 -twenty percent ou t s ide f i t t e d ranges, f o r any combinat ion o f v a r i a b l e s , w i th no apparent problems. The present t e r t i a r y c rusher model i s cons idered s a t i s f a c t o r y f o r s i m u l a t i o n purposes. Note t ha t the model d i f f e r s from tha t proposed by Whiten i n the f o l l o w i n g ways: (a) use o f a d i f f e r e n t equa t ion to desc r ibe primary breakage (b) more model parameters r e q u i r i n g p r e d i c t i o n (c) use o f d i f f e r e n t r e l a t i o n s f o r p r e d i c t i n g model parameters (d) use o f a d i f f e r e n t r e l a t i o n f o r p r e d i c t i n g c rusher cu r ren t draw I t shou ld be noted t ha t the behav iour o f parameter K2 as a func t ion o f c rusher gap i s not what would be expec ted , i n tha t the base l i n e f o r the func t ion decreases w i t h i n c r e a s i n g gap. (see F igure 19 (d ) ) . An a l t e r n a t i v e express ion was developed f o r parameter K2 which does * -behave as would be expec ted , but which r e s u l t s i n a s . i g h i f i c a n t r l o s s o f p r e d i c t i n g accuracy over the range o f data sampled. For t h i s reason the a l t e r n a t i v e K2 express ion i s not used. The a l t e r n a t i v e i s expressed by the e q u a t i o n : K2 =.' 8:9T6337 c+"^34v56163^GV!:18.18497^e'Xp(-^1;.74922 : (G- .891776) 2 ) (44) I t s behaviour i s dep ic t ed g r a p h i c a l l y i n F igure 2 1 / ' 4 .4 The Secondary Screen Model The Whiten screen model was analysed i n d e t a i l and found to be d i scon t inuous i n nature (see page 9 ) . An a l t e r n a t i v e e f f i c i e n c y equat ion was d e r i v e d from s t a t i s t i c a l - m e c h a n i c a l c o n s i d e r a t i o n s and f i t t e d to the observed sc reen ing data to produce the model proposed i n t h i s t h e s i s . The d e r i v a t i o n i s presented i n Appendix G. - 70 -Tertiary Crusher Gap - (cm) Figure 21 Behavior o f A l t e r n a t i v e K2 R e l a t i o n (a) Model D e s c r i p t i o n The de r i ved screen e f f i c i e n c y equat ion i s continuous over any s i z e range o f i n t e r e s t and makes the f o l l o w i n g assumptions: (a) the sc reen ing opera t ion i s a t steady s t a t e (b) the p a r t i c l e volume diameter i s e f f e c t i v e l y p r o p o r t i o n a l to the geometric mean diameter and independent of p a r t i c l e shape f ac to r s (c) p a r t i c l e s w i t h i n a narrow s i z e f r a c t i o n are not d i s t i n g u i s h e d from other p a r t i c l e s w i t h i n the same s i z e f r a c t i o n . The l a t t e r assumption becomes more r e a l i s t i c as the mean p a r t i c l e s i z e decreases and the p a r t i c l e popu la t ion i n c r e a s e s . The general form o f the e f f i c i e n c y equat ion i s expressed as: - 71 -1-Ci Y l = + C i i = 1 to n-1 (45) l + e x p [ x 5 0 3 _ X i 3 ] where Yj i s the p r e d i c t e d weight f r a c t i o n o f feed r e p o r t i n g to the o v e r s i z e product and C-j i s an a u x i l l i a r y func t ion in t roduced to ex-p l a i n the sho r t c i r c u i t i n g o f unders ize m a t e r i a l , such as mois t f i n e s , to the o v e r s i z e product . The p a r t i c l e s i z e X-j i s represented by the geometric mean o f the s i z e range i n q u e s t i o n . An a l t e r n a t i v e and use-f u l form o f the e f f i c i e n c y equat ion i s : Ui = Ff-j F ^ ' 3 ••••.3 i = 1 to n-1 (46) - g - u ( i + e x p r X 5 0 J ' V ] where un- i s the p r e d i c t e d weight f r a c t i o n o f feed r e p o r t i n g to the unders ize product . The pan s i z e m a t e r i a l (ma te r i a l pass ing the s m a l l e s t s c r e e n , -53y f o r t h i s p ro j ec t ) i s p r e d i c t e d by s e t t i n g x-j=0 as f o l l o w s : Y pan = ~ + c ' i = cons tant j = n (47) l+exprx-so 3-, a J For data ob ta ined around the Brenda Mines l t d . s c reen ing c i r c u i t , the a u x i l l i a r y func t ion has been se t equal to z e r o . The screen model parameters are p r e d i c t e d from the equa t ions : % 0 = 6.543503 - 7.342139.;^ + 2 . 8 5 5 7 7 6 V (48) - 4 . 6 4 8 8 1 x l 0 " 5 S 2 - 1 . 3 0 3 6 5 5 x l 0 " 2 2 T 7 and a = 1.238414 + 0.4822109- <f - 1 .002221xlO" 2 S (49) + 1 . 1 6 3 8 7 1 x l 0 - 7 T 2 I t i s convenient at t h i s stage to e x p l a i n how an e q u i v a l e n t screen opening , f e , was determined f o r the composite screens employed - 72 -i n t e s t s 17 to 21 . The two feed end panels o f the lower deck c o n s i s t e d o f 5/8 i n . x 3-1/2 i n . s l o t s , w h i l e the three d ischarge-end panels c o n s i s t e d o f 1/2 in., x 3-1/2 i n . s l o t s . . The f i r s t two fee t o f the feed end o f the upper deck were blanked o f f by a p r o t e c t i v e rubber s t r i p , e f f e c t i v e l y removing the corresponding sc reen ing area i n the feed end p a n e l . o f the lower deck. Us ing a Simplex d i r e c t search (see page 47), values f o r the model parameters " x ; 5 0 " and "a" were determined f o r each t e s t , i n c l u d i n g t e s t s 17 to 21 . However, the constants used i n equat ions 4 8 and 49. were i n i t i a l l y determined f o r t e s t s 25 to 30 o n l y , ( e x c l u d i n g "i. t e s t s 17 to 21) us ing r eg res s ion analyses conducted w i th the computer program ALLRED (see Appendix D(a)),. Runs 25 to 30 i n v o l v e d uniform screen openings i n the lower deck. F o l l o w i n g t h i s , equat ions 48 and 49 were used to back c a l c u l a t e values f o r <()'e f o r runs 17 to 2 1 , w i t h two es t imates per run be ing o b t a i n e d , one f o r each equa t i on . These were averaged to y i e l d a f i n a l es t imate o f the e q u i v a l e n t screen opening f o r the composite screen decks o f f e = 1.5 cm. T h i s value was subsequent ly used f o r f i t t i n g t e s t s 17 to 21 i n the f i n a l model. (b) Model Behav io r Figures 22(a) and 22(b) d e p i c t how screen ing e f f i c i e n c y depends on X 5 0 and "a" when the a u x i l l i a r y func t ion Ci = 0. Note tha t the i n t e r -cept a t X i = 0 i s not equal to z e r o , but a f i n i t e va lue which i s a func t ion o f x 5 0 and " a " . Because the Brenda Mines L t d . concen t ra to r i s l o c a t e d i n a s e m i - a r i d c l i m a t e , the Brenda ore i s cons idered to be r e l a t i v e l y d ry . Consequent ly , the assumption t ha t Cq- = 0 was used dur ing model b u i l d i n g . - 73 -Figure 22 (a) Behavior o f Screen E f f i c i e n c y as a Funct ion o f Parameter x 5 0 (a=2.0 cm 3) - 74 -Figure 22 (b) Behavior o f Screen E f f i c i e n c y as a Funct ion o f Parameter a ( x 5 0 = 1 . 9 2 cm) - 75 -Although the e f f i c i e n c y equat ion i s being u t i l i z e d f o r double deck screens w i th r e c t angu l a r openings , i t i s f e l t t ha t the equat ion has wider a p p l i c a t i o n s . The equat ion should be a p p l i c a b l e to screens o f va r ious d e s i g n , w i t h uniform openings o f any convent iona l s i z e and shape. In f a c t , equat ion (45) appears to be s u i t a b l e as a cyclone e f f i c i e n c y equa t ion . I t i s expected tha t f o r wet o r e s , the a u x i l l i a r y func t ion Cj w i l l no longer be n e g l i g i b l e . I f t h i s proves t o be t r u e , i t i s a n t i c i -pated tha t Ci w i l l be a func t ion o f both feed moisture content and p a r t i -c l e s i z e . A p o s s i b l e f u n c t i o n a l form proposed f o r C-j i s : Ci = a 0 m e x p ( - a ! ( J L )) i = 1 to n (50) >• X50 where m i s the mois ture content o f the screen f eed , ao and a i are cons tan t s . (c) Model Accuracy and Range The computer program used to f i t the secondary screen model , c a l l e d SCRN5, i s presented i n Appendix H. Th i s program i s a m o d i f i c a t i o n o f the Simplex s imultaneous search program TURKEY,, used to f i t both crusher models. I t f i t s a l l screen data se t s s imul t aneous ly by m i n i m i z i n g an o b j e c t i v e f u n c t i o n o f the form: O.F . = ? . " . ( O i i - O i i ) 2 + z E (u i - j -u - j j ) 2 (51) i = l j= l J J i = l j = l J J f o r k runs and n screen s i z e f r a c t i o n s . Al though s i z e f r a c t i o n v a r i a n c e s , SOJ and SUJ , were a v a i l a b l e f o r repeat runs , they were not used as we igh t ing f ac to r s i n the above o b j e c t i v e f u n c t i o n . Consequent ly , the coa r se r s i z e s ( j= l to 5) were p r e f e r e n t i a l l y weighted dur ing f i t t i n g o f the model. This .was cons idered - 76 -acceptable because the f i n e m a t e r i a l present i n the measured o v e r s i z e stream t y p i c a l l y comprised 1 to 1-1/2 percent o f the t o t a l f l o w . I t was cons idered more important to a c c u r a t e l y p r e d i c t those s i z e f r a c t i o n s c o n t a i n i n g the bulk o f product f l o w r a t e , than to have a more s t a t i s t i c a l l y v a l i d model w i t h a very s i g n i f i c a n t l o s s o f p r e d i c t i n g accuracy . Despi te the o b j e c t i v e func t ion employed, the screen e f f i c i e n c y equat ion i s judged to perform s a t i s f a c t o r i l y over a l l s i z e ranges. The mean RSS a s s o c i a t e d w i th the p r e d i c t e d o v e r s i z e s i z e d i s t r i b u t i o n s i s 1.19, w i t h a s tandard d e v i a t i o n o f 1.69, w h i l e the mean RSS f o r the unders ize d i s t r i b u t i o n s i s 2 . 2 6 , w i th a. s tandard d e v i a t i o n o f 4 . 1 1 . Graphica l 'per formance o f the screen model i s presented i n F igures 2 3 ( a ) , - ( b ) and ( c ) , which r e -p resen t , r e s p e c t i v e l y , , the b e s t , wors t and second worst p r e d i c t i o n s . The secondary screen model can be s a t i s f a c t o r i l y e x t r a p o l a t e d a t l e a s t twenty percent beyond the l i m i t s o f the f i t t e d data ranges. 4.5 The Primary Fines Model The model proposed f o r the pr imary f i n e s stream i s e m p i r i c a l . I t c o n s i s t s o f two components, one to p r e d i c t the primary f i n e s s i z e d i s t r i b u t i o n and the o ther to p r e d i c t the s o l i d s f l o w r a t e . The model was developed from s i x samples taken over a time pe r iod o f one week and from d a i l y f low ra tes taken over a consecut ive three month p e r i o d . The on ly measurable ope ra t ing v a r i a b l e a v a i l a b l e f o r q u a n t i f y i n g the pr imary f i ne s was t ime . The pr imary f i n e s model was necessary to improve upon the v general s i m u l a t i o n and to i n v e s t i g a t e the p o s s i b i l i t y t ha t the primary f i ne s c h a r a c t e r i s t i c s were a c y c l i c f u n c t i o n of t ime . Th i s s u s p i c i o n Figure 23 (a) Performance o f Secondary Screen Mode l , Best P r e d i c t i o n - 78 -Figure 23 (b) Performance o f Secondary Screen Mode l , Worst P r e d i c t i o n - 79 -Figure 23 (c) Performance o f Secondary Screen Model Second Worst P r e d i c t i o n - 80 -arose from i n t a n g i b l e , unrecorded observa t ions o f the c y c l i c i n f l uence o f mine ope ra t ing procedures on concen t ra to r feed c h a r a c t e r i s t i c s and performance over a p e r i o d o f seve ra l weeks. Al though the q u a n t i t y o f data ob ta ined was very smal l . , a c o n s i s t e n t t r end f o r the model parame-t e r s was observed. (a) Model D e s c r i p t i o n The pr imary f i ne s d a i l y f l owra t e was analysed both g r a p h i c a l l y and by r eg re s s ion w i th respec t to time as expressed by both the day o f the week and the day o f the month. The day o f the week can be represen t -ed by consecut ive i n t e r g e r s from 1 to 7 and the day o f the month by consecut ive i n t ege r s from 1 to 30 (o r 31 ) . In both cases , no c o r r e l a t i o n cou ld be found and the c o n c l u s i o n was drawn t ha t the primary f i n e s f lowra te was random. Consequent ly , p r e d i c t i o n o f the f i ne s f lowra te i s based around a random number genera tor us ing the observed mean d a i l y f low ra te o f 248.71 tph a t a s tandard d e v i a t i o n o f 83.88 tph . I t was found tha t the pr imary f i n e s samples taken over the s i x day p e r i o d cou ld be c h a r a c t e r i z e d by a common s i z e d i s t r i b u t i o n equa t ion . Th i s form i s desc r ibed by the e q u a t i o n : Y . 1 °Y . = b 0 e b l - i - b 0 e b 2 X i i = 1 to n-1 (52) i - i c l where Y C 1 - represents the cumulat ive weight f r a c t i o n f i n e r than screen s i z e X-j. The parameters b 0 and b i were found to be s t r o n g l y c o r r e l a t e d to the day o f the week as expressed by in tegers from 1 to 7 and b 2 was found to be r e l a t e d to the parameter b 0 . The r e l a t i o n s developed to p r e d i c t these parameters a r e : - 81 -b(j = ABS(3.225629 - 2.263788 D + 0.538710 D 2 - 4.088134 x 1 0 _ 2 D 3 ) (53) bi = 1.146195 + 0.72933 D - 0.1829856 D 2 + 1.339609 x 1 0 _ 2 D 3 (54) and b 2 = -4 .491863 + 5.034085 In ( b 0 ) (55) These r e l a t i o n s are dep ic t ed g r a p h i c a l l y i n Figures 24(a) and 2 4 ( b ) . Table 8 presents the sampling schedule f o r the primary f i ne s stream. MON TUE WED THUR FRI SAT SUN Day of Week Figure 24(a) Behaviour o f Pr imary Fines Parameters b 0 and b i -21 Parameter Figure 24(b) Behaviour o f Pr imary Fines Parameter b 2 - 82 -TABLE 8 Primary Fines Sampling Schedule Sample Number Sample Date (1975) Day Coded Day + D Comments PF1 (31) Aug. 11 . Monday 1 - Aug. 12.' Tuesday 2 No pr imary f i ne s dur ing day s h i f t PF2 (32) Aug. 13. , Wednesday 3 PF3 (33) Aug. 14/ Thursday 4 PF4 (34) Aug. 15 ' F r i day 5 PF5 (35) Aug. 16 Saturday 6 PF6 (36) Aug. 17 / Sunday 7 (b) Model Accuracy The pr imary f i n e s s i z e d i s t r i b u t i o n model has been f i t t e d by another v a r i a t i o n o f the simultaneous search program TURKEY, l i s t e d i n Appendix I . The program f o r the f i t t e d model , c a l l e d PF , i s a l so presented i n Appendix I , a long w i th model p r e d i c t i o n s f o r a l l runs. A s t a t i s t i c a l a n a l y s i s o f model performance cannot be p resen ted , o ther than to say t ha t the model p r e d i c t i o n s e x h i b i t e d a mean RSS o f 28.2 and a s tandard d e v i a t i o n o f 19.8 f o r a l l t e s t s . On the bas i s o f the data c o l l e c t e d , the model i s cons idered s a t i s f a c t o r y f o r s i m u l a t i o n purposes. Al though i t w i l l n o t be e x p l a i n e d i n d e t a i l , an a l t e r n a t i v e pr imary f i n e s model was cons ide red . The s i z e d i s t r i b u t i o n equat ion (equat ion (52)) found to be common to a l l data se ts was employed. Op-timum values f o r parameters b 0 , b x and b 2 were determined f o r each data se t by d i r e c t search methods and a mean and s tandard d e v i a t i o n f o r each - 83 -parameter were determined. These means and s tandard d e v i a t i o n s may then be used i n a random number genera tor , so tha t the primary f i ne s s i z e a n a l y s i s becomes random i n na tu re , ra ther , than c y c l i c . In the absence o f a s t a t i s t i c a l bas i s e n a b l i n g a choice between the two approaches, i . e . random versus c y c l i c , the l a t t e r was chosen. - 84 -CHAPTER V SIMULATION QF THE CRUSHING PLANT 5.1 The S imu la t i on Programs S i m u l a t i o n o f the secondary c rush ing p l a n t i n v o l v e s cons t ruc -t i o n o f an o v e r a l l framework u t i l i z i n g the i n d i v i d u a l models as sub-programs o r sub rou t i ne s . The f low diagram f o r the Brenda c rush ing p l a n t s i m u l a t i o n i s dep i c t ed i n F igure 25 . As the secondary crushers are open c i r c u i t , on ly a s i n g l e pass i s r e q u i r e d . S i m u l a t i o n of the c l o s e d t e r t i a r y c ru sh ing loop i s accomplished by assuming an i n i t a l t e r t i a r y c rusher d ischarge o f z e r o . Th i s i s blended wi th d ischarge from the secondary crushers and the combined stream i s sent to the screens where i t i s s p l i t i n t o o v e r s i z e and unders ize p roduc t s . The o v e r s i z e stream goes to the t e r t i a r y crushers and a new es t imate o f t e r t i a r y crusher i s produced. Th i s process i s repeated u n t i l the combined screen unders ize f lowra te approaches the secondary c rush ing p l a n t feedrate to w i t h i n a s p e c i f i e d accuracy . The c i r c u i t - c o n v e r g e s e s s e n t i a l l y to steady s t a t e w i t h i n f i f t e e n to twenty i t e r a t i o n s . Two computer programs were w r i t t e n f o r s i m u l a t i o n o f the secon-dary c rush ing p l a n t . The i n i t i a l program, c a l l e d M2, i s the more com-prehensive o f the two. I t enables c o n t r o l over the number o f process u n i t s f o r a given o p e r a t i o n , the r e l a t i v e feed s p l i t t o each u n i t and c o n t r o l o f i n d i v i d u a l u n i t o p e r a t i n g s e t t i n g s . Under M2, i t would be p o s s i b l e to "operate" any o f the f i v e secondary sc reens , each w i th a d i f f e r e n t screen opening. The program a l s o con ta ins an ex tens ive output s e c t i o n . However, M2 proved to be too l a r g e f o r the U . B . C . BASIC language - 85 -I Simulation Control | I Data 1 T 1 J l _ . L . L_. PRIMARY FINES MODEL I PLANT FEED SECONDARY CRUSHER MODEL Blend Secondary/Tertiary Crusher Products l SECONDARY SCREEN MODEL TERTIARY CRUSHER MODEL I !_ I Convergence Determining | I Cr i ter ia I I , I Blend Screen Unders ize/Pr imary Fines Products " - R O D MILL F E E D -I : 1 I Output of Plant Operating | I Data I 1 Figure 25 S i m u l a t i o n Flow Diagram - 86 -compi l e r and consequently r equ i r ed sepa ra t ion i n t o f i v e subprograms before i t cou ld be executed . Th i s proved d i f f i c u l t and c o s t l y , so M2 has been t e m p o r a r i l y s h e l v e d . Program M2 i s presented i n Appendices J (a ) and J ( b ) , w i t h sample o u t p u t s - f o r two s i m u l a t i o n s . The program M2 was r ep laced w i t h a s i m p l i f i e d v e r s i o n c a l l e d PGM2. Th i s program s imula tes the secondary c rush ing p l a n t on the assump-t i o n tha t when two or more process u n i t s are i n p a r a l l e l , the feed streams are e q u a l l y d i v i d e d . Furthermore, s i m i l a r process un i t s must operate w i th i d e n t i c a l ope ra t ing s e t t i n g s . The output s e c t i o n presents only e s s e n t i a l ope ra t ing c o n d i t i o n s and product s i z e d i s t r i b u t i o n s . A l i s t i n g o f PGM2 and two sample outputs are presented i n Appendices J ( c ) and J ( d ) . The f i r s t sample output was performed under, the .same:operat ing c o n d i t i o n s as the f i r s t output from M2, thus e n a b l i n g a comparison o f the two programs. The convergence c r i t e r i o n f o r PGM2 i s taken as the absolute d i f f e r e n c e i n f low ra te between the secondary c rush ing p l a n t feed and the combined secondary screens unders ize product s treams. T h i s value i s c u r r e n t l y se t a t 0.01 tph or approximate ly .0007 percent o f the p l a n t feed r a t e . Choice o f t h i s c r i t e r i o n w i l l i n f l uence the number o f i t e r a -t i o n s t o (and thus ra te o f . . ) convergence. T h i s and o the r s i m u l a t i o n parameters , such as the number o f u n i t s to be s i m u l a t e d , can be changed by a l t e r i n g the s i m u l a t i o n program i t s e l f . 5.2 Methodology Employed to Study the S i m u l a t i o n Program PGM2 To acqui re output from the s i m u l a t i o n program PGM2, a f u l l two-l e v e l f a c t o r i a l design was employed. A t o t a l o f f i v e v a r i a b l e s were manipulated over t h e i r observed ope ra t i ng ranges to produce t h i r t y - t w o - 87 -i n d i v i d u a l s i m u l a t i o n s . ( 2 5 = 32) . The v a r i a b l e s chosen f o r the study and the t o t a l span o f t h e i r ope ra t ing ranges are dep ic ted i n Table 9. Of these v a r i a b l e s , only the p l a n t feed s i z e d i s t r i b u t i o n i s u n c o n t r o l l a -b l e i n p r a c t i c e . However, the coarses t and f i n e s t s i z e d i s t r i b u t i o n s ( r e s p e c t i v e l y , secondary crusher t e s t s number 2 and 5) were used to ob ta in endpoint va lues . The coded design ma t r ix f o r t h i s study i s p re -sented i n Table 10 and the coding system i s a v a i l a b l e from Table 9. TABLE 9 Opera t ing Ranges o f V a r i a b l e s S tud ied w i t h Program PGM2 Opera t ing Ranges S tud ied V a r i a b l e Low Midpo in t High U n i t P l a n t Feedrate 1255.4 1417.1 1578.8 tph P l a n t Feed S i z e 1 73.3 (5) 83.6 (4) 92.9 (2) % + 1 inch D i s t r i b u t i o n Secondary Crusher 2.540 3.16 3.785 cm Gap Secondary Screen 1.27 1.43 1.59 cm Opening T e r t i a r y Crusher 0.495 0.788 1.080 cm Gap Coded Value -1 0 +1 — The f a c t o r i a l design y i e l d s in fo rma t ion regard ing the endpoints o f the observed data ranges. I t i s a l so d e s i r a b l e to study behaviour i n the in te rmedia te ranges. To accomplish t h i s , a second study was conducted 1 Plant feed size d i s t r i b u t i o n i s quantif ied by the % + 1 inch material i n the d i s t r i b u t i o n . The number i n parentheses i s the number of- the secondary crusher run from which the feed size d i s t r i bu t i on i s taken. - 88 -TABLE 10 Coded Two-Level F u l l F a c t o r i a l Design M a t r i x Used f o r Secondary Crushing P l a n t S imu la t i on Study Secondary Secondary T e r t i a r y P l a n t % + 1 inch Crusher Screen Crusher Run Feedrate i n feed Gap. Opening Gap. Number ( tph) (%) (cm) (cm) (cm) 1 _-, _- , .-, _-, _- , 2 1 -1 -1 -1 -1 3 -1 1 -1 -1 -1 4 1 1 -1 -1 -1 5 -1 -1 1 _1 _"l 6 1 _1 1 -1 _1 7 -1 1 1 -1 -1 8 1 1 1 -1 _1 9 -1 -1 _] 1 _1 10 1 -1 -1 1 -1 11 -1 1 _1 1 -1 12 1 1 -1 1 -1 13 -1 -1 1 1 -1 14 1 -1 1 1 -1 15 = 1 1 1 1 -1 16 1 1 1 1 _1 17 -1 -1 -1 -1 1 18 1 -1 -1 -1 1 19 -1 1 -1 _1 1 20 1 1 -1 -1 1 21 -1 -1 1 _1 1 22 1 -1 1 _1 1 23 -1 1 1 -1 1 24 1 1 1 -1 1 25 -1 -1 -1 1 1 26 1 -1 -1 1 1 27 -1 1 -1 1 1 28 1 1 -1 1 1 29 -1 -1 1 1 1 30 1 -1 1 1 1 31 -1 1 1 1 1 32 1 1 1 1 1 - 89 -accord ing to a n o n - f a c t o r i a l design us ing the same f i v e v a r i a b l e s . The design mat r ix f o r the in te rmedia te range s tudy , performed i n three p a r t s , i s presented i n coded form i n Table 11. Although the i n t e r m e d i -ate range study i s f a r from being complete , i t should provide a s u f f i c i -ent d e s c r i p t i o n o f s i m u l a t i o n behaviour i n the midpoint r eg ion f o r the purpose o f t h i s t h e s i s . S tudies were a l s o conducted to see how the program PGM2 would behave under e x t r a p o l a t i o n o f the f i v e v a r i a b l e s . The conc lus ions from these s t u d i e s v e r i f y what has a l ready been desc r ibed (pages 62 , 66., 76) concerning e x t r a p o l a t i o n o f i n d i v i d u a l models. A weak p o i n t i n the s i m u l a t i o n i s the secondary c rusher model. Th i s model i s bound by e x t r a -p o l a t i o n r e s t r a i n t s a l ready desc r ibed f o r i t s upper l i m i t s . The secon-dary screen and t e r t i a r y crushermode 1.Is appear to f u n c t i o n w e l l when e x t r a p o l a t e d , w i t h no apparent problems i n performance. I t was observed tha t f o r runs where the s i m u l a t i o n exper ienced obvious problems dur ing e x t r a p o l a t i o n , the number o f i t e r a t i o n s to con-vergence was g r e a t l y i n c r e a s e d . Convergence i t e r a t i o n s f o r these runs were t y p i c a l l y i n the range o f 40 to 50 , n e a r l y three times the number otherwise observed. Th i s c o n s i s t e n t t r end was used as a p r e l i m i n a r y i n d i c a t o r f o r convergence problems. Problems occur red f o r e x t r a p o l a t i o n o f the secondary c rusher v a r i a b l e s o n l y . - 90 -TABLE 11 Coded Intermediate Range Two-Level Design M a t r i x Used f o r Secondary Crushing P l an t S i m u l a t i o n Study Secondary Secondary T e r t i a r y % + 1 inch P l a n t Crusher Screen Crusher Run i n feed Feedrate Gap Opening Gap Number (%) (tph) (cm) (cm) (cm) 1 0 0 0 0 0 2 1 0 0 0 0 3 -1 0 0 0 0 4 0 1 0 0 0 5 0 -1 0 0 0 6 0 0 1 0 0 7 0 0 -1 0 0 8 0 0 0 1 0 9 0 0 0 -1 0 10 0 0 0 0 1 11 0 0 0 0 -1 12 0 0 0 1 1 13 0 0 0 1 -1 14 0 0 0 -1 1 15 0 0 0 -1 -1 16 0 0 1 0 1 17 0 0 1 0 -1 •18 0 0 -1 0 1 19 0 0 -1 0 -1 20 0 0 1 1 0 21 0 0 1 -1 0 22 0 0 -1 1 0 23 0 0 -1 -1 0 24 1 1 0 0 0 25 1 -1 0 0 0 26 -1 1 0 0 0 27 -1 -1 0 0 0 - 91 -CHAPTER VI DISCUSSION 6.1 A n a l y s i s o f S imu la t i on Output (a) General A major reason f o r conduct ing the study o f the secondary c rush ing p l a n t s i m u l a t i o n was to ensure tha t the computer program was f u n c t i o n i n g c o r r e c t l y and e f f i c i e n t l y . A p r e l i m i n a r y a n a l y s i s o f the e f f e c t s o f the major ope ra t ing v a r i a b l e s on p l a n t behavior was a l so conducted, a l though the output was ob ta ined l a r g e l y to t e s t the performance o f the s i m u l a t i o n over the data ranges sampled. Computer output from PGM2 i s presented i n Appendices K(a) and K ( b ) . For convenience , the p e r t i n e n t i n fo rma t ion from these outputs are summarized . i n Tables 12 and 13. Note tha t these summary t ab l e s (Tables 12 and 13) have not been repor ted i n the same order as t h e i r coded design mat r ices (Tables 10 and 11 r e s p e c t i v e l y ) . The o rder was changed to f a c i l i t a t e computer programming. In t o t a l , f i f t y - n i n e s i m u l a -t i o n s were o b t a i n e d , t h i r t y - t w o f o r the f u l l f a c t o r i a l design and twenty-seven f o r the in te rmed ia te : ranges des ign . The average cos t f o r a s i n g l e s i m u l a t i o n i s 20 cents on normal computing p r i o r i t y . The cos t savings between an i n - p l a n t t e s t and a s i m u l a t i o n i s e v i d e n t . 1 At U . B . C , computer usage i s charged according to p r i o r i t y l e v e l s . A l l remote and in te rac t ive terminals are considered high p r i o r i t y and charged at a rate factor of l.h. Batch jobs are rated normal p r i o r i t y , with a rate factor of 1.0 and jobs run between 12:00 pirn, and 6 :00 a.m. are rated low p r i o r i t y , with a rate factor of o.6'. - 92 -TABLE 12 Summary of Two-Level Fac to r i a l Design Simulation Study Run Number % + 1 inch in P lant Feed % Plant Feedrate (TPH) ] Secondary Crusher Gap (cm) NDEPENDENT ' Secondary Screen Gap (cm) Te r t i a r y Crusher Gap (cm) Screen Feedrate (TPH) % + 1 inch in Screen Feed (%) Te r t i a r y Crusher Feedrate (TPH) % + 1 inch in Te r t i a r y Crusher Feed (%) 56-1/2 inch in Screen Undersize (%) Screen E f f i c i e n c y {%) DEPENDENT Plant Reduction Ratio C i r cu la t ing Load Secondary Crusher Current (Amperes) Te r t i a r y Crusher Current, (Amperes) 1 2 3 4 5 c 92.85 92.85 92.85 92.85 92.85 09 OC 1255.4 1578.8 1255.4 1578.8 1255.4 2.54 2.54 3.785 3.785 2.54 1.27 1.27 1.27 1.27 1.59 -.495 .495 .495 .495 .495 573.76 739.43 637.88 822.14 522.98 32.53 32.98 36.71 36.66 40.01 403.35 529.59 483.50 632.98 339.88 57.96 57.57 60.54 59.52 76.95 79.51 79.87 79.11 80.56 61.38 97.10 96.90 97.55 97.05 97.40 32.45 32.60 32.29 32.88 25.05 1.29 1.34 1.54 1.60 1.08 23.68 29.26 14.56 20.15 57.96 57.57 49.60 57.88 0 7 8 9 10 3£ . OD 92.85 92.85 92.85 92.85 no oc 1578.8 1255.4 1578.8 1255.4 1578.8 i o r r A 2.54 3.785 3.785 2.54 2.54 1.59 1.59 1.59 1.27 1.27 .495 .495 .495 1.080 1.080 675.10 582.82 745.94 564.92 727.30 41.51 45.40 45.59 32.25 32.69 449.17 414.67 537.72 392.30 514.42 77.99 79.75 79.06 58.05 57.77 64.24 63.38 64.39 80.00 80.03 97.25 97.75 97.55 97.95 96.80 26.22 ' 25.87 26.28 32.65 32.78 1.14 1.32 1.36 1.25 1,30 29.26 14.56 20.15 23.68 *t 1 . Oh 47.69 45.78 52.60 38.92 & K AO 1 1 12 13 14 15 y<:. 8b 92.85 92.85 92.85 92.85 no ntz 1255.4 1578.8 '1255.4 1578.8 1255.4 3.785 3.785 2.54 2.54 3.785 1.27 1.27 1.59 1.59 1.59 1.080 1.080 1.080 1.080 1.080 628.28 808.60 513.55 660.95 571.45 36.44 36.48 38.88 40.54 44.47 471.50 616.05 328.09 431.48 400.48 60.70 59.86 76.07 77.63 79.32 79.57 80..85 60.35 64.18 63.02 97.45 97.00 97.30 97.15 97.70 32.48 33.00 24.63 26.20 25.72 1.50 1.56 1.05 1.09 1.28 "14.56 20.15 23.68 29.26 14 <ifi 40. 0 j 43.31 51.32 35.36 41.09 lb 17 18 19 20 9 1 91.8b 73.30 73.30 73.30 73.30 "7 o in 1578.8 1255.4 1578.8 1255.4 1578.4 3. 785 2.54 2.54 3.785 3.785 1.59 1.27 1.27 1.27 1.27 1.080 .495 .495 .495 .495 731.24 518.59 666.54 566.65 722.88 44.86 28.17 28.63 31.72 31.89 519.35 334.39 438.48 394.47 508.92 78.95 54.6 54.40 56.96 56.63 64.43 80.09 79.80 79.07 79.54 97.45 96.50 96.40 97.05 96.80 26.30 5.68 5.66 5.61 5.64 1.32 1.07 1.11 1.26 1.29 1 T • JU 20.15 23.68 29.26 14.56 ?0 IS oy • j / 45.95 41.33 47.10 44.66 c i ni c 22 . 23 24 25 26 97 3. 3073.30 73.30 73.30 73.30 73.30 70 on 1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 2.54 2.54 3.785 3.785 2.54 2; 54 1.59 1.59 1.59 1.59 1.27 1.27 .495 .495 . .495 .495 1.080 1.080 473.79 606.17 514.91 658.69 511.37 655.62 34.91 36.17 38.9 40.23 27.73 28.25 278.39 363.01 329.78 428.66 325.36 424.83 74.27 75.49 75.92 77.27 54.49 54.49 61.30 63.64 59.87 63.53 80.48 80.31 96.95 96.85 97.40 97.25 96.35 96.25 4.35 4.51 4.25 4.51 5.71 5.70 0.39 0.92 1.05 1.09 1.04 1.08 23.68 29.26 14.56 20.15 23.68 29.26 J 1 . U 1 38.23 42.92 41.08 46.56 35.21 40 7? CI 28 29 30 31 00 15. JU 73.30 73.30 73.30 73.30 "70 on 1255.4 1578.8 1255.4 1578.8 .1255.4 3.785 3.785 2.54 2.54 3.785 1.27 1.27 1.59 1.59 1.59 1.080 1.080 1.080 1.080 1.080 557.77 711.08 464.84 592.90 507.26 31.37 31.58 34.37 34.93 37.76 383.36 494.15 267.20 346.42 320.22 57.05 56.81 74.74 74.73 74.77 79.59 80.00 63.42 63.39 58.15 96.95 96.70 96.95 96.85 97.30 5.64 5.67 4.50 4.50 4.12 1.22 1.25 0.85 0.88 1.02 14.56 20.15 23.68 29.26 14 56 i 38.43 44.57 31.99 36.38 O.A 0 0 / J . 30 1578.8 3.785 T.59 1.080 644.92 39.22 411.45 76.84 63.44 97.25 4.50 1.04 20.15 39.98 i - 93 -TABLE.13 Run Number 1 2 3 4 5 6 7 8 9 n 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Summary of Two-Level- Intermediate Ranges Design Simulation Study % + 1 inch in Plant Feed 92.85 92.85 92.85 73.3 73.3 73.3 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 83.6 Plant Feedrate (TPH) 1417.1 1578.8 1255.4 1417.1 1578.8 1255.4 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 1578.8 1255.4 1417.1 1417.1 1417.1 1417.1 1417.1 1417.1 INDEPENDENT Secondary Crusher Gap (cm) 3.16 3.16 3.16 3.16 3.16 3.16 3.16 3.16 3.16 3.16 3.785 3.785 2.54 2.54 3.785 3.785 2.54 2.54 3.16 3.16 3.785 2.54 3.16 3.16 3.16 3.16 141771 1X76 Secondary Screen Opening (cm) 1.43 1.43 1.43 1.43 1.43 1.43 1.59 1.27 1.59 1.27 1.43 1.43 1.43 1.43 1.59 1.27 1.59 1.27 1.43 1.43 1.43 1.43 1.59 1.27 1.43 1.43 1.43 Te r t i a r y Crusher Gap (cm) .788 .788 .788 .788 .788 Screen Feedrate (TPH) .788 1.080 .495 .495 1.080 1.080 .495 1.080 .495 .788 604.58 680.33 531.32 539.60 603.26 475.70 590.21 662.41 604.59 650.68 % + 1 inch in screen Feed 33.24 33.47 32.88 27.70 27.98 .788 .788 .788 .788 .788 .788 .788 .788 .788 1.080 .495 672.87 684.38 621.19 632.02 580.00 644.41 538.49 594.31 663.00 519.32 27.52 39.66 32.12 40.83 31.74 35.86 36.29 32.64 33.15 38.92 ,788 629.07 580.46 544.84 604.78 632.84 644.49 590.44 33.53 34.54 30.19 31.73 31.34 34.52 31.05 35.39 30.68 33.10 33.66 31.58 Ter t i a ry Crusher Feedrate (TPH) 401.45 455.71 350.30 320.24 359.38 280.78 383.48 473.74 401.46 459.08 486.81 501.20 422.22 435.75 370.72 451.24 318.60 388.61 434.05 335.30 432.07 371.30 326.77 401.70 436.77 450.85 383.77 % -i- 1 inch in Ter t i a ry Crusher Feed ',%) 62.58 62,47 62,34 58,34 58.72 58,28 76.29 56,13 76.85 56,24 61.96 61.94 60.03 60.10 76.12 59.86 72.94 57.71 60.58 60.67 62.82" 60.67 73,76 57,74 60 06 60.11 60.72 %-l/2 inch in Screen Undersize 77.13 77.28 76.96 77.83 78.18 77.87 60.45 77.84 60.61 78.39 73.15 72.65 73.71 73.16 60.93 81.43 58.63 81.88 76.33 76.31 76.09 76.83 59.52 81.44 73.08 '72.52 76.25 Screen E f f i c i ency (%) DEPENDENT Plant Reduction Ratio 95.90 95.80 95.80 95.00 94.80 94.55 97.40 97.15 97.50 97.20 95.7 95.6 96.30 95.55 97.00 96.60 96.40 96.45 95.70 C i r cu l a t i ng Load 31.48 31.54 31.41 5.52 5.54 5.52 13.58 17.49 13.62 17.62 16.44 16.33 16.56 16.44 13.69 18.30 13.18 18.40 17.15 17.15 17.10 17.27 13.38 18.30 16.42 16.30 1.13 1.15 1.12 .90 .91 .89 1.08 1.34 1.13 1.30 1.37 1.41 1.19 1.23 1.05 17.13 1.27 .90 1.10 1.10 1.07 1.22 1.05 .92 1.13 1.23 1.27 1.080 Secondary Crusher Current (Amperes) Te r t i a r y Crusher Current (Amperes) 21.93 24.72 19.14 21.93 24.72 19.14 21.93 21.93 21.93 21.93 17.36 17.36 26.47 26.47 17.36 17.36 26.47 26.47 24.72 19.14 17.36 26.47 21.93 21.93 21.93 21.93 42.23 45.24 39.40 37.73 39.90 35.55 38.43 49.06 45.05 42.62 44.16 50.58 40.58 45.95 40.53 44.99 37.64 41.52 44.04 38.57 21.93 43.93 40.56 38.10 42.25 41.39-47.79 41.25 - 94 -A l l s i m u l a t i o n s appear to run c o r r e c t l y , w i t h no evidence o f convergence problems. Th i s obse rva t ion i s f u r t h e r enhanced by the speed a t which the s i m u l a t i o n s converged to s t e a d y - s t a t e , a l l w i t h i n twenty-two i t e r a t i o n s , w i t h an average o f t e n . There are fou r ope ra t ing v a r i a b l e s whose values are generated by the s i m u l a t i o n around the t e r t i a r y c rush ing loop and over which the programmer has no d i r e c t c o n t r o l . These v a r i a b l e s are ones which were measured du r ing the exper imenta l .phase o f the p r o j e c t and i nco rpo ra t ed i n t o the models. Of these v a r i a b l e s , on ly the t e r t i a r y c rusher feedrate was observed to exceed the f i t t e d data range. Seven runs , or four teen percent o f the t o t a l , exceeded the upper l i m i t o f the sampled range by more than twenty percent . These seven t e s t s were t r e a t e d w i t h extreme s u s p i c i o n , and i n f a c t , none o f these s i m u l a t i o n s were used i n subsequent ana lyses . The remaining three v a r i a b l e s , secondary screen f eed ra t e , and percent +1 inch i n the screen and t e r t i a r y crusher feeds , were found to remain w i t h i n t h e i r r e s p e c t i v e measured data ranges f o r a l l t e s t s . Crushing p l a n t behaviour may be measured by the f o l l o w i n g depen-dent v a r i a b l e s ( c a l l e d responses) : (1) percent -1 /2 inch m a t e r i a l i n p l a n t product (2) p l a n t r educ t ion r a t i o (3) c i r c u l a t i n g load r a t i o f o r the t e r t i a r y c rush ing l o o p . (4) secondary screen e f f i c i e n c y 1 The term " t e r t i a ry crushing loop" i s used to denote the closed loop containing both the t e r t i a r y crushers and the secondary screens. 2 The c i r c u l a t i n g load r a t i o i s defined as the; r a t i o of the t e r t i a r y crusher product to new plant feed (secondary crusher product; see Figure 2 5 , page 85 ) . - 95 -The f i n a l p l a n t product ( rod m i l l feed) i s taken to be the unders ize stream from the secondary screens . The p l a n t r educ t ion r a t i o , a l though s t r i c t l y speaking not a t rue r educ t ion r a t i o , can be used as a measure o f both the p l a n t work output and p l a n t e f f i c i e n c y i n terms o f s i z e r e -d u c t i o n . Th i s response i s de f ined i n t h i s study as the r a t i o : n _ percent - 1/2 inch i n p l a n t product percent - 1/2 inch i n p l a n t feed The pr imary f i n e s stream has been neg lec ted f o r these s t u d i e s , because i t has no i n f l uence on the behaviour o f the secondary c rush ing p l a n t . However, the primary f i n e s w i l l i n f l uence the feed to the f i n e ore b i n s . For the purpose o f t h i s s tudy , the screen opening i s de f ined as the wid th o f the s l o t s i n the lower screen deck. These s l o t s have a u n i -form l eng th o f 3-1/2 i n c h e s . The screen opening i s used synonymously w i t h screen aper tu re . The screen e f f i c i e n c i e s are not output ted by the s i m u l a t i o n p ro -gram and have been computed s e p a r a t e l y f o r both study des igns . For conven-i e n c e , the computed e f f i c i e n c i e s are i n c l u d e d i n Tables 12 and 13. The screen e f f i c i e n c i e s were c a l c u l a t e d w i t h respec t to the p r e d i c t e d o v e r s i z e p r o d u c t 1 by the s tandard A l l i s - C h a l m e r s p rocedure 2 o u t l i n e d i n the 1 The screen e f f i c i enc ie s are computed with respect to the oversize product because the screen e f f ic iency equation (equation ) i s defined i n terms of t h i s same product. Screen e f f i c i enc ie s computed with respect to the undersize product are t y p i c a l l y i n the range of 77 to 78 percent"when computed by the All is-Chalmers method. These lower e f f i c i enc i e s are bel ieved to be due to the rectangular screen openings permit t ing passage of slabby or p la ty p a r t i c l e s . 2 This procedure i s summarized as fol lows: (1) obtain a sample of the desired screen product (2) determine the percentage of misplaced mater ia l ( i . e . undersize mater ia l i n the oversize product) (3) subtract t h i s value from 100 to obtain screen e f f ic iency i n percent, - 96 -p u b l i c a t i o n "Screen ing Mach inery" v . The amount o f m a t e r i a l i n the o v e r s i z e product pass ing the des ignated screen opening was determined g r a p h i c a l l y . (b) P l a n t Feedrate The i n f l uence o f p l a n t feedrate on responses i s dep ic t ed i n Figure 26. The p l a n t feedrate does not appear to e x e r t any i n f l u e n c e on e i t h e r p l a n t r educ t ion r a t i o , screen e f f i c i e n c y o r the s i z e q u a l i t y o f the f i n a l product . However, i t does e x e r t a smal l i n f l u e n c e on the c i r c u l a t i n g load r a t i o , which inc reases s l i g h t l y w i t h i n c r e a s i n g p l a n t f eedra te . Th i s i s not an unreasonable obse rva t ion i f the c lo sed t e r t i a r y c rush ing loop does not approach i t s maximum c a p a c i t y . Since the s i m u l a -t i o n study was conducted w i t h i n the data ranges over which the screen model was f i t t e d and the screen e f f i c i e n c i e s are both high and cons tan t , i t i s reasonable to assume tha t n e g l i f i b l e b l i n d i n g occurs and the screen s p l i t i s " c l e a n " . The increase i n c i r c u l a t i n g load r a t i o may then be a t t r i b u t e d to d e t e r i o r a t i o n o f c rush ing a c t i o n w i t h i n the secondary crushers w i th the i n c r e a s i n g p l a n t f eedra te . Th i s hypothes is i s supported by observa-t i o n s made dur ing sampl ing . I t i s b e l i e v e d tha t the secondary crushers are nea r ing t h e i r p h y s i c a l l i m i t s a t the upper feedrate t e s t e d and tha t t h e i r c rush ing a c t i o n may be d e t e r i o r a t i n g due to crowding phenomena. Th i s would r e s u l t i n a coa r se r product a t h ighe r feedrates and thus a s l i g h t bu i ldup i n the c i r c u l a t i n g l o a d . T e r t i a r y c rush ing a c t i o n should not d e t e r i o r a t e when the c i r c u l a t i n g l o a d inc reases because the inc reased t e r t i a r y c rusher feedrates are s t i l l w i t h i n the p h y s i c a l l i m i t s of. the machines. 1 The term "binding" i s used i n the sense of physical.blockage of screen apertures by e i ther wedging of pa r t i c l e s between c lo th wires or buildup of layers of pa r t i c l e s preventing access to the screen deck. 100i 38-\ 95 a 90-^ U § 8 5 ^ i 8 ^ X u CM 75 \ z 70 hi O a: UJ a 65-^ 12 10 8-I 601 MOO °/o+1 Inch in Plant Feed =83 .6 Secondary Crusher Gap =3.16 cm Secondary Screen Opening = 1.43 cm Ter t ia ry Crusher Gap =.788 cm r 8 5 1220 11240 ' 1260 ' l280 1 1300' 1320 ' 1340 ' 1360 1 1380' 1400 ' l 4 2 0 ' 1440 ' 1460114*80' 1500 1 1520 1 1540 1 1560 1 1580 1 1600 . PLANT FEEDRATE ( t p h ) •1.4 95 90 H.3 o m m h-2 n 80 m -n 3! n m 75 ^ -< H.1 S3 n c z Q O > D 70 3J > M.o g Y65 r.9 r60 Figure 26 The Inf luence o f P l a n t Feedrate on S i m u l a t i o n Responses - 98 -(c) P l a n t Feed S i z e D i s t r i b u t i o n In most c rush ing p l a n t s , the opera tor has no e x p l i c i t c o n t r o l over the p l a n t feed s i z e d i s t r i b u t i o n . However, t h i s i s an important v a r i a b l e and al though not c o n t r o l l a b l e , i t s i n f luence should be known. F igure 27 dep i c t s the e f f e c t o f the percent plus 1 inch m a t e r i a l i n the p l a n t feed ( i . e . r e l a t i v e feed coarseness) on the responses. The feed s i z e appears to have l i t t l e i n f l uence on e i t h e r the screen e f f i c i e n c y o r the q u a l i t y o f the f i n a l product . Th i s i s not an unreasonable obse rva t ion i f , as i s the case f o r t h i s s tudy , the u n i t s around the t e r t i a r y c rush ing loop do not approach t h e i r maximum p h y s i c a l l i m i t s . F i n a l product s i z e q u a l i t y should not change app rec i ab ly i f the screen e f f i c i e n c y remains constant (which i t does) and the t e r t i a r y c rush ing a c t i o n does not d e t e r i o r a t e . F igure 27 i n d i c a t e s a cons ide rab le inc rease i n p l a n t r educ t ion r a t i o w i th i n c r e a s i n g p l an t feed s i z e . Th i s i s to be expected because the p l a n t must work harder to reduce the coa r se r feed to the same pass ing screen s i z e . S imu l t aneous ly , the i n c r e a s i n g p l a n t feed s i z e would produce a coa r se r secondary c rusher product and thus increase the c i r c u l a t i n g load r a t i o ( as observed i n F igure 27) . (d) Secondary Crusher Gap The i n f l uence o f the secondary crusher gap on responses i s de-p i c t e d i n F igure 28 . The c rusher gap has v i r t u a l l y no e f f e c t upon p l a n t r educ t ion r a t i o , screen e f f i c i e n c y o r the f i n a l product s i z e q u a l i t y . However, i t does e x e r t a s u b s t a n t i a l i n f l u e n c e on c i r c u l a t i n g l o a d r a t i o . Opening o f the secondary c rusher gap produces a coarse r c rusher p roduc t , 100i 95 U 90i a O or Q. 38 36 34 32 30 - 28 85^ -z J 8 0 1 eg 75 ^  Z UJ u or LJ Q- 70-65-26 5 24 or z 22 O § 2 0 a UJ K 18 \ 16 14 12 10 8 60 r 100 Plant Feedrate =1417.1 tph Secondary ' Crusher Gap . = 3.16 cm Secondary Screen Opening = 1.43 cm T e r t i a r y C rusher Gap =.788 cm "70 1 72 )&74 I 76 ' 78 1 80 1 82 1 84 1 86 PERCENT t1 INCH IN PLANT FEED I-85 CV) O I- 2 m z •1.4 95 •90 -1.3 -1.2 o 80 75 m -n 31 o m z o M.1 23 n c z D O > H.o 5 70 65 h.9 r 6 0 .