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UBC Theses and Dissertations

The synthesis of a free-piston power saw Fandrich, Helmut Edward 1970

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THE SYNTHESIS OF A FREE-PISTON POWER SAW by HELMUT EDWARD FANDRICH B.A.Sc., U n i v e r s i t y of B r i t i s h Columbia, 1960 M.A.Sc., U n i v e r s i t y of B r i t i s h Columbia, 1962 ENGINEER, Stanford U n i v e r s i t y , 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of MECHANICAL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d standard: UNIVERSITY OF BRITISH COLUMBIA February, 1970 In p resen t i ng t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia , I agree t ha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r re fe rence and study a f t e r May 1, 1973 unless t h i s d i r e c t i o n i s countermanded by me and the Head of the Department of Mechanical Eng ineer ing before tha t da te . I f u r t h e r agree t ha t permiss ion f o r ex tens i ve copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s a f t e r May 1, 1973. I t i s understood tha t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed w i thou t my w r i t t e n p e r m i s s i o n . HELMUT EDWARD FANDRICH Department o f Mechanical Eng ineer ing The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8 , Canada ABSTRACT The o b j e c t of t h i s study was t o apply the technique of s y n t h e s i s t o the design of a sm a l l power saw. The study produced experimental data on optimum chain speeds, engine v i b r a t i o n s , noise l e v e l s , and heat t r a n s f e r c o e f f i c i e n t s f o r r e c i p r o c a t i n g c y l i n d e r heads, and l e d to a simple f r e e - p i s t o n c o n f i g u r a t i o n i n which a p i s t o n o s c i l l a t e d between a mixture of a i r and f u e l i n one end of a c l o s e d c y l i n d e r and a s p r i n g i n the other. The f e a s i b i l i t y of developing the c o n f i g u r a t i o n i n t o a p r a c t i c a l r e c i p r o c a t i n g engine was v e r i f i e d by design-i n g , b u i l d i n g and t e s t i n g a prototype. The prototype i n c o r p o r a t e d such novel f e a t u r e s as i n s t a n t , e f f o r t l e s s s t a r t i n g and stopping, automatic t h r o t t l -i n g , s e l f - c o o l i n g , compression i g n i t i o n of a carbureted a i r -f u e l m i x t u r e , and a balanced engine. U n c o n t r o l l e d i g n i t i o n t i m i n g reduced engine e f f i c i e n c y , and the l a c k of i n e r t i a made engine s t a l l i n g easy and c a r b u r e t o r adjustment d i f f i c u l t . The computed r e s u l t s suggest t h a t a developed 3 l b f r e e - p i s t o n power saw w i l l produce 1.0 hp at 6,400 cpm and have a s p e c i f i c f u e l consumption of .9 lb/shp-hr. i i i TABLE OF CONTENTS Chapter Page 1. FORMULATION 1 1.1 I n t r o d u c t i o n 1 1.2 S p e c i f i c a t i o n f o r the Design Envelope 26 2. SYNTHESIS 6 3 2.1 Wood C u t t i n g Devices . ; 63 2.2 E v a l u a t i o n o f E x i s t i n g Engines 77 2.3 S y n t h e s i s o f A l t e r n a t i v e s 91 2.4 S y n t h e s i s of the F r e e - p i s t o n power Saw 107 3. DETAILING 118 3.1 Dimensional A n a l y s i s 118 3.2 Automatic T h r o t t l i n g 145 3.3 Design o f Components 156 3.3.1 G e n e r a l C o n s i d e r a t i o n s 156 3.3.2 Bounce S p r i n g 158 3.3.3 S y n c h r o n i z i n g Mechanism 172 3.3.4 A r r e s t i n g Mechanism 184 3.3.5 C o o l i n g System 190 3.3.6 Combustion System 197 3.4 F a b r i c a t i o n of P a r t s 206 4. EVALUATION 216 4.1 Performance C h a r a c t e r i s t i c s o f the F r e e - p i s t o n Saw 216 . i v Page 4.2 C o n c l u s i o n s . . 237 4.3 Summary 241 REFERENCES 247 APPENDICES I C u t t i n g Speed T e s t Data 257 I I Chain Saw V i b r a t i o n T e s t Data 258 I I I C h ain Saw Noise T e s t Data 259 IV Data from the Q u e s t i o n n a i r e on the Use of Power Saws 260 V T y p i c a l Power Saw Performance Data . . . . 261 VI Data f o r Heat T r a n s f e r from R e c i p r o c a t i n g Heads 262 VII FPS Pr o t o t y p e T e s t Data . 263 V LIST OF TABLES Table Page I S p e c i f i c a t i o n s f o r a sm a l l power saw 61 I I C h a r a c t e r i s t i c s of the co n v e n t i o n a l and Wankel engines 81 I I I S c a l i n g c h a r a c t e r i s t i c s f o r s i m i l a r engines 129 IV S i z e of m a t e r i a l r e q u i r e d to s t o r e 175 i n - l b of energy 166 V C a p a c i t y and optimum s i z e of bands 179 VI M a t e r i a l s s u i t a b l e f o r c y l i n d e r heads and b l o c k s 197 V I I M a t e r i a l s s u i t a b l e f o r p i s t o n s 202 V I I I Performance c h a r a c t e r i s t i c s of the f r e e -p i s t o n power saw 237 v i LIST OF FIGURES F i g u r e Page 1.1 O u t l i n e of the comprehensive d e s i g n e n g i n e e r s task , 10 1.2 C u t t i n g w i t h one of the o r i g i n a l one-man c h a i n saws 17 1.3 Sketches of the c h i s e l - t o o t h and c h i p p e r -t o o t h c h a i n s 1^ 1.4 T y p i c a l l i s t of c h a i n saw s p e c i f i c a t i o n s , c i r c . 1950 1 9 1.5 T y p i c a l t r e e h a r v e s t i n g machine 24 1.6 Apparatus used i n c h a i n speed t e s t s 33 1.7 Schematic r e p r e s e n t a t i o n of m u f f l e r and e l e c t r i c a l e q u i v a l e n t ">3 1.8 A c c i d e n t s r e p o r t e d to Quebec Pulp and Paper A s s o c i a t i o n ^6 1.9 R e s u l t s of q u e s t i o n n a i r e on the importance o f saw c h a r a c t e r i s t i c s ^0 2.1 Diagrams i l l u s t r a t i n g hot-gas c y c l e 85 2.2 S t i r l i n g thermal engine schematic drawing . . . 88 2.3 Sketches of the unbalanced l e v e r engine . . . . 9 ^ 2.4 A s k e t c h o f the o s c i l l a t i n g f r e e - p i s t o n engine 101 2.5 T y p i c a l r e c i p r o c a t i n g - b l a d e saws 115 2.6 E x i s t i n g f r e e - p i s t o n c o n f i g u r a t i o n s 117 3.1 F r e e body diagram o f the f r e e - p i s t o n power saw 157 3.2 Photographs of heat t r a n s f e r t e s t apparatus 19 5 3.3 F r e e - p i s t o n power saw assembly s k e t c h 207 v i i F i g u r e Page 3.4 Photograph of the t r a n s f e r p o r t machining o p e r a t i o n 209 3.5 Photographs of s y n c h r o n i z i n g and a r r e s t i n g mechanism assemblies 212 3.6 Photographs of FPS components . 214 3.7 Photograph of a l l FPS p a r t s 215 4.1 Photographs of the instrumented FPS 222 4.2 Photographs of the FPS, w i t h a fixed-throw c r a n k s h a f t 222 4.3 Photographs of the FPS w i t h an o s c i l l a t -i n g c rankshaft 2 30 4.4 Subassembly photographs of a conventional power saw and the FPS 2 39 v i i i LIST OF GRAPHS Graph Page 1.1 Power saw performance trends 22 1.2 Optimum power as a f u n c t i o n of t r e e s i z e 31 1.3 Importance of sprocket s i z e on c u t t i n g r a t e s - 35 1.4 Importance of j o i n t on c u t t i n g r a t e s 35 1.5 C u t t i n g r a t e v a r i a t i o n s 35 1.6 -Importance of bar l e n g t h on c u t t i n g r a t e s 35 1.7 Importance of wood species on c u t t i n g r a t e s . 36 1.8 Gear d r i v e c u t t i n g r a t e s 36 1.9 S p e c i f i c energy as a f u n c t i o n of c h a i n speed 36 1.10 V i b r a t i o n damage l e v e l s as a f u n c t i o n of frequency 40 1.11 V i b r a t i o n amplitude w h i l e c u t t i n g versus counterweight s i z e 44 1.12 V i b r a t i o n amplitude w h i l e c u t t i n g and w h i l e unloaded 44 1.13 E f f e c t of bar on amplitude w i t h s e v e r a l d i f f e r e n t counterweights 45 1.14 E f f e c t of bar on v i b r a t i o n amplitude 46 1.15 E f f e c t of speed on v i b r a t i o n amplitude . . . . 46 1.16 E f f e c t of rubber i n s u l a t i o n on v i b r a t i o n amplitude 47 1.17 Noise l e v e l readings of t y p i c a l power saws 50 i x Graph Page 1.18 State of Washington standard f o r indus-t r i a l noise 51 1.19 T e n t a t i v e Swedish noise l e v e l l i m i t s f o r power saws 52 2.1 S p e c i f i c energy r e q u i r e d by v a r i o u s wood c u t t i n g devices 77 2.2 Power of a Wankel engine compared w i t h c o n v e n t i o n a l engines 82 2.3 Computed p i s t o n p o s i t i o n f o r the un-balanced l e v e r engine 98 2.4 Blade and p i s t o n p o s i t i o n as a f u n c t i o n of compression r a t i o 103 3.1 Power as a f u n c t i o n of p i s t o n area f o r t y p i c a l power saws 122 3.2 S p e c i f i c power as a f u n c t i o n of bore s i z e . . 125 3.3 S p e c i f i c weight as a f u n c t i o n of bore s i z e 125 3.4 S p e c i f i c power as a f u n c t i o n of p i s t o n speed 133 3.5 S p e c i f i c power as a f u n c t i o n of engine speed 133 3.6 P o r t areas of t y p i c a l power saws versus stroke/bore r a t i o s 135 3.7 P o r t heights versus square r o o t of s t r o k e / bore r a t i o s 137 3.8 S p e c i f i c power and BMEP versus p o r t area r a t i o s 141 3.9 Flow area versus stroke f o r i d e a l FPS . . . . 149 3.10 P i s t o n s t r o k e s as a f u n c t i o n of time f o r i d e a l FPS 152 3.11 Stroke v a r i a t i o n caused by sudden load changes 163 X Graph Page 3.12 Maximum load t r a n s m i t t e d by bands 181 3.13 Heat t r a n s f e r curve f o r r e c i p r o c a t i n g c y l i n d e r heads 196 3.14 C a l c u l a t e d thermal l o s s e s from com-b u s t i o n chambers 200 4.1 Prototype engine t r a c e s (experimental). . . . 223 4.2 Prototype engine t r a c e s without combustion (computed) 224 4.3 E f f e c t of leakage, f r i c t i o n and damping on t r a c e s (computed) 225 4.4 Prototype engine t r a c e s w i t h combustion . . . 226 4.5 Crank engine performance (experimental and computed) 229 4.6 Experimental engine p o s i t i o n t r a c e s (experimental) 2 32 4.7 Experimental engine p o s i t i o n t r a c e s (computed) 233 ACKNOWLEDGEMENTS Of the many people a s s o c i a t e d w i t h t h i s t h e s i s , the author would l i k e t o s i n g l e out the f o l l o w i n g f o r s p e c i a l r e c o g n i t i o n : Mr. A.F.B. M i l l i g a n and Mr. J.C. St a i n s b y f o r s e t t i n g up the Canadien Chain Saw F e l l o w s h i p and Grant; Mr. Pe t e r G. Dueck f o r c o n t i n u i n g the f i n a n c i a l support; Dr. E.G. Hauptmann f o r s u p e r v i s i o n o f the p r o j e c t ; Dr. C. B r o c k l e y , Dr. J.P. Duncan, Dr. N. E p s t e i n , and P r o f . W.O. Richmond f o r a c t i n g on the s u p e r v i s o r y committee A s p e c i a l thanks t o my w i f e f o r her h e l p i n p r o o f r e a d i n g the t h e s i s . 1 1. FORMULATION 1.1 I n t r o d u c t i o n This study evolved a c o n f i g u r a t i o n f o r a sm a l l prime mover t o be used i n a c l a s s of a p p l i c a t i o n s such as power saws. S t a r t i n g w i t h a f o r m u l a t i o n of the b a s i c power saw requirements, the study continued w i t h a s y n t h e s i s of s e v e r a l a l t e r n a t i v e s t o the conventional r e c i p r o c a t i n g engine. Synthesis was f o l l o w e d w i t h an o p t i m i z a t i o n of the most promising a l t e r n a t i v e and a d e t a i l design of the components. The study concluded w i t h a v e r i f i c a t i o n of the i d e a by t e s t i n g an a c t u a l prototype. The end r e s u l t was a l i g h t - w e i g h t , v i b r a t i o n l e s s , q u i c k - s t a r t i n g , s e l f -t h r o t t l i n g , f r e e - p i s t o n machine t h a t departed " r a d i c a l l y " from e x i s t i n g power saws. In the c o n f i g u r a t i o n optimized and b u i l t , a p i s t o n bounces between a s p r i n g i n one end of a closed c y l i n d e r and a volume of f u e l and a i r i n the other end. A blade i s attached d i r e c t l y t o the o s c i l l a t i n g p i s t o n . By i g n i t i n g the mixture during the compression s t r o k e , a simple prime mover i s t h e o r e t i c a l l y p o s s i b l e . Engineering design i s an i t e r a t i v e decision-making process ap p l y i n g s c i e n t i f i c p r i n c i p l e s and u t i l i z i n g prac-t i c a l techniques i n order to d e f i n e a d e v i c e , a process, or a system i n s u f f i c i e n t d e t a i l to permit i t s p h y s i c a l r e a l -2 * i z a t i o n [1.1, 1.2] . A good d e s i g n permits manufacture by the most economical method and i n the s h o r t e s t p o s s i b l e time and r e s u l t s i n a f u n c t i o n a l , o f t e n p a t e n t a b l e product t h a t not o n l y meets the s t i p u l a t e d c o n d i t i o n s but a l s o i n c o r p o r a t e s a e s t h e t i c appeal [1.3, 1.4, 1.5], A good c r e a t i v e l y - d e s i g n e d product i s a unique, o f t e n s t a r t l i n g combination o f e n g i n e e r i n g p r i n c i p l e s and known d a t a . The d e v i c e i s u s e f u l and b e n e f i c i a l and ve r y l i k e l y t o be dra m a t i c , s p e c t a c u l a r and newsworthy. I t s a t i s f i e s the maker and f a s c i n a t e s the use r [1.6, 1.7]. A good d e s i g n e r i s a g e n e r a l i s t who i s motivated by v e r y broad concepts of human a c t i v i t y , thought and behaviour. He communicates w e l l . He understands the c r e a t i v e p r o c e s s . He m a i n t a i n s a d e l i c a t e b alance between h i s a b i l i t y t o s y n t h e s i z e , t o a n a l y z e , and t o e v a l u a t e . He i s t h o r o u g h l y f a m i l i a r w i t h the environment i n which h i s product w i l l be made, s o l d , used and s e r v i c e d . A r n o l d [1.8] c a l l e d t h i s g e n e r a l i s t a "comprehensive d e s i g n e r " . Although each d e s i g n p r o j e c t has i t s own h i s t o r y , the sequence of events common to a l l p r o j e c t s forms a p a t t e r n t h a t can be s t u d i e d p r o f i t a b l y . By examining t h i s p a t t e r n engineers have o b t a i n e d an i n s i g h t i n t o the methodology of d e s i g n by which thoughts about needs are * References i n p a r e n t h e s i s r e f e r t o B i b l i o g r a p h y a t end of t h i s t h e s i s . 3 p r o j e c t e d i n t o i d e a s about t h i n g s [1.9, 1.10]. The p a t t e r n l e a d s t o the standard r e c i p e : a n a l y z e , t h e o r i z e , d e l i n e a t e and modify [1.11]. The use o f t h i s r e c i p e r e s u l t s i n a c o n v e n t i o n a l s o l u t i o n t h a t i s u s u a l l y p h y s i c a l l y r e a l i z a b l e , e c o n o m i c a l l y worthwhile, and f i n a n -c i a l l y f e a s i b l e but not n e c e s s a r i l y the b e s t one p o s s i b l e . To a r r i v e a t a more o p t i m a l solution,, e s p e c i a l l y to a complex problem, i t i s n ecessary t o add a c r e a t i v e o r i n v e n t i v e p rocess to the r e c i p e . The i n v e n t i v e process has the f o l l o w i n g steps [1.12, 1.13, 1.14, 1.15]: 1. p r e p a r a t i o n - g a t h e r i n g s k i l l s and f o r m u l a t i n g the problem, 2. p e r s p i r a t i o n - t h i n k i n g d e l i b e r a t e l y and i n t e n s e l y about the problem, 3. i n c u b a t i o n - a p e r i o d of mental r e s t a f t e r d e l i b e r a t e t h i n k i n g has f a i l e d , 4. i n s p i r a t i o n - the sudden i d e a o r r e o r g a n i z a t i o n which i s the s o l u t i o n , 5. v e r i f i c a t i o n - f o l l o w i n g through w i t h g e n e r a l i z a -t i o n s , e v a l u a t i o n s and e l a b o r a t i o n s . As the scope of h i s c r e a t i v e work depends upon h i s s t o r e of knowledge, the p r o g r e s s i v e d e s i g n e r endeavours to be p e r c e p t i v e and to e n l a r g e h i s v i e w p o i n t s through study, e x p e r i e n c e , and o b s e r v a t i o n . By being aware of h i s e motional b l o c k s and c o n s c i o u s of h i s p r e d i s p o s i t i o n to 4 p a r t i c u l a r images, methods or way of t h i n k i n g , he overcomes h i s b i g g e s t o b s t a c l e to o r i g i n a l i t y because a b i l i t y to r e c a l l the r i g h t images and the a b i l i t y to modify images e f f e c t i v e l y are two e s s e n t i a l i n g r e d i e n t s of c r e a t i v i t y [1.12, 1.16]. In c o n t r a s t to the c r e a t i v e mental processes are these non-creative processes [1.15]: 1. o b s e r v a t i o n - studying p e r c e i v e d o b j e c t s and circum-stances , 2. r e f l e c t i o n - reviewing the content of the mind, 3. remembering - r e c a l l i n g past experiences and pre-v i o u s l y acquired i d e a s , 4. reasoning - determining the consequences of assumed c o n d i t i o n s and courses of a c t i o n , 5. judgment - f o r m u l a t i n g d e c i s i o n s . But no new s o l u t i o n s are p o s s i b l e without s t i m u l a t i o n . What s t i m u l a t e s us? Niemann [1.17] suggests excitement over a new phenomenon, a new r e a l i z a t i o n , a new requirement, the f r u i t f u l anger over an incomplete t h i n g or the l i v e l y d i f f e r -ence of o p i n i o n w i t h other experienced people. Less i n f l u e n t i a l , but nevertheless s a t i s f a c t o r y , i s the s t i m u l a t i o n t h a t comes through reading w i t h an a l e r t a t t i t u d e and the unrest t h a t comes through c r i t i c i s m of the present, by p r e s e n t a t i o n of new p o i n t s of view and by hearing others express t h e i r wishes. 5 C r e a t i v i t y i s only a f a i r l y recent i n c l u s i o n i n engineering courses. Perhaps the e a r l i e s t f o r m u l a t i o n of the c r e a t i v e design process was f o r General E l e c t r i c Company's "Cre a t i v e Engineering Program" e s t a b l i s h e d i n 1937 [1.18, 1.19]. The f o l l o w i n g steps were formulated: 1. D e f i n i t i o n of the problem, 2. M a n i p u l a t i o n of elements bearing on s o l u t i o n . 3. P e r i o d r e s u l t i n g i n the i n t u i t i v e i d e a , 4. The idea i s shaped to p r a c t i c a l u s e f u l n e s s . [1.19, p. 9] From about 1940 to 1960, c r e a t i v i t y was emphasized i n the hope t h a t b e t t e r t e c h n o l o g i c a l designs would r e s u l t . Roadblocks to c r e a t i v e a c t i v i t y were i n v e s t i g a t e d not only by designers but by authors g e n e r a l l y . E r i c h Fromm [1.20] c l e a r l y demonstrates t h a t although each person has a strong need f o r s e c u r i t y , to be a member of a group, t o belong to something, he expresses t h i s need p o s i t i v e l y or n e g a t i v e l y . He becomes a f r e e productive i n d i v i d u a l or he forms psycho-l o g i c a l b l o c k s . These bl o c k s form f i l t e r s t h a t d i s t o r t the in f o r m a t i o n he r e c e i v e s from the ou t s i d e world, i n h i b i t f r e e a s s o c i a t i o n w i t h i n h i s b r a i n , and prevent c l e a r communi-c a t i o n to other s . In the l a t e f i f t i e s and e a r l y s i x t i e s , t h o u g h t f u l i n d i v i d u a l s began to r e a l i z e t h a t there was c o n s i d e r a b l y more to the design process than a n a l y s i s or even c r e a t i v i t y . Observing the a c t i o n s of h i s f e l l o w man, T i e l h a r d de Chardin [1.21] f e l t t h a t man i s obsessed by the need to depersonal-6 i z e a l l t h a t he most a d m i r e s , p a r t l y b e c a u s e o f a n a l y s i s , t h a t m a r v e l l o u s i n s t r u m e n t o f s c i e n t i f i c r e s e a r c h t o w h i c h we owe a l l o u r a d v a n c e s b u t w h i c h , b r e a k i n g down s y n t h e s i s a f t e r s y n t h e s i s , a l l o w s one s o u l a f t e r a n o t h e r t o e s c a p e , l e a v i n g us c o n f r o n t e d w i t h a p i l e o f d i s m a n t l e d m a c h i n e r y . [ 1 . 2 1 , p. 283] A r n o l d [ 1 . 7 , 1.18] was p e r h a p s one o f t h e f i r s t e n g i n e e r s t o r e c o g n i z e t h e n e e d f o r a more c o m p r e h e n s i v e v i e w o f t h e d e s i g n p r o c e s s when i n 19 59 he i n c l u d e d s u c h t o p i c s as p s y c h o l o g y o f t h e m i n d , a e s t h e t i c s , d e c i s i o n t h e o r y and o p e r a t i o n s r e s e a r c h i n h i s t h e o r y o f d e s i g n . T h i s c o m p r e h e n s i v e v i e w h a s now become an i m p o r t a n t c o n c e p t i n t h e p h i l o s o p h y o f d e s i g n . The s o l u t i o n t o t h e r a p i d l y c h a n g i n g and i n c r e a s i n g l y c o m p l e x p r o b l e m s o f e n g i n e e r i n g d e s i g n r e q u i r e s a f l e x i b l e a p p r o a c h . To a c h i e v e f l e x i b i l i t y y e t a t t h e same t i m e t o a r r i v e a t a c o n c r e t e s o l u t i o n , t h e e n g i n e e r i s e n c o u r a g e d t o g e n e r a t e s e v e r a l a l t e r n a t i v e s , c h o o s e t h e b e s t , and t h e n o p t i m i z e t h e c o n f i g -u r a t i o n u s i n g r a t i o n a l t e c h n i q u e s . I n f o r m a t i o n f e e d b a c k c o n t i n u a l l y c h a l l e n g e s h i s d e c i s i o n s , m a k i n g t h e d e s i g n p r o c e s s n o t an "open i n f o r m a t i o n l o o p " s y s t e m where t h e s o l u t i o n h y p o t h e t i c a l l y d o e s n o t a f f e c t t h e e n v i r o n m e n t , b u t a " s o c i o - t e c h n i c a l f e e d b a c k " s y s t e m where t h e s o l u t i o n a n t i c i p a t e s t h e d y n a m i c i n t e r a c t i o n o f d e s i g n , man and e n v i r o n m e n t [ 1 . 2 2 ] . The d y n a m i c f e e d b a c k s y s t e m g r e a t l y i n c r e a s e s t h e number o f v a r i a b l e s and t h e number o f d e c i s i o n s r e q u i r e d . The r e s u l t i s t h a t " t h e s k i l l o f t h e d e s i g n e r i s 7 measured by h i s a b i l i t y to i d e n t i f y l i m i t s and to make appro-p r i a t e compromises" [1.21, p. 9], Even as o p t i m i z a t i o n techniques, d e c i s i o n theory, systems a n a l y s i s , operations r e s e a r c h , c y b e r n e t i c imagin-a t i o n , value eng i n e e r i n g , r e l i a b i l i t y engineering and program e v a l u a t i o n review techniques are being i n v e s t i g a t e d and a p p l i e d , some s o c i a l s c i e n t i s t s are c o n s i d e r i n g the e f f e c t t h a t too much .emphasis on methods has on the i n d i v i d u a l because the process of sy n t h e s i s i s e s s e n t i a l l y i n d i v i d u a l -i s t i c . Jacques E l l u l [1.23] suggests t h a t o p t i m i z a t i o n techniques when a p p l i e d to managerial o r g a n i z a t i o n s lead to s t a n d a r d i z a t i o n and r a t i o n a l i z a t i o n of economic and a d m i n i s t r a t i v e l i f e . He quotes Antoine Mas to expand h i s p o i n t : s t a n d a r d i z a t i o n means r e s o l v i n g i n advance a l l the problems t h a t might p o s s i b l y impede the f u n c t i o n i n g of an o r g a n i z a t i o n . I t i s not a matter of l e a v i n g i t to i n s p i r a t i o n , i n g e n u i t y , nor even i n t e l l i g e n c e to f i n d a s o l u t i o n a t the moment some d i f f i c u l t y a r i s e s ; i t i s r a t h e r i n some way to a n t i c i p a t e both the d i f f i c u l t y and i t s r e s o l u t i o n . From then on s t a n d a r d i z -a t i o n c r e a t e s i m p e r s o n a l i t y , i n the sense t h a t o r g a n i z a t i o n r e l i e s more on methods and i n -s t r u c t i o n s than on i n d i v i d u a l s . [1.23, P. 11] But some engineering educators are o p t i m i s t i c about the changing nature of engineering design. Thimm [1.22] b e l i e v e s t h a t : systematic t r a i n i n g i n operations research and d e c i s i o n theory w i l l improve o v e r a l l engineering performance; i t might even save the world from t e c h n o l o g i c a l p o l l u t i o n and e c o l o g i c a l catastrophe. [1.22, p. 12] 8 So c i e t y i s expecting the designer t o take more r e s p o n s i b i l i t y not only a g a i n s t e r r o r s but a l s o f o r e f f l u -ents of an unhealthy nature. At the t h i r d annual McMaster U n i v e r s i t y design seminar, F.R. Duncan [1.24] c l o s e d h i s remarks on the l e g a l r e s p o n s i b i l i t y of the designer w i t h the remark t h a t , " I t s j u s t not safe t o leave design e r r o r s f l o a t i n g around any more" [1.24, p. 36]. At the same seminar A l l c u t [1.25] mentioned t h a t w h i l e e t h i c s r e l a t e e n t i r e l y to people and design deals o n l y w i t h t h i n g s , the r e l a t i o n s h i p between the two i s e s s e n t i a l l y t h a t of cause and e f f e c t and "considerable judgment based on experience i s r e q u i r e d to combine these two f a c t o r s i n the r i g h t p r o p o r t i o n s " [1.25, p. 38], The emphasis on c r e a t i v i t y i s a s s o c i a t e d w i t h the G e s t a l t theory of p e r c e p t i o n developed around the 1920's [1.26]. The crux of the theory i s t h a t i t i s important to examine the t o t a l i t y of a problem, not merely i t s components. In p e r c e p t i o n the whole i s g r e a t e r than the sum of i t s p a r t s . To per c e i v e the t o t a l i t y or i m p l i c a t i o n of the s o l u t i o n r e q u i r e s a " t o t a l " approach t o problem s o l v i n g . What i s c a l l e d the " t o t a l " approach i s an a l l i a n c e between i n t e l l e c t and i n t u i t i o n , between v e r t i c a l t h i n k i n g based on l o g i c l e a d i n g to a co n v e n t i o n a l s o l u t i o n and l a t e r a l t h i n k i n g based on i n t u i t i v e awareness l e a d i n g t o r a d i c a l s o l u t i o n s . This approach i n t e g r a t e s what C P . Snow c a l l s the "two c u l t u r e s " [1.27] and leads t o new d i s c o v e r i e s , 9 unusual s o l u t i o n s , and comprehensive understanding of the problems. In the " t o t a l " approach to c r e a t i v e d e s i g n , i l l u s -t r a t e d on F i g u r e 1.1, the engineer goes through f i v e stages [1.28, 1.2]: 1. Problem f o r m u l a t i o n , 2. Concept s y n t h e s i s , 3. C o n f i g u r a t i o n o p t i m i z a t i o n , 4. Element des i g n , and 5. Performance e v a l u a t i o n . I f i t i s i n i t i a t e d a f t e r the problem i s c l e a r l y understood and the design envelope i s e x p l i c i t l y formulated, s y n t h e s i s can lead to a number of concepts which t e n t a t i v e l y s a t i s f y the requirements of f u n c t i o n , environment and economy. Each of the concepts i s subjected to c r i t i c a l s c i e n t i f i c a n a l y s i s and judged on sound engineering p r i n -c i p l e s . For the most promising concept, an optimum c o n f i -g u r a t i o n i s devised and the elements of the c o n f i g u r a t i o n are designed using the best engineering p r a c t i c e . F i n a l l y a working model i s c o n s t r u c t e d and the performance evaluated. Throughout the d e s i g n , feedback i s used to c o r r e c t d e c i s i o n s made at any of the e a r l i e r stages. In a p p l y i n g the f i v e s t e p s , c o n f l i c t s occur between c r e a t i v e s y n t h e s i s and l o g i c a l a n a l y s i s . One d i f f i c u l t y i s t h a t the c r e a t i v e step r e q u i r e s a breadth of knowledge and understanding and an a b i l i t y to r e l a t e d i v e r s e elements, E x p e r i m e n t a l General Knowledge P e r s o n a l E x p e r i e n c e 1 F i e l d Study 10 J Step 1. F o r m u l a t i o n F o r m u l a t i o n of Design Envelope S c i e n t i f i c P r i n c i p l e s C r e a t i v e ^ A b i l i t y Concept 1 7E Concept 2 S c i e n t i f i c Knowledge f l New Informa-t i o n G e n e r a l f a c t s p r i n c i p l e s , t e c h n i q u e s h New Informa-t i o n Step 2. S y n t h e s i s E n g i n e e r i n g Judgment Step 3. O p t i m i z a t i o n E n g i n e e r i n g Judgment Proposed Design | C o n s t r u c t i o n and T e s t i n g of |_J Working Model Step 4 . D e l i n e a t i o n Step 5. E v a l u a t i o n F i g u r e 1.1 O u t l i n e of the Comprehensive Design E n g i n e e r ' s Task 11 whereas the a n a l y t i c step r e q u i r e s a depth of s p e c i a l i z e d knowledge, an a b i l i t y to use mathematics, and an a b i l i t y to r e cognize and remember s p e c i f i c f a c t s . To be e f f e c t i v e the c r e a t i v e engineer must be able to o s c i l l a t e f r e e l y between the c r e a t i v e step and a n a l y t i c a l step, between imag i n a t i o n and reason. Imagination evolves new combin-a t i o n s of ideas and reason evaluates each combination. In order to be c r e a t i v e and evolve new ideas the mind must be f r e e t o a l t e r n a t e between a l l aspects of the problem whereas i n order t o evaluate l o g i c a l l y the mind must not depart from a systematic step-by-step sequence. This c o n f l i c t between c r e a t i v e s y n t h e s i s and l o g i c a l a n a l y s i s i s r e s o l v e d by a l l o w i n g the mind complete freedom to produce i d e a s , s o l u t i o n s , p o s s i b i l i t i e s and guess work at any time w h i l e employing a system of n o t a t i o n to record a l l design i n f o r m a t i o n f o r l o g i c a l a n a l y s i s . Thus imagination i s u n r e s t r i c t e d i n the mind and l o g i c i s preserved on paper. Once s t a r t e d , the system of n o t a t i o n must be used f l e x i b l y as a guide, not d o g m a t i c a l l y as a r i t u a l . One engineering h e u r i s t i c s technique used to generate s o l u t i o n s t o problems i s to p o s t u l a t e a g e n e r a l -i z e d model of the design process i n the form of a " t r e e " [1.28]. Each s o l u t i o n to some design concept w i l l , i n g e n e r a l , g i v e r i s e to a s e r i e s of s u b s i d i a r y problems each of which has (usually) more than one p o s s i b l e s o l u t i o n . 