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Digital simulation of a crushing plant Hatch, Christopher 1977

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DIGITAL SIMULATION OF A CRUSHING PLANT  by Christopher Hatch,  B.A.Sc.  U n i v e r s i t y o f B r i t i s h C o l u m b i a , Canada,  1973  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department o f Mineral  Engineering  We a c c e p t t h i s t h e s i s as conforming t o the r e q u i r e d  THE UNIVERSITY OF BRITISH COLUMBIA (c}  Christopher Hatch,  1977  standard.  In presenting this thesis in partial  fulfilment of the requirements for  an advanced degree at the University of B r i t i s h 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 B r i t i s h Columbia  2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  Date  -  ii -  ABSTRACT To improve upon the u n d e r s t a n d i n g 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 r e e n i n g p r o c e s s , the Brenda Mines L i m i t e d secondary c r u s h i n g p l a n t was simulated.  The p l a n t c o n s i s t s o f two s t a g e s 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 e e n i n g employed i n c l o s e d c i r c u i t w i t h the l a t t e r c r u s h i n g stage. A c q u i s i t i o n o f p l a n t d a t a was c a r r i e d out a c c o r d i n g t o  full  o r m o d i f i e d f a c t o r i a l d e s i g n s i n t e n d e d t o c o v e r normal o p e r a t i n g The  u n i t s sampled i n c l u d e a Symons Nordberg 7 - f o o t s t a n d a r d  ranges.  cone  c r u s h e r , a Symons Nordberg 7 - f o o t s h o r t - h e a d cone c r u s h e r and two Allis-Chalmers 8ft.x20ft.  double deck v i r b r a t i n g s c r e e n s .  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 t o steady s t a t e as was p o s s i b l e . All  samples were s c r e e n e d a t the p l a n t u s i n g a s t a n d a r i z e d  procedure.  Raw data o b t a i n e d around the screens was l a t e r a d j u s t e d by means o f a l e a s t squares t e c h n i q u e t h a t assumes a l l measured v a l u e s are i n e r r o r . The models developed t o d e s c r i b e both c r u s h i n g o p e r a t i o n s m o d i f i c a t i o n s o f those used a t Mt. I s a Mines L i m i t e d . meters were e m p i r i c a l l y f i t t e d t o the observed d a t a . s a t i s f a c t o r y performance.  The model p a r a Both models gave  The model proposed f o r the v i b r a t i n g s c r e e n s  was d e r i v e d from s m a l 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 t o perform s a t i s f a c t o r i l y . short-head crushers  are  and the s c r e e n s  Models f o r  the  can be e x t r a p o l a t e d a p p r o x i m a t e l y  twenty p e r c e n t beyond t h e i r f i t t e d data  ranges.  The f i t t e d models were combined t o 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 t h e complete secondary c r u s h i n g p l a n t . s i m u l a t i o n was performed i n accordance w i t h a f u l l modified to i n c l u d e intermediate ranges.  A s t u d y o f the  factorial  design  O p e r a t i n g v a r i a b l e s whose  values were generated d u r i n g 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 r a n g e s , w i t h the e x c e p t i o n o f the s h o r t - h e a d c r u s h e r f e e d r a t e . 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 o u t p u t shows t h a t the conform to e x p e c t e d and observed p l a n t b e h a v i o r .  Pre-  results  Further analysis  w i t h r e s p e c t t o s h o r t - h e a d c r u s h e r power draw i n d i c a t e s t h a t i t may be p o s s i b l e to i n c r e a s e 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 . economic advantage o f a d i g i t a l  The  s i m u l a t i o n i s demonstrated by t h e  t h a t the average c o s t f o r one computer run i s a p p r o x i m a t e l y twenty cents.  fact  - iv -  TABLE OF CONTENTS Page ABSTRACT  ii  LIST OF FIGURES  viii  LIST OF TABLES  xii  LIST OF SYMBOLS  xiv  ACKNOWLEDGEMENTS  xix  CHAPTER I  :: INTRODUCTION  1.1  Statement o f O b j e c t i v e s  1  1.2  Literature  3  (a)  Survey  Summary o f Comminution D i s t r i b u t i o n F u n c t i o n s  4  1.3  The Cone C r u s h e r Model  6  1.4  The V i b r a t i n g Screen Model  7  CHAPTER I I 2.1  2.2  2.3 CHAPTER I I I  DATA ACQUISITION Description of Crushing Plant (a)  Introduction  10  (b)  The P r i m a r y C r u s h e r  10  (c)  The Secondary C r u s h e r  12  (d)  The Secondary Screens  12  (e)  The T e r t i a r y Crushers  13  (f)  General  14  Procedures  f o r A c q u i s i t i o n o f Raw Data  (a)  Introduction  15  (b)  Secondary C r u s h e r Sampling  29  (c)  T e r t i a r y C r u s h e r Sampling  32  (d)  Secondary Screen Sampling  36  (e)  P r i m a r y Fines Sampling  41  Sample S c r e e n i n g  42  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 C r u s h e r 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 C r u s h e r C u r r e n t  57  (d)  Model A c c u r a c y and Range  58  4.3  4.4  4.5  CHAPTER V  The T e r t i a r y C r u s h e r 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 C r u s h e r C u r r e n t  64  (d)  Model A c c u r a c y and Range  64  The Secondary Screen Model  69  (a)  Model D e s c r i p t i o n  70  (b)  Model B e h a v i o r  72  (c)  Model A c c u r a c y and Range  75  The P r i m a r y F i n e s Model  76  (a)  Model D e s c r i p t i o n  80  (b)  Model A c c u r a c y  82  SIMULATION OF THE CRUSHING PLANT  5.1  The S i m u l a t i o n Programs  84  5.2  Methodology Employed t o Study the S i m u l a t i o n Program PGM2  86  CHAPTER VI 6.1  6.2  DISCUSSION 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 z e D i s t r i b u t i o n  98  (d)  Secondary C r u s h e r Gap  98  (e)  Secondary Screen Opening  101  (f)  T e r t i a r y C r u s h e r 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 Current  110  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  116  - vi -  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 Crushing Plant  Secondary  (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  127 131  Measured (Raw) Data  C.  D.  E.  (a)  S i z e D i s t r i b u t i o n s f o r Secondary Samples  Crusher  (b)  Size Distributions for Tertiary Samples  (c)  S i z e D i s t r i b u t i o n s f o r Secondary Samples  (d)  S i z e D i s t r i b u t i o n s f o r P r i m a r y Screens U n d e r s i z e Samples  142  (e)  F l o w r a t e Record f o r P r i m a r y Screens U n d e r s i z e Stream  143  Crusher Screens  135 137 139  Adjustment o f Secondary Screen Data (a)  L i s t i n g o f the Program SCREEN, a Program Developed f o r Adjustment o f Raw Screen Data  147  (b)  A d j u s t e d Data f o r the Secondary Screens  152  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 L i n e a r Regression A n a l y s i s  169  (b)  TRANS4, a Support Program f o r ALLREDD t o P e r m i t Data T r a n s f o r m a t i o n  173  Summary o f t h e Secondary C r u s h e r 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 C r u s h e r M o d e l , SECRUSH  180  (c)  Output from SECRUSH - Model P r e d i c t i o n s f o r Observed Data  183  - vii Page F.  Summary o f t h e T e r t i a r y C r u s h e r Model (a)  L i s t i n g o f t h e 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 C r u s h e r M o d e l , 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 E q u a t i o n  H.  Summary o f Secondary Screen Model  I.  J.  (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 M o d e l , SCRN3  217  (c)  Output from SCRN3 - Model P r e d i c t i o n s f o r Observed Data  220  Summary.of the P r i m a r y F i n e s 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 P r i m a r y F i n e s M o d e l , PF  236  (c)  Output from PF - Model P r e d i c t i o n s f o r Observed Data  238  Secondary C r u s h i n g P l a n t S i m u l a t i o n (a)  Main Program M2  243  Subprogram SCMS (Secondary Crusher)  247  Subprogram TCMS ( T e r t i a r y Crusher)  249  (iv)  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  (ii) (iii)  L.  Programs  L i s t i n g o f the S i m i l a t i o n Program M2 (i)  K.  203  Output from S i m u l a t i o n  Studies  (a)  Full  F a c t o r i a l Design Study  (b)  I n t e r m e d i a t e Ranges Study  Computation o f E f f e c t s o f S i m u l a t i o n V a r i a b l e s on Responses  272 302 329  - viii  -  LIST OF FIGURES Figure  Page  1  Schematic R e p r e s e n t a t i o n  o f a Cone C r u s h e r  6  2  Geometric C o n s i d e r a t i o n s  for Derivation of Screening  Probability  7  3  Efficiency  Curve f o r Whiten Screen Model  4  G e n e r a l i z e d C r u s h i n g P l a n t Flowsheet  5  M o d i f i c a t i o n s t o Secondary and T e r t i a r y  9 11 Crusher  Mantles (a)  Standard  14  Crushers  6  (b) S h o r t - h e a d Crushers F a c t o r i a l Design Used f o r Sampling Schedules  7  General Views o f t h e Brenda C r u s h i n g P l a n t  18  (a)  P h y s i c a l L o c a t i o n s o f C r u s h i n g P l a n t Components  (b)  I n t e r i o r View o f t h e S e c o n d a r y / T e r t i a r y  Crusher  Building  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 The Secondary C r u s h i n g P l a n t C o n t r o l Room  21 22  (e) 8  19  L o c a t i o n o f Sample (a)  Points  Secondary C r u s h i n g P l a n t Flowsheet Showing Sample L o c a t i o n s  (b)  Sample P o i n t f o r Secondary C r u s h e r Feed  (c)  Sample P o i n t f o r Secondary C r u s h e r P r o d u c t , Secondary Screen Feed and T e r t i a r y Crusher Product  24 25  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 O v e r s i z e and U n d e r s i z e Products Sample P o i n t f o r P r i m a r y Screens U n d e r s i z e Product (Primary Fines)  27  Sample S c r e e n i n g S t a t i o n  28  (f) (g)  27  - ix -  Figure 9  E x p e r i m e n t a l Design f o r Secondary  Crushers  10  E x p e r i m e n t a l Design f o r T e r t i a r y  11  Segregation  12  Combined E x p e r i m e n t a l Design f o r Secondary  13  Schematic Diagram f o r Mass Balance o f a Secondary Screen  14  Computational Procedure Component, B l  f o r P r i m a r y Breakage  15  Computational Procedure Component, B2  f o r Secondary  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 F u n c t i o n  Crushers  Trends w i t h i n Screen Surge B i n Screens  Breakage  Components, B l and B2 17  C l a s s i f i c a t i o n Function c(x)  18  (a) (b)  19  20  Performance o f Secondary C r u s h e r M o d e l , Best P r e d i c t i o n Performance o f Secondary C r u s h e r M o d e l , Worst P r e d i c t i o n  B e h a v i o r o f T e r t i a r y C r u s h e r Model Parameters (a)  Parameter a  (b)  Parameter 3  (c)  Parameter k l  (d)  Parameter k2  (a)  Performance o f T e r t i a r y C r u s h e r M o d e l , Best P r e d i c t i o n  (b)  Performance o f T e r t i a r y C r u s h e r M o d e l , Worst P r e d i c t i o n  21  B e h a v i o r o f A l t e r n a t i v e k2 R e l a t i o n  22  (a)  B e h a v i o r o f Screen E f f i c i e n c y as a F u n c t i o n o f Parameter x (a=2.0 cm ) 3  5 0  (b)  B e h a v i o r o f Screen E f f i c i e n c y as a F u n c t i o n o f Parameter a ( x = 1 . 9 2 cm) 5 0  - x -  Fi gure  23  Page  (a) (b) (c)  24  Performance o f Secondary Screen M o d e l , Best P r e d i c t i o n  77  Performance o f Secondary Screen M o d e l , Worst P r e d i c t i o n  78  Performance o f Secondary Screen M o d e l , Second Worst P r e d i c t i o n  79  B e h a v i o r o f P r i m a r y F i n e s Model Parameters (a)  Parameters b  (b)  Parameter b  0  and  b  81  1  2  25  S i m u l a t i o n Flow Diagram  85  26  The I n f l u e n c e o f P l a n t Feedrate on S i m u l a t i o n Responses  97  The I n f l u e n c e o f P e r c e n t + 1 Inch i n P l a n t Feed on S i m u l a t i o n Responses  99  27  28 29 30 31  The I n f l u e n c e o f Secondary C r u s h e r Gap on S i m u l a t i o n Responses  100  The I n f l u e n c e o f Secondary Screen Opening on S i m u l a t i o n Responses  102  The I n f l u e n c e o f T e r t i a r y C r u s h e r Gap on S i m u l a t i o n Responses  104  (a) (b)  32  B e h a v i o r o f R a t i o A as a F u n c t i o n o f T e r t i a r y C r u s h e r Gap  106  B e h a v i o r o f R a t i o A as a F u n c t i o n o f P a r t i c l e Size  106  B e h a v i o r o f T e r t i a r y C r u s h e r C u r r e n t Draw as a F u n c t i o n o f F e e d r a t e f o r Constant C r u s h e r Gap  111  33  I n d i c a t e d C a p a c i t y I n c r e a s e s f o r T e r t i a r y Crushers  1-13  34  The I n f l u e n c e o f S i m u l a t i o n V a r i a b l e s on T e r t i a r y C r u s h e r C u r r e n t Draw and F e e d r a t e  115  - xi -  Figure  Page  Al  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 I n c l i n e d V i b r a t i n g Screens  132  Gl  Schematic R e p r e s e n t a t i o n  205  G2  Comparison o f Observed and P r e d i c t e d Screen Response  o f a V i b r a t i n g Screen  209  - xii -  LIST OF TABLES  Table  Page  1  Thermal O v e r l o a d S e t t i n g s  2  Representative  3  Summary o f O p e r a t i n g D a t a ; Secondary Sampling Phase  4  5  6 7  f o r Crushers  U n i t s Sampled  Summary o f O p e r a t i n g D a t a ; . . T e r t i a r y Sampling Phase  17 Crusher 32 Crusher  41  S c r e e n i n g Procedures f o r Secondary C r u s h i n g P l a n t Samples  43  G e n e r a l i z e d T a b l e o f Data O b t a i n e d Around a 46  8  P r i m a r y F i n e s Sampling Schedule  9  O p e r a t i n g Ranges o f V a r i a b l e s S t u d i e d w i t h Program PGM2 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 C r u s h i n g P l a n t S i m u l a t i o n Study  11  12 13  36  Summary o f O p e r a t i n g D a t a ; Secondary Screen Sampling Phase  Screen  10  15  82  87  88  Coded Two-Level I n t e r m e d i a t e Range Design M a t r i x Used f o r Secondary C r u s h i n g P l a n t S i m u l a t i o n Study  90  Summary o f Two-Level F u l l S i m u l a t i o n Study  92  Summary o f Two-Level  F a c t o r i a l Design  I n t e r m e d i a t e 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  I n d i c a t e d C a p a c i t y I n c r e a s e s f o r T e r t i a r y Crushers  112  - xiii  -  Table  Page  Al  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  127  A2  Design S p e c i f i c a t i o n s f o r Symons Nordberg Cone Crushers  129  A3  O p e r a t i n g S p e c i f i c a t i o n s f o r Symons Nordberg Cone Crushers  130  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 P r i m a r y and Secondary V i b r a t i n g Screens  131  Bl  F l o w r a t e Record f o r Primary Screens U n d e r s i z e Stream; A u g u s t , 1975  143  B2  F l o w r a t e Record f o r P r i m a r y Screens U n d e r s i z e Stream; September, 1975  144  B3  F l o w r a t e Record f o r P r i m a r y Screens U n d e r s i z e Stream;. O c t o b e r , 1975  145  - xiv -  LIST OF SYMBOLS Unit  Symbol A.  GENERAL TERMINOLOGY =  counter  n  =  number o f screen  size  n-1  =  number o f screen  sizes  x  =  screen s i z e (lower l i m i t o f size fraction)  centimeter  variables fractions  dimensionless dimension l e s s  G  =  c r u s h e r c l o s e s i d e s e t t i n g o r gap  centimeter  T  =  unit  tons/hour  S  =  percent + 1 inch material feed s t r e a m .  feedrate  =  secondary screen  Yc  =  cumulative weight f r a c t i o n screen  =  in unit weight percent centimeter  <}>  RSS  B.  dimensi o n l e s s  i,j  opening  r e s i d u a l sum o f squares two v e c t o r s  passing dimensionless  between dimensionless  THE WHITEN SCREEN MODEL m  =  number o f random passes a p a r t i c l e makes a t openings w h i l e p a s s i n g o v e r a screen deck  dimensionless  1  =  l e n g t h o f screen  feet  a  =  screen opening (square mesh)  inch  w  =  w i d t h o f screen  feet  =  an e f f i c i e n c y  dimensionless  =  a loading constant  dimensionless  V  =  volumetric feedrate  ton/hour  b  =  screen  inch  s  =  particle  ki k  2  2  constant  cloth wire size  diameter  inch  - xv Symbol C.  Unit  DATA ADJUSTMENT PROCEDURE FOR SECONDARY SCREENS F  =  measured screen  0  =  measured screen o v e r s i z e flowrate  U  f.j  o.j  u.j  =  =  =  =  =  =  Sf.  So^  Su.  Y.  =  =  =  measured screen flowrate  feedrate  undersize  ton/hour product ton/hour product ton/hour  measured w e i g h t 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  dimensionless  measured w e i g h t 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  dimensionless  measured w e i g h t 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 u n d e r s i z e product  dimensionless  a symbol used i n c o n j u n c t i o n w i t h any o f the above s c r e e n v a r i a b l e s t o denote an a d j u s t e d o r p r e d i c t e d val ue  dimensionless  a symbol used i n c o n j u n c t i o n w i t h any o f the above screen v a r i a b l e s t o denote a program search v a r i a b l e  dimensionless  standard deviation of i t h s i z e f r a c t i o n o f measured s c r e e n f e e d  dimensionless  standard d e v i a t i o n of 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  dimensionless  standard deviation of i t h s i z e f r a c t i o n o f measured screen undersize product  dimensionless  =  ordinate value f o r i t h s i z e f r a c t i o n o f a d j u s t e d screen e f f i c i e n c y curve  =  w e i g h t 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  dimensionless  - xvi -  Symbol D.  Unit  THE SIMULATION MODELS (a)  The C r u s h e r Model F  =  c r u s h e r feed  vector  X  =  vector describing instantaneous crusher contents  weight percent weight percent  weight percent  P  =  crusher product  B  =  t o t a l breakage m a t r i x  dimensionless  Bl  =  p r i m a r y breakage component m a t r i x  dimensionless  B2  =  secondary breakage component m a t r i x  dimensionless  C  =  c l a s s i f i c a t i o n matrix  dimensionless  CX  =  proportion of crusher contents be broken  BCX  x  =  =  x.  =  Yp n  =  proportion o f crusher a c t u a l l y broken  =  =  weight percent  contents weight  percent  centimeter  lower s i z e l i m i t o f p a r t i c l e fraction i  centimeter  size  v a l u e o f p r i m a r y breakage d i s t r i bution function for p a r t i c l e s i z e dimensionless  i  v a l u e o f secondary breakage d i s t r i bution function for p a r t i c l e s i z e x  a  to  g e o m e t r i c mean s i z e o f l a r g e s t p a r t i c l e entering crusher ( d e f i n e d as the geometric mean s i z e o f the s m a l l e s t screen f r a c t i o n p a s s i n g 100 p e r c e n t i n 1/2 screen r a t i o )  x  Ys .  vector  dimensionless  i  l i n e a r combination (model parameter)  coefficient dimensionless  y  =  model c o n s t a n t  dimensionless  3  =  model parameter  dimensionless  - XVI1  -  Symbol  i  a  Unit =  model c o n s t a n t  =  i t h element o f secondary matrix  =  centimeter breakage dimensionless  i t h element o f p r i m a r y breakage matrix  dimensionless  c(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 function  dimensionless  C ^ )  =  i t h element o f c l a s s i f i c a t i o n matrix diagonal  dimensionless dimensionless  n  F(x )  =  intermediate  Kl  =  model parameter  centimeter  K2  =  model parameter  centimeter  C  =  predicted crusher  i  calculation  vector  current  amperes  The Screen Model =  =  =  x  50  =  e q u i v a l e n t s c r e e n opening composite screen  for centimeter  g e o m e t r i c mean s i z e o f p a r t i c l e s i z e range i  centimeter  w e i g h t f r a c t i o n o f feed to o v e r s i z e product  dimensionless  reporting  model parameter ( p a r t i c l e s i z e a t which 50 p e r c e n t o f feed reports to oversize product)  centimeter  a  =  model parameter  cubic  Ci  =  a u x i l l i a r y f u n c t i o n to account f o r s h o r t - c i r c u i t i n g o f undersize material into oversize product  dimensionless weight percent  o f feed  centimeter  m  =  moisture content  a  =  proposed model parameter  dimensionless  0 ai  =  proposed model parameter  dimensionless  - xvm  -  Symbol  Uni t  The P r i m a r y F i n e s Model Yc.j  =  cumulative weight percent screen s i z e i  passing weight percent  °  =  model parameter  dimensionless  bi  =  model parameter  dimensionless  b  =  model parameter  dimensionless  b  2  - xix -  ACKNOWLEDGEMENTS The a u t h o r w i s h e s t o e x t e n d h i s g r a t i t u d e 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 ,  and a p p r e c i a t i o n  P r o f e s s o r A . L . M u l a r , whose  and encouragement was i n v a l u a b l e t h r o u g h o u t .  to  guidance  Thanks are a l s o extended  t o v a r i o u s f a c u l t y members and graduate s t u d e n t s o f t h e Department o f M i n e r a 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 M r . H. F. S o l b e r g f o r s t i m u l a t i n g conversations  concerning m o d e l l i n g techniques  and t o M r s . S. M a i r o f  the Department o f Computer S c i e n c e f o r many hours o f c o n s u l t a t i o n r e g a r d i n g the BASIC language a t  U.B.C.  The a u t h o r a l s o wishes t o e x p r e s s h i s g r a t i t u d e personnel  a t the Brenda Mines L t d . c o n c e n t r a t o r ,  both Mr. J . A u s t i n , M i l l  t o the  operating  and e s p e c i a l l y t o  thank  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 , C r u s h e r  Foreman, f o r t h e i r p a t i e n c e  and s u p p o r t 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  s u p p o r t o f both the N a t i o n a l Research C o u n c i l  of  Canada and the Canada C e n t e r f o r M i n e r a l s and Energy T e c h n o l o g y i s greatly appreciated.  Without t h e i r s u p p o r t ,  t h i s s t u d y w o u l d n o t have  been p o s s i b l e . The a u t h o r 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 a scholarship.  support  i n the form o f  - 1 -  CHAPTER 1  INTRODUCTION  1.1  Statement o f O b j e c t i v e s The comminution process  i s one o f the most i m p o r t a n t compon-  e n t s o f the m i n e r a l p r o c e s s i n g i n d u s t r y , and c e r t a i n l y t h e most c o s t l y . In c o n v e n t i o n a 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 o u t i n two s t a g e s : coarse s i z e r e d u c t i o n through c r u s h i n g and f i n e through g r i n d i n g .  reduction  I t i s g e n e r a l l y accepted t h a t the c o s t o f s i z e  r e d u c t i o n i n c r e a s e s w i t h d e c r e a s i n g p a r t i c l e s i z e , so t h a 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 . i s e v i d e n t t h a t improvement i n c r u s h i n g e f f i c i e n c y  Therefore,  it  s h o u l d produce  the most s i g n i f i c a n t g a i n s f o r the t o t a l o p e r a t i o n i n terms o f dec r e a s e d o p e r a t i n g c o s t s and i n c r e a s e d c o n t r o l o f subsequent  (downstream)  operations. E x t e n s i v e o n - l i n e s t u d i e s o f an o p e r a t i n g p r o c e s s 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 s p e c t  p r o d u c t i o n and p l a n t e f f i c i e n c y . conducted u s i n g a d i g i t a l  Consequently, o f f - l i n e  simulation  In t h i s a p p r o a c h , i n d i v i d u a l  o f f e r an a t t r a c t i v e  for to  lost  studies alternative.  p r o c e s s u n i t s are m o d e l l e d m a t h e m a t i c a l l y .  The models may be used f o r a general s i m u l a t i o n t o p e r m i t s t u d y and o p t i m i z a t i o n o f a p r o c e s s w i t h o u t any o f the problems w i t h i n - p l a n t t e s t i n g and a t a minimal  cost.  associated  - 2 -  T h i s p r o j e c t i s concerned w i t h the a p p l i c a t i o n o f computer s i m u l a t i o n methods t o an o p e r a t i n g c r u s h i n g p l a n t .  off-line 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)  t o o b t a i n o p e r a t i n g models f o r each o f t h e t h r e e u n i t studied:  operations  secondary c r u s h i n g , t e r t i a r y c r u s h i n g and secondary  screening. (b)  t o combine the models developed f o r i n d i v i d u a l  units in a  g e n e r a l program capable o f s i m u l a t i n g the s t e a d y s t a t e operation of the e n t i r e crushing p l a n t . (c)  t o t e s t the s i m u l a t i o n program o v e r normal o p e r a t i n g ranges and t o perform p r e l i m i n a r y a n a l y s e s o f c r u s h i n g p l a n t performance w i t h r e s p e c t to a l l o f the major m a n i p u l a t a b l e and n o n - m a n i p u l a t a b l e (but measurable)  operating variables.  Once a g e n e r a l 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 , are numerous s t u d i e s t h a t may be performed.  there  Several p o s s i b i l i t i e s  are: (a)  e v a l u a t i o n o f equipment wear on p l a n t performance  and p r o d u c t  quality. (b)  optimization of plant operating variables with respect plant capacity or final  to  product q u a l i t y .  (c)  evaluation of alternative c i r c u i t  (d)  proposal and/or e v a l u a t i o n of p l a n t c o n t r o l  (e)  a d e t a i l e d s t u d y o f p l a n t b e h a v i o u r l e a d i n g t o a comprehensive o p e r a t i n g manual.  configurations. strategies.  - 3 -  1.2  Literature  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 a r e a o f comminution has been documented of operating et al  Ik 5)  v  (Pi)  .  I n i t i a l work on c i r c u i t d e s i g n and c o n t r o l  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  .  More r e c e n t l y , Whiten e t a l  undertaken  (12) ' ' have s i m u l a t e d an  v  o p e r a t i n g c r u s h i n g p l a n t u s i n g models developed f o r cone and v i b r a t i n g s c r e e n s .  by Lynch  crushers  T h i s i s the most comprehensive e f f o r t  c r u s h i n g 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  towards  f o r the  studies  (3) conducted d u r i n g t h i s a successful  project.  "program"  Gurun  v  1  has c l a i m e d development  for simulating crushing p l a n t s ,  i n f o r m a t i o n has been p u b l i s h e d to enable s a t i s f a c t o r y the  of  but too  little  evaluation  of  system. A considerable  volume o f l i t e r a t u r e  has been g e n e r a t e d c o n -  c e r n i n g the s u b j e c t s o f c r u s h i n g 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 r u s h i n g and s c r e e n i n g i s a v a i l a b l e  (2M  i n t e x t b o o k s by T a g g a r v has prepared ldndka  KX  ' and G a u d i n  (25) v  .  In a d d i t i o n ,  Marshall  a c r i t i q u e o f e x i s t i n g crushing l a w s , w h i l e Suzuki  ' have attempted t o r e l a t e c r u s h i n g e f f i c i e n c y t o  conditions.  F e r r a r a and P r e t i ^ ^ have undertaken  of screening  k i n e t i c s and have d e r i v e d two e q u a t i o n s u s e f u l  2  design and a n a l y s i s o f e x p e r i m e n t a l Chalmerspublication a good g e n e r a l  screening  and  operating  a detailed  results.  (11)  v  study  for  screen  The A l l i s  on commercial s c r e e n i n g has been found t o be  reference f o r p r a c t i c a l screening  applications.  - 4 -  P r e s e n t a t i o n o f a comprehensive s u r v e y o f p u b l i s h e d  literature  c o n c e r n i n g mathematical m o d e l l i n g , r e g r e s s i o n a n a l y s e s and computer methods i s n o t 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 .  Excellent  t e x t b o o k s 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 M u l a r and B u l l  (modelling techniques)  v  and by H i m m e l b l a u ^ ^ ( s t a t i s t i c a l t e c h n i q u e s ) .  The f i e l d o f r e g r e s s i o n  1 0  a n a l y s i s has been very t h o r o u g h l y covered i n the t e x t by D r a p e r and Smith  v  Mular^,  .  The r e a d e r i s r e f e r r e d t o papers by N e l d e r and Mead and M u l a r and B u l l ^  methods employed i n t h i s  (a)  ,  f o r d e s c r i p t i o n s o f the b a s i c computer  study.  Summary o f Comminution D i s t r i b u t i o n F u n c t i o n s There have been a number o f mathematical f u n c t i o n s  to d e s c r i b e 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 One  v  o f the most u s e f u l  developed  phenomena.  f u n c t i o n s 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 c o a l and r e l a t i v e l y f i n e l y  c r u s h e d ore i s the R o s i n - R o m m l e r  v  equation Yc = 1 - e x p ( - ( | ) )  (1)  b  T h i s f u n c t i o n has a s t a t i s t i c a l b a s i s in  g i v e n by F i s h e r and T i p p e t ^ ^ 1  1928. S e v e r a l v a r i a t i o n s o f t h i s e q u a t i o n have s i n c e been p r o p o s e d .  (23) In  1951, W e i b u l r  ' r e p o r t e d a more g e n e r a l Yc = 1 - exp ( -  In  1956, B r o a d b e n t ^ ^ 1  (  x  ^  form )  b  )  (2)  used a m o d i f i c a t i o n by E p s t e i n ^ ^ w i t h the Yc = 1 - e x p ( - ( ^ ) (3) a__ 2 0  b  1 - exp  (-1)  form  "  - 5 -  A n o t h e r f u n c t i o n which has widespread Gaudin-Schuhmann^ '-^ 15  (4)  C  i s u s u a l l y a p p l i c a b l e t o p a r t o f the  d e t e r i o r a t e s f o r the coarse s i z e s equation  the  equation Yc = ( £ )  This function  application is  i s employed e x t e n s i v e l y  d a t a o n l y and  involved in crushing.  However,  i n the m i n e r a l p r o c e s s i n g  field.  A d i s t r i b u t i o n sometimes c i t e d , but n o t i n f r e q u e n t use the R o l l e r ^ ^ 2  is  function Yc = aTx e x p ( - | )  A distribution by Gaudin and M e l o y ^ distributions  the  1 3 , 1  (5)  function with a t h e o r e t i c a l ^  i n 1962.  The f u n c t i o n  b a s i s was  describes  c r e a t e d by t h e mechanism o f s i n g l e f r a c t u r e  derived  size  and  is  e x p r e s s e d as Yc = 1 - ( 1 - |  )  (6)  b  ( 21 22) A more g e n e r a l  modification of this equation,  used d u r i n g t h i s p r o j e c t  i n the  by B e r g s t r o n r  '  ,was  form  Yc = 1 - ( 1 - ( £ ) ) C  b  (7)  - 6 -  1.3  The Cone C r u s h e r Model  (1 32) The cone c r u s h e r model developed by Whiten e t a l as a s t a r t i n g p o i n t f o r the c r u s h e r models developed i n t h i s The Whiten model i s shown s c h e m a t i c a l l y i n F i g u r e 1. b u i l t around t h e two o p e r a t i o n s  study.  The model  is  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 l o w e r t r i a n g u l a r m a t r i x which d e s c r i b e s i s a d i a g o n a l m a t r i x which d e s c r i b e s breakage.  served  p a r t i c l e breakage and C  the p r o b a b i l i t y o f  particle  F r e p r e s e n t s the new c r u s h e r feed v e c t o r , P r e p r e s e n t s  c r u s h e r product v e c t o r and X r e p r e s e n t s the c r u s h e r c o n t e n t s a t any g i v e n  vector  instant.  Figure 1  Schematic R e p r e s e n t a t i o n  o f a Cone C r u s h e r  To o b t a i n the m a t r i x form o f the m o d e l , mass b a l a n c e s taken around nodes 1 and 2 i n F i g u r e 1 as  the  are  follows:  (1)  X = F + BCX  ( )  (2)  X = CX + P  (g)  8  - 7 -  S o l v i n g f o r P g i v e s the m a t r i x e q u a t i o n : P = [ T - C] [ T - B C ] " ? "  (10)  1  which r e p r e s e n t s the f i n a l i z e d  1.4  form o f the cone c r u s h e r model.  The V i b r a t i n g Screen Model The model developed by Whiten to s i m u l a t e v i b r a t i n g s c r e e n s  i s based on the p r o b a b i l i t y c o n s i d e r a t i o n s p a s s i n g thorugh a square a p e r t u r e ,  of a spherical  particle  ( 25)  f i r s t proposed by G a u d i n  i n 1938.  v  i 11  . . .  1  I  1 a- s -I  *"  »  V ) Q  Figure 2  b  *  Geometric C o n s i d e r a t i o n s 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 F i g u r e 2 , the area o f the b a s i c s e p a r a t i n g the s c r e e n i s ( a + b ) . 2  (a-s)  2  A p a r t i c l e of size ' s  1  must f a l l  i n t o an a r e a  to pass through the s c r e e n w i t h o u t t o u c h i n g the w i r e s .  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  PO)  =  [(IS) ] 2  2  unit of  The  be:  (n)  - 8 -  and f o r 'm' random t r i a l s :  P(m) = [ ( f ^ - ) ] " 2  (12)  1  T h i s r a t i o r e p r e s e n t s the l o w e r l i m i t o f p r o b a b i l i t y o f p a s s a g e , as passage c a n a l s o o c c u r when a p a r t i c l e i s d e f l e c t e d through the h o l e after  s t r i k i n g a wire. The  efficiency  curve f o r the screen can be r e p r e s e n t e d  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 n o t p a s s i n g the s c r e e n  i n terms  ( i . e . of entering  the o v e r s i z e p r o d u c t ) e x p r e s s e d by the e q u a t i o n :  E(s)  = [1 - ( § = f ) f  (13)  2  Whiten found t h a t the number o f t r i a l s , ' m ' , t h a t a p a r t i c l e performs i n p a s s i n g o v e r the screen can be e x p r e s s e d by the e q u a t i o n : m = ki lf  (14)  2  where:  f  =  ]  (  1 a w ki k V 2  The  load f a c t o r "f" w i l l  towards z e r o f o r v e r y l a r g e feed  w i t h the s t e e p g r a d i e n t o f the c u r v e .  2  E(s)ds - Si  tend  curve i s  r e q u i r e d o v e r each s c r e e n s i z e f r a c t i o n to overcome problems  s  )  rates.  To use t h i s m o d e l , an average o f the e f f i c i e n c y  S 2  5  = screen length = screen aperture = screen width = e f f i c i e n c y constant = loading constant = v o l u m e t r i c feed r a t e  be u n i t y f o r low feed r a t e s and w i l l  Average E ( s ) = s {  ]  associated  The f o l l o w i n g t e c h n i q u e was a p p l i e d : (16)  - 9 -  T h i s e q u a t i o n r e p r e s e n t s a w e i g h t e d average over a s c r e e n i n t e r v a l  . J l,3i)  which i s e v a l u a t e d u s i n g computer a p p r o x i m a t i o n methods  Particle Figure 3  Efficiency  ( cm )  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 i n F i g u r e 3.  Size , s  curve(13) f o r t h i s model i s  presented  Any t h e o r y o f v i b r a t i n g screens s h o u l d 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 t h e screen opening w i l l  r e p o r t to the c o a r s e p r o d u c t .  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  c u r v e o f F i g u r e 3.  It  i s e v i d e n t t h a t i n o r d e r t o use t h i s c u r v e , 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 o b s e r v e d . i n t o f o u r s e p a r a t e zones as  Whitens screen model can be d i v i d e d  follows:  (a)  a l l complete s i z e f r a c t i o n s c o a r s e r than the s c r e e n opening  (b)  t h e s i z e f r a c t i o n c o n t a i n i n g the screen o p e n i n g . T h i s can be subdivided i n t o : (i) a p o r t i o n c o a r s e r than the s c r e e n opening (ii) a p o r t i o n f i n e r than the s c r e e n opening  (c)  those complete s i z e f r a c t i o n s f i n e r than the s c r e e n o p e n i n g , but c o a r s e 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 h a t t h i s model p r o v i d e s an adequate d e s c r i p t i o n  o f screen b e h a v i o r , e x c e p t i n the sub-mesh  ranges.  - 10 -  CHAPTER I I DATA ACQUISITION  2.1  Description of Crushing Plant (a)  Introduction E x p e r i m e n t a l d a t a f o r t h i s p r o j e c t were o b t a i n e d from the  secondary c r u s h i n g p l a n t a t the Brenda Mines L t d . c o n c e n t r a t o r Peachland, B . C .  This operation  near  r e c o v e r s s e p a r a t e c h a l c o p y r i t e and  m o l y b d e n i t e c o n c e n t r a t e s through c o n v e n t i o n a l m i l l i n g o f a low grade porphyry type o r e .  M i n i n g i s by the open p i t method and d a i l y  c a p a c i t y averages 30,000  (b)  plant  tpd.  The P r i m a r y C r u s h e r The t o t a l  size reduction.  Brenda c r u s h i n g p l a n t c o n s i s t s o f t h r e e s t a g e s o f  The p l a n t f l o w s h e e t i s d e p i c t e d i n F i g u r e 4.  The  p r i m a r y c r u s h e r i s a 60 i n . x 89 i n . g y r a t o r y c r u s h e r d r i v e n by a 700 Hp motor and i s capable o f r e d u c i n g r u n - o f - m i n e ore t o -7 i n c h s i z e the  r a t e o f 3,000 t p h .  at  The crushed p r o d u c t f a l l s onto two 78 i n c h  apron f e e d e r s and i s d i s c h a r g e d onto two c o n v e y o r s , each f e e d i n g an 8 ft.  x 20 f t .  the s c r e e n s ,  double deck v i b r a t i n g s c r e e n .  The u n d e r s i z e p r o d u c t  a t - 3 / 4 i n c h , i s conveyed t o the m i l l  the coarse p r o d u c t i s conveyed to a 45,000 ton l i v e The secondary c r u s h i n g p l a n t ,  f i n e ore b i n s , w h i l e stockpile.  c o n s i s t i n g o f two s t a g e s o f c r u s h i n g  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 i g u r e 4 . primarily with this  from  s e c t i o n o f the o v e r a l l  This thesis  plant.  is  concerned  LEGEND  Figure 4  Generalized  Crushing Plant  Flowsheet  1 2 3  P r i m a r y Crusher (1) Primary Screens (2) Coarse Ore Stockpile  4 5  Secondary Crushers (2) Surge Bin  6 7  Secondary Screens (5) Surge Bin  8  Tertiary  Crushers  (4)  - 12 -  (c)  The Secondary C r u s h e r The secondary c r u s h i n g c i r c u i t c o n s i s t s o f two Symons Nordberg  7 f o o t s t a n d a r d heavy duty cone c r u s h e r s o p e r a t i n g i n p a r a l l e l open circuit.  Feed i s r e c l a i m e d d i r e c t l y from the c o a r s e ore s t o c k p i l e by  two 4 8 - i n c h c o n v e y o r s , each i n c o r p o r a t i n g f o u r 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.  T h i s m a t e r i a l i s then passed t o two 5 4 - i n c h t r a n s f e r  and i n t o the c r u s h e r s .  The feed e n t e r s an i n v e r t e d c o n i c a l  belts  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 t o a s s i s t d i s t r i b u t i o n around the c r u s h i n g chamber.  The chamber i t s e l f  consists  o f a coarse type concave and mantle w i t h a nominal c l o s e s i d e o f 1-1/4  i n c h and a throw o f 3 - 5 / 8 i n c h .  d r i v e n by s i n g l e , 350 Hp  The c o u n t e r s h a f t s  synchronous motors.  i n uniform  setting  are d i r e c t l y  The c r u s h e d p r o d u c t  passes through a s l o p e d d i s c h a r g e compartment and onto a 7 2 - i n c h c o n v e y o r . T h i s conveyor then d i s c h a r g e s onto a 6 0 - i n c h conveyor which empties a 1600 ton surge b i n ahead o f the secondary  (d)  into  screens.  The Secondary Screens The secondary s c r e e n i n g 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 s c r e e n s o p e r a t i n g i n p a r a l l e l .  The upper deck o f  each s c r e e n 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 t h 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 b l a n k e d o f f w i t h rubber m a t t i n g t o e l i m i n a t e e x c e s s i v e wear n o r m a l l y encountered when feed p a r t i c l e s f a l l screen.  As a r e s u l t ,  onto  the  the e f f e c t i v e s c r e e n i n g area i s reduced by  a p p r o x i m a t e l y 10 p e r c e n t .  The lower deck c o n s i s t s o f f i v e p a n e l s o f  woven w i r e c l o t h w i t h s l o t s 3-1/2 i n c h l o n g by v a r i o u s w i d t h s .  F o r the  - 13 -  purpose o f t h i s t h e s i s ,  the w i d t h o f t h e l o w e r deck s l o t w i l l  r e f e r r e d to as t h e s c r e e n o p e n i n g .  be  T h 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 s c r e e n i s s l o p e d a t 2 0 ° 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 i n 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 screen. directs  emptying d i r e c t l y onto the upper deck o f the  respective  The u n d e r s i z e p r o d u c t f a l l s i n t o a s l o p e d compartment which i t onto a s h o r t 4 8 - i n c h t r a n s f e r  b e l t , where i t i s conveyed  through two l o n g e r b e l t s t o the f i n e ore b i n s .  The u n d e r s i z e p r o d u c t  blended w i t h the p r i m a r y screen u n d e r s i z e p r o d u c t ( p r i m a r y f i n e s ) the t r a n s f e r p o i n t between the two l o n g e r c o n v e y o r s . falls  is  at  The o v e r s i z e p r o d u c t  i n t o a s l o p e d 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 u n d e r s i z e d i s c h a r g e .  After transfer to a longer, 48-inch  b e l t , the o v e r s i z e i s t r a n s p o r t e d t o a second 1600 ton surge b i n ahead o f the t e r t i a r y (e)  crushers.  The T e r t i a r y Crushers The t e r t i a r y c r u s h i n g c i r c u i t c o n s i s t s o f f o u r Symons Nordberg  7 f o o t heavy duty s h o r t - h e a d cone c r u s h e r s o p e r a t i n g i n p a r a l l e l and i n c l o s e d c i r c u i t w i t h the secondary s c r e e n s .  With the e x c e p t i o n o f the  c r u s h i n g 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 r u s h e r s .  Feed i s r e c l a i m e d from the c r u s h e r  b i n by f o u r v a r i a b l e c o n t r o l v i b r a t i n g f e e d e r s , 54-inch transfer  b e l t emptying d i r e c t l y i n t o i t s  surge  each s u p p l y i n g a s h o r t , respective  crusher.  As w i t h the secondary c r u s h e r s , feed e n t e r s an i n v e r t e d c o n i c a l 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 t o the m a n t l e .  chute  The c r u s h i n g  chamber c o n s i s t s o f a coarse concave and medium mantle, w i t h a nominal  - 14 -  c l o s e s i d e s e t t i n g o f .27 i n c h e s and a throw o f 3 - 5 / 8 i n c h e s . counter shafts  are d i r e c t l y d r i v e n by 300 Hp m o t o r s .  The  Crushed p r o d u c t  passes through a s l o p e d d i s c h a r g e chamber onto the same 7 2 - i n c h conveyor as the secondary c r u s h e r p r o d u c t and i s t r a n s p o r t e d t o the surge b i n ahead o f t h e (f)  screens.  General The o p e r a t i n g p e r s o n n e l a t the Brenda p l a n t have  subsequently  m o d i f i e d the shape o f the c r u s h i n g chambers i n both the secondary and t e r t i a r y crushers.  These m o d i f i c a t i o n s a f f e c t  the mantles o n l y and  c o n s i s t o f b u i l d i n g up the l o w e r c o n i c a l s e c t i o n s o f each m a n t l e .  The  m o d i f i c a t i o n s t o the secondary c r u s h e r mantles are s u b s t a n t i a l l y d i f f e r e n t t o those f o r the t e r t i a r y c r u s h e r s .  These m o d i f i c a t i o n s , d e p i c t e d  i n F i g u r e 5 , are b e l i e v e d to a c h i e v e a b e t t e r c r u s h i n g a c t i o n and h i g h e r capacity.  (a) Standard C r u s h e r  Figure 5  (b) S h o r t - h e a d C r u s h e r  M o d i f i c a t i o n s to Crusher Mantles  i  - 15 -  All  secondary and t e r t i a r y c r u s h e r s have a thermal  p r o t e c t i o n f e a t u r e which w i l l  s h u t down a g i v e n c r u s h e r when the motor  w i n d i n g temperature exceeds a m a n u a l l y determined s e t p o i n t feature protects be a h i n d r a n c e  value.  This  the c r u s h e r motors from s u s t a i n e d o v e r l o a d i n g , but may  in other aspects,  c o n t i n u e to r i s e a f t e r  as the motor w i n d i n g t e m p e r a t u r e s may  a surge i n f e e d r a t e has a l r e a d y p a s s e d .  p r e s e n t thermal o v e r l o a d s e t p o i n t s , presented  overload  i n Table  i n terms o f c u r r e n t  draw,  The are  I.  TABLE 1 Thermal O v e r l o a d S e t t i n g s  Crusher Number  Crushing Ci r c u i t  Crusher Type  Sustained Full-Load (amperes)  f o r Crushers  Thermal O v e r l o a d Current (amperes)  Power Draw (Horsepower)  Voltage (Volts)  1  Secondary  Standard  48  67.5  350  4160  2 •  Secondary  Standard  48  74.3  350  4160  Tertiary  Short-head  42  60.4  300  4160  3 - 6  More d e t a i l e d d e s c r i p t i o n s o f t h e major process presented 2.2  i n Appendix A .  Procedures (a)  u n i t s sampled are  f o r A c q u i s i t i o n - o f Raw Data  Introduction Only the secondary c r u s h i n g p l a n t was sampled.  d e s i r a b l e t o s i m u l a t e the p r i m a r y c r u s h i n g p l a n t , c r u s h e r and the two p r i m a r y s c r e e n s ,  c o n s i s t i n g o f the p r i m a r y  but the d i f f i c u l t y  s c r e e n i n g the p r i m a r y c r u s h e r feed (ROM ore)  I t would be  o f s a m p l i n g and  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 n a t u r e o f the p r i m a r y c r u s h i n g p l a n t o p e r a t i o n would p r e s e n t c o n s i d e r a b l e d i f f i c u l t y t o model development, as i t would depend upon m i n i n g 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 e n s u r e s  continuous and c o n t r o l l a b l e o p e r a t i o n throughout the secondary  crushing  plant. The u n i t o p e r a t i o n s  sampled i n the secondary c r u s h i n g p l a n t  were secondary c r u s h i n g , t e r t i a r y c r u s h i n g and secondary s c r e e n i n g . s a m p l i n g each o p e r a t i o n , t h e assumption was made t h a t a l l u n i t s  In  within  the s p e c i f i e d o p e r a t i o n behave i n a s i m i l a r manner to the u n i t sampled. T h i s assumption was made w i t h the knowledge t h a t a l l u n i t s w i t h i n each o p e r a t i o n were p h y s i c a l l y " s i m i l a r " . operation  Obviously, units within a specified  ( i . e . secondary c r u s h i n g ) w i l l  differently, differences  behave d i f f e r e n t l y when  set  but t h i s case i s i r r e l e v a n t to the a s s u m p t i o n , as t h e s e 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,  differences  i n wear r a t e s and p a t t e r n s w i l l  cause b e h a v i o u r a l d i f f e r e n c e s ,  thus  d e v i a t i o n from the a s s u m p t i o n .  A t p r e s e n t , wear phenomena are beyond  o p e r a t o r c o n t r o l , although s t u d y 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. A n o t h e r f a c t o r which may cause d e v i a t i o n from the above t i o n i s p a r t i c l e s i z e s e g r e g a t i o n w i t h i n the surge b i n s . t h e r e 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 . t h a t s c r e e n s fed from the outermost  feeders  1  At p r e s e n t ,  However, i t i s known  produce p r o d u c t s i z e  b u t i o n s which d i f f e r s l i g h t l y from t h e c e n t r a l l y fed screen.. 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  assump-  i n feed s i z e  or  i n screen b e h a v i o r .  1  This observation applies to the Brenda surge bins only.  It  distriisjiot  distributions  C u r r e n t o p i n i o n favours t h e former c a s e .  As  - 17 -  s a m p l i n g 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 assumption was made.  ".similarity"  T a b l e 2 i n d i c a t e s the u n i t s chosen f o r  representation  o f each o p e r a t i o n .  TABLE 2 R e p r e s e n t a t i v e U n i t s Sampled Unit Operation  U n i t Sampled  Comments  Secondary C r u s h i n g  #1 S t a n d a r d  Feed s l i g h t l y f i n e r , e a s i e r s a m p l i n g  T e r t i a r y Crushing  #2 S h o r t - h e a d  Minimized bin segregation  Secondary S c r e e n i n g  #2 and 4 Screens  Chosen as most r e p r e s e n t a t i v e "average" s c r e e n f e e d .  Samples o f the p r i m a r y s c r e e n s u n d e r s i z e p r o d u c t ( t o be  of  referred  t o as " p r i m a r y f i n e s " ) were taken o v e r a p e r i o d o f seven d a y s . As mentioned e a r l i e r , s e g r e g a t i o n e f f e c t s w i t h i n both surge b i n s .  were known t o o c c u r  However, no attempts were made t o sample o r s i m u l a t e  t h i s b e h a v i o u r , 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 s a m p l i n g schedule f o r each u n i t o p e r a t i o n was c o n s t r u c t e d according to a f u l l process v a r i a b l e s ) .  