^8 88 1 9 0 92 94 96 98 100 Figure 27 The Inf luence o f Percent +1.Inch in P l a n t - F e e d on S i m u l a t i o n Responses r100 381 36-34| —I 32-3 0 -• 28-26-O < 24-z 22^ O h-^ 201 Q LU K 181 16 i -z < 14-1 12-101 8--Q-Plant Feedrate =1417.1 tph °/0 +1 inch in Plant Feed. . = 83.6 Secondary Screen Opening = 1.43 cm Ter t iary Crusher Gap =.788 cm -o-2.5 ' 2.6 1 2.7 1 2.8 1 2.9 1 1 0 1 3.'l 1 3.2 1 3.3 1 3!4 1 3.5 1 3.6 1 3.7 1 3.8 SECONDARY CRUSHER G A P ( c m ) H95 Y90 85 in n XI m m z 80 m -n r- 3! n m 3 70 -2 -11 M F65 r60 2.4 T 3.9 1 4.0 Figure 28 The Inf luence o f Secondary Crusher Gap on S i m u l a t i o n Responses - 101 -which i n tu rn r e s u l t s i n an increase i n the c i r c u l a t i n g l o a d . I f the c losed t e r t i a r y c rush ing loop i s not ope ra t ing near i t s maximum c a p a c i t y , then i t w i l l be capable o f absorbing and b reak ing the a d d i t i o n a l l oad imposed by the secondary c rushe r s . Th i s behavior w i l l r e s u l t i n a con-s t an t p l a n t r educ t ion r a t i o , screen e f f i c i e n c y and f i n a l product s i z e q u a l i t y , independent o f the secondary c rusher performance. The a b i l i t y o f one or more process u n i t s t o ac t as a b u f f e r and e i t h e r p a r t i a l l y o r t o t a l l y absorb performance changes i n another u n i t ope ra t ion i s an important p roper ty o f any c i r c u i t . In the Brenda secon-dary c rush ing p l a n t , the t e r t i a r y c rush ing loop i s capable o f compensating f o r almost any change i n p l a n t feed c h a r a c t e r i s t i c s o r secondary c rusher performance. Such compensation was observed f o r changes i n p l a n t feed s i z e when the f i n a l product s i z e q u a l i t y was mainta ined desp i t e s i g n i f i -cant changes i n p l a n t r educ t ion r a t i o and: c i r c u l a t i n g load (see F igure 27 ) . Wi th in the t e r t i a r y c rush ing loop the u n i t opera t ions a l s o have some mu-t u a l a b i l i t y to compensate f o r performance changes i n each o t h e r , as d i scussed l a t e r . (e) Secondary Screen Opening The secondary screens appear to e x e r t the most marked e f f e c t s upon c rush ing p l a n t performance, as i l l u s t r a t e d i n F igure 29. R e f e r r i n g to the f i g u r e , as the screen opening i n c r e a s e s , the unders ize ( f i n a l ) product f i n e s s must o b v i o u s l y decrease ( i . e . becomes c o a r s e r ) . Th i s enables more m a t e r i a l to be d i scharged from the t e r t i a r y c rush ing l o o p , so the c i r c u l a t i n g load r a t i o decreases. With the p l a n t producing a coa r se r p roduc t , l e s s work i s r e q u i r e d f o r s i z e r educ t ion and the p l a n t r educ t ion r a t i o must a l s o decrease . Figure 29 The Inf luence o f Secondary Screen Opening on S i m u l a t i o n Responses - 103 -The screen opening appears to e x e r t a smal l i n f l uence on screen e f f i c i e n c y , caus ing a minimum to occur a t the middle o f t h e . s t u d i e d range. However, t h i s e f f e c t i s s m a l l , and i n view o f t h i s , i t cannot be s t a t e d wi th c e r t a i n t y whether the e f f e c t i s a t t r i b u t a b l e to d i f f e r e n t screen openings or to computat ional e r r o r . 1 ( f ) T e r t i a r y Crusher Gap S u r p r i s i n g trends are observed when the t e r t i a r y c rusher gap i s a l t e r e d . These trends are dep ic t ed i n F igure 30. C l e a r l y , an "optimum" ope ra t ing s e t t i n g i s i n d i c a t e d i n the midpoin t r e g i o n . A n a l y s i s o f the computer output confirms tha t the t e r t i a r y crusher product i s f i n e r f o r a gap o f 0.788 cm. than f o r gaps o f e i t h e r 1.080 cm. o r 0.495 cm. The be-h a v i o r o f the three responses , p l a n t r educ t ion r a t i o , c i r c u l a t i n g load r a t i o and f i n a l product s i z e i s such t h a t : (a) ., as t h e - f i n a l product "becomes,f iner , .morerwork i s r equ i r ed f o r breakage and the p l a n t r educ t ion r a t i o inc reases s l i g h t l y (b) f o r a f i x e d screen opening , more m a t e r i a l leaves the t e r t i a r y c rush ing loop as the f i n a l product becomes f i n e r , hence the c i r c u l a t i n g load decreases These observa t ions c o i n c i d e w i t h expected b e h a v i o r , but they do not e x p l a i n the maxima/minima i n the three responses as a f u n c t i o n o f the c rusher gap (see F igure 30) . Note tha t screen e f f i c i e n c y s i m i l a r l y a-ppears to decrease very s l i g h t l y near the midpoint o f the range s t u d i e d . The maxima/minima trends may be caused by changes i n the amount o f n e a r - s c r e e n - s i z e m a t e r i a l produced by changes i n the crusher gap. The r e l a t i v e amounts o f m a t e r i a l i n the s i z e s c l o s e s t to the screen opening may be measured by the r a t i o : 1 Computational error arises during graphical approximation of the amount of undersize material i n the oversize product. This error i s bel ieved to be of the order of 0.2 to 0.5 percent. 100i 951 . 9 0 1 38 3 6 H 34 32 30 U z> Q °851 a. < z ^ 8 0 -z u z rvj 75-H Z UJ (J70-ir UJ a. 65-~ 28 26 < 24{ | 22H ^ 2 0 i Q UJ 181 < 16 14 12-10-8 60H Plant Feedrate =1417.1 tph °/0 +1 Inch in Plant Feed = 83.6 Secondary Crusher Gap = 3.16 cm Secondary Screen Opening =1.43 cm —i— .5 100 M.4 te5 90 -1.3 85 </> O SJ m m z 80 m |_ JJ n m M.2 11 r75 O -< O 3D o c o O > D 5 -1.0 7 0 „° 65 6 0 T • .6 TERTIARY .7 CRUSHER .8 GAP ( c m ) .9 1,0 1.1 Figure 30 The Inf luence o f T e r t i a r y Crusher Gap" on S i m u l a t i o n Responses - 105 -^ _ cumulat ive percent pass ing screen opening i n screen feed cumulat ive percent r e t a i n e d on screen opening s i z e i n screen feed 2 The behav io r o f t h i s r a t i o i s dep ic t ed i n F igure 31(a) . C l e a r l y , a maximum i s noted to occur i n the midpoin t reg ion o f the t e r t i a r y c rusher gap range s t u d i e d . Th i s i n d i c a t e s t h a t l a r g e r q u a n t i t i e s o f m a t e r i a l are pass ing the screen opening i n the midpoin t r eg ion o f the c ru she r gap than are pass ing a t the eridpoint r e g i o n s . In o the r words, there must be more n e a r - s c r e e n - s i z e m a t e r i a l being produced f o r a gap o f 0.788 cm. than f o r e i t h e r 0.495 cm. or 1.080 cm. The use o f s l o t t e d screens i n the lower screen deck permits passage o f s i g n i f i c a n t q u a n t i t i e s o f s labby o r p l a t y p a r t i c l e s i n the s i z e ranges j u s t above the screen opening (near - sc reen-s i z e ranges) . Thus, i f -more h e a r - s c r e e n - s i z e - m a t e r i a l i s be ing -p ro -duced, more w i l l pass. Both the percent - 1 /2 i n c h , i n the f i n a l product and the p l a n t r educ t ion r a t i o w i l l i nc rease w h i l e the c i r c u l a t i n g load r a t i o w i l l decrease. Fur thermore, i f the amount o f n e a r - s c r e e n - s i z e mater-i a l r i s e s to a maximum and then decreases , the responses must f o l l o w the t r end a c c o r d i n g l y . The r a t i o A ( n e a r - s c r e e n - s i z e m a t e r i a l ) a l s o appears to be i n -f luenced by the screen opening , as i n d i c a t e d i n Figure 31(b) . Th i s i s not an unreasonable obse rva t ion c o n s i d e r i n g t ha t "A" i s computed w i t h respect to the screen opening. A g a i n , a maximum i s observed near the midpoin t o f the range o f screen openings s t u d i e d . Th i s i n d i c a t e s t ha t 1 Values of cumulative percent passing and retained on the screen opening size were computed graphica l ly . 2 The screen feed represents the combined secondary and t e r t i a r y crusher products. However, as the secondary crusher product-is constant for a given s imulat ion, any changes i n the screen feed are due to changes i n the t e r t i a r y crusher product. -106-1 -TERTIARY CRUSHER G A P ( c m ) Figure 31(a) Behav io r o f R a t i o A as a Funct ion o f T e r t i a r y Crusher Gap .701 —. 1 > 1 1 1 ' 1 1 1 ' 1 > 1 • 1 1 — 1.25 1.30. 1.35 1.40 1.45 1.50 1.55 1.60 1.65 PARTICLE SIZE (cm) Figure 31(b) Behav io r of R a t i o A as a Func t ion o f P a r t i c l e S i z e - 107 -regard less o f the gap s e t t i n g , the t e r t i a r y crushers tend to produce a product w i t h a maximum amount o f m a t e r i a l around the 1.43 cm. s i z e . However, a screen opening o f 1.43 cm. may not n e c e s s a r i l y be an "optimum" f o r p l a n t opera t ion because o f the i n f luence o f o ther f a c t o r s . These observa t ions have an impor tant impact on c rush ing p l a n t o p e r a t i o n . C l e a r l y , an "optimum" s e t t i n g f o r the t e r t i a r y c rusher gap i s i n d i c a t e d c lose to 0.800 cm. Th i s value i s "optimum" f o r the f o l l o w i n g reasons: (a) a maximum product f ineness i s i n d i c a t e d (b) a minimum c i r c u l a t i n g load i s i n d i c a t e d A minimum i n the c i r c u l a t i n g load r a t i o means a maximum c a p a c i t y to absorb changes i in e i t h e r p l a n t feed c h a r a c t e r i s t i c s o r secondary c rusher o p e r a t i o n . Furthermore, the "optimum" e f f e c t o f t e r t i a r y c rusher gap appears to be i n f l u e n c e d by the screen opening s i z e . By ope ra t i ng a t an "optimum" combinat ion o f c rusher gap and screen opening , i t may be p o s s i b l e to r e a l i z e s i g n i f i c a n t improvements i n both f i n a l product f ineness and p l a n t s t a b i l i t y . (g) E f f e c t s o f V a r i a b l e s on Reponses The e f f e c t s o f manipulated v a r i a b l e s upon responses have been computed f o r the t w o - l e v e l f a c t o r i a l design study and are i n c l u d e d i n Appendix L . For convenience , these e f f e c t s have been ranked acco rd ing to magnitude and are presented i n Table 14. A measure o f pure e r r o r f o r the c rush ing p l a n t i s n o t . a v a i l a b l e , so there i s no means to e s t a b l i s h s t a t i s t i c a l l y which e f f e c t s are s i g n i -f i c a n t . The c u t - o f f po in t f o r de te rmining the s i g n i f i c a n c e o f an e f f e c t - 108 -TABLE 14 Summary of E f fect s of Simulation Variables on Responses %- l/2 inch in Product Plant Reduction Ci rcul at ing Screen E f f i c i e n c y Ratio Load Ratio Var iable E f f e c t Variable E f fec t Var iable E f f e c t Var iable E f fec t Code Code Code Code 4 -17.2838 2 24.1781 2 .2475 2 .4719 1 1.5113 4 -4.0581 3 .2075 4 .3469 1/4 1.035 2/4 -2.7994 4 -.2075 3 .3281 2/3 .92 1 .3719 1 .0413 1 -.2594 1/2/3/4 -.7275 1/2 .2681 5 -.03875 2/3 .1281 1/2/3 -.6363 1/4 .1944 2/3 .035 1/2 -.1219 2 .595 1/2/3/4 -.1856 2/4 -.01 2/4 -.1219 2/3/4 .5588 2/3 .1819 3/4 -.01 1/4 .1156 2/4 .4838 2/3/4 .1369 1/2 .00875 2/3/4 .0906 1/3 .3613 1/3/4 -.1369 1/2/3/4 -.00375 2/4/5 -.0844 1/2/4 -.32 3/4 .1006 1/4 -.00375 1/2/4 .0781 4/5 -.3063 1/2/4 .0981 2/3/4 -.0025 2/3/4/5 .0719 2/3/4/5 .2938 3 .0981 1/2/3/5 .0025 1/2/3/4/5 -.0719 1/2/3/4/5 -.29 1/2/3 .0931 1/2/3/4/5 .0025 1/3/5 .0656 1/2/3/5 -.2813 4/5 -.0869 1/4/5 -.0025 1/2/5 . -.0656 2/3/5 .2625 2/4/5 -.0706 1/5 -.0025 1/4/5 .0594 1/3/4/5 .2325 1/2/4/5 .0444 1/3 -.00125 1/3/4/5 -.0594 3 -.235 2/3/4/5 .0406 1/2/3 .00125 1/2/3/4 -.0531 1/3/5 .1963 1/4/5 .0381 1/2/4 -.00125 1/5 -.0531 3/5 -.1875 1/2/3/5 -.0344 1/3/4 -.00125 2/5 .0531 3/4/5 -.1763 2/3/5 .0331 2/5 -.00125 3/5 -.0531 1/2/4/5 .15 1/2/5 .0319 3/5 -.00125 2/3/5 -.0531 5 .1375 1/2/3/4/5 -.0294 4/5 -.00125 1/2/3/5 .0531 1/2/5 .1138 1/5 .0281 2/3/5 .00125 1/2/4/5 .0469 2/5 -.105 1/3 -.0219 2/4/5 .00125 3/4/5 .0469 2/4/5 -.0789 5 .0156 3/4/5 .00125 3/4 .0406 1/3/4 -.065 1/3/4/5 .0069 2/3/4/5 -.00125 1/2/3 .0344 1/2 .0513 3/4/5 .0069 1/2/4/5 2 . 7 8 x l 0 " 1 7 4/5 -.0344 1/4/5 .05 3/5 -.0031 1/2/5 - 2 . 7 8 x l 0 - 1 7 5 -.0219 1/5 .0288 1/3/5 -.00063 1/3/4/5 0 1/3/4 -.0156 3/4 .0238 2/5 .00063 1/3/5 0 1/3 -.0031 Key to Var iable Code 1 = Factor code f o r P lant Feedrate 2 = Factor code fo r % + 1 inch in P lant Feed 3 = Factor code f o r Secondary Crusher Gap 4 = Factor code f o r Secondary Screen Opening 5 = Factor code f o r Te r t i a r y Crusher Gap. - 109 -i s thus a r b i t r a r y and made on the bas i s o f the e f f e c t ' s magnitude and sharp changes i n the magnitude o f adjacent e f f e c t s i n Table 14. Without a s t a t i s t i c a l b a s i s , i n most cases i t i s only p o s s i b l e to i n f e r the s i g n i f i c a n c e o f a s p e c i f i e d e f f e c t . The e f f e c t s i n d i c a t e d i n Table 13 tend to conf i rm the t rends a l ready observed f o r the f i v e main e f f e c t s presented i n F igures 26 through 30. The on ly v a r i a b l e w i t h a s i g n i f i c a n t e f f e c t upon the f i n a l product s i z e appears to be the screen opening. Th i s confirms the f i n d i n g s from Figure 29 (page 102).. The remaining main e f f e c t s and a l l i n t e r a c t i o n e f f e c t s appear to be i n s i g n i f i c a n t . However, some o f the e f f e c t s w i th l a r g e r magnitudes may be s i g n i f i c a n t ( i . e . p l a n t f e e d r a t e ) , but as there are no sharp d i f f e r ences between the magnitudes o f these e f f e c t s , t h e i r r e l a t i o n s h i p w i t h f i n a l product s i z e may be complex. The p l a n t r educ t ion r a t i o appears t o be s i g n i f i c a n t l y e f f e c t e d by both percent +_1 inch i n p l an t feed and screen opening. Th i s t rend i s c l e a r l y observed i n Figures 27 (page 9.9 ) and 29 (page!02). The i n t e r -a c t i o n between these two v a r i a b l e s a l s o appears to be s i g n i f i c a n t . A l l o ther e f f e c t s are judged to be i n s i g n i f i c a n t . The c i r c u l a t i n g l o a d r a t i o appears t o be r e a d i l y e f f e c t e d by percent + 1 inch i n p l a n t f eed , secondary crusher gap and secondary screen opening, as a l s o observed i n F igures 27 , 28 (page 100) and 29. Other e f f e c t s appear to be i n s i g n i f i c a n t , i n c l u d i n g the t e r t i a r y c rusher gap. However, t h i s c o n t r a d i c t s the maxima/minima trends observed i n Figure 30 (page~104)\ The c o n t r a d i c t i o n may occur because these trends are n o n - l i n e a r , w i t h the maxima/minima o c c u r r i n g i n the midpoint o f the - no -v a r i a b l e range s t u d i e d . The method fo r . computing e f f e c t s assumes a l i n e a r behav io r over the range. Since the computations i n v o l v e the endpo in t s , the maxima/minima behav ior f o r the t e r t i a r y c rusher gap i s not n o t i c e d . The magnitudes o f e f f e c t s on the screen e f f i c i e n c y are smal l and sharp changes i n magnitude are not noted . Th i s i n d i c a t e s t h a t the screen e f f i c i e n c y may be l a r g e l y independent o f the ope ra t ing v a r i a b l e s over the ranges t e s t e d . T h i s obse rva t ion tends to conf i rm the t rends i n d i c a t e d i n F igures 26 through 30. I f the l a r g e r e f f e c t s are s i g n i f i -can t , t h e i r i n t e r a c t i o n s are l i k e l y to be complex. (h) T e r t i a r y Crusher Current One aspect o f t h i s study not y e t cons idered i s the c rusher cu r r en t draw. The cu r r en t draws f o r both secondary and t e r t i a r y crushers are p r e d i c t e d from an equa t ion o f the form: C = a 0 - a x G + a 2 T (37 , 43) Th i s equat ion i n d i c a t e s t ha t c rusher cu r ren t decreases w i th i n c r e a s i n g gap, inc reases w i t h feedrate and i s independent o f the feed s i z e d i s t r i -b u t i o n . The behav ior o f the t e r t i a r y c rusher cu r r en t versus feedrate at d i f f e r e n t gaps i s presented i n F igure 32. I t may be assumed t ha t the t e r t i a r y c rusher feedrate can be e x t r a p o l a t e d ten percent beyond the upper l i m i t o f i t s f i t t e d data range. Th i s i s not an unreasonable assumption c o n s i d e r i n g t ha t the c rusher u t i l i z e s a coarse concave w i th the mantle m o d i f i c a t i o n s dep ic ted i n F igure 5 (page 14) . T h i s assumption i s p e r t i n e n t to the ensuing d i s c u s s i o n . - i n -Figure 32 Behavior o f T e r t i a r y Crusher Curren t Draw as a Funct ion o f Feedrate f o r Constant Gap - 112 -The t e r t i a r y crushers are p r e s e n t l y ra ted at a maximum cu r r en t draw o f 42.0 amperes. However, F igure 32 i n d i c a t e s t ha t an inc rease i n c rusher cur ren t w i l l enable an inc rease i n capac i ty throughput , w i t h l a r g e s t c a p a c i t y gains i n d i c a t e d f o r the s m a l l e s t gap s e t t i n g s . I f a maximum s u s t a i n a b l e cur ren t draw o f 47 amperes were p o s s i b l e , the c a p a c i t y inc reases i n d i c a t e d would be s u b s t a n t i a l . The i n d i c a t e d c a p a c i t y i n -creases assuming a ten percent feedrate. e x t r a p o l a t i o n and a 47 ampere cu r r en t draw are presented i n Table 15 and g r a p h i c a l l y i n F igure 33. . TABLE 15 Ind i ca t ed Capac i ty Increases f o r T e r t i a r y Crushers Crusher Gap (cm..) Maximum Curren t Increase (amperes) Maximum Ind ica t ed Capac i ty Increase (tph) Maximum Ind ica t ed Capac i ty Increase per Ampere (tph/amp) .495 5.0 90 18.0 .788 3.7 66 17.84 1.080 0.9 16 17.78 I t i s not known whether the e x i s t i n g 300,. Hp" motors w i l l operate under a continuous cu r r en t draw o f 47 amperes, but i t i s known tha t they w i l l s u s t a i n cur ren t s as high as 49.3 amperes f o r shor t p e r i o d s . Th i s obse rva t ion i n d i c a t e s t ha t i t may be p o s s i b l e t o inc rease the maximum continuous cu r r en t draw f o r the t e r t i a r y motors. I f t h i s i s not p o s s i b l e , then c o n s i d e r a t i o n o f l a r g e r motors , such as the 350 Hp secondary c rush -e r motors , may be a v i a b l e a l t e r n a t i v e . These have a maximum cont inuous cu r r en t r a t i n g o f 48 amps. S u b s t i t u t i o n o f the l a r g e r motors would pe r -mi t the h ighe r cu r ren t draws proposed w h i l e s t i l l m a i n t a i n i n g a smal l s a fe ty margin . - 113 -Current Increase (amperes) Figure 33 Ind i ca t ed Capac i ty Increases For T e r t i a r y Crushers The c a p a c i t y inc reases i n d i c a t e d by F igure 3'3 represent a p o s s i b l e upper l i m i t , depending upon the upper cu r r en t l e v e l f i n a l l y chosen. How-e v e r , i t must be remembered t h a t these inc reases are sub jec t to the p h y s i c a l l i m i t s o f the crushers be ing cons ide red . A d e f i n i t e c a p a c i t y l i m i t cannot be s t a t e d because t h i s v a r i e s f o r va r ious a p p l i c a t i o n s o f the same machine. However, reference to pub l i shed Symons Nordberg capa-c i t y char t s (Appendix A) i n d i c a t e s tha t f o r crushers o f the type under c o n s i d e r a t i o n , maximum capac i t y throughputs are i n the order o f 450 tph . Th i s l i m i t corresponds c l o s e l y t o the ten percent e x t r a p o l a t i o n i n feed-ra te assumed i n F igure 33. Furthermore, i t i s b e l i e v e d tha t the crushers a t the Brenda p l a n t are capable o f hand l ing throughputs l a r g e r than i n -d i c a t e d by the Nordberg char t s due to t h e i r modi f i ed c rush ing chamber - 114 -c o n f i g u r a t i o n s . I t i s the re fore reasonable to suggest t h a t , a l though the i n d i c a t e d l i m i t i n g c a p a c i t i e s may not be r e a l i z e d i n p r a c t i c e ( e s p e c i a l l y f o r s m a l l e r gaps) , s u b s t a n t i a l c a p a c i t y inc reases w i l l be ach ieved . The e f f e c t s , o f ope ra t ing v a r i a b l e s upon the t e r t i a r y c rusher feedrate and cu r r en t draw are shown g r a p h i c a l l y i n F igure 34 f o r constant t e r t i a r y c rusher gap. These e f f e c t s are as expected and have been d i s -cussed i n prev ious s e c t i o n s . For example, an inc rease i n p l a n t feedrate r e s u l t s i n a d i r e c t increase i n the t e r t i a r y c rusher feedra te and cu r ren t draw. Increases i n the pi antfeed s i z e d i s t r i b u t i o n r e s u l t i n an inc reased c i r c u l a t i n g l o a d r a t i o (see F igure 27) and thus an inc rease i n t e r t i a r y c rusher feedrate and cu r r en t . The f a c t t ha t the t e r t i a r y crushers are so r e a d i l y a f f e c t e d by c i r c u i t changes elsewhere e x p l a i n s why these u n i t s are so useful as a b u f f e r f o r p l a n t performance. They have the a b i l i t y to e i t h e r damp out shor t term o r c y c l i c d i s turbances o r compensate f o r more permanent changes. For i n s t a n c e , the a b i l i t y to inc rease the t e r t i a r y c rusher cu r r en t draw above the present maximum l e v e l can be d i r e c t l y t r a n s l a t e d i n t o inc reases i n c i r c u l a t i n g l o a d c a p a c i t y , which cou ld be used to smooth out p e r i o d i c changes i n p l a n t feed c h a r a c t e r i s t i c s o r enable h igher p l a n t feedra tes . The secondary screens a l so p l ay a pa r t i n the b u f f e r i n g r o l e i n tha t they r e t a i n changes i n p l an t feed c h a r a c t e r i s t i c s o r ope ra t i ng s e t t i n g s ( i . e . secondary c rusher gap) u n t i l the t e r t i a r y crushers have had the necessary time to compensate f o r these changes. The t e r t i a r y crushers are the l i m i t i n g opera t ion i n the t e r t i a r y i TERTIARY CRUSHER FEEDRATE (below, in tph) and CURRENT DRAW (above, in amperes) Figure 34 The Inf luence o f P l a n t Opera t ing V a r i a b l e s on T e r t i a r y Crusher Current Draw and F p e d r a t P - 116 -c rush ing l o o p . Each secondary screen i s capable o f hand l ing 1000 t p h , y i e l d i n g a combined c a p a c i t y o f approximate ly 5000 tph . To meet t h i s l e v e l , the t e r t i a r y crushers would be r e q u i r e d to operate at c a p a c i t i e s r o f the order o f 1250 t p h , which i s w e l l beyond t h e i r c a p a b i l i t y . Th i s obse rva t ion adds f u r t h e r importance to the study o f the t e r t i a r y crusher c a p a c i t y - c u r r e n t increases because Figure 32 i n d i c a t e s t h a t an inc rease i n c rusher cu r r en t can be t r a n s l a t e d i n t o e i t h e r an increase i n p l an t c a p a c i t y , or an increase i n the p l a n t ' s a b i l i t y to handle coa r se r feeds. On the bas i s o f obse rva t ions taken dur ing sampling o f the se-condary c r u s h e r s , i t i s b e l i e v e d tha t the p h y s i c a l c apac i t y o f these crushers w i l l be reached w e l l before t h e i r r a t ed maximum s u s t a i n a b l e cu r r en t draws. The h ighes t cu r ren t draw recorded dur ing sampling was 32.0 amperes a t a gap o f 2.54 cm. and a feedrate o f 782.3 tph . A t t h i s l e v e l , the c rusher was shaking very h e a v i l y and was o b v i o u s l y approaching i t s maximum throughput . S tudies were not undertaken to determine which u n i t ope ra t ion i s l i m i t i n g w i t h respec t to t o t a l p l a n t c a p a c i t y . I t i s b e l i e v e d tha t the l i m i t i n g opera t ion w i l l be e i t h e r secondary o r t e r t i a r y c rush ing and tha t i t may a l t e r n a t e between the two depending upon opera t ing c o n d i t i o n s . 6.2 P o t e n t i a l A p p l i c a t i o n s f o r the S i m u l a t i o n Programs Al though a p p l i c a t i o n s o f the c rush ing p l a n t s i m u l a t i o n were l i m i t e d i n t h i s t h e s i s , there are s eve ra l t ha t warrant a b r i e f d e s c r i p t i o n . Perhaps the most obvious i s o f f - l i n e o p t i m i z a t i o n , where the best combina-t i o n o f manipulable v a r i a b l e s w i th respect to a s p e c i f i e d o b j e c t i v e i s sought. The o p t i m i z a t i o n could be performed us ing a s u i t a b l e d i r e c t - 117 -search program. Instead o f sea rch ing f o r constants p e r m i t t i n g the best f i t f o r a s i n g l e model , the search would i nco rpo ra t e the e n t i r e s i m u l a -t i o n and search f o r the values o f the s p e c i f i e d manipulable (ope ra t ing) v a r i a b l e s t ha t s a t i s f y the p r e s c r i b e d o b j e c t i v e . The o b j e c t i v e - f u n c t i o n would be based on one o r more o f the d e s i r e d responses , such as f ineness o f the f i n a l product sub jec t to p l a n t throughput r e s t r i c t i o n s . Imple-mentation o f such a program requ i r e s the i d e n t i f i c a t i o n o f c o n s t r a i n t s to ensure tha t - the i n d i v i d u a l models remain w i t h i n t h e i r acceptable v a r i a b l e ranges. I t may a l s o be d e s i r a b l e to conduct a s e r i e s o f o p t i m i z a -t i o n s t u d i e s to determine how the optimum p l a n t s e t t i n g s vary w i t h p l a n t feed s i z e d i s t r i b u t i o n . Another a p p l i c a t i o n ' o f . t h e s i m u l a t i o n system, perhaps o f more long term i n t e r e s t , i s the study and comparison o f a l t e r n a t e c i r c u i t c o n f i g u r a -t i o n s . With the present program i t i s p o s s i b l e to s imula te the e x i s t i n g Brenda c i r c u i t w i t h the view o f a l t e r i n g the number o f un i t s i n a given o p e r a t i o n . For example, i t may be d e s i r a b l e t o study the c rush ing p l a n t w i t h the a d d i t i o n o f a t h i r d secondary c rusher o r w i th on ly four secondary screens o p e r a t i n g . Another aspect o f i n t e r e s t i s the s tudy o f new c i r c u i t c o n f i g u r a t i o n s and t h e i r comparison w i t h the e x i s t i n g c i r c u i t . Th i s a p p l i c a t i o n cou ld be o f p a r t i c u l a r i n t e r e s t to those i n v o l v e d w i t h the design and c o n s t r u c t i o n o f c rush ing p l a n t s . A f a r more d e t a i l e d study o f the e x i s t i n g c rush ing p l a n t cou ld be undertaken w i t h the o b j e c t i v e o f comp i l i ng a comprehensive ope ra t ing manual. Th i s manual would document i n f o r m a t i o n such as recommended ope ra t ing s e t t i n g s and maximum opera t ing t o l e r a n c e s . I t would be compiled - 118 -o f f - l i n e , and once completed, cou ld be checked aga ins t ac tua l ope ra t i ng behav io r f o r accuracy and r e l i a b i l i t y . I t i s not expected tha t such a manual would be t o t a l l y accurate or f o o l p r o o f , but when used w i t h d i s -c r e t i o n , i t cou ld prove to be ext remely useful as a supplement to eve ry -day manual c o n t r o l . A f i n a l a p p l i c a t i o n o f the s i m u l a t i o n could i n v o l v e a study o f equipment wear e f f e c t s . E v a l u a t i o n o f the e f f e c t s o f equipment wear on p l a n t performance and product q u a l i t y cou ld be achieved by i n c r e -menta l ly v a r y i n g e i t h e r c rusher gap, the screen opening , o r a combination o f the three over a d e s i r e d range and a n a l y s i n g the s i m u l a t i o n output . I f the s imula t ed e f f e c t s o f equipment wear cou ld be r e l a t e d to known or measurable ra tes o f wear, then the ra tes o f change i n p l a n t behavior cou ld be p r e d i c t e d . Th i s f a c t cou ld then be used to c o n s t r u c t , modify o r supplement a maintenance schedule f o r the e n t i r e p l a n t . Such a schedule would be useful as a f u r t h e r supplement to manual c o n t r o l . - 119 -SUMMARY AND CONCLUSIONS The s i m u l a t i o n o f an ope ra t ing c rush ing p l a n t , c o n s i s t i n g o f two stages o f c rush ing and one stage o f s c r e e n i n g , has been undertaken. An i n - p l a n t sampling program enabled a c q u i s i t i o n o f data cove r ing normal ope ra t i ng ranges f o r a l l three major process u n i t s i n v o l v e d . The data acqu i red f o r s c reen ing were subsequently adjusted by means o f a s t a t i s t i -ca l method. E s t a b l i s h e d models were modi f i ed and used to s imula t e both secondary and t e r t i a r y c rush ing p rocesses , w h i l e a new model was used to desc r ibe the v i b r a t i n g sc reens . A l l three models are s e m i - e m p i r i c a l i n na ture . The models were combined i n sequence to enable s i m u l a t i o n o f the secondary c rush ing p l a n t . P r e l i m i n a r y s tud i e s were conducted on the s i m u l a t i o n s to ensure the system was f u n c t i o n i n g p r o p e r l y . A n a l y s i s o f the r e s u l t s has confirmed tha t the s i m u l a t i o n program i s f u n c t i o n i n g s u c c e s s f u l l y and has demonstrated the advantages o f d i g i t a l s i m u l a t i o n as a modern a n a l y t i c a l t o o l . The f o l l o w i n g conc lus ions can be drawn from t h i s s tudy: (1) The l a r g e p a r t i c l e s i z e s i n v o l v e d i n the c rush ing ope ra t ion not on ly make sampling extremely d i f f i c u l t , but in t roduce a high degree o f process e r r o r . The l a rge p a r t i c l e s i z e s produce h igh f requencies o f s h o r t - t e r m f l u c t u a t i o n s i n some f lowstreams, hence the concept o f steady s t a t e must be cons idered i n a b road , "average" sense and only over per iods g r e a t l y exceeding the f l u c t u a t i o n p e r i o d . Large sample s i z e s (400 to 1500 lb /sample) are r e q u i r e d to ensure r ep re sen t a t i ve s amp l ing , thus r e s t r i c t i n g the q u a n t i t y o f data taken to the minimum r e q u i r e d f o r model development. (2) The data adjustment procedure used f o r the secondary screens data i s an e f f i c i e n t , s t a t i s t i c a l l y v a l i d method f o r c o r r e c t i n g u n r e l i a b l e data ob ta ined around a three (o r more) product u n i t o p e r a t i o n . - 120 -(3) The Whiten c rusher model was judged to d e s c r i b e adequately the performance o f both the secondary and t e r t i a r y c r u s h e r s , a f t e r s u i t a b l e m o d i f i c a t i o n s such as s u b s t i t u t i o n o f the Gaudin-Meloy primary breakage equa t i on . (4) The Whiten v i b r a t i n g screen model was judged to be u n s a t i s f a c -t o r y . The model 's d i scon t inuous nature i s cons idered to s e r i o u s -l y impede i t s u t i l i t y . An a l t e r n a t i v e model , which i s continuous over a l l p a r t i c l e s i z e s , was used. (5) The mathematical l i m i t s o f a l l models were e s t a b l i s h e d and the ex ten t to which each model can be e x t r a p o l a t e d beyong i t s f i t t e d data range before i t s t a r t s ma l func t ion ing was a l s o determined. The models used i n the s i m u l a t i o n program g e n e r a l l y func t ioned w e l l when manipulable v a r i a b l e s were e x t r a p o l a t e d 15 or 20 percent beyond t h e i r f i t t e d ranges. (6) The models developed f o r s i m u l a t i o n o f the Brenda Mines L t d . c rush ing p l a n t are s e m i - e m p i r i c a l i n na tu re . They are not n e c e s s a r i l y a p p l i c a b l e to o ther c rush ing o p e r a t i o n s . (7) Development o f mathematical models f o r s i m u l a t i o n o f c rush ing p l an t s i s time consuming and c o s t l y . I t i s the re fore impera t ive to have f i r m l y e s t a b l i s h e d o b j e c t i v e s and procedures before under tak ing such a p r o j e c t . (8) Once a d i g i t a l s i m u l a t i o n has been ob t a ined , i t can be a ve r sa -t i l e t o o l f o r a n a l y s i s o f c rush ing p l a n t o p e r a t i o n . The f o l l o w i n g advantages can be r e a l i z e d through the use o f d i g i t a l s i m u l a t i o n : (a) speed - a s i m u l a t i o n can be prepared and run on a computer w i t h i n 5 minutes . (b) cos t - one complete s i m u l a t i o n o f the Brenda c rush ing p l a n t w i l l cos t approximate ly 20<t (c) no i n t e r f e r e n c e w i th p l a n t opera t ion (d) d i v e r s i t y o f the types o f s tud ie s a v a i l a b l e . (9) The s i m u l a t i o n program must be used w i t h cau t ion and not b l i n d l y . Th i s i s e s p e c i a l l y t rue when ope ra t i ng v a r i a b l e s are used out -s ide t h e i r f i t t e d ranges. A l i t t l e "common sense" a p p l i e d i n con junc t ion w i t h the s i m u l a t i o n may prove i n v a l u a b l e to the user . (10) For the Brenda Mines L t d . c rush ing o p e r a t i o n , i t may be p o s s i b l e to inc rease p l a n t c a p a c i t y f o r some opera t ing ^condi t ions by i n -c reas ing , the power draw to the t e r t i a r y c rushe r s . (11) An "optimum" s e t t i n g f o r t e r t i a r y c rusher gap i s i n d i c a t e d i n the midpoin t region o f the gap range s t u d i e d . - 121 -RECOMMENDATIONS FOR FURTHER WORK The f o l l o w i n g suggest ions are made regard ing f u r t h e r work i n the f i e l d o f c rush ing p l a n t s i m u l a t i o n : (1) Inves t i ga t e the p o t e n t i a l o f us ing the screen model e f f i c i e n c y equat ion to r ep lace the p a r a b o l i c c l a s s i f i c a t i o n equat ion c u r r e n t l y employed i n the c rusher models. I t i s b e l i e v e d tha t the p r o b a b i l i t y o f a p a r t i c l e be ing c l a s s i f i e d i s a continuous func t ion f o r a l l s i z e s and would be b e t t e r approximated by a continuous equa t ion . (2) Perform an o f f - l i n e o p t i m i z a t i o n study to determine optimum s e t t i n g s f o r a l l manipulable ope ra t ing v a r i a b l e s . I t may a l so be useful to perform seve ra l o p t i m i z a t i o n s t u d i e s to determine how the optimum ope ra t ing v a r i a b l e s change w i t h changes i n p l a n t feed s i z e d i s t r i b u t i o n . (3) Perform d e t a i l e d s t u d i e s o f the Brenda Mines L t d . c rush ing p l a n t and compile a comprehensive p l a n t ope ra t ing manual. These s tud i e s may o r may not i n v o l v e s tud ies i n t o the e f f e c t s o f equ ip -ment wear on p l a n t performance. I f such a manual were compi l ed , i t cou ld prove to be a very usefu l supplement to both manual c o n t r o l and p l a n t maintenance. (4) Perform s i m u l a t i o n s t u d i e s on a l t e r n a t e c i r c u i t c o n f i g u r a t i o n s and compare t h e i r performance w i t h tha t o f the e x i s t i n g c i r c u i t . (5) Combine t h i s c rush ing p l an t s i m u l a t i o n program w i t h the program developed to s imula te the Brenda Mines L t d . g r i n d i n g c i r c u i t . In t h i s manner, i t would be p o s s i b l e to s imula te the e n t i r e comminution c i r c u i t . (6) Inves t i ga t e the p o s s i b i l i t i e s o f i n c r e a s i n g the cu r r en t draw on the t e r t i a r y c r u s h e r s , e i t h e r by m o d i f i c a t i o n o f the e x i s t i n g motors o r by replacement w i t h l a r g e r ones. Then perform t e s t s to determine whether the i n d i c a t e d capac i t y increases were r e a l i z e d . (7) Tes t the screen e f f i c i e n c y equat ion under d i f f e r e n t c o n d i t i o n s and f o r d i f f e r e n t screen types to determine the equat ions t h e o r e t i c a l v a l i d i t y and general a p p l i c a b i l i t y . A l s o i n v e s t i -gate the a p p l i c a b i l i t y o f the screen e f f i c i e n c y equat ion to cyclone c l a s s i f i c a t i o n . (8) Perform f u r t h e r i n v e s t i g a t i o n s i n t o the time behav io r o f the pr imary f ines stream i n an e f f o r t to improve upon the proposed f i ne s model. - 122 -Perform t e s t s to p r e d i c t maximum capac i t y l i m i t s f o r each u n i t ope ra t ion and the product q u a l i t y o r p l a n t performance a t these l i m i t s . Th i s should a l s o enable i d e n t i f i c a t i o n o f the l i m i t i n g ope ra t ion on t o t a l p l a n t c a p a c i t y . Perform t e s t s to s tudy the i n f l u e n c e o f t e r t i a r y crusher gap on p l a n t performance. 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FERRARA, G. and PRETI, U . , "A C o n t r i b u t i o n to Screening K i n e t i c s " , 11th I n t . M i n i . P roc . Congress , C a g l i a r i , I t a l y , 1975, Paper no. 7. GLUCK, S. E . , " V i b r a t i n g Screens : Surface S e l e c t i o n and Capac i ty C a l c u l a t i o n " , Chem. E n g . , March 1965 , .pp . 179-182. - 1 2 5 -(28) "Screening Mach ine ry" , Tech. In fo . B u l l . PM1.1 , A l l i s - C h a l m e r s Manufactur ing C o . , June 1963, pp. 41-71. (29) NELDER, J . . A . and MEAD, R. A . , "A Simplex Method f o r Funct ion M i n i m i z a t i o n " . Comput. J . , v o l . 7 , 1965, pp. 308-313. (30) MULAR, A. L . , BRADBURN., R . , FLINTOFF, B. and LARSEN, C . , "Mass Balance o f a G r i n d i n g C i r c u i t " , Can. Ins t . M i n . Metal 1. B u l l . , v o l . 6 9 , no. 776, 1976, pp. 124-129. (31) HART, J . e t a l . "Computer Approx ima t ions" , N i l e y , New Y o r k , 1968. (32) WHITEN, W. J . , "The Use o f M u l t i - D i m e n s i o n a l Cubic S p l i n e Funct ions f o r Regress ion and Smoothing", Aus t . Comp. J . , v o l . 3 , 1971, pp. 81-88. (33) DRAPER, N . , and SMITH, H . , " A p p l i e d Regression A n a l y s i s " , W i l e y , New Y o r k , 1966. - 126 -v APPENDIX A MAJOR EQUIPMENT SPECIFICATIONS FOR SECONDARY CRUSHING PLANT (a) Secondary and T e r t i a r y Crushers (b) Primary and Secondary V i b r a t i n g Screens - 127 -MAJOR EQUIPMENT SPECIFICATIONS FOR SECONDARY  CRUSHING PLANT (a) Secondary and T e r t i a r y Crushers A l l crushers i n the secondary c rush ing p l a n t are 7 f t . Symons Nordberg heavy duty cone c rushe r s . With the excep t ion o f the c rush ing chamber c o n f i g u r a t i o n , a l l crushers are s i m i l a r . The secondary crushers u t i l i z e the "s tandard" c rush ing chamber c o n f i g u r a t i o n w i th coarse concave and mant le , w h i l e the t e r t i a r y crushers use the "shor t -head" c o n f i g u r a -t i o n w i th a coarse concave and medium mantle . The reader should note the m o d i f i c a t i o n s made to both "s tandard" and shor t -head" mantles des-c r i b e d on page 14. In a d d i t i o n to c rusher s p e c i f i c a t i o n s desc r ibed i n Table 1 (page 15) and under the i n d i v i d u a l u n i t opera t ion d e s c r i p t i o n s , the f o l l o w i n g in fo rmat ion i s p resen ted : TABLE AI A d d i t i o n a l S p e c i f i c a t i o n s f o r Secondary and T e r t i a r y Crushers S p e c i f i c a t i o n Secondary Crushers (Standard) T e r t i a r y Crushers (Short-Head) Motor sheave diameter Countershaf t sheave diameter Motor speed Countershaf t speed Mantle throw ' . 26-1/2 i n . 42-1/2 i n . 710 rpm 443 rpm 3-5/8 i n . 26-1/2 i n . 42-1/2 i n . 712 rpm 444 rpm 3-5/8 i n . A l l u n i t s w i t h i n a s p e c i f i e d u n i t opera t ion are p h y s i c a l l y s i m i l a r . - 128 -Figure A l Design S p e c i f i c a t i o n s f o r Symons Nordberg Cone Crushers - 129 -TABLE A2 Design S p e c i f i c a t i o n s f o r Symons Nordberg Cone Crushers STANDARD CONE CRUSHERS Size A B C D n^iiiiHiMiaw E F Keyway G H Recommended Horsepower (Electric) Full Load RPM Weight lbs. 9.900 (4,491 Kg.) 2 It. •-. (610 mml 4'-6" (1372 mm) 4'-3%" (1311 mm) 5'-0/,6" 11526 mm) V-1%" (340 mm) r-5" (432 mm) '3y,6" (87 mm) %"X 7 /,6" (22mmx11 mm) 4'-3%" (1318mm) 2'-8" (813mm] 30-50 575 3 ft. (914 mm) 5'-8" (1727 mm| 5'-10/2" (1791 mm| 6'-0%" (1838 mm) V-5%" (450 mm) •V-9/4" (540 mm] 3'5/6" (100 mm) V'x/2" (25mmxl3 mm) 5'-6/2" (1994mm) 3'-8" i [1118mm] j 75-100 580 22,000 (9,979 Kg.) 4 ft. (1219mm) 7'-0" (1778 mm) 8'-2/2" (2502 mml 6'-7/4" (2013 mm) 2'-0/e" (613 mm) 2'-0" (610 mml 47/,6": (113mm) 1/s"x9/,6" (29 mmx14mm| 6'-11/4" (2115 mm) 4'-0" (1219mm) 100-150 485 37.100 (16,828 Kg.) 4/4 ft. (1295 mm| 7'-6" (2286 mm| 8'-4/4" (2546 mm) 6'-83/4" (2051 mm] 2'-0/e" (613 mm) 2'-3" (686 mml 47/,o" (113 mm) 1/a"x9/t6" (29mmx14mm) 6'-11/2" (2121 mm) 4'-3/2" (1308 mml 150-200 485 47,100 (21,364 Kg.) 5 ft. (1524 mm| 8'63/4" (2610 mm| 10'-5%" (3191mm) 6'-0'/>" (1842 mm) V-6" (457 mm| ; ' 2'-6" (762 mm) 57/,6" (138 mm) 13/e"x"/,6" |35mmx17mm) 8'-23/4" (2508 mm) 4'-6" (1372 mm| 200-250 485 91,600 (41,549 Kg.) 5/2 ft. Heavy Duty (1676 mm) 8'-9/4" (2673 mm| 9'-9/4" (2978 mm) 8'-1" (2464 mml 2-7/4" (794 mm| 2'-7/2" (800 mm) 57/,6" (138 mm) 1%"x'/,s" |35mmx17mm| 9'-3/2" (2832 mm) 4'-6" (1372 mm) 200-250 485 92,600 (•12.003 Kg.) 7 ft. Heavy Duty (2134 mm) 10'-53/8" (3185 mm) 1V-3" |3429mm) 9'-8%" ! 3'-43/8" . (2962 mm) j (1026 mml 1 2'-11/2" (902 mm). ' 6/2" (165 mm) 1/2"x3/4" (38mmx19mm) 11'-2/2" (3416mm) 6'-0" (1829 mm) 300-350 435 148,500 (67.359 Kg.) 7 ft. Extra Heavy Duty (2134 mm) 13'-2/4" (4020 mm) 10'-10/4" (3308 mm| 9'-8%" | 3'-43/8" (2962 mml j [1026 mm] 2'-11/2" (902 mm) 6/2" | 1/2"x3/4" (165mm) (38mmx19mm) 1V-2/2" (3416 mml jjMiiaaiiurgHBE 6'-0" (1829 mm) 300-350 435 191,200 (86,728 Kg.) SHORT HEAD CONE CRUSHERS Size 2 ft. . (610 mm| A 4'-6" (1372 mm) B 4'-3%" (1311 mm) c 5'-0/,6" (1526 mm) D V-1%" (340 mm) E F Keyway G K Recommended Horsepowei (Electric) 30-50 Full ' Load RPM 575 Weight Ihs. 10,100 (4,581 Kg.) V-5" (432 mm) 37/,6'" (87 mm] 78"x7,e" • 22 mmx11 mm) 4'-37/8" (1318mm) 2'-8" (813 mm) 3 ft. (914 mm| 5'-8" (1727 mm) 5'-10/2" (1791 mm) 6'-03/8" (1838 mm| V-5%" (450 mm) V-9/4" (540 mm) 3,5/,6" (100 mm) V'x/2" (25 mmx13 mm) 5'-6/2" (1994 mm) 3-8" (1118mm) 75-100 580 23,200 (10,523 Kg.) : 4/4 ft. : |1295mm) 7'- 6" (2286 mml 8'-4/4" (2546 mm) 6'-83/4" (2051 mm) 2'-0/8" (613 mm) 2'-3" (686 mm) 47/,6" (113 mm) 1/8"X!/16" (29mmx14mm) 6'-11/2" (2121 mm] 4'-3/2" (1308 mm) 150-200 485 47,400 (21,500 Kg.) 5 ft. (1524 mm) 8'-7/4" (2622 mm) 10'-53/4" (3185 mm) 6'-0/2" . (1842 mm) V-6" (457 mm) 2'-6" (762 mm) 57/,6'' (138 mm) 1 3/ 8"X ' / l6" (35mmx17mm) 8'-2%" (2508 mm) 4'-6" (1372 mm| 200-250 485 92,900 (42.139 Kg.) V 5/ 2 ft. ' Heavy Duty ' (1676 mm) 8'-9/4" (2673 mm) 9'-9/4" (297Bmm) 8'-1" (2464 mm) 2'-7/4" (794 mml 2'-7/2" (800 mm|-57/,e" (138 mm) 13 /B"X" / , 6 " |35mmx17mm| 9'-3/2" (2832 mm| 4'-6" (1372 mm) 200-250 485 93.900 (42.593 Kg.l 7 ft. Heavy Duty (2134 mm) 10'-2%" (3115 mm) 11'-3/2" (3442 mm) 9'-8%" (2962 mm| 3'-4%" (1026 mm| 2'-11/2" (902 mm| 6/2" (165 mm) 1/2"x3/4" |38mmx19mm) IV-2/2" (3416 mm) 6'-0" (1829 mm) 300-350 435 154,600 (70.126 Kg.l ,' 7 ft. Extra .' Heavy Duty XLa'A , .: (2134 mm] | ( 3 8 4 2 l™> 11'-10%" (3626 mm) 9'-8%" (2962 mm) 3'-43/8" i (1026 mm| 2'-11/2" (902 mm) 6/2" (165 mm) 1/2"x3/4" (38 mmx19mm) IV-2/2" (3416 mm) 6'-0" (1829 mml 300-350 435 197.300 189,495 Kg.] THE DATA SHOWN ON THIS PAGE SHOULD NOT BE USED FOR CONSTRUCTION PURPOSES. CONSULT NORDBERG —DIVISION OF REX CHAINBELT INC. BEFORE DESIGNING OR BUILDING A CRUSHING PLANT USING SYMONS STANDARD OR SHORT HEAD CONE CRUSHERS OR PURCHASING ELECTRIC MOTORS, ETC. TABLE A3 Opera t ing S p e c i f i c a t i o n s f o r Symons Nordberg Cone Crushers S T A N D A R D S Y M O C O N E C R U S H E R S — O P E N C IRCU IT CAVITIES FEED OPENINGS PRODUCT SIZES • CAPACITIES a S i n Type of Recommended Minimum Discharge Feed opening With Minimum Recommended Discharge Setting A Capacities in Tons (2000 lb. Per Hour Passii >. Through the Crusher at Indicated Discharge Setting A Cavity Setting A B B Closed Side Open Side W (6 mm) w (10 mm) Vj" (13 mm) w (16 mm) Hr> (19 mm) w (22 mm) 1" (25 mm) 1V«" (32 mm) 114" (38 mm) 2" (51 mm) 2 W (64 mm) mmmtmmtamt 2 f t (610 mm) Fine Coarse Extra Coarse V (6 mm) ' V," (10 mm) V (13 mm) 2 V (57 mm) 2 V (70 mm) 3 V (83 mm) 3 V (95 mm) 3 V (89 mm) 4" (102 mm) 18 20 20 25 25 25 30 30 30 35 35 40 40 45 50 45 50 55 50 60 70 60 75 80 3 ft. (914 mm) Fine Coarse Extra Coarse '/," (10 mm) V (13 mm) V (19 mm) 3 V (86 mm) 4 V (105 mm) 4 V (124 mm) 5%"(144mm) 6 V (175 mm) 7 V (191 mm) 40 50 50 60 60 70 75 75 75 90 90 80 100 100 120 120 140 140 4 f t (1219 mm) Fine Medium Coarse Extra Coarse V (10 mm) V (13 mm) V (19 mm) y," (19 mm) 5" (127 mm) 5 'V (143 mm) 6 V (156 mm) 6 V (171mm) 7 V (187 mm) 8 V (210 mm) 8%"(227mm) | 9 V (248 mm) 70 90 100 110 n o 130 140 140 140 140 150 150 150 150 175 175 175 170 200 200 200 220 260 260 300 300 Wt ft. (1295 mm) Fine Medium Coarse Extra Coarse '/," (13 mm) V (16 mm) V (19 mm) 1" (25 mm) 4 V (114 mm) 5 V (137 mm) 7 V (187 mm) 8 V (210 mm) 9" (229 mm) 10" (254 mm) 1 0 V (264mm) 1 1 V (286mm) 120 140 140 150 160 160 160 175 175 175 190 200 200 200 240 240 240 250 275 300 350 350 5 f t (1524 mm) Fine Medium Coarse Extra Coarse '/," (16 mm) V (19 mm) V," (22 mm) 1" (25 mm) 6 V (171 mm) 7'/," (191 mm) 8 V (222 mm) 9 V (235 mm) 9 V (248 mm) 10'/," (267 mm) 1 1 V (292 mm) 1 2 V (311mm) 160 175 175 200 220 220 230 250 250 250 250 275 285 285 300 325 350 • . 