12 The d e s i g n i s complete when a l l branches of the t r e e t e r m i n a t e . T h i s happens when the f o l l o w i n g r u l e s are f o l l o w e d : 1. When a number of a l t e r n a t i v e s o l u t i o n s are p r e -sented, any one may be accepted and the r e s t i g n o r e d . 2. A l l the problems dependent on the c h o i c e of a p a r t i c u l a r a l t e r n a t i v e s o l u t i o n , must, however, be s o l v e d . 3. A p a r t i c u l a r branch of the t r e e must be f o l l o w e d u n t i l a s o l u t i o n i s reached which does not have a dependent problem. P r o v i d e d t h a t t h i s s o l u t i o n i s the p r e f e r r e d one a t t h i s p o i n t , the branch t e r m i n a t e s . [1.28, p. 54] F a c t o r a n a l y s i s i s another i n t e r e s t i n g technique which attempts to s o l v e the b a s i c d i f f i c u l t y of combining l o g -i c a l a n a l y s i s w i t h c r e a t i v e thought [1.28, 1.29, 1.30]. T h i s technique r e q u i r e s a t a b l e or m a t r i x where a l l parameters concerned w i t h f e a t u r e s or f u n c t i o n s d e s i r e d are l i s t e d v e r t i c a l l y . A l l p o s s i b l e means of a c h i e v i n g each f u n c t i o n are l i s t e d h o r i z o n t a l l y w i t h r e f e r e n c e t o the c o n f l i c t i n g demands of the o t h e r f u n c t i o n s . The p a r t i a l s o l u t i o n s are then combined by permuta-t i o n to g i v e s e v e r a l a l t e r n a t i v e whole s o l u t i o n s . T h i s procedure i s the r e v e r s e of c o n v e n t i o n a l d e s i g n methods i n which a s i n g l e s o l u t i o n i s c o n c e i v e d as a "whole w i t h the d e t a i l s b e i n g worked out l a t e r . As the work proceeds, many more id e a s are added. Incomplete, q u e s t i o n a b l e or c o n f l i c t i n g i n f o r m a t i o n i s sub-s t a n t i a t e d by a l i t e r a t u r e s e a r c h , by c o n s u l t i n g e x p e r i e n c e d persons o r by performing experiments. New i d e a s are encour-aged by l o o k i n g a t e x i s t i n g d e s i g n s , viewing the problem from a new v i e w p o i n t , comparing the problem w i t h o t h e r s o l u t i o n s , i d e n t i f y i n g w i t h the o b j e c t being designed, f a n t a s i z i n g an i d e a l s o l u t i o n , u s i n g f r e e a s s o c i a t i o n , and b r a i n s t o r m i n g [1.14, 1.28, 1.31]. T h i s l a t t e r method i s b e s t s u i t e d t o a d e s i g n team w i t h w e l l d e f i n e d r e s p o n s i b i l i t i e s and occurs when each person u n c r i t i c a l l y r e c o r d s any i d e a or s o l u t i o n t h a t o c c u r s to him a f t e r b e i n g c o n f r o n t e d w i t h the problem, or a f t e r l o o k i n g a t examples, drawings and r e p o r t s of e x i s t i n g d e s i g n s . R e l a t i o n s h i p s between s o l u t i o n s can be c l a r i f i e d w i t h t r e n d p l o t s or new s o l u t i o n p l o t s . A t r e n d p l o t shows how shape and performance have changed over the years t o -geth e r w i t h the reason f o r the changes. A new s o l u t i o n p l o t i s a means of comparing the range of e x i s t i n g s o l u t i o n s , or new p r o p o s a l s i n r e l a t i o n t o shape or performance. These p l o t s can be used t o f i n d areas where new combinations of shape and performance can be sought. More l o g i c a l and c a r e -f u l thought i s g i v e n to aspects of the problem where no s o l u t i o n s have appeared. I f the i m a g i n a t i o n comes t o a h a l t and no s o l u t i o n seems p o s s i b l e , Jones suggests the f o l l o w -i n g procedure: 1. Write down the c o n d i t i o n s which would make a s o l u t i o n p o s s i b l e , 2. Write down a phrase d e s c r i b i n g the d i f f i c u l t y and s u b s t i t u t e a l t e r n a t i v e s f o r each word, 3. W r i t e down the consequences of not f i n d i n g a S o l u t i o n . n oo CAI [1.28, p. 64] 14 Because i t safeguards a g a i n s t wasting time on a system t h a t i s not f e a s i b l e or goes o u t s i d e the d e s i g n envelope, a continuous check t h a t the p o s s i b l e s o l u t i o n s are indeed a c c e p t a b l e i s kept up i n p a r a l l e l w i t h a l l o t h e r d e s i g n a c t i v i t y . I f an unaccept-a b l e s o l u t i o n i s d e t e c t e d work on i t ceases. From among the a l t e r n a t i v e s s y n t h e s i z e d the b e s t one i s chosen f o r o p t i m i z a t i o n and d e t a i l d e s i g n i n g . The optimum d e s i g n i s o n l y achieved when ex p e r i e n c e and i n g e n u i t y are blended w i t h d e s i g n p h i l o s o p h y , m a t e r i a l s e l e c t i o n and the p r o d u c t i o n methods a v a i l a b l e . T h i s b l e n d i n g i n i t i a l l y i n v o l v e s rough sketches and order-of-magnitude c a l c u l a t i o n s and f i n a l l y uses d e t a i l e d a n a l y s i s . The f a c t s of l i f e i n a mass-production economy make the i n t r o d u c t i o n of new concepts v e r y c o s t l y and r i s k y . I t i s n a t u r a l t o p r e f e r s t a b i l i t y and t o seek i t . T h i s p r e f e r e n c e f o r s t a b i l i t y means t h a t i n n o v a t i o n s and i n v e n t i o n s , i f they are t o become p r o d u c t i o n items, w i l l have t o f i t i n w i t h the c u r r e n t market c a p a b i l i t i e s and the e s t a b l i s h e d means of p r o -d u c t i o n , maintenance and s e r v i c i n g as w e l l as f i n a n c i a l r e -sources a v a i l a b l e {1.4, 1.32]. Where i t i s p o s s i b l e to va r y the p r o p e r t i e s o f the elements or of i n p u t s or some asp e c t s o f environment so as to e f f e c t the p r o p e r t i e s o f the system, i t i s p o s s i b l e to choose a combination o f v a r i a b l e s which y i e l d the b e s t system p e r f o r -mance. F o r the case i n which a mathematical r e l a t i o n s h i p connects o v e r a l l c o s t and the v a r i a b l e s t o be o p t i m i z e d , c a l -15 c u i u s , l i n e a r programming or dynamic programming methods are p o s s i b l e . Where v a r i a b l e s are not m a t h e m a t i c a l l y connected, o t h e r t e c h n i q u e s to f i n d the b e s t " s t r a t e g y of s e a r c h " , t h a t i s , the p a t t e r n of moves l i k e l y t o l e a d most q u i c k l y to the summit, are used [1.33]. The c r u c i a l elements and u n c e r t a i n f e a t u r e s of the optimum s o l u t i o n are i d e n t i f i e d and an attempt i s made to determine how the d e s i g n can be m o d i f i e d t o y i e l d a workable system i n case the c r u c i a l elements cannot be r e a l i z e d . The r e s u l t w i l l be a h i e r a r c h y of p o s s i b l e d e s i g n s , s t a r t i n g w i t h the most f a v o u r a b l e and p r o c e e d i n g t o l e s s f a v o u r a b l e a l t e r -n a t i v e arrangements. In cases where a c e r t a i n c r u c i a l element has few or no a l t e r n a t i v e r e a l i z a t i o n s so t h a t no adequate path of r e t r e a t i s a v a i l a b l e i n the event t h a t the element proves u n a v a i l a b l e e x p e r i m e n t a l work i s i n i t i a t e d i n o r d e r to demonstrate the f e a s i b i l i t y of t h i s element. T h i s i s to safeguard a g a i n s t f a i l u r e of the whole d e s i g n a t a l a t e r d a t e . I t i s unwise to work on some branches of the d e s i g n t r e e to the p o i n t of f i n e d e t a i l w h i l e t h e r e are s t i l l u n r e s o l v e d problems a t a 'higher' (that i s , more a b s t r a c t ) l e v e l , a l t h o u g h f o r s m a l l p r o j e c t s , the i n f o r m a t i o n r e q u i r e d may be o b t a i n e d from t e s t s on an a c t u a l p r o t o t y p e . The d e s i g n t r e e and o t h e r approaches to s y s t e m a t i c d e s i g n can be p r o f i t a b l y s t u d i e d and a p p l i e d i n e n g i n e e r i n g d e s i g n c o u r s e s . T y p i c a l of the c r e a t i v e d e s i g n p r o j e c t s under-16 taken on a graduate l e v e l i s de P e n d e r * s Ph.D. t h e s i s , Genesis  of a Machine: A P r o d u c t i o n Paper C u t t e r [1.34]. In h i s t h e s i s he d e s c r i b e s the e v o l u t i o n o f the machine from an i d e a t o an o p e r a t i n g p r o t o t y p e : The emphasis i s on the d e c i s i o n s , methods, c r i t e r i a , and r e s u l t s i n c o r p o r a t e d i n the machine r a t h e r than on a n a l y t i c a l a s p e c t s of the d e s i g n . The primary c r i t e r i a g u i d i n g the d e s i g n was t o p r o v i d e a machine more economical f o r u s e r s t o own. [ A b s t r a c t , r e f . (1.34)] The u s u a l i n d u s t r i a l approach to s m a l l engine de-s i g n i s not s y s t e m a t i c but by t r i a l and e r r o r . S o l u t i o n s are sought o n l y to urgent problems without a study of the t o t a l i t y of the d e s i g n . P r e s s u r e i s ex e r t e d on the d e s i g n e r to g et s p e c i f i c s o l u t i o n s immediately. Consequently concepts change s l o w l y and breakthroughs seldom o c c u r . Such has been the case w i t h the development o f the power saw. When the f i r s t German saws were imported i n t o B r i t i s h Columbia i n 1937, they weighed about 12 0 l b s and produced about 5 hp (rated a t 8 hp). When World War I I c u t the supply o f saws and spare p a r t s and the d e a l e r , D.J. Smith Equipment, found i t nec e s s a r y t o make h i s own u n i t s , he c o p i e d the imported saw. In 1943 he brought out a 90 l b v e r s i o n and then a l i m i t e d number of one-man c h a i n saws. By 19 45 the d e a l e r had become I n d u s t r i a l E n g i n e e r i n g L i m i t e d , Power Machinery L i m i t e d had formed, and Vancouver was the c e n t e r o f the North American c h a i n saw i n d u s t r y . 17 When they brought out the s u c c e s s f u l one-man chain saw shown on F i g u r e 1.2, Power Machinery L i m i t e d became a strong competitor w i t h I n d u s t r i a l Engineering L i m i t e d f o r the power saw market. With competition came more r a p i d progress. The problem areas on e x i s t i n g saws were i n v e s t i g a t e d by both Fig u r e 1.2 C u t t i n g w i t h one of the o r i g i n a l one man power saws companies independently. The manual rope and p u l l e y s t a r t i n g system was replaced w i t h an automatic r e c o i l rewind mechanism i n 1946. 18 When the Cox chipper chain came on the market i n 1948, i t s value i n reducing f r i c t i o n and saw blade l o a d i n g was immediately recognized. Whereas the standard chain r e q u i r e d an e x t e r n a l f o r c e to feed the t e e t h much l i k e the f o r c e r e q u i r e d t o cut w i t h the co n v e n t i o n a l t a b l e saw, the chipper chain r e q u i r e d no such f o r c e , because the s e l f - f e e d i n g a c t i o n o r i g i n a t e d from the shape of the t e e t h , as shown on Fi g u r e F i g u r e 1.3 Sketches of the c h i s e l - t o o t h ( l e f t ) and the ch i p p e r - t o o t h ( r i g h t ) chains 1.3. Because the s e l f - f e e d i n g reduced bar and chain f r i c t i o n , the need f o r a f o o l p r o o f automatic o i l i n g system, i n use sinc e about 1946, was not as c r i t i c a l . The s e l f - e n e r g i z i n g c e n t r i f u g a l c l u t c h was added t o the saws i n 1949. This c l u t c h a u t o m a t i c a l l y engaged when the engine speed reached a predetermined l e v e l and disengaged when the speed dropped below t h i s l e v e l ; the amount of pre-c o m p r e s s i o n o f t h e s p r i n g s a c t i n g a g a i n s t c e n t r i f u g a l f o r c e d e t e r m i n e d t h e e n g a g e m e n t s p e e d . B y t h i s t i m e some a t t e n t i o n w a s g i v e n t o a e s t h e t i c s . A s w e l l a s b e i n g p a i n t e d f o r t h e f i r s t t i m e , t h e u n i t s w e r e s h a p e d m o r e a t t r a c t i v e l y . A l s o e m p h a s i z e d w e r e t h e a u t o m a t i c s y s t e m s , a s s h o w n b y t h e l a s t f o u r i t e m s o f a t y p i c a l l i s t o f s p e c i f i c a t i o n s , F i g u r e 1 . 4 . S P E C I F I C A T I O N S Main Bearings ...Ball and needle - Standard malces Connecting Rod Bearings Needle and Bronze Guide Bar Alloy steel, heat treated, hard tipped Cutting Chain. Alloy steel, heat treated, chipper type General Construction Cast Magnesium Starting Mechanism Automatic recoil ^ Drive Gilmer Belt - no lubrication necessary </ Clutch Automatic ^ Chain Oiler Automatic V F i g u r e 1 .4 T y p i c a l l i s t o f c h a i n saw s p e c i f i c a t i o n s , c i r c . 1 9 5 0 * T h e G i l m e r b e l t was o n e o f s e v e r a l s p e e d r e d u c e r s u s e d t o k e e p t h e c h a i n s p e e d l o w . N o t u n t i l 1 9 5 3 h a d I n d u s t r i a l E n g i n e e r i n g L i m i t e d a d v a n c e d t h e c h a i n - c u t t e r b a r t e c h n o l o g y f a r e n o u g h t o make a d i r e c t - d r i v e c h a i n saw p r a c -t i c a l . B y u s i n g a h i g h - s p e e d c h a i n a n d s t e l l a r - t i p p e d b a r Motor Single cylinder, 2 cycle, air cooled Power 4 H.P. at 4000 R.P.M. Cylinder Aluminum, chrome plated and honed Crankshaft Forged alloy steel, machined, heat-treated and precision ground. Connecting Rod Same as above Piston Aluminum - 3 ring Carburetor Float type - Tillotson Ignition Flywheel type - Wico Lubrication Oil and gasoline mixed * S p e c i f i c a t i o n s f o r t h e P . M . " R o c k e t " c h a i n s a w , r e f . [ 1 . 3 5 ] . they e l i m i n a t e d the need f o r Gilmer b e l t s , chain d r i v e s , b e v e l gears, spur gears or other speed reducers. When I n d u s t r i a l Engineering L i m i t e d brought out t h e i r d i r e c t d r i v e chainsaw, Power Machinery L i m i t e d was behind i n t h e i r chain technology, having supported the development of a T i l l o t s o n a l l - p o s i t i o n c a r b u r e t o r . The lead gave I n d u s t r i a l Engineering L i m i t e d a name and a market which t h e i r competition could not match even w i t h the i n t r o d u c t i o n of an a l l - p o s i t i o n c a r b u r etor a year l a t e r . The a l l p o s i t i o n diaphragm carburetor w i t h a b u i l t -i n diaphragm f u e l pump ended many f u e l metering problems. When the T i l l o t s o n diaphragm f u e l pump became a v a i l a b l e i n June 19 54, Power Machinery L i m i t e d [1.36] announced t h a t the new car b u r e t o r would be s o l d a t the o p t i o n of the buyer. By November the new carburetor was standard equipment. The quick changeover can be b e t t e r understood i f one con-s i d e r s the problems encountered w i t h the two types of o l d e r c a r b u r e t o r s — t h e f l o a t type using g r a v i t y feed and the diaphragm type u s i n g a p r e s s u r i z e d f u e l tank. The f l o a t type c a r b u r e t o r operated only when u p r i g h t ; i n one design t h i s requirement was met by manually s w i v e l l i n g the carburet or when the engine was turned f o r bucking, and i n the other design by manually s w i v e l l i n g the blade and chain w h i l e keeping the engine u p r i g h t . The p r e s s u r i z e d tank type c a r b u r e t o r r e q u i r e d c o n t i n u a l adjustment because the i n l e t and o u t l e t check v a l v e s c o n t r o l l i n g the tank pressure f r e -21 q u e n t l y plugged or l e a k e d , c a u s i n g the p r e s s u r e to exceed or f a l l below the proper working p r e s s u r e . S i n c e the i n t r o d u c t i o n o f the a l l p o s i t i o n c a r b u r e t o r no major change has o c c u r r e d , although c o n t i n u a l r efinement o f d e s i g n , m a t e r i a l s , and manufacturing techniques have reduced the weight of the saw and i n c r e a s e d the speed of the engine. In 1945 when they were i n t r o d u c e d , the one-man saws weighed about 34 l b s and produced about 2 1/2 hp a t 3800 3 rpm from a 4.5 i n d i s p l a c e m e n t . Ten years l a t e r a 22 l b 3 saw produced 4 hp a t 6000 rpm from a 6,2 i n d i s p l a c e m e n t . In 1963 a 16 l b saw produced 4 1/2 hp a t 7500 rpm from a 5.8 i n d i s p l a c e m e n t . Now i n 1969 the s m a l l 6 1/2 l b saws 3 produce 2 hp a t 9000 rpm from a 2.8 i n d i s p l a c e m e n t . These t r e n d s , p l o t t e d on Graph 1.1, show t h a t e n g i n e e r s have i n c r e a s e d the power per u n i t d i s p l a c e m e n t by g r a d u a l l y r a i s -i n g the r e l i a b l e o p e r a t i n g speed although a t the expense of brake mean e f f e c t i v e p r e s s u r e . N e v e r t h e l e s s , s i n c e the power saws were i n t r o d u c e d , the method of c u t t i n g has not changed. Although the i n t r o d u c t i o n of the power saw to wood-lands o p e r a t i o n i n E a s t e r n Canada dates from 1929 when a 4 hp German machine weighing 80 l b s was t e s t e d , i t was not u n t i l the one-man saw became commercially a v a i l a b l e t h a t the use of the power saw became g e n e r a l . For example, Brown [1.37] r e p o r t s t h a t i n the pulpwood l i m i t s o f E a s t e r n Canada d u r i n g the 1950-51 season l e s s than 4% of the wood was c u t , 22 9000. SPEED (RPM) 3000 BMEP (PSI) 50i-40 30 20 j i i ^ DRY WEIGHT (LBS) 120r 60 -OB— 1935 • TWO MAN * . \ /ONE MAN LIGHTWEIGHTS—• 1945 1955 YEAR 1965 1975 Graph 1.1 Power Saw Performance Trends w i t h power saws. This increased to 55% during the 1954-55 season and to 97% during the 1957-58 season. Over the same e i g h t year p e r i o d the production went up from 1.67 to 2.44 cords per man per day, l a r g e l y due t o the extended use of the power saw. Now because the t o t a l i t y of the wood c u t t i n g o p e r a t i o n i s being considered^a new r e v o l u t i o n i s sweeping the pulpwood l o t s of Eastern Canada. Instead of f e l l i n g pulpwood t r e e s and then bucking them i n t o 8 f o o t lengths w i t h a p o r t a b l e power saw, the operators are t u r n i n g to a semi-mechanized or t o t a l l y mechanized h a r v e s t i n g system. In the semi-mechanized system the t r e e s are f e l l e d and topped w i t h power saws; f u r t h e r processing i s done by machines. In the t o t a l l y mechanized system shears mounted on t r a c t o r s or s p e c i a l h a r v e s t i n g machines delimb, c u t , and buck the t r e e s . The speed a t which the t o t a l l y mechanized system i s expected to be introduced i n the l i m i t e d pulpwood areas i n Eastern Canada, i s shown by the f o l l o w i n g s t a t i s t i c s [1.38]: whereas only 8% of the pulpwood produced i n 1966 was harvested by the t o t a l l y mechanized system, by 1970 t h i s p r o p o r t i o n i s f o r e -c a s t to be 20% and by 1975 i t i s to be 75%. As an example of the f u l l y mechanized c u t t i n g system, the t r e e harvester of F i g u r e 1.5 walks up to a t r e e , wraps a delimbing head around the trunk and sends the delimbing head f l y i n g up the t r e e r i d i n g on a t e l e s c o p i n g mast. As the head moves up i t removes a l l branches and shears the top 24 i The operator places open bottom shear on the tree at ground level. He then en-circles the tree with the delimbing arms. As the tree decreases in diameter, cutting edges follow. When the top diameter measures about three inches, operator tops the tree by actuating the hydrau-lically operated topping shear. After trunk is sheared at the bottom, the tree ( rests on the shears cupped by the curved , shoe that holds it in position while the operator r swings it to bunching position. The operator i tilts the mast forward, opens the delimber grapple jaws and the tree drops to the ground. Figure 1.5 T y p i c a l t r e e h a r v e s t i n g machine [1.39] 25 o f f a t any d e s i r e d p o i n t . The head then r e t u r n s p a r t way and h o l d s the trunk w h i l e some l a r g e r shears s n i p the t r e e o f f a t ground l e v e l . The head and bottom shears d e p o s i t the t r e e on the ground i n a p r e - e s t a b l i s h e d p a t t e r n and the c y c l e i s complete. Although t h i s machine i s capable of 80-100 cords per day, i n p r a c t i c e i t has averaged 22 cords per man-day. T h i s p r o d u c t i o n compares w i t h 2.6 cords per man-day f o r a good power saw t i m b e r j a c k and 1.67 cords per man-day f o r a good axeman [1.37, 1.40, 1.41]. These p r o -d u c t i o n f i g u r e s c o u l d suggest the v a l u e of the " t o t a l " approach to the problem of h a r v e s t i n g wood. Even though the technology of shear c u t t i n g i s not new, the h a r v e s t i n g systems were not developed u n t i l a l l h a r v e s t i n g requirements were c o n s i d e r e d as one concept. One wonders what the out-come would have been had the " t o t a l " approach been a p p l i e d b e f o r e the power saw was i n t r o d u c e d t o the p r o f e s s i o n a l l o g g e r . Would the power saw be now r e l e g a t e d t o the c a s u a l user? The v a l u e of a p p l y i n g the " t o t a l " approach to wood h a r v e s t i n g i s e v i d e n t from the b r i e f h i s t o r y j u s t g i v e n . How the f o r m u l a t i o n of a d e s i g n envelope of a power saw engine was based on the " t o t a l i t y " o f the problem i s the s u b j e c t of the next s e c t i o n . 26 1 . 2 S p e c i f i c a t i o n s f o r t h e D e s i g n E n v e l o p e A n a c c u r a t e f o r m u l a t i o n o f t h e d e s i g n p r o b l e m i n t h e l i g h t o f a l l t h e c o m p l e x a n d c o n f l i c t i n g r e q u i r e m e n t s o f r e a l l i f e i s a n i m p o r t a n t f i r s t s t e p i n c r e a t i v e l y s o l v i n g a n y t e c h n i c a l p r o b l e m . A s l o n g a s t h e f i r s t s t a g e o f t h e a n a l y s i s i s i n c o m p l e t e , a n d t h e p r o b l e m s a r e n o t c o r r e c t l y s t a t e d , i t i s u s e l e s s t o p r o f f e r s o l u t i o n s . A n d b e f o r e t h e p r o b l e m s c a n b e c o r r e c t l y p o s e d , a n e x a c t d e s c r i p t i o n o f t h e e x p e c t e d r e q u i r e m e n t s a n d i m p o s e d c o n d i t i o n s m u s t b e g i v e n . T h e a n a l y s i s o f w h a t s a w o p e r a t o r s e x p e c t i n a c h a i n s a w , w h a t g o v e r n m e n t g u i d e l i n e s s u g g e s t a n d e n f o r c e , a n d w h a t f a c t o r s e x p e r i e n c e h a s s h o w n t o b e i m p o r t a n t , r e s u l t e d i n t h e f o l l o w i n g l i s t o f c h a r a c t e r i s t i c s w h i c h w e r e c o n s i d e r e d t o b e p a r t o f t h e d e s i g n e n v e l o p e : 1 . s p e e d a n d p o w e r , 2 . e n v i r o n m e n t a l c o n t r o l , 3 . a l l o w a b l e n o i s e l e v e l s , 4 . a l l o w a b l e v i b r a t i o n l e v e l s , 5 . s p a r k a r r e s t o r r e g u l a t i o n s , 6 . s a f e t y p r e c a u t i o n s , 7 . i m p o r t a n c e o f c o s t , a p p e a r a n c e , r e l i a b i l i t y , w e i g h t , e a s e o f s t a r t i n g , e a s e o f h a n d l i n g , e a s e o f m a i n t e n a n c e , l o w f u e l a n d o i l c o n s u m p t i o n , a n d l o n g o p e r a t i n g l i f e . W a l l a c e [ 1 . 