f a c t o r i a l d e s i g n i n v o l v i n g two f a c t o r s F o r both c r u s h i n g o p e r a t i o n s ,  c l o s e s i d e s e t t i n g (gap)  and f e e d r a t e ,  s c r e e n opening and feed r a t e .  (controllable  the f a c t o r s were  and f o r s c r e e n i n g the f a c t o r s  With two f a c t o r s ,  r u n s , s c h e d u l e d a c c o r d i n g t o the p a t t e r n  crusher were  the design, i n v o l v e s f o u r  o u t l i n e d i n F i g u r e 6.  Additional  runs were s c h e d u l e d to c o v e r the c e n t e r p o i n t area f o r each s a m p l i n g s c h e d u l e . In each c a s e , the measured dependent v a r i a b l e was the p r o d u c t s i z e d i s t r i b u t i o n .  - 18 -  Figure 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 r u s h i n g p l a n t , i t i s u s e f u l t o d i s c u s s the p h y s i c a l l a y o u t o f the Brenda p l a n t a t t h i s p o i n t . 7(a) t o ( e ) .  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 i g u r e s  The t o t a l c r u s h i n g p l a n t i s housed i n t h r e e s e p a r a t e  b u i l d i n g s and i n t e r c o n n e c t e d through a network o f e n c l o s e d c o n v e y o r s . The c r u s h i n g p l a n t i s s e p a r a t e from the main c o n c e n t r a t o r . b u i l d i n g houses the p r i m a r y c r u s h e r and s c r e e n s , secondary s c r e e n s  and a f f i l i a t e d  The f i r s t  the second houses  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 t h e combined secondary and t e r t i a r y c r u s h e r s w i t h dust c o n t r o l systems. l i e s the t r a n s f e r  their  Between the s c r e e n i n g and c r u s h i n g b u i l d i n g s  t o w e r , where m i x i n g o f the screen u n d e r s i z e and p r i m a r y  f i n e s streams t a k e s p l a c e d u r i n g t r a n s p o r t t o the f i n e ore b i n s to the m i l 1.  the  attached  - 19 -  Primary  F i g u r e 7(a)  Crusher  Physical Locations o f Crushing Plant  Components  F i g u r e 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 Building  Crusher  - 21 -  F i g u r e 7(d)  D e t a i l e d View o f the  Interior  Screen  of a  Secondary  - 22 -  F i g u r e 7(e)  The Secondary  C r u s h i n g P l a n t C o n t r o l Room  - 23 -  The p r i m a r y c r u s h i n g c i r c u i t f a l l s the m i n i n g department  under the j u r i s d i c t i o n o f  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 m a n u a l l y c o n t r o l l e d from a s i n g l e control  room l o c a t e d i n the c r u s h i n g b u i l d i n g .  A more d e t a i l e d  s c h e m a t i c o f the c r u s h i n g p l a n t showing sample p o i n t l o c a t i o n s i s g i v e n in Figure 8(a).  Photographs o f sample p o i n t s and work areas are shown  i n F i g u r e s 8(b); through 8(h)  respectively.  P r i o r t o i n i t i a t i n g the s a m p l i n g program, a sample s c r e e n i n g station  ( F i g u r e 8(g)) was l o c a t e d i n the g r i n d i n g bay o f t h e main con-  centrator.  I t was i m p o s s i b l e t o s i t u a t e  a screening station  within  the secondary c r u s h i n g p l a n t b u i l d i n g s because o f Brenda maintenance policy.  The c r u s h i n g p l a n t s s u p p o r t t h e i r own maintenance f o r c e ,  te from the main c o n c e n t r a t o r ,  separa-  and m a i n t a i n t h e i r own i n v e n t o r y .  f o r c e i s h e a v i l y o r i e n t e d towards p r e v e n t i v e m a i n t e n a n c e , 1  This  so t h a 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 o c c u p i e d by e i t h e r p a r t s i n v e n t o r y o r workshops.  The g r i n d i n g bay was chosen  the s c r e e n i n g s t a t i o n as i t o f f e r e d the o n l y l o c a t i o n w i t h room t h a t would n o t 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 .  for  sufficient This  meant  t h a t a l l samples taken throughout the secondary c r u s h i n g p l a n t had t o be t r a n s p o r t e d  to and s t o r e d i n the g r i n d i n g bay.  These s c r e e n i n g  f a c i l i t i e s were s h a r e d f o r a s h o r t p e r i o d w i t h Brenda r e s e a r c h  personnel  e x e c u t i n g a s a m p l i n g program around one o f the rod m i l l s . Few h e l p e r s were a v a i l a b l e t o a s s i s t the a u t h o r d u r i n g the  course  o f the d a t a a c q u i s i t i o n program and n e a r l y a l l s a m p l i n g was done alone and by hand.  1  I t i s current operating p r a c t i c e to shut down the e n t i r e secondary crushing plant for a minimum of four hours on d a y s h i f t , Monday through F r i d a y , to carry out maintenance repairs and i n s p e c t i o n s .  LEGEND Screens )  a.  Coarse Ore S t o c k p i l e  A. Secondary C r u s h e r Feed  b.  Secondary C r u s h e r s  c.  Secondary Screen Surge B i n  B. Secondary and T e r t i a r y Crusher Products,Secondary Screen Feed  d.  Secondary  e.  T e r t i a r y C r u s h e r Surge B i n  C. Secondary Screen O v e r s i z e Product  f.  T e r t i a r y Crushers  D. T e r t i a r y C r u s h e r Feed  Screens  N o s . 4 , 6 - 2 0 r e f e r t o conveyors referenced i n t e x t  10  E . Secondary Screen U n d e r s i z e Product  ll  EEL mr  fi-  f2  t o F i n e Ore B i n s  Screens  F i g u r e 8(a)  Secondary C r u s h i n g 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 C r u s h e r  Product,Secondary  Screen Feed and T e r t i a r y C r u s h e r P r o d u c t  F i g u r e 8(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  - 27 -  F i g u r e 8(e)  Sample P o i n t s f o r Secondary Screen and U n d e r s i z e  Figure 8(f)  Oversize  Products  Sample P o i n t f o r P r i m a r y Screens Product (Primary  Fines)  Undersize  - 28 -  F i g u r e 8(g)  Sample S c r e e n i n g S t a t i o n  - 29 -  (b)  Secondary C r u s h e r Sampling The c r u s h e r s e l e c t e d f o r s a m p l i n g was number 1 s t a n d a r d .  feed t o t h i s c r u s h e r i s b e l i e v e d t o be s l i g h t l y f i n e r  1  than the feed t o  the second m a c h i n e , a f a c t t h a t would a i d i n s c r e e n i n g o f the s i z e ranges.  The  upper  A M e r r i c k weightometer i s l o c a t e d on each o f the two  c r u s h e r feed b e l t s drawing from the c o a r s e ore s t o c k p i l e , but a t  the  time o f s a m p l i n g , the conveyor b e l t i n g t o number 2 s t a n d a r d had j u s t been r e p l a c e d , and i t s weightometer n o t y e t c a l i b r a t e d . The sample p o i n t s f o r the number 1 s t a n d a r d are shown i n F i g u r e 8 ( a ) , (b) and ( c ) .  The sample p o i n t f o r the c r u s h e r f e e d was on number  6 conveyor l o c a t e d i n the access s h a f t t o the r e c l a m a t i o n t u n n e l s the coarse ore s t o c k p i l e .  under  The c r u s h e r p r o d u c t was sampled on number  14 c o n v e y o r 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 s c h a r g e onto number 13 conveyor which i n t u r n d i s c h a r g e s onto number 14 b e l t , but as number 13 conveyor i s e n c l o s e d and i n a c c e s s i b l e o v e r i t s e n t i r e l e n g t h , s a m p l i n g 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 t h a t the c r u s h e r was o p e r a t i n g a t steady s t a t e when sampled and t h a t the time l a g between the feed and p r o d u c t sample p o i n t s had negligible effect.  T h i s time l a g , i n a c t u a l i t y , was o f the o r d e r o f  90 seconds. The s a m p l i n g procedure adopted f o r the secondary c r u s h e r s t a b u l a t e d as (1)  is  follows:  the secondary s c r e e n b i n was drawn down s u f f i c i e n t l y t o r e c e i v e a p p r o x i m a t e l y 20 minutes o f d i s c h a r g e from number 1 s t a n d a r d crusher.  .1 Due t o segregation effects on the coarse ore s t o c k p i l e .  - 30 -  (2)  the e n t i r e secondary c r u s h i n g p l a n t was shut down. ( I t i s c o n v e n i e n t i f s t e p s 1 and 2 can be s c h e d u l e d t o c o i n c i d e w i t h the m i l l f i n e ore b i n s b e i n g f u l l ) .  (3)  t h e c l o s e s i d e s e t t i n g o f number 1 s t a n d a r d was a d j u s t e d recorded.  and  (4)  number 1 s t a n d a r d was s t a r t e d and feed run through u n t i l was s t a b i l i z e d a t t h e d e s i r e d f e e d r a t e .  operation  (5)  number 1 s t a n d a r d was h e l d a t t h i s f e e d r a t e f o r a p p r o x i m a t e l y 10 minutes t o 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)  d u r i n g t h i s p e r i o d , c u r r e n t draw was measured o v e r a p e r i o d o f a p p r o x i m a t e l y 4-5 minutes f o r number 1 s t a n d a r d motor.  (7)  a f t e r 10 m i n u t e s , t h e feed and d i s c h a r g e b e l t s were shut down s i m u l t a n e o u s l y and l o c k e d o u t . ( N o t e : the p r e v i o u s t i m e l a g assumption).  (8)  tonnage and time measurements were r e c o r d e d f o r f e e d r a t e c a l c u l a t i o n .  (9)  a 1 0 - f o o t s e c t i o n o f p r o d u c t was taken from number 14 b e l t and s t o r e d i n a c o v e r e d 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 r u s h i n g p l a n t may be r e s t a r t e d , minus number 1 s t a n d a r d c r u s h e r ) .  (10)  a 2 0 - f o o t s e c t i o n o f feed was taken from number 6 b e l t and s t o r e d i n two covered 4 5 - g a l l o n drums i n the access s h a f t .  (11)  a f t e r e v e r y second t e s t , the s t o r e d samples were removed t o g r i n d i n g bay f o r s c r e e n i n g . In a l l , t h e r e were e i g h t t e s t s conducted around the  crushers.  F i g u r e 9 d e p i c t s the comparison between  and s a m p l i n g s c h e d u l e o b t a i n e d .  secondary  the s c h e d u l e d d e s i g n  There were no p a r t i c u l a r  i n p r e p a r i n g , o p e r a t i n g o r s a m p l i n g the number 1 . s t a n d a r d  difficulties crusher.  D i s c r e p a n c i e s between s c h e d u l e d and observed d e s i g n p o i n t s are be due t o . e i t h e r  the c o n s i d e r a b l e s h o r t term f l u c t u a t i o n s  f e e d r a t e o r the d i f f e r e n t  the  in  operating personalities of different  believed.to  crusher operators.  31  The c r u s h e r gaps were a d j u s t e d  u s i n g the 4 p o i n t l e a d w e i g h t t e c h n i q u e  .  B e t t e r p r e c i s i o n c o u l d have been o b t a i n e d , but o n l y at t h e expense o f t i m e , w h i c h , i n terms o f p l a n t shutdown, i s a v e r y e x p e n s i v e commodity. The s h o r t term f l u c t u a t i o n s coarse n a t u r e o f t h e feed  i n f e e d r a t e are a t t r i b u t e d  to the  extremely  and are beyond c o n t r o l o f the p r e s e n t o p e r a t i o n .  4.0H E u CL o 0 03  sz  3.5H  A - D e s i g n Point  %  3.0-1  © - O b s e r v e d Point  ©  to Z5 -6 1  2.5H i  550  i  i  600  i  i  i  i  i  Crusher  Figure 9  i  i  i  i  700  T  I ' l l  750  Feedrate  1  800  I  I  1  I  850  (tph)  gap, f e e d r a t e ,  and c u r r e n t draw o b t a i n e d  p e r c e n t o f . + .1 i n c h i n  around the secondary c r u s h e r f o r the  runs performed are summarized i n T a b l e 3.  1  T-1  E x p e r i m e n t a l Design f o r Secondary Crushers  Measured v a l u e s o f feed  i  650  eight  The p e r c e n t o f + 1 i n c h  This procedure i n v o l v e s a t t a c h i n g a c y l i n d r i c a l l e a d weight, w i t h a diameter s e v e r a l times that of the estimated gap, to a wire cord. While the crusher i s running, hut empty, the weight, i s q u i c k l y lowered between the: mantle and concave, u n t i l no more crushing a c t i o n i s f e l t . The weight i s withdrawn and the t h i n n e s t p a r t of the f l a t t e n e d d i s c i s a measure of the crusher gap at that p o i n t . This procedure i s repeated at four e q u i d i s t a n t points to l o c a t e the minimum gap.  - 32 -  material  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 c o a r s e n e s s o f the feed s i z e d i s t r i b u t i o n . is  This variable  determined g r a p h i c a l l y from t h e measured s i z e d i s t r i b u t i o n s o f a l l  unit feeds.  A complete s i z e a n a l y s i s o f each sample taken around the  secondary c r u s h e r s  i s p r e s e n t e d i n Appendix B ( a ) . TABLE 3 Summary o f O p e r a t i n g Data Secondary C r u s h e r Sampling Phase  Run Number  INDEPEf\ DENT Feedrate Close Side S e t t i n g (tph) (cm) (inch)  % + 1 inch i n Feed  DEPENDENT C u r r e n t Draw (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 C r u s h e r Sampling In comparison w i t h the secondary c r u s h e r s , s a m p l i n g around  the t e r t i a r y c r u s h e r s was c o n s i d e r a b l y more d i f f i c u l t .  The surge b i n  ahead o f the t e r t i a r y c r u s h e r s p e r m i t t e d t h e i r o p e r a t i o n f o r s u b s t a n t i a l p e r i o d s under non-steady s t a t e c o n d i t i o n s . Weightometers were n o t mounted on the t e r t i a r y c r u s h e r feed b e l t s , so measurement o f f e e d r a t e was o b t a i n e d i n d i r e c t l y .  I t was  - 33 -  observed t h a t when the surge b i n 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 s c h a r g e d almost d i r e c t l y i n t o the f e e d e r f o r number 2 s h o r t - h e a d c r u s h e r .  F o r t h i s r e a s o n , the number  2 c r u s h e r was chosen t o r e p r e s e n t the t e r t i a r y c i r c u i t .  Fortunately,  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 t h a t f l o w r a t e s onthatbelt  c o u l d be o b t a i n e d .  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 f e e d e r . D e s i r e d f e e d r a t e s to.number 2 s h o r t - h e a d 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 r u s h e r feed was on the number 2 s h o r t - h e a d feed b e l t (number 11 b e l t ) the c r u s h e r .  d i r e c t l y p r i o r to discharge  into  T h i s n e c e s s i t a t e d removal o f t h e conveyor c o v e r p l a t e .  The p r o d u c t was sampled on number 14 b e l t i n the t r a n s f e r t o w e r , a t same l o c a t i o n as the secondary c r u s h e r p r o d u c t .  the  The l o c a t i o n o f the  t e r t i a r y c r u s h e r sample p o i n t s i s i n d i c a t e d on F i g u r e s 8 ( a ) ,  (c) and  ( d ) , pages 24 t o 2 6 . The f o l l o w i n g s a m p l i n g procedure was adopted f o r the number 2 short-head  crusher:  (1)  the secondary s c r e e n b i n was f i l l e d duration o f the t e s t .  to s u p p l y feed f o r the  (2)  the t e r t i a r y surge b i n was emptied u n t i l feeder t h r o a t s were visible. The b i n was a l s o checked f o r dead s t o r a g e .  (3)  the e n t i r e secondary c r u s h i n g p l a n t was shut down.  (4)  the c l o s e s i d e s e t t i n g o f number.2 s h o r t - h e a d c r u s h e r was a d j u s t e d and r e c o r d e d .  (5)  number 2 s h o r t - h e a d c r u s h e r was s t a r t e d . Several screens were s t a r t e d s h o r t l y a f t e r w a r d s t o s u p p l y f e e d . t o number 16 belt.  - 34 -  (6)  number 16 b e l t weightometer tonnage r e a d i n g s were r e l a y e d t o the o p e r a t o r (no i n t e g r a t i o n i n c o n t r o l room)., who a d j u s t e d the s c r e e n feeders u n t i l the d e s i r e d f l o w r a t e a c h i e v e d . Number 16 b e l t was m a i n t a i n e d a t t h i s r a t e as c l o s e l y as p o s s i b l e f o r a p p r o x i m a t e l y TO m i n u t e s . Adjustments were made as r e q u i r e d .  (7)  d u r i n g the t e s t p e r i o d , c u r r e n t and power draws were m o n i t o r e d and r e c o r d e d , as were t o n n a g e / t i m e r e a d i n g s f o r the w e i g h t o m e t e r .  (8)  numbers 1 1 , 14 and 16 b e l t s were shut down s i m u l t a n e o u s l y and locked out.  (9)  a measured l e n g t h o f p r o d u c t was taken from number 14 b e l t and s t o r e d i n a c l o s e d drum i n the t r a n s f e r tower. The c r u s h i n g p l a n t c o u l d 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 s h o r t - h e a d .  (10)  a measured l e n g t h o f feed was taken from number 11 b e l t and s t o r e d i n a c l o s e d drum by the c r u s h e r .  (11)  the t e r t i a r y surge b i n was i n s p e c t e d f o r a c c u m u l a t i o n ( c o n d i t i o n s permitting).  (12)  the samples were removed t o the m i l l possible.  g r i n d i n g bay as soon as  There were ten runs conducted around, the number 2 s h o r t - h e a d crusher.  A comparison o f the s c h e d u l e d a n d . o b s e r v e d . f a c t o r l e v e l s i s  p r e s e n t e d i n F i g u r e 10.  I t i s e v i d e n t t h a t the observed s a m p l i n g  s c h e d u l e was unable t o f o l l o w c l o s e l y the d e s i g n schedule and t h a t observed data p o i n t s are n o t a p p l i c a b l e t o a f u l l The  2  n  factorial  the  design.  c r u s h e r gap, a d j u s t e d by the l e a d w e i g h t t e c h n i q u e appears t o be  well  c o n t r o l l e d and r e l i a b l e .  good. (a)  (b)  S e v e r a l - p o s s i b l e , reasons  However, c o n t r o l o f the f e e d r a t e was n o t f o r t h i s are as  follows:  f o r a f i x e d f e e d r a t e , changes i n feed s i z e d i s t r i b u t i o n s t o ; the secondary s c r e e n s w i l l cause changes i n o v e r s i z e p r o d u c t f l o w r a t e and thus changes i n c r u s h e r f e e d r a t e . These changes can o c c u r q u i t e r a p i d l y on a s m a l l s c a l e , r e s u l t i n g i n high f r e q u e n c i e s o f s h o r t term f l u c t u a t i o n s i n . c r u s h e r f e e d r a t e . a c c u m u l a t i o n 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 r u s h e r f e e d r a t e l e s s than i n d i c a t e d by the weightometer on number 16 belt.  - 35 -  (c)  o c c u r r e n c e o f a " f r e e f e e d i n g " c o n d i t i o n , where dead s t o r a g e o r accumulated m a t e r i a l l i n i n g the f e e d e r t h r o a t s p o r a d i c a l l y s l i d e s i n t o the f e e d e r . T h i s r e s u l t s i n h i g h e r than i n d i c a t e d f e e d r a t e s and s u b s t a n t i a l n o n - s t e a d s t a t e b e h a v i o u r . This i s b e l i e v e d t o be the major f a c t o r c o n t r i b u t i n g t o d e v i a t i o n from the d e s i g n s s c h e d u l e .  (d)  s e v e r a l o p e r a t o r s were s u s p e c t e d 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 t o s l i p w h i l e r e a d i n g s were b e i n g .taken o u t s i d e the c o n t r o l room.  4V E u  1.0  -00  :  0  •9H  © c  -i  -£=  -  7  i/l  .6-  6  .5^ .4 150  O A-Design Point ©-Observed Point - 4 —r—i—l—|  200  1-  ->—  1  I—r-  250  Crusher F i g u r e 10  t — i — I — r -  300  -i—|—i—r-  350  Feedrate  f  1—i  r—,  400  • — ,  450  (tph)  E x p e r i m e n t a l Design f o r T e r t i a r y Crushers  Because f e e d r a t e  measurements  o b t a i n e d from the number 16  b e l t weightometer were judged to be i n e r r o r , the c r u s h e r  feedrates  were back c a l c u l a t e d from the measured sample w e i g h t s , l e n g t h s b e l t speeds r e s p e c t i v e l y .  and  T h i s was done f o r both feed and p r o d u c t  s a m p l e s , w i t h the c a l c u l a t e d f e e d r a t e s b e i n g averaged t o y i e l d a f i n a l value f o r each r u n .  T h i s averaged f e e d r a t e  work p e r t a i n i n g to the t e r t i a r y  crushers.  was used f o r a l l  subsequent  - 36 -  T a b l e 4 summarizes o p e r a t i n g data f o r the t e r t i a r y s a m p l i n g phase.  The f e e d r a t e v a l u e s measured from the  crusher  weightometer  on number 16 b e l t are p r e s e n t e d f o r c o m p a r i s o n . TABLE 4 Summary o f O p e r a t i n g Data T e r t i a r y C r u s h e r Sampling Phase  Run Number  INDEPENDENT Feedrates Close Side S e t t i n g Calc. Avg. #16 b e l t (cm) (inch) (TPH) (TPH)  %+l in  inch feed  DEPENDENT Current (amps)  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 a n a l y s e s o f a l l samples taken f o r the crushers (d)  tertiary  are p r e s e n t e d i n Appendix B ( b ) . Secondary Screen Sampling I t i s known t h a t p a r t i c l e s i z e s e g r e g a t i o n e f f e c t s  the secondary s c r e e n surge b i n .  Although these effects-have  occur w i t h i n n o t been  a c c u r a t e l y q u a n t i f i e d , the s e g r e g a t i o n t r e n d s which have been observed are d e p i c t e d i n F i g u r e 1 1 .  In an attempt t o m i n i m i z e these  effects,  - 37 -  screens number 2 and 4 were chosen as r e p r e s e n t a t i v e behaviour.  o f secondary s c r e e n  I t i s f e l t t h a t the feed s i z e d i s t r i b u t i o n s t o these  screens  most c l o s e l y r e p r e s e n t s both t h e s i z e d i s t r i b u t i o n o f feed to the b i n and the most p r o b a b l e "average" feed d i s t r i b u t i o n t o a l l o f the  h s i  Coarsest  F i g u r e 11  1 4|  13 i  1 21  Fine  Finest  Fine  screens.  11 i — Coarsest 1  S e g r e g a t i o n Trends w i t h i n Screen Surge B i n  Sampling o f the secondary screens was undertaken i n two phases. During the f i r s t phase ( A u g u s t , 1 9 7 5 ) , both the p r i m a r y and secondary c r u s h i n g p l a n t s were undergoing e x t e n s i v e maintenance programs.  Con-  s e q u e n t l y , no changes i n l o w e r deck screen panels were a v a i l a b l e and s a m p l i n g had to be c a r r i e d out on the screens  as they were.  A l l screens  had composite l o w e r d e c k s , so the most " u n i f o r m " o f numbers 2 and 4 s c r e e n s was s e l e c t e d , f o r s a m p l i n g .  T h i s was the number 2 s c r e e n , w i t h  a l o w e r 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 t h r e e d i s c h a r g e end p a n e l s o f 1/2 i n . x " 3-1/2 i n . openings.  - 38 -  D u r i n g the second phase o f s a m p l i n g (December, 1 9 7 5 ) , 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 t h u n i f o r m openings i n the l o w e r deck.  The number 2 s c r e e n c o n t a i n e d o n l y 1/2 i n . x  3-1/2 i n . o p e n i n g s , w h i l e the number 4 s c r e e n c o n t a i n e d o n l y 5/8 i n . x  3-1/2 i n . o p e n i n g s .  each  The same s a m p l i n g procedures were used f o r  phase. F i v e samples were taken d u r i n g the f i r s t phase.  With s c r e e n  feedrate. b e i n g the o n l y m a n i p u l a b l e v a r i a b l e , . t h e sample s c h e d u l e was simple.  Sampling c o n s i s t e d o f t h r e e c e n t e r p o i n t r e p e a t r u n s , a h i g h  feedrate  run and a low f e e d r a t e  run.  D u r i n g the second phase, two  m a n i p u l a b l e v a r i a b l e s were a v a i l a b l e , so a m o d i f i e d 2 d e s i g n was c o n s t r u c t e d .  S i x t e s t s were r u n :  s i z e and t h r e e a t the s m a l l e r .  n  factorial  t h r e e a t the l a r g e r s c r e e n  The combined sample s c h e d u l e  1  f o r both  phases i s d e p i c t e d , i n F i g u r e 12.  1.25  1.30  1.35  Screen F i g u r e 12  1  1.40  1.45  Opening  1.50 1.55  1.60  1.65  (cm)  Combined E x p e r i m e n t a l Design f o r Secondary Screens  C a l c u l a t i o n 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  s a m p l i n g o f s c r e e n 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 r e s p e c t t o measuring f e e d r a t e sample f o r a n a l y s i s .  and t o p h y s i c a l l y o b t a i n i n g a  However, the " p e r c e n t maximum f e e d r a t e "  could  be a c c u r a t e l y measured and c o n t r o l l e d ' f o r each o f the feeders drawing 1  from the b i n ( w i t h o u t knowledge o f t h e a c t u a l v a l u e ) thus e n a b l i n g s c r e e n feedrate  to be h e l d c o n s t a n t 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 o c c u r s w i t h i n the b i n , a p p r o x i m a t i o n s o f the t r u e feed t o the s c r e e n s were made by s a m p l i n g t h e feed t o the b i n .  test  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 r u s h e r p r o d u c t samples were t a k e n . Sampling o f the s c r e e n o v e r s i z e and u n d e r s i z e p r o d u c t streams p r e s e n t e d no p r o b l e m s .  Easy access t o each stream was o b t a i n e d i n the  t r a n s f e r t o w e r , where both o v e r s i z e (number 16) and u n d e r s i z e (number 18) conveyors are open and r u n n i n g p a r a l l e l .  L o c a t i o n s o f the sample p o i n t s  are p r e s e n t e d i n F i g s . 8(a) and 8 ( e ) , pages 24  and 2 7 .  An attempt was made t o m i n i m i z e the e f f e c t s  o f surge b i n r e s i d e n c e  time and b e l t l a g t o ensure t h a t feed m a t e r i a l sampled on number 14 b e l t would c o r r e s p o n d t o the p r o d u c t m a t e r i a l sampled on numbers 16 and 18 b e l t s .  T h i s was a c c o m p l i s h e d through the use o f p a i n t e d rock  The s a m p l i n g procedure adopted f o r the secondary s c r e e n s  tracers.  i s o u t l i n e d as  fol1ows:  1  Control of screen feedrate i s achieved t h r o u g h . c o n t r o l l i n g current to the v i b r a t i n g feeder discharging onto the desired u n i t .  - 40 -  (1)  s t a r t by o p e r a t i n g the secondary c r u s h i n g p l a n 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 i n u n t i l the h i g h l e v e l alarm comes o n . Shut down the e n t i r e c r u s h i n g p l a n t , e n s u r i n g number 14 b e l t i s f u l l y l o a d e d .  (2)  take the feed sample from number 14 b e l t and s t o r e drum.  (3)  s p r a y about 20 f e e t o f f e e d - m a t e r i a l j u s t ahead o f the cut with b r i g h t , fluorescent p a i n t .  (4)  s t a r t e n t i r e c r u s h i n g 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 s c r e e n s and c r u s h e r s - a r e t o be r u n n i n g under normal o p e r a t i n g c o n d i t i o n s .  (5)  s e t feeders feedrate.  (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 ) . shut down a l l but the t e s t s c r e e n .  (7)  a l l o w time f o r o t h e r screens t o  (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 a g a i n . 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 , u s i n g t r i p chords.  (9)  sample numbers 16 and 18 b e l t s and s t o r e the samples i n c o v e r e d drums. Record r e s i d e n c e time o f t r a c e r s .  f o r t e s t screen t o d e s i r e d percentage  i n a covered sample  o f maximum  When d e t e c t e d ,  clear.  O p e r a t i n g d a t a f o r both o f t h e screen s a m p l i n g phases are sented i n T a b l e 5.  Screen f e e d r a t e s can be determined by assuming s t e a d y -  s t a t e around a screen and summing ,the o v e r s i z e and u n d e r s i z e flowrates.  pre-  product  - 41 -  TABLE 5 Summary o f O p e r a t i n g Data Secondary Screen Sampling Phases  ...Run Number  INDEPENDENT Feedrate Screen Opening % max. stph cm. inches  Sample Phase  % + 1 inch i n feed  356.8  47.29  40  353.4  33.65  1.50  40  345.4  43.26  16/27  1.50  60  563.7  34.81  1  16/27  1.50  20  157.8  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  17  1  • 16/27 •  1.50  40  18  1  16.27  1.50  19  1  16/27  20  1  21  .  Complete s i z e a n a l y s e s o f a l l samples taken f o r the screens i s presented (e)  22.86  .  secondary  i n Appendix B ( c ) .  P r i m a r y F i n e s Sampling Sampling o f the p r i m a r y f i n e s stream was  straightforward.  The f l o w o f t h i s stream i s d i s c r e t e and depends upon m i n i n g methods and ore haulage  r a t e s a t the mine.  F l o w r a t e a t any g i v e n time  be r e l i a b l y measured, because t h e r e are f r e q u e n t , ore does not f l o w .  However, the t o t a l  l o n g p e r i o d s when  d a i l y tonnage o f p r i m a r y  has been r e c o r d e d f o r a c o n s e c u t i v e p e r i o d o f 96 days and i s i n Appendix B ( e ) .  cannot  fines  presented  Samples o f the p r i m a r y f i n e s stream were taken o v e r 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 p r i m a r y f i n e s b l e n d w i t h the  screens undersize product.  The sample procedure  secondary  consisted of passing  two l a r g e sample buckets through the d i s c h a r g e stream t h a t f a l l s conveyor head p u l l e y .  The samples were taken as c l o s e t o 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 t h e c o n s t r a i n t s haulage.  from  o f mine  On the second day, the mine was down d u r i n g the day s h i f t ,  so  no sample was t a k e n . . In a l l , s i x samples were t a k e n , and t h e i r s i z e analyses  2.3  are p r e s e n t e d  i n Appendix B ( d ) .  Sample S c r e e n i n g A f t e r the samples were t r a n s p o r t e d . t o  the s c r e e n i n g  station  i n the g r i n d i n g b a y , they were s i z e d on a G i l son s c r e e n i n g machine. The s c r e e n i n g s t a t i o n ( F i g u r e 8 ( g ) , page28')  was j o i n t l y shared w i t h  the Brenda r e s e a r c h  personnel  screen  (Canadian T y l e r S i e v e s ) was d e s i r e d .  r a t i o o f 1/2  d u r i n g the e a r l y stages o f t h e p r o j e c t .  the + 1/2 i n c h s i z e f r a c t i o n s , G i l s o n s c r e e n s i n the 1/2 were u n a v a i l a b l e and a l t e r n a t e s c r e e n s were used.  A  However, f o r ratio  series  The a p p r o p r i a t e  1/2  r a t i o s c r e e n s i z e s were l a t e r o b t a i n e d 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  distributions.  The s c r e e n 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 T a b l e 6.  - 43 -  TABLE 6 S c r e e n i n g Procedure f o r Secondary C r u s h i n g P l a n t Samples  Intended 1/2 r a t i o Screen S i z e s ( i n y)  Actual Screen S i z e s used. ( U n i t s variable)  S c r e e n i n g Method  10 i n .  - By hand, u s i n g s p e c i a l l y f a b r i c a t e d , square mesh  templates.  870,400u  8 in.  435,200y  6 in.  - Particles individually sized.  108,800y  4 in.  - 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 in.  217,600y  27,200y 13,600y 6,800y  1-1/2  in.  sample drum u n t i l e n t i r e screened.  sampled  Size fractions held in  3/4 i n .  plastic pails until  full;  pails  1/4 i n .  weighed on T o l e d o w e i g h s c a l e ; - 1 / 4 1  in.  f r a c t i o n retained, other  fractions  di s c a r d e d . - U s i n g G i l son square mesh s c r e e n s  3,400y  6 mesh  - By r o t a p machine u s i n g s t a n d a r d  l,700y  10 mesh  1/2 r a t i o (square mesh) s i e v e  850y  20 mesh  425y  35 mesh  then d r i e d .  212y  65 mesh  approx. 350-400 g m . , then dry s c r e e n e d .  106y  150 mesh  D u p l i c a t e samples s t o r e d f o r  53y  270 mesh  reference.  37y  400 mesh  - Samples r i f f l e d  1  screens.  t o approx. 5-10 l b s .  Further r i f f l e d  to future  - Suspect approx. 1 t o 1-1/2% m o i s t u r e c o n t e n t p r i o r to  pan  Tyler  drying.  pan  Toledo weighscale;. range from 0 to 75 l b . i n 2 oz. graduations. Scale c a l i b r a t e d both before and after screening program and found to be accurate to w i t h i n 2-1/2 oz. at maximum d e f l e c t i o n .  - 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 o b t a i n e d around the secondary  crushers.  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 r u s h e r f e e d r a t e s were  found by a v e r a g i n g the f l o w r a t e s c a l c u l a t e d from feed and p r o d u c t w e i g h t s . No f u r t h e r adjustments  o f t e r t i a r y c r u s h e r data were attempted.  Adjust-  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 r u s h e r 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 h a t d i r e c t s a m p l i n g o f the v i b r a t i n g  s c r e e n feed was i m p o s s i b l e .  C o n s e q u e n t l y , a sample o f t h i s f l o w s t r e a m  was approximated by a n o t h e r sample taken from the feed t o the s c r e e n surge b i n .  However, due t o p a r t i c l e s e g r e g a t i o n e f f e c t s  known t o o c c u r  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. A l t h o u g h d i r e c t s a m p l i n g o f both o v e r s i z e and u n d e r s i z e p r o d u c t streams was e a s i l y a c c o m p l i s h e d , both o f these samples are a l s o s u b j e c t t o e x perimental  error.  To m i n i m i z e the above e x p e r i m e n t a l e r r o r , a data procedure was d e v i s e d .  adjustment  T h 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 t h a t a l l measured data are i n e r r o r and f i n d s  adjusted  data p o i n t s which m i n i m i z e a l e a s t squares c r i t e r i o n , e x p r e s s e d  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 t a n d a r d  deviation  a s s o c i a t e d w i t h the i t h measured d a t a p o i n t and M | i s computed u s i n g the minimum number o f s e a r c h v a r i a b l e s which p e r m i t c a l c u l a t i o n o f a l l data p o i n t s .  T h 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  c o n d i t i o n s d e p i c t e d i n F i g u r e 13.  state  As an example , i f one c o n s i d e r s  g e n e r a l i z e d d a t a 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 a t  the steady  state: F = 0 +U i fi  = ( 0 / F ) OJ. + ( U / F )  where F , 0 , U , f | ,  = 1 to n  (18)  U i  o-j and u-j have been measured around the s c r e e n .  t h a t one o f the v a r i a b l e s f. -, o.j o r u - i s unnecessary n  a mass b a l a n c e c a l c u l a t i o n .  n  Note  f o r completion o f  F u r t h e r m o r e , one o f the f l o w r a t e s F , 0 o r U  can a l s o be c o n s i d e r e d to be  redundant. F,f:  (No. 14 Belt)'  O.O, (No.18 Belt)  F i g u r e 13  (No. 16 Belt)  Schematic Diagram f o r Mass Balance o f a Secondary Screen  - 46 -  TABLE 7 G e n e r a l i z e d Table o f Data O b t a i n e d Around Screen  Weight P e r c e n t R e t a i n e d on S i z e Size i 1  Undersize  Feed  Oversize  ' I  0,  U.  0  U  2 3 4  n Flowrates  After careful  c o n s i d e r a t i o n , the a b s o l u t e  v a l u e s o f the  following  were d e f i n e d as search v a r i a b l e s : 0 , U , Oj and u-j , f o r i = 1 t o n 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 data p o i n t . as  Adjusted data.points  can be computed from s e a r c h  1.  adjusted  variables  follows:  6 =6 U = 0 F = 6 +U = pi Uj. = Ui fi  °h  = (1-  u  .)ci,  6+U  . n-1 ~ 1-E 0,i=l  i  = 1 to n - 1  i  0+U  1  "n  +  (^)u ;  (19)  - 47 -  The  adjusted  data p o i n t s may be determined by f i n d i n g  combination o f s e a r c h v a r i a b l e s which m i n i m i z e s the f o l l o w i n g  the objective  function: O.F.  ="  (!i^i)  i=l + (0 -  So-j  +  S  ( J-H)2  2  u  i=l  6 ) + (U - U )  where S o j , Su^ and Sfj ith  2  n +  T  .  Sui  (fiifi)  i=l  2  S-fj (20)  2  are the s t a n d a r d d e v i a t i o n s a s s o c i a t e d w i t h  the  s i z e f r a c t i o n o f the measured o v e r s i z e , u n d e r s i z e and feed streams (6 29)  respectively.  A m o d i f i c a t i o n o f the s i m p l e x d i r e c t search method^  '  '  was employed t o f i n d the s e t o f search v a r i a b l e s t h a t would m i n i m i z e equation  (20). T e s t s numbers 1 7 , 18 and 19 are r e p e a t runs where o p e r a t i n g  v a r i a b l e s were s e t t o the same l e v e l s .  From these r e p e a t s ,  estimates  o f s t a n d a r d 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 p r o d u c t s i z e d i s t r i b u t i o n s . Su-j  These e s t i m a t e s  o f So-,- ,  and Sfj; are then i n t r o d u c e d i n t o the o b j e c t i v e f u n c t i o n to e n a b l e  the s e a r c h program t o m i n i m i z e w i t h r e s p e c t t o the s t a t i s t i c a l p r e c i s i o n i n h e r e n t t o the s a m p l i n g 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 r e a t e d t o perform the screen data  ment i s c a l l e d SCREEN and i s w r i t t e n i n the BASIC l a n g u a g e . 1  o f t h i s program i s p r e s e n t e d i n Appendix C ( a ) . r e p r e s e n t s the f i n a l ,  fully  adjusted  adjust-  A listing  The o u t p u t from SCREEN  s c r e e n data used i n development  o f the screen m o d e l .  1  A l l computer programs used during t h i s project are w r i t t e n i n U . B . C . BASIC, with.the exception of p l o t t i n g p r o g r a m s w h i c h are w r i t t e n 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 -  I n c o r p o r a t e d w i t h i n SCREEN i s a s h o r t s u b r o u t i n e used t o c a l c u l a t e o r d i n a t e v a l u e s f o r the c o r r e s p o n d i n g s c r e e n e f f i c i e n c y F o r the purpose o f t h i s t h e s i s , the s c r e e n e f f i c i e n c y  curve.  curve i s d e f i n e d  as the p l o t o f the w e i g h t f r a c t i o n o f f e e d i n s i z e range i r e p o r t i n g t o the o v e r s i z e p r o d u c t versus the l o g a r i t h m o f the g e o m e t r i c mean o f p a r t i c l e s i z e range i . as  The o r d i n a t e o f the e f f i c i e n c y  curve i s computed  follows: Yi=°L° f^O+U) The a d j u s t e d s c r e e n d a t a ,  a t e s , i s presented  i = l t o n-1:  complete w i t h e f f i c i e n c y  i n Appendix C ( b ) .  (21)  curve o r d i n -  - 49 -  CHAPTER IV MODEL DEVELOPMENT  4.1  Summary o f Development Procedures All  strategy.  f o u r models were developed a c c o r d i n g t o the same b a s i c  This strategy  c o n s i s t s o f f o u r s t a g e s and i s summarized as  f ol1ows: (a)  propose a model form  (b)  determine c o n s t a n t s t h a t e n a b l e the model t o f i t o b s e r v e d  (c)  quantitatively relate operating variables.  (d)  e s t i m a t e how w e l l model performs and modify as n e c e s s a r y s a t i s f a c t o r y performance i s a c h i e v e d  c o n s t a n t s i n f i t t e d models t o  data  measured  until  The c r u s h e r models proposed are based on a model t e s t e d by Whiten^  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 m a t r i x B~, i n the e m p i r i c a l r e l a t i o n s developed t o p r e d i c t model parameters and i n t h e c r u s h e r c u r r e n t e q u a t i o n . t o the t e r t i a r y c r u s h e r s secondaries.  differs  The model  adapted  a p p r e c i a b l y from t h a t developed the  The d i s c o n t i n u o u s n a t u r e o f W h i t e n ' 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 d e s c r i b e secondary s c r e e n s .  the  The p r i m a r y 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 v a l u e s o f a l l unknown model parameters t h a t would enable a " b e s t f i t " o f the proposed model to the observed d a t a . set.  T h i s was done f o r each  These "optimum" parameters were then a n a l y s e d both g r a p h i c a l l y and  u s i n g s i m p l e hand c a l c u l a t o r r e g r e s s i o n a n a l y s e s t o determine  i  data  i f any  These were modified Simplex type d i r e c t searches. The program developed for parameter searches i s c a l l e d BRCRUSH and i s w r i t t e n 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 p a r a m e t e r s . parameters  t o be f i x e d as t r u e c o n s t a n t s  terms o f the r e m a i n i n g p a r a m e t e r s ,  T h i s u s u a l l y e n a b l e d some and o t h e r s t o be e x p r e s s e d i n  thus r e d u c i n g the number o f  t o be r e l a t e d t o o p e r a t i n g v a r i a b l e s .  parameters  D i r e c t searches were again c a r r i e d  out t o f i n d "optimum" v a l u e s f o r the new s e t o f  parameters.  With the "optimum" v a l u e s f o r the new s e t o f p a r a m e t e r s , complete r e g r e s s i o n a n a l y s i s was performed t o determine with operating variables.  relationships  A BASIC language computer program c a l l e d ALLREDD  was used t o perform the m u l t i - v a r i a b l e r e g r e s s i o n a n a l y s e s .  A complete  l i s t i n g o f the program ALLREDD and a d a t a t r a n s f o r m a t i o n program, TRANS 4 , i s i n c l u d e d i n Appendix D. the model parameters  a  U s i n g ALLREDD, e q u a t i o n s  called  relating  t o observed o p e r a t i n g v a r i a b l e s were d e v e l o p e d .  A f t e r an approximate model form had been f o u n d , a " s i m u l t a n e o u s " S i m p l e x s e a r c h was conducted f o r v a l u e s o f c o n s t a n t s  i n the model t h a t  would m i n i m i z e 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 s e a r c h .  This  was conducted s i m u l t a n e o u s l y on a l l v a l i d d a t a s e t s p e r t i n e n t t o model under development.  search the  The computer program w r i t t e n to perform t h i s  s e a r c h i s c a l l e d TURKEY and uses t h e s i m p l e x d i r e c t . s e a r c h method p r e v i o u s l y referrenced.  T h i s program was a l t e r e d t o i n c o r p o r a t e the model under  development and the v a r i o u s m o d i f i c a t i o n s are p r e s e n t e d p r i a t e appendices.  i n the  appro-  Output from t h i s program c o n s t i t u t e d a model.  However,  n o t 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 s e v e r a l forms before an a c c e p t a b l e model was e s t a b l i s h e d . All  computer programs u s i n g the Simplex search method ( i n c l u d i n g  SCREEN) employ a f i t t i n g t e c h n i q u e 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 data p o i n t s .  r e s i d u a l sum o f squares between observed and p r e d i c t e d  The sum o f squares are c a l c u l a t e d u s i n g the p r o d u c t  d i s t r i b u t i o n s expressed  size  i n w e i g h t f r a c t i o n r e t a i n e d on s i z e r a t h e r than  s i z e f r a c t i o n mass f l o w s .  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 n o t  be w e i g h t e d d u r i n g 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 r e p e a t 4.2  data.  The Secondary C r u s h e r Model The b a s i s f o r t h e cone c r u s h e r model i s the assumption  that  p a r t i c l e s e n t e r i n g the c r u s h e r s p l i t i n t o . p o r t i o n s t h a t e i t h e r l e a v e c r u s h e r unharmed o r are b r o k e n .  Those p a r t i c l e s which are broken  then  have the same c h o i c e o f e i t h e r b e i n g broken again o r l e a v i n g the C o n s e q u e n t l y , the operations:  the  crusher.  c r u s h i n g phenomenon can be d i v i d e d i n t o two b a s i c  t h a t o f p a r t i c l e breakage and t h a 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 i g u r e 1, page 6 , the c r u s h e r model can be e x p r e s s e d by a s i n g l e breakage z o n e , r e p r e s e n t e d 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 t h a t z o n e , r e p r e s e n t e d by C. (see  From mass b a l a n c e s  aroundnodes  1 and 2  F i g u r e 1, page 6 ) , the p r o d u c t v e c t o r i s p r e d i c t e d from the  equation: P = [T - C] [T - B C ~ ] ~ T  (.10)  which r e p r e s e n t s the f i n a l i z e d m a t r i x form o f the model. m a t r i x [ I - BZ] must always be n o n - s i n g u l a r ( d e t e r m i n a n t  Note t h a t  f 0 ) , as a u n i t  element on the d i a g o n a l o f B" C] i m p l i e s both no breakage and no of that s i z e (a)  the  discharge  fraction.  The Breakage M a t r i x , B" Whiten d i v i d e d the breakage m a t r i x i n t o two components,  i  each  - 52 -  presumably d e s c r i b i n g a d i f f e r e n t e n t s are l o w e r  type o f c r u s h i n g a c t i o n .  Both compon-  triangular.  The f i r s t  component, B l , d e s c r i b e d the mechanism o f p r i m a r y  breakage by g i v i n g the p r o d u c t d i s t r i b u t i o n r e l a t i v e l a r g e s t o r i g i n a l feed p a r t i c l e .  t o the s i z e o f  T h i s component forms an (n-1)  by  the  (n-1)  s t e p m a t r i x . w h i c h was n o r m a l i z e d w i t h r e s p e c t t o 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 .  Consequently,  elements o f the f i r s t first  the e n t i r e m a t r i x can-be computed once  column are known.  T h i s i s done by d i s p l a c i n g  column o v e r one column and down one row f o r s u c c e s s i v e  w i t h z e r o s o c c u p y i n g empty l o c a t i o n s shown d i a g r a m a t i c a l l y  in Figure  i n the a r r a y .  size  T h i s procedure  the the  fractions, is  14.  0 0  b f i r s t column  b. n  n  b  n-1  b  n-2  b  n-3  known  F i g u r e 14  Computational  Procedure f o r P r i m a r y Breakage. Component, BT  - 53 -  The elements o f the f i r s t column o f the B l m a t r i x are from the m o d i f i e d Gaudin-Meloy p r i m a r y breakage Y  equation : 1  = 1 - (1 - (•*!)?)*  p  where y and 3 were determined w i t h y = 2 . 0 and 3 = 6 . 0 . i  b  computed  =  Y  (7) t o be c o n s t a n t f o r the secondary  crushers  These elements are computed as f o l l o w s :  p ( i ) - p(i+1) Y  1  =  1  t  0  n  _  1  Y p ( ) = 1.0  (23)  o  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  to be independent o f the o r i g i n a l p a r t i c l e normalizable.  assumed  s i z e and c o n s e q u e n t l y ,  However, t h i s m a t r i x can be e m p i r i c a l l y c a l c u l a t e d  the elements o f the f i r s t row are known.  procedure  n e  Rosin-RammTer d i s t r i b u t i o n Y  The  i s shown i n F i g u r e 15.  The elements o f the f i r s t column o f the B2" m a t r i x are from , t  adding  p r e d i c t e d above the s i z e b e i n g broken t o t h a t s i z e .  computational  calculated  function:  = 1 - exp ( - ( | L ) )  (24)  V  s  once  T h i s i s a c h i e v e d by d i s p l a c i n g  the f i r s t column sideways t o form an (n-1) by (n-1) m a t r i x , then the m a t e r i a l  not  where S" and v are model c o n s t a n t s found t o have the v a l u e s o f 2 . 0 cm and 0.664 r e s p e c t i v e l y . a  1  i  =  Y  -s(i)  The method o f computing B2~ elements i s :  " s(i+1) Y  1  =  1  t  0  n-"  1  (25)'  This breakage equation d i f f e r s from t h a t used by Whiten. He used a m o d i f i c a t i o n of the Rosin-Rammler equation proposed by B r o a d b e n t U ^ ' (equation ( 3 ) , page h ) . From p r e l i m i n a r y analyses, t h i s equation d i d not appear to be s a t i s f a c t o r y f o r our data.  - 54 -  B2  (1,1)  l  a  =  a  l  a a  3  a  4  ->  a  a  a  2  3  •  a  • ai  l 2  3  a a  a  2  3  a  •  B2=  a  l  .0  n  0  ° 1 a-|+a  i  —  2  a  2  3  a  3  a  3  a  l  a  4  a  4  a  4  2  + a  0 2  + a  3  0  •  m i  a  first  V  n  a  n  a  n  ••  •• n  n  a  V ' -  n  column known  F i g u r e 15  Computation Procedure f o r Secondary Component, B2  However, i f the d i s t r i b u t i o n f u n c t i o n i s r e w r i t t e n y where y  Breakage  as:  = exp [ - ( i i ) ] S"  (26)  v  s  i s the c u m u l a t i v e f r a c t i o n c o a r s e r than s i z e x - j , then  s  computation a  i  the  becomes: =  y;s(i+l) - V s ( i )  i = 1 to  n-1  (27)  where y  s(o)  =  0  E q u a t i o n (27) was found t o s i m p l i f y computations BRCRUSH and TURKEY.  i n the s e a r c h  programs  +  a  n  - 55 -  To o b t a i n the t o t a l  breakage m a t r i x , the two components  summed i n l i n e a r c o m b i n a t i o n a c c o r d i n g B = a B T + (1-a) where « , the  to:  B2  (28)  l i n e a r combination c o e f f i c i e n t , was found t o be  to the c r u s h e r  gap and f e e d r a t e by the  related  equation:  a = -0.91489 + 0.21729 G+ 0.000626T + 0.0056345 The r e l a t i v e  contributions  F i g u r e 16  (29)  o f the two breakage components  p r e s e n t e d g r a p h i c a l l y i n F i g u r e 16. size d i s t r i b u t i o n is included for  are  A typical  secondary  crusher  comparison.  