375 400 450 5V2ft. (1676 mm) Fine Medium Coarse Extra Coarse y," (16 mm) '/," (22 mm) 1" (25 mm) I V (38 mm) 7'/," (181mm) 7 V (197 mm) 8 V (219 mm) 9 V (241 mm) 9 V (251mm) 1 0 V (276 mm) 13V," (343 mm) 1 4 V (368 mm) 180 200 235 275 275 300 300 300 375 375 350 400 450 450 450 500 500 700 800 7 a (2134 mm) Fine Medium Coarse Extra Coarse V (19 mm) 1" (25 mm) I V (32 mm) I V ' (38 mm) 10" (254 mm) 11" (279 mm) 1 1V (292 mm) 12 V (324 mm) 1 3 V (343 mm) 14V (378 mm) 1 6 V (425 mm) 18V (460 mm) 370 400 500 500 600 620 750 750 750 800 850 850 1100 1200 1200 1400 1400 SHORT H E A D S Y M O N S C O N E C R U S H E R S - C L O S E D C I R C U I T F E E D O P E N I N G S • P R O D U C T S IZES • CAPACITIES*IN TONS (2000 lbs.] PER H O U R BASED ON CLOSED CIRCUIT OPERATION Type of Cavity Recom-mended Feed Opening With Min. Recommended Discharge Setting C Note 1: Note 2: Net Finished Product (Screen Undersize) Approx. Total TPH Passing Through Crusher (Net Finished Product rcul ting Load) Size Minimum Discharge Setting D D W (3 mm) X." (5 mm) W (6 mm) W (10 mm) w (13 mm) w (16 mm) (19 nm) 1" (25 mm) C Closed Side Open Side Note 1 Note 2 Note 1 Note 2 Note 1 Note 2 Note 1 Note 2 Note 1 Note 2 Note 1 Note 2 Note 1 Note 2 Note 1 Note 2 2 ft. (610 mm) Fine Coarse V (3 mm) X," (5 mm) V (19 mm) ' I V (35 mm) ' I V (38 mm) 2" (51mm) 18 10 20 22 13 13 26 26 14 18 21 27 20 25 30 40 25 30 35 45 3 ft. (914 mm) Fine Medium Coarse V (3 mm) V (3 mm) V (6 mm) V," (13 mm) I V (41mm) 1" (25 mm) 1 2" (51mm) 2" (51mm) 3" (76 mm) 45 45 40 40 30 30 35 60 60 70 40 40 45 60 60 75 50 55 60 75 80 90 80 90 105 1 85 95 110 80 100 120 4% f t (1295 mm) Fine Medium Coarse Extra Coarse V (3 mm) V (6 mm) V (8 mm) '/," (16 mm) I V (29 mm) 2 V (64 mm) I V (41mm) 3" (76 mm) 2 V (70 mm) 4" (102 mm) 4 V (121mm) 5 V (140 mm) 20 60 35 40 70 80 50 55 100 110 75 80 80 110 120 120 100 105 110 150 160 165 125 125 140 140 160 160 210 210 150 175 175 170 240 240 200 200 250 250 5 ft. (1524 mm) Fine Medium Med. Coarse Coarse Extra Coarse V ' (5 mm) V (6 mm) V (10 mm) V (10 mm) V (13 mm) 1" (25mm) 2 ' i " (64mm) I V (44 mm) 3 V (83 mm) 2\," (65 mm) 3 V (98 mm) 3 V (83 mm) 4 V (117 mm) 4 V (105 mm) 5 V (143mm) 100 75 150 150 no 120 120 160 180 180 180 150 150 150 200 225 225 225 175 180 180 220 240 260 270 270 220 250 270 290 290 230 260 260 260 280 300 300 5% f t (1676 mm) Fine Medium Coarse Extra Coarse V ' (5 mm) V (6 mm) V (10 mm) V (13 mm) I V (35 mm) 2 V (70 mm) 2 V (54 mm) 3 V (89 mm) 3 V (95 mm) 5 V (133 mm) 6" (152 mm) 7 V (184 mm) 65 130 180 180 135 135 W 200 200 210 170 175 175 175 230 230 260 260 210 210 220 220 240 250 330 330 245 250 250 270 350 350 280 320 320 300 360 360 7 ft. (2134 mm) Fine Medium Coarse Extra Coarse V (5 mm) V," (10 mm) V (13 mm) V (16 mm) 2" (51mm) 3 V (95 mm) 3 V (98 mm) 5 V (146 mm) 5" (127 mm) 7" (178 mm) 6 V ' (160mm) 8 ' 4 " (210mm) 240 320 240 360 360 300 300 450 450 450 360 450 500 550 600 450 500 500 560 620 550 520 580 650 C A P A C I T I E S S H O W N A R E B A S E D O N R E S U L T S S E C U R E D IN A C T U A L P R A C T I C E . T H E F I G U R E S S H O W N A P P L Y T O S H O R T T O N S O F M A T E R I A L W E I G H I N G 1 0 0 P O U N D S P E R C U B I C F O O T , A N D A R E B A S E D O N A P R O P E R L Y G R A D E D F E E D . F A C T O R S W H I C H M A Y A F F E C T C A P A C I T Y I N C L U D E . »IZE O F F E E D , F R I A B I L I T Y , T O U G H N E S S A N D M O I S T U R E C O N T E N T . T O A C H I E V E O P T I M U M R E S U L T S T H E C R U S H E R S E T T I N G C M A Y V A R Y D E P E N D I N G O N T H E N A T U R E O F T H E M A T E R I A L A N D S P E C I F I C A T I O N D E S I R E D . - 131 -Design s p e c i f i c a t i o n s f o r the e n t i r e f a m i l y o f Symons Nordberg cone c r u s h e r s , i n c l u d i n g the 7 f t . s tandard and shor t -head models are presented i n F igure A l and Table A2 ( T a b l e A2 re fe r s to Figure A l )... G e n e r a l i z e d ope ra t i ng data f o r both c rusher types i s presented i n Table A 3 . (b) Primary and Secondary V i b r a t i n g Screens A l l s c reen ing i n the Brenda c rush ing p l a n t i s done on A l l i s -Chalmers double deck R i p l - F l o i n c l i n e d v i b r a t i n g screens . The pr imary and secondary s c r e e n s , desc r ibed on pages 10 and 12 r e s p e c t i v e l y , are i d e n t i c a l , w i th the excep t ion tha t the secondary screens are the heavy duty v e r s i o n w h i l e the pr imary screens are the e x t r a heavy duty v e r s i o n . A d d i t i o n a l ope ra t ing s p e c i f i c a t i o n s f o r these screens are presented i n Table A4. TABLE A4 A d d i t i o n a l S p e c i f i c a t i o n s f o r Primary and Secondary V i b r a t i n g Screens S p e c i f i c a t i o n Primary Screen Secondary Screen Make A l l i s - C h a l m e r s A l l i s - C h a l m e r s Model double deck R i p l - F l o double deck R i p l - F l o Vers ion e x t r a heavy duty heavy duty Nominal Dimensions 8 f t . x 20 f t . 8 f t . x 20 f t . Motor 2x25 Hp @ 1800 rpm 2x25 Hp @ 1800 rpm Dr i ve d i r e c t , b e l t d i r e c t , b e l t V i b r a t i o n Frequency 850 rpm 850 rpm V i b r a t i o n Ampli tude 3/8 i n . 3/8 i n . I n c l i n a t i o n 20° 20° Upper Deck s t r i p s o f punched p l a t e s t r i p s o f punched p l a t e S l o t Dimensions - 1-1/16 i n . x 3 i n . Lower Deck 5 panels wi re c l o t h 5 panels wi re c l o t h (4 f t . x 8 f t . ) (4 f t . x 8 f t . ) S l o t Dimensions 3/4 i n . x 3-1/16 i n . 1/2 i n . or 5/8 i n . x 3-1/16 i n . w i re diameter - 3/8 i n . -..132 -MODEL SH SCREEN SIZES and DIIVIENSIONS i C A B L E tCABLE S T I F F E N E R F R A M E A T S P R I N G B A S E S S U B S T I T U T E D F O R ( B O T H S I D E S ) . S I Z I N G D E C K SINGLE and DOUBLE DECK . . . 20° SLOPE Screen Size (ft) Mech. No. A ft-in. B ft-in. C ft-in. • ft-in. E ft-in. F ft-in. G in. H ft-in. K ft-in. L ft-in. M ft-in. 4x 8 4x 10 4 x 12 4 x 14 2- 4 3- 4 3-4 3-4 4-0'A 4-0/4 4-0/4 4-0V4 7-10% 9- 9 % 11- 8 13- 6% ?.-10/2 3- 6% 4- 3 4-11% 3- 0 % 3- 0 % 3- 0 % 3- 0 % 0-15% 0-153/s 0-153/a 0-153/a 2-10% 2-10% 2-10% 2-10% 81/4 81/4 81/4 81/4 0-20% 0-20% 0-203A 0-203/4 2-103/g 2-103/8 2-10% 2-10% 2- 91/4 2- 9 % 2- 9'/4 2- 9% 2- 8 2- 8 2- 8 2- 8 5x 10 5x 12 5 x 14 5x 14 5 x 16 3-4 3-4 3- 4 4- 4 4-4 5-0V4 5-01/4 5-0V4 5-Oi/j 5-OiA 9- 9% l i - 3 13- 6% 13- 6% 15- 51/s 3- 6% 4- 3 4-11% 4- 11% 5- 7% 3- 0 % 3- 0 % 3- 0 % - 3 - 6 3- 6 0-153/a 0-153/a 0-153/s O-I81/2 0-18'/2 2-10% 2-10% 2- 10% 3- 33/8 3- 33/8 83/8 8'/8 7% 83/8 83/8 0-20% 0-20% 0-20% 2- 1% 2- 1% 3- 4% 3- 4% 3- 4% 3- 5% 3- 5% 3- 3/s 3- 3% 3- 3 % 3- 3/2 3- 3/2 3- 1 % 3- 1 % 3- 1% 3- 3% 3- 3% 6x 12 6x 14 6x 16 6 x 2 0 4-4 4-4 4- 4 5- 5 6-oy 4 6-0% 6-01/4 6-01/4 11- 8 13- 6% 15- 51/s 19- 2i/4 4- 3 4- 11% 5- 7% 6- 11 '% 3- 6 3- 6 3- 6 3-10% O-I81/2 0-18/2 0-181/2 0-211/4 3- 33/8 3- 3% 3- 33/8 3- 83/4 83/a 83/8 83/s 73/4 2- 1% 2- 1% 2- 1% 2- 6 3-111/4 3-111/4 3- 111/4 4- 2 3- 9/2 3- 9/2 3- 91/2 3-113/4 3- 9% 3- 9%, 3- 9% 3-10% 7 x 14 7 x 16 7 x 20 5-5 5-5 • 5-5 7-0/4 7-01/4 7-01/4 13- 8/ 4 15- 6% 19- 3 % 4- 11% 5- 8 6- 111/4 4- 93/4 4- 9 % 4- 9% 0-24 0-24 0-24 4- 61/4 4- 61/4 4- 61/4 123/4 123/4 113/4 2-10 2-10 2- 9 5- 2% 5- 2% 5- 2% 4- 53/4 4- 53/4 4- 53/4 4- 3/2 4- 3/2 4- 3y 2 8 x 16 8 x 2 0 8 x 20 5-5 5- 5 6- 5 8-0V4 8-0/> 8-0V4 15- 6% 19- 3 % 19- 3 % 5- 8 6- 111/4 6-II1/4 4- 93/4 5- OVz 5- 31/8 0-24 2- 13/8 2- 3 4- 61/4 4- 8 4-111/4 123/4 IIV4 111/4 2-10 2- 10 3- 0 % 5- 2% 5- 2% 5- 4% 4-11.3/4 4- 11% 5- 21/, 4- 9/2 4- 9y 2 4-11/2 Screen Size (ft) N ft-in. P • in. Q ft-in. R ft-in. S in. T in. U in. A-A ft-in. B-B ft-in. C-C ft-in. D-D ft-in. E E ft-in. WT.-D.D. floor mt. 4 x 8 4 x 10 4 x 12 4x 14 4-1/4 4-1% 4-1% 4-1% 16% 16% 16% 16% 5- 2 7- 0 % 8- 11% 10- 9 % 4- 8 / 2 5- 8/2 6- 8/2 7- 8/2 3 % 3 % 3 % 3 % 53/s 5% 53/, 53/4 6% 6% 6% 6% 0- 6 /4 0- 8 0- 8 0- 8 2-3% 2- 4% 3- 0/2 3-8'% 0- 9 1- 10 1-10 1-10 6- 31/2 6- 5% 7- 11% 10- 2/2 5-1 5-1 5-1 5-1 4900 5200 5300 6300 5 x 10 5x 12 5 x 14 5 x 14 5 x 16 5-1% 5-1% 5-1% 5-1% 5-1% 16% 163/s 163/8 163/8 16% 7- 0 % 8- 11/8 10- 9 % 10- 9 % 12- 8/4 5- 8 / 2 6- 8/2 7- 8/2 7- 9% 8- 9% 3 % 3% 3% 3 % 3 % 53/4 53/4 53/, 7/a 7/s 6% 6% 6% 6% 6% 0- 8 0- 8 0- 8 0- 7 0- 8 2- 43/4 3- 0% 3-8'% 3- 3 % 4- 4 '% 1-10 1-10 1-10 1- 9% 1-10 6- 6'% 8- 4% 10- 2% 10- 3% 12- 1% 6-1 6-1 6-1 6-1 6-1 6475 6950 7300 7550 8800 6x 12 6 x 14 6 x 1 6 6 x 20 6-13/4 6-1% 6-1% 6-13/4 163/s 163/s 163/s 163/8 8-11 Vs 10- 9 % 12- 8 / 4 16- 53/8 6- 9% 7- 9 % 8- 9% 10-9% 3 % 3% 3 % 4/t 7/s 7/s 7/8 8 6% 6% 6% 6% 0- 8 0- 7 0- 8 1- 5/2 3-1/2 3- 8 '% 4- 4 % 4-1/4 1-10 1- 9% 1-10 4- 1/B 8- 4'% 10- 3% 12- 1% 11- 3% 7-1 7-1 7-1 7-1 8500 8840 9100 13400 7 x 14 7 x 16 7 x 2 0 7-2 7-2 7-2 16/4 16/4 16/4 10-11 12- 9% 16- 63/4 8- 0 9- 0 11-1 7/4 7 !A 7/4 8 8 8 9/2 9% 9/2 0- 9% 0- 9% 1- 6% 3- 4% 4- 0 % 4 -1% 2- 2 2- 2 4- 2% 9- 43/4 11- 2/4 11- 3/4 8-1 8-1 8-1 14100 15100 17600 8 x 1 6 8 x 20 8 x 20 - - - 9-1% 9-0 11-1 7/2 8/2 8/2 8 / 3 8 8/4 10 9/2 91/2 0- 9% 1- 6% 0-11% 4-0% 4-1% 4-7/. 2- 2 4- 2% 2- 8% 11- 2/4 11- 3/4 12- 9% 9-1 9-1 9-1 17000 19600 21900 Figure A2 Design S p e c i f i c a t i o n s f o r A l l i s - C h a l m e r s R i p l - F l o I n c l i n e d V i b r a t i n g Screens - 133 -Design s p e c i f i c a t i o n s f o r the e n t i r e f ami ly o f R i p l - F l o screens are presented i n F igure A2 . The s i n g l e and double deck screens are i d e n -t i c a l , w i t h the excep t ion tha t a s t i f f e n e r frame i s used i n the s i n g l e deck v e r s i o n where the lower deck i s used i n the double deck v e r s i o n . - 134 -APPENDIX B MEASURED (RAW) DATA S i z e D i s t r i b u t i o n s f o r Secondary Crusher Samples S i z e D i s t r i b u t i o n s f o r T e r t i a r y Crusher Samples S i z e D i s t r i b u t i o n s f o r Secondary Screens Samples S i z e D i s t r i b u t i o n s f o r Primary Screens Unders ize Samples Flowrate Record f o r Pr imary Screens Unders ize S t re - 135 -L e v i c e : DS2D t a s k : 39 USERID: RALU 12: 51: 30 0.9-04-77 U n i v e r s i t y of B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS2D f SIGN RALU t ENTER USER PASSWORD. » i **LAST SIGNON WAS: 12:41:44 f USES "RALU" SIGNED ON AT 12:50:05 ON SUN SEP 04/77 * RUN *BAS.IC * EXECUTION BEGINS , ?UBC BASIC SYSTEM GET APEND RUN SECONDARY CRUSHEH SAMPLE S I Z E ANALYSES SIZE ANALYSES REPORTED IN HEIGHT PERCENT RETAINED ON SIZE t a s k : FEED SIZE DISTRIBUTIONS • • • SIZE (CM) 21.76 10. 88 5. 2. 44 72 1.36 0.68 0. 34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 RUN NO. 1 1.5 20.5 28 .5 29.4 13.3 3.41 0.91 0. 48 0. 38 0. 4 1 0.36 0.3 0.24 0.31 RUN NO. 2 3 35 36. 5 18.35 4.7 0.94 0.29 0.22 0. 17 0.17 0. 18 0.16 0. 13 0.19 RUN NO. 3 0 .5 23.5 28 27.5 13.26 2.72 0.97 0.79 0.66 0.57 0.56 0.42 0.28 0.27 RUN NO. 4 0 24 29 30.. 6 1.1.95 1.94 0.68 0.37 0.29 0.26 0.27 0.24 0.18 0*22 SIZE (CM) 21.76 10. 88 5.44 2. 72 1.36 0. 68 0.34 0. 17 0. 085 0.0425 0.0212 0.0106 0.0053 - 0 . 0 0 5 3 RUN NO, 5 1 16.5 28. 5 27 .3 12.6 4.65 2. 25 2 1.65 1.32 1.02 0. 64 0. 3 0.27 RUN NO. 6 4 27 26. 5 23. 6 10. 8 3 1.05 1.05 0.81 0.73 0.6 0.42 0.25 0.19 RUN NO, 7 0 30 29.5 26.4 9.1 1.8 0.76 0.52 0.37 0.39 0.4 0.3 0.23 0.23 RUN NO. 8 0 26 30 29.4 8.9 1.87 0.73 0.62 0.56 0.58 0.51 0.37 0.23 0.23 - 136 -PRODUCT SIZE DISTRIBUTIONS SIZE (CM) 21.76 10.88 5. 44 2.72 1.36 0.68 0. 34 0.17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 SIZE (CM) 21.76 10.88 5. 44 2.72 1 .36 0.68 0. 34 0.17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 RUN NO. 1 0 0 17 45 23. 9 6.05 2. 24 1. 56 1. 07 0. 87 0.69 0.59 0. 46 0. 57 RUN NO. . 5 0 0 26 37 18.2 6 3.2 2. 65 2 1.71 1.29 0.91 0.51 0.53 RUN NO. 2 0 0 24 42. 5 17. 6 6. 15 2 .75 1.97 1.33 1.04 0.82 0.65 0.52 0.67 RUN NO. 6 0 0 16 39 21 9 3.9 3.2 2.4 1.87 1.43 1.05 0.61 0.54 RUN NO. 3 0 0 16 39 .5 22 .5 8.2 4 2.8 2 1.47 1.28 0.98 0.63 0.64 RUN NO. 7 0 0 23 42 .5 19. 1 5.4 2.8 1 .95 1.3 1 .07 1.05 0.8 0.53 0.5 RUN NO. 4 0 0 31 42 15.9 4.4 2.05 1.25 0.89 0.68 0.56 0.47 0.35 0.45 RUN NO. 8 0 0 20 39 22.7 7.3 2.9 2.35 1.6 1*27 1.09 0.82 0.51 0.46 r ?STOP! I- ? AT LINE "690" IN PROGRAM "APEND" i- ? PROGRAM ENDS : MTS i CONTROL *PRINT* HOLD PRINT=TN FOfiM=8X11 * *PRINT* ASSIGNED RFS NUMBER 661805 I COPY *flSOURCE*a)SP TO *PSINT* - 161 -e v i c e : DS48 t a s k : 246 USEHID: BALU 10:20:16 09-06-77 U n i v e r s i t y o f B r i t i s h Coiutabia Computing C e n t r e - d e v i c e : DS48 task.: 246 SIGN RALU ENTER USER PASSWORD. * * L A S T SIGNON WAS: 10:10:51 USER "RALU" SIGNED ON AT 10:19:17 ON TUB SEP 06/77 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM ? GET APPE RUN TERTIARY CRUSHER SAMPLE SIZE ANALYSES SIZE ANALYSES REPORTED IN WEIGHT PERCENT RETAINED ON SIZE FEED SIZE DISTRIBUTIONS SIZE {CM) 21. 76 10.88 5. 44 2.72 1. 36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 SIZE (CM) 21. 76 10.88 5. 44 2.72 1.36 0.68 0. 34 0.17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 .RUN NO. 9 0 0 12 43 39 3.62 0.76 0. 42 0.24 0. 2 0. 19 0. 15 0. 12 0.3 RUN NO. 14 0 0 2 55 38.6 1. 88 0.53 0.41 0.31 0.26 0.21 0. 19 0. 18 0.43 RUW NO. 10 0 0 19 44.5 31.5 2.82 0.66 0.25 0.21 0.18 0. 18 0.19 0. 17 0.34 RUN NO. 15 0 0 14 52 31 1.21 0.38 0.26 0. 17 0. 16 0.15 0. 14 0. 14 0.39 RUN NO. 1 1 0 0 22 47.5 27.1 1. 66 0. 38 0.24 0. 18 0. 18 0. 18 0. 15 O. 14 0. 29 RUN NO. 16 0 0 6 37 .5 51.8 3. 18 0. 58 0. 22 0. 12 0. 1 0. 09 0, 09 0. 1 0.22 RUN NO. 12 0 0 23 38.5 32.6 2.85 0.89 0.46 0.35 0.27 0.23 0.22 0.22 0.41 RUN NO. 16A 0 0 15 47 34.9 1.4 0 .5 0.26 0,2 0.16 0. 13 0.12 0.11 0.22 RUN NO. 13 0 0„ 16 46.5 32 .2 J . 56 Q. 46 0.26 Q. 19 0. 16 0. 14 D. 13 a . 13 0.27 •RUN NO. 16B 0 o. 20 57 21.05 0.85 0,. 22 0.15 0.. 11 0. 1 Q. 11 0. 1 0. 12 0. 19 - 138 -PRODUCT SIZE DISTRIBUTIONS SIZE RUN NO. RUN NO. (CM) 9 .10 21.76 0 0 10.88 0 0 5.44 0 0 2.72 0 0 1. 36 38.5 42 0.68 34 .5 31 0.34 10 9.6 0.17 6 5.8 0.085 3.4 3.4 0.0425 2.55 2 .55 0.0212 1.9 2 0.0106 1.31 1.47 0.0053 0.89 1.08 -0 .0053 0.95 1.1 SIZE RUN NO. SDN NO. (CM) 14 15 21.76 0 0 10.88 0 0 5.44 0 0 2.72 43 16 1.36 42 42 0.68 7.4 19.7 0.34 2.35 7.4 0. 17 1.55 4.3 0.085 1 2.9 0.0425 0.75 2.35 0.0212 0.69 1.85 0.0106 0.54 1.45 0.0053 0.37 1.01 -0 .0053 0.35 1.04 RUN NO. RUN NO. RUB NO.: 11 12 13 o o a 0 0 0, 0 0 0 2 5 .5 10 47.5 38.5 42 26.5 26.7 23.5 8.5 10.3 8.7 4 .7 6.2 5.1 3 .2 4.2 3.2 2.25 2 .9 2.25 1. 9 2.05 .1.75 1.4 1.5 1.27 1.02 1.05 1 1.03 1.1 .1.23 RUN NO. RUN NO. RUN NO.. 16 16A 16t\ 0 0 0 0 0 0, 0 0 0 6 15 23 36 45 41 29.5 19.6 17.8 10.5 7.4 5.9 5.7 4 3 .6 3. 5 2 .7 2.3 2 .5 1.95 1.75 2.1 1.62 1.5 1.6 1.06 1.2 1. 16 0.77 Q.91 1. 44 0.9 1.04 ?STOP! ? AT LINE "690'1 IN PROGRAM "APPE" ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FQRM=8X11 •PRINT* ASSIGNED RFS NUMBER 662260 $C *SOURCE*a)SP *PRINT* - 13y -e v i c e : DS40 t a s k : 237 USESID: BALU 09:53:41 09-06-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS40 • SIGN RALU ' ENTER USER PASSWORD. t a s k : 23' r **LAST SIGNON WAS: 09:40:31 r USER "RALU" SIGNED ON AT .09: 52: 35 ON TUE SEP 06/77 f RUN *BASIC • EXECUTION BEGINS r ?UBC BASIC SYSTEM , ? . GET APEND RUN SECONDARY SCREENS SAMPLE SIZE ANALYSES SIZE ANALYSES REPORTED IN WEIGHT PERCENT RETAINED ON SIZE FEED SIZE DISTRIBUTIONS S I Z E (CM) 21.76 10. 88 5.44 2 .72 1.36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 - 0 . 0 0 5 3 RUN NO. 17 0 0 17 38 20.2 9.3 4.5 3. 1 2.3 1.8 1.4 1 0.7 0.7 RUN N O . 18 0 0 14 3 2.5 28 .5 12 4 2.4 1.65 1.4 1. 15 0.92 0.67 0.81 RUN NO. 19 0 0 12 31 30 13 5 2. 6 1.6 1.3 1.2 0. 85 0. 63 0. 82 RUN NO, 20 0 0 10 31 29. 5 15 5.1 2.9 9 3 08 0 . 7 7 0.62 0.83 RUN NO, 21 0 0 10 24 31 17.5 6.1 3 .6 2 .3 1.7 1.37 0. 98 0.71 0. 74 S U N so;. 25 0 0 11 27 28. 1 16. 9 5.9 3.3 2.3 1.65 1.29 0.96 0.68 0.92 SIZE RUN NO., SUN NO. (CM) 26 27 21.76 0 0 10.88 0 0 5.44 10 12 2.72 24.5 28 1.36 29.5 28.5 0.68 18.3 15.7 0.34 6.4 5.8 0 .17 3.7 3.1 0.085 2.3 2 0.0425 1.55 1.4 0.0212 1.15 1.15 0.0106 0.9 0.77 0.0053 0.72 0.65 -0 .0053 0.98 0.93 RUN N O . , RUN NO. RUN NO. 28 29 30 0 0 0 0 0 0 8 11 11 23 2 9 24 32 28 29 .5 18.8 15.3 17 6 5.7 6 3. 6 3.2 3 .7 2. 4 2.2 2 .5 1.95 1.7 1.8 1.3 1.3 1.4 1.05 1 1.1 0.8 0.75 0.8 1.1 0.85 1.2 - 140 -OVERSIZE PRODUCT DISTRIBUTIONS SIZE SUN NO. RUN NO. RUN NO. RUN NO. RUN NO. RUN NO. (CM) 17 18 19 20 21 25 21.76 0 0 0 0 0 0 10.88 0 0 0 0 0 0 5.44 26 16 22 15 15 14 2.72 46.5 45 45 51 .5 39 45 1.36 25.3 36.4 31.4 31. 25 41.6 35 0.68 1. 1 1.62 0. 88 1.29 2.44 4.82 0.34 0.25 0.28 0,21 0.28 0.54 0.38 0. 17 0. 16 0.15 0. 09 0.14 0.32 0.15 0.085 0. 13 0. 1 0. 07 0. 1 1 0.23 0. 1 1 0.0425 0. 13 0.09 0. 07 0.07 0.2 0.09 0.0212 0. 13 0.08 0. 06 0.08 0. 17 0.09 0.0106 0. 1 0.07 0. 06 0.08 0.15 0.08 0.0053 0.08 0.07 0. 06 0.Q7 0. 14 0.09 -0 .0053 0. 12 0. 14 0. 1 0.13 0.21 0.19 S I Z E SUN NO. SUN NO. RUN NO. RUN NO. RUN NO. (CM) 26 27 28 29 30 21.76 0 0 0 0 0 10. 88 0 0 0 0 0 5. 44 14 18 16 22 21 2.72 31 40 47 55.5 54 1. 36 49 39.2 33.2 20. 4 22.7 0.68 4.92 1.6 2. 37 0.9 8 1.07 0.34 0. 44 0.34 0. 49 0.32 0.31 0. 17 0. 18 0.18 0. 19 0.16 0.19 0. 085 0.09 0.14 0. 12 0.11 0.13 0.0425 0.08 0.12 0. 11 0.11 0. 12 0.0212 0.07 0.11 0. 1 0.1 0.11 0.0106 0.05 0.1 0. 1 0. 1 0.11 0.0053 0.05 0.1 0.12 0.08 0. 1 -0 .0053 0.12 0.11 0,2 0.14 0. 16 UNDERSIZE PRODUCT DISTRIBUTIONS S I Z E RUN NO. RUN NO. RUN NO. RUN NO. RUN NO. RUN NO. (CM) 17 18 19 20 21 25 21.76 0 0 0 0 0 0 10.88 0 0 0 0 0 0 5.44 0 0 0 0 0 0 2.72 2 0 0 0 0 0 1. 36 31 36 42 32 30 11 0.68 30. 5 36 29.5 34 33.5 39 0.34 10.3 10. 1 8 11.7 13 17. 5 - 141 -0.17 6.7 5.4 5 .3 7.3 7 .7 9.7 0.Q85 5 3 .5 4 4.5 . 4 .5 6.1 0.0425 3.9 2.4 3. 3 3.3 3. 2 4.6 0.0212 3.4 2.1 2 .7 2.5 2 .7 3.9 0.0106 2. 9 1 .7 2. 1 1.85 2. 1 2.6 1 0.0053 2 1.35 1.58 1.3 1.5 2.4 -0 .0053 2.3 1.45 1.52 1.55 1.8 3.19 SIZE RUN NO. . RUN NO. {CM) 26 27 21.76 0 0 10.88 0 0 5.44 0 0 2.72 0 0 1.36 9 21 0.68 41 45 0.34 19 15.2 0.17 11.1 7 0.085 6.8 3 .3 0.0425 3.8 2.3 0.0212 3.3 1.7 0.0106 2.25 1.4 0.0053 1.65 1.2 -0 .0053 2.1 1.9 RUN NO. RUN NO. RUN NO. 28 29 30 0 0 0 0 0 0 0 0 0 0 0 0 30 32 34 36 32. 5 32.2 13 11.5 12.6 6.3 6.5 5.2 4. 2 4.2 3.4 2 .9 3.6 3 .2 2. 4 2.8 2 .5 1. 9 2.4 2 .3 1.52 1.9, 2 1. 78 2.6 2.6 ?STOP! ? AT LINE "900" IN PROGRAM "APEND" ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FORH=8X11 •PRINT* ASSIGNED RFS NUMBER 662239 $C *SOURCE*SSP *PRINT* - 142 -e v i c e : DS40 t a s k : 237 USERID: RALU 10:06:27 09-06-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS4Q task SIGN HALO ENTER USER PASSWORD. • • L A S T SIGNON WAS: 09:57:33 USER "RALU" SIGNED ON AT 10:05:52 ON TUE SEP 06/77 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM GET PEND RUN PHIMARY SCREENS UNDERSIZE (PRIMARY FINES) SAMPLE SIZE ANALYSES S I Z E ANALYSES REPORTED IN WEIGHT PERCENT RETAINED ON SIZE SIZE RUN NO. RUN NO. RUN NO. RUN NO. RUN NO. EUN NO. (CM) 31 32 33 34 35 36 21.76 0 0 0 0 0 0 10. 88 0 0 0 0 0 0 5. 44 0 0 0 0 0 0 2.72 0 0 0 0 0 0 1.36 6 0 22 33 22 25 0.68 13 0 31 34 29 26 0.34 15 0 15. 5 10.2 15 13.5 0. 17 15 0 9 6 10. 7 9.5 0.085 15.5 0 8 4.8 7.5 7.8 0.0425 14 0 5 .9 3 . 1 5.6 5 .9 0.0212 9.9 0 3.9 2.9 3.8 4 .7 0.0106 6.2 0 2.4 2.6 2.7 3 .5 0.0053 3.55 0 1.34 1.85 1.95 2.3 -0 .0053 1.85 0 0.96 1.55 1.75 1.8 ?STOP! • • • • ' • • • • a t • • • • • • • • • • « • • • * • • * • ' • • • * * • ? AT LINE "336" IN PROGRAM "PEN D" ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FORH=8X11 *PRINT* ASSIGNED RFS NUMBER 662250 $C *SOURCE*SSP *PRINT* - 143 -TABLE B l Flowrate Record f o r Primary Screens Unders ize Stream Augus t , 1975 Flowrates Percent Ove r s i ze Unders ize .Feed Fines i n Feed Date Day ( tons) ( tons) ( tons) (%) 1 F r i 19,724 6,185 25,909 23.87 2 Sat 24,130 7,867 31,997 24.59 3 Sun 20,716 6,528 27,244 23.96 4 Mon S ta tua to ry Ho l iday 5 Tue 32,944 11,128 " 44,072 25.25 6 Wed 10,934 3,274 14,208 23.04 7 Thur 27,062 10,053 37,115 27.09 8 F r i 11,994 3,307 15,301 21.61 9 Sat 25,557 8,031 33,588 23.91 10 Sun 27,564 8,375 35,939 23.30 11 Mon 20,955 7,322 28,277 25.89 12 Tue 15,495 3,988 19,483 20.47 13 Wed 22,625 2,161 24,786 8.72 14 Thur 25,156 2,156 27,724 9.26 15 F r i 14,225 5,875 20,100 29.23 16 Sat 19,781 7 ,768 27,549 28.20 17 Sun 25,045 8,231 33,276 24.74 18 Mon 20,282 6,906 27,188 25.40 19 Tue 7,010 2,069 9,079 22.79 20 Wed 26,314 8,766 35,080 24.99 21 Thur 16,366 5,941 22,307 26.63 22 F r i 7,613 3,292 10,905 30.19 23 Sat 10,996 4,236 15,232 27.81 24 Sun 24,232 6,022 30,642 19.65 25 Mon 24,620 6,423 31,043 20.69 26 Tue 22,637 4,877 27,514 17.73 27 Wed 14,087 3,197 17,284 18.50 28 Thur 36,057 8,278 44,335 18.67 29 F r i 24,243 6,390 30,633 20.86 30 Sat 24,837 3,728 28,565 13.05 31 Sun 24,774 7,484 32,258 23.20 - 144 -TABLE B2 Flowrate Record f o r Primary Screens Undersize Stream September, 1975 Flowrates Percent Overs ize Unders ize Feed Fines i n Feed Date Day ( tons) ( tons) ( tons) (*) 1 Mon S ta tua to ry Ho' iday 2 Tue: 25,514 6,658 32,172 20.70 3 Wed 24,378 5,411 29,789 18.16 4 Thur 24,561 7,135 31,696 22.51 5 F r i 23,740 5*999 29,739 20.17 6 Sat 20,875 6,330 27,205 23.27 7 Sun 21,181 5,901 27,082 21.79 8 Mon 6,164 1,503 7,667 19.60 9 Tue 5,992 1,858 7,850 23.67 10 Wed 23,850 7,283 31,133 23.39 11 Thur 19,137 5,487 24,624 22.28 12 F r i 22,794 3,724 26,518 14.04 13 Sat 23,912 6,161 30,073 20.49 14 Sun 22,738 5,777 28.515 20.26 15 Mon 23,662 5,788 29,450 19.65 16 Tue 20,435 6,199 26,634 23.27 17 Wed 12,303 3,273 15,576 21.01 18 Thur 29,195 - 8,291 37,486 22.12 19 F r i 19,802 4,744 24,546 19.33 20 Sat 32,402 8,340 40,742 20.47 21 Sun 28,679 7,363 36.042 20.43 22 Mon 20,332 6,075 26,407 23.01 23 Tue.: 12,867 3,448 16.315 21.13 24 Wed 18,560 5,311 23,871 22.25 25 Thur 17,756 4,901 22,657 21.63 26 F r i 24,691 6,852 31,543 21.72 27 Sat 27,608 9,265 36,873 25.13 28 Sun 20,480 4,600 25,080 18.34 29 Mon 21,498 6,391 27,889 22.92 30 Tue,. 15,167 4,648 19,815 . 23.46 \ - 145 -TABLE B3 Flowrate Record f o r Primary Screens Unders ize Stream October , 1975 Flowrates Percent Overs i ze Unders ize Feed Fines i n Feed Date Day ( tons) ( tons) ( tons) (*) 1 Wed 24,368 7,850 32,218 24.37 2 Thur 21,554 6,354 27,908 22.77 3 F r i 18,250 5,184 23,434 22.12 4 Sat 20,640 5,978 26,618 22.46 5 Sun 20,142 5,770 25,912 22.27 6 Mon 20,926 5,818 26,744 21.75 7 Tue 16,502 5,048 21,550 23.42 8 Wed 23,868 7,108 30,976 22.95 9 Thur 22,651 6,339 28,990 21.87 10 F r i 18,653 4,292 22,945 18.71 11 Sat 26,843 6,762 33,605 20.12 12 Sun 22 ,295 6,048 28,343 21.34 13 Mon S ta tua to ry Ho" iday 14 Tue 21,605 5,380 26,985 19.94 15 Wed 27,194 5,502 32,696 16.83 16 Thur 10,099 2,429 12,528 19.39 17 F r i 22,476 4,748 27,224 17.44 18 Sat 28,487 7,618 36,105 21.10 19 Sun 29,378 8,166 37,544 21.75 20 Mon 19,541 4,913 24,454 20.10 21 Tue 15,818 5,669' 21,487 26.38 22 Wed 29,927 9,633 39,560 24.35 23 Thur 22,211 7,149 29,360 24.35 24 F r i 14,975 5,393 20,368 26.48 25 Sat 27,906 8,455 36,361 23.25 26 Sun 17,917 3,955 21,872 18.08 27 Mon 28,471 6,475 34,946 18.53 28 Tue 16,614 5,271 21,885 24.08 29 Wed 15,863 4,680 20,543 22.78 30 Thur 27,725 6,287 34,003 18.46 31 F r i 22,313 11,978 34,291 34.93 - 146 -APPENDIX C ADJUSTMENT OF SECONDARY SCREEN DATA L i s t i n g o f the Program SCREEN - a program developed f o r adjustment o f raw screen da ta . Adjus ted Data f o r the Secondary Screens - 147 -1 * * * PROGRAM. SCREEN :SCEEEN DATA ADJUSTMENT PROGRAM 2 * 3 * 9 DIM G(20,20) ,H(20,20) ,K(20 ,20) ,1 (20 ,20) ,V(20 ,20) 10 DIM F(20,20) ,U(20,20) ,0 (20 ,20) ,A{1,40) ,C(45) ,T{2 ,20) , E(35,10) 12 DIM D(1,40) ,X{40,40) , ¥ { 4 0 , 1 ) , 2 (1 ,40) ,Q(40,40) 14 READ N1,N2,A3,A2 16 HEAD M3,M4 18 READ A 1 , 8 1 , V 1 , G 2 , M 2 20 MAT A=ZEE(1,N1) 22 MAT D=ZEB(1,N1) 24 MAT X=ZEE(N1 + 1,N1) 26 MAT Y=ZER (N1 + 1,1) 28 MAT Z=ZER(1,N1) 29 MAT Q=ZER (N1 + 1 ,N1) 30 P I L E SSF ,SSO,SSD,SV10 ,TONS,DUMP,ASF2 ,AS02 ,ASU2,AKX2,VAE 40 MAT BEAD F I L E 1 ,F(N2,A3) 50 MAT HEAD F I L E 2 ,0(N2,A3) 60 MAT READ FILE 3 ,U(N2,A3) 70 MAT SEAD F I L E 4 , E { N 1, 11) 80 MAT READ F I L E 5 , T ( 2 , 1 1 ) 82 MAT HEAD F I L E 11,Y(N2,3) 85 A9=A2 90 POR 1=1 TO N1 100 A (1 , I ) = E ( I , A9) 110 NEXT I 12 0 MAT F=( .01)*F 130 MAT O=(.01) *0 140 MAT U= (.01) *U 210 * CALCULATION OF INITIAL STARTING VALUES 215 FOB 1=1 TO N1 220 D(1 , I ) =ABS(G2*A (1,1) ) 225 NEXT I 230 * SET UP INITIAL SIMPLEX 240 FOR J=1 TO N1 250 FOE I = 1 TO J+1 260 I F I=J+1 THEN 290 270 X ( I ,J )=A (1, J) - (2/(3* 1) ) *D (1,J) 280 GO TO 300 290 X ( T , J ) = A ( 1 , J ) + ((2/(J*-1) ) * D ( 1 , J ) * J ) 300 NEXT I 310 FOR I = 3*2 TO N1+1 320 X ( I ,J )=A (1,J) 330 NEXT I 340 NEXT J 350 * CALCULATION OF STD. DEV'N OF OBJECTIVE FUNCTION 360 Z8=0 361 Z9=0 370 T3=1.E70 380 FOR 1=1 TO N1+1 390 H=I 400 GO SUB 1310 410 Y(I ,1)=Y1 420 NEXT I 430 GO SUB 1720 440 T1=0 441 T2=0 44 5 FOR 1=1 TO N1+1 450 T1=T1 + Y ( I , 1 ) 455 NEXT I - 148 -460 T1=T1/(N1+1) 465 FOR 1=1 TO N1 • 1 470 T2=T2+ (Y <I, 1)-T1) **2 480 NEXT I 490 T4=SQR (T2/N1) 500 IF T4>1.E-6 THEN 750 510 GO TO 590 520 * PRINTOUT SECTION 530 PHINT 540 PRINT "CYCLE LIMIT STOP CBITERION=";M2;"STD. DEVIATION=" ; T4 550 PRINT 560 PR I NT" HIGH= " ; Y (H , 1) , "2ND HIGH=";Y(S, 1} ,"LOW= n ; Y (L, 1) 570 PRINT 580 GO TO 600 590 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y ( L , 1 ) 593 PRINT 595 PRINT "STANDARD DEVIATION=";T4 600 H=L 610 GO SUB 1310 620 PRINT 622 A10=0 624 A11 = 0 625 PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS=»;Z9 626 A12=0 630 PRINT 635 PRINT "RUN NO.=";A2 695 PRINT " ADJUSTED SIZE DISTRIBUTIONS" 70 0 PRINT 701 A 15=0 702 A16=0 703 A17=0 705 PRINT " M I A S . F E E D " , " A D J . FEED" 708 PRINT 710 FOR J=1 TO N2 711 PRINT F{J ,A2)*100 ,C(2*N2*J)*100 712 A15=A15 + C{2*N2 + J) *1O0 713 A 10=A 10 + (F ( J , A2) * 100—C (2*N2+J) * 1 00) **2 714 NEXT J 715 PRINT 716 PRINT "RESIDUAL SUM SQUARES=";A 10 , " ","SUN FEED=";A15 717 PRINT 718 PRINT " M E A S . O / S " , " A D J . 0 / S " r " " , " M E A S . U / S " , " A D J . U / S " 719 PRINT 720 FOR J=1 TO N2 722 PRINT O {J, A2) *100, C{J) *100, " " , U (J , A 2) * 100 # C (N 2* J) * 1 00 723 A11=A11+ (0 (J,A2) *100-C (J) *100) **2 724 A12=A12 + (U (J,A2) *100-C(N2+J) *100)**2 725 NEXT J 726 PRINT 727 PRINT "RESIDUAL SUM SQRS=";A 11," " , "RESIDUAL SUM SQRS=";A12 728 FOR J=1 TO N2 729 A16=A16 + C (J) *100 730 A17=A17 + C(N2+J)*100 731 NEXT J 732 PRINT 733 PRINT " ","SUM 0/S=";A16," " , " " ,"SUM U/S=";A17 73 4 PRINT 735 PRINT " ADJUSTED FLOWRATES" 74 0 PRINT 744 PRINT "FEED=";ABS(X{H,27) ) *ABS (X (H,28) ) ;"{";T(1 ,A9) +T (2, A9) - 149 -745 PRINT 746 PRINT "0/S=";ABS(X(H,27)) ;"{";T(1 ,A9) ; ") " 747 PRINT « U / S = » ; A B S (X(H,28) ) < n , T ( 2 , A 9 ) ; ") " 748 PRINT 749 GO TO 1580 750 IF Z9>M2 THEN 530 752 IF Z9>M3 THEN 756 754 GO TO 766 756 M3=M3+M4 758 M5=CMD ("SEMPTY DUMPSD") 760 MAT WRITE F I L E 6 ,X 762 M6=CMD ("%SAVE DUMPSD") 764 PRINT " Z 9 = » ; Z 9 766 IF T4>T3 THEN 770 76 8 T3=T4 76 9 *EEFLECTION 77 0 MAT Q = (1) *X 780 FOE J = 1 TO N1 790 P1=0 800 FOR I = 1 TO N1+1 810 IF I = H THEN 830 820 P1 = P1 + X ( I .J ) /N1 830 NEXT I 840 Z (1, J)= (1 + A1) *P1-At*X {H, J) 850 X (H,J)=Z (1 ,J) 860 D(1.J)=P1 870 NEXT J 880 GO SOB 1310 89 0 MAT X = (1) *Q 900 Y=Y1 910 IF Y>=Y(L,1) THEN 1000 920 * EXPANSION 93 0 FOR J = 1 TO N1 940 X ( H , J ) = (1 + V1)*Z (1, J) —V1*D (1 , J) 950 NEXT J 960 GO SOB 1310 970 IF Y 1 > ¥ ( L , 1 ) THEN 10 10 980 Y{H, 1) =Y1 990 GO TO 430 1000 I F Y>Y(S,1) THEN 1060 1010 Y (H,1)=Y 10 20 FOR J=1 TO N1 1030 X (H,J)=Z (1,J) 1040 NEXT J 1050 GO TO 430 1060 I F Y>Y(H,1) THEN 1120 1070 FOR J = 1 TO N1 10 80 X (H,J) =Z (1,J) 1090 NEXT J 1100 Y (H, 1)=Y 11 10 * CONTRACTION 1120 FOR J=1 TO N1 1130 X (H,J) = B1*X (H, J) *(1-B1) *D(1 ,J) 1140 NEXT J 1150 GO SUB 1310 1160 I F ¥ 1 > Y ( H , 1 ) THEN 1200 1170 Y (H,1) = Y1 1180 GO TO 430 1190 * REDUCE SIZE OF SIMPLEX 1200 FOE J=1 TO N1 - IDU -1210 FOR 1=1 TO N1+1 1220 X ( I , J ) = ( Q ( I , J ) + Q ( L , J ) ) / 2 1230 NEXT I 1240 NEXT J 1250 Z8=Z8+1 1260 PRINT 1270 PRINT "STEP CHANGE";Z8 1280 PRINT 1290 GO TO 380 1300 CONSTRAINT SECTION 1310 Z1=0 1320 Z2=0 13 21 FOR J=1 TO N1-2 1322 I F X(H,J)>170 THEN: X (H , J) = 1 70 1323 I F X(H,J)<-170 THEN : X (H,3) = - 170 13 28 NEXT J 1330 FOR J=1 TO N2-1 1340 C (J)=EXP (X (H,J) ) / ( E X P (X (H, J) ) +EXP (-X (H, J) ) ) 1342 C(J )=INT(C(J ) *100000 + . 5)/100000 13 45 A5=N2-1+J 13 50 C (N2+J) =EXP (X{H,A5) ) / ( E X P (X (H,A5) ) +EXP(-X (H,A5) ) ) 1355 C(N2+J)=INT(C(N2+J) *100000 + .5) /100000 1360 Z1=Z1+C(J) 1370 Z2=Z2+C (N2+J) 1380 NEXT J 1390 C(N2-1)= 1-Z1 1400 C (2*N2) = 1-Z2 1410 C A L C U L A T I O N OF FEED DISTRIBUTION 14 20 Z3=ABS (X(H,28) ) / (ABS (X (H,27)) *ABS (X (H,2 8) )) 1430 Z4=1-Z3 1440 FOR J=1 TO N2 1450 C (2*N2 + J)=Z4*C (J) +Z3*C (N2+J) 1455 C(2*N2 + J) =INT (C(2*N2+J)*10O000+.5)/100000 1460 NEXT J 1470 C (3*N2)=Z4*C (N2) +Z3*C(2*N2) 1480 C A L C U L A T I O N OF OBJECTIVE FUNCTION 1490 F2=0 1500 FOR J=1 TO N2 1510 F2=F2+ ( (U (J,A2) -C(N2+J) ) **2) / V ( J , 3} + ( (0 ( J , A2) - C (J ) ) * * 2} / V (J , 1520 F2=F2*.3333* ( ( F { J , A 2 ) - C (2*N2 + J) ) * * 2 ) / V ( J , 1) 15 30 NEXT J 1540 F 2 - F 2 * <T{1, A9) - ABS (X (H,27) ) ) **2+{T (2, A9) -ABS{X(H, 28) ) ) **2 1550 Y1 = F2 1560 Z9=Z9+1 1561 FOR J=1 TO 3*N2 1562 I F C ( J ) < 1 . E - 8 THEN:C(J)=0 1565 NEXT J 1570 RETURN 1579 * DATA FILE STORAGE SECTION 1580 HAT READ F I L E 7 ,G(11,N2) 1582 MAT READ F I L E 8,H(11,N2) 1584 MAT READ F I L E 9 ,L(11 ,N2) 1586 MAT BEAD F I L E 10,K(11,N2) 1590 FOR J=1 TO N2 1592 G (A9,J)=C (2*N2 + J) *100 1594 H (A9, J) =C (J) *100 1596 L (A9,J)=C(N2+J) *100 1598 NEXT J 1600 A15=CMD("%EMPTY ASF23D") 16 02 MAT WRITE FILE 7 ,G - 151 -1604 A 16=CMD("%SAVE ASF23D") 1606 A 17=CMD ("%EMPTY AS023ID") 1608 MAT WRITE F I L E 8 ,H 1610 A18=CMD{"%SAVE ASO23D") 1612 A19=CME{"%EMPTY ASU22JD") 1614 MAT WRITE F I L E 9 , L 1616 A20=CMD {"%SAVE ASU23D") 1617 PRINT "^T.FRACTION REPORTING TO O/S" 1618 A21=X(H,27)+X(H,28) 1619 PRINT 1620 FOR J=1 TO N2 1622 I F C(2*N2*J)=0 THEN 1626 1624 GO TO 1630 1626 K (A9,J) =1 1627 PRINT K<A9,J) 1628 GO TO 1632 16 30 K (A9, J) = (C (J) *X (H,27) ) / (C(2*N2+J) *A21) 16 31 PRINT K (A9,J) 1632 NEXT J 1634 A22=CMD ("%EMPTY AKX23D") 1636 MAT WRITE FILE 10,K 1638 A23=CMDf"%SAVE AKX2SD") 1640 STOP 1715 * OBJECTIVE FUNCTION MAGNITUDE LISTING (ORDER SEARCH) 1720 I F Y ( 1 , 1)>Y(2, 1) THEN 1770 1740 S=1 1741 1=1 1750 H=2 1760 GO TO 1790 1770 S=2 1771 L=2 1780 H=1 1790 FOR 1=3 TO N1+1 1800 I F Y ( I , 1) >Y (I , 1) THEN 1820 1810 1=1 1820 I F Y<I,1) <Y{S, 1) THEN 1880 1830 I F ¥ ( I , 1) <Y (H, 1) THEN 1870 1840 S=H 1850 H=I 1860 GO TO 1880 1870 S=I 1880 NEXT I 1890 RETURN 1900 DATA 28 ,14 ,11 ,11 1910 DATA 1100,300 1920 DATA 1 , . 5 , 2 , . 0 1,10 2000 END END—OF-FILE - \i>d -e v i c e : DS40 t a s k : 237 USERID: RALU 09:59:05 09-06-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS40 t a s k : 237 SIGN RALU ENTER USER PASSWORD. , * * L A S T SIGNON WAS: 09: 57:08 USER "RALU" SIGNED ON AT 09:57:33 ON TUE SEP 06/77 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM GET ADP RUN ADJUSTED SIZE ANALYSES FOR SECONDARY SCREEN SAMPLES SIZE ANALYSES REPORTED IN HEIGHT PERCENT RETAINED ON SIZE R U N N U M B E R S 17 SIZE MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5. 44 17 16.803 2.72 38 30.487 1. 36 20. 2 27.221 0.68 9.3 11.649 0.34 4.5 3.919 0.17 3. 1 2.633 0. 085 2.3 1,909 0.0425 1.8 1.523 0.0212 1.4 1.325 0.0106 1 1.053 0.0053 0.7 0.717 -0 .0053 0.7 0.?6 RESIDUAL SUM OF SQUARES= 112.0938 FEED SUM= 99.999 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UN DERSIZE UNDERSIZE 21. 76 0 0 0 0 10.88 0 0 0 0 5. 44 26 26.226 0 0 2.72 46.5 46.497 2 1.94 1. 36 25.3 25. 116 31 30.975 0.68 1.1 1.084 30.5 30.488 0.34 0.25 0.251 10.3 10.461 0. 17 0.16 0. 161 6 .7 7.041 0. 085 0.13 0. 12 5 5 . 1 0.0425 0. 13 0. 124 3. 9 4.018 0.0212 0. 13 0. 125 3.4 3.464 0.0106 0.1 0. 1 2. 9 2.752 0.0053 0.08 0.077 2 1.859 - 153 -.' -0 .0053 0.12 0.119 2.3 1.902 OVERSIZE SUH= 100 UNDERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.08537 : UNDERSIZE= 0.37478 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE S I Z E (CM) 21.76 10.88 5. 44 2. 72 1.36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 ADJUSTED ORDINATE 1 1 0.9999932 0.9771518 0.5911507 5.962006E-2 0.0410346 3.917661E-2 4.027422E-2 5.216432E-2 6.044299E-2 6.084479E-2 6.880553E-2 0. 1003671 ADJUSTED FLOW RATES : FLOWSTREAM MEASURED FEED 356.8 OVERSIZE 228.6 UNDERSIZE 128.2 ADJUSTED 356. 7998 228.6001 128.1997 R U N N U M B E R S 18 SIZE MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5. 44 14 8. 855 2.72 32. 5 24.79 1. 36 28. 5 36.193 0.68 12 17.012 0. 34 4 4. 462 0.17 2.4 2.469 0.085 1.65 1.613 0.0425 1.4 1. 158 0.0212 1.15 1.064 0.0106 0.9 2 0.909 0.0053 0.67 0.68 - 154 --0 .0053 0.81 0.795 RESIDUAL SUM OF SQUARES^ 170.5035 FEED SUM= 100 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 21.76 0 0 0 0 10.88 0 0 0 0 5. 44 16 16.064 0 0 2.72 45 44.974 0 0 1.36 36.4 36.357 36 35.991 0.68 1.62 1. 621 36 35.917 0. 34 0.28 0.285 10. 1 9.592 0. 17 0. 15 0. 154 5. 4 5.313 0.085 0.1 0.093 3. 5 3. 479 0.0425 0.09 0.088 2. 4 2. 473 0.0212 0.08 0.082 2. 1 2.27 0.0106 0.07 0.074 1. 7 1 .935 0.0053 0.07 0.07 1. 35 1. 429 -0 .0053 0.14 0. 138 1. 45 1.601 OVERSIZE SUM= 100 UNDERSIZE SUfl= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0 . 0 0 6 74 : UNDERSIZE= 0 . 3 9 1 5 4 ORDINATE VALUES FOR SCEEEN EFFICIENCY CURVE SIZE ADJUSTED (CM) OBDINATE 21.76 1 10.88 1 5. 44 0.9999734 2.72 1.000019 1.36 0.5537156 0.68 5.252318E- 2 0. 34 3 .520778E- 2 0. 17 3 .438135E- 2 0.085 3.178132E- 2 0.0425 4. 188875E- 2 0.0212 4.248108E- 2 0.0106 4. 487363E- 2 0.0053 5.674302E- 2 -0 .0053 9.573511E- 2 ADJUSTED FLOWRATES: FLOWSTREAM MEASURED ADJUSTED FEED 353.4 353.3993 OVERSIZE 194.8 194 .8 UNDERSIZE 158.6 158. 5993 - 155 -HUN NUMBER= 19 SIZE MEASURED ADJUSTED (CM) PEED FEED 2 1 . 7 6 0 0 1 0 . 8 8 0 0 5 . 4 4 12 14 . 21 2 . 7 2 31 2 9 . 0 5 4 1. 36 30 3 5 . 12 0 . 6 8 13 1 0 . 9 9 7 0 . 34 5 2 . 97 0 . 17 2 . 6 1 .922 0 . 0 8 5 1.6 1 .395 0 . 0 4 2 5 1.3 1 . 2 0 7 0 . 0 2 1 2 1.2 0 . 9 9 9 0 . 0 1 0 6 0 . 8 5 0 . 7 8 6 0 . 0 0 5 3 0 . 6 3 0 . 6 0 7 - 0 . 0 0 5 3 0 . 8 2 0 . 7 3 3 RESIDUAL SUM OF SQUARES= 4 3 . 5 8 1 2 8 FEED SUM= 100 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 2 1 . 7 6 0 0 0 0 1 0 . 88 0 0 0 0 5 . 4 4 22 2 2 . 0 0 9 0 0 2 . 7 2 45 4 5 . 0 0 1 0 0 1 . 36 3 1 . 4 3 1 . 3 5 7 42 4 1 . 9 7 6 0 . 6 8 0 . 8 8 0 . 8 9 7 2 9 . 5 2 9 . 3 9 8 0 . 3 4 0 . 2 1 0 . 2 1 1 8 7 . 9 9 8 0 . 1 7 0 . 0 9 0 . 0 9 3 5 . 3 5 . 2 5 3 0 . 0 8 5 0 . 0 7 0 . 0 7 2 4 3 . 8 0 6 0 . 0 4 2 5 0 . 0 7 0 . 0 7 2 3 . 3 3 . 2 7 4 0 . 0 2 1 2 0 . 0 6 0 . 0 6 2 2 . 7 2 . 7 0 7 0 . 0 1 0 6 0 . 0 6 0 . 0 6 1 2 . 1 2 . 108 0 . 0 0 5 3 0 . 0 6 0 . 0 6 1 1. 58 1 .601 - 0 . 0 0 5 3 0 . 1 0 . 104 1. 52 1 . 8 7 9 OVERSIZE SUM= 100 UNDERSIZE SUH= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0 . 0 0 2 2 6 : UNDERSIZE= 0 . 18094 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE ADJUSTED (CM) ORDINATE 2 1 . 7 6 1 1 0 . 8 8 1 5 . 4 4 0 . 9 9 9 9 7 3 9 2 . 7 2 0 . 9 9 9 9 9 7 1 .36 0 . 5 7 6 4 5 1 1 15b -0. 68 0. 0526624 0.34 4. 586786E-2 0. 17 3. 124007E-2 0.085 3. 332274E-2 0.0425 3. 851303E-2 0.0212 4. 006901E-2 0.0106 0. 050106 0.0053 6. 488191E-2 -0 .0053 9. 160219E-2 ADJUSTED FLOWRATES: FLOWSTREAM MEASURED FEED 345.4 OVERSIZE 223 UNDERSIZE 122.4 ADJUSTED 345. 401 223.0006 122.4004 RUN NUMBER = 20 S I Z E (CM) 21.76 10. 88 5.44 2. 72 1.36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 MEASURED FEED 0 0 10 31 29. 5 15 5.1 2 . 9 1.9 1.3 1.08 0.77 0.62 0.83 ADJUSTED FEED 0 0 7.82 26. 991 31.611 16. 947 5.732 3.569 2.204 1.54 1.242 0. 867 0.631 0. 844 RESIDUAL SUM OF SQUARES = 30.10458 FEED SUM = 99.998 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 21.76 0 0 0 0 10.88 0 0 0 0 5. 44 15 14.923 0 0 2.72 51.5 51. 506 0 0 1.36 31. 25 31.204 32 32.059 0.68 1.29 1.401 34 34.064 0.34 0.28 0.277 11.7 11.738 0. 17 0. 14 0. 139 7.3 7.346 0.085 0. 11 0. 1 14 4. 5 4.505 0.0425 0.07 0.073 3. 3 3. 156 - 1 0 / -0.0212 0.0106 0.0053 -0 .0053 0.08 0.08 0.07 0. 13 0.08 0.081 0.072 0. 13 2. 5 1. 85 1.3 1. 55 2. 522 1.732 1.247 1.631 O V E R S I Z E SUM= 100 U N D E R S I Z E SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.020442 : UNDESSIZE= 0.055676 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE S I Z E ADJUSTED (CM) ORDINATE 21. 76 1 10.88 1 5.44 1.000025 2.72 1.000001 1.36 0.5172895 0.68 4.332185E- 2 0.34 2 .532417E- 2 0. 17 2.040938E- 2 0.085 2.710534E- 2 0.0425 0.0248407 0.0212 3.375437E- 2 0.0106 4.895844E- 2 0.0053 5.979499E- 2 -0 .0053 0.0806763 A D J U S T E D F L O W R A T E S : F L O W S T R E A M M E A S U R E D F E E D 563.7 O V E R S I Z E 295.4 U N D E R S I Z E 268.3 ADJUSTED 563.6995 295.3992 268.3003 R U N NU MBER= 21 S I Z E M E A S U R E D A D J U S T E D ( C M ) F E E D F E E D 21.76 0 0 10.88 0 0 5.44 10 6.386 2 .72 24 16.474 1.36 31 34.978 0.68 17.5 21.107 0.34 6.1 7.788 0.17 3.6 4.416 0.085 2.3 2.845 0.0425 1.7 1.954 Ibb -0.0212 0.0106 0.0053 -0 .0053 1.37 0.98 0.71 0.74 1. 484 1.026 0.728 0.812 RESIDUAL SUM OF SQUARES= 102.434 FEED SUM= 99.998 SIZE (CM) 21.76 10.88 5. 44 2.72 1. 36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 MEASURED OVERSIZE 0 0 15 39 41. 6 2.44 0.54 0.32 0.23 0.2 0.17 0. 15 0.14 0.21 ADJUSTED OVERSIZE 0 0 15. 154 39.092 41,301 2. 52 0.534 0.324 0.232 0. 195 0. 149 0.151 0. 14 0.208 OVERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE^ 0.128508 : UNDERSIZE= 2.27989 MEASURED UNDERSIZE 0 0 0 0 30 33.5 13 7. 7 4.5 3.2 2.7 2. 1 1. 5 1.8 ADJUSTED UNDERSIZE 0 0 0 0 30.372 3 4.646 13.072 7.397 4.749 3.235 2.457 1.663 1. 157 1.252 UNDERSIZE SUIi= 100 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE ADJUSTED (CM) ORDINATE 21.76 1 10.88 1 5. 44 1.000039 2.72 1.000017 1.36 0.4976044 0.68 5.031444E- 2 0. 34 2 .889575E- 2 0.17 3.091965E- 2 0.085 3.436563E- 2 0.0425 4.205607E- 2 0.0212 4.231272E- 2 0.0106 6.202235E- 2 0.0053 8. 104295E- 2 -0 .0053 0. 1079463 ADJUSTED FLOW RATES: FLOWSTREAM MEASURED FEED 157.8 OVERSIZE 66.5 ADJUSTED 1 5 7 . 7 9 9 3 6 6 . 5 0 0 3 - 159 -UNDERSIZE 91.3 91.299 RUN NUMBER= 25 SIZE MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5. 44 11 10.232 2.72 27 32. 908 1.36 28. 1 28.582 0.68 16. 9 13.974 0.34 5.9 4. 984 0. 17 3.3 2.714 0.085 2.3 1.716 0.0425 1.65 1.3 0.0212 1.29 1.118 0.0106 0.96 0.768 0.0053 0.68 0. 702 -0 .0053 0.92 1.003 RESIDUAL SUM OF SQUARES= 46.00792 FEED SUM= 100.00 1 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 21.76 0 0 0 0 10. 88 0 0 0 0 5. 44 14 13. 977 0 0 2.72 45 44. 955 0 0 1.36 35 35. 027 11 10.977 0.68 4.82 4.846 39 38.908 0.34 0.38 0.387 17.5 17.542 0. 17 0.15 0. 152 9.7 9.712 0. 085 0.1 1 0. 114 6. 1 6.092 0.0425 0.09 0.091 4.6 4.602 0.0212 0.09 0.092 3. 9 3.921 0.0106 0.08 0.081 2.61 2.643 0.0053 0.09 0.091 0 2. 4 2.372 -0 .0053 0.19 0. 187 3. 19 3.231 OVERSIZE SUM= 100 UNDERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.004044 : UNDERSIZE= 0.014964 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE ADJUSTED (CM) ORDINATE 21.76 10.88 1 1 - IDU -5. 44 0. 9999516 2.72 1. 000005 1. 36 0. 8970897 0.68 0. 2538565 0. 34 5. 684058E- 2 0. 17 4. 099768E- 2 0.085 4. 863099E- 2 0.0425 5. 124171E- 2 0.0212 6. 023814E- 2 0.0106 0. 0772057 0.0053 9. 4 8 92 05 E - 2 -0 .0053 0. 1365175 ADJUSTED FLOWRATES: FLOWSTREAM MEASURED FEED 1044 .5 OVERSIZE 764.6 ONDERSIZE 279.9 ADJUSTED 10 44.501 764,5999 279.9007 RUN NUMBER= 26 S I Z E MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5.44 10 5.63 2 .72 24.5 11.984 1.36 29. 5 29.015 0.68 18.3 27.03 0.34 6.4 9.785 0.17 3.7 5.758 0. 085. 2.3 4.397 0.0425 1.55 2.469 0.0212 1.15 1.313 0.0106 0.9 0.882 0.0053 0.72 0.718 -0 .0053 0.98 1,018 RESIDUAL SUM OF SQUARES= 273.1592 FEED SUM= 99.999 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 21.76 0 0 0 0 10.88 0 0 0 0 5. 44 14 14. 449 0 0 2.72 31 30.756 0 0 1.36 49 48.983 9 16.267 0.68 4.92 4. 756 • 41 41.251 0.34 0.44 0.425 19 15.76 - lb I -0.17 0.18 0.201 11.1 9.306 0.085 0.09 0.081 . 6. 8 7.153 0.0425 0.08 0.058 3.8 4.008 0.0212 0.07 0.061 3 .3 2.113 0.0106 0.05 0.051 2. 25 1.412 0.0053 0.05 0.058 1.65 1.14 - 0 . 0 0 5 3 0.12 0.121 2.1 1.59 OVERSIZE SUfl = 100 UNDERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.2897 : UNDEfiSIZE= 69.38761 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE S I Z E ADJUSTED (CM) ORDINATE 21.76 1 10.88 1 5.44 • 1.000036 2.72 1.000032 1.36 0.6578227 0.68 6.856174E- 2 0.34 1.692443E- 2 0. 17 1.360224E- 2 0.085 7.178184E- 3 0.0425 9.153621E- 3 0.0212 1.810303E- 2 0.0106 2.253137E- 2 0.0053 3. 147673E- 2 -0 .0053 4.633391E- 2 ADJUSTED FLOHSATES: FLOWSTREAM MEASURED FEED 562 .8 OVERSIZE 219.3 UNDERSIZE 343.5 ADJUSTED 56 2. 80 53 219.3027 343.5026 RUN NU MBER= 27 SIZE (CM) 21.76 10. 88 5. 44 2.72 1.36 0.68 0.34 MEASURED FEED 0 0 12 28 2 8 . 5 1 5 . 7 5 . 8 ADJUSTED FEED 0 0 9 . 7 0 2 21.343 3 0 . 7 5 2 1 . 7 7 5 6 . 9 5 3 - ID t i -0. 17 3. 1 3.453 0.085 2 1.617 0.0425 1.4 1. 117 0.0212 1.15 1.016 0.0106 0.77 0.715 0.0053 0.65 0.623 -0 .0053 0.93 0.936 RESIDUAL SUM OF SQUARES= 93.26712 FEED SUM= 100 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 21.76 0 0 0 0 10.88 0 0 0 0 5. 44 18 18. 156 0 0 2.72 40 39.94 0 0 1.36 39. 2 39.139 21 21. 122 0.68 1.6 1.597 45 4 4.933 0. 34 0.34 0. 325 15.2 14.559 0. 17 0.18 0. 182 7 7.207 0.085 0.14 0. 137 3.3 3 . 315 0.0425 0.12 0.114 2.3 2.269 0.0212 0. 11 0 . 102 1.7 2.064 0.0106 0. 1 0. 1 1.4 1.421 0.0053 0. 1 0.099 1.2 1.224 -0 .0053 0. 11 0. 109 1.9 1.886 O V E R S I Z E S U M = 100 U N D E R S I Z E SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.032006 : UNDERSIZE= 0,607998 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE ADJUSTED (CM) ORDINATE 21.76 1 10. 88 1 5.44 1.000032 2.72 1.000018 1.36 0.6801734 0.68 3 .919239E- 2 0. 34 2 .497849E- 2 0. 17 0.0281663 0. 085 4.527574E- 2 0.0425 5.453894E- 2 0.0212 5.364898E- 2 0.0106 7.473929E- 2 0.0053 8.491847E- 2 -0 .0053 6.220451E- 2 ADJUSTED FLOWRATES: FLOSSTREAM MEASURED ADJUSTED - ID J FEED 279.2 279.2006 OVERSIZE 149.2 149.2009 UNDERSIZE 130 129.9997 RUN NUMBER= 28 SIZE MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5.44 8 7. 506 2.72 23 21.895 1.36 32 31. 329 0.68 18. 8 20. 16 0.34 6 7.852 0. 17 3.6 3.251 0. 085 2.4 2. 154 0.0425 1.95 1.485 0.0212 1.3 1. 194 0.0106 1.05 0.915 0.0053 0.8 0.928 -0 .0053 1.1 1.332 RESIDUAL SUM OF SQUARES= 7.693017 FEED SUM= 100.001 SIZE (CM) 21. 76 10.88 5.44 2 .72 1.36 0.68 0. 34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0 .0053 MEASURED OVERSIZE 0 0 16 47 33.2 2.37 0.49 0.19 0.12 0.1 1 0. 1 0.1 0.12 0.2 ADJUSTED OVERSIZE 0 0 16. 127 47.041 33.095 2.321 0.502 0.221 0. 107 0.059 0. 104 0.098 0. 127 0. 198 MEASURED UNDERSIZE 0 0 0 0 30 36 13 6. 3 4. 2 2. 9 2. 4 1.9 1. 52 1. 78 ADJUSTED UNDERSIZE 0 0 0 0 29.791 35.693 14.251 5.89 3.936 2.726 2. 143 1.626 1.625 2.319 OVER SIZE SUM= 100 UNDERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.035184 : UNDERSIZE= 2.413674 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM) ADJUSTED ORDINATE - 164 -21.76 1 10.88 1 5. 44 1.000031 2.72 1 1. 36 0.491682 0.68 5.358621E- 2 0.34 2.975718E- 2 0. 17 3.164053E- 2 0. 085 2.312099E- 2 0.0425 1.849243E- 2 0.0212 4.054128E- 2 0.0106 4.985095E- 2 0.0053 6.369776E- 2 -0 .0053 6.919863E- 2 ADJUSTED FLOWRATES: FLOWSTREAM MEASURED FEED 1 0 0 4 . 2 OVERSIZE 4 6 7 . 4 UNDERSIZE 5 3 6 . 8 ADJUSTED 1 0 0 4 . 2 4 6 7 . 3997 5 3 6 . 7 9 9 8 RUN NUMBER= 29 S I Z E MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5. 44 11 10.497 2.72 29 26. 405 1.36 28 26.646 0.68 15.3 17. 815 0.34 5.7 6. 198 0. 17 3.2 3.588 0.085 2. 2 2.4 0.0425 1.7 1. 938 0.0212 1.3 1. 42 0.0106 1 1.327 0.0053 0.75 0.788 -0 .0053 0.85 0. 976 RESIDUAL SUM OF SQUARES= 15.77942 FEED SUM= 99.998 SIZE ' MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 2 1 . 7 6 0 0 0 0 1 0 . 8 8 0 0 0 0 5 . 4 4 22 2 2 . 0 6 9 0 0 2 . 7 2 5 5 . 5 5 5 . 5 1 5 0 0 - Ibb -1.36 20. 4 20. 36 4 32 32.345 0.68 0.98 0.981 32.5 • 3 3.084 0.34 0.32 0. 325 11.5 11.526 0. 17 0. 16 0. 159 6. 5 6.699 0.085 0. 11 0. 106 4.2 4.481 0.0425 0.11 0. 101 3.6 3.605 0.0212 0. 1 0.09 2.8 2.626 0.0106 0. 1 0.072 2. 4 2.466 0.0053 0.08 0.079 1. 9 1.432 -0.0053 0.14 0. 139 2. 6 1.736 OVERSIZE SUM= 100 UNDERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.007292 : UNDERSIZE= 1.579496 ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE ADJUSTED (CM) ORDINATE 21.76 1 10. 88 1 5.44 0.9999835 2.72 0.999999 1.36 0.3635017 0.68 2.619139E-2 0.34 2.494062E- 2 0. 17 2.107755E-2 0.085 2.100729E- 2 0.0425 2.478809E-2 0.0212 3.014599E- 2 0.0106 2.580697E-2 0.0053 4.768439E-2 -0.0053 6.771093E-2 ADJUSTED FLOWRATES: FLOWSTREAM MEASURED FEED 498.7 OVERSIZE 237.2 UNDERSIZE 261.5 ADJUSTED 498. 6997 237. 1999 261.4998 RUN NUMBER= 30 SIZE MEASURED ADJUSTED (CM) FEED FEED 21.76 0 0 10.88 0 0 5.44 11 9.127 2.72 24 24.994 - Ibb -1. 36 2 9 . 5 29. 109 0.68 17 17.956 0. 34 6 6. 356 0.17 3.7 3.353 0.085 2.5 2.301 0.0425 1.8 2.065 0.0212 1.4 1. 429 0.0106 1.1 1.215 0.0053 0.8 0.833 -0 .0053 1.2 1. 263 RESIDUAL SUM OF SQUARES= 5. 939077 FEED SUM= 100.001 SIZE MEASURED ADJUSTED MEASURED ADJUSTED (CM) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE 21.76 0 0 0 0 10.88 0 0 0 0 5. 44 21 20.077 0 0 2.72 54 54.982 0 0 1.36 22. 7 22.773 34 34.39 0.68 1.07 0.967 32.2 32 .115 0.34 0.31 0.305 12.6 1 1.399 0. 17 0.19 0. 183 5. 2 5.995 0.085 0. 13 0. 117 3. 4 4. 121 0.0425 0.12 0.113 3 . 2 3.691 0 . 0 2 1 2 0.1 1 0. 116 2. 5 2.524 0.0106 0.11 0. 1 13 2.3 2. 133 0.0053 0. 1 0.096 2 1. 448 -0 .0053 0.16 0. 158 2.6 2. 184 OVERSIZE SUM = 100 UNDERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 1. 832548 : UNDERSIZE= 3. 500898 ORDINATE VALUES FOR SCREEN EFFICIENCY CUR VE SIZE ADJUSTED (CM) ORDINATE 21.76 1 10.88 1 5.44 0.9999554 2.72 0.9999877 1.36 0.3556336 0.68 2.448086E- 2 0.34 2 . 1 8 1 3 5 2 E - 2 0. 17 2.481004E- 2 0. 085 2.3 11421E- 2 0.0425 0.0248753 0.0212 3.690079E- 2 0.0106 4. 227777E- 2 0.0053 5.238852E- 2 -0 .0053 5.686645E- 2 ADJUSTED FLOWRATES: - 167 -FLOSSTREAM MEASURED ADJUSTED F E E D 265.3 265.3008 O V E R S I Z E 120.6 120.6003 UNDERSIZE 144.7 144. 