1 1 ] s u g g e s t s t h a t t h e d e s i g n e r s h o u l d a l w a y s c o n s i d e r t h e w o r s t s e t o f c i r c u m s t a n c e s w h i c h c a n o c c u r 27 -and design a c c o r d i n g l y because "sooner or l a t e r any machinery may be loaded to the l i m i t of i t s c a p a b i l i t i e s " . [1.11, p. 23]. Even though the worst set of circumstances should be con-s i d e r e d , a good f o r m u l a t i o n of the design envelope w i l l i n -sure a g a i n s t overdesigning. Before undertaking a new design p r o j e c t i t i s of course necessary to know i f a market e x i s t s f o r the proposed item. I f the item i s to compete w i t h e x i s t i n g u n i t s , i t must possess some unique c h a r a c t e r i s t i c h i g h l y d e s i r e d by pros-p e c t i v e u s e rs. Not only must t h i s c h a r a c t e r i s t i c be s u i t a b l e f o r the environment i n which i t w i l l operate, but i t must a l s o be economically and a e s t h e t i c a l l y a t t r a c t i v e . In a d d i -t i o n to possessing a unique c h a r a c t e r i s t i c , the new item must compare favourably w i t h f e a t u r e s and c h a r a c t e r i s t i c s of e x i s t i n g u n i t s . I f the market i s very c o m p e t i t i v e , i t may be necessary to design a u n i t f o r a s p e c i f i c a p p l i c a t i o n before i t becomes s a l e a b l e . To achieve a low-cost product, the design should always be r e l a t e d t o mass-production techniques. A simple, mass-produced p a r t w i l l c o s t l e s s to make than a manually machined p a r t . I f i t can be made and assembled on an auto-matic assembly l i n e , a new saw can have a b r i g h t f u t u r e . Because how and where the product i s used determines many of the requirements, a d e c i s i o n to design the saw f o r the c a s u a l user was made e a r l y i n the design study. The machine was to be of s p e c i f i c i n t e r e s t to 4 groups of 28 people who r e q u i r e a small p o r t a b l e d e v i c e : 1. t r e e pruners such as o r c h a r d i s t s , gardeners, 2. c o n s t r u c t i o n workers such as c a r p e n t e r s , plumbers, e l e c t r i c i a n s , 3. d e m o l i t i o n crews, 4..casual operators such as campers, farmers, hunters. By assuming th a t the time between cuts i s independent of the s i z e of the cut and power, and by u s i n g average values of c o s t , wages, s p e c i f i c c u t t i n g r a t e s , and r a t i o s of c u t -t i n g t i m e - t o - i d l e time, i t was p o s s i b l e to set up an equation l i n k i n g cost to the s i z e of cut and power s u p p l i e d . More s p e c i f i c a l l y , the f o l l o w i n g assumptions were used: 1. a c a p i t a l c o s t of s i x t y d o l l a r s per horsepower (hp),* a working load of "N" days per year, and a d e p r e c i -a t i o n i n "W" working days w i t h 6% annual i n t e r e s t , = (60) (hp) | (.06) (60) (hp) W N 2. an o p e r a t i n g c o s t equal to 1.3 times the annual d e p r e c i a t i o n c o s t 11.42] (1.3)(60)(hp) ] W ' 2 3. an average s p e c i f i c c u t t i n g r a t e (SCR) of 3 i n / sec-hp {1.43] . *Based on the l i s t p r i c e f o r Canadian 270 w i t h 30 i n c h bar and c h a i n , A p r i l 1, 1964. 4. a 1:3 r a t i o of c u t t i n g t i m e - t o - i d l e time f o r a 5 hp machine i n 14 i n diameter timber [1.44], j c u t t i n g time = (|^ ;) A, i d l e time = 3 g ^ P ) A = 40J , 5. an operator's wage of t h i r t y d o l l a r s a day. Adding the d e p r e c i a t i o n , i n t e r e s t , o p e r a t i n g expenses and wages, the formula f o r the d a i l y c o s t i s : COST = 30. + 3 * 6 N h P + 1 3 8 w h P [$/day] Taking the c y c l e time to be equal t o the sum of c u t t i n g time based on the assumed s p e c i f i c c u t t i n g r a t e and i d l e time which i s assumed to be constant, the production r a t e equation i s : RATE = jArea/cycle) = A { inf. (time/cycle) a sec 3 T p + 4 0 where A i s the area i n sq i n per cut. The c o s t of generating a surface i s obtained by d i v i d i n g the cost by production r a t e : PRODUCTION COST - 4™ + + i£L + ^ 1 + I ^ J E + 1.6 r $ W 1000 i n 2 30 The equation f o r optimum power based on minimum c o s t i s obtained by d i f f e r e n t i a t i n g the above equation and s e t t i n g the r e s u l t equal to zero: optimum 14.4 + 552 NA WA For t r e e s and round wood the equation becomes > _ diameter ^"optimum Jl8.3. T N 702 W This equation i s p l o t t e d on Graph 1.2. I f the pruner cuts branches t h a t average 3 i n diameter, or i f the carpenter cuts boards t h a t average 1 x 8 2 i n , or i f the farmer averages 7 i n between c u t s , then a 1 hp saw w i l l be the l e a s t expensive s i z e . As w e l l as c o s t i n g more to purchase and operate, a l a r g e r machine i s l e s s f l e x i b l e to handle and harder to c o n t r o l . Below 1 hp a chain saw may become more of a toy than a t o o l , e s p e c i a l l y s i n c e 50% of the brake horsepower never reaches the c u t t i n g p o i n t but i s absorbed by the sproc-k e t , c h a i n and guide-bar [1.43].' The need f o r ensuring t h a t t r a n s m i s s i o n l o s s e s on a small saw are kept to a minimum and t h a t the maximum amount of engine power i s a v a i l a b l e f o r a c t u a l l y c u t t i n g the wood, i s evident from these c o n s i d e r a t i o n s . 31 0 , 5 10 15 TREE DIAMETER ( i N ) Graph 1.2 Optimum power as a f u n c t i o n of t r e e s i z e The engine speed should be as low as convenient and the torque as high as p r a c t i c a l . In a d d i t i o n a curve of the power as a f u n c t i o n of speed should be f l a t . The f l a t power curve ensures t h a t the saw cuts at a constant r a t e over a wide speed range. This s p e c i f ic a t i o n ' ^ i s e s p e c i a l l y s i g n i f i c a n t f o r c a s u a l users who l a c k the experience r e -q u i r e d t o keep the saw running a t a constant speed even i f they knew what the optimum speed was. U s u a l l y c a s u a l users do not cut wood i n extremes of weather. Except i n s p e c i f i c areas and i s o l a t e d cases the saw w i l l not be used i f the temperature drops below 0° F or goes above 100° F. L i k e w i s e i t s use i n snow, or heavy r a i n w i l l be q u i t e l i m i t e d . Optimum power i s not the only performance s p e c i f i -c a t i o n r e q u i r e d ; the chain speed or the s h a f t torque must a l s o be s p e c i f i e d . The values s p e c i f i e d w i l l depend on the kinematic r a t i o s of the chain and sprocket, the c o n s t r u c t i o n of the c h a i n and of the t e e t h , and the p h y s i c a l p r o p e r t i e s of the wood. To approach the optimum combination of f a c t o r s , the author set up a s e r i e s of t e s t s on t y p i c a l chain saws. The data f o r each t e s t i n c l u d e d the time r e q u i r e d by each c u t , the area of the c u t , the type of work, the engine speed, and the s p e c i f i c a t i o n of the c h a i n , bar and sprocket. Power was obtained from engine performance curves drawn from dynamometer data taken before and a f t e r the t e s t . The apparatus i s shown on F i g u r e 1.6 and the data i s i n Appendix I. The f o l l o w i n g v a r i a b l e s were i n v e s t i g a t e d : 1. types of wood - maple, hemlock, and cedar, 2. c h a i n p i t c h e s - .375, .404, and .500 i n , 3. sprocket s i z e s - 7, 8, and 9 t o o t h 4. j o i n t s - .025, .030, and .040 i n , 5. bar lengths - 15 i n and 2 4 i n , 6. types of saw - d i r e c t d r i v e and gear d r i v e , 7. speed range - 4,500 - 7,000 rpm. F i g u r e 1.6 Apparatus used i n the c h a i n speed t e s t s The r e s u l t s , drawn on Graphs 1.3 to 1.9, l e d to the f o l l o w -i n g c o n c l u s i o n s : 1. The minimum s p e c i f i c energy r e q u i r e d to cut hemlock 2 was 1,600 i n - l b / i n and to cut maple i t was 3,700 i n - l b / i n 2 (Graph 1.3). The minimum energy occurred at the lowest speed t e s t e d and c o i n c i d e d w i t h the speed f o r most r a p i d c u t t i n g (Graph 1.5). 2. When c u t t i n g hemlock, the s p e c i f i c energy was not a f f e c t e d very much by the sprocket s i z e but when c u t t i n g maple, the s p e c i f i c energy was lower f o r the s m a l l e r sprocket (Graph 1.3). 3. Because i t precedes the c u t t e r . t o o t h i n t o the k e r f , the depth gauge t o o t h determines the depth of c u t or " b i t e " ( F i g u r e 1.3). The d i s t a n c e the depth gauge t e e t h are below the c u t t e r t e e t h i s known as j o i n t . The t e s t s showed t h a t the minimum j o i n t produced the most e f f i c i e n t c u t s (Graph 1.4). 4. The s h o r t e r bar c u t s f a s t e r than the l o n g e r one (Graph 1.6). 5. The c u t t i n g r a t e f o r cedar was o n l y - s l i g h t l y l e s s than t h a t f o r hemlock but about double t h a t f o r maple (Graph 1.7). 6. F o r the gear d r i v e saw, the c u t t i n g r a t e depended c on the number of t e e t h p a s s i n g a g i v e n p o i n t (Graph 1.8). 7. Although the gear d r i v e w i t h a 24 i n bar c u t s l i g h t l y f a s t e r than the d i r e c t d r i v e w i t h the same l e n g t h bar, i t c u t 15% slower than the d i r e c t d r i v e w i t h a 15 i n bar (Graph 1.9). V i b r a t i o n l e v e l s must a l s o be s p e c i f i e d t o ensure t h a t the o p e r a t o r w i l l not e x p e r i e n c e damaging v i b r a t i o n l e v e l s when h a n d l i n g the saw. Prolonged exposure to e x c e s s i v e v i b r a t i o n produces a v a s c u l a r d i s t u r b a n c e o f the hands known as Raynaud's phenomenon, air-hammer d i s e a s e , or "white f i n g e r s " . During a v a s c u l a r d i s t u r b a n c e b l o o d 35 5000 4000 3000 2000 HEMLOCK .025 .375 PITCH 15 IN BAR 10001 5000 6000 S P E E D (RPH) 7000 5000 B— X 4000 30001— 2000 1000' 5000 6000 S P E E D (RPH) Graph 1 3 Impdrtance of sprocket Graph 1.4 Importance of j o i n t s i z e 10 7 TOOTH ,375 PITCH ,040 JOINT 15" BAR 3000 Graph 1.5 6000 SPEED (RPI'i) C u t t i n g r a t e s 7000 5000 6000 7000 SPEED (P.PC) . Graph 1.6 Importance of bar length ' 10 8 TOOTH .404 PITCH .025 JOIMT 24 IN BAR 8 TOOTO .375 PITCH .040 JOINT 15 IN BAR MAPLE I 1 „„. • ••• """" 5000 6000 • . .  SPEED (RPil) Graph 1.7 Importance of wood species 7000 36 , 7 TOOTH -.500 PITCH 24 IN BAR 9 TOOTH .404 PITCH 2 4 IN BAR 7 TOOTH . 404 PITCH! 15 IN BAR HEMLOCK. . 030 J'JI 3:1 CLA;-RLDUC: 60M 7000 SPEED (P\PM) Graph 1.8 S p e c i f i c c u t t i n g r a t e Graph 1.9 S p e c i f i c energy as a f u n c t i o n of chain speed 37 c i r c u l a t i o n d e c r e a s e s s i g n i f i c a n t l y t o t h e e x t e n t t h a t t h e f i n g e r s t u r n w h i t e , b e c o m e s t i f f , a c h e , l o s e t h e i r f e e l i n g , a n d b e c o m e u s e l e s s [ 1 . 4 5 ] . T h i s c o n d i t i o n i s o n l y t e m p o r a r y , a l t h o u g h o n c e t h e y a r e d a m a g e d t h e h a n d s w i l l n e v e r a g a i n b e n o r m a l a n d t h e s p a s m s may b e t r i g g e r e d b y c o n d i t i o n s o t h e r t h a n v i b r a t i o n , s u c h a s e x p o s u r e t o c o l d . D u r i n g some c o o l a n d damp d a y s o n t h e c o a s t a l a r e a s o f B r i t i s h C o l u m b i a , 25%* o f t h e l o g g e r s i n a p a r t i c u l a r l o c a t i o n may e x p e r i e n c e t h i s p h e n o m e n o n . Due t o t h e t e m -p o r a r y n a t u r e o f t h e c o n d i t i o n a d a y o r t w o away f r o m t h e p o w e r s a w , o r a c h a n g e i n w e a t h e r c o n d i t i o n s w i l l b e s u f f i -c i e n t t o a l l o w t h e f i n g e r s t o r e t u r n t o n o r m a l . I n A u s t r a l i a , a m e d i c a l s t u d y b y G r o u n d s [ 1 . 4 6 ] s h o w e d t h a t i n a g r o u p o f 22 t i m b e r f e l l e r s u s i n g c h a i n s a w s , R a y n a u d ' s p h e n o m e n o n o c c u r r e d i n 20 o f t h e m . I n a l l b u t o n e o f t h e s e 20 c a s e s , t h e f i r s t t r o u b l e o c c u r r e d f r o m 1 t o 6 y e a r s a f t e r t h e y s t a r t e d u s i n g c h a i n s a w s . O n c e a f f l i c t e d , t h e s e men t y p i c a l l y e x p e r i e n c e d i n t e r m i t t e n t p a i n f u l p a l l o r o f t h e f i n g e r s , w h i l e d r i v i n g t h e i r c a r s , w h i l e w o r k i n g o r h u n t i n g i n c o l d w e a t h e r , o r w h e n w a t c h i n g f o o t b a l l . T h i s 91% i n c i d e n c e o f t h e d i s e a s e a f t e r a n a v e r a g e e x p o s u r e o f o n l y 3 1 / 2 y e a r s i s i n d i c a t i v e o f t h e s e v e r i t y o f t h e v i b r a t i o n p r o b l e m . N o t o n l y a r e t h e m e d i c a l a u t h o r i t i e s a w a r e o f t h i s d a n g e r , b u t l o g g e r s t h e m s e l v e s * U n o f f i c i a l s t a t i s t i c f r o m t h e W o r k m a n ' s C o m p e n s a t i o n B o a r d O f f i c e , V a n c o u v e r , B r i t i s h C o l u m b i a . are b e g i n n i n g t o r e a l i z e the e x t e n t of the d i s a b l i n g and permanent damage t h a t can occur from h a n d l i n g the c h a i n saws e s p e c i a l l y the powerful l i g h t w e i g h t ones. In May 1968, a group of l o g g e r s i n Washington S t a t e went on s t r i k e t o pro-t e s t the use of saws they f e l t were v i b r a t i n g e x c e s s i v e l y . In g e n e r a l t h e r e i s a r e l a t i o n s h i p between the nature o f v i b r a t i o n and the i n c i d e n c e of d i s e a s e : The evidence i n g e n e r a l suggests t h a t i f any t o o l produces h i g h amplitudes a t the lower f r e q u e n c i e s o f , f o r example, 40 to 125 c y c l e s per second (2,400 to 7,500 rpm) , i t i s l i k e l y t o produce Ray-naud's phenomenon, p a r t i c u l a r l y i f i t i s i n con-t i n u a l use . . . the s a l i e n t f a c t o r i s not so much the t o o l , as the heaviness of the work expressed i n terms of speed of working e x e r t i o n , and g r i p r e q u i r e d . [1.46, p. 272] Ground s t a t e s t h a t : the damage done to the v a s c u l a t u r e of the hands bears some r e l a t i o n t o the energy absorbed. The energy E of a wave motion of frequency F and am-p l i t u d e A i s g i v e n by the e q u a t i o n E = KA2F2 where K i s a c o n s t a n t . On t h i s assumption, the noxious e f f e c t s o f a v i b r a t i n g t o o l w i l l i n c r e a s e g r e a t l y w i t h i n c r e a s i n g frequency, u n t i l a l i m i t i s reached beyond which the s k i n w i l l f a i l to conduct the v i b r a t i o n , a n d i f the handles are a p p r o p r i a t e l y i n s u l a t e d t h i s l i m i t w i l l be lower. [1.46, p. 272] The engine v i b r a t i o n s are the r e s u l t of p e r i o d i c f o r c e s a c t i n g on the mass of the machine. The p r e s e n t t r e n d to l i g h t w e i g h t saws has decreased the v i b r a t i n g mass w i t h -out d e c r e a s i n g the p e r i o d i c f o r c e to the same e x t e n t . Conse q u e n t l y the e x p e c t a t i o n i s t h a t the amplitude of v i b r a t i o n should i n c r e a s e . But because the newer saws are designed t o o p e r a t e a t h i g h e r s p e e d s , t h e a m p l i t u d e may n o t h a v e i n c r e a s e d w h i l e t h e e n e r g y i m p a r t e d t o t h e m a c h i n e p r o b a b l y h a s . T h i s e n e r g y u l t i m a t e l y d e t e r m i n e s t h e a m o u n t o f damage d o n e t o t h e v a s c u l a t u r e o f t h e h a n d s . T h o m p s o n [ 1 . 4 4 ] a t M c C u l l o c h C o r p o r a t i o n a l s o i n -v e s t i g a t e d t h e e f f e c t s o f c h a i n saw v i b r a t i o n o n o p e r a t o r s h e a l t h . He c o n c l u d e d : 1 . T h e r e i s d a n g e r o f p h y s i c a l i n j u r y t o t h e h a n d s a n d a r m s f r o m l a r g e a m p l i t u d e saw v i b r a t i o n s a t f r e q u e n c i e s a b o v e 1 0 , 0 0 0 r p m . 2 . H i g h s p e e d v i b r a t i o n c a n b e t o l e r a t e d f r o m a h e a l t h s t a n d p o i n t i f t h e a m p l i t u d e i s l o w e n o u g h . 3 . D i s a g r e e a b l e v i b r a t i o n s a n d i n j u r i o u s v i b r a t i o n s a r e n o t n e c e s s a r i l y t h e same . . . T h e r e a s o n s a w s h a v e n o t c a u s e d m o r e i n j u r y a p p e a r s t o b e b e c a u s e (1) t h e r e l a t i v e l y l o w s p e e d o f m o s t s a w s a n d (2) t h e f a c t t h a t t h e o p e r a t o r i s c o n t i n -u a l l y c h a n g i n g h i s g r i p , a l t e r i n g h i s b o d y p o s i t i o n a n d o p e r a t i n g t h e saw i n t e r m i t t e n t l y . [ 1 . 4 4 , p . 8] He s u g g e s t e d t h a t f o r c o n t i n u o u s o p e r a t i o n t h e v e l o c i t y s h o u l d b e b e l o w . 7 5 i p s ; a t 1 0 , 0 0 0 cpm t h e p e r m i s s i b l e a m p l i t u d e w o u l d b e . 0 0 1 i n . He c o m p a r e d t h i s t o t h e R u s s i a n p e r m i s s i b l e l i m i t w h i c h i s . 0 0 3 2 i n a t 5 , 5 0 0 cpm w i t h a m a n d a t o r y 5 - 1 0 m i n r e s t p e r i o d a f t e r 4 5 - 5 0 m i n o f c o n t i n u o u s w o r k . T h i s l i m i t , T h o m p s o n ' s l i m i t a n d t h e damage l i m i t f o r c o n t i n u o u s o p e r a t i o n i s d r a w n o n G r a p h 1 . 1 0 . T h e n e c e s s i t y f o r r e s t p e r i o d s i s i m p e r a t i v e f o r t h e l i g h t w e i g h t s a w s a s t h e y a r e r u n f o r a g r e a t e r p o r t i o n o f a working day. Then a l s o , they are f r e q u e n t l y used a t h i g h speeds; f o r example d u r i n g l i m b i n g , the op e r a t o r may open the t h r o t t l e wide and use the machine • D • - D AMPLITUDE OF SAWS TESTED AT IDLING SPEED D AMPLITUDE OF g SAWS TESTED AT OPERATING D S "EED • D * : ° R Co/v'f7w,','*''''i... • L I M I T SET IN RUSSIA 1,Juous £••'•> BR^ioN  2000 4000 FREQUENCY (CPM) L I M I T SUGGESTED BY THOMPSON. ^ m " ™ ^ o o T ™ l ^ B ^ o o o ^ , , ^ 10000 Graph 1.10 V i b r a t i o n damage l e v e l s as a f u n c t i o n o f frequency as an axe. Not o n l y do the saws run f a s t e r but they a l s o r e q u i r e l e s s time f o r a c u t . T h i s means t h a t the o p e r a t o r makes more cu t s per day and more c u t s r e q u i r e more c o n t r o l and p r e s s u r e on the handles. No s t u d y o f e n g i n e v i b r a t i o n w o u l d b e c o m p l e t e w i t h -o u t a t l e a s t a c u r s o r y a n a l y s i s o f v i b r a t i o n c a u s e s . I n a p o w e r saw m o s t o f t h e v i b r a t i o n s a r e c a u s e d b y e n g i n e u n -b a l a n c e , p i s t o n c l e a r a n c e s , a n d r o u g h c u t t i n g c h a i n s . M a n u -f a c t u r i n g a n d d e s i g n t o l e r a n c e s d e t e r m i n e p i s t o n c l e a r a n c e s a n d c h a i n o p e r a t i o n , b u t t h e e n g i n e u n b a l a n c e i s a n i n h e r e n t c h a r a c t e r i s t i c o f t h e s i n g l e c y l i n d e r t w o - s t r o k e e n g i n e . T h e r e c i p r o c a t i n g m o t i o n o f t h e p i s t o n s e t s u p a n u n b a l a n c e a l o n g t h e p i s t o n c e n t e r l i n e . T h e u n b a l a n c e i n t h i s d i r e c t i o n c a n b e l a r g e l y e l i m i n a t e d b y a d d i n g a c o u n t e r -w e i g h t o n t h e c r a n k s h a f t . B u t t h i s c o u n t e r w e i g h t s e t s u p a n u n b a l a n c e i n a p l a n e p e r p e n d i c u l a r t o t h e o r i g i n a l p i s t o n d i r e c t i o n . T h u s t h e a d d i t i o n o f c o u n t e r w e i g h t s d e c r e a s e s t h e a m p l i t u d e o f v i b r a t i o n o n o n e p l a n e b u t i n c r e a s e s i t i n a n o t h e r . A s e r i e s o f t e s t s w e r e p e r f o r m e d b y t h e a u t h o r t o d e t e r m i n e t h e e f f e c t o f a c h a n g e i n t h e c o u n t e r w e i g h t s i z e o n v i b r a t i o n l e v e l s . I n o n e t e s t , 4 s i m i l a r s a w s w i t h v e r t i c a l c y l i n d e r s w e r e u s e d ; t h e y w e r e i d e n t i c a l e x c e p t f o r t h e c o u n t e r b a l a n c i n g m a s s w h i c h v a r i e d f r o m 197 g r a m s t o 24 8 g r a m s . T h e 197 g r a m m a s s b a l a n c e d 53% o f t h e r e c i p r o -c a t i n g u n b a l a n c e a n d t h e 249 g r a m m a s s b a l a n c e d 76% o f t h e u n b a l a n c e . I n a n o t h e r t e s t 6 s a w s w e r e c o m p a r e d . F o r b o t h t e s t s r o o t - m e a n - s q u a r e v i b r a t i o n l e v e l r e a d i n g s w e r e t a k e n w i t h t h e saw c u t t i n g a n d w i t h i t u n l o a d e d e i t h e r w i t h o r w i t h o u t a b a r a n d c h a i n . F r o m t h e d a t a o b t a i n e d ( shown i n 42 Appendix I I ) , Graphs 1.10 - 1.16 were drawn and the f o l l o w -i n g c o n c l u s i o n s were made: 1. The v i b r a t i o n amplitude v a r i e s from .013 t o .030 i n and i s i n the area where damage to the hands w i l l occur i f saws are used c o n t i n -uously without the p r o t e c t i o n a f f o r d e d by gloves (Graph 1.10) . 2. The e f f e c t of l a r g e r counterweights i s to lower perp e n d i c u l a r v i b r a t i o n s i n the re a r handle, and t o r a i s e both h o r i z o n t a l and v e r t i c a l v i b r a t i o n s i n the f r o n t handle (Graph 1.11). 3. The c u t t i n g a c t i o n c o n t r i b u t e s to the v i b r a t i o n amplitudes i n both planes but e s p e c i a l l y t o the h o r i z o n t a l component (Graph 1.12). 4. The guide bar lowers the h o r i z o n t a l component of c y l i n d e r v i b r a t i o n but does not a f f e c t the v e r t i c a l component, probably because by moving the center of g r a v i t y forward, the a d d i t i o n a l mass increase s the r a d i u s from the center of r o t a t i o n t o the center of the accelerometer, negating the e f f e c t of the increased mass (Graph 1.13). The change i n the v i b r a t i o n i s more pronounced than i n d i c a t e d because the v i b r a t i o n s caused by the c u t t i n g a c t i o n were not accounted f o r . 5. Whereas i n the c y l i n d e r the v e r t i c a l v i b r a t i o n i s independent of i n i t i a l p i s t o n unbalance, i n the handle the p e r p e n d i c u l a r v i b r a t i o n i s dependent on the amount of p i s t o n unbalance. I f the p i s t o n i s l i g h t l y overbalanced so t h a t the unbalance i s mainly h o r i z o n t a l , the a d d i t i o n of the bar r e -duces the p e r p e n d i c u l a r amplitude, and i f the p i s -ton i s balanced normally so t h a t the v e r t i c a l and h o r i z o n t a l imbalance are n e a r l y equal, the bar does not change the amplitude (Graph 1.14). 6. V i b r a t i o n l e v e l s reach a minimum value around 6,000 rpm and are very high d u r i n g engine i d l e , p o s s i b l y due t o e r r a t i c combustion (Graph 1.15). 7. Contrary to e x p e c t a t i o n s , the v i b r a t i o n i n s u l a -t i o n rubber on the handles a c t u a l l y increased the v i b r a t i o n amplitudes (Graph 1.16). I t i s obvious t h a t the optimum counterweight w i l l be a compromise between keeping e i t h e r the h o r i z o n t a l or the v e r t i c a l v i b r a t i o n s low. The f o r e g oing r e s u l t s suggest t h a t the l a r g e s t unbalance should be i n a plane w i t h the h i g h e s t i n e r t i a or i n a plane where the v i b r a t i o n i s l e a s t d i s t u r b i n g . In a c h ain saw a p p l i c a t i o n the highest i n e r t i a i s u s u a l l y i n the d i r e c t i o n of the bar and the l e a s t d i s -t u r b i n g v i b r a t i o n s are p e r p e n d i c u l a r to the arm. No c h ain saw e x h i b i t s o n l y t r a n s l a t i o n a l v i b r a t i o n s ; a l l e x h i b i t a r o c k i n g motion as w e l l . Indeed when the unbalanced f o r c e i s l o c a t e d at some d i s t a n c e from the 44 MASS BALANCED (%) - ' I1ASS BALANCED (%) Graph 1.11 V i b r a t i o n amplitude w h i l e c u t t i n g versus counter-weight s i z e Graph 1.12 V i b r a t i o n amplitude w h i l e c u t t i n g and running unloaded 50 60 70 w50 60 70 MASS BALANCED (%)' HASS BALANCED (%) ? 02 -L i J .03 50 1 1 REAR HANDLE VERTICAL .02 -CUTTING Graph 1.13 L U 1=1 S= 01 .0 NOT CUTTING^  CUTTING *m -60 70 50 60 70 MASS BALANCED (I) MAGS BALANCED (%) E f f e c t of adding bar on the amplitude w i t h s e v e r a l counterweights .03 CYLINDER VERTICAL .02 -ijj r a .01 WITHOUT BAR CUTTING V.'ITH BAR •03|— LONGITUDINAL E U J ca I— .021-H A G G H _ 1 CX-• 0 1 r * E . A J 46 WITHOUT BAR CU I IlilG 0 ' A H FRONT HANDLE RESULTANT OF VERT• AND LONG C U T T I N G WITHOUT BAR C U T T I N G WITHOUT BAR Graph 1.14 E f f e c t of the bar on v i b r a t i o n amplitude .02 0 'REAR HANDLE 1 PERPENDICULAR — " • • — - — —fi dm 2 4 6 S P E E D (RPM x 10"3) .061] "ILI" l I i CYLINDER V E R T I C A L S P E E D (RPM x 10"J) .oc .04 .02 0 CYLINDER LONGITUDINAL 4 6 S P E E D (RPM x 10~J) !i P L L J (RPM / 10 J) Graph 1.15 E f f e c t of speed on v i b r a t i o n amplitude c e n t e r of i n e r t i a , a l a r g e r o c k i n g couple may be s e t up. T h i s f a c t can be used t o advantage when the unbalanced f o r c e i s l a r g e i n o n l y one pla n e . In such a s i t u a t i o n t h e r e e x i s t s a p o i n t which undergoes v e r y l i t t l e t r a n s l a t i o n a l motion„ .03 ~ J)2 Q_ < 1 REAR HANDLE - PERPENDICULAR TO GRIP --NO BAR mBB-a»««*'s WITHOUT INSULATION WITH RUBBER Graph 1.16 E f f e c t of rubber i n s u l a t i o n o f v i b r a t i o n amplitude F i n d i n g the optimum handle p o s i t i o n c e r t a i n l y begins w i t h an a n a l y s i s o f the mode of v i b r a t i o n s and weight d i s -t r i b u t i o n . I t i s then necessary to check where v i b r a t i o n s can be reduced o r , i f i t i s advantageous, to have o n l y a v e r t i c a l o r a h o r i z o n t a l unbalance and then l o c a t e one handle a t a v i b r a t i o n mode and the o t h e r handle a t a low amplitude l o c a t i o n but p a r a l l e l to the l a r g e s t component a t t h a t l o c a t i o n . The weight must be d i s t r i b u t e d to r e s u l t i n the o v e r a l l minimum v i b r a t i o n l e v e l s . No f a c t o r a ccentuates v i b r a t i o n s as much as poor weight and l o a d d i s t r i b u t i o n and no system absorbs v i b r a t i o n as much as s p e c i a l shock absorbing g l o v e s , u s u a l l y made of foam and l e a t h e r . A l s o , f l e e c e gloves keep the hand warm and dry and a l l o w f o r crimping i n the palm of the hand where the v i b r a t i o n i n s u l -a t i n g m a t e r i a l i s most e f f e c t i v e l y used. Instead of l i n i n g a glove the i n s u l a t i n g m a t e r i a l could be wrapped around the handle. Because high pressure i s exerted on the handle, t h i s method i s not always as e f f e c t i v e as i t could be. A t h i r d method of reducing v i b r a t i o n t r a n s m i s s i o n i s to a t t a c h the handle not s o l i d l y t o the engine frame but f l e x i b l y to some i n s u l a t i n g m a t e r i a l . The f l e x i b l e handle supposedly reduces the v i b r a t i o n l e v e l s t r a n s m i t t e d to the hand. Observations during a s e r i e s of v i b r a t i o n l e v e l t e s t s v e r i f i e d t h i s e x p e c t a t i o n ; when comparing the l e v e l s of two s i m i l a r saws, the v i b r a t i o n i n the machine w i t h the f l e x i b l e handle was lower than or equal to the v i b r a t i o n i n the machine w i t h the s o l i d handle. * Exposure to high l e v e l i n d u s t r i a l noise " l i m i t s speech communication, changes a t t i t u d e s and behaviour, and impairs hearing."