R e l a t i v e C o n t r i b u t i o n s o f Breakage F u n c t i o n Components, B l and B2  are product  - 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 i a g o n a l elements o f the c l a s s i f i c a t i o n m a t r i x (C)  are o b t a i n e d following (1)  from a d i s c r e t e f u n c t i o n o f p a r t i c l e  particles  above a c e r t a i n x  i  s i z e K2 are always b r o k e n ,  or: (30)  > K2  p a r t i c l e s below a c e r t a i n s i z e K l are n o t b r o k e n , pass through the c r u s h e r , so t h a t : c(x-j) = 0  (3)  the  assumptions:  c(x.j) = 1.0 (2)  s i z e based on  but (31)  x-j < Kl  p a r t i c l e s between these s i z e s are broken a c c o r d i n g t o 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 e x p r e s s e d by: c(x ) = l 1  (^J<2)2 K l - K2  The c l a s s i f i c a t i o n f u n c t i o n  Kl < x . < K2  c(x-j) i s d e p i c t e d i n F i g u r e 17.  11  x u _Q O _Q O £_  Q_  K1  Particle F i g u r e 17  K2  Size , x  C l a s s i f i c a t i o n Function,  c(x)  (32)  - 57 -  The d i a g o n a l elements  o f the C m a t r i x are c a l c u l a t e d as  the  mean v a l u e s o f c ( x ) o v e r the s i z e range i n q u e s t i o n a c c o r d i n g t o :  C(x) = J  c(x)dx  X  2  X  -  X  (33)  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 t o c a l c u l a t e the C e l e m e n t s : (i)  F ( x ) + Kl - 1/3(K1 - K2)  Kl > x.,-  i  (ii)  F ( X i ) = x.. - V 3 ( x - K 2 ) ; i  ^  K 1  K 2  (Kl - K 2 P (iii)  (  1  V  F(x -) = x ;1  )  C  (  l  )  "  3  4  )  K2 < X i  i  x ^ - x  The two p a r a m e t e r s ,  (  1 i  +  =  *o"-l  1  1  K l and K 2 , are p r e d i c t e d from the  equations:  K l = 44.5875 - 33.5157 G+ 5.677T.G + 0.1221 S  (35)  K2 = -22.8812 + 23.7981 G - 3.7319 G - 0.02798S  (36)  2  and ;  (c)  2  The C r u s h e r C u r r e n t .  The secondary c r u s h e r c u r r e n t draw can be p r e d i c t e d from the  c r u s h e r gap and f e e d r a t e by the  equation:  C = 20.6182 - 7.323393 G+ 0.0345158T  (37)  T h i s r e l a t i o n i s s i m p l e and agrees w i t h what i s e x p e c t e d f o r i n f l u e n c e o f gap and f e e d r a t e on c u r r e n t draw.  I t was observed t h a 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 measured c u r r e n t o v e r the ranges s t u d i e d . t i a l l y different  the  upon the  E q u a t i o n (3 7) i s  from t h a t proposed by W h i t e n ^ .  substan-  - 58 -  (d)  Model A c c u r a c y and Range The computer program used f o r f i t t i n g the secondary  model (TURKEY) i s p r e s e n t e d  i n Appendix E .  The program f i n d s model  parameters t h a t m i n i m i z e the sum o f the square o f the (RSS)  crusher  differences.  between measured and p r e d i c t e d p r o d u c t s i z e d i s t r i b u t i o n s .  presented  Also  i n Appendix E i s the computer program f o r t h e f i t t e d m o d e l ,  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 r u n s .  I t i s not p o s s i b l e  t o t e s t f o r l a c k o f f i t o f the model because o f the absence o f r e p e a t runs.  T h u s , i t i s n o t p o s s i b l e t o determine  the r e l a t i v e  contributions  o f the RSS components due to l a c k o f f i t and t o random e r r o r .  The o b v i o u s  method f o r e v a l u a t i o n o f the secondary c r u s h e r 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 r u n .  A mean RSS o f 1 3 . 5 , w i t h a s t a n d a r d  d e v i a t i o n o f 1 6 . 3 , was o b s e r v e d .  C r u s h e r c u r r e n 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  model i s judged t o 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 p u r p o s e s , it  crusher  although  i s f e l t t h a 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 m a t r i x  section. 18(a)  The g r a p h i c a l performance  o f the model i s d e p i c t e d i n F i g u r e s  and ( b ) , r e p r e s e n t i n g the b e s t and the w o r s t model p r e d i c t i o n s . The secondary c r u s h e r 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 e q u a t i o n t o d e s c r i b e p r i m a r y breakage  (b)  use o f d i f f e r e n t  (c)  use o f a 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 r e l a t i o n f o r p r e d i c t i n g c r u s h e r c u r r e n t draw  There i s no doubt t h a t e r r o r has been i n t r o d u c e d d u r i n g s a m p l i n g o f the secondary c r u s h e r s .  Both the e x t r e m e l y l a r g e p a r t i c l e  sizes  - 59 -  F i g u r e 18(a)  Performance o f Secondary C r u s h e r M o d e l , Best P r e d i c t i o n  - 60 -  F i g u r e 18(b)  Performance o f Secondary C r u s h e r M o d e l , Worst P r e d i c t i o n  - 61 -  i n v o l v e d and the h i g h frequency o f s h o r t term f l u c t u a t i o n s made a c c u r a t e  sampling very d i f f i c u l t .  of sampling,and interference o f samples were o b t a i n e d .  i n feedrate  F u r t h e r m o r e , due t o the  difficulty  w i t h p l a n t o p e r a t i o n , o n l y a s m a l l number  F o r these r e a s o n s ,  the a c c u r a c y o f the  cone  c r u s h e r model s h o u l d n o t be e x p e c t e d to e q u a l t h a t o f a r o d o r b a l l mill  m o d e l , u n l e s s a much l a r g e r sample p o p u l a t i o n has been a c q u i r e d . There i s c o n s i d e r a b l e 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 d a t a range o v e r which t h e model was f i t t e d . it  i s useful  t o know how a model w i l l behave when o p e r a t i n g  are s e t beyond the f i t t e d data range.  However, variables  T h i s knowledge becomes  essential  i n a m u l t i - m o d e l 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 v a l u e s f o r o p e r a t i n g v a r i a b l e s which may span w e l l beyond the fitted  data ranges w h i l e approaching a convergence. S t u d i e s were conducted on the secondary c r u s h e r model t o  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 r a n g e s .  t h a t a l l c o m b i n a t i o n s o f o p e r a t i n g v a r i a b l e s c o u l d be  see  I t was found  extrapolated  twenty p e r c e n t below the lower l i m i t s o f the f i t t e d d a t a ranges w i t h no a p p a r e n t problems.  However, t h i s was n o t t r u e 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 s e r i o u s p r o b l e m s , such as p r e d i c t i n g n e g a t i v e v a l u e s where p o s i t i v e ones are m a n d i t o r y , w e r e observed t o o c c u r .  Since  parameters were observed t o be f u n c t i o n s o f two o r more o p e r a t i n g 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 i m p l e e x t r a p o l a t i o n i s cult.  However, i t has been p o s s i b l e t o make the f o l l o w i n g  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 :  diffi-  individual  - 62 -  (a)  f e e d r a t e t o + .20%, i f the gap and % + 1 i n c h do not exceed the upper l i m i t o f the sampled d a t a range.  (b)  gap t o + 7%, i f the f e e d r a t e and % + 1 i n c h 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 i n c r e a s e s as T and S d e c r e a s e .  (c)  % + 1 i n c h t o + 5.5%, i f the gap and f e e d r a t e . do not exceed the upper l i m i t o f the observed data range.  I t was n o t p o s s i b l e t o e x t r a p o l a t e  c o m b i n a t i o n s o f two o r more o p e r a t i n g  v a r i a b l e s beyond +2%. 4.3  The T e r t i a r y C r u s h e r Model The model proposed f o r the t e r t i a r y c r u s h e r s  to t h a t r e p o r t e d f o r the secondary c r u s h e r s . the e q u a t i o n s  i s very s i m i l a r  The d i f f e r e n c e  developed t o p r e d i c t t h e model parameters as  o f the o p e r a t i n g v a r i a b l e s . meter r e q u i r e d p r e d i c t i o n .  l i e s in functions  I t was a l s o found t h a t an a d d i t i o n a l  para-  The'..matrix form o f the model, remains e x -  p r e s s e d i n terms o f the c r u s h e r feed by the P = [ I - C] [ I - B C ]  _ 1  equation: (10)  F  ( 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  m a t r i x comprised o f two components-, both o f which are l o w e r t r i a n g u l a r . The breakage  component m a t r i c e s 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 i m p o r t a n t d i f f e r e n c e  arises  i n the use o f the m o d i f i e d  Gaudin-Meloy d i s t r i b u t i o n f u n c t i o n t o d e s c r i b e p r i m a r y breakage. function  i s expressed Y  p(i) =  1  This  as:  " *1  (7)  - (  I t was found t h a t the parameter  e, determined t o be c o n s t a n t  for  the  - 63 -  secondary c r u s h e r s , e x h i b i t e d t o o much v a r i a t i o n to be h e l d f o r the t e r t i a r y c r u s h e 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 t o the l i n e a r c o m b i n a t i o n c o e f f i c i e n t a. meter Y) a l t h o u g h s t i l l  constant  constant,  In a d d i t i o n , the  i s l a r g e r by a f a c t o r o f two.  paraThe  parameters i n v o l v e d i n the Gaudin-Meloy p r i m a r y breakage e q u a t i o n expressed  are  as: = 4.0  Y  (38)  and 3 = 27.4583 + 43.97832 EXP (-2599.762 ai&'.766 3)  (39)  The secondary breakage e q u a t i o n e x p r e s s e d by the Rosin-Rammler distribution Y  s ( 1  function: )  = 1 - exp ( - ( | r ) )  (2.4)  v  remains unchanged.  The v a l u e s o f the parameters a r e :  S" = 2 . 0 , c m .  and v = 0 . 6 6 4 . The l i n e a r c o m b i n a t i o n 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 r u s h e r f e e d r a t e by the e q u a t i o n : a = 0.1133812 + 1.178078 x 1 0 H + (: ) (40) l+3.632176xl0~ (T-299.381) -  0  ,  5  1  8  0  7  6  lt  (b)  2  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 m a t r i x i s a l s o d e f i n e d and c a l c u l a t e d as  d e s c r i b e d f o r t h e secondary c r u s h e r . m o d e 1 . classification  The d i f f e r e n c e between  m a t r i c e s l i e s w i t h the e q u a t i o n s t h a t p r e d i c t the  meters K l and K 2 .  F o r the t e r t i a r y c r u s h e r s ,  para-  these parameters can be  p r e d i c t e d from the feed s i z e and c r u s h e r gap by the Kl = -1.793265 + 0.05284647 S  the  equations: (41 )  - 64 -  and K2 = 6.331619 - 0.8040997 G _  1.042385  {  -j 1 7.966.98  1 + 2.996623(G-0.7135176)  (  4  2  )  2  I t s h o u l d be n o t e d t h a t the model i s v e r y s e n s i t i v e t o roundo f f e r r o r i n the parameter e q u a t i o n c o n s t a n t s .  Attempts were made to  r o u n d - o f f a l l e q u a t i o n c o n s t a n t s w i t h v e r y s i g n i f i c a n t l o s s o f model accuracy.  The b e h a v i o u r s o f t h e f o u r model parameters are  depicted  g r a p h i c a l l y i n F i g u r e 19. (c)  The C r u s h e r C u r r e n t The t e r t i a r y  c r u s h e r c u r r e n t i s p r e d i c t e d from the  gap and f e e d r a t e by the  crusher  equation:  C = 27.55756 - 9.608871 G+ .0.0554204 T T h i s r e l a t i o n has t h e same form as t h a t developed f o r the c r u s h e r m o d e l . . As b e f o r e , have a n e g l i g i b l e e f f e c t  (43) secondary  the feed s i z e d i s t r i b u t i o n was observed  upon the c r u s h e r c u r r e n t draw.  to  This expression  i s again c o n s i d e r a b l y 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 r u s h e r (d)  current.  Model A c c u r a c y and Range The computer program used to f i t the t e r t i a r y c r u s h e r model  (TURKEY) i s p r e s e n t e d  i n Appendix F.  As w i t h t h e secondary  crusher  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 t h e sum o f the squares o f the d i f f e r e n c e s s i z e d i s t r i b u t i o n s (RSS).  between measured, and p r e d i c t e d  Also presented  product  i n Appendix F i s the  f o r the f i t t e d m o d e l , c a l l e d . T E R C R , w i t h p r e d i c t i o n s f o r a l l  program  fitted  - 65 -  (a) Parameter a  (b) Parameter 3  (c)  (d) Parameter K2  Parameter K l  F i g u r e 19  B e h a v i o r o f T e r t i a r y C r u s h e r Model  Parameters  - 66 -  t e s t runs.  As no r e p e a t  runs were a v a i l a b l e , a l a c k o f f i t t e s t  cannot  be p e r f o r m e d . D u r i n g development o f the t e r t i a r y c r u s h e r m o d e l , two data s e t s were n o t e d t o 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 These data s e t s r e p r e s e n t t e s t s numbered 14 and 16B.  It is  others.  suspected  t h a t the c r u s h e r gap was r e a d i n c o r r e c t l y w h i l e p r e p a r i n g f o r t e s t n o . 16B and t h a t the t r u e . g a p  i s somewhat l a r g e r than was r e c o r d e d .  Data  from t e s t n o . 16B seems t o c o n f i r m 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 b e h a v i o u r was observed when a gap s i z e o f .85 cm. was used i n p l a c e o f the r e c o r d e d .762 cm.  No obvious reason can be d i s c e r n e d f o r severe  d e v i a t i o n s n o t e d from t e s t n o . 14.  Due t o these s u b s t a n t i a l l y d e v i a n t  b e h a v i o u r s , d a t a s e t s numbered 14 and.16B were d e l e t e d f o r development o f the f i n a l m o d e l . As a r e s u l t o f the bad data s e t s , c o n s i d e r a b l e d i f f i c u l t y e x p e r i e n c e d i n development o f t h e parameter p r e d i c t i n g r e l a t i o n s .  was Several  s e t s o f a l t e r n a t i v e r e l a t i o n s were d e v e l o p e d , t e s t e d and e v e n t u a l l y d i s carded.  The f i n a l  model e n a b l e s 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 2 5 . 7 and a s t a n d a r d 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 i g u r e s 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 b e s t and w o r s t runs r e s p e c t i v e l y . S e v e r a l o f the a l t e r n a t i v e model forms d e v e l o p e d gave  better  p r e d i c t i n g performance o v e r the d a t a range to which they were f i t t e d . However, these forms were c o n s i d e r a b l y 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 p r e s e n t 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  least  F i g u r e 20(a)  Performance  o f T e r t i a r y Crusher Model, Best  Prediction  Figure  20(b)  Performance o f T e r t i a r y C r u s h e r M o d e l , Worst  Prediction,  - 69 twenty p e r c e n t o u t s i d e f i t t e d r a n g e s ,  f o r any c o m b i n a t i o n o f v a r i a b l e s ,  w i t h no apparent p r o b l e m s . The p r e s e n t t e r t i a r y f o r s i m u l a t i o n purposes.  c r u s h e r model i s c o n s i d e r e d  satisfactory  Note t h a t the model d i f f e r s from t h a t  proposed  by Whiten i n t h e f o l l o w i n g ways: (a)  use o f a d i f f e r e n t e q u a t i o n to d e s c r i b e p r i m a r y  (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  (d)  use o f a d i f f e r e n t  breakage  r e l a t i o n s f o r p r e d i c t i n g model parameters r e l a t i o n f o r p r e d i c t i n g crusher current  I t s h o u l d be n o t e d t h a t the b e h a v i o u r o f parameter function  o f c r u s h e r gap i s n o t what would be e x p e c t e d ,  draw  K2 as a  i n t h a t the base  l i n e f o r the f u n c t i o n decreases w i t h i n c r e a s i n g gap.  (see  An a l t e r n a t i v e e x p r e s s i o n was developed f o r parameter  K2 which does  behave as would be e x p e c t e d , but which r e s u l t s  the  K2 e x p r e s s i o n i s n o t used.  19(d)). * -  in a s.ighificantrloss of  p r e d i c t i n g a c c u r a c y o v e r the range o f data sampled. alternative  Figure  F o r t h i s reason  The a l t e r n a t i v e  the  i s e x p r e s s e d by  equation: K2 =.' 8:9T6337 +"^34v56163^GV!:18.18497^e'Xp(-^1;.74922 ( G - . 8 9 1 7 7 6 ) ) c  2  :  (44)  Its behaviour i s depicted g r a p h i c a l l y in Figure 2 1 / '  4.4  The Secondary Screen Model The Whiten s c r e e n model was a n a l y s e d i n d e t a i l and found to be  d i s c o n t i n u o u s i n n a t u r e (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 e q u a t i o n  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 t o observed s c r e e n i n g data t o produce the model proposed i n t h i s The d e r i v a t i o n i s p r e s e n t e d  i n Appendix G.  thesis.  the  - 70 -  Tertiary F i g u r e 21  (a)  Crusher  Gap - ( c m )  B e h a v i o r o f A l t e r n a t i v e K2 R e l a t i o n  Model D e s c r i p t i o n The d e r i v e d s c r e e n e f f i c i e n c y e q u a t i o n i s c o n t i n u o u s o v e r 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 s c r e e n i n g o p e r a t i o n i s a t steady  state  (b)  the p a r t i c l e volume d i a m e t e r 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 t o the g e o m e t r i c mean d i a m e t e r and independent o f p a r t i c l e shape factors  (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 o t h e r 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 p o p u l a t i o n  increases.  The general form o f the e f f i c i e n c y  equation i s expressed  as:  - 71 -  1-Ci  =  Y l  l+exp[x  5 0  + Ci  3_  X i  i = 1 t o n-1  (45)  3]  where Yj i s the p r e d i c t e d w e i g h t f r a c t i o n o f feed r e p o r t i n g t o the o v e r s i z e p r o d u c t and C-j i s an a u x i l l i a r y f u n c t i o n i n t r o d u c e d t o e x p l a i n the s h o r t c i r c u i t i n g o f u n d e r s i z e m a t e r i a l , such as m o i s t to the o v e r s i z e p r o d u c t .  The p a r t i c l e s i z e X-j i s r e p r e s e n t e d by the  g e o m e t r i c mean o f t h e s i z e range i n q u e s t i o n . ful  form o f the e f f i c i e n c y Ui  =  An a l t e r n a t i v e  and use-  equation i s :  Ff-j  -g-  fines,  ^ '  F  u(i+expr  ••••.3  3  X 5 0 J  i  =  1  to  n-1  (46)  'V]  where u - i s the p r e d i c t e d w e i g h t f r a c t i o n o f feed r e p o r t i n g t o the n  undersize product.  The pan s i z e m a t e r i a l  s c r e e n , -53y f o r t h i s p r o j e c t ) Y  pan  =  ~ l+exprx-so -, a  +  c  ( m a t e r i a l p a s s i n g the s m a l l e s 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 : 'i  =  constant  j = n  (47)  3  J  For d a t a o b t a i n e d around the Brenda Mines l t d . s c r e e n i n g c i r c u i t , the a u x i l l i a r y f u n c t i o n  has been s e t equal t o z e r o .  The  screen model parameters are p r e d i c t e d from the e q u a t i o n s : %  0  = 6.543503 - 7.342139.;^ + 2 . 8 5 5 7 7 6 V -4.64881xl0" S 5  2  - 1.303655xl0" T 2 2  (48)  7  and a  = 1.238414 + 0.4822109- <f - 1 . 0 0 2 2 2 1 x l O " S 2  + 1.163871xl0- T 7  (49)  2  I t i s c o n v e n i e n t a t t h i s stage t o e x p l a i n how an e q u i v a l e n t screen o p e n i n g , f e , was determined f o r the composite s c r e e n s employed  - 72 -  i n t e s t s 17 t o 2 1 .  The two feed end panels o f the l o w e r deck  o f 5/8 i n . x 3-1/2 i n . s l o t s , w h i l e the t h r e e d i s c h a r g e - e n d 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 . .  consisted  panels  The f i r s t two f e e t o f the  feed end o f the upper deck were b l a n k e d o f f by a p r o t e c t i v e rubber effectively  strip,  removing the c o r r e s p o n d i n g s c r e e n i n g a r e a i n the feed end  p a n e l . o f the l o w e r deck.  U s i n g a S i m p l e x d i r e c t search  (see page 4 7 ) ,  v a l u e s f o r the model parameters " x ; " and " a " were determined f o r each 5 0  t e s t , i n c l u d i n g t e s t s 17 t o 2 1 .  However, the c o n s t a n t s used i n  equations  4 8 and 49. were i n i t i a l l y determined f o r t e s t s 25 t o 30 o n l y , ( e x c l u d i n g "i.  t e s t s 17 t o 21) u s i n g r e g r e s s i o n  a n a l y s e s conducted w i t h the  computer  program ALLRED (see Appendix D(a)),.  Runs 25 to 30 i n v o l v e d u n i f o r m  s c r e e n openings i n the l o w e r deck.  Following t h i s , equations  48 and  49 were used t o back c a l c u l a t e v a l u e s f o r <()'e f o r runs 17 t o 2 1 , w i t h two e s t i m a t e s per run b e i n g o b t a i n e d , one f o r each e q u a t i o n . were averaged to y i e l d a f i n a l  estimate  o f the e q u i v a l e n t screen  f o r the composite s c r e e n decks o f f e = 1.5  cm.  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 (b)  5 0  T h i s v a l u e was  opening subsequently  model.  Model B e h a v i o r F i g u r e s 22(a)  on X  These  and 22(b)  d e p i c t how s c r e e n i n g e f f i c i e n c y depends  and " a " when the a u x i l l i a r y f u n c t i o n Ci = 0.  Note t h a t the  inter-  cept a t X i = 0 i s n o t equal to z e r o , but a f i n i t e v a l u e which i s a f u n c t i o n of x  5 0  and " a " .  Because the Brenda Mines L t d . c o n c e n t r a t o r  is  located  i n a s e m i - a r i d c l i m a t e , the Brenda ore i s c o n s i d e r e d t o be r e l a t i v e l y dry.  C o n s e q u e n t l y , the assumption t h a t C - = 0 was used d u r i n g model  building.  q  - 73 -  F i g u r e 22 (a)  B e h a v i o r o f Screen E f f i c i e n c y as a F u n c t i o n o f Parameter x (a=2.0 cm ) 3  5 0  - 74 -  F i g u r e 22 (b)  B e h a v i o r o f Screen E f f i c i e n c y as a F u n c t i o n o f Parameter a ( x = 1 . 9 2 cm) 5 0  - 75 -  A l t h o u g h the e f f i c i e n c y  e q u a t i o n i s b e i n g u t i l i z e d f o r double  deck s c r e e n s w i t h r e c t a n g u l a r o p e n i n g s , i t i s f e l t t h a t the e q u a t i o n has w i d e r a p p l i c a t i o n s .  The e q u a t i o n s h o u l d be a p p l i c a b l e t o s c r e e n s o f  v a r i o u s d e s i g n , w i t h u n i f o r m openings o f any c o n v e n t i o n a l s i z e and shape. In f a c t , e q u a t i o n (45) appears t o be s u i t a b l e as a c y c l o n e e f f i c i e n c y equation. I t i s e x p e c t e d t h a t f o r wet o r e s , the a u x i l l i a r y f u n c t i o n Cj will  no l o n g e r be n e g l i g i b l e .  pated t h a t C i w i l l cle  size.  I f t h i s proves t o be t r u e ,  i t is  antici-  be a f u n c t i o n o f both f e e d m o i s t u r e c o n t e n t and p a r t i -  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 )) X50  i = 1 to n  (50)  where m i s the m o i s t u r e c o n t e n t o f the s c r e e n f e e d , ao and a i are (c)  constants.  Model A c c u r a c y and Range The computer program used to f i t the secondary s c r e e n m o d e l ,  c a l l e d SCRN5, i s p r e s e n t e d i n Appendix H .  T h i s program i s a m o d i f i c a t i o n  o f the S i m p l e x s i m u l t a n e o u s s e a r c h program TURKEY,, used t o f i t both c r u s h e r models.  I t f i t s a l l screen data s e t s s i m u l t a n e o u s l y 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 O.F. for  form:  = ? . " . (Oii-Oii) i=l j=l J  k runs and n s c r e e n s i z e  J  2  + z E i=l j=l  (ui-j-u-jj) J  2  J  (51)  fractions.  A l t h o u g h s i z e f r a c t i o n v a r i a n c e s , SOJ and S U J , were a v a i l a b l e for  r e p e a t r u n s , they were n o t used as w e i g h t i n g f a c t o r s  objective function.  Consequently, the coarser s i z e s (j=l  p r e f e r e n t i a l l y w e i g h t e d d u r i n g f i t t i n g o f the model.  i n the above t o 5) were  This.was considered  - 76 -  acceptable  because the f i n e m a t e r i a l p r e s e n t i n the measured  stream t y p i c a l l y comprised 1 t o 1-1/2  p e r c e n t o f the t o t a l  oversize  flow.  was c o n s i d e r e d more i m p o r t a n t t o a c c u r a t e l y p r e d i c t those s i z e  It fractions  c o n t a i n i n g the b u l k o f product f l o w r a t e , than t o 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 v e r y 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 a c c u r a c y .  Despite  the o b j e c t i v e f u n c t i o n employed, the screen e f f i c i e n c y e q u a t i o n t o perform s a t i s f a c t o r i l y o v e r a l l s i z e r a n g e s . w i t h 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  deviation of 4.11.  judged  The mean RSS a s s o c i a t e d i s 1.19, w i t h a s t a n d a r d  d e v i a t i o n o f 1 . 6 9 , w h i l e the mean RSS f o r the u n d e r s i z e i s 2 . 2 6 , w i t h a. s t a n d a r d  is  distributions  Graphical'performance  the screen model i s p r e s e n t e d i n F i g u r e s 2 3 ( a ) , ( b ) -  of  and ( c ) , which r e -  p r e s e n t , r e s p e c t i v e l y , , the b e s t , w o r s t and second w o r s t  predictions.  The secondary screen model can be s a t i s f a c t o r i l y  extrapolated  a t l e a s t twenty p e r c e n t beyond the l i m i t s o f the f i t t e d d a t a r a n g e s . 4.5  The P r i m a r y F i n e s Model The model proposed f o r the p r i m a r y f i n e s stream i s e m p i r i c a l .  It consists  o f two components,  one t o p r e d i c t the p r i m a r y f i n e s  d i s t r i b u t i o n and the o t h e r t o p r e d i c t the s o l i d s f l o w r a t e . was developed from  size  The model  s i x samples taken over a time p e r i o d o f one week  and from d a i l y f l o w r a t e s taken o v e r a c o n s e c u t i v e t h r e e month p e r i o d . The o n l y measurable  operating variable available for quantifying  the  p r i m a r y f i n e s was t i m e . The p r i m a r y f i n e s model was n e c e s s a r y general  s i m u l a t i o n and to i n v e s t i g a t e  fines characteristics  to improve upon the  the p o s s i b i l i t y t h a t the  were a c y c l i c f u n c t i o n o f t i m e .  v  primary  This suspicion  F i g u r e 23 (a)  Performance o f Secondary Screen M o d e l , Best P r e d i c t i o n  - 78 -  F i g u r e 23 (b)  Performance o f Secondary Screen M o d e l , Worst P r e d i c t i o n  - 79 -  F i g u r e 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 o b s e r v a t i o n s o f the c y c l i c o f mine o p e r a t i n g procedures performance  on c o n c e n t r a t o r  over a p e r i o d o f s e v e r a l weeks.  influence  feed c h a r a c t e r i s t i c s  and  A l t h o u g h the q u a n t i t y o f  d a t a o b t a i n e d was v e r y s m a l l . , a c o n s i s t e n t t r e n d f o r the model paramet e r s was o b s e r v e d . (a)  Model D e s c r i p t i o n The p r i m a r y f i n e s d a i l y f l o w r a t e was a n a l y s e d b o t h g r a p h i c a l l y  and by r e g r e s s i o n w i t h r e s p e c t  to time as e x p r e s s e d by both the day o f  the week and the day o f the month. ed by c o n s e c u t i v e i n t e r g e r s consecutive integers c o u l d be found  The day o f t h e week can be r e p r e s e n t -  from 1 t o 7 and the day o f the month by  from 1 to 30 ( o r 3 1 ) .  In both c a s e s , no c o r r e l a t i o n  and the c o n c l u s i o n was drawn t h a t the p r i m a r y f i n e s  f l o w r a t e was random.  C o n s e q u e n t l y , p r e d i c t i o n o f the f i n e s f l o w r a t e  based around a random number g e n e r a t o r  is  u s i n g the observed mean d a i l y  flow r a t e o f 248.71 tph a t a s t a n d a r d d e v i a t i o n o f 83.88 t p h . I t was found t h a t the p r i m a r y f i n e s samples taken o v e r the s i x day p e r i o d c o u l d 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 e q u a t i o n . T h i s form i s d e s c r i b e d by the Y . 1 °Y . = b e i - i 0  c  b l  equation:  -i - b e 0  b 2 X  i  i = 1 to n-1  (52)  l  where Y - r e p r e s e n t s the c u m u l a t i v e w e i g h t f r a c t i o n f i n e r than C1  s i z e X-j.  The parameters b  0  and b i were found t o be s t r o n g l y  to the day o f the week as e x p r e s s e d by i n t e g e r s was found to be r e l a t e d t o the parameter b . 0  to p r e d i c t these parameters  are:  from 1 t o 7  The r e l a t i o n s  screen  correlated and b  2  developed  - 81 -  b(j = ABS(3.225629 - 2.263788 D + 0.538710 D  2  - 4.088134 x 1 0 D ) _ 2  bi = 1.146195 + 0.72933 D - 0.1829856 D + 1.339609 x 1 0 D 2  _ 2  3  (53) (54)  3  and b  2  = - 4 . 4 9 1 8 6 3 + 5.034085 In ( b )  (55)  0  These r e l a t i o n s are d e p i c t e d g r a p h i c a l l y i n F i g u r e s 24(a)  and 2 4 ( b ) .  T a b l e 8 p r e s e n t s the s a m p l i n g s c h e d u l e f o r the p r i m a r y f i n e s  MON  TUE  WED  THUR  FRI  SAT  stream.  SUN  Day of Week F i g u r e 24(a)  B e h a v i o u r o f P r i m a r y F i n e s Parameters b  -21  Parameter F i g u r e 24(b)  B e h a v i o u r o f P r i m a r y F i n e s Parameter b  2  0  and b i  - 82 -  TABLE 8 Primary F i n e s Sampling Schedule  Sample Number  Sample Date (1975)  PF1  (31)  Aug.  11  -  Aug.  12.'  PF2  (32)  Aug.  13.  PF3  (33)  Aug.  PF4  (34)  PF5 PF6  1  . Monday Tuesday  2  Wednesday  3  14/  Thursday  4  Aug.  15'  F r i day  5  (35)  Aug.  16  Saturday  6  (36)  Aug.  17 /  Sunday  7  (b)  ,  No p r i m a r y d u r i n g day  fines shift  Model A c c u r a c y The p r i m a r y f i n e s  a n o t h e r v a r i a t i o n o f the Appendix I .  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  simultaneous  search  statistical  The program f o r the f i t t e d m o d e l , c a l l e d P F , i s  analysis  o f model performance  than to say t h a t the model p r e d i c t i o n s  (52))  timum v a l u e s  f o r a l l runs. other  On the b a s i s o f the  data  The s i z e d i s t r i b u t i o n  alternative equation  found t o be common t o a l l d a t a s e t s was employed. 0  x  and b  2  and  f o r s i m u l a t i o n purposes.  n o t be e x p l a i n e d i n d e t a i l , an  f o r parameters b , b  A  e x h i b i t e d a mean RSS o f 28.2  c o l l e c t e d , the model i s c o n s i d e r e d s a t i s f a c t o r y  p r i m a r y f i n e s model was c o n s i d e r e d .  also  cannot be p r e s e n t e d ,  a standard d e v i a t i o n o f 19.8 f o r a l l t e s t s .  Although i t w i l l  by  program TURKEY, l i s t e d i n  p r e s e n t e d i n Appendix I , a l o n g w i t h model p r e d i c t i o n s  (equation  Comments  Coded Day + D  Day  were determined  f o r each  Opdata  s e t by d i r e c t s e a r c h methods and a mean and s t a n d a r d d e v i a t i o n f o r each  - 83 -  parameter were d e t e r m i n e d .  These means and s t a n d a r d d e v i a t i o n s may then  be used i n a random number g e n e r a t o r , so t h a t the p r i m a r y f i n e s s i z e a n a l y s i s becomes random i n n a t u r e ,  r a t h e r , than c y c l i c .  In the  absence  o f a s t a t i s t i c a l b a s i s e n a b l i n g a c h o i c e between the two approaches, random v e r s u s c y c l i c ,  the l a t t e r was c h o s e n .  i.e.  - 84 -  CHAPTER V SIMULATION QF THE CRUSHING PLANT  5.1  The S i m u l a t i o n Programs S i m u l a t i o n o f the secondary c r u s h i n g p l a n t i n v o l v e s c o n s t r u c -  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 subprograms o r s u b r o u t i n e s .  The flow diagram f o r the Brenda c r u s h i n g  plant simulation i s depicted i n Figure 25.  As the secondary  are open c i r c u i t , o n l y 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 o f the  c l o s e d t e r t i a r y c r u s h i n g l o o p i s a c c o m p l i s h e d by assuming an t e r t i a r y crusher discharge of zero. the secondary c r u s h e r s  inital  This i s blended with discharge  and the combined stream i s s e n t t o the  where i t i s s p l i t i n t o o v e r s i z e and u n d e r s i z e p r o d u c t s . stream goes t o the t e r t i a r y c r u s h e r s and a new e s t i m a t e crusher i s produced.  crushers  T h i s process i s r e p e a t e d u n t i l  screens  The o v e r s i z e of t e r t i a r y  the combined s c r e e n  u n d e r s i z e f l o w r a t e approaches  the secondary c r u s h i n g p l a n t f e e d r a t e  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 t o  state within fifteen  t o twenty  from  to steady  iterations.  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 s e c o n dary c r u s h i n g p l a n t . p r e h e n s i v e o f t h e two.  The i n i t i a l  program, c a l l e d M2, i s the more com-  I t e n a b l e s c o n t r o l o v e r t h e number o f p r o c e s s  u n i t s f o r a g i v e n 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 control of individual  unit operating settings.  and  Under M2, i t would be  p o s s i b l e t o " o p e r a t e " any o f the f i v e secondary s c r e e n s , each w i t h a d i f f e r e n t screen opening. section.  The program a l s o c o n t a i n s an e x t e n s i v e  However, M2 proved t o be too l a r g e f o r the U . B . C . BASIC  output language  - 85 -  I Simulation Control | I  Data  PLANT  FEED  1  T  J  1  SECONDARY CRUSHER MODEL  l_.  Blend Secondary/Tertiary Crusher Products  TERTIARY CRUSHER MODEL  l SECONDARY  SCREEN  MODEL  L.  L_.  I  PRIMARY FINES MODEL  I I Convergence Determining I Criteria I ,  !_ | I I  Blend S c r e e n U n d e r s i z e / P r i m a r y Fines Products "-ROD  MILL  I  FEED-  1 Output of Plant Operating | I Data I  I  :  1  Figure  25  Simulation  Flow Diagram  - 86 -  c o m p i l e r and c o n s e q u e n t l y it  c o u l d be e x e c u t e d .  temporarily shelved.  required separation  T h i s proved d i f f i c u l t  i n t o f i v e subprograms and c o s t l y , so M2 has  Program M2 i s p r e s e n t e d i n Appendices J ( a )  J ( b ) , w i t h sample o u t p u t s - f o r  before been  and  two s i m u l a t i o n s .  The program M2 was r e p l a c e d 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.  T h i s program s i m u l a t e s  the secondary c r u s h i n g p l a n t on the  t i o n t h a t when two o r more process are e q u a l l y d i v i d e d . identical  u n i t s are i n p a r a l l e l , the feed streams  Furthermore, s i m i l a r process  operating settings.  u n i t s must o p e r a t e w i t h  The o u t p u t s e c t i o n p r e s e n t s o n l y e s s e n t i a l  o p e r a t i n g c o n d i t i o n s and p r o d u c t 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 p r e s e n t e d i n Appendices J ( c ) first  assump-  and J ( d ) .  sample output was performed under, the . s a m e : o p e r a t i n g  The  conditions  as  the f i r s t o u t p u t from M2, thus e n a b l i n g a comparison o f the two programs. The convergence difference  c r i t e r i o n f o r PGM2 i s taken as the  i n f l o w r a t e between the secondary c r u s h i n g p l a n t f e e d and  the combined secondary s c r e e n s u n d e r s i z e currently set feed r a t e .  absolute  product streams.  T h i s value  a t 0.01 tph o r a p p r o x i m a t e l y .0007 p e r c e n t o f the  Choice o f t h i s c r i t e r i o n w i l l  t i o n s t o (and thus r a t e o f . . )  convergence.  is  plant  i n f l u e n c e the number o f  itera-  T h i s and o t h e r s i m u l a t i o n  p a r a m e t e r s , such as the number o f u n i t s t o 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 5.2  itself.  Methodology Employed t o Study the S i m u l a t i o n Program PGM2 To a c q u i r e o u t p u t from the s i m u l a t i o n program PGM2, a f u l l  level  f a c t o r i a l d e s i g n was employed.  A total  of five variables  m a n i p u l a t e d over t h e i r observed o p e r a t i n g ranges t o produce  two-  were  thirty-two  - 87 -  individual  simulations.  and the t o t a l  (2  5  = 32).  The v a r i a b l e s chosen f o r the  study  span o f t h e i r o p e r a t i n g ranges are d e p i c t e d i n T a b l e 9.  Of these v a r i a b l e s , o n l y 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 ble in practice.  However, the c o a r s e s t and f i n e s t s i z e  ( r e s p e c t i v e l y , secondary c r u s h e r t e s t s number obtain endpoint values.  distributions  2 and 5)  were used  The coded d e s i g n m a t r i x f o r t h i s s t u d y i s  to pre-  s e n t e d i n T a b l e 10 and the c o d i n g system i s a v a i l a b l e from Table 9.  TABLE 9 O p e r a t i n g Ranges o f V a r i a b l e s S t u d i e d w i t h Program PGM2  Variable  O p e r a t i n g Ranges S t u d i e d Midpoint High  Low  P l a n t Feedrate P l a n t Feed S i z e Distribution  1255.4 1  1417.1  73.3  (5)  83.6  Unit  1578.8 (4)  92.9  tph (2)  % + 1 inch  Secondary C r u s h e r Gap  2.540  3.16  3.785  cm  Secondary Screen Opening  1.27  1.43  1.59  cm  Tertiary Gap  0.495  0.788  1.080  cm  Crusher  Coded Value  -1  0  +1  The f a c t o r i a l d e s i g n y i e l d s i n f o r m a t i o n r e g a r d i n g the o f the observed d a t a ranges. the i n t e r m e d i a t e  1  ranges.  It is also desirable  —  endpoints  to study b e h a v i o u r i n  To a c c o m p l i s h t h i s , a second s t u d y was  conducted  Plant feed s i z e d i s t r i b u t i o n i s q u a n t i f i e d by the % + 1 inch m a t e r i a l 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 s i z e d i s t r i b u t i o n 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 C r u s h i n g P l a n t S i m u l a t i o n Study  Run Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  Plant Feedrate (tph)  % + 1 inch i n feed (%)  _-,  _-,  1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 =1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1  -1 1 1 -1 _1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1  1  1  Secondary Crusher Gap. (cm)  .-, -1 -1 -1 1 1 1 1  _]  -1 _1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1  Secondary Screen Opening (cm)  Tertiary Crusher Gap. (cm)  _-,  _-,  -1 -1 -1 _1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 _1 -1 _1 _1 -1 -1 1 1 1 1 1 1 1  -1 -1 -1 _"l _1 -1 _1 _1 -1 -1 -1 -1 -1 -1 _1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1  1  - 89 -  a c c o r d i n g t o a n o n - f a c t o r i a l d e s i g n u s i n g the same f i v e The d e s i g n m a t r i x f o r the i n t e r m e d i a t e parts, ate  i s presented  variables.  range s t u d y , performed i n t h r e e  i n coded form i n T a b l e 11.  A l t h o u g h the  intermedi-  range study i s f a r from b e i n g c o m p l e t e , i t s h o u l d p r o v i d e a  suffici-  e n t d e s c r i p t i o n o f s i m u l a t i o n b e h a v i o u r i n the m i d p o i n t r e g i o n f o r purpose o f t h i s  the  thesis.  S t u d i e s were a l s o conducted t o 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 . from these s t u d i e s  v e r i f y what has a l r e a d y been d e s c r i b e d (pages 62 , 66.,  76) c o n c e r n i n g 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. s i m u l a t i o n i s t h e secondary c r u s h e r model. polation restraints  The c o n c l u s i o n s  A weak p o i n t i n the  T h i s model i s bound by e x t r a -  a l r e a d y d e s c r i b e d f o r i t s upper l i m i t s .  dary s c r e e n and t e r t i a r y crushermode .Is 1  The s e c o n -  appear t o 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 t h a t f o r runs where the s i m u l a t i o n e x p e r i e n c e d obvious problems d u r i n g 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 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 t o 5 0 , n e a r l y t h r e e times the otherwise observed.  t o con-  number  T h i s c o n s i s t e n t t r e n d 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 p r o b l e m s .  Problems o c c u r r e d f o r e x t r a p o l a t i o n  o f the secondary c r u s h e r v a r i a b l e s o n l y .  - 90 -  TABLE 11 Coded I n t e r m e d i a t e Range Two-Level Design M a t r i x Used f o r Secondary C r u s h i n g P l a n t S i m u l a t i o n Study  Run Number  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 •18 19 20 21 22 23 24 25 26 27  % + 1 inch i n feed (%) 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 -1  Plant Feedrate (tph)  0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 -1  Secondary Crusher Gap (cm)  0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 1 1 -1 -1 1 1 -1 -1 0 0 0 0  Secondary Screen Opening (cm)  Tertiary Crusher Gap (cm)  0 0 0 0 0 0 0 1 -1 0 0 1 1 -1 -1 0 0 0 0 1 -1 1 -1 0 0 0 0  0 0 0 0 0 0 0 0 0 1 -1 1 -1 1 -1 1 -1 1 -1 0 0 0 0 0 0 0 0  - 91 -  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 A major reason f o r c o n d u c t i n g the study o f the secondary c r u s h i n g  p l a n t s i m u l a t i o n was t o ensure c o r r e c t l y and e f f i c i e n t l y .  t h a t the computer program was f u n c t i o n i n g  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 o p e r a t i n g v a r i a b l e s on p l a n t b e h a v i o r was a l s o c o n d u c t e d , a l t h o u g h the o u t p u t was o b t a i n e d l a r g e l y t o t e s t the performance o f the s i m u l a t i o n over the d a t a ranges sampled. Computer output from PGM2 i s p r e s e n t e d i n Appendices K(a) and K(b).  F o r c o n v e n i e n c e , the p e r t i n e n t  are summarized . i n T a b l e s 12 and 13.  i n f o r m a t i o n from these  outputs  Note t h a t these summary t a b l e s  ( T a b l e s 12 and 13) have n o t been r e p o r t e d i n the same o r d e r as coded d e s i g n m a t r i c e s ( T a b l e s 10 and 11 r e s p e c t i v e l y ) .  their  The o r d e r was  changed t o 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 d e s i g n and t w e n t y -  seven f o r the i n t e r m e d i a t e : ranges d e s i g n .  The average c o s 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 c o s t s a v i n g s  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 i n t e r a c t i v e terminals are considered high p r i o r i t y and charged at a rate f a c t o r of l.h. Batch jobs are r a t e d normal p r i o r i t y , w i t h a r a t e f a c t o r of 1.0 and jobs run between 1 2 : 0 0 pirn, and 6 : 0 0 a.m. are r a t e d low p r i o r i t y , w i t h a rate f a c t o r of o.6'.  - 92 -  TABLE 12 Summary o f Two-Level F a c t o r i a l Design S i m u l a t i o n Study ] NDEPENDENT  Run Number  % + 1 inch in Plant Feed  % 1 2 3 4 5 c 0 7 8 9 10 1 1 12 13 14 15 lb 17 18 19 20 1 c9 1 22 . 23 24 25 26 CI 97 28 29 30 31 00  92.85 92.85 92.85 92.85 92.85 09 OC 3£ . OD 92.85 92.85 92.85 92.85 y<:. 8b no oc 92.85 92.85 92.85 92.85 91.8b no ntz 73.30 73.30 73.30 73.30 "7 o 30 in 73. 73.30 73.30 73.30 73.30 73.30 70 on 15. JU 73.30 73.30 73.30 73.30 / J . on 30 "70  DEPENDENT  Plant Feedrate  Secondary' Crusher Gap  Secondary Screen Gap  Tertiary Crusher Gap  Screen Feedrate  (TPH)  (cm)  (cm)  (cm)  (TPH)  1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 1255.4 iorr A 1578.8 '1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 1255.4 1578.4 1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 1255.4 1578.8 .1255.4 1578.8  2.54 2.54 3.785 3.785 2.54 2.54 3.785 3.785 2.54 2.54 3.785 3.785 2.54 2.54 3.785 3. 785 2.54 2.54 3.785 3.785 2.54 2.54 3.785 3.785 2.54 2; 54 3.785 3.785 2.54 2.54 3.785 3.785  1.27 1.27 1.27 1.27 1.59 1.59 1.59 1.59 1.27 1.27 1.27 1.27 1.59 1.59 1.59 1.59 1.27 1.27 1.27 1.27 1.59 1.59 1.59 1.59 1.27 1.27 1.27 1.27 1.59 1.59 1.59 T.59  -.495 573.76 .495 739.43 .495 637.88 .495 822.14 522.98 .495 .495 675.10 .495 582.82 .495 745.94 1.080 564.92 1.080 727.30 1.080 628.28 1.080 808.60 1.080 513.55 1.080 660.95 1.080 571.45 1.080 731.24 .495 518.59 .495 666.54 .495 566.65 .495 722.88 .495 473.79 .495 . 606.17 .495 514.91 .495 658.69 1.080 511.37 1.080 655.62 1.080 557.77 1.080 711.08 1.080 464.84 1.080 592.90 1.080 507.26 1.080 644.92  % + 1 inch i n Screen Feed  (%) 32.53 32.98 36.71 36.66 40.01 41.51 45.40 45.59 32.25 32.69 36.44 36.48 38.88 40.54 44.47 44.86 28.17 28.63 31.72 31.89 34.91 36.17 38.9 40.23 27.73 28.25 31.37 31.58 34.37 34.93 37.76 39.22  Te r t i a r y Crusher Feedrate (TPH) 403.35 529.59 483.50 632.98 339.88 449.17 414.67 537.72 392.30 514.42 471.50 616.05 328.09 431.48 400.48 519.35 334.39 438.48 394.47 508.92 278.39 363.01 329.78 428.66 325.36 424.83 383.36 494.15 267.20 346.42 320.22 411.45  % + 1 inch in Tertiary Crusher Feed  (%)  57.96 57.57 60.54 59.52 76.95 77.99 79.75 79.06 58.05 57.77 60.70 59.86 76.07 77.63 79.32 78.95 54.6 54.40 56.96 56.63 74.27 75.49 75.92 77.27 54.49 54.49 57.05 56.81 74.74 74.73 74.77 76.84  i  56-1/2 inch in Screen Undersize  (%) 79.51 79.87 79.11 80.56 61.38 64.24 63.38 64.39 80.00 80.03 79.57 80..85 60.35 64.18 63.02 64.43 80.09 79.80 79.07 79.54 61.30 63.64 59.87 63.53 80.48 80.31 79.59 80.00 63.42 63.39 58.15 63.44  Screen Efficiency  Plant Reduction Ratio  Circulating Load  {%) 97.10 96.90 97.55 97.05 97.40 97.25 97.75 97.55 97.95 96.80 97.45 97.00 97.30 97.15 97.70 97.45 96.50 96.40 97.05 96.80 96.95 96.85 97.40 97.25 96.35 96.25 96.95 96.70 96.95 96.85 97.30 97.25  32.45 32.60 32.29 32.88 25.05 26.22 ' 25.87 26.28 32.65 32.78 32.48 33.00 24.63 26.20 25.72 26.30 5.68 5.66 5.61 5.64 4.35 4.51 4.25 4.51 5.71 5.70 5.64 5.67 4.50 4.50 4.12 4.50  1.29 1.34 1.54 1.60 1.08 1.14 1.32 1.36 1.25 1,30 1.50 1.56 1.05 1.09 1.28 1.32 1.07 1.11 1.26 1.29 0.39 0.92 1.05 1.09 1.04 1.08 1.22 1.25 0.85 0.88 1.02 1.04  Secondary Crusher Current  Tertiary Crusher Current,  (Amperes)  (Amperes)  23.68 29.26 14.56 20.15  57.96 57.57 49.60 57.88  29.26 14.56 20.15 23.68 "14.56 20.15 23.68 29.26 14 <ifi 1 T • JU 20.15 23.68 29.26 14.56 ?0 IS 23.68 29.26 14.56 20.15 23.68 29.26 14.56 20.15 23.68 29.26 14 56 20.15  i  *t 1 . Oh 47.69 45.78 52.60 38.92 40. j &K0 AO 43.31 51.32 35.36 41.09 oy • j / 45.95 41.33 47.10 44.66 c i ni J1.U1 38.23 42.92 41.08 46.56 35.21 40 7? 38.43 44.57 31.99 36.38 O.A 0 0 39.98  - 93 -  TABLE.13 Summary o f Two-Level- Intermediate Ranges Design Simulation Study INDEPENDENT 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  % + 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  Secondary Crusher Gap  Secondary Screen Opening  Tertiary Crusher Gap  Screen Feedrate  (TPH)  (cm)  (cm)  (cm)  (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  141771  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  1X76  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  .788 .788 .788 .788 .788 .788 1.080 .495 .495 1.080 1.080 .495 1.080 .495 .788 .788 .788 .788 .788 .788 .788 .788 .788 .788 1.080 .495 ,788  604.58 680.33 531.32 539.60 603.26 475.70 590.21 662.41 604.59 650.68 672.87 684.38 621.19 632.02 580.00 644.41 538.49 594.31 663.00 519.32 629.07 580.46 544.84 604.78 632.84 644.49 590.44  % + 1 inch i n screen Feed  Tertiary Crusher Feedrate (TPH)  33.24 33.47 32.88 27.70 27.98 27.52 39.66 32.12 40.83 31.74 35.86 36.29 32.64 33.15 38.92 33.53 34.54 30.19 31.73 31.34 34.52 31.05 35.39 30.68 33.10 33.66 31.58  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  DEPENDENT % -i- 1 inch in T e r t i a r y Crusher Feed  % - l / 2 inch in Screen Undersize  ',%) 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  Screen Efficiency  Plant Reduction Ratio  Circulating Load  (%) 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  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  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 17.13  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 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  Tertiary Crusher Current  (Amperes)  (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 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 43.93 40.56 38.10 42.25 41.3947.79 41.25  - 94 -  All  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 e v i d e n c e o f  convergence p r o b l e m s .  T h i s o b s e r v a t i o n i s f u r t h e r enhanced by the  a t which the s i m u l a t i o n s converged t o s t e a d y - s t a t e , i t e r a t i o n s , w i t h an average o f t e n .  speed  a l l w i t h i n twenty-two  There are f o u r o p e r a t i n g v a r i a b l e s  whose v a l u e s are generated by t h e s i m u l a t i o n around the t e r t i a r y c r u s h i n g loop  and o v e r which t h e 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 d u r i n g the e x p e r i m e n t a l .phase o f the p r o j e c t and i n c o r p o r a t e d i n t o the models. crusher feedrate  Of t h e s e v a r i a b l e s , o n l y the  tertiary  was observed t o exceed the f i t t e d data r a n g e .  