7005 ?STOP! ? AT LINE "910" IN PROGRAM "A DP" ? PROGRAM ENDS M T S CONTROL *PRINT* HOLD PRINT=TN F0RM=8X11 *PRINT* ASSIGNED RFS NUMBER 662240 $C *S0URCE*3SP *PSINT* - 168 -APPENDIX D LISTING OF COMPUTER PROGRAMS ALLREDD, a program f o r m u l t i - v a r i a b l e l i n e a r r eg re s s ion ana lyses . TRANS4, a support program f o r ALLREDD to permit data t r ans format ion - 169 -1,*** PROGRAM NAME: ALLREDD 2 * 3 * 10 DIM X (1.0,7) , Y ( 4 0 , 1 ) ,2 (10 ,7) ,P (7, 40) , Q (7, 7) , B (6 4 , 7) , T (7 , 1) , F { 40 , 7) 15 DIM G (40,7) , H (64,5) 19 PRINT "INPUT NO. OF RUNS AND NO. .OF INDEPENDENT VARIABLES: N ,K" 20 INPUT » , K 30 MAT X=HDM(N,K*1) 40 MAT Y=RDM(N,1) 45 MAT G=8DM(N,K+1) 50 MAT Z=RDM(N,K+1) 55 MAT F=RDM{N , K> 1) SO MAT B=RDM (2**K,K) 7 0 MAT H=RDM(2**K,5) 375 W9=CMD("%SET CHD=13") 376 PRINT W9 377 PRINT 378 PRINT 379 * * * T H E DATA IS READ FROM EXTERNAL F I L E S * * * 380 F I L E PARA,MCC 381 MAT READ F I L E 1 ,X(N,K + 1) 382 MAT READ FILE 2 ,Y(N,1) 388 ***CALCULATE FLAGS TO DETERMINE I F FACTORS ARE TO BE 389 ***INCLUDED IN THE FIT EQUATION*** 390 FOR J=1 TO K 394 F1=2**(K-J+1) 395 F2=2** (J-1) 400 A=1 n o T=0 4 20 FOR 1=1 TO FT 430 A=-A 4 40 FOR M=1 TO F2 450 T=T+1 460 B ( T , J ) = ( 1 - A ) /2 470 NEXT M 4 72 NEXT I 474 NEXT J 478 ***CALCULATE AVERAGE RESPONSE AND SUM OF Y ( J , 1 ) - Y A V G SQUARED*** 480 Y2=0 4 82 FOR J=1 TO N 484 Y2=Y2 + Y ( J , 1 ) 486 NEXT J 4 88 Y2=Y2/N 4 90 S2=0 492 FOR J=1 TO N 494 S2=S2+(Y ( J , 1)-Y2) **2 495 NEXT J 496 ***LOCATION FOR ANY DESIRED TRANSFORMATIONS OF DATA*** 4 97 P=0 498 PRINT "FIT N O . " , " S S R " , " R * * 2 f l , " S S R / D F 1 " , " V A R I A B L E CODE" 4 99 PRINT 500 £ 1 = 0 510 FOR M=1 TO N 520 FOR M1=1 TO K+1 530 Z (M,M1) =X (M,M1) 540 NEXT M1 550 NEXT B 552 MAT G=Z 555 FOR 1=1 TO 2**K 560 MAT Z=RDM (N,K*1) - 170 -562 MAT Z=G 563 ***SHIFT DATA TO FORM A N BY T*1 MATRIX*** 565 T=0 570 FOR J=1 TO K 5 80 I F B ( I , J ) = 0 THEN 650 590 T=T+1 5 00 FOR L=1 TO N 510 Z (L,T+1) =Z(L,J+1) 520 NEXT L 5 50 NEXT J 553 ***REDIMENSION Z WHILE RETAINING ITS VALUES*** 555 MAT F=Z 560 T=T+1 5 65 IF T=1 THEN 1310 570 MAT Z=RDM{N,T) 571 FOR J=1 TO T 572 FOR L=1 TO N 573 Z ( L , J ) = F ( L , J) 574 NEXT L 575 NEXT J 5 7 7 ***CALCULATE (TEN (Z) *Z) * * - 1 AND TIN (Z) * Y * * * 5 80 MAT P=RDM{T,N) 5 90 MAT P=TRN(Z) 700 MAT Q=RDM (T,T) 710 MAT Q=P*Z 720 MAT T=RDM (T , 1) 730 MAT T=P*Y 740 MAT P=RDM(T,T) 750 MAT P=INV(Q) 753 I F P=0 THEN 769 754 PRINT 755 PRINT "(VAR/COVAH M A T R I X ) / S E * * 2 M 756 PRINT 757 IF T>5 THEN 760 758 MAT PRINT P 759 GO TO 769 760 FOR L=1 TO T 761 PRINT P ( L , 1) ,P (L,2) ,P ( L , 3) , P (L, 4) ,P (L,5) 762 IF T>6 THEN 765 763 PRINT P ( L , 6 ) 764 GO TO 766 765 PRINT P (L,6) ,P{L,7 ) 766 PRINT 767 NEXT L 768 * * * C A L C 0 L A T E MATRIX OF COEFFICIENTS*** 769 MAT Q=RDM(T,1) 770 MAT Q=P*T 794 ***CALCULATE DEGREES OF FREEDOM ASSOCIATED WITH SSR*** 795 S3=0 300 FOR L=1 TO K 310 S3=S3+B(I,L) 320 NEXT L 330 S3=N-S3-1 528 ***CALCULATED VALUES OF RESPONSES AND SSR*** 330 S0=0 340 S1=0 344 I F E1=0 THEN 960 345 PRINT 346 PRINT "Y-OBS" , " Y - C A L C " , "RESIDUAL" 360 FOR J=1 TO N - 171 -370 ¥1 = 0 380 if OR L=1 TO T I000 Y1=Y1+Q (L, 1) *Z ( J , L ) 1030 NEXT L 1040 S0=S0+ (Y (3 , 1) - Y 1) **2 1050 S1=S1*(Y1-Y2)**2 106 0 I F E1=0 THEN 1070 306 1 PRINT Y ( J , 1) ,Y1 ,Y ( J , 1)-Y 1 1070 NEXT J 1190 IF P=0 THEN 1260 1200 MAT P=RDM (1,T) 1205 PRINT 1210 PRINT "COEFFICIENTS OF F I T EQUATION" I 22 0 PRINT 1230 MAT P=TRN(Q) 1235 IF T>5 THEN 1242 1240 MAT PRINT P 1241 GO TO 1250 1242 PRINT P(1,1) ,P{1,2) ,P{1,3) ,P (1 ,4} , P (1,5) 1243 IF T>6 THEN 1246 1244 PRINT P(1,6) 1245 GO TO 1250 1246 PRINT P (1,6) ,P<1 ,7) 1250 IF P=1 THEN 1700 1255 ***STORE OUTPUT VALUES FOR SORTING*** 1260 H(I ,1 )=I 1270 H(I,2)=S0 1280 H(I ,3)=S1/S2 1290 H(I ,4 )=S0/S3 1300 GO TO 1355 1310 H(I ,1 )=I 1320 H (I,2)=S2 1340 H(I ,3 )=0 .00 1350 H(I ,4)=S2 1355 E=0 1356 FOR M=1 TO K 1357 E=E*B(I,M) *(10** (K-M) ) 1358 NEXT M 1359 H(I ,5) =E 1360 NEXT I 1490 ***SORTING ROUTINE*** 1500 FOR J=1 TO 2**K 1510 B1=0 1520 FOR I=J TO 2**K 1530 IF H(I,4)<C=B1 THEN 1560 154 0 B1=H (1,4) 1550 .11=1 1560 NEXT I 1570 FOR L=1 TO 5 1580 T1=H ( J , L ) 1590 H ( J , L ) = H ( I 1 , L ) 1600 H(I1,L)=T1 1610 NEXT L 1620 NEXT J 1630 FOR 1=1 TO 2**K 1640 PRINT H ( I , 1) ,H (1,2) , H(I ,3) , H (1,4) , H ( I , 5) 1650 NEXT I 1700 PRINT 1710 PRINT "INPUT F I T EQUATION FOR WHICH MORE INFORMATION IS DESIRED" 172 0 INPUT I - 172 -1722 IF 1=0 THEN 1960 1725 PRINT " I F RESIDUALS ARE DESIRED ENTER 1; I F NOT ENTER 0" 1726 INPUT E1 !730 IF 1=0 THEN 1960 1740 P=1 1750 GO TO 560 1960 PRINT 197 0 PRINT 1980 STOP 1990 END END-OF-F.IL E - 173 -* * * PROGRAM: T1ANS4 * DIM A (20 ,20) ,C(20 ,20) : PRINT "ENTER NUMBER OF RUNS,N" INPUT N > K=5 PRINT "NUMBER OF OPERATING VARIABLES=»;K ' MAT A=ZER{N,K+1) MAT C=ZER(N,K+1) 1 PRINT "INPUT VARIABLE CODE; G=2,T=3,S=4 " ' INPUT B , D , E , F , G FILE SE1,PARA MAT READ F I L E 1 ,C(N,K*1) PRINT "INPUT POWER CODE,P=1ST VAR,Q=2ND VAR,R=3RD VAH" INPUT P , Q , R , S , T FOR J=1 TO N A (J, 1)=C (J,1) 0 A ( J , 2 ) = C ( J , B ) * * P 0 A ( J , 3 ) = C ( J , D ) **Q 5 A (J,4) =C ( J , E) **R 6 A (J , 5) =C (J , F) **S 7 A (J ,6) =C (J,G) * * T 0 NEXT J !0 PRINT CMD ("%EMPTY PARA5)D") 0 MAT WRITE F I L E 2,A 0 PRINT CMD("%SAVE PARA3D") 0 STOP 0 END !ND-OF-FILE - 174 -APPENDIX E SUMMARY OF THE SECONDARY CRUSHER MODEL L i s t i n g o f the Model F i t t i n g Program TURKEY L i s t i n g o f the Secondary Crusher Model , SECRUSH Output from SECRUSH - Model P r e d i c t i o n s f o r Observed Data - 175 -1 * * * PROGRAM; TURKEY :SECONDARY CRUSHER VERSION 2 * 3 * 29 DIM N (3,10) , J (22) 30 DIM A(1,22) ,D(1 ,22) ,X<22,22) , Z (1,22) ,Y (22, 1) ,Q (22,22) 33 DIM K(22) ,V(22) ,S{22) ,H{22) ,G(22) ,R{22) 36 DIM P(15,15) , F ( 1 5 , 1 5 ) , T { 1 5 , 1 5 ) ,W{15,1) 3 8 READ N1,N2,A3 4 0 R ( 0 ) = 0 70 MAT P=ZER(N2,A3) 1 10 MAT Z=ZER (1 , N1) 120 MAT Y=Z ER (N1 + 1, 1) 130 MAT D=ZER(1,N1) 140 MAT X=ZER(N1+1,N1) 150 SAT Q=ZER(N1 + 1,N1) 171 F I L E SCF,SCP,STVAL,SCOV,DUMP 172 MAT READ F I L E 1 ,F(N2,A3) 173 MAT READ F I L E 2,T<N2,A3) 175 MAT READ F I L E 3 ,A(1 ,N1) 178 MAT READ F I L E 4,N(3,A3) 180 MAT READ W ( » 2 , 1 ) 182 READ A2,S1 184 READ A 1 , B 1 , V 1 , G 2 , H 2 186 FOR 1=1 TO N2 188 S (I)=S1*A2** (1-1) 190 NEXT I 192 S2=SQE (S (1) *S (2) ) 200 M3=500 208 * INITIAL VALUES INPUTTED 210 * CALCULATION OF INITIAL STARTING VALUES 215 FOR .1=1 TO N1 220 D (1 ,I )=ABS(G2*A(1,I ) ) 225 NEXT I 230 * SET UP INITIAL SIMPLEX 2 40 FOR J=1 TO N1 2 50 FOR I = 1 TO J+1 260 I F I=J + 1 THEN 290 27 0 X ( I ,J ) =A (1, J) - ( 2 / ( J + 1) ) *D(1 , J) 280 GO TO 300 2 90 X ( I , J ) =A (1, J) + { (2/(J+1) ) *D(1 , J) *J) 3 00 NEXT I 310 FOR I = J+2 TO N1+1 3 20 X ( I . J ) =A (1, J) 3 30 NEXT I 340 NEXT J 350 * CALCULATION OF STD. DEV* N OF OBJECTIVE FUNCTION 360 Z8=0 361 Z9=0 370 T3=1.E70 3 80 FOR 1=1 TO N1+1 390 H=I 400 GO SUB 1310 4 10 Y (1,1) =Y1 420 NEXT I 430 GO SOB 1720 4 40 T1=0 441 T2=0 4 45 FOR 1=1 TO N1+1 450 T1=T1 + Y ( I , 1 ) 455 NEXT I - 176 -460 T1=T1/(N1+1) 465 FOR 1=1 TO N1+1 470 T2=T2+(Y (I . 1)-T1) **2 480 NEXT I 490 T4=SQR (T2/N1) 500 I F T4>1.E-6 THEN 730 510 GO TO 590 520 * PRINTOUT SECTION 530 PRINT 540 PRINT "CYCLE LIBIT STOP CRITERION=";M2;"STD.DEVIATION 3 ";T4 5 50 PRINT 560 PRINT"HIGH=»;Y (H,1) ,"2ND HIGH=";Y (S , 1) ,"LOW=";Y (1,1) 570 PRINT 580 GO TO 600 590 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE OF";Y{L,1 ) 593 PRINT 595 PRINT "STANDARD DEV IATION="; T4 6 00 H=L 610 GO SUB 1310 6 20 PRINT 630 PRINT 635 PRINT "ALPHA CONSTANTS" 640 PRINT "A1 = ";ABS (X{H r1) ) , " A2=" ; X (H , 2) , "A3="; X (H, 3) ,"A4=";X (H,4) 642 PRINT 650 PRINT "K1 CONSTANTS" 655 PRINT "A5=";X (H,5) , »A6 = " ; X (H, 6) ,"A7=" ;X (H ,7) , "A 8= "; X (H,8) 660 PRINT 665 PRINT "K2 CONSTANTS" 670 PRINT "A9=";X(H,9) ,"A10=";X (H, 10) , » A 1 1="; X(H, 11) ,"A12=";X (H,12) 675 PRINT 6 90 PRINT 695 PRINT 696 PRINT 700 PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS =";Z9 7 02 FOR 1=1 TO A3 704 A9=0 705 PRINT 706 PRINT "RUN N O . " ; I 7 07 PRINT 708 PRINT " S I Z E " , " M E A S . PR0D","P8ED. PROD", "DIFFERENCE" 7 09 PRINT 711 PRINT 712 FOR J=1 TO N2-1 714 PRINT S (J+1) r T (J , I ) , P ( J , I ) , T ( J , I ) - P ( J , I ) 716 A9=A9+ ( T ( J , I ) - P (J , I ) ) **2 718 NEXT J 719 PRINT " P A N " , T ( N 2 , I ) , P ( N 2 , I ) , ( T ( N 2 , I ) - P ( N 2 , I ) ) 720 PRINT 721 A9=A9+ (T(N2,I) - P (N2,I) ) **2 722 PRINT "RESIDUAL SUM SQUARES=";A9 7 23 PRINT 724 NEXT I 729 STOP 730 I F Z9>M2 THEN 530 732 I F Z9>M3 THEN 736 734 GO TO 745 736 M3=M3+300 738 M4=CMD("%EMPTY DUMP3D") 740 MAT WRITE F I L E 5.X 742 M5=CMD("ISAVE DUMPSID") - 177 -7 4.3 PRINT "Z9=";Z9 745 I F T4>T3 THEN 770 750 T3=T4 760 * REFLECTION 770 MAT Q = (1) *X 7 80 FOR J = 1 TO N1 790 P1 = 0 800 FOR 1 = 1 TO N1+1 810 I F I = H THEN 830 820 P1=P1+X {I, J) /N1 8 30 NEXT I 840 Z (1,J) = (1 + A1) *P1-A1*X (H,J) 850 X <H,J)=Z (1 ,J ) 860 D(1,J)=P1 870 NEXT J 880 GO SOB 1310 890 MAT X = (1) *Q 900 Y=Y1 910 I F Y>=Y(L,1) THEN 1000 920 * EXPANSION 930 FOR J = 1 TO N1 9 40 X (H,J) = (1 + V1) *Z (1 , J ) - V1*D <1, J) 950 NEXT J 960 GO SOB 1310 970 I F Y1>Y{L,1) THEN 1010 980 Y (H, 1) = Y1 9 90 GO TO 4 30 1000 IF Y>Y(S,1) THEN 1060 1010 Y{H,1)=Y 1020 FOR J=1 TO N1 1030 X (H, J)=Z (1, J) 1040 NEXT J 1050 GO TO 430 1060 IF Y>Y(H,1) THEN 1120 1070 FOR J = 1 TO N1 1080 X (H, J) =Z <1 , J) 1090 NEXT J 1100 Y(H,1)=Y 1110 * CONTRACTION 1120 FOR J=1 TO N1 1 130 X (H, J) = B1*X (H, J) + (1-B1) *D{1, J) 1140 NEXT J 1150 GO SUB 1310 1160 IF Y1>Y(H,1) THEN 1200 1 170 Y (H f 1) =Y1 1180 GO TO 430 1190 * REDUCE SIZE OF SIMPLEX 1200 FOR J=1 TO N1 1210 FOR 1=1 TO N1+1 1220 X(.I ,J) = (Q(I ,J ) * Q ( L , J ) ) / 2 1230 NEXT I 1240 NEXT J 1250 Z8=Z8+1 1260 PRINT 1270 PRINT "STEP CHANGE";Z8 1280 PBINT 1290 GO TO 380 1300 * ESTIMATION OF NEW VALUES FOR UNKNOWNS 1305 *PREDICTION OF FINAL PRODUCT 1310 F2=0 - 178 -1311 FOB K=1 TO A3 1312 11=0 1314 L2=1 1318 L4=0 1322 L5=0 1 326 Z1=X (H, 1) + X (H, 2) *N (1 , K) + X (H,3) *N (2,K) + X (H,4) *N (3 ,K) 1327 Z4=X (H,5) +X(H,6) *N (1,K) +X(H,7) *N (1,K)**2+X (H , 8) *N (3 , K) 1 328 Z5=X (H,9) +X (H,10) *N(1,KJ + X (H, 1 1) *N (1,K) **2 + X (H,12)*N (3,K) 1341 FOR U=1 TO N2-1 1342 L1 = 1-{1-(S <U+1)/S2)**2)**6 1346 K{U)=L2-L1 1350 L2=L1 1354 L4=EXP{-{ (S (0+1)/2) **.664) ) 1362 J(U)=L4-L5 1366 L5=L4 1368 NEXT 0 14 82 FOR U=1 TO N2 1484 I F S{U)>Z5 THEN 1506 1486 I F S(CJ)<Z4 THEN 1498 1490 H(U)=S (U) - (S<0) -Z5)**3 / (3* ( (Z4-Z5) **2)) 1494 GO TO 1510 1498 H (0) =Z 4- (Z4-Z5) /3 1502 GO TO 1510 1 506 H (U) =S (0) 1510 NEXT 0 1512 Z6=0 1514 FOR 0=1 TO N2-1 1518 V (0) = (H(U)-H(U+1) ) / (S (O)-S (0+1) ) 1522 A5=0 1526 B5=0 1530 FOR V=1 TO 0-1 1534 A5=A5+ (Z1*K (U-V+1) + (1-Z1) * J (U) )*R(V) 1538 B5=B5 + J{?) 1540 NEXT V 1544 G (•) = (F (0,K) +A5) / {1- (Z1*K < 1) + < 1-Z1) * (B5* J(U) ) ) *V (0) ) 1546 R (0) =V (U) *G (U) 1548 P (U,K)=G (U) -R{0) 1549 Z6=Z6 + P(U,K) 1550 NEXT U 1608 P(N2,K)=100-Z6 1630 * CALCULATION OF OBJECTIVE FUNCTION FOR POLYGON VERTICES 1650 FOR U=1TO N2-1 1655 F2 = F2+W (U, 1) * (T (U, K) -P (U,K) ) **2 1660 NEXT U 1670 F2=F2+100* (T <U, K) - P (U, K) ) **2 1675 NEXT K 1680 Y1=F2 1690 Z9=Z9+1 1710 RETURN 1715 * OBJECTIVE FUNCTION MAGNITUDE LISTING (ORDER SEARCH) 1720 I F Y(1 ,1 )>Y(2 ,1 ) THEN 1770 1740 S=1 1741 L=1 1750 H=2 1760 GO TO 1790 1770 S=2 1771 L=2 1780 H=1 1790 FOR 1=3 TO N1+1 1800 I F Y ( I , 1) >Y ( L , 1) THEN 1820 - 179 -1810 L=I 1820 I F Y ( I , 1) <Y (S, 1) THEN 1880 1830 I F Y {I, 1) <Y(H, 1) THEN 1870 1840 S=H 1850 H=I 1860 GO TO 1880 1870 S=I 1880 NEXT I 1890 RETURN 1895 DATA 12,14,8 1896 DATA 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1,1 1900 DATA . 5 , 4 3 . 5 2 1950 DATA 1 , . 5 , 2 , . 0 1 , 1 0 2000 END E N D - O F - F I L E - I tfU -1 *** PROGRAM: SECRUSE :SECONDARY CRUSHER HODEL 2 * 3 * 10 DIM J (15) ,K (15) , V (15) ,S (15) , H (15) RG (15) ,R (15) 20 DIM P (15, 15) ,F (15,15) ,T(15,15) ,N (3, 15) 22 HEAD N2,A2,S1,A3,A4 24 MAT P=ZER(N2,A3) 50 FILE SCF,SCP,SCOV 60 MAT READ 2ILE 1,F(N2,A3) 70 MAT READ TILE 2,T(N2,A3) 80 MAT READ TILE 3,N(3,A3) 85 * READ MODEL CONSTANTS 90 READ A20,&21,A22,A23 95 BEAD A30,131,A32,A33 100 BEAD A40,A41,A42,A43 110 READ A60,A61,A62 115 FOR 1=1 TO N2 120 S(I) =S1*Jk2** (1-1) 130 NEXT I 140 S2=SQR (S (1) *S (2) ) 150 IF A4=0 THEN 205 160 A3 = A4 170 GO TO 210 200 *CALCUIA1'I0N OF PREDICTED DISTRIBUTION 205 A4=1 206 PRINT 207 PRINT "COMPUTED VALUES OF MODEL PABAMETERS" 20 8 PRINT 210 FOR K=A4 TO A3 23 0 L2=1 250 15=0 255 Z1=A20+A21*N (1 ,K) +A22*N(2,K) +A23*N (3,K) 27 0 FOR U=1 TO N2-1 280 11 = 1- (1- (S (U+1) /S2) **2) **6 290 K<U)=12-11 300 12=11 310 L4 = EXP (~( (S (U+1)/2) **.664) ) 320 J(U)=14-15 33 0 15=14 340 NEXT ..0 350 Z4=A30 + A31*N (1,K) +A32*N (1 ,K) **2*A33*N (3,K) 360 Z5=A40+A41*N (1,K) +A42*N (1.K) **2+A43*N (3,K) 37 0 FOR U=1 TO N2 380 IF S{U)>Z5 THEN 440 390 IF S (U) <2,4 THEN 420 400 H(U) =S (U)- (S (U) -Z5) * 0*3/ (3* ( (Z4-Z5) **2) ) 410 GO TO 450 420 H(U) =Z4-(Z4-Z5)/3 430 GO TO 450 440 H(U)=S(U) 450 NEXT U 455 Z6=0 46 0 FOR U=1 20 N2-1 470 V(U)=(H{U)-H(U*1))/<S(U)-S(U+1)) 480 A5=0 490 B5=0 495 R(0)=0 500 FOR V=1 TO U-1 510 A5 = A5+{Z1*K (U-V+1) +(1-2 1) * J (U) ) *R(V) 520 B5=B5+J(V) - 181 -530 NEXT V 540 G{U) = (F (U,K) +A5)/ (1- (Z1*K (1) + (1-31) * (B5*J (U) ) ) *V (U) ) 550 R (U) =V (U) *G (U) 560 P (U, K) =G (U)-R(U) 565 Z6=Z6 + P{0,K) 570 NEXT U 610 P(N2,K)=100-Z6 620 C(K)=A60-i-A61*N(1,K) + A62*N(2,K) 630 PRINT "RON NUMBER=";K 635 Z1=INT{Z1*100000+.5) /100000 636 Z4=INT{Z4*100000+.5)/100000 637 Z5 = INT (Z5*100000 + . 5)/100000 640 PRINT " A L P H A = " ; Z 1 " ; " K 1 = " ; Z 4 ; T A B (32) ;"K2=";Z5 650 NEXT K 654 FOR J=1 TO N2 655 S •( J) =INT (S (J) *1 Q000-* . 5) /10000 656 NEXT J 66 0 PRINT«***************** *********** *********************************** 70 0 *PRINTOUT SECTION 701 PRINT 702 PRINT "SIZE ANALYSES REPORTED AS K T . PERCENT RETAINED ON S I Z E " 703 PRINT 704 P R I N T " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 710 FOR K=A4 TO A3 720 A9=0 722 PRINT 724 PRINT "RliN NUMBER="; K 726A18=0 727 FOR J=1 TO N2 728 A18=A18+P (J,K) 729 NEXT J 735 PRINT 740 PRINT "SIZE","MEASURED","PREDICTED","DIFFERENCE" 741 PRINT " (CM.) ","PRODUCT","PRODUCT" 750 PRINT 755 FOR J=1 TO N2 756 P (J ,K) =INT(P (J ,K) *1O00 + . 5)/1000 757 NEXT J 76 0 FOR J=1 TO N2-1 770 PRINT S{«3+1) , T ( J , K ) , P ( J , K ) , T (J , K ) - P ( J , K) 780 A9=A9+(T ( J , K ) - P (J,K) ) **2 790 NEXT J 79 2 A9=A9+ (T(N2,K) - P (N2,K) ) **2 796 PRINT "PAN" ;T AB (14) ?T{N2,K) ;TAB{29) ;P (N2,K) ; TAB (44) ;T (N2 , K ) - P (N2 , K) 800 PRINT 804 PRINT T A £ ( 3 1 ) ; " S U M = » ; A 1 8 810 PRINT "RESIDUAL SUM OF SQUARES=";A9 820 PRINT 821 PRINT "PREDICTED CUBSENT=" ; C (K) 822 PRINT 826 PRINT "OPERATING CONDITIONS ; " 830 PRINT 835 PRINT "GAP= "; N (1 , K) , "FEEDRATE=" ; N (2 ,K) , " ","% +1INCH IN FEED=" ; N (3 ,K) 83 8 PRINT " {CM.) " , " <TPH) « 84 0 PRINT 850 PRINT " . . 880 NEXT K 90 0 STOP 910 DATA 1 4 , . 5 , 4 3 . 5 2 , 8 , 0 930 DATA - . 9 1 4 8 9 , . 2 1 7 2 9 , . 0 0 0 6 2 6 , . 0 0 5 6 3 4 - mz -935 DATA 4 4 . 5 8 7 5 , - 3 3 . 5 1 5 7 , 5 . 6 7 7 1 , . 1 2 2 1 940 DATA - 2 2 . 8 8 1 2 , 2 3 . 7 9 8 1 , - 3 . 7 3 1 9 , - . 0 2 7 9 8 945 DATA 20 .6182 , -7 .323393 , .0345158 1000 END END-OF-FILE - 183 -l e v i c e : DS40 t a s k : 2241 USERID: RALU 09:04:34 08-16-77 U n i v e r s i t y of B r i t i s h Columbia Computing C e n t r e - a e v i c e : DS40 t a s k : 224 I SIGN RALU £ ENTER USER PASSWORD, ft **LAST SIGNCN WAS: 08:37:01 » USER "RALU" SIGNED ON AT 09:03:10 ON TUE AUG 16/77 » RUN *BASIC ft EXECUTION BEGINS & ?UBC BASIC SYSTEM > ? : GET SECRUSH : RUN COMPUTED VALUES OF MODEL PARAMETERS RUN NUMBER= 1 A.LPHA= 0. 68-923 RUN NUMBER= 2 ALPHA= 0.73686 RUN NUMBER= 3 ALPHA= 0.68529 RUN NUMBER= 4 ALPHA= 0.78095 RUN NUMBEB= 5 ALPHA= 0.82483 RUN NUMBER= 6 AIPHA= 0.59324 RUN NUMBER= 7 ALPHA= 0.73797 SUN NUMBER= 8 ALPHA= 0.52012 K1= 5-58928 K1= 6.66409 K1= 5, 356 27 K1= 9.1991 K1= 8.2317 K1= 6, 19388 K1= 6.16672 K1= 6.7067 K2= 12.75747 K2= 12.39 765 K2= 12.75868 K2= 11.49089 K2= 11.62927 K2= 1 1. 1725 K2= 12.60 702 K2= 1 1.05499 *************************************************************** SIZE ANALYSES REPORTED AS WT. PERCENT RETAINED ON SIZE * * * * * * * * * * * * * * * * * * * * * * : * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN NUMBER= 1 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT, 2 1. 76 0 0 0 10.88 0 0.085 -0 .085 5.44 17 17.018 -0 .018 2.72 45 43. 112 1. 888 1.36 23.9 22.689 1.211 0.68 6.05 7.727 - 1 . 6 7 7 0.34 2.24 3. 1 36 -0 .896 0. 17 1.56 1.817 -0 .257 0.085 1.07 1.238 -0 .168 0.0425 0.87 0.968 -0 .098 0.0212 0.69 0.721 -0 .031 0.0106 0.59 0.532 0. 058 0.0053 0.46 0.389 0. 071 PAN 0.57 0.568 0. 002 SUM= 100 RESIDUAL SUE OF SQUARES= 8.767006 - 184 -PREDICTED CURRENT 3 21-09676 OPERATING CONDITIONS: GAP= 3.239 FEE DRATE 3 701.1 % +1INCH IN F E E D 3 81.9 (CM.) (TPH) RON NUMBER3 2 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0. 12 -0 .12 5.44 24 29. 174 -5 .174 2.72 42. 5 38.365 4. 135 1.36 17. 6 17.095 0. 505 0.68 6.15 6.426 -0 .276 0.34 2.75 3.046 -0 .296 0. 17 1.97 1.851 0. 119 0.085 1.33 1.21 0. 12 0.0425 1.04 0. 844 0. 196 0.0212 0.82 0.616 0.204 0.0106 0.65 0. 441 0.209 0.0053 0.52 0.309 0.211 PAN 0.67 0.502 0. 168 SUM 3 100 RESIDUAL SUE OF SQUARES 3 44.52674 PEEDICTED CURRENT 3 23.12155 OPERATING CONDITIONS: GAP= 3.086 FEEDRATE 3 727.3 % +1INCH IN F E E D 3 93.7 (CM.) (TP H) RUN NUMBER3 3 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0.09 - 0 . 0 9 5.44 16 16.051 -0 .051 2.72 39.5 42.248 - 2 . 7 48 1.36 22. 5 23. 29 8 -0 .798 0.68 8.2 7.348 0. 852 0.34 4 3.365 0. 635 0. 17 2.8 2.232 0.568 0.085 2 1.586 0. 414 0.0425 1.47 1. 172 0. 298 0.0212 1.28 0.95 0.33 0.0106 0.98 0.671 0.309 0.0053 0.63 0. 441 0. 189 - 185 -PAN 0.64 0.549 0. 091 SUM 3 100 RESIDUAL SUfi OF SQUARES 3 10.15935 PREDICTED CURRENT 3 22.56656 OPERATING CONDITIONS: G A P 3 3 .15 F E E D R A T E 3 724 . 8 % +1INCH IN F E E D 3 82 (CM.) {TPH) RUN NUMBER3 4 SIZE MEASURED PREDICTED DIFFERENCE '{CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0.033 -0 .033 5.44 31 31. 57 6 -0 .576 2.72 42 41.059 0. 941 1.36 15. 9 17.456 -1 .556 0.68 4.4 4.282 0. 118 0. 34 2.05 1.846 0. 204 0. 17 1.25 1.058 0. 192 0.085 0.89 0.728 0. 162 0.0425 0.68 0. 544 0. 136 0.0212 0.56 0. 454 0.106 0.0106 0.47 0.358 0. 112 0.0053 0.35 0.256 0. 094 PAN 0.45 0.351 0. 09 9 SUM 3 100 RESIDUAL SUM OF SQUARES 3 3 . 819043 PREDICTED CURBENT 3 15.10533 OPERATING CONDITIONS: G A P 3 3 . 7 4 7 FEEDRATE 3 6 3 5 . 3 % +1INCH IN F E E D 3 8 5 . 9 (CM.) (TPH) RUN NUMBER3 5 SIZE (CM.) 2 1 . 7 6 1 0 . 8 8 5 . 4 4 2 . 7 2 1. 36 0 . 6 8 0 . 3 4 0 . 17 0 . 0 8 5 MEASURED PRODUCT 0 0 26 37 1 8 . 2 6 3 . 2 2 . 6 5 2 PREDICTED PRODUCT DIFFERENCE 0 0.019 25.641 37. 09 18.389 6.951 3.259 2.542 1.979 0 -0 .019 0. 359 - 0 . 0 9 -0 .189 -0 .951 -0 .059 0. 108 0. 021 - 186 -0.0425 1.71 1. 529 0. 181 0.0212 1.29 1.154 0. 136 0.0106 0.91 0.726 0. 184 0.0053 0.51 0. 355 0. 155 PAN 0.53 0. 365 0. 165 SUM= 100 RESIDUAL SUB OP SQUARES 3 1.229413 PREDICTED CURRENT 3 20.14593 OPERATING CONDITIONS: G A P 3 3.785 FEEDRATE 3 789.4 % +1INCH IN F E E D 3 75.1 (CM.) (TPH) RUN NUMBER3 6 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0.001 -0 .001 5.44 16 16.657 -0 .657 2.72 39 39.043 -0 .043 1 .36 21 2 1. 428 -0 .428 0.68 9 8.528 0. 472 0.34 3.9 4. 284 -0 .384 0. 17 3.2 3 . 136 0. 064 0.085 2. 4 2. 189 0.21 1 0.0425 1.87 1.637 0.233 0.0212 1.43 1. 19 0.24 0.0106 1.05 0.8 0.25 0.0053 0.61 0.493 0. 117 PAN 0.54 0.613 -0 .073 SUM 3 100 RESIDUAL SUC OF SQUARES 3 1. 228947 PREDICTED CURRENT 3 29.01849 OPERATING CONDITIONS: G A P 3 2.54 FEEDRATE 3 782.3 % +1INCH IN F E E D 3 82.8 (CB.) (TPH) RUN NUMBER3 7 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0.117 -0 .117 5.44 23 21.359 1. 641 2.72 42 .5 43.196 -0 .696 1.36 19.1 19.673 -0 .573 - 187 -0.68 5.4 6. 4 33 -1 .033 0.34 2.8 3.051 -0 .251 0.17 1.95 1. 862 0. 088 0.085 1.3 1.221 0. 079 0.0425 1.07 0.941 0. 129 0.0212 1.05 0.7 56 0. 294 0.0106 0.8 0. 529 0. 271 0.0053 0.53 0.376 0. 154 PAN 0.5 0.484 0. 016 SUM= 100 RESIDUAL SUfi OP SQUARES= 4. 86388 PREDICTED CURRENT^ 22.76645 OPERATING CONDITIONS: GAP= 3.2 FEEDRATF= 741.2 % +1INCII IN FEED= 87.6 (Ca.) {TPH) RUN NUMBER = 8 SIZE MEASURED PREDICTED DIFFERENCE {CM.) PEODUCT PRODUCT 21.76 0 0 0 10.88 0 0 0 5.44 20 19.364 0. 636 2.72 39 42. 373 -3 .373 1.36 22. 7 18.216 4. 48 4 0 .68 7.3 7.017 0. 283 0.34 2.9 3.886 -0 .986 0. 17 2.35 2.702 -0 .352 0.085 1.6 1.9 49 -0 .349 0.0425 1.27 1.497 -0 .227 0.0212 1.09 1. 107 - 0 . 0 1 7 0.0106 0. 82 0.755 0.065 0.0053 0.51 0.476 0. 034 PAN 0.46 0.658 -0 .198 SUM= 100 RESIDUAL SUM OF SQUARES^ 33. 28227 PREDICTED COERENT= 23.68235 OPERATING CONDITIONS: GAP= 2.54 FEEDRATE= 627.7 fo +1INCH IN FEED= 87 {CM.) (TPH) r ?STOP! ^ ? AT LINE "900" IN PROGRAM "SECRUSH" t ? PROGRAM ENDS : MTS * CONTROL *PRINT* HOLD P«INT=TN FORM=8X11 It *PRINT* ASSIGNED RFS NUMBER 664582 I COPY *MSOUBCE*aSP *PRINT* - 188 -APPENDIX F SUMMARY OF THE TERTIARY CRUSHER MODEL L i s t i n g o f the Model F i t t i n g Program TURKEY L i s t i n g o f the T e r t i a r y Crusher Mode l , TERCR Output from TERCR - Model P r e d i c t i o n s f o r Observed Data - i «y -1 * * * PROGRAM: TURKEY :TERTIARY CRUSHER VERSION 2 * 3 * 29 DIM N (3, 10) , J (22) 30 DIM A(1 ,22) ,D (1 ,22) , X (22,22) ,Z (1 ,22) ,Y (22, 1) ,Q (22, 22) 33 DIM K (22) , V (22) ,S(22) ,H (22) , G (22) ,R(22) 36 DIM P(15,15) ,F{15,15) , T (15,15) ,W (15,1) 3 8 READ N1,N2,A3 70 MAT P=ZER(N2,A3) 110 MAT Z=ZER (1 ,N1) 120 MAT Y=ZER (N1 + 1, 1) 130 MAT D=ZER(1,N1) 140 MAT X=ZER (N1+-1 , N1) 150 MAT Q=ZER (N1 + 1 ,N1) 171 F I L E T C F , T C P , T C O V C , S T V A L 172 MAT READ F I L E 1 ,F(N2,A3) 173 HAT READ FILE 2 ,T(N2,A3) 175 MAT READ F I L E 3 , N (3,13) 178 MAT READ F I L E 4 ,A(1 ,N1) 182 READ A2,S1,M3 184 READ A 1 , B 1 , V 1 , G 2 , M 2 186 FOR 1=1 TO N2 188 S (I) =S1*A2** (I-1) 190 NEXT I 192 S2=SQR(S(1) *S{2) ) 208 * INITIAL VALUES INPUTTED 210 * CALCULATION OF INITIAL STARTING VALUES 215 FOR 1=1 TO N1 220 D(1 , I )=ABS(G2*A(1 , I ) ) 225 NEXT I 230 * SET UP INITIAL SIMPLEX 240 FOR J=1 TO N1 250 FOR I = 1 TO J+1 260 I F I=J+1 THEN 290 270 X ( I , J ) = A ( 1 , J ) - ( 2 / ( J + 1) ) *D(1 ,J ) 280 GO TO 300 290 X ( I , J ) = A ( 1 , J ) + { (2 / (J+1) )*D(1 ,J ) *J) 300 NEXT I 310 FOR I = J+2 TO N1+1 320 X (I , J) = A (1 ,J ) 330 NEXT I 3 40 NEXT J 350 * CALCULATION OF STD. , D E V N OF OBJECTIVE FUNCTION 360 Z8=0 361 Z9=0 370 T3=1.E70 3 80 FOR 1=1 TO N1+1 390 H=I 400 GO SUB 1310 410 Y (I,1)=Y1 420 NEXT I 430 GO SUB 1720 440 T1=0 441 T2=0 445 FOR 1=1 TO N1+1 450 T1 = T1 + Y (1,1) 4 55 NEXT I 460 T1=T1/(N1+1) 465 FOR 1=1 TO N1+1 470 T2 = T2+(Y (I , 1)-T1) **2 - 190 -480 NEXT I 490 T4=SQR (T2/N1) 500 I F T4>1.E-6 THEN 730 510 GO TO 590 520 * PRINTOUT SECTION 530 PRINT 540 PRINT "CYCLE LIMIT STOP C R I T E R I O N = « ; M 2 ; " S T D . D E V I A T I O N ^ " ; T 4 550 PRINT 560 PRI NT" HIGH= "; Y (H, 1) , » 2 N D HIGH=»;Y (S, 1) , "LOW=" ; Y (L , 1) 570 PRINT 580 GO TO 600 590 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y ( L , 1 ) 593 PRINT 595 PRINT "STANDARD DEVIATION=";T4 600 H=L 610 GO SUB 1310 620 PRINT 630 PRINT 635 PRINT "ALPHA CONSTANTS" 6 40 PRINT "A1 = ";ABS (X (H , 1) ) , "A2=" ; X (H ,2) , "A3=";X (H,3) ,"A4 = " ; X (H,4) 6 42 PRINT 645 PRINT "A5=";X(H,5) 650 PRINT "BETA CONSTANTS" 652 PRINT 655 PRINT "A6=";ABS (X (H,6) ) ,"A7=";X (H,7) , "A8="; X (H, 8) , " A 9 = » ; X (H,9) 662 PRINT 6 65 PRINT "K1 CONSTANTS" 668 PRINT 670 PRINT "A10=";X (H, 10) ,"A11=";X (H, 1 1) 678 PRINT 6 80 PRINT "K2 CONSTANTS" 6 82 PRINT 6 85 PRINT "A12=";X|H,12) , " A 13=" ; X (H , 1 3) , » A 1 4 = " ; X{H, 14) ,"A15=" ;X (H,15) 688 PRINT 690 PRINT "A16 = " ; X (H„16) , " A17=";X (H, 17) 695 PRINT 6 96 PRINT 700 PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS = » ; Z 9 7 02 FOR 1=1 TO A3 703 PRINT "##############################################################" 704 A9=0 705 PRINT 706 PRINT "RUN N O . " ; I 7 0 7 PRINT 7 08 PRINT "SIZE","HEAS.PROD","PRED.PROD","DIFFERENCE" 7 09 PRINT 711 PRINT 712 FOR J=1 TO N2-1 714 PRINT S (J + 1) , T (J , I ) , P ( J , I ) , T ( J , I ) - P { J , I ) 716 A 9 = A 9 * < T ( J , I ) - P ( J , I ) ) * * 2 718 NEXT J 719 PRINT « P A N " , T ( N 2 , I ) , P { N 2 , I ) , C T < N 2 , I ) - P ( N 2 , I ) ) 720 PRINT 721 A9=A9+ (T (N2,I) - P ( N 2 , I ) ) **2 722 PRINT "RESIDUAL SUM SQUARES=";A9 7 23 PRINT 724 NEXT I 729 STOP 730 I F Z9>M2 THEN 530 732 I F Z9>M3 THEN 736 - i y i -734 GO TO 745 736 B3=H3+300 745 I F T4>T3 THEN 770 750 T3=T4 760 * REFLECTION 770 MAT Q = (1) *X 780 FOR J = 1 TO N1 790 P1=0 800 FOR I = 1 TO N1+1 810 I F I = H THEN 830 820 P1 = P1 + X ( I , J ) /N1 830 NEXT I 84 0 Z {1 , J ) = <1+A1) *P1~A1 *X (H, J) 850 X (H, J) =Z (1, J) 860 D (1,J)=P1 870 NEXT J 880 GO SUB 1310 890 MAT X = (1) *Q 900 ¥=Y1 910 I F Y>=Y{L,1) THEN 1000 9 20 * EXPANSION 930 FOR J = 1 TO N1 940 X(H,J)=(1+V1)*Z (1,.J) - V1*D(1 , J ) 950 NEXT J 960 GO SUB 1310 970 I F Y1>Y(L,1) THEN 1010 980 Y (H, 1) =Y1 990 GO TO 430 1000 I F Y>Y(S.1) THEN 1060 1010 Y(H,1)=Y 1020 FOR J=1 TO N1 1030 X (H, J) =Z (1 , J) 1040 NEXT J 1050 GO TO 430 1060 I F Y>Y(H,1) THEN 1120 1070 FOR J = 1 TO N1 1080 X(H,J)=2 (1,J) 1090 NEXT J 1100 Y (H, 1) =Y 1110 * CONTRACTION 1 120 FOR J=1 TO N1 1 130 X (H, J) =B1*X (H, J) + (1-B1) *D{1, J) 1140 NEXT J 1150 GO SUB 1310 1160 I F Y1>Y{H,1) THEN 1200 1170 Y(H.1)=Y1 1180 GO TO 430 1190 * REDUCE SIZE OF SIMPLEX 1200 FOR J=1 TO N1 1210 FOR 1=1 TO .N1 + 1 1220 X ( I , J ) =<Q(I ,J)+Q(L,J) ) / 2 1230 NEXT I 1240 NEXT J 1250 28=28+1 1260 PRINT 1270 PRINT "STEP C HANGE";Z8 1280 PRINT 1290 GO TO 380 1300 * ESTIMATION OF NEW VALUES FOR UNKNOWNS 1305 *PREDICTION OF FINAL PRODUCT - 192 -1310 F2=0 1311 FOR K=1 TO A3 1312 I F K=6 THEN:K=7 1313 I F K=10 THEN 1675 1314 L2=1 1318 L5=0 1320 Z20=X (H,3) / (1+X(H,4) * ( N ( 2 , K ) - X (H,5)) **2) 1325 Z1=Z20 + ABS(X{H,1)) +X(H, 2)*N (2, K) 1330 Z2=ABS (X (H,6) } +X (H,7) *EXP(X (H, 8) *Z1**X (H,9) ) 1335 Z4=X(H,10)+X(H,11) *N(3,K) 1337 Z23=(X(H,14) / (1 + X(H,15)* (N (1 , K ) - X (H, 16) ) **2) )**X (H,17) 1338 Z5=X(H,12) *X(H,13) * N ( 1 , K ) - Z 2 3 1341 FOR 0=1 TO N2-1 1342 11 = 1- (1- (S (D+1J/S2) **4) **Z2 1346 K(U)=L2-L1 1350 L2=L1 1354 L4=EXP(-{<S(U+1)/2) **.664)) 1362 J<D)=I4-L5 1366 L5=L4 1368 NEXT 0 1482 FOR 0=1 TO N2 1484 I F Si(0)>Z5 THEN 1506 1486 I F S(0)<Z4 THEN 1498 1490 H (U) =S (U) - (S (0) -Z5) **3/{3* { (Z4-Z5) **2) ) 1494 GO TO 1510 1498 H (U) = Z 4 - ( Z 4 - Z 5 ) / 3 1502 GO TO 1510 1506 H (U) =S {0) 1510 NEXT 0 1512 Z6=0 1514 FOR 0=1 TO N2-1 1518 V (U)= {H (U)-H (0 + 1) ) /{S (U)-S (0 + 1)) 1522 A5=0 1526 B5=0 1530 FOR V=1 TO 0-1 1534 A5=A5+ (Z1*K (U-V+1) + (1-Z1) * J (U) ) *B (V) 1538 B5=B5+J(V) 1540 NEXT V 1544 G (U) = (F (U,K) +A5) / ( 1- (Z1 *K (1) * (1-Z1) * (B5 + J(U) ) ) *V (U) ) 1546 R(0)=V(U) *G(U) 1548 P (0,K)=G (U)-B (U) 1549 Z6=Z6 + P(U,K) 1550 NEXT 0 1608 P(N2,K)=100-Z6 1630 * CALCULATION OF OBJECTIVE FUNCTION FOR POLYGON VERTICES 1635 P10=0 1636 P11=0 1640 IF Z4<=0 THEN:P10=2*EXP (10* (-Z4) )-1 1645 IF Z4>=Z5 THEN:P11=2*EXP(10*(Z4-Z5))-1 1650 FOR U=1 TO N2 1655 F2=F2+ CT (U,K) -P{U,K) ) **2+P10 + P11 1660 NEXT U 1675 NEXT K 1680 Y1=F2 1690 Z9=Z9+1 1710 RETURN 1715 * OBJECTIVE FUNCTION MAGNITUDE LISTING (ORDER SEARCH) 1720 I F Y{1, 1)>Y(2 f 1) THEN 1770 1740 S=1 1741 L=1 - 193 -1750 H=2 1760 GO TO 1790 1770 S=2 1771 L=2 1780 H=1 1790 FOB 1=3 TO N1+1 1800 I F Y ( I , 1) >Y (L, 1) THEN 1820 1810 L=I 1820 I F Y ( I , 1) <Y(S, 1) THEN 1880 1830 I F Y (1,1) <Y(H, 1) THEN 1870 1840 S=H 1850 H=I 1860 GO TO 1880 1870 S=I 1880 NEXT I 1890 RETOBN 1895 DATA 17,14,10 1900 DATA . 5 , 4 3 . 5 2 , 1 0 0 0 1950 DATA 1 , . 5 , 2 , . 0 1 , 1 0 2000 END E N D - O F - F I L E - iy4 -1 * * * PROGRAM: TERCR :TERTIARY CRUSHER MODEL 2 * 3 * 10 DIM J (15) , K (15) , V (15) ,S (15) , H (15| , G (15} ,R (15) 20 DIM P(15,15) ,F (15 ,15 ) ,T{15,15) ,N(3 ,15) 22 BEAD N 2 , A 2 , S 1 , A 3 , A 4 24 MAT P=ZER(N2,A3) 50 F I L E TCF,TCP,TCOVC,CONST 60 MAT READ F I L E 1,F(N2,A3) 70 MAT READ F I L E 2 ,T(N2,A3) 80 MAT READ F I L E 3,N{3,A3) 85 * READ MODEL CONSTANTS 90 READ A20 ,A21 ,A22 ,A23 ,A24 95 BEAD A30,A31,A32,A33 100 HEAD A40,A41 105 READ A50 # A51, # A52,A53, A54,A55 110 READ A60,&61,A62 115 FOR 1=1 TO N2 120 S(I) =S1*A2**{I-1) 130 NEXT I 140 S2=SQR (S (1) *S(2) ) 150 IF A4=0 THEN 205 160 A3=A4 170 GO TO 210 20 0 *CALCULATION OF PREDICTED DISTRIBUTION 205 A4=1 206 PRINT 207 PRINT "COMPUTED VALUES OF MODEL PARAMETERS" 208 PRINT 210 FOR K=A4 TO A3 220 IF K=6 THEN:K=7 225 IF K=10 THEN 660 230 L2=1 250 L5=0 255 Z1 = A20 + A21*N (2,K) + (A22/ (1+A23* (N (2, K)-A24) **2) ) 260 Z7=A30+A31*EXP{A32*Z1**A33) 270 FOR U=1 TO N2-1 28 0 L1 = 1 - 4 1 - ( S (U+1)/S2) **4) **Z7 290 K(U)=L2-L1 30 0 L2=L1 31 0 L4=EXP {- ( (S (Ut 1) /2) * * . 664) ) 320 J(U)=L4-15 330 L5=L4 340 NEXT U 350 Z4=A40 + A41*N (3,K) 360 Z5=A50*A51*N(1,K)-(A52/(1+A53*(N (1,K)-A54) **2) ) **A55 37 0 FOE U=1 TO N2 380 IF S(U)>Z5 THEN 440 390 IF S(U)<Z4 THEN 420 400 H(U) =S(U)-(S(U) -Z5) **3/{3*( (Z4-Z5) **2) ) 410 GO TO 450 420 H(U) =Z4-(Z4-Z5) / 3 430 GO TO 450 440 H(U)=S(U) 450 NEXT U 455 Z6=0 46 0 FOE U=1 TO N2-1 470 V(U) = {H(U)-H(U+1) ) / (S{U) -S (U*1) ) 480 A5=0 490 B5=0 - 195 -495 B(0)=0 500 FOB V=1 TO U-1 510 A5=A5+ (Z1*K (U-V+1) * (1-Z1) * J (U) )*R(V) 520 B5=B5 + J(V) 530 NEXT V 540 G (0) =(F (U , K) + A5) / {1 - (Z 1 *K ( 1) • (1 - Z 1) * (B5+J { 0) ) ) * V (U) ) 550 R(U)=V (U)*G (U) 560 P(U ,K )=G(U)-R{U) 565 Z6=Z6+P(U,K) 570 NEXT 0 610 P(N2,K)=100-Z6 620 C{K)=A60*A61*N(1,K) *A62*N(2,K) 630 PRINT "BON NUMBER 3 ";K 635 Z1=INT(Z1*100000*.5)/100000 64 0 PBINT " A L P H A 3 " ; Z1;TAB{ 18) ; " B E T A = " ; Z 7 , " K 1 3 " ; Z 4 , » K 2 = " ; Z 5 650 NEXT K 660 P R I N T " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 700 *PRINTOUT SECTION 701 PRINT 702 PRINT "SIZE ANALYSES REPORTED AS ST. PERCENT RETAINED ON SIZE" 703 PRINT 704 P R I N T " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * " 705 PRINT 710 FOR K=A4 TO A3 715 IF K=6 THEN:K=7 716 I F K=10 THEN;STOP 72 0 A9=0 722 PRINT 724 PRINT "RUN NUMBER=";K 726 A18=0 727 FOR J=1 TO N2 728 A18=A18 + P{J ,K) 729 NEXT J 735 PRINT 740 PBINT "SIZE","MEASURED","PREDICTED","DIFFERENCE" 741 PRINT " (CM.) ","PRODUCT","PRODUCT" 750 PRINT 755 FOR J=1 TO N2 756 P ( J , K ) = I N T ( P ( J , K ) * 1000+. 5) / I 000 757 S{ J) =1 NT (S ( J) *10000 + .5) /10000 758 NEXT J 76 0 FOR J=1 TO N2-1 770 PRINT S (J+1) , T ( J , K ) , P ( J , K ) , T {J , K ) - P ( J , K) 780 A 9 = A 9 * ( T ( J , K ) - P ( J , K ) ) **2 790 NEXT J 792 A9=A9+(T(N2,K)-P(N2,K)) **2 796 PRINT "PAN";TAB (14) ; T (N2,K) ;TAB (29) ;P (N2,K) ; TAB (44) ; T ( N 2 , K ) - P (N2 ,K) 800 PRINT 804 PRINT TAB(31);"SUH=";A18 810 PRINT "RESIDUAL SUM OF SQUARES=";A9 820 PRINT 821 PRINT "PREDICTED CURRENT 3 ";C (K) 822 PRINT 826 PRINT "OPERATING CONDITIONS:" 830 PRINT 835 PRINT "GAP=";N (1,K) , " F E E D R A T E 3 " ;N (2, K) , " " , » $ +1INCH IN FEED—" ; N (3 ,K) 838 PRINT " (CM. ) " , 1 ' (TPH) " 840 PRINT 850 PBINT " . . . . . . . . . . . . . . . . . . . " 880 NEXT K - 196 -900 STOP 910 DATA 1 4 , . 5 , 4 3 . 5 2 , 1 0 . 0 930 DATA . 1 133812,1. 178078E-4 , .518076 ,3 .632176E-4 ,299 .381 935 DATA 27 .4583 ,43 .97832 , -2599 .762 ,16 .766 29 940 DATA -1 .793265 ,5 .284647E-2 94 5 DATA 6 .331619 , - .8040997 ,1 .042385 ,2 .996623 , .7135176 ,17 .96698 950 DATA 27 .55756 , -9 .608871 ,5 .542041E-2 1000 END E N D - O P - F I L E - 197 -e v i c e : DS20 t a s k : 2227 USER.ID: RALU 13:49:26 08-16-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS20 t a s k : 222' • SIGN RALU ' ENTER USER PASSWORD. ' **LAST SIGNON WAS: 13:45:35 l- USER "RALU" SIGNED ON AT 13:47:46 ON TUE AUG 16/77 : RUN *BASIC '• EXECUTION BEGINS - ?UBC BASIC SYSTEM • ?  GET TERCR RUN COMPUTED VALUES OF MODEL PARAMETERS RUN NUMBER3 1 ALPHA 3 0.66668 BETA 3 29.87378 K1 = 1. 377523 K2= 3.69241 9 RUN NUMBER= 2 ALPHA 3 0.55844 BETA 3 65.35574 K1 = 1. 773872 K2= 3.860186 RUN NUMBER3 3 ALPHA 3 0.44047 B E T A 3 71.31435 K1 = 2. 196643 K 2 3 3.860481 RUN NUMBER3 4 A L P H A 3 0.39154 B E T A 3 71.41962 K1 = 1. 641756 K2= 3.992796 RUN NUMBER3 5 ALPHA 3 0.55131 B E T A 3 66.46409 K1 = 1. 905988 K2= 5.458353 RUN NUMBER3 7 ALPHA 3 0.36837 B E T A 3 71.43051 K1 = 2. 011681 K2= 5.742872 RUN NUMBER3 8 ALPHA 3 0.42698 BETA 3 71.36399 K1 = 0. 796212 K2= 5.5 94 909 RON NUMBER3 9 ALPHA 3 0.24368 B E T A 3 71.43661 K1 = 1. 853141 K2= 5.443298 *************************************************************** SIZE ANALYSES REPORTED AS WT. PERCENT RETAINED ON SIZE * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN NUMBER3 1 SIZE MEASURED PREDICTED DIFFER (CM.), PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0 0 5.44 0 0 0 2.72 0 1. 137 - 1 . 1 3 7 1.36 38. 5 39.171 -0 .671 0.68 34 .5 35. 102 -0 .602 0.34 10 13.493 -3 .493 0.17 6 4.009 1.991 0.085 3.4 2.306 1. 094 0.0425 2.55 1.557 0.993 0.0212 1.9 1.077 0. 823 0.0106 1.31 0.723 0. 587 0.0053 0.89 0.487 0.403 PAN 0.95 0.938 0.012 SUM 3 100 - 198 -RESIDUAL SOB OF SQUARES 3 21.63788 PREDICTED CURRENT 3 37.05207 OPERATING CONDITIONS: G A P 3 0.737 FEEDRATE 3 299.1 % *1INCH IN F E E D 3 60 (CM.) {TPH) RUN NUMBER3 2 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0 0 5.44 0 0 0 2.72 0 2.377 - 2 . 3 7 7 1.36 42 42. 22 -0 .22 0.68 31 30.339 0. 661 0.34 9.6 12.306 - 2 . 7 06 0. 17 5.8 4.394 1. 406 0.085 3.4 2.692 0.708 0.0425 2.55 1.817 0. 733 0.0212 2 1.25 0.75 0.0106 1.47 0.881 0.589 0.0053 1.08 0.613 0. 467 PAN 1.1 1. 109 -0 .009 SUM 3 100 RESIDUAL SUM OF SQUARES 3 17.60087 PREDICTED CURRENT 3 36. 21502 OPERATING CONDITIONS: G A P 3 0.673 FEEDRATE 3 272.9 % +1INCH IN F E E D 3 67.5 (CM.) (TPH) RUN NUMBER3 3 SIZE (CM.) MEASURED PRODUCT PREDICTED PRODUCT DIFFERENCE 21.76 0 0 0 10.88 0 0 0 5.44 0 0 0 2.72 2 4. 106 - 2 . 1 0 6 1. 36 47.5 45.497 2.003 0.68 26 .5 26.237 0.263 0.34 8.5 9.478 -0 .978 0.17 4.7 4.851 -0 .151 0.085 3.2 3.208 -0 .008 0.0425 2.25 2. 196 0.054 0.0212 1.9 1.5 0.4 0.0106 1.4 1.002 0.398 - 199 -0.0053 1.02 0,686 0.334 PAN 1.03 1.239 -0 .209 SUM= 100 RESIDUAL SUH OF SQUARES= 9.97232 PREDICTED CUR8ENT= 39.44431 OPERATING CONDITIONS: GAP= 0.762 FEEDRATE= 346.6 % +1INCH IN FEED= 75 .5 (CM.) (TPH) RUN NUMBER= 4 SIZE MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0 0 5.44 0 0 0 2.72 5.5 2. 425 3.075 1.36 38. 5 39.972 -1 .472 0.68 26.7 26.459 0. 241 0. 34 10. 3 13.314 -3 .014 0. 17 € .2 6.023 - - 0.177 0.085 4.2 3.873 0. 327 0.0425 2.9 2.607 0.29 3 0.0212 2.05 1.759 0.291 0.0106 1.5 1.208 0. 292 0.G053 1.05 0.853 0. 197 PAN 1.1 1,509 - 0 . 4 0 9 S0M= 100 RESIDUAL SUM OF SQUARES= 21.36483 PREDICTED CURRENT= 34.78816 OPERATING CONDITIONS: GAP= 0.66 FEEDRATE= 244.9 % +1INCH IN FEED= 65 (CM.) (TPH) R U N NUMBER= 5 S I Z E MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10,88 0 0 0 5.44 0 0 0 2.72 10 11.359 -1 .359 1.36 42 45.983 -3 .983 0.68 23 ,5 22. 883 0. 617 0.34 8.7 7.901 0.799 0. 17 5. 1 3.329 1.771 - 200 -0.085 3.2 2. 117 1. 083 0.0425 2 .25 1.437 0. 813 0.0212 1. 75 0. 976 0.774 0.0106 1.27 0.67 0. 6 0.0053 1 0.476 0. 524 PAN 1.23 2.871 -1 .641 SUM 3 100 RESIDUAL SUM OF SQUARES 3 27.62709 PREDICTED CURRENT 3 35.35787 OPERATING CONDITIONS: GAP= 1.08 FEEDRATE 3 328 % +1INCH IN F E E D 3 70 (CM.) (TPH) RUN NUMBER3 7 SIZE MEASURED PREDICTED DIFFERENCE (CM.), PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0 0 5.44 0 0.002 -0 .002 2.72 16 15.624 0.376 1.36 42 43.889 -1 .889 0.68 19.7 19.608 0. 092 0.34 7.4 7.785 -0 .385 0.17 4.3 4. 271 0.029 0.085 2.9 2.835 0. 065 0.0425 2.35 1.936 0. 414 0.0212 1.85 1.313 0. 537 0.0106 1.45 0.891 0. 559 0.0053 1.01 0.621 0.389 PAN 1.04 1.226 - 0 . 1 8 6 SUM 3 100 RESIDUAL SUM OF SQUARES 3 4.829619 PREDICTED CURRENT 3 36.09653 OPERATING CONDITIONS: G A P 3 0.495 FEEDRATE 3 239 .9 % *1INCH IN F E E D 3 72 (CM.) (TPH) RUN NUMBER3 8 S I Z E MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10.88 0 0 0 5.4 4 0 0 0 2.72 6 5.775 0. 225 - 201 -1.36 36 39.967 -3 .967 0.68 29 .5 23. 426 6.074 0. 34 10.5 15.91 -5 .41 0. 17 5.7 5. 877 - 0 . 1 7 7 0.085 3.5 3.083 0.417 0.0425 2 .5 2.007 0. 493 0.0212 2.1 1.334 0. 766 0.0106 1.6 0.893 0.707 0,0053 1.16 0.614 0.546 PAN 1.44 1.114 0.326 SUM= 100 RESIDUAL SUB OF SQUARES= 83.88855 PREDICTED CURRENT= 41.90415 OPERATING CONDITIONS: GAJP= 0.521 FEEDRATE= 3 49.2 % +1INCH IN FEED= 49 (CM.) (TPH) HUN NUMBER= 9 SI2E MEASURED PREDICTED DIFFERENCE (CM.) PRODUCT PRODUCT 21.76 0 0 0 10,88 0 0 0 5.44 0 0 0 2.72 15 11.755 3.245 1. 36 45 44. 897 0. 103 0.68 19.6 18.063 1. 537 0.34 7.4 9. 124 -1 .724 0. 17 4 5. 355 -1 .355 0.085 2.7 3.624 -0 .924 0.0425 1.95 2. 445 - 0 . 4 9 5 0.0212 1.62 1. 626 - 0 . 0 06 0.0106 1.06 1.086 -0 .026 0.0053 0.77 0.729 0.041 PAN 0.9 1.295 -0 .395 SUM= 100 RESIDUAL SUM OF SQUARES= 18. 96842 PREDICTED CURRENT= 41.76555 OPEBATING CONDITIONS: GAP= 0,953 FEEDRATE= 421.6 % +1INCH IN FEED= 69 (CM.) (TPH) • ?STOP! y ? AT LINE "716" IN PROGBAM "TERCB" y ? PROGRAM ENDS : MTS \ CONTROL *PRINT* HOLD PRINT=TN F0RM=8X11 t *PRINT* ASSIGNED RFS NUMBER 664962 - 202 APPENDIX G DERIVATION OF A SCREEN EFFICIENCY  EQUATION by A . L . Mular and C . C . Hatch - 203 -DERIVATION OF A SCREEN EFFICIENCY EQUATION By A. L. Mular* and C. t). Hatch** INTRODUCTION Interest in crushing plant simulation (1 ,2 ) has stimulated the development of an eff ic iency equation for vibrat ing screens as reported by Whiten (2)• Whitens equation appears to be a modification of one proposed by Gaudin (3] many years ago. More recently, Ferrara and Pret i (4) summarized the l i terature which dealt with screening kinet ics and proposed the use of alternative equations based part ly upon mechanism. Gaudins expression was employed. ( The purpose of this note is to derive a new efficiency equation and show * *•* how well i t f i t s screening data acquired at the Brenda Mines Limited secondary crushing plant . PARTICLE SIZE AND SCREEN INEFFICIENCY Consider a screen deck onto which is fed part ic les of various sizes, and shapes per unit time. A screen analysis of a representative portion of feed may be performed to determine the feed size d i s tr ibut ion . The size of part ic les trapped between any two sieves i s often reported as the geometric mean size of the two sieves, i . e . , = ^jxTx"^" . However, not a l l of these part ic les are of size X^. The actual size of a single part i c l e is perhaps better defined with, respect to i t s centroid by 3 dimensions. On this basis , the probabi l i ty that a part i c l e trapped between sieves X.. and + ^ has exactly the same dimensions as any other par t i c l e in this size range cannot be very large. S t i l l , in a pract i ca l * Professor of Mineral Engineering, University of Br i t i sh Columbia, Vancouver Research Assistant, Department of Mineral Engineering, University of B. C , Vancouver * * * Peachland, B. C. ; : i - 204 -sense, no attempt i s made to distinguish between part ic les in the size range. For that matter, in a prac t i ca l screen operation, we seldom distinguish between indiv idual part ic les in the feed to a screen, except to determine the proportion of to ta l feed that passes or does not pass through the screen openings. Such information i s used to calculate gross screening eff ic iency. Continuous screens which operate in crushing plants are seldom 100% e f f i c i e n t . This suggests that a proportion of certain size fractions fed to a screen can be "bypassed" to the oversize stream. I f c, = fract ion of feed of a narrow size range that "bypasses" to the coarse stream, then an eff ic iency equation may be corrected accordingly. When o^ part ic les of a narrow size range report to the oversize stream, while f^ part ic les of the same size range are being fed to the screen, the fract ion of the feed part ic les which are not involved in bypassing is given by o. - c . f . Y. - c. f. - c . f . 1 - C 1 v 6 1 1 1 1 o. where = ^— , c^ is a measure of ineff ic iency for each size fract ion i , and i i s the most probable fraction of that portion of a narrow feed size range not involved in bypassing that reports to the oversize. A suitable expression for P^ i s necessary at this stage. DERIVATION OF AN EXPRESSION FOR P. l Figure 1 i s a diagram of a vibrating screen being fed with F part ic les per unit time, where the part ic les have a continuous d is tr ibut ion of s izes. Assume that in one retention time period, T, F part ic les (not involved i n bypassing) are fed to a vibrating screen at steady state. Consider, i n i t i a l l y , a narrow size fract ion of these part ic les . Let the number of part ic les of geometric mean size X. be F . , whereT*F. = F. After time T, U. part ic les of 1 X X X size have passed through the screen, while - U\ part ic les have been retained as part of the oversize stream. The number of par t i c l e s , U^, that pass - 205 -F , # r . © o t o o d t i F - U = 2 F ; - U : ©OOOO © U , U ; U = 2 U ; F I G U R E 1 S C H E M A T I C R E P R E S E N T A T I O N O F A VIBRATING S C R E E N 206 -through the screen, among other things, depends on par t i c l e dimensions, p a r t i c l e orientation at any time on the screen, size of the screen opening, extent of crowding, mechanical factors -such as slope and throw, the value of T , and the moisture content of the feed. One thing that can be certain is that a given p a r t i c l e either passed or did not pass through the screen, although, because s ize i s measured with standard sieves, that par t i c l e cannot be d i s -tinguished indiv idual ly within the geometric mean size range measured by X^. Let each feed par t i c l e in the size range be tagged with an identifying number, Zj w h e r e ^ Z j = F^. I f a par t i c l e passes through the screen, assign a value of 1 to Zy Otherwise the value of Z.. i s zero. For example, suppose there are 8 p a r t i c l e s , i . e . , F^ = 8; the following might occur: Z l Z2 Z 3 Z 4 Z 5 Z 6 Z 7 Z 8 (identifying numbers) 1 0 1 1 0 0 0 0 This means that part ic les Z^, Z^ and passed through the screen, while the others did not. It i s obvious that there is a large number of d i s t inct sequences that may occur. Another way to characterize the s ituation i s to group F^ part ic les according to whether they pass the screen or do not as follows: Pass (1) Do Not Pass (0) Z l Z 3 Z 4 ' , Z2 Z 5 Z 6 Z 7 Z 8 Again we note that a large number of d i s t inct sequences is possible, including (a) a l l part ic les pass, (b) no part ic les pass, etc. There are F J ways to write the Z^ identifying numbers on a l ine , as the f i r s t posi t ion may be chosen in F^ ways, the second in F ^ - l ways and so on. But many of these sequences are not distinguishable because of the way part i c l e size i s measured. For example, interchanging the order Z^ Z^ Z^ to Z^ Z^ Z^ is not a distinguishable sequence. Of interest are the number of d i s t inc t sequences that are possible; not the per-mutations. Each d i s t inc t sequence can be permuted in IL! (F . - IK) ! ways. I f l\L is the to ta l number of d i s t inct sequences, then W . U . ! ( F . ~ U . ) ! = F . ! l . i i i l so that F . ! " i " U . ! ( F . - U . ) . ~ - t & 2 ) " 1 v 1 xJ • -- 207 -Thus there are VL d i s t inc t ways that the F^ par t i c l e s might d i s t r ibute to the undersize stream. I f we now cover the complete range of s izes involved in the feed, then the to ta l number of d i s t inc t ways of d i s t r i b u t i n g feed part ic les to the undersize stream i s W, where F . ! _ I f ItT _ II 1 7T h - K n / / v i ' v U . ! ( F . - U.) I a l l x a l l x i - i xJ Taking the natural log of both sides of equation 3 resu l t s i n (G-3) InW = E (InF.! - l n U . l - l n ( ( F . - U. ) ! ) ) "CM) a l l x 1 1 i i To f i n d the most probable way to d i s t r ibute par t i c l e s to the undersize, make 9 InW 3Ui a maximum, subject to the following conditions: (a) U = EIL = constant at steady state, where U i s the t o t a l number of p a r t i c l e s reporting to the undersize stream, i n time T . (b) V = ^ U i V i = constant at steady state, where V i s the t o t a l volume of the undersize stream and V\ i s the average volume^per p a r t i c l e of the s ize fract ion i n the undersize stream, both i n time T . As shown below, the solut ion to the above problem resembles the solution to obtain the Fermi-Dirac d i s t r i c u t i o n function--a well known expression that describes the probab i l i t y that an electron occupies an energy state of a given energy. Using the approximation that mj.