** I f the operator i s exposed t o high l e v e l noise f o r a c o n s i d e r a b l e l e n g t h of time not o n l y w i l l the noise con-t r i b u t e to f a t i g u e but i t may permanently damage the ear. * Author's u n o f f i c i a l observations during v i b r a t i o n l e v e l t e s t s a t Pe E l , Washington, June 22, 1967. ** From a t a l k by B.P. Carton presented to Truck Loggers' Convention, Vancouver, January 20, 19 67. 49 What we are concerned w i t h here i s the impairment of the workman's a b i l i t y t o hear and understand normal speech. The degree of impairment depends on many f a c t o r s , i n c l u d i n g the type of n o i s e , the i n t e n s i t y of the n o i s e , and the d u r a t i o n of exposure. The sound l e v e l i s g e n e r a l l y expressed as the l o g a r -i t h e m i c r a t i o of the energy i n the measured p r e s s u r e wave to the energy i n a standard p r e s s u r e wave, u s u a l l y the t h r e s h o l d o f h e a r i n g a t 1000 cps. Thus 0 dB r e p r e s e n t s the t h r e s h o l d of h e a r i n g , 60 dB r e p r e s e n t s c o n v e r s a t i o n a l speech, and 140 dB r e p r e s e n t s the t h r e s h o l d o f p a i n . To reduce the p o s s i b i l i t y of h e a r i n g impairment from long-term exposure t o h i g h l e v e l n o i s e , the Workman's Compensation Board of B r i t i s h Columbia adopted A c c i d e n t P r e v e n t i o n R e g u l a t i o n 12.28 i n 1966. T h i s r e g u l a t i o n s t a t e s i n p a r t t h a t where the n o i s e l e v e l s exceed the Board c r i t e r i a , and the circumstances are such t h a t a hazard to h e a r i n g e x i s t s , the n o i s e s h a l l be reduced t o a c c e p t a b l e l e v e l s by e n g i n e e r i n g means. Where r e d u c t i o n by e n g i n e e r i n g means i s not p r a c t i c a l , adequate ear p r o t e c t i o n s h a l l be p r o v i d e d and s h a l l be worn. [1.47, p. 4] The broad-band n o i s e l e v e l c r i t e r i a f o r h e a r i n g c o n s e r v a t i o n adopted by the Workman's Compensation Board, the damage r i s k c r i t e r i a suggested by Baranek [1.48] and the n o i s e l e v e l r e a d i n g s a t the o p e r a t o r ' s ear of t y p i c a l saws are shown i n Graph 1.17. The da t a f o r the n o i s e l e v e l r e a d i n g s shown i n i n Appendix I I I . The n o i s e i n t e n s i t y d ecreases w i t h d i s t a n c e away from the saw. For example, where the o p e r a t o r i s exposed to an i n t e n s i t y o f 105 dBA, an obs e r v e r a t 23 f t i s exposed to 82 dBA and a t 50 f t he i s exposed t o 75 dBA [1.49]. 120 a 100 o CO 1 1 I I I I I I J 1 1 1 M M M WITHOUT BAR OH DYNAMOMETER BARAMEK 801 100 B . CV,,W6,RKMTI^,,,CO,M,P,E^ T ' I I I 1 1 1 1 1 I I I I 1111 1000 FREQUENCY (CPS) 10000 Graph 1.17 Noise l e v e l r e a d i n g s of t y p i c a l power saws Because the e x t e n t of h e a r i n g impairment depends on the l e n g t h of exposure, the n o i s e c r i t e r i a should accommodate v a r y i n g amounts of exposure. The S t a t e of Washington 51 100 1000 10000 FREQUENCY (CPS) Graph 1.18 State of Washington standard f o r i n d u s t r i a l noise Graph 1.19 T e n t a t i v e Swedish noise l e v e l l i m i t s O c c u p a t i o n a l H e a l t h Standards c r i t e r i a does t h i s by s p e c i f y -i n g the n o i s e l e v e l i n terms of a l l o w a b l e exposure i n hours per week without ear p r o t e c t i o n , Graph 1.18. But because the l e n g t h o f exposure does not v a r y a g r e a t d e a l from o p e r a t o r to o p e r a t o r , the Swedish c r i t e r i a f o r c h a i n saws s p e c i f i e s the n o i s e l e v e l s i n terms of the amount of p r o -t e c t i o n g i v e n to the e a r , Graph 1.19. A p r o p e r l y designed m u f f l e r of e i t h e r the r e a c t i v e or d i s s i p a t i v e type reduces the exhaust n o i s e s i g n i f i c a n t l y . The d i s s i p a t i v e m u f f l e r c o n t a i n s flow r e s i s t i v e m a t e r i a l such as f i b r e g l a s s or asbestos to absorb the energy r e l e a s e d when the exhaust p o r t s open. But when exhaust p a r t i c l e s c l o g the p e r f o r a t i o n s , not o n l y i s the s i l e n c i n g e f f e c t i v e -ness l o s t , but the r e s i s t a n c e to exhaust flow i s i n c r e a s e d . Since the p o r t e d two-stroke engine i s v e r y s e n s i t i v e t o b a c k p r e s s u r e , a s m a l l i n c r e a s e i n flow r e s i s t a n c e produces a l a r g e power drop. T h i s type of m u f f l e r then, i s not v e r y s u i t a b l e on a power saw. The r e a c t i v e m u f f l e r i s timed to pass o n l y the f r e -q uencies below i t s resonant frequency. I t s e f f e c t i v e n e s s i n r e d u c i n g n o i s e l e v e l i s l i m i t e d by the volume or s i z e p o s s i b l e . E f f e c t i v e n e s s can be understood i n terms o f an e l e c t r i c a l analogue (low pass f i l t e r ) as shown on F i g u r e 1.7. The c u r r e n t (volume of gas exhausted) flows from the source i n t o the c a p a c i t o r ( m u f f l e r volume) and i s d i s -charged through the inductance c o i l ( t a i l p i p e ) . To be e f f e c t i v e at low f r e q u e n c i e s , the c a p a c i t o r and inductance must be l a r g e . The optimum volume f o r a power saw i s i n the order of 10 times the engine displacement and the optimum len g t h of the t a i l p i p e i s i n the order of 12 f t [1.44, 1.50]. Obviously a compromise between s i z e and e f f e c t i v e n e s s i s necessary. from exhaust. But exhaust noises are only p a r t of the noise p i c t u r e . McCulloch's experience [1.44] shows t h a t without the exhaust noise the accumulated aerodynamic no i s e of the c o o l i n g a i r fan and the mechanical noise of be a r i n g s , t h r u s t I t i s g e n e r a l l y assumed t h a t engine noise comes L V= Vo lume of C a v i t y - c m 5 H=Amb ien t P r e s s u r e - U I O ' d y n e s / c m ' P = D e n s i t y of A i r - L Z I x l O ^ g m / c m 1 i - L e n g t h of T u b e - c m A -Area of T u b e - c m ' F r e q u e n c y F i g u r e 1.7 Schematic r e p r e s e n t a t i o n of m u f f l e r and e l e c t r i c a l e q u i v a l e n t [1.50] w a s h e r s , g e a r s , v i b r a t i n g p a n e l s , p i s t o n s l a p , c h a i n a n d s p r o c k e t n o i s e s a r e a r o u n d 100 d B a t 3 f t f r o m t h e s a w . B e t t e r e n g i n e b a l a n c e a n d c l o s e r t o l e r a n c e s c a n r e d u c e some o f t h i s n o i s e . O t h e r r e d u c t i o n s c a n b e a c c o m p l i s h e d b y s t i f f e n i n g o r i n s u l a t i n g t h e v i b r a t i n g p a n e l s a n d b y a e r o -d y n a m i c a l l y d e s i g n i n g t h e f a n a n d c o w l i n g f o r q u i e t n e s s . T h e m u f f l e r o n t h e p o w e r saw h a s a d u a l p u r p o s e . I t r e d u c e s t h e n o i s e t o a n a c c e p t a b l e l e v e l a n d p r e v e n t s t h e e s c a p e o f s p a r k s , c a r b o n d e p o s i t s a n d o t h e r s u b s t a n c e s l i k e l y t o c a u s e a f i r e . R e t e n t i o n i s a c h i e v e d i f t h e l a r g e s p a r k s i m p i n g e o n a s o l i d s u r f a c e a n d b r e a k u p b e f o r e t h e y l e a v e t h e m u f f l e r . T h e s o l i d s u r f a c e may b e a w a l l , a b a f f l e , o r a s c r e e n . W h a t e v e r i s u s e d a s t h e i m p i n g e m e n t s u r f a c e m u s t b e p o s i t i o n e d i n s u c h a f a s h i o n t h a t p a r t i c l e s c a n n o t t r a v e l i n a s t r a i g h t l i n e f r o m t h e p o r t t o t h e m u f f l e r e x h a u s t . T h e S o c i e t y o f A u t o m o t i v e E n g i n e e r s , i n c o n j u n c t i o n w i t h t h e P o w e r Saw M a n u f a c t u r e r s A s s o c i a t i o n , d r a f t e d a m u f f l e r s t a n d a r d [ 1 . 5 1 ] . To b e a c c e p t a b l e t h e m u f f l e r m u s t h a v e a n 80% r e t e n t i o n o f p a r t i c l e s t h a t c a n b e r e t a i n e d o n a n ASTM#30 ( . 0 2 3 i n ) s c r e e n a n d a 100% r e t e n t i o n o f p a r t i c l e s t h a t c a n b e r e t a i n e d o n a n ASTM#16 ( . 0 4 7 i n ) s c r e e n . A l t h o u g h i n m o s t w a y s s i m i l a r t o t h e S A E - P S M A , t h e C a l i f o r n i a s t a n d a r d [ 1 . 5 2 ] s p e c i f i e s 90% r e t e n t i o n i n b o t h c a t e g o r i e s . A u s t r a l i a a c c e p t s a m u f f l e r i f p i n e n e e d l e s w i t h 6% m o i s t u r e c o n t e n t d o n o t i g n i t e a f t e r b e i n g h e l d i n c o n t a c t w i t h t h e m u f f l e r f o r 30 s e c d u r i n g a w i d e o p e n t h r o t t l e , n o l o a d e n g i n e t e s t [ 1 . 5 3 ] . I n W a s h i n g t o n S t a t e t h e e x h a u s t g a s m u s t i m p i n g e o n 3 s u r f a c e s b e f o r e e x h a u s t i n g f r o m t h e m u f f l e r , o r t h e m u f f l e r m u s t c o n t a i n t w o s t a g g e r e d s o l i d b a f f l e s , o r 2 p e r f o r a t e d b a f f l e s w i t h h o l e s l e s s t h a n . 1 8 7 i n d i a m e t e r o r 2 o r m o r e s c r e e n s w i t h h o l e s l e s s t h a n o r e q u a l t o . 0 3 0 i n d i a m e t e r , [ 1 . 5 4 ] . I n t h e s t a t e o f M a i n e , o n l y o n e p e r f o r a t e d b a f f l e i s r e q u i r e d b u t t h e h o l e s m u s t b e l e s s t h a n . 0 8 0 i n d i a m e t e r a n d s p a c e d a r o u n d t h e p e r i p h e r y , o r i f s c r e e n s a r e u s e d , 3 a r e r e q u i r e d a n d t h e h o l e s m u s t b e l e s s t h a n . 0 3 0 i n d i a m e t e r [ 1 . 5 5 ] . M o s t s t a n d a r d s a l s o r e q u i r e a m u f f l e r t h a t i s d e s i g n e d a n d made o f a m a t e r i a l t h a t w i l l n o t a l l o w e x c e s s i v e s h e l l t e m p e r a t u r e s ; t h e S A E -PSMA s t a n d a r d l i m i t s t h i s t e m p e r a t u r e t o 8 5 0 ° F . T h e a r r e s t e r s h o u l d o p e r a t e f o r a m i n i m u m o f 8 h o u r s b e f o r e c l e a n i n g i s n e c e s s a r y a n d h a v e a l i f e e x p e c t a n c y o f 50 h o u r s . No e l e c t r i c , p n e u m a t i c , o r e n g i n e p o w e r t o o l i s a s d a n g e r o u s a s o n e w i t h r a p i d l y m o v i n g , s h a r p l y f i l e d t e e t h , s u c h a s a p o w e r s a w . A n d y e t no t o o l h a s a s f e w p r o t e c t i v e g u a r d s . L i t t l e i m a g i n a t i o n i s r e q u i r e d t o v i s u a l i z e how much i n j u r y c a n o c c u r i n a m i s h a p a n d l i t t l e p e r s u a s i o n i s r e q u i r e d t o a c c e p t a c c i d e n t s t a t i s t i c s . A b r e a k d o w n o f t h e a c c i d e n t s r e p o r t e d t o t h e Q u e b e c P u l p a n d P a p e r S a f e t y A s s o c i a t i o n i s g i v e n i n F i g u r e 1 . 8 . Branching ; 1455 1956 T Y P E O F A C C I D E N T 1957 Bucking 1955 1956 1957 While clearing, saw kicked back^ or defected, ^s.-.c-^s"-' ': : 1 Branching '• with- saw, kicked/ : back, cut through or deflected. 1 Branch hit accelerator startutg saw, i 1 5 8 8 . 31 0 .1 Saw kicked back or chain jumped due to touching branch 5 Saw cut through log striking worker. 2 Foot slipped and leg hit saw. . 3 Placed foot on tree, beside. saw, chain jumped. - Total %. Percentage 3 1.19* 13 2.34* 40 6.92% Tota l Percentage -, 1 " l l 4.36% 29 35 16 82 14.80% 73 45 3 123 : 21.28% Fell ing Saw kicked back' or saw chain • ; jumped due to touching branch, tree log, other ob-struction or punching. .. : 53 As tree fell it pushed,saw chain' which hit operator. . ; 7 Falling branch hit saw or opcr-' ator causing fall on saw. {10 Pushing tree, with one hand • while holding saw with other, j 4 Hi t by companion's saw while i helping by pushing tree. i 10 After, felling, hit by saw while i cutting hinge, attached to j ....-. stump. . .-;'•)' i 12 Hi t chain saw while getting away; . from falling tree. ! 2 131 41 11 : 10 13. 2 7 130 36 6 6 10 2 5 Miscellaneous Preparing, adjusting or repair-' ingsaw. ) Starting motor.' • . • I Hit chain acadentally while : handling. Cham broke striking operator. • Burns, gasoline spilled on ^ . clothing ignited. j* Working too close to com com-; panion, hitby saw; . Foreign body in eye. ^ Tota l . Percentage ."Hit by companion's tree. ; 3 11 17., 4 18 10 1 17 9 0 • 1 ** 0 2 0 i 6 5 • 3 14 55 45 5.557o 9.92% 7.78% 37 58(4 x) 71 (4x) • ' ' • . T o t a l -•' : Percentage Chang ing Position : Fall with chain at rest, hit saw i 98 ! 38.88% 215 38.80% 195 33.73% .. Kick-back (felling). 14 68"% 10 46% 12.88% 73x 28.96%, 91x 16.42% 70x 12.11% Tota l 252x 554fx> 578(5x) teeth. . ! -4 • 15 17 Fell with chain in motion. ': 7 . 1 2 •• 9 Hit self with saw in motion. 5 . .13 8 . Tota l To 40 34 Note: (xy Indicates mat figures include fuui! accident Percentage • 6.34% 5.88% P O W E R S A W K I C K - B A C K , H I T B Y C O M P A N I O N ' S T R E E Age of Injured Employees 1955 1956 1957 Nature of Injury 1955 1956 1957 •/ 20 vears old and under 64 .143 • I48x Cut 106 291 295 .f 21 to 25 71 • 142 (2x) 154x Laceration 26 76 108 26 to 30 •• • 46 96 23x Amputation 1 1 1 31 to 35 .. 26 56 59x Bruise , 15 105 38 36 to 45 30 -• 61 x 79x Fracture : 29x 30(5x1 . 3S(5x' 46 to 70 13x 47(2x) 43 Foreign body in eye 5 4 5 Unknown 2 9 12 Strain 16 31 23 : ,r • . .  ._ ,— Sprain 54 . 16 25 : . Tota l 252x ,554(5x) 578(5x) T o t a l .'.-V-.-2 5 2 X. , „ ,A ..554:5x.i .578(5x' Part of Body Injured I.ength of T i m e Employed Before Accident.; '• Finger 10 30 41 Less than 1 week ' •' 30 '90x 96 Hand 11 41 43 1 to 2 weeks 13 . 88 104 Arm 18 30 34 2 to 4 " . 68 98 136 Elbow 10 4 Over 4 78 19! 137(2* Torso . 30 56x 43 Uhknown 45x 8 V M \ : 105(3? Head 21x 21 1\ • 34 (4 x) Eye 11 7 Tota l • 252x 554i5i,-i 578 (5> Multiple 14 23 43 Foot 15 2.6 34 Leg 72 147 146x Knee 48 138 135 Toe 1 8 14 — -Tota l 252.x 554 15xi 578(5x1 / Note: (x) Indicates that l i i 'ures include: fatal accident. F i g u r e 1.8 Accidents reported to Quebec Pulp and Paper A s s o c i a t i o n [1.37] An a n a l y s i s of these s t a t i s t i c s i n d i c a t e s t h a t the moving chain was r e s p o n s i b l e f o r two t h i r d s of the i n j u r i e s and a t h i r d of the f a t a l i t i e s . The three f a t a l i t i e s as w e l l as 40% of the a c c i d e n t s (1957) were caused b.y kickback; t h i s r e a c t i o n occurs when the top of the moving chain a c c i d e n t -a l l y h i t s a f o r e i g n o b j e c t and causes the whole machine to k i c k back out of c o n t r o l . The remainder of the a c c i d e n t s occurred when the chain jumped out of the guidebar, or when the operator or a s s i s t a n t a c c i d e n t a l l y h i t the chain i n t r y i n g t o escape from f a l l i n g branches or t r e e s or were pushed i n t o the chain by the branch or t r e e , or when the operator or a s s i s t a n t were too c a r e l e s s . I t i s obvious t h a t i n the hands of an inexperienced operator the chain saw has a high p o t e n t i a l f o r h u r t i n g and maiming. The s t a t i s t i c s show t h a t 75% of the a c c i d e n t s occur w i t h i n 4 weeks a f t e r the operator s t a r t s work w i t h a chain saw. Though somewhat s a f e r than the bar type chain saw, the bow type i s unpopular because i t i s expensive and cumbersome. A l s o c o n s i d e r a b l y s a f e r than the c h a i n type saw because there i s p r a c t i c a l l y no chance of kickback, the r e c i p r o c a t i n g blade saw i s unpopular because i t does not feed as e a s i l y as does the chipper t o o t h chain nor does i t remove the sawdust as q u i c k l y . Consequently, the operator must e x e r t c o n s i d e r a b l e e f f o r t t o keep the saw c u t t i n g r a p i d l y . The e f f o r t causes f a t i g u e which i n t u r n makes him more prone to a c c i d e n t s . 5 8 I t i s always d i f f i c u l t t o a v o i d back f a t i g u e when f o r c i b l y c o n t r o l l i n g a v i b r a t i n g machine. F a t i g u e can be reduced by p r o p e r l y b a l a n c i n g the saw and p r o p e r l y d e s i g n i n g the handles. Maximum o p e r a t o r comfort and minimum back f a t i g u e r e s u l t when the g r i p conforms to the shape of the hand and the l o c a t i o n l i n e s up w i t h the guide bar and the engine c e n t e r of g r a v i t y . Good balance and good c o n t r o l d u r i n g v e r t i c a l c u t t i n g r e q u i r e t h a t the f r o n t handlebar be forward of the c e n t e r o f g r a v i t y . In t h i s arrangement the f r o n t hand i s used as a p i v o t and the r e a r hand as a c o n t r o l . The engine c o n t r o l s must be grouped so t h a t u n i n t e n t i o n a l f i n g e r movements are kept t o a minimum, and t h a t q u i c k n a t u r a l movements of the index f i n g e r and thumb c o n t r o l the t h r o t t l e , c h a i n o i l e r , and i g n i t i o n c u t - o f f . The c o n t r o l s must a l s o a u t o m a t i c a l l y reduce power when the f i n g e r s are a c c i d e n t a l l y or p u r p o s e l y removed. Some o p e r a t o r s t h i n k t h a t the h i g h e r the power, the f a s t e r the c u t , the l e s s the f a t i g u e . But w i t h more power f o r a g i v e n weight, the o p e r a t o r spends l e s s time c u t t i n g and more time moving from cu t to c u t . Because the saw c u t s f a s t e r he must c o n t r o l the saw more. T h e r e f o r e i t cannot be maintained t h a t a high-power-to-weight r a t i o means l e s s f a t i g u e , e s p e c i a l l y i f the v i b r a t i o n l e v e l s i n c r e a s e as the saw weight d e c r e a s e s . Other means of r e d u c i n g f a t i g u e must be found because most e x p e r t s agree t h a t f a t i g u e i s a prime 59 c a u s e o f a c c i d e n t s . To d e t e r m i n e t h e i m p o r t a n c e o f a n u m b e r o f c o n t r o l l a b l e saw c h a r a c t e r i s t i c s , a q u e s t i o n n a i r e was d i s t r i b u t e d t o a n u m b e r o f p r o f e s s i o n a l a n d c a s u a l u s e r s . R e s p o n s e s w e r e f e w , b u t r e p l i e s w e r e r e c e i v e d f r o m O n t a r i o , New B r u n s w i c k , t h e Q u e e n C h a r l o t t e I s l a n d s , a n d f r o m t h e l o c a l a r e a . T h e q u e s -t i o n n a i r e a s k e d t h e u s e r t o i n d i c a t e t o w h a t e x t e n t t h e s t a t e d c h a r a c t e r i s t i c s b o t h e r e d o r a f f e c t e d h i m , o r how i m p o r t a n t h e c o n s i d e r e d t h e m t o b e . He was a s k e d t o e v a l u a t e t h e m a c c o r d i n g t o f o u r d e g r e e s : v e r y m u c h , q u i t e a l o t , s o m e w h a t , a n d n o t a t a l l . B y a s s i g n i n g a v a l u e o f 3 , 2 , 1 a n d 0 t o t h e s e d e g r e e s , b y t o t a l l i n g e a c h c a t e g o r y a n d d i v i d i n g b y t h e n u m b e r o f r e s p o n s e s (7 f o r t h e p r o f e s s i o n a l l o g g e r c u t t i n g p u l p w o o d ) , a n i m p o r t a n c e f a c t o r was d e t e r -m i n e d . T h e c h a r a c t e r i s t i c s m e n t i o n e d a n d t h e r e s u l t s o b t a i n e d a r e s h o w n o n F i g u r e 1 . 9 . The o r i g i n a l d a t a i s s h o w n i n A p p e n d i x I V . T h e l o g g e r s c o n s i d e r e d e a s y s t a r t i n g , r e l i a b i l i t y a n d l o w w e i g h t a s ' t h e m o s t i m p o r t a n t c h a r a c t e r i s t i c s , a n d a p p e a r a n c e , s m e l l a n d n o i s e a s t h e l e a s t i m p o r t a n t . Two l o g g e r s e x p r e s s e d p e r s o n a l s u g g e s t i o n s f o r i m p r o v e m e n t s t o e x i s t i n g s a w s , B o t h s u g g e s t e d a f u e l f i l t e r i n g s y s t e m t o k e e p o u t s a w d u s t . O t h e r s u g g e s t i o n s i n c l u d e d a m o r e r u g g e d a i r f i l t e r , a b e t t e r c h a i n , t i n k e r p r o o f c a r b u r e t o r a d j u s t -m e n t s a n d s e l f - c l e a n i n g p o r t s . E v e n t h o u g h u s e r s d i d n o t c o n s i d e r a p p e a r a n c e t o b e i m p o r t a n t , i f o t h e r t h i n g s a r e e q u a l o r u n k n o w n , t h e y a r e C h a r a c t e r i s t i c s Imp N o t > o r t a n t V e r y Im p o r t a n t E a s y s t a r t i n g R e l i a b i l i t y Low w e i g h t a n d s i z e L o n g , t r o u b l e - f r e e l i f e Low i n i t i a l c o s t i 9 9 9 9 > Low f u e l c o n s u m p t i o n E a s y m a i n t e n a n c e Low u p k e e p c o s t Low o i l c o n s u m p t i o n N e a t a p p e a r a n c e 9 9 9 9 9 W e i g h t V i b r a t i o n S m e l l N o i s e 5 9 9 9 • F i g u r e 1 . 9 R e s u l t s o f q u e s t i o n n a i r e o n t h e i m p o r t a n c e o f saw c h a r a c t e r i s t i c s m o r e l i k e l y t o b u y a n a t t r a c t i v e , f u n c t i o n a l l y a r r a n g e d saw t h a n a n u n a t t r a c t i v e o n e . F o r t h e c a s u a l u s e r , t h e p u r c h a s e p r i c e i s o f t e n t h e m a i n , c o n s i d e r a t i o n . I n c o m p a r i s o n w i t h o t h e r c a s u a l s a w s t h a t s e l l f o r 100 t o 200 d o l l a r s , a new .saw s h o u l d s e l l b e l o w 200 d o l l a r s . I f t h e p r i c e i s h i g h e r t h a n f o r t h e c o n v e n t i o n a l s a w , t h e c a s u a l u s e r w i l l h a v e t o b e c o n v i n c e d o f t h e s a w ' s m e r i t s b e f o r e he p a y s t h e e x t r a p r i c e . To s u m m a r i z e w h a t t h e o p e r a t i n g c h a r a c t e r i s t i c s o f a p o w e r saw s h o u l d b e l i k e , o n e c a n s a y t h a t t h e c a s u a l u s e r requires and wants a simple one-handed t o o l that can be c a r r i e d into a tree, pushed into a t i g h t corner or carried long distances. For safety and convenience, he wants i t to be powerful, s e l f - s t a r t i n g and f a s t stopping because i n awkward situations such as when a tree pruner i s precariously perched oh a branch or a carpenter i s accurately cutting the overhang of a roof, hand s t a r t i n g i s essentially, d i f f i c u l t and dangerous. As with a l l hand t o o l s , the operator wants to experience the minimum amount of fatigue and the maximum protection to his health so that noise l e v e l s and v i b r a t i o n amplitudes must be low. To make i t easy to handle, the machine must be l i g h t i n weight and small i n s i z e . I t should be inexpensive to own and operate. Its source of power must be safe, r e l i a b l e and r e a d i l y a v a i l a b l e . Table 1 S p e c i f i c a t i o n s for a Small Power Saw 1. power - 1 hp, 2. chain speed - less than 2000 fpm i f a chain i s used, 3. weight - less than 4 l b s , 4. cost - less than 2:00 d o l l a r s , 5. v i b r a t i o n amplitude - less than .002 i n at 7000 rpm, 6. noise l e v e l - below 110 dBA, 7. safety - automatic stopping i f t r i g g e r i s released, 8. appearance - a e s t h e t i c a l l y pleasing, 9. s p e c i f i c f u e l consumption - less than 1.2 lb/bhp-hr, 10. f u e l tank capacity - 7 in-3 - enough for 10 min continuous f u l l power cutting, 11. o i l - i f mixed with f u e l , rates should be at l e a s t 50:1, 12. s t a r t e r - s e l f - s t a r t i n g . T h e s p e c i f i c a t i o n s f o r t h e d e s i g n e n v e l o p e h a v e b e e n s u m m a r i z e d i n T a b l e I. T h e f o r m u l a t i o n o f t h e s p e c i f i -c a t i o n s c o n s t i t u t e s o n l y t h e f i r s t s t e p i n t h e d e s i g n p r o c e s s . The n e x t s t e p i s t o a s c e r t a i n a l l p o s s i b l e means o f a c h i e v i n g t h e d e s i r e d o u t p u t , w i t h i n t h e s p e c i f i e d l i m i t a t i o n s . T h i s s t e p , t h e a n a l y s i s o f s u i t a b l e p o w e r s o u r c e s a n d p o s s i b l e c u t t i n g d e v i c e s , i s t h e s u b j e c t o f t h e f o l l o w i n g c h a p t e r . 63 2 . S Y N T H E S I S 2 . 1 Wood C u t t i n g D e v i c e s F i n d i n g t h e b e s t s o u r c e o f p o w e r f o r t h e w o o d c u t t i n g d e v i c e r e q u i r e d a n e v a l u a t i o n o f t h e many s o u r c e s a v a i l a b l e . T h e t a s k o f e l i m i n a t i n g t h e l e s s d e s i r a b l e a n d a c c e p t i n g t h e m o r e r e a s o n a b l e was e x p e d i a t e d w i t h t h e h e l p o f t h e f o l l o w i n g c r i t e r i a : t h e m a c h i n e a n d i t s s o u r c e o f p o w e r m u s t b e r e -l i a b l e , s a f e , i n e x p e n s i v e a n d p o r t a b l e . S o l a r e n e r g y w a s t h e f i r s t s o u r c e t o b e e v a l u a t e d . N o t o n l y i s t h i s s o u r c e f r e e a n d u n i v e r s a l l y a v a i l a b l e , b u t i t s c o n v e r s i o n i n t o w o r k h a s r e c e n t l y r e c e i v e d much s t u d y . I t i s p o s s i b l e t o u s e s o l a r e n e r g y i n t h e f o l l o w i n g w a y s : 1 . t o h e a t b o i l e r s , a i r h e a t e r s o r e n e r g y a b s o r b i n g m a t e r i a l s d i r e c t l y , 2 . t o g r o w v e g e t a t i o n ( e s p e c i a l l y a l g a e ) a n d t h e n b u r n i t a s f u e l , 3 . t o p h o t o l y z e w a t e r a n d t h e n b u r n t h e h y d r o g e n a n d o x y g e n p r o d u c e d , a n d 4 . t o p o w e r a n e n e r g y c o n v e r t e r a n d t h e n u s e t h e e l e c t r i c i t y . When t h e s u n i s a t t h e z e n i t h t h e s o l a r p o w e r r e a c h i n g a h o r i z o n t a l p l a t e a t s e a l e v e l i s a b o u t 1 / 1 0 h p / f t 2 . B e c a u s e c o n v e r s i o n e f f i c i e n c y i s o n l y 2 a b o u t 10%, a c o l l e c t o r a r e a o f 100 f t i s r e q u i r e d t o produce 1 hp. According to T h i r r i n g [2.1], during a sunny day the t o t a l d a i l y energy reaching the ea r t h at the 50th p a r a l l e l v a r i e s from a peak of 570 gram-calories per sq cm i n June to a low of 100 gram-calories per sq cm i n December The c a p r i c e cloud cover p r e v a l e n t i n many areas reduces the r a d i a t i o n and makes s o l a r power u n r e l i a b l e . The drawbacks of c a p r i c e cloud cover can be over-come when the cloudy i n t e r v a l s are s h o r t . Thermal energy can be st o r e d i n melted s a l t o r , i f f i r s t converted i n t o e l e c t r i c a l energy, i n b a t t e r i e s . One hp-hr can be stored i n 25 l b s of Na 2SO 4.10H 2O [2.1], i n a 20 l b z i n c - a i r b a t t e r y [2.2] or i n 70 l b s of l e a d - a c i d storage b a t t e r i e s . Although i t would not be very p o r t a b l e , even without an i n t e g r a t e d storage d e v i c e , s o l a r power i s f e a s i b l e f o r a s t a t i o n a r y power p l a n t , as was shown by the small p i s t o n engine b u i l t i n I t a l y to pump i r r i g a t i o n water. Using a f l a t p l a t e as a c o l l e c t o r and sulphur d i o x i d e as a working m a t e r i a l , i t converted s o l a r energy i n t o work at an e f f i c -iency of 10%. Because s o l a r power i s not p o r t a b l e , i t d i d not meet the design requirements so no f u r t h e r a n a l y s i s was undertaken. Although f e a s i b l e i n windy areas and p r a c t i c a l i n undeveloped c o u n t r i e s , l a c k i n g a more s u i t a b l e source, wind power i s not r e l i a b l e and not p o r t a b l e [2.3], Power from t i d e s and waves and from h y d r a u l i c p o t e n t i a l i s a l s o not p o r t a b l e . Nuclear energy i s not only too expensive but a l s 65 t o o h e a v y ; t h e p e r f o r m a n c e t a r g e t f o r t h e 500 w a t t S . N . A . P . -10A r e a c t o r - t h e r m o e l e c t r i c u n i t i s 200 l b s p e r k i l o w a t t - h o u r [ 2 . 