Seven r u n s ,  or f o u r t e e n p e r c e n t 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 p e r c e n t .  These seven t e s t s were t r e a t e d  with  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 a n a l y s e s . feedrate,  The r e m a i n i n g t h r e e v a r i a b l e s , secondary s c r e e n  and p e r c e n t +1 i n c h i n the s c r e e n and t e r t i a r y c r u s h e r f e e d s , were  found t o 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 . C r u s h i n g p l a n t b e h a v i o u r may be measured by the f o l l o w i n g dent v a r i a b l e s ( c a l l e d  depen-  responses):  (1)  percent -1/2 inch material i n p l a n t product  (2)  plant reduction r a t i o  (3)  c i r c u l a t i n g load r a t i o  (4)  secondary s c r e e n  f o r the t e r t i a r y c r u s h i n g l o o p .  efficiency  1  The term " t e r t i a r y crushing loop" i s used t o 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  stream from the secondary s c r e e n s .  feed)  i s taken to be the  undersize  The p l a n t r e d u c t i o n r a t i o , a l t h o u g h  s t r i c t l y s p e a k i n g n o t a t r u e r e d u c t i o n r a t i o , can be used as a measure o f both the p l a n t work o u t p u t and p l a n t e f f i c i e n c y duction.  i n terms o f s i z e r e -  T h i s response i s d e f i n e d i n t h i s study as the n _ p e r c e n t - 1/2 i n c h i n p l a n t p e r c e n t - 1/2 i n c h i n p l a n t  ratio:  product feed  The p r i m a r y f i n e s s t r e a m has been n e g l e c t e d f o r these  studies,  because  i t has no i n f l u e n c e on the b e h a v i o u r o f the secondary c r u s h i n g  plant.  However, the p r i m a r y f i n e s w i l l  i n f l u e n c e the feed to the  fine  ore b i n s . F o r the purpose o f t h i s s t u d y , the screen opening i s d e f i n e d as the w i d t h o f the s l o t s i n the l o w e r screen deck. form l e n g t h o f 3-1/2 i n c h e s . screen  These s l o t s have a u n i -  The screen opening i s used synonymously w i t h  aperture. The s c r e e n e f f i c i e n c i e s are n o t o u t p u t t e d by t h e s i m u l a t i o n p r o -  gram and have been computed s e p a r a t e l y f o r both study d e s i g n s .  F o r 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 T a b l e s 12 and 13.  The  s c r e e n 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 r e s p e c t to the p r e d i c t e d o v e r s i z e product  1  by the s t a n d a r d A l l i s - C h a l m e r s p r o c e d u r e  2  o u t l i n e d i n the  1  The screen e f f i c i e n c i e s are computed w i t h respect t o the oversize product because the screen e f f i c i e n c y equation (equation ) i s defined i n terms of t h i s same product. Screen e f f i c i e n c i e s computed w i t h respect to the undersize product are t y p i c a l l y i n the range o f 77 to 78 percent"when computed by the A l l i s - C h a l m e r s method. These lower e f f i c i e n c i e s are b e l i e v e d to be due to the rectangular screen openings p e r m i t t i n g passage of slabby or p l a t y p a r t i c l e s .  2  This procedure i s summarized as f o l l o w s : (1) obtain a sample o f the d e s i r e d screen product (2) determine the percentage of misplaced m a t e r i a l ( i . e . undersize m a t e r i a l i n the oversize product) (3) subtract t h i s value from 100 to obtain screen e f f i c i e n c y  i n percent,  - 96 -  publication "Screening Machinery"  v  .  The amount o f m a t e r i a l i n the  o v e r s i z e p r o d u c t p a s s i n g the d e s i g n a t e d s c r e e n opening was determined graphically. (b)  Plant  Feedrate  The i n f l u e n c e o f p l a n t f e e d r a t e F i g u r e 26.  The p l a n t f e e d r a t e  on responses  does n o t appear t o 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 e d u c t i o n r a t i o , s c r e e n e f f i c i e n c y o f the f i n a l  product.  o r the s i z e q u a l i t y  However, i t does e x e r t a s m a l l i n f l u e n c e on the  c i r c u l a t i n g l o a d r a t i o , which i n c r e a s e s feedrate.  is depicted in  T h i s i s n o t an unreasonable  s l i g h t l y with increasing plant o b s e r v a t i o n i f the c l o s e d t e r t i a r y  c r u s h i n g l o o p does n o t approach i t s maximum c a p a c i t y .  S i n c e the s i m u l a -  t i o n s t u d y was conducted w i t h i n the data ranges o v e r which t h e s c r e e n model was f i t t e d and the s c r e e n e f f i c i e n c i e s are both high and c o n s t a n t , reasonable is "clean".  to assume t h a t n e g l i f i b l e b l i n d i n g  o c c u r s and the screen  The i n c r e a s e i n c i r c u l a t i n g l o a d r a t i o may then be  t i o n s made d u r i n g s a m p l i n g .  is split  attributed  t o d e t e r i o r a t i o n o f c r u s h i n g a c t i o n w i t h i n the secondary c r u s h e r s the i n c r e a s i n g p l a n t f e e d r a t e .  it  with  T h i s h y p o t h e s i s i s s u p p o r t e d by o b s e r v a I t i s b e l i e v e d t h a t the secondary  are n e a r i n g t h e i r p h y s i c a l l i m i t s a t the upper f e e d r a t e  crushers  t e s t e d and t h a t  t h e i r c r u s h i n g a c t i o n may be d e t e r i o r a t i n g due t o crowding phenomena. T h i s would r e s u l t i n a c o a r s e r p r o d u c t a t h i g h e r f e e d r a t e s and thus a s l i g h t b u i l d u p i n the c i r c u l a t i n g l o a d . 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 i n c r e a s e s because the  t e r t i a r y c r u s h e r f e e d r a t e s are s t i l l  1  T e r t i a r y crushing action should increased  w i t h i n the p h y s i c a l l i m i t s of. the machines.  The term "binding" i s used i n the sense of physical.blockage of screen apertures by e i t h e r wedging of p a r t i c l e s between c l o t h wires or buildup of layers of p a r t i c l e s preventing access to the screen deck.  100i  MOO  38-\  •1.4 95  95  a 90-^  90  H.3  U  §85^  r85  h-2 n S3 n m c m o  80  i ^  z m Q -n 3! H.1 n O m > D 75 ^ -< 3J  8  X  u  75 \  >  CM  M.o g  z 70 hi O  70  a:  UJ  12  a  65-^  °/o+1 Inch in Plant Feed =83.6 Secondary Crusher Gap =3.16 cm Secondary Screen Opening = 1.43 cm Tertiary Crusher Gap =.788 cm  10 8-I  Y65  r60  601 1220 1240 ' 1260 'l280 1300' 1320 ' 1340 ' 1360 1380' 1400 ' l 4 2 0 ' 1440 ' 1460 14*80' 1500 1520 1540 1560 1580 1600 . PLANT FEEDRATE (tph) 1  1  Figure 26  1  1  The I n f l u e n c e o f P l a n t Feedrate on S i m u l a t i o n  1  1  Responses  1  1  1  r.9  - 98 -  (c)  P l a n t Feed S i z e  Distribution  In most c r u s h i n g p l a n t s , the o p e r a t o r has no e x p l i c i t c o n t r o l o v e r 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 i m p o r t a n t  v a r i a b l e and a l t h o u g h not c o n t r o l l a b l e , i t s i n f l u e n c e s h o u l d be known. F i g u r e 27 d e p i c t s the e f f e c t o f the p e r c e n t p l u s 1 i n c h 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 c o a r s e n e s s )  s i z e appears t o have l i t t l e the q u a l i t y o f the f i n a l if,  on the r e s p o n s e s .  The feed  i n f l u e n c e on e i t h e r the s c r e e n e f f i c i e n c y  product.  T h i s i s n o t an unreasonable  or  observation  as i s the case f o r t h i s s t u d y , the u n i t s around the t e r t i a r y c r u s h i n g  l o o p do n o t 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 s h o u l d n o t change a p p r e c i a b l y i f the s c r e e n e f f i c i e n c y constant  remains  (which i t does) and the t e r t i a r y c r u s h i n g a c t i o n does n o t  deteriorate. F i g u r e 27 i n d i c a t e s a c o n s i d e r a b l e i n c r e a s e i n p l a n t r e d u c t i o n r a t i o w i t h i n c r e a s i n g p l a n t feed s i z e .  T h i s i s t o be e x p e c t e d because  the  p l a n t must work h a r d e r t o reduce the c o a r s e r feed to the same p a s s i n g s c r e e n size.  S i m u l t a n e o u s l y , the i n c r e a s i n g p l a n t feed s i z e would produce a  c o a r s e r secondary c r u s h e r p r o d u c t and thus i n c r e a s e the c i r c u l a t i n g l o a d r a t i o ( as o b s e r v e d i n F i g u r e 2 7 ) . (d)  Secondary C r u s h e r Gap The i n f l u e n c e o f the secondary c r u s h e r gap on responses i s de-  p i c t e d in Figure 28.  The c r u s h e r gap has v i r t u a l l y no e f f e c t  reduction r a t i o , screen e f f i c i e n c y  o r the f i n a l  However, i t does e x e r t a s u b s t a n t i a l  upon p l a n t  product s i z e q u a l i t y .  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 r u s h e r gap produces a c o a r s e r c r u s h e r  product,  100i  r  38  100  36 95  •1.4 95  34 32  U 90i  a O or  30 28  -  Q. 85^  z  -  I-85  26  CV)  eg  80  z 22 O  K  18  \  16  Z UJ  u  n c  m -n  z D O >  H.o 5 70  14 Plant F e e d r a t e Secondary ' Crusher Secondary Screen Tertiary Crusher  12 65-  23  o m z 75 o  or  LJ 70Q-  -1.2 o  31 M.1  §20 a  75 ^ UJ  O 2 m z  I-  5 24 or  J801  -1.3  •90  10  =1417.1 tph Gap . = 3.16 cm Opening = 1.43 cm Gap = . 7 8 8 cm  65  h.9  8 r60  60 "70  1  72 )&74  F i g u r e 27  I 76 ' 78 PERCENT t1  1  80 INCH  1  82 84 IN PLANT 1  1  The I n f l u e n c e o f P e r c e n t +1.Inch  86 FEED  88  1  in Plant-Feed  90  92  94  on S i m u l a t i o n  96 Responses  98  100  ^.8  r100  381 36H95  34| —I  32Y90  30• 28-  85  in  26-  n  O < 24-  m m z  XI  80  z 22^ O h^ 201  r-  Q LU K  m -n -11 3! n m  181 -Q-  iz 16 <  -o70  14-1 12-  Plant Feedrate =1417.1 tph °/ +1 inch in Plant Feed. . = 8 3 . 6 Secondary Screen Opening 1.43 cm T e r t i a r y Crusher Gap =.788 cm 0  101  F65  =  8r60 2.4  2.5 T' 2.6  1  2.7  1  F i g u r e 28  2.8 2.9 10 SECONDARY 1  1  1  3.'l 3.2 CRUSHER 1  1  3.3 3!4 GAP 1  1  3.5  1  3.6  1  3.7  1  3.8  (cm)  The I n f l u e n c e o f Secondary C r u s h e r Gap on S i m u l a t i o n  Responses  3.9  1  4.0  3  -2  M  - 101 -  which i n t u r n r e s u l t s  i n an i n c r e a s e i n the c i r c u l a t i n g l o a d .  I f the  c l o s e d t e r t i a r y c r u s h i n g l o o p i s n o t o p e r a t i n g n e a r i t s maximum c a p a c i t y , then i t w i l l  be capable o f a b s o r b i n g and b r e a k i n g the a d d i t i o n a l l o a d  imposed by the secondary c r u s h e r s .  This behavior w i l l  s t a n t p l a n t reduction r a t i o , screen e f f i c i e n c y q u a l i t y , independent o f the secondary c r u s h e r The  r e s u l t i n a con-  and f i n a l  product s i z e  performance.  a b i l i t y o f one o r more p r o c e s s u n i t s t o a c 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 o p e r a t i o n i s an i m p o r t a n t p r o p e r t y o f any c i r c u i t .  unit  In the Brenda s e c o n -  dary c r u s h i n g p l a n t , the t e r t i a r y c r u s h i n g l o o p i s capable o f compensating for  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  performance.  Such compensation was o b s e r v e d f o r changes i n p l a n t  s i z e when the f i n a l cant changes  crusher  p r o d u c t s i z e q u a l i t y was m a i n t a i n e d d e s p i t e  feed  signifi-  i n p l a n t r e d u c t i o n r a t i o and: c i r c u l a t i n g l o a d (see F i g u r e 2 7 ) .  W i t h i n the t e r t i a r y c r u s h i n g l o o p the u n i t o p e r a t i o n s a l s o have some mut u a l a b i l i t y t o compensate f o r performance changes i n each o t h e r , discussed (e)  as  later. Secondary Screen Opening The  secondary screens appear to e x e r t the most marked  upon c r u s h i n g p l a n t performance, as i l l u s t r a t e d i n F i g u r e 2 9 .  effects Referring  to the f i g u r e , as the screen opening i n c r e a s e s , the u n d e r s i z e ( f i n a l ) p r o d u c t f i n e s s must o b v i o u s l y d e c r e a s e ( i . e . becomes c o a r s e r ) .  This  enables  more m a t e r i a l to be d i s c h a r g e d from the t e r t i a r y c r u s h i n g 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 p r o d u c i n g a c o a r s e r  p r o d u c t , l e s s work i s r e q u i r e d f o r s i z e r e d u c t i o n and the p l a n t r e d u c t i o n r a t i o must a l s o  decrease.  F i g u r e 29  The I n f l u e n c e o f Secondary Screen Opening on S i m u l a t i o n Responses  - 103 -  The screen opening appears t o e x e r t a s m a l l i n f l u e n c e on s c r e e n efficiency,  c a u s i n g a minimum t o o c c u r a t the middle o f t h e . s t u d i e d  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  w i t h c e r t a i n t y whether the e f f e c t openings o r t o c o m p u t a t i o n a l (f)  error.  to d i f f e r e n t  stated  screen  1  T e r t i a r y C r u s h e r Gap S u r p r i s i n g trends  altered.  is attributable  range.  These t r e n d s  are observed when the t e r t i a r y c r u s h e r gap i s  are d e p i c t e d i n F i g u r e 30.  C l e a r l y , an "optimum"  o p e r a t i n g s e t t i n g i s i n d i c a t e d i n the m i d p o i n t r e g i o n .  A n a l y s i s o f the  computer o u t p u t c o n f i r m s t h a t the t e r t i a r y c r u s h e r p r o d u c t 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. h a v i o r o f the t h r e e r e s p o n s e s , r a t i o and f i n a l  The be-  plant reduction r a t i o , c i r c u l a t i n g load  p r o d u c t s i z e i s such t h a t :  (a) ., as t h e - f i n a l p r o d u c t " b e c o m e s , f i n e r , . m o r e r w o r k i s r e q u i r e d f o r breakage and the p l a n t r e d u c t i o n r a t i o i n c r e a s e s s l i g h t l y (b)  f o r a f i x e d s c r e e n o p e n i n g , more m a t e r i a l l e a v e s the t e r t i a r y c r u s h i n g l o o p as the f i n a l p r o d u c t becomes f i n e r , hence the c i r c u l a t i n g l o a d decreases  These o b s e r v a t i o n s c o i n c i d e w i t h e x p e c t e d 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 t h r e e responses c r u s h e r gap (see F i g u r e 3 0 ) . ppears t o decrease  as a f u n c t i o n o f the  Note t h a t s c r e e n e f f i c i e n c y s i m i l a r l y  v e r y s l i g h t l y n e a r the m i d p o i n t o f the range  studied.  The maxima/minima t r e n d s may be caused by changes i n the of near-screen-size  a-  amount  m a t e r i a l produced by changes i n the c r u s h e r 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 t o the s c r e e n opening may be measured by the  1  ratio:  Computational e r r o r arises during g r a p h i c a l approximation of the amount of undersize m a t e r i a l i n the oversize product. This e r r o r i s b e l i e v e d to be of the order of 0.2 to 0.5 percent.  100i  100  38 36H  951  M.4 te5  34 32  .901 U  -1.3  90  30 ~ 28  z>  Q  °851 a. < z ^80z  85  26 < 24{ |  80  22H  |_ ^20i  u z rvj  75-  Q UJ  </> M.2 O O 3D SJ o m c m z m JJ n m  (J70ir UJ  14  a.  1265-  108  D -1.0  7 0 „°  Plant Feedrate °/ +1 Inch in Plant Feed Secondary Crusher Gap Secondary Screen Opening 0  =1417.1 tph = 83.6 = 3.16 cm =1.43 cm  65  60H  60 T  —i—  .5  F i g u r e 30  • .6 TERTIARY  .7 CRUSHER  The I n f l u e n c e o f T e r t i a r y  .8 GAP  .9  (cm)  C r u s h e r Gap" on S i m u l a t i o n  1,0 Responses  1.1  o  O >  r75 O -<  181 < 16  H Z UJ  11  5  -  105 -  ^ _ c u m u l a t i v e p e r c e n t p a s s i n g screen opening i n screen feed c u m u l a t i v e p e r c e n t r e t a i n e d on screen opening s i z e i n s c r e e n  feed  2 The  b e h a v i o r o f t h i s r a t i o i s d e p i c t e d i n F i g u r e 31(a)  .  Clearly,  a maximum i s n o t e d t o o c c u r i n the m i d p o i n t r e g i o n o f the t e r t i a r y gap range s t u d i e d .  crusher  This indicates that l a r g e r quantities of material  are  p a s s i n g the s c r e e n opening i n the m i d p o i n t r e g i o n o f the c r u s h e r gap than are p a s s i n g a t the e r i d p o i n t r e g i o n s . near-screen-size  In o t h e r w o r d s , t h e r e must be more  m a t e r i a l b e i n g produced f o r a gap o f 0.788 cm. than  e i t h e r 0.495 cm. o r 1.080 cm.  The use o f s l o t t e d screens  for  i n the l o w e r  screen deck p e r m i t s 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 l a b b y 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 s i z e ranges).  Thus, if-more h e a r - s c r e e n - s i z e - m a t e r i a l  duced, more w i l l  pass.  Both the p e r c e n t - 1 / 2 i n c h ,  and the p l a n t r e d u c t i o n r a t i o w i l l ratio will ial  decrease.  (near-screen-  i s being-pro-  i n the f i n a l  product  i n c r e a s e w h i l e the c i r c u l a t i n g l o a d  F u r t h e r m o r e , i f the amount o f n e a r - s c r e e n - s i z e  r i s e s t o a maximum and then d e c r e a s e s ,  the responses  mater-  must f o l l o w  the  trend accordingly. The  ratio A (near-screen-size  m a t e r i a l ) a l s o appears t o be i n -  f l u e n c e d by the s c r e e n o p e n i n g , as i n d i c a t e d i n F i g u r e 3 1 ( b ) . n o t an unreasonable  This  is  o b s e r v a t i o n c o n s i d e r i n g t h a t " A " i s computed w i t h  r e s p e c t t o the s c r e e n o p e n i n g .  A g a i n , a maximum i s observed n e a r  m i d p o i n t o f the range o f screen openings s t u d i e d .  This indicates  the that  1  Values of cumulative percent passing and r e t a i n e d on the opening s i z e were computed g r a p h i c a l l y .  screen  2  The screen feed represents the combined secondary and t e r t i a r y crusher products. However, as the secondary crusher p r o d u c t - i s constant for a given s i m u l a t i o n , 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 F i g u r e 31(a)  CRUSHER  GAP  (cm)  B e h a v i o r o f R a t i o A as a F u n c t i o n o f T e r t i a r y C r u s h e r Gap  .701  —.  1.25  1  Figure  >  1.30.  31(b)  1  1  1.35  1  '  1.40 PARTICLE  1  1  1.45 SIZE  1  '  1.50 (cm)  1  >  1.55  B e h a v i o r o f R a t i o A as a F u n c t i o n o f P a r t i c l e Size  1  •  1.60  1  1—  1.65  -  - 107 -  regardless  o f the gap s e t t i n g , the t e r t i a r y c r u s h e r s tend t o produce  a p r o d u c t 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 s c r e e n opening o f 1.43 cm. may n o t n e c e s s a r i l y be an "optimum" f o r p l a n t o p e r a t i o n because o f the i n f l u e n c e o f o t h e r  factors.  These o b s e r v a t i o n s have an i m p o r t a n t impact on c r u s h i n g p l a n t operation.  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 r u s h e r gap  i s i n d i c a t e d c l o s e t o 0.800 cm.  T h i s v a l u e i s "optimum" f o r the  following  reasons: (a)  a maximum p r o d u c t f i n e n e s s  is indicated  (b)  a minimum c i r c u l a t i n g l o a d 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 l o a d r a t i o means a maximum c a p a c i t y t o absorb c h a n g e s i i n 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 operation.  crusher  F u r t h e r m o r e , the "optimum" e f f e c t o f t e r t i a r y c r u s h e r gap  appears t o be i n f l u e n c e d by the s c r e e n opening s i z e .  By o p e r a t i n g a t an  "optimum" c o m b i n a t i o n o f c r u s h e r gap and s c r e e n o p e n i n g , i t may be p o s s i b l e t o 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 fineness  and  plant 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 m a n i p u l a t e d 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 d e s i g n study and are i n c l u d e d i n Appendix L .  For c o n v e n i e n c e , these e f f e c t s  to magnitude and are p r e s e n t e d  have been ranked a c c o r d i n g  i n T a b l e 14.  A measure o f pure e r r o r f o r the c r u s h i n g p l a n t i s n o t . a v a i l a b l e , so t h e r e i s no means t o 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 ficant.  are  signi-  The c u t - o f f p o i n t f o r d e t e r m i n i n g 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 f e c t s o f Simulation V a r i a b l e s on Responses % - l / 2 inch in Product Variable Code  Effect  4 1 1/4 2/3 1/2/3/4 1/2/3 2 2/3/4 2/4 1/3 1/2/4 4/5 2/3/4/5 1/2/3/4/5 1/2/3/5 2/3/5 1/3/4/5 3 1/3/5 3/5 3/4/5 1/2/4/5 5 1/2/5 2/5 2/4/5 1/3/4 1/2 1/4/5 1/5 3/4  -17.2838 1.5113 1.035 .92 -.7275 -.6363 .595 .5588 .4838 .3613 -.32 -.3063 .2938 -.29 -.2813 .2625 .2325 -.235 .1963 -.1875 -.1763 .15 .1375 .1138 -.105 -.0789 -.065 .0513 .05 .0288 .0238  P l a n t Reduction Ratio Variable Effect Code  Ci rcul a t i n g Load Ratio Variable Effect Code  Variable Code  Effect  2 24.1781 4 -4.0581 2/4 -2.7994 1 .3719 .2681 1/2 .1944 1/4 1/2/3/4 -.1856 2/3 .1819 2/3/4 .1369 1/3/4 -.1369 3/4 .1006 1/2/4 .0981 3 .0981 1/2/3 .0931 -.0869 4/5 2/4/5 -.0706 1/2/4/5 .0444 2/3/4/5 .0406 1/4/5 .0381 1/2/3/5 -.0344 2/3/5 .0331 1/2/5 .0319 1/2/3/4/5 -.0294 .0281 1/5 1/3 -.0219 5 .0156 1/3/4/5 .0069 3/4/5 .0069 3/5 -.0031 1/3/5 -.00063 2/5 .00063  2 3 4 1 5 2/3 2/4 3/4 1/2 1/2/3/4 1/4 2/3/4 1/2/3/5 1/2/3/4/5 1/4/5 1/5 1/3 1/2/3 1/2/4 1/3/4 2/5 3/5 4/5 2/3/5 2/4/5 3/4/5 2/3/4/5 1/2/4/5 1/2/5 1/3/4/5 1/3/5  2 4 3 1 2/3 1/2 2/4 1/4 2/3/4 2/4/5 1/2/4 2/3/4/5 1/2/3/4/5 1/3/5 1/2/5 . 1/4/5 1/3/4/5 1/2/3/4 1/5 2/5 3/5 2/3/5 1/2/3/5 1/2/4/5 3/4/5 3/4 1/2/3 4/5 5 1/3/4 1/3  .4719 .3469 .3281 -.2594 .1281 -.1219 -.1219 .1156 .0906 -.0844 .0781 .0719 -.0719 .0656 -.0656 .0594 -.0594 -.0531 -.0531 .0531 -.0531 -.0531 .0531 .0469 .0469 .0406 .0344 -.0344 -.0219 -.0156 -.0031  .2475 .2075 -.2075 .0413 -.03875 .035 -.01 -.01 .00875 -.00375 -.00375 -.0025 .0025 .0025 -.0025 -.0025 -.00125 .00125 -.00125 -.00125 -.00125 -.00125 -.00125 .00125 .00125 .00125 -.00125 2.78xl0" -2.78xl00 0  Screen E f f i c i e n c y  1 7 1 7  Key t o V a r i a b l e Code 1 2 3 4 5  = = = = =  Factor Factor Factor Factor Factor  code code code code code  for for for for for  P l a n t Feedrate % + 1 inch i n P l a n t Feed Secondary Crusher Gap Secondary Screen Opening T e 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 b a s i s o f the e f f e c t ' s sharp changes  i n the magnitude o f a d j a c e n t  effects  magnitude  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 o n l y p o s s i b l e to i n f e r significance of a specified The e f f e c t s  i n d i c a t e d i n T a b l e 13 t e n d t o c o n f i r m the presented  upon the  relationship with final  findings  and a l l i n t e r a c t i o n  However, some o f the e f f e c t s  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 ) , are no sharp d i f f e r e n c e s  final  T h i s c o n f i r m s the  from F i g u r e 29 (page 102).. The r e m a i n i n g main e f f e c t s appear to be i n s i g n i f i c a n t .  trends  i n F i g u r e s 26  The o n l y 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  p r o d u c t s i z e appears t o be the screen o p e n i n g .  effects  the  effect.  a l r e a d y observed f o r the f i v e main e f f e c t s through 30.  and  with  but as t h e r e  between the magnitudes o f these e f f e c t s ,  their  p r o d u c t s i z e may be complex.  The p l a n t r e d u c t i o n 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 p e r c e n t  +_1  i n c h i n p l a n t feed and s c r e e n o p e n i n g .  i s c l e a r l y observed i n F i g u r e s 27 (page 9.9 ) and 29 ( p a g e ! 0 2 ) .  This trend 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 t o be s i g n i f i c a n t . other effects  All  are judged t o 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 p e r c e n t + 1 i n c h i n p l a n t f e e d , secondary c r u s h e r gap and secondary screen o p e n i n g , as a l s o observed i n F i g u r e s 2 7 , 28 (page 100) and 2 9 . Other e f f e c t s gap.  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  crusher  However, t h i s c o n t r a d i c t s t h e maxima/minima t r e n d s observed i n  F i g u r e 30 (page~104)\  The c o n t r a d i c t i o n may o c c u r because these t r e n d s  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 m i d p o i n t o f the  - no v a r i a b l e range s t u d i e d .  The method f o r . computing e f f e c t s  a l i n e a r b e h a v i o r o v e r the range.  assumes  S i n c e the computations i n v o l v e  the  e n d p o i n t s , the maxima/minima b e h a v i o r f o r the t e r t i a r y c r u s h e r gap i s not n o t i c e d . The magnitudes o f e f f e c t s  on the s c r e e n e f f i c i e n c y are s m a l l  and sharp changes i n magnitude are not n o t e d . screen e f f i c i e n c y  This indicates that  the  may be l a r g e l y independent o f the o p e r a t i n g v a r i a b l e s  o v e r the ranges t e s t e d .  T h i s o b s e r v a t i o n tends t o c o n f i r m the  i n d i c a t e d i n F i g u r e s 26 through 30.  I f the l a r g e r e f f e c t s a r e  trends signifi-  c a n 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 a s p e c t o f t h i s study n o t y e t c o n s i d e r e d i s t h e  c u r r e n t draw.  The c u r r e n t draws f o r both secondary and t e r t i a r y  are p r e d i c t e d from an e q u a t i o n o f the C = a  crusher  0  form:  - a G + a T x  crushers  ( 3 7 , 43)  2  T h i s e q u a t i o n i n d i c a t e s t h a t c r u s h e r c u r r e n t decreases w i t h i n c r e a s i n g gap, i n c r e a s e s w i t h f e e d r a t e bution.  and i s independent o f the feed s i z e  The b e h a v i o r o f the t e r t i a r y c r u s h e r c u r r e n t v e r s u s  distri-  feedrate  a t d i f f e r e n t gaps i s p r e s e n t e d i n F i g u r e 3 2 . I t may be assumed t h a t the t e r t i a r y c r u s h e r f e e d r a t e  can be  e x t r a p o l a t e d ten p e r c e n t beyond the upper l i m i t o f i t s f i t t e d d a t a T h i s i s n o t an unreasonable assumption c o n s i d e r i n g t h a t the  range.  crusher  u t i l i z e s a c o a r s e concave w i t h the mantle m o d i f i c a t i o n s d e p i c t e d i n F i g u r e 5 (page 1 4 ) . T h i s assumption i s p e r t i n e n t t o the e n s u i n g d i s c u s s i o n .  - in -  F i g u r e 32  B e h a v i o r o f T e r t i a r y C r u s h e r C u r r e n t Draw as a F u n c t i o n o f Feedrate f o r C o n s t a n t Gap  -  The t e r t i a r y  crushers  draw o f 42.0 amperes.  112 -  are p r e s e n t l y r a t e d a t a maximum c u r r e n t  However, F i g u r e 32 i n d i c a t e s t h a t an i n c r e a s e  crusher current w i l l  enable an i n c r e a s e  in capacity throughput,  with  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 . maximum s u s t a i n a b l e increases  If a  c u r r e n t draw o f 47 amperes were p o s s i b l e , the  i n d i c a t e d would be s u b s t a n t i a l .  in  capacity  The i n d i c a t e d c a p a c i t y i n -  c r e a s e s assuming a ten p e r c e n t f e e d r a t e . e x t r a p o l a t i o n and a 47 ampere c u r r e n t draw are p r e s e n t e d  i n T a b l e 15 and g r a p h i c a l l y i n F i g u r e 3 3 .  . TABLE 15 I n d i c a t e d C a p a c i t y I n c r e a s e s f o r T e r t i a r y Crushers  C r u s h e r Gap (cm..)  Maximum Current Increase (amperes)  Maximum Indicated Capacity I n c r e a s e (tph)  Maximum Indicated Capacity I n c r e a s e 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 n o t known whether the e x i s t i n g 300,. Hp" motors w i l l under a c o n t i n u o u s c u r r e n t draw o f 47 amperes, will  sustain  currents  but i t i s known t h a t they  as h i g h as 49.3 amperes f o r s h o r t p e r i o d s .  o b s e r v a t i o n i n d i c a t e s t h a t i t may be p o s s i b l e t o i n c r e a s e c o n t i n u o u s c u r r e n t draw f o r the t e r t i a r y motors.  c u r r e n t r a t i n g o f 48 amps. mit  the maximum  Hp  secondary  crush-  These have a maximum c o n t i n u o u s  S u b s t i t u t i o n o f the l a r g e r motors would p e r -  the h i g h e r c u r r e n t draws proposed w h i l e s t i l l  margin.  This  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 m o t o r s , such as the 350 e r m o t o r s , may be a v i a b l e a l t e r n a t i v e .  operate  maintaining a small  safety  - 113 -  Current Increase (amperes) F i g u r e 33  I n d i c a t e d C a p a c i t y I n c r e a s e s F o r T e r t i a r y Crushers  The c a p a c i t y i n c r e a s e s upper l i m i t , ever,  i n d i c a t e d by F i g u r e 3'3 r e p r e s e n t a p o s s i b l e  depending upon the upper c u r r e n t l e v e l  i t must be remembered t h a t these i n c r e a s e s  physical  l i m i t s o f the c r u s h e r s b e i n g c o n s i d e r e d .  finally  chosen.  are s u b j e c t A definite  to  How-  the  capacity  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 v a r i o u s a p p l i c a t i o n s o f the same machine. c i t y charts  However, r e f e r e n c e  t o p u b l i s h e d Symons Nordberg capa-  (Appendix A) i n d i c a t e s t h a t f o r c r u s h e r s  c o n s i d e r a t i o n , maximum c a p a c i t y throughputs T h i s l i m i t corresponds  o f the type  under  are i n the o r d e r o f 450 t p h .  c l o s e l y t o the ten p e r c e n t e x t r a p o l a t i o n i n f e e d -  r a t e assumed i n F i g u r e 3 3 .  F u r t h e r m o r e , i t i s b e l i e v e d t h a t the  a t the Brenda p l a n t are capable o f h a n d l i n g throughputs d i c a t e d by the Nordberg c h a r t s  crushers  l a r g e r than i n -  due to t h e i r m o d i f i e d c r u s h i n g chamber  - 114 -  configurations.  It is therefore  r e a s o n a b l e t o suggest t h a t , a l t h o u g h  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 n o t 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 smaller gaps), substantial  capacity increases w i l l  be  achieved. The e f f e c t s , o f o p e r a t i n g v a r i a b l e s upon the t e r t i a r y feedrate  and c u r r e n t draw are shown g r a p h i c a l l y i n F i g u r e 34 f o r  t e r t i a r y c r u s h e r gap.  These e f f e c t s  cussed i n p r e v i o u s s e c t i o n s .  Increases  constant  are as e x p e c t e d and have been d i s -  F o r e x a m p l e , an i n c r e a s e i n p l a n t  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 crusher feedrate draw.  crusher  feedrate  and c u r r e n t  i n the pi a n t f e e d 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 i n c r e a s e d  c i r c u l a t i n g l o a d r a t i o (see F i g u r e 27) and t h u s an i n c r e a s e i n t e r t i a r y crusher feedrate  and c u r r e n t .  The f a c t t h a t the t e r t i a r y c r u s h e r s 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 u s e f u l 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 t o e i t h e r damp out  s h o r t term o r c y c l i c d i s t u r b a n c e s o r compensate f o r more permanent  changes.  F o r i n s t a n c e , the a b i l i t y t o i n c r e a s e the t e r t i a r y c r u s h e r c u r r e n t draw above the p r e s e n t 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  increases  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 c o u l d 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 e n a b l e h i g h e r p l a n t The secondary screens  a l s o p l a y a p a r t i n the b u f f e r i n g r o l e i n t h a t  they r e t a i n 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 o p e r a t i n g (i.e.  feedrates.  settings  secondary c r u s h e r gap) u n t i l the t e r t i a r y c r u s h e r s have had the  n e c e s s a r y time t o compensate f o r these changes. The t e r t i a r y c r u s h e r s are the l i m i t i n g o p e r a t i o n i n the  tertiary  i  TERTIARY  CRUSHER  F i g u r e 34  FEEDRATE (below, in tph)  and  CURRENT  DRAW  (above, in  The I n f l u e n c e o f P l a n t O p e r a t i n g V a r i a b l e s on T e r t i a r y C r u s h e r C u r r e n t Draw and F p e d r a t P  amperes)  - 116 -  crushing loop.  Each secondary screen i s capable o f h a n d l i n g 1000 t p h ,  y i e l d i n g a combined c a p a c i t y o f a p p r o x i m a t e l y 5000 t p h .  To meet t h i s  l e v e l , the t e r t i a r y c r u s h e r s would be r e q u i r e d t o o p e r a t e a t c a p a c i t i e s r o f the o r d e r 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 .  This  o b s e r v a t i o n adds f u r t h e r importance t o 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 i n c r e a s e s because F i g u r e 32 i n d i c a t e s t h a t an i n c r e a s e i n c r u s h e r c u r r e n t can be t r a n s l a t e d i n t o e i t h e r an i n c r e a s e i n p l a n t c a p a c i t y , o r an i n c r e a s e i n t h e p l a n t ' s  a b i l i t y t o handle c o a r s e r  feeds.  On the b a s i s o f o b s e r v a t i o n s taken d u r i n g s a m p l i n g o f the condary c r u s h e r s , i t i s b e l i e v e d t h a t the p h y s i c a l crushers w i l l c u r r e n t draws. 32.0  se-  c a p a c i t y o f these  be reached w e l l b e f o r e t h e i r r a t e d maximum s u s t a i n a b l e The h i g h e s t c u r r e n t draw r e c o r d e d d u r i n g s a m p l i n g was  amperes a t a gap o f 2 . 5 4 cm. and a f e e d r a t e o f 782.3 t p h .  At this  l e v e l , the c r u s h e r was s h a k i n g v e r y h e a v i l y and was o b v i o u s l y a p p r o a c h i n g its  maximum t h r o u g h p u t . S t u d i e s were n o t undertaken to determine which u n i t o p e r a t i o n  is  l i m i t i n g with respect to t o t a l plant capacity.  the l i m i t i n g o p e r a t i o n w i l l  It i s believed that  be e i t h e r secondary o r t e r t i a r y c r u s h i n g and  t h a t i t may a l t e r n a t e between the two depending upon o p e r a t i n g 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 A l t h o u g h a p p l i c a t i o n s o f the c r u s h i n g 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 , t h e r e are s e v e r a l t h a t w a r r a n t 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 b e s t combina-  t i o n o f m a n i p u l a b l e v a r i a b l e s w i t h r e s p e c t to a s p e c i f i e d o b j e c t i v e sought.  The o p t i m i z a t i o n c o u l d be performed u s i n g a s u i t a b l e  direct  is  - 117 -  search program. fit  I n s t e a d o f s e a r c h i n g f o r c o n s t a n t s p e r m i t t i n g the  f o r a s i n g l e m o d e l , the search would i n c o r p o r a t e  the e n t i r e  t i o n and s e a r c h f o r the v a l u e s o f the s p e c i f i e d m a n i p u l a b l e variables that satisfy  the p r e s c r i b e d o b j e c t i v e .  The  simula-  (operating)  objective-function  would be based on one o r more o f the d e s i r e d r e s p o n s e s , such as o f the f i n a l mentation  product  subject  to p l a n t throughput  o f such a program r e q u i r e s  the  i d e n t i f i c a t i o n of  tion studies  I t may a l s o be d e s i r a b l e  t o determine  fineness  restrictions.  t o ensure t h a t - t h e i n d i v i d u a l models remain w i t h i n t h e i r v a r i a b l e ranges.  best  Imple-  constraints  acceptable  t o conduct a s e r i e s  of optimiza-  how the optimum p l a n t s e t t i n g s v a r y 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 s y s t e m , perhaps o f more l o n g  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 tions.  With the p r e s e n t program i t i s p o s s i b l e t o s i m u l a t e 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 u n i t s operation.  in a given  For example, i t may be d e s i r a b l e t o s t u d y the c r u s h i n g  w i t h the a d d i t i o n o f a t h i r d secondary c r u s h e r o r w i t h o n l y f o u r screens operating. configurations  Another aspect o f i n t e r e s t  d e s i g n and c o n s t r u c t i o n  of crushing  secondary  i s t h e s t u d y o f new c i r c u i t  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 .  a p p l i c a t i o n c o u l d be o f p a r t i c u l a r i n t e r e s t  plant  This  to those i n v o l v e d w i t h the  plants.  A f a r more d e t a i l e d s t u d y o f the e x i s t i n g c r u s h i n g p l a n t c o u l d be undertaken manual.  w i t h the o b j e c t i v e o f c o m p i l i n g a comprehensive  T h i s manual would document i n f o r m a t i o n such as  o p e r a t i n g s e t t i n g s and maximum o p e r a t i n g t o l e r a n c e s .  operating  recommended  I t would be c o m p i l e d  - 118 -  off-line,  and once c o m p l e t e d , c o u l d be checked a g a i n s t a c t u a l  b e h a v i o r f o r a c c u r a c y and r e l i a b i l i t y .  operating  I t i s n o t e x p e c t e d t h a t such a  manual would be t o t a l l y a c c u r a t e o r f o o l p r o o f , but when used w i t h  dis-  c r e t i o n , i t c o u l d prove t o be e x t r e m e l y u s e f u l as a supplement t o e v e r y day manual  control.  A final  a p p l i c a t i o n o f the s i m u l a t i o n c o u l d 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 p r o d u c t q u a l i t y c o u l d be a c h i e v e d by i n c r e m e n t a l l y v a r y i n g e i t h e r c r u s h e r gap, the screen o p e n i n g , o r a c o m b i n a t i o n o f the t h r e e o v e r 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 o u t p u t . I f the s i m u l a t e d e f f e c t s  o f equipment wear c o u l d be r e l a t e d to known  o r measurable r a t e s o f wear, then the r a t e s o f change i n p l a n t b e h a v i o r c o u l d be p r e d i c t e d .  T h i s f a c t c o u l d then be used t o c o n s t r u c t ,  o r supplement a maintenance s c h e d u l e f o r the e n t i r e p l a n t .  modify  Such a  s c h e d u l e would be u s e f u l 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 o p e r a t i n g c r u s h i n g p l a n t , c o n s i s t i n g o f two s t a g e s o f c r u s h i n g and one s t a g e o f s c r e e n i n g , has been  undertaken.  An i n - p l a n t s a m p l i n g program e n a b l e d a c q u i s i t i o n o f data c o v e r i n g normal o p e r a t i n g ranges f o r a l l t h r e e major p r o c e s s u n i t s i n v o l v e d .  The data  a c q u i r e d f o r s c r e e n i n g were s u b s e q u e n t l y a d j u s t e d by means o f a s t a t i s t i c a l method.  E s t a b l i s h e d models were m o d i f i e d and used to s i m u l a t e both  secondary and t e r t i a r y c r u s h i n g p r o c e s s e s , w h i l e a new model was used t o d e s c r i b e the v i b r a t i n g s c r e e n s . in nature.  A l l t h r e e models are s e m i - e m p i r i c a l  The models were combined i n sequence t o enable s i m u l a t i o n  o f the secondary c r u s h i n g p l a n t .  P r e l i m i n a r y s t u d i e s were conducted on  the s i m u l a t i o n s t o ensure the system was f u n c t i o n i n g p r o p e r l y .  Analysis  o f the r e s u l t s has c o n f i r m e d t h a 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 as a modern a n a l y t i c a l  the advantages  of d i g i t a l simulation  tool.  The f o l l o w i n g c o n c l u s i o n s can be drawn from t h i s  study:  (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 r u s h i n g o p e r a t i o n n o t o n l y make s a m p l i n g e x t r e m e l y d i f f i c u l t , but i n t r o d u c e a h i g h degree o f process e r r o r . The l a r g e p a r t i c l e s i z e s produce h i g h f r e q u e n c i e s 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 l o w s t r e a m s , hence the concept o f steady s t a t e must be c o n s i d e r e d i n a b r o a d , "average" sense and o n l y o v e r p e r i o d s g r e a t l y e x c e e d i n g 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 t o 1500 l b / s a m p l e ) are r e q u i r e d t o ensure r e p r e s e n t a t i v e s a m p l i n g , 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 t o 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 s c r e e n s 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 d a t a o b t a i n e d around a t h r e e ( o r more) p r o d u c t u n i t operation.  - 120 -  (3)  The Whiten c r u s h e r model was judged t o d e s c r i b e a d e q u a t e l y 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 p r i m a r y breakage e q u a t i o n .  (4)  The Whiten v i b r a t i n g s c r e e n model was judged t o be u n s a t i s f a c tory. The m o d e l ' s d i s c o n t i n u o u s n a t u r e i s c o n s i d e r e d t o 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 m o d e l , which i s c o n t i n u o u s o v e r 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 e x t e n t t o 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 d a t a range before i t s t a r t s m a l f u n c t i o n i n g was a l s o d e t e r m i n e d . 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 f u n c t i o n e d w e l l when m a n i p u l a b l e v a r i a b l e s were e x t r a p o l a t e d 15 o r 20 p e r c e n t beyond t h e i r f i t t e d r a n g e s .  (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 r u s h i n g p l a n t are s e m i - e m p i r i c a l i n n a t u r e . They are n o t n e c e s s a r i l y applicable to other crushing operations.  (7)  Development o f mathematical models f o r s i m u l a t i o n o f c r u s h i n g p l a n t s i s time consuming and c o s t l y . It i s therefore imperative 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 u n d e r t a k i n g 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 o b t a i n e d , i t can be a v e r s a t i l e t o o l f o r a n a l y s i s o f c r u s h i n g 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)  c o s t - one complete s i m u l a t i o n o f the Brenda c r u s h i n g p l a n t w i l l c o s t a p p r o x i m a t e l y 20<t  (c)  no i n t e r f e r e n c e w i t h p l a n t o p e r a t i o n  (d)  d i v e r s i t y o f the types o f s t u d i e 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 c a u t i o n and n o t b l i n d l y . T h i s i s e s p e c i a l l y t r u e when o p e r a t i n g v a r i a b l e s are used o u t s i d e 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 c o n j u n c t i o n 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)  F o r the Brenda Mines L t d . c r u s h i n g o p e r a t i o n , i t may be p o s s i b l e t o i n c r e a s e p l a n t c a p a c i t y f o r some o p e r a t i n g ^ c o n d i t i o n s by i n c r e a s i n g , the power draw t o the t e r t i a r y c r u s h e r s .  (11)  An "optimum" s e t t i n g f o r t e r t i a r y c r u s h e r gap i s i n d i c a t e d i n the m i d p o i n t r e g i o n 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 suggestions  are made r e g a r d i n g f u r t h e r work i n  the f i e l d o f c r u s h i n g p l a n t s i m u l a t i o n : (1)  I n v e s t i g a t e the p o t e n t i a l o f u s i n g the screen model e f f i c i e n c y e q u a t i o n to r e p l a c e the p a r a b o l i c c l a s s i f i c a t i o n e q u a t i o n c u r r e n t l y employed i n t h e c r u s h e r models. It i s believed that the p r o b a b i l i t y o f a p a r t i c l e b e i n g c l a s s i f i e d i s a c o n t i n u o u s f u n c t i o n f o r a l l s i z e s and would be b e t t e r approximated by a continuous equation.  (2)  Perform an o f f - l i n e o p t i m i z a t i o n study t o determine optimum s e t t i n g s f o r a l l manipulable operating v a r i a b l e s . I t may a l s o be u s e f u l to perform s e v e r a l o p t i m i z a t i o n s t u d i e s t o determine how the optimum o p e r a t i n g 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 r u s h i n g p l a n t and c o m p i l e a comprehensive p l a n t o p e r a t i n g manual. These s t u d i e s may o r may n o t i n v o l v e s t u d i e s i n t o the e f f e c t s o f e q u i p ment wear on p l a n t performance. I f such a manual were c o m p i l e d , i t c o u l d prove to be a v e r y u s e f u l supplement t o 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 t h a 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 r u s h i n g p l a n t s i m u l a t i o n program w i t h the program developed t o s i m u l a t e 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 t o s i m u l a t e the e n t i r e comminution c i r c u i t .  (6)  I n v e s t i g a 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 c u r r e n 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 t o determine whether the i n d i c a t e d c a p a c i t y i n c r e a s e s were realized.  (7)  T e s t the s c r e e n e f f i c i e n c y e q u a t i o n 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 s c r e e n types t o determine the e q u a t i o n s t h e o r e t i c a l v a l i d i t y and g e n e r a l a p p l i c a b i l i t y . Also 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 s c r e e n e f f i c i e n c y e q u a t i o n t o 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 b e h a v i o r o f the p r i m a r y f i n e s stream i n an e f f o r t t o improve upon the proposed f i n e s model.  - 122 -  Perform t e s t s t o p r e d i c t maximum c a p a c i t y l i m i t s f o r each u n i t o p e r a t i o n and the p r o d u c t q u a l i t y o r p l a n t performance a t these limits. T h i s s h o u l d 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 o p e r a t i o n 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 t o s t u d y the i n f l u e n c e o f t e r t i a r y c r u s h e r gap on p l a n t performance. T h i s s h o u l d enable i d e n t i f i c a t i o n o f an "optimum" gap s e t t i n g and may i n d i c a t e how t h i s "optimum" i n t e r acts with other manipulable operating v a r i a b l e s , e s p e c i a l l y screen opening.  - 123 BIBLIOGRAPHY  WHITEN, W. J . , "The S i m u l a t i o n o f C r u s h i n g P l a n t s w i t h Models Developed U s i n g M u l t i p l e S p l i n e R e g r e s s i o n " . J . South A f r . I n s t . M i n . Metal 1 . , v o l . 7 2 , 1972 pp. 254-264. WHITEN, W. J . and WALTER, G. W., "An E x a m i n a t i o n o f T e r t i a r y S c r e e n i n g Using S i m u l a t i o n " , P r o c . A u s t . I n s t . M i n . Metal 1 . , no. 2 6 1 , M a r c h , 1977. GURUN, T . , Design o f C r u s h i n g P l a n t Flowsheets by S i m u l a t i o n , " A p p l . o f Comp. Math i n the M i n i . I n d . " , I n t . 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M e c h . , v o l . 18, 1951, pp. 293-297. TAGGART,. A. F . , "Handbook  o f M i n e r a l D r e s s i n g " , W i l e y , New Y o r k ,  GAUDIN, A . M . , " P r i n c i p l e s o f M i n e r a l D r e s s i n g " , New Y o r k , 1939, pp. 143-152.  1954  McGraw-Hill,  FERRARA, G. and PRETI, U . , "A C o n t r i b u t i o n to S c r e e n i n g K i n e t i c s " , 11th I n t . M i n i . P r o c . C o n g r e s s , C a g l i a r i , I t a l y , 1975, Paper n o . 7. GLUCK, S. E . , " V i b r a t i n g S c r e e n s : Surface S e l e c t i o n and C a p a c i t y C a l c u l a t i o n " , Chem. E n g . , March 1 9 6 5 , . p p . 179-182.  -125  -  (28)  "Screening Machinery", Tech. Info. B u l l . PM1.1, A l l i s - C h a l m e r s M a n u f a c t u r i n g C o . , June 1963, pp. 4 1 - 7 1 .  (29)  NELDER, J . . A . and MEAD, R. A . , "A Simplex Method f o r F u n c t i o n Minimization". 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 " , C a n . I n s t . M i n . Metal 1. B u l l . , v o l . 6 9 , n o . 776, 1976, pp. 124-129.  (31)  HART, J . e t a l . "Computer A p p r o x i m a t i o n s " , 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 C u b i c S p l i n e F u n c t i o n s f o r R e g r e s s i o n and Smoothing", A u s t . Comp. J . , v o l . 