* = j l n j - j , equation 4 becomes ' InW = Z • (Fj lnF. - ( F . - l y i n C F - U ) - U InU ) ( ( G _ 5 ) a l l x The LaGrange mul t ip l i er method may be used to find, a maximum subject to conditions (a) and (b). Thus 3(lnW + ct(U - ZU..} + B(V - IU..V.)) hu7 = 0 (G-6) l so that equation 6 becomes InfF. - U.) - InU. - a - BV. = 0 (G-7) - 208 -The probable f rac t ion , P . , of par t i c l e s of volume V. that reports to the oversize stream i s given as P. = 1 - 1 U. (G-8) F i 1 + e~a-^i where P. refers to par t i c l e s that are not involved in bypassing. A value for a may be found from boundary conditions in terms of 3. When P. i s 0.5 V. = V so that - a = 3 V 5 { ) . On subst i tut ion into equation 8, we have 1 ' 1 5 0 > P. = i , 3fV -V 1 1 + eP(V50 V (6-9) On the assumption that volume shape factors are constant, Equations 1 and 9 may be combined and expressed in terms of an average "volume" diameter so that (1 - c ) Y = c + ... ,(G-10) 1 + exp(kCX^ 0- X p ) The value of X.^  and hence X 5 Q i s proportional to geometric mean sizes i . Equation 10 has been tested using data gathered around secondary screens at Brenda Mines Limited, with c^ equal to zero. A typica l resu l t i s shown i n Figure 2. I t i s expected that for wet ores, fines w i l l s t i ck to coarse rock and c. w i l l not be zero for some s ize ranges. In this case, c^ may depend upon moisture content. Other factors may include the. percentage open area of the screen, the amplitude and frequency of v i b r a t i o n , the slope, and the retention time of sol ids on the screen. ACKNOWLEDGEMENT This study i s supported by a grant from the Canada Centre for Metals and Minerals Technology. LOG PARTICLE SIZE, MICRONS F I G U R E 2 COMPARISON O F O B S E R V E D AND PREDICTED S C R E E N 210 REFERENCES 1. GURUN, T . , "Design of Crushing Plant Flowsheets by Simulation", 10th APCOM Symposium, published by South African Institute of Mining and Metallurgy, Johannesburg, 1973. 2. WHITEN, W . J . , "The Simulation of Crushing Plants with Models Developed Using Multiple Spline Regression", 10th APCOM Symposium, and J . S . A . I . M . M . , May, 1972, p. 257. 3. GAUDIN, A . M . , Principles of Mineral Dressing, McGraw-Hill, New York, 1939, p. 145. 4. TERRARA, G . , and PRETI, U . , "A Contribution to Screening Kinetics", 11th IMPC, C a g l i a r i , I ta ly , 1975. - 211 -APPENDIX H SUMMARY.OF SECONDARY SCREEN MODEL L i s t i n g o f the Model F i t t i n g Program SCRN5 L i s t i n g o f the Secondary Screen Mode l , SCRN3 Output from SCRN3 - Model P r e d i c t i o n s f o r Observed Data - 212 -1 * * * PROGRAM: SCRN5 : SECONDARY SCREENS MODEL FITTING PROGRAM 2 * 3 * 27 DIM T (20) , E (20) , V{20) 28 DIM P(20,20) ,R (20,20) ,8(20,20) ,S{20) ,K(20,20) 29 DIM N{20, 20) ,0(20,20) ,0 (20,20) , F ( 2 0 , 20) 30 DIM A (1 ,22) ,D(1 ,22) , X (22,22) , Z (1, 22) , Y (22, 1) ,Q{22,22) 36 DIM L{20,4) 38 READ N 1 , N 2 , A 2 , S 1 , A 5 45 READ M3,M4 50 READ A3,AH 70 READ A 1 , S 1 , V 1 , G 2 , M 2 90 MAT R=ZER(A5,N2) 95 MAT W=ZER(A5,N2) 110 MAT Z=ZER(1,N1) 120 MAT Y=ZER(N1 + 1, 1) 130 MAT D=ZER(1,N1) 140 MAT X=ZER(N1+1,N1) 150 MAT Q=ZER(N1 + 1,N1) 170 F I L E AKX2,SV7,DUMP,ASF2,AS02,ASU2,OP,OP2 172 MAT READ F I L E 1 ,K(A5,N2) 173 MAT READ F I L E 2 , A ( 1, N1) 175 MAT READ F I L E 4 ,F(A5,N2) 176 MAT READ F I L E 5 ,0(A5,N2) 177 MAT READ F I L E 6 ,0(A5,N2) 178 MAT READ F I L E 7 , L ( A 5 , 3 ) 179 MAT READ F I L E 8 ,N(3,A5) 182 S2 = SQR (S1* (S1*A2) ) 186 FOR 1=1 TO N2 190 S(I) =S1*A2**I 19 2 NEXT I 194 FOR J=1 TO N2-1 196 T(J) =S2*A2** ( J - 1) 198 NEXT J 208 * I N I T I A L VALUES INPUTTED 210 * CALCULATION OF INITIAL STARTING VALUES 215 FOR 1=1 TO N1 220 D(1,I ) =ABS (G2*A(1,I) ) 225 NEXT I 23 0 * SET UP INITIAL SIMPLEX 24 0 FOR J=1 TO N1 250 FOR I = 1 TO J+1 260 IF I=J+1 THEN 290 27 0 X ( I , J ) = A ( 1 , J ) - (2/(J+1)) *D(1,J) 280 GO TO 300 290 X ( I , J )=A(1 ,J ) + ( ( 2 / ( J + 1) ) * D ( 1 , J ) *J) 300 NEXT I 310 FOR I = J+2 TO N1+1 320 X ( I , J) =A (1, J) 330 NEXT I 340 NEXT J 350 * CALCULATION OF STD. DEV'N OF OBJECTIVE FUNCTION 360 Z8=0 361 Z9=0 370 T3=1.E70 380 FOR 1=1 TO N1+1 390 H=I 400 GO SUB 1310 410 Y ( I , 1)=Y1 420 NEXT I - Z\6 -430 GO SOB 1720 440 T1=0 441 T2=0 445 FOR 1=1 TO N1+1 450 T1=T1+Y (1,1) 455 NEXT I 460 T1=T1/(N1+1) 465 FOR 1=1 TO N1 + 1 470 T2=T2+(Y {I, 1)-T1) **2 480 NEXT I 490 T4=SQR (T2/N1) 500 IF T4>1.E-6 THEN 730 510 GO TO 590 52 0 * PRINTOUT SECTION 530 PRINT 540 PRINT "CYCLE LIMIT STOP CHITERION=";M2;"STD.DEVIATION=";T4 55 0 PRINT 560 PRINT"HIGH=";Y(H, 1) , "2ND HIGH=»; Y (S, 1) , "LOW-"; Y (L, 1) 575 PRINT 580 GO TO 600 590 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y ( L , 1 ) 593 PRINT 595 PRINT "STANDARD DEVIATION=";T4 600 H=L 610 GO SUB 1310 620 PRINT 623 PRINT "RELATION CONSTANTS" 626 PRINT "FOR PARAMETER A" 627 PRINT 62 9 PRINT "A1 = » ; X ( H , 1 ) , "A2=";X (H,2) , "A3="; X {H, 3) ,"A4=";X (H,4) 630 PRINT 63 1 PRINT "FOR PARAMETER X50" 632 PRINT 633 PRINT "A5=";X (H,5) ,"A6=";X (H,6) , "A7="; X (H,7) , » A8=" ; X (H , 8) 63 4 PRINT "A9=";X(H,9) 63 6 PRINT 639 PRINT 640 PRINT "NUMBEE OF OBJECTIVE FUNCTION CALCULATIONS=" ; Z9 64 2 FOR I=A3 TO A4 643 A8=0 644 A9=0 645 A10=0 646 PRINT 64 9 PRINT "RUN NR. " ; I 65 0 PHINT 651 PRINT "RESPONSE IS WEIGHT FRACTION TO OVERSIZE" 652 PRINT 653 PRINT "SIZE","ADJUSTED","PREDICTED" 65 4 FOR J=1 TO N2-1 655 PRINT S(J) ,K ( I , J) , P ( I , J) 656 A8=A8+(K (I , J ) - P ( I , J) ) **2 657 NEXT J 658 PRINT "PAN",K(I ,N2) , P ( I , N 2 ) 659 A8=A8+(K ( I , N 2 ) - P ( I , N 2 ) ) **2 660 PRINT 661 PRINT "RESIDUAL SUM SQUARES=";A8 662 PRINT 663 GO SUB 700 664 PRINT "MODEL PERFORMANCE" 665 PRINT - 214 -66 6 PBINT " S I Z E " , " A D J . 0 / S " , " P R E D . 0 / S " , " A D J . 0 / S " , " P R E D . U/S» 667 PRINT 66 8 FOR J=1 TO N2-1 669 PRINT S(J) ,0 ( I , J ) ,R ( I , J ) ,U ( I , J ) , W ( I , J) 670 A9=A9* (R (I , J) -0 ( I , J) ) **2 671 A10=A10* (W ( I , J ) - U (I , J) ) **2 67 2 NEXT J 673 PRINT "PAN",0 (I,N2) , R ( I , N 2 ) ,0(1,N2) ,W(I,N2) 674 A9=A9+ (R ( I , N2) -0 (I,N2) ) **2 675 A10=A10+ (I? (I,N2) -U (I,N2) ) **2 676 PRINT " " , " ","SUM 0/S=";A20," ","SUM U / S = » ; B 2 0 677 PRINT "RESIDUAL SUM SQUARES:0/S=";A9,"U/S=";A10 678 PRINT 679 PRINT " F L O W R A T E S : O / S = " ; E ( I ) / 1 0 0 , " U / S = " ; V ( I ) / 1 0 0 680 PRINT 682 Z2 = X (H, 1) + X(H,2) *N(1,1) **2+X (H,3) *N (2,1) *X (H ,4) *N (3,1) **2 68 3 Z21 = X(H,5) +X(H,6) *N(1,I)+X (H,7) *N(1 ,I ) **2 68 4 Z3=Z21 +X (H,8) *N (2,1) **2 + X (H,9) *N (3,1) **7 686 PRINT " A = " ; Z 2 , " X 5 0 = " ; Z 3 , " C - » ; Z 1 , " B = " ; Z 4 687 PRINT 688 NEXT I 689 PRINT " 690 STOP 700 A20=0 705 B2 0=0 710 FOR J=1 TO N2 712 A20=A20*R(I,J) 714 B20=B20 + W ( I , J) 716 NEXT J 718 RETURN 730 IF Z9>M2 THEN 530 732 I F Z9>M3 THEN 736 734 GO TO 745 736 M3=H3*M4 73 8 M5=CMD("%EMPTY DUMPSD") 74 0 MAT WRITE F I L E 3 ,X 74 2 M6=CMD(»%SAVE DUMPSD") 74 3 PRINT "Z9=";Z9 745 IF T4>T3 THEN 770 75 0 T3 = T4 76 0 * REFLECTION 770 MAT Q = (1)*X 780 FOR J = 1 TO N1 790 P1=0 80 0 FOR I •= 1 TO N1 + 1 810 IF I = H THEN 830 820 P1=P1 + X ( I , J) /N1 830 NEXT I 840 Z (1, J) = (1 + A1) *P1-A1*X (H, J) 850 X (H, J) =Z (1 ,J ) 860 D(1,J)=P1 870 NEXT J 880 GO SUB 1310 890 MAT X = (1) *Q 900 Y=Y1 910 IF Y>=Y(L,1) THEN 1000 920 * EXPANSION 93 0 FOR J = 1 TO N1 94 0 X (H, J) = (1 + Y1) *Z (1, J) - V 1 * D ( 1 , J) 95 0 NEXT J - 215 -960 GO SUB 1310 970 IF Y1>Y(L,1) THEN 1010 980 Y(H,1)=Y1 990 GO TO 430 1000 I F Y>Y(S,1) THEN 1060 10 10 Y (H, 1) =Y 1020 FOR J=1 TO N1 1030 X (H,J) = Z ( 1 , J ) 1040 NEXT J 1050 GO TO 430 1060 I F Y>Y{H,1) THEN 1120 1070 FOR J = 1 TO N V 1080 X (H, J) =Z (1 , J) 1090 NEXT J 1100 Y (H , 1) = Y 1110 * CONTRACTION 1120 FOR J=1 TO N1 1130 X(H,J)=B1*X (H,J) + (1-B1) *D(1 ,J) 1140 NEXT J 1150 GO SUB 1310 1160 I F Y1>Y(H,1) THEN 1200 1170 Y (H, 1) =Y1 1180 GO TO 430 1190 * REDUCE SIZE OF SIMPLEX 1200 FOR J=1 TO N1 1210 FOR 1=1 TO N1+1 1220 X ( I , J ) = (Q(I ,J ) + Q ( L , J ) ) / 2 1230 NEXT I 12 40 NEXT J 1250 Z8=Z8*1 1260 PRINT 1270 PRINT "STEP CHANGE";Z8 1280 PRINT 1290 GO TO 380 1300 * ESTIMATION OF NEW VALUES FOR UNKNOWNS 13 10 F2=0 13 15 FOR K=A3 TO A4 13 18 C2=L(K,2) * L ( K , 3 ) 13 25 Z2=X (H, 1) +X (H,2 ) *N (1,K) **2 + X (H, 3) *N (2,K) *X{H, 4) *N <3,K)**2 13 30 Z30=X (H,5) +X <H,6) *N (1 ,K) +X (H,7) *N (1,K) **2 1331 Z3=Z30+X (H,8) *N (2,K) **2+X (H,9) *N(3,K) **7 1337 V(K)=0 1338 E{K)=0 1340 FOR J=1 TO N2-1 1345 C1= (Z3**3-T(J) **3 ) /Z2 1350 I F C K - 1 7 0 THEN:C1=-170 1355 I F C1>170 THEN:C1=170 1360 P <K,J) = (1/(1 + EXP (C1) ) ) 1370 R (K, J) = (P (K, J) * F (K, J) *C2) 1373 E (K) =E (K) +R (K, J) 1375 W (K,J) = (1-P{K, J)>*F (K, J) *C2 1378 V <K) = V (K) +W (K, J) 1385 NEXT J 1386 B10={1/(H-EXP{Z3**3/Z2) )) 1387 R(K,N2)=B10*F(K,N2)*C2 1388 W (K,N2) =(1-B10) *F(K,N2) *C2 1389 E <K)=E (K) +R (K f N2) 1390 V (K)=V (K) *W (K,N2) 1391 FOR J=1 TO N2 1392 R (K,J) = (R (K, J) / E ( K ) ) *100 - 216 -1393 i (K,J) = (I{K, J ) / V ( K ) ) *100 1394 F2=F2+ (0 (K, J) -R (K, J) ) **2+ (U (K,J) -W (K, J) ) **2 1395 NEXT J 1396 NEXT K 1397 Y1 = F2 1400 Z9=Z9+1 1405 RETURN 1715 * OBJECTIVE FUNCTION MAGNITUDE LISTING {ORDER SEARCH) 1720 I F Y(1,1)>Y (2,1) THEN 1770 1740 S=1 1741 L=1 1750 H=2 1760 GO TO 1790 1770 S=2 1771 L=2 17 80 H=1 1790 FOR 1=3 TO N1+1 1800 I F Y ( I , 1 ) >Y{L, 1) THEN 1820 1810 L=I 1820 I F Y ( I , 1) <Y (S, 1) THEN 1880 1830 I F Y f l , 1) <Y (H, 1) THEN 1870 1840 S=H 1850 H=I 1860 GO TO 1880 1870 S=I 1880 NEXT I 1890 RETURN 1900 DATA 9 , 1 4 , . 5 , 4 3 . 5 2 , 1 1 1910 DATA 1100,290 1920 DATA 1,11 1930 DATA 1 , . 5 , 2 , . 0 1 , 3 0 END—OF-FILE - 217 -1 * * * PROGRAM: SCR'N.3 : SECONDARY SCREEN MODEL 2 * 3 * 10 DIM T (20) , N (20) ,W (20) , Y (20) ,S (20) 20 DIM F (20,20) ,0 (20,20) ,0 (20,20) , L { 2 0 , 5) ,M (5,20) , K (20,20) 25 * READ MODEL CONSTANTS 3 0 READ N 2 , S 1 , A 2 , A 3 HQ READ B1,B2 42 READ A20 ,A21 ,A22 ,A23 ,A24 '45 READ A30,A31,A32,A33 46 PRINT 1 1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 7 PRINT 48 PRINT "SIZE ANALYSES REPORTED AS WT. PERCENT RETAINED ON SIZE" H9 PRINT " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * " 50 FILE A S F 2 , £ S 0 2 , A S U 2 , O P , A K X 2 , O P 2 60 MAT READ F I L E 1,F(A3,N2) 70 MAT READ F I L E 2,0(A3,N2) 80 MAT READ F I L E 3,U(A3,N2) 90 MAT READ F I L E 4 , L ( A 3 , 3 ) 100 HAT READ F I L E 5,K(A3,N2) 105 MAT READ F I L E 6,M(3,A3) 110 FOR J=1 TO N2 112 S{J) =S1*A2**J 114 NEXT J 1 16 S2=SQR{S (1) *S (2) ) 118 FOR J=1 TO N2-1 120 I (J) =S2*A2** (J-2) 130 NEXT J 131 FOR K=B1 TO B2 132 Z1 = A20 + A21*M (1,K) +A22*M (1,K) **2>A23*M (2,K) **2+A24*a (3 ,K)**7 136 Z2=A3 0+A31*M (1 ,K) **2+A32*M (2,K) +A33*M (3 ,K) **2 140 FOR J=1 TO N2-1 150 C1= (Z 1 **3—T (J) **3) / Z 2 160 IF C K - 1 7 0 THEN: C 1=—170 170 I F C1>170 THEN:C1=170 210 I (J ) •= 1/( 1 + EXP (C1) ) 220 NEXT J 230 A9=0 240 A10=0 242 A15=0 244 A16=0 260 FOR J=1 T€ N2-1 270 N (J) = (Y { J) * F (K, J) *L (K , 1) ) /100 280 W (J)= ( (1-1 (J) ) *F {K, J) * L (K, 1) ) /100 282 A15=A15 + N(J) 284 A16=A16 + W(J) 310 NEXT J 311 B10=1/(1+EXP (Z1**3/Z2) ) 312 N (N2) = (B10*F(K,N2) *I (K,1) ) /100 314 R (N2) = ( (1-B10) *F(K,N2) *L (K,1) ) /100 3 16 A15=A15*N(N2) 318 A16-=A16*W (N2) 3 20 FOR J=1 TO N2 322 N (J) = (N (J) / A 15) * 1 00 324 W{J) = (W(J)/A16)*100 326 A9=A9*<N<J)-0 (K, J) ) **2 328 A10=A10+ (« (J ) -U (K,J) ) **2 329 S (J) =INT (S (J) *10000+.5) /10000 3 30 NEXT J 331 PRINT - 218 -332 PBINT "BON NUMBER=";.K 334 PBINT 336 PRINT "PARAMETER X50="; Z 1,"PARAMETER A=";Z2 338 PRINT 340 PRINT "SIZE","MEASURED","PREDICTED" 342 PRINT " ( C £ l . ) " , " Y 0 / S » , " Y 0/S" 344 A8=0 350 PRINT 354 FOR J=1 TO N2 355 Y (J)=INT (Y(J) *10000000 + . 5)/1 0000000 356 K (K, J) =.INT (K (K, J) * 10000000+. 5) /10000000 357 NEXT J 3 60 FOR J=1'TO N2-1 370 PRINT S {J) , K ( K , J ) ,Y<*7) 380 A8=A8+ (K {¥., J ) - Y (J) ) **2 390 NEXT J 400 PRINT "PAN" ;TAB{14) ;R(K,N2) ; TAB (29) ; B10 410 A8=A8+(K(&,N2)-B10)**2 4 20 PRINT 430 PRINT "RESIDUAL SUM SQUARES-";A8 4 40 PRINT 4 50 PRINT 460 PRINT "SIZE","MEASURED","PREDICTED","MEASURED","PREDICTED" 461 PRINT " (CM.) " , "OVERSIZE", "OVERSIZE", "UNDERSIZE", "UNDERSIZE" 462 PRINT TAB(16) ; "PRODUCT" ; TAB (31) ; "PRODUCT";TAB (46) ;"PRODUCT";TAB (61) ;"PRO 470 PRINT 475 A17=0 476 A18=0 4 80 FOR J=1 TO N2 485 A17=A17 + N(J) 486 A18 = A18 + W(J) 488 N (J) =INT (N (J) * 1000 + .5) /1000 489 W (J) =INT (S (J) *1000 + .5) /1 000 490 NEXT J 492 FOR J=1 TO N2-1 495 PRINT S (J) , 0 ( K , J ) ,N(J) ,U (K,J) , W (J) 5 00 NEXT J 510 PRINT "PAU";TAB (14) ;0 (K,N2) ; TAB (29) ;N (N2) ; TAB (44) ;U (K,N2) ;TAB (59) ;W (N2) 520 PRINT 530 PRINT T A B ( 3 1 ) ; " S U M = » ; A 1 7 ; T A B ( 6 1 ) ; " S U M = " ; A 1 8 540 PRINT 545 A10=1 NT(A 10*10000 0 + .5) /100000 550 PRINT "RESIDUAL SUMS OF SQUARES: O V E R S I Z E 3 " ; A 9 , " UNDERSIZE 3 ";A10 560 PRINT 565 A15=INT(A 15*1000•.5) /1000 566 A16=INT(Al6*1000+.5)/1000 570 PRINT "FLOWBATES: PREDICTED: O V E R S I Z E 3 " ; A 1 5 , " U N D E R S I Z E 3 " ; A 1 6 571 PRINT " MEASURED : O V E R S I Z E 3 " ; L (K,2) , " U N D E R S I Z E 3 " ; L ( K , 3 ) 575 PRINT 576 PRINT "OPERATING CONDITIONS:" 577 PRINT 578 PRI NT"APEIsTURE=" ; M (1, K) , " % +1 INCH IN F E E D 3 " ; M (2,K) , " F E E D R A T E 3 " ; M (3, K) 579 PRINT " ( C f i . ) " , " « , " ( T P H ) " 5 80 PRINT 5 82 PRINT " . , . . . , . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . , . . . . , . , . . . . . . " 585 NEXT K 5 86 PRINT 589 PRINT 590 STOP 500 DATA 1 4 , 4 3 . 5 2 , . 5 , 11 - 219 -510 DATA 1,11 520 DATA 6.54350 3,-7.342139,2.85577 6,~4.64881E-5,-1.303655E 630 DATA 1. 238414,.4822109,- 1.002221E-2,1. 163871E-7 7 00 END EN D-OF-FILE i e v i c e : DS40 t a s k : 2241 USEBID: BALU 09:13:22 03-16-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS40 t a s k : 224 ft SIGN RALU ft ENTER USER PASSWORD. 7 # **1AST SIGNON WAS: 09:07:46 # USER "RALU" SIGNED ON AT 09:11:37 ON TUE AUG 16/77 # BUN *EASIC '4 EXECUTION BEGINS 5 ?UBC BASIC SYSTEM : GET SCBN3 : BUN ********************************** SIZE ANALYSES REPORTED AS WT. PERCENT RETAINED ON SIZE * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN NUMBERS 1 PARAMETER X50= 1.851731 PARAMETER A= 1.86 4255 SIZE MEASURED PB EDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 0.9999932 1 2.72 0.9771518 1 1.36 0.5911507 0.6012195 0.68 0.0596201 0.0507471 0.34 0.0410346 0.0340184 0.17 0.0391766 0.0323449 0.085 0.0402742 0.0321414 0.0425 0.0521643 0.032116 0.0212 0.060443 0.0321129 0.0106 0.0608448 0.0321125 0.0053 0.0688055 0.0321124 PAN 0.1003671 3.211241E-2 BESIDUAL SUM SQUABES= 8.899353E-3 SIZE (CM.) 21.76 10.88 5.44 2.72 1.36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 MEASUBED OVERSIZE PRODUCT 0 0 26. 226 46.497 25. 116 1.084 0.251 0.161 0.12 0. 124 0.125 0. 1 0.077 PBEDICTED OVERSIZE PRODUCT 0 0 25. 971 47.121 25.295 0.914 0.206 0. 132 0.095 0.076 0.066 0.052 0.0 36 MEASURED UNDERSIZE PRODUCT 0 0 0 1. 94 30.975 30.488 10.461 7.04 1 5. 1 '4. 018 3. 464 2.752 1.859 PREDICTED UNDERSIZE PRODUCT 0 0 0 0 30.752 31.326 10.725 7.218 5.234 4.176 3.633 2.887 1.966 - 221 -PAN 0.119 0.038 SUM 3 100 RESIDUAL SDHS OF SQUARES: OVERSIZE 3 0.53545 FLOWRATES: PREDICTED: O V E R S I Z E 3 230.847 MEASURED : O V E R S I Z E 3 228.599 OPERATING CONDITIONS: APERTURE 3 1.5 % +1 INCH IN F E E D 3 47.29 (CM.) 1. 902 2.083 SUM 3 100 UNDERSIZE 3 4.7 50 5 UNDERSIZE 3 125.9 47 UNDERSIZE 3 128.2 FEEDRATE 3 356.79 9 (TPH) RUN NUMBER3 2 PARAMETER X 5 0 3 1.903061 PARAMETER A 3 2.00 0677 SIZE MEASURED PREDICTED (CM.) Y O/S Y O/S 2 1.76 1 1 10.88 1 1 5.44 0.9999734 1 2.72 1.000019 1 1.36 0.5537156 0.5277841 0.68 0.0525232 0.0474072 0.34 0.0352078 0.0326293 0.17 0.0343813 0.031129 0.085 0.0317813 0.0309462 0.0425 0.0418887 0.0309235 0.0212 0.042481 1 0.0309206 0.0106 0.0448736 0.03092 03 0.0053 0.056743 0.0309202 PAN 0.0957351 0.0309202 RESIDUAL SUH SQUARES 3 6.' 032904E-3 SIZE MEASURED PREDICTED MEASURED PREDICTED (CM.) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE PRODUCT PRODUCT PRODUCT PRODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 16.064 16.408 0 0 2.72 44.974 45.934 0 0 1. 36 36.3 57 35. 395 35.991 37. 129 0.68 1.621 1.494 35.917 3 5.205 0.34 0.285 0. 27 9. 592 9.377 0. 17 0. 154 0. 142 5.313 5.197 0.085 0.093 0.092 3.479 3.396 0.0425 0.088 0.066 2.473 2.438 0.0212 0.082 0.061 2. 27 2.24 0.0106 0.074 0.052 1. 935 1.914 0.0053 0.07 0. 039 1. 429 1.432 PAN 0.138 0.046 1. 60 1 1 .673 - 222 -SUM 3 100 RESIDUAL SUES OF SQUARES: OVERSIZE 3 1.99318 FLOWRATES: PREDICTED: OVER S I Z E - 190.725 MEASURED : OVERSIZE 3 194.801 OPERATING CONDITIONS: APERTURE 3 1.5 % +1 INCH IN F E E D 3 33.65 (CM.) SUM 3 100 UNDERSIZE 3 1.87557 UNDERSIZE 3 162.675 UNDERSIZE 3 158.6 FEEDRATE 3 353. 401 (TPH) RUN NUMBER3 3 PARAMETER X 5 0 3 1.868715 PARAMETER A= 1.903713 SIZE MEASURED PREDICTED (CM.), Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 0.9999739 1 2.72 0.999997 1 1.36 0.5764511 0.5767445 0.68 0.0526624 0.0492317 0.34 0.0458679 0.0332623 0.17 0.03124O1 0.0316579 0.085 0.0333227 0.0314627 0.0425 0.038513 0.0314384 0.0212 0.040069 0.0314353 0.0106 0.050106 0.031435 0.0053 0.0648819 0.0314349 PAN 0.0916022 0.0314349 RESIDUAL SUB SQUARES 3 5 .386394E-3 SIZE (CM.), 21.76 10.88 5.44 2.72 1 .36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 PAN MEASURED OVERSIZE PRODUCT 0 0 22.009 45.001 31.357 0.897 0.211 0.093 0.072 0.072 0.062 0.061 0.061 0. 104 PREDICTED OVERSIZE PRODUCT 0 0 22.06 5 45. 115 31.452 0. 841 0. 153 0.094 0.068 0.059 0.049 0.038 0.03 0.0 36 MEASURED UNDERSIZE PRODUCT 0 0 0 0 41.976 29.398 7. 998 5. 253 3. 80 6 3.274 2. 707 2. 108 1. 601 1. 879 PREDICTED UNDERSIZE PRODUCT 0 0 0 0 41.755 29.37 8.065 5.228 3.7 95 3.284 2.718 2.138 1.651 1.994 SUM 3 100 SUM 3 100 - LLZ -RESIDUAL SUES OF SQUARES; OVERSIZE 3 0.03811 FLOWRATES; PREDICTED: O V E R S I Z E 3 222.438 MEASURED : O V E R S I Z E 3 222.9 99 OPERATING CONDITIONS: APERTURE 3 1.5 % +1 INCH IN F E E D 3 43.26 (CM.) UNDERSIZE 3 0.07175 UNDERSIZE 3 122.961 UNDERSIZE 3 122.4 FEEDRATE 3 345.399 (TPH) RUN NUMBER3 4 PARAMETER X50= 1.897101 PARAMETER A 3 2.011498 SIZE (CM.) 21.76 10,88 5.44 2.72 1.36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 PAN MEASURED Y O/S 1 1 1.000025 1.000001 0.5172895 0.0433218 0.0253242 0.0204094 0.0271053 0.02484O7 0.0337544 0.0489584 0.059795 0.0806763 PREDICTED Y O/S 1 1 1 1 0.53562 53 0.0496335 0.0342557 0.0326914 0.0325008 0.0 32 477 0.0324741 0.0324737 0.0324737 3. 247 365E-2 RESIDUAL SUM SQUARES 3 4 .037417E-3 SIZE (CM.) MEASURED OVERSIZE PRODUCT PREDICTED OVERSIZE PRODUCT MEASURED UNDERSIZE PRODUCT PRE DICTED UNDERSIZE PRODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 14.923 14. 717 0 0 2.72 51.506 50.797 0 0 1.36 31.204 31. 865 32.059 31. 32 4 0.68 1.401 1.583 34.064 34. 368 0.34 0.277 0.37 11.738 11.812 0. 17 0. 139 0. 22 7.346 7.367 0.085 0.114 0. 135 4.505 4.55 0.0425 0.073 0.094 3. 156 3.179 0.0212 0.08 0.076 2. 522 2.564 0.0106 0.081 0. 053 1.732 1.79 0.0053 0.072 0.039 1. 247 1.303 PAN 0. 13 0.052 1.631 1.743 SUM 3 100 SUM 3 100 RESIDUAL SUSSS OF SQUARES: OVERSIZE 3 1.03941 UNDERSIZE 3 0.66238 FLOWBATES: PREDICTED: OV£RSIZE= 299.521 UNDERSIZE= 264.17 MEASURED : OVERSIZE= 295.4 UNDEBSIZE= 268.3 OPERATING CONDITIONS: APERTURE= 1.5 % +1 INCH IN FEED= 34.81 FEEDBATE= 563.7 (CM.) (TPH) RUN NUMBER= 5 PARAMETEB X50= 1.931496 PARAMETEE A= 2. 097179 SIZE MEASUEED PBEDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 1.000039 1 2 .72 1.000017 1 1.36 0.4976044 0.4891528 0.68 0.0503144 0.0468922 0.34 0.0288957 0.032833 0.17 0.0309196 0.0313916 0.085 0.0343656 0.0312158 0.0425 0.0420561 O.0311939 0.0212 0.0423127 0.0311912 0.0106 0.0620223 0.0311908 0.0053 0.0810429 0.0311908 PAN 0.1079463 3.119077E-2 R E S I D U A L S U M S Q U A H E S = 9 . 6 7 7 6 8 9 E - 3 SIZE (CM.) 21.76 10.88 5.44 2.72 1.36 0.68 0.34 O. 17 0.085 0.0425 0.0212 0.0106 0.0053 P A N M E A S U R E D O V E R S I Z E P E O D U C T 0 0 15.154 39.092 41. 301 2. 52 0. 534 0.324 0.232 0. 195 0. 149 0. 151 0.14 0.208 PBEDICTED OVEBSIZE PEODUCT 0 0 15. 34 39.573 41.099 2.378 0.614 0. 333 0.213 0. 146 0.111 0.077 0.055 0.061 SUM= 100 MEASURED UNDEBSIZE PRODUCT 0 0 0 0 30.372 34.6 46 13.072 7.397 4. 749 3. 235 2 .457 1. 66 3 1. 157 1.252 PREDICTED UNDERSIZE PEGDUCT 0 0 0 0 30.613 34.466 12.905 7.328 4.722 3.243 2.463 1.703 1 .208 1.348 SUM= 100 RESIDUAL SUMS OF SQUABES: OVEBSIZE= 0.37167 UNDERSIZE= 0.13751 FLOWBATES: PBEDICTED: OVERSIZE= 65.692 MEASURED : OVERSIZE= 66 .5 UNDEBSIZE= 92.105 UNDERSIZE- 91.3 - CdO -OPERATING CONDITIONS: APERTURE 3 1.5 % +1 INCH IN (CM.) F E E D 3 22.86 FEEDRATE 3 157.8 ( T P H ) RUN NUMBER3 6 PARAMETER X 5 0 3 1.561736 PARAMETER A= 1.71079 SIZE MEASURED PREDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 0.9999516 1 2.72 1.000005 1 1.36 0.8970897 0.8734989 0.68 0.2538565 0.1535962 0.34 0,0568406 0.1032582 0.17 0.0409977 0.0981108 0.085 0.048631 0.0974837 0.0425 0.0512417 0.0974056 0.0212 0.0602381 0.0973959 0.0106 0.0772057 0.0973946 0.0053 0.094892 0.0973945 PAN 0.1365175 9.739446E-2 R E S I D U A L S U B S Q U A R E S 3 2 . 3 8 6 8 0 2 E - 2 SIZE (CM.) M E A S U R E D O V E R S I Z E P R O D U C T P R E D I C T E D O V E R S I Z E P R O D U C T M E A S U R E D U N D E R S I Z E P R O D U C T PREDICTED UNDERSIZE PRODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 13.977 14.275 0 0 2.72 44.955 45. 91 1 0 0 1.36 35.027 34. 832 10.977 12. 766 0.68 4. 846 2.994 38.908 41.759 0.34 0.387 0.718 17.5 42 15.78 0. 17 0.152 0.371 9.712 8.6 42 0.085 0.114 0. 233 6. 092 5.468 0.0425 0.091 0. 177 4. 602 4. 143 0-0212 0.092 0 . 1 52 3.921 3.563 0.0106 0.081 0. 104 2.643 2.447 0.0053 0.091 0.095 2.372 2.237 PAN 0. 187 0.136 3. 231 3.195 SUM 3 100 SUM 3 100 RESIDUAL SUHS OF SQUARES: OVERSIZE 3 4.6559 UNDERSIZE 3 16.36493 FLOWRATES : PREDICTED: OVERSIZE 3 748.668 UNDERSIZE 3 295,838 MEASURED : O V E R S I Z E 3 764.6 UNDERSIZE 3 279.899 OPERATING CONDITIONS; - LLXi -APEHTURE= 1.27 % +1 INCH IN FEED= 43.14 FEEDEATE= 1044.499 (CM.) {TPH) BON NUMBEB= 7 PARAMETEB X50= 1 . 8 0 7 7 7 4 PARAMETER A= 1.873238 SIZE MEASURED PBEDICTED (CM.) y o /s Y O/S 21.76 1 1 10.88 1 1 5.44 1.000036 1 2.72 1.000032 1 1.36 0.6578227 0.6557206 0.68 0.0685617 0.0642195 0.34 0.0169244 0.043335 0. 17 0.0136022 0.0412326 0.085 0.0071782 0.0409767 0.0425 0.0091536 0.0409448 0.0212 0.018103 0.0409409 0.0106 0.0225314 0.0409404 0.0053 0.0314767 0.0409403 PAN 0.04 6333 9 4.094029E-2 RESIDUAL SUe SQUARES^ 4 .616365E-3 SIZE MEASURED PREDICTED MEASURED PBEDICTED (OS. ) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE PRODUCT PBODUCT PBODUCT PBODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 14.449 14.261 0 0 2 .72 30.756 30.355 0 0 1. 36 48.983 48.192 16.267 16. 506 0.68 4.756 4.397 41.251 41.795 0.34 0.425 1.074 15.76 15. 468 0. 17 0.201 0.601 9.306 9.122 0.085 0.081 0.456 7. 153 6.968 0.0425 0.058 0.256 4 . 008 3.913 0.0212 0.061 0.136 2.113 2.081 0.0106 0.051 0.091 1. 412 1.398 0.0053 0.058 0.074 1. 14 1.138 PAN 0.121 0. 106 1. 59 1.613 SUM= 100 SUM= 100 RESIDUAL SUfiS OF SQUARES; 0VERSI2E= 1.720 65 UNDERSIZE= 0.51761 FLOWRATES: PREDICTED; OVERSIZE= 222.189 MEASURED ; OVERSIZE= 219.3 UNDERSI2£= 340.603 UNDEBSIZE= 343.5 OPERATING CONDITIONS; APEBTUBE= 1.27 % +1 INCH IN FEED= 17.94 FEEDBATE= 562.8 (CM.) - 227 -(TPH) BUN HUHBEB= 8 PARAMETER X50= 1.780231 PARAMETER A= 1.714055 SIZE MEASURED PREDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 1.000032 1 2.72 1.00001S 1 1.36 0.6801734 0.7025081 0.68 0.0391924 0.0588161 0.34 0.0249785 0.0381724 0.17 0.0281663 0.0361426 0.085 0.0 452757 0.0358962 0.0425 0.0545389 0.0358656 0.0212 0.053649 0.0358617 0.0106 0.0 747393 0.0358613 0.0053 0.0849185 0.0358612 PAN 0.062204 5 3.586119E-2 RESIDUAL SUE SQUARES 3 6 .486773E-3 SIZE MEASURED PREDICTED MEASURED PREDICTED (CM.) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE PRODUCT PRODUCT PRODUCT PRODUCT 2 1. 76 0 0 0 0 10.88 0 0 0 0 5.44 18.156 17.791 0 O 2.72 39.94 39.137 0 0 1.36 39.139 39.612 21.122 20. 12 0.68 1.597 2.348 44.933 45. 076 0.34 0.325 0. 487 14.559 14.709 0. 17 0.182 0.229 7. 207 7.32 0.085 0. 137 0. 106 3.315 3.429 0.0425 0.114 0.073 2. 269 2.369 0.0212 0. 102 0.067 2. 064 2.154 0.0106 0. 1 0.047 1. 421 1.516 0.0053 0.099 0.041 1. 224 1.321 PAN 0. 109 0.062 1. 886 1.986 SUM= 100 SUM 3 100 RESIDUAL SUMS OF SQUARES: OVERSIZE 3 1.60747 UNDERSIZE 3 1 . 1 1887 FLOWRATES : PREDICTED; O V E R S I Z E 3 152.259 UNDERSIZE 3 126 .9 42 MEASURED : OVER S I Z E 3 149.2 UNDERSIZE 3 130 OPERATING CONDITIONS: APERTURE 3 1.27 % +1 INCH IN F E E D 3 31.05 FEEDRATE 3 279.2 (CM.) (TPH) - 228 -RUN NUMBER= 9 PARAMETER X50= 1.914758 PARAMETER A= 2.280206 SIZE MEASURED PREDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 1.000031 1 2.72 1 1 1.36 0.491682 0.5103823 0.68 0.0535862 0.0636451 0.34 0.0297572 0.0460911 0.17 0.0316405 0.0442514 0.085 0.023121 0.0440264 0.0425 0.0184924 0.0439984 0.0212 0.0405413 0.0439949 0.0106 0.0498509 0.0439944 0.0053 0.0636978 0.0439944 PAN 0.0691986 4.399436E-2 RESIDUAL SUM SQUARES= 3 .03401E-3 SIZE MEASURED PREDICTED MEASURED PREDICTED (CM.) OVERSIZE OVERSIZE UNDEBSIZE UNDERSIZE PRODUCT PRODUCT PRODUCT PRODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 16.127 15.791 0 0 2.72 47.041 46.064 0 0 1.36 33.095 33. 64 29.791 29. 235 0.68 2.321 2.699 35.6 93 35.977 0.34 0.502 0.761 14.251 14.275 0.17 0.221 0.303 5. 89 5.922 0.085 0. 107 0.2 3. 936 3.925 0.0425 0.059 0. 137 2.726 2.706 0.0212 0.104 0.111 2. 143 2.176 0.0106 0.098 0.085 1.626 1 .667 0.0053 0.127 0.086 1. 625 1.691 PAN 0. 198 0. 123 2.319 2.427 SUM= 100 SUM= 100 RESIDUAL SUBS OF SQUARES: OVERSIZE= 1.60408 UNDERSIZE = 0 .41089 FLQWRATES : PREDICTED: OVERSIZE= 477.317 UNDERSIZE= 526 .893 *3EASURED : OVERSIZE= 467.402 UNDESSIZE= 536 .8 OPERATING CONDITIONS: APESTURE= 1.59 % +1 INCH IN FEED= 29.4 FEEDRATE= 1004.202 (CM.) (TPH) - 229 -RON NUMBER— 10 PARAMETER X50= 2.024891 PARAMETER A= 2.116617 SIZE MEASURED PREDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 0.9999835 1 2.72 0.999999 1 1.36 0.3635017 0.3632929 0 .68 0.0261914 0.0292463 0.34 0.0249406 0.0204327 0.17 0.0210775 0.0195329 0.085 0.0210073 0.0194232 0.0425 0.0247881 0.0194095 0.0212 0.030146 0.0194078 0.0106 0.025807 0.0194076 0.0053 0.0476844 0.0194076 PAN 0.06771O9 1.940757E-2 RESIDUA! SUM SQUARES 3 3 .352573E-3 SIZE MEASURED PREDICTED MEASURED PREDICTED (CM.) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZE PRODUCT PRODUCT PRODUCT PRODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 22.06 9 22.112 0 0 2.72 55.515 55.622 0 0 1.36 20.364 20.392 32.3 45 32. 299 0. 68 0.981 1.098 33.084 3 2. 92 4 0.34 0.325 0.267 11.526 1 1.559 0. 17 0.159 0.148 6.699 6.697 0.085 0.106 0.098 4.48 1 4.48 0.0425 0. 101 0.079 3. 605 3.618 0.0212 0.09 0.058 2. 626 2.651 0.0106 0.072 0.0 54 2.466 2.477 0.0053 0. 079 0.032 1.432 1.471 PAN 0. 139 0.04 1. 73 6 1.823 SUM 3 100 SUM 3 100 RESIDUAL SUFiS OF SQUARES; OVERSIZE 3 0.04514 UNDERSIZE 3 0. 0 3866 FLOWRATES ; PREDICTED: O V E R S I Z E 3 236.742 UNDERSIZE 3 261. 95 MEASURED : O V E R S I Z E 3 237.2 UNDERSIZE= 261. 5 OPERATING CONDITIONS: APERTURE 3 1.59 % +1 INCH IN F E E D 3 36.9 FEEDRATE 3 498. 7 (CM.) (TPH) RUN NUMBER3 11 PARAMETER X50= 2.035057 - Z6\J -PARAMETER A 3 2.123725 SIZE MEASURED PREDICTED (CM.) Y O/S Y O/S 21.76 1 1 10.88 1 1 5.44 0.9999554 1 2.72 0.9999877 1 1.36 0.3556336 0.3501449 0.68 0.0244809 0.0279286 0,34 0.0218135 0.0 195277 0. 17 0.02481 0.0186698 0.085 0.0231142 0.0185652 0.0425 0.0248753 0.0185522 0.0212 0.0369008 0.0185505 0.0106 0.0 422778 0.0185503 0.0053 0.0523885 0.0185503 PAN 0.0568664 1.855029E-2 RESIDUAL SUB SQUARES 3 3 .658492E-3 SIZE MEASURED PREDICTED MEASURED PREDICT EI (CM.) OVERSIZE OVERSIZE UNDERSIZE UNDERSIZl PRODUCT PRODUCT PRODUCT PRODUCT 21.76 0 0 0 0 10.88 0 0 0 0 5.44 20.077 20.206 0 0 2.72 54.982 55.333 0 0 1.36 22.773 22. 564 34.39 3 4. 5 0.68 0.967 1.11 32.1 15 31. 834 0. 34 0.305 0.275 11.399 1 1.366 0.17 0. 183 0. 139 5. 995 6.001 0.085 0.1 17 0.095 4. 121 4. 119 0.0425 0. 113 0.085 3.691 3.696 0.0212 0. 116 0.059 2. 524 2.558 0.0106 0.113 0.05 2. 133 2.175 0.0053 0.0 96 0.034 1. 448 1.491 PAN 0. 158 0.052 2. 184 2.261 SUM 3 100 SUM 3 100 RESIDUAL SUBS OF SQUARES: OVERSIZE 3 0.23007 UNDERSIZE 3 0. 10316 FLOWRATES : PREDICTED: OVER S I Z E 3 119.838 UNDERSIZE 3 145. 4 66 MEASURED : O V E R S I Z E 3 120.601 UNDERSIZE 3 144. 701 OPERATING CONDITIONS: APERTURE 3 1.59 % +1 INCH IN F E E D 3 34.12 FEEDRATE 3 265. 302 (CM.) (TPH) ^ ?STOPI ^ 1 AT LINE "590" IN PROGRAM "SCRN3" + ? PROGRAM E1IDS - 231 -APPENDIX I SUMMARY OF PRIMARY FINES MODEL L i s t i n g o f the Model F i t t i n g Program TURKEY L i s t i n g o f the Primary Fines Mode l , PF Output from PF - Model P r e d i c t i o n s f o r Observed Data - 232 -1 * * * PROGRAM: TURKEY :PRIMARY FINES MODEL FITTING VERSION 2 * 3 * 2 9 DIM N (3, 10) , J (2 2) 30 DIM A(1,22) ,D{1,22) ,X(22 ,22) , Z (1,22) ,Y (22,1) ,Q{22,22) 33 DIM K(22) , V (22) ,S (22) ,H{22) ,G{22) , R(22) 36 DIM P(15 , 15) , F (15,15) , T (15, 15) , H (15, 1) 3 8 READ N1,N2,A3 7 0 MAT P=ZER(N2,A3) 80 MAT F=ZER{N2,A3) 110 MAT Z=ZEE(1,N1) 120 MAT Y=ZER(N 1*1,1) 130 MAT D=ZER (1,N1) 140 MAT X=ZER (N1+1,N1) 150 MAT Q=ZER (N1 + 1 , N1) 171 F I L E PFSD 172 MAT READ F I L E 1,T(N2,A3) 173 FOR J=1 TO N1 175 READ A (1, J) 178 NEXT J 182 READ A2,S1,M3 184 READ A 1 , B 1 , V 1 , G 2 , M 2 186 FOR 1=1 TO H2 188 S (I) =S 1 *A2** ( I - 1) 190 NEXT I 192 S2=SQR (S (1) *S (2) ) 208 * INITIAL VALUES INPUTTED 210 * CALCULATION OF INITIAL STARTING VALUES 215 FOR 1=1 TO N1 220 D (1,I)=ABS(G2*A (1,1)) 225 NEXT I 230 * SET UP INITIAL SIMPLEX 240 FOR J=1 TO N1 250 FOR 1 = 1 TO J +1 260 I F I=J+1 THEN 290 270 X ( I , J ) = A (1,J) - (2/{J+1) ) *D (1, J) 280 GO TO 300 290 X (I ,J)=A (1,J) + ( (2/(J+1) ) *D (1,J) *J) 300 NEXT I 310 FOR I = J+2 TO N1+1 320 X ( I , J) = A (1 , J) 330 NEXT I 340 NEXT J 350 * CALCULATION OF STD. DEV'N OF OBJECTIVE FUNCTION 360 Z8=0 361 Z9=0 370 T3=1. E70 3 80 FOR 1=1 TO N1+1 3 90 H=I 400 GO SUB 1310 410 Y (I,1) = Y1 4 20 NEXT I 430 GO SUB 1720 440 T1=0 441 T2=0 445 FOR 1=1 TO N1+1 450 T1=T1+Y (1,1) 455 NEXT I 460 T1=T1/(N1+1) 4 65 FOR 1=1 TO N1+1 - Z66 -470 T2=T2+ (Y ( I , 1) -T1) **2 480 NEXT I 490 T4=SQR (T2/N1) 500 I F T4>1.E-6 THEN 730 5 10 GO TO 590 520 * PRINTOUT SECTION 530 PRINT 540 PRINT "CYCLE LIMIT STOP CRITERION = ";M 2;"STD.DEVIATION=" ; T4 550 PBINT 560 PRINT"HIGH=";Y (H, 1} ,"2ND HIGH=";Y (S,1) ,"LOW=" ; Y (L , 1) 570 PRINT 580 GO TO 600 590 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE OF";Y{L,1 ) 5 93 PRINT 5 95 PRINT "STANDARD DEVIATION=";T4 6 00 H=L 610 GO SUB 1310 6 20 PRINT 630 PRINT 6 35 PRINT " EQUATION CONSTANTS " 6 42 PRINT "A1 = ";X(H,1) , "A2 = " ; X (H, 2) ,"A3 = ",-X (H,3) , "A4=";X (H,4) 645 PRINT 650 PRINT "B1=";X(H,5) ,"B2=";X (H,6) ,"B3 = " ; X ( H ,7) , "B4= "; X <H, 8) 652 PRINT 655 PRINT "C1 = " ;X(H,9) , "C2=" ; X (H , 10 ) 662 PRINT 672 PRINT 6 90 PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS="; Z9 700 FOR 1=1 TO A3 702 I F 1=2 THEN:I=3 7 03 PRINT " # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # » 704 A9=0 705 PRINT 706 PRINT "RUN N O . " ; I 707 PRINT 708 PBINT "B=";H(I) ,"X 0=";R(I) ,"X 50=";G{I) 709 PBINT 710 PRINT 711 PRINT " S I Z E " , " M E A S . P R O D . " , " P R E D . P R O D . " , " D I F F E R ENC E» 712 PRINT 713 FOB J=1 TO N2-1 714 PRINT S{J + 1) , T ( J , I ) f P { J / I ) , T ( J , I ) - P ( J , I ) 7 16 A9=A9+ (T ( J , I ) -P ( J , I ) ) **2 718 NEXT J 719 PBINT "PAN" , T ( N 2 , I ) , P ( N 2 , I ) , ( T ( N 2 , I ) - P { N 2 , I ) ) 720 PBINT 721 A9=A9+<T(N2,I)-P(N2,I) ) **2 722 PRINT "RESIDUAL SUM SQUABES=";A9 723 PBINT 724 NEXT I 729 STOP 730 I F Z9>H2 THEN 530 732 I F Z9>M3 THEN 736 734 GO TO 745 736 M3=M3+300 745 I F T4>T3 THEN 770 75 0 T3=T4 760 * REFLECTION 770 MAT Q = (1) *X 780 FOB J = 1 TO N1 - 234 -790 P1=0 800 FOR I = 1 TO N1+1 8 10 I F I = H THEN 830 820 P1=P1+X ( I ,J ) /N1 830 NEXT I 8 40 Z (1,J) = (1+A 1) *P1-A1*X (H,J) 850 X (H,J)=Z (1 , J) 860 D (1,J)=P1 8 70 NEXT J 880 GO SUB 1310 890 MAT X = (1) *Q 900 Y=Y1 910 I F Y>=Y(L,1) THEN 1000 920 * EXPANSION 930 FOR J = 1 TO N1 940 X (H,J) = (1+V1) * Z ( 1 , J ) - V 1 * D (1 , J ) 950 NEXT J 960 GO SUB 1310 970 I F Y1>Y(L,1) THEN 1010 980 Y (H, 1) -Y1 990 GO TO 430 1000 IF Y>Y(S,1) THEN 1060 1010 Y{H,1)=Y 1020 FOR J=1 TO N1 1030 X (H,J)=Z (1,J) 1040 NEXT J 1050 GO TO 430 1060 I F Y>Y ( H f 1) THEN 1120 1070 FOR J = 1 TO N1 1080 X(H,J )=Z (1,J) 1090 NEXT J 1 100 Y(H,1)=Y 1110 * CONTRACTION 1120 FOR J=1 TO N1 1 130 X (H, J)=B1*X (H, J) + (1-.B1) *D (1, J) 1 140 NEXT J 1150 GO SUB 1310 1160 I F Y1>Y(H,1) THEN 1200 1170 Y{H,1)=Y1 1 180 GO TO 430 1190 * REDUCE SIZE OF SIMPLEX 1200 FOR J=1 TO N1 1210 FOR 1=1 TO N1+1 1220 X ( I , J ) ={Q(I,J) +Q ( L , J ) ) /2 1230 NEXT I 1240 NEXT J 1250 Z8=Z8+1 1260 PRINT 1270 PRINT "STEP CHANGE";Z8 1280 PRINT 1290 GO TO 380 1300 * ESTIMATION OF NEW VALUES FOR UNKNOWNS 1305 *PREDICTION OF FINAL PRODUCT 1310 F2=0 1311 FOR K=1 TO A3 1312 I F K=2 THEN:K=3 1313 A21=100 1314 H (K) =X (H, 1} +X (H,2) *K*X tH,3) *K**2 + X (H ,4) *K**3 1315 G (K) =X (H,5) +X (H,6) *K + X <H,7) *K**2+X (H,8) *K**3 1316 I F H(K)<0 THEN:H (K) = ABS (H (KJ) - C30 -1 3 1 7 H ( K ) = X { H , 9 ) +X ( H , 10) * L O G ( H (K) ) 1 3 1 8 FOR J = 1 TO 4 1 3 2 0 F ( J , K ) = 1 0 0 1 3 2 5 N E X T J 1 3 2 6 A 2 2=0 1 3 3 0 F O R - t J = 5 TO N 2 - 1 1 3 3 2 K ( J ) =H (K) * E X P (G (K) * S ( J + 1 ) ) - H (K) * E X P ( R (K) *S ( J + 1) ) 1 3 3 5 F ( J , K) = (K ( J ) / (1+K ( J ) ) ) * 1 0 0 1 3 3 7 N E X T J 1 3 3 8 P ( 1 , K ) = 0 1 3 4 0 F O R J = 2 T O N 2 - 1 1 3 4 1 P ( J , K ) = F ( J - 1 , K ) - F ( J , K ) 1 3 4 2 A 2 2 = A 2 2 + P ( J , K ) 1 3 4 4 N E X T J 1 3 4 6 P ( N 2 , K ) = 1 0 0 - A 2 2 1 5 1 0 P 1 0 = 0 1 5 1 4 A 5 0 = P ( N 2 , K ) 1 5 1 5 I F P ( N 2 , K ) < - 1 6 T H E N : A 5 0 = - 1 6 1 5 2 0 I F P ( N 2 , K ) < = 0 T H E N : P 1 0 = 2 * E X P { 1 0* ( - A 5 0 ) ) - 1 1 5 4 4 FOR J = 1 TO N2 1 5 4 9 F 2 = F 2 + (T {J, K) - P ( J , K) ) * * 2 + P 10 1 6 5 0 N E X T J 1 6 7 5 N E X T K 1 6 8 0 Y 1 = F 2 1 6 9 0 Z 9 = Z 9 + 1 1 7 1 0 R E T U R N 1 7 1 5 * O B J E C T I V E F U N C T I O N M A G N I T U D E L I S T I N G ( O R D E R S E A R C H ) 1 7 2 0 I F Y { 1 , 1 ) > Y ( 2 , 1 ) T H E N 1 7 7 0 1 7 4 0 S=1 1 7 4 1 L = 1 1 7 5 0 H=2 1 7 6 0 GO T O 1 7 9 0 1 7 7 0 S = 2 1 7 7 1 L = 2 1 7 8 0 H=1 1 7 9 0 F O R 1 = 3 TO N1+1 1 8 0 0 I F Y ( I , 1) > Y ( L , 1 ) T H E N 1 8 2 0 1 8 1 0 L = I 1 8 2 0 I F Y ( I , 1) <Y ( S , 1) T H E N 1 8 8 0 1 8 3 0 I F Y ( I , 1) <Y ( H , 1) T H E N 1 8 7 0 1 8 4 0 S=H 1 8 5 0 H = I 1 8 6 0 GO TO 1 8 8 0 1 8 7 0 S = I 1 8 8 0 N E X T I 1 8 9 0 R E T U R N 1 8 9 5 D A T A 1 0 , 1 4 , 7 1 8 9 8 D A T A 2 . 9 9 6 4 3 3 , - 2 . 3 9 1 7 8 4 , . 6 2 1 6 0 0 8 , - 4 . 9 5 0 0 9 3 E - 2 1 8 9 9 D A T A 1 . 4 4 0 1 6 7 , . 6 2 0 9 3 4 5 , - . 1 8 8 5 8 6 5 , 1 . 5 0 1 7 5 9 E - 2 1 9 0 0 D A T A - 3 . 8 7 5 7 , 4 . 9 5 1 9 0 1 D A T A . 5 , 4 3 . 5 2 , 1 0 0 0 1 9 5 0 D A T A 1 , . 5 , 2 , . 0 1 , 1 0 2 0 0 0 E N D E N D - O P - ' F I L E - Z6b -1 * * * PROGRAM: PF ;PRIMARY FINES MODEL 2 * 3 * 10 DIM S (15) , H (15) , G (15) ,R (15) , K (22) 20 DIM P(15,15) , T { 1 5 , 15) ,V (22) , J(22) ,B(60) 30 READ N2,A3 35 DATA 14,7 40 MAT P=ZER(N2,A3) 52 X0=-1 54 B0=83.88 56 A0=248. 71 60 F I L E PFSD,CONST 62 FOR J=1 TO 56 64 READ F I L E 2 ,B(J) 66 NEXT J 70 MAT READ F I L E 1 ,T(N2,A3) 110 READ A2,S1 115 DATA . 5 , 4 3 . 5 2 120 FOR J=1 TO N2 130 S(J)=S1*A2**(J-1) 140 NEXT J 3 00 FOR K=1 TO A3 310 IF K=2 THEN;K=3 330 H (K) = ABS (B (47) +B(4 8) *K+B{49) *K**2+B(50) *K**3) 340 G (K) = B (51) + B{52) *K+B (53)*K**2 + B (54) *K**3 360 R (K)=B(55) +B(56) *LOG(H (K) ) 370 A22=0 410 FOR J=1 TO N2-1 420 K (J) =H (K) *EXP (G (K) *S (J + 1) ) - H (K) *EXP (R (K) *S(J+ 1) ) 430 7 (J) = (K ( J ) / ( 1 + K (J)} ) *100 435 I F J=1 THEN 460 440 P (J ,K) =V ( J - 1 ) - V (J) 450 A22=A22 + P (J,K) 46 0 NEXT J 470 P(1 ,K) =100-V (1) 480 P(N2 f K)=1O0-A22 485 FOR J=1 TO N2 4 90 P ( J , K ) = I N T ( P ( J , K ) *100 + . 5 ) / 1 0 0 495 NEXT J 510 NEXT K 620 PRINT 630 PRINT 6 35 PRINT " EQUATION CONSTANTS " 642 PRINT "A1 = " ; B (47) , " A2=" ; B (48) , 1 1 A 3="; B (49) , " A 4 = » ; B (50) 64 5 PRINT 650 PRINT "B1 = ";B(51) , "B2="; B (52) , " B3= 0 ; B (5 3) ,"B4=";B (54) 652 PRINT 655 PRINT "C1=";B(55) ,"C2=";B(56) 662 PRINT 670 FOR 1=1 TO A3 6 80 I F 1=2 THEN:1=3 730 A9=0 740 PRINT 750 PRINT "RON NO. = " M 760 PRINT 770 PRINT "B=";H(I) ,"X 0=";R(I) ,"X 50=";G(I) 780 PRINT 790 PRINT 800 PRINT " S I Z E " , " M E A S . P R O D . " , " P R E D . P R O D . " , " D I F F E R E N C E " 810 PRINT - LSI -820 FOB J=1 TO N2-1 830 PBINT S (J+1) , T (J , I ) ,P ( J , I ) , T ( J , I ) - P (J , I ) 840 A9 = A9+ ( T ( J , I ) - P (J , I ) ) **2 850 NEXT J 860 PRINT "PSN",T (N2,I) , P ( N 2 , I ) , T (N2,I ) -P (N2,I) 870 PRINT 880 A9=A9+(T(N2,I) -P(N2,I) ) **2 890 PRINT "RESIDDAL SUM OF SQUARES=";A9 900 PRINT 902 GO SUB 2500 904 PRINT "FLOWRATE (AVERAGE OVER DAY IN TPH)=";Q 906 PBINT 9 07 PRINT " . . . . . . . . . . . . . . . . . . . . . . . , . . . . . , . . . " 910 NEXT I 2500 I F X0>=0 THEN 2540 2510 X30=X0 2520 GO SUB 2630 2530 X0=B30 2540 X30=0 2550 GO SUB 2630 2560 X10=R30 2570 X30=0 2580 GO SUB 2630 2590 X20=R30 26 00 Y0=SQR (-2*LOG (X10) ) * (COS (6. 2 83184*X2 0) ) 2610 Q=A0+Y0*BO 2620 BETUBN 2630 IF X30<0 THEN 2680 2640 R10=B0*R30 2650 R20=R10-INT(R10/B10)*B10 2660 R30=R20/B10 2670 RETURN 2680 R0=7E13 2690 B10=10**9.03089987 2700 R30=-X30 2710 GO TO 2640 3000 END E N D - O F - F I L E i e v i c e : DS24 t a s k : 31 USERID: RALU 10:19:33 09-08-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS24 t SIGN R ALU t ENTER USER PASSWORD. t * * L A S T SIGNON WAS: 10:16:35 \ USER "RALU" SIGNED ON AT 10:18:28 ON THU SEP 08/77 \ RUN *BASIC \ EXECUTION BEGINS ?UBC BASIC SYSTEM • ?  : GET PF RUN t a s k : 31 EQUATION CONSTANTS A1= 3. 225629 A 2= -2.263788 A3= 0.5387101 A4= B1 = 1.146159 B2= 0.72933 C1= -4.491863 C2= 5.034085 B3= - 0 . 1 8 2 9 8 5 6 B4 = -4 .088134E-2 1.339609E-2 RUN NO.= 1 B= 1. 45967 X 0= - 2 . 587921 X 50= 1.705899 S I Z E 21.76 10. 88 5.44 2.72 1.36 0. 68 0. 34 0. 17 0.085 0.0425 0.02125 0. 010625 0.0053125 PAN M E A S . PRO D. 0 0 0 0 6 13 15 15 15. 5 14 9.9 6.2 3.55 1. 8.5 PRED. PROD, 0 0 0.01 0.65 5.67 12. 18 14. 82 16. 42 16.23 13.29 9.09 5. 44 3 3.22 R E S I D U A L S U M O F S Q U A R E S = 7.7028 F L O W R A T E ( A V E R A G E O V E R DAY I N T P H ) = 321.7097 R U N N O . = 3 B= 0.1788597 X 0= -13 .1563 X 50= 2.048973 DIFFERENCE 0 0 -0 .01 -0 .6 5 0. 33 0. 82 0. 18 - 1 . 4 2 - 0 . 7 3 0.71 0. 81 0. 76 0. 55 - 1 . 3 7 SIZE 21 .76 10.88 MEAS. PROD. 0 0 PR ED.PROD. 0 0 DIFFERENCE 0 0 - 239 -5. 44 0 0.01 -0.01 2.72 0 2.07 -2.07 1. 36 22 23.55 -1.55 0.68 31 32. 5 -1.5 0. 34 15.5 15. 57 -0.07 0.17 9 7.32 1. 68 0. 085 8 5.6 2. 4 0.0425 5.9 4.88 1.02 0.02125 3.9 3.59 0.31 0.010625 2.4 2.25 0. 15 0.0053125 1.34 1.27 0. 07 PAN 0.96 1. 38 -0.42 RESIDUAL SUM OF SQUARES= 18.8651 FLOWRATE (AVERAGE OVER DAY IN TPH)= 293.4845 RUN NO.= 4 B= 0.1734328 X 0= -13.31 14 X 50= 1.993 059 SIZE MEAS.PRO D. PRED, PROD. DIFF ERENCE 21.76 0 0 0 10.88 0 0 0 5.44 0 0.01 -0.01 2. 72 0 2.48 -2.48 1.36 33 25. 23 7.77 0. 68 34 32.07 1. 93 0.34 10. 2 14. 86 -4.66 0. 17 6 6.96 -0.96 0.085 4.8 5. 38 -0.58 0.0425 3. 1 4.73 -1.63 0.02125 2.9 3.5 -0.6 0.010625 2.6 2. 19 0. 41 0.0053125 1.85 1. 24 0.61 PAN 1.55 1. 35 0.2 RESIDUAL SUM OF SQUARES= 96.819 FLOWRATE (AVERAGE OVER DAY IN TPH)= 288.0897 RUN NO.= 5 B= 0.264274 X 0= -11.19107 X 50= 1.89268 SIZE MEAS.PROD. PRED.PROD., DIFFERENCE 2 1.76 0 0 0 10.88 0 0 0 5. 44 0 0.01 -0.01 2.72 0 2. 14 -2.14 1. 36 22 20. 24 1. 76 0.68 29 28.71 0.29 - Z4U -0. 34 15 15.7 - 0 . 7 0. 17 10.7 8. 67 2. 03 0. 085 7.5 7. 3 0. 2 0.0425 5.6 6.35 - 0 . 7 5 0.02125 3.8 4.63 -0 .83 0.010625 2.7 2.88 - 0 . 1 8 0. 0053 125 1.95 1.62 0.33 PAN 1.75 1. 76 - 0 . 01 RESIDUAL SUM OF SQUARES= 13.8051 FLOWRATE (AVERAGE OVER DAY IN TPH)= 283.6669 RUN NO.= 6 B= 0.2060952 X 0= -12 .44 278 X 50= 1.828213 SIZE MEAS. PROD. PflED.PROD. DIFFERENCE 21.76 0 0 0 10. 88 0 0 0 5.44 0 0.02 - 0 . 0 2 2.72 0 3. 23 -3 .23 1.36 25 25. 51 -0 .51 0.68 26 29. 57 - 3 . 5 7 0.34 13. 5 14. 1 - 0 . 6 0. 17 9.5 7. 17 2. 33 0.085 7.8 5,94 1. 86 0.0425 5.9 5. 27 0. 63 0.02125 4.7 3.89 0. 81 0.010625 3.5 2. 44 1. 06 0.0053125 2.3 1.37 0. 93 PAN 1.8 1.5 0.3 RESIDUAL SUM OF SQUARES^ 35.8183 FLOWRATE (AVERAGE OVER DAY IN TPH)= 219.4101 RUN NO.= 7 B= 0.2463917 X 0= -11.54377 X 50= 1.880033 SIZE MEAS.PROD. PRED. PROD. DIFFERENCE 2 1.76 0 0 0 10.88 0 0 0 5. 44 0 0.01 - 0 . 0 1 2.72 0 2.37 - 2 . 3 7 1.36 23 21.56 1. 44 0.68 25 29. 12 -4 .12 0.34 13 15. 34 - 2 . 3 4 0. 17 10 8.26 1.74 0.085 8.5 6.91 1. 59 0.0425 6.3 6.04 0.26 i - t I 0.02125 0.010625 0.0053125 PAN 5.3 3.9 2.7 2.3 4.41 2.75 1.55 1. 68 0. 89 1. 15 1. 15 0.6 2 RESIDUAL SUM OF SQUARES= 39.5854 FLOWRATE (AVERAGE OVER DAY IN TPH) = 355.3625 ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FORM=8X11 •PRINT* ASSIGNED RFS NUMBER 663938 $C *S0URCE*3SP *PRINT* - 242 -APPENDIX J SECONDARY CRUSHING PLANT SIMULATION PROGRAMS (a) L i s t i n g o f the S imu la t i on Program M2 ( i ) Main Program M2 ( i i ) Subprogram SCMS (Secondary Crusher) ( i i i ) Subprogram TCMS ( T e r t i a r y Crusher) ( i v ) Subprogram PRNT1 ( P r i n t o u t ) (v) Subprogram PRNT2 ( P r i n t o u t ) (b) Sample Outputs from Program M2 (2) (c) L i s t i n g o f the S imu la t i on Program PGM2 (d) Sample Outputs . f rom Program PGM2 (2) - £ t J -1 * * * PROGRAM: M2 :CRUSHING PLANT SIMULATION PROGRAM 2 * 3 * 10 * * DATA INPUT SECTION * * 20 DIM A(1,20) f D(1 ,20) , E (20,30) 30 DIM R (20) , V (20) , Y (20) ,F(30) 40 DIM S(20) ,T{20) , L (30) ,M (20) , N (20) , G (2 0) ,H (2 0) , J (20) , K (20) 50 DIM P(20) ,0(15) 70 READ S1 ,R1 ,P (10) ,P (7) ,P (8) ,P{9) , P (13) ,P (14) 80 DATA 4 3 . 5 2 , . 5 , 1 4 , 2 , 5 , 4 , 5 0 , . 0 1 90 F I L E X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 100 MAT E=ZER{P(10) ,24) 130 PRINT "ENTER PLANT FEEDRATE (STPH) " 140 INPUT L{1) 150 PRINT 160 FOR J=1 TO P(10) 170 READ E ( J , 1 ) 175 NEXT J 180 DATA 3 , 3 5 , 3 6 . 5, 18. 3 5 , 4 . 7 , . 9 4 , . 2 9 , . 2 2 , . 17 , . 17 , . 18 , . 16 , . 1 3 , . 19 185 FOR J=1 TO 9 187 READ F(J ) 189 NEXT J 191 DATA 1.238414, . 4822109, - 1. 00 2221E-2, 1. 163871E-7, 6. 543503 193 DATA - 7 . 3 4 2 1 3 9 , 2 . 8 5 5 7 7 6 , - 4 . 6 4 8 8 1 E - 5 , - 1 . 3 0 3 6 5 5 E - 2 2 220 FOR J=1 TO (P{7) +P (8) +P (9) ) 230 READ M(J) 235 WRITE F I L E 4,M(J) 240 NEXT J 260 RESTORE F I L E 4 280 PRINT "ENTER SECONDARY CRUSHER GAPS (CM.)" 285 FOR J = 1 TO P(7) 290 INPUT N(J) 29 5 NEXT J 300 PRINT "ENTER SECONDARY SCREEN OPENINGS (CM.)," 305 FOR J=(P{7)+1) TO (P(7)+P{8)) 310 INPUT N(J) 315 NEXT J 320 PRINT "ENTER TERTIARY CRUSHER GAPS (CM.)" 325 FOB J= (P (7)+P (8)+1) TO (P (7)+P (8)+P{9) ) 330 INPUT N<J) 333 NEXT J 34 0 PRINT 345 PBINT "**************************#*#***^ 350 FOR J=1 TO (P{7)+P (8)+P (9) ) 355 WRITE F I L E 5 ,N(J) 36 0 NEXT J 365 RESTORE F I L E 5 37 0 FOR J=1 TO P(10) 380 S (J)=S1*R1** (J-1) 390 NEXT J 400 P (12)=SQB (S (1) *S (2) ) 410 FOR J=1 TO P (10) -1 420 T(J)=P( 12) *R1** (J-1) 43 0 NEXT J 43 2 FOR J=1 TO P{10) 433 W R I T E F I L E 2 ,S (J ) 434 NEXT J 436 RESTORE F I L E 2 440 FOR J=6 TO P{10) - 244 -450 P{6) =P (6) +E ( J , 1) 460 NEXT J 47 0 P{15)=0 48 0 * * SECONDARY CRUSHER SECTION * * 490 HAT A=ZER(1,P(10)) 495 P(1)=0 50 0 FOR J=1 TO 4 505 P(1)=P(1) + E ( J , 1 ) 510 NEXT J 515 MAT WRITE F I L E 1 , E 52 0 RESTORE F I L E 1 525 L(4)=0 53 0 FOR 1=1 TO P(7) 532 L (1+1) =L (1) *M (I) 544 WRITE F I L E 3 , L (1 + 1) 54 6 RESTORE F I L E 3 548 P{1 1) =1 550 WRITE F I L E 7 , P { 1) ,P ( 10) , P (1 1) , P ( 1 2) 55 2 RESTORE F I L E 7 555 CALL SCMS 55 8 MAT READ F I L E 1 ,E 55 9 RESTORE F I L E 1 560 FOR J=1 TO P(10) 570 A (1 , J) =A (1, J) + E ( J , 1 + 1) * L (1 + 1) 580 NEXT J 585 L (4)=L (4)+L (1+1) 590 NEXT I 600 FOR J=1 TO P(10) 610 E(J ,4)=A (1 f J) / L ( 4 ) 620 NEXT J 625 I(22)=0 640 * * BLEND SECONDARY AND TERTIARY CROSHER PRODUCTS * * 660 L(5)=L(4) +L (22) 67 0 FOR J=1 TO P(10) 680 E (J,5) = (E (J,4) * L (4) + E (J,22) * L (22) ) / L (5) 690 NEXT J 730 * * SECONDARY SCREENS SECTION * * 740 L(17)=0 750 L(11)=0 755 P{2)=0 76 0 FOR J=1 TO 4 770 P(2)=P(2)+E(J ,5) 78 0 NEXT J 800 MAT A=ZER (1 r P (10) ) 810 MAT D=ZER(1,P (10) ) 82 0 FOR 1=1 TO P(8) 830 L(23+I)=L<5) *M (2 + 1) 840 GOSUB 3860 850 FOR J=1 TO P(10) 86 0 A (1 , J ) = A (1, J) +E ( J , 11+1) *L{1 1 + 1) 870 D (1 »J) =D (1,J) +E(J ,5*I) * L (5 + 1) 880 NEXT J 890 L(17)=L(17) +L(11+I) 900 1(1 1) = L (11) +L (5 + 1) 910 NEXT I 912 I F L{17)<=0 THEN:L{17)=1 914 IF L(11)<=0 THEN:L(11) = 1 92 0 FOR J=1 TO P(10) 930 E(J ,17 ) =A (1 r J ) / L (17) 940 E ( J , 1 1 ) = D ( 1 r J ) / L ( 1 1 ) - 245 -950 NEXT J 96 0 P(4)=0 970 FOB J=6 TO P(10) 980 P (4)=P{4) + E ( J , 1 1) 990 NEXT 3 1000 * * CALCULATION OF CONVERGENCE CRITERION ** 1010 P(15)=P(15) +1 1020 I F ABS (L (1) -L{11) ) <P(14) THEN 1240 1030 I F P(15)>=P(13) THEN 1240 1040 * * TERTIARY CBUSHEB SECTION * * 1050 L(22) =0 1060 P{3)=0 1070 FOR J=1 TO 4 1080 P (3) = P (3) + E ( J f 17) 1090 NEXT J 1100 MAT A=ZER (1,P (10) ) 1102 FOR 1=1 TO P(9) 1103 P(11)=I 1104 L ( 17+1) =L (17) *M (7+1) 1106 WRITE F I L E 7 ,P (3) r P (10) , P (11) , P (12) 1108 RESTORE F I L E 7 1110 MAT WRITE F I L E 1,E 1112 RESTORE F I L E 1 1114 WRITE F I L E 3,L(17+I) 1116 RESTORE F I L E 3 1130 CALL TCMS 1135 MAT READ F I L E 1 ,E 1136 RESTORE F I L E 1 1140 FOR J=1 TO P (10) 1150 A(1 ,3)=A (1 ,J )+E (J,17*1)*1(17+1) 1160 NEXT J 1170 L(22)=L{22)+L(17+I) 1180 NEXT I 1190 FOR J=1 TO P(10) 1200 E (J ,22) =A (1, J) / L (22) 1210 NEXT J 1220 GO TO 660 1230 * * PRIMARY FINES BLENDING SECTION * * 1240 GO TO 1255 1250 *PUT A GOSUB COMMAND TO PRIMARY FINES MODEL HERE 1251 *NOTE:PRIMARY FINES MODEL NOT INCLUDED IN THIS PROGRAM 1255 L(23)=0 1260 L(29)=L (11)+L(23) 1270 FOR J=1 TO P (10) 1280 E (J r 24) = (E ( J , 11) *L(11) * E ( J , 23) * L (23)) / L (29) 1290 NEXT J 1330 FOR J=6 TO P(10) 1340 P (5) =P{5) +E(J,24) 1350 NEXT J 1355 GO TO 4590 3859 * * SECONDARY SCREENS SUBROUTINE * * 3860 Z8=F(1) +F (2) *N (2+1) **2 + F{3) *P (2) +F{4) *L(23+I) **2 3880 Z9=F(5) +F(6) *N (2+1) +F(7) *N(2 + I) **2 + F(8)*P (2)**2+F (9) *L(23+I) **7 3890 FOR J=1 TO P (10)-1 3900 Y (J) = 1/(1+EXP{ (Z9**3-T (J) **3) /Z8) ) 3910 NEXT J 3920 A3=0 3930 B3=0 3940 FOR J=1 TO P(10)-1 3950 J ( J ) = <Y (J) * L (23+1) *E(J,5) ) /100 3960 K{J)=( (1-Y (J) ) * L (23+1) * E ( J , 5 ) ) /100 39 70 A3=A3+J (J) 3980 B3=B3 + K(J) 3990 NEXT J 3995 B1 0=1/(1 + EXP (29**3/28) ) 4000 J (P (10) )= (810*L (23+1) * E (P (10) ,5) ) /100 40 10 K(P (10) ) = ( (1-B10)*L (23 + 1) * E (P (10) ,5) ) /100 4020 A3 = A3 + JfP{10) ) 4030 B3=B3+K(P{10)) 4040 L(11 + I)=A3 4045 I F A3<=0 THEN:A3=1 4050 L(5 + I) = B3 40 55 I F B3<=0 THEN:B3=1 40 6 0 FOR J=1 TO P(10) 4070 E(J r 11+I) = (J (J) /A3) *100 4080 E (J,5+1) = (K (J) /B3) * 100 4090 NEXT J 4100 RETURN 4590 FOR 1=1 TO (8+P (7) + 2*P (8) +P (9)) 45 92 FOR J=1 TO P{10) 4594 E ( J , I ) = I N T ( E (J , I ) *1 00000+. 