4 ] . C o n s e q u e n t l y w i n d p o w e r , h y d r a u l i c p o t e n t i a l , a n d n u c l e a r e n e r g y w e r e n o t a n a l y z e d . I t i s p o s s i b l e t o u s e f u e l c e l l s a n d b a t t e r i e s t o p o w e r a n e l e c t r i c p o w e r s a w . A l t h o u g h i t h a s a w e i g h t a d v a n t a g e o v e r t h e s t o r a g e b a t t e r y a n d a n e f f i c i e n c y a d v a n t a g e o v e r t h e h e a t e n g i n e , t h e f u e l c e l l i s t o o e x p e n s i v e f o r t h e c o m m e r c i a l m a r k e t . T h e r o o m t y p e c e l l s s u c h a s H 2 ~ ° 2 r e < 3 u i x e e x p e n s i v e e l e c t r o - c a t a l y s t s , a n d e x p e n s i v e f u e l , w e i g h 100 l b s p e r k i l o w a t t - h o u r a n d a c h i e v e 50% e f f i c i e n c i e s [ 2 . 5 ] . H i g h t e m p e r a t u r e c e l l s s u c h a s a l k a l i - h a l o g e n w i t h a 5 l b p e r k i l o w a t t - h o u r r a t i n g show some p r o m i s e f o r c o m m e r c i a l d e v e l o p -m e n t b u t c o n t a i n m e n t i s d i f f i c u l t [ 2 . 6 ] , S t o r a g e b a t t e r i e s a r e l e s s e x p e n s i v e b u t h e a v i e r t h a n f u e l c e l l s . C o n v e n t i o n a l b a t t e r i e s w e i g h 70 - 200 l b s p e r k i l o w a t t - h o u r , z i n c - a i r b a t t e r i e s w e i g h 20 l b s p e r k i l o w a t t -h o u r [ 2 . 2 ] , o r g a n i c - e l e c t r o l y t e b a t t e r i e s may a p p r o a c h 5 l b s p e r k i l o w a t t - h o u r [ 2 . 7 ] , a n d a new e x p e r i m e n t a l L i t h i u m -T e l l u r i u m b a t t e r y w e i g h s 2 l b s p e r k i l o w a t t - h o u r [ 2 . 8 ] . B e s i d e s f u e l c e l l s a n d b a t t e r i e s , p h o t o v o l t a i c , t h e r m i o n i c a n d t h e r m o -e l e c t r i c c o n v e r t e r s c a n b e u s e d t o g e n e r a t e e l e c t r i c i t y . P h o t o -v o l t a i c c o n v e r t e r s o p e r a t i n g w i t h 15% e f f i c i e n c i e s r e q u i r e a h i g h t e m p e r a t u r e h e a t s o u r c e t o s u p p l y r a d i a n t e n e r g y . T h e c o n v e r t e r s c a n b e c o m p a c t ; a p r o d u c t i o n t y p e 10 0 w a t t c o n -v e r t e r u s i n g a r a d i o - i s o t o p e a s t h e s o u r c e o f h e a t c a n b e h o u s e d i n a 2 i n d i a m e t e r s p h e r e [ 2 . 9 , 2 . 1 0 ] . A t h e r m i o n i c c o n v e r t e r t r a n s f o r m s t h e r m a l e n e r g y i n t o e l e c t r i c a l e n e r g y b y u t i l i z i n g t h e t h e r m i o n i c e m i s s i o n o f e l e c t r o n s . E f f i c -i e n c i e s o f 4 -19% c a n b e o b t a i n e d d e p e n d i n g o n t h e m a t e r i a l s a n d t h e t e m p e r a t u r e u s e d [ 2 . 1 1 ] . A t h e r m o e l e c t r i c g e n e r a t o r u t i l i z i n g t h e t h e r m o c o u p l e p r i n c i p l e , c o n v e r t s t h e r m a l e n e r g y i n t o e l e c t r i c a l e n e r g y a t e f f i c i e n c i e n c e s o f 2 -10% [ 2 . 1 2 ] . T h e m a g n e t o - h y d r o d y n a m i c g e n e r a t o r , a d e v i c e u s i n g 5 p 0 0 ° F p l a s m a j e t s t o c o n d u c t e l e c t r i c i t y i n a m a g n e t i c f u e l , a n d t h e e l e c t r o - g a s - d y n a m i c g e n e r a t o r s u i t a b l e f o r v o l t a g e s a b o v e 5 0 , 0 0 0 v o l t s a r e b o t h s t i l l i n t h e e x p e r i m e n -t a l s t a g e [ 2 . 1 3 , 2 . 1 4 ] . A l l t h e a b o v e m e n t i o n e d f u e l c e l l s a n d b a t t e r i e s a r e i n t h e m s e l v e s h e a v y a n d i n o r d e r t o p r o d u c e w o r k , r e q u i r e a n e l e c t r o m e c h a n i c a l d e v i c e s u c h a s a m o t o r w h i c h f u r t h e r i n c r e a s e s t h e w e i g h t . A t y p i c a l e l e c t r i c r e c i p r o c a -t i n g s a w , t h e 1 h p W e l l s a w 4 0 0 , w i t h a n 8 i n b l a d e , w e i g h s 8 l b s [ 2 . 1 5 ] , B e c a u s e b a t t e r i e s a n d f u e l c e l l s w i t h a n e l e c t r i c m o t o r w o u l d b e h e a v i e r a n d m o r e c u m b e r s o m e t h a n e x i s t i n g p o w e r s a w s , t h e y do n o t m e e t t h e d e s i g n r e q u i r e m e n t s . E n e r g y may b e s t o r e d a s p o t e n t i a l e n e r g y d u e t o g r a v i t y o r p r e s s u r e , o r a s k i n e t i c e n e r g y , s t r a i n e n e r g y , i n t e r n a l t h e r m a l e n e r g y , o r c h e m i c a l e n e r g y . I t i s p o s s i b l e t o c o m p a r e t h e e n e r g y s t o r i n g a b i l i t y o n a w e i g h t b a s i s b y a s s u m i n g t y p i c a l s i z e s a s s h o w n b e l o w : 67 1. K i n e t i c energy: K. E . . = 1/2 (RCO)2 f o r R = r a d i u s = 3 i n c h oj - speed = 9,000 rpm K.E. = 860 f t - l b / l b mass 2. S t r a i n energy: S.E. 2Ep f o r s t e e l rods, S P S.E. f o r s t e e l s p r i n g s , S.E. f o r rubber, S.E. = s t r e s s = 200,000 p s i 7 = modulus = 10 p s i 3 = d e n s i t y = .28 l b / i n = 240 f t - l b / l b mass = 100 f t - l b / l b mass = 4,000 f t - l b / l b mass 3. G r a v i t y p o t e n t i a l : For 100 f t above datum, P.E. = 100 f t - l b / l b mass 4. Compressed a i r p o t e n t i a l : where Wk = work out i n expanding a volume of gas from P to Pa according to law pVY = constant Pa = pressure of atmosphere pa = d e n s i t y of atmosphere Y = r a t i o of s p e c i f i c heats = 1.4 ' r = compression r a t i o = 9 Energy based on a i r weight o n l y : Wk = 80,000 f t - l b / l b a i r I f s tored i n aluminum sphere, ( s t r e s s / p r e s s = 230): Wk = 2,600 f t - l b / l b mass. 5. Thermal energy i n s a l t : For Na 2S0 4.10H 2O, Heat of Fusion = 104 B t u / l b Energy = 80,000 f t - l b / l b mass 6. Hydrocarbon f u e l : Heat of Combustion = 18,000 B t u / l b With 20% e f f i c i e n c y , Wk = 2,800,000 f t - l b / l b mass Of a l l the energy s t o r i n g devices considered, the hydrocarbon f u e l has the highest energy-to-weight r a t i o and r e q u i r e s only a small storage volume. The fundamental o b j e c t i v e of the device i s to cut a piece of wood w i t h a minimum expenditure of energy and i n the s h o r t e s t p o s s i b l e time. By ap p l y i n g a f o r c e l a r g e enough to exceed the rupture s t r e n g t h of the wood f i b r e s a piece of wood can be broken, by app l y i n g a shear load l a r g e enough to exceed the shear s t r e s s at f a i l u r e the piece can be c u t , by app l y i n g an abrasive m a t e r i a l the wood can be eroded, and by ap p l y i n g a hot wire or flame the piece can be burned. Wood 69 e x h i b i t s p r o n o u n c e d v i s c o - e l a s t i c c h a r a c t e r i s t i c s . U n d e r s u d d e n l y a p p l i e d l o a d s t h e r e i s a n i m m e d i a t e d e f o r m a t i o n a p p r o x i m a t i n g t h e c l a s s i c a l d e f o r m a t i o n p a t t e r n s , f o l l o w e d b y a l o g a r i t h m i c i n c r e a s e w i t h t i m e [ 2 . 1 6 ] . T h i s c h a r a c t e r -i s t i c means t h a t t h e f a s t e r t h e l o a d i s a p p l i e d o r t h e c u t i s m a d e , t h e h i g h e r t h e s t r e s s w i l l b e . C o n s e q u e n t l y t h e s p e c i f i c e n e r g y w i l l i n c r e a s e a s t h e c u t t i n g s p e e d i s i n c r e a s e d . U n d e r t h e i n f l u e n c e o f a n a p p l i e d b e n d i n g m o m e n t , t h e o u t e r f i b r e s i n a p i e c e o f wood c a n b e b r o k e n i f t h e moment i s l a r g e e n o u g h . F o r r o u n d wood t h e r e q u i r e d moment v a r i e s w i t h t h e d i a m e t e r c u b e d a n d f o r D o u g l a s f i r i t i s g i v e n b y : * M = 400 d 3 [ i n - l b ] w h e r e t h e d i a m e t e r (d) i s g i v e n i n i n c h e s . T h e a m o u n t o f w o r k r e q u i r e d t o b r e a k a g i v e n t r e e i n c r e a s e s a s t h e l e v e r a r m b e t w e e n t h e p o i n t o f a p p l i c a t i o n a n d g r o u n d i n c r e a s e s . T h e r e l a t i o n s h i p b e t w e e n w o r k p e r u n i t a r e a a n d l e v e r a r m f o r D o u g l a s f i r i s g i v e n b y : S p e c i f i c Work = . 3 9 I [ i n - l b / i n 2 ] a n d t h e r e q u i r e d f o r c e i s g i v e n b y : * F o r d e n s e s t r u c t u r a l w o o d , e . g . D o u g l a s f i r , s o u t h e r n p i n e , M a r k s H a n d b o o k [ 2 . 1 6 ] , g i v e s t h e f o l l o w i n g v a l u e s : S = 2000 p s i , S i m p a c t = 4000 p s i , E = 1 . 7 6 x 106 p s i . P = < o o d i I l b ] I where the l e v e r arm (Z) i s given i n inches. When a f o r c e i s a p p l i e d 8 1/2 f t from the ground on a 10 i n diameter Douglas f i r t r e e the f o l l o w i n g w i l l be r e q u i r e d to f e l l the t r e e : bending moment = ,400,000 i n - l b , f o r c e = 4,000 l b , 2 s p e c i f i c energy = 39 xn-lb/xn Because l i t t l e energy i s r e q u i r e d and the type of surface produced i s unimportant, f e l l i n g t r e e s by breaking them i s an a t t r a c t i v e way t o c l e a r l a n d . This i s done mechan i c a l l y by p u l l i n g two long chains attached to a very l a r g e and heavy s t e e l b a l l . Two t r a c t o r s , t r a v e l l i n g some d i s t a n c e a p a r t , p u l l the f r e e end of the chains and topple the t r e e s between them. The reason f o r having the b a l l diameter l a r g e i s to keep the f o r c e s low (by m a i n t a i n i n g s u i t a b l e ground clearance), and the reason f o r having the b a l l heavy i s to prevent the chains from r i d i n g along the tops of the t r e e s and breaking o f f only the t r e e t o p s . Such a device was used at the Portage Mountain Dam s i t e where two 385 hp t r a c t o r s t r a v e l l i n g 75-8 0 f t apart p u l l e d an 8 f t diameter, 9 ton s t e e l b a l l and c l e a r e d 9 acres of f o r e s t per hour. Trees up to 4 f t diameter were toppled [2.17]. Because the energy a p p l i e d to the t r e e i s d i s t r i b u t e d over a l a r g e volume,it i s not s u r p r i s i n g t h a t many ragged s p l i n t e r s p r o t r u d e on the p a r t i n g s u r f a c e and many minute c r a c k s occur on the i n s i d e of the wood. The wood broken by t h i s method i s t h e r e f o r e of a low grade. When h e l d a g a i n s t a r o t a t i n g d i s c , wood heats up, becomes b r i t t l e and d i s i n t e g r a t e s . I t i s by t h i s method t h a t Yu [2.18] c u t wood d u r i n g experiments a t the U n i v e r s i t y of B r i t i s h Columbia. He found t h a t a t low feed r a t e s f r i c t i o n does not generate s u f f i c i e n t heat to r a i s e the wood t o i t s i g n i t i o n temperature; t h e r e f o r e wood i s removed by a t t r i t i o n . He c a l c u l a t e d t h a t a t h i g h feed r a t e s the i g n i t i o n temperature i s reached, so t h a t the wood i s removed by b u r n i n g as w e l l as by a t t r i t i o n . A t a feed r a t e o f 2 4 i n /min, Yu r e q u i r e d a l o a d i n g f o r c e of 5 l b s and a s p e c i f -2 2 i c c u t t i n g energy of 100,000 i n - l b / i n . At 16 i n /min, he r e q u i r e d a f o r c e of 7 0 l b s and a s p e c i f i c energy of 2 300,000 i n - l b / i n . These v a l u e s a re f o r c u t t i n g a c r o s s the g r a i n of a f i r board 1 i n t h i c k , w i t h a moisture c o n t e n t of 72%. The s u r f a c e of the wood produced by a f r i c t i o n d i s c i s smooth, p o l i s h e d and s t r a i g h t . The k e r f i s narrow and c l e a n . But the f r i c t i o n d i s c i s p r a c t i c a l o n l y i f ample power i s a v a i l a b l e . The k i n e t i c energy of a water j e t can c u t wood i f the v e l o c i t y i s h i g h enough t o s t r e s s the wood t i s s u e s beyond t h e i r r u p t u r e s t r e n g t h s . Because the water j e t r e c e i v e s i t s k i n e t i c energy as i t passes through a very small n o z z l e , t h usable energy i s i n a h i g h l y confined and c o n t r o l l e d form. The j e t i s a c u t t e r t h a t i s not l i a b l e t o wear, does not r e q u i r e d a i l y maintenance by h i g h l y s k i l l e d personnel, and produces high q u a l i t y surfaces w i t h a n e g l i g i b l e l o s s of m a t e r i a l . But c u t t i n g w i t h water j e t s has one major d i s -advantage. U n l i k e the bending method of breaking wood and l i k e the f r i c t i o n d i s c method, the high v e l o c i t y j e t method causes a complete breakdown of the m a t e r i a l being removed. Because i t r e q u i r e s energy i n p r o p o r t i o n to the amount of breakdown, the j e t - c u t t i n g method i s h i g h l y i n e f f i c i e n t . Bryan [2.19] at the U n i v e r s i t y of Michigan found t h a t the energy r e q u i r e d by t h i s method was at l e a s t 50 times higher than normally obtained w i t h the c o n v e n t i o n a l power saw. This puts the s p e c i f i c energy r e q u i r e d a t about 100,000 2 2 i n - l b / i n . At a feed r a t e of about 5 i n /min and w i t h a pressure of 30,000 p s i he was able to penetrate 1 i n of 2 maple and generate 2 0 i n of surface area per min. At a 2 feed r a t e of about 100 i n /min, the .010 i n diameter j e t 2 generated 6 0 i n /min but the p e n e t r a t i o n was only .3 i n . E x t r a p o l a t i n g from the r e s u l t s produced by the .010 j e t , he p r e d i c t e d t h a t a .040 j e t would cut 16 i n stock. A number of other researchers have i n v e s t i g a t e d c u t t i n g w i t h water j e t s [2.20, 2.21]. Some of t h e i r f i n d i n g s are l i s t e d below: 73 1. The depth of p e n e t r a t i o n i s i n v e r s e l y p r o p o r t i o n a l to the f e e d i n g speed; the area of c u t f i r s t i n c r e a s e s w i t h i n c r e a s e d f e e d i n g speed, reaches a maximum, and then a t a c e r t a i n p o i n t begins t o decrease. 2. When the j e t passes through the same c u t many times, a " c r i t i c a l depth" i s reached a t which p o i n t the k i n e t i c energy of the j e t s w i l l be completely exhausted by the f o r c e s o f f r i c t i o n a g a i n s t the w a l l s of the cu t and a g a i n s t the so c a l l e d "water c u s h i o n " . 3. In b l i n d h o l e s a t depths g r e a t e r than 10 h o l e d i a m e t e r s , the water p r e s s u r e reaches a c o n s t a n t v a l u e of about 1/10 of the supply p r e s s u r e . 4. The maximum p r e s s u r e on a t a r g e t p l a t e i s h a l f o f the supply p r e s s u r e a t a d i s t a n c e o f about 350 n o z z l e d i a m e t e r s . 5. The p r e s s u r e d i s t r i b u t i o n on a t a r g e t p l a t e decreases r a d i c a l l y from p o i n t of impact u n t i l a t a r a d i u s o f 2.6 j e t r a d i i the p r e s s u r e i s zero. 6. The d e s t r u c t i v e c a p a b i l i t y of j e t s drops s l o w l y w i t h i n c r e a s i n g d i s t a n c e between headpiece and sample; when sample i s moved 5-25 cms, the d e s t r u c t i v e e f f e c t i s reduced 15-20%. 7. The width of k e r f i n wood i s approximately equal to the diameter of the n o z z l e opening. As w e l l as by b r e a k i n g the f i b r e s , c r u s h i n g the t i s s u e s , o r wearing p a r t i c l e s away, wood can be c u t by shear-i n g t h e f i b r e s w i t h s h a r p b l a d e s . I t i s b y t h i s l a t t e r m e t h o d t h a t m o s t o f t h e p r u n i n g i n g a r d e n s a n d o r c h a r d s a n d m o s t o f t h e f e l l i n g , l i m b i n g a n d c u t t i n g i n a m e c h a n i z e d h a r v e s t i n g s y s t e m i s c a r r i e d o u t . T h e t h i c k n e s s o f t h e b l a d e a n d i t s c u t t i n g a n g l e a f f e c t s t h e c u t t i n g f o r c e a n d s p e c i f i c e n e r g y r e q u i r e d . J o h n s t o n [2.22] f o u n d t h a t a . 2 5 0 i n t h i c k k n i f e a t a c u t t i n g a n g l e o f 4 5 ° r e q u i r e d a f o r c e o f 5,06 0 l b s a n d a 2 s p e c i f i c e n e r g y o f 817 i n - l b / i n t o c u t a 4 . 6 i n s p r u c e c a n t . A . 7 5 0 i n t h i c k k n i f e r e q u i r e d a max imum f o r c e o f 2 9,470 l b s a n d a s p e c i f i c e n e r g y o f 1,520 i n - l b / i n t o c u t a s i m i l a r c a n t . The e f f e c t o f t h e c u t t i n g a n g l e b e l o w 4 5 ° was i n s i g n i f i c a n t . B a s e d o n h i s e x p e r i m e n t a l r e s u l t s , J o h n s t o n came u p w i t h t h e f o l l o w i n g d e s i g n f o r m u l a w h i c h g i v e s t h e max imum f o r c e r e q u i r e d t o c u t f r e s h s p r u c e i n t h e d i a m e t e r r a n g e o f 3 - 6 i n s [ 2 . 2 3 , 2 . 2 4 ] : F o r c e = 3,000 + 2,300 t d - 3,400 t [ l b ] w h e r e t i s k n i f e t h i c k n e s s ( i n c h ) a n d d i s l o g d i a m e t e r ( i n c h ) . A t y p i c a l e x a m p l e o f a c o m m e r c i a l s h e a r i s t h e R o a n o k e T r e e S h e a r [ 2 . 2 5 ] . T h e s h e a r i n g s p e e d o f M o d e l T F - 1 0 , w e i g h -i n g 3,400 l b s e x c l u s i v e o f t h e c r a w l e r t r a c t o r o n w h i c h i t i s m o u n t e d , v a r i e s f r o m 5 - 1 0 s e c p e r t r e e d e p e n d i n g o n t h e t r e e d i a m e t e r . A 6 i n d i a m e t e r h y d r a u l i c c y l i n d e r w o r k i n g o n a max imum o p e r a t i n g p r e s s u r e o f 2^100-2^00 p s i s u p p l i e s t h e f o r c e t o t h e 1 1 /4 i n t h i c k b l a d e w h i c h o p e n s u p t o c u t 26 i n d i a m e t e r t r e e s . A t 12 s e c f o r a 25 i n d i a m e t e r t r e e , t h e .75 2 f e e d r a t e i s 2,500 i n / m i n a n d t h e max imum c u t t i n g f o r c e i s 6 8 , 0 0 0 l b s . C h o p p i n g w i t h a n a x e , o n e o f t h e f i r s t wood c u t t i n g m e t h o d s u s e d b y m a n , i s v e r y e f f i c i e n t a n d q u i t e f a s t . A n e x p e r i e n c e d l u m b e r j a c k c a n c u t a 14 i n d i a m e t e r w h i t e p i n e l o g i n 3 1 . 3 s e c [ 2 . 2 6 ] . A t t h i s r a t e h e c u t s 2 . . . 300 i n / m i n a n d i f h i s p o w e r d u r i n g t h i s t i m e a v e r a g e s .4 hp [ 2 . 2 7 ] , t h e s p e c i f i c e n e r g y f o r c h o p p i n g i s 530 2 i n - l b / i n . E v e n t h o u g h h i s r a t e i s h i g h f o r s h o r t p e r i o d s , t h e a x e m a n c a n n o t m a i n t a i n t h i s r a t e ; a f t e r a s h o r t t i m e , he m u s t t a k e a r e s t . M a c h i n e s o n t h e o t h e r h a n d , r e q u i r e n o r e s t p e r i o d s . A n o t h e r m e t h o d o f c u t t i n g wood ( f o r w h i c h l i t t l e i n f o r m a t i o n w a s a v a i l a b l e ) i s b y d r i l l i n g c l o s e l y s p a c e d h o l e s . I n s t e a d o f t h e s h a v i n g s b e i n g r e m o v e d a s w i t h a c o n v e n t i o n a l b i t , t h e y c a n b e p r e s s e d a g a i n s t t h e p e r i m e t e r o f t h e h o l e b y s p e c i a l w i n g - a n d - s p u r c u t t e r s t o g i v e a d d e d f o r w a r d t h r u s t a n d r e d u c e t h e p o w e r r e q u i r e d [ 2 . 2 8 ] . U l t r a s o n i c s c o u l d p o s s i b l y b e u s e d t o c u t w o o d . T h e m e c h a n i c a l f r i c t i o n p r o d u c e d b y a v i b r a t i n g t o o l c o u l d b e s u f f i c i e n t t o s t r e s s t h e f i b r e s b e y o n d t h e i r t e n s i l e l i m i t a n d t h u s p r o d u c e a r u p t u r e . E v e n t h o u g h u l t r a s o n i c s i s u s e d t o p u s h s c r e w s i n t o p l a s t i c s [ 2 . 2 9 ] , i t s c u t t i n g p o t e n t i a l i n w o o d i s y e t t o b e d e t e r m i n e d . T h e m e t h o d o f wood c u t t i n g r e q u i r i n g t h e s m a l l e s t a m o u n t o f e x t e r n a l e n e r g y i s b u r n i n g . O n c e t h e i g n i t i o n temperature of the wood i s reached w i t h the a i d of a flame or hot band, the c u t t i n g a c t i o n can be s e l f s u s t a i n i n g . I f r a p i d combustion i s maintained w i t h a l e n g t h of hot wire or s t e e l band and a c o n t r o l l e d supply of oxygen, the cut can be completed before combustion i n the v i c i n i t y of the cut becomes s e l f - s u s t a i n i n g . This concept was e x p e r i -mentally proved f e a s i b l e by c u t t i n g w i t h an oxygen-acetylene t o r c h . The most popular method of c u t t i n g wood i s w i t h a saw because the s p e c i f i c energy r e q u i r e d i s low and the c u t t i n g r a t e i s d i r e c t l y p r o p o r t i o n a l to the power a v a i l a b l e . Johnston [2.30] found t h a t f o r feed r a t e s from 2 600-2,300 i n /min he r e q u i r e d a s p e c i f i c energy of about 2 1460 i n - l b / i n to c r o s s - c u t white spruce lumber. The energy r e q u i r e d to cut white pine was 18% lower, w h i l e t o cut y e l l o w b i r c h i t was 23% higher. As has been shown i n Chapter 1, the energy r e q u i r e d to cut wood w i t h a chain saw depends on the j o i n t of the c h a i n , the chain speed, the r a t e of c u t t i n g and the species of t r e e . For hemlock the minimum 2 s p e c i f i c energy r e q u i r e d was 1,650 i n - l b / i n at a feed r a t e 2 of 700 i n /min. This s p e c i f i c energy i s shown on Graph 2.1, w i t h the s p e c i f i c energy r e q u i r e d by the other c u t t i n g d e v i c e s . Before the choice of a wood c u t t i n g device was f i n a l i z e d , the e x i s t i n g engines were evaluated. This e v a l u a t i o n i s the subject of the next s e c t i o n . 77 Graph 2.1 S p e c i f i c e n e r g i e s r e q u i r e d by v a r i o u s wood c u t t i n g d e v i c e s 2.2 E v a l u a t i o n of E x i s t i n g Engines In the e v o l u t i o n of the i n t e r n a l combustion engine many types and c o n f i g u r a t i o n s have emerged as p o s s i b l e a l t e r n a -t i v e s t o the c o n v e n t i o n a l r e c i p r o c a t i n g engine. The Wankel, gas t u r b i n e , and S t i r l i n g engines, f a m i l i a r to the engine d e s i g n e r as concepts t h a t have overcome some of the d i s a d -vantages of r e c i p r o c a t i n g engines were e v a l u a t e d as p o s s i b l e s m a l l power u n i t s . Other types proposed by i n v e n t o r s such as T s c h u d i , Mercer, L l e w e l l y n , Dotto, Lim, James, Yoto, Gursted, V i r m e l , Kauretz, U n s i n , Rajakaruna and Selwood were c o n s i d e r e d but not e v a l u a t e d as none of them appeared p r o m i s i n g . The gas t u r b i n e has the advantages of a r e l a t i v e l y c o n s t a n t torque a t a l l speeds, v i b r a t i o n l e s s o p e r a t i o n and a h i g h power-to-weight r a t i o . Although i n p r i n c i p l e the weight per horsepower v a r i e s w i t h the square r o o t of the horse power, i n p r a c t i c e the t u r b i n e and compressor e f f i c i e n -c i e s d e t e r i o r a t e r a p i d l y below 500 hp so t h a t the promised g a i n i n weight per horsepower tends to be c a n c e l l e d out. Disadvantages of t h i s engine are the hi g h f u e l consumption and the slow r a t e of a c c e l e r a t i o n . A number of s m a l l gas t u r b i n e s have been b u i l t or are proposed. S o l l a r ' s f e a s i b i l i t y study of s m a l l gas t u r b i n e s i n d i c a t e d t h a t a 20 hp gas t u r b i n e t u r n i n g a t 100,000 rpm w i l l have a s p e c i f i c f u e l consumption of 1.04 l b / s h p - h r and w i l l c o s t $1,400 i n q u a n t i t i e s of 2,000 u n i t s per year [ 2 . 3 1 ] . An 80 hp t u r b i n e i n a t r a c t o r w i t h a r e d u c t i o n gear to 2,000 rpm weighs 90 l b s [ 2 . 3 2 ] . A two-stage t u r b i n e d r i v e n by mercury vapour and d r i v i n g an a l t e r n a t o r i n a h e r m e t i c a l l y s e a l e d package 7 i n diameter by 18 i n long, weighs 60 l b s and produces 4 k i l o w a t t a t 3,600 rpm [ 2 . 3 3 ] . V o l v o ' s 250 hp automotive gas t u r b i n e , i n c l u d i n g t r a n s m i s s i o n , weighs 800 l b s [ 2 . 3 4 J . Ford's 400 hp gas t u r b i n e s f o r t r u c k s are to c o s t 10-15 $/hp. [ 2 . 