3 , 1971, pp. 8 1 - 8 8 .  (33)  DRAPER, N . , and SMITH, H . , " A p p l i e d R e g r e s s i o n New Y o r k , 1966.  A n a l y s i s " , Wiley,  - 126 -  v APPENDIX A MAJOR EQUIPMENT SPECIFICATIONS (a) (b)  FOR SECONDARY CRUSHING PLANT  Secondary and T e r t i a r y Crushers P r i m a r y 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 All  crushers  i n t h e secondary c r u s h i n g p l a n t are 7 f t .  Nordberg heavy duty cone c r u s h e r s .  With the e x c e p t i o n o f the  chamber c o n f i g u r a t i o n , a l l c r u s h e r s  are s i m i l a r .  u t i l i z e the "standard"  crushing  The secondary  crushers  c r u s h i n g chamber c o n f i g u r a t i o n w i t h coarse  and m a n t l e , w h i l e the t e r t i a r y c r u s h e r s  use the " s h o r t - h e a d "  t i o n w i t h a coarse concave and medium m a n t l e . the m o d i f i c a t i o n s made t o both " s t a n d a r d " c r i b e d on page 14.  Symons  concave  configura-  The r e a d e r s h o u l d note  and s h o r t - h e a d "  mantles  des-  In a d d i t i o n t o c r u s h e r s p e c i f i c a t i o n s d e s c r i b e d i n  T a b l e 1 (page 15) and under the i n d i v i d u a l the f o l l o w i n g i n f o r m a t i o n i s  unit operation  descriptions,  presented:  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 C r u s h e r s Secondary Crushers (Standard)  Specification Motor sheave  diameter  Countershaft  sheave  Motor speed Countershaft Mantle throw  All  speed  diameter  '  .  T e r t i a r y Crushers (Short-Head)  26-1/2 i n .  26-1/2 i n .  42-1/2 i n .  42-1/2 i n .  710 rpm  712 rpm  443 rpm  444 rpm  3-5/8 i n .  3-5/8 i n .  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 o p e r a t i o n 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 Cone Crushers  f o r Symons Nordberg  -  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 ^niiiiHiMiaw  Size  B  A  V-1%" r-5" %"X /,6" '3y, " 5'-0/, " 4'-3%" 4'-6" 2 It. •-. (610 mml (1372 mm) (1311 mm) 11526 mm) (340 mm) (432 mm) (87 mm) (22mmx11 mm) 3' / " V'x/ " •V-9/4" V-5%" 5'-10/" 6'-0%" 5'-8" 3 ft. (914 mm) (1727 mm| (1791 mm| (1838 mm) (450 mm) (540 mm] (100 mm) (25mmxl3 mm) 7  6  6  5  6  2  2  Recommended Full Horsepower Load RPM (Electric)  H  G  Keyway  F  E  D  C  2'-8" 4'-3%" (1318mm) (813mm]  30-50  Weight lbs.  9.900 575 (4,491 Kg.)  3'-8" i 75-100 5'-6/ " (1994mm) [1118mm] j  22,000 580 (9,979 Kg.)  4'-0" 6'-11/ " (2115 mm) (1219mm)  100-150  37.100 485 (16,828 Kg.)  6'-11/ " 4'-3/ " (2121 mm) (1308 mml  2  2'-0" 2'-0/ " 6'-7/ " 8'-2/ " 7'-0" 4 ft. (1219mm) (1778 mm) (2502 mml (2013 mm) (613 mm) (610 mml 6'-83/" 2'-3" 2'-0/ " 8'-4/ " 7'-6" 4/ ft. (1295 mm| (2286 mm| (2546 mm) (2051 mm] (613 mm) (686 mml  4 /, ": 1/s"x /,6" (113mm) (29 mmx14mm| 4/,o" 1/a"x /t6" (113 mm) (29mmx14mm)  150-200  47,100 485 (21,364 Kg.)  ' 2'-6" V-6" 8'63/" 10'-5%" 6'-0'/>" 5 ft. (1524 mm| (2610 mm| (3191mm) (1842 mm) (457 mm| (762 mm)  5 /, " 8'-2 / " 4'-6" 1 /e"x"/,6" 200-250 (138 mm) |35mmx17mm) (2508 mm) (1372 mm|  91,600 485 (41,549 Kg.)  5/ ft. 2'-7/ " 2-7/ " 9'-9/ " 8'-1" 8'-9/4" Heavy Duty (2673 mm| (2978 mm) (2464 mml (794 mm| (800 mm) (1676 mm)  5 /, " 1%"x'/,s" 4'-6" 9'-3/ " (138 mm) |35mmx17mm| (2832 mm) (1372 mm)  200-250  92,600 485 (•12.003 Kg.)  6'-0" 7 ft. 11'-2/ " 1/ "x3/ " 9'-8%" ! 3'-43/" . 2'-11/ " ' 6/2" 10'-53/" Heavy Duty (3185 mm) |31V-3" 429mm) (2962 mm) j (1026 mml (902 mm). (165 mm) (38mmx19mm) (3416mm) (1829 mm) (2134 mm) 1  300-350  148,500 435 (67.359 Kg.)  7 ft. Extra 13'-2/ " 10'-10/" 9'-8%" | 3'-43/" 2'-11/ " Heavy Duty (4020 mm) (3308 mm| (2962 mml j [1026 mm] (902 mm) (2134 mm)  300-350  191,200 435 (86,728 Kg.)  4  4  4  e  4  2  e  4  ;  2  2  4  4  8  8  9  6  7  9  2  8  4  2  2  7  3  3  6  4  7  6  2  2  2  4  4  7  2  4  6/2" | 1/ "x3/ " 6'-0" 1V-2/ " (165mm) (38mmx19mm) (3416 mml (1829 mm) 2  4  2  jjMiiaaiiurgHBE  SHORT HEAD CONE CRUSHERS Size  B  A  Keyway  F  D  E  V-1%" (340 mm)  V-5" (432 mm)  8  V-5%" (450 mm)  (540 mm)  4  2'-3" 2'-0/ " (613 mm) (686 mm)  c  Recommended Full ' Horsepowei Load RPM (Electric)  K  G  Weight Ihs.  8  30-50  575  10,100 (4,581 Kg.)  2  75-100  580  23,200 (10,523 Kg.)  4'-3/ " 6'-11/2" 1/8"X!/16" (1308 mm) 150-200 (29mmx14mm) (2121 mm] 8'-2%" 4'-6" 2'-6" 1 / "X'/l6" 5 /, '' 200-250 (762 mm) (138 mm) (35mmx17mm) (2508 mm) (1372 mm|  485  47,400 (21,500 Kg.)  485  92,900 (42.139 Kg.)  4'-6" 5 / ft. 5/,e" 9'-3/ " 8'-9/ " 2'-7/ " 2'-7/ " 1 /B"X"/,6" 8'-1" 9'-9/ " 200-250 ' Heavy Duty (2673 mm) (297Bmm) (2464 mm) (794 mml (800 mm|- (138 mm) |35mmx17mm| (2832 mm| (1372 mm) ' (1676 mm)  485  93.900 (42.593 Kg.l  300-350  435  154,600 (70.126 Kg.l  300-350  435  197.300 189,495 Kg.]  5'-0/, " 4'-3%" 4'-6" ft. . (610 mm| (1372 mm) (1311 mm) (1526 mm) 5'-10/ " 6'-03/" 5'-8" 3 ft. (914 mm| (1727 mm) (1791 mm) (1838 mm| 6'-83/" 8'-4/ " 7'- 6" : 4/ ft. : |1295mm) (2286 mml (2546 mm) (2051 mm) 2  6  2  4  4  8  8'-7/ " 10'-53/4" 6'-0/ " . V-6" 5 ft. (1524 mm) (2622 mm) (3185 mm) (1842 mm) (457 mm) 2  4  V  2'-8" 78"x7,e" • 4'-3 / " (1318mm) (813 mm) (87 mm] 22 mmx11 mm) 3 /, " 3-8" 5'-6/ " V'x/ " (100 mm) (25 mmx13 mm) (1994 mm) (1118mm) 7  3 /,6'" 7  ,5  V-9/4"  6  2  4 /, " (113 mm) 7  2  6  7  3  6  8  7  2  4  4  4  3  2  2  7 ft. 6'-0" IV-2/2" 6/2" 1/2"x3/ " 3'-4%" 2'-11/ " 10'-2%" 11'-3/ " 9'-8%" Heavy Duty (3115 (3442 mm) (2962 mm| (1026 mm| (902 mm| (165 mm) |38mmx19mm) (3416 mm) (1829 mm) m m ) (2134 mm) ,' 7 ft. Extra 11'-10%" 9'-8%" 3'-43/" 2'-11/2" .' Heavy Duty X ' , (3626 mm) (2962 mm)i (1026 mm| (902 mm) .: (2134 mm] | ( ™> L  A  a 3842l  4  2  2  8  6/ " 6'-0" IV-2/2" 1/2"x3/ " (165 mm) (38 mmx19mm) (3416 mm) (1829 mml 2  4  T H E DATA SHOWN ON THIS PAGE S H O U L D NOT B E USED FOR CONSTRUCTION PURPOSES. C O N S U L T NORDBERG —DIVISION O F REX CHAINBELT INC. B E F O R E DESIGNING OR BUILDING A C R U S H I N G PLANT USING SYMONS STANDARD OR SHORT HEAD CONE C R U S H E R S OR PURCHASING ELECTRIC MOTORS, ETC.  TABLE A3 O p e r a t i n g S p e c i f i c a t i o n s f o r Symons N o r d b e r g Cone C r u s h e r s STANDARD  SYMO  T y p e of Cavity  Sin  mmmtmmtamt  CONE  CRUSHERS — O P E N  Recommended Minimum Discharge Setting A  B Closed Side  W  60 60  70 75 75  75 90 90  80 100 100  120 120  140 140  70  90 100  110 no  130 140 140 140  140 150 150 150  150 175 175 175  170 200 200 200  220 260 260  300 300  120  140 140  150 160 160  160 175 175  175 190 200 200  200 240 240 240  250 275 300  350 350  (191 mm) (235 mm) (267 mm) (311mm)  160  175 175  200 220 220  230 250 250 250  250 275 285 285  300 325 350  375 400 450  (197 (241 (276 (368  180  200  235 275  275 300 300  300 375 375  400 500  500 600  620 750 750  4 V (105 mm) 5%"(144mm) 7 V (191 mm)  4ft (1219 mm)  Fine Medium Coarse Extra Coarse  V V V y,"  (10 (13 (19 (19  mm) mm) mm) mm)  5" (127 mm) 6 V (156 mm) 7 V (187 mm) 8%"(227mm)  5'V 6V 8 V | 9 V  (143 mm) (171mm) (210 mm) (248 mm)  Wt ft. (1295 mm)  Fine Medium Coarse Extra Coarse  '/," V V 1"  (13 (16 (19 (25  mm) mm) mm) mm)  4V 7 V 9" 10V  (114 mm) (187 mm) (229 mm) (264mm)  5 V 8 V 10" 11V  (137 mm) (210 mm) (254 mm) (286mm)  5ft (1524 mm)  Fine Medium Coarse Extra Coarse  '/," V V," 1"  (16 (19 (22 (25  mm) mm) mm) mm)  6 V 8 V 9 V 11V  (171 (222 (248 (292  mm) mm) mm) mm)  7'/," 9 V 10'/," 12V  5V ft. (1676 mm) 2  Fine Medium Coarse Extra Coarse  y," '/," 1" IV  (16 (22 (25 (38  mm) mm) mm) mm)  7'/," 8 V 9 V 13V,"  (181mm) (219 mm) (251mm) (343 mm)  7 V 9 V 10V 14V  7a (2134 mm)  Fine Medium Coarse Extra Coarse  V 1" IV IV'  (19 (25 (32 (38  mm) mm) mm) mm)  10" 11V 13V 16V  (254 (292 (343 (425  11" (279 mm) 12 V (324 mm) 1 4 V (378 mm) 1 8 V (460 mm)  Recommended Minimum Discharge Setting C  Type of Cavity  CLOSED  18  mm) mm) mm) mm)  370  ( 2 0 0 0 lbs.]  PER  HOUR  (19 mm) (38 mm)  2 ft. (610 mm)  Fine Coarse  V (3 mm) X," (5 mm)  3 ft. (914 mm)  Fine Medium Coarse  V V V  (3 mm) (3 mm) (6 mm)  V," (13 mm) 1" (25 mm) 2" (51mm)  4% ft (1295 mm)  Fine Medium Coarse Extra Coarse  V V V '/,"  (3 mm) (6 mm) (8 mm) (16 mm)  IV IV 2 V 4 V  5 ft. (1524 mm)  Fine Medium Med. Coarse Coarse Extra Coarse  V' V V V V  (5 mm) (6 mm) (10 mm) (10 mm) (13 mm)  5% ft (1676 mm)  Fine Medium Coarse Extra Coarse  V' V V V  7 ft. (2134 mm)  Fine Medium Coarse Extra Coarse  V V," V V  (29 mm) (41mm) (70 mm) (121mm)  Note 1: Note 2:  W (3 mm)  D Open Side  '  IV 2"  (35 mm) (51mm)  I V 1 2" 3"  (41mm) (51mm) (76 mm)  2 V 3" 4" 5 V  (64 mm) (76 mm) (102 mm) (140 mm)  1" (25mm) IV (44 mm) 2\," (65 mm) 3 V (83 mm) 4 V (105 mm)  2'i" 3 V 3 V 4 V 5 V  (64mm) (83 mm) (98 mm) (117 mm) (143mm)  (5 mm) (6 mm) (10 mm) (13 mm)  IV 2V 3 V 6"  (35 mm) (54 mm) (95 mm) (152 mm)  2 V 3V 5V 7 V  (70 mm) (89 mm) (133 mm) (184 mm)  (5 mm) (10 mm) (13 mm) (16 mm)  2" (51mm) 3 V (98 mm) 5" (127 mm) 6 V ' (160mm)  3 V 5 V 7" 8' "  (95 mm) (146 mm) (178 mm) (210mm)  4  ON  BASED  Feed Opening With Min. R e c o m m e n d e d Discharge Setting C  V IV  •  .  350 400 450 450 750 800 850 850  2W (64 m m )  450 500 500  700 800  1100 1200 1200  1400 1400  CIRCUIT  • CAPACITIES*IN TONS  D Closed Side  2" (51 m m )  50 50  (86 mm) (124 mm) (175 mm)  Size  114" (38 mm)  40  3 V 4 V 6 V  -  1V«" (32 m m )  60 75 80  '/," (10 mm) V (13 mm) V (19 mm)  SIZES  1" (25 mm)  w (22 mm)  50 60 70  Fine Coarse Extra Coarse  CRUSHERS  Hr> (19 m m )  45 50 55  3 ft. (914 mm)  • PRODUCT  w (16 m m )  40 45 50  2 V (70 mm) 3 V (95 mm) 4" (102 mm)  CONE  mm)  35 35 40  (57 mm) (83 mm) (89 mm)  OPENINGS  Vj" (13 mm)  w  30 30 30  2 V 3 V 3 V  SYMONS  a  25 25 25  V (6 mm) ' V," (10 mm) V (13 mm)  FEED  SIZES • CAPACITIES  20 20  Fine Coarse Extra Coarse  HEAD  (10  (6 m m )  2 ft (610 mm)  SHORT  PRODUCT  OPENINGS  Capacities in Tons (2000 lb. Per Hour Passii >. Through the Crusher at Indicated Discharge Setting A  B Open Side  mm) mm) mm) mm)  FEED  CAVITIES  CIRCUIT  Feed o p e n i n g With Minimum Recommended Discharge Setting A  Note 1  18  '  Note 1  10  45 45 20  60  35 40  Note 2  Note 1  Note  20 22  13 13  26 26  40 40  30 30 35  70 80  100  65  CIRCUIT  W (10 mm)  W (6 m m )  X." (5 mm)  Note 2  CLOSED  OPERATION  Net Finished Product (Screen Undersize) Approx. Total T P H Passing Through Crusher (Net F i n i s h e d Product  2  Note 2  Note 2  Note 1  14 18  21 27  20 25  30 40  60 60 70  40 40 45  60 60 75  50 55 60  75 80 90  50 55  100 110  75 80 80  110 120 120  100 105 110  150 160 165  75  150 150  no 120 120  160 180 180 180  150 150 150  200 225 225 225  135 135 W  200 200 210  170 175 175 175  240  360 360  300 300  130  180 180  240  320  CAPACITIES S H O W N A R E B A S E D ON 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 . THE FIGURES SHOWN APPLY TO SHORT TONS OF MATERIAL WEIGHING 100 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 INCLUDE. »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 MOISTURE CONTENT. TO ACHIEVE OPTIMUM RESULTS THE CRUSHER SETTING C M A Y VARY DEPENDING O N T H E NATURE O F T H E MATERIAL AND SPECIFICATION DESIRED.  Note 1  w (13 m m )  w (16 mm) Note 1  25 30  Note 2  (19 Note 1  rcul ting Load) nm)  1" (25 mm)  Note 2  Note 1  Note 2  85 95 110  80  100 120  200 200  250 250  250 270 290 290  230 260 260  260 280 300 300  270 350 350  280 320 320  300 360 360  550  520 580 650  35 45 80 90 105  125 125 140 140  160 160 210 210  175 180 180  220 240 260 270 270  230 230 260 260  210 210 220 220  240 250 330 330  450 450 450  360  450 500 550 600  1 150 175 175  220  245 250 250  450  170 240 240  500 500 560 620  - 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 t a n d a r d and s h o r t - h e a d models  p r e s e n t e d i n F i g u r e A l and T a b l e A2 ( T a b l e A2 r e f e r s  t o F i g u r e A l )...  G e n e r a l i z e d o p e r a t i n g d a t a f o r both c r u s h e r types i s p r e s e n t e d (b)  P r i m a r y and Secondary V i b r a t i n g All  are  i n Table A3.  Screens  s c r e e n i n g i n the Brenda c r u s h i n g 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 s c r e e n s . secondary s c r e e n s ,  The p r i m a r y and  d e s c r i b e d 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 t h the e x c e p t i o n t h a t the secondary s c r e e n s are the heavy duty v e r s i o n w h i l e the p r i m a r y s c r e e n s are the e x t r a heavy duty v e r s i o n . o p e r a t i n g s p e c i f i c a t i o n s f o r t h e s e s c r e e n s are p r e s e n t e d  Additional  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 P r i m a r y and Secondary Vibrating Specification Make Model Version Nominal Dimensions Motor D r i ve V i b r a t i o n Frequency V i b r a t i o n Amplitude Inclination Upper Deck S l o t Dimensions Lower Deck S l o t Dimensions wire  diameter  Screens  P r i m a r y Screen Allis-Chalmers double deck R i p l - F l o e x t r a heavy duty 8 f t . x 20 f t . 2x25 Hp @ 1800 rpm direct, belt 850 rpm 3/8 i n . 20° s t r i p s o f punched p l a t e  -  5 panels w i r e c l o t h (4 f t . x 8 f t . ) 3/4 i n . x 3-1/16 i n .  -  Secondary Screen Allis-Chalmers double deck R i p l - F l o heavy duty 8 f t . x 20 f t . 2x25 Hp @ 1800 rpm direct, belt 850 rpm 3/8 i n . 20° s t r i p s o f punched p l a t e 1-1/16 i n . x 3 i n . 5 panels wire c l o t h (4 f t . x 8 f t . ) 1/2 i n . o r 5/8 i n . x 3-1/16 i n . 3/8 i n .  -..132 -  MODEL SH SCREEN SIZES and DIIVIENSIONS i  S T I F F E N E R  tCABLE  F R A M E  S U B S T I T U T E D SIZING  CABLE  AT  FOR  SPRING  ( B O T H  B A S E S  S I D E S )  .  D E C K  SINGLE and DOUBLE DECK . . . 20° SLOPE 2-103/g 2-103/8 2-10% 2-10%  2222-  91/4 9% 9'/ 9%  2222-  83/  0-20% 0-20% 0-20% 2- 1% 2- 1%  33333-  4% 4% 4% 5% 5%  33333-  3/s 3% 3% 3/2 3/2  3- 1 % 3- 1 % 3- 1 % 3- 3 % 3- 3 %  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%  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- 3/2 4- 3/2 4- 3y  123/4 IIV4 111/4  2-10 2- 10 3- 0 %  5- 2 % 5- 2 % 5- 4 %  4-11.3/4 4- 1 1 % 5- 2 /,  4- 9/2 4- 9 y 4-11/2  0-15% 0-153/s 0-153/a 0-153/a  2-10% 2-10% 2-10% 2-10%  3- 6 % 4- 3 4-11% 4- 1 1 % 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'/  2-10% 2-10% 2- 1 0 % 3- 33/8 3- 33/8  3 11% 7% 11'%  3- 6 3- 6 3- 6 3-10%  O-I81/2 0-18/2 0-181/2 0-211/4  3333-  33/8 3% 33/8 83/ 4  7% 83/ 8/ 83/a 83/8 83/s 73/4  4- 1 1 % 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  15- 6% 19- 3 % 19- 3 %  5- 8 6- 111/4 6-II1/4  4- 9 / 5- OVz 5- 31/8  0-24 2- 13/8 2- 3  4- 61/4 4- 8 4-111/4  Q ft-in.  R ft-in.  C ft-in.  4x 8 4 x 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%  5x 5x 5 x 5x 5 x  10 12 14 14 16  3-4 3-4 3- 4 4- 4 4-4  5-0V4 5-01/4 5-0V 5-Oi/j 5-OiA  9li131315-  6 x 12 6 x 14 6 x 16 6x20  4-4 4-4 4- 4 5- 5  6-oy 6-0% 6-01/4 6-01/4  11- 8 13- 6% 15- 51/s 19- 2i/4  4456-  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 / 15- 6 % 19- 3 %  8 x 16 8x20 8 x 20  5-5 5- 5 6- 5  8-0V4 8-0/> 8-0V4  N ft-in.  •  P in.  Screen Size (ft)  0-20% 0-20% 0-203A 0-203/4  ?.-10/ 3- 6 % 4- 3 4-11%  B ft-in.  4  81/4 81/4 81/4 81/4  F ft-in.  A ft-in.  4  K ft-in.  E ft-in.  Mech. No.  2  9% 3 6% 6% 51/s  4  2  3  4  M ft-in.  H ft-in.  • ft-in. 3- 0 % 3- 0 % 3- 0 % 3- 0 %  Screen Size (ft)  G in.  8  8'/8  8  3  8  S in.  T in.  U in.  A-A ft-in.  B-B ft-in.  C-C ft-in.  L ft-in.  4  /4  1  D-D ft-in.  EE ft-in.  8 8 8 8  2  2  WT.-D.D. floor mt.  4 x 4 x 4 x 4x  8 10 12 14  4-1/4 4-1% 4-1% 4-1%  16% 16% 16% 16%  5- 2 7- 0 % 8- 1 1 % 10- 9 %  4- 8 / 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- 1 1 % 10- 2/2  5-1 5-1 5-1 5-1  4900 5200 5300 6300  5 x 5x 5 x 5 x 5 x  10 12 14 14 16  5-1% 5-1% 5-1% 5-1% 5-1%  7- 0 % 8- 11/8 10- 9 % 10- 9 % 12- 8/4  5- 8 / 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%  00000-  8 8 8 7 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  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 8  6% 6% 6% 6%  0001-  8 7 8 5/2  3-1/2 3- 8 ' % 4- 4 % 4-1/4  1-10 1- 9 % 1-10 4- 1/B  8500 8840 9100 13400  7/4 7A 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 %  4'% 3% 1% 3% 43/4 2/4 3/4  7-1 7-1 7-1 7-1  8- 0 9- 0 11-1  810121191111-  8-1 8-1 8-1  14100 15100 17600  9-1% 9-0 11-1  7/2 8/2 8/2  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  6 x 12 6 x 14 6x16 6 x 20  6-13/4 6-1% 6-1% 6-13/4  16% 163/s 163/8 163/8 16% 163/s 163/s 163/s 163/8  7 x 14 7 x 16 7x20  7-2 7-2 7-2  16/4 16/4 16/4  10-11 12- 9 % 16- 63/  -  -  8x16 8 x 20 8 x 20  -  F i g u r e A2  4  2  2  !  7/8  8/3  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 are p r e s e n t e d  i n Figure A2.  family o f R i p l - F l o screens  The s i n g l e and double deck s c r e e n s are  t i c a l , with the exception that a s t i f f e n e r  frame i s used i n the  iden-  single  deck v e r s i o n where the l o w e r 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 C r u s h e r Samples Size 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 S i z e D i s t r i b u t i o n s f o r P r i m a r y Screens Samples F l o w r a t e Record f o r P r i m a r y Screens  Samples  Undersize  Undersize Stre  - 135 L e v i c e : DS2D task: 39 USERID: RALU 12: 51: 30 0.9-04-77 U n i v e r s i t y o f B r i t i s h C o l u m b i a Computing C e n t r e - d e v i c e : DS2D f SIGN RALU t ENTER USER PASSWORD. » i * * L A S T SIGNON WAS: 12:41:44 f USES "RALU" SIGNED ON AT 12:50:05 ON SUN SEP 0 4 / 7 7 * RUN *BAS.IC * EXECUTION BEGINS , ?UBC BASIC SYSTEM  task:  GET APEND RUN SECONDARY CRUSHEH SAMPLE S I Z E ANALYSES S I Z E ANALYSES REPORTED IN HEIGHT PERCENT RETAINED ON SIZE ••• FEED S I Z E  DISTRIBUTIONS  SIZE (CM)  RUN NO. 1  RUN NO. 2  RUN NO. 3  RUN NO. 4  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  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  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  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  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)  RUN NO, 5  RUN NO. 6  RUN NO, 7  RUN NO. 8  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  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  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  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  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 S I Z E  DISTRIBUTIONS  SIZE (CM)  RUN NO. 1  RUN NO. 2  RUN NO. 3  RUN NO. 4  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  0 0 17 45 23. 9 6.05 2. 24 1. 56 1. 07 0. 87 0.69 0.59 0. 46 0. 57  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  0 0 16 39.5 22.5 8.2 4 2.8 2 1.47 1.28 0.98 0.63 0.64  0 0 31 42 15.9 4.4 2.05 1.25 0.89 0.68 0.56 0.47 0.35 0.45  SIZE (CM)  RUN NO. . 5  RUN NO. 6  RUN NO. 7  RUN NO. 8  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  0 0 26 37 18.2 6 3.2 2. 65 2 1.71 1.29 0.91 0.51 0.53  0 0 16 39 21 9 3.9 3.2 2.4 1.87 1.43 1.05 0.61 0.54  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  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 * * P R I N T * ASSIGNED RFS NUMBER 661805 I COPY *flSOURCE*a)SP TO *PSINT*  -  161 -  e v i c e : DS48 task: 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 C o i u t a b i a C o m p u t i n g C e n t r e - d e v i c e : DS48 SIGN RALU ENTER USER PASSWORD.  task.:  * * L A S T SIGNON WAS: 10:10:51 USER "RALU" SIGNED ON AT 10:19:17 ON TUB SEP 0 6 / 7 7 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM ? GET APPE RUN  TERTIARY CRUSHER SAMPLE S I Z E ANALYSES S I Z E ANALYSES REPORTED IN WEIGHT PERCENT RETAINED ON S I Z E  FEED S I Z E  DISTRIBUTIONS  SIZE {CM)  .RUN NO. 9  RUW NO. 10  RUN NO. 1 1  RUN NO. 12  RUN NO. 13  2 1 . 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  0 0 12 43 39 3.62 0.76 0. 42 0.24 0. 2 0. 19 0. 15 0. 12 0.3  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  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  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  0 0„ 16 46.5 32.2 J . 56 Q. 46 0.26 Q. 19 0. 16 0. 14 D . 13  SIZE (CM)  RUN NO. 14  RUN NO. 15  RUN NO. 16  RUN NO. 16A  •RUN NO. 16B  2 1 . 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  0 0 2 55 38.6 1. 88 0.53 0.41 0.31 0.26 0.21 0. 19 0. 18 0.43  0 0 14 52 31 1.21 0.38 0.26 0. 17 0. 16 0.15 0. 14 0. 14 0.39  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  0 0 15 47 34.9 1.4 0.5 0.26 0,2 0.16 0 . 13 0.12 0.11 0.22  0  a . 13  0.27  o. 20 57 21.05 0.85 0,. 22 0.15 0.. 11 0. 1 Q. 11 0. 1 0. 12 0. 19  246  - 138 PRODUCT S I Z E  DISTRIBUTIONS  SIZE (CM)  RUN NO. 9  RUN NO. .10  RUN NO. 11  RUN NO. 12  RUB NO.: 13  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  0 0 0 0 38.5 34.5 10 6 3.4 2.55 1.9 1.31 0.89 0.95  0 0 0 0 42 31 9.6 5.8 3.4 2.55 2 1.47 1.08 1.1  o  o  a  0 0 2 47.5 26.5 8.5 4.7 3.2 2.25 1. 9 1.4 1.02 1.03  0 0 5.5 38.5 26.7 10.3 6.2 4.2 2.9 2.05 1.5 1.05 1.1  0, 0 10 42 23.5 8.7 5.1 3.2 2.25 .1.75 1.27 1 .1.23  SIZE (CM)  RUN NO. 14  SDN NO. 15  RUN NO. 16  RUN NO. 16A  RUN NO.. 16t\  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  0 0 0 43 42 7.4 2.35 1.55 1 0.75 0.69 0.54 0.37 0.35  0 0 0 16 42 19.7 7.4 4.3 2.9 2.35 1.85 1.45 1.01 1.04  0 0 0 6 36 29.5 10.5 5.7 3. 5 2.5 2.1 1.6 1. 16 1. 44  0 0 0 15 45 19.6 7.4 4 2.7 1.95 1.62 1.06 0.77 0.9  0 0, 0 23 41 17.8 5.9 3.6 2.3 1.75 1.5 1.2 Q.91 1.04  ?STOP! ? AT LINE "690' IN PROGRAM "APPE" ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FQRM=8X11 • P R I N T * ASSIGNED RFS NUMBER 662260 $C *SOURCE*a)SP *PRINT* 1  e v i c e : DS40 task: University of B r i t i s h • SIGN RALU ' ENTER USER PASSWORD.  - 13y 237 USESID: BALU 09:53:41 09-06-77 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS40  task:  23'  r * * L A S T SIGNON WAS: 0 9 : 4 0 : 3 1 r USER "RALU" SIGNED ON AT . 0 9 : 52: 35 ON TUE SEP 06/77 RUN *BASIC • EXECUTION BEGINS r ?UBC BASIC SYSTEM , . GET APEND RUN f  ?  SECONDARY SCREENS SAMPLE S I Z E ANALYSES S I Z E ANALYSES REPORTED IN WEIGHT PERCENT RETAINED ON SIZE  FEED S I Z E  DISTRIBUTIONS  SIZE (CM)  RUN NO. 17  RUN N O .  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  0 0 17 38 20.2 9.3 4.5 3. 1 2.3 1.8 1.4 1 0.7 0.7  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. 19  RUN NO, 20  RUN NO, 21  SUN  0 0 14 3 2.5 28.5 12 4 2.4 1.65 1.4 1. 15 0.92 0.67 0.81  0 0 12 31 30 13 5 2. 6 1.6 1.3 1.2 0. 85 0. 63 0. 82  0 0 10 31 29. 5 15 5.1 2.9 9 3 08 0.77 0.62 0.83  0 0 10 24 31 17.5 6.1 3.6 2.3 1.7 1.37 0. 98 0.71 0. 74  0 0 11 27 28. 1 16. 9 5.9 3.3 2.3 1.65 1.29 0.96 0.68 0.92  RUN N O . , 26  SUN NO. 27  RUN N O . , 28  RUN NO. 29  RUN NO. 30  0 0 10 24.5 29.5 18.3 6.4 3.7 2.3 1.55 1.15 0.9 0.72 0.98  0 0 12 28 28.5 15.7 5.8 3.1 2 1.4 1.15 0.77 0.65 0.93  0 0 8 23 32 18.8 6 3. 6 2. 4 1.95 1.3 1.05 0.8 1.1  0 0 11 29 28 15.3 5.7 3.2 2.2 1.7 1.3 1 0.75 0.85  0 0 11 24 29.5 17 6 3.7 2.5 1.8 1.4 1.1 0.8 1.2  18  so;.  25  - 140 -  OVERSIZE PRODUCT DISTRIBUTIONS SIZE (CM)  SUN NO. 17  RUN NO. 18  RUN NO. 19  RUN NO. 20  RUN NO. 21  RUN NO. 25  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  0 0 26 46.5 25.3 1. 1 0.25 0. 16 0. 13 0. 13 0. 13 0. 1 0.08 0. 12  0 0 16 45 36.4 1.62 0.28 0.15 0. 1 0.09 0.08 0.07 0.07 0 . 14  0 0 22 45 31.4 0. 88 0,21 0. 09 0. 07 0. 07 0. 06 0. 06 0. 06 0. 1  0 0 15 51.5 31. 25 1.29 0.28 0.14 0. 1 1 0.07 0.08 0.08 0.Q7 0.13  0 0 15 39 41.6 2.44 0.54 0.32 0.23 0.2 0. 17 0.15 0. 14 0.21  0 0 14 45 35 4.82 0.38 0.15 0. 1 1 0.09 0.09 0.08 0.09 0.19  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  SUN NO. 26 0 0 14 31 49 4.92 0. 44 0. 18 0.09 0.08 0.07 0.05 0.05 0.12  SUN NO. 27 0 0 18 40 39.2 1.6 0.34 0.18 0.14 0.12 0.11 0.1 0.1 0.11  RUN NO. 28 0 0 16 47 33.2 2. 37 0. 49 0. 19 0. 12 0. 11 0. 1 0. 1 0.12 0,2  RUN NO. 29 0 0 22 55.5 20. 4 0.9 8 0.32 0.16 0.11 0.11 0.1 0. 1 0.08 0.14  RUN NO. 30 0 0 21 54 22.7 1.07 0.31 0.19 0.13 0. 12 0.11 0.11 0. 1 0. 16  UNDERSIZE PRODUCT DISTRIBUTIONS SIZE (CM)  RUN NO. 17  RUN NO. 18  RUN NO. 19  RUN NO. 20  RUN NO. 21  RUN NO. 25  21.76 10.88 5.44 2.72 1. 36 0.68 0.34  0 0 0 2 31 30. 5 10.3  0 0 0 0 36 36 10. 1  0 0 0 0 42 29.5 8  0 0 0 0 32 34 11.7  0 0 0 0 30 33.5 13  0 0 0 0 11 39 17. 5  0.17 0.Q85 0.0425 0.0212 0.0106 0.0053 -0.0053  6.7 5 3.9 3.4 2. 9 2 2.3  5.4 3.5 2.4 2.1 1 .7 1.35 1.45  SIZE {CM)  RUN NO. . 26  RUN 27  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  0 0 0 0 9 41 19 11.1 6.8 3.8 3.3 2.25 1.65 2.1  0 0 0 0 21 45 15.2 7 3.3 2.3 1.7 1.4 1.2 1.9  NO.  - 141 5.3 4 3. 3 2.7 2. 1 1.58 1.52  7.3 4.5 . 3.3 2.5 1.85 1.3 1.55  7.7 4.5 3. 2 2.7 2. 1 1.5 1.8  RUN NO. 28  RUN NO. 29  RUN NO. 30  0 0 0 0 30 36 13 6.3 4. 2 2.9 2. 4 1. 9 1.52 1. 78  0 0 0 0 32 32. 5 11.5 6.5 4.2 3.6 2.8 2.4 1.9, 2.6  0 0 0 0 34 32.2 12.6 5.2 3.4 3.2 2.5 2.3 2 2.6  ?STOP! ? AT L I N E "900" IN PROGRAM "APEND" ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FORH=8X11 • P R I N T * ASSIGNED RFS NUMBER 662239 $C *SOURCE*SSP *PRINT*  9.7 6.1 4.6 3.9 2.6 1 2.4 3.19  -  142 -  e v i c e : DS40 task: 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 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS4Q SIGN HALO ENTER USER PASSWORD. • • L A S T SIGNON WAS: 0 9 : 5 7 : 3 3 USER "RALU" SIGNED ON AT 10:05:52 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM  task  ON TUE SEP 0 6 / 7 7  GET PEND RUN  PHIMARY SCREENS UNDERSIZE SIZE  (PRIMARY FINES)  SAMPLE SIZE ANALYSES  ANALYSES REPORTED IN WEIGHT PERCENT RETAINED ON S I Z E  SIZE (CM)  RUN NO. 31  RUN NO. 32  RUN NO. 33  RUN NO. 34  RUN NO. 35  EUN NO. 36  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  0 0 0 0 6 13 15 15 15.5 14 9.9 6.2 3.55 1.85  0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 22 31 15. 5 9 8 5.9 3.9 2.4 1.34 0.96  0 0 0 0 33 34 10.2 6 4.8 3. 1 2.9 2.6 1.85 1.55  0 0 0 0 22 29 15 10. 7 7.5 5.6 3.8 2.7 1.95 1.75  0 0 0 0 25 26 13.5 9.5 7.8 5.9 4.7 3.5 2.3 1.8  •  • • • ' • • • • a t  ?STOP! ? 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 F l o w r a t e Record f o r P r i m a r y Screens U n d e r s i z e Stream A u g u s t , 1975  Date  Day  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun  Oversize (tons) 19,724 24,130 20,716 32,944 10,934 27,062 11,994 25,557 27,564 20,955 15,495 22,625 25,156 14,225 19,781 25,045 20,282 7,010 26,314 16,366 7,613 10,996 24,232 24,620 22,637 14,087 36,057 24,243 24,837 24,774  Flowrates Undersize (tons) 6,185 7,867 6,528 Statuatory Holiday 11,128 " 3,274 10,053 3,307 8,031 8,375 7,322 3,988 2,161 2,156 5,875 7,768 8,231 6,906 2,069 8,766 5,941 3,292 4,236 6,022 6,423 4,877 3,197 8,278 6,390 3,728 7,484  .Feed (tons)  Percent F i n e s i n Feed (%)  25,909 31,997 27,244  23.87 24.59 23.96  44,072 14,208 37,115 15,301 33,588 35,939 28,277 19,483 24,786 27,724 20,100 27,549 33,276 27,188 9,079 35,080 22,307 10,905 15,232 30,642 31,043 27,514 17,284 44,335 30,633 28,565 32,258  25.25 23.04 27.09 21.61 23.91 23.30 25.89 20.47 8.72 9.26 29.23 28.20 24.74 25.40 22.79 24.99 26.63 30.19 27.81 19.65 20.69 17.73 18.50 18.67 20.86 13.05 23.20  - 144 TABLE B2 F l o w r a t e Record f o r P r i m a r y Screens U n d e r s i z e Stream September,  Date  Day  Oversize (tons)  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  Mon Tue: Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue.: Wed Thur Fri Sat Sun Mon Tue,.  25,514 24,378 24,561 23,740 20,875 21,181 6,164 5,992 23,850 19,137 22,794 23,912 22,738 23,662 20,435 12,303 29,195 19,802 32,402 28,679 20,332 12,867 18,560 17,756 24,691 27,608 20,480 21,498 15,167  Flowrates Undersize (tons)  1975  Percent F i n e s i n Feed (*)  Feed (tons)  S t a t u a t o r y Ho' i d a y 32,172 6,658 5,411 29,789 7,135 31,696 5*999 29,739 27,205 6,330 27,082 5,901 7,667 1,503 1,858 7,850 7,283 31,133 24,624 5,487 3,724 26,518 6,161 30,073 28.515 5,777 5,788 29,450 26,634 6,199 15,576 3,273 37,486 8,291 4,744 24,546 40,742 8,340 7,363 36.042 6,075 26,407 3,448 16.315 5,311 23,871 4,901 22,657 6,852 31,543 9,265 36,873 4,600 25,080 6,391 27,889 19,815 4,648  .  \  20.70 18.16 22.51 20.17 23.27 21.79 19.60 23.67 23.39 22.28 14.04 20.49 20.26 19.65 23.27 21.01 22.12 19.33 20.47 20.43 23.01 21.13 22.25 21.63 21.72 25.13 18.34 22.92 23.46  - 145 -  TABLE B3 F l o w r a t e Record f o r P r i m a r y Screens U n d e r s i z e Stream O c t o b e r , 1975  Date  Day  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri Sat Sun Mon Tue Wed Thur Fri  Oversize (tons) 24,368 21,554 18,250 20,640 20,142 20,926 16,502 23,868 22,651 18,653 26,843 22 ,295 21,605 27,194 10,099 22,476 28,487 29,378 19,541 15,818 29,927 22,211 14,975 27,906 17,917 28,471 16,614 15,863 27,725 22,313  Flowrates Undersize (tons)  Feed (tons)  32,218 7,850 6,354 27,908 5,184 23,434 5,978 26,618 5,770 25,912 26,744 5,818 5,048 21,550 7,108 30,976 6,339 28,990 4,292 22,945 6,762 33,605 28,343 6,048 S t a t u a t o r y Ho" i d a y 5,380 26,985 5,502 32,696 2,429 12,528 4,748 27,224 36,105 7,618 37,544 8,166 4,913 24,454 5,669' 21,487 9,633 39,560 7,149 29,360 5,393 20,368 8,455 36,361 3,955 21,872 6,475 34,946 21,885 5,271 20,543 4,680 6,287 34,003 34,291 11,978  Percent F i n e s i n Feed (*) 24.37 22.77 22.12 22.46 22.27 21.75 23.42 22.95 21.87 18.71 20.12 21.34 19.94 16.83 19.39 17.44 21.10 21.75 20.10 26.38 24.35 24.35 26.48 23.25 18.08 18.53 24.08 22.78 18.46 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 s c r e e n data. A d j u s t e d Data f o r the Secondary Screens  - 147 1 * * * PROGRAM. SCREEN :SCEEEN DATA ADJUSTMENT PROGRAM 2 * 3 * 9 DIM G ( 2 0 , 2 0 ) , H ( 2 0 , 2 0 ) , K ( 2 0 , 2 0 ) , 1 ( 2 0 , 2 0 ) , V ( 2 0 , 2 0 ) 10 DIM F ( 2 0 , 2 0 ) , U ( 2 0 , 2 0 ) , 0 ( 2 0 , 2 0 ) , A { 1 , 4 0 ) , C ( 4 5 ) , T { 2 , 2 0 ) , E ( 3 5 , 1 0 ) 12 DIM D ( 1 , 4 0 ) , X { 4 0 , 4 0 ) , ¥ { 4 0 , 1 ) , 2 ( 1 , 4 0 ) , Q ( 4 0 , 4 0 ) 14 READ N 1 , N 2 , A 3 , A 2 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 S S F , S S O , S S D , S V 1 0 , T O N S , D U M P , A S F 2 , A S 0 2 , A S U 2 , A K X 2 , V A E 40 MAT BEAD F I L E 1 , F ( N 2 , A 3 ) 50 MAT HEAD F I L E 2 , 0 ( N 2 , A 3 ) 60 MAT READ F I L E 3 , U ( N 2 , A 3 ) 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 1 1 , Y ( N 2 , 3 ) 85 A9=A2 90 POR 1=1 TO N1 100 A (1 , I ) = E ( I , A9) 110 NEXT I 12 0 MAT F = ( . 0 1 ) * F 130 MAT O=(.01) *0 140 MAT U= (.01) *U 210 * CALCULATION OF I N I T I A L STARTING VALUES 215 FOB 1=1 TO N1 220 D ( 1 , I ) =ABS(G2*A (1,1) ) 225 NEXT I 230 * SET UP I N I T I A L 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 S T D . DEV'N OF OBJECTIVE FUNCTION 360 Z8=0 361 Z9=0 370 T 3 = 1 . E 7 0 380 FOR 1=1 TO N1+1 390 H=I 400 GO SUB 1310 410 Y ( I , 1 ) = Y 1 420 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  460 465 470 480 490 500 510 520 530 540 550 560 570 580 590 593 595 600 610 620 622 624 625 626 630 635 695 70 0 701 702 703 705 708 710 711 712 713 714 715 716 717 718 719 720 722 723 724 725 726 727 728 729 730 731 732 733 73 4 735 74 0 744  - 148 T1=T1/(N1+1) FOR 1=1 TO N1 • 1 T2=T2+ (Y <I, 1 ) - T 1 ) **2 NEXT I T4=SQR (T2/N1) I F T 4 > 1 . E - 6 THEN 750 GO TO 590 * PRINTOUT SECTION PHINT PRINT "CYCLE LIMIT STOP CBITERION=";M2;"STD. DEVIATION=" ; T4 PRINT PR I NT" HIGH= " ; Y (H , 1) , "2ND HIGH=";Y(S, 1} , " L O W = ; Y ( L , 1) PRINT GO TO 600 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y ( L , 1 ) PRINT PRINT "STANDARD DEVIATION=";T4 H=L GO SUB 1310 PRINT A10=0 A11 = 0 PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS=»;Z9 A12=0 PRINT PRINT "RUN NO.=";A2 PRINT " ADJUSTED S I Z E DISTRIBUTIONS" PRINT A 15=0 A16=0 A17=0 PRINT " M I A S . F E E D " , " A D J . FEED" PRINT FOR J=1 TO N2 PRINT F { J , A 2 ) * 1 0 0 , C ( 2 * N 2 * J ) * 1 0 0 A15=A15 + C{2*N2 + J) *1O0 A 10=A 10 + (F ( J , A2) * 100—C (2*N2+J) * 1 00) **2 NEXT J PRINT PRINT "RESIDUAL SUM SQUARES=";A 10 , " " , " S U N FEED=";A15 PRINT PRINT " M E A S . O / S " , " A D J . 0 / S " " " , " M E A S . U / S " , " A D J . U / S " PRINT FOR J=1 TO N2 PRINT O {J, A2) * 1 0 0 , C{J) *100, " " , U (J , A 2) * 100 C (N 2* J) * 1 00 A11=A11+ (0 ( J , A 2 ) * 1 0 0 - C (J) *100) **2 A12=A12 + (U ( J , A 2 ) *100-C(N2+J) *100)**2 NEXT J PRINT PRINT "RESIDUAL SUM SQRS=";A 1 1 , " " , "RESIDUAL SUM SQRS=";A12 FOR J=1 TO N2 A16=A16 + C (J) *100 A17=A17 + C(N2+J)*100 NEXT J PRINT PRINT " ","SUM 0 / S = " ; A 1 6 , " " , " " , " S U M U/S=";A17 PRINT PRINT " ADJUSTED FLOWRATES" PRINT PRINT "FEED=";ABS(X{H,27) ) *ABS (X (H,28) ) ; " { " ; T ( 1 , A 9 ) +T (2, A9) n  r  #  - 149 745 PRINT 746 PRINT " 0 / S = " ; A B S ( X ( H , 2 7 ) ) ; " { " ; T ( 1 , A 9 ) ; ") " 747 PRINT « U / S = » ; A B S (X(H,28) ) < , T ( 2 , A 9 ) ; ") " 748 PRINT 749 GO TO 1580 750 I F Z9>M2 THEN 530 752 I F 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 I F 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) * P 1 - A t * X {H, J) 850 X ( H , J ) = Z ( 1 , J ) 860 D ( 1 . J ) = P 1 870 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 I F 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 - B 1 ) * 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 S I Z E OF SIMPLEX 1200 FOE J=1 TO N1 n  -  1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 13 21 1322 1323 13 28 1330 1340 1342 13 45 13 50 1355 1360 1370 1380 1390 1400 1410 14 20 1430 1440 1450 1455 1460 1470 1480 1490 1500 1510 1520 15 30 1540 1550 1560 1561 1562 1565 1570 1579 1580 1582 1584 1586 1590 1592 1594 1596 1598 1600 16 02  IDU -  FOR 1=1 TO N1+1 X(I,J) = (Q(I,J)+Q(L,J))/2 NEXT I NEXT J Z8=Z8+1 PRINT PRINT "STEP CHANGE";Z8 PRINT GO TO 380 C O N S T R A I N T SECTION Z1=0 Z2=0 FOR J=1 TO N1-2 I F X ( H , J ) > 1 7 0 THEN: X (H , J) = 1 70 I F X ( H , J ) < - 1 7 0 THEN : X (H,3) = - 170 NEXT J FOR J=1 TO N2-1 C (J)=EXP (X ( H , J ) ) / ( E X P (X (H, J) ) +EXP (-X (H, J) ) ) C ( J ) = I N T ( C ( J ) *100000 + . 5 ) / 1 0 0 0 0 0 A5=N2-1+J C (N2+J) =EXP (X{H,A5) ) / ( E X P (X (H,A5) ) +EXP(-X (H,A5) ) ) C(N2+J)=INT(C(N2+J) *100000 + . 5 ) / 1 0 0 0 0 0 Z1=Z1+C(J) Z2=Z2+C (N2+J) NEXT J C ( N 2 - 1 ) = 1-Z1 C (2*N2) = 1-Z2 C A L C U L A T I O N OF FEED DISTRIBUTION Z3=ABS (X(H,28) ) / (ABS (X (H,27)) *ABS (X (H,2 8) )) Z4=1-Z3 FOR J=1 TO N2 C (2*N2 + J)=Z4*C (J) +Z3*C (N2+J) C(2*N2 + J) =INT ( C ( 2 * N 2 + J ) * 1 0 O 0 0 0 + . 5 ) / 1 0 0 0 0 0 NEXT J C (3*N2)=Z4*C (N2) +Z3*C(2*N2) C A L C U L A T I O N OF OBJECTIVE FUNCTION F2=0 FOR J=1 TO N2 F2=F2+ ( (U ( J , A 2 ) -C(N2+J) ) **2) / V ( J , 3} + ( (0 ( J , A2) - C (J ) ) * * 2} / V (J , F 2 = F 2 * . 3 3 3 3 * ( ( F { J , A 2 ) - C (2*N2 + J) ) * * 2 ) / V ( J , 1) NEXT J F 2 - F 2 * <T{1, A9) - ABS (X (H,27) ) ) **2+{T (2, A9) - A B S { X ( H , 28) ) ) **2 Y1 = F2 Z9=Z9+1 FOR J=1 TO 3*N2 I F C ( J ) < 1 . E - 8 THEN:C(J)=0 NEXT J RETURN * DATA F I L E STORAGE SECTION HAT READ F I L E 7 , G ( 1 1 , N 2 ) MAT READ F I L E 8 , H ( 1 1 , N 2 ) MAT READ F I L E 9 , L ( 1 1 , N 2 ) MAT BEAD F I L E 1 0 , K ( 1 1 , N 2 ) FOR J=1 TO N2 G ( A 9 , J ) = C (2*N2 + J) *100 H (A9, J) =C (J) *100 L (A9,J)=C(N2+J) *100 NEXT J A15=CMD("%EMPTY ASF23D") MAT WRITE F I L E 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 . F R A C T I O N 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 ( A 9 , J ) =1 1627 PRINT K<A9,J) 1628 GO TO 1632 16 30 K (A9, J) = (C (J) *X (H,27) ) / ( C ( 2 * N 2 + J ) *A21) 16 31 PRINT K ( A 9 , J ) 1632 NEXT J 1634 A22=CMD ("%EMPTY AKX23D") 1636 MAT WRITE F I L E 10,K 1638 A23=CMDf"%SAVE AKX2SD") 1640 STOP 1715 * OBJECTIVE FUNCTION MAGNITUDE LISTING 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 2 8 , 1 4 , 1 1 , 1 1 1910 DATA 1100,300 1920 DATA 1 , . 5 , 2 , . 0 1,10 2000 END END—OF-FILE  (ORDER  SEARCH)  -  e v i c e : DS40 task: U n i v e r s i t y of B r i t i s h SIGN RALU ENTER USER PASSWORD. ,  \i>d 237 USERID: RALU 09:59:05 09-06-77 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS40  * * L A S T SIGNON WAS: 09: 57:08 USER "RALU" SIGNED ON AT 0 9 : 5 7 : 3 3 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM  task:  ON TUE SEP 0 6 / 7 7  GET ADP RUN ADJUSTED S I Z E  ANALYSES FOR SECONDARY SCREEN SAMPLES  S I Z E ANALYSES REPORTED IN HEIGHT PERCENT RETAINED ON S I Z E  RUN  NUMBERS  17  SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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  0 0 17 38 20. 2 9.3 4.5 3. 1 2.3 1.8 1.4 1 0.7 0.7  0 0 16.803 30.487 27.221 11.649 3.919 2.633 1,909 1.523 1.325 1.053 0.717 0.?6  RESIDUAL SUM OF  SQUARES= 112.0938  FEED SUM= 9 9 . 9 9 9  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UN DERSIZE  ADJUSTED UNDERSIZE  2 1 . 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 26 46.5 25.3 1.1 0.25 0.16 0.13 0. 13 0. 13 0.1 0.08  0 0 26.226 46.497 25. 116 1.084 0.251 0 . 161 0. 12 0. 124 0. 125 0. 1 0.077  0 0 0 2 31 30.5 10.3 6.7 5 3. 9 3.4 2. 9 2  0 0 0 1.94 30.975 30.488 10.461 7.041 5. 1 4.018 3.464 2.752 1.859  237  -0.0053  - 153 -.' 0.119  0.12  OVERSIZE SUH= 100 RESIDUAL SUM OF SQUARES: :  OVERSIZE= UNDERSIZE=  ADJUSTED ORDINATE  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  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  0.08537 0.37478  ADJUSTED FLOW RATES : FLOWSTREAM  MEASURED  ADJUSTED  FEED  356.8  356. 7998  OVERSIZE  228.6  228.6001  UNDERSIZE  128.2  128.1997  RUN  NUMBERS  1.902  UNDERSIZE SUM= 100  ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM)  2.3  18  SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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 14 32. 5 28. 5 12 4 2.4 1.65 1.4 1.15 0.9 2 0.67  0 0 8. 855 24.79 36.193 17.012 4. 462 2.469 1.613 1. 158 1.064 0.909 0.68  -0.0053  - 154 0.795  0.81  RESIDUAL SUM OF SQUARES^  170.5035  FEED SUM= 100  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  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  0 0 16 45 36.4 1.62 0.28 0. 15 0.1 0.09 0.08 0.07 0.07 0.14  0 0 16.064 44.974 36.357 1. 621 0.285 0 . 154 0.093 0.088 0.082 0.074 0.07 0 . 138  0 0 0 0 36 36 10. 1 5. 4 3. 5 2. 4 2. 1 1. 7 1. 35 1. 45  0 0 0 0 35.991 35.917 9.592 5.313 3. 479 2 . 473 2.27 1 .935 1. 429 1.601  OVERSIZE SUM= 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 (CM)  ADJUSTED OBDINATE  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  1 1 0.9999734 1.000019 0.5537156 5.252318E- 2 3.520778E- 2 3.438135E- 2 3.178132E- 2 4. 188875E- 2 4.248108E- 2 4. 487363E- 2 5.674302E- 2 9.573511E- 2  ADJUSTED FLOWRATES: FLOWSTREAM  MEASURED  ADJUSTED  FEED  353.4  353.3993  OVERSIZE  194.8  194.8  UNDERSIZE  158.6  158. 5993  UNDERSIZE  SUfl= 100  - 155 -  HUN NUMBER=  19  SIZE (CM)  MEASURED PEED  ADJUSTED FEED  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  0 0 12 31 30 13 5 2.6 1.6 1.3 1.2 0.85 0.63 0.82  0 0 1 4 . 21 29.054 3 5 . 12 10.997 2 . 97 1.922 1.395 1.207 0.999 0.786 0.607 0.733  RESIDUAL SUM OF SQUARES= 4 3 . 5 8 1 2 8  FEED SUM= 100  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  21.76 1 0 . 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  0 0 22 45 31.4 0.88 0.21 0.09 0.07 0.07 0.06 0.06 0.06 0. 1  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  0 0 0 0 42 29.5 8 5.3 4 3.3 2.7 2. 1 1. 58 1. 52  0 0 0 0 41.976 29.398 7.998 5.253 3.806 3.274 2.707 2 . 108 1.601 1.879  OVERSIZE RESIDUAL  SUM OF SQUARES: :  SUM= 100 OVERSIZE= UNDERSIZE=  ORDINATE VALUES FOR SCREEN SIZE (CM)  ADJUSTED ORDINATE  21.76 10.88 5.44 2.72 1.36  1 1 0.9999739 0.999997 0.5764511  UNDERSIZE 0.00226 0 . 18094  EFFICIENCY CURVE  SUH=  100  15b  0. 68 0.34 0 . 17 0.085 0.0425 0.0212 0.0106 0.0053 -0.0053  0. 4. 3. 3. 3. 4. 0. 6. 9.  -  0526624 586786E-2 124007E-2 332274E-2 851303E-2 006901E-2 050106 488191E-2 160219E-2  ADJUSTED FLOWRATES: FLOWSTREAM  MEASURED  ADJUSTED  FEED  345.4  3 4 5 . 401  OVERSIZE  223  223.0006  UNDERSIZE  122.4  122.4004  RUN NUMBER = 20 SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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  0 0 10 31 29. 5 15 5.1 2.9 1.9 1.3 1.08 0.77 0.62 0.83  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 (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  21.76 10.88 5. 44 2.72 1.36 0.68 0.34 0. 17 0.085 0.0425  0 0 15 51.5 31. 25 1.29 0.28 0. 14 0. 11 0.07  0 0 14.923 51. 506 31.204 1.401 0.277 0. 139 0. 1 14 0.073  0 0 0 0 32 34 11.7 7.3 4. 5 3. 3  0 0 0 0 32.059 34.064 11.738 7.346 4.505 3 . 156  -  0.0212 0.0106 0.0053 -0.0053  0.08 0.08 0.07 0. 13 OVERSIZE  1 0 /  -  0.08 0.081 0.072 0. 13 SUM=  2. 5 1. 85 1.3 1. 55  100  RESIDUAL SUM OF SQUARES: OVERSIZE= : UNDESSIZE=  UNDERSIZE  0.020442 0.055676  ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM)  ADJUSTED ORDINATE  2 1 . 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  1 1 1.000025 1.000001 0.5172895 4.332185E2.532417E2.040938E2.710534E0.0248407 3.375437E4.895844E5.979499E0.0806763  ADJUSTED  2 2 2 2 2 2 2  FLOWRATES:  FLOWSTREAM  MEASURED  ADJUSTED  FEED  563.7  563.6995  OVERSIZE  295.4  295.3992  UNDERSIZE  268.3  268.3003  RUN  NU MBER=  21  SIZE (CM)  MEASURED FEED  ADJUSTED FEED  21.76 10.88 5.44 2.72 1.36 0.68 0.34 0.17 0.085 0.0425  0 0 10 24 31 17.5 6.1 3.6 2.3 1.7  0 0 6.386 16.474 34.978 21.107 7.788 4.416 2.845 1.954  2 . 522 1.732 1.247 1.631 SUM=  100  Ibb 1.37 0.98 0.71 0.74  0.0212 0.0106 0.0053 -0.0053 RESIDUAL  SUM OF SQUARES=  1. 484 1.026 0.728 0.812 102.434  FEED SUM= 9 9 . 9 9 8  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  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  0 0 15 39 41. 6 2.44 0.54 0.32 0.23 0.2 0.17 0. 15 0.14 0.21  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  0 0 0 0 30 33.5 13 7. 7 4.5 3.2 2.7 2. 1 1. 5 1.8  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  OVERSIZE SUM= 100 RESIDUAL  SUM OF SQUARES: :  OVERSIZE^ UNDERSIZE=  ORDINATE VALUES FOR SCREEN SIZE (CM)  ADJUSTED ORDINATE  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  1 1 1.000039 1.000017 0.4976044 5.031444E- 2 2.889575E- 2 3.091965E- 2 3.436563E- 2 4.205607E- 2 4.231272E- 2 6.202235E- 2 8. 104295E- 2 0. 1079463  UNDERSIZE SUIi= 100 0.128508 2.27989  EFFICIENCY CURVE  ADJUSTED FLOW RATES: FLOWSTREAM  MEASURED  ADJUSTED  FEED  157.8  157.7993  OVERSIZE  66.5  66.5003  - 159 UNDERSIZE  RUN  91.3  91.299  NUMBER= 25  SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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  0 0 11 27 28. 1 16. 9 5.9 3.3 2.3 1.65 1.29 0.96 0.68 0.92  0 0 10.232 32. 908 28.582 13.974 4. 984 2.714 1.716 1.3 1.118 0.768 0. 702 1.003  RESIDUAL SUM OF SQUARES=  46.00792  FEED SUM= 100.00 1  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  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  0 0 14 45 35 4.82 0.38 0.15 0.1 1 0.09 0.09 0.08 0.09 0.19  0 0 13. 977 44. 955 35. 027 4.846 0.387 0 . 152 0. 114 0.091 0.092 0.081 0.091 0. 187  0 0 0 0 11 39 17.5 9.7 6. 1 4.6 3. 9 2.61 2. 4 3. 19  0 0 0 0 10.977 38.908 17.542 9.712 6.092 4.602 3.921 2.643 2.372 3.231  0  OVERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= : UNDERSIZE=  UNDERSIZE 0.004044 0.014964  ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM)  ADJUSTED ORDINATE  21.76 10.88  1 1  SUM= 100  -  5. 44 2.72 1. 36 0.68 0. 34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0.0053  0. 1. 0. 0. 5. 4. 4. 5. 6. 0. 9. 0.  IDU -  9999516 000005 8970897 2538565 684058E- 2 099768E- 2 863099E- 2 124171E- 2 023814E- 2 0772057 4 8 92 05 E - 2 1365175  ADJUSTED FLOWRATES: FLOWSTREAM  MEASURED  ADJUSTED  FEED  1044.5  10 44.501  OVERSIZE  764.6  764,5999  ONDERSIZE  279.9  279.9007  RUN NUMBER= 26 SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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  0 0 10 24.5 29. 5 18.3 6.4 3.7 2.3 1.55 1.15 0.9 0.72 0.98  0 0 5.63 11.984 29.015 27.03 9.785 5.758 4.397 2.469 1.313 0.882 0.718 1,018  RESIDUAL  SUM OF SQUARES= 2 7 3 . 1 5 9 2  FEED SUM= 9 9 . 9 9 9  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  21.76 10.88 5. 44 2.72 1.36 0.68 0.34  0 0 14 31 49 4.92 0.44  0 0 14. 449 30.756 48.983 4. 756 0.425  0 0 0 0 9 41 19  0 0 0 0 16.267 41.251 15.76  •  0.17 0.085 0.0425 0.0212 0.0106 0.0053 -0.0053  0.18 0.09 0.08 0.07 0.05 0.05 0.12  lb I -  0.201 0.081 . 0.058 0.061 0.051 0.058 0.121  11.1 6. 8 3.8 3.3 2. 25 1.65 2.1  OVERSIZE SUfl = 100 RESIDUAL SUM OF SQUARES: OVERSIZE= : UNDEfiSIZE=  UNDERSIZE SUM= 100 0.2897 69.38761  ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM)  ADJUSTED ORDINATE  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  1 1 1.000036 1.000032 0.6578227 6.856174E- 2 1.692443E- 2 1.360224E- 2 7.178184E- 3 9.153621E- 3 1.810303E- 2 2.253137E- 2 3. 147673E- 2 4.633391E- 2  ADJUSTED FLOHSATES: FLOWSTREAM  MEASURED  9.306 7.153 4.008 2.113 1.412 1.14 1.59  ADJUSTED  FEED  562.8  56 2. 80 53  OVERSIZE  219.3  219.3027  UNDERSIZE  343.5  343.5026  RUN NU MBER= 27 SIZE (CM)  MEASURED FEED  ADJUSTED FEED  21.76 10. 88 5. 44 2.72 1.36 0.68 0.34  0 0 12 28 28. 5 15.7 5.8  0 0 9.702 21.343 30.75 21.775 6.953  -  0 . 17 0.085 0.0425 0.0212 0.0106 0.0053 -0.0053 RESIDUAL SUM OF  3. 1 2 1.4 1.15 0.77 0.65 0.93  IDti  -  3.453 1.617 1. 117 1.016 0.715 0.623 0.936  SQUARES= 9 3 . 2 6 7 1 2  FEED SUM= 100  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  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  0 0 18 40 39. 2 1.6 0.34 0.18 0.14 0.12 0. 11 0. 1 0. 1 0. 11  0 0 18. 156 39.94 39.139 1.597 0. 325 0. 182 0. 137 0.114 0 . 102 0. 1 0.099 0. 109  0 0 0 0 21 45 15.2 7 3.3 2.3 1.7 1.4 1.2 1.9  0 0 0 0 2 1 . 122 4 4.933 14.559 7.207 3 . 315 2.269 2.064 1.421 1.224 1.886  OVERSIZE  RESIDUAL SUM OF SQUARES: :  SUM =  100  OVERSIZE= UNDERSIZE=  UNDERSIZE  0.032006 0,607998  ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM)  ADJUSTED ORDINATE  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  1 1 1.000032 1.000018 0.6801734 3.919239E- 2 2.497849E- 2 0.0281663 4.527574E- 2 5.453894E- 2 5.364898E- 2 7.473929E- 2 8.491847E- 2 6.220451E- 2  ADJUSTED FLOWRATES: FLOSSTREAM  MEASURED  ADJUSTED  SUM=  100  -  ID J  FEED  279.2  279.2006  OVERSIZE  149.2  149.2009  UNDERSIZE  130  129.9997  RUN NUMBER= 28 SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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  0 0 8 23 32 18. 8 6 3.6 2.4 1.95 1.3 1.05 0.8 1.1  0 0 7. 506 21.895 31. 329 20. 16 7.852 3.251 2. 154 1.485 1. 194 0.915 0.928 1.332  RESIDUAL SUM OF SQUARES=  7.693017  FEED SUM=  100.001  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  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  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  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  0 0 0 0 30 36 13 6. 3 4. 2 2. 9 2. 4 1.9 1. 52 1. 78  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 RESIDUAL SUM OF SQUARES: :  SUM= 100 OVERSIZE= UNDERSIZE=  UNDERSIZE 0.035184 2.413674  ORDINATE VALUES FOR SCREEN EFFICIENCY CURVE SIZE (CM)  ADJUSTED ORDINATE  SUM= 100  - 164 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  1 1 1.000031 1 0.491682 5.358621E- 2 2.975718E- 2 3.164053E- 2 2.312099E- 2 1.849243E- 2 4.054128E- 2 4.985095E- 2 6.369776E- 2 6.919863E- 2  ADJUSTED FLOWRATES: FLOWSTREAM  MEASURED  ADJUSTED  FEED  1004.2  1004.2  OVERSIZE  467.4  467. 3997  UNDERSIZE  536.8  536.7998  RUN NUMBER=  29  SIZE (CM)  MEASURED FEED  ADJUSTED FEED  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  0 0 11 29 28 15.3 5.7 3.2 2. 2 1.7 1.3 1 0.75 0.85  0 0 10.497 26. 405 26.646 17. 815 6. 198 3.588 2.4 1. 938 1. 42 1.327 0.788 0. 976  RESIDUAL SUM OF SQUARES=  SIZE (CM) 21.76 10.88 5.44 2.72  '  15.77942  FEED SUM= 9 9 . 9 9 8  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  0 0 22 55.5  0 0 22.069 55.515  0 0 0 0  ADJUSTED UNDERSIZE 0 0 0 0  1.36 0.68 0.34 0. 17 0.085 0.0425 0.0212 0.0106 0.0053 -0.0053  20. 4 0.98 0.32 0. 16 0. 11 0.11 0. 1 0. 1 0.08 0.14  - Ibb 20. 36 4 0.981 0. 325 0. 159 0. 106 0. 101 0.09 0.072 0.079 0. 139  OVERSIZE SUM= 100 RESIDUAL SUM OF SQUARES: OVERSIZE= 0.007292 : UNDERSIZE= 1.579496 ORDINATE VALUES FOR SCREEN SIZE (CM)  ADJUSTED ORDINATE  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  1 1 0.9999835 0.999999 0.3635017 2.619139E- 2 2.494062E- 2 2.107755E- 2 2.100729E- 2 2.478809E- 2 3.014599E- 2 2.580697E- 2 4.768439E- 2 6.771093E- 2  EFFICIENCY CURVE  ADJUSTED FLOWRATES: FLOWSTREAM  MEASURED  ADJUSTED  FEED  498.7  498. 6997  OVERSIZE  237.2  237. 1999  UNDERSIZE  261.5  261.4998  RUN  NUMBER= 30  SIZE (CM)  MEASURED FEED  ADJUSTED FEED  21.76 10.88 5.44 2.72  0 0 11 24  0 0 9.127 24.994  32 32.5 11.5 6. 5 4.2 3.6 2.8 2. 4 1. 9 2. 6  32.345 • 3 3.084 11.526 6.699 4.481 3.605 2.626 2.466 1.432 1.736  UNDERSIZE SUM= 100  1. 