5) /100000 4596 NEXT J 4598 NEXT I 4600 MAT WRITE F I L E 1,E 4610 RESTORE F I L E 3 4615 FOR J=1 TO (8 + P (7)+3*P (8)+P (9)) 4620 WRITE F I L E 3 , L ( J ) 4625 NEXT J 4670 P(16)=ABS (L(1)-L{11)) 46 80 RESTORE F I L E 7 46 85 FOR J=1 TO 16 4690 WRITE F I L E 7,P{J) 4695 NEXT J 4697 RESTORE F I L E 1 46 98 RESTORE F I L E 2 46 9 9 RESTORE F I L E 3 4700 RESTORE F I L E 4 4701 RESTORE F I L E 5 4702 RESTORE F I L E 6 4703 RESTORE F I L E 7 4710 CHAIN PRNT1 48 00 STOP 4810 END END-OF-FILE - £4/ -3480 DIM E{20,30) ,L(30) ,S(20) ,K(20) , J (20 ) ,R(20) 3482 DIM H (20) , V (20) , G (20) ,P (20) ,0 (15) ,N ( 1 5) ,Q (15) 34 84 F I L E X 1 , X 2 , X 3 , X 5 , X 6 , X 7 3485 READ F I L E 6 , P (1) , P { 10) , P (1 1) , P { 1 2) 34 86 RESTORE F I L E 6 34 87 I=P(11) 34 88 FOR J=1 TO 5 3489 READ F I L E 4,N (J) 3490 NEXT J 3491 RESTORE F I L E 4 3492 MAT READ F I L E 1 , E (P (10) ,24) 3493 RESTORE F I L E 1 3494 FOR J=1 TO P{10) 3495 READ F I L E 2,S (J) 34 96 NEXT J 3497 RESTORE F I L E 2 3498 READ F I L E 3,L(1+I) 34 99 RESTORE F I L E 3 35 01 FOR J=1 TO 12 3502 READ Q (J) 3504 NEXT J 3505 DATA - . 9 1 4 8 9 , . 2 1 7 2 9 , . 0 0 0 6 2 6 , . 0 0 5 6 3 4 , 4 4 . 5 8 7 5 , - 3 3 . 5 1 5 7 3506 DATA 5. 6 7 7 1 , . 1 2 2 1 , - 2 2 . 8 8 1 2 , 2 3 . 7 9 8 1 , - 3 . 7 3 1 9 , 0 2 7 9 8 3507 Z1=Q(1)+Q(2)*N(I)+Q{3) *L(1 + I) +Q(4)*P(1) 350 8 Z2=Q{5) +0 (6)*N (I) +Q (7) *N(I) **2+Q{8) *P (1) 3509 Z3=Q(9) + Q {1 0) *N (I) +Q (1 1) *N (I) **2+Q {12 ) *P (1) 3510 RESTORE 3511 L2=1 3513 L4=0 3515 FOR J=1 TO P(10)-1 352 0 L1 = 1- (1- (S (J + 1) / P (12) ) **2) **6 35 30 K(J)=L2-L1 3540 L2=L1 3550 L3=EXP(- ( (S(J+1) /2 ) **.664)) 3560 J ( J ) = L 3 - L 4 35 70 L4=L3 3580 NEXT J 35 90 FOR J=1 TO P(10) 3600 I F S(J)>Z3 THEN 3660 3610 I F S(J)<Z2 THEN 3640 3620 H (J)=S (J) - (S (J) -Z3) * * 3 / (3* ( (Z2-Z3) **2)) 3630 GO TO 3670 3640 H (J) = Z 2 - ( Z 2 - Z 3 ) / 3 3650 GO TO 3670 36 6 0 H (J)=S (J) 36 70 NEXT J 3675 R(0)=0 3678 Z20=0 36 80 FOR 0=1 TO P(10)-1 36 90 V(U) = (H(U)-H(U+1)) / (S(0) -S(U+1) ) 3710 A1=0 3720 B1=0 373 0 FOR J=1 TO 11-1 374 0 A 1 = A 1+ (Z1*K (D-J+1) + {1-Z 1) * J (U) ) *R (J) 3750 B1 = B1+J(J) 3760 NEXT J 3770 G (U) = (E (0, 1) + A 1 ) / ( 1 - (Z1*K(1) + {1 - Z 1) *{B1 + J (U) ) ) * V (U) ) 3780 R(U)=V(U)*G (0) 3790 E ( U , 1 + 1) =G (U)-R (U) 3800 Z20=Z20+E(0,1+I) - £48 -3810 NEXT U 3820 E(P(10) ,1+I) = 100-Z20 3830 0{I) =20.6182-7. 323393*N (I) + . 0345158*L (1 3836 WRITE F I L E 5,0 (I) 3840 MAT WRITE F I L E 1,E 3846 RESTORE F I L E 1 3855 RETURN END-OF- FILE 10 DIM W (30) ,K (20) , J (20) ,H {20) , V (20) , G (20) ,R (20) ,0 (15) 20 DIM E{20,30) ,P{20) ,S (20) ,L(30) ,N(15) 30 FILE X 1 , X 2 , X 3 , X 5 , X 6 , X 7 40 READ F I L E 6,P{3) , P (10) , P (11) , P ( 12) 45 RESTORE F I L E 6 50 I=P{11) 55 MAT READ F I L E 1, E (P { 1 0) , 24) 60 RESTORE F I L E 1 65 FOR 3=1 TO P(10) 70 READ F I L E 2,S (J) 75 NEXT J 80 RESTORE F I L E 2 85 READ F I L E 3,1(17 + 1) 90 RESTORE F I L E 3 95 FOB J=1 TO 11 100 READ F I L E 4 ,N(J) 105 NEXT J 110 RESTORE FILE 4 195 FOR 3=1 TO 17 197 BEAD H (9+3) 199 NEXT 3 201 DAT A. 1133812, 1. 178078E-4 , .518076 ,3 .632176E-4 ,299 .381 203 DATA 27. 4583,43. 97832, -2599.762, 16.76629 205 DATA -1 .793265 ,5 .284647E-2 206 DATA6. 331619 , - . 80409 97, 1.0 42385,2.9966 2 3 , . 7135176, 17. 9 6698 210 BESTOBE 4130 L2=1 4150 L4=0 4160 Z4=W (10) *W{1 1) * L (17+1) + (W (12) / { 1 + W (13) *{L (17 + 1) -W (14) ) **2) ) 4170 Z5=Wf15) +W(16) * E X P ( » ( 1 7 ) * Z 4 * * H ( 1 8 ) ) 4180 Z6=W (19)+W{20) *P{3) 4190 Z3 0=(W (23) / (1 + W{24) *(N (7 + 1) -W (2 5) ) **2)) **W (26 ) 4200 Z7=W (21)+W (22) *N (7+1)-Z30 4232 IF Z5<0 THEN:Z5=0 4234 I F Z5>600 THEN:Z5=600 4240 FOB 3=1 TO P(10)-1 425 0 L1 = 1-{1- (S (3+1) / P (12.) ) **4) **Z5 4260 K(3)=L2-L1 4270 L2=L1 4280 L3=EXP(- ({S(3+1)/2) * * . 664) ) 42 90 3 (3)=L3-L4 4300 L4=L3 4310 NEXT 3 4320 FOB 3=1 TO P{10) 4330 I F S(3)>Z7 THEN 4390 4340 IF S{J)<Z6 THEN 4370 4350 H (3)=S{3)- (S (3) -27) **3/(3*( (Z6-Z7)**2)) 4360 GO TO 4400 4370 H (3)=Z6-{Z6-Z7) /3 4380 GO TO 4400 4390 H (3)=S (3) 4400 NEXT 3 4410 Z20=0 44 20 FOB 0=1 TO P{10)-1 44 30 V (U)= (H (U) -H{0+1) ) / (S {0)-S {U+1) ) 4440 A1=0 4450 B1=0 44 55 B(0}=0 44 6 0 FOR 3=1 TO U-1 4470 A1=A1+ <Z4*K {U-3+1) + (1-Z4) *3 (0) ) *R (3) - £ D U -4480 B1 = B1 + J (J ) 4490 NEXT J 4500 G(0) = ( E ( U , 1 7 ) + A 1 ) / ( 1 - (Z4*K{1) +(1-Z4)* (B1+J(U) ) ) *V (0) ) 4510 R (0) = V (U) *G (D) 4520 E ( 0 , 17 + I)=G (U)-R (U) 45 3 0 Z20=Z20+E(U,17+1) 4540 NEXT U 4550 E(P(10) , 17 + 1) = 100-220 4560 0 (2 + I) = 27. 55756-9. 608871*N (7 + 1) + 5.542041E-2*L (17+1) 4565 WHITE F I L E 5,0(2+1) 4570 MAT WRITE F I L E 1 ,E 4575 RESTORE F I L E 1 45 80 RETURN END-OF— FILE - 251 -1370 DIM I (30) , E ( 2 0 , 3 0 ) , S ( 2 0 ) ,L{30) , M (15) , N (15) , 0 { 10) ,P(20) 1372 F I L E X 1 , X 2 , X 3 , X 4 , X 5 , X 6 - , X 7 1373 FOB J=1 TO 16 1374 BEAD F I L E 7,P{J) 1375 NEXT 3 1376 MAT BEAD F I L E 1 , E (P (10) ,8+P (7) + 2*P (8) *P (9) ) 1377 FOB J=1 TO P(10) 1378 BEAD F I L E 2 ,S (J ) 1379 NEXT 3 1380 FOB J = l TO 8*P (7)+3*P (8)+P{9) 1381 BEAD F I L E 3 , L ( J ) 1382 NEXT J 1383 FOB J=1 TO P (7) *P (8)+P (9) 13 84 BEAD F I L E 4 ,H(J) 1385 NEXT J 13 86 FOR J=1 TO P (7)+P (8)+P (9) 1387 READ F I L E 5 ,N(J) 13 88 NEXT J 13 89 FOR J=1 TO P(7)+P{9) 1390 BEAD F I L E 6 ,0 (J ) 1391 NEXT J 1392 IF P(16)<P(14) THEN 1420 1393 PRINT "CYCLE LIMIT SET AT";P(13),"NUMBER OF CYCLES=";P(15) 1394 PRINT » ","CONVERGENCE CRITERION^";P{16) 1410 GO TO 1460 1420 PRINT 1430 PRINT "CONVERGENCE CRIT EBION MINIMUM^";P{16) 14 40 PBINT » NUMBER OF CYCLES=";P(15} 1450 PBINT 1460 PBINT "ALL SIZE DISTRIBUTIONS MEASURED IN % RETAINED ON SIZE" 1470 PBINT 1490 PBINT " * * * * * ANALYSIS OF PLANT FEED * * * * * * 1510 PRINT "SCREEN S I Z E " , " F E E D SIZE ANALYSIS" 1530 FOB J=1 TO P{10)-1 1540 PRINT S (J+1) , E (J,1) 1550 I (23}=I (23) +E(J , 1} 1560 NEXT J 1570 PRINT "PAN",E(P (10) , 1} 1580 I(23)=I{23)+E(P(10) ,1) 1590 PBINT 1600 PBINT "SUM",1(23) 1610 PBINT 1620 PRINT "PLANT FEEDRATE ( STPH) = " ; L {1) , " » ,"% MINUS .54 INCH IN FEED = « ; P ( ( 1630 PBINT 1650 PBINT " * * * * * SECONDARY CRUSHING OUTPUT * * * * * * 1660 PBINT 1670 PBINT "NUMBER OF CRUSHERS OPERATING=";P(7) 1680 PRINT 1690 PRINT "FEED SPLIT B ATI OS=" ; M (1) , M (2 ) 17 00 PRINT 1710 PBINT "PBODUCT SIZE ANALYSES" 1730 PRINT "SIZE","CRUSHER NR.1","CRUSHES NR.2","COMBINED OUTPUT" 1750 FOB J=1 TO P{10)-1 1760 PRINT S (J + 1) , E (J,2) , E ( J , 3 ) , E ( J , 4) 1770 1(1) =1(1) +E (J ,2) 1780 I (2)=I (2) +E(J,3) 1790 I (3) =1(3) +E (J ,4) 1800 NEXT J 1810 PRINT » P A N " , E f P (10) ,2) ,E(P(10) ,3) ,E(P{10) ,4) 1820 I (1)=I(1) * E ( P ( 1 0 ) ,2) - Z5Z -1830 I (2 )=I (2 )+E(P(10) ,3 ) 1840 I(3)=I(3)+E(P(10) ,4) 1850 PRINT 1860 PRINT "SUM", 1(1) , I (2) , I (3) 1870 PRINT 1890 PRINT " "/ 'OPERATING D A T A " , " NUMBER 1", "NUMBER 2", "COMBINED" 1910 PRINT "CLOSE SIDE SETTING (IN CM.) " , N (1) , N (2) , " - " 1930 PRINT "FLOWRATES"," (IN STPH) " , L (2) , L (3) , L (4) 1950 PRINT "CURRENT DRAW","(IN AMPER ES) " ,0 (1) ,0(2) , "N. A. " 1970 PRINT 1980 PRINT " * * * * * SECONDARY SCREENING OUTPUT * * * * * " 1990 PRINT 2000 PRINT "NUMBER OF SCREENS OPERATING=";P(8) 2010 PRINT 2020 PRINT "SCREEN 1","SCREEN 2","SCREEN 3","SCREEN 4","SCREEN 5" 2030 PRINT "FEED SPLIT RATIOS" 2040 PRINT M (3) ,M (4) ,M (5) ,M (6) ,M (7) 2060 PRINT "FEEDRATES TO IN DIVIDUAL SCREENS (STPH) " 2070 PRINT L (24) , L (25) , L (26) , L (27) , L (28) 20 90 PRINT 2100 PRINT "OVERSIZE PRODUCT SIZE ANALYSIS" 2120 M5=CMD("%SET COLWIDTH=11") 2130 PRINT "SIZE","SCRN 1","SCRN 2","SCRN 3","SCRN 4","SCRN 5","COMB'D" 2150 FOR J=1 TO P(10) -1 2160 PRINT S (J+1) , E (J,12) , E ( J , 13) , E ( J , 14) , E ( J , 15) , E (J , 16) , E ( J , 17) 2170 I (4)=I (4) +E ( J , 12) 2180 1(5) =1 (5) +E ( J , 13) 21 90 I (6) =1 (6) +E(J , 14) 2200 I (7) =1(7) +E(J , 15) 2210 I<8)=I (8) +E(J , 16) 2220 I (9) =1 (9) +E ( J , 17) 2230 NEXT J 2235 N2=P(10) 22 40 PRINT "PAN",E(N2, 12) , E (N2, 1 3) , E (N 2, 14) , E (N 2 , 1 5) , E (N 2 , 16) , E (N2 , 17) 2250 FOR J=1 TO P{8) +1 22 60 I (3*J) =1 (3+J) +E (P( 10) , 1 1+J) 2270 NEXT J 22 75 PRINT 2280 PRINT " S U M " , ! (4) ,1(5) ,1(6), I (7) ,1(8),1(9) 22 90 PRINT 2300 PRINT " ","OPERATING DATA" 2350 PRINT " ","FLOWRATES (STPH)" 2360 PRINT " " , L (12) , L (13) , L (14) , L (15) , L (1 6) , L (17) 2370 PRINT 2377 RESTORE F I L E 1 23 78 RESTORE F I L E 2 2379 RESTORE F I L E 3 23 80 RESTORE F I L E 4 23 81 RESTORE F I L E 5 23 82 RESTORE F I L E 6 2383 RESTORE F I L E 7 23 85 CHAIN PRNT2 2386 STOP 2387 END E N D - O F - F I L E - Zb-i -2390 DIM I{30) , E { 2 0 , 30) ,S (20) , L (30) , M (15) , N (15) ,0(10) , P (20) 2392 F I L E X 1 r X 2 , X 3 , X 4 , X 5 , X 6 , X 7 2393 FOE J=1 TO 16 23 94 BEAD F I L E 7 ,P (J) 2395 NEXT J 2396 MAT BEAD F I L E 1 , E (P (10) , 8 +P (7) + 2*P (8) +P {9)) 2397 FOB J=1 TO P{10) 2398 BEAD F I L E 2,S{J) 2399 NEXT J 2400 FOB J=1 TO 8 + P (7)+3*P {8)+P (9) 2401 BEAD F I L E 3 , L ( J ) 2402 NEXT J 24 0 3 FOB J=1 TO P (7)+P (8)+P (9) 2405 BEAD F I L E 4,M(J) 2406 NEXT J 2407 FOB J=1 TO P (7) +P (8) +P (9) 24 08 BEAD F I L E 5 ,N(J) 2409 NEXT J 24 10 FOB J=1 TO P(7)+P(9) 2411 BEAD F I L E 6 , 0 ( J ) 2412 NEXT J 2420 PBINT "UNDEBSIZE SIZE ANALYSES" 2425 M7=CMD("$SET COLWIDTH=11") 24 30 FOB J=1 TO P(10)-1 2440 PRINT S(J+1) , E (J,6) , E (J ,7) , E ( J , 8 ) , E ( J , 9 ) , E ( J , 1 Q ) , E ( J , 1 1 ) 2450 1 (10) =1 (10) +E (J,6) 2460 I(11)=I (11)+E(J,7) 2470 I ( 12) =1 (12) +E (J ,8) 2480 I (13)=I (13) +E(J,9) 2490 I (14) =1 (14)+E ( J , 10) 2500 I (15) = I (15) + E ( J , 11) 2510 NEXT J 2515 N2=P(10) 2520 PBINT "PAN" r E(N2,6) , E (N2,7) , E (N2 ,8) , E (N2, 9) ,E (N2, 10) ,E{N2,11) 2530 PBINT 2540 FOB J = 1 TOP (8) + 1 2550 I (9 + J) =1 (9+J) +E (P{10) ,5+J) 2560 NEXT J 2570 PBINT "SUM",I (10) , I (11) ,1 (12) , I (13) , I (14) , I (15) 2580 PBINT 2590 PRINT " ","OPEBATING DATA" 2610 PBINT " " ,"SCBEEN OPENING (CM.)" 2620 PBINT " ",N(3) ,N(4) ,N(5) ,N{6) ,N{7) , " - " 2640 PRINT " ","FLOHHATES (STPH)" 2650 PRINT " » , L (6) , L (7) , L (8) , L (9) , L (10) , L (11) 2660 PRINT 2670 PRINT"fo MINUS .54 INCH MAT'L IN CRUSHING PLANT PR ODUCT=»; P (4) 2690 PRINT 27 00 PRINT " * * * * * TEBTIAHY CRUSHING OUTPUT * * * « * " 2710 PRINT 2720 PBINT "NUMBER OF CEUSHEBS OPEBATING=";P(9) 2740 PBINT " FEED SPLIT RATIOS=" ; M (8) , M (9) , M (10) , M ( 11) 27 50 PBINT 2760 PEINT "PBODUCT SIZE ANALYSES" 2780 PBINT "SIZE","CRUSHER 1","CBUSHER 2", "CRUSHER 3","CRUSHES 4","COMBINED' 2800 FOB J=1 TO P(10)-1 2810 PRINT S (J + 1) , E (J,18) , E (J ,19) , E ( J , 2 0 ) , E ( J , 2 1 ) , E ( J , 2 2 ) 2820 I (16) =1 (16) +E(J , 18) 2830 I (17)=I <17) +E ( J , 19) 28 40 I (18) =1 (18)+E(J,20) - 254 -2850 I{19)=I{19) + E ( J , 2 1 ) 2860 I (20)=I (20)+E (J,22) 2870 NEXT J 2880 PRINT « P A N " , E ( P { 1 0 ) , 18) , E (P (10) , 19) , E (P {1 0) ,20) , E (P { 10) ,2 1) , E (P (1 0) ,22] 2890 FOR J=1 TO P (9) +1 2900 I (15+J)=1 (15+J) +E(P(10),17+J) 2910 NEXT J 2920 PRINT 2930 PRINT "SUM",I (16) ,1 (17) ,1 (18) ,1 (19) ,1 (20) 294 0 PRINT 2950 PRINT » ","OPERATING DATA" 297 0 PRINT " " , "CLOSE SIDE SETTING (CM.)" 2980 PRINT " ",N{8) ,N{9) ,N(10) ,N (11) , » - " 3000 PRINT ™ ","FLOWRATES (STPH)" 3010 PRINT " » , L (18) ,L{19) , L (20) , L (21) , L (22) 3030 PRINT " " , "CURRENT DRAWS (AMPERES) " 3040 PRINT " ",0 (3) ,0 (4) ,0 (5) ,0(6) , " N . A . " 3050 PRINT 3060 PRINT "PERCENT CIRCULATING LOAD="; (L(22 ) / I (4 ) ) 3080 PRINT 30 90 M6=CMD("%SET COLWIDTH=15") 3100 PRINT " * * « * * PRIMARY FINES OUTPUT * * * * * * 3130 PRINT 3140 PRINT "SCREEN S I Z E " , " S I Z E ANALYSIS" 3160 FOR J - 1 TO P{10)-1 3170 PRINT S (J + 1) , E (J,23) 3180 1(21) =1 (21)+E (J,23) 3190 NEXT J 3200 PRINT "PAN",E(P (10) ,23) 3210 I<21)=I (21) +E(P (10) ,23) 3220 PRINT 3230 PRINT " S U M " , ! (21) 3240 PRINT 3250 PRINT "DAILY FLOWRATE (STPH, INTERMITTENT) ="; L (23) 3260 PRINT 3280 PRINT " * * * * * ROD MILL FEED ANALYSIS 3290 PRINT 3300 PRINT "SCREEN S I Z E " , " S I Z E ANALYSIS" 33 20 FOR J= 1 TO P (1 0) - 1 3330 PRINT S (J+1) , E (J,24) 33 40 I (22) =1(22) +E(J,24) 3350 NEXT J 3360 PRINT "PAN",E(P(10) ,24) 3370 I (22)=I (22) +E(P (10) ,24) 3380 PRINT 3390 PRINT "SUM",I (22) 34 00 PRINT 3410 PRINT "ROD MILL FEED FLOWRATE (STPH)=";L(29) 34 20 PRINT 3425 PRINT "SECONDARY CRUSHING PLANT REDUCTION RATIO=";P(4) /P(6) 3430 PRINT »% MINUS .54 INCH M A T ' ! IN ROD HILL FEED=";P(5) 3450 PRINT 3460 STOP E N D - O F - F I L E INVALID COMMAND. , MISSING OR ILLEGAL PARAMETERS. COMMAND IGNORED. - -d e v i c e : DS49 task; 50 USERID: RALU 13:42:3 9 09-08-77 U n i v e r s i t y o f B r i t i s h Co lumbia Computing C e n t r e - d e v i c e : DS49 t a s k : # SIGN RALU # ENTER USER PASSWORD. # * * L A S T SIGNON WAS: 13:21:23 # USER "RALU" SIGNED ON AT 13:40:27 ON THU SEP 08/77 f RUN *BASIC # EXECUTION BEGINS & ?UBC BASIC SYSTEM 6 ? : GET M2 : RUN ENTER PLANT FEEDRATE (STPH) ? 1454.6 ENTER SECONDARY CRUSHER GAPS (CM.) ? 3 .08 ? 3 .08 ENTER SECONDARY SCREEN OPENINGS (CM.) ? 1.59 ? 1.59 ? 1 .59 ? 1.59 ? 1 .59 ENTER TERTIARY CRUSHER GAPS (CM.) ? .81 ? . 81 ? .81 ? .81 *********************************** ***************************** CONVERGENCE CRITERION MINIMUM= 2.586723E-3 NUMBER OF CYCLES= 10 ALL SIZE DISTRIBUTIONS MEASURED IN % RETAINED ON SIZE * * * * * ANALYSIS OF PLANT FEED * * * * * SCREEN SIZE FEED SIZE ANALYSIS 21.76 3 10.88 35 5.44 36.5 2.72 18.35 1.36 4.7 0.68 0.94 0.34 0.29 0.17 0.22 0.085 0.17 0.0425 0,17 0.02125 0.18 0.010625 0.16 0.0053125 0.13 PAN 0.19 SUM 100 PLANT FEEDRATE (STPH)= 1454.6 % MINUS .54 INCH IN FEED * * * * * SECONDARY CRUSHING OUTPUT * * * * * - 256 -NUMBER OF CRUSHERS OPERATING 3 2 FEED SPLIT RATIOS 3 0.5 0.5 PRODUCT SIZE SIZE 21.76 10. 88 5.44 2.72 1.36 0.68 0.34 0. 17 0.085 0.0425 0.02125 0.010625 0.0053125 PAN ANALYSES CRUSHER NR.1 0 0.11915 28.51169 38. 50253 17.28089 6.54267 3.12138 1.90209 1.2438 0.86689 0.63114 0.45016 0.31553 0.51209 CRUSHER NR.2 0 0.11915 28,51169 38.50253 17.28089 6.54267 3.12138 1.90209 1.2438 0.86689 0.63114 0.45016 0.31553 0.51209 COMBINED OUTPUT 0 0. 11915 28.51169 38.50253 17.28089 6. 54267 3. 12138 1. 90209 1.24 38 0. 86689 0.63114 0.45016 0.31553 0.51209 SUM 100 100 100 OPERATING DATA NUMBER 1 CLOSE SIDE SETTING (IN CM.) 3.08 FLOWRATES (IN STPH) 727.3 CURRENT DRAW {IN AMPERES) 23.16549 NUMBER 2 3.08 727.3 23.16549 COMBINED 1454.6 N. A. * * * * * SECONDARY SCREENING OUTPUT * * * * * NUMBER OF SCREENS OPERATING 3 5 SCREEN 1 SCREEN 2 SCREEN 3 SCREEN 4 SCREEN 5 FEED SPLIT RATIOS 0.2 0.2 0. 2 0. 2 0 .2 FEEDRATES TO INDIVIDUAL SCREENS (STPH) 577.5805 577.5805 577.5805 577. 5805 577.5805 OVERSIZE PRODUCT SIZE ANALYSIS SIZE SCRN 1 SCRN 2 SCRN 3 SCRN 4 SCRN 5 COMB' D 21. 76 0 0 0 0 0 0 10.88 0. 12092 0.12092 0. 12092 0. 12092 0. 12 092 0.12092 5. 44 28.9354 28. 9354 28.9354 28.9354 28 ,9354 28.9354 2.72 46.82823 46.82823 46.82823 46. 82 823 46 .82823 46. 82 823 1.36 22.49981 22.49981 22.49981 22. 49981 22 .49981 22.49981 0.68 0.91858 0.91858 0.91858 0.9 1858 0. 9185 8 0.91858 0. 34 0.26406 0.26 4 06 0.26406 0.26406 0. 26406 0.26406 0. 17 0.14589 0. 14589 0.14589 0.145 89 0. 14589 0.14589 0. 085 0.09658 0.09658 0.09658 0.09658 0. 09658 0.0 9658 0.0425 0.06515 0.06515 0.06515 0.06515 0. 0651 5 0.06515 0.02125 0.04396 0.04396 0.04396 0.04396 0. 04396 0.04396 0.010625 0.02928 0.02928 0.02928 0.02928 0. 0292 8 0.02928 0.0053125 0.01931 0.01931 0. 01931 0.01931 0. 0193 1 0.01931 PAN 0.03281 0.03281 0.03281 0.03281 0 .03281 0.03281 SUM 99.99998 99.99998 99.99998 99.99998 99.99998 99.9999* OPERATING DATA FLOWRATES (STPH) - ZS/ -286.66 286.66 286.66 286.66 286.66 1433.3 UNDERSIZE SIZE ANALYSES 21.76 0 0 ' 0 0 0 0 10. 88 0 0 0 0 0 0 5.44 0 0 0 0 0 0 2.72 0 0 0 0 0 0 1.36 37.84707 37. 8 4707 37.84707 37.84707 37.847 07 37.84707 0. 68 29.17259 29.17259 29.17259 29.17259 29.17259 29. 17259 0.34 12.1076 12,1076 12.1076 12. 1076 12.1076 12. 1076 0. 17 7.00373 7.00373 7. 00373 7.00373 7.0037 3 7.00373 0.085 4.66311 4,66311 4. 6631 1 4.66311 4.66311 4.66311 0.0425 3. 14783 3.14783 3.14783 3.147 83 3. 14783 3.14783 0.02125 2. 12438 2.12438 2.12438 2.12438 2.12438 2.12438 0.010625 1.41477 1.41477 1. 41477 1.41477 1.41477 1.41477 0.0053125 0.93334 0.93334 0.93334 0.933 34 0.93334 0.9 3334 PAN ' 1.58559 1.58559 1.58559 1.58559 1. 58559 1.58559 SUM 100 100 100 100 100 100 OPERATING DATA SCREEN OPENING (CM.) 1.59 1.59 1.59 1.5 9 1 .59 — FLOWRATES (STPH) 290.9205 290.9205 290.9205 290.9205 290.9205 1454.603 % MINUS .54 INCH MAT'L IN CRUSHING PLANT PRODUCT= 62.15293 ***** TERTIARY CRUSHING OUTPUT ***** NUMBER OF CRUSHERS OPERATING^ 4 FEED SPLIT RATIOS= 0.25 0 .25 0.25 0.25 PRODUCT SIZE ANALYSES SIZE CRUSHER 1 CRUSHER 2 CRUSHES 3 CRUSHER 4 COMBINED 2 1 . 76 0 0 0 0 0 10.88 0 0 0 0 0 5.44 0 0 0 0 0 2. 72 7.75351 7.75351 7.75351 7.75351 7.75351 1.36 43.37161 43.37161 43. 37161 43.37161 43.37161 0.68 23,88481 23.88481 23.88481 23. 88481 23.88481 0.34 9.38383 9.38383 9.38383 9.38383 9.38383 0. 17 5.32335 5.32335 5.32335 5.32335 5.32335 0.085 3.56671 3.56671 3. 56671 3.56671 3.56671 0.0425 2 . 37998 2.37998 2. 37998 2.37998 2.37998 0.02125 1. 5594 1.5594 1.5594 1.5594 1.5594 0.010625 1.00823 1.00823 1.00823 1.00823 1.00823 0.0053125 0.64631 0.64631 0.64631 0.6 46 31 0.64631 PAN 1.12227 1.12227 1.12227 1. 12227 1. 12227 SUM 100 100 100 100 100 OPERATING DATA CLOSE SIDE SETTING (CM.) 0.81 0.81 0.81 0.81 -FLOWHATES (STPH) 358.3256 358.3 256 358.3256 358.3 256 1433.302 CURRENT DRAWS (AMPERES) 35.37048 35.37048 35.37048 35. 37048 N.A. - 258 -PERCENT CIRCULATING LOAD= 0.9853582 * * * * * PRIMARY FINES OUTPUT * * * * * SCREEN SIZE 21.76 10.88 5.44 2.72 1.36 0 . 6 8 0.34 0. 17 0.085 0.0425 0.02125 0.010625 0.0053125 PAN SUM SIZE ANALYSIS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 DAILY FLOUR ATE (STPH,INTERMITTENT) = 0 * * * * * ROD MILL FEED ANALYSIS * * * * * SCREEN SIZE 21.76 10.88 5. 44 2.72 1. 36 0.68 0. 34 0. 17 0.085 0.0425 0.02125 0.010625 0.0053125 PAN SUM SIZE ANALYSIS 0 0 0 0 37.84707 29.17259 12. 1076 7.00373 4.66311 3. 14783 2. 12438 1.41477 0.93334 1.58559 100 ROD MILL FEED FLOWRATE (STPH)= 1454.603 SECONDARY CRUSHING PLANT REDUCTION RATIO= 25.36854 % MINUS ,54 INCH HftTVL IN ROD MILL FEED= 62.15293 + 7STOP! # ? AT LINE "3460" IN PROGRAM "PRNT2" + ? PROGRAM ENDS : HTS # CONTROL *PRINT* HOLD PRINT=TN FORM=8X11 # *PRINT* ASSIGNED RFS NUMBER 664246 # $C * SOURCE* 3>S P * PRINT* d e v i c e : DS48 t a s k : 49 USERID: RALU 14:23:24 09-08-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS48 t a s k : 4' # SIGN RALU # ENTER USER PASSWORD. # * * L A S T SIGNON WAS: 14:15:53 # USER "RALU" SIGNED ON AT 14:18:45 ON THU SEP 08/77 # RUN *BASIC # EXECUTION BEGINS & ?UBC BASIC SYSTEH S. ? — : GET M2 : .250 DATA . 6 , . 4 , . 2 5 , . 2 , . 1 , . 2 , . 2 5 , . 3 , . 2 , . 15 , .35 : RUN ENTER PLANT FEEDRATE (STPH) ? 1275 ENTER SECONDARY CRUSHER GAPS (CM.) ? 2.8 ? 3 .25 ENTER SECONDARY SCREEN OPENINGS (CM.) ? 1.4 ? 1.5 ? 1.27 ? 1.5 ? 1 .59 ENTER TERTIARY CRUSHER GAPS (CM.) ? . 9 ? . 82 ? .74 ? 1. 00 ************************************************$$*$£*********** CONVERGENCE CRITERION MINIMUM3 1. 509731 E-3 NUMBER OF C Y C L E S 3 12 ALL SIZE DISTRIBUTIONS MEASURED IN % RETAINED ON SIZE * * * * * ANALYSIS OF PLANT FEED * * * * * SCREEN SIZE FEED SIZE ANALYSIS 21.76 3 10.88 35 5.44 36.5 2.72 18.35 1.36 4.7 0.68 0.94 0.34 0.29 0 .17 0.22 0.085 0.17 0.0425 0.17 0.02125 0.18 0.010625 0.16 0.0053125 0.13 PAN 0.19 SUM 100 PLANT FEEDRATE ( S T P H ) 3 1275 % MINUS .54 INCH IN F E E D 3 2.4^ * * * * * SECONDARY CRUSHING OUTPUT NUMBER OF CRUSHERS OPERATING 3 2 - 260 -* * * * * FEED SPLIT RATIOS 3 0.6 0.4 PRODUCT SIZE S I Z E 21.76 10. 88 5.44 2.72 1 .36 0.68 0.34 0. 17 0.085 0.0425 0.02125 0.010625 0.0053125 PAN SUM ANALYSES CRUSHER NR. 1 0 0.04222 27.17139 38.33784 17.51018 6.88696 3.42821 2. 13384 1.406 0.97584 0.70258 0.49634 0.34511 0.56349 100 CRUSHER NR.2 0 0.14436 30.36988 36.01817 16.06379 6.64779 3.5558 2.30361 1.54156 1.07084 0.76583 0.53745 0.3715 0.60941 99.99999 OPERATING DATA NUMBER 1 CLOSE SIDE SETTING (IN CM.) 2 .8 FLOWRATES (IN STPH) 765 CURRENT DRAW (IN AMPERES) 26.51729 * * * * * SECONDARY SCREENING OUTPUT * * * * * NUMBER OF SCREENS OPERATING 3 5 COMBINED OUTPUT 0 0. 08307 28.45079 37.40997 16.93162 6. 79129 3. 47925 2. 20175 1. 46022 1.01 384 0.72788 0.51278 0. 35567 0.58186 99. 99999 NUMBER 2 3.25 510 14.42023 COMBINED 1275 N. A. , SCREEN 1 SCREEN 2 SCREEN 3 FEED SPLIT RATIOS 0.25 0.2 0.1 FEEDRATES TO INDIVIDUAL SCREENS (STPH) 679.3038 543.4431 271.7215 SCREEN 4 0. 2 54 3. 4431 SCREEN 5 0.25 679.3038 OVERSIZE PRODUCT SIZE ANALYSIS SIZE SCRN 1 SCRN 2 SCRN 3 SCRN 4 SCRN 5 COMBED 21.76 0 0 0 0 0 0 10.88 0.06797 0.07389 0.06648 0.0 73 89 0.08275 0.07344 5. 44 23.28013 25.3077 22.766 86 25. 3077 28.34012 25. 15217 2.72 37.57377 40. 84624 36.74537 40.84624 45.74052 40.59521 1. 36 35.76178 31. 17531 37.72987 31. 17531 23.9556 31. 53637 0.68 1.7474 1.3562 1.45718 1.3562 0.97155 1.38767 0.34 0.60817 0.48016 0. 48059 0.48016 0. 35132 0.4 862 0. 17 0. 326 0.25798 0.25588 0.25798 0. 18929 0.26088 0.085 0.21481 0.17004 0.16846 0.17004 0. 12481 0. 17192 0.0425 0.14456 0.11444 0.11336 0.1 1444 0. 084 0.1157 0.02125 0.09702 0.07681 0.07608 0.07681 0.05638 0.07765 0.010625 0.06427 0.05088 0.0504 0.Q5088 0.03735 0.05144 0.0053125 0.04218 0.03339 0.03308 0.03339 0.0245 1 0.0 3376 PAN 0.07194 0.05695 0.05641 0. 05 695 0.04181 0.05758 SUM 100 99.99999 100 99.99999 100 99.9999 OPERATING DATA - Zb\ -FLOWRATES (STPH) 389.5477 286.6707 159.3319 286.6707 319.9958 1442.217 UNDERSIZE SIZE ANALYSES 21.76 0 0 0 0 0 0 10. 88 0 0 0 0 0 0 5.44 0 0 0 0 0 0 2. 72 0 0 0 0 0 0 1.36 23.91498 30.18743 20.75459 30.18743 36.722 6 4 29.77215 0.68 31.6475 29.17689 32.9935 29.17689 26.55065 29.33469 0. 34 16.63636 15.22077 17.31821 15. 22077 13.76251 15.31641 0. 17 9. 38 93 8.58395 9.77199 8.5 83 95 7.7566 5 8.63856 0.085 6.22685 5.69224 6.48046 5.69224 5. 14324 5.7285 0.0425 4.19379 3.83369 4.36459 3 .83369 3.46391 3.85812 0.02125 2.81507 2.57335 2.92971 2.57335 2.32513 2.58974 0.010625 1.86477 1 .70465 1. 94071 1.70465 1.54022 1,71551 0.0053125 1.22395 1.11885 1.2738 1.1 1885 1.01093 1 . 12598 PAN 2.08743 1.90819 2.17244 1.90819 1.72413 1. 92035 SUM 100 100 100 100 100 100 OPERATING DATA SCREEN OPENING (CM.) 1.4 1.5 1. 27 1.5 1 .59 -FLOWRATES (STPH) 289.7561 256.7724 112.3896 256.7724 359.308 1274.998 % MINUS .54 INCH MAT'L IN CRUSHING PLANT PRODUCT= 70.22785 * * * * * TERTIARY CRUSHING OUTPUT * * * * * NUMBER OF CRUSHERS OPERATING^ 4 FEED SPLIT RATIOS= 0.3 0.2 0. 15 0. 35 PRODUCT SIZE ANALYSES SIZE CRUSHER 1 CRUSHER 2 CRUSHER 3 CRUSHER 4 COMBINED 21.76 0 0 0 0 0 10. 88 0 0 0 0 0 5.44 0 0 0 0.00024 0.00008 2.72 8.88153 4.75241 1.25504 10.62722 7. 52272 1.36 42.19728 48.68096 38.5474 42. 03039 42.888 12 0. 68 19.53891 26.48171 25.05363 18.28921 21.31728 0.34 10.76471 9.88285 14.07278 10. 38 286 10.9509 0. 17 6.34421 3.67131 7.30771 6.33626 5. 95137 0.085 4.25599 2.27477 4.78136 4.27532 3.94532 0.0425 2.84043 1.50692 3. 18313 2.85491 2.6302 0.02125 1. 86145 0.98773 2.08533 1.87103 1.72364 0.0106 25 1. 20375 0.63929 1.34834 1 .20994 1.1147 1 0.0053125 0.77179 0.41026 0.8644 0.77576 0.71476 PAN 1.33997 0.71178 1.50088 1. 34686 1.24088 SUM 100 99.99999 100 100 99.99998 OPERATING DATA CLOSE SIDE SETTING (CM.) 0.9 0.82 0. 74 1 FLOWRATES (STPH) 432.6646 288.4431 216.3323 504.7754 CURRENT DRAWS (AMPERES) 35.6926 30. 86697 28.8385 37. 52888 1442.215 N . A . - 262 -PERCENT CIRCULATING LOAD= 1.131149 * * * * * PRIMARY FINES OUTPUT * * * * * SCREEN SIZE 21.76 10. 88 5.44 2.72 1.36 0. 68 0.34 0. 17 0.085 0.0425 0.02125 0.010625 0.0053125 PAN SUM SIZE ANALYSIS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 DAILY FLOWRATE (STPH,INTERMITTENT)= 0 * * * * * ROD MILL FEED ANALYSIS * * * * * SCREEN SIZE 21.76 10.88 5. 44 2 .72 1. 36 0.68 0. 34 0. 17 0. 085 0.0425 0.02125 0.010625 0.0053125 PAN SUM SIZE ANALYSIS 0 0 0 0 29.77215 29.33469 15.31641 8.63856 5.7285 3.85812 2.58974 1.71551 1.12598 1.92035 100 ROD MILL FEED FLOWRATE (STPH)= 1274.998 SECONDARY CRUSHING PLANT REDUCTION RATIO= 28.6644 3 % MINUS .54 INCH fflAT*L IN ROD MILL FEED= 70.22785 + ?STOP! # ? AT LINE "3460" IN PROGRAM "PRNT2" + ? PROGRAM ENDS : MTS # CONTROL *PRINT* HOLD PRINT=TN F0RM=8X11 # *PRINT* ASSIGNED RFS NUMBER 664325 # $C *SOURCE*5)SP *PRINT* - £ 0 J -1 * * * PROGRAM: PGM2 :CRUSHING PLANT SIMULATION PROGRAM 2 * 3 * 10 DIMA (14) , B{14) ,C(14) , D{14) , F (1 4) ,0 (14) ,P (58) ,Q (14) 20 DIM K(14) ,J (14) ,G (14) ,V{14) ,R(14) ,S{14) ,T(14) ,H( 14) ,Y{14) 3 0 F I L E CONST 32 FOR J=1 TO 56 34 READ F I L E 1,P{J) 36 NEXT J 40 READ C 2 , C 3 , C 5 , S 1 , R 1 , N 2 , M 1 50 DATA 2 , 4 , 5 , 4 3 . 5 2 , . 5 , 1 4 , 1 0 0 53 X0=-1 56 BQ=83.88 60 DATA 3 , 3 5 , 3 6 . 5 , 18. 3 5 , 4 . 7 , . 9 4 , . 2 9 , . 2 2 , . 17 , . 1 7 , . 1 8 , . 16 , . 1 3 , . 19 65 V1=0 70 FOR J=1 TO N2 80 READ A (J) 85 IFJ>4THEN91 90 V1=V1+A (J) 91 S (J) =S1*B1** (J-1) 92 Q (J) =INT ( (S (J) /2) *1 0000+. 5)/10000 9 3 IFJ=1 THEN 105 9 4 T (J- 1) =SQB (S (1) *S (2) ) *H1** (J-2) 105 NEXT J 107 Q(N2)=-Q (N2-1) 108 S2=SQR(S{1) *S(2) ) 110 PRINT "ENTER PLANT FEEDRATE" 112 INPUT A 114 PBINT "ENTEB:2-CB GAP,2-SCBN OPEN»G,3-CR GAP" 115 INPUT Q2,S ,Q3 116 PRINT "IF SIMULATION OF PBIMABY FINES DESIRED,ENTER 1;IF NOT,ENTER 0" 118 INPUT J5 120 I F J5=0 THEN 128 122 PBINT "ENTER DAY OF WEEK:MON=1,TUE= 2,WED=3,THU=4,FBI=5,SAT= 6,SUN=7" 125 INPUT J1 128 PBINT "IF ANOTHEB RUN IS DESIRED, ENTEB 1; IF NOT, ENTEB 0" 130 INPUT J6 240 21=P (1) *P (2) *Q2+P (3) * (A/C2) *P (4) *V1 250 Z2=P{5) +P(6) *Q2 + P (7) *Q2**2+P (8) *V1 260 Z3=P (9) *P (10) *Q2*P (11) *Q2**2 + P (12) *V1 270 L2=1 280 L4=0 2 90 FOR 1=1 TO N2-1 300 L1= 1- (1- (S (1+ 1)/S2) **2) **6 310 K(I)=L2-L1 320 L2=L1 330 L3=EXP(- ( (S (1 + 1) /2) **.664) ) 3 40 J ( I ) = L 3 - L 4 350 L4=L3 360 NEXT I 370 FOR J=1 TO N2 380 I F S(J)>Z3 THEN 440 390 I F S(J)<Z2 THEN 420 400 H (J) =S (J) - (S {J) - Z 3) **3/(3*{ (Z2-Z3) **2) ) 410 GO TO 450 420 H(J) =Z2- ( Z 2 - Z 3 ) / 3 430 GO TO 450 440 H(J)=S(J) 450 NEXT J 460 R(0)=0 - 264 -4 70 £20=0 4 80 FOR 0=1 TO N2-1 490 V (U) = (H (U) —H (0+1 )) / (S (0) -S (U+1) ) 500 A1 = 0 510 B1=0 520 FOR 1=1 TO U-1 530 A1=A 1+ (Z1*K (U-I* 1) * (1-Z1) * J (U) ) *R (I) 540 B1=B1+J(I) 550 NEXT I 560 G(U) = (A (0)+A1) / (1- (Z1*K(1) + (1-Z1) *(B1+J(U) ) )*V(0) ) 570 R (0) = V (D) *G (0) 580 B(0)=G(U)-R(U) 590 Z20=Z20 + B(U) 600 NEXT U 610 B(N2)=100-Z20 6 20 12=1 NT ( (P{13) *P(14) *Q2+P (15) * (A/C2) )*100+.5)/100 6 30 C=0 640 Z25=0 650 D=A+C 660 V2=0 670 FOR J=1 TO N2 680 D (J) = (A*B (J) *C*C (J) ) /D 690 I F J>4 THEN 710 700 V2=V2 + D(J) 710 NEXT J 720 Z8=P (17) +P(18) *S**2+P(19) *V2+P(20)* (D/C5) **2 730 Z9=P (21) +P (22) *S + P (23) *S**2 + P (24) *V2**2+P (25) *{D/C5) **7 7 40 C=0 760 FOR 1=1 TO N2-1 770 Y (I) =1/{1+EXP{ (Z9**3-T (I) **3)/Z8) ) 780 J (I) = (Y (I) * (D/C5) *D (I) ) /100 790 K(I)= ( (1-Y(I) ) * (D/C5) *D(I) )/100 800 C=C+J(I) 820 NEXT I 830 B10=1/(1+EXP(Z9**3/Z8)) 8 40 J (N2) = (B10* (D/C5) *D (N2) ) /100 850 K (N2) = ( (1-B10) *(D/C5) *D (N2) ) /100 860 C=C + J(N2) 870 F=(D/C5)-C 875 V3=0 880 FOR 1=1 TO N2 890 0(1) = (J (I) /C) *100 900 F (I) = (K (I) /F) * 100 901 K{I)=0 902 IF I>4 THEN 908 903 V3=V3+0(I) 908 NEXT I 910 C=C*C5 911 F=F*C5 920 IF ABS(A-F) <.01THEN950 930 Z25=Z25+1 940 IF Z25>M1 THEN 950 945 GO TO 1000 950 IF J5=0 THEN 988 952 A0=248.71 956 GO SOB 2500 958 A22=0 960 J2=ABS (P (47)+P (48) * J 1+ P ( 49) * J 1**2+P (50) *J1**3) 962 J3=P{51) +P{52) *J1 + P(5 3) *J1**2+P{54) *J1**3 964 J4 = P (55)+P (56) *LOG (J2) - Zbb -966 FOR 1=1 TO N2-1 970 J12=J2*EXP (J3*S (1+1) ) - J 2 * E X P (J4*S (1 + 1) ) 972 J(I ) = 100*J12/(1+J12) 974 IF 1=1 THEN 9 82 976 K (I) =J ( I - 1) - J (I) 980 A22=A22 + K(I) 982 NEXT I 984 K(1) = 100-J(1) 986 K(N2) =100-A22 988 IF J5=0 THEN;K=0 989 FOE 1=1 TO N2 990 & ( ! ) - <K*K (I) +F*F (I) ) / (F+K) 991 NEXT I 992 GO TO 1500 1000 Z4=P(26)+P(27)*(C/C3)+P(28) / (1+P(29)*( (C/C3) -P (30) )**2) 1010 Z5=P (31) +P{32) *EXP{P (33) *Z4**P (34) ) 1020 Z6 = P{35)+P(36)*V3 103 0 Z7=P (37) +P (3 8) *Q3- (P (39) / (1 +P (40)* (Q3-P (41)) * * 2} ) **P (42) 1040 I3=INT { (P{43) +P (44) *Q3 + P{45) * (C/C3) ) *100 + . 5) /100 1090 L2=1 1100 L4=0 1110 FOR 1=1 TO N2-1 1120 L1 = 1- (1- (S (1 + 1) /S2) **4) **Z5 1130 K(I )=L2-L1 1140 L2=L1 1 150 L3=EXP(-( (S (1+1 )/2) **.664)) 1160 J ( I ) = L 3 - L 4 1170 L4=L3 1180 NEXT I 1190 FOR J=1 TO N2 1200 IF S(J)>Z7 THEN 1260 1210 IF S(J)<Z6 THEN 1240 1220 H(J)=S ( J ) - (S(J) -Z7) **3 / (3*({Z6-Z7) **2) ) 1230 GO TO 1270 1240 H ( J ) = Z 6 - ( Z 6 - Z 7 ) / 3 1250 GO TO 1270 1260 H(J)=S(J) 127 0 NEXT J 128 0 R(0) =0 1290 Z20=0 1300 FOR 0=1 TO N2-1 1310 V (U) = (H (U) - H (U+ 1) ) / ( S (U) - S (U+1) ) 1320 A1=0 133 0 B1 = 0 1340 FOR 1=1 TO U-1 1350 A1 = A1+ (Z4*K (U-I+1) +( 1-Z4) *J(0) ) *R{I) 1360 B1=B1+J(I) 1370 NEXT I 1380 G (0) = (0 (0) +A1) / (1— (Z4*K (1) + (1 -Z4)* (B1 + J(U) ) ) *V (U) ) 1390 R(0)=V(U) *G{0) 1400 C (0)=G (U)-R (U) 1410 Z20=Z20 + C (U) 142 0 NEXT D 1430 C(N2)=100-Z20 1440 GO TO 650 1500 PRINT "NUMBER OF CYCLES="; Z25 , "CONVERGENCE CRITERION 3 "; ABS (A-F) 1505 PRINT 1516 V4=0 1517 V5=0 1520 H10=CH.D(«JtSET COLWIDTH=8") - 266 -1525 PRINT"* RETAINED:" 1 5 2 7 P R I N T " S I Z E » , " 2 C R F » , » 2 CRP","S F » , » S U / S " , » S O/S","3 CRP","P F","RMF« 15.31 F0RJ=1T0N2 1533 F10=INT (A (J) *1000 + .5) /1000 1534 F20=INT (B (J) * 1000*. 5) /1000 1535 F30=INT{D(J) *1000+.5) /1000 1536 F40=INT (F <J) *1000+.5) /1000 1537 F50=INT{0(J)*1000+.5)/1000 1538 F60=INT (C (J) * 1000 + . 5) /1000 153 9 F7 0=.INT{K(J)*1000+.5)/1000 154 0 F80=INT{R{J) * 1000+.5) /1000 1544 P R I N T Q ( J ) , F 1 0 , F 2 0 , F 3 0 , F 4 0 , F 5 0 , F 6 0 , F 7 0 , F 8 0 1553 IFJ<6THEN1565 1555 V4=V4+F(J) 1560 V5=V5+F10 1565 NEXTJ 1582 A=INT (A* 1 00 +. 5) /100 1 583 D=INT{D*100+.5)/100 1584 C=TNT(C*100 + . 5 ) / 1 0 0 1 585 F=INT(F*100 + . 5 ) / 1 0 0 1591 K=.INT(K*100+.5) /1 00 1593 PRINT 1595 S10=0 1600 S20=0 1605 S30=0 1610 S40=0 1615 S5 0=0 1620 S60=0 1625 S70=0 1630 S80=0 1633 PRINT"% PASSING:" 1634PRINT"SIZE","2 CRF","2 CRP","S F " , " S U / S " , " S O/S" ,"3 C R P " , " P F" ,"RMF" 1635 FORJ=N2T01STEP-1 1640 S10=S10+A(J) 1645 S20=S20+B(J) 1647 S21=INT(S20*1000 + .5 ) /1000 1650 S30=S30 + D{J) 1652 S31 = INT{S30*100 0 + . 5 ) / 1 0 00 1655 S40=S40*F(J) 1657 S41=INT(S40*1000+.5)/1000 1660 S50=S50 + O(J) 1662 S51 = INT (S50*1000 + .5 ) /1000 1665 S60=S60 + C(J) 1667 S61=INT{S60*1000+.5)/1000 1670 S70=S70 + K(J) 1672 S71=INT<S70*1000+.5)/10 00 1675 S80=S80 + R{J) 1677 S81=INT(S80*1000+.5) /1000 1678 S90 = INT(S (J) * 1 0000+ . 5) /10000 1680 PRINTS9 0 ,S10 ,S21 ,S3 1 ,S41 ,S51 ,S61 ,S71 ,S81 1685 NEXTJ 1690 PRINT 2000 PRINT " " , " " , " ","OPERATING CONDITIONS" 2015 PRINT"TONNAGES:" 2020 PRINT" " , A , A , D , F , C , C , K , K + F 2035 PRINT"% +1 INCH:" 2040 PRINT" " , V 1 , " " , V 2 , " " , " " ,V3 2055 PRINT"CRDSHER CURRENTS:" 2060 PRINT" " , I 2 , " " , " " , " " , " ",13 2065IFI2>67.5THEN:PRINT"(2-CR CURRENT EXCEEDS OVERLOAD MAXIMUM OF 67.5 AMPS) - Zbl -2070XFI3>60.3THEN:PRINT"(3-CR CUB BENT EXCEEDS OVERLOAD MAXIMUM OF 2080 PRINT"SETS;" ,"2 Cfi SET=";Q2,"SCRN OP=";S,"3 CR SET=";Q3 2085 PRINT "%-1/2 INCH IN FEED=";V5 ," » , " % - 1 / 2 INCH IN SCREEN U/S 2090 PRINT »% - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED=";V4/V5 2095 PRINT "% CIRCULATING LOAD=»;C/A 2097 PRINT 2100 I F J6=0 THEN 2120 2110 GO TO 110 2120 STOP 2500 IF X0>=0 THEN 2540 2510 X30=X0 2520 GO SUB 2630 2530 X0=R30 254 0 X30=O 2550 GO SUB 2630 2560 X10=R30 2570 X30=0 2580 GO SUB 2630 2590 X20=R30 2600 Y0=SQR {-2*LOG <X10) }* (COS (6. 283184*X20) ) 2610 K=A0+Y0*B0 2620 RETURN 2630 IF X30<0 THEN 2680 2640 R10=R0*R30 2650 R20=R10-INT (R10/B10) *B10 2660 R30=R20/B10 267 0 RETURN 2680 B0=7E13 2690 B10=10**9.03089987 2700 B30=-X30 2710 GO TO 2640 4000 END END-OF-FILE - 268 -d e v i c e : DS22 t a s k : 521 USERID: RALU 13:42:19 08-17-77 U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e - d e v i c e : DS22 t a s k : 52 # SIGN RALU # ENTER USER PASSWORD. ? # **LAST SIGNON WAS: 13:10:34 # USER "RALU" SIGNED ON AT 13:40:07 ON WED AUG 17/77 # RUN *BASIC # EXECUTION BEGINS 5 ?UBC BASIC SYSTEM 6 ?  : GET PGM2 : RUN ENTER PLANT FEEDRATE ? 1454 .6 ENTER:2-CR GAP,2-SCRN OPEN'G,3-CR GAP ? 3 . 0 8 , 1 .59 , .81 IF SIMULATION OF PRIMARY FINES DESIRED,ENTER 1;IF NOT,ENTER 0 ? 1 ENTER DAY OF WEEK:MON=1,TUE 3 2,WED 3 3 ,THU=4,FRI=5 ,SAT 3 6,SUN=7 ? 3 I F ANOTHER RUN IS DESIRED, ENTER 1; IF NOT, ENTER 0 ? 1 NUMBER OF C Y C L E S 3 9 CONVERGENCE CRITERION 3 2 .728776E-3 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 3 0 0 0 0 0 0 0 10.88 35 0. 119 0.06 0 0,121 0 0 0 5.44 36. 5 28.512 14.361 0 28. 935 0 0.008 0.001 2.72 18.35 38.503 23.241 0 46.828 7.754 2.071 0.375 1.36 4.7 17.281 30.23 37.847 22.5 43. 372 23. 547 35.257 0. 68 0.94 6. 543 15. 15 29. 173 0.919 23.88 5 32. 498 2 9.775 0.34 0. 29 3. 121 6.23 12. 108 0.264 9. 384 15.571 12. 73 5 0. 17 0. 22 1. 902 3.6 7.004 0.146 5.323 7.323 7.062 0.085 0. 17 1. 244 2.397 4.663 0.097 3.567 5.604 4.834 0.0425 0. 17 0. 867 1.618 3, 148 0.065 2.38 4.879 3.461 0.0212 0. 18 0.631 1.092 2. 124 0.044 1.559 3.593 2.39 0.0106 0. 16 0. 45 0. 727 1. 4 15 0.029 1.008 2.251 1 .566 0.0053 0. 13 0. 316 0. 48 0.933 0.019 0.646 1. 271 0.994 -0 .0053 0. 19 0.512 0.815 1. 586 0.033 1 .122 1.384 1.549 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0. 19 0.512 0.0106 0.32 0. 828 0.0212 0. 48 1. 278 0.0425 0.66 1. 909 0.085 0. 83 2. 776 0. 17 1 4. 02 0.34 1.22 5. 922 0.68 1.51 9.043 1.36 2. 45 15.586 2. 72 7. 15 32.867 5.44 25.5 71.369 10.88 62 99.881 21.76 97 100 43.52 100 100 S F S U/S S O/S 0. 815 1. 586 0.033 1. 295 2.519 0.052 2. 0 22 3.934 0.081 3. 114 6. 058 0. 125 4.731 9.206 0.191 7. 128 13.869 0.287 10.728 20.873 0.433 16.958 32. 98 0,697 32.108 62. 153 1.616 62.338 100 24. 115 85.579 100 70. 944 99. 94 100 99. 879 100 100 100 100 100 100 3 CRP P F RMF 1.122 1.384 1 .549 1.769 2.655 2.543 2.777 4.905 4.11 4. 3 36 8.499 6. 5 6.716 13.377 9.961 10.283 1 8. 981 14.795 15.606 26.304 21.856 24.99 41.876 34. 591 48.875 74.373 64.366 92.246 97. 921 99.623 100 99.992 99.999 100 100 100 1 00 100 100 100 100 100 OPERATING CONDITIONS - 269 -TONNAGES: 1454.6 1454.6 2887.9 1454.6 1 433. 3 1433.3 321 .71 1 776. 31 % +1 INCH: 92.85 37.66239 75.88456 CRUSHES CURRENTS: 23. 17 3 9.63 SETS: 2 CR SET= 3.08 SCEN OP= 1. 59 3 CR SET= 0.81 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 62.15294 % -1 /2 INCH RATIO, SCREEN U/S TO PLANT FEED= 25.36855 % CIRCULATING LOAD= 0.9853568 ENTER PLANT FEEDRATE 1250 ENTER:2-CR GAP,2-SCRN OPEN»G,3-CR GAP 2 . 8 5 , 1 . 4 , . 9 5 I F SIMULATION OF PRIMARY FINES DESIRED,ENTER 1;IF NOT,ENTER 0 1 ENTER DAY OF WEEK:MON=1,TUE=2,NED=3,THU=4,FRI=5,SAT=6,SUN=7 3 IF ANOTHER BUN IS DESIRED, ENTEE 1; I F NOT, ENTER 0 0 NUMBER OF CYCLES= 10 CONVERGENCE CBITEBION= 3.393379E-3 % RETAINED: SIZE 2 CBF 2 CEP S F S U/S S O/S 3 CEP P F RMF 21.76 3 0 0 0 0 0 0 0 10.88 35 0. 057 0.026 0 0.047 0 0 0 5.44 36 .5 26.673 12.01 0 21.849 0 0.008 0.001 2.72 18 .35 37.076 20. 974 0 38. 154 7.784 2.071 0.33 1.36 4. 7 17. 177 30.745 23. 69 36. 524 41.859 23.547 23. 668 0.68 0. 94 7. 255 14.974 31.089 1 .774 2 1. 29 7 32.498 31.313 0.34 0. 29 3. 91 8. 323 17. 669 0.668 1 1. 93 8 15.571 17.335 0. 17 0. 22 2. 53 4. 422 9.407 0.338 5.971 7.323 9.075 0.085 0. 17 1. 691 2. 891 6. 153 0.219 3.874 5.604 6.065 0.0425 0. 17 1. 169 1.943 4. 136 0. 147 2,578 4.879 4.254 0.0212 0. 18 0. 83 1. 302 2. 771 0.099 1.689 3.5 93 2.902 0.0106 0. 16 0. 579 0. 861 1. 833 0.065 1.093 2.251 1.899 0.0053 0. 13 . 0.398 0. 564 1.201 0.043 0.701 1.271 1.212 - 0 . 0 0 5 3 0. 19 0. 655 0.964 2.051 0.073 1.216 1.384 1.945 % PASSING: SIZE 2 CBF 2 CEP S F S U/S S O/S 3 CEP P F RMF 0.0053 0.. 19 0. 655 0.964 2.051 0.073 1.216 1. 384 1.945 0.0106 0.32 1. 053 1. 5 28 3.252 0.116 1 .917 2.655 3.157 0.0212 0.48 1.632 2. 389 5. 085 0.181 3.01 4.905 5.056 0.0425 0.66 2. 461 3. 692 7.856 0.28 4.699 8.499 7.959 0.085 0. 83 3.631 5.635 11. 992 0.427 7.277 13.377 12.213 0. 17 1 5. 322 8. 526 18. 145 0.647 11.151 18.981 18.278 0. 34 1.2.2 7. 85 2 12.948 27.552 0.985 17. 122 26.304 27.354 0.68 1.51 11.762 21,271 45. 221 1.6 52 2 9.06 41.876 44.688 1.36 2. 45 19.017 36.245 76. 31 3.427 50.357 74. 373 76.001 2.72 7. 15 36.194 66.99 100 3 9.95 92.216 97. 92 1 99.669 5.44 25.5 73. 27 87.964 100 78. 105 100 99.992 99. 999 10.88 62 99.943 99.974 100 99.953 100 100 100 21.76 97 100 100 100 100 100 100 100 43.52 100 100 100 100 100 100 100 100 OPERATING CONDITIONS TONNAGES: 1250 1250 2776 1250 1526 1526 236.75 1486.75 - 270 -% +1 INCH: 92.85 33.01009 60.04972 CRUSHER CURRENTS: 21.32 39.57 SETS: 2 CR SET= 2.85 SCRN OP= 1.4 3 CR SET= 0.95 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 76. 30968 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT EEED= 31.14681 % CIRCULATING LOAD= 1.2208 # 7STOPI + ? AT LINE "2120" IN PROGRAM "PGM2" + ? PROGRAM ENDS : MTS # CONTROL * PRINT* HOLD PR INT=TN FOSM=8X11 # *PRINT* ASSIGNED RFS NUMBER 665816 # COPY *MSQURCE*dSP *PRINT* - 271 -APPENDIX K OUTPUT FROM SIMULATION STUDIES F u l l F a c t o r i a l Design Study Intermediate Ranges Study - zrz -(a) F u l l F a c t o r i a l Design Study . . B E E S . , , . 1. . B E E S . . . 2. . BEES. . . 3. . B E E S . . . 4. . BEES. . , 5 . . B E E S . . . 6 . . BEES. . . 7. .BEES. RFS NO. 186975 UNIVERSITY OF B C COMPUTING CENTRE MTS{A3 * * * T H E PAPERTAPE PUNCH S READER ARE DOWN * * * $SIGN RALU T=2M PRINT=TN FORM=8X11 P=60 273 RRRRRRRRRRR RRRRRRRR RRRR RR RR RR RR R R RR RRRRRRRRRRRR RRRRRRRRRRR RR RR RR RR RR RR RR RR RR RR AAAAAAAAAA AAAAAAAAAAAA A A A A AA A A AA A A AAAAAAAAAAAA AA.AAAAA AAAAA AA A A AA AA A A A A AA A A AA A A LL L L LL L L LL L L LL LL L L LL L L L L L L L L L L L L L L L L L L L L L L L L UU UU UU UU UU UU UU UU uu uu uu uu uu uu uu uu uu uu uu uu uuuuuuuuuuuu uouuuuuuuu * * L A S T SIGNON WAS: 21:27:31 USER "RALU" SIGNED ON AT 2 1:28:50 ON WED SEP 07/77 $RUN *BASIC EXECUTION BEGINS UBC BASIC SYSTEM %GET PGM2 110 PRINT 112 READ A 114 115 READ Q2,S ,Q3 1 16 1 18 READ J5 120 I F J5=0 THEN 130 122 128 130 READ J6 2098 PRINT " 3010 DATA 1 2 5 5 . 4 , 2 . 5 4 , 1 . 2 7 , . 4 9 5 , 0 , 1 3020 DATA 1 5 7 8 . 8 , 2 . 5 4 , 1 , 2 7 , . 4 9 5 , 0 , 1 3030 DATA 1 2 5 5 . 4 , 3 . 7 8 5 , 1 . 2 7 , . 4 9 5 , 0 , 1 3040 DATA 1 5 7 8 . 8 , 3 . 7 8 5 , 1 . 2 7 , . 4 9 5 , 0 , 1 3050 DATA 1 2 5 5 . 4 , 2 . 5 4 , 1 . 5 9 , . 4 9 5 , 0 , 1 - Zl<\ -3060 3070 3080 3090 3100 3110 3120 3130 3140 3150 3 160 %RUN DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA 1578 .8 ,2 . 1 2 5 5 , 4 , 3 . 1578 .8 ,3 . 1255 .4 ,2 . 1578 .8 ,2 . 1255 .4 ,3 . 1578 .8 ,3 . 1255 .4 ,2 . 1578 .8 ,2 . 1255 .4 ,3 . 1578 .8 ,3 . 54,1 785, 785, 54,1 54, 1 785, 785, 54,1 54,1 785, 785, . 5 9 , . 1 .59, 1 .59 , .27 ,1 . 2 7 , 1 1. 27, 1 .27, . 5 9 , 1 .59 ,1 1. 59, 1.59, 495 ,0 , 1 . 495 ,0 , 1 . 495 ,0 ,1 . 0 8 , 0 , 1 . 0 8 , 0 , 1 1 .08 ,0 ,1 1 .08 ,0 ,1 . 08 ,0 , 1 . 0 8 , 0 , 1 1 .08 ,0 , 1 1 .08 ,0 ,0 NUMBER OF CYCLES= 11 CONVERGENCE CRITERION= 3.458869E-3 %SET COLWIDTH % RETAINED: = 8 SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 3 0 0 0 0 0 . 0 0 10.88 35 0 0 0 0 0 0 0 5. 44 36.5 28.384 12.422 0 22.088 0.0 02 0 0 2.72 18.35 35,327 20.172 0 35.869 8.381 0 0 1.36 4.7 16.261 3 0.85 20.493 3 8.909 42.202 0 20.493 0.68 0.94 7. 258 1 4. 26 30.555 1.58 19.708 0 30.555 0.34 0.29 4. 155 8.505 18. 645 0.615 1 1.889 0 18.645 0.17 0.22 2.768 4.691 10.30 7 0.321 6.188 0 10.307 0.085 0. 17 1. 869 3.09 6.791 0.21 4.04 0 6.791 0.0425 0. 17 1.291 2. 077 4.566 0.141 2.689 0 4.566 0.0212 0. 18 0.911 1.389 3.054 0.094 1.762 0 3.054 0.0106 0. 16 0.631 0.917 2.016 0.062 1.14 0 2.016 0.0053 0. 13 0.432 0.6 1.318 0.041 0.731 0 1. 318 -0 .0053 0. 19 0.714 1.026 2.254 0.07 1.269 0 2.254 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0. 19 0.714 1.026 2.254 0.07 1.269 0 2.254 0.0106 0.32 1.145 1.625 3.573 0.11 1.999 0 3.573 0.0212 0.48 1.776 2.543 5.588 0. 173 3. 139 0 5.588 0.0425 0.66 2.687 3.932 8.642 0.267 4.901 0 8.642 0.085 0.83 3.978 6.009 13. 208 0. 408 7 .59 0 13.208 0. 17 1 5. 847 9.1 19.999 0.618 1 1.63 0 19. 999 0.34 1.22 8.615 13.791 30.307 0.94 17. 818 0 30.307 0.68 1.51 12.77 22.295 48. 951 1.554 2 9.707 0 48. 951 1.36 2.45 20.027 36.555 79.507 3.134 49.415 0 79.507 2.72 7. 15 36.289 67 .405 100 42.043 91.617 0 100 5.44 25.5 71.616 87.578 100 77. 912 99.998 0 100 10. 88 62 100 100 100 100 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES • 1255.4 1255.4 2868.8 1255. 4 1613.4 1613.4 0 1255.4 % +1 INCH: 92.85 32.59477 CRUSHER CURRENTS: 23.68 S E T S : 2 CR SET= 2.54 SCRN OP= 1.27 %-1/2 INCH IN FEED= 2.45 % - 1 / 2 INCH RATIO, SCREEN U/S 57.9569 45. 16 3 CR S£T= 0.495 IS-1/2 INCH IN SCREEN U/S= 79. 50652 TO PLANT FEED= 32.4 516 4 % CIRCULATING LOAD= 1.285168 - n/o -NUMBER OF CYCLES= 12 CONVERGENCE CRITERION= 1. 022953E-4 %5ET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 3 0 0 0 0 0 0 0 10. 88 35 0 0 0 0 0 0 0 5.44 36.5 29.02 12.394 0 21.63 0.002 0 0 2.72 18.35 36.925 20.591 0 35. 937 8.417 0 0 1. 36 4.7 16.656 30.989 20. 13 39.082 41.671 0 20. 13 0.68 0.94 6.785 13. 587 29. 62 1.637 18.656 0 29.62 0.34 0.29 3.546 8.275 18.5 0.655 1 1.8 0 18. 5 0.17 0.22 2.268 4.796 10.748 0.36 6 .68 0 10.748 0.085 0. 17 1.51 3. 185 7. 139 0.238 4.433 0 7. 139 0.0425 0. 17 1.048 2. 141 4.799 0. 16 2.955 0 4.799 0.0212 0. 18 0.751 1.43 3.206 0.107 1.937 0 3. 206 0.0106 0.16 0.528 0.943 2. 114 0.07 1.252 0 2.1 14 0.0053 0. 13 0. 365 0.616 1.381 0.046 0.803 0 1.381 - 0 . 0053 0. 19 0.598 1.054 2.364 0.079 1.394 0 2.364 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.19 0.598 1.054 2. 364 0.079 1.394 0 2.364 0.0106 0.32 0.963 1.67 3.745 0.124 2.1 97 0 3.745 0.0212 0.48 1.491 2.613 5.858 0. 195 3 .4 5 0 5.858 0.0425 0.66 2. 242 4.043 9.064 0.301 5.386 0 9.064 0.085 0.83 3.29 6. 184 13. 864 0.461 8.342 0 13.864 0. 17 1 4. 8 9.369 21.003 0.698 12. 775 0 21.003 0.34 1.22 7.068 14. 165 31. 751 1.0 59 19.455 0 31.751 0.68 1.51 10.614 22. 44 50.25 1.714 31.255 0 50. 25 1 .36 2.45 17.398 3 6.027 79. 87 3.351 49.911 0 79.87 2.72 7. 15 34.0 54 67.016 100 42.433 91. 581 0 100 5.44 25.5 70.98 87.606 100 78. 37 99.998 0 100 10. 88 62 100 100 100 100 100 0 100 21. 76 97 100 100 100 100 1 00 0 100 4 3. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES i : 1578.8 1578.8 3697. 17 1578. 8 2118.37 2118.37 0 1578.8 % +1 INCH: 92.85 32.98435 57.56726 CRUSHER CURRENTS: 29.26 52.15 SETS: 2 CR SET= 2.54 SCRN OP= 1.27 3 CR SET= 0.495 %-1/2 INCH IN FEED= 2.45 %-l/2 INCH IN SCREEN U/S= 79.87011 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 32.60004 % CIRCULATING LOAD= 1.34176 NUMBER OF CYCLES^ 12 CONVERGENCE C8ITERION= 2.881162E-4 %5ET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF - Zlb -21.76 3 0 0 0 0 0 0 0 10.88 35 0.034 0.013 0 0.022 0 0 0 5.44 36.5 49.038 19.304 0 31.835 0.0 03 0 0 2.72 18.35 32.081 17.392 0 28. 