3 5 ] . These examples i n d i c a t e t h a t the gas t u r b i n e i s not competitive costwise w i t h the conventional r e c i p r o c a t i n g engine. Of the numerous r o t a r y engines proposed during the l a s t decade only the Wankel has emerged as a p r a c t i c a l a l t e r n a t i v e t o the p i s t o n engine. F a c t o r i e s i n Japan and Germany are producing them on an assembly l i n e b a s i s , and companies i n I t a l y , France and England are planning to do the same. Some recent design changes found necessary to improve the performance and r e l i a b i l i t y [2.36] show up some weaknesses of the Wankel: 1. i n t a k e p o r t s were moved to the si d e s so t h a t the ove r l a p between i n t a k e and exhaust p o r t s was reduced, thereby improving f u e l consumption, 2. the t r o i c h o i d a l t r a c k was sprayed w i t h s p e c i a l m a t e r i a l and se a l s were made of more s u i t a b l e m a t e r i a l s to reduce apex s e a l c h a t t e r i n g ( N i t r i t e d c a s t i r o n , molybdenum spray and chrome-p l a t i n g had p r e v i o u s l y been t r i e d ) , 3. the heat flow path from the unsymmetrically heated r o t o r and t r a c k was changed to reduce d i s t o r t i o n . To evaluate the f e a s i b i l i t y of using the Wankel engine i n a power saw, the performance c h a r a c t e r i s t i c s of an i n d u s t r i a l Wankel engine producing 6.6 hp at 5,500 rpm 80 was compared with an i n d u s t r i a l two-stroke engine producing 3 hp at 5,000 rpm and a conventional power saw producing 5.8 hp at 7,000 rpm. The information on the Wankel and i n d u s t r i a l engines was obtained from Go-Power Corporation [2.37] and the information on the power saw, from Power Machinery Limited. The Wankel engine used i n t h i s comparison was the f i r s t production version of a single rotor a i r cooled F i c h t l and Sachs KM37 i n d u s t r i a l u n i t . The scavenging charge i n t h i s engine heats up as i t passes through the rotor before entering the cylinder, to keep the temperatures down to acceptable l e v e l s [2.38]. The governor, although very necessary on the Wankel, i s an unattractive feature for loggers. The two-cycle i n d u s t r i a l u n i t used i n the compar-isons was an a i r cooled, diecast, reed-valve-ported McCulloch Series 49 i n d u s t r i a l engine, a type commonly used i n chain saws, scooters and outboard motors. The chain saw was a sand cast, piston-ported Canadien 275 complete with bar and chain. The c h a r a c t e r i s t i c s of the three engines are l i s t e d i n Table I I . The p o s i t i v e features of the Wankel engine,when used i n a power saw, would be: 1. lower v i b r a t i o n l e v e l s , 2. smoother torque, 3. lower f u e l consumption, 4. lower o i l consumption, 5. lower s t a r t i n g torque, 6. lower noise l e v e l . 81 T a b l e I I C h a r a c t e r i s t i c s o f t h e C o n v e n t i o n a l a n d W a n k e l E n g i n e s I n d u s t r i a l W a n k e l C h a i n Saw 3 D i s p l a c e m e n t ( i n ) 4 . 9 6 . 6 7 . 4 M a x i m u m p o w e r ( s h p ) 3 . 0 @ 5,000 rpm 6 . 6 @ 5,500 rpm 5 . 8 @ 7,000 rpm W e i g h t ( l b / h p ) 4 . 0 5 . 2 3 . 7 S p e c i f i c f u e l c o n s u m p t i o n ( l b s / s h p - h r ) 1 .1 0 . 7 1 . 0 L i s t p r i c e ( $ / h p ) 33 60 60 C o m p r e s s i o n r a t i o 6 8 . 5 5 . 7 V i b r a t i o n a m p l i t u d e a t 4000 r p m [ 2 . 3 8 ] . 0 1 7 ( t y p i c a l ) . 0 0 2 5 . 0 1 4 R a t i o o f max imum t o mean t o r q u e [ 2 . 3 9 ] 7 . 0 3 . 5 7 . 0 Number o f n o i s e p u l s e s p e r c y c l e 1 3 1 The n e g a t i v e f e a t u r e s w o u l d b e : 1 . h i g h e r c o s t , 2 . m o r e w e i g h t , 3 . g r e a t e r c o m p l e x i t y , 4 . r e d u c e d r e l i a b i l i t y * T h e l a s t f e a t u r e c a n b e i m p r o v e d b y m o r e d e v e l o p m e n t w o r k o n t h e s e a l i n g , c o o l i n g a n d c o m b u s t i o n s y s t e m s . G r a p h 2 . 2 82 shows t h a t the power-speed c h a r a c t e r i s t i c of the Wankel engine i s q u i t e c l o s e t o t h a t of a chain saw engine, although the power i n the Wankel drops f a s t e r as the engine slows down. As the operator c o n t r o l s the engine speed by the amount of load he a p p l i e s to the saw, the Wankel engine, as ported, would be harder to keep at the optimum speed, espec-i a l l y s i nce the governor cuts i n as the engine develops maximum power. As the negative f a c t o r s are important to a power saw operator, other engines were evaluated. .SPEED (RPM) Graph 2.2 Power of a Wankel engine compared w i t h con-v e n t i o n a l engines Although invented by S t i r l i n g i n 1816, the q u i e t h o t - a i r c y c l e engine was not a p r a c t i c a l high speed engine u n t i l very r e c e n t l y . The innovations which made the o l d concept p r a c t i c a l are: 83 1. use of hydrogen or helium as the working gas, 2. increased knowledge of compact heat exchanges, 3. i n v e n t i o n of the rhombic d r i v e , 4. i n v e n t i o n of " r o l l s o c k " p o s i t i v e s e a l s . P h i l i p s [2.40] b u i l t a 440 l b hot-gas engine t h a t developed 50 hp at 2,500 rpm. By using l i g h t - w e i g h t m a t e r i a l s , by o p e r a t i n g the engine at high speeds, and by designing f o r low weight and high power, one would expect the weight to power r a t i o of the hot gas engine to be competit i v e w i t h e x i s t i n g two-stroke engines. The inherent c h a r a c t e r i s t i c s of the e x t e r n a l com-b u s t i o n engine g i v e the S t i r l i n g engine the f o l l o w i n g p o s i t i v e f e a t u r e s : 1. smokefree combustion w i t h a great v a r i e t y of f u e l s , 2. exhaust temperatures only a few degrees above the incoming a i r temperature, 3. low s p e c i f i c f u e l consumption (.52 l b / s h p - h r ) , 4. low peak torque (3.5 times mean output torque r e s u l t -i ng p a r t l y from two pulses per r e v o l u t i o n ) , 5. low p i s t o n v e l o c i t i e s (750-800 fps) , 6. low noise l e v e l s ( i n a u d i b l e at 100-300 f t ) , 7. low v i b r a t i o n l e v e l s (rhombic d r i v e r e s u l t i n g i n a balanced engine). Some of the negative c h a r a c t e r i s t i c s t h a t produce a heavier and more expensive engine are: 84 1. more complicated mechanisms such as seals, power and speed control devices, regenerator, o i l pump and an a u x i l i a r y compressor for the working gas, 2. higher forces i n the drive mechanism and cylinder, 3. long delay i n st a r t i n g cold engine (1-2 min), 4. larger cooling system (approximately double con-ventional engine requirements). The hot-gas engine i s based on the well known p r i n c i p l e of compressing gas at a low temperature (Figure 2.IB) and expanding i t at a high temperature (Figure 2.ID). When a high temperature i s required, the gas i s forced into a hot region (Figure 2.1C) and when a low temperature i s required, into a cold region (Figure 2.1A). What makes the modern engine work so well i s an e f f e c t i v e regenerator situated between the hot and cold regions. This regenerator stores most of the heat rejected at the end of the expansion stroke and returns i t to the gas at the end of the compression stroke. In order to get the most work out of a cycle, the power piston stroke and the displacer piston stroke must overlap, and the cold volume must go to zero. At a given r a t i o between the hot and cold space temperatures and the r a t i o between the maximum hot and maximum cold volumes, there e x i s t optimum values of piston phase angle and swept volume. These conditions were analyzed by Kirkley [2.41], Creswick [2.42] analyzed the heat and mass flow i n the i d e a l i s o t h e r m a l S t i r l i n g c y c l e and made the f o l l o w i n g o b s e r v a t i o n s : 1. Heat must be r e j e c t e d from a l l surfaces during compression and added everywhere during expansion to maintain a constant temperature. A B C D  F i g u r e 2.1 Diagrams i l l u s t r a t i n g the hot-gas c y c l e 2. Because more mass i s i n the expansion space during expansion than during compression, more heat i s added than i s r e j e c t e d . The reverse i s t r u e f o r the compression space. 3. The dead spaces r e j e c t as much heat as they take i n , thus they have no u s e f u l f u n c t i o n i n the i d e a l i s o -thermal c y c l e . 86 4 . T h e p e a k h e a t f l u x f a r e x c e e d s t h e a v e r a g e r a t e o f h e a t a d d i t i o n ; t h e r e f o r e , h e a t t r a n s f e r s u r f a c e s s h o u l d b e d e s i g n e d t o a c c o m m o d a t e t h e i n s t a n t a n e o u s h e a t a d d i t i o n r a t e s r a t h e r t h a n t h e a v e r a g e n e t r a t e . 5 . T h e t o t a l a m o u n t o f h e a t d e p o s i t e d o r p i c k e d u p i n o n e " b l o w " o f t h e r e g e n e r a t o r i s s e v e r a l t i m e s g r e a t e r t h a n t h e n e t a m o u n t t r a n s f e r r e d f r o m t h e e n v i r o n m e n t p e r c y c l e . A t l e a s t f i v e e n g i n e a r r a n g e m e n t s a r e p o s s i b l e : o p p o s e d , V e e , o i l c o l u m n , d o u b l e a c t i n g a n d r h o m b i c d r i v e [ 2 . 4 3 ] . I n t h e o p p o s e d p i s t o n c o n f i g u r a t i o n , t h e h i g h p r e s s u r e s a c t i n g o n t h e p i s t o n s ( i n t h e o r d e r o f 100 a t m o -s p h e r e s ) m u s t b e b a l a n c e d b y i n t r o d u c i n g a h i g h a v e r a g e p r e s s u r e i n t h e l a r g e c r a n k c a s e . I n t h e V e e a r r a n g e m e n t t h e c r a n k c a s e i s m o r e c o m p a c t , b u t t h e l a r g e d e a d s p a c e b e t w e e n p i s t o n s a n d t h e l a c k o f f l o w s y m m e t r y r e d u c e t h e r m o d y n a m i c e f f i c i e n c i e s . D r i v i n g t h e p o w e r p i s t o n s w i t h a c o l u m n o f o i l o v e r c o m e s some o f t h e s e d e f i c i e n c i e s b u t t h e o i l m u s t b e c i r c u l a t e d , c o o l e d , d e g a s s e d a n d f i l t e r e d . I n t h e d o u b l e a c t i n g e n g i n e e a c h o f f o u r p i s t o n s p e r f o r m s t h e w o r k o f a d i s p l a c e r a n d a p o w e r p i s t o n a l t e r n a t e l y , a s t h e g a s i s f o r c e d f r o m o n e c y l i n d e r t o a n o t h e r t h r o u g h t h e r e g e n e r a t o r ; i n t h i s a r r a n g e m e n t a l i m i t t o t h e v a r i a t i o n i n h o t a n d c o l d v o l u m e s a f f e c t s t h e r m o d y n a m i c e f f i c i e n c i e s . I n t h e r h o m b i c 87 d r i v e c o n f i g u r a t i o n , a b a l a n c e d e n g i n e w i t h o u t a p r e s s u r i z e d c r a n k c a s e i s p o s s i b l e b e c a u s e t h e d i s p l a c e r p i s t o n i s e a s i l y s e a l e d w i t h a r o l l i n g d i a p h r a p h m ; t h i s c o n f i g u r a t i o n i s t h e r m o d y n a m i c a l l y f a v o u r a b l e a n d t e c h n i c a l l y a p p e a l i n g b e c a u s e o f i t s s i m p l i c i t y . A l l o f t h e b a s i c c o m p o n e n t s o f a h o t - g a s e n g i n e i n a r h o m b i c d r i v e c o n f i g u r a t i o n w e r e e v a l u a t e d w i t h a v i e w t o d e s i g n i n g t h e m f o r a p o w e r saw a p p l i c a t i o n . The a r r a n g e m e n t o f t h e s e c o m p o n e n t s i s shown i n t h e s c h e m a t i c d i a g r a m F i g u r e 2 . 2 . T h e m a i n c o m p o n e n t i s , o f c o u r s e , t h e r e g e n e r a t o r . T h e r m a l s t r e s s c a n b e a v o i d e d b y d i v i d i n g t h e a n n u l a r s p a c e i n t o a n u m b e r o f s m a l l e r c h a m b e r s n o t c o n t i n u o u s w i t h t h e c y l i n d e r w a l l . B e s t p e r f o r m a n c e c a n b e o b t a i n e d w i t h a m a t r i x c o n s i s t i n g o f a r a n d o m l y p a c k e d m a s s o f c o p p e r w i r e s a p p r o x i m a t e l y . 0 0 1 i n d i a m e t e r b y 2 i n l o n g , a r r a n g e d b e t w e e n t w o s l e e v e s o f c o m p r e s s e d p a p e r a n d r e t a i n e d o n t h e e n d s b y a c o a r s e w i r e g a u z e [ 2 . 4 4 ] . T h e a i r u s e d i n c o m b u s t i o n e n t e r s t h e p r e h e a t e r o n t h e o u t s i d e o f t h e h o t a i r d u c t s a n d s p i r a l s i n t o t h e b u r n e r . O n c e i n t h e b u r n e r t h e a i r i s s p r a y e d w i t h a t o m i z e d f u e l , i g n i t e d , a n d t h e h o t g a s l e a v e s t h r o u g h t h e i n s i d e o f t h e h o t - a i r d u c t t o b e i n s u l a t e d b y t h e i n c o m i n g a i r . A l t e r i n g t h e mean p r e s s u r e o f t h e w o r k i n g g a s c o n t r o l s t h e e n g i n e o u t p u t w i t h o u t a f f e c t i n g t h e t h e r m a l e f f i c i e n c y . The c o n t r o l s y s t e m c o n s i s t s o f a m e t h o d f o r a d m i t t i n g a n d w i t h d r a w i n g g a s f r o m t h e w o r k i n g c y c l e a n d a thermostat to c o n t r o l the heater temperature. An a u x i l i a r y compressor f o r c e s gas i n t o the working c y c l e and a low pres-sure r e c e i v e r tank (below the lowest maximum c y c l e pressure) accepts excess gas. By using a low d e n s i t y gas such as hydro-gen, flow l o s s e s are r e l a t i v e l y s m a l l , heat t r a n s f e r c o e f f i c -i e n t s are h i g h , and the response to t h r o t t l e i s f a s t . I Schematic diagram of rhombic drive mechanism. J = power pistonT 6 — displacer piston. 5-5' = cranks in two shafts rotating in opposite senses and coupled by gears 10-10'. 4-4' c con-rods pivoted from ends of yoke 3 fixed to the hollow power-piston rod 2. 9-9' = con-rods pivoted from ends of yoke 8 fixed to displacer-piston rod, which runs through the hollow power-piston rod, 11 and 12= gas-tight stuffing-boxes. /.'* ** buffer space containing gas at high buffer pressure. F i g u r e 2. 2 S t i r l i n g thermal engine schematic drawing [2.40] 89 T h e r o l l i n g d i a p h r a g m h a s a d d e d g r e a t l y t o t h e e f f i c i e n c y o f t h e m o d e r n h o t - g a s e n g i n e . I t m a i n t a i n s a p o s i t i v e s e a l b e t w e e n t h e p i s t o n a n d c y l i n d e r w a l l s s o t h a t n o w o r k i n g g a s c a n e s c a p e f r o m t h e c y l i n d e r . A s t h e d i a p h r a g m i s s u p p o r t e d o n a n o i l c u s h i o n , i t s f u n c t i o n i s c o n f i n e d t o s e p a r a t i n g t h e f l u i d i n t h e c u s h i o n f r o m t h e w o r k i n g g a s a b o v e t h e p i s t o n . A c r o s s t h e d i a p h r a g m t h e r e i s o n l y a p r e s s u r e d i f f e r e n c e o f a b o u t 5 a t m o s p h e r e s . T h e r e a l d i f f e r e n c e i n p r e s s u r e s ( 5 0 - 1 0 0 a t m o s p h e r e s ) i s c a r r i e d b y a s e c o n d c o n v e n t i o n a l s e a l . T h i s s e a l s e p a r a t e s t h e o i l c u s h i o n u n d e r t h e d i a p h r a g m f r o m t h e s p a c e c o n t a i n i n g t h e d r i v i n g m e c h a n i s m . B y d e s i g n i n g s t e p s i n t h e p i s t o n a n d i n t h e c y l i n d e r w a l l , t h e o i l c u s h i o n v o l u m e b e c o m e s i n d e p e n d e n t o f t h e s t r o k e , a n d b y d e s i g n i n g s u i t a b l e o r i f i c e s , t h e p r e s s u r e c a n b e made s e l f - r e g u l a t i n g . T h e e n d u r a n c e o f t h e r o l l i n g d i a p h r a m s d e p e n d s d i r e c t l y o n t h e p r e s s u r e a c r o s s t h e d i a p h r a g m a n d i n v e r s e l y o n t h e t h i c k n e s s , t e m p e r a t u r e a n d p i s t o n c l e a r a n c e ; ( P o l y u r e t h a n e r u b b e r d i a p h r a g m s l a s t f o r a b o u t a y e a r ) [ 2 . 4 6 ] . A p o w e r saw e n g i n e s h o u l d b e a i r - c o o l e d . To a c h i e v e t h e h i g h c o o l i n g r a t e r e q u i r e d < i n a h o t - g a s e n g i n e , a l a r g e s u r f a c e a r e a a n d a l a r g e b l o w e r a r e r e q u i r e d . I f t h e t e m p e r -a t u r e s a r e n o t k e p t l o w , e f f i c i e n c y a n d p o w e r i s l o w . S c a l i n g l a w s i n d i c a t e t h a t f o r s i m i l a r e n g i n e s , w e i g h t s a r e p r o p o r t i o n a l t o d i s p l a c e m e n t . I f a c o n s t a n t p i s t o n s p e e d i s m a i n t a i n e d , t h e n t h e p o w e r - t o - w e i g h t r a t i o 90 g o e s u p a s t h e d i s p l a c e m e n t g o e s d o w n . A l s o , t h e r a t i o o f t h e s u r f a c e a r e a - t o - v o l u m e g o e s up s o t h a t v e r y s m a l l c y l i n d e r s w i l l h a v e a r e l a t i v e l y h i g h h e a t t r a n s f e r (a c h a r a c t e r i s t i c d e s i r e d i n t h e h o t g a s e n g i n e . ) B a s e d o n t h e s e o b s e r v a t i o n s , i t i s e x p e c t e d t h a t a s m a l l e n g i n e w o u l d h a v e a h i g h p o w e r - t o - w e i g h t r a t i o ( i f c l e a r a n c e s c a n b e s c a l e d d o w n . ) B a s e d o n t h e P h i l i p s 40 h p e n g i n e ( s c a l i n g f a c t o r m = . 3 6 ) , a 5 hp e n g i n e r u n n i n g a t 4 , 5 0 0 r p m w o u l d w e i g h 20 l b s a n d o c c u p y t h e same v o l u m e a s a c y l i n d e r 5 i n d i a m e t e r b y 12 i n l o n g . A S t i r l i n g c y c l e p o w e r saw w o u l d r u n q u i e t l y , s m o k e - f r e e , n e a r l y v i b r a t i o n l e s s a n d w i t h a c o o l e x h a u s t . The m a c h i n e w o u l d c o s t m o r e a n d b e m o r e c o m p l e x a n d h e a v i e r t h a n a c o n v e n t i o n a l t w o - s t r o k e e n g i n e . T h e d e l a y i n s t a r t -i n g w o u l d b e i n c o n v e n i e n t , b u t t h e d e l a y w o u l d b e v e r y s h o r t w h e n t h e saw was h o t . S e c o n d a r y f a c t o r s s u c h a s i t s a b i l i t y t o b u r n a v a r i e t y o f f u e l s e f f i c i e n t l y , t o o p e r a t e a t a l o w e r s p e e d a n d t o i g n i t e f u e l w i t h o u t h i g h p r e s s u r e f u e l pumps o r t i m e d m a g n e t o s , w o u l d p r e s e n t some a d v a n t a g e s , b u t f a c t o r s s u c h a s s p e c i a l s e a l s , c o m p l i c a t e d p o w e r a n d s p e e d c o n t r o l s , a n d t h e r e q u i r e m e n t o f a p r e s s u r i z e d g a s s y s t e m w o u l d p r e s e n t m a i n t e n a n c e a n d c o s t d i s a d v a n t a g e s . A c h a i n saw i s v e r y o f t e n a b u s e d . F o r t h i s r e a s o n i t s h o u l d b e s i m p l e , r u g g e d a n d f o o l p r o o f . I f a n y o f t h e c o m p l i c a t e d c o n t r o l s o r s e a l s o n t h e h o t - g a s e n g i n e w e r e t o m a l f u n c t i o n , t h e e n g i n e w o u l d n o t r u n a n d w o u l d r e q u i r e a competent mechanic f o r r e p a i r s . Because the saw would cost at l e a s t twice as much as the c o n v e n t i o n a l engine and weigh about 50% more, i t i s d o u b t f u l t h a t i t would be accepted i n the g e n e r a l c o m p e t i t i v e market. Nevertheless, f o r l i m i t e d markets, where m u l t i f u e l c a p a c i t y and freedom from noise and v i b r a t i o n i s paramount, the S t i r l i n g c y c l e power saw might be the answer. But f o r the purpose of t h i s p r o j e c t , the S t i r l i n g c y c l e engine d i d not meet the design r e q u i r e -ments so t h a t the a n a l y s i s was d i s c o n t i n u e d . 2.3 Synthesis of A l t e r n a t i v e s As the e v a l u a t i o n of the gas t u r b i n e , Wankel and S t i r l i n g engines f a i l e d to i n d i c a t e an engine t h a t would be c o m p e t i t i v e w i t h the two-stroke c y c l e engine p r e s e n t l y used e x t e n s i v e l y i n p o r t a b l e power saws, the next stage i n the design program was to s y n t h e s i z e some new engine arrange-ments. The s y n t h e s i s s t a r t e d w i t h a c o n s i d e r a t i o n of the b a s i c problem areas i n the e x i s t i n g power saws and concluded w i t h a f e a s i b i l i t y check. No p a r t i n high-speed engines i s as important as the connecting rod bearings. And yet no. p a r t f a i l s as o f t e n . To produce as much power as p o s s i b l e from a given weight, designers have gone to higher and higher speeds, u n t i l the f a t i g u e l i f e of the connecting rod bearings i s o f t e n reached w i t h i n the u s e f u l l i f e of the saw. The high loadings and l a r g e number of c y c l e s cause the bearings to f a i l and the engine to stop. An engine without a crank would be i d e a l . 92 The c r a n k l e s s r o t a t i n g f r e e p i s t o n engine concept, based on the ide a t h a t a weight at the end of a h o r i z o n t a l l e v e l causes an unbalanced moment, meets t h i s requirement. I f the l e v e r were allowed to r o t a t e and i f the weight were moved up whenever the weight reaches i t s lowest p o i n t ( i . e . when the l e v e r i s v e r t i c a l ) , then the l e v e r would continue to r o t a t e . By using a p i s t o n as the weight and a c y l i n d e r as a l e v e r , an engine i s t h e o r e t i c a l l y p o s s i b l e . An a n a l y s i s of the energy present i n such a system y i e l d e d the f o l l o w i n g equation f o r the k i n e t i c energy: 0 2 M V 2 K.E. = (I + 1 + M R ) + ? P c p p 2 2 Where I i s the i n e r t i a of the c y l i n d e r about c 1 center of r o t a t i o n , I i s the i n e r t i a of the p i s t o n about P center of r o t a t i o n , Vp i s the v e l o c i t y of the p i s t o n , M i s the mass of the p i s t o n , P R i s the d i s t a n c e from the p i s t o n center of g r a v i t y , to i s the angular v e l o c i t y of c y l i n d e r . Assuming t h a t the p i s t o n experienced only a cen-t r i f u g a l f o r c e ( g r a v i t a t i o n a l f o r c e and gas f o r c e n e g l i g i b l e ) then the d i f f e r e n t i a l equation i s : 93 2M Ru> V = _ _ J 2 P d t I + 1 + M R< C p p 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 t h e c y l i n d e r would slow down as the p i s t o n moved away from t h e c e n t e r o f r o t a t i o n and speed up as t h e p i s t o n moved towards t h e c e n t e r . I n o r d e r t o g e t work o u t , a p l a n e t a r y g e a r and a one-way c l u t c h t h a t a l l o w e d t h e c y l i n d e r t o a c c e l e r a t e o n l y i f the o u t p u t arm a l s o a c c e l e r a t e d was p o s t u l a t e d . On c l o s e r e x a m i n a t i o n i t became o b v i o u s t h a t t h e system would s l o w down and s t o p u n l e s s t h e work p u t i n t o t h e system t h r o u g h c o m b u s t i o n c o u l d a c c e l e r a t e t h e c y l i n d e r . T h i s r e a l i z a t i o n l e d t o an a n a l y s i s o f t h e energy i n v o l v e d i n moving t h e p i s t o n a g a i n s t the c e n t r i f u g a l f o r c e . The o b s e r v a t i o n was made t h a t i f t h e system c o u l d be a r r a n g e d so t h a t w h i l e t h e p i s t o n was moving away from t h e c e n t e r o f r o t a t i o n t h e c y l i n d e r r o t a t e d more s l o w l y t h a n when th e p i s t o n was moving toward t h e c e n t e r o f r o t a t i o n , n e t work ou t c o u l d be p o s s i b l e . Combustion must o c c u r when t h e p i s t o n was f u r t h e s t from t h e c e n t e r o f r o t a t i o n , so t h a t t h e energy r e l e a s e d i n c o m b u s t i o n would move t h e p i s t o n a g a i n s t t h e c e n t r i f u g a l f o r c e . But t h i s arrangement l a c k e d a r e a c t i o n f o r c e and w i t h o u t one no system c o u l d work. T h e r e f o r e the n e x t s t e p was t o p o s t u l a t e an arrangement whereby g r a v i t y would g i v e t h e r e q u i r e d r e a c t i o n f o r c e . I n t h i s s i m p l e a r r a n g e -ment t h e p i s t o n moved a g a i n s t a g r a v i t y f o r c e , as i n F i g u r e 94 2 . 3 . A s l o n g a s t h e p i s t o n r e m a i n e d o n t h e l e f t s i d e o f t h e c e n t e r o f r o t a t i o n , t h e o u t p u t t o r q u e was p o s i t i v e . e a F i g u r e 2 . 3 S k e t c h e s o f t h e u n b a l a n c e d l e v e r e n g i n e I n p r i n c i p l e t h e e n g i n e o p e r a t e d a s f o l l o w s : a s t h e c y l i n d e r r o t a t e d c o u n t e r c l o c k w i s e o n s h a f t " 0 " , t h e p i s t o n m o v e d t o w a r d e n d " A " a s shown i n F i g u r e 2 . 3 . I n t h i s p o s i t i o n t h e p i s t o n w e i g h t a c c e l e r a t e d t h e c y l i n d e r . A t t h e e n d o f t h e s t r o k e t h e c o m p r e s s e d m i x t u r e i n e n d " A " i g n i t e d a n d t h e p r e s s u r e a c c e l e r a t e d t o w a r d s e n d " B ' . ' B u t t h e c y l i n d e r was a l s o r o t a t i n g , s o when t h e p i s t o n h a d p a s s e d t h r o u g h t h e c e n t e r o f r o t a t i o n , t h e g r a v i t a t i o n a l p u l l o n t h e p i s t o n a g a i n e x e r t e d a p o s i t i v e t o r q u e o n t h e s h a f t . I f t h e c y c l e c o n t i n u e d o n e n d "B" a s i t h a d d o n e o n e n d " A " , a n d i f t h e e a r t h ' s g r a v i t a t i o n a l p u l l was a u g m e n -t e d b y s w i n g i n g t h e c y l i n d e r a b o u t a n o t h e r c e n t e r , a c o m p a c t e n g i n e was t h e o r e t i c a l l y p o s s i b l e . 95 A s i m p l e c a l c u l a t i o n s h o w e d t h a t f o r a c y l i n d e r a s s e m b l y r o t a t i n g a t 1 , 0 0 0 rpm a b o u t a n a x i s 6 i n f r o m t h e c e n t e r o f t h e c y l i n d e r r o t a t i o n , t h e c e n t r i f u g a l a c c e l e r -a t i o n was a p p r o x i m a t e l y 150 g . I f c o m b u s t i o n r a i s e d a 1 l b p i s t o n a d i s t a n c e o f 1 i n a n d i f t h e c y l i n d e r s r o t a t e d a t 6 , 0 0 0 r p m , a 4 c y l i n d e r e n g i n e w o u l d p r o d u c e a b o u t 10 h p . A n a n a l y s i s o f t h e s y s t e m p r o d u c e d t w o s i m u l t a n -e o u s e q u a t i o n s ; o n e d e s c r i b e d t h e p i s t o n a c c e l e r a t i o n a n d t h e o t h e r d e s c r i b e d t h e c y l i n d e r a c c e l e r a t i o n : 2 ri R 2 2 dR = A ( P » - P ) + Leo c o s 9 + R(CO+(JO ) ± y[2 ~ (co+co )+ L u s i n 9 ] d t 2 O 0 r\ A - (Leo s i n e ± u[RW+R+Lu c o s 8 ] ) = — * • d t ^ = ( C 2 d T ^+UQ) + L w 2 s i n 8 ] [ c o s e + ~ + 5_ ± y s i n e ] d t \ + A (P - P » ) s i n e - T I / [ I W + I +-S . -R r £ 1/ \ ° q W i ) W h e r e R = [R + RW + LW c o s 6 ] [ c o s 8 + ^ + _ ± u s i n 6 ] R = i s d i m e n s i o n l e s s p i s t o n p o s i t i o n , r i s p i s t o n p o s i t i o n ( f r o m c e n t e r o f r o t a t i o n ) , s i s r e f e r e n c e s t r o k e d 8 co i s a n g u l a r s p e e d o f c y l i n d e r = ^ , 6 i s a n g u l a r p o s i t i o n o f c y l i n d e r ( f r o m r o t a t i n g a r m ) , 96 de OJ i s a n g u l a r s p e e d o f r o t a t i n g arm = ° d t I L = — i s d i m e n s i o n l e s s l e n g t h o f r o t a t i n g arm, I i s l e n g t h o f r o t a t i n g a rm, t i s t i m e , OJ W = —°- i s d i m e n s i o n l e s s a n g u l a r s p e e d r a t i o , OJ u i s c o e f f i c i e n t o f f r i c t i o n , A'P. Mps A = i s p i s t o n a r e a r a t i o , A 1 i s p i s t o n a r e a , P^ i s a t m o s p h e r i c p r e s s u r e , Mp i s mass o f p i s t o n , P ' P = —r— i s p r e s s u r e r a t i o i n r i g h t c y l i n d e r , r P a p 1 L P p = i s p r e s s u r e r a t i o i n l e f t c y l i n d e r , L P a T o u t 2 i s o u t p u t t o r q u e r a t i o , I = — ° — j i s i n e r t i a o f r o t a t i n g arm a s s e m b l y , L Mps I ' ( LMps" q LMps — 3 — i s i n e r t i a o f c y l i n d e r - p i s t o n a s s e m b l y . B e c a u s e t h e g a s f o r c e s p r e s e n t i n t h e s e e q u a t i o n s a r e h i g h l y n o n - l i n e a r , t h e e q u a t i o n s w e r e s o l v e d b y s t e p - w i s e c o m p u t e r i n t e g r a t i o n u s i n g t h e R u n g e - K u t t a s u b r o u t i n e . 