36 0.68 0. 34 0.17 0.085 0.0425 0.0212 0.0106 0.0053 -0.0053  - Ibb 29. 109 17.956 6. 356 3.353 2.301 2.065 1. 429 1.215 0.833 1. 263  29. 5 17 6 3.7 2.5 1.8 1.4 1.1 0.8 1.2  RESIDUAL SUM OF SQUARES= 5. 939077  FEED SUM= 100.001  SIZE (CM)  MEASURED OVERSIZE  ADJUSTED OVERSIZE  MEASURED UNDERSIZE  ADJUSTED UNDERSIZE  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  0 0 21 54 22. 7 1.07 0.31 0.19 0. 13 0.12 0.1 1 0.11 0. 1 0.16  0 0 20.077 54.982 22.773 0.967 0.305 0. 183 0. 117 0.113 0. 116 0 . 1 13 0.096 0. 158  0 0 0 0 34 32.2 12.6 5. 2 3. 4 3.2 2. 5 2.3 2 2.6  0 0 0 0 34.39 32.115 1 1.399 5.995 4 . 121 3.691 2.524 2 . 133 1 . 448 2 . 184  OVERSIZE SUM =  100  RESIDUAL SUM OF SQUARES: OVERSIZE= UNDERSIZE= :  ORDINATE VALUES FOR SCREEN SIZE (CM)  ADJUSTED ORDINATE  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  1 1 0.9999554 0.9999877 0.3556336 2.448086E- 2 2.181352E- 2 2.481004E- 2 2.3 11421E- 2 0.0248753 3.690079E- 2 4. 227777E- 2 5.238852E- 2 5.686645E- 2  ADJUSTED FLOWRATES:  UNDERSIZE 1. 832548 3 . 500898  EFFICIENCY CUR VE  SUM= 100  - 167 FLOSSTREAM  MEASURED  ADJUSTED  FEED  265.3  265.3008  OVERSIZE  120.6  120.6003  UNDERSIZE  144.7  144. 7005  ?STOP! ? AT LINE "910" IN PROGRAM "A DP" ? PROGRAM ENDS MTS  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 regression analyses. TRANS4, a s u p p o r t program f o r ALLREDD to permit data transformation  - 169 1,*** PROGRAM NAME: ALLREDD 2 * 3 * 10 DIM X (1.0,7) , Y ( 4 0 , 1 ) , 2 ( 1 0 , 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 N O . . O F 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 F I L E 2 , Y ( N , 1 ) 388 * * * C A L C U L A T E FLAGS TO DETERMINE I F FACTORS ARE TO BE 389 ***INCLUDED IN THE F I T 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 * * * C A L C U L A T E 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 " F I T N O . " , " S S R " , " R * * 2 , " 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) f l  562 563 565 570 5 80 590 5 00 510 520 5 50 553 555 560 5 65 570 571 572 573 574 575 577 5 80 5 90 700 710 720 730 740 750 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 794 795 300 310 320 330 528 330 340 344 345 346 360  - 170 MAT Z=G * * * S H I F T DATA TO FORM A N BY T*1 MATRIX*** T=0 FOR J=1 TO K I F B ( I , J ) = 0 THEN 650 T=T+1 FOR L=1 TO N Z (L,T+1) = Z ( L , J + 1 ) NEXT L NEXT J ***REDIMENSION Z WHILE RETAINING ITS V A L U E S * * * MAT F=Z T=T+1 IF T=1 THEN 1310 MAT Z=RDM{N,T) FOR J=1 TO T FOR L=1 TO N Z ( L , J ) = F ( L , J) NEXT L NEXT J * * * C A L C U L A T E (TEN (Z) *Z) * * - 1 AND TIN (Z) * Y * * * MAT P=RDM{T,N) MAT P=TRN(Z) MAT Q=RDM ( T , T ) MAT Q=P*Z MAT T=RDM (T , 1) MAT T=P*Y MAT P=RDM(T,T) MAT P=INV(Q) I F P=0 THEN 769 PRINT PRINT "(VAR/COVAH M A T R I X ) / S E * * 2 PRINT I F T>5 THEN 760 MAT PRINT P GO TO 769 FOR L=1 TO T PRINT P ( L , 1) , P (L,2) , P ( L , 3) , P (L, 4) , P (L,5) IF T>6 THEN 765 PRINT P ( L , 6 ) GO TO 766 PRINT P (L,6) , P { L , 7 ) PRINT NEXT L * * * C A L C 0 L A T E MATRIX OF C O E F F I C I E N T S * * * MAT Q=RDM(T,1) MAT Q=P*T * * * C A L C U L A T E DEGREES OF FREEDOM ASSOCIATED WITH S3=0 FOR L=1 TO K S3=S3+B(I,L) NEXT L S3=N-S3-1 ***CALCULATED VALUES OF RESPONSES AND SSR*** S0=0 S1=0 I F E1=0 THEN 960 PRINT PRINT "Y-OBS" , " Y - C A L C " , "RESIDUAL" FOR J=1 TO N M  SSR***  - 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 S 1 = S 1 * ( Y 1 - Y 2 ) * * 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 I F 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 I F 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 I F T>6 THEN 1246 1244 PRINT P ( 1 , 6 ) 1245 GO TO 1250 1246 PRINT P (1,6) ,P<1 ,7) 1250 I F P=1 THEN 1700 1255 ***STORE OUTPUT VALUES FOR SORTING*** 1260 H ( I , 1 ) = I 1270 H ( I , 2 ) = S 0 1280 H ( I , 3 ) = S 1 / S 2 1290 H ( I , 4 ) = S 0 / S 3 1300 GO TO 1355 1310 H ( I , 1 ) = I 1320 H ( I , 2 ) = S 2 1340 H ( I , 3 ) = 0 . 0 0 1350 H ( I , 4 ) = S 2 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 I F 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 ( I 1 , L ) = T 1 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 172 0 INPUT I  IS  DESIRED"  - 172 1722 I F 1=0 THEN 1960 1725 PRINT " I F RESIDUALS ARE DESIRED ENTER 1726 INPUT E1 !730 I F 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  1; I F NOT ENTER 0"  - 173 ***  PROGRAM:  T1ANS4  * DIM A ( 2 0 , 2 0 ) , C ( 2 0 , 2 0 ) : 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) PRINT "INPUT VARIABLE CODE; G=2,T=3,S=4 " ' INPUT B , D , E , F , G F I L E 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 1  - 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 C r u s h e r M o d e l , SECRUSH Output from SECRUSH - Model P r e d i c t i o n s Observed Data  for  - 175 :SECONDARY CRUSHER  1 * * * PROGRAM; TURKEY VERSION 2 * 3 * 29 DIM N (3,10) , J (22) 30 DIM A ( 1 , 2 2 ) , D ( 1 , 2 2 ) , X < 2 2 , 2 2 ) , Z (1,22) , Y (22, 1) ,Q (22,22) 33 DIM K(22) , V ( 2 2 ) ,S{22) ,H{22) ,G(22) ,R{22) 36 DIM P ( 1 5 , 1 5 ) , F ( 1 5 , 1 5 ) , T { 1 5 , 1 5 ) ,W{15,1) 3 8 READ N 1 , N 2 , A 3 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 S C F , S C P , S T V A L , S C O V , D U M P 172 MAT READ F I L E 1 , F ( N 2 , A 3 ) 173 MAT READ F I L E 2,T<N2,A3) 175 MAT READ F I L E 3 , A ( 1 , N 1 ) 178 MAT READ F I L E 4 , N ( 3 , A 3 ) 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 * I N I T I A L VALUES INPUTTED 210 * CALCULATION OF I N I T I A L STARTING VALUES 215 FOR .1=1 TO N1 220 D ( 1 , I ) = A B S ( G 2 * A ( 1 , I ) ) 225 NEXT I 230 * SET UP I N I T I A L 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 T 3 = 1 . E 7 0 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  - 176 460 465 470 480 490 500 510 520 530 540 5 50 560 570 580 590 593 595 6 00 610 6 20 630 635 640 642 650 655 660 665 670 675 6 90 695 696 700 7 02 704 705 706 7 07 708 7 09 711 712 714 716 718 719 720 721 722 7 23 724 729 730 732 734 736 738 740 742  T1=T1/(N1+1) FOR 1=1 TO N1+1 T2=T2+(Y ( I . 1)-T1) **2 NEXT I T4=SQR (T2/N1) I F T 4 > 1 . E - 6 THEN 730 GO TO 590 * PRINTOUT SECTION PRINT PRINT "CYCLE L I B I T 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 PRINT P R I N T " H I G H = » ; Y (H,1) ,"2ND HIGH=";Y (S , 1) ,"LOW=";Y (1,1) PRINT GO TO 600 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y { L , 1 ) PRINT PRINT "STANDARD DEV IATION="; T4 H=L GO SUB 1310 PRINT PRINT PRINT "ALPHA CONSTANTS" PRINT "A1 = ";ABS (X{H 1) ) , " A2=" ; X (H , 2) , "A3="; X (H, 3) ,"A4=";X (H,4) PRINT PRINT "K1 CONSTANTS" PRINT "A5=";X (H,5) , »A6 = " ; X (H, 6) ,"A7=" ;X (H ,7) , "A 8= " ; X (H,8) PRINT PRINT "K2 CONSTANTS" PRINT "A9=";X(H,9) ,"A10=";X (H, 10) , » A 1 1="; X ( H , 11) ,"A12=";X (H,12) PRINT PRINT PRINT PRINT PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS =";Z9 FOR 1=1 TO A3 A9=0 PRINT PRINT "RUN N O . " ; I PRINT PRINT " S I Z E " , " M E A S . PR0D","P8ED. PROD", "DIFFERENCE" PRINT PRINT FOR J=1 TO N2-1 PRINT S (J+1) T ( J , I ) , P ( J , I ) , T ( J , I ) - P ( J , I ) A9=A9+ ( T ( J , I ) - P ( J , I ) ) **2 NEXT J PRINT " P A N " , T ( N 2 , I ) , P ( N 2 , I ) , ( T ( N 2 , I ) - P ( N 2 , I ) ) PRINT A9=A9+ ( T ( N 2 , I ) - P (N2,I) ) **2 PRINT "RESIDUAL SUM SQUARES=";A9 PRINT NEXT I STOP I F Z9>M2 THEN 530 I F Z9>M3 THEN 736 GO TO 745 M3=M3+300 M4=CMD("%EMPTY DUMP3D") MAT WRITE F I L E 5.X M5=CMD("ISAVE DUMPSID") 3  r  r  - 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 ) = P 1 870 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 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) =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 I F Y1>Y(H,1) THEN 1200 1 170 Y ( H 1) =Y1 1180 GO TO 430 1190 * REDUCE S I Z E 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 f  - 178 1311 1312 1314 1318 1322 1 326 1327 1 328 1341 1342 1346 1350 1354 1362 1366 1368 14 82 1484 1486 1490 1494 1498 1502 1 506 1510 1512 1514 1518 1522 1526 1530 1534 1538 1540 1544 1546 1548 1549 1550 1608 1630 1650 1655 1660 1670 1675 1680 1690 1710 1715 1720 1740 1741 1750 1760 1770 1771 1780 1790 1800  FOB K=1 TO A3 11=0 L2=1 L4=0 L5=0 Z1=X ( H , 1) + X ( H , 2) *N (1 , K) + X (H,3) *N (2,K) + X (H,4) *N (3 ,K) Z4=X (H,5) +X(H,6) *N (1,K) +X(H,7) *N (1,K)**2+X (H , 8) *N (3 , K) Z5=X (H,9) +X (H,10) * N ( 1 , K J + X ( H , 1 1) *N (1,K) **2 + X (H,12)*N (3,K) FOR U=1 TO N2-1 L1 = 1 - { 1 - ( S <U+1)/S2)**2)**6 K{U)=L2-L1 L2=L1 L4=EXP{-{ (S (0+1)/2) **.664) ) J(U)=L4-L5 L5=L4 NEXT 0 FOR U=1 TO N2 I F S{U)>Z5 THEN 1506 I F S(CJ)<Z4 THEN 1498 H(U)=S ( U ) - ( S < 0 ) - Z 5 ) * * 3 / ( 3 * ( ( Z 4 - Z 5 ) **2)) GO TO 1510 H (0) =Z 4- (Z4-Z5) / 3 GO TO 1510 H (U) =S (0) NEXT 0 Z6=0 FOR 0=1 TO N2-1 V (0) = (H(U)-H(U+1) ) / (S (O)-S (0+1) ) A5=0 B5=0 FOR V=1 TO 0-1 A5=A5+ (Z1*K (U-V+1) + (1-Z1) * J (U) )*R(V) B5=B5 + J{?) NEXT V G (•) = (F (0,K) +A5) / {1- (Z1*K < 1) + < 1-Z1) * (B5* J(U) ) ) *V (0) ) R (0) =V (U) *G (U) P (U,K)=G (U) -R{0) Z6=Z6 + P ( U , K ) NEXT U P(N2,K)=100-Z6 * CALCULATION OF OBJECTIVE FUNCTION FOR POLYGON VERTICES FOR U=1TO N2-1 F2 = F2+W ( U , 1) * (T (U, K) - P (U,K) ) **2 NEXT U F2=F2+100* (T <U, K) - P (U, K) ) **2 NEXT K Y1=F2 Z9=Z9+1 RETURN * OBJECTIVE FUNCTION MAGNITUDE LISTING (ORDER SEARCH) I F Y ( 1 , 1 ) > Y ( 2 , 1 ) THEN 1770 S=1 L=1 H=2 GO TO 1790 S=2 L=2 H=1 FOR 1=3 TO N1+1 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 1 2 , 1 4 , 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 END-OF-FILE  -  I tfU -  1 *** PROGRAM: SECRUSE :SECONDARY CRUSHER HODEL 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 HEAD N2,A2,S1,A3,A4 24 MAT P=ZER(N2,A3) 50 F I L E SCF,SCP,SCOV 60 MAT READ 2 I L E 1,F(N2,A3) 70 MAT READ T I L E 2,T(N2,A3) 80 MAT READ T I L E 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 R  120 S(I) =S1*Jk2** (1-1)  130 140 150 160 170 200 205 206 207 20 8 210 23 0 250 255 27 0 280  NEXT I S2=SQR (S (1) *S (2) ) I F A4=0 THEN 205 A3 = A4 GO TO 210 *CALCUIA1'I0N OF PREDICTED DISTRIBUTION A4=1 PRINT PRINT "COMPUTED VALUES OF MODEL PABAMETERS" PRINT FOR K=A4 TO A3 L2=1  15=0  Z1=A20+A21*N (1 ,K) +A22*N(2,K) +A23*N (3,K) FOR U=1 TO N2-1 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 I F S{U)>Z5 THEN 440 390 I F S (U) <2,4 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 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) 0  - 181 530 NEXT V 540 G{U) = (F (U,K) + A 5 ) / (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 ( N 2 , K ) = 1 0 0 - Z 6 620 C(K)=A60-i-A61*N(1,K) + A62*N(2,K) 630 PRINT "RON NUMBER=";K 635 Z1=INT{Z1*100000+.5) / 1 0 0 0 0 0 636 Z4=INT{Z4*100000+.5)/100000 637 Z5 = INT (Z5*100000 + . 5 ) / 1 0 0 0 0 0 640 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) / 1 0 0 0 0 656 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 " S I Z E " , " M E A S U R E D " , " P R E D I C T E D " , " D I F F E R E N C E " 741 PRINT " (CM.) ","PRODUCT","PRODUCT" 750 PRINT 755 FOR J=1 TO N2 756 P ( J , K ) =INT(P ( J , K ) *1O00 + . 5 ) / 1 0 0 0 757 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 2 0 . 6 1 8 2 , - 7 . 3 2 3 3 9 3 , . 0 3 4 5 1 5 8 1000 END END-OF-FILE  - 183 l e v i c e : DS40 task: 2241 USERID: RALU 09:04:34 08-16-77 U n i v e r s i t y o f B r i t i s h C o l u m b i a Computing C e n t r e - a e v i c e : DS40 I SIGN RALU £ ENTER USER PASSWORD, ft » » ft &  * * L A S T SIGNCN WAS: 0 8 : 3 7 : 0 1 USER "RALU" SIGNED ON AT 0 9 : 0 3 : 1 0 ON TUE AUG 16/77 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM  > ?  : GET SECRUSH : RUN COMPUTED VALUES OF MODEL PARAMETERS RUN NUMBER= 1 A.LPHA= 0. 68-923 RUN NUMBER= 2  K1=  5-58928  K2=  12.75747  ALPHA= 0.73686  K1=  6.66409  K2=  12.39 765  K1=  5, 356 27  K2=  12.75868  K1=  9.1991  K2=  11.49089  K1=  8.2317  K2=  11.62927  K1=  6, 19388  K2=  1 1. 1725  K1=  6.16672  K2=  12.60 702  K1=  6.7067  K2=  1 1.05499  RUN NUMBER= 3 ALPHA= 0.68529 RUN NUMBER= 4 ALPHA= 0.78095 RUN NUMBEB= 5 ALPHA= 0 . 8 2 4 8 3 RUN NUMBER= 6 AIPHA= 0.59324 RUN NUMBER= 7 ALPHA= 0.73797 SUN NUMBER= 8 ALPHA= 0.52012  *************************************************************** SIZE  ANALYSES REPORTED AS WT. PERCENT RETAINED ON S I Z E  **********************:*************************  ****************  RUN NUMBER= 1 SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT,  DIFFERENCE  2 1. 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  0 0 17 45 23.9 6.05 2.24 1.56 1.07 0.87 0.69 0.59 0.46 0.57  0 0.085 17.018 43. 112 22.689 7.727 3. 1 36 1.817 1.238 0.968 0.721 0.532 0.389 0.568  0 -0.085 -0.018 1. 888 1.211 -1.677 -0.896 -0.257 -0.168 -0.098 -0.031 0. 058 0. 071 0. 002  RESIDUAL  SUE OF SQUARES=  SUM= 100 8.767006  task:  224  - 184 PREDICTED  CURRENT  OPERATING  CONDITIONS:  GAP= 3 . 2 3 9 (CM.)  3  21-09676  FEE DRATE (TPH)  RON NUMBER  3  3  701.1  % +1INCH IN F E E D  81.9  3  93.7  2  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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  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  0 0. 12 29. 174 38.365 17.095 6.426 3.046 1.851 1.21 0. 844 0.616 0. 441 0.309 0.502  0 -0.12 -5.174 4. 135 0. 505 -0.276 -0.296 0. 119 0. 12 0. 196 0.204 0.209 0.211 0. 168  RESIDUAL SUE OF  SQUARES  PEEDICTED CURRENT OPERATING  3  3  3  SUM 44.52674  3  100  23.12155  CONDITIONS:  GAP= 3 . 0 8 6 (CM.)  RUN NUMBER  FEEDRATE (TP H)  3  3  727.3  % +1INCH IN F E E D  3  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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 16 39.5 22. 5 8.2 4 2.8 2 1.47 1.28 0.98 0.63  0 0.09 16.051 42.248 23. 29 8 7.348 3.365 2.232 1.586 1. 172 0.95 0.671 0. 441  0 -0.09 -0.051 - 2 . 7 48 -0.798 0. 852 0. 635 0.568 0. 414 0. 298 0.33 0.309 0. 189  PAN  - 185 0.549  0.64  SUM RESIDUAL  SUfi OF SQUARES  PREDICTED CURRENT OPERATING GAP 3.15 (CM.)  3  3  100  10.15935  3  22.56656  CONDITIONS: FEEDRATE 724.8 {TPH)  3  % +1INCH IN F E E D  3  RUN NUMBER  3  0. 091  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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  0 0 31 42 15. 9 4.4 2.05 1.25 0.89 0.68 0.56 0.47 0.35 0.45  0 0.033 31. 57 6 41.059 17.456 4.282 1.846 1.058 0.728 0. 544 0. 454 0.358 0.256 0.351  0 -0.033 -0.576 0. 941 -1.556 0. 118 0. 204 0. 192 0. 162 0. 136 0.106 0. 112 0. 094 0. 09 9  SUM OF SQUARES  PREDICTED  82  3  85.9  4  SIZE '{CM.)  RESIDUAL  3  CURBENT  3  SUM 3 . 819043  3  3  100  15.10533  OPERATING CONDITIONS: GAP 3 . 7 4 7 (CM.)  FEEDRATE (TPH)  3  RUN NUMBER  3  3  635.3  % +1INCH IN F E E D  5  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  21.76 10.88 5.44 2.72 1. 36 0.68 0.34 0 . 17 0.085  0 0 26 37 18. 2 6 3.2 2.65 2  0 0.019 25.641 37. 09 18.389 6.951 3.259 2.542 1.979  0 -0.019 0. 359 -0.09 -0.189 -0.951 -0.059 0. 108 0. 021  - 186 0.0425 0.0212 0.0106 0.0053 PAN  1.71 1.29 0.91 0.51 0.53  RESIDUAL SUB OP  1. 529 1.154 0.726 0. 355 0. 365  SQUARES  PREDICTED CURRENT  3  0. 0. 0. 0. 0.  181 136 184 155 165  SUM= 100 1.229413  3  20.14593  OPERATING CONDITIONS: GAP 3.785 (CM.)  FEEDRATE 789.4 (TPH)  3  RUN NUMBER  % +1INCH IN F E E D  3  3  3  75.1  3  82.8  6  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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  0 0 16 39 21 9 3.9 3.2 2. 4 1.87 1.43 1.05 0.61 0.54  0 0.001 16.657 39.043 2 1. 428 8.528 4. 284 3 . 136 2. 189 1.637 1. 19 0.8 0.493 0.613  0 -0.001 -0.657 -0.043 -0.428 0. 472 -0.384 0. 064 0.21 1 0.233 0.24 0.25 0. 117 -0.073  RESIDUAL SUC OF SQUARES PREDICTED CURRENT  3  SUM 1. 228947  3  3  100  29.01849  OPERATING CONDITIONS: G A P 2.54 (CB.)  FEEDRATE (TPH)  3  RUN NUMBER  3  3  782.3  % +1INCH IN F E E D  7  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  21.76 10.88 5.44 2.72 1.36  0 0 23 42.5 19.1  0 0.117 21.359 43.196 19.673  0 -0.117 1. 641 -0.696 -0.573  - 187 0.68 0.34 0.17 0.085 0.0425 0.0212 0.0106 0.0053 PAN  5.4 2.8 1.95 1.3 1.07 1.05 0.8 0.53 0.5  6 . 4 33 3.051 1. 862 1.221 0.941 0 . 7 56 0. 529 0.376 0.484  RESIDUAL SUfi OP SQUARES= PREDICTED CURRENT^  -1.033 -0.251 0. 088 0. 079 0. 129 0. 294 0. 271 0. 154 0. 016  SUM= 100 4. 86388  22.76645  OPERATING CONDITIONS: GAP= 3 . 2 (Ca.)  FEEDRATF= 7 4 1 . 2 {TPH)  % +1INCII IN FEED=  87.6  RUN NUMBER = 8 SIZE {CM.)  MEASURED PEODUCT  PREDICTED PRODUCT  DIFFERENCE  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  0 0 20 39 22. 7 7.3 2.9 2.35 1.6 1.27 1.09 0. 82 0.51 0.46  0 0 19.364 42. 373 18.216 7.017 3.886 2.702 1.9 49 1.497 1. 107 0.755 0.476 0.658  0 0 0. 636 -3.373 4. 48 4 0. 283 -0.986 -0.352 -0.349 -0.227 -0.017 0.065 0. 034 -0.198  RESIDUAL SUM OF SQUARES^ PREDICTED COERENT=  SUM= 100 3 3 . 28227  23.68235  OPERATING CONDITIONS: GAP= 2 . 5 4 {CM.)  FEEDRATE= 6 2 7 . 7 (TPH)  r ?STOP! ^ ? AT LINE "900" IN PROGRAM "SECRUSH" t ? PROGRAM ENDS : MTS * CONTROL *PRINT* HOLD P « I N T = T N FORM=8X11 It *PRINT* ASSIGNED RFS NUMBER 664582 I COPY *MSOUBCE*aSP *PRINT*  fo +1INCH IN FEED= 87  - 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 C r u s h e r M o d e l , TERCR Output from TERCR - Model P r e d i c t i o n s Observed Data  for  -  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 ( 2 2 ) , H (22) , G (22) , R ( 2 2 ) 36 DIM P ( 1 5 , 1 5 ) , F { 1 5 , 1 5 ) , T (15,15) ,W (15,1) 3 8 READ N 1 , N 2 , A 3 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 ( N 2 , A 3 ) 173 HAT READ F I L E 2 , T ( N 2 , A 3 ) 175 MAT READ F I L E 3 , N (3,13) 178 MAT READ F I L E 4 , A ( 1 , N 1 ) 182 READ A 2 , S 1 , M 3 184 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 * I N I T I A L VALUES INPUTTED 210 * CALCULATION OF I N I T I A L STARTING VALUES 215 FOR 1=1 TO N1 220 D ( 1 , I ) = A B S ( G 2 * A ( 1 , I ) ) 225 NEXT I 230 * SET UP I N I T I A L 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 T 3 = 1 . E 7 0 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  - 190 480 490 500 510 520 530 540 550 560 570 580 590 593 595 600 610 620 630 635 6 40 6 42 645 650 652 655 662 6 65 668 670 678 6 80 6 82 6 85 688 690 695 6 96 700 7 02 703 704 705 706 707 7 08 7 09 711 712 714 716 718 719 720 721 722 7 23 724 729 730 732  NEXT I T4=SQR (T2/N1) I F T 4 > 1 . E - 6 THEN 730 GO TO 590 * PRINTOUT SECTION PRINT 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 PRINT PRI NT" HIGH= " ; Y (H, 1) , » 2 N D HIGH=»;Y (S, 1) , "LOW=" ; Y (L , 1) PRINT GO TO 600 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y ( L , 1 ) PRINT PRINT "STANDARD DEVIATION=";T4 H=L GO SUB 1310 PRINT PRINT PRINT "ALPHA CONSTANTS" PRINT "A1 = ";ABS (X (H , 1) ) , "A2=" ; X (H ,2) , "A3=";X (H,3) ,"A4 = " ; X (H,4) PRINT PRINT "A5=";X(H,5) PRINT "BETA CONSTANTS" PRINT PRINT "A6=";ABS (X (H,6) ) ,"A7=";X (H,7) , "A8="; X (H, 8) , " A 9 = » ; X (H,9) PRINT PRINT "K1 CONSTANTS" PRINT PRINT "A10=";X (H, 10) ,"A11=";X (H, 1 1) PRINT PRINT "K2 CONSTANTS" PRINT PRINT " A 1 2 = " ; X | H , 1 2 ) , " A 13=" ; X (H , 1 3) , » A 1 4 = " ; X{H, 14) ,"A15=" ;X (H,15) PRINT PRINT "A16 = " ; X ( H „ 1 6 ) , " A17=";X (H, 17) PRINT PRINT PRINT "NUMBER OF OBJECTIVE FUNCTION CALCULATIONS = » ; Z 9 FOR 1=1 TO A3 PRINT "##############################################################" A9=0 PRINT PRINT "RUN N O . " ; I PRINT PRINT " S I Z E " , " H 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 " PRINT PRINT FOR J=1 TO N 2 - 1 PRINT S (J + 1) , T ( J , I ) , P ( J , I ) , T ( J , I ) - P { J , I ) A9=A9*<T(J,I)-P(J,I))**2 NEXT J PRINT « P A N " , T ( N 2 , I ) , P { N 2 , I ) , C T < N 2 , I ) - P ( N 2 , I ) ) PRINT A9=A9+ (T (N2,I) - P ( N 2 , I ) ) **2 PRINT "RESIDUAL SUM SQUARES=";A9 PRINT NEXT I STOP I F Z9>M2 THEN 530 I F Z9>M3 THEN 736  -  iyi  -  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 ) / N 1 830 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 ) = P 1 870 NEXT J 880 GO SUB 1310 890 MAT X = (1) *Q 900 ¥ = Y 1 910 I F Y>=Y{L,1) THEN 1000 9 20 * EXPANSION 930 FOR J = 1 TO N1 940 X ( H , J ) = ( 1 + V 1 ) * 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 S I Z E 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 1311 1312 1313 1314 1318 1320 1325 1330 1335 1337 1338 1341 1342 1346 1350 1354 1362 1366 1368 1482 1484 1486 1490 1494 1498 1502 1506 1510 1512 1514 1518 1522 1526 1530 1534 1538 1540 1544 1546 1548 1549 1550 1608 1630 1635 1636 1640 1645 1650 1655 1660 1675 1680 1690 1710 1715 1720 1740 1741  F2=0 FOR K=1 TO A3 I F K=6 THEN:K=7 I F K=10 THEN 1675 L2=1 L5=0 Z20=X ( H , 3 ) / ( 1 + X ( H , 4 ) * ( N ( 2 , K ) - X (H,5)) **2) Z1=Z20 + ABS(X{H,1)) +X(H, 2)*N (2, K) Z2=ABS (X (H,6) } +X (H,7) *EXP(X (H, 8) *Z1**X (H,9) ) Z4=X(H,10)+X(H,11) *N(3,K) Z 2 3 = ( X ( H , 1 4 ) / ( 1 + X ( H , 1 5 ) * ( N (1 , K ) - X (H, 16) ) **2) ) * * X (H,17) Z5=X(H,12) * X ( H , 1 3 ) * N ( 1 , K ) - Z 2 3 FOR 0=1 TO N2-1 11 = 1- ( 1 - (S (D+1J/S2) **4) **Z2 K(U)=L2-L1 L2=L1 L4=EXP(-{<S(U+1)/2) * * . 6 6 4 ) ) J<D)=I4-L5 L5=L4 NEXT 0 FOR 0=1 TO N2 I F Si(0)>Z5 THEN 1506 I F S(0)<Z4 THEN 1498 H (U) =S (U) - (S (0) - Z 5 ) * * 3 / { 3 * { (Z4-Z5) **2) ) GO TO 1510 H (U) = Z 4 - ( Z 4 - Z 5 ) / 3 GO TO 1510 H (U) =S {0) NEXT 0 Z6=0 FOR 0=1 TO N2-1 V (U)= {H (U)-H (0 + 1) ) / { S (U)-S (0 + 1)) A5=0 B5=0 FOR V=1 TO 0-1 A5=A5+ (Z1*K (U-V+1) + (1-Z1) * J (U) ) *B (V) B5=B5+J(V) NEXT V G (U) = (F (U,K) +A5) / ( 1- (Z1 *K (1) * (1-Z1) * (B5 + J(U) ) ) *V (U) ) R(0)=V(U) *G(U) P (0,K)=G (U)-B (U) Z6=Z6 + P ( U , K ) NEXT 0 P(N2,K)=100-Z6 * CALCULATION OF OBJECTIVE FUNCTION FOR POLYGON VERTICES P10=0 P11=0 I F Z4<=0 THEN:P10=2*EXP (10* (-Z4) )-1 I F Z4>=Z5 T H E N : P 1 1 = 2 * E X P ( 1 0 * ( Z 4 - Z 5 ) ) - 1 FOR U=1 TO N2 F2=F2+ CT (U,K) - P { U , K ) ) **2+P10 + P11 NEXT U NEXT K Y1=F2 Z9=Z9+1 RETURN * OBJECTIVE FUNCTION MAGNITUDE LISTING (ORDER SEARCH) I F Y { 1 , 1 ) > Y ( 2 1) THEN 1770 S=1 L=1 f  - 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 1810 L=I 1820 I F Y ( I , 1) < Y ( S , 1) THEN 1830 I F Y (1,1) <Y(H, 1) THEN 1840 S=H 1850 H=I 1860 GO TO 1880 1870 S=I 1880 NEXT I 1890 RETOBN 1895 DATA 1 7 , 1 4 , 1 0 1900 DATA . 5 , 4 3 . 5 2 , 1 0 0 0 1950 DATA 1 , . 5 , 2 , . 0 1 , 1 0 2000 END END-OF-FILE  1820 1880 1870  -  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 ( 1 5 , 1 5 ) , F ( 1 5 , 1 5 ) , T { 1 5 , 1 5 ) , N ( 3 , 1 5 ) 22 BEAD N 2 , A 2 , S 1 , A 3 , A 4 24 MAT P=ZER(N2,A3) 50 F I L E T C F , T C P , T C O V C , C O N S T 60 MAT READ F I L E 1 , F ( N 2 , A 3 ) 70 MAT READ F I L E 2 , T ( N 2 , A 3 ) 80 MAT READ F I L E 3 , N { 3 , A 3 ) 85 * READ MODEL CONSTANTS 90 READ A 2 0 , A 2 1 , A 2 2 , A 2 3 , A 2 4 95 BEAD A 3 0 , A 3 1 , A 3 2 , A 3 3 100 HEAD A40,A41 105 READ A 5 0 A 5 1 , A 5 2 , A 5 3 , A54,A55 110 READ A 6 0 , & 6 1 , A 6 2 115 FOR 1=1 TO N2 120 S(I) =S1*A2**{I-1) 130 NEXT I 140 S2=SQR (S (1) *S(2) ) 150 I F 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 I F K=6 THEN:K=7 225 I F K=10 THEN 660 230 L2=1 250 L5=0 255 Z1 = A20 + A21*N (2,K) + ( A 2 2 / (1+A23* (N (2, K ) - A 2 4 ) **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 ) = L 2 - L 1 30 0 L2=L1 31 0 L4=EXP {- ( (S (Ut 1) / 2 ) * * . 664) ) 320 J ( U ) = L 4 - 1 5 330 L5=L4 340 NEXT U 350 Z4=A40 + A41*N (3,K) 360 Z 5 = A 5 0 * A 5 1 * N ( 1 , K ) - ( A 5 2 / ( 1 + A 5 3 * ( N ( 1 , K ) - A 5 4 ) **2) ) **A55 37 0 FOE U=1 TO N2 380 I F S(U)>Z5 THEN 440 390 I F S(U)<Z4 THEN 420 400 H(U) = S ( U ) - ( S ( U ) - Z 5 ) * * 3 / { 3 * ( (Z4-Z5) **2) ) 410 GO TO 450 420 H(U) = Z 4 - ( Z 4 - Z 5 ) / 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 #  #  - 195 495 500 510 520 530 540 550 560 565 570 610 620 630 635 64 0 650 660 700 701 702 703 704 705 710 715 716 72 0 722 724 726 727 728 729 735 740 741 750 755 756 757 758 76 0 770 780 790 792 796 800 804 810 820 821 822 826 830 835 838 840 850 880  B(0)=0 FOB V=1 TO U-1 A5=A5+ (Z1*K (U-V+1) * (1-Z1) * J (U) ) * R ( V ) B5=B5 + J ( V ) NEXT V G (0) =(F (U , K) + A5) / {1 - (Z 1 *K ( 1) • (1 - Z 1) * (B5+J { 0) ) ) * V (U) ) R(U)=V (U)*G (U) P(U,K)=G(U)-R{U) Z6=Z6+P(U,K) NEXT 0 P(N2,K)=100-Z6 C{K)=A60*A61*N(1,K) * A 6 2 * N ( 2 , K ) PRINT "BON NUMBER ";K Z1=INT(Z1*100000*.5)/100000 PBINT " A L P H A " ; Z 1 ; T A B { 18) ; " B E T A = " ; Z 7 , " K 1 " ; Z 4 , » K 2 = " ; Z 5 NEXT K PRINT"***************************************** *PRINTOUT SECTION PRINT PRINT " S I Z E ANALYSES REPORTED AS S T . PERCENT RETAINED ON S I Z E " PRINT PRINT"************************************************************ ***" PRINT FOR K=A4 TO A3 I F K=6 THEN:K=7 I F K=10 THEN;STOP A9=0 PRINT PRINT "RUN NUMBER=";K A18=0 FOR J=1 TO N2 A18=A18 + P { J , K ) NEXT J PRINT PBINT " S I Z E " , " M E A S U R E D " , " P R E D I C T E D " , " D I F F E R E N C E " PRINT " (CM.) ","PRODUCT","PRODUCT" PRINT FOR J=1 TO N2 P ( J , K ) = I N T ( P ( J , K ) * 1000+. 5) / I 000 S{ J) =1 NT (S ( J) *10000 + .5) / 1 0 0 0 0 NEXT J FOR J=1 TO N2-1 PRINT S (J+1) , T ( J , K ) , P ( J , K ) , T {J , K ) - P ( J , K) A 9 = A 9 * ( T ( J , K ) - P ( J , K ) ) **2 NEXT J A 9 = A 9 + ( T ( N 2 , K ) - P ( N 2 , K ) ) **2 PRINT "PAN";TAB (14) ; T (N2,K) ;TAB (29) ; P (N2,K) ; TAB (44) ; T ( N 2 , K ) - P ( N 2 , K ) PRINT PRINT T A B ( 3 1 ) ; " S U H = " ; A 1 8 PRINT "RESIDUAL SUM OF SQUARES=";A9 PRINT PRINT "PREDICTED C U R R E N T " ; C (K) PRINT PRINT "OPERATING CONDITIONS:" PRINT PRINT "GAP=";N (1,K) , " F E E D R A T E " ;N ( 2 , K) , " " , » $ +1INCH IN FEED—" ; N (3 ,K) PRINT " (CM. ) " , ' (TPH) " PRINT PBINT " . . . . . . . . . . . . . . . . . . . " NEXT K 3  3  3  3  3  1  - 196 900 STOP 910 DATA 1 4 , . 5 , 4 3 . 5 2 , 1 0 . 0 930 DATA . 1 1 3 3 8 1 2 , 1 . 1 7 8 0 7 8 E - 4 , . 5 1 8 0 7 6 , 3 . 6 3 2 1 7 6 E - 4 , 2 9 9 . 3 8 1 935 DATA 2 7 . 4 5 8 3 , 4 3 . 9 7 8 3 2 , - 2 5 9 9 . 7 6 2 , 1 6 . 7 6 6 29 940 DATA - 1 . 7 9 3 2 6 5 , 5 . 2 8 4 6 4 7 E - 2 94 5 DATA 6.331619,-.8040997,1.042385,2.996623,.7135176,17.96698 950 DATA 2 7 . 5 5 7 5 6 , - 9 . 6 0 8 8 7 1 , 5 . 5 4 2 0 4 1 E - 2 1000 END END-OP-FILE  - 197 e v i c e : DS20 task: 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 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS20 • SIGN RALU ' ENTER USER PASSWORD. ' : '• -  * * L A S T SIGNON WAS: 1 3 : 4 5 : 3 5 USER "RALU" SIGNED ON AT 1 3 : 4 7 : 4 6 ON TUE AUG 16/77 RUN *BASIC EXECUTION BEGINS ?UBC BASIC SYSTEM  •  ?  l  task:  222'  GET TERCR RUN COMPUTED VALUES OF MODEL PARAMETERS RUN NUMBER 1 ALPHA 0.66668 RUN NUMBER= 2 ALPHA 0.55844 RUN NUMBER 3 ALPHA 0.44047 RUN NUMBER 4 ALPHA 0.39154 RUN NUMBER 5 ALPHA 0.55131 RUN NUMBER 7 ALPHA 0.36837 RUN NUMBER 8 A L P H A 0.42698 RON NUMBER 9 ALPHA 0.24368 3  3  3  BETA  3  29.87378  K1 =  1. 377523  K2=  3.69241 9  BETA  3  65.35574  K1 = 1. 773872  K2=  3.860186  BETA  3  71.31435  K1 = 2. 196643  K2  3  3.860481  BETA  3  71.41962  K1 =  1. 641756  K2=  3.992796  BETA  3  66.46409  K1 =  1. 905988  K2=  5.458353  BETA  3  71.43051  K1 = 2. 011681  K2=  5.742872  BETA  3  71.36399  K1 = 0. 796212  K2=  5 . 5 94 909  BETA  3  71.43661  K1 = 1. 853141  K2=  5.443298  3  3  3  3  3  3  3  3  3  3  3  3  *************************************************************** S I Z E ANALYSES REPORTED AS WT. PERCENT RETAINED ON S I Z E *********************************************  RUN NUMBER  3  1  SIZE (CM.),  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFER  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  0 0 0 0 38. 5 34.5 10 6 3.4 2.55 1.9 1.31 0.89 0.95  0 0 0 1. 137 39.171 35. 102 13.493 4.009 2.306 1.557 1.077 0.723 0.487 0.938  0 0 0 -1.137 -0.671 -0.602 -3.493 1.991 1. 094 0.993 0. 823 0. 587 0.403 0.012  SUM  3  100  - 198 RESIDUAL  SOB OF SQUARES  PREDICTED CURRENT OPERATING  3  21.63788  3  37.05207  CONDITIONS:  GAP 0.737 (CM.)  FEEDRATE {TPH)  3  RUN NUMBER  3  3  299.1  % *1INCH IN F E E D  60  2  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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  0 0 0 0 42 31 9.6 5.8 3.4 2.55 2 1.47 1.08 1.1  0 0 0 2.377 42. 22 30.339 12.306 4.394 2.692 1.817 1.25 0.881 0.613 1. 109  0 0 0 -2.377 -0.22 0. 661 - 2 . 7 06 1. 406 0.708 0. 733 0.75 0.589 0. 467 -0.009  RESIDUAL SUM OF  SQUARES  PREDICTED CURRENT OPERATING  3  3  3  SUM 17.60087  3  100  36. 21502  CONDITIONS:  GAP 0.673 (CM.)  FEEDRATE (TPH)  3  RUN NUMBER  3  3  272.9  % +1INCH IN F E E D  3  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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 0 0 2 47.5 26.5 8.5 4.7 3.2 2.25 1.9 1.4  0 0 0 4. 106 45.497 26.237 9.478 4.851 3.208 2. 196 1.5 1.002  0 0 0 -2.106 2.003 0.263 -0.978 -0.151 -0.008 0.054 0.4 0.398  3  67.5  - 199 0.0053 PAN  1.02 1.03  0,686 1.239  0.334 -0.209  SUM= 100 RESIDUAL  SUH OF SQUARES=  PREDICTED CUR8ENT= OPERATING  9.97232  39.44431  CONDITIONS:  GAP= 0.762 (CM.)  FEEDRATE= 3 4 6 . 6 (TPH)  % +1INCH IN FEED=  75.5  RUN NUMBER= 4 SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  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.G053 PAN  0 0 0 5.5 38. 5 26.7 10. 3 €.2 4.2 2.9 2.05 1.5 1.05 1.1  0 0 0 2. 425 39.972 26.459 13.314 6.023 3.873 2.607 1.759 1.208 0.853 1,509  S0M= RESIDUAL SUM OF SQUARES= 2 1 . 3 6 4 8 3 PREDICTED  CURRENT=  OPERATING  CONDITIONS:  GAP= 0 . 6 6 (CM.)  RUN  NUMBER=  DIFFERENCE  0 0 0 3.075 -1.472 0. 241 -3.014 - - 0.177 0. 327 0.29 3 0.291 0. 292 0. 197 -0.409  100  34.78816  FEEDRATE= (TPH)  244.9  % +1INCH IN FEED= 65  5  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  21.76 10,88 5.44 2.72 1.36 0.68 0.34 0 . 17  0 0 0 10 42 23,5 8.7 5. 1  0 0 0 11.359 45.983 22. 883 7.901 3.329  0 0 0 -1.359 -3.983 0. 617 0.799 1.771  - 200 0.085 0.0425 0.0212 0.0106 0.0053 PAN RESIDUAL  3.2 2.25 1. 75 1.27 1 1.23  2. 117 1.437 0. 976 0.67 0.476 2.871  SUM OF SQUARES  PREDICTED CURRENT OPERATING  3  3  SUM 27.62709  3  1. 083 0. 813 0.774 0. 6 0. 524 - 1 .641 100  35.35787  CONDITIONS:  GAP= 1.08 (CM.)  FEEDRATE (TPH)  RUN NUMBER  3  3  328  % +1INCH IN F E E D  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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  0 0 0 16 42 19.7 7.4 4.3 2.9 2.35 1.85 1.45 1.01 1.04  0 0 0.002 15.624 43.889 19.608 7.785 4. 271 2.835 1.936 1.313 0.891 0.621 1.226  0 0 -0.002 0.376 -1 . 8 8 9 0. 092 -0.385 0.029 0. 065 0. 414 0. 537 0. 559 0.389 -0.186  SUM OF SQUARES  PREDICTED CURRENT OPERATING  70  3  72  7  SIZE (CM.),  RESIDUAL  3  3  3  SUM 4.829619  3  100  36.09653  CONDITIONS:  GAP 0.495 (CM.)  FEEDRATE (TPH)  3  RUN NUMBER  3  3  239.9  % *1INCH IN F E E D  8  SIZE (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  21.76 10.88 5.4 4 2.72  0 0 0 6  0 0 0 5.775  0 0 0 0. 225  1.36 0.68 0 . 34 0 . 17 0.085 0.0425 0.0212 0.0106 0,0053 PAN  RESIDUAL SUB OF  -3.967 6.074 -5.41 -0.177 0.417 0. 493 0. 766 0.707 0.546 0.326  SUM= 100 SQUARES= 8 3 . 8 8 8 5 5  PREDICTED CURRENT= OPERATING  - 201 39.967 23. 426 15.91 5. 877 3.083 2.007 1.334 0.893 0.614 1.114  36 29.5 10.5 5.7 3.5 2.5 2.1 1.6 1.16 1.44  41.90415  CONDITIONS:  GAJP= 0.521 (CM.)  FEEDRATE= 3 4 9 . 2 (TPH)  % +1INCH IN FEED= 49  HUN NUMBER= 9 SI2E (CM.)  MEASURED PRODUCT  PREDICTED PRODUCT  DIFFERENCE  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  0 0 0 15 45 19.6 7.4 4 2.7 1.95 1.62 1.06 0.77 0.9  0 0 0 11.755 44. 897 18.063 9. 124 5. 355 3.624 2. 445 1. 626 1.086 0.729 1.295  0 0 0 3.245 0. 103 1. 537 -1.724 -1.355 -0.924 -0.495 - 0 . 0 06 -0.026 0.041 -0.395  RESIDUAL SUM OF SQUARES= PREDICTED CURRENT=  SUM= 18. 96842  100  41.76555  OPEBATING CONDITIONS: GAP= 0 , 9 5 3 (CM.)  FEEDRATE= 4 2 1 . 6 (TPH)  • ?STOP! y ? AT L I N E "716" IN PROGBAM "TERCB" y ? PROGRAM ENDS : MTS \ CONTROL *PRINT* HOLD PRINT=TN F0RM=8X11 t *PRINT* ASSIGNED RFS NUMBER 664962  % +1INCH IN FEED=  69  -  202  APPENDIX G DERIVATION OF A SCREEN EFFICIENCY EQUATION by A . L . M u l a r and  C.C.  Hatch  - 203 -  DERIVATION OF A SCREEN EFFICIENCY EQUATION  By A. L . Mular* and C. t). Hatch**  INTRODUCTION i n crushing plant simulation ( 1 , 2 ) has stimulated the development  Interest  of an e f f i c i e n c y equation f o r v i b r a t i n g screens as reported by Whiten (2)• Whitens equation appears to be a modification of one proposed by Gaudin (3] More r e c e n t l y , Ferrara and P r e t i (4) summarized the l i t e r a t u r e  many years ago.  which dealt with screening k i n e t i c s and proposed the use of a l t e r n a t i v e equations based p a r t l y upon mechanism. (  Gaudins expression was employed.  The purpose of t h i s note i s to derive a new e f f i c i e n c y equation and show * *•*  how well i t f i t s  screening data acquired at the Brenda Mines Limited  secondary  crushing p l a n t . PARTICLE SIZE AND SCREEN INEFFICIENCY Consider a screen deck onto which i s fed p a r t i c l e s of various sizes, and shapes per unit time.  A screen analysis of a representative p o r t i o n of feed  may be performed to determine the feed size d i s t r i b u t i o n .  The s i z e of p a r t i c l e s  trapped between any two sieves i s often reported as the geometric mean s i z e of the two s i e v e s , i . e . , of s i z e X^.  = ^jxTx"^" .  However, not a l l of these p a r t i c l e s are  The actual s i z e of a single p a r t i c l e i s perhaps b e t t e r defined with,  respect to i t s  centroid by 3 dimensions.  a p a r t i c l e trapped between sieves X.. and  On t h i s b a s i s , the p r o b a b i l i t y that +  ^ has exactly the same dimensions as  any other p a r t i c l e i n t h i s size range cannot be very l a r g e .  *  Still,  in a practical  Professor of Mineral Engineering, U n i v e r s i t y of B r i t i s h Columbia, Vancouver Research A s s i s t a n t , Department of Mineral Engineering, U n i v e r s i t y of B. C , Vancouver  ***  Peachland, B. C.  ;:i  - 204 -  sense, no attempt i s made to d i s t i n g u i s h between p a r t i c l e s i n the s i z e range. For that matter, i n a p r a c t i c a l screen operation, we seldom d i s t i n g u i s h between i n d i v i d u a l p a r t i c l e s i n the feed to a screen, except to determine the proportion of t o t a l feed that passes or does not pass through the screen openings. information i s used to c a l c u l a t e gross screening  Such  efficiency.  Continuous screens which operate i n crushing plants are seldom 100% efficient.  This suggests that a proportion of c e r t a i n s i z e f r a c t i o n s fed to  a screen can be "bypassed" to the oversize stream.  I f c, = f r a c t i o n of feed  of a narrow s i z e range that "bypasses" to the coarse stream, then an e f f i c i e n c y equation may be corrected accordingly.  When o^ p a r t i c l e s of a narrow s i z e  range report to the oversize stream, while f^ p a r t i c l e s of the same s i z e range are being fed to the screen, the f r a c t i o n of the feed p a r t i c l e s which are not involved i n bypassing i s given by o.  - c.f.  Y. - c.  f.  - c.f.  1  1  where  =  1  1  -  C  v  1  1  6  o. ^— , c^ i s a measure of i n e f f i c i e n c y for each s i z e f r a c t i o n i , and i  i s the most probable f r a c t i o n of that p o r t i o n of a narrow feed s i z e range not involved i n bypassing that reports to the oversize. for  A suitable  expression  P^ i s necessary at t h i s stage.  DERIVATION OF AN EXPRESSION FOR P. l Figure 1 i s a diagram of a v i b r a t i n g screen being fed with F p a r t i c l e s per  unit time, where the p a r t i c l e s have a continuous d i s t r i b u t i o n of s i z e s .  Assume that i n one retention time p e r i o d , T , F p a r t i c l e s (not involved i n bypassing)  are fed to a v i b r a t i n g screen at steady s t a t e .  a narrow s i z e f r a c t i o n of these p a r t i c l e s .  Let the number of p a r t i c l e s of  geometric mean s i z e X. be F . , whereT*F. = F. 1  size  X  X  After time T , U. p a r t i c l e s o f X  have passed through the screen, while  r e t a i n e d as part of the oversize stream.  Consider, i n i t i a l l y ,  - U\ p a r t i c l e s have been  The number of p a r t i c l e s , U^, that pass  - 205  -  F,  #  r. © otoodti  ©OOOO  F-U=2F;-U:  ©  U,U; U =2 U ; FIGURE 1 SCHEMATIC REPRESENTATION OF A VIBRATING SCREEN  206 -  through the screen, among other t h i n g s , depends on p a r t i c l e dimensions, particle  o r i e n t a t i o n at any time on the screen, s i z e 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 c e r t a i n i s  that  a given p a r t i c l e either passed or d i d not pass through the screen, although, because s i z e i s measured with standard sieves, that p a r t i c l e cannot be d i s tinguished i n d i v i d u a l l y within the geometric mean s i z e range measured by X^. Let each feed p a r t i c l e i n the s i z e range be tagged with an i d e n t i f y i n g number, Zj w h e r e ^ Z j = F ^ . of  1 to Zy  I f a p a r t i c l e passes through the screen, assign a value  Otherwise the value of Z.. i s zero.  8 particles, i . e . , Z  F^ = 8; the following might occur:  l  Z  1  2  Z  0  3  Z  1  4  Z  1  5  Z  6  0  Z  0  7  Z  8  0  This means that p a r t i c l e s Z ^ , Z^ and others d i d not.  For example, suppose there are  ( i d e n t i f y i n g numbers) 0  passed through the screen, while the  It i s obvious that there i s  a large number o f d i s t i n c t  sequences that may occur. Another way to characterize the s i t u a t i o n i s to group F^ p a r t i c l e s according to whether they pass the screen or do not as Pass (1) Z  l  Z  3  Z  Do Not Pass  4  '  ,  Z  2  Z  5  Z  6  Z  7  Z  follows:  (0) 8  Again we note that a large number of d i s t i n c t sequences i s (a)  a l l p a r t i c l e s pass,  (b) no p a r t i c l e s pass,  etc.  p o s s i b l e , including  There are F J ways to  write the Z^ i d e n t i f y i n g numbers on a l i n e , as the f i r s t p o s i t i o n may be chosen i n F^ ways, the second i n F ^ - l ways and so on.  But many of these sequences are  not d i s t i n g u i s h a b l e because of the way p a r t i c l e s i z e i s measured.  For example,  interchanging the order Z^ Z^ Z^ to Z^ Z^ Z^ i s not a d i s t i n g u i s h a b l e  sequence.  Of i n t e r e s t are the number of d i s t i n c t sequences that are p o s s i b l e ; not the permutations.  Each d i s t i n c t sequence can be permuted i n I L ! ( F . - IK) ! ways.  If  l\L i s the t o t a l number of d i s t i n c t sequences, then W.U.!(F.~ l  .  i  i  U.)!  i  so that  =  F.! l  F.! "i  "  U. F.! (  1  v  1  U.).~  x  J  -  t  •  &  -  2  )  "  - 207 -  Thus there are VL d i s t i n c t ways that the F^ p a r t i c l e s might d i s t r i b u t e to the undersize stream. feed,  I f we now cover the complete range o f s i z e s involved i n the  then the t o t a l number of d i s t i n c t ways of d i s t r i b u t i n g feed p a r t i c l e s  to  the undersize stream i s W, where  _  hi -  If  7T  ItT  / / all x n  v  F.!  K  _  1  II  ' all x v  J  Taking the n a t u r a l log of both sides o f equation 3 r e s u l t s InW  =  E all x  (InF.! - lnU.l 1  1  (G-3)  U . ! ( F . - U.) I i - i x in  "CM)  - ln((F.- U.)!)) i i  To f i n d the most probable way to d i s t r i b u t e p a r t i c l e s to the u n d e r s i z e , make 9 InW 3Ui  a maximum, subject to the following  (a)  conditions:  U = EIL = constant at steady s t a t e , where U i s the t o t a l number o f p a r t i c l e s r e p o r t i n g to the undersize stream, i n time T .  (b)  V = ^ i i U  V  =  constant at steady s t a t e , where V i s the t o t a l volume  o f the undersize stream and V\ i s the average volume^per p a r t i c l e of the s i z e f r a c t i o n i n the undersize stream, both i n time T . As shown below, the s o l u t i o n to the above problem resembles  the s o l u t i o n to obtain  the Fermi-Dirac d i s t r i c u t i o n f u n c t i o n - - a well known expression that describes  the  p r o b a b i l i t y that an e l e c t r o n occupies an energy s t a t e of a given energy. Using the approximation that mj.* = j l n j - j , equation 4 becomes ' InW =  Z • (FjlnF. all x  ( F . - l y i n C F - U ) - U InU )  ( ( G  _  5 )  The LaGrange m u l t i p l i e r method may be used to find, a maximum subject to (a) and (b).  conditions  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 r a c t i o n , P . , of p a r t i c l e s o f volume V . that reports to the o v e r s i z e stream i s given as U.  P.  =  1 -  1  F  (G-8)  i  1  e~ -^i a  +  where P. r e f e r s to p a r t i c l e s that are not involved i n bypassing. may be found from boundary conditions i n terms o f 3. so that - a = 3 V P. i  5 { )  =  .  When P. i s 0.5  On s u b s t i t u t i o n into equation 8, we have  ,  3fV  1  5  0  >  (6-9)  V  P(V  V. = V '  1  -V 1  1 + e 50  A value f o r a  On the assumption that volume shape f a c t o r s are constant, Equations 1 and 9 may be combined and expressed i n terms o f an average "volume" diameter so that (1 - c ) Y  =  c  +  ...  ,(G-10)  1 + exp(kCX^ - X p ) 0  The value o f X.^ and hence X  5 Q  i s p r o p o r t i o n a l to geometric mean s i z e s i .  Equation 10 has been tested using data gathered around secondary screens at Brenda Mines L i m i t e d , with c^ equal to zero.  A t y p i c a l r e s u l t i s shown i n  F i g u r e 2. I t i s expected that f o r wet o r e s , fines w i l l s t i c k to coarse rock and c. w i l l not be zero f o r some s i z e ranges.  In t h i s case, c^ may depend upon moisture content.  Other f a c t o r s may include the. percentage open area o f the screen, the amplitude and frequency o f v i b r a t i o n , the slope,  and the r e t e n t i o n time o f s o l i d s on the  screen.  ACKNOWLEDGEMENT This study i s supported by a grant from the Canada Centre f o r Metals and Minerals Technology.  LOG PARTICLE SIZE, MICRONS  FIGURE 2 COMPARISON O F OBSERVED AND PREDICTED SCREEN  210  REFERENCES  1.  GURUN, T . , "Design of Crushing Plant Flowsheets by Simulation", 10th APCOM Symposium, published by South A f r i c a n I n s t i t u t e of Mining and Metallurgy, Johannesburg, 1973.  2.  WHITEN, W . J . , "The Simulation of Crushing Plants with Models Developed Using M u l t i p l e Spline Regression", 10th APCOM Symposium, and J . S . A . I . M . M . , May, 1972, p. 257.  3.  GAUDIN, A . M . , P r i n c i p l e s of Mineral Dressing, McGraw-Hill, New York, 1939, p. 145.  4.  TERRARA, G . , and PRETI, U . , "A Contribution to Screening K i n e t i c s " , 11th IMPC, C a g l i a r i , I t a l y , 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 M o d e l , SCRN3 Output from SCRN3 - Model P r e d i c t i o n s Observed Data  for  - 212 : SECONDARY SCREENS MODEL FITTING  1 * * * PROGRAM: SCRN5 2 * 3 * 27 DIM T (20) , E (20) , V{20) 28 DIM P ( 2 0 , 2 0 ) , R (20,20) ,8(20,20) ,S{20) , K ( 2 0 , 2 0 ) 29 DIM N{20, 20) , 0 ( 2 0 , 2 0 ) ,0 (20,20) , F ( 2 0 , 20) 30 DIM A (1 ,22) , D ( 1 , 2 2 ) , X (22,22) , Z (1, 22) , Y (22, 1 ) , Q { 2 2 , 2 2 ) 36 DIM L { 2 0 , 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 A K X 2 , S V 7 , D U M P , A S F 2 , A S 0 2 , A S U 2 , O P , O P 2 172 MAT READ F I L E 1 , K ( A 5 , N 2 ) 173 MAT READ F I L E 2 , A ( 1, N1) 175 MAT READ F I L E 4 , F ( A 5 , N 2 ) 176 MAT READ F I L E 5 , 0 ( A 5 , N 2 ) 177 MAT READ F I L E 6 , 0 ( A 5 , N 2 ) 178 MAT READ F I L E 7 , L ( A 5 , 3 ) 179 MAT READ F I L E 8 , N ( 3 , A 5 ) 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 I N I T I A L STARTING VALUES 215 FOR 1=1 TO N1 220 D ( 1 , I ) =ABS ( G 2 * A ( 1 , I ) ) 225 NEXT I 23 0 * SET UP I N I T I A L SIMPLEX 24 0 FOR J=1 TO N1 250 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 300 290 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 S T D . 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  PROGRAM  - Z\6  430 440 441 445 450 455 460 465 470 480 490 500 510 52 0 530 540 55 0 560 575 580 590 593 595 600 610 620 623 626 627 62 9 630 63 1 632 633 63 4 63 6 639 640 64 2 643 644 645 646 64 9 65 0 651 652 653 65 4 655 656 657 658 659 660 661 662 663 664 665  -  GO SOB 1720 T1=0 T2=0 FOR 1=1 TO N1+1 T1=T1+Y (1,1) NEXT I T1=T1/(N1+1) FOR 1=1 TO N1 + 1 T2=T2+(Y {I, 1)-T1) **2 NEXT I T4=SQR (T2/N1) IF T 4 > 1 . E - 6 THEN 730 GO TO 590 * PRINTOUT SECTION PRINT PRINT "CYCLE LIMIT STOP CHITERION=";M2;"STD.DEVIATION=";T4 PRINT PRINT"HIGH=";Y(H, 1) , "2ND HIGH=»; Y (S, 1) , " L O W - " ; Y ( L , 1) PRINT GO TO 600 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y ( L , 1 ) PRINT PRINT "STANDARD DEVIATION=";T4 H=L GO SUB 1310 PRINT PRINT "RELATION CONSTANTS" PRINT "FOR PARAMETER A" PRINT PRINT "A1 = » ; X ( H , 1 ) , "A2=";X (H,2) , "A3="; X {H, 3) , " A 4 = " ; X (H,4) PRINT PRINT "FOR PARAMETER X50" PRINT PRINT "A5=";X (H,5) ,"A6=";X (H,6) , "A7="; X (H,7) , » A8=" ; X (H , 8) PRINT "A9=";X(H,9) PRINT PRINT PRINT "NUMBEE OF OBJECTIVE FUNCTION CALCULATIONS=" ; Z9 FOR I=A3 TO A4 A8=0 A9=0 A10=0 PRINT PRINT "RUN NR. " ; I PHINT PRINT "RESPONSE I S WEIGHT FRACTION TO OVERSIZE" PRINT PRINT " S I Z E " , " A D J U S T E D " , " P R E D I C T E D " FOR J=1 TO N2-1 PRINT S ( J ) , K ( I , J) , P ( I , J) A8=A8+(K ( I , J ) - P ( I , J) ) **2 NEXT J PRINT " P A N " , K ( I , N 2 ) , P ( I , N 2 ) A8=A8+(K ( I , N 2 ) - P ( I , N 2 ) ) **2 PRINT PRINT "RESIDUAL SUM SQUARES=";A8 PRINT GO SUB 700 PRINT "MODEL PERFORMANCE" PRINT  -  66 6 667 66 8 669 670 671 67 2 673 674 675 676 677 678 679 680 682 68 3 68 4 686 687 688 689 690 700 705 710 712 714 716 718 730 732 734 736 73 8 74 0 74 2 74 3 745 75 0 76 0 770 780 790 80 0 810 820 830 840 850 860 870 880 890 900 910 920 93 0 94 0 95 0  214  -  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 » PRINT FOR J=1 TO N2-1 PRINT S(J) ,0 ( I , J ) ,R ( I , J ) , U ( I , J ) , W ( I , J) A9=A9* (R ( I , J) - 0 ( I , J) ) **2 A10=A10* (W ( I , J ) - U ( I , J) ) **2 NEXT J PRINT "PAN",0 (I,N2) , R ( I , N 2 ) ,0(1,N2) , W ( I , N 2 ) A9=A9+ (R ( I , N2) -0 (I,N2) ) **2 A10=A10+ (I? (I,N2) - U (I,N2) ) **2 PRINT " " , " ","SUM 0 / S = " ; A 2 0 , " ","SUM U / S = » ; B 2 0 PRINT "RESIDUAL SUM S Q U A R E S : 0 / S = " ; A 9 , " U / S = " ; A 1 0 PRINT PRINT " F L O W R A T E S : O / S = " ; E ( I ) / 1 0 0 , " U / S = " ; V ( I ) / 1 0 0 PRINT Z2 = X (H, 1) + X ( H , 2 ) *N(1,1) **2+X (H,3) *N (2,1) *X (H ,4) *N (3,1) **2 Z21 = X(H,5) +X(H,6) * N ( 1 , I ) + X (H,7) * N ( 1 , I ) **2 Z3=Z21 +X (H,8) *N (2,1) **2 + X (H,9) *N (3,1) **7 PRINT "A=";Z2,"X50=";Z3,"C-»;Z1,"B=";Z4 PRINT NEXT I PRINT " STOP A20=0 B2 0=0 FOR J=1 TO N2 A20=A20*R(I,J) B20=B20 + W ( I , J) NEXT J RETURN I F Z9>M2 THEN 530 I F Z9>M3 THEN 736 GO TO 745 M3=H3*M4 M5=CMD("%EMPTY DUMPSD") MAT WRITE F I L E 3 , X M6=CMD(»%SAVE DUMPSD") PRINT "Z9=";Z9 I F T4>T3 THEN 770 T3 = T4 * REFLECTION MAT Q = (1)*X FOR J = 1 TO N1 P1=0 FOR I •= 1 TO N1 + 1 I F I = H THEN 830 P1=P1 + X ( I , J) /N1 NEXT I Z (1, J) = (1 + A1) * P 1 - A 1 * X ( H , J) X ( H , J) =Z (1 , J ) D(1,J)=P1 NEXT J GO SUB 1310 MAT X = (1) *Q Y=Y1 I F Y>=Y(L,1) THEN 1000 * EXPANSION FOR J = 1 TO N1 X (H, J) = (1 + Y1) *Z (1, J) - V 1 * D ( 1 , J) NEXT J  - 215 960 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 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 ) = B 1 * 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 C 2 = 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= ( Z 3 * * 3 - T ( J ) * * 3 ) / Z 2 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 B 1 0 = { 1 / ( H - E X P { Z 3 * * 3 / Z 2 ) )) 1387 R ( K , N 2 ) = B 1 0 * F ( K , N 2 ) * C 2 1388 W (K,N2) =(1-B10) * F ( K , N 2 ) *C2 1389 E <K)=E (K) +R (K 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 f  - 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 B 1 , B 2 42 READ A 2 0 , A 2 1 , A 2 2 , A 2 3 , A 2 4 '45 READ A 3 0 , A 3 1 , A 3 2 , A 3 3 46 PRINT * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4 7 PRINT 48 PRINT " S I Z E ANALYSES REPORTED AS WT. PERCENT RETAINED ON S I Z E " H9 PRINT "****************************************************************" 50 F I L E 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 ( A 3 , N 2 ) 70 MAT READ F I L E 2 , 0 ( A 3 , N 2 ) 80 MAT READ F I L E 3 , U ( A 3 , N 2 ) 90 MAT READ F I L E 4 , L ( A 3 , 3 ) 100 HAT READ F I L E 5 , K ( A 3 , N 2 ) 105 MAT READ F I L E 6 , M ( 3 , A 3 ) 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 I F 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) ) / 1 0 0 280 W (J)= ( ( 1 - 1 (J) ) *F {K, J) * L (K, 1) ) / 1 0 0 282 A15=A15 + N(J) 284 A16=A16 + W(J) 310 NEXT J 311 B10=1/(1+EXP (Z1**3/Z2) ) 312 N (N2) = ( B 1 0 * F ( K , N 2 ) * I (K,1) ) / 1 0 0 314 R (N2) = ( (1-B10) * F ( K , N 2 ) * L (K,1) ) / 1 0 0 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 ) / A 1 6 ) * 1 0 0 326 A9=A9*<N<J)-0 (K, J) ) **2 328 A10=A10+ ( « ( J ) - U ( K , J ) ) **2 329 S (J) =INT (S (J) *10000+.5) / 1 0 0 0 0 3 30 NEXT J 331 PRINT 11  - 218 332 334 336 338 340 342 344 350 354 355 356 357 3 60 370 380 390 400 410 4 20 430 4 40 4 50 460 461 462 470 475 476 4 80 485 486 488 489 490 492 495 5 00 510 520 530 540 545 550 560 565 566 570 571 575 576 577 578 579 5 80 5 82 585 5 86 589 590 500  PBINT "BON NUMBER=";.K PBINT PRINT "PARAMETER X50="; Z 1,"PARAMETER A=";Z2 PRINT PRINT " S I Z E " , " M E A S U R E D " , " P R E D I C T E D " PRINT " ( C £ l . ) " , " Y 0 / S » , " Y 0 / S " A8=0 PRINT FOR J=1 TO N2 Y (J)=INT (Y(J) *10000000 + . 