682 7.857 0 0 1.36 4,7 10.628 30.538 20.893 3 6. 798 43.461 0 20.893 0.68 0.94 3. 38 2 1 2. 188 28. 966 1.298 17.905 0 28.966 0.34 0. 29 1.528 7.488 18. 229 0.516 11.357 0 18.229 0.17 0.22 0.964 4.401 10.739 0.287 6.633 0 10.739 0.085 0, 17 0.647 2.944 7. 185 0.191 4.434 0 7. 185 0.0425 0. 17 0.481 1.983 4. 84 0.128 2.959 0 4.84 0.0212 0. 18 0.381 1.326 3. 235 0.086 1 .939 0 3. 235 0.0106 0. 16 0. 289 0.874 2. 133 0.057 1 .253 0 2. 1 33 0.0053 0. 13 0.213 0.571 1.394 0. 037 0.804 0 1. 394 -0 .0053 0.19 0.334 0.977 2.386 0.0 63 1.395 0 2.386 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.19 0.334 0.977 2.386 0.063 1.395 0 2.386 0,0106 0.32 0.547 1.548 3.779 0.1 2.199 0 3.779 0.0212 0.48 0.836 2.422 5. 913 0. 157 3.452 0 5.913 0.0425 0.66 1.217 3.74 8 9. 148 0. 243 5.391 0 9. 148 0.085 0.83 1.698 5.731 13.988 0.371 8.349 0 13.988 0. 17 1 2. 345 8.675 21.173 0.562 12.784 0 21.173 0.34 1.22 3. 309 13.076 31. 913 0.849 19.416 0 31.913 0.6 8 1.51 4. 837 20. 564 50.142 1.365 30.773 0 50. 142 1.36 2.45 8.219 32.753 79. 107 2.663 4 8.678 0 79.107 2.7 2 7. 15 18.847 63.29 100 39.461 92. 139 0 100 5.44 25.5 50.928 80.683 100 68.143 99.997 0 100 10.88 62 99.966 99.987 100 99. 978 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 1 00 0 100 1255.4 3189.38 1255.4 36.70966 1933.98 1933.98 0 60.53894 OPERATING CONDITIONS TONNAGES: 1255.4 % + 1 INCH: 92.85 CRUSHER CURRENTS: 14.56 49.6 SETS: 2 CR S E T 3 3.785 SCRN O P 3 1.27 3 CR S E T 3 0.495 %-1/2 INCH IN F E E D 3 2.45 %-1/2 INCH IN SCREEN U / S 3 79.10722 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 32.28866 % CIRCULATING LOAD 3 1. 540 529 1255.4 NUMBER OF C Y C L E S 3 12 CONVERGENCE CRITERION 3 9.081121E-3 %SET COLWIDTH=8 % RETAINED; SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CEP P F RMF 21.76 3 0 0 0 0 0 0 0 10. 88 35 0.034 0.013 0 0.021 0 0 0 5.44 36.5 50.294 19.318 0 31.364 0.0 03 0 0 2.72 18.35 33.018 17. 328 0 28. 134 7.545 0 0 1.36 4.7 10.509 30.446 19.443 37. 30 7 42.878 0 19.443 0.68 0.94 2 .9 12.247 29.423 1.537 18.076 0 29.423 0,34 0.29 1.055 7.569 18.708 0.623 1 1. 63 0 18.708 0. 17 0.22 0.597 4.41 10.932 0.344 6.788 0 10.932 0.085 0. 17 0.389 2.944 7.299 0.228 4.537 0 7.299 - Cll -0.0425 0. 17 0. 306 1.982 4. 914 0.1 53 3.027 0 4.914 0.0212 0.18 0.26 7 1. 324 3. 284 0. 102 1.984 0 3. 284 0.0106 0. 16 0.215 0.873 2. 164 0.068 1.283 0 2.164 0.0053 0. 13 0. 165 0,57 1.414 0.044 0.822 0 1.414 - 0 . 0053 0. 19 0. 251 0.976 2. 42 0.076 1.428 0 2.42 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0. 19 0. 251 0.976 2. 42 0.076 1.428 0 2.42 0.0106 0. 32 0.417 1 .54 6 3 . 834 0. 12 2.25 0 3. 834 0.0212 0.48 0.63 2 2.419 5, 998 0. 187 3.533 0 5.998 0.0425 0.66 0.899 3.74 3 9.281 0.29 5.517 0 9.281 0.085 0.83 1.205 5.7 25 14. 196 0. 443 8.543 0 14. 196 0. 17 1 1. 594 8.669 21.495 0.671 13. 08 0 21.495 0.34 1.22 2. 191 13.079 32.426 1^015 19.868 0 32.426 0.68 1.51 3.246 20.648 51.134 1.638 31.499 0 51.13 4 1.36 2.45 6. 145 32.894 80.557 3. 174 49. 574 0 80.557 2 .72 7. 15 16.654 63.34 100 40.481 92.452 0 100 5.44 25.5 49.672 80.669 100 68.615 99.997 0 100 10. 88 62 99.966 99.987 100 99.979 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578. 8 1578. 8 4110.7 1578.79 2531.91 2531.91 0 1578.79 % + 1 INCH: 92.85 36.65974 59.51919 CRUSHER CURRENTS: 20.15 57.88 S E T S : 2 CR SET= 3. 785 SCRN OP= 1. 27 3 CR SET= 0.495 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 80.55686 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 32.88035 % CIRCULATING LOAD= 1.603693 NUMBER OF C Y C L E S 3 14 %SET COLHIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21.76 3 0 10. 88 35 0 5.44 36.5 28.384 2.72 18. 35 35.3 27 1.36 4.7 16.261 0.68 0.94 7.258 0.34 0.29 4. 155 0. 17 0.22 2.768 0.085 0. 17 1.86 9 0.0425 0. 17 1.291 0.0212 0. 18 0.91 1 0.0106 0. 16 0.631 0.0053 0. 13 0.432 -0 .0053 0. 19 0.714 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0. 19 0.714 CONVERGENCE CRITERION 3 S F S U/S S O/S 0 0 0 O 0 0 13.629 0 26.215 26. 38 0 50. 74 29.774 38. 62 1 21.604 14.653 29.611 0.84 5.645 1 1. 514 0.225 3.307 6.752 0. 126 2.217 4. 527 0.084 1.5 3.064 0.057 1.014 2.071 0.038 0.676 1.381 0.026 0.446 0.912 0.017 0.758 1.548 0.029 S F S U/S S O/S 0.758 1.548 0. 029 9.099711E-3 3 CRP P F RMF 0 0 0 0 0 0 0.004 0 0 18. 118 0 0 4 2.251 0 38.621 21.482 0 29.6 11 7.021 0 11.514 3.805 0 6.752 2.539 0 4.527 1.693 0 3.064 1.11 0 2.071 0.718 0 1. 381 0.46 0 0.912 0.7 99 0 1.548 3 CRP P F RMF 0.799 0 1.548 - Z/b -0.0106 0.32 1.145 1.204 2.459 0.0 46 1.259 0 2.459 0.0212 0. 48 1.776 1.881 3. 84 0.071 1.977 0 3. 84 0.0425 0.66 2.687 2.895 5.911 0. 1 1 3 .087 0 5.911 0.085 0. 83 3.978 4.395 8. 975 0. 166 4.78 0 8.975 0.17 1 5. 847 6.612 13.502 0.25 7.319 0 13.502 0.34 1.22 8.615 9.919 20.254 0.376 11.124 0 20.254 0.68 1.51 12.77 15. 564 31.767 0.602 18. 144 0 31.767 1.36 2.45 20.027 30.217 61.37 9 1.442 3 9.62 7 0 61.379 2.72 7. 15 36.289 59. 991 100 23.046 81.878 0 100 5. 44 25.5 71.6 16 86.371 100 73.785 99.996 0 100 10. 88 62 100 100 100 100 100 0 100 21.76 97 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES I 1255. 4 1255.4 2614.92 1255.41 1359.52 1359.52 0 1255.41 % +1 INCH: 92.85 CRUSHER CURRENTS: 23. 68 SETS: 2 CR SET= 2.54 SCRN OP= 1. 59 3 CR 5S-1/2 INCH IN FEED= 2.45 %-1 /2 INCH IN SCREEN U/S= 61. 37 867 % - 1 / 2 INCH fiATIO, SCREEN U/S TO PLANT FEED= 25.05252 % CIRCULATING LOAD= 1.082938 40.0091 76. 95447 41.64 SET= 0.495 NUMBER OF CYCLES= 11 %SET COL»IDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21. 76 3 0 10. 88 35 0 5. 44 36.5 29.02 2.72 18.35 36.925 1.36 4.7 16.656 0.68 0.94 6.785 0.34 0.29 3.546 0.17 0.22 2.268 0.085 0. 17 1.51 0.0425 0. 17 1.048 0.0212 0. 18 0.751 0.0106 0.16 0.528 0.0053 0.13 0.365 - 0 . 0053 0.19 0. 598 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0. 19 0.598 0.0106 0. 32 0. 963 0.0212 0.48 1.491 0.0425 0.66 2.242 0.085 0.83 3.29 0. 17 1 4.8 0.34 1.22 7.068 0.68 1.51 10.614 1 .36 2.45 17.398 2.72 7. 15 34.0 54 CONVERGENCE CRITERION= S F S U/S S O/S 0 0 0 0 0 0 13. 576 0 25.505 27. 935 0 52. 482 27.642 35.764 20.506 12.35 25.552 0.75 6.225 13. 01 0.263 4.073 8.52 0. 1 65 2.769 5.793 0.111 1.869 3.911 0.075 1.255 2.6 25 0.05 0.831 1. 738 0.033 0.545 1.141 0.022 0.93 1.946 0.0 37 S F S U/S S O/S 0.93 1.946 0.037 1.475 3.087 0.059 2.306 4. 825 0.0 93 3. 561 7.45 0. 1 43 5.43 11. 361 0.218 8. 199 17.154 0.329 12. 271 25. 674 0.494 18.4 97 38.684 0.757 30. 847 64.236 1.507 58.489 100 22.013 3. 756307E-4 3 CRP P F RMF 0 0 0 0 0 0 0.004 0 0 2 0. 035 0 0 37.296 0 35.764 17.241 0 25.552 8.58 0 13. 01 5.659 0 8.52 3.875 0 5.793 2.591 0 3.911 1 .698 0 2.625 1.097 0 1.738 0.703 0 1. 141 1.222 0 1.946 3 CRP P F RMF 1.222 0 1.946 1.925 0 3.087 3.022 0 4.825 4.72 0 7.45 7.311 0 11.361 11.185 0 17. 154 16.844 0 25.674 25. 424 0 38.684 42.665 0 64.236 79. 961 0 100 - <:/y -5.44 25.5 70.98 86.424 100 74.495 99.996 0 100 10. 88 62 100 100 100 100 100 0 100 21. 76 97 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 1578.8 3375.49 1578.8 1796.69 1796.69 0 7 7 . 9 8 6 9 8 OPERATING CONDITIONS TONNAGES: 1578.8 % +1 INCH: 92.85 CRUSHER CURRENTS: 29.26 SETS: 2 CR S E T 3 2.54 %--\/2 INCH IN F E E D 3 2.45 %-1/2 INCH IN SCREEN U / S 3 64. 23609 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 26.21881 % CIRCULATING LOAD 3 1.13801 1 5 7 8 . 8 4 1.51059 SCRN OP= 1.59 47.69 3 CR S E T 3 0.495 NUMBER OF C Y C L E S 3 12 %SET COLHIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21. 76 3 0 10.88 35 0.034 5.44 36.5 49.038 2.72 18.35 32.081 1.36 4.7 10.628 0.68 0.94 3.382 0. 34 0.29 1. 528 0.17 0.22 0.964 0.085 0. 17 0.647 0.0425 0. 17 0.481 0.0212 0. 18 0.381 0.0106 0. 16 0.289 0.0053 0. 13 0.213 - 0 . 0053 0. 19 0.334 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.19 0.334 0.0 106 0.32 0.547 0,0212 0.48 0.836 0.0 425 0.66 1.217 0.085 0.83 1.698 0. 17 1 2. 345 0.34 1.22 3. 309 0.68 1.51 4. 837 1 .36 2.45 8.219 2 .72 7. 15 18.847 5.44 25.5 50.928 10. 88 62 99.966 21. 76 97 100 43. 52 100 100 TONNAGES 1255.4 1255.4 % + 1 INCH: CONVERGENCE CRITERION 3 S F S U/S S O/S 0 0 0 0.015 0 0.026 21.129 0 37.121 24.252 0 42.608 26.593 36.62 19.004 11.269 25.334 0.623 5.572 12.652 0.213 3.686 8.378 0.134 2.522 5.733 0.091 1.707 3. 88 0.062 1. 147 2.6 07 0.042 0.76 1.727 0.Q28 0.499 1.134 0.018 0.851 1. 934 0.031 S F S U/S S O/S 0.851 1.-934 0.031 1.349 3.068 0.049 2. 109 4,795 0.076 3.256 7.403 0.1 18 4.963 11. 283 0. 18 7.485 17.015 0.271 1 1, 17 25. 393 0.405 16.742 38. 045 0.618 28.011 63. 38 1.241 54.604 100 20.245 78.856 100 62.853 99.985 100 99.974 100 100 100 100 100 100 OPERATING CONDITIONS 2914.09 1255. 41 1658. 68 7.995972E-3 3 CRP P F RMF 0 0 0 0 0 0 0.006 0 0 18.327 0 0 38.676 0 36. 62 17.238 0 25.334 8.632 0 12. 652 5.746 0 8.378 3.94 0 5.733 2.635 0 3. 88 1.726 0 2.607 1.116 0 1.727 0.715 0 1. 134 1.242 0 1.934 3 CRP P F RMF 1.242 0 1.934 1 .957 0 3.068 3.073 0 4.795 4.799 0 7.403 7.434 0 11.283 1 1.374 0 17.015 17. 12 0 25.393 25.752 0 38.045 42.99 0 63. 38 81.667 0 100 99.994 0 100 100 0 100 100 0 100 ' 100 0 100 1658,68 0 1255.4-- £ O U -92.85 45.39591 79.7547 CRUSHER CURRENTS: 14. 56 45.78 SETS: 2 CR SET= 3.785 SCRN 0P= 1.59 3 CR SET= 0.495 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 63.37956 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 25.86921 56 CIRCULATING LOAD= 1.321236 NUMBER OF CYCLES= 10 CONVERGENCE CRITERION= 5. 993138E-3 38SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CHP P F RMF 21. 76 3 0 0 0 0 0 0 0 10.88 35 0.034 0.014 0 0.025 0 0 0 5. 44 36.5 50.294 21.2 93 0 36.923 0.006 0 0 2 .72 18.35 33.018 24. 287 0 42. 115 17. 879 0 0 1.36 4.7 10.509 26. 353 35.605 19.562 37. 983 0 35.605 0.68 0.94 2 .9 10.815 24.643 0.665 16.625 0 24.643 0. 34 0.29 1.055 5.689 13.108 0.243 9.09 0 13. 108 0.17 0.22 0.597 3.812 8. 795 0. 155 6.1 73 0 8.795 0.085 0. 17 0. 389 2.61 6.022 0.106 4.241 0 6.022 0.0425 0. 17 0. 306 1.765 4.073 0.071 2.836 0 4.073 0.0212 0. 18 0.267 1.185 2.733 0.048 1.858 0 2.7 33 0.0106 0.16 0.215 0.784 1.809 0.032 1.201 0 1.809 0.0053 0. 13 0. 165 0.514 1.186 0.021 0.77 0 1. 186 - 0 . 0053 0. 19 0. 251 0.878 2.025 0.035 1.337 0 2.025 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.19 0.251 0.878 2.025 0.035 1.337 0 2.025 0. 0106 0. 32 0.417 1.392 3.211 0.056 2.107 0 3.211 0.0212 0.48 0.632 2. 176 5.02 0.088 3.308 0 5.02 0.0425 0.66 0.899 3.36 7.753 0. 136 5.167 0 7.753 0.085 0.83 1.205 5. 126 1 1. 826 0.2 07 8.003 0 11.826 0. 17 1 1.594 7.736 17. 849 0.3 13 12.244 0 17.849 0.34 1.22 2. 19 1 11.5 48 26. 644 0.468 18.417 0 26.644 0.68 1.51 3. 246 17.237 39.752 0.711 27.507 0 39.752 1 .36 2.45 6. 145 28.052 64. 395 1.375 44. 132 0 64.395 2.72 7. 15 16.654 54.405 100 20. 937 82. 115 0 100 5.4 4 25.5 49.672 78.692 100 63.052 99.994 0 100 10. 88 62 99.966 99.986 100 99.975 100 0 100 21 .76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3729.68 1578.79 2150.88 2150.88 0 1578.79 % +1 INCH: 92.85 45.59491 79.06251 CRUSHER CURRENTS: 20. 15 52.6 S E T S : 2 CR SET= 3 .?85 SCRN OP= 1.59 3 CR SET= 0.495 %-1/2 INCH IN FEED= 2.45 SS-1/2 INCH IN SCREEN U/S= 64.39515 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 26.28373 % CIRCULATING LOAD= 1.362351 - Zo\ -NUMBER OP CYCLES= 7 CONVERGENCE CRITERION 3 2.802705E-4 %SET COL¥IDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 3 0 0 0 0 0 0 0 10.88 35 0 0 0 0 0 0 0 5.44 36.5 28.384 12.616 0 22.708 0 0 0 2.72 18.35 35.327 19.631 0 35. 337 7.075 0 0 1.36 4.7 16.261 30.396 19.999 38.714 4 1. 704 0 19.999 0.68 0.94 7.258 14.753 31. 132 1.65 20.75 0 31.132 0. 34 0.29 4. 155 8.775 18.943 0.64 12.471 0 18.943 0.17 0.22 2.768 4.72 10.212 0. 326 6.282 0 10.212 0.085 0. 17 1. 869 3.093 6.6 94 0.212 4.073 0 6.694 0.0425 0.17 1.291 2.079 4. 499 0. 1 43 2.709 0 4.499 0.0212 0. 18 0.911 1.391 3. 01 0.095 1.775 0 3.01 0.0106 0. 16 0.631 0.918 1.987 0.063 1.148 0 1.987 0.0053 0. 13 0. 432 0.601 1.3 0.041 0.736 0 1. 3 - 0 . 0053 0. 19 0.714 1.Q27 2. 223 0.07 1.278 0 2.223 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP p F RMF 0.0053 0.19 0.714 1.0 27 2. 223 0.07 1.2 78 0 2.223 0.0106 0. 32 1. 145 1.628 3.523 0.1 12 2.014 0 3.523 0.0212 0.48 1.776 2.546 5.51 0. 175 3 . 162 0 5.51 0.0 4 25 0.66 2.687 3 .937 8.52 0.27 4.937 0 8.52 0.085 0.83 3.978 6.016 13. 019 0.413 7.645 0 13.019 0. 17 1 5. 847 9. 109 19.713 0.6 25 11.718 0 19.713 0.34 1.22 8.615 13.829 29.926 0.951 18 . 0 29.926 0.68 1.51 12.77 22.604 48. 869 1 .591 30. 471 0 48.869 1 .36 2.45 20.027 37. 357 80.00 1 3.241 51.221 0 80.001 2.72 7. 15 36.289 67.753 100 41. 954 92. 925 0 100 5.44 25.5 71.616 87.384 100 77.292 100 0 100 10. 88 62 100 100 100 1 00 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 1 00 100 100 1 00 0 100 OPERATING CONDITIONS TONNAGES: 1255.4 1255.4 2824.59 1255. 4 1569. 19 1569.19 0 1255.4 % +1 INCH: 92.85 32.24706 58.04566 CRUSHER CURRENTS: 23.68 38.92 S E T S : 2 CR S E T 3 2.54 SCRN O P 3 1.27 3 CR SET= 1.08 %-1/2 INCH IN F E E D 3 2. 45 5S-1/2 INCH IN SCREEN U/S= 80.00063 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 32.65332 % CIRCULATING LOAD 3 1.249952 NUMBER OF C Y C L E S 3 11 CONVERGENCE CRITERION 3 2 .594253E-4 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.?6 3 0 0 0 0 0 0 0 10. 88 35 0 0 0 0 0 0 0 5.44 36.5 29.02 12.599 0 22. 266 0 0 0 - 282 -2.72 18. 35 36.925 1.36 4.7 16.656 0.68 0.94 6.785 0.3 4 0.29 3.546 0, 17 0. 22 2.268 0.085 0. 17 1.51 0.0425 0. 17 1.048 0.0212 0.18 0.751 0.0106 0. 16 0.528 0.0053 0.13 0.365 - 0 . 0053 0. 19 0. 598 % PASSING: SIZE 2 CBF 2 CRP 0.0053 0. 19 0.59 8 0.0106 0.32 0.963 0.0212 0.48 1.491 0.0425 0.66 2.242 0.085 0.83 3.29 0.17 1 4.8 0.34 1.22 7.068 0.68 1.51 10.614 1.36 2.45 17.398 2.72 7. 15 34.054 5.44 25.5 70.98 10. 88 62 100 21. 76 97 100 43.52 100 100 20.088 0 35.501 30.511 19.698 38.807 13.884 29.796 1.674 8.481 18. 658 0.672 4.891 10.787 0.368 3.245 7. 16 0.2 42 2.181 4.813 0. 163 1.457 3.215 0. 109 0.961 2. 119 0.072 0.628 1.385 0.047 1.074 2.37 0.08 S F S U/S S O/S 1.07 4 2 .37 0.08 1.702 3.754 0. 127 2. 662 5. 874 0.1 99 4. 12 9. 088 0.307 6.301 13. 901 0.47 9.547 21.061 0.712 14.438 31. 847 1.08 22.918 50. 505 1.752 36. 802 80.302 3.426 67.313 100 42.233 87.401 100 77.734 100 100 100 100 100 100 100 100 100 7.17 0 0 4 1.141 0 19.698 19.33 0 29.796 12. 267 0 18.658 6.904 0 10.787 4.577 0 7. 16 3.051 0 4. 813 1.999 0 3.215 1 .293 0 2. 119 0.829 0 1.385 1 .439 0 2. 37 3 CRP P F RMF 1.439 0 2.37 2.268 0 3.754 3.561 0 5.874 5.561 0 9.088 8.612 0 13.901 13.189 0 21.061 20.092 0 31.847 32. 359 0 50.505 51.689 0 80.302 92. 83 0 100 100 0 100 100 0 100 100 0 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578. 8 1578. 8 3636.49 1578. 8 2057.69 2057.69 0 1578.8 % +1 INCH: 92.85 32.68742 57.76741 CRUSHER CURRENTS: 29. 26 45 .69 SETS; 2 CR SET= 2.54 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 80.30151 % - 1 / 2 INCH RATIO, SCREEN D/S TO PLANT FEED= 32.77613 % CIRCULATING LOAD= 1.30 3325 NUMBER OF CYCLES= 11 CONVERGENCE CRITERION= 1.350034E-4 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 3 0 0 0 0 0 0 0 10. 88 35 0.034 0.014 0 0.023 0 0 0 5. 44 36.5 49.038 19.597 0 32.642 0 0 0 2 .72 18.35 32.081 16.831 0 28.035 6.68 0 0 1.36 4.7 10.628 30. 118 20.426 36.569 4 3. 091 0 20.426 0.68 0.94 3. 382 12. 47 29. 2 1.333 18. 519 0 29.2 0.34 0. 29 1. 528 7.679 18.416 0.532 1 1.773 0 18.416 0.17 0.22 0.96 4 4.479 10.766 0.293 6.818 0 10.766 0.085 0. 17 0. 647 2.991 7.192 0.195 4.551 0 7. 192 0.0425 0. 17 0. 481 2.015 4. 845 0. 131 3.036 0 4.845 0.0212 0. 18 0.381 1.347 3.238 0.088 1 .989 0 3.238 0.0106 0.16 0.289 0.888 2. 135 0.0 58 1.286 0 2. 135 0.0053 0. 13 0. 213 0.58 1.395 0.038 0.825 0 1. 395 - 0 . 0 053 0.19 0.334 0.993 2.388 0.065 - 1.432 0 2. 388 55 PASSING: SIZE 2 CRF 2 CRP S F S 0/S S O/S 3 CRP P F RMF 0.0053 0. 19 0. 334 0.993 2. 388 0.065 1.432 0 2.388 0.0106 0. 32 0.547 1.573 3.782 0.102 2.2 56 0 3.782 0.0212 0.48 0.836 2.461 5.917 0. 16 3.542 0 5.917 0.0425 0.66 1.217 3.807 9. 155 0.2 48 5.532 0 9. 155 0.085 0.83 1.698 5.822 14 0.379 8.568 0 14 0. 17 1 2. 345 8.813 21. 192 0.573 13. 119 0 21.192 0.34 1.22 3.309 13.292 31. 958 0.867 19.937 0 31.958 0.68 1.51 4. 837 2 0. 971 50.374 1.398 31.71 0 50.374 1 .36 2.45 8.219 33. 44 79. 574 2.732 50.229 0 79.574 2 .72 7. 15 18.847 63.558 100 39.301 9 3.32 0 100 5.44 25.5 50.928 80.389 100 67. 336 100 0 100 10. 88 62 99.966 99.986 100 99. 977 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 3141.38 1255. 4 1885.98 1 885.98 0 1255.4 % +1 INCH: 92.85 36.44163 60.69901 CRUSHER CURRENTS: 14.56 43.31 S E T S : 2 CR SET= 3.785 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH IN FEED= 2.45 %-l/2 INCH IN SCREEN D/S= 79.57359 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 32.47902 % CIRCULATING LOAD= 1. 502294 NUMBER OF CYCLES= 12 5SSET COLHIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21.76 3 0 10. 88 35 0.034 5.44 36.5 50.294 2.72 18.35 33.018 1.36 4.7 10.509 0.68 0.94 2. 9 0.34 0.29 1.055 0. 17 0. 22 0.597 0.085 0. 17 0.389 0.0425 0. 17 0. 306 0.0212 0. 18 0.267 0.0106 0. 16 0.215 0.0053 0. 13 0. 165 - 0 . 0053 0. 19 0. 251 % PASSING; SIZE 2 CRF 2 CRP 0.0053 0. 19 0. 251 0.0106 0.32 0.417 0.0212 0.48 0.632 0.0425 0.66 0.899 CONVERGENCE CRITERION= S F S U/S S O/S 0 0 0 0.013 0 0.022 19.64 0 32. 223 16.831 0 27. 615 29.993 19. 146 36.943 12.46 2 9. 49 4 1.546 7.727 18.806 0.628 4.498 10.977 0.347 3. 00 1 7.327 0.2 3 2.021 4. 934 0.155 1.35 3.296 0. 103 0.89 2. 172 0.068 0.581 1. 419 0.044 0.995 2.429 0.076 S F S U/S S O/S 0.995 2.429 0.076 1.576 3.848 0.121 2. 466 6.02 0. 1 89 3.816 9.316 0.292 4.066208E-3 3 CRP P F RMF 0 0 0 0 0 0 0 0 0 6.46 0 0 42.477 0 19.146 1 8.585 0 29.494 12.001 0 18.806 6.997 0 10.977 4.675 0 7.327 3.1 19 0 4.934 2.044 0 3.296 1.322 0 2. 172 0.847 0 1.419 1 .471 0 2.429 3 CRP P F RMF 1.471 0 2.429 2.319 0 3.848 3.641 0 6.02 5.685 0 9.316 - £ O t -0. 085 0.83 1. 205 5.837 14.25 0.446 8.804 0 14. 25 0.17 1 1.594 8.838 21.577 0.6 76 13.479 0 21. 577 0.34 1.22 2. 191 13.336 32.554 1. 0 23 20. 476 0 32.554 0.68 1.51 3.246 21.063 51.36 1.651 32.478 0 51. 36 1.36 2.45 6. 145 33.5 23 80.854 3. 197 51. 063 0 80.854 2 .72 7. 15 16.654 6 3.516 100 40.141 93. 54 0 100 5.44 25.5 49.6 72 80.347 100 67.755 100 0 100 10. 88 62 99.966 99.987 100 99.978 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPEHATING CONDITIONS TONNAGES: 1578.8 1578.8 4042.99 1578.8 2464.19 2464.19 0 % +1 INCH: 92.85 36. 48407 CHUSHES CURRENTS: 20. 15 51. 32 SETS: 2 CR SET= 3.785 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH IN FEED= 2.45 55-1/2 INCH IN SCREEN U/S= * - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 33.0016 % CIRCULATING LOAD= 1.560799 1578.8 59.85941 80.85393 NUMBER OF C Y C L E S 3 13 CONVERGENCE CRITERION 3 5 .688607E-3 9JSET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 3 0 0 0 0 0 0 0 10. 88 35 0 0 0 0 0 0 0 5.44 36.5 28.384 13. 877 0 27.153 0 0 0 2.72 18. 35 35.327 24.998 0 48. 912 15. 118 0 0 1.36 4.7 16.261 30.868 39,653 22.463 44. 84 0 39.653 0.68 0.94 7.258 15.361 30.489 0.889 23.113 0 30.489 0.34 0.29 4. 155 5.579 11. 176 0.225 6.942 0 11.176 0. 17 0. 22 2.768 3. 117 6.249 0.12 3.451 0 6.249 0.085 0.17 1.869 2.074 4. 158 0.079 2.269 0 4. 158 0.0425 0. 17 1. 291 1.404 2. 816 0.054 1.512 0 2. 816 0.0212 0.18 0.911 0. 952 1.908 0.036 0.991 0 1.908 0.0106 0. 16 0.631 0.636 1.276 0.024 0.641 0 1. 276 0.0053 0.13 0. 432 0. 42 1 0. 8 44 0.016 0.411 0 0.844 - 0 . 0053 0. 19 0.714 0.714 1.431 0. 027 0.713 0 1. 431 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP p F RMF 0.0053 0. 19 0.714 0.714 1.431 0.027 0.713 0 1.431 0.0106 0. 32 1. 145 1. 135 2. 275 0.043 1.124 0 2.275 0.0212 0.48 1.776 1.771 3.551 0.068 1.765 0 3. 551 0.0425 0.66 2.687 2.722 5.459 0. 104 2.756 0 5.459 0.085 0. 83 3.978 4. 126 8.275 0.158 4.268 0 8. 275 0.17 1 5. 847 6.2 12. 433 0.237 6.537 0 12.433 0. 34 1.22 8.615 9.316 18.682 0.357 9.9 87 0 18.682 0.68 1.51 12.77 14. 895 29.858 0. 582 16. 929 0 29.858 1. 36 2.45 20.027 30.256 60.34 7 1.4 72 40. 042 0 60.347 2.72 7. 15 36.289 61. 124 100 23. 935 84.882 0 100 5.44 25.5 71.616 86.123 100 72. 84 7 1 00 0 100 10. 88 62 100 100 100 100 100 0 100 21. 76 97 100 100 100 100 100 0 100 - 28t> -43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 2567.75 1255. 41 1312.3** 1312.34 0 1255. 41 % +1 INCH: 92.85 38. 87593 76.06522 CRUSHER CURRENTS: 23.68 35.36 SETS: 2 CR SET= 2.54 SCRN OP= 1. 59 3 CR SET= 1.08 %-1/2 INCH IN FEED= 2.45 %-'\/2 INCH IN SCREEN U/S= 60. 34678 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 24.63134 % CIRCULATING LOAD= 1.045356 NUMBER OF CYCLES= 9 CONVERGENCE C R ITER ION = 9. 187785E-3 %SET COLRIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 3 0 0 0 0 0 0 0 10.88 35 0 0 0 0 0 0 0 5. 44 36.5 29.02 13.864 0 26.546 0 0 0 2.72 18.35 36.925 26.678 0 51,081 17.304 0 0 1.36 4,7 16.656 27.987 35.817 20.825 3 8. 353 0 35.817 0.68 0.94 6,785 12.739 25. 816 0.777 18. 185 0 25.816 0. 34 0.29 3. 546 6.336 12. 96 8 0.269 8.888 0 12.968 0.17 0.22 2. 268 4. 116 8. 433 0. 167 5.807 0 8.4 33 0.085 0. 17 1.51 2.796 5.728 0.1 13 3. 971 0 5.728 0.0425 0. 17 1.048 1.887 3. 867 0.076 2.655 0 3.867 , 0.0212 0. 18 0.751 1.267 2.597 0.051 1.74 0 2.597 0.0106 0. 16 0.528 0.839 1.72 0.034 1.125 0 1.72 0.0053 0. 13 0.365 0.551 1.129 O.022 0.721 0 1. 129 -0 .0053 0.19 0.598 0.94 1.925 0.038 1.252 0 1.925 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.19 0. 598 0.94 1.925 0.038 1.252 0 1.925 0.0106 0.32 0.963 1.491 3.054 0.06 1.973 0 3.054 0.0212 0.48 1.49 1 2.33 4.774 0. 0 94 3.098 0 4.774 0.0425 0.66 2.242 3.597 7.371 0.145 4.837 0 7.371 0.085 0.83 3.29 5.485 11.238 0.221 7.492 0 11.238 0.17 1 4. 8 8.28 16.966 0.334 11.464 0 16.966 0.34 1.22 7.068 12.396 25. 4 0. 502 17.271 0 25.4 0.68 1.51 10.614 18.732 38.367 0.771 26. 159 0 38.367 1.36 2.45 17.398 31. 471 64. 183 1.548 44.344 0 64.183 2.72 7. 15 34.054 59.458 100 22.373 82.696 0 100 5.44 25.5 70.98 86.136 100 73. 454 100 0 100 10. 88 62 100 100 100 100 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3304.74 1578.81 1725.93 1725.93 0 % +1 INCH: 92.85 40.54165 77.62738 CRUSHER CURRENTS: 29.26 41.09 1578.81 - 28b -SETS: 2 CR SET= 2.5ft SCRN 0P= 1.59 3 CB SET= 1.08 X - 1 / 2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 64.183 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED = 26.197 14 % CIRCULATING LOAD= 1.093191 NUMBER OF CYCLES= 12 CONVERGENCE C R I T E R I O N 5.279837E-3 %SET COLWIDTH= % BETAINED: SIZE 2 CBF 2 CRP S F S U/S S O/S 3 CEP P F BMF 21.76 3 0 0 0 0 0 0 0 10. 88 35 0.034 0.015 0 0.027 0 0 0 5.44 36.5 49.038 21.545 0 38.431 0 0 0 2.72 18.35 32.081 22. 907 0 40. 86 15. 718 0 0 1.36 4.7 10.628 27.133 36.983 19.414 40.068 0 36.983 0.68 0.94 3. 382 1 1.655 25.7 0.647 18. 138 0 25.7 0.34 0.29 1.528 5.615 12. 50 4 0.215 8.817 0 12.504 0. 17 0. 22 0.964 3.674 8. 191 0. 135 5.799 0 8. 191 0.085 0.17 0.647 2.51 5.597 0.091 3 .97 0 5.597 0. 0 425 0. 17 0. 481 1.699 3.789 0.062 2.655 0 3.789 0.0212 0.18 0.381 1.143 2. 547 0.042 1 .739 0 2.547 0.0106 0. 16 0.289 0.757 1.689 0.028 1. 124 0 1.689 0.0053 0. 13 0.213 0.497 1. 109 0.018 0.721 0 1.109 - 0 . 0053 0. 19 0. 334 0.848 1. 891 0.031 1.251 0 1. 891 % PASSING: SIZE 2 CBF 2 CEP S F S U/S S O/S 3 CEP P F EMF 0.0053 0. 19 0. 334 0.848 1.891 0.031 1.251 0 1.891 0.0106 0.32 0.547 1.346 3 0.049 1.972 0 3 0.0212 0.48 0.836 2. 103 4.689 0.077 3.0 96 0 4.689 0.0425 0.66 1.217 3.246 7.236 0. 1 18 4.835 0 7.236 0.085 0.83 1.698 4.945 11.025 0. 18 7.49 0 11.025 0.17 1 2. 345 7.455 16.622 0.271 1 1. 46 0 16.622 0. 34 1. 22 3. 309 11. 13 24.813 0.406 17.259 0 24.813 0.68 1.51 4.837 16.744 37.317 0.621 26. 076 0 37.317 1.36 2.45 8.219 28.399 63.017 1.269 44.213 0 63.017 2.72 7.15 18.847 55.532 100 20.683 84.282 0 100 5.44 25.5 50.928 78.44 100 61.543 100 0 100 10. 88 62 99.966 99.985 100 99.973 100 0 100 21. 76 97 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 2857.3 1255. 41 1601. 9 1601.9 0 1255. 41 % +1 INCH: 92.85 44.46782 79.31724 CBUSHEB CUBRENTS: 14.56 SETS: 2 CB SET= 3.785 SCBN OP= 1.59 %--\/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 63.01705 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 25.72124 % CIRCULATING LOAD= 1.276008 39. 37 3 CR SET= 1.08 NUMBER OF CYCLES= 14 CONVEEGENCE CRITERION^ 2. 882275E-3 - 287 -%5ET C0LWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S O/S S O/S 3 CRP P F RMF 21.76 •3 0 0 0 0 0 0 0 10. 88 35 0.034 0.015 0 0.026 0 0 0 5.44 36.5 50.294 21.718 0 38. 22 3 0 0 0 2 .72 18.35 33.018 23.129 0 40.706 15.613 0 0 1.36 4.7 10.509 26.523 35.567 19.651 3 8.694 0 35.567 0.68 0.94 2 .9 11.049 24.701 0.675 17.243 0 24.701 0.34 0.29 1.055 5.80 5 13. 118 0.246 9.414 0 13. 118 0.17 0. 22 0.597 3. 883 8.786 0.157 6.381 0 8.786 0.085 0.17 0.389 2.658 6.015 0.107 4.383 0 6.015 0.0425 0. 17 0.306 1.798 4.068 0.072 2.931 0 4.068 0.0212 0. 18 0. 267 1.207 2.73 0.049 1.921 0 2.73 0.0106 0. 16 0. 215 0.798 1.807 0.032 1.242 0 1.807 0.0053 0.13 0. 165 0.524 1. 185 0.021 0.7 96 0 1. 185 - 0 . 0053 0.19 0.251 0.894 2.022 0.036 1.382 0 2.022 % PASSING: SIZE 2 CRF 2 CRP S F S O/S S O/S 3 CRP P F RMF 0.0053 0. 19 0.251 0.894 2.022 0.036 1.382 0 2.0 22 0.0106 0.32 0.417 1.417 3.207 0.057 2.178 0 3.207 0.0212 0.48 0.632 2.216 5.014 0.089 3.419 0 5.014 0.0 425 0.66 0.899 3.422 7.744 0. 138 5.34 0 7.744 0.085 0.83 1.205 5.22 11.813 0.21 8.271 0 11.813 0.17 1 1. 594 7.878 17.828 0.317 12.654 0 17.828 0.34 1.22 2. 191 11.762 26.614 0.4 74 19.036 0 26.614 0.68 1.51 3.246 17.566 39. 73 3 0.72 28.45 0 39.733 1.36 2.45 6. 145 28.616 64.43 3 1.395 45.693 0 64.433 2.72 7.15 16.654 55.139 100 21. 045 84.387 0 100 5.44 25.5 49.672 7 8.268 100 61.751 100 0 100 10. 88 62 99,966 99.985 100 99.974 100 0 100 21. 76 97 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING I CONDITIONS TONNAGES ' Z 1578.8 1578.8 3656. 18 1578.8 2077. 38 2077.38 0 1578. 8 % +1 INCH: 92.85 44. 86086 78.95482 CRUSHER CURRENTS: 20. 15 45. 96 SETS: 2 CR SET= 3.785 SCRN OP= 1. 59 3 CR SET= 1.08 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 64.43347 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 26.29938 % CIRCULATING LOAD= 1.315797 STOP! AT LINE "2120" IN PR0GBAM "PGM2" PROGRAM ENDS 60 DATA 1,16. 5 , 2 8 . 5 , 2 7 . 3 , 1 2 . 6 , 4 . 6 5 , 2 . 25 ,2 . 0, 1.65,1 . 32 , 1 . 0 2 , . 6 4 , . 3 , . 27 3010 DATA 1 2 5 5 . 4 , 2 . 5 4 , 1 , 2 7 , . 4 9 5 , 0 , 1 3020 DATA 1 5 7 8 . 8 , 2 . 5 4 , 1 . 2 7 , . 4 9 5 , 0 , 1 3030 DATA 1 2 5 5 . 4 , 3 . 7 8 5 , 1 . 2 7 , . 4 9 5 , 0 , 1 3040 DATA 1 5 7 8 . 8 , 3 . 7 8 5 , 1 . 2 7 , . 4 9 5 , 0 , 1 3050 DATA 1 2 5 5 . 4 , 2 . 5 4 , 1 . 5 9 , . 4 9 5 , 0 , 1 3060 DATA 1 5 7 8 . 8 , 2 . 5 4 , 1 . 5 9 , , 4 9 5 , 0 , 1 3070 DATA 1 2 5 5 . 4 , 3 . 7 8 5 , 1 . 5 9 , . 4 9 5 , 0 , 1 3080 DATA 1 5 7 8 . 8 , 3 . 7 8 5 , 1 . 5 9 , . 4 9 5 , 0 , 1 - -.»» -3090 DATA 1255. 4 , 2 . 5 4 , 1 . 2 7 , 1 . 0 8 , 0,1 3100 DATA 1578. 8 , 2 . 5 4 , 1 . 2 7 , 1 . 0 8 , 0, 1 3110 DATA 1255. 4 , 3 . 7 8 5 , 1 .27 ,1 .08 1,0,1 3120 DATA 1578. 8 , 3 . 7 8 5 , 1 . 27, 1 .08 ,0 , 1 3130 DATA 1255 .4 ,2 .54 ,1 . 5 9 , 1 . 0 8 , 0,1 3140 DATA 1578. 8 , 2 . 5 4 , 1 . 5 9 , 1 . 0 8 , 0,1 3150 DATA 1255. 4 , 3 . 7 8 5 , 1 .59 ,1 .08 i ,0 ,1 3160 DATA 1578. 8 , 3 . 7 8 5 , 1 .59 ,1 .08 , 0 , 0 8.RUN NUMBER OF C Y C L E S 3 10 CONVERGENCE CRITERION 3 4. 297657E-3 SI SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16. 5 0.002 0.001 0 0.002 0 0 0 5.44 28.5 11.286 5.465 0 10.594 0.001 0 0 2.72 27.3 38.024 22.702 0 44.009 8.321 0 0 1.36 12.6 21.595 31.065 19.913 41.532 39.954 0 19.913 0.68 4.65 9.915 17.985 34. 869 2.138 25.559 0 34.869 0.34 2.25 5.56 9.853 19, 53 0.771 13. 883 0 19.53 0. 17 2 4. 204 4.479 8.898 0. 3 32 4.738 0 8.8 98 0.085 1.65 3.125 2.882 5.727 0.212 2.6 55 0 5.727 0.0425 1.32 2.295 2.009 3. 991 0. 1 48 1.74 0 3.991 0.0212 1.02 1.656 1,39 1 2.763 0. 102 1.142 0 2.763 0.0106 0.64 1.05 0.888 1.765 0.065 0.737 0 1.765 0.0053 0.3 0.562 0.514 1.021 0.038 0.468 0 1.021 -0 .0053 0.27 0.726 0.76 6 1.522 0.056 0.804 0 1. 522 % PASSING: SIZE 2 CRF 2 CRP S F S 0/S S O/S 3 CRP P F RMF 0.0053 0.27 0.726 0.766 1.522 0.056 0.8 04 0 1. 522 0.0106 0.57 1.288 1. 28 2. 542 0.094 1.272 0 2.542 0.0212 1.21 2.338 2.168 4.308 0.16 2.008 0 4.308 0.0425 2.23 3.994 3 .559 7.071 0.262 3.151 0 7.071 0.085 3.55 6.289 5. 567 11.062 0.41 4 .89 0 11.062 0.17 5.2 9.414 8. 45 16.789 0.6 22 7.545 0 16.789 0.34 7.2 13.618 12.929 25.687 0.954 12.282 0 25.687 0.68 9.45 19.178 22.782 45. 218 1.7 25 26. 165 0 45.218 1.36 14. 1 29.093 40.767 80.087 3.863 51.724 0 80.087 2.72 26.7 50.688 71 .833 100 45.396 91.678 0 100 5.44 54 88.712 94.534 100 89.404 99.999 0 100 10.88 82. 5 99.998 99.999 100 99.998 100 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1255.4 1255.4 2592.96 1255.4 1337. 57 1337.57 0 1255. 4 % +1 INCH: 73.3 28. 16746 54.60446 CRUSHER CURRENTS: 23.68 41.33 SETS: 2 CR SET= 2.54 SCRN OP= 1. 27 3 CR S E T 3 0.495 %--\/2 INCH IN F E E D 3 14.1 %-1/2 INCH IN SCREEN U / S 3 80.08693 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 5.67 9924 % CIRCULATING L O A D 3 1.065453 - 289 -NUMBER OF C Y C L E S 3 8 CONVERGENCE CRITERION 3 7.813911E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16.5 0. 002 0.001 0 0.002 0 0 0 5.44 28.5 11.39 5.396 0 10.254 0.001 0 0 2.72 27.3 39.144 23.234 0 44. 148 8.912 0 0 1.3 6 12.6 22.088 31.557 20.202 41.778 40. 081 0 20.202 0.68 4.65 9.675 15.063 29.726 1.8 65 19.914 0 29. 726 0.34 2.25 5. 159 8. 975 18. 13 0.735 12. 41 0 18. 13 0. 17 2 3.86 5.259 10.647 0.408 6.5 17 0 10.647 0.085 1.65 2.875 3 .588 7. 267 0.277 4.23 0 7.267 0.0425 1.32 2. 125 2 .49 5.042 0. 192 2.818 0 5.042 0.0212 1.02 1.544 1.705 3. 453 0. 131 1.85 0 3.453 0.0106 0.64 0.977 1.091 2.211 0.084 1. 194 0 2.211 0.0053 0.3 0.516 0.645 1.306 0.0 5 0.761 0 1.306 - 0 . 0053 0.27 0. 645 0.996 2.017 0.077 1.312 0 2.017 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.27 0. 645 0.996 2.017 0.077 1.312 0 2.017 0.0106 0.57 1.161 1.641 3.323 0.126 2.073 0 3.323 0.0212 1.21 2. 138 2.732 5.533 0.211 3.267 0 5. 533 0.0425 2.23 3.68 2 4. 437 8.986 0.3 42 5.117 0 8.986 0.085 3 .55 5. 806 6.927 14.028 0.534 7.935 0 14.028 0.17 5.2 8.682 10.515 21. 295 0.8 11 1 2. 165 0 21.295 0.34 7.2 12.542 15.773 31,942 1.219 18.682 0 31.942 0.68 9.45 17.701 24.749 50.071 1.954 31.092 0 50.071 1.36 14. 1 27.376 39.812 79.798 3.8 18 51.006 0 79.798 2.72 26.7 49.464 71. 369 100 45.597 91.087 0 100 5.44 54 88.608 94.603 100 89.744 99.999 0 100 10.88 82.5 99.998 99.999 100 99.998 100 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 1578. 8 3332.71 1578.79 1753. 91 1753.91 0 54.40342 OPERATING CONDITIONS TONNAGES: 1578.8 % *1 INCH: 73.3 CRUSHER CURRENTS: 29. 26 SETS: 2 CR S E T 3 2.54 %-1/2 INCH IN F E E D 3 14.1 %-1/2 INCH IN SCREEN U/S= 79.79757 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 5.659402 % CIRCULATING L O A D 3 1.110913 1578.79 28.63106 SCRN OP= 1.27 47. 1 3 CR S E T 3 0.495 NUMBER OF C Y C L E S 3 11 CONVERGENCE CRITERION 3 2. 885293E-3 %SET COLWIDTH 38 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10.88 16.5 0.02 0.009 0 0.016 0 0 0 5.44 28.5 24.445 10.833 0 19.451 0.002 0 0 - 290 -2.72 27.3 36.592 20.88 0 37. 492 8.379 0 0 1. 36 12.6 18.472 31.471 20. 932 39. 855 41.812 0 20.932 0.68 4.65 7.317 14.486 30.661 1.616 20. 19 0 30.661 0.34 2.25 3.626 8.367 18. 117 0.61 12. 139 0 18. 117 0.17 2 2.828 4.653 10.098 0.321 6.105 0 10.098 0.085 1.65 2. 182 3. 169 6.879 0. 217 3.954 0 6. 879 0.0425 1. 32 1.666 2.205 4.787 0. 151 2.634 0 4.787 0.0212 1.02 1. 244 1. 514 3.287 0.104 1 .729 0 3. 287 0.0106 0.64 0.784 0.969 2. 104 0.066 1.116 0 2. 104 0.0053 0.3 0. 392 0.57 1.237 0.039 0.711 0 1. 237 - 0 . 0 053 0.27 0.43 0.875 1. 898 0.06 1.228 0 1.898 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.27 0. 43 0.875 1.898 0.06 1.228 0 1.898 0.0106 0.57 0.822 1. 445 3. 136 0.099 1.94 0 3. 136 0.0212 1.21 1.607 2.414 5. 239 0.165 3.056 0 5.2 39 0.0425 2.23 2.851 3. 92 8 8.526 0.269 4 .7 85 0 8. 526 0.085 3.55 4.517 6. 133 13.313 0.42 7.419 0 13.313 0. 17 5.2 6.699 9.302 20.192 0.638 11. 373 0 20. 192 0.34 7.2 9,527 13.9 55 30.289 0.959 17.478 0 30.289 0.68 9.45 13.153 22.322 48.406 1.569 29.618 0 48.406 1.36 14.1 20.471 3 6. 80 8 79.068 3. 185 49.807 0 79.068 2.72 26.7 38.943 68. 279 100 43.04 91. 62 0 100 5.44 54 75.535 89.159 100 80.533 99.998 0 100 10. 88 82.5 99.98 99.991 100 99.984 100 0 100 21.76 99 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES 1255.4 1255.4 2833.26 1255.4 1577. 86 1577.86 0 1255.4 % +1 INCH: 73.3 31.7212 56. 95966 CRUSHER CURRENTS: 14.56 44.66 S E T S : 2 CR SET= 3.785 SCRN OP= 1.27 3 CR SET= 0.495 X - 1 / 2 INCH IN FEED= 14.1 ? « - 1 / 2 INCH IN SCREEN U/S= 79.06755 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.6076 28 % CIRCULATING LOAD= 1. 256858 NUMBER OF C¥CLES= 11 %SET COLIIDTH=8 % RETAINED: S I Z E 2 C R F 2 CRP 21.76 1 0 10. 88 16.5 0.02 5.44 28.5 24.777 2,7 2 27.3 37.345 1.36 12.6 18.664 0.68 4.65 7.088 0.34 2.25 3.331 0. 17 2 2. 586 0.085 1.65 2.007 0.0425 1.32 1. 54 8 0.0212 1.02 1.166 0.0106 0.64 0.734 CONVERGENCE CRITERION.= S F S U/S S O/S 0 0 0 0.009 0 0.016 10.824 0 19.218 21. 062 0 37.397 31.444 20.464 39.96 13.703 29.242 1.6 52 8.184 17. 898 0.65 4.893 10.726 0. 368 3. 369 7.388 0.2 52 2.34 5. 131 0. 175 1.601 3.512 0. 1 2 1.026 2.249 0.077 6. 590481E-3 3 CRP P F RMF 0 0 0 0 0 0 0.002 0 0 8.434 0 0 41.357 0 20.464 18.834 0 29.242 11.947 0 17.898 6.6 82 0 10.726 4.425 0 7.388 2.954 0 5. 131 1.939 0 3.512 1.252 0 2.249 - £ 3 I -0.0053 0.3 0.36 0.607 1.33 0.045 0.798 0 1.33 - 0 . 0053 0.27 0.374 0.939 2.06 0.07 1.378 0 2.06 % PASSING: SIZE 2 CRF 2 CRP S F s g/s S O/S 3 CRP P F RMF 0.0053 0.27 0.374 0. 939 2.06 0.07 1.378 0 2.06 0.0106 0.57 0.734 1.546 3. 391 0. 1 16 2.176 0 3.391 0.0212 i . 21 1.468 2.572 5.64 0. 192 3.428 0 5.64 0.0425 2.23 2.634 4. 173 9. 151 0.312 5.366 0 9.151 0.085 3.55 4. 182 6.513 14. 282 0.487 8.32 0 14.282 0.17 5.2 6. 19 9.881 21. 67 0.739 12.745 0 21.67 0. 34 7.2 8.775 14.774 32.396 1. 107 19.426 0 32.396 0.68 9.45 12.106 22.958 50. 294 1.756 3 1. 374 0 50.294 1.36 14. 1 19.194 36.661 79.536 3.409 50.208 0 79.536 2.72 26.7 37.858 68.105 100 43.369 91. 564 0 100 5. 4 4 54 75.203 89. 168 100 80.766 99,998 0 100 10.88 82.5 99.98 99.991 100 99.984 100 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578. 8 1578. 8 3614. 47 1578. 79 2035.67 2035.67 0 1578.79 % +1 INCH: • 73.3 31.8946 56.63086 CROSHER CURRENTS: 20.15 51.01 SETS: 2 CR SET= 3. 785 SCRN OP= 1. 27 3 CR SET= 0.495 %-1/2 INCH IN FEED= 14.1 %-1/2 INCH IN SCREEN U/S= 79.53588 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.640843 % CIRCULATING LOAD= 1.289378 NUMBER OF CYCLES= 22 CONVERGENCE CRITERION= 3.593712E-3 %5EH COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16.5 0.002 0.001 0 0.003 0 0 0 5. 44 28.5 11.286 5.982 0 12. 72 5 0.002 0 0 2.72 27.3 38.024 28.927 0 6 1. 53 9 18.672 0 0 1. 36 12.6 21.595 31. 801 38. 701 24.022 43.307 0 38. 701 0.68 4.65 9.915 16.293 29.856 1.002 23. 482 0 29.856 0.34 2.25 5.56 5.914 10. 934 0.255 6.314 0 10.934 0.17 2 4.204 3 .57 4 6.6 15 0. 147 2.865 0 6.615 0.085 1.65 3. 125 2. 53 1 4.684 0.1 04 1.861 0 4.684 0.0425 1.32 2.295 1.8 3.331 0.074 1.242 0 3.331 0.0212 1. 02 1.656 1.261 2.334 0.052 0.816 0 2. 334 0.0106 0.64 1.05 0. 804 1.488 0.033 0.527 0 1.488 0.0053 0. 3 0.562 0 . 455 0.843 0.019 0.335 0 0. 843 - 0 . 0053 0.27 0.726 0.656 1. 213 0.027 0.576 0 1.213 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.27 0.726 0.656 1.213 0.027 0.576 0 1.213 0.0106 0. 57 1.288 1.111 2.056 0.045 0.911 0 2.056 0.02 12 1.21 2. 338 1.915 3.544 0.078 1.438 0 3.544 0.0425 2. 23 3. 994 3.176 5.878 0.13 2.254 0 5. 878 - Z3Z -0.085 3.55 6. 289 4.976 9. 209 0.204 3.4 96 0 9.209 0. 17 5.2 9.414 7.507 13. 894 0.307 5.358 0 13.894 0.34 7.2 13.6 18 1 1.082 20.508 0.455 8.222 0 20.508 0.68 9.45 19.178 16.996 31. 44 3 0.709 14.537 0 31.443 1.36 14. 1 29.09 3 33.289 61.299 1.711 38. 019 0 61.299 2.72 26.7 50.688 65.09 100 25.734 81.326 0 100 5.4 4 54 88.712 94.017 100 87.272 99.998 0 100 10.88 82.5 99.998 99.999 100 99.997 100 0 100 21. 76 99 100 100 100 100 100 0 100 43,52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES 1255.4 1255.4 2368.97 1255.4 1113.57 1113.57 0 1255. 4 % +1 INCH: 73.3 34.91014 74. 26633 CRUSHER CURRENTS 23. 68 38. 23 SETS: 2 CR SET = 2.54 SCRN OP= 1, 59 3 CR SET= 0.495 Jt-1/2 INCH IN FEED= 14.1 %-1/2 INCH IN SCREEN U/S= 61.29 869 % - 1 / 2 INCH RATIO, SCREEN D/S TO PLANT FEED= 4.347424 % CIRCULATING LOAD= 0.8870241 NUMBER OF CYCLES= 13 %SET COLHIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21. 76 1 0 10.88 16.5 0. 002 5.44 28.5 11.39 2.72 27.3 39.144 1.36 12.6 22.088 0.68 4.65 9. 675 0.34 2. 25 5. 159 0.17 2 3.86 0.085 1.65 2. 875 0.0425 1.32 2. 125 0.0212 1.02 1.54 4 0.0106 0.64 0.977 0.0053 0.3 0.516 -0 .0053 0.27 0.645 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.27 0. 645 0.0106 0.57 1. 161 0.0212 1.21 2. 138 0.0425 2.23 3.682 0.085 3.55 5.806 0. 17 5.2 8.682 0.34 7.2 12.542 0.68 9.45 17.701 1 .36 14. 1 27.376 2.72 26.7 49.464 5.44 54 88.608 10. 88 82.5 99.998 21.76 99 100 CONVERGENCE CRITERION 3 S F S U/S S O/S 0 0 0 0.001 0 0.002 5.934 0 12.386 30.233 0 63. 106 29.833 36.357 22.738 15.042 28.00 1 0.952 6.32 11.875 0.281 4.086 7.684 0. 173 2.895 5.444 0. 122 2.041 3. 839 0.086 1.417 2. 666 0.06 0.905 1.702 0.038 0.521 0.98 0.022 0.772 1.452 0.033 S F S U/S S O/S 0.772 1. 452 0.033 1.293 2.432 0.055 2. 198 4. 134 0.093 3.615 6.799 0.152 5.656 10.638 0.239 8.551 16.08 3 0.361 12. 636 23. 767 0.534 18.957 35.642 0.815 33.999 63. 643 1.767 63. 832 100 24.505 94.065 100 87.611 99.999 100 99.998 100 100 100 5 . 7 0 9 5 0 9 E - 3 3 CRP P F RMF 0 0 0 0 0 0 0.002 0 0 2 0. 545 0 0 3 8.253 0 36.357 20. 878 0 28.001 7.583 0 11.875 4.331 0 7.684 2.915 0 5.444 1.95 0 3.839 1.28 0 2.666 0.826 0 1.702 0.527 0 0.98 0.91 0 1.452 3 CRP P F RMF 0.91 0 1.452 1.436 0 2.432 2.263 0 4. 134 3.543 0 6.799 5.4 93 0 10.638 8.408 0 16.083 12.739 0 23.767 20. 322 0 35.642 41.2 0 63.643 79.453 0 100 99.998 0 100 100 0 100 100 0 100 - 293 -43.52 100 100 100 100 100 100 0 100 1578. 8 3030, 83 1578. 81 1452.03 1452,03 0 75.49482 OPERATING CONDITIONS TONNAGES: 1578.8 % +1 INCH: 73.3 CRUSHER CURRENTS: 29.26 S E T S : 2 CR SET= 2.54 %-1/2 INCH IN FEED= 14.1 5 8 - 1 / 2 INCH IN SCREEN U/S= 63. 64277 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED = 4.513672 % CIRCULATING LOAD= 0.9197048 1578.81 36.16846 SCRN OP= 1.59 42.92 3 CR SET= 0.495 NUMBER OF CYCLES^ 14 CONVERGENCE CRITERION 3 6,034896E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16,5 0.02 0.01 0 0.019 0 0 0 5.44 28,5 24.445 11.922 0 23, 268 0.003 0 0 2.72 27.3 36.592 26.969 0 52. 634 17.81 0 0 1.36 12.6 18.472 31.16 40. 125 22.628 4 3. 234 0 40.125 0.68 4.65 7.317 15. 133 30.115 0.874 22.571 0 30. 115 0.34 2.25 3.626 5. 2 10.444 0.209 6.698 0 10.444 0. 17 2 2. 828 3.09 6.212 0. 1 19 3.339 0 6. 212 0.085 1.65 2. 182 2. 192 4. 408 0.084 2.2 02 0 4.408 0.0425 1. 32 1.666 1 .566 3. 148 0.06 1.47 0 3. 148 0.0212 1.02 1.244 1. 101 2. 214 0.042 0.965 0 2.214 0.0106 0. 64 0.784 0.702 1.411 0.027 0.623 0 1.411 0.0053 0.3 0. 392 0.395 0.794 0.015 0.397 0 0.794 - 0 . 0053 0. 27 0. 43 0.561 1. 128 0.021 0.685 0 1. 128 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.27 0.43 0.561 1. 128 0.021 0.6 85 0 1. 128 0.0106 0.57 0.822 0.956 1.921 0.037 1.082 0 1.921 0.0212 1. 21 1.607 1 .657 3.332 0.063 1 .706 0 3. 332 0.0425 2.23 2.851 2.759 5. 547 0. 105 2.671 0 5.547 0.085 3.55 4.517 4.324 8.695 0.165 4.141 0 8.695 0.17 5.2 6.699 6.517 13. 10 3 0. 249 6.344 0 13.103 0. 34 7. 2 9.527 9.607 19.315 0.368 9.683 0 19.315 0.68 9.45 13.153 14. 807 29.759 0.577 16.381 0 29.759 1.36 14. 1 20.471 29. 94 59. 875 1.451 38.952 0 59,875 2.72 26.7 38.943 6 1. 1 100 24.079 82.186 0 100 5. 44 54 75.535 88.068 100 76.713 9 9.997 0 100 10.88 82.5 99.98 99.99 100 99.981 100 0 100 21. 76 99 100 100 100 100 100 0 100 43,52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 2574. 53 1255. 41 131 9. 13 1319. 13 0 % +1 INCH: 73.3 38.90009 75.92106 CRUSHER CURRENTS: 14.56 4 1. 08 1255. 41 - zy4 -SETS: 2 CR SET= 3.785 SCRN O P 3 1.59 3 CR SET= 0.495 %-1/2 INCH IN FEED= 14.1 %-1/2 INCH IN SCREEN U/S= 59. 87487 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 4.246445 % CIRCULATING LOAD= 1.050765 NUMBER OF CYCLES= 11 CONVERGENCE CRITERION 3 5 .781114E-3 %SET COLBIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S 0/S S O/S 3 CRP P F RMF 21. 76 1 0 0 0 0 0 0 0 10.88 16.5 0.02 0.01 0 0.018 0 0 0 5.44 28.5 24.777 1 1.879 0 22. 818 0.004 0 0 2.72 27.3 37.345 28. 34 0 54.434 20.048 0 0 1,36 12.6 18.664 28.519 36.473 21.195 37. 593 0 36.473 0.68 4.65 7.088 12. 559 25.368 0.766 17.597 0 25.368 0. 34 2.25 3.331 5. 987 12.213 0.255 8.433 0 12. 213 0.17 2 2. 586 4.096 8.363 0. 167 5.487 0 8.363 0.085 1.65 2. 007 2.917 5. 958 0.1 18 3.755 0 5.958 0.0425 1.32 1.548 2.051 4. 188 0.083 2.514 0 4. 188 0.02 12 1.02 1. 166 1.418 2.895 0.057 1 .649 0 2. 895 0.0106 0.64 0.734 0.906 1.851 0.037 1.065 0 1.851 0.0053 0.3 0. 36 0.526 1.075 0.021 0.68 0 1.075 - 0 . 0053 0.27 0.374 0.792 1.617 0.032 1.176 0 1.617 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.27 0. 374 0.792 1.617 0.0 32 1.176 0 1.617 0.0106 0.57 0. 734 1.318 2.692 0.053 1 .856 0 2.692 0.0212 1.21 1.468 2.224 4. 542 0.09 2.921 0 4.542 0.0425 2.23 2.634 3.642 7.437 0.147 4.57 0 7.437 0.085 3.55 4. 182 5.693 11.625 0.23 7.083 0 11.625 0. 17 5.2 6. 19 8.61 17.583 0.348 10.839 0 17.583 0.34 7.2 8.775 12.706 25. 946 0.514 16.325 0 25.946 0.68 9.45 12.106 18.693 38. 159 0.769 24.758 0 38. 159 1.36 14. 1 19.194 31. 252 63.527 1. 535 42.355 0 63.527 2.72 26.7 37.858 59.771 100 22. 73 79. 949 0 100 5.44 54 75.203 88. 1 11 100 77.164 99.996 0 100 10. 88 82.5 99.98 99.99 100 99.982 100 0 100 21.76 99 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3293. 45 1578. 81 1714.64 1714.64 0 1578.81 % + 1 INCH: 73.3 40.22867 77.27044 CRUSHER CURRENTS: 20.15 46.56 S E T S : 2 CR SET= 3.785 SCRN OP= 1.59 3 CR SET= 0.495 %-1/2 INCH IN FEED= 14.1 S-1/2 INCH IN SCREEN U/S= 63. 52686 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 4.50 54 51 % CIRCULATING LOAD= 1. 08604 NUMBER OF CYCLES= 7 CONVERGENCE CRITERION 3 6.477077E-3 - 295 -%SET C0LWIDTH=8 % RETAINED: S I.Z E 2 CRF 2 CRP 21. 76 1 0 10.88 16.5 0. 002 5.44 28.5 11.286 2.72 27.3 38.024 1.36 12.6 21.595 0.68 4.65 9.915 0.34 2.25 5.56 0.17 2 4. 204 0.085 1.65 3. 125 0.0425 1.32 2.295 0.0212 1.02 1.656 0.0106 0.64 1.05 0.0053 0.3 0.562 -0 .0053 0.27 0.726 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.27 0.726 0.0106 0. 57 1.288 0.0212 1.21 2.338 0.0 4 25 2. 23 3. 994 0.085 3.55 6.289 0. 17 5.2 9.414 0.34 7.2 13.6 18 0.68 9.45 19.178 1.36 14.1 29.093 2.72 26.7 50.688 5.44 54 88.712 10. 88 82.5 99.998 21.76 99 100 43. 52 100 100 S F S U/S S O/S 0 0 0 0.001 0 0.002 5.541 0 10.887 22. 191 0 43.597 30.713 19.525 41.505 18.812 35. 96 7 2.263 10.177 19. 892 0.8 06 4. 392 8.602 0.33 2.788 5.463 0.208 1.945 3.81 0. 145 1.35 2.645 0.101 0.862 1.689 0.064 0.496 0.971 0.037 0.733 1.437 0.055 S F S U/S S O/S 0.733 1.4 37 0.055 1.229 2.408 0.092 2.09 1 4.097 0.156 3.441 6.741 0.257 5.385 10.551 0.402 8.173 16.014 0.61 12. 565 24.617 0.94 22.742 44,509 1.746 4 1.554 80.475 4.009 72. 266 100 45.514 94. 457 100 89. 111 99.999 100 99.998 100 100 100 100 100 100 3 CRP P F RMF 0 0 0 0 0 0 0 0 0 6.919 0 0 39.507 0 19.525 27.393 0 35.967 14.632 0 19.892 4.573 0 8.602 2.463 0 5.463 1.606 0 3.81 1.055 0 2.645 0.68 0 1.689 0.432 0 0.971 0.74 0 1.437 3 CRP P F RMF 0.74 0 1.437 1 . 1 72 0 2. 408 1.852 0 4.097 2 .907 0 6,741 4.514 0 10.551 6.977 0 16.014 11.549 0 24.617 26. 181 0 44.509 53. 574 0 80.475 93.081 0 100 100 0 100 100 0 100 100 0 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1255.4 1255. 4 2556. 83 1255. 39 1301.44 1301.44 0 1255.39 % +1 INCH: 73.3 27.73363 54.48603 CRUSHER CURRENTS: 23.68 35.21 S E T S : 2 CR SET= 2.54 SCRN OP= 1.27 3 CR SET= 1.08 %-l/2 INCH IN FEED= 14.1 %-*\/2 INCH IN SCREEN U/S= 80.4754 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.707475 % CIRCULATING LOAD= 1.036674 NUMBER OF CYCLES= 10 CONVERGENCE CRITERION^ 8. 572892E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16.5 0. 002 0.001 0 0.002 0 0 0 5.44 28.5 11.39 5.486 0 10.582 0 0 0 2.7 2 27.3 39.144 22.761 0 43.907 7.539 0 0 1 .36 12. 6 22.088 31. 026 19.685 41. 562 39.33 0 19.685 0.68 4.65 9.675 15. 504 30.107 1.936 2 0. 92 0 30. 107 - Zyb -0.34 2.25 5. 159 9.247 18. 378 0.764 13.045 0 18.378 0. 17 2 3.86 5.338 10.634 0.419 6.7 12 0 10.634 0.085 1.65 2. 875 3.631 7.234 0.283 4.332 0 7. 234 0.0425 1.32 2.125 2.519 5.0 19 0.196 2.884 0 5.019 0.0212 1. 