97 The n u m b e r o f d e s i g n c h o i c e s a v a i l a b l e t o t h e e n g i n e e r i s r e f l e c t e d i n t h e n u m b e r o f p a r a m e t e r s i n t h e e q u a t i o n s a s w e l l a s t h e c o m b u s t i o n c o n d i t i o n s . I n c h o o s i n g a p p r o p r i a t e p a r a m e t e r s , t r e n d s f r o m p r e v i o u s r e s u l t s a n d q u a l i t a t i v e p r e d i c t i o n s b a s e d o n e x i s t i n g a n d e x p e c t e d f o r c e c h a n g e s w e r e u s e d . B u t e v e n a f t e r a l l p a r a m e t e r s w e r e v a r i e d w i t h i n p r a c t i c a l l i m i t s a n d a l a r g e n u m b e r o f c o m b i n a t i o n s w e r e i n v e s t i g a t e d , no s t a b l e c y c l e s w e r e d i s c o v e r e d . The c o m p u t e d r e s u l t s i n d i c a t e d t h e k i n e t i c e n e r g y o f t h e p i s t o n w o u l d i n c r e a s e u n t i l t h e c y l i n d e r h e a d w o u l d b e b l o w n o f f , a s s h o w n b y t y p i c a l r e s u l t s d r a w n o n G r a p h 2 . 3 . T h e f i n a l s t e p b e f o r e a b a n d o n i n g t h e c r a n k l e s s r o t a t i n g e n g i n e c o n c e p t was t o l i n e a r i z e t h e s y s t e m . T h i s m e a n t t h a t t h e g a s f o r c e was r e p l a c e d b y a l i n e a r s p r i n g . The r e s u l t i n g d i f f e r e n t i a l e q u a t i o n s w e r e s o l v e d u s i n g D u h a m m e l 1 s I n t e g r a l t o g i v e : R = ~2 2 (cosuJt^-costot-^) P -oo 2 k 2 ' w h e r e P = rr— - (OJ+CO ) Mp o k = s p r i n g r a t e T h e f o l l o w i n g a r e r e s u l t s o f t h e l i n e a r s y s t e m : 2 1 . I f ( O J + C O O ) i s g r e a t e r t h a n k / m ^ , t h e s y s t e m i s u n s t a b l e , 98 Graph 2.3 Computed p i s t o n p o s i t i o n s - unbalanced l e v e r engine 2 . I f (o)+too) = k / n i p , t h e n p = 0 a n d R = L ( l - c o s o j t ) t h e c y c l e i s s i n u s o i d a l . 2 2 3 . I f p = OJ a n d k / m ^ = ( O J + O J O ) + OJ , t h e c y c l e f r e q u e n c y o f t h e p i s t o n i s t h e same a s t h a t o f t h e c y l i n d e r ; V. t h e s o l u t i o n b y d o u b l e i n t e g r a t i o n i s R = — s i n u t + (R .+ 4) COSOJt. l 2 4 . I f p = O J , t h e max imum p i s t o n d i s p l a c e m e n t i s a p e r i o d i c f u n c t i o n i n c r e a s i n g o r d e c r e a s i n g f r o m c y c l e t o c y c l e . I t i s p o s s i b l e t o o b t a i n a s t a b l e c y c l e f o r a p a r t i c u l a r v a l u e o f p a n d OJ i f p<oj f o r p a r t o f t h e c y c l e a n d p>oj f o r t h e r e m a i n i n g p a r t . I n a n e n g i n e t h e v a l u e o f p i s i n c r e a s e d w h e n c o m b u s t i o n s u d d e n l y r a i s e s t h e g a s p r e s s u r e , a n d i s d e c r e a s e d w h e n t h e e x h a u s t p o r t o p e n s . S i n c e t h e c y c l e m u s t be s t a b l e f o r a t l e a s t a s m a l l v a r i a t i o n i n s p e e d , c o n d i t i o n s 2 a n d 3 a r e n o t s u i t a b l e a n d c o n d i t i o n 4 b e c o m e s t h e o n l y w o r k a b l e s o l u t i o n . To a c h i e v e a s t a b l e c y c l e t h e i g n i t i o n t i m i n g a n d p r e s s u r e i n c r e a s e m u s t b e r e l a t e d t o t h e c y l i n d e r p o s i t i o n when t h e p i s t o n i s a t t h e t o p d e a d c e n t e r . T h e o p t i m u m a n g u l a r p o s i t i o n d e p e n d s o n t h e s p e e d a n d t h e r e q u i r e d p r e s s u r e i n c r e a s e d e p e n d s o n t h e w o r k r e m o v e d f r o m t h e c y c l e . T h e s e r e q u i r e m e n t s a r e d i f f i c u l t , i f n o t i m p o s s i b l e , t o a c h i e v e i n p r a c t i c e . The c o n c e p t o f a c r a n k l e s s , r o t a t i n g , f r e e -p i s t o n e n g i n e was t h e r e f o r e a b a n d o n e d . 100 As has been shown, the p u r s u i t of a p r a c t i c a l r o t a t i n g free-pist'on engine r e q u i r e d many branches of the d e c i s i o n t r e e . Some l e d to dead ends but others opened up a l t e r n a t e p o s s i b i l i t i e s . When i t became obvious t h a t s t a b l e c y c l e s were d i f f i c u l t to achieve i n the r o t a t i n g f r e e c y l i n d e r engine, the a l t e r n a t e p o s s i b i l i t y of using r e c i p r o c a t i n g motion d i r e c t l y was i n v e s t i g a t e d . Experience had shown t h a t a p i s t o n bouncing i n a clo s e d c y l i n d e r could be made i n t o a workable engine i f the p i s t o n and c y l i n d e r were synchronized and i f automatic t h r o t t l i n g were i n c o r p o r -ated. No major problem w i t h s e a l i n g and combustion was envisioned as long as con v e n t i o n a l p i s t o n s , c y l i n d e r s and r i n g s were t o be used. A number of a l t e r n a t e s f o r automatic t h r o t t l i n g were conceived but dis c a r d e d because they were too complicated or too u n r e l i a b l e . Connecting the t h r o t t l e d i r e c t l y to the • p i s t o n was not s u i t a b l e because the d i f f e r e n c e between no load and f u l l load strokes was s m a l l . A wedge or a r o t a t i n g v a l v e complicated the engine. A device s e n s i t i v e to the scavenging chamber pressure was too u n r e l i a b l e . F i n a l l y a l e v e r arrangement t h a t was simple and s e n s i t i v e to stroke was conceived. A d e s c r i p t i o n of t h i s arrangement w i t h reference to Figu r e 2.4 f o l l o w s . In the p o s i t i o n drawn, the scavenging charge enters the top c y l i n d e r from the top scavenging chamber, whi l e the i n t a k e charge enters the bottom scavenging chamber from F i g u r e 2.4 A sketch of the o s c i l l a t i n g f r e e - p i s t o n engine 102 t h e i n t a k e p a s s a g e , a n d c o m b u s t i o n o c c u r s i n t h e b o t t o m c y l i n d e r . T h e g a s f o r c e i n t h e b o t t o m c y l i n d e r p u s h e s t h e c y l i n d e r a s s e m b l y down a n d t h e p i s t o n a s s e m b l y u p . T h e r e s u l t i n g m o t i o n m o v e s t h e b l a d e a g a i n s t a l o a d a n d u n c o v e r s t h e t h r o t t l e p o r t t o a d m i t a f r e s h c h a r g e i n t o t h e i n t a k e p a s s a g e . F u r t h e r m o t i o n o f t h e p i s t o n a n d c y l i n d e r u n c o v e r s t h e b o t t o m e x h a u s t p o r t a n d t h e n t h e t o p i n t a k e a n d t h e b o t t o m t r a n s f e r p o r t s . T h e n i t c l o s e s t h e t h r o t t l e p o r t . T h e m o t i o n c o n t i n u e s u n t i l a l l t h e k i n e t i c e n e r g y i n t h e p i s t o n a n d c y l i n d e r h a s b e e n a b s o r b e d b y t h e c o m p r e s s i o n o f t h e g a s e s . C o m b u s t i o n t h e n o c c u r s i n t h e t o p c y l i n d e r a n d t h e c y c l e r e p e a t s . When t h e a n g l e (8) b e t w e e n t h e c o n n e c t i n g r o d a n d p i s t o n r o d i s l e s s t h a n 4 5 ° , a s m a l l m o v e m e n t i n t h e p i s t o n r e s u l t s i n a c o r r e s p o n d i n g b u t l a r g e r m o v e m e n t i n t h e b l a d e . B e c a u s e i t i s a n i n h e r e n t p a r t o f t h e b l a d e , t h e t h r o t t l e c o u l d b e d e s i g n e d t o r e m a i n c l o s e d f o r a g r e a t e r p o r t i o n o f t h e c y c l e when t h e p i s t o n m o v e m e n t b e c o m e s l a r g e r . A p l o t o f t h e p i s t o n s t r o k e a n d b l a d e s t r o k e a s a f u n c t i o n o f t h e c o m -p r e s s i o n r a t i o i l l u s t r a t e s t h e s e n s i t i v i t y , o f t h e a r r a n g e m e n t , G r a p h 2 . 4 . F o r e x a m p l e , when t h e l o a d i s s u d d e n l y r e m o v e d , a n d t h e p i s t o n s t o p s a t a c o m p r e s s i o n r a t i o o f 50 i n s t e a d o f 1 0 , t h e p i s t o n s t r o k e i n c r e a s e s 13% a n d t h e b l a d e s t r o k e i n c r e a s e s 57%. A f t e r t h e c o n c e p t w a s r e f i n e d , a c o m p u t e r p r o g r a m u s i n g t h e R u n g e - K u t t a s u b r o u t i n e was s e t u p t o s o l v e t h e t w o Graph 2.4 Blade and piston p o s i t i o n as a function of compression r a t i o coupled equations derived from a force analysis without f r i c t i o n . The analysis resulted i n the following equations d 2Y 2 v r £ (P -P») A d 2X — 2 = <W A m at Where Y i s the dimensionless blade p o s i t i o n (= , s X i s the dimensionless cylinder p o s i t i o n I' L i s the connecting rod leng t h (= — ) , s i s a reference s t r o k e , A P. A i s the reduced p i s t o n area (= ^ ^~) i F i s the net load on the saw (= rr^—) , M s ' P P 1 i s the gas pressure i n r i g h t c y l i n d e r (=p—) , 3. P p i s the gas pressure i n the l e f t c y l i n d e r JC p i JL (= |T-> , a m m i s the mass r a t i o (= , m c m i s P m i s c P i s a the atmospheric pressure. The pressures i n the c y l i n d e r s were c a l c u l a t e d w i t h the i s e n t r o p i c equation: P r = 4.74 ( S F ) ( C R ) 1 , 4 Where CR i s the compression r a t i o ( f u n c t i o n of x+y), S F i s the scavenging f a c t o r . The f o l l o w i n g observations were made from the computed r e s u l t s : 1. When no t h r o t t l i n g , no bounce and no s y n c h r o n i z a t i o n was used and the a p p l i e d load was below the f u l l l o a d : 105 (a) the engine s t a l l e d when the a p p l i e d load exceeded the f u l l l o a d , (b) the c y c l e s were q u i t e s t a b l e f o r a very heavy c y l i n d e r , e.g. c y l i n d e r mounted to heavy base. 2. When the combustion pressure depended on the blade s t r o k e : (a) the c y c l e s s t a b i l i z e d f o r a heavy c y l i n d e r at compression r a t i o s t h a t depended on the load a p p l i e d ( f o r no load the l e f t compression r a t i o was 55 and the r i g h t was 87), (b) the c y c l e s were unstable when the c y l i n d e r and p i s t o n weights were equal, (c) the compression r a t i o f l u c t u a t e d f o r a medium weight c y l i n d e r and a heavy l o a d . 3. When automatic t h r o t t l i n g and a u x i l i a r y bounce chambers were used: (a) the c y c l e was unstable f o r c y l i n d e r weights l e s s than 10 times the p i s t o n weight, (b) the a d d i t i o n of the bounce chamber made the c y c l e s more un s t a b l e . 4. When the c y l i n d e r and p i s t o n were synchronized but no t h r o t t l i n g was used: (a) f o r a l a r g e load the c y c l e s were s t a b l e , (b) f o r a sm a l l load the compression r a t i o kept i n c r e a s i n g . 106 When t h e r e s u l t s o f t h e i d e a l c y c l e a r e a p p l i e d t o a p r a c t i c a l e n g i n e , t h e f o l l o w i n g t w o c o n d i t i o n s a r e r e -q u i r e d f o r s t a b l e c y c l e s : 1 . t h e c y l i n d e r m u s t b e v e r y h e a v y , f a s t e n e d t o a h e a v y f r a m e o r s y n c h r o n i z e d w i t h t h e p i s t o n , 2 . t h e i n t a k e m u s t b e t h r o t t l e d d u r i n g p a r t l o a d o p e r a t i o n . T h e s e r e q u i r e m e n t s w e r e m e t b y s y n c h r o n i z i n g t h e p i s t o n a n d c y l i n d e r w i t h a r a c k a n d p i n i o n g e a r a r r a n g e m e n t . A d e t a i l e d f o r c e a n a l y s i s y i e l d e d t h e f o l l o w i n g e q u a t i o n f o r t h e a c c e l e r a t i o n o f t h e p i s t o n : ,2 V f 0 - F f 7 2-1 = A ( P , - P ) + = f — d t 2 r t i + d ] r— 1 + d ^ ! ) 2 d + d ) - 1 W h e r e f , = — i s t h e sum o f t h e f r i c t i o n f o r c e b e t w e e n 1 ms t h e p i s t o n a n d c y l i n d e r , a n d b e t w e e n t h e f r a m e a n d c y l i n d e r , V f ~ = - i s t h e f r i c t i o n f o r c e b e t w e e n t h e b l a d e '2 ms f . a n d f r a m e , '3 f = i s t h e f r i c t i o n f o r c e b e t w e e n t h e p i s t o n 3 ms c a n d f r a m e , F ' F = — i s t h e l o a d o n b l a d e , ms i s t h e r a t i o o f c y l i n d e r - t o - p i s t o n g e a r m d i a m e t e r s (= —£• f o r b a l a n c e d e n g i n e ) , m c 107 by: F n m m m i s the reduced mass. (= —P— ) . m +m p c The normal force against the bladeguide i s given F - f When the piston i s at the end of i t s stroke so that (6) approaches 90°, the normal force on the guide i s very high i f the saw load i s high. But 9 only approaches 90° when the saw i s unloaded, so the normal force i s not as high as might f i r s t be expected. When the force i s high, the stroke i s short. The blade makes two cutting strokes for every piston cycle and i s connected to the piston with a connecting rod containing two bearings. I t was sur-mised that i f these two bearings could be eliminated,the arrangement would have even fewer moving parts. Consequently basic engine requirements were again considered i n hopes of achieving even a simpler design. 2.4 Synthesis of the Free-Piston Power Saw (FPS) The synthesis of the new power saw started with a simple concept and ended with a p r a c t i c a l arrangement. The concept was based on a piston bouncing i n a closed cylinder f i l l e d with gas. By adding energy to the gas, the piston bounce can be maintained and work removed. By providing 108 t h e c y l i n d e r w i t h i n t a k e a n d e x h a u s t p o r t s a n d b y u s i n g t h e e x h a u s t p u l s e s t o s c a v e n g e t h e c y l i n d e r , a s i m p l e i n t e r n a l c o m b u s t i o n e n g i n e i s t h e o r e t i c a l l y p o s s i b l e . T h o u g h p o s s i b l e i n t h e o r y a n d a t t a i n a b l e i n p r a c t i c e , t h e i d e a o f t u n i n g t h e i n t a k e a n d e x h a u s t m a n i f o l d s t o s c a v e n g e t h e c y l i n d e r i s a s s o c i a t e d w i t h l o n g m a n i f o l d s a n d l o w a i r f l o w s . H i g h e r f l o w s a r e p o s s i b l e i f a s c a v e n g i n g pump i s u s e d . A pump c a n b e i n c o r p o r a t e d i n t o t h e d e s i g n w i t h o u t i n c r e a s i n g t h e n u m b e r o f m o v i n g p a r t s i f o n e e n d o f t h e c y l i n d e r i s d e s i g n e d a s a s c a v e n g i n g c h a m b e r w h i l e t h e o t h e r r e m a i n s a s a c o m b u s t i o n c h a m b e r . S i n c e i t i s n o t c o n n e c t e d t o t h e c y l i n d e r , t h e p i s t o n i s f r e e t o r e c i p r o c a t e w i t h i n t h e c y l i n d e r a n d t o a c c e l e r a t e m o r e r a p i d l y w h e n t h e c y l i n d e r m o t i o n i s i m p e d e d b y a n e x t e r n a l l o a d . B e c a u s e a r e a c t i o n f o r c e i s r e q u i r e d f o r s t a b l e c y c l e s , t h e p i s t o n c o u l d b e m o u n t e d s o t h a t t h e m o u n t t r a n s m i t s t h e g a s f o r c e , t h e c u t t i n g f o r c e , t h e l o a d i n g f o r c e , a n d t h e b e n d i n g moment c a u s e d b y t h e f e e d i n g f o r c e . W i t h t h e s e l f - f e e d i n g t e e t h , t h e b e n d i n g moment i s s m a l l b u t t h e r e a c t i o n f o r c e c a u s e d b y t h e g a s p r e s s u r e s i s s t i l l v e r y h i g h . I n v e r s i o n s u g g e s t s t h a t t h e h i g h r e a c t i o n f o r c e i s d u e t o a n u n b a l a n c e d m a s s . T h i s p r o b l e m i s o v e r c o m e b y a l l o w i n g t h e c y l i n d e r m a s s t o c o u n t e r - b a l a n c e t h e p i s t o n m a s s . The p i s t o n a n d c y l i n d e r c a n b e s y c h r o n i z e d w i t h a r a c k a n d p i n i o n , b e l t a n d p u l l e y , o r c o n n e c t i n g r o d a n d c r a n k s h a f t a r r a n g e m e n t . 109 I f r i g i d l y attached to the moving c y l i n d e r , the c a r b u r e t o r makes f u e l metering d i f f i c u l t . I t i s p o s s i b l e t o e l i m i n a t e t h i s problem by mounting the c a r b u r e t o r j e t on the s t a t i o n a r y base and then a l l o w i n g the v e n t u r i to move over the j e t , or by mounting the complete ca r b u r e t o r on the base and connecting i t to the i n t a k e manifold w i t h a f l e x i b l e or t e l e s c o p i c tube. I f the saw blade i s connected to the p i s t o n i n s t e a d of to the c y l i n d e r , the weights are brought c l o s e r together, so t h a t s m a l l e r counterweights are r e q u i r e d . This arrangement has a p o t e n t i a l f o r e f f i c i e n t scavenging, good c a r b u r e t i o n , and v i b r a t i o n l e s s o p e r a t i o n . I t l a c k s , however, a s a t i s f a c t o r y t h r o t t l i n g system. When the amount of energy added during each c y c l e j u s t equals the amount of work removed, the c y c l e i s s t a b l e . When the amount added exceeds the amount removed, the p i s t o n - c y l i n d e r a c c e l e r a t i o n i n c r e a s e s u n t i l the extremely high gas pressure causes so much gas to leak from the c y l i n d e r t h a t the p i s t o n impacts the c y l i n d e r head. Because f a i l u r e can occur w i t h i n 2 or 3 c y c l e s (1/30 sec) manual t h r o t t l i n g i s too slow and the engine must be designed to t h r o t t l e i t s e l f i n s t a n t a n e o u s l y . To a l i m i t e d extent the arrangement i s i n h e r e n t l y s e l f - t h r o t t l i n g , because the l e n g t h of time the p o r t s remain open i s i n v e r s e l y p r o p o r t i o n a l t o the p i s t o n c y l i n d e r v e l o c i t y which increa s e s when the energy added exceeds the work removed. As the v e l o c i t y i n c r e a s e s , the p o r t s remain 110 open f o r s h o r t e r durations, so t h a t l e s s charge e n t e r s . A l s o more energy i s d i s s i p a t e d through f r i c t i o n and l o s t through increased heat t r a n s f e r . The end r e s u l t of increased t h r o t t l i n g , f r i c t i o n , and heat t r a n s f e r i s t h a t there i s an upper l i m i t to the p i s t o n v e l o c i t y even without e x t e r n a l t h r o t t l i n g . Maximum torque i n c o n v e n t i o n a l engines occurs at about 4,500 rpm and f r e e wheeling speed occurs a t 9,500 rpm. This o b s e r v a t i o n concurs w i t h a c a l c u l a t e d r e s u l t based on the assumptions t h a t the energy r e l e a s e d v a r i e s i n v e r s e l y w i t h mean p i s t o n speed and f r i c t i o n removes 10% of k i n e t i c energy. At the upper speed l i m i t (2.2 times higher than a t maximum torque) the i d e a l gas equation f o r i s e n t r o p i c compression p r e d i c t s t h a t the maximum compression r a t i o w i l l be 180 and t h a t the maximum pressure w i l l be 800 atmospheres. The upper speed l i m i t and t h e r e f o r e the maximum pressures can be reduced by i n c r e a s i n g the s e n s i -t i v i t y of t h r o t t l i n g t o speed, the f r i c t i o n at higher speeds, and the heat t r a n s f e r a t higher speeds. Of the three means l i s t e d , only t h r o t t l i n g l i m i t s the speed e f f i c i e n t l y . The stroke becomes more s e n s i t i v e to the k i n e t i c energy i n the p i s t o n - c y l i n d e r assembly i f the bounce chamber i s r e p l a c e d by a spring^, s i n c e the energy absorbed by the s p r i n g i s p r o p o r t i o n a l to the d e f l e c t i o n squared. For example, to increase the energy absorbed to 5 times the o r i g i n a l value, a s p r i n g w i l l d e f l e c t 123% more, whereas ' the stroke of an i d e a l gas w i l l i n c rease only 16%. The engine becomes s e l f - t h r o t t l i n g i f the piston s k i r t can cover the transfer ports when the stroke i s long. This means that for long strokes the ports w i l l be open only for a short time. For very long strokes, the piston can uncover an a u x i l i a r y bleed port to r e c i r c u l a t e the scavenging charge into the carburetor and so reduce the scavenging charge flow and increase the f u e l - a i r r a t i o . The synthesis of the bleed port created confidence i n the concept because i t was reasoned that even i f the piston s k i r t f a i l e d to t h r o t t l e the intake properly, the bleed port would act as a safety valve. A force analysis of the arrangement yielded the following d i f f e r e n t i a l equation: AP - £ Y + r ( f e 2 + ( F ± y N 1+d Where Y i s the dimensionless piston p o s i t i o n (= —) , A s ) , P i s the resultant pressure r a t i o on piston m i s the reduced mass (= m P i s the mass of piston assembly, m c i s the mass of cylinder assembly, k i s t h e s p r i n g r a t e , r ' s r i s t h e d a m p i n g c o e f f i c i e n t (= — ^ ~ ) i F 1 F i s t h e e x t e r n a l l o a d o n saw (= — ) , ms N i s t h e n o r m a l l o a d o n saw (= — ) , ms u i s t h e c o e f f i c i e n t o f f r i c t i o n , d i s t h e r a t i o o f c y l i n d e r - t o - p i s t o n g e a r d 1 d i a m e t e r s (= —) . T h i s e q u a t i o n w a s u s e d i n a c o m p u t e r p r o g r a m t o s o l v e f o r t h e p i s t o n p o s i t i o n a s a f u n c t i o n o f t i m e . P r e s -s u r e s d u r i n g c o m p r e s s i o n w e r e c a l c u l a t e d u s i n g t h e f o l l o w i n g i s e n t r o p i c e q u a t i o n : 1 4 1 4 ( c R r r - * - ( C R £ r - 4 W h e r e C R ^ i s t h e c o m p r e s s i o n r a t i o i n t h e c o m b u s t i o n c h a m b e r , C R £ i s t h e c o m p r e s s i o n r a t i o i n t h e s c a v e n g i n g c h a m b e r . C o m b u s t i o n w a s a s s u m e d t o o c c u r w h e n t h e c o m p r e s s i o n r a t i o i n t h e c o m b u s t i o n c h a m b e r r e a c h e d 7 . 4 . A f t e r t h i s t i m e a n d u n t i l t h e e x h a u s t p o r t w a s u n c o v e r e d , t h e p r e s s u r e s w e r e c a l c u l a t e d a c c o r d i n g t o t h e i s e n t r o p i c e q u a t i o n : P = 4 . 7 4 (SF) ( C R r ) Y - ( C R £ ) 1 * 4 113 Where y 1 S the r a t i o of s p e c i f i c heats and SF i s the scavenging factor. The scavenging factor was inserted so that the combustion could be related to the scavenging and combustion e f f i c i e n c i e s . When the t h r o t t l e was completely open and a l l the exhaust gases were scavenged, the scavenging factor was 1.0 and the cylinder pressure, when the exhaust port opened, was 69.6 p s i a . When the t h r o t t l e was completely closed so that no fresh charge was admitted to the cy l i n d e r , or when combustion did not occur, the scavenging factor was 0.211. The load on the blade was either applied gradually or held constant. The f r i c t i o n and damping forces were added aft e r the program was debugged. Values of spring sizes f o r the program were based 3 on the assumed output of a 0.8 i n engine (1 i n bore by 1 i n stroke). When the mean e f f e c t i v e pressure was 50 p s i , each cycle of the engine released 40 i n - l b of energy. Assuming that the compression of the fresh charge requires one fourth of the energy released and that t h i s energy i s stored i n the spring, the spring rate should be 20 ppi. When i t d e f l e c t s to 1.5 in,the spring w i l l absorb 22 i n - l b of energy. The free length of a t y p i c a l spring (.95 i n O.D., .10 i n wire diameter) i s 2 1/2 i n . If a short overload spring (.62 i n O.D., .12 i n wire, free length 1.33 i n , rate 400 ppi) i s inserted inside the main one, a l l of the combustion energy released i n one cycle can be absorbed during a 1 p i s t o n stroke of 1.5 i n . But an e v a l u a t i o n showed t h a t the optimum s p r i n g (minimum weight) would have no pre-compression but would be long enough t o remain i n contact w i t h the p i s t o n . The f o l l o w i n g types of t h r o t t l i n g were i n v e s t i g a t e d (a) d i r e c t l y p r o p o r t i o n a l to s t r o k e , (b) d i r e c t l y p r o p o r t i o n a l to stroke w i t h random com-bu s t i o n pressure v a r i a t i o n s (because combustion i n two-stroke engines i s q u i t e e r r a t i c as shown by the r e s u l t s of an e a r l i e r t h e s i s [2.47],) (c) p r o p o r t i o n a l to area of p o r t open w i t h random pres-sure v a r i a t i o n s . The f o l l o w i n g c o n c l u s i o n s were drawn from the computed r e s u l t s : (a) the exact s p r i n g r a t e i s not c r i t i c a l , (b) the f r i c t i o n f o r c e s are not c r i t i c a l , (c) o v e r l o a d i n g immediately s t a l l s the engine, (d) the engine i s s e l f - s t a r t i n g even under f u l l l o a d , (e) the exact t h r o t t l i n g r a t e and e r r a t i c combustion are not c r i t i c a l , (f) c o n d i t i o n s are more c r i t i c a l i f the saw cuts on the r e t u r n s t r o k e , (g) a bounce chamber i s not necessary, (h) a s y n c h r o n i z i n g mechanism i s r e q u i r e d , (i) s t i f f e r s p rings produce higher speeds 115 ( j ) t h e s p e e d i s n e a r l y i n d e p e n d e n t o f l o a d (or s t r o k e ) , (k) t h e e n g i n e c a n go t h r o u g h a number o f c y c l e s b e f o r e s t a r t i n g . The r e s u l t s showed t h a t a f r e e - p i s t o n r e c i p r o c a t i n g b l a d e saw was t h e o r e t i c a l l y p o s s i b l e and a c o m p a r i s o n w i t h t h e c o m m e r c i a l power b l a d e saws a v a i l a b l e on t h e m a r k e t ( F i g u r e 2.5) showed t h a t t h e new saw c o u l d be c o m p e t i t i v e . Of t h e ones a v a i l a b l e , o n l y t h e W r i g h t t w o - s t r o k e power saw i s c o m p l e t e l y p o r t a b l e . The e l e c t r i c - p o w e r e d t y p e s s u c h as t h e e l e c t r i c j i g saw, s a b r e saw and r e c i p r o c a t i n g b l a d e saws r e q u i r e a c o r d and a power s u p p l y w h i l e t h e p n e u m a t i c o r t h e h y d r a u l i c t y p e s r e q u i r e a h o s e and a t a n k . F i g u r e 2.5 T y p i c a l r e c i p r o c a t i n g b l a d e saws 116 A l a r g e number o f p u b l i c a t i o n s on t h e f r e e p i s t o n e n g i n e s a r e a v a i l a b l e ; t h e N a t i o n a l R e s e a r c h C o u n c i l ' s B i b l i o g r a p h y on F r e e - P i s t o n E n g i n e s ( A p r i l , 1964) l i s t s 282 r e f e r e n c e s . The s t a n d a r d c o n v e n t i o n a l f r e e - p i s t o n e n g i n e has a s t a t i o n a r y c y l i n d e r and two r e c i p r o c a t i n g p i s t o n s w h i c h come t o g e t h e r d u r i n g t h e c o m p r e s s i o n s t r o k e and move a p a r t d u r i n g t h e power s t r o k e , F i g u r e 2.6 [2.99]. T h i s c o n c e p t has be e n u s e d t o d r i v e an a i r c o m p r e s s o r , a l i n e a r g e n e r a t o r , a f l u i d pump, and a t u r b i n e . I n a n o t h e r c o n f i g u r a t i o n more c l o s e l y r e l a t e d t o t h e r e c i p r o c a t i n g b l a d e saw i t has b e ^ n u s e d i n a p i l e d r i v e r , F i g u r e 2.6 [2.50]. The h e a d o f t h e p i l e d r i v e r i s s i m i l a r i n many ways t o t h e h e a d o f t h e p o r t -a b l e M o t o r b o r r r o c k d r i l l , b u t t h e r o c k d r i l l p i s t o n i s c o n n e c t e d t o a c o n v e n t i o n a l t w o - s t r o k e c o n n e c t i n g r o d and c r