5 ) / 1 0000000 K (K, J ) =.INT (K (K, J ) * 10000000+. 5) /10000000 NEXT J FOR J = 1 ' T O N2-1 PRINT S {J) , K ( K , J ) ,Y<*7) A8=A8+ (K {¥., J ) - Y (J) ) **2 NEXT J PRINT "PAN" ;TAB{14) ; R ( K , N 2 ) ; TAB (29) ; B10 A8=A8+(K(&,N2)-B10)**2 PRINT PRINT "RESIDUAL SUM S Q U A R E S - " ; A 8 PRINT PRINT PRINT " S I Z E " , " M E A S U R E D " , " P R E D I C T E D " , " M E A S U R E D " , " P R E D I C T E D " PRINT " (CM.) " , " O V E R S I Z E " , " O V E R S I Z E " , "UNDERSIZE", "UNDERSIZE" PRINT TAB(16) ; "PRODUCT" ; TAB (31) ; "PRODUCT";TAB (46) ;"PRODUCT";TAB (61) ;"PRO PRINT A17=0 A18=0 FOR J=1 TO N2 A17=A17 + N(J) A18 = A18 + W(J) N (J) =INT (N (J) * 1000 + .5) / 1 0 0 0 W (J) =INT ( S (J) *1000 + . 5 ) / 1 000 NEXT J FOR J=1 TO N2-1 PRINT S (J) , 0 ( K , J ) , N ( J ) , U ( K , J ) , W (J) NEXT J PRINT "PAU";TAB (14) ;0 (K,N2) ; TAB (29) ;N (N2) ; TAB (44) ; U (K,N2) ;TAB (59) ;W (N2) PRINT PRINT T A B ( 3 1 ) ; " S U M = » ; A 1 7 ; T A B ( 6 1 ) ; " S U M = " ; A 1 8 PRINT A10=1 NT(A 10*10000 0 + . 5 ) / 1 0 0 0 0 0 PRINT "RESIDUAL SUMS OF SQUARES: O V E R S I Z E " ; A 9 , " UNDERSIZE ";A10 PRINT A15=INT(A 1 5 * 1 0 0 0 • . 5 ) / 1 0 0 0 A16=INT(Al6*1000+.5)/1000 PRINT "FLOWBATES: PREDICTED: O V E R S I Z E " ; A 1 5 , " U N D E R S I Z E " ; A 1 6 PRINT " MEASURED : O V E R S I Z E " ; L (K,2) , " U N D E R S I Z E " ; L ( K , 3 ) PRINT PRINT "OPERATING CONDITIONS:" PRINT PRI NT"APEIsTURE=" ; M ( 1 , K) , " % +1 INCH IN F E E D " ; M (2,K) , " F E E D R A T E " ; M (3, K) PRINT " ( C f i . ) " , " «,"(TPH)" PRINT PRINT " . , . . . , . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . , . . . . , . , . . . . . . " NEXT K PRINT PRINT STOP DATA 1 4 , 4 3 . 5 2 , . 5 , 11 3  3  3  3  3  3  3  3  - 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 task: 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 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS40 ft SIGN RALU ft ENTER USER PASSWORD.  task:  7  # # # '4 5  **1AST SIGNON WAS: 0 9 : 0 7 : 4 6 USER "RALU" SIGNED ON AT 0 9 : 1 1 : 3 7 ON TUE AUG 16/77 BUN * E A S I C EXECUTION BEGINS ?UBC BASIC SYSTEM  : GET SCBN3 : BUN  ********************************** SIZE ANALYSES REPORTED AS WT. PERCENT RETAINED ON S I Z E **************************************************************** RUN NUMBERS 1 PARAMETER X50=  1.851731  PARAMETER A= 1.86 4255  SIZE (CM.)  MEASURED Y O/S  PB EDICTED Y O/S  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  1 1 0.9999932 0.9771518 0.5911507 0.0596201 0.0410346 0.0391766 0.0402742 0.0521643 0.060443 0.0608448 0.0688055 0.1003671  1 1 1 1 0.6012195 0.0507471 0.0340184 0.0323449 0.0321414 0.032116 0.0321129 0.0321125 0.0321124 3.211241E-2  BESIDUAL  SUM SQUABES=  8.899353E-3  SIZE (CM.)  MEASUBED OVERSIZE PRODUCT  PBEDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  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 26. 226 46.497 25. 116 1.084 0.251 0.161 0.12 0. 124 0.125 0. 1 0.077  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  0 0 0 1. 94 30.975 30.488 10.461 7.04 1 5. 1 '4. 018 3. 464 2.752 1.859  0 0 0 0 30.752 31.326 10.725 7.218 5.234 4.176 3.633 2.887 1.966  224  - 221 PAN  0.119  SUM RESIDUAL  SDHS OF SQUARES:  OPERATING  CONDITIONS:  APERTURE (CM.)  1.5  RUN NUMBER  3  % +1 INCH  3 3  0.53545  3  3  UNDERSIZE UNDERSIZE UNDERSIZE  47.29  FEEDRATE (TPH)  3  3 3  3  3  100  4 . 7 50 5  125.9 47 128.2  356.79 9  2  PARAMETER X 5 0  1.903061  PARAMETER A  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  2 1.76 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  1 1 0.9999734 1.000019 0.5537156 0.0525232 0.0352078 0.0343813 0.0317813 0.0418887 0.042481 1 0.0448736 0.056743 0.0957351  1 1 1 1 0.5277841 0.0474072 0.0326293 0.031129 0.0309462 0.0309235 0.0309206 0.03092 03 0.0309202 0.0309202  RESIDUAL  SUM  230.847 228.599  IN F E E D  2.083  100  3  OVERSIZE  FLOWRATES: PREDICTED: O V E R S I Z E MEASURED : O V E R S I Z E  3  1. 902  0.038  3  SUH SQUARES  3  3  2 . 0 0 0677  6.'032904E-3  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  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  0 0 16.064 44.974 3 6 . 3 57 1.621 0.285 0. 154 0.093 0.088 0.082 0.074 0.07 0.138  0 0 16.408 45.934 3 5 . 395 1.494 0. 27 0. 142 0.092 0.066 0.061 0.052 0. 039 0.046  0 0 0 0 35.991 35.917 9. 592 5.313 3.479 2.473 2. 27 1. 935 1. 429 1. 60 1  0 0 0 0 37. 129 3 5.205 9.377 5.197 3.396 2.438 2.24 1.914 1.432 1 .673  - 222 SUM RESIDUAL  SUES OF SQUARES:  OVERSIZE  FLOWRATES: PREDICTED: OVER S I Z E MEASURED : O V E R S I Z E  3  100  3  1.99318  3  190.725 194.801  SUM UNDERSIZE UNDERSIZE UNDERSIZE  3 3  3  3  100  1.87557  162.675 158.6  OPERATING CONDITIONS: APERTURE (CM.)  3  1.5  RUN NUMBER  3  % +1 INCH IN F E E D  3  33.65  FEEDRATE (TPH)  3 5 3 . 401  3  PARAMETER X 5 0  1.868715  PARAMETER A= 1.903713  SIZE (CM.),  MEASURED Y O/S  PREDICTED Y O/S  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  1 1 0.9999739 0.999997 0.5764511 0.0526624 0.0458679 0.03124O1 0.0333227 0.038513 0.040069 0.050106 0.0648819 0.0916022  1 1 1 1 0.5767445 0.0492317 0.0332623 0.0316579 0.0314627 0.0314384 0.0314353 0.031435 0.0314349 0.0314349  RESIDUAL  3  3  SUB SQUARES  3  5.386394E-3  SIZE (CM.),  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  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  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  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  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  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  FLOWRATES; PREDICTED: O V E R S I Z E MEASURED : O V E R S I Z E OPERATING  CONDITIONS:  APERTURE (CM.)  1.5  3  RUN NUMBER  3  3 3  -  0.03811  3  222.438 2 2 2 . 9 99  % +1 INCH IN F E E D  FEEDRATE (TPH)  3  0.07175  3  122.961 122.4  3 3  345.399  4  PARAMETER X50=  1.897101  PARAMETER A  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  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  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  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  UNDERSIZE UNDERSIZE  43.26  3  UNDERSIZE  SUM SQUARES  3  3  2.011498  4.037417E-3  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PRE DICTED UNDERSIZE PRODUCT  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  0 0 14.923 51.506 31.204 1.401 0.277 0 . 139 0.114 0.073 0.08 0.081 0.072 0. 13  0 0 14. 717 50.797 31. 865 1.583 0.37 0. 22 0 . 135 0.094 0.076 0. 053 0.039 0.052  0 0 0 0 32.059 34.064 11.738 7.346 4.505 3. 156 2. 522 1.732 1. 247 1.631  0 0 0 0 31. 32 4 34. 368 11.812 7.367 4.55 3.179 2.564 1.79 1.303 1.743  SUM RESIDUAL  SUSSS OF SQUARES:  100  3  OVERSIZE  3  1.03941  SUM UNDERSIZE  3  3  0.66238  100  FLOWBATES:  PREDICTED: OV£RSIZE= MEASURED : OVERSIZE=  OPERATING  CONDITIONS:  APERTURE= (CM.)  1.5  RUN NUMBER=  299.521 295.4  % +1 INCH IN FEED=  34.81  UNDERSIZE= UNDEBSIZE=  FEEDBATE= (TPH)  563.7  5  PARAMETEB X50=  1.931496  PARAMETEE A= 2. 097179  SIZE (CM.)  MEASUEED Y O/S  PBEDICTED Y O/S  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  1 1 1.000039 1.000017 0.4976044 0.0503144 0.0288957 0.0309196 0.0343656 0.0420561 0.0423127 0.0620223 0.0810429 0.1079463  1 1 1 1 0.4891528 0.0468922 0.032833 0.0313916 0.0312158 O.0311939 0.0311912 0.0311908 0.0311908 3.119077E-2  RESIDUAL  264.17 268.3  SUM SQUAHES=  9.677689E-3  SIZE (CM.)  MEASURED OVERSIZE PEODUCT  PBEDICTED OVEBSIZE PEODUCT  MEASURED UNDEBSIZE PRODUCT  PREDICTED UNDERSIZE PEGDUCT  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  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  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  0 0 0 0 30.372 3 4 . 6 46 13.072 7.397 4. 749 3. 235 2.457 1. 66 3 1. 157 1.252  0 0 0 0 30.613 34.466 12.905 7.328 4.722 3.243 2.463 1.703 1 .208 1.348  PAN  SUM= 100 RESIDUAL  SUMS OF SQUABES:  OVEBSIZE=  FLOWBATES: PBEDICTED: OVERSIZE= MEASURED : OVERSIZE=  0.37167  65.692 66.5  SUM= 100 UNDERSIZE= UNDEBSIZE= UNDERSIZE-  0.13751  92.105 91.3  -  OPERATING  CONDITIONS:  APERTURE (CM.)  1.5  3  % +1 INCH IN F E E D  CdO  -  22.86  3  FEEDRATE (TPH)  RUN NUMBER  3  6  PARAMETER X 5 0  1.561736  PARAMETER A= 1.71079  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  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  1 1 0.9999516 1.000005 0.8970897 0.2538565 0,0568406 0.0409977 0.048631 0.0512417 0.0602381 0.0772057 0.094892 0.1365175  1 1 1 1 0.8734989 0.1535962 0.1032582 0.0981108 0.0974837 0.0974056 0.0973959 0.0973946 0.0973945 9.739446E-2  RESIDUAL  157.8  3  3  SUB SQUARES  3  2.386802E-2  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  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  0 0 13.977 44.955 35.027 4. 846 0.387 0.152 0.114 0.091 0.092 0.081 0.091 0. 187  0 0 14.275 45. 91 1 34. 832 2.994 0.718 0.371 0. 233 0. 177 0 . 1 52 0. 104 0.095 0.136  0 0 0 0 10.977 38.908 17.5 42 9.712 6. 092 4. 602 3.921 2.643 2.372 3. 231  0 0 0 0 12. 766 41.759 15.78 8 . 6 42 5.468 4 . 143 3.563 2.447 2.237 3.195  SUM RESIDUAL  SUHS OF SQUARES:  FLOWRATES :  OPERATING  OVERSIZE  PREDICTED: O V E R S I Z E MEASURED : O V E R S I Z E CONDITIONS;  3 3  100  3  3  4.6559  748.668 764.6  SUM UNDERSIZE UNDERSIZE UNDERSIZE  3 3  3  3  100  16.36493  295,838 279.899  -  APEHTURE= (CM.)  1.27  BON NUMBEB=  % +1 INCH  IN FEED=  LLXi  -  43.14  FEEDEATE= {TPH)  7  PARAMETEB X50=  1.807774  PARAMETER A= 1.873238  SIZE (CM.)  MEASURED y o/s  PBEDICTED Y O/S  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  1 1 1.000036 1.000032 0.6578227 0.0685617 0.0169244 0.0136022 0.0071782 0.0091536 0.018103 0.0225314 0.0314767 0.04 6333 9  1 1 1 1 0.6557206 0.0642195 0.043335 0.0412326 0.0409767 0.0409448 0.0409409 0.0409404 0.0409403 4.094029E-2  RESIDUAL  1044.499  SUe  SQUARES^  4.616365E-3  SIZE (OS.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PBODUCT  MEASURED UNDERSIZE PBODUCT  PBEDICTED UNDERSIZE PBODUCT  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  0 0 14.449 30.756 48.983 4.756 0.425 0.201 0.081 0.058 0.061 0.051 0.058 0.121  0 0 14.261 30.355 48.192 4.397 1.074 0.601 0.456 0.256 0.136 0.091 0.074 0. 106  0 0 0 0 16.267 41.251 15.76 9.306 7. 153 4 . 008 2.113 1. 412 1. 14 1. 59  0 0 0 0 16. 506 41.795 15. 468 9.122 6.968 3.913 2.081 1.398 1.138 1.613  SUM= 100 RESIDUAL  SUfiS OF SQUARES; 0VERSI2E=  FLOWRATES:  PREDICTED; OVERSIZE= MEASURED ; OVERSIZE=  OPERATING  CONDITIONS;  APEBTUBE=  1.27  1.720 65  222.189 219.3  % +1 INCH IN FEED=  17.94  SUM= 100 UNDERSIZE= 0.51761 UNDERSI2£= UNDEBSIZE=  FEEDBATE=  340.603 343.5  562.8  - 227 (CM.)  (TPH)  BUN HUHBEB= 8 PARAMETER X50=  1.780231  PARAMETER A= 1.714055  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  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  1 1 1.000032 1.00001S 0.6801734 0.0391924 0.0249785 0.0281663 0.0 452757 0.0545389 0.053649 0.0 747393 0.0849185 0.062204 5  1 1 1 1 0.7025081 0.0588161 0.0381724 0.0361426 0.0358962 0.0358656 0.0358617 0.0358613 0.0358612 3.586119E-2  RESIDUAL SUE SQUARES  3  6.486773E-3  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  2 1. 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  0 0 18.156 39.94 39.139 1.597 0.325 0.182 0. 137 0.114 0. 102 0. 1 0.099 0. 109  0 0 17.791 39.137 39.612 2.348 0. 487 0.229 0. 106 0.073 0.067 0.047 0.041 0.062  0 0 0 0 21.122 44.933 14.559 7. 207 3.315 2. 269 2 . 064 1. 421 1. 224 1. 886  0 0 O 0 20. 12 45. 076 14.709 7.32 3.429 2.369 2.154 1.516 1.321 1.986  SUM= 100 RESIDUAL SUMS OF SQUARES: FLOWRATES :  OVERSIZE  PREDICTED; O V E R S I Z E MEASURED : OVER S I Z E  3  3  3  1.60747  152.259 149.2  SUM UNDERSIZE UNDERSIZE UNDERSIZE  3 3  3  1 . 1 1887  126 . 9 42 130  OPERATING CONDITIONS: APERTURE (CM.)  3  1.27  % +1 INCH IN F E E D  3  31.05  FEEDRATE (TPH)  3  3  279.2  100  - 228 -  RUN NUMBER= 9 PARAMETER X50=  1.914758  PARAMETER A= 2.280206  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  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  1 1 1.000031 1 0.491682 0.0535862 0.0297572 0.0316405 0.023121 0.0184924 0.0405413 0.0498509 0.0636978 0.0691986  1 1 1 1 0.5103823 0.0636451 0.0460911 0.0442514 0.0440264 0.0439984 0.0439949 0.0439944 0.0439944 4.399436E-2  RESIDUAL SUM SQUARES=  3.03401E-3  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDEBSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  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  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  0 0 15.791 46.064 33. 64 2.699 0.761 0.303 0.2 0. 137 0.111 0.085 0.086 0. 123  0 0 0 0 29.791 3 5 . 6 93 14.251 5. 89 3. 936 2.726 2. 143 1.626 1. 625 2.319  0 0 0 0 29. 235 35.977 14.275 5.922 3.925 2.706 2.176 1 .667 1.691 2.427  SUM= 100 RESIDUAL SUBS  OF SQUARES:  OVERSIZE=  FLQWRATES :  PREDICTED: OVERSIZE= *3EASURED : OVERSIZE=  OPERATING  CONDITIONS:  APESTURE= (CM.)  1.59  % +1 INCH  1.60408  477.317 467.402  IN FEED=  29.4  SUM= 100 UNDERSIZE = 0 . 4 1 0 8 9 UNDERSIZE= 526 .893 UNDESSIZE= 536 . 8  FEEDRATE= (TPH)  1004.202  - 229 RON NUMBER—  10  PARAMETER X50= 2.024891  PARAMETER A= 2.116617  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  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  1 1 0.9999835 0.999999 0.3635017 0.0261914 0.0249406 0.0210775 0.0210073 0.0247881 0.030146 0.025807 0.0476844 0.06771O9  1 1 1 1 0.3632929 0.0292463 0.0204327 0.0195329 0.0194232 0.0194095 0.0194078 0.0194076 0.0194076 1.940757E-2  RESIDUA! SUM SQUARES  3  3.352573E-3  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICTED UNDERSIZE PRODUCT  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  0 0 22.06 9 55.515 20.364 0.981 0.325 0.159 0.106 0. 101 0.09 0.072 0. 079 0. 139  0 0 22.112 55.622 20.392 1.098 0.267 0.148 0.098 0.079 0.058 0 . 0 54 0.032 0.04  0 0 0 0 3 2 . 3 45 33.084 11.526 6.699 4.48 1 3. 605 2. 626 2.466 1.432 1. 73 6  0 0 0 0 32. 299 3 2. 92 4 1 1.559 6.697 4.48 3.618 2.651 2.477 1.471 1.823  SUM RESIDUAL  SUFiS OF SQUARES;  FLOWRATES ;  OVERSIZE  PREDICTED: O V E R S I Z E MEASURED : O V E R S I Z E  3 3  100  3  3  0.04514  236.742 237.2  SUM UNDERSIZE  3  0. 0 3866  UNDERSIZE 261. 95 UNDERSIZE= 261. 5 3  OPERATING CONDITIONS: APERTURE (CM.)  3  1.59  RUN NUMBER  3  11  % +1 INCH  IN  FEED  3  36.9  FEEDRATE (TPH)  3  3  498. 7  100  - Z6\J -  PARAMETER X50=  2.035057  PARAMETER A  SIZE (CM.)  MEASURED Y O/S  PREDICTED Y O/S  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  1 1 0.9999554 0.9999877 0.3556336 0.0244809 0.0218135 0.02481 0.0231142 0.0248753 0.0369008 0.0 422778 0.0523885 0.0568664  1 1 1 1 0.3501449 0.0279286 0.0 195277 0.0186698 0.0185652 0.0185522 0.0185505 0.0185503 0.0185503 1.855029E-2  RESIDUAL  SUB SQUARES  3  3  2.123725  3.658492E-3  SIZE (CM.)  MEASURED OVERSIZE PRODUCT  PREDICTED OVERSIZE PRODUCT  MEASURED UNDERSIZE PRODUCT  PREDICT EI UNDERSIZl PRODUCT  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  0 0 20.077 54.982 22.773 0.967 0.305 0 . 183 0.1 17 0. 113 0. 116 0.113 0.0 96 0. 158  0 0 20.206 55.333 22. 564 1.11 0.275 0 . 139 0.095 0.085 0.059 0.05 0.034 0.052  0 0 0 0 34.39 3 2 . 1 15 11.399 5. 995 4. 121 3.691 2. 524 2. 133 1. 448 2. 184  0 0 0 0 3 4. 5 31. 834 1 1.366 6.001 4. 119 3.696 2.558 2.175 1.491 2.261  SUM RESIDUAL  SUBS OF SQUARES: O V E R S I Z E  FLOWRATES :  PREDICTED: OVER S I Z E MEASURED : O V E R S I Z E  3 3  100  3  3  0.23007  119.838 120.601  SUM UNDERSIZE UNDERSIZE UNDERSIZE  3 3  3  0. 10316  145. 4 66 144. 701  OPERATING CONDITIONS: APERTURE (CM.)  3  1.59  % +1 INCH IN  FEED  3  ^ ?STOPI ^ 1 AT LINE "590" IN PROGRAM "SCRN3" + ? PROGRAM E1IDS  34.12  FEEDRATE (TPH)  3  265.  3  302  100  - 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 P r i m a r y F i n e s M o d e l , PF Output from PF - Model P r e d i c t i o n s Observed Data  for  - 232 1 * * * PROGRAM: TURKEY :PRIMARY FINES MODEL FITTING 2 * 3 * 2 9 DIM N (3, 10) , J (2 2) 30 DIM A ( 1 , 2 2 ) , D { 1 , 2 2 ) , X ( 2 2 , 2 2 ) , Z (1,22) , Y (22,1) , Q { 2 2 , 2 2 ) 33 DIM K(22) , V (22) , S (22) ,H{22) ,G{22) , R(22) 36 DIM P ( 1 5 , 15) , F (15,15) , T (15, 15) , H (15, 1) 3 8 READ N 1 , N 2 , A 3 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 ( N 2 , A 3 ) 173 FOR J=1 TO N1 175 READ A ( 1 , J) 178 NEXT J 182 READ A 2 , S 1 , M 3 184 READ A 1 , B 1 , V 1 , G 2 , M 2 186 FOR 1=1 TO H2 188 S (I) =S 1 * A 2 * * ( I - 1) 190 NEXT I 192 S2=SQR (S (1) *S (2) ) 208 * I N I T I A L VALUES INPUTTED 210 * CALCULATION OF I N I T I A L STARTING VALUES 215 FOR 1=1 TO N1 220 D (1,I)=ABS(G2*A ( 1 , 1 ) ) 225 NEXT I 230 * SET UP I N I T I A L 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  VERSION  - Z66 -  470 480 490 500 5 10 520 530 540 550 560 570 580 590 5 93 5 95 6 00 610 6 20 630 6 35 6 42 645 650 652 655 662 672 6 90 700 702 7 03 704 705 706 707 708 709 710 711 712 713 714 7 16 718 719 720 721 722 723 724 729 730 732 734 736 745 75 0 760 770 780  T2=T2+ (Y ( I , 1) -T1) **2 NEXT I T4=SQR (T2/N1) I F T 4 > 1 . E - 6 THEN 730 GO TO 590 * PRINTOUT SECTION PRINT PRINT "CYCLE LIMIT STOP CRITERION = " ; M 2;"STD.DEVIATION=" ; T4 PBINT PRINT"HIGH=";Y (H, 1} ,"2ND HIGH=";Y (S,1) ,"LOW=" ; Y (L , 1) PRINT GO TO 600 PRINT"CONVERGENCE AT OBJECTIVE FUNCTION VALUE O F " ; Y { L , 1 ) PRINT PRINT "STANDARD DEVIATION=";T4 H=L GO SUB 1310 PRINT PRINT PRINT " EQUATION CONSTANTS " PRINT "A1 = " ; X ( H , 1 ) , "A2 = " ; X (H, 2) ,"A3 = ",-X (H,3) , "A4=";X (H,4) PRINT PRINT "B1=";X(H,5) ,"B2=";X (H,6) ,"B3 = " ; X ( H ,7) , "B4= " ; X <H, 8) PRINT PRINT "C1 = " ; X ( H , 9 ) , "C2=" ; X (H , 10 ) PRINT PRINT PRINT "NUMBER OF O B J E C T I V E FUNCTION CALCULATIONS="; Z9 FOR 1=1 TO A3 I F 1=2 THEN:I=3 PRINT " # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # » A9=0 PRINT PRINT "RUN N O . " ; I PRINT PBINT " B = " ; H ( I ) , " X 0 = " ; R ( I ) , " X 50=";G{I) PBINT PRINT 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» PRINT FOB J=1 TO N2-1 PRINT S{J + 1) , T ( J , I ) P { J / I ) , T ( J , I ) - P ( J , I ) A9=A9+ (T ( J , I ) - P ( J , I ) ) **2 NEXT J PBINT "PAN" , T ( N 2 , I ) ,P(N2,I),(T(N2,I)-P{N2,I)) PBINT A 9 = A 9 + < T ( N 2 , I ) - P ( N 2 , I ) ) **2 PRINT "RESIDUAL SUM SQUABES=";A9 PBINT NEXT I STOP I F Z9>H2 THEN 530 I F Z9>M3 THEN 736 GO TO 745 M3=M3+300 I F T4>T3 THEN 770 T3=T4 * REFLECTION MAT Q = (1) *X FOB J = 1 TO N1 f  - 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) * P 1 - A 1 * 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) - Y 1 990 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 ) = 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 S I Z E 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) f  -  C30  -  1 3 1 7 H ( K ) = X { H , 9 ) +X ( H , 1 0 ) * L O G ( H ( K ) ) 1 3 1 8 FOR J=1 TO 4 1320 F ( J , K ) = 1 0 0 1 3 2 5 NEXT J 1 3 2 6 A2 2=0 1 3 3 0 FOR-tJ=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 1337 NEXT J 1338 P ( 1 , K ) = 0 1 3 4 0 FOR J=2 TO N 2 - 1 1341 P ( J , K ) = F ( J - 1 , K ) - F ( J , K ) 1342 A22=A22 + P ( J , K ) 1344 NEXT J 1346 P(N2,K)=100-A22 1510 P10=0 1514 A50=P(N2,K) 1515 I F P ( N 2 , K ) < - 1 6 THEN: A50=-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 F O R J = 1 TO N 2 1 5 4 9 F 2 = F 2 + (T {J, K) - P ( J , K) ) * * 2 + P 10 1650 NEXT J 1 6 7 5 NEXT K 1680 Y1=F2 1690 Z9=Z9+1 1710 RETURN 1715 * O B J E C T I V E FUNCTION MAGNITUDE L I S T I N G (ORDER SEARCH) 1720 I F Y { 1 ,1)>Y ( 2 , 1 ) THEN 1770 1 7 4 0 S=1 1741 L=1 1 7 5 0 H=2 1 7 6 0 GO T O 1 7 9 0 1770 S=2 1771 L=2 1 7 8 0 H=1 1 7 9 0 FOR 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 1810 L=I 1 8 2 0 I F Y ( I , 1) <Y ( S , 1) T H E N 1880 1 8 3 0 I F Y ( I , 1) <Y ( H , 1) T H E N 1870 1 8 4 0 S=H 1850 H=I 1 8 6 0 GO T O 1 8 8 0 1870 S=I 1880 NEXT I 1 8 9 0 RETURN 1 8 9 5 DATA 10,14,7 1898 DATA 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 DATA 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 DATA -3.8757,4.95 1 9 0 1 DATA .5,43.52,1000 1 9 5 0 DATA 1,.5,2,.01,10 2 0 0 0 END END-OP-'FILE  - Z6b 1 * * * PROGRAM: PF ;PRIMARY FINES MODEL 2 * 3 * 10 DIM S (15) , H (15) , G (15) ,R (15) , K (22) 20 DIM P ( 1 5 , 1 5 ) , T { 1 5 , 15) , V (22) , J ( 2 2 ) , B ( 6 0 ) 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 ( N 2 , A 3 ) 110 READ A 2 , S 1 115 DATA . 5 , 4 3 . 5 2 120 FOR J=1 TO N2 130 S ( J ) = S 1 * A 2 * * ( J - 1 ) 140 NEXT J 3 00 FOR K=1 TO A3 310 I F 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 ( N 2 K ) = 1 O 0 - A 2 2 485 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) , A 3="; B (49) , " A 4 = » ; B (50) 64 5 PRINT 650 PRINT "B1 = ";B(51) , "B2="; B (52) , " B 3 = ; 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 "SIZE","MEAS.PROD.","PRED.PROD.","DIFFERENCE" 810 PRINT f  1 1  0  -  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 ( N 2 , I ) - P (N2,I) 870 PRINT 880 A 9 = A 9 + ( T ( N 2 , I ) - P ( N 2 , 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 I F 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 END-OF-FILE  i e v i c e : DS24 task: 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 C o l u m b i a C o m p u t i n g 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: 1 0 : 1 6 : 3 5 \ USER "RALU" SIGNED ON AT 10:18:28 \ RUN *BASIC \ EXECUTION BEGINS ?UBC BASIC SYSTEM • : GET PF RUN  ON THU SEP 0 8 / 7 7  ?  EQUATION CONSTANTS A1= 3. 225629 A 2= - 2 . 2 6 3 7 8 8  A3= 0.5387101  A4= - 4 . 0 8 8 1 3 4 E - 2  B1 = 1.146159  B2= 0.72933  B3=  B4 = 1.339609E-2  C1=  C2= 5 . 0 3 4 0 8 5  -4.491863  -0.1829856  RUN NO.= 1 B=  1. 45967  X 0= - 2 . 587921 X 50=  1.705899  SIZE  M E A S . P R O D.  PRED. PROD,  DIFFERENCE  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  0 0 0 0 6 13 15 15 15. 5 14 9.9 6.2 3.55 1. 8.5  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  0 0 -0.01 -0.6 5 0. 33 0. 82 0. 18 -1.42 -0.73 0.71 0. 81 0. 76 0. 55 -1.37  RESIDUAL FLOWRATE  RUN  NO.=  SUM O F SQUARES= (AVERAGE  OVER  7.7028  DAY I N T P H ) =  321.7097  3  B= 0 . 1 7 8 8 5 9 7  X 0= - 1 3 . 1 5 6 3  X 50=  2.048973  SIZE  MEAS. PROD.  PR ED.PROD.  DIFFERENCE  21 .76 10.88  0 0  0 0  0 0  task:  31  - 239 0 0 22 31 15.5 9 8 5.9 3.9 2.4 1.34 0.96  5. 44 2.72 1. 36 0.68 0. 34 0.17 0. 085 0.0425 0.02125 0.010625 0.0053125 PAN  0.01 2.07 23.55 32. 5 15. 57 7.32 5.6 4.88 3.59 2.25 1.27 1. 38  -0.01 -2.07 -1.55 -1.5 -0.07 1. 68 2. 4 1.02 0.31 0. 15 0. 07 -0.42  RESIDUAL SUM OF SQUARES= 18.8651 FLOWRATE  RUN B=  (AVERAGE OVER DAY IN TPH)=  293.4845  NO.= 4 0.1734328  X 0= -13.31 14  X 50= 1.993 059  SIZE  MEAS.PRO D.  PRED, PROD.  DIFF ERENCE  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  0 0 0 0 33 34 10. 2 6 4.8 3. 1 2.9 2.6 1.85 1.55  0 0 0.01 2.48 25. 23 32.07 14. 86 6.96 5. 38 4.73 3.5 2. 19 1. 24 1. 35  0 0 -0.01 -2.48 7.77 1. 93 -4.66 -0.96 -0.58 -1.63 -0.6 0. 41 0.61 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 10.88 5. 44 2.72 1. 36 0.68  0 0 0 0 22 29  0 0 0.01 2. 14 20. 24 28.71  0 0 -0.01 -2.14 1. 76 0.29  0. 34 0. 17 0. 085 0.0425 0.02125 0.010625 0 . 0053 125 PAN  RESIDUAL SUM OF SQUARES= FLOWRATE  - Z4U 15.7 8. 67 7. 3 6.35 4.63 2.88 1.62 1. 76  15 10.7 7.5 5.6 3.8 2.7 1.95 1.75  -0.7  2. 03  0. 2 -0.75 -0.83 -0.18 0.33 - 0 . 01  13.8051  (AVERAGE OVER DAY INTPH)=  283.6669  RUN NO.= 6 B=  0.2060952  X 0= - 1 2 . 4 4 278 X 50=  1.828213  SIZE  MEAS. PROD.  PflED.PROD.  DIFFERENCE  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  0 0 0 0 25 26 13. 5 9.5 7.8 5.9 4.7 3.5 2.3 1.8  0 0 0.02 3. 23 25. 51 29. 57 14. 1 7. 17 5,94 5. 27 3.89 2. 44 1.37 1.5  0 0 -0.02 -3.23 -0.51 -3.57 -0.6 2. 33 1. 86 0. 63 0. 81 1. 06 0. 93 0.3  RESIDUAL SUM OF SQUARES^ 3 5 . 8 1 8 3 FLOWRATE  (AVERAGE OVER DAY  INTPH)=  219.4101  X 0= - 1 1 . 5 4 3 7 7 X 50=  1.880033  RUN NO.= 7 B=  0.2463917  SIZE  MEAS.PROD.  PRED. PROD.  DIFFERENCE  2 1.76 10.88 5. 44 2.72 1.36 0.68 0.34 0 . 17 0.085 0.0425  0 0 0 0 23 25 13 10 8.5 6.3  0 0 0.01 2.37 21.56 29. 12 15. 34 8.26 6.91 6.04  0 0 -0.0 1 -2.37 1. 44 -4.12 -2.3 4 1.74 1. 59 0.26  i-t I  0.02125 0.010625 0.0053125 PAN  5.3 3.9 2.7 2.3  RESIDUAL SUM OF SQUARES= FLOWRATE  4.41 2.75 1.55 1. 68 39.5854  (AVERAGE OVER DAY IN TPH) = 355.3625  ? PROGRAM ENDS MTS CONTROL *PRINT* HOLD PRINT=TN FORM=8X11 • P R I N T * ASSIGNED RFS NUMBER 663938 $C *S0URCE*3SP *PRINT*  0. 89 1. 15 1. 15 0.6 2  - 242 -  APPENDIX J SECONDARY CRUSHING PLANT SIMULATION PROGRAMS (a)  Listing (i) (ii) (iii) (iv) (v)  o f the S i m u l a t i o n Program M2  Main Program M2 Subprogram SCMS (Secondary Crusher) Subprogram TCMS ( T e r t i a r y Crusher) Subprogram PRNT1 ( P r i n t o u t ) Subprogram PRNT2 ( P r i n t o u t )  (b)  Sample Outputs from Program M2 (2)  (c)  Listing  (d)  Sample O u t p u t s . f r o m Program PGM2 (2)  o f the S i m u l a t i o n Program PGM2  -  £ t J  -  1 * * * PROGRAM: M2 :CRUSHING PLANT SIMULATION PROGRAM 2 * 3 * 10 * * DATA INPUT SECTION * * 20 DIM A ( 1 , 2 0 ) D ( 1 , 2 0 ) , E (20,30) 30 DIM R (20) , V (20) , Y (20) , F ( 3 0 ) 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 ( 1 5 ) 70 READ S 1 , R 1 , 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 X1,X2,X3,X4,X5,X6,X7 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 , . 1 7 , . 1 7 , . 1 8 , . 1 6 , . 1 3 , . 19 185 FOR J=1 TO 9 187 READ F ( J ) 189 NEXT J 191 DATA 1 . 2 3 8 4 1 4 , . 4822109, - 1. 00 2 2 2 1 E - 2 , 1. 1 6 3 8 7 1 E - 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 f  260 280 285 290 29 5 300 305 310 315 320 325 330 333 34 0 345 350 355 36 0 365 37 0 380 390 400 410 420 43 0 43 2  RESTORE F I L E 4 PRINT "ENTER SECONDARY CRUSHER GAPS ( C M . ) " FOR J = 1 TO P(7) INPUT N(J) NEXT J PRINT "ENTER SECONDARY SCREEN OPENINGS (CM.)," FOR J=(P{7)+1) TO (P(7)+P{8)) INPUT N(J) NEXT J PRINT "ENTER TERTIARY CRUSHER GAPS ( C M . ) " FOB J= (P (7)+P (8)+1) TO (P (7)+P (8)+P{9) ) INPUT N<J) NEXT J PRINT PBINT "**************************#*#***^ FOR J=1 TO (P{7)+P (8)+P (9) ) WRITE F I L E 5 , N ( J ) NEXT J RESTORE F I L E 5 FOR J=1 TO P(10) S (J)=S1*R1** (J-1) NEXT J P (12)=SQB (S (1) *S (2) ) FOR J=1 TO P (10) - 1 T ( J ) = P ( 12) * R 1 * * (J-1) NEXT J FOR J=1 TO P{10)  433  WRITE  FILE  2,S(J)  434 NEXT J 436 RESTORE F I L E 2 440 FOR J=6 TO P{10)  - 244 450 460 47 0 48 0 490 495 50 0 505 510 515 52 0 525 53 0 532 544 54 6 548 550 55 2 555 55 8 55 9 560 570 580 585 590 600 610 620 625 640 660 67 0 680 690 730 740 750 755 76 0 770 78 0 800 810 82 0 830 840 850 86 0 870 880 890 900 910 912 914 92 0 930 940  P{6) =P (6) +E ( J , 1) NEXT J P{15)=0 * * SECONDARY CRUSHER SECTION ** HAT A = Z E R ( 1 , P ( 1 0 ) ) P(1)=0 FOR J=1 TO 4 P(1)=P(1) + E ( J , 1 ) NEXT J MAT WRITE F I L E 1 , E RESTORE F I L E 1 L(4)=0 FOR 1=1 TO P(7) L (1+1) =L (1) *M (I) WRITE F I L E 3 , L (1 + 1) RESTORE F I L E 3 P{1 1) =1 WRITE F I L E 7 , P { 1) , P ( 10) , P (1 1) , P ( 1 2) RESTORE F I L E 7 CALL SCMS MAT READ F I L E 1 , E RESTORE F I L E 1 FOR J=1 TO P(10) A (1 , J) =A (1, J) + E ( J , 1 + 1) * L (1 + 1) NEXT J L (4)=L (4)+L (1+1) NEXT I FOR J=1 TO P(10) E ( J , 4 ) = A (1 J) / L ( 4 ) NEXT J I(22)=0 ** BLEND SECONDARY AND TERTIARY CROSHER PRODUCTS L ( 5 ) = L ( 4 ) +L (22) FOR J=1 TO P(10) E ( J , 5 ) = (E ( J , 4 ) * L (4) + E ( J , 2 2 ) * L (22) ) / L (5) NEXT J ** SECONDARY SCREENS SECTION ** L(17)=0 L(11)=0 P{2)=0 FOR J=1 TO 4 P(2)=P(2)+E(J,5) NEXT J MAT A=ZER (1 P (10) ) MAT D=ZER(1,P (10) ) FOR 1=1 TO P(8) L(23+I)=L<5) *M (2 + 1) GOSUB 3860 FOR J=1 TO P(10) A (1 , J ) = A (1, J) +E ( J , 11+1) *L{1 1 + 1) D (1 »J) =D ( 1 , J ) + E ( J , 5 * I ) * L (5 + 1) NEXT J L ( 1 7 ) = L ( 1 7 ) +L(11+I) 1(1 1) = L (11) +L (5 + 1) NEXT I I F L{17)<=0 THEN:L{17)=1 I F L(11)<=0 THEN:L(11) = 1 FOR J=1 TO P(10) E ( J , 1 7 ) =A (1 J ) / L (17) E(J,11)=D(1 J)/L(11) f  r  r  r  **  - 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 { 1 1 ) ) <P(14) THEN 1240 1030 I F P(15)>=P(13) THEN 1240 1040 * * TERTIARY CBUSHEB SECTION ** 1050 L ( 2 2 ) =0 1060 P{3)=0 1070 FOR J=1 TO 4 1080 P (3) = P (3) + E ( J 17) 1090 NEXT J 1100 MAT A=ZER ( 1 , P (10) ) 1102 FOR 1=1 TO P(9) 1103 P ( 1 1 ) = I 1104 L ( 17+1) =L (17) *M (7+1) 1106 WRITE F I L E 7 , P (3) 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 ( 1 7 + 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 ( 2 2 ) = L { 2 2 ) + L ( 1 7 + I ) 1180 NEXT I 1190 FOR J=1 TO P(10) 1200 E ( J , 2 2 ) =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 ( 2 3 ) = 0 1260 L ( 2 9 ) = L (11)+L(23) 1270 FOR J=1 TO P (10) 1280 E ( J 2 4 ) = (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 , 2 4 ) 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 ( 1 0 ) - 1 3900 Y (J) = 1/(1+EXP{ ( Z 9 * * 3 - T (J) **3) / Z 8 ) ) 3910 NEXT J 3920 A3=0 3930 B3=0 3940 FOR J=1 TO P ( 1 0 ) - 1 3950 J ( J ) = <Y (J) * L (23+1) *E(J,5) ) / 1 0 0 f  r  r  3960 K { J ) = ( (1-Y (J) ) * L (23+1) * E ( J , 5 ) ) / 1 0 0 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) ) / 1 0 0 40 10 K(P (10) ) = ( ( 1 - B 1 0 ) * L (23 + 1) * E (P (10) ,5) ) /100 4020 A3 = A3 + J f P { 1 0 ) ) 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 1 1 + I ) = (J ( J ) / A 3 ) *100 4080 E (J,5+1) = (K (J) / B 3 ) * 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) / 1 0 0 0 0 0 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 { 1 1 ) ) 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 r  - £4/ 3480 3482 34 84 3485 34 86 34 87 34 88 3489 3490 3491 3492 3493 3494 3495 34 96 3497 3498 34 99 35 01 3502 3504 3505 3506 3507 350 8 3509 3510 3511 3513 3515 352 0 35 30 3540 3550 3560 35 70 3580 35 90 3600 3610 3620 3630 3640 3650 36 6 0 36 70 3675 3678 36 80 36 90 3710 3720 373 0 374 0 3750 3760 3770 3780 3790 3800  DIM E { 2 0 , 3 0 ) , L ( 3 0 ) , S ( 2 0 ) , K ( 2 0 ) , J ( 2 0 ) , R ( 2 0 ) DIM H (20) , V (20) , G (20) , P (20) , 0 (15) , N ( 1 5) , Q (15) FILE X1,X2,X3,X5,X6,X7 READ F I L E 6 , P (1) , P { 10) , P (1 1) , P { 1 2) RESTORE F I L E 6 I=P(11) FOR J=1 TO 5 READ F I L E 4 , N (J) NEXT J RESTORE F I L E 4 MAT READ F I L E 1 , E (P (10) ,24) RESTORE F I L E 1 FOR J=1 TO P{10) READ F I L E 2 , S (J) NEXT J RESTORE F I L E 2 READ F I L E 3 , L ( 1 + I ) RESTORE F I L E 3 FOR J=1 TO 12 READ Q (J) NEXT J 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 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 Z1=Q(1)+Q(2)*N(I)+Q{3) *L(1 + I) +Q(4)*P(1) Z2=Q{5) +0 (6)*N (I) +Q (7) *N(I) **2+Q{8) *P (1) Z3=Q(9) + Q {1 0) *N (I) +Q (1 1) *N (I) **2+Q {12 ) *P (1) RESTORE L2=1 L4=0 FOR J=1 TO P ( 1 0 ) - 1 L1 = 1- ( 1 - (S (J + 1) / P (12) ) **2) **6 K(J)=L2-L1 L2=L1 L3=EXP(-((S(J+1)/2) **.664)) J(J)=L3-L4 L4=L3 NEXT J FOR J=1 TO P(10) I F S ( J ) > Z 3 THEN 3660 I F S ( J ) < Z 2 THEN 3640 H (J)=S (J) - (S (J) - Z 3 ) * * 3 / (3* ( (Z2-Z3) **2)) GO TO 3670 H (J) = Z 2 - ( Z 2 - Z 3 ) / 3 GO TO 3670 H (J)=S (J) NEXT J R(0)=0 Z20=0 FOR 0=1 TO P ( 1 0 ) - 1 V(U) = ( H ( U ) - H ( U + 1 ) ) / ( S ( 0 ) - S ( U + 1 ) ) A1=0 B1=0 FOR J=1 TO 11-1 A 1 = A 1+ (Z1*K (D-J+1) + {1-Z 1) * J (U) ) *R (J) B1 = B1+J(J) NEXT J G (U) = (E (0, 1) + A 1 ) / ( 1 - (Z1*K(1) + {1 - Z 1) *{B1 + J (U) ) ) * V (U) ) R(U)=V(U)*G (0) E ( U , 1 + 1) =G (U)-R (U) Z20=Z20+E(0,1+I)  - £48 3810 NEXT U 3820 E ( P ( 1 0 ) ,1+I) = 100-Z20 3830 0{I) = 2 0 . 6 1 8 2 - 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- F I L E  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 ( 3 0 ) , N ( 1 5 ) 30 F I L E 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 F I L E 4 195 FOR 3=1 TO 17 197 BEAD H (9+3) 199 NEXT 3 201 DAT A. 1133812, 1. 1 7 8 0 7 8 E - 4 , . 5 1 8 0 7 6 , 3 . 6 3 2 1 7 6 E - 4 , 2 9 9 . 3 8 1 203 DATA 27. 4 5 8 3 , 4 3 . 9 7 8 3 2 , - 2 5 9 9 . 7 6 2 , 16.76629 205 DATA - 1 . 7 9 3 2 6 5 , 5 . 2 8 4 6 4 7 E - 2 206 DATA6. 3 3 1 6 1 9 , - . 80409 9 7 , 1.0 4 2 3 8 5 , 2 . 9 9 6 6 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 I F Z5<0 THEN:Z5=0 4234 I F Z5>600 THEN:Z5=600 4240 FOB 3=1 TO P ( 1 0 ) - 1 425 0 L1 = 1-{1- (S (3+1) / P (12.) ) **4) * * Z 5 4260 K ( 3 ) = L 2 - L 1 4270 L2=L1 4280 L 3 = E X P ( - ({S(3+1)/2) * * . 664) ) 42 90 3 ( 3 ) = L 3 - L 4 4300 L4=L3 4310 NEXT 3 4320 FOB 3=1 TO P{10) 4330 I F S(3)>Z7 THEN 4390 4340 I F S{J)<Z6 THEN 4370 4350 H ( 3 ) = S { 3 ) - (S (3) -27) * * 3 / ( 3 * ( ( Z 6 - Z 7 ) * * 2 ) ) 4360 GO TO 4400 4370 H ( 3 ) = Z 6 - { Z 6 - Z 7 ) / 3 4380 GO TO 4400 4390 H (3)=S (3) 4400 NEXT 3 4410 Z20=0 44 20 FOB 0=1 TO P { 1 0 ) - 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)  -  £DU -  4480 B1 = B1 + J ( J ) 4490 NEXT J 4500 G(0) = ( E ( U , 1 7 ) + A 1 ) / ( 1 - (Z4*K{1) + ( 1 - Z 4 ) * (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. 5 5 7 5 6 - 9 . 608871*N (7 + 1) + 5 . 5 4 2 0 4 1 E - 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— F I L E  - 251 1370 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 13 84 1385 13 86 1387 13 88 13 89 1390 1391 1392 1393 1394 1410 1420 1430 14 40 1450 1460 1470 1490 1510 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1650 1660 1670 1680 1690 17 00 1710 1730 1750 1760 1770 1780 1790 1800 1810 1820  DIM I (30) , E ( 2 0 , 3 0 ) , S ( 2 0 ) , L { 3 0 ) , M (15) , N (15) , 0 { 10) , P ( 2 0 ) FILE X1,X2,X3,X4,X5,X6-,X7 FOB J=1 TO 16 BEAD F I L E 7 , P { J ) NEXT 3 MAT BEAD F I L E 1 , E (P (10) ,8+P (7) + 2*P (8) *P (9) ) FOB J=1 TO P(10) BEAD F I L E 2 , S ( J ) NEXT 3 FOB J = l TO 8*P (7)+3*P (8)+P{9) BEAD F I L E 3 , L ( J ) NEXT J FOB J=1 TO P (7) *P (8)+P (9) BEAD F I L E 4 , H ( J ) NEXT J FOR J=1 TO P (7)+P (8)+P (9) READ F I L E 5 , N ( J ) NEXT J FOR J=1 TO P(7)+P{9) BEAD F I L E 6 , 0 ( J ) NEXT J I F P(16)<P(14) THEN 1420 PRINT "CYCLE LIMIT SET AT";P(13),"NUMBER OF CYCLES=";P(15) PRINT » ","CONVERGENCE CRITERION^";P{16) GO TO 1460 PRINT PRINT "CONVERGENCE CRIT EBION MINIMUM^";P{16) PBINT » NUMBER OF CYCLES=";P(15} PBINT PBINT " A L L S I Z E DISTRIBUTIONS MEASURED IN % RETAINED ON S I Z E " PBINT PBINT " * * * * * ANALYSIS OF PLANT FEED ****** PRINT "SCREEN S I Z E " , " F E E D S I Z E ANALYSIS" FOB J=1 TO P { 1 0 ) - 1 PRINT S (J+1) , E ( J , 1 ) I (23}=I (23) + E ( J , 1} NEXT J PRINT " P A N " , E ( P (10) , 1} I ( 2 3 ) = I { 2 3 ) + E ( P ( 1 0 ) ,1) PBINT PBINT "SUM",1(23) PBINT PRINT "PLANT FEEDRATE ( STPH) = " ; L {1) , " » ,"% MINUS . 5 4 INCH IN FEED = « ; P ( ( PBINT PBINT " * * * * * SECONDARY CRUSHING OUTPUT * * * * * * PBINT PBINT "NUMBER OF CRUSHERS OPERATING=";P(7) PRINT PRINT "FEED S P L I T B ATI OS=" ; M (1) , M (2 ) PRINT PBINT "PBODUCT SIZE ANALYSES" PRINT "SIZE","CRUSHER NR.1","CRUSHES NR.2","COMBINED OUTPUT" FOB J=1 TO P { 1 0 ) - 1 PRINT S (J + 1) , E ( J , 2 ) , E ( J , 3 ) , E ( J , 4) 1(1) = 1 ( 1 ) +E ( J , 2 ) I (2)=I (2) + E ( J , 3 ) I (3) =1(3) +E ( J , 4 ) NEXT J PRINT » P A N " , E f P (10) ,2) , E ( P ( 1 0 ) ,3) , E ( P { 1 0 ) ,4) I (1)=I(1) * E ( P ( 1 0 ) ,2)  - Z5Z 1830 I ( 2 ) = I ( 2 ) + E ( P ( 1 0 ) , 3 ) 1840 I ( 3 ) = I ( 3 ) + E ( P ( 1 0 ) ,4) 1850 PRINT 1860 PRINT "SUM", 1(1) , I (2) , I (3) 1870 PRINT 1890 PRINT " " / ' O P E R A T I N G 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 " , " S C R E E N 3 " , " S C R E E N 4 " , " S C R E E N 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 S I Z E ANALYSIS" 2120 M5=CMD("%SET COLWIDTH=11") 2130 PRINT " S I Z E " , " S C R N 1","SCRN 2","SCRN 3","SCRN 4","SCRN 5 " , " C O M B ' D " 2150 FOR J=1 TO P ( 1 0 ) - 1 2160 PRINT S (J+1) , E ( J , 1 2 ) , 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 " P A N " , E ( N 2 , 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 END-OF-FILE  - Zb-i 2390 2392 2393 23 94 2395 2396 2397 2398 2399 2400 2401 2402 24 0 3 2405 2406 2407 24 08 2409 24 10 2411 2412 2420 2425 24 30 2440 2450 2460 2470 2480 2490 2500 2510 2515 2520 2530 2540 2550 2560 2570 2580 2590 2610 2620 2640 2650 2660 2670 2690 27 00 2710 2720 2740 27 50 2760 2780 2800 2810 2820 2830 28 40  DIM I{30) , E { 2 0 , 30) , S (20) , L (30) , M (15) , N (15) , 0 ( 1 0 ) , P (20) FILE X1 X2,X3,X4,X5,X6,X7 FOE J=1 TO 16 BEAD F I L E 7 , P (J) NEXT J MAT BEAD F I L E 1 , E (P (10) , 8 +P (7) + 2*P (8) +P {9)) FOB J=1 TO P{10) BEAD F I L E 2 , S { J ) NEXT J FOB J=1 TO 8 + P (7)+3*P {8)+P (9) BEAD F I L E 3 , L ( J ) NEXT J FOB J=1 TO P (7)+P (8)+P (9) BEAD F I L E 4 , M ( J ) NEXT J FOB J=1 TO P (7) +P (8) +P (9) BEAD F I L E 5 , N ( J ) NEXT J FOB J=1 TO P ( 7 ) + P ( 9 ) BEAD F I L E 6 , 0 ( J ) NEXT J PBINT "UNDEBSIZE S I Z E ANALYSES" M7=CMD("$SET COLWIDTH=11") FOB J=1 TO P ( 1 0 ) - 1 PRINT S(J+1) , E ( J , 6 ) , E ( J , 7 ) , E ( J , 8 ) , E ( J , 9 ) , E ( J , 1 Q ) , E ( J , 1 1 ) 1 (10) =1 (10) +E ( J , 6 ) I(11)=I (11)+E(J,7) I ( 12) =1 (12) +E ( J , 8 ) I (13)=I (13) + E ( J , 9 ) I (14) =1 (14)+E ( J , 10) I (15) = I (15) + E ( J , 11) NEXT J N2=P(10) PBINT " P A N " E ( N 2 , 6 ) , E (N2,7) , E (N2 ,8) , E (N2, 9) ,E (N2, 10) , E { N 2 , 1 1 ) PBINT FOB J = 1 TOP (8) + 1 I (9 + J) =1 (9+J) +E (P{10) ,5+J) NEXT J PBINT " S U M " , I (10) , I (11) ,1 (12) , I (13) , I (14) , I (15) PBINT PRINT " " , " O P E B A T I N G DATA" PBINT " " , " S C B E E N OPENING ( C M . ) " PBINT " " , N ( 3 ) ,N(4) , N ( 5 ) ,N{6) ,N{7) , " - " PRINT " " , " F L O H H A T E S (STPH)" PRINT " » , L (6) , L (7) , L (8) , L (9) , L (10) , L (11) PRINT PRINT"fo MINUS . 5 4 INCH MAT'L IN CRUSHING PLANT PR ODUCT=»; P (4) PRINT PRINT " * * * * * TEBTIAHY CRUSHING OUTPUT ***«*" PRINT PBINT "NUMBER OF CEUSHEBS OPEBATING=";P(9) PBINT " FEED SPLIT RATIOS=" ; M (8) , M (9) , M (10) , M ( 11) PBINT PEINT "PBODUCT S I Z E ANALYSES" PBINT "SIZE","CRUSHER 1","CBUSHER 2", "CRUSHER 3","CRUSHES 4","COMBINED' FOB J=1 TO P ( 1 0 ) - 1 PRINT S (J + 1) , E ( J , 1 8 ) , E ( J , 1 9 ) , E ( J , 2 0 ) , E ( J , 2 1 ) , E ( J , 2 2 ) I (16) =1 (16) + E ( J , 18) I (17)=I <17) +E ( J , 19) I (18) =1 ( 1 8 ) + E ( J , 2 0 ) r  r  - 254 -  2850 I{19)=I{19) + E ( J , 2 1 ) 2860 I (20)=I (20)+E ( J , 2 2 ) 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 ( 1 0 ) , 1 7 + J ) 2910 NEXT J 2920 PRINT 2930 PRINT " S U M " , I (16) ,1 (17) ,1 (18) ,1 (19) ,1 (20) 294 0 PRINT 2950 PRINT » ","OPERATING DATA" 297 0 PRINT " " , "CLOSE SIDE SETTING ( C M . ) " 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 ( 2 2 ) / 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 { 1 0 ) - 1 3170 PRINT S (J + 1) , E ( J , 2 3 ) 3180 1(21) =1 (21)+E ( J , 2 3 ) 3190 NEXT J 3200 PRINT " P A N " , 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 , 2 4 ) 33 40 I (22) =1(22) + E ( J , 2 4 ) 3350 NEXT J 3360 PRINT " P A N " , E ( P ( 1 0 ) , 2 4 ) 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 R A T I O = " ; P ( 4 ) / P ( 6 ) 3430 PRINT »% MINUS .54 INCH M A T ' ! I N ROD HILL FEED=";P(5) 3450 PRINT 3460 STOP END-OF-FILE 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 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS49 # SIGN RALU # ENTER USER PASSWORD.  task:  # * * L A S T SIGNON WAS: 1 3 : 2 1 : 2 3 # USER "RALU" SIGNED ON AT 1 3 : 4 0 : 2 7 ON THU SEP 0 8 / 7 7 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 . 5 8 6 7 2 3 E - 3 NUMBER OF CYCLES= 10 ALL SIZE DISTRIBUTIONS MEASURED IN % RETAINED ON SIZE ***** ANALYSIS OF PLANT FEED ***** SCREEN S I Z E FEED S I Z E 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  SECONDARY CRUSHING  OUTPUT  % MINUS .54 *****  INCH IN FEED  - 256 NUMBER OF CRUSHERS  OPERATING  FEED SPLIT  0.5  RATIOS  3  2  3  0.5  PRODUCT S I Z E ANALYSES SIZE CRUSHER NR.1 21.76 0 10. 88 0.11915 5.44 28.51169 2.72 38. 50253 1.36 17.28089 0.68 6.54267 0.34 3.12138 0. 17 1.90209 0.085 1.2438 0.0425 0.86689 0.02125 0.63114 0.010625 0.45016 0.0053125 0.31553 PAN 0.51209 SUM  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  100  100  OPERATING DATA CLOSE SIDE SETTING (IN CM.) FLOWRATES (IN STPH) CURRENT DRAW {IN AMPERES) *****  NUMBER OF SCREENS OPERATING SCREEN 1 SCREEN 2 FEED SPLIT RATIOS 0.2 0.2 FEEDRATES TO INDIVIDUAL 577.5805 577.5805 OVERSIZE PRODUCT SIZE SIZE SCRN 1 21. 76 0 10.88 0. 12092 5. 44 28.9354 2.72 46.82823 22.49981 1.36 0.68 0.91858 0. 34 0.26406 0 . 17 0.14589 0. 085 0.09658 0.0425 0.06515 0.02125 0.04396 0.010625 0.02928 0.0053125 0.01931 PAN 0.03281 SUM  99.99998  3  100  NUMBER 1 3.08 727.3 23.16549  SECONDARY SCREENING OUTPUT  NUMBER 2 3.08 727.3 23.16549  COMBINED 1454.6 N . A.  *****  5 SCREEN 3  0. 2 SCREENS (STPH) 577.5805  ANALYSIS SCRN 2 0 0.12092 28. 9354 46.82823 22.49981 0.91858 0.26 4 06 0 . 14589 0.09658 0.06515 0.04396 0.02928 0.01931 0.03281 99.99998  OPERATING DATA FLOWRATES (STPH)  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  SCRN 3 0 0. 12092 28.9354 46.82823 22.49981 0.91858 0.26406 0.14589 0.09658 0.06515 0.04396 0.02928 0. 01931 0.03281 99.99998  SCREEN 4  SCREEN 5  0. 2  0.2  577. 5805  577.5805  SCRN 4 0 0. 12092 28.9354 46. 82 823 22. 49981 0 . 9 1858 0.26406 0 . 1 4 5 89 0.09658 0.06515 0.04396 0.02928 0.01931 0.03281 99.99998  SCRN 5 0 0. 12 092 28 , 9 3 5 4 46 .82823 22 . 4 9 9 8 1 0. 9185 8 0. 26406 0 . 14589 0 . 09658 0 . 0651 5 0. 04396 0. 0292 8 0. 0193 1 0 .03281 99.99998  COMB' D 0 0.12092 28.9354 46. 82 823 22.49981 0.91858 0.26406 0.14589 0.0 9658 0.06515 0.04396 0.02928 0.01931 0.03281 99.9999*  - ZS/ 286.66  286.66  UNDERSIZE S I Z E ANALYSES 21.76 0 0 ' 10. 88 0 0 5.44 0 0 2.72 0 0 1.36 37.84707 37. 8 4707 0. 68 29.17259 29.17259 0.34 12.1076 12,1076 0. 17 7.00373 7.00373 0.085 4.66311 4,66311 0.0425 3. 14783 3.14783 0.02125 2. 12438 2.12438 0.010625 1.41477 1.41477 0.0053125 0.93334 0.93334 PAN ' 1.58559 1.58559 100  SUM  *****  286.66  286.66  1433.3  0 0 0 0 37.84707 29.17259 12.1076 7. 00373 4. 6631 1 3.14783 2.12438 1. 41477 0.93334 1.58559  0 0 0 0 37.84707 29.17259 12. 1076 7.00373 4.66311 3 . 1 4 7 83 2.12438 1.41477 0.933 34 1.58559  0 0 0 0 3 7 . 8 4 7 07 29.17259 12.1076 7.0037 3 4.66311 3. 14783 2.12438 1.41477 0.93334 1. 58559  0 0 0 0 37.84707 29. 17259 12. 1076 7.00373 4.66311 3.14783 2.12438 1.41477 0.9 3334 1.58559  100  OPERATING DATA SCREEN OPENING (CM.) 1.59 1.59 FLOWRATES (STPH) 290.9205 290.9205 % MINUS .54  286.66  100  100  100  1.59  1.5 9  1 .59  —  290.9205  290.9205  290.9205  1454.603  INCH MAT'L IN CRUSHING  TERTIARY CRUSHING  PLANT PRODUCT= 6 2 . 1 5 2 9 3  OUTPUT  *****  NUMBER OF CRUSHERS OPERATING^ 4 FEED SPLIT RATIOS= 0 . 2 5  0.25  PRODUCT SIZE ANALYSES SIZE CRUSHER 1 2 1 . 76 0 10.88 0 5.44 0 2 . 72 7.75351 1.36 43.37161 0.68 23,88481 0.34 9.38383 0. 17 5.32335 0.085 3.56671 0.0425 2 . 37998 0.02125 1. 5594 0.010625 1.00823 0.0053125 0.64631 PAN 1.12227 SUM  100  CRUSHER 2 0 0 0 7.75351 43.37161 23.88481 9.38383 5.32335 3.56671 2.37998 1.5594 1.00823 0.64631 1.12227 100  CRUSHES 3 0 0 0 7.75351 43. 37161 23.88481 9.38383 5.32335 3. 56671 2. 37998 1.5594 1.00823 0.64631 1.12227 100  OPERATING DATA CLOSE SIDE SETTING (CM.) 0.81 0.81 0.81 FLOWHATES (STPH) 358.3256 3 5 8 . 3 256 358.3256 CURRENT DRAWS (AMPERES) 35.37048 35.37048 35.37048  0.25 CRUSHER 4 0 0 0 7.75351 43.37161 23. 88481 9.38383 5.32335 3.56671 2.37998 1.5594 1.00823 0 . 6 46 31 1. 12227  0.25 COMBINED 0 0 0 7.75351 43.37161 23.88481 9.38383 5.32335 3.56671 2.37998 1.5594 1.00823 0.64631 1. 12227  100  100  0.81  -  358.3 256  1433.302  35. 37048  N.A.  100  - 258 PERCENT CIRCULATING  LOAD=  0.9853582  *****  PRIMARY  FINES OUTPUT  SCREEN 21.76 10.88 5.44 2.72 1.36  SIZE  SIZE 0 0 0 0 0 0 0 0 0 0 0 0 0  0.68  0.34 0 . 17 0.085 0.0425 0.02125 0.010625 0.0053125 PAN SUM DAILY *****  ANALYSIS  0  0 FLOUR ATE (STPH,INTERMITTENT) = 0 ROD MILL FEED ANALYSIS  SCREEN 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  *****  *****  S I Z E 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= 2 5 . 3 6 8 5 4 % MINUS , 5 4 INCH HftTVL IN ROD MILL FEED= 6 2 . 1 5 2 9 3 + # + : # # #  7STOP! ? AT LINE "3460" IN PROGRAM "PRNT2" ? PROGRAM ENDS HTS CONTROL *PRINT* HOLD PRINT=TN FORM=8X11 * P R I N T * ASSIGNED RFS NUMBER 664246 $C * SOURCE* 3>S P * PRINT*  d e v i c e : DS48 task: 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 C o l u m b i a C o m p u t i n g C e n t r e - d e v i c e : DS48 # SIGN RALU # ENTER USER PASSWORD.  task:  4'  # * * L A S T SIGNON WAS: 1 4 : 1 5 : 5 3 # USER "RALU" SIGNED ON AT 1 4 : 1 8 : 4 5 ON THU SEP 0 8 / 7 7 # RUN *BASIC # EXECUTION BEGINS & ?UBC BASIC SYSTEH S. ? — : GET M2 : .250 DATA . 6 , . 4 , . 2 5 , . 2 , . 1 , . 2 , . 2 5 , . 3 , . 2 , . 1 5 , . 3 5 : 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 MINIMUM 1. 509731 E - 3 NUMBER OF C Y C L E S 12 3  3  ALL S I Z E DISTRIBUTIONS MEASURED I N % RETAINED ***** ANALYSIS SCREEN 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 PLANT  ON SIZE  OF PLANT FEED ***** FEED S I Z E ANALYSIS 3 35 36.5 18.35 4.7 0.94 0.29 0.22 0.17 0.17 0.18 0.16 0.13 0.19 100  FEEDRATE ( S T P H )  3  1275  % MINUS .54  INCH  IN F E E D  3  2.4^  *****  SECONDARY CRUSHING  NUMBER OF CRUSHERS OPERATING FEED SPLIT  RATIOS  2  3  0.6  3  0.4  PRODUCT S I Z E ANALYSES SIZE CRUSHER NR. 1 21.76 0 10. 88 0.04222 5.44 27.17139 2.72 38.33784 1 .36 17.51018 0.68 6.88696 0.34 3.42821 0. 17 2. 13384 0.085 1.406 0.0425 0.97584 0.02125 0.70258 0.010625 0.49634 0.0053125 0.34511 PAN 0.56349 SUM  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  100  OPERATING DATA CLOSE SIDE SETTING (IN CM.) FLOWRATES (IN STPH) CURRENT DRAW (IN AMPERES) *****  SECONDARY SCREENING  NUMBER OF SCREENS  - 260 *****  OUTPUT  99.99999  99. 99999  NUMBER 1 2.8 765 26.51729  NUMBER 2 3.25 510 14.42023  OUTPUT  OPERATING  3  SUM  100  1275 N . A. ,  5  ANALYSIS SCRN 2 0 0.07389 25.3077 40. 84624 31. 17531 1.3562 0.48016 0.25798 0.17004 0.11444 0.07681 0.05088 0.03339 0.05695 99.99999  OPERATING DATA  COMBINED  *****  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 OVERSIZE PRODUCT S I Z E SIZE SCRN 1 21.76 0 10.88 0.06797 5. 44 23.28013 37.57377 2.72 1. 36 35.76178 0.68 1.7474 0.34 0.60817 0 . 17 0. 326 0.085 0.21481 0.0425 0.14456 0.02125 0.09702 0.010625 0.06427 0.0053125 0.04218 PAN 0.07194  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  SCRN 3 0 0.06648 22.766 86 36.74537 37.72987 1.45718 0. 48059 0.25588 0.16846 0.11336 0.07608 0.0504 0.03308 0.05641 100  SCREEN 4  SCREEN 5  0. 2  0.25  54 3. 4431  679.3038  SCRN 4 0 0.0 73 89 25. 3077 40.84624 31. 17531 1.3562 0.48016 0.25798 0.17004 0.1 1444 0.07681 0.Q5088 0.03339 0. 05 695 99.99999  SCRN 5 0 0.08275 28.34012 45.74052 23.9556 0.97155 0. 35132 0. 18929 0. 12481 0 . 084 0.05638 0.03735 0.0245 1 0.04181 100  COMBED 0 0.07344 25. 15217 40.59521 31. 53637 1.38767 0.4 862 0.26088 0 . 17192 0.1157 0.07765 0.05144 0.0 3376 0.05758 99.9999  - Zb\ FLOWRATES 389.5477 UNDERSIZE 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  (STPH) 286.6707  159.3319  286.6707  319.9958  1442.217  S I Z E ANALYSES 0 0 0 0 0 0 0 0 23.91498 30.18743 31.6475 29.17689 16.63636 15.22077 9. 38 93 8.58395 6.22685 5.69224 4.19379 3.83369 2.81507 2.57335 1.86477 1 .70465 1.22395 1.11885 2.08743 1.90819  0 0 0 0 20.75459 32.9935 17.31821 9.77199 6.48046 4.36459 2.92971 1. 94071 1.2738 2.17244  0 0 0 0 30.18743 29.17689 15. 22077 8.5 83 95 5.69224 3 .83369 2.57335 1.70465 1.1 1885 1.90819  0 0 0 0 36.722 6 4 26.55065 13.76251 7.7566 5 5 . 14324 3.46391 2.32513 1.54022 1.01093 1.72413  0 0 0 0 29.77215 29.33469 15.31641 8.63856 5.7285 3.85812 2.58974 1,71551 1 . 12598 1. 92035  SUM  100  100  OPERATING DATA SCREEN OPENING (CM.) 1.4 1.5 FLOWRATES (STPH) 289.7561 256.7724 % MINUS .54 *****  100  1 .59  -  112.3896  256.7724  359.308  1274.998  PLANT PRODUCT=  *****  NUMBER OF CRUSHERS OPERATING^ 4 FEED SPLIT RATIOS= 0 . 3 0 . 2  0 . 15  SUM  100  CRUSHER 2 0 0 0 4.75241 48.68096 26.48171 9.88285 3.67131 2.27477 1.50692 0.98773 0.63929 0.41026 0.71178 99.99999  100  1.5  OUTPUT  PRODUCT S I Z E ANALYSES SIZE CRUSHER 1 21.76 0 10. 