02 1. 544 1.725 3.437 0. 134 1 .893 0 3. 437 0.0106 0.64 0.977 1.10 4 2.2 0. 086 1.222 0 2.2 0.0053 0.3 0. 516 0.652 1.299 0.051 0.779 0 1.299 -0 .0053 0. 27 0.645 1.007 2.006 0.078 1.343 0 2.006 % PASSING: SIZE 2 CRF 2 CfiP S F S O/S S O/S 3 CRP P F RMF 0.0053 0.27 0.645 1.007 2. 006 0.078 1.343 0 2.006 0.0106 0.57 1. 161 1.659 3 .3 05 0. 129 2. 122 0 3.305 0.0212 1.21 2. 138 2.763 5. 506 0.215 3.344 0 5.506 0.0425 2.23 3.682 4.488 8.943 0.349 5.237 0 8.943 0.085 3.55 5.806 7.007 13. 961 0.545 8.122 0 13.961 0. 17 5. 2 8.682 10.637 21. 196 0.828 12.454 0 21. 196 0.34 7.2 12.542 15.976 31.829 1.2 47 19.166 0 31.829 0.68 9.45 17.701 25. 223 50.208 2.011 32.211 0 50.208 1.36 14. 1 27.376 40.727 80,315 3.947 53.131 0 80.315 2.72 26.7 49.464 71.753 100 45.509 9 2. 461 0 100 5.44 54 88.608 94.513 100 89.416 100 0 100 10. 88 82.5 99.998 99.999 100 99.998 100 0 100 21.76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3278. 11 1578. 79 1699.32 1699.32 0 1578.79 % + 1 INCH: 73.3 28. 24717 54. 49091 CRUSHER CURRENTS: 29.26 40.72 SETS: 2 CR SET= 2.54 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH IN FEED= 14.1 X - 1 / 2 INCH IN SCREEN U/S= 80.31493 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.696095 % CIRCULATING LOAD= 1.076336 NUMBER OF C Y C L E S 3 7 CONVERGENCE CRITERION 3 2. 161942E-3 %SET COL¥IDTH=8 % RETAINED: S I Z E 2 CRF 2 CRP S F S D/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16. 5 0. 02 0 .009 0 0.016 0 0 0 5.44 28.5 24.445 1 1.004 0 20.013 0 0 0 2.72 27.3 36.592 20.354 0 37. 018 7.061 0 0 1.36 12. 6 18.472 30. 989 20.407 39.652 41. 236 0 20.407 0.68 4.65 7.317 15.038 31.338 1.694 21.359 0 31.338 0.34 2.25 3.626 8.66 1 18. 461 0.638 12.783 0 18.461 0. 17 2 2.828 4.668 9.973 0.326 6.175 0 9. 973 0.085 1.65 2, 182 3. 16 6.7 53 0.219 3.962 0 6.753 0.0425 1. 32 1.666 2.2 4.7 0. 152 2.637 0 4.7 0.0212 1.02 1.244 1.511 3.23 0. 105 1.7 3 0 3.23 0.0106 0.64 0.784 0.967 2.067 0.067 1.1 17 0 2.067 0.0053 0.3 0.392 0.568 1.214 0. 039 0.712 0 1.214 - 0 . 0053 0.27 0.43 0.869 1.858 0.06 1.229 0 1.858 - 297 -% PASSING: SIZE 2 CSF 2 CEP S F S O/S S O/S 3 CRP P F RMF 0.0053 0.27 0. 43 0.869 1.858 0.06 1.229 0 1.858 0.0106 0,57 0.822 1. 437 3.071 0. 1 1.941 0 3.071 0.0212 1. 21 1.607 2.404 5.138 0.167 3.058 0 5. 138 0.0425 2.23 2.851 3.916 8. 368 0.271 4.788 0 8.368 0.085 3. 55 4.517 6.116 13.068 0.424 7.425 0 13.068 0.17 5.2 6.699 9.276 19.821 0.643 1 1. 386 0 19.821 0.34 7.2 9.527 13.945 29.794 0.968 17.561 0 29.794 0.68 9.45 13.153 22. 60 5 48.255 1.606 30.344 0 48.255 1.36 14. 1 20.471 3 7.6 44 79.593 3.3 51.703 0 79.593 2.72 26.7 38.943 68.633 100 42.952 92.939 0 100 5.44 54 75.535 88.987 100 79.971 100 0 100 10.88 82.5 99.98 99.991 100 99.984 100 0 100 21.76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES 1255.4 1255. 4 2788.84 1255.4 1533.43 1533.43 0 1255. 4 % +1 INCH: 73.3 31.36743 57.04753 CRUSHER CURRENTS; 14.56 38.43 S E T S : 2 CR SET= 3.785 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH IN FEED= 14.1 %--\/2 INCH IN SCREEN U/S= 79.59293 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.644889 % CIRCULATING LOAD= 1.221467 NUMBER OF CYCLES= 11 CONVERGENCE CRITERION= 8, 589651E-4 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 1 0 0 0 0 0 0 0 10.88 16.5 0.02 0. 009 0 0.016 0 0 0 5.44 28.5 24.777 11.002 0 19.791 0 0 0 2.72 27.3 37.345 20.571 0 37.002 7.173 0 0 1. 36 12.6 18.664 30.952 20.004 39.697 40.768 0 20.004 0.68 4.65 7.088 14.019 29.449 1.695 19. 556 0 29,449 0.34 2.25 3. 33 1 8.397 18.073 0.668 12.444 0 18.073 0.17 2 2.586 4. 988 10.761 0. 377 6.907 0 10.761 0.085 1.65 2.007 3.43 7.403 0.2 57 4.567 0 7.403 0.0425 1.32 1. 54 8 2. 382 5. 141 0. 178 3 .048 0 5.141 0.0 212 1.02 1. 166 1.63 3.518 0. 122 2.001 0 3.518 0.0106 0.64 0.734 1.044 2. 253 0.078 1.292 0 2. 253 0.0053 0. 3 0.36 0.618 1.333 0.046 0.823 0 1.333 -0 .0053 0.27 0.374 0.957 2.065 0.072 1.422 0 2.065 % PASSING: SIZE 2 CRF 2 CRP S F S U / S S O/S 3 CRP P F RMF 0.0053 0.27 0.374 0.957 2.065 0.0 72 1.4 22 0 2.065 0.0106 0.57 0.734 1.574 3 .3 98 0. 1 18 2.246 0 3.398 0.0212 1.21 1.468 2.618 5.651 0.196 3.537 0 5.651 0.0425 2.23 2.634 4.24 9 9.169 0.318 5.538 0 9. 169 0.085 3.55 4. 182 6.63 1 14.31 0.497 8.587 0 14.31 0. 17 5.2 6. 19 10.061 21.713 0.754 13. 154 0 21.713 0.34 7.2 8.775 15.049 32. 47 4 1.131 2 0. 06 0 32.474 - <-ya -0.68 9.45 12.106 23.446 50.548 1.799 32.504 0 50.548 1.36 14. 1 19. 194 37.466 79. 996 3.4 94 52.06 0 79.996 2.72 26.7 37.858 68.4 18 100 43.192 92. 827 0 100 5. 44 54 75.203 88.989 100 80.193 100 0 100 10.88 82.5 99.98 99.991 100 99.984 100 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES 1578.8 1578.8 3555.39 1578.8 1976.59 1976.59 0 1578.8 % . * 1 I NCfl : 73.3 31.5 82 21 56. 80847 CRUSHER CURRENTS • 20. 15 44.57 S E T S : 2 CR SET = 3.785 SCRN OP= 1. 27 3 CR SET= 1.08 %-1/2 INCH IN FEED= 14.1 %--\/2 INCH IN SCREEN 0/S= 79.99632 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.6734 98 % CIRCULATING LOAD= 1.251957 NUMBER OF C Y C L E S 3 14 CONVERGENCE CRITERION 3 5 .082472E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21. 76 1 0 10.88 16.5 0.00 2 5. 44 28.5 11.286 2 .72 27.3 38.024 1.36 12.6 21.595 0.68 4.65 9.915 0.34 2. 25 5.56 0.17 2 4. 204 0.085 1.65 3. 125 0.0425 1.32 2.295 0.0212 1.02 1.656 0.0106 0.64 1.05 0.0053 0.3 0.562 - 0 . 0053 0.27 0.726 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.27 0.726 0.0106 0. 57 1.288 0.0212 1.21 2.338 0.0425 2.23 3. 99 4 0.085 3.55 6.289 0. 17 5.2 9.414 0.34 7.2 13.618 0.68 9.45 19.178 1.36 14. 1 29.093 2.72 26.7 50.688 5.44 54 88.712 10. 88 82.5 99.998 21.76 99 100 43. 52 100 100 S F S U/S S O/S 0 0 0 0.001 0 0.003 6. 096 0 13.257 28. 27 0 61.476 30. 532 36.576 23.433 16.792 30. 192 1.0 52 6 .343 11.506 0.279 3.869 7.024 0. 163 2.734 4.965 0. 1 14 1.938 3.519 0.081 1.353 2.457 0.056 0.863 1.567 0.0 36 0.492 0.8 94 0.021 0.717 1.301 0.03 S F S O/S S O/S 0.717 1.301 0.03 1.209 2. 195 0.05 2.072 3.762 0.0 86 3. 425 6.219 0.1 43 5. 36 3 9.7 38 0.224 8.097 14.702 0.338 1 1. 966 21.727 0.501 18,309 33.232 0.779 35.10 1 63. 424 1.831 65,633 100 25.265 93. 903 100 86.741 99.999 100 99.997 100 100 100 100 100 100 3 CRP P F RMF 0 0 0 0 0 0 0 0 0 16.813 0 0 4 1. 03 0 36.576 24. 869 0 30.192 7.263 0 11. 506 3 .475 0 7.024 2.275 0 4.965 1.518 0 3.519 0.997 0 2.457 0.644 0 1.567 0.41 0 0.894 0.7 06 0 1.301 3 CRP P F RMF 0.706 0 1.301 1.116 0 2. 195 1.76 0 3.762 2.757 0 6.219 4.275 0 9.738 6.55 0 14. 702 10.025 0 21.727 17.288 0 33. 232 42.157 0 63.424 83. 187 0 100 100 0 100 100 0 100 100 0 100 100 0 100 OPERATING CONDITIONS - 299 -1255.4 2324. 19 1255. 41 1068.78 1068.78 0 74.73526 TONNAGES: 1255.4 % +1 INCH: 73.3 CRUSHER CURRENTS: 23.68 SETS: 2 CR SET= 2.54 %-1/2 INCH IN FEED= 14.1 %-1/2 INCH IN SCREEN U/S= 63.42425 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 4.49 8174 % CIRCULATING LOAD= 0.8513462 1255.41 34.36715 SCRN OP= 1.59 31 . 99 3 CR SET= 1.08 NUMBER OF CYCLES= 12 CONVERGENCE CRITERION= 0. 0087265 %SET COLWIDTH % RETAINED: = 8 SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16.5 0. 002 0.001 0 0.003 0 0 0 5.44 28.5 11. 39 6.066 0 12.977 0 0 0 2.72 27.3 39.144 28. 863 0 61.749 17.149 0 0 1.36 12.6 22.088 30. 449 36 .613 23. 426 39. 976 0 36.613 0.68 4.65 9.675 16.128 29.374 1.0 36 23.482 0 29.374 0.34 2.25 5. 159 6. 34 11. 653 0.286 7.686 0 11.653 0. 17 2 3. 86 3.935 7.239 0.17 4.019 0 7.239 0.085 1.65 2.875 2.779 5. 112 0.119 2.668 0 5. 112 0.0425 1.32 2. 125 1. 965 3.616 0.0 84 1.783 0 3.616 0.0212 1.02 1.54 4 1.369 2. 519 0.059 1.17 0 2.519 0.0106 0. 64 0.977 0.874 1.608 0.037 0.756 0 1. 608 0.0053 0.3 0.516 0.5 0.92 0.021 0.481 0 0.92 - 0 . 0053 0. 27 0.645 0.732 1.346 0.031 0.831 0 1. 346 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0. 27 0.645 0.732 1.346 0.031 0.831 0 1.3 46 0.0106 0.57 1.16 1 1.231 2.266 0.053 1.312 0 2.266 0.0212 1.21 2. 138 2. 105 3. 873 0.09 2.068 0 3. 873 0.0425 2.23 3.682 3 . 474 6.393 0.1 49 3 .238 0 6.393 0.085 3. 55 5.806 5.439 10.008 0.233 5.021 0 10.008 0.17 5.2 8.682 8.218 15. 121 0.3 53 7.689 0 15.121 0.34 7.2 12.542 12. 152 22.359 0.523 11.708 0 22.359 0.68 9.45 17.701 18.493 34.013 0.809 19.394 0 34.013 1. 36 14. 1 27.376 3 4.621 6 3.387 1.8 45 42.876 0 63.387 2.72 26.7 49.464 65.07 100 25. 272 82.851 0 100 5.44 54 88.608 93.933 100 87. 02 100 0 100 10. 88 82.5 99.998 99.999 100 99.997 1 00 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 1578.8 2964.48 1578.81 1385.67 1385.67 0 OPERATING CONDITIONS TONNAGES: 1578.8 % +1 INCH: 73.3 CRUSHER CURRENTS: 29.26 SETS; 2 CR SET= 2.54 %-1/2 INCH IN FEED= 14.1 1-1/2 INCH IN SCREEN U/S= 63.38681 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 4.495518 34. 9299 SCRN OP= 1. 59 74.72843 36.38 3 CR SET= 1.08 1578.81 % CIRCULATING LOAD 3 0.8776729 - 300 -NUMBER OF C Y C L E S 3 12 CONVERGENCE CRITERION 3 9 .78447E-3 JSSET COLWIOTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CSP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16.5 0.02 0.01 0 0.02 0 0 0 5.44 28.5 24.445 12. 1 0 23. 959 0 0 0 2.72 27.3 36.592 25.65 0 50.79 14.926 0 0 1.36 12.6 18.472 32.725 41.849 23. 783 46.695 0 41 .849 0.68 4.65 7.317 15. 186 2 9.778 0.884 22.898 0 29.778 0.34 2.25 3.626 5.11 10.112 0.208 6 .565 0 10. 112 0. 17 2 2.828 2.963 5.868 0. 1 15 3.0 94 0 5. 868 0.085 1.65 2. 182 2.101 4. 162 0.081 2.022 0 4.162 0.0425 1.32 1.666 1.506 2.984 0.058 1.35 0 2. 984 0.0212 1.02 1.244 1.063 2. 107 0.041 0.886 0 2.107 0.0106 0.64 0.784 0.677 1.341 0.026 0.572 0 1.341 0.0053 0.3 0. 39 2 0.378 0.749 0.015 0.36.4 0 0.749 -0 .0053 0.27 0. 43 0.53 1.05 0.02 0.628 0 1.05 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.27 0. 43 0.53 1.05 0.02 0.628 0 1.05 0.0106 0.57 0.822 0.908 1.799 0.035 0.992 0 1.799 0.0212 1.21 1.607 1.585 3.14 0.061 1.564 0 3. 14 0.0425 2.23 2.851 2. 649 5. 247 0. 102 2.451 0 5.2 47 0.085 3.55 4.517 4.155 8.231 0.16 3 .8 0 8. 231 0.17 5.2 6.699 6.256 12. 393 0.2 41 5; 823 0 12.393 0.34 7.2 9.527 9.219 18.261 0.356 8.917 0 18.261 0.68 9.45 13.153 14.329 28. 374 0.564 15.482 0 28.374 1. 36 14. 1 20.471 29. 515 58. 151 1.448 38.38 0 58.151 2 .72 26.7 38.943 62. 24 100 25.231 85.074 0 100 5. 44 54 75.535 87. 89 100 76.021 100 0 100 10.88 82.5 99.98 99.99 100 99. 98 100 0 100 2 1 . 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES; 1255.4 % +1 INCH: 73.3 CRUSHER CURRENTS: 14.56 SETS: 2 CR S E T 3 3.785 SCRN X -1/2 INCH IN FEED= 14.1 1255.4 2536.28 1255.41 1280.87 1280.87 0 1255.41 37.75965 74.7687 5 O P 3 1. 59 34. 93 3 CR S E T 3 1.08 %-1/2 INCH IN SCREEN U / S 3 58.15109 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 4. 124191 % CIRCULATING LOAD 3 1.020288 NUMBER OF C Y C L E S 3 10 CONVERGENCE CRITERION 3 6.044243E-3 XSET COLBIDTH 3 8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF - cJU I -21.76 1 0 10. 88 16. 5 0. 02 5. 44 28.5 24.777 2.72 27.3 37.345 1.36 12. 6 18.664 0.68 4. 65 7.088 0.34 2.25 3.331 0. 17 2 2.586 0.085 1.65 2.007 0.0425 1.32 1. 54 8 0.0212 1.02 1. 166 0.0 106 0.64 0.734 0.0053 0.3 0.36 - 0 . 0053 0.27 0.374 % PASSING: SIZE 2 CBF 2 CRP 0.0053 0.27 0.374 0.0106 0.57 0.734 0.0212 1.21 1.468 0.0425 2.23 2. 634 0.085 3.55 4. 182 0.17 5.2 6. 19 0. 34 7.2 8.775 0.68 9.45 12.106 1.36 14. 1 19.194 2.72 26.7 37.858 5. 44 54 75.203 10.88 82.5 99.98 21. 76 99 100 43.52 100 100 0 0 0 0.01 0 0.019 12. 131 0 23.769 27. 076 0 53.051 28.912 36.554 21.581 13.015 25.75 0.798 6 . 081 12. 149 0.261 4. 119 8.237 0.169 2.932 5. 863 0. 1 19 2.062 4. 124 0.084 1.4 27 2.853 0.058 0.912 1. 824 0. 037 0.529 1.058 0.022 0.793 1.587 0.032 S F S U/S S O/S 0.793 1.587 0.032 1. 322 2. 645 0.054 2.234 4.469 0.091 3.661 7. 322 0.1 49 5.723 11.446 0.233 8.655 17,31 0.352 12.774 25.547 0.521 18.855 37. 696 0.782 31.871 63.446 1.58 60.783 100 23.161 87.859 100 76.212 99.99 100 99.981 100 100 100 100 100 100 0 0 0 0 0 0 0 0 0 17.226 0 0 38. 743 0 36.554 18.701 0 25.75 8.72 0 12.149 5 .59 0 8. 237 3.818 0 5.863 2.556 0 4. 124 1.676 0 2.853 1 .083 0 1.824 0.691 0 1.058 1.196 0 1.587 3 CRP P F BMF 1 . 1 96 0 1.587 1 .887 0 2.645 2. 97 0 4. 469 4.646 0 7.322 7.2 02 0 11.446 11. 02 0 17.31 16.61 0 25. 547 2 5. 33 0 37.696 44. 031 0 63.446 82.774 0 100 100 0 100 100 0 100 100 0 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578. 8 1578. 8 3224.58 1578. 81 1645. 78 1645.78 0 % +1 INCH: 73.3 39.21749 76.8391 CBUSHEB CUBBENTS: 20. 15 SETS: 2 CR SET= 3.785 SCRN OP= X - 1 / 2 INCH IN FEED= 14.1 % - 1 / 2 INCH RATIO, SCREEN U/S TO % CIRCULATING LOAD= 1.042425 1578.81 1. 59 39. 98 3 CR SET= 1.08 - 1 / 2 INCH IN SCREEN U/S= 63. 44553 PLANT FEED= 4.4996 83 STOP! AT LINE "2120" IN PR0GBAM "PGM2" PROGRAM ENDS 5SLOGOFF 0FF AT 21:29:24 0N 09-07-77 EXECUTION TEBMINATED - 302 -I n te rme d i a te Ran ge s S tu dy . .MOON...1..MOON...2..MOON...3..MOON...4..MOON. ..5..MOON...6..MOON...1 RFS NO. 186974 UNIVERSITY OF B C COMPUTING CENTRE * * * T H E PAPERTAPE PUNCH S READER ARE DOWN * * * $SIGN RALU T=2M PRINT=TN FORM=8X11 P=60 303 -RRRRRRRRRRR RRRRRRRRRRRR RR RR RR RR RR RR RRRRRRRRRRRR RRRRRRRRRRR RR RR RR RR RR RR RR RR RR RR AAAAAAAAAA AAAAAAAAAAAA AA AA AA AA AA A A AAAAAAAAAAAA AAAAAAAAAAA A A A A A A A A A A A A A AA A A AA A A LL L L LL LL LL LL LL LL LL L L L L L L L L L L L L L L LLLLLLLLLLLL UU UU UU UU UU UU UU UU UU UU UU UU UU UU UU UU UU UU UU UU uuuuuuuuuuuu uuuuuuuuuu * * L A S T SIGNON WAS: 21:13:15 USER "RALU" SIGNED ON AT 21:27:31 ON WED SEP 07/77 $RUN *BASIC EXECUTION BEGINS UBC BASIC SYSTEM %GET_PGM2 110 PRINT 112 READ A 114 115 READ Q2,S ,Q3 1 16 118 READ J5 120 IF J5=0 THEN 130 122 128 130 READ J6 2 098 PRINT " 3230 DATA 1 417. 1, 3. 16, 1. 4 3 , . 788 ,0 , 1 3240 DATA 1 5 7 8 . 8 , 3 . 1 6 , 1 . 4 3 , . 7 8 8 , 0 , 1 3250 DATA 1 2 5 5 . 4 , 3 . 1 6 , 1 . 4 3 , . 7 8 8 , 0 , 0 %RUN NUMBER OF C Y C L E S 3 9 - 304 -CONVERGENCE CRITERION = 1. 285836E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 c a p S F S U / S S O/S 3 CRP P F RMF 2 1. 76 3 0 0 0 0 0 0 0 1 0. 88 35 0. 13 4 0.063 0 0. 1 18 0 0 0 5. 44 36.5 29.558 13.856 0 26.085 0 0 0 2.72 18.35 38.206 19.322 0 36. 374 2.658 0 0 1.36 4.7 16. 958 28.692 22.874 33. 826 39. 047 0 22.874 0.68 0.94 6.372 15. 478 30.944 1.83 23. 515 0 30.944 0.3 4 0.29 3.025 8.774 17.914 0.708 13.848 0 17.914 0.17 0.22 1.841 4.717 9.65 0.3 63 7.254 0 9.65 0.085 0. 17 1. 204 3.088 6.319 0.236 4.75 0 6.319 0.0425 0. 17 0.841 2.074 4.245 0. 159 3. 163 0 4.245 0.0212 0. 18 0.614 1.389 2. 843 0.106 2.073 0 2. 843 0.0106 0. 16 0.439 0.918 1.879 0.07 1.34 0 1.879 0.0053 0. 13 0. 309 0.601 1.23 0.046 0.86 0 1.23 -0 .0053 0. 19 0.5 1.027 2. 102 0.078 1.492 0 2. 102 % PASSING: SIZE 2 CRF 2 CRP S F S U / S S O/S 3 CRP P F RMF 0.0053 0. 19 0.5 1.027 2. 102 0. 078 1.492 0 2.102 0.0106 0.32 0.808 1.628 3.332 0.1 24 2.352 0 3.332 0.0212 0.48 1.248 2. 546 5. 211 0. 195 3.692 0 5.211 0.0425 0.66 1.86 2 3 .935 8.054 0.301 5.765 0 8.054 0.085 0.83 2.703 6.01 12.299 0.4 59 8.928 0 12.299 0.17 1 3.907 9.098 18.618 0.6 95 13.679 0 18.618 0.34 1.22 5.748 13,814 28. 268 1.058 2 0. 933 0 28.268 0.68 1.51 8.773 22.588 46. 182 1.767 34.781 0 46.182 1 .36 2.45 15.144 38.066 77. 126 3.597 58. 295 0 77.126 2,72 7. 15 32.102 66.758 100 37.423 97.342 0 100 5.44 25.5 70.308 86.081 100 73.797 100 0 100 10. 88 62 99.866 99.937 100 9 9. 882 100 0 100 21.76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417.1 1417.1 3022.88 1417.1 1605,78 1605.78 0 1417.1 % +1 INCH: 92.85 33. 2416 62. 57728 CRUSHER CURRENTS: 21..93 42.23 S E T S : 2 CR S E T 3 3.16 SCRN O P 3 1.43 3 CR S E T 3 0.788 %-1/2 INCH IN F E E D 3 2.45 %--\/2 INCH IN SCREEN U/S= 77. 12594 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 31.4 7998 % CIRCULATING LOAD 3 1, 133145 NUMBER OF C Y C L E S 3 8 CONVERGENCE CRITERION 3 7.729005E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S D/S S O/S 3 CRP P F RMF 21.76 3 0 0 0 0 0 0 0 10.88 35 0.134 0.062 0 0.116 0 0 0 5.44 36.5 29.87 13.863 0 25. 871 0 0 0 2.72 18.35 39.022 19.549 0 36. 482 2.683 0 0 - 305 -1.36 4.7 17.169 28. 688 22.714 33.862 38. 665 0 22.714 0.68 0.94 6. 133 14.906 30.019 1.816 2 2.505 0 30.019 0.34 0. 29 2.715 8.631 17.765 0.72 13.756 0 17.765 0.17 0.22 1.586 4.858 10.02 0.386 7.692 0 10.02 0.085 0. 17 1.02 3.207 6.617 0.254 5.101 0 6.6 17 0.0425 0. 17 0.716 2. 155 4. 446 0. 17 3.401 0 4.446 0.0212 0. 18 0.532 1. 441 2.974 0.114 2.228 0 2.974 0.0106 0. 16 0.386 0.952 1.963 0.075 1.441 0 1.963 0.0053 0. 13 0. 275 0.623 1.2 85 0. 049 0.924 0 1. 285 - 0 . 0053 0. 19 0.44 1 1.064 2. 196 0.084 1.604 0 2. 196 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0. 19 0. 44 1 1.064 2. 196 0.084 1.604 0 2. 196 0.0 106 0. 32 0.716 1.687 3.481 0.133 2.5 28 0 3.481 0.0212 0.48 1. 102 2. 639 5. 444 0.208 3 .97 0 5.444 0.0425 0.66 1.634 4.08 8.418 0.322 6.198 0 8.4 18 0.085 0.83 2.351 6.235 12. 864 0. 493 9.599 0 12.864 0. 17 1 3.371 9.442 19.481 0.746 14.7 0 19.481 0.34 1.22 4.957 14. 3 29.50 2 1. 132 22.391 ^  0 29.502 0.68 1.51 7.672 22.931 47.267 1 . 8 53 36. 147 0 47.267 1.36 2.45 13.805 37.837 77.286 3.669 58.652 0 77.286 2 .72 7.15 30.974 66.525 100 37.531 97.317 0 100 5.44 25.5 69.996 86.074 100 74.013 100 0 100 10. 88 62 99.866 99.938 100 99.384 100 0 100 21. 76 97 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3401.63 1578. 81 1822. 82 1 822.82 0 1578. 81 % +1 INCH: 92.85 33. 475 62. 46882 CRUSHER CURRENTS; 24.72 45. 24 SETS: 2 CB SET= 3.16 SCRN OP= 1.43 3 CR SET= 0.788 %-'\/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 77.28592 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 31.545 27 % CIRCULATING LOAD= 1.15456 NUMBER OF CYCLES= 8 CONVERGENCE CRITERION= 5.849005E-3 %SET COL¥IDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21.76 3 0 10. 88 35 0.134 5.44 36.5 29.244 2.72 18.35 37.396 1.36 4.7 16.752 0.68 0.94 6. 60 9 0.34 0.29 3. 333 0. 17 0.22 2.095 0.085 0. 17 1.386 0.0 425 0. 17 0.964 0.0212 0. 18 0.695 0.0106 0. 16 0.492 0.0053 0. 13 0.342 S F S U/S S O/S 0 0 0 0.063 0 0.1.2 13.82 0 26.201 19 0 36.023 28.839 23.038 34. 037 17.199 34. 165 1. 998 9.193 18.64 1 0.728 4. 156 8.4 44 0.314 2.618 5. 322 0. 196 1 .756 3.569 0.132 1. 18 2.399 0.088 0.783 1.592 0.059 0.515 1.047 0.039 3 CRP P F RMF 0 0 0 0 0 0 0 0 0 2.518 0 0 39.669 0 23.038 26.686 0 34. 165 14.444 0 18.641 6.002 0 8. 444 3.722 0 5.322 2.465 0 3.569 1.615 0 2.399 1 .045 0 1.592 0.67 0 1.047 - ,5110 -- 0 . 0053 0. 19 0. 558 0.877 1.783 0.066 1 .163 0 1.783 % PASSING: SIZE 2 CRF 2 CRP S F S 0/S S O/S 3 CRP P F RMF 0.0053 0. 19 0. 558 0.877 1.783 0.066 1 .163 0 1.783 0.0106 0.32 0.901 1. 393 2.83 0. 104 1. 833 0 2.83 0.0212 0.48 1. 392 2. 176 4.423 0.163 2.878 0 4. 423 0.0425 0.66 2.088 3.357 6.822 0.252 4.493 0 6.822 0.085 0. 83 3.052 5.112 10.391 0.383 6.959 0 10.391 0.17 1 4. 438 7.731 15.713 0.58 10.681 0 15.713 0.34 1.22 6.532 1 1.886 24.156 0.893 16.683 0 24.156 0.68 1.51 9.865 21.08 42. 798 1.621 31. 127 0 42.798 1. 36 2.45 16.474 38.278 76,962 3.619 57.813 0 76.962 2 .72 7. 15 33.22 6 67.117 100 37.656 97.482 0 100 5.44 25.5 70.622 86. 117 100 73.679 100 0 100 10. 88 62 99.866 99.937 100 99. 88 100 0 100 2 1. 76 97 100 100 100 100 1 00 0 100 43.52 100 100 100 100 100 100 0 100 1 2 5 5 . 4 2 6 5 6 . 6 1 2 5 5 . 4 1 1 4 0 1 . 2 1 4 0 1 . 2 0 6 2 . 3 4 4 1 7 OPERATING CONDITIONS TONNAGES: 1255.4 % +1 INCH: 92.85 CR0SHER CURRENTS: 19. 14 SETS: 2 CR SET= 3. 16 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 76.96212 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 31.41311 % CIRCULATING LOAD= 1.116138 1 2 5 5 . 4 1 3 2 . 88279 SCRN OP= 1.43 39. 4 3 CR SET= 0.788 STOP! AT LINE "2120" IN PROGRAM "PGM2" PROGRAM ENDS 60 DATA 1, 16. 5 ,28. 5 , 2 7 . 3 , 1 2 . 6 , 4 . 6 5 , 2 . 2 5 , 2 . 0 ,1 .65 ,1 . 32 , 1 .02 , .64 , . 3 , . 2 7 3260 DATA 1417. 1,3. 1 6 , 1 . 4 3 , . 7 8 8 , 0 , 1 3 270 DATA 1 5 7 8 . 8 , 3 . 1 6 , 1 . 4 3 , . 7 8 8 , 0 , 1 3280 DATA 1 2 5 5 . 4 , 3 . 1 6 , 1 . 4 3 , . 7 8 , 0 , 0 %RUN NUMBER OF C Y C L E S 3 11 CONVERGENCE CRITERION 3 6.104166E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S 0/S S O/S 3 CRP P F RMF 21.76 1 0 0 0 0 0 0 0 10. 88 16.5 0. 067 0.035 0 0.0 74 0 0 0 5.44 28.5 12.215 6.416 0 13.514 0 0 0 2.72 27.3 38.31 21.244 0 44.747 2,365 0 0 1 .36 12.6 22.816 29.238 22. 168 37.059 36.343 0 22.168 0.68 4.65 9.853 20.768 37.121 2.678 32.844 0 37. 121 0.34 2.25 4.977 10. 287 18.76 0.914 16.162 0 18.76 0. 17 2 3.63 4.152 7.587 0.352 4.729 0 7.587 0.085 1.65 2.692 2. 674 4.887 0.225 2.653 0 4.887 0.0 425 1.32 1.997 1. 877 3.431 0. 158 1.745 0 3. 431 0.0212 1.02 1.458 1.31 2.395 0. 1 1 1.147 0 2.395 0.0106 0. 64 0.922 0.835 1.527 0.07 0.74 0 1.527 0.0 053 0.3 0.48 0. 475 0. 868 0.04 0.469 0 0.868 -0 .0053 0.27 0.583 0.687 1.256 0.058 0.803 0 1.256 - JU/ -% PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0. 27 0.583 0.687 1. 256 0.058 0.803 0 1.256 0.0106 0.57 1.063 1. 162 2. 124 0.098 1.272 0 2. 124 0.0212 1.21 1.985 1.998 3.651 0.168 2.012 0 3.651 0.0425 2.23 3. 443 3.308 6.046 0.278 3 . 159 0 6.046 0.085 3.55 5.439 5. 185 9.477 0.436 4.9 04 0 9. 477 0.17 5.2 8. 131 7. 859 14.364 0.662 7.557 0 14.364 0.34 7.2 11.762 12.011 21.951 1.014 12.286 0 21.951 0.68 9.45 16.739 22.298 40.711 1.927 2 8. 44 8 0 40.711 1. 36 14. 1 26.592 43.066 77.832 4.606 61.291 0 77.832 2.72 26.7 49.408 72.304 100 41.665 97.635 0 100 5.44 54 87.717 93.549 100 86.412 100 0 100 10.88 8:2.5 99.933 99.965 100 99.926 100 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417.1 1417.1 2698.05 1417.11 1280.95 1280.95 0 1417.11 % +1 INCH: 73.3 27.69564 58. 33516 CRUSHER CURRENTS; 21.93 37. 73 SETS: 2 CR SET= 3.16 SCRN OP= 1,43 3 CR SET= 0.788 55-1/2 INCH IN FEED= 14.1 X - 1 / 2 INCH IN SCREEN U/S= 77. 83 157 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 5.51997 % CIRCULATING LOAD= 0.9039235 NUMBER OF C,YCLES= 7 %5ET COLHIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21.76 1 0 10. 88 16.5 0.067 5.44 28.5 12.27 2.72 27.3 38.821 1.36 12.6 23.091 0.68 4.65 9.759 0.34 2.25 4.781 0.17 2 3. 456 0.085 1.65 2. 564 0.0425 1.32 1.909 0.0212 1. 02 1.4 0.0106 0.64 0.884 0.0 053 0.3 0. 456 -0 .0053 0.27 0. 541 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.27 0. 541 0,0 106 0,57 0.997 0.0212 1.21 1.881 0.0425 2.23 3.282 0.085 3. 55 5. 19 0. 17 5. 2 7.754 CONVERGENCE CRITERION= S F S U/S S O/S 0 0 0 0.035 0 0.074 6 .423 0 13.476 21.526 0 45. 169 28.906 21.817 36.691 18. 576 33. 272 2. 436 10. 036 18.347 0.908 4.918 9.0 1 0.425 3.267 5.986 0.28 2. 277 4. 172 0.195 1. 572 2. 881 0. 1 35 1.005 1.841 0. 086 0.583 1.069 0.05 0.876 1.605 0.075 S F S U/S S O/S 0.876 1.605 0.075 1.459 2.674 0. 125 2.464 4.515 0.211 4.036 7.3 96 0.346 6 .313 11.568 0.541 9.58 17.554 0.822 1. 188215E-3 3 CRP P F RMF 0 0 0 0 0 0 0 0 0 2.532 0 0 35.292 0 21.817 28.26 0 33.272 15.807 0 18. 347 6.524 0 9.01 4.039 0 5.986 2.681 0 4.172 1.761 0 2. 881 1.137 0 1.841 0.723 0 1.069 1.244 0 1.605 3 CRP P F RMF 1.244 0 1.605 1.967 0 2. 674 3.103 0 4.515 4, 864 0 7. 396 7.546 0 11.568 11.585 0 17.554 - 308 -0.34 7.2 11.21 1 4. 498 2 6.56 4 1.246 18. 11 0 26. 56 4 0*68 9.45 15.991 2 4. 534 44.91 1 2. 1 54 33.917 0 44. 911 1.36 14. 1 25.75 43. 1 1 78.183 4.591 62. 176 0 78. 183 2.72 26.7 48.841 7 2.0 16 100 41. 281 97.468 0 100 5.44 54 87.662 93.542 100 86. 45 100 0 100 10. 88 82.5 99.933 99, 965 100 99.926 100 0 100 21. 76 99 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1578. 8 1578.8 3016.32 1578.8 1437.52 1 437.52 0 1578. 8 % +1 INCH: 73. 3 27.9842 58.71876 CRUSHES CURRENTS: 24.72 39 .9 SETS: 2 CR S E T 3 3.16 SCRN O P 3 1. 43 3 CR S E T 3 0.788 X - 1 / 2 INCH IN F E E D 3 14.1 %-^/2 INCH IN SCREEN U/S 78. 18288 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 5. 544885 % CIRCULATING LOAD= 0.9105143 NUMBER OF C Y C L E S 3 9 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21.76 1 0 10. 88 16.5 0.067 5. 44 28.5 12.16 2.72 27.3 37.8 1.36 12.6 22.543 0.68 4.65 9.947 0.34 2.25 5. 172 0. 17 2 3.80 4 0.085 1.65 2. 82 0.0425 1.32 2.084 0.0212 1.02 1.516 0.0106 0.64 0.959 0.0053 0.3 0. 504 - 0 . 0053 0.27 0.624 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.27 0.624 0.0106 0. 57 1.128 0.0212 1.21 2.087 0.0425 2.23 3.603 0.085 3.55 5.687 0. 17 5. 2 8.506 0.34 7.2 12.31 0.68 9.45 17.482 1.36 14. 1 27.43 2.72 26.7 49.973 5.44 54 87.773 10. 88 82.5 99.933 21.76 99 100 4 3. 52 100 100 CONVERGENCE CRITERION 3 S F S 0/S S O/S 0 0 0 0.035 0 0.075 6.418 0 13.592 21.065 0 44.611 29.222 22. 133 37. 145 20.79 1 37.016 2.657 10.257 18.627 0.901 4.203 7.648 0.352 2.723 4.957 0.2 27 1.912 3. 481 0. 1 59 1.334 2.428 0.1 11 0.851 1. 549 0.071 0.484 0.882 0.04 0.703 1.28 0.059 S F S U/S S O/S 0.703 1.28 0.059 1. 188 2. 162 0.099 2.039 3.711 0.17 3.373 6. 139 0.281 5.285 9.62 0.44 8.009 14. 577 0.667 12. 212 22.22 5 1.019 22 .469 40. 851 1.921 43. 26 77. 867 4.577 72.481 100 41.722 93.546 100 86.333 99.965 100 99. 925 100 100 100 100 100 100 1. 500984E-3 3 CRP P F RMF 0 0 0 0 0 0 0 0 0 2.3 59 0 0 3 6.6 86 0 22. 13 3 32.913 0 37.016 15. 941 0 18.627 4 .649 0 7.648 2.6 16 0 4.957 1 .721 0 3.481 1.132 0 2.428 0.73 0 1.549 0.4 62 0 0.882 0.792 0 1.28 3 CRP P F RMF 0.7 92 0 1.28 1.2 54 0 2. 162 1.984 0 3.711 3*1 16 0 6. 139 4.837 0 9.62 7.453 0 14.577 12. 101 0 22.22 5 28. 042 0 40.851 60. 955 0 77.867 97. 641 0 100 100 0 100 100 0 100 100 0 100 100 0 100 - juy -OPERATING CONDITIONS TONNAGES: 1255. 4 1255.4 2378.52 1255.4 1123. 13 1 123. 13 0 1255.4 % +1 INCH: 73.3 27.51852 58. 27794 CRUSHER CURRENTS: 19. 14 35. 55 SETS: 2 CR S E T 3 3 .16 SCRN OP= 1.43 3 CR S E T - 0.788 X - 1 / 2 INCH IN F E E D 3 14.1 %-1/2 INCH IN SCREEN U/S= 77. 86688 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 5.522473 % CIRCULATING LOAD 3 0.8946392 STOP! AT LINE PROGRAM 60 DATA 3010 DATA 3020 DATA 3030 DATA 3040 DATA 3 05 0 DATA 3060 DATA 3070 DATA 3080 DATA 3 090 DATA 3100 DATA 3120 DATA 3130 DATA 3140 DATA 3150 DATA 3160 DATA 3170 DATA 3180 DATA 3190 DATA 3200 DATA 3210 DATA 3220 DATA SRUN "2120 ENDS 0 ,24 , 1417 1417 1417 1417 1417 1417 1417 1417 1417 1417 1417 1417 157 8 1255 1417 1417 1417 1417 1417 1417 1417 " IN PROGRAM "PGM2" 29 3 0 . 6 , 1 1 . 9 5 , 1 . 9 4 , . 6 8 , . 3 7 , . 2 9 , . 2 6 , . 2 7 , . 2 4 , . 1 8 , . 2 2 3. 16, 1 . 5 9 , 1 . 0 8 , 0 , 1 3. 1 6 , 1 . 2 7 , . 4 9 5 , 0 , 1 3. 1 6 , 1 . 5 9 , . 495 ,0 , 1 3 . 1 6 , 1 . 2 7 , 1 . 0 8 , 0 , 1 3 . 7 8 5 , 1 . 43, 1 .08 ,0 ,1 3 . 7 8 5 , 1 . 4 3 , . 4 9 5 , 0 , 1 2 . 5 4 , 1 . 4 3 , 1 . 0 8 , 0 , 1 2 . 5 4 , 1 . 4 3 , . 4 9 5 , 0 , 1 3 . 7 8 5 , 1 . 5 9 , . 7 8 8 , 0 , 1 3 .785 , 1. 2 7 , . 788,0,1 2 . 5 4 , 1 . 5 9 , . 7 8 8 , 0 , 1 2 . 5 4 , 1 . 2 7 , . 7 8 8 , 0 , 1 3 . 1 6 , 1 . 4 3 # . 7 8 8 , 0 , 1 3 . 1 6 , 1 . 4 3 , . 7 8 8 , 0 , 1 3 . 7 8 5 , 1 . 4 3 , . 7 8 8 , 0 , 1 2 . 5 4 , 1 . 4 3 , . 7 8 8 , 0 , 1 3. 1 6 , 1 . 5 9 , . 7 8 8 , 0 , 1 3 . 1 6 , 1 . 2 7 , . 7 8 8 , 0 , 1 3 . 1 6 , 1 . 4 3 , 1 . 0 8 , 0 , 1 3 . 1 6 , 1 . 4 3 , . 4 9 5 , 0 , 1 3 . 1 6 , 1 . 4 3 , . 7 8 8 , 0 , 0 NUMBER OF C Y C L E S 3 11 CONVERGENCE CRITERION 3 8. 348205E-3 %SET COL«IDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U / S S O/S 3 CRP P F RMF 21.76 0 0 0 0 0 0 0 0 10. 88 24 0.092 0.044 0 0.085 0 0 0 5.44 29 17.377 8. 345 0 16.054 0 0 0 2.72 30.6 45.283 31.269 0 60. 156 18. 322 0 0 1.36 11.95 21.881 30.565 39.546 22. 26 7 38 .587 0 39.546 0.68 1.94 6.507 13.561 27.378 0.7 96 20. 078 0 27. 378 0.34 0.68 3.041 5.741 11.70 1 0.235 8.236 0 11.701 0. 17 0.37 1.791 3.459 7.056 0.135 5 0 7.056 0.085 0.29 1.202 2.338 4.771 0.091 3.388 0 4.771 0.0425 0.26 0.853 1.586 3.237 0.062 2.264 0 3. 237 0.0212 0.27 0.654 1.08 6 2.215 0.042 1.484 0 2.215 0.0 106 0.24 0.487 0.733 1.495 0.0 28 0.96 0 1.495 0.0 05 3 0.18 0. 338 0.482 0.984 0.019 0.615 0 0.984 -0 .0053 0. 22 0. 495 0.792 1.6 16 0.031 1.067 0 1.616 - JIU -% PASSING: SIZE 2 CRF 2 c a p S F S 0/S S O/S 3 CRP P F RMF 0.0053 0. 22 0.495 0.792 1.616 0.031 1.067 0 1.616 0.0106 0.4 0.833 1.27 4 2. 6 0.0 49 1.6 82 0 2.6 0.0212 0.64 1.32 2.007 4.096 0.078 2.642 0 4.096 0.0425 0.91 1.974 3.093 6. 31 0.1 2 4. 126 0 6.31 0.085 1. 17 2. 828 4.679 9.547 0. 182 6.39 0 9.547 0.17 1.46 4.03 7.017 14.318 0.273 9.778 0 14.318 0.34 1.83 5. 82 10.4 76 21. 374 0.408 1 4. 777 0 21.374 0.68 2.51 8.86 1 16. 217 33.076 0.643 23. 013 0 33.076 1.36 4.45 15.368 29.778 60.454 1.439 43.091 0 60.454 2.72 16.4 37.248 60.343 100 23.706 81.678 0 100 5. 44 47 82.531 91.611 100 83.862 100 0 100 10. 88 76 99.908 99.956 100 99.915 100 0 100 21. 76 100 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417.1 1417.1 2951.04 1417.11 1533.93 1533.93 0 1417.11 % +1 INCH: 83.6 39.65729 76. 29437 CRUSHER CURRENTS: 21.93 38.43 SETS: 2 CR SET= 3.16 SCRN OP= 1.59 3 CR SET= 1.08 £ - 1 / 2 INCH IN FEED= 4.45 %-1/2 INCH IN SCREEN U/S= 60.45366 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 13.5 8509 % CIRCULATING LOAD= 1.082443 NUMBER OF CYCLES= 11 CONVERGENCE CRITERION^ 3, 166374E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 0 0 0 0 0 0 0 0 10. 88 24 0.092 0.039 0 0.068 0 0 0 5. 44 29 17.377 7.436 0 12.996 0.001 0 0 2.72 30.6 45.283 24. 641 0 43.068 9.204 0 0 1.36 11.95 21.881 32.811 22. 163 40.774 40. 984 0 22. 163 0.68 1.94 6.507 13.769 30. 09 1. 564 19,199 0 30.09 0. 34 0.68 3.041 8.107 18. 142 0.604 11.897 0 18. 142 0.17 0.37 1.791 4. 469 10.022 0.315 6.471 0 10.022 0.085 0.29 1.202 2.946 6.61 0.207 4.251 0 6. 61 0.0425 0.26 0.853 1,98 5 4. 453 0. 139 2.831 0 4.453 0.0212 0. 27 0.654 1.342 3.01 0.094 1 .856 0 3.01 0.0106 0.24 0. 487 0.896 2.009 0.0 63 1.201 0 2.009 0.0053 0. 18 0. 338 0.585 1.313 0.041 0.7 7 0 1.313 -0 .0053 0.22 0.495 0.97 5 2. 188 0.068 1 .335 0 2. 188 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.22 0. 495 0.975 2. 188 0,068 1.335 0 2. 188 0.0106 0.4 0.833 1.561 3.501 0.109 2.105 0 3. 501 0.0212 0.64 1.32 2. 456 5.51 0. 172 3.306 0 5.51 0.0 425 0.91 1.974 3 .798 8.521 0.266 5. 162 0 8. 521 0.085 1.17 2. 828 5.783 12. 974 0.405 7.992 0 12.974 0. 17 1. 46 4.03 8.729 19. 584 0.612 12. 243 0 19.584 0.34 1.83 5.82 13.198 29.606 0.927 18.715 0 29.606 - 3 1 1 -0.68 2. 51 8.861 21.305 47. 748 1.5 31 30.611 0 47.748 1.36 4.45 15.368 35.074 77. 837 3.0 94 49. 81 1 0 77.837 2.72 16.4 37.248 67. 884 100 43.868 90.795 0 100 5.44 47 82.531 92. 525 100 86. 93 5 99.999 0 100 10. 88 76 99.908 99.961 100 99.932 100 0 100 21.76 100 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES 1417. 1 1417.1 3312.06 1417.1 1894.96 1894.96 0 1417.1 % *1 INCH: 83.6 3 2. 11551 56. 13227 CRUSHER CURRENTS 21. 93 49.06 SETS: 2 CR SET = 3.16 SCRN OP= 1.27 3 CR SET= 0.495 %-l/2 INCH IN FEED= 4.45 X - 1 / 2 INCH IN SCREEN U/S= 77. 83733 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 17.49154 % CIRCULATING LOAD= 1.33721 NUMBER OF CYCLES= 12 CONVERGENCE CRITERION= 4. 986511E-3 %SET COLIIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 0 0 0 0 0 0 0 0 10. 88 24 0.092 0.043 0 0.081 0 0 0 5.44 29 17.377 8. 147 0 15.337 0.002 0 0 2.72 30.6 45.283 32.639 0 61.442 21. 481 0 0 1.36 11. 95 21.881 30. 019 39.385 21.754 37. 201 0 39.385 0.68 1.94 6.507 12.851 26. 567 0.7 47 18.45 0 26.567 0. 34 0.68 3.041 5.677 11.849 0.23 8.003 0 11.849 0.17 0.37 1.791 3.503 7. 318 0. 135 5.013 0 7.318 0.085 0. 29 1. 202 2.376 4.96,5 0.091 3.412 0 4.9 65 0.0425 0.26 0.853 1.611 3.367 0.062 2.28 0 3.367 0.0212 0.27 0.654 1.101 2.3 0.042 1 .495 0 2.3 0.0106 0.24 0.487 0.742 1. 551 0. 029 0.967 0 1.551 0.0053 0. 18 0.338 0.488 1.019 0.019 0.62 0 1.019 -0 .0053 0.22 0.495 0.803 1.678 0.031 1.075 0 1.678 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.22 0.495 0.803 1.678 0.031 1,075 0 1.678 0.0106 0.4 0. 833 1.291 2.697 0.05 1.695 0 2.697 0.0212 0.64 1.32 2.033 4.248 0.078 2.662 0 4.2 48 0.0425 0.91 1.974 3.134 6.548 0.1 2 4.157 0 6.548 0.085 1.17 2.828 4.745 9.915 0. 182 6 .437 0 9.915 0. 17 1. 46 4.03 7. 121 14. 88 0.274 9.849 0 14. 88 0.34 1.83 5.82 10.624 22. 199 0.409 14. 862 0 22.199 0.68 2. 51 8. 861 16.3 3 4.04 8 0.639 22. 865 0 34.048 1.36 4.45 15.368 29.151 60.615 1.386 41. 315 0 60.615 2.72 16.4 37.248 59. 171 100 23. 14 78.516 0 100 5.44 47 82.531 91.81 100 84.582 99.998 0 100 10. 88 76 99.908 99.957 100 99.919 100 0 100 21.76 100 100 100 100 100 100 0 100 43. 52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS - 312 -TONNAGES: 1417.1 1417. 1 3022.94 1417. 1 1605.84 1605.84 0 1417.1 % +1 INCH: 83.6 40.82937 76.86012 CRUSHER CURRENTS: 21.93 4 5. 05 SETS: 2 CR S E T 3 3.16 SCRN OP= 1.59 3 CR SET= 0.495 %-1/2 INCH IN F E E D 3 4.45 36-1/2 INCH IN SCREEN D / S 3 60.61469 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 13.62128 % CIRCULATING LOAD 3 1.133187 NUMBER OF C Y C L E S 3 10 CONVERGENCE CRITERION 3 4.665336E-3 1SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 0 0 0 0 0 0 0 0 10. 88 24 0.092 0.04 0 0.071 0 0 0 5.44 29 17.377 7.569 0 13. 41 0 0 0 2.72 30.6 45.283 24. 135 0 42. 76 7.815 0 0 1.36 11.95 21.881 32. 311 21.615 40.565 40.359 0 21.615 0.68 •1.94 6.507 14. 155 30.402 1.618 20.058 0 30.402 0.34 0.68 3.041 8. 354 18. 368 0.6 26 12.454 0 18.368 0. 17 0.37 1.791 4.557 10.042 0. 324 6.691 0 10.042 0.085 0.29 1. 202 2.998 6.608 0.212 4.3 83 0 6.608 0.0425 0.26 0.853 2.019 4.45 0. 142 2. 918 0 4.45 0.0212 0.27 0.654 1.365 3.009 0.096 1.913 0 3.009 0.0106 0.24 0.487 0.91 1 2.008 0.064 1.238 0 2.008 0.0053 0. 18 0. 338 0.595 1,312 0.042 0.794 0 1.312 - 0 . 0053 0.22 0.495 0.992 2. 187 0.07 1.376 0 2. 187 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.22 0. 495 0.992 2. 187 0.07 1 .3 76 0 2. 187 0.0106 0.4 0.833 1.587 3. 499 0. 1 12 2 .17 0 3.499 0.0212 0.64 1.32 2. 498 5.5 07 0. 176 3 .408 0 5.507 0.0425 0.91 1.974 3.863 8.516 0.272 5.321 0 8.516 0.085 1.17 2. 828 5.882 12.966 0.415 8.239 0 12.966 0.17 1.46 4.03 8.879 19.574 0.626 12.622 0 19.574 0.34 1.83 5. 82 13.436 29.616 0.95 19.313 0 29.616 0.68 2.51 8.861 21.79 47, 98 3 1. 576 31.767 0 47.983 1. 36 4.45 15.368 35.945 78. 385 3. 1 94 51.825 0 78.385 2.72 16.4 37.248 68.256 100 43.759 92. 185 0 100 5.44 47 82.531 92.391 100 86.519 100 0 100 10. 88 76 99.908 99.96 100 99. 929 100 0 100 21. 76 100 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417. 1 1417. 1 3253. 41 1417. 1 1836.31 1836.31 0 1417.1 % +1 INCH: 83.6 31.74408 56. 24121 CRUSHER CURRENTS: 21.93 42.62 SETS: 2 CR SET= 3.16 SCRN O P 3 1.27 3 CR S E T 3 1.08 %-1/2 INCH IN F E E D 3 4.45 %-1/2 INCH IN SCREEN U / S 3 78.38514 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 17.61464 - J I J -% CIRCULATING LOAD 3 1. 295822 NUMBER OF C Y C L E S 3 11 CONVERGENCE CRITERION 3 1.09 27 31 E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21.76 0 0 0 0 0 0 0 0 10. 88 24 0.022 0.009 0 0.016 0 0 0 5.44 29 31,949 13.457 0 23.251 0 0 0 2.72 30.6 41.327 22.394 0 38.691 8.616 0 0 1.36 11.95 17.442 31.645 26,853 35. 133 4 1. 982 0 26.853 0.68 1.94 4. 145 12.688 28. 152 1.434 1 8.905 0 28.152 0.34 0.68 1.704 7.229 16.398 0.557 11.249 0 16.398 0. 17 0. 37 0.947 4. 201 9.55 0.308 6.569 0 9.55 0.085 0.29 0.65 2.818 6.408 0.205 4.396 0 6.408 0.0425 0.26 0.491 1.905 4.332 0. 139 2.934 0 4.332 0.0212 0.27 0.419 1.29 2.933 0.0 94 1.924 0 2.933 0.0106 0.24 0.336 0.862 1. 96 0.063 1.245 0 1. 96 0.0053 0.18 0.241 0.564 1.281 0.041 0.798 0 1.281 - 0 . 0053 0.22 0. 326 0,938 2. 134 0.068 1.384 0 2. 134 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP p F RMF 0.0053 0. 22 0.326 0.938 2. 134 0.068 1.384 0 2. 134 0.0106 0.4 0.567 1.502 3. 415 0. 109 2. 182 0 3.415 0.0212 0.64 0. 903 2.36 4 5.375 0.172 3.426 0 5.375 0.0425 0.91 1. 322 3.654 8.308 0.266 5 .35 0 8.308 0.085 1. 17 1. 814 5.558 12. 64 0.405 8.284 0 12. 64 0.17 1.46 2. 463 8.376 19.048 0.61 12. 68 0 19.048 0.34 1.83 3.41 1 12. 577 28.598 0. 918 19.248 0 28.598 0.68 2,51 5. 115 19.806 44. 996 1.475 30.498 0 44.996 1.36 4. 45 9.26 32.494 73. 147 2.909 49.402 0 73.147 2.72 16.4 26.702 64.139 100 38.042 91. 384 0 100 5.44 47 68.029 86.533 100 76.733 100 0 100 10.88 76 99.978 99.991 100 99.984 100 0 100 21.76 100 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES 1417. 1 1417. 1 3364. 34 1417.1 1947.24 1947.24 0 1417. 1 % +1 INCH: 83.6 35.86076 61 . 95837 CRUSHER CURRENTS 17. 36 44. 16 SETS: 2 CR SET 3 3.785 SCRN OP= 1. 43 3 CR S E T 3 1.08 K - 1 / 2 INCH IN F E E D 3 4.45 %-1/2 INCH IN SCREEN U/S= 73.1473 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 3 16.4376 % CIRCULATING LOAD 3 1.374102 NUMBER OF C Y C L E S 3 12 CONVERGENCE CRITERION 3 9 .566123E-4 %SET COLSIDTH 3 8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF - 3 1 4 -21. 76 0 0 10. 88 24 0.022 5.44 29 31.949 2.72 30.6 41.327 1.36 11.95 17.442 0.68 1. 94 4. 145 0.34 0.68 1.704 0. 17 0. 37 0.947 0.085 0.29 0.65 0.0425 0. 26 0.49 1 0.0212 0.27 0,419 0.0 106 0. 24 0.336 0.0053 0. 18 0.241 - 0 . 0053 0.22 0.326 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.22 0.326 0.0106 0.4 0.567 0.0212 0.64 0.903 0.0425 0.91 1. 322 0.085 1. 17 1.814 0.17 1.46 2.463 0.34 1.83 3. 41 1 0.68 2.51 5. 115 1.36 4.45 9.26 2.72 16.4 26.702 5.44 47 68.029 10. 88 76 99.978 21.76 100 100 43. 52 100 100 0 0 0 0.009 0 0.016 13.232 0 22.586 23.045 0 39.335 31.971 27.355 35.233 12. 378 27. 917 1 .394 7.03 16.212 0. 539 4.116 9.513 0.301 2.765 6.392 0.201 1. 86 9 4.322 1 0.136 1.266 2. 927 0.092 0.846 1.956 0.061 0.553 1.279 0.04 0.921 2. 129 0.067 S F S U/S S O/S 0.921 2. 129 0.067 1.474 3. 408 0. 107 2.32 5.363 0.168 3.586 8.29 0.26 5.455 12.612 0.3 96 8.219 19.003 0.597 12.335 28.516 0.897 19.364 44.728 1. 436 31.742 72.645 2.83 63.713 100 38.063 86.758 100 77. 398 99.991 100 99.984 100 100 100 100 100 100 0 0 0 0 0 0 0.002 0 0 10.123 0 0 42.241 0 27.355 18. 197 0 27.917 10.794 0 16.212 6.355 0 9. 513 4.26 0 6.392 2.843 0 4. 322 1.864 0 2.927 1 .206 0 1. 956 0.773 0 1.279 1.341 0 2. 129 3 CRP P F RMF 1.341 0 2. 129 2.1 15 0 3.408 3.321 0 5.363 5.185 0 8.29 8.028 0 12.612 12.288 0 19.003 18.643 0 28.516 29.437 0- 44.728 4 7.634 0 72.645 89.875 0 100 99.998 0 100 100 0 100 100 0 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417. 1 1417. 1 3421. 88 1417. 1 2004.78 2004.73 0 1417.1 % +1 INCH: 83.6 36.28699 61.9368 CRUSHER CURRENTS: 17.36 50.58 SETS: 2 CR SET= 3.785 SCRN OP= 1.43 3 CR SET= 0.495 %-1/2 INCH IN FEED= 4.45 %-1/2 INCH IN SCREEN U/S= 72.64464 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 16.32464 % CIRCULATING LOAD= 1.414706 NUMBER OF CYCLES= 10 CONVERGENCE CRITERION= 8.31629E-3 5SSET COLMIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S D/S S O/S 3 CRP P F RMF 21. 76 0 0 0 0 0 0 0 0 10.88 24 0.001 0 0 0.001 0 0 0 5. 44 29 17.021 7.766 0 14.282 0 0 0 2.72 30.6 43.679 24.877 0 45. 751 9.101 0 0 1. 36 11.95 21.35 31.939 26.287 36.682 40.825 0 26.287 0.68 1.94 6.933 14.258 29.277 1.6 57 20.405 0 29.277 0. 34 0.68 3. 64 7.94 16. 65 0.631 1 1.547 0 16. 65 0.17 0.37 2. 291 4.441 9.333 0.336 6.245 0 9.333 0.085 0.29 1.563 2.954 6.209 0.222 4.121 0 6. 209 - J i u -0.0425 0.26 1.098 1.995 4. 193 0.15 2.747 0 4. 193 0.0212 0.27 0.816 1.352 2.841 0. 102 1.801 0 2,841 0.0106 0.24 0.592 0. 904 1.9 0.068 1.166 0 1.9 0.0053 0.18 0.405 0.59 1 1.243 0.044 0.748 0 1.243 -0 .0053 0.22 0.61 1 0.983 2.067 0.074 1.296 0 2.067 % PASSING: SIZE 2 CRF 2 CRP S F S O/S S O/S 3 CRP P F RMF 0.0053 0.22 0.611 0.983 2.067 0.074 1.296 0 2.067 0.0106 0.4 1.016 1.575 3. 31 0.1 18 2.043 0 3.31 0.0212 0.64 1.608 2.479 5.21 0.1 87 3.209 0 5. 21 0.0425 0.91 2.424 3.83 8.052 0.288 5.011 0 8.052 0.085 1. 17 3.522 5.825 12.245 0.438 7.757 0 12.245 0.17 1.46 5.085 8.779 18.454 0.661 11.878 0 18.454 0.34 1.83 7.376 13.22 27.787 0.997 18. 123 0 27.787 0.68 2.51 11.0 17 2 1. 16 44. 437 1,628 29 .67 0 44.437 1. 36 4.45 17.95 35.418 73.713 3.2 85 50.075 0 73.713 2.72 16.4 39.3 6 7.357 100 39.967 90.899 0 100 5.44 47 82.979 92.234 100 85.718 100 0 100 10. 88 76 99.999 100 100 99.999 100 0 100 21. 76 100 100 100 100 100 100 0 100 43.52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417. 1 1417. 1 3105. 96 1417. 09 1688. 87 1688.87 0 1417. 09 % +1 INCH: 83.6 32.64294 60.03292 CRUSHER CURRENTS: 26.47 40.58 SETS: 2 CR SET= 2.54 SCRN OP= 1. 43 3 CR SET= 1.08 %-1/2 INCH IN FEED= 4.45 %-1/2 INCH IN SCREEN U/S= 73.71343 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 16.56482 % CIRCULATING LOAD= 1.191779 NUMBER OF C Y C L E S 3 11 CONVERGENCE CRITERION 3 5. 94 7501 E-3 %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 21. 76 0 0 0 0 0 0 0 0 10. 88 24 0.001 0 0 0.001 0 0 0 5.44 29 17.021 7.633 0 13. 84 0.001 0 0 2.72 30.6 43.679 25.515 0 46. 26 10.748 0 0 1.36 11. 95 21.35 32.292 26 . 837 36.727 41. 189 0 26.837 0.68 1.94 6. 933 13.802 28 . 822 1.59 19.386 0 28.822 0. 34 0.68 3.64 7.696 16 .417 0.6 06 10.994 0 16.417 0.17 0.37 2.291 4.378 9. 359 0.329 6.075 0 9.359 0.085 0.29 1.563 2.921 6. 247 0.218 4.026 0 6.247 0.0425 0.26 1,098 1.97 3 4. 219 0.147 2.684 0 4.219 0.0212 0.27 0.816 1.337 2. 858 0,1 1.76 0 2, 858 0.0106 0.24 0.59 2 0.894 1. 911 0.067 1.139 0 1.911 0.0053 0. 18 0. 405 0.585 1. 25 0.044 0.731 0 1.25 - 0 . 0053 0.22 0.61 1 0.972 2. 079 0.073 1.266 0 2.079 % PASSING: SIZE 2 CRF 2 CRP S F S U/S S O/S 3 CRP P F RMF 0.0053 0.22 0.61 1 0.972 2. 079 0.073 1.266 0 2.079 - 316 -0.0106 0. 4 1.016 1.557 3.33 0. 116 1 .997 0 3 • 3 3 0.0212 0.64 1.608 2. 451 5.241 0. 183 3.137 0 5. 241 0.0425 0.91 2. 424 3.788 8.099 0.282 4.897 0 8.099 0.085 1. 17 3.522 5.761 12,318 0.43 7.581 0 12.318 0.17 1.46 5.085 8.682 18. 565 0.648 1 1.607 0 18.565 0.34 1.83 7. 376 13.061 27.924 0.976 17.682 0 27.924 0.68 2.51 11.0 17 20.757 44. 341 1.583 28.676 0 44.341 1.36 4.45 17.95 34. 559 73.163 3,173 48. 062 0 73. 163 2.72 16.4 39.3 66.851 100 39. 9 89.251 0 100 5. 44 47 82.979 92.366 100 86. 16 99.999 0 100 10.88 76 99.999 100 100 99.999 100 0 100 21. 76 100 100 100 100 100 100 0 100 4 3,52 100 100 100 100 100 100 0 100 OPERATING CONDITIONS TONNAGES: 1417. 1 1417. 1 3160.08 1417. 09 1742.99 1742.99 0 1417.09 % +1 INCH: 83.6 33.14914 60.10027 CRUSHER CURRENTS: 26.47 46.95 SETS: 2 CR SET= 2.54 SCRN OP= 1. 43 3 CR SET= 0.495 %-1/2 INCH IN FEED = 4.45 %-1/2 INCH IN SCREEN U/S= 73.16263 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 16.44104 % CIRCULATING LOAD= 1.229 97 NUMBER OF CYCLES= 8 CONVERGENCE CRITERION= 8.444003E-4 %SET COL¥IDTH=8 % RETAINED: S I Z E 2 C R F 2 C R P S F S U / S S O / S 3 C R P P F R M F 21. 76 0 0 0 0 0 0 0 0 10. 88 24 0.022 0.011 0 0.021 0 0 0 5. 44 29 31.949 15,612 0 30.531 0 0 0 2.72 30.6 41.327 23. 299 0 45.565 6.072 0 0 1.36 11.95 17.442 30.542 39.073 22. 39 43.062 0 39. 073 0.68 1.94 4. 145 1 4.05 27.88 3 0.832 23.517 0 27.883 0. 34 0.68 1.704 5.947 1 1. 914 0.246 10.002 0 11.914 0.17 0.37 0.947 3.477 6.971 0. 137 5.893 0 6.971 0.085 0.29 0.65 2.34 8 4.709 0.092 3.971 0 4.709 0.0425 0.26 0.491 1. 596 3.2 0.063 2.651 0 3.2 0.0212 0.27 0.419 1.093 2. 193 0.043 1.738 0 2. 193 0.0106 0.24 0.336 0.739 1. 481 0.029 1.124 0 1.481 0.0053 0. 18 0.241 0.486 0. 975 0.019 0.72 0 0.975 - 0 . 0053 0. 22 0. 326 0.798 1.601 0.031 1 .25 0 1.601 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.22 0.326 0.0106 0.4 0.567 0.0212 0.64 0.903 0.0425 0.91 1.322 0.085 1.17 1.814 0. 17 1.46 2. 463 0.34 1.83 3. 41 1 0.68 2.51 5. 115 1.36 4.45 9.26 2.72 16.4 26.702 S F S U/S S O/S 0.798 1.601 0.031 1. 285 2.576 0.05 2.023 4.058 0.079 3. 117 6.25 0.1 22 4.713 9.451 0. 185 7.06 1 14. 159 0.277 10.537 21,13 0.414 16.485 33.044 0.66 30.535 60.927 1.492 61. 078 100 23.882 3 CRP P F RMF 1.25 0 1.601 1. 97 0 2.576 3.094 0 4.058 4. 832 0 6. 25 7.483 0 9.451 11.454 0 14. 159 17.348 0 21. 13 27.35 0 33.044 50,866 0 60.927 93. 928 0 100 - 3 1 7 -5.44 47 68.029 84.377 100 10.88 76 99.978 99.989 100 21. 76 100 100 100 100 43.52 100 100 100 100 69.447 100 0 99. 979 100 0 100 100 0 100 100 0 100 100 100 100 OPERATING CONDITIONS TONNAGES: 1417. 1 1417. 1 2899.99 1417. 1 1482.89 1482.89 0 1417.1 % +1 INCH: 83.6 38.92235 76.11784 CRUSHER CURRENTS: 17.36 4 0.53 SETS: 2 CR SET= 3.785 SCRN OP= 1. 59 3 CR S E T 3 0.788 %-1/2 INCH IN F E E D 3 4.45 %-1/2 INCH IN SCREEN U/S= 60.927 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT FEED= 13.69146 % CIRCULATING LOAD- 1.046426 NUMBER OF C Y C L E S 3 9 %SET COLBIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP 21.76 0 0 10. 88 24 0.022 5.44 29 31.949 2.72 30.6 41.327 1. 36 1 1.95 17.442 0.68 1.94 4. 145 0.34 0.68 1.704 0.17 0.37 0.947 0.085 0.29 0.65 0.0425 0.26 0. 49 1 0.0212 0.27 0.419 0.0106 0.24 0.336 0.0053 O. 18 0. 241 - 0 . 0053 0.22 0.326 % PASSING: SIZE 2 CRF 2 CRP 0.0053 0.22 0.326 0.0106 0.4 0.567 0.0212 0.64 0.903 0.0425 0. 91 1.322 0.085 1. 17 1.814 0. 17 1.46 2.463 0.34 1.83 3.411 0.68 2. 51 5. 115 1 .36 4.45 9.26 2.72 16.4 26.702 5.44 47 68.029 10. 88 76 99.978 21.76 100 100 43. 52 100 100 TONNAGES 1417. 1 1417. 1 % +1 INCH: CONVERGENCE CRITERION 3 S F S U/S S O/S 0 0 0 0.01 0 0.0 18 14. 052 0 25.084 19.472 0 34. 76 28.777 18.571 36.791 14. 561 30.976 1.674 8.908 19.404 0.668 4.80 9 10.499 0.342 3.176 6.937 0.224 2. 142 4.678 0. 151 1.447 3. 159 0. 102 0.96 4 2. 106 0.068 0. 63 1.375 0.044 1.051 2. 296 0.074 S F S U/S S O/S 1.051 2. 296 0.074 1.681 3.671 0.1