88 0 5.44 0 2.72 8.88153 1.36 42.19728 0. 68 19.53891 0.34 10.76471 0. 17 6.34421 0.085 4.25599 0.0425 2.84043 0.02125 1. 86145 0.0106 25 1. 20375 0.0053125 0.77179 PAN 1.33997  100  1. 27  INCH MAT'L IN CRUSHING  TERTIARY CRUSHING  100  CRUSHER 3 0 0 0 1.25504 38.5474 25.05363 14.07278 7.30771 4.78136 3. 18313 2.08533 1.34834 0.8644 1.50088  0. 35 CRUSHER 4 0 0 0.00024 10.62722 42. 03039 18.28921 10. 38 286 6.33626 4.27532 2.85491 1.87103 1 .20994 0.77576 1. 34686  100  OPERATING DATA CLOSE SIDE SETTING (CM.) 0.9 0.82 0. 74 FLOWRATES (STPH) 432.6646 288.4431 216.3323 CURRENT DRAWS (AMPERES) 35.6926 30. 86697 28.8385  70.22785  100  COMBINED 0 0 0.00008 7. 52272 42.888 12 21.31728 10.9509 5. 95137 3.94532 2.6302 1.72364 1.1147 1 0.71476 1.24088 99.99998  1 504.7754  1442.215  37. 52888  N.A.  - 262 PERCENT CIRCULATING LOAD= *****  PRIMARY FINES OUTPUT  SCREEN 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 DAILY *****  FLOWRATE  SIZE 0 0 0 0 0 0 0 0 0 0 0 0 0  *****  ANALYSIS  0 0 (STPH,INTERMITTENT)=  ROD MILL FEED ANALYSIS  SCREEN 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  1.131149  0  *****  S I Z E 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= 7 0 . 2 2 7 8 5 + ?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*  -  1 *** 2 *  3 *  10 20 30 32 34 36 40 50 53 56 60 65 70 80 85 90 91 92 93 94 105 107 108 110 112 114 115 116 118 120 122 125 128 130 240 250 260 270 280 2 90 300 310 320 330 3 40 350 360 370 380 390 400 410 420 430 440 450 460  PROGRAM:  PGM2  :CRUSHING  £ 0  J  -  PLANT SIMULATION  PROGRAM  DIMA (14) , B{14) , C ( 1 4 ) , D{14) , F (1 4) , 0 (14) , P (58) ,Q (14) DIM K(14) , J ( 1 4 ) ,G (14) ,V{14) ,R(14) ,S{14) , T ( 1 4 ) , H ( 14) ,Y{14) F I L E CONST FOR J=1 TO 56 READ F I L E 1,P{J) NEXT J READ C 2 , C 3 , C 5 , S 1 , R 1 , N 2 , M 1 DATA 2 , 4 , 5 , 4 3 . 5 2 , . 5 , 1 4 , 1 0 0 X0=-1 BQ=83.88 DATA 3 , 3 5 , 3 6 . 5 , 18. 3 5 , 4 . 7 , . 9 4 , . 2 9 , . 2 2 , . 1 7 , . 1 7 , . 1 8 , . 1 6 , . 1 3 , . 19 V1=0 FOR J=1 TO N2 READ A (J) IFJ>4THEN91 V1=V1+A (J) S (J) =S1*B1** (J-1) Q (J) =INT ( (S ( J ) / 2 ) *1 0000+. 5 ) / 1 0 0 0 0 IFJ=1 THEN 105 T (J- 1) =SQB (S (1) *S (2) ) * H 1 * * (J-2) NEXT J Q(N2)=-Q (N2-1) S2=SQR(S{1) *S(2) ) PRINT "ENTER PLANT FEEDRATE" INPUT A PBINT " E N T E B : 2 - C B GAP,2-SCBN O P E N » G , 3 - C R GAP" INPUT Q 2 , S , Q 3 PRINT " I F SIMULATION OF PBIMABY FINES DESIRED,ENTER 1;IF NOT,ENTER 0" INPUT J5 I F J5=0 THEN 128 PBINT "ENTER DAY OF WEEK:MON=1,TUE= 2,WED=3,THU=4,FBI=5,SAT= 6,SUN=7" INPUT J1 PBINT "IF ANOTHEB RUN IS DESIRED, ENTEB 1; IF NOT, ENTEB 0" INPUT J6 21=P (1) *P (2) *Q2+P (3) * (A/C2) *P (4) *V1 Z2=P{5) +P(6) *Q2 + P (7) *Q2**2+P (8) *V1 Z3=P (9) *P (10) *Q2*P (11) *Q2**2 + P (12) *V1 L2=1 L4=0 FOR 1=1 TO N2-1 L1= 1- (1- (S (1+ 1)/S2) **2) **6 K(I)=L2-L1 L2=L1 L 3 = E X P ( - ( (S (1 + 1) /2) * * . 6 6 4 ) ) J(I)=L3-L4 L4=L3 NEXT I FOR J=1 TO N2 I F S ( J ) > Z 3 THEN 440 I F S ( J ) < Z 2 THEN 420 H (J) =S (J) - (S {J) - Z 3) * * 3 / ( 3 * { (Z2-Z3) **2) ) GO TO 450 H(J) =Z2- ( Z 2 - Z 3 ) / 3 GO TO 450 H(J)=S(J) NEXT J 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 ) + A 1 ) / ( 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 I F I>4 THEN 908 903 V3=V3+0(I) 908 NEXT I 910 C=C*C5 911 F=F*C5 920 I F ABS(A-F) <.01THEN950 930 Z25=Z25+1 940 I F Z25>M1 THEN 950 945 GO TO 1000 950 I F 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 I F 1=1 THEN 9 82 976 K (I) =J ( I - 1) - J (I) 980 A22=A22 + K(I) 982 NEXT I 984 K(1) = 1 0 0 - J ( 1 ) 986 K(N2) =100-A22 988 I F 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 Z 4 = P ( 2 6 ) + P ( 2 7 ) * ( C / C 3 ) + P ( 2 8 ) / ( 1 + P ( 2 9 ) * ( ( C / C 3 ) - P (30) )**2) 1010 Z5=P (31) +P{32) *EXP{P (33) *Z4**P (34) ) 1020 Z6 = P { 3 5 ) + P ( 3 6 ) * V 3 103 0 Z7=P (37) +P (3 8) * Q 3 - (P (39) / (1 +P (40)* (Q3-P (41)) * * 2} ) * * P (42) 1040 I3=INT { (P{43) +P (44) *Q3 + P{45) * ( C / C 3 ) ) *100 + . 5) / 1 0 0 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 ) = L 2 - L 1 1140 L2=L1 1 150 L 3 = E X P ( - ( ( S (1+1 ) / 2 ) * * . 6 6 4 ) ) 1160 J ( I ) = L 3 - L 4 1170 L4=L3 1180 NEXT I 1190 FOR J=1 TO N2 1200 IF S ( J ) > Z 7 THEN 1260 1210 I F S ( J ) < Z 6 THEN 1240 1220 H(J)=S ( J ) - (S(J) -Z7) * * 3 / ( 3 * ( { Z 6 - Z 7 ) **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 - Z 4 ) * (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 C Y C L E S = " ; Z25 , "CONVERGENCE C R I T E R I O N " ; ABS (A-F) 1505 PRINT 1516 V4=0 1517 V5=0 1520 H10=CH.D(«JtSET COLWIDTH=8") 3  - 266 1525 PRINT"* RETAINED:" 1 5 2 7 P R I N T " 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","RMF« 15.31 F0RJ=1T0N2 1533 F10=INT (A (J) *1000 + .5) / 1 0 0 0 1534 F20=INT (B (J) * 1000*. 5) / 1 0 0 0 1535 F30=INT{D(J) *1000+.5) / 1 0 0 0 1536 F40=INT (F <J) *1000+.5) / 1 0 0 0 1537 F 5 0 = I N T { 0 ( J ) * 1 0 0 0 + . 5 ) / 1 0 0 0 1538 F60=INT (C (J) * 1000 + . 5) / 1 0 0 0 153 9 F7 0=.INT{K(J)*1000+.5)/1000 154 0 F80=INT{R{J) * 1000+.5) / 1 0 0 0 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) / 1 0 0 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:" 1 6 3 4 P R I N T " 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 " ,"RMF" 1635 FORJ=N2T01STEP-1 1640 S10=S10+A(J) 1645 S20=S20+B(J) 1647 S21=INT(S20*1000 + . 5 ) / 1 0 0 0 1650 S30=S30 + D{J) 1652 S31 = INT{S30*100 0 + . 5 ) / 1 0 00 1655 S40=S40*F(J) 1657 S 4 1 = I N T ( S 4 0 * 1 0 0 0 + . 5 ) / 1 0 0 0 1660 S50=S50 + O(J) 1662 S51 = INT (S50*1000 + . 5 ) / 1 0 0 0 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) / 1 0 0 0 1678 S90 = INT(S (J) * 1 0000+ . 5) /10000 1680 PRINTS9 0 , S 1 0 , S 2 1 , S 3 1 , S 4 1 , S 5 1 , S 6 1 , S 7 1 , S 8 1 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 I N C H : " 2040 PRINT" " , V 1 , " " , V 2 , " " , " " , V 3 2055 PRINT"CRDSHER CURRENTS:" 2060 PRINT" " , I 2 , " " , " " , " " , " ",13 2 0 6 5 I F I 2 > 6 7 . 5 T H E N : P R I N T " ( 2 - C R CURRENT EXCEEDS OVERLOAD MAXIMUM OF 6 7 . 5 AMPS)  - Zbl 2 0 7 0 X F I 3 > 6 0 . 3 T H E N : P R I N T " ( 3 - C R CUB BENT EXCEEDS OVERLOAD MAXIMUM OF 2080 P R I N T " S E T S ; " , " 2 Cfi SET=";Q2,"SCRN O P = " ; S , " 3 CR SET=";Q3 2085 PRINT "%-1/2 INCH I N F E E D = " ; V 5 , " » , " % - 1 / 2 INCH IN SCREEN U/S 2090 PRINT »% - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT F E E D = " ; V 4 / V 5 2095 PRINT "% CIRCULATING L O A D = » ; C / A 2097 PRINT 2100 I F J6=0 THEN 2120 2110 GO TO 110 2120 STOP 2500 I F 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 I F 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 task: 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 C o l u m b i a Computing C e n t r e - d e v i c e : DS22 # SIGN RALU # ENTER USER PASSWORD. ? # * * L A S T SIGNON WAS: 13:10:34 # USER "RALU" SIGNED ON AT 1 3 : 4 0 : 0 7 ON WED AUG 17/77 # RUN *BASIC # EXECUTION BEGINS 5 ?UBC BASIC SYSTEM 6  task:  ?  : GET PGM2 : RUN ENTER PLANT FEEDRATE ? 1454.6 ENTER:2-CR G A P , 2 - S C R N O P E N ' G , 3 - C R GAP ? 3.08, 1.59,.81 I F SIMULATION OF PRIMARY FINES DESIRED,ENTER 1 ; I F NOT,ENTER 0 ? 1 ENTER DAY OF WEEK:MON=1,TUE 2,WED 3 , T H U = 4 , F R I = 5 , S A T 6,SUN=7 ? 3 I F ANOTHER RUN I S DESIRED, ENTER 1; I F NOT, ENTER 0 ? 1 3  NUMBER OF C Y C L E S  3  9  3  3  CONVERGENCE C R I T E R I O N  3  2.728776E-3  % RETAINED: SIZE 2 CRF 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 0.0212 0. 18 0.0106 0. 16 0.0053 0. 13 - 0 . 0 0 5 3 0. 19  2 CRP 0 0. 119 28.512 38.503 17.281 6. 543 3. 121 1. 902 1. 244 0. 867 0.631 0. 45 0. 316 0.512  S F 0 0.06 14.361 23.241 30.23 15. 15 6.23 3.6 2.397 1.618 1.092 0. 727 0. 48 0.815  S U/S 0 0 0 0 37.847 29. 173 12. 108 7.004 4.663 3, 148 2. 124 1. 4 15 0.933 1. 586  S O/S 0 0,121 28. 935 46.828 22.5 0.919 0.264 0.146 0.097 0.065 0.044 0.029 0.019 0.033  3 CRP 0 0 0 7.754 43. 372 23.88 5 9. 384 5.323 3.567 2.38 1.559 1.008 0.646 1 .122  P F 0 0 0.008 2.071 23. 547 32. 498 15.571 7.323 5.604 4.879 3.593 2.251 1. 271 1.384  RMF 0 0 0.001 0.375 35.257 2 9.775 12. 73 5 7.062 4.834 3.461 2.39 1 .566 0.994 1.549  % PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0.32 0.0212 0. 48 0.0425 0.66 0.085 0. 83 0. 17 1 0.34 1.22 0.68 1.51 1.36 2. 45 2. 72 7 . 15 5.44 25.5 10.88 62 21.76 97 43.52 100  2 CRP 0.512 0. 828 1. 278 1. 909 2. 776 4. 02 5. 922 9.043 15.586 32.867 71.369 99.881 100 100  S F 0. 815 1. 295 2. 0 22 3. 114 4.731 7. 128 10.728 16.958 32.108 62.338 85.579 99. 94 100 100  S U/S 1. 586 2.519 3.934 6. 058 9.206 13.869 20.873 32. 98 62. 153 100 100 100 100 100  S O/S 0.033 0.052 0.081 0 . 125 0.191 0.287 0.433 0,697 1.616 24. 115 7 0 . 944 99. 879 100 100  3 CRP 1.122 1.769 2.777 4. 3 36 6.716 10.283 15.606 24.99 48.875 92.246 100 100 1 00 100  P F 1.384 2.655 4.905 8.499 13.377 1 8. 981 26.304 41.876 74.373 97. 921 99.992 100 100 100  RMF 1 .549 2.543 4.11 6. 5 9.961 14.795 21.856 34. 591 64.366 99.623 99.999 100 100 100  OPERATING  CONDITIONS  52  - 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 . 4 5 %-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 E N T E R : 2 - C R GAP,2-SCRN O P E N » G , 3 - C R GAP 2.85,1.4,.95 I F SIMULATION OF PRIMARY FINES DESIRED,ENTER 1 ; I F NOT,ENTER 0 1 ENTER DAY OF WEEK:MON=1,TUE=2,NED=3,THU=4,FRI=5,SAT=6,SUN=7 3 I F ANOTHER BUN IS DESIRED, ENTEE 1; I F NOT, ENTER 0 0 NUMBER OF CYCLES=  10  CONVERGENCE CBITEBION=  3.393379E-3  % S I ZRETAINED: E 2 CBF 21.76 3 10.88 35 5.44 36 . 5 2.72 18 . 3 5 1.36 4. 7 0.68 0. 94 0.34 0. 29 0 . 17 0. 22 0.085 0. 17 0.0425 0. 17 0.0212 0. 18 0. 16 0.0106 0.0053 0. 13 - 0 . 0 0 5 3 0. 19  2 CEP 0 0. 057 26.673 37.076 17. 177 7. 255 3. 91 2. 53 1. 691 1. 169 0. 83 0. 579 . 0.398 0. 655  S F 0 0.026 12.01 20. 974 30.745 14.974 8. 323 4. 422 2. 891 1.943 1. 302 0. 861 0. 564 0.964  S U/S 0 0 0 0 23. 69 31.089 17. 669 9.407 6. 153 4. 136 2. 771 1. 833 1.201 2.051  S O/S 0 0.047 21.849 38. 154 36. 524 1 .774 0.668 0.338 0.219 0 . 147 0.099 0.065 0.043 0.073  3 CEP 0 0 0 7.784 41.859 2 1. 29 7 1 1. 93 8 5.971 3.874 2,578 1.689 1.093 0.701 1.216  P F 0 0 0.008 2.071 23.547 32.498 15.571 7.323 5.604 4.879 3 . 5 93 2.251 1.271 1.384  RMF 0 0 0.001 0.33 23. 668 31.313 17.335 9.075 6.065 4.254 2.902 1.899 1.212 1.945  % PASSING: SIZE 2 CBF 0.. 19 0.0053 0.0106 0.32 0.0212 0.48 0.0425 0.66 0.085 0. 83 0 . 17 1 0. 34 1.2.2 0.68 1.51 1.36 2. 45 2.72 7. 15 5.44 25.5 10.88 62 97 21.76 43.52 100  2 CEP 0. 655 1. 053 1.632 2. 461 3.631 5. 322 7. 85 2 11.762 19.017 36.194 73. 27 99.943 100 100  S F 0.964 1. 5 28 2. 389 3. 692 5.635 8. 526 12.948 21,271 36.245 66.99 87.964 99.974 100 100  S U/S 2.051 3.252 5. 085 7.856 11. 992 18. 145 27.552 45. 221 76. 31 100 100 100 100 100  S O/S 0.073 0.116 0.181 0.28 0.427 0.647 0.985 1.6 52 3.427 3 9.95 78. 105 99.953 100 100  3 CEP 1.216 1 .917 3.01 4.699 7.277 11.151 17. 122 2 9.06 50.357 92.216 100 100 100 100  P F 1. 384 2.655 4.905 8.499 13.377 18.981 26.304 41.876 74. 373 97. 92 1 99.992 100 100 100  RMF 1.945 3.157 5.056 7.959 12.213 18.278 27.354 44.688 76.001 99.669 99. 999 100 100 100  1526  236.75  1486.75  OPERATING TONNAGES: 1250  1250  2776  CONDITIONS 1250  1526  - 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 . 4 5 %-1/2 INCH IN SCREEN U/S= 7 6 . 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 Full  Factorial  Design Study  I n t e r m e d i a t e Ranges Study  - zrz -  (a)  Full  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. . B E E S . RFS NO. 186975 UNIVERSITY OF B C COMPUTING CENTRE MTS{A3 273  * * * T H E PAPERTAPE PUNCH S READER ARE DOWN * * * $SIGN RALU T=2M PRINT=TN FORM=8X11 P=60  RRRRRRRRRRR RRRRRRRR RRRR 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 AA AAAAAAAAAAAA AA.AAAAA AAAAA AA AA AA AA AA AA AA AA AA AA  LL LL LL LL LL LL LL LL LL LL LLLLLLLLLLLL LLLLLLLLLLLL  uu uu uu uu uu uu uu uu uu uu uu uu uuuuuuuuuuuu uouuuuuuuu UU UU UU UU UU UU UU UU  * * L A S T SIGNON WAS: 2 1 : 2 7 : 3 1 USER "RALU" SIGNED ON AT 2 1:28:50 ON WED SEP 0 7 / 7 7 $RUN *BASIC EXECUTION BEGINS UBC BASIC SYSTEM %GET PGM2 110 PRINT 112 READ A 114 115 READ Q 2 , S , Q 3 1 16 1 18 READ J 5 120 I F J5=0 THEN 130 122 128 130 READ J 6 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. 1255,4,3. 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.  NUMBER OF CYCLES=  54,1 . 5 9 , . 785, 1 . 5 9 , 785, 1 . 5 9 , 54,1 . 2 7 , 1 54, 1 . 2 7 , 1 785, 1. 2 7 , 785, 1 . 2 7 , 54,1 . 5 9 , 1 54,1 . 5 9 , 1 785, 1. 5 9 , 785, 1 . 5 9 ,  495,0, 1 . 495,0, 1 .495,0,1 .08,0,1 .08,0,1 1.08,0,1 1.08,0,1 . 08,0, 1 .08,0,1 1.08,0, 1 1.08,0,0  11  CONVERGENCE CRITERION=  3.458869E-3  %SET COLWIDTH = 8 % RETAINED: SIZE 2 CRF 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 0.0212 0. 18 0.0106 0. 16 0.0053 0. 13 - 0 . 0 0 5 3 0. 19  2 CRP 0 0 28.384 35,327 16.261 7. 258 4. 155 2.768 1. 869 1.291 0.911 0.631 0.432 0.714  S F 0 0 12.422 20.172 3 0.85 1 4. 26 8.505 4.691 3.09 2. 077 1.389 0.917 0.6 1.026  S U/S 0 0 0 0 20.493 30.555 18. 645 10.30 7 6.791 4.566 3.054 2.016 1.318 2.254  S O/S 0 0 22.088 35.869 3 8.909 1.58 0.615 0.321 0.21 0.141 0.094 0.062 0.041 0.07  3 CRP 0. 0 0.0 02 8.381 42.202 19.708 1 1.889 6.188 4.04 2.689 1.762 1.14 0.731 1.269  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 20.493 30.555 18.645 10.307 6.791 4.566 3.054 2.016 1. 318 2.254  % PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0.32 0.0212 0.48 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1.36 2.45 2.72 7. 15 5.44 25.5 10. 88 62 21.76 97 4 3 . 52 100  2 CRP 0.714 1.145 1.776 2.687 3.978 5. 847 8.615 12.77 20.027 36.289 71.616 100 100 100  S F 1.026 1.625 2.543 3.932 6.009 9.1 13.791 22.295 36.555 67.405 87.578 100 100 100  S U/S 2.254 3.573 5.588 8.642 13. 208 19.999 30.307 48. 951 79.507 100 100 100 100 100  S O/S 0.07 0.11 0 . 173 0.267 0. 408 0.618 0.94 1.554 3.134 42.043 77. 912 100 100 100  3 CRP 1.269 1.999 3 . 139 4.901 7.59 1 1.63 17. 818 2 9.707 49.415 91.617 99.998 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.254 3.573 5.588 8.642 13.208 19. 999 30.307 48. 951 79.507 100 100 100 100 100  OPERATING CONDITIONS TONNAGES • 1255.4 1255.4 2868.8 1255. 4 1613.4 1613.4 0 1255.4 % +1 INCH: 92.85 32.59477 57.9569 CRUSHER CURRENTS: 23.68 45. 16 SETS: 2 CR SET= 2.54 SCRN OP= 1.27 3 CR S£T= 0.495 %-1/2 INCH I N FEED= 2 . 4 5 IS-1/2 INCH IN SCREEN U/S= 7 9 . 50652 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 3 2 . 4 516 4  - n/o % CIRCULATING LOAD=  NUMBER OF CYCLES=  1.285168  12  CONVERGENCE CRITERION=  1. 022953E-4  %5ET COLWIDTH=8 % RETAINED: SIZE 2 CRF 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. 17 0.085 0.0425 0. 17 0.0212 0. 18 0.0106 0.16 0.0053 0. 13 - 0 . 0053 0. 19  2 CRP 0 0 29.02 36.925 16.656 6.785 3.546 2.268 1.51 1.048 0.751 0.528 0. 365 0.598  S F 0 0 12.394 20.591 30.989 13. 587 8.275 4.796 3. 185 2 . 141 1.43 0.943 0.616 1.054  S U/S 0 0 0 0 20. 13 29. 62 18.5 10.748 7 . 139 4.799 3.206 2. 114 1.381 2.364  S O/S 0 0 21.63 35. 937 39.082 1.637 0.655 0.36 0.238 0. 16 0.107 0.07 0.046 0.079  3 CRP 0 0 0.002 8.417 41.671 18.656 1 1.8 6.68 4.433 2.955 1.937 1.252 0.803 1.394  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 20. 13 29.62 18. 5 10.748 7. 139 4.799 3. 206 2.1 14 1.381 2.364  % PASSING: SIZE 2 CRF 0.0053 0.19 0.0106 0.32 0.48 0.0212 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1 .36 2.45 7. 15 2.72 5.44 25.5 10. 88 62 21. 76 97 4 3. 52 100  2 CRP 0.598 0.963 1.491 2. 242 3.29 4. 8 7.068 10.614 17.398 3 4 . 0 54 70.98 100 100 100  S F 1.054 1.67 2.613 4.043 6 . 184 9.369 14. 165 22. 44 3 6.027 67.016 87.606 100 100 100  S U/S 2. 364 3.745 5.858 9.064 13. 864 21.003 31. 751 50.25 79. 87 100 100 100 100 100  S O/S 0.079 0.124 0 . 195 0.301 0.461 0.698 1.0 59 1.714 3.351 42.433 78. 37 100 100 100  3 CRP 1.394 2.1 97 3.4 5 5.386 8.342 12. 775 19.455 31.255 49.911 91. 581 99.998 100 1 00 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.364 3.745 5.858 9.064 13.864 21.003 31.751 50. 25 79.87 100 100 100 100 100  OPERATING CONDITIONS TONNAGES i : 1578.8 1578.8 3 6 9 7 . 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 . 5 4 SCRN OP= 1.27 3 CR SET= 0.495 %-1/2 INCH I N FEED= 2 . 4 5 %-l/2 INCH IN SCREEN U/S= 79.87011 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 3 2 . 6 0 0 0 4 % CIRCULATING LOAD= 1.34176  NUMBER OF CYCLES^  12  %5ET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP  CONVERGENCE C8ITERION=  S F  S U/S  S O/S  2.881162E-4  3 CRP  P F  RMF  - Zlb  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  -  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  0 0.034 49.038 32.081 10.628 3. 38 2 1.528 0.964 0.647 0.481 0.381 0. 289 0.213 0.334  0 0.013 19.304 17.392 30.538 1 2. 188 7.488 4.401 2.944 1.983 1.326 0.874 0.571 0.977  0 0 0 0 20.893 28. 966 18. 229 10.739 7. 185 4. 84 3. 235 2. 133 1.394 2.386  0 0.022 31.835 28. 682 3 6. 798 1.298 0.516 0.287 0.191 0.128 0.086 0.057 0. 037 0 . 0 63  0 0 0.0 03 7.857 43.461 17.905 11.357 6.633 4.434 2.959 1 .939 1 .253 0.804 1.395  0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 20.893 28.966 18.229 10.739 7. 185 4.84 3. 235 2. 1 33 1. 394 2.386  % PASSING: SIZE 2 CRF 0.0053 0.19 0,0106 0.32 0.0212 0.48 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.6 8 1.51 1.36 2.45 2.7 2 7. 15 5.44 25.5 10.88 62 21.76 97 43. 52 100  2 CRP 0.334 0.547 0.836 1.217 1.698 2. 345 3. 309 4. 837 8.219 18.847 50.928 99.966 100 100  S F 0.977 1.548 2.422 3.74 8 5.731 8.675 13.076 20. 564 32.753 63.29 80.683 99.987 100 100  S U/S 2.386 3.779 5. 913 9. 148 13.988 21.173 31. 913 50.142 79. 107 100 100 100 100 100  S O/S 0.063 0.1 0. 157 0. 243 0.371 0.562 0.849 1.365 2.663 39.461 68.143 99. 978 100 100  3 CRP 1.395 2.199 3.452 5.391 8.349 12.784 19.416 30.773 4 8.678 92. 139 99.997 100 100 1 00  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.386 3.779 5.913 9. 148 13.988 21.173 31.913 50. 142 79.107 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1255.4 1255.4 3 1 8 9 . 3 8 1255.4 1933.98 1933.98 0 1255.4 % + 1 INCH: 92.85 36.70966 60.53894 CRUSHER CURRENTS: 14.56 49.6 SETS: 2 CR S E T 3 . 7 8 5 SCRN O P 1.27 3 CR S E T 0.495 %-1/2 INCH I N F E E D 2 . 4 5 %-1/2 INCH IN SCREEN U / S 7 9 . 1 0 7 2 2 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT F E E D 32.28866 % CIRCULATING LOAD 1. 540 529 3  3  3  3  3  3  3  NUMBER OF C Y C L E S %SET COLWIDTH=8 % RETAINED; SIZE 2 CRF 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  3  12  2 CRP 0 0.034 50.294 33.018 10.509 2.9 1.055 0.597 0.389  CONVERGENCE C R I T E R I O N  S F 0 0.013 19.318 17. 328 30.446 12.247 7.569 4.41 2.944  S U/S 0 0 0 0 19.443 29.423 18.708 10.932 7.299  3  S O/S 0 0.021 31.364 28. 134 37. 30 7 1.537 0.623 0.344 0.228  9.081121E-3  3 CEP 0 0 0 . 0 03 7.545 42.878 18.076 1 1. 63 6.788 4.537  P F 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 19.443 29.423 18.708 10.932 7.299  -  0.0425 0.0212 0.0106 0.0053 - 0 . 0053  0. 17 0.18 0. 16 0. 13 0. 19  % PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0. 32 0.0212 0.48 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1.36 2.45 2.72 7 . 15 5.44 25.5 10. 88 62 21.76 97 43. 52 100  Cll  -  0. 306 0.26 7 0.215 0. 165 0. 251  1.982 1. 324 0.873 0,57 0.976  4 . 914 3. 284 2. 164 1.414 2. 42  0.1 53 0. 102 0.068 0.044 0.076  3.027 1.984 1.283 0.822 1.428  0 0 0 0 0  4.914 3. 284 2.164 1.414 2.42  2 CRP 0. 251 0.417 0.63 2 0.899 1.205 1. 594 2. 191 3.246 6. 145 16.654 49.672 99.966 100 100  S F 0.976 1 .54 6 2.419 3.74 3 5 . 7 25 8.669 13.079 20.648 32.894 63.34 80.669 99.987 100 100  S U/S 2. 42 3 . 834 5, 998 9.281 14. 196 21.495 32.426 51.134 80.557 100 100 100 100 100  S O/S 0.076 0. 12 0. 187 0.29 0. 443 0.671 1^015 1.638 3. 174 40.481 68.615 99.979 100 100  3 CRP 1.428 2.25 3.533 5.517 8.543 13. 08 19.868 31.499 49. 574 92.452 99.997 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF  2.42  3. 834 5.998 9.281 14. 196 21.495 32.426 51.13 4 80.557 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1578. 8 1578. 8 4 1 1 0 . 7 1 5 7 8 . 7 9 2531.91 2531.91 0 1578.79 % + 1 INCH: 92.85 36.65974 59.51919 CRUSHER CURRENTS: 20.15 57.88 SETS: 2 CR SET= 3. 785 SCRN OP= 1. 27 3 CR SET= 0.495 %-1/2 INCH IN FEED= 2 . 4 5 %-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  CONVERGENCE  CRITERION  3  9.099711E-3  %SET COLHIDTH=8 % RETAINED: SIZE 2 CRF 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 0.0212 0. 18 0.0106 0. 16 0.0053 0. 13 - 0 . 0 0 5 3 0. 19  2 CRP 0 0 28.384 3 5 . 3 27 16.261 7.258 4. 155 2.768 1.86 9 1.291 0.91 1 0.631 0.432 0.714  S F 0 O 13.629 26. 38 29.774 14.653 5.645 3.307 2.217 1.5 1.014 0.676 0.446 0.758  S U/S 0 0 0 0 38. 62 1 29.611 1 1. 514 6.752 4. 527 3.064 2.071 1.381 0.912 1.548  S O/S 0 0 26.215 50. 74 21.604 0.84 0.225 0. 126 0.084 0.057 0.038 0.026 0.017 0.029  3 CRP 0 0 0.004 18. 118 4 2.251 21.482 7.021 3.805 2.539 1.693 1.11 0.718 0.46 0 . 7 99  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 38.621 2 9 . 6 11 11.514 6.752 4.527 3.064 2.071 1. 381 0.912 1.548  % PASSING: SIZE 2 CRF 0.0053 0. 19  2 CRP 0.714  S F 0.758  S U/S 1.548  S O/S 0. 029  3 CRP 0.799  P F 0  RMF 1.548  - Z/b 0.0106 0.0212 0.0425 0.085 0.17 0.34 0.68 1.36 2.72 5. 44 10. 88 21.76 43.52  0.32 0. 48 0.66 0. 83 1 1.22 1.51 2.45 7 . 15 25.5 62 97 100  1.145 1.776 2.687 3.978 5. 847 8.615 12.77 20.027 36.289 7 1 . 6 16 100 100 100  1.204 1.881 2.895 4.395 6.612 9.919 15. 564 30.217 59. 991 86.371 100 100 100  2.459 3. 84 5.911 8. 975 13.502 20.254 31.767 61.37 9 100 100 100 100 100  0 . 0 46 0.071 0. 1 1 0. 166 0.25 0.376 0.602 1.442 23.046 73.785 100 100 100  1.259 1.977 3.087 4.78 7.319 11.124 18. 144 3 9.62 7 81.878 99.996 100 100 100  0 0 0 0 0 0 0 0 0 0 0 0 0  2.459 3. 84 5.911 8.975 13.502 20.254 31.767 61.379 100 100 100 100 100  OPERATING CONDITIONS TONNAGES I 1255. 4 1255.4 2 6 1 4 . 9 2 1255.41 1359.52 1359.52 0 1255.41 % +1 INCH: 92.85 40.0091 76. 95447 CRUSHER CURRENTS: 23. 68 41.64 SETS: 2 CR SET= 2 . 5 4 SCRN OP= 1. 59 3 CR SET= 0 . 4 9 5 5S-1/2 INCH IN FEED= 2 . 4 5 %-1 / 2 INCH IN SCREEN U/S= 6 1 . 37 867 % - 1 / 2 INCH fiATIO, SCREEN U / S TO PLANT FEED= 25.05252 % CIRCULATING LOAD= 1.082938  NUMBER OF CYCLES= 11  CONVERGENCE CRITERION= 3. 756307E-4  %SET COL»IDTH=8 % RETAINED: SIZE 2 CRF 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 0.0212 0. 18 0.0106 0.16 0.0053 0.13 - 0 . 0053 0.19  2 CRP 0 0 29.02 36.925 16.656 6.785 3.546 2.268 1.51 1.048 0.751 0.528 0.365 0. 598  S F 0 0 13. 576 27. 935 27.642 12.35 6.225 4.073 2.769 1.869 1.255 0.831 0.545 0.93  S U/S 0 0 0 0 35.764 25.552 13. 01 8.52 5.793 3.911 2 . 6 25 1. 738 1.141 1.946  S O/S 0 0 25.505 52. 482 20.506 0.75 0.263 0. 1 65 0.111 0.075 0.05 0.033 0.022 0 . 0 37  3 CRP 0 0 0.004 2 0. 035 37.296 17.241 8.58 5.659 3.875 2.591 1 .698 1.097 0.703 1.222  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 35.764 25.552 13. 01 8.52 5.793 3.911 2.625 1.738 1. 141 1.946  % PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0. 32 0.0212 0.48 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1 .36 2.45 2.72 7. 15  2 CRP 0.598 0. 963 1.491 2.242 3.29 4.8 7.068 10.614 17.398 34.0 54  S F 0.93 1.475 2.306 3. 561 5.43 8. 199 12. 271 18.4 97 30. 847 58.489  S U/S 1.946 3.087 4. 825 7.45 11. 361 17.154 25. 674 38.684 64.236 100  S O/S 0.037 0.059 0.0 93 0. 1 43 0.218 0.329 0.494 0.757 1.507 22.013  3 CRP 1.222 1.925 3.022 4.72 7.311 11.185 16.844 25. 424 42.665 79. 961  P F 0 0 0 0 0 0 0 0 0 0  RMF 1.946 3.087 4.825 7.45 11.361 17. 154 25.674 38.684 64.236 100  -  5.44 10. 88 21. 76 43.52  25.5 62 97 100  70.98 100 100 100  86.424 100 100 100  100 100 100 100  <:/y -  74.495 100 100 100  99.996 100 100 100  0 0 0 0  100 100 100 100  OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3375.49 1578.8 1796.69 1796.69 0 1578. 8 % +1 INCH: 92.85 4 1.51059 77.98698 CRUSHER CURRENTS: 29.26 47.69 SETS: 2 CR S E T 2.54 SCRN OP= 1.59 3 CR S E T 0.495 %--\/2 INCH IN F E E D 2.45 %-1/2 INCH IN SCREEN U / S 64. 23609 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT F E E D 26.21881 % CIRCULATING L O A D 1.13801 3  3  3  3  3  3  NUMBER OF C Y C L E S  3  12  CONVERGENCE  CRITERION  3  7.995972E-3  %SET COLHIDTH=8 % RETAINED: SIZE 2 CRF 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. 18 0.0212 0.0106 0. 16 0.0053 0. 13 - 0 . 0053 0. 19  2 CRP 0 0.034 49.038 32.081 10.628 3.382 1. 528 0.964 0.647 0.481 0.381 0.289 0.213 0.334  S F 0 0.015 21.129 24.252 26.593 11.269 5.572 3.686 2.522 1.707 1. 147 0.76 0.499 0.851  S U/S 0 0 0 0 36.62 25.334 12.652 8.378 5.733 3. 88 2 . 6 07 1.727 1.134 1. 934  S O/S 0 0.026 37.121 42.608 19.004 0.623 0.213 0.134 0.091 0.062 0.042 0.Q28 0.018 0.031  3 CRP 0 0 0.006 18.327 38.676 17.238 8.632 5.746 3.94 2.635 1.726 1.116 0.715 1.242  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 36. 62 25.334 12. 652 8.378 5.733 3. 88 2.607 1.727 1. 134 1.934  % PASSING: SIZE 2 CRF 0.0053 0.19 0.0 106 0.32 0,0212 0.48 0 . 0 425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1 .36 2.45 2.72 7. 15 5.44 25.5 10. 88 62 21. 76 97 43. 52 100  2 CRP 0.334 0.547 0.836 1.217 1.698 2. 345 3. 309 4. 837 8.219 18.847 50.928 99.966 100 100  S F 0.851 1.349 2. 109 3.256 4.963 7.485 1 1, 17 16.742 28.011 54.604 78.856 99.985 100 100  S U/S 1.-934 3.068 4,795 7.403 11. 283 17.015 25. 393 38. 045 63. 38 100 100 100 100 100  S O/S 0.031 0.049 0.076 0.1 18 0. 18 0.271 0.405 0.618 1.241 20.245 62.853 99.974 100 100  3 CRP 1.242 1 .957 3.073 4.799 7.434 1 1.374 17. 12 25.752 42.99 81.667 99.994 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 1.934 3.068 4.795 7.403 11.283 17.015 25.393 38.045 63. 38 100 100 100 100 ' 100  0  1255.4-  OPERATING  TONNAGES 1255.4 % + 1 INCH:  1255.4  2914.09  CONDITIONS 1255. 41 1658. 68 1658,68  -  £OU -  92.85 45.39591 79.7547 CURRENTS: 14. 56 45.78 SETS: 2 CR SET= 3 . 7 8 5 SCRN 0P= 1.59 3 CR SET= 0.495 %-1/2 INCH IN FEED= 2 . 4 5 %-1/2 INCH IN SCREEN U/S= 6 3 . 3 7 9 5 6 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 25.86921 56 CIRCULATING LOAD= 1.321236 CRUSHER  NUMBER OF CYCLES=  10  CONVERGENCE CRITERION= 5. 993138E-3  38SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 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 0.0212 0. 18 0.0106 0.16 0.0053 0. 13 - 0 . 0053 0. 19  2 CRP 0 0.034 50.294 33.018 10.509 2.9 1.055 0.597 0. 389 0. 306 0.267 0.215 0. 165 0. 251  S F 0 0.014 2 1 . 2 93 24. 287 26. 353 10.815 5.689 3.812 2.61 1.765 1.185 0.784 0.514 0.878  S U/S 0 0 0 0 35.605 24.643 13.108 8. 795 6.022 4.073 2.733 1.809 1.186 2.025  S O/S 0 0.025 36.923 42. 115 19.562 0.665 0.243 0. 155 0.106 0.071 0.048 0.032 0.021 0.035  3 CHP 0 0 0.006 17. 879 37. 983 16.625 9.09 6.1 73 4.241 2.836 1.858 1.201 0.77 1.337  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 35.605 24.643 13. 108 8.795 6.022 4.073 2.7 33 1.809 1. 186 2.025  % PASSING: SIZE 2 CRF 0.0053 0.19 0. 0106 0. 32 0.0212 0.48 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1 .36 2.45 2.72 7. 15 5.4 4 25.5 10. 88 62 21.76 97 43. 52 100  2 CRP 0.251 0.417 0.632 0.899 1.205 1.594 2. 19 1 3. 246 6. 145 16.654 49.672 99.966 100 100  S F 0.878 1.392 2. 176 3.36 5 . 126 7.736 1 1 . 5 48 17.237 28.052 54.405 78.692 99.986 100 100  S U/S 2.025 3.211 5.02 7.753 1 1. 826 17. 849 26. 644 39.752 64. 395 100 100 100 100 100  S O/S 0.035 0.056 0.088 0. 136 0.2 07 0.3 13 0.468 0.711 1.375 20. 937 63.052 99.975 100 100  3 CRP 1.337 2.107 3.308 5.167 8.003 12.244 18.417 27.507 44. 132 82. 115 99.994 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.025 3.211 5.02 7.753 11.826 17.849 26.644 39.752 64.395 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1578.8 1578.8 3 7 2 9 . 6 8 1578.79 2 1 5 0 . 8 8 2 1 5 0 . 8 8 0 1578.79 % +1 INCH: 92.85 45.59491 79.06251 CRUSHER CURRENTS: 20. 15 52.6 SETS: 2 CR SET= 3 . ? 8 5 SCRN OP= 1.59 3 CR SET= 0.495 %-1/2 INCH I N FEED= 2 . 4 5 SS-1/2 INCH IN SCREEN U/S= 6 4 . 3 9 5 1 5 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 2 6 . 2 8 3 7 3 % CIRCULATING LOAD= 1.362351  - Zo\  -  NUMBER OP CYCLES= 7  CONVERGENCE C R I T E R I O N  %SET COL¥IDTH=8 % RETAINED: SIZE 2 CRF 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 0.0212 0. 18 0.0106 0. 16 0.0053 0. 13 - 0 . 0053 0. 19  2 CRP 0 0 28.384 35.327 16.261 7.258 4. 155 2.768 1. 869 1.291 0.911 0.631 0. 432 0.714  S F 0 0 12.616 19.631 30.396 14.753 8.775 4.72 3.093 2.079 1.391 0.918 0.601 1.Q27  S U/S 0 0 0 0 19.999 31. 132 18.943 10.212 6.6 94 4. 499 3. 01 1.987 1.3 2. 223  S O/S 0 0 22.708 35. 337 38.714 1.65 0.64 0. 326 0.212 0. 1 43 0.095 0.063 0.041 0.07  3 CRP 0 0 0 7.075 4 1. 704 20.75 12.471 6.282 4.073 2.709 1.775 1.148 0.736 1.278  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 19.999 31.132 18.943 10.212 6.694 4.499 3.01 1.987 1. 3 2.223  % PASSING: SIZE 2 CRF 0.0053 0.19 0.0106 0. 32 0.0212 0.48 0 . 0 4 25 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1 .36 2.45 2.72 7. 15 5.44 25.5 10. 88 62 21.76 97 43. 52 100  2 CRP 0.714 1. 145 1.776 2.687 3.978 5. 847 8.615 12.77 20.027 36.289 71.616 100 100 100  S F 1.0 27 1.628 2.546 3.937 6.016 9. 109 13.829 22.604 37. 357 67.753 87.384 100 100 1 00  S U/S 2. 223 3.523 5.51 8.52 13. 019 19.713 29.926 48. 869 80.00 1 100 100 100 100 100  S O/S 0.07 0.1 12 0. 175 0.27 0.413 0 . 6 25 0.951 1 .591 3.241 41. 954 77.292 1 00 100 100  3 CRP p F 1.2 78 0 2.014 0 0 3 . 162 4.937 0 7.645 0 11.718 0 18 .0 30. 471 0 51.221 0 92. 925 0 100 0 100 0 100 0 1 00 0  RMF 2.223 3.523 5.51 8.52 13.019 19.713 29.926 48.869 80.001 100 100 100 100 100  3  2.802705E-4  OPERATING CONDITIONS TONNAGES: 1255.4 1255.4 2 8 2 4 . 5 9 1255. 4 1569. 19 1569.19 0 1255.4 % +1 INCH: 92.85 32.24706 58.04566 CRUSHER CURRENTS: 23.68 38.92 SETS: 2 CR S E T 2.54 SCRN O P 1.27 3 CR SET= 1.08 %-1/2 INCH IN F E E D 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 2 . 6 5 3 3 2 % CIRCULATING L O A D 1.249952 3  3  3  3  3  NUMBER OF C Y C L E S  3  11  CONVERGENCE C R I T E R I O N  %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 2 CRP S F 21.?6 3 0 0 10. 88 35 0 0 5.44 36.5 29.02 12.599  S U/S 0 0 0  3  S O/S 0 0 22. 266  2.594253E-4  3 CRP 0 0 0  P F 0 0 0  RMF 0 0 0  - 282 2.72 1.36 0.68 0.3 4 0, 17 0.085 0.0425 0.0212 0.0106 0.0053 - 0 . 0053  18. 35 4.7 0.94 0.29 0. 22 0. 17 0. 17 0.18 0. 16 0.13 0. 19  36.925 16.656 6.785 3.546 2.268 1.51 1.048 0.751 0.528 0.365 0. 598  20.088 30.511 13.884 8.481 4.891 3.245 2.181 1.457 0.961 0.628 1.074  0 19.698 29.796 18. 658 10.787 7. 16 4.813 3.215 2. 119 1.385 2.37  35.501 38.807 1.674 0.672 0.368 0.2 42 0. 163 0. 109 0.072 0.047 0.08  7.17 4 1.141 19.33 12. 267 6.904 4.577 3.051 1.999 1 .293 0.829 1 .439  0 0 0 0 0 0 0 0 0 0 0  0 19.698 29.796 18.658 10.787 7 . 16 4. 813 3.215 2. 119 1.385 2. 37  % PASSING: SIZE 2 CBF 0.0053 0. 19 0.0106 0.32 0.0212 0.48 0.0425 0.66 0.085 0.83 0.17 1 0.34 1.22 0.68 1.51 1.36 2.45 2.72 7 . 15 5.44 25.5 10. 88 62 21. 76 97 43.52 100  2 CRP 0.59 8 0.963 1.491 2.242 3.29 4.8 7.068 10.614 17.398 34.054 70.98 100 100 100  S F 1.07 4 1.702 2. 662 4. 12 6.301 9.547 14.438 22.918 36. 802 67.313 87.401 100 100 100  S U/S 2.37 3.754 5. 874 9. 088 13. 901 21.061 3 1 . 847 50. 505 80.302 100 100 100 100 100  S O/S 0.08 0. 127 0.1 99 0.307 0.47 0.712 1.08 1.752 3.426 42.233 77.734 100 100 100  3 CRP 1.439 2.268 3.561 5.561 8.612 13.189 20.092 32. 359 51.689 92. 83 100 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.37 3.754 5.874 9.088 13.901 21.061 31.847 50.505 80.302 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1578. 8 1578. 8 3 6 3 6 . 4 9 1578. 8 2057.69 2 0 5 7 . 6 9 0 1578.8 % +1 INCH: 92.85 32.68742 57.76741 CRUSHER CURRENTS: 29. 26 45.69 SETS; 2 CR SET= 2 . 5 4 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=  %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 21. 76 3 10. 88 35 5. 44 36.5 2.72 18.35 4.7 1.36 0.68 0.94 0.34 0. 29 0.17 0.22 0.085 0. 17 0.0425 0. 17 0. 18 0.0212 0.0106 0.16  S F 0 0.014 19.597 16.831 3 0 . 118 12. 47 7.679 4.479 2.991 2.015 1.347 0.888  2 CRP 0 0.034 49.038 32.081 10.628 3 . 382 1. 528 0.96 4 0. 647 0. 481 0.381 0.289  S U/S 0 0 0 0 20.426 29. 2 18.416 10.766 7.192 4. 845 3.238 2. 135  S O/S 0 0.023 32.642 28.035 36.569 1.333 0.532 0.293 0.195 0. 131 0.088 0 . 0 58  1.350034E-4  3 CRP 0 0 0 6.68 4 3. 091 18. 519 1 1.773 6.818 4.551 3.036 1 .989 1.286  P F 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 20.426 29.2 18.416 10.766 7. 192 4.845 3.238 2. 135  0.0053 0. 13 - 0 . 0 053 0.19  0. 213 0.334  0.58 0.993  1.395 2.388  0.038 0.065 -  0.825 1.432  0 0  1. 395 2. 388  55 PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0. 32 0.0212 0.48 0.0425 0.66 0.085 0.83 0. 17 1 0.34 1.22 0.68 1.51 1 .36 2.45 2.72 7. 15 5.44 25.5 10. 88 62 21.76 97 43. 52 100  2 CRP 0. 334 0.547 0.836 1.217 1.698 2. 345 3.309 4. 837 8.219 18.847 50.928 99.966 100 100  S F 0.993 1.573 2.461 3.807 5.822 8.813 13.292 2 0. 971 33. 44 63.558 80.389 99.986 100 100  S 0/S 2. 388 3.782 5.917 9. 155 14 21. 192 31. 958 50.374 79. 574 100 100 100 100 100  S O/S 0.065 0.102 0. 16 0.2 48 0.379 0.573 0.867 1.398 2.732 39.301 67. 336 99. 977 100 100  3 CRP 1.432 2 . 2 56 3.542 5.532 8.568 13. 119 19.937 31.71 50.229 9 3.32 100 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.388 3.782 5.917 9. 155 14 21.192 31.958 50.374 79.574 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 3 1 4 1 . 3 8 1255. 4 1885.98 1 885.98 0 1255.4 % +1 INCH: 92.85 36.44163 60.69901 CRUSHER CURRENTS: 14.56 43.31 SETS: 2 CR SET= 3 . 7 8 5 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH I N FEED= 2.45 %-l/2 INCH IN SCREEN D/S= 7 9 . 5 7 3 5 9 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 3 2 . 4 7 9 0 2 % CIRCULATING LOAD= 1. 502294  NUMBER OF CYCLES=  12  CONVERGENCE CRITERION= 4 . 0 6 6 2 0 8 E - 3  5SSET COLHIDTH=8 % RETAINED: SIZE 2 CRF 21.76 3 10. 88 35 5.44 36.5 18.35 2.72 1.36 4.7 0.68 0.94 0.34 0.29 0. 17 0. 22 0.085 0. 17 0.0425 0. 17 0.0212 0. 18 0.0106 0. 16 0.0053 0. 13 - 0 . 0053 0. 19  2 CRP 0 0.034 50.294 33.018 10.509 2. 9 1.055 0.597 0.389 0. 306 0.267 0.215 0. 165 0. 251  S F 0 0.013 19.64 16.831 29.993 12.46 7.727 4.498 3. 00 1 2.021 1.35 0.89 0.581 0.995  S U/S 0 0 0 0 19. 146 2 9. 49 4 18.806 10.977 7.327 4. 934 3.296 2. 172 1. 419 2.429  S O/S 0 0.022 32. 223 27. 615 36.943 1.546 0.628 0.347 0.2 3 0.155 0. 103 0.068 0.044 0.076  3 CRP 0 0 0 6.46 42.477 1 8.585 12.001 6.997 4.675 3 . 1 19 2.044 1.322 0.847 1 .471  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 19.146 29.494 18.806 10.977 7.327 4.934 3.296 2. 172 1.419 2.429  % PASSING; SIZE 2 CRF 0.0053 0. 19 0.0106 0.32 0.0212 0.48 0.0425 0.66  2 CRP 0. 251 0.417 0.632 0.899  S F 0.995 1.576 2 . 466 3.816  S U/S 2.429 3.848 6.02 9.316  S O/S 0.076 0.121 0. 1 89 0.292  3 CRP 1.471 2.319 3.641 5.685  P F 0 0 0 0  RMF 2.429 3.848 6.02 9.316  -  0 . 085 0.17 0.34 0.68 1.36 2.72 5.44 10. 88 21.76 43. 52  0.83 1 1.22 1.51 2.45 7. 15 25.5 62 97 100  1. 205 1.594 2. 191 3.246 6 . 145 16.654 49.6 72 99.966 100 100  5.837 8.838 13.336 21.063 3 3 . 5 23 6 3.516 80.347 99.987 100 100  £ O t  14.25 21.577 32.554 51.36 80.854 100 100 100 100 100  -  0.446 0.6 76 1. 0 23 1.651 3. 197 40.141 67.755 99.978 100 100  8.804 13.479 20. 476 32.478 51. 063 93. 54 100 100 100 100  0 0 0 0 0 0 0 0 0 0  14. 25 21. 577 32.554 51. 36 80.854 100 100 100 100 100  OPEHATING CONDITIONS TONNAGES: 1578.8 1578.8 4 0 4 2 . 9 9 1578.8 2464.19 2464.19 0 1578.8 % +1 INCH: 92.85 36. 48407 59.85941 CHUSHES CURRENTS: 20. 15 5 1 . 32 SETS: 2 CR SET= 3 . 7 8 5 SCRN OP= 1.27 3 CR SET= 1.08 %-1/2 INCH I N FEED= 2 . 4 5 55-1/2 INCH IN SCREEN U/S= 80.85393 * - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 3 3 . 0 0 1 6 % CIRCULATING LOAD= 1.560799  NUMBER OF C Y C L E S  3  13  CONVERGENCE C R I T E R I O N  3  5.688607E-3  9JSET COLWIDTH=8 % RETAINED: SIZE 2 CRF 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 0.0212 0.18 0.0106 0. 16 0.0053 0.13 - 0 . 0053 0. 19  2 CRP 0 0 28.384 35.327 16.261 7.258 4. 155 2.768 1.869 1. 291 0.911 0.631 0. 432 0.714  S F 0 0 13. 877 24.998 30.868 15.361 5.579 3 . 117 2.074 1.404 0. 952 0.636 0 . 42 1 0.714  S U/S 0 0 0 0 39,653 30.489 11. 176 6.249 4. 158 2. 816 1.908 1.276 0 . 8 44 1.431  S O/S 0 0 27.153 48. 912 22.463 0.889 0.225 0.12 0.079 0.054 0.036 0.024 0.016 0. 027  3 CRP 0 0 0 15. 118 44. 84 23.113 6.942 3.451 2.269 1.512 0.991 0.641 0.411 0.713  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 39.653 30.489 11.176 6.249 4. 158 2. 816 1.908 1. 276 0.844 1. 431  % PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0. 32 0.48 0.0212 0.0425 0.66 0.085 0. 83 0.17 1 0 . 34 1.22 0.68 1.51 1. 36 2.45 2.72 7. 15 5.44 25.5 10. 88 62 21. 76 97  2 CRP 0.714 1. 145 1.776 2.687 3.978 5. 847 8.615 12.77 20.027 36.289 71.616 100 100  S F 0.714 1. 135 1.771 2.722 4. 126 6.2 9.316 14. 895 30.256 61. 124 86.123 100 100  S U/S 1.431 2. 275 3.551 5.459 8.275 12. 433 18.682 29.858 60.34 7 100 100 100 100  S O/S 0.027 0.043 0.068 0. 104 0.158 0.237 0.357 0. 582 1.4 72 23. 935 72. 84 7 100 100  3 CRP 0.713 1.124 1.765 2.756 4.268 6.537 9 . 9 87 16. 929 40. 042 84.882 1 00 100 100  p F 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 1.431 2.275 3. 551 5.459 8. 275 12.433 18.682 29.858 60.347 100 100 100 100  43.52  100  100  100  - 28t> 100 100  100  0  100  OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 2 5 6 7 . 7 5 1255. 41 1312.3** 1312.34 0 1255. 41 % +1 INCH: 92.85 3 8 . 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 . 4 5 %-'\/2 INCH IN SCREEN U/S= 6 0 . 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 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 0.0212 0. 18 0.0106 0. 16 0.0053 0. 13 - 0 . 0 0 5 3 0.19  2 CRP 0 0 29.02 36.925 16.656 6,785 3. 546 2. 268 1.51 1.048 0.751 0.528 0.365 0.598  S F 0 0 13.864 26.678 27.987 12.739 6.336 4. 116 2.796 1.887 1.267 0.839 0.551 0.94  S U/S 0 0 0 0 35.817 25. 816 12. 96 8 8. 433 5.728 3. 867 2.597 1.72 1.129 1.925  S O/S 0 0 26.546 51,081 20.825 0.777 0.269 0. 167 0.1 13 0.076 0.051 0.034 O.022 0.038  3 CRP 0 0 0 17.304 3 8. 353 18. 185 8.888 5.807 3. 971 2.655 1.74 1.125 0.721 1.252  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 35.817 25.816 12.968 8.4 33 5.728 3.867 , 2.597 1.72 1. 129 1.925  % PASSING: SIZE 2 CRF 0.0053 0.19 0.0106 0.32 0.0212 0.48 0.0425 0.66 0.085 0.83 0.17 1 0.34 1.22 0.68 1.51 1.36 2.45 2.72 7 . 15 5.44 25.5 10. 88 62 21.76 97 43. 52 100  2 CRP 0. 598 0.963 1.49 1 2.242 3.29 4. 8 7.068 10.614 17.398 34.054 70.98 100 100 100  S F 0.94 1.491 2.33 3.597 5.485 8.28 12.396 18.732 31. 471 59.458 86.136 100 100 100  S U/S 1.925 3.054 4.774 7.371 11.238 16.966 25. 4 38.367 64. 183 100 100 100 100 100  S O/S 0.038 0.06 0. 0 94 0.145 0.221 0.334 0. 502 0.771 1.548 22.373 73. 454 100 100 100  3 CRP 1.252 1.973 3.098 4.837 7.492 11.464 17.271 26. 159 44.344 82.696 100 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 1.925 3.054 4.774 7.371 11.238 16.966 25.4 38.367 64.183 100 100 100 100 100  TONNAGES: 1578.8 1578.8 % +1 INCH: 92.85 CRUSHER CURRENTS: 29.26  OPERATING CONDITIONS 3304.74  1578.81  1725.93  1725.93 0  40.54165  77.62738 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 . 4 5 %-1/2 INCH IN SCREEN U/S= 6 4 . 1 8 3 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED = 2 6 . 1 9 7 14 % CIRCULATING LOAD= 1.093191  NUMBER OF CYCLES= 12  CONVERGENCE C R I T E R I O N  %SET COLWIDTH= % BETAINED: SIZE 2 CBF 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. 0 425 0. 17 0.0212 0.18 0.0106 0. 16 0.0053 0. 13 - 0 . 0053 0. 19  2 CRP 0 0.034 49.038 32.081 10.628 3. 382 1.528 0.964 0.647 0. 481 0.381 0.289 0.213 0. 334  S F 0 0.015 21.545 22. 907 27.133 1 1.655 5.615 3.674 2.51 1.699 1.143 0.757 0.497 0.848  S U/S 0 0 0 0 36.983 25.7 12. 50 4 8. 191 5.597 3.789 2. 547 1.689 1. 109 1. 891  S O/S 0 0.027 38.431 40. 86 19.414 0.647 0.215 0. 135 0.091 0.062 0.042 0.028 0.018 0.031  3 CEP 0 0 0 15. 718 40.068 18. 138 8.817 5.799 3.97 2.655 1 .739 1. 124 0.721 1.251  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  BMF 0 0 0 0 36.983 25.7 12.504 8. 191 5.597 3.789 2.547 1.689 1.109 1. 891  % PASSING: SIZE 2 CBF 0.0053 0. 19 0.0106 0.32 0.0212 0.48 0.0425 0.66 0.085 0.83 0.17 1 0. 34 1. 22 0.68 1.51 1.36 2.45 2.72 7.15 5.44 25.5 10. 88 62 97 21. 76 43.52 100  2 CEP 0. 334 0.547 0.836 1.217 1.698 2. 345 3. 309 4.837 8.219 18.847 50.928 99.966 100 100  S F 0.848 1.346 2 . 103 3.246 4.945 7.455 11. 13 16.744 28.399 55.532 78.44 99.985 100 100  S U/S 1.891 3 4.689 7.236 11.025 16.622 24.813 37.317 63.017 100 100 100 100 100  S O/S 0.031 0.049 0.077 0 . 1 18 0. 18 0.271 0.406 0.621 1.269 20.683 61.543 99.973 100 100  3 CEP 1.251 1.972 3 . 0 96 4.835 7.49 1 1. 46 17.259 26. 076 44.213 84.282 100 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  EMF 1.891 3 4.689 7.236 11.025 16.622 24.813 37.317 63.017 100 100 100 100 100  5.279837E-3  OPERATING CONDITIONS TONNAGES: 1255. 4 1255. 4 2 8 5 7 . 3 1255. 41 1601. 9 1601.9 0 1255. 41 % +1 INCH: 92.85 44.46782 79.31724 CBUSHEB CUBRENTS: 14.56 39. 37 SETS: 2 CB SET= 3 . 7 8 5 SCBN OP= 1.59 3 CR SET= 1.08 %--\/2 INCH IN FEED= 2 . 4 5 %-1/2 INCH IN SCREEN U/S= 6 3 . 0 1 7 0 5 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 25.72124 % CIRCULATING LOAD= 1.276008  NUMBER OF CYCLES= 14  CONVEEGENCE CRITERION^ 2. 882275E-3  - 287 %5ET C0LWIDTH=8 % RETAINED: SIZE 2 CRF 21.76 •3 10. 88 35 5.44 36.5 2.72 18.35 4.7 1.36 0.68 0.94 0.34 0.29 0.17 0. 22 0.085 0.17 0.0425 0. 17 0.0212 0. 18 0.0106 0. 16 0.0053 0.13 - 0 . 0053 0 . 1 9  2 CRP 0 0.034 50.294 33.018 10.509 2.9 1.055 0.597 0.389 0.306 0. 267 0. 215 0. 165 0.251  S F 0 0.015 21.718 23.129 26.523 11.049 5.80 5 3. 883 2.658 1.798 1.207 0.798 0.524 0.894  S O/S 0 0 0 0 35.567 24.701 13. 118 8.786 6.015 4.068 2.73 1.807 1. 185 2.022  S O/S 0 0.026 38. 22 3 40.706 19.651 0.675 0.246 0.157 0.107 0.072 0.049 0.032 0.021 0.036  3 CRP 0 0 0 15.613 3 8.694 17.243 9.414 6.381 4.383 2.931 1.921 1.242 0 . 7 96 1.382  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 35.567 24.701 13. 118 8.786 6.015 4.068 2.73 1.807 1. 185 2.022  % PASSING: SIZE 2 CRF 0.0053 0. 19 0.0106 0.32 0.48 0.0212 0 . 0 425 0.66 0.085 0.83 0.17 1 0.34 1.22 0.68 1.51 1.36 2.45 2.72 7.15 5.44 25.5 10. 88 62 97 21. 76 43.52 100  2 CRP 0.251 0.417 0.632 0.899 1.205 1. 594 2. 191 3.246 6 . 145 16.654 49.672 99,966 100 100  S F 0.894 1.417 2.216 3.422 5.22 7.878 11.762 17.566 28.616 55.139 7 8.268 99.985 100 100  S O/S 2.022 3.207 5.014 7.744 11.813 17.828 26.614 39. 73 3 64.43 3 100 100 100 100 100  S O/S 0.036 0.057 0.089 0. 138 0.21 0.317 0.4 74 0.72 1.395 21. 045 61.751 99.974 100 100  3 CRP 1.382 2.178 3.419 5.34 8.271 12.654 19.036 28.45 45.693 84.387 100 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.0 22 3.207 5.014 7.744 11.813 17.828 26.614 39.733 64.433 100 100 100 100 100  OPERATING I CONDITIONS TONNAGES ' Z 1578.8 1578.8 3 6 5 6 . 18 1 5 7 8 . 8 2077. 38 2077.38 0 1578. % +1 INCH: 92.85 4 4 . 86086 78.95482 CRUSHER CURRENTS: 20. 15 4 5 . 96 SETS: 2 CR SET= 3 . 7 8 5 SCRN OP= 1. 59 3 CR SET= 1.08 %-1/2 INCH IN FEED= 2.45 %-1/2 INCH IN SCREEN U/S= 6 4 . 4 3 3 4 7 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT FEED= 2 6 . 2 9 9 3 8 % CIRCULATING LOAD= 1.315797  8  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 . 2 5 , 2 . 0, 1 . 6 5 , 1 . 3 2 , 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 3100 3110 3120 3130 3140 3150 3160 8.RUN  DATA DATA DATA DATA DATA DATA DATA DATA  1255. 4 , 2 . 5 4 , 1 . 2 7 , 1 . 0 8 , 0,1 1578. 8 , 2 . 5 4 , 1 . 2 7 , 1 . 0 8 , 0, 1 1255. 4 , 3 . 7 8 5 , 1 . 2 7 , 1 . 0 8 1,0,1 1578. 8 , 3 . 7 8 5 , 1 . 2 7 , 1 . 0 8 , 0 , 1 1 2 5 5 . 4 , 2 . 5 4 , 1 . 5 9 , 1 . 0 8 , 0,1 1578. 8 , 2 . 5 4 , 1 . 5 9 , 1 . 0 8 , 0,1 1255. 4 , 3 . 7 8 5 , 1 . 5 9 , 1 . 0 8 i , 0 , 1 1578. 8 , 3 . 7 8 5 , 1 . 5 9 , 1 . 0 8 , 0 , 0  NUMBER OF C Y C L E S  3  10  CONVERGENCE  CRITERION  3  4. 297657E-3  SI SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 21.76 1 10. 88 16. 5 5.44 28.5 2.72 27.3 1.36 12.6 0.68 4.65 0.34 2.25 0. 17 2 1.65 0.085 0.0425 1.32 0.0212 1.02 0.0106 0.64 0.0053 0.3 - 0 . 0 0 5 3 0.27  2 CRP 0 0.002 11.286 38.024 21.595 9.915 5.56 4. 204 3.125 2.295 1.656 1.05 0.562 0.726  S F 0 0.001 5.465 22.702 31.065 17.985 9.853 4.479 2.882 2.009 1,39 1 0.888 0.514 0.76 6  S U/S 0 0 0 0 19.913 34. 869 19, 53 8.898 5.727 3. 991 2.763 1.765 1.021 1.522  S O/S 0 0.002 10.594 44.009 41.532 2.138 0.771 0. 3 32 0.212 0. 1 48 0. 102 0.065 0.038 0.056  3 CRP 0 0 0.001 8.321 39.954 25.559 13. 883 4.738 2 . 6 55 1.74 1.142 0.737 0.468 0.804  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 19.913 34.869 19.53 8.8 98 5.727 3.991 2.763 1.765 1.021 1. 522  % PASSING: SIZE 2 CRF 0.0053 0.27 0.57 0.0106 0.0212 1.21 0.0425 2.23 0.085 3.55 0.17 5.2 0.34 7.2 0.68 9.45 1.36 14. 1 26.7 2.72 5.44 54 10.88 82. 5 21. 76 99 43.52 100  2 CRP 0.726 1.288 2.338 3.994 6.289 9.414 13.618 19.178 29.093 50.688 88.712 99.998 100 100  S F 0.766 1. 28 2.168 3.559 5 . 567 8. 45 12.929 22.782 40.767 71.833 94.534 99.999 100 100  S 0/S 1.522 2. 542 4.308 7.071 11.062 16.789 25.687 45. 218 80.087 100 100 100 100 100  S O/S 0.056 0.094 0.16 0.262 0.41 0.6 22 0.954 1.7 25 3.863 45.396 89.404 99.998 100 100  3 CRP 0 . 8 04 1.272 2.008 3.151 4.89 7.545 12.282 26. 165 51.724 91.678 99.999 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 1. 522 2.542 4.308 7.071 11.062 16.789 25.687 45.218 80.087 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1255.4 1255.4 2 5 9 2 . 9 6 1255.4 1337. 57 1337.57 0 1255. % +1 INCH: 73.3 2 8 . 16746 54.60446 CRUSHER CURRENTS: 23.68 41.33 SETS: 2 CR SET= 2 . 5 4 SCRN OP= 1. 27 3 CR S E T 0.495 %--\/2 INCH IN F E E D 14.1 %-1/2 INCH IN SCREEN U / S 80.08693 % - 1 / 2 INCH RATIO, SCREEN U / S TO PLANT F E E D 5 . 6 7 9924 % CIRCULATING L O A D 1.065453 3  3  3  3  3  4  - 289 NUMBER OF C Y C L E S  3  8  CONVERGENCE C R I T E R I O N  3  7.813911E-3  %SET COLWIDTH=8 % RETAINED: SIZE 2 CRF 21.76 1 10. 88 16.5 5.44 28.5 27.3 2.72 1.3 6 12.6 0.68 4.65 0.34 2.25 0. 17 2 0.085 1.65 0.0425 1.32 0.0212 1.02 0.0106 0.64 0.0053 0.3 - 0 . 0053 0 . 2 7  2 CRP 0 0. 002 11.39 39.144 22.088 9.675 5. 159 3.86 2.875 2. 125 1.544 0.977 0.516 0. 645  S F 0 0.001 5.396 23.234 31.557 15.063 8. 975 5.259 3.588 2.49 1.705 1.091 0.645 0.996  S U/S 0 0 0 0 20.202 29.726 18. 13 10.647 7 . 267 5.042 3. 453 2.211 1.306 2.017  S O/S 0 0.002 10.254 44. 148 41.778 1.8 65 0.735 0.408 0.277 0. 192 0. 131 0.084 0.0 5 0.077  3 CRP 0 0 0.001 8.912 40. 081 19.914 12. 41 6 . 5 17 4.23 2.818 1.85 1. 194 0.761 1.312  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 0 0 0 0 20.202 29. 726 18. 13 10.647 7.267 5.042 3.453 2.211 1.306 2.017  % PASSING: SIZE 2 CRF 0.0053 0.27 0.57 0.0106 0.0212 1.21 0.0425 2.23 0.085 3.55 0.17 5.2 0.34 7.2 0.68 9.45 14. 1 1.36 26.7 2.72 5.44 54 10.88 82.5 21. 76 99 43.52 100  2 CRP 0. 645 1.161 2. 138 3.68 2 5. 806 8.682 12.542 17.701 27.376 49.464 88.608 99.998 100 100  S F 0.996 1.641 2.732 4. 437 6.927 10.515 15.773 24.749 39.812 71. 369 94.603 99.999 100 100  S U/S 2.017 3.323 5.533 8.986 14.028 21. 295 31,942 50.071 79.798 100 100 100 100 100  S O/S 0.077 0.126 0.211 0 . 3 42 0.534 0.8 11 1.219 1.954 3 . 8 18 45.597 89.744 99.998 100 100  3 CRP 1.312 2.073 3.267 5.117 7.935 1 2. 165 18.682 31.092 51.006 91.087 99.999 100 100 100  P F 0 0 0 0 0 0 0 0 0 0 0 0 0 0  RMF 2.017 3.323 5. 533 8.986 14.028 21.295 31.942 50.071 79.798 100 100 100 100 100  OPERATING CONDITIONS TONNAGES: 1578. 8 3 3 3 2 . 7 1 1578.79 1753. 91 1753.91 0 1578.8 1578.79 % *1 INCH: 28.63106 73.3 54.40342 CRUSHER CURRENTS: 47. 1 29. 26 SCRN OP= 1.27 SETS: 2 CR S E T 2.54 3 CR S E T 0.495 %-1/2 INCH IN F E E D 14.1 %-1/2 INCH IN SCREEN U/S= 7 9 . 7 9 7 5 7 % - 1 / 2 INCH RATIO, SCREEN U/S TO PLANT F E E D 5.659402 % CIRCULATING L O A D 1.110913 3  3  3  3  3  NUMBER OF C Y C L E S %SET COLWIDTH 8 % RETAINED: SIZE 2 CRF 21.76 1 10.88 16.5 5.44 28.5  3  11  CONVERGENCE C R I T E R I O N  3  2. 885293E-3  3  2 CRP 0 0.02 24.445  S F 0 0.009 10.833  S U/S 0 0 0  S O/S 0 0.016 19.451  3 CRP 0 0 0.002  P F 0 0 0  RMF 0 0 0  - 290 2.72 1. 36 0.68 0.34 0.17 0.085 0.0425 0.0212 0.0106 0.0053 - 0 . 0 053  27.3 12.6 4.65 2.25 2 1.65 1. 32 1.02 0.64 0.3 0.27  % PASSING: SIZE 2 CRF 0.0053 0.27 0.0106 0.57 0.0212 1.21 0.0425 2.23 0.085 3.55 0. 17 5.2 0.34 7.2 0.68 9.45 1.36 14.1 26.7 2.72 5.44 54 10. 88 82.5 21.76 99 43. 52 100  36.592 18.472 7.317 3.626 2.828 2. 182 1.666 1. 244 0.784 0. 392