a n k s h a f t , [2.51]. The f r e e p i s t o n e n g i n e h a s b e e n u s e d as a r e f r i g e r a n t c o m p r e s s o r , [2.52], The c y l i n d e r a s s e m b l y i s p i v o t e d so t h a t t h e c e n t e r l i n e o f t h e e n g i n e c o m p r e s s o r p a s s e s t h r o u g h t h e c e n t e r o f p e r c u s s i o n o f t h e s u s p e n d e d mass. I t u s e s f u e l i n j e c t i o n f o r s a t i s f a c t o r y s t a r t i n g on t h e f i r s t s t r o k e and a p r o x i m i t y p l u g f o r p o s i t i v e i g n i t i o n . A l t h o u g h t h e f r e e p i s t o n e n g i n e c o n c e p t i s n o t new, i t s a p p l i c a t i o n t o a r e c i p r o c a t i n g b l a d e saw i s . I n d e e d many o f t h e f r e e - p i s t o n e n g i n e f e a t u r e s s u c h as v i b r a t i o n -f r e e o p e r a t i o n , i n s t a n t s t a r t i n g and s t o p p i n g , m u l t i f u e l c a p a c i t y , and s i m p l i c i t y a r e p r e s e n t i n t h e b l a d e saw a p p l i -c a t i o n and make t h e saw v e r y u n i q u e . How piston and hammer operates W h e n the e x p l o s i o n takes place, the p i s t o n is d r i v e n u p w a r d s ; i t goes t h r o u g h its cyc le at constant speed. T h e h a m m e r is d r i v e n d o w n w a r d s at the same t ime, a n d strikes the d r i l l . "When the p i s t o n moves u p -w a r d s , i t u n c o v e r s the gas d u c t , a n d gas f r o m the c o m b u s t i o n c h a m b e r f lows i n t o the space b e l o w the h a m m e r f lange. T h e gas pressure a c t i n g here o n the unders ide of the h a m m e r f lange, t o g e t h e r w i t h the recoi l f r o m the d r i l l , t h r o w s the h a m m e r b a c k u p to its s t a r t i n g p o s i t i o n . T h e m e a n pressure i n the gas chamber b e l o w the h a m m e r f lange is a u t o m a t i c a l l y regulated b y a s p r i n g - l o a d e d v a l v e so that the h a m -m e r is a lways k e p t i n t i m e w i t h the p i s t o n . COMPRESSOR INLET r B O U N C E , \ CYLINDER — MECHANICAL DRIVE GAS COLLECTOR EXHAUST - C O M P R E S S O R g DISCHARGE DIESEL- 1 CYLINDER COMPRESSOR CYLINDER L I F T I N G F I N G E R M E C H A N I S M C O M P R E S S I O N T A N K B O U N C E C H A M B E R V E N T D R I V I N G H E A D A - "Free- -head" r o c k d r i l l B - F r e e - p i s t o n t u r b o s e t C - P i l e d r i v e r D - F r e o n c o m p r e s s o r POWER CYLINDER P ISTON COUNTER CHAMBER BOUNCE CHAMBER C O M P R E S S O R F i g u r e 2.6 E x i s t i n g f r e e - p i s t o n c o n f i g u r a t i o n s 118 3. DETAILING COMPONENTS 3.1 D i m e n s i o n a l A n a l y s i s A l t h o u g h i t c o n t r i b u t e s l i t t l e t o t h e u n d e r s t a n d i n g o f t h e mechanisms t a k i n g p l a c e i n s i d e an e n g i n e , s i m i l i t u d e f a c i l i t a t e s t h e i n t e r p r e t a t i o n o f t e s t r e s u l t s and e x t e n d s t h e r a n g e o f s i z e s e n g i n e s c a n be s c a l e d by c o r r e l a t i n g p e r f o r m a n c e i n t e r m s o f d i m e n s i o n l e s s v a r i a b l e s and r a t i o s . The t w o - s t r o k e e n g i n e d e s i g n e r u s e s t h e f o l l o w i n g r a t i o s : 1. s c a l i n g f a c t o r ( s p e c i f i e d b o r e / r e f e r e n c e b o r e ) m 2. s t r o k e / b o r e s/b 3. e x h a u s t p o r t a r e a / p i s t o n a r e a Ae/Ap 4. i n t a k e p a r t a r e a / p i s t o n a r e a A i / A p 5. e x h a u s t p o r t a r e a / t r a n s f e r p o r t a r e a A e / A t 6. e x h a u s t h e i g h t / s t r o k e E x H t / s 7. t r a n s f e r h e i g h t / s t r o k e T r H t / s 8. i n t a k e h e i g h t / s t r o k e I n H t / s He d e t e r m i n e s what s i z e s t o u s e b y : 1. o b s e r v i n g how s i z e v a r i a t i o n a f f e c t s e n g i n e p e r f o r -mance, 2. c o r r e l a t i n g p e r f o r m a n c e i n t e r m s o f d i m e n s i o n l e s s v a r i a b l e s t h a t c a n be e x t r a p o l a t e d t o new s i z e s , 3. d e d u c i n g f r o m t h e c o r r e l a t i o n new d i m e n s i o n s t h a t w i l l g i v e r i s e t o t h e r e q u i r e d p e r f o r m a n c e . I n s m a l l e n g i n e d e s i g n , e l a b o r a t e p e r f o r m a n c e p r e d i c t i o n s a r e u s u a l l y n o t w a r r a n t e d b e c a u s e b y b u i l d i n g a n d t e s t i n g a n a c t u a l e n g i n e m o r e a c c u r a t e r e s u l t s a r e o b t a i n e d a t l e s s c o s t . A f a m i l y o f s i m i l a r e n g i n e s h a s t h e same b o r e / s t r o k e r a t i o , mean p i s t o n s p e e d a n d g e o m e t r y . The d e d u c t i o n t h a t t h e v o l u m e t r i c e f f i c i e n c y r e m a i n s t h e same f o r s i m i l a r e n g i n e s c a n b e shown t o b e v a l i d , p r o v i d e d t h e * i n l e t a n d e x h a u s t c o n d i t i o n s r e m a i n t h e s a m e . U n d e r F l o w / c y c l e = K f ^ P y j ^ = ^At = K^A S_ J m = K ( E x H t ) ( w i d t h ) — = K 3 ( K 4 s ) (K 5 TTb) m m = K, s 2 b b m / i K, s 2 b TT T TH.CC F l o w / c y c l e b T r , s , , , V o l . E f f . = — = — = Ky (g-) = c o n s t a n t D i s p l a c e m e n t Trb^  P — 3 W h e r e AP i s p r e s s u r e a c r o s s p o r t , p i s d e n s i t y u p s t r e a m , t i s t i m e , i s t h e mean p i s t o n s p e e d , A i s p o r t a r e a K ' s a r e c o n s t a n t s s i s p i s t o n s t r o k e b i s c y l i n d e r b o r e 120 such conditions the r a t i o of the amount of gas trapped i n the cylinder to the amount entering remains constant. For a constant pressure drop across the ports and a constant o r i f i c e c o e f f i c i e n t , the mass of charge flowing through a port i s proportional to the length of time the port i s open. When the mean piston v e l o c i t y remains constant (valid for s i m i l a r engines), the length of time the port remains open i s proportional to the length of the stroke so that volumetric e f f i c i e n c y = constant The weight of gas displaced per cycle and there-fore the weight of fresh charge supplied i s proportional to the engine displacement. At a constant mean piston v e l o c i t y the engine speed varies inversely with the stroke so that the weight of the mixture supplied, as well as the energy supplied per u n i t time ( i f the combustion e f f i c i e n c y remains constant), varies with the bore diameter squared so that 2* Energy supplied a m where m i s the scaling factor and i s defined as the r a t i o of any two s i m i l a r dimensions. * 2 Weicfht = V f _ = b s 2 fm = time 1/N 6 2s 8 Energy = ( H e a t i n g value) (Eff.) (Weight/time) cycle = K g'(Kgbs) = K 9bs I f t h e a i r / f u e l r a t i o , f r i c t i o n mean e f f e c t i v e p r e s s u r e a n d v o l u m e t r i c e f f i c i e n c y a r e u n a l t e r e d a s t h e e n g i n e s i z e i s c h a n g e d , t h e n t h e i n d i c a t o r d i a g r a m s w i l l b e s i m i l a r a n d t h e b r a k e mean e f f e c t i v e p r e s s u r e w i l l b e c o n s t a n t : bmep = c o n s t a n t . P o w e r w i l l b e p r o p o r t i o n a l t o t h e r a t i o o f t h e d i a m e t e r s s q u a r e d s o t h a t 2 * s h p a m . On G r a p h 3 . 1 t h e s h a f t h o r s e p o w e r o f t y p i c a l p o w e r saw * * e n g i n e s i s p l o t t e d a s a f u n c t i o n o f p i s t o n a r e a . * , (BMEP) (Vd) (N) . 2 , . . . . s h p = — —-—- = k , n ( B M E P ) (bs ) (N) 3 3 0 0 0 = K 1 Q ( B M E P ) b 2 ^ = K i ; L b 2 W h e r e V d i s e n g i n e d i s p l a c e m e n t , BMEP i s b r a k e mean e f f e c t i v e p r e s s u r e , a n d N i s e n g i n e s p e e d ** U n p u b l i s h e d d a t a f r o m P o w e r M a c h i n e r y L t d . , s h o w n i n A p p e n d i x V . 122 2 3 P I S T O N A R E A ( S Q I N ) Graph 3.1 Power as a f u n c t i o n of p i s t o n area f o r t y p i c a l power saws When considered on a displacement b a s i s , the power of a g e o m e t r i c a l l y s i m i l a r engine i s i n v e r s e l y p r o p o r t i o n a l to the bore: Vd a - * m When compared on a weight b a s i s , a small engine performs b e t t e r than a b i g one because the weight of an engine i s p r o p o r t i o n a l to 3 dimensions (volume), whereas power i s p r o p o r t i o n a l to only two dimensions (area). This Sh£ Vd K l l b ' TT, 2 4 b s K 13 123 means t h a t the weight per u n i t horsepower f o r a g e o m e t r i c a l l y s i m i l a r engine v a r i e s d i r e c t l y w i t h the bore: Though i t i s p o s s i b l e i n medium and l a r g e bore engines, the idea of reducing the weight-to-power r a t i o by decreasing the bore diameter cannot always be u t i l i z e d f o r bores l e s s than 2 i n . Such small engines are i n e f f i c i e n t f o r the f o l l o w i n g four reasons: 1. Very small c y l i n d e r s have a high r e l a t i v e heat l o s s because the r a t i o of exposed surface area to volume i s very high d u r i n g combustion. Con-sequently a l a r g e percentage of heat i s t r a n s f e r r e d to the c y l i n d e r head and block. 2. The i n l e t manifold i s s h o r t . As i t can mix w i t h the a i r f o r only a short time, much of the f u e l goes through the engine unevaporated and unburned. 3. The c y l i n d e r w a l l temperatures w i l l be lower. This r e s u l t s i n higher o i l v i s c o s i t y . The high v i s c o s i t y o i l and high r e l a t i v e t o l e r a n c e s con-t r i b u t e to an abnormally high f r i c t i o n mean e f f e c t i v e pressure. Wt shp a m Wt shp 4. The e f f e c t i v e Reynolds number corresponding to gas flows may be so low t h a t v i s c o u s f o r c e s add an i n c r e -ment to fo r c e s r e s i s t i n g gas flow [3.1]. Because small bore engines are i n e f f i c i e n t , the power per u n i t displacement of t y p i c a l power saws does not depend on bore s i z e (Graph 3.2) and the weight per horsepower a c t u a l l y i n c r e a s e s as the c y l i n d e r bores are made smaller (Graph 3.3). w i l l be the same at s i m i l a r p i s t o n p o s i t i o n s provided the mean p i s t o n speeds are the same, the i n d i c a t o r diagrams are the same, and no s e r i o u s feedback of v i b r a t o r y f o r c e s occurs. Under these c o n d i t i o n s Stresses due to gas pressure and i n e r t i a of p a r t s * mechanical s t r e s s = constant gas f o r c e S t r e s s due to gas f o r c e s area = K 15 S t r e s s due to a c c e l e r a t i n g f o r c e s = (mass)(acc) 125 ro £ 9 LU 5 : LU O < _ J D_ CO LU 3: o .8 .7 .4 • eh —ms a A .6 - A _ , _ l . BORE (IN ) .8 CL. X CQ o CL. \ \— X ID t—i L U 1.8 2.2 2J5 BORE ( IN) Graph 3.2 Specific'power as a f u n c t i o n of bore Graph 3.3 S p e c i f i c weight as a f u n c t i o n of bore Even though the a p p l i e d s t r e s s e s remain constant, higher s t r e s s r a t i n g s are p o s s i b l e f o r small c y l i n d e r s i z e s because the one piece c o n s t r u c t i o n and t h i n n e r s e c t i o n s have higher a l l o w a b l e working s t r e s s e s . The gas side heat t r a n s f e r c o e f f i c i e n t v a r i e s i n v e r s e l y w i t h the bore when the Reynolds number remains constant [3.1] . 1 * h a — m K K K h = Nu( r) = K i 6 R e ( z > = -j-16 ( i f R e y n o l d s n u m b e r i n c r e a s e s b e c a u s e t h e p i s t o n s p e e d i n -c r e a s e s , t h e N u s s e l t n u m b e r a n d t h e r e f o r e t h e h e a t t r a n s f e r c o e f f i c i e n t w i l l b e l a r g e r . ) To k e e p t h e t h e r m a l e f f i c i e n c y h i g h a n d c o o l i n g s y s t e m c a p a c i t y l o w , i t i s d e s i r a b l e t o h o l d t h i s h e a t t r a n s f e r c o e f f i c i e n t t o a m i n i m u m . U n l e s s d e s i g n c h a n g e s a r e i n c o r p o r a t e d t o k e e p f l o w p a t h s s h o r t , t h e t e m p e r a t u r e o f t h e p a r t s ( T w ) e x p o s e d t o t h e h o t g a s e s w i l l r i s e a s t h e c y l i n d e r s i z e i s i n c r e a s e d s o t h a t T a m . w W a l l t e m p e r a t u r e s a r e l i m i t e d b y c o n s i d e r a t i o n s o f s t r e n g t h a n d d u r a b i l i t y o f t h e m a t e r i a l a n d i n t h e c a s e o f t h e c y l i n d e r b o r e , b y t h e n e c e s s i t y o f m a i n t a i n i n g a b e a r i n g s u r f a c e f r e e f r o m e x c e s s i v e f r i c t i o n a n d w e a r . N o t o n l y d o e s t h e w a l l t e m p e r a t u r e g o u p a s t h e b o r e i n c r e a s e s b u t t h e t e m p e r a t u r e d i f f e r e n c e a c r o s s t h e w a l l a l s o i n c r e a s e s : T - T a m w c ** C o n v e c t i o n t o w a l l = Q = K 17 a l s o = h ( T - T ) g w K 16 (T -T ) ; T = T - K n , £ = K n _ b Z g w w g 16 17 * * C o n d u c t i o n t h r o u g h w a l l = £ = K ' = £ (T - T ) ^ A 17 Z w c i Z T —T = K, _ — = K, n b w c 17 K 18 Given that the stresses due to thermal expansion i n the s o l i d body of a given material are proportional to the difference i n temperature between two points i n a body, the thermal stress w i l l vary with the bore: thermal stress a m . Lower wall temperatures also mean lower compression temper-atures and consequently lower compression pressures as well as lower l o c a l hot spot temperatures. The lower temperature and shorter flame t r a v e l length w i l l reduce the tendency for the mixture i n the cylin d e r to detonate. Smaller cylinders can thus be operated at a higher compression r a t i o before s e l f - i g n i t i o n occurs, so that compression r a t i o a — c m Cen t r i f u g a l forces i n rot a t i n g parts such as the crankshaft are inversely proportional to engine s i z e , c e n t r i f u g a l force a 2 * * m Deflections of parts due to mechanical forces are porportional to stresses and part length, d e f l e c t i o n a m *** Thermal stress W W = K x 9 K 1 8 b = K 1 9 b ** 2 mv2 K20 C e n t r i f u g a l force = mrw = s/2 *** Deflection = £(strain) = —(stress) = K„,£ hi Z x 128 N a t u r a l f r e q u e n c y o f v i b r a t i o n i s i n v e r s e l y p r o p o r t i o n a l t o t h e l e n g t h o f t h e p a r t 1 * f r e q u e n c y a — W e a r i n e n g i n e s i s c a u s e d b y f o r e i g n m a t t e r , c o r r o s i o n , a n d i n some c a s e s , d i r e c t m e t a l l i c c o n t a c t . T h e d e p t h o f c o r r o s i v e w e a r p e r . u n i t t i m e i s i n d e p e n d e n t o f t h e b e a r i n g s i z e . H o w e v e r , t h e d e p t h o f w e a r w h i c h c a n b e t o l e r -a t e d i s p r o p o r t i o n a l t o t h e s i z e o f t h e p a r t i n q u e s t i o n : w e a r damage a — . F o r a f a m i l y o f s i m i l a r e n g i n e s ( c o n s t a n t s t r o k e / b o r e r a t i o ) t h e e f f e c t o f t h e c y l i n d e r s i z e o n e n g i n e p e r f o r m a n c e a r e s u m m a r i z e d i n T a b l e I I I . F o r a c o n s t a n t d i s p l a c e m e n t e n g i n e t h e f o l l o w i n g l i s t o f c h a r a c t e r i s t i c s s u m m a r i z e s t h e e f f e c t o f t h e b o r e / s t r o k e r a t i o o n e n g i n e p e r f o r m a n c e : 1 . A l o n g - s t r o k e e n g i n e w i l l h a v e a h i g h e r t h e r m a l e f f i c i e n c y t h a n a s h o r t - s t r o k e e n g i n e . T h e a m o u n t o f s u r f a c e a r e a e x p o s e d t o t h e e x t r e m e l y h i g h g a s t e m p e r a t u r e a t t h e b e g i n n i n g o f t h e p o w e r s t r o k e F r e q u e n c y o f v i b r a t i o n o f4 u n i f o r m beam = C /gE I 'w£3 K = K „ „ / ~~T 22 / m 22 3 3 m m . m 129 Table I I I S c a l i n g C h a r a c t e r i s t i c s f o r S i m i l a r Engines energy s u p p l i e d a 2 m shp, fhp a 2 m weight per shp a m d e f l e c t i o n of p a r t s a m w a l l temperature a m temperature across w a l l a m thermal s t r e s s a m fmep, bmep = e s t b e a r i n g pressures e s t mechanical s t r e s s e s = e s t power per u n i t displacement a 1/m maximum compression r a t i o a 1/m wear damage a 1/m heat t r a n s f e r c o e f f i c i e n t a 1/m n a t u r a l v i b r a t i o n frequency a 1/m c e n t r i f u g a l f o r c e a 1/m depends l a r g e l y on the p i s t o n f o r c e and c y l i n d e r head areas and c o n t r o l s much of the heat t r a n s m i s s i o n from the combustion volume. The p i s t o n area to c y l i n d e r displacement r a t i o v a r i e s i n v e r s e l y w i t h the s t r o k e : combustion surface area 1 . a _ d isplacement The a d v i s a b i l i t y of using a low bore/stroke r a t i o to decrease surface area i s obvious, but what i s not so obvious i s the advantage gained through a s h o r t e r 130 flame t r a v e l d i s t a n c e . Because combustion i s com-p l e t e d sooner and t h e r e f o r e c l o s e r to the optimum crank angle, combustion pressures are higher. Higher pressures and lower heat t r a n s m i s s i o n r e s u l t i n higher thermal e f f i c i e n c i e s . (The co n v e n t i o n a l techniques of using a domed or c o n i c a l combustion chamber to reduce the surface-to-volume r a t i o and to shorten the flame t r a v e l d i s t a n c e , and using a squish area to promote t u r b u l e n t combustion cannot be used i n the f r e e - p i s t o n engine.) 2. A small bore engine w i l l operate w i t h a c o o l e r p i s t o n than one w i t h a l a r g e bore. The heat flow path from the p i s t o n crown to the nearest cooled surface shortens as the bore decreases so t h a t the temperature d i f f e r e n c e a l s o decreases: T, - T a b h c For a detonation l i m i t e d spark i g n i t i o n engine, the c o o l e r p i s t o n and c y l i n d e r , and the s h o r t e r flame t r a v e l d i s t a n c e , a l l o w the engine to run at a higher compression r a t i o . For a compression i g n i t i o n engine, the c o o l e r c y l i n d e r n e c e s s i t a t e s a higher compression r a t i o before i g n i t i o n occurs. 3. The f o r c e s due to gas pressures w i l l be lower f o r a small bore than f o r a la r g e bore. Since f o r c e i s proportioned to area, a smaller p i s t o n area r e s u l t s 131 i n a smaller force. In terms of stroke, the r e l a t i o n -ship i s force -, a - ' displacement S 4. If the stroke i s i n i t i a l l y very short, more fu e l w i l l probably be trapped i n the cylinder as the stroke i s increased. Since the charge i s deflected upwards into the chamber, the longer stroke pro-duces a longer flow path so i t seems probable that a long stroke w i l l increase fuel-residue mixing and decrease short c i r c u i t i n g . 5. As the bore/stroke r a t i o decreases, higher piston speeds w i l l be required to maintain the same output. If the displacement and brake mean e f f e c -t i v e pressure remain the same, the rpm must also remain constant. A longer stroke at a constant speed means the average piston v e l o c i t y w i l l be higher. Because i t depends on v e l o c i t y and not on rpm, the f r i c t i o n mean e f f e c t i v e pressure and the heat generated by the rin g f r i c t i o n w i l l be higher. If the piston v e l o c i t y i s already c r i t i c a l , the higher v e l o c i t y may cause the l u b r i c a t i o n between the rings and cylinder to break down. But i f the mean piston v e l o c i t y remains constant, the power of a long stroke, constant brake mean e f f e c t i v e pres-sure engine w i l l decrease as the stroke increases: bhp 1 V, s . d  A p l o t of s p e c i f i c power as a f u n c t i o n of stroke f o r t y p i c a l power saws d i d not v e r i f y t h i s r e l a t i o n s h i p . This i s not s u r p r i s i n g s i n c e the brake mean e f f e c t i v e pressure and mean p i s t o n speed v a r i e s from manufacturer to manufacturer and from engine to engine. The power of t y p i c a l saws as a f u n c t i o n of the mean p i s t o n speed and the rpm i s shown on Graph 3.4 and 3.5. These curves a l s o i n c l u d e a small model a i r c r a f t engine 3 (.10 i n , .14 hp) and a small u t i l i t y engine (1.26 i n ^ , .5 hp). A longer stroke permits the design of l a r g e r p o r t areas. As a long stroke engine has a high w a l l surface/volume r a t i o , the usable area f o r por t s i s a l s o l a r g e . When the r a t i o s of the po r t width/circumference and p o r t h e i g h t / s t r o k e remain constant, the r a t i o of the po r t a r e a / p i s t o n area i s a f u n c t i o n of the stroke/bore r a t i o , .MEAN P I S T O N S P E E D ( F P M ) •' Graph 3.4 S p e c i f i c power as a f u n c t i o n of p i s t o n speed Graph 3.5 S p e c i f i c power as a f u n c t i o n o f engine speed p o r t a r e a p i s t o n a r e a 134 A p l o t o f t h e e x h a u s t a r e a s a s a f u n c t i o n o f t h e s t r o k e / b o r e r a t i o s , v e r i f i e d t h e a b o v e s u p p o s i t i o n b u t a p l o t o f t h e t r a n s f e r p o r t a r e a s d i d n o t v e r i f y i t , G r a p h 3 . 6 . A n u n s u c c e s s f u l a t t e m p t w a s made t o c o r r e l a t e p o w e r a s a f u n c t i o n o f f l o w t h r o u g h p o r t s b y f i r s t d e t e r -m i n i n g t h e f a c t o r s i n f l u e n c i n g f l o w . T h e d e r i v e d r e l a t i o n -s h i p , was t h e n . s e t e q u a l t o a c o n s t a n t s o t h a t : D e f i n e I p o r t w i d t h _ w A w i d t h + b r i d g e ~ w+y ~ 23 p o r t w i d t h + b r i d g e _ w+y A. R c i r c u m f e r e n c e irb 24 ' p o r t w i d t h _ w_ _ K K ' ' c i r c u m f e r e n c e Trb 23 24 p o r t a r e a A _ w (H t ) _ . (H t ) (w) , s , .: „ j - ~ _ ~ . n „ « — ^ o w l u ) p i s t o n a r e a b v b ' K25 <l> * * R a t i o o f f l o w t h r o u g h o r i f i c e ( V f ) t o d i s p l a c e m e n t ( V ^ ) V f A a ^ t ,A w a ' , H t s , v , s w H t > 2 , a . V T = K~T = ( A ) ( C ) ( s ~ ) * = K 2 6 ( b ) ( C ) d p p m m w h e r e § = 2/r I±i\ r - r P y \ (continued on next page ) 135: < LU CC < in < x X LU CC < CC LU LL. CO < < LU < .2 o CO = .35 (§•)-*** A p v b > T D 9 ^ A i A p = . 2 8 (g) a • PORTED & o REED V A L V E • A S P E C I A L J L .8 1.0 STROKE/BORE RATIO 12 G r a p h 3 . 6 P o r t a r e a s o f t y p i c a l p o w e r s a w s v e r s u s s t r o k e / b o r e r a t i o 136 1. when piston v e l o c i t y ( c m) 1 S constant, 2. when rpm i s constant, Ht s These variables were used to correlate the port heights of t y p i c a l saws as shown on Graph 3.7. What t h i s graph v e r i f i e s i s that the port height decreases as the bore/stroke r a t i o decreases. The next step i n the port design was to ascertain the shape and sizes of the intake, transfer and exhaust ports. For e f f e c t i v e scavenging, the design objective should be to secure high values of flow c o e f f i c i e n t and scavenging *(continued from l a s t page) a i s v e l o c i t y of sound = 49v/Tr~ r ^ i s pressure r a t i o across port C i s mean piston v e l o c i t y m ^ 1 v f a * (a) when ^— = and ^ — = K^g m d then Ht V A s = K27\/F V f (b) when = K^7 and N = d then — = K-^/b -s 30 r -X ID I — I LU X cc LU LL. co < CC r -X CD 1—1 LU X LU < I— LU ^ «, O «0 CC I— CO ht. 25 .lb' x. 1.1 12 1.3 14 BORE 'STROKE Graph 3.7 Typical port heights versus the square root of bore/stroke ratio e f f i c i e n c y . T h i s o b j e c t i v e r e q u i r e s t h a t the p o r t areas be l a r g e . But f o r expansion s t r o k e u t i l i z a t i o n , the d e s i g n o b j e c t i v e should be to s a c r i f i c e o n l y a s m a l l p o r t i o n of the expansion s t r o k e t o the scavenging p r o c e s s , and a s m a l l p o r t i o n o f the i n t a k e s t r o k e t o the c h a r g i n g p r o c e s s . T h i s o b j e c t i v e r e q u i r e s a low v a l u e of the exhaust p o r t h e i g h t / s t r o k e r a t i o and a low v a l u e of the i n t a k e p o r t h e i g h t / s t r o k e r a t i o , g i v i n g r i s e to s m a l l p o r t a r e a s . Since these o b j e c t i v e s oppose each ot h e r to q u i t e a degree, the two-s t r o k e c y l i n d e r p o r t d e s i g n i n v o l v e s a g r e a t d e a l of com-promise between e f f i c i e n t scavenging and a h i g h power/dis-placement r a t i o . But s i n c e power was more important than e f f i c i e n c y , the d e s i g n o b j e c t i v e was to achieve a h i g h power/weight r a t i o . The compromise can be more e a s i l y understood and the e f f e c t o f st r o k e / b o r e r a t i o on p o r t a r e a s / p i s t o n area r a t i o can be more e a s i l y p r e d i c t e d i f we assume t h a t the t o t a l width of a s e t of p o r t s w i l l be p r o p o r t i o n a l t o the c i r c u m f e r e n c e and t o the f r a c t i o n of t h i s c i r c u m f e r e n c e devoted t o p o r t i n g . Based on t h i s assumption the area r a t i i s p r o p o r t i o n a l to the p o r t h e i g h t / b o r e r a t i o . I - K s <!r>- K s <"><!> P  I t i s e v i d e n t t h a t f o r a f i x e d r a t i o of p o r t h e i g h t / s t r o k e , the p o r t a r e a / p i s t o n area r a t i o tends t o be p r o p o r t i o n a l to the s t r o k e / b o r e r a t i o as a l r e a d y shown on Graph 3.6. 139 Based on the c o n s i d e r a t i o n s p r e v i o u s l y d i s c u s s e d , the bore/stroke r a t i o f o r the f r e e - p i s t o n r e c i p r o c a t i n g blade engine was chosen as ^ = 1.35 s When the bore i s 1.250 i n the s t r o k e should be equal to 0.9 3 i n . For t h i s bore/stroke r a t i o , Graph 3.7 suggests t h a t the exhaust h e i g h t / s t r o k e r a t i o should be ExHt = . 3 0 s Graph 3.6 suggests t h a t the exhaust a r e a / p i s t o n area r a t i o should be The exhaust gases f l o w out through the p o r t s not only during the blowdown p e r i o d but a l s o during the scaveng-i n g p e r i o d . Scavenging should s t a r t when the pressure i n the c y l i n d e r has dropped to the pressure i n the scavenging chamber. I f the t r a n s f e r ports open too soon, burnt gases w i l l rush i n t o the chamber and prevent proper scavenging. As most of the burnt gases w i l l have exhausted by the time the t r a n s f e r p o r t s are uncovered,the f r e s h charge f o r c e s out only a f r a c t i o n of the o r i g i n a l mass of burnt gases. On the compression stroke the c y l i n d e r pres-sure w i l l b u i l d up and exceed the crankcase pressure i f the 140 t r a n s f e r p o r t s a r e t o o h i g h ; when t h i s happens t h e gas w i l l f l o w from t h e c y l i n d e r i n t o t h e c r a n k c a s e and reduce the s c a v e n g i n g e f f i c i e n c y . I f t h e t r a n s f e r p o r t a r e a i s t o o s m a l l , t h e c y l i n d e r w i l l n o t be c o m p l e t e l y scavenged by t h e ti m e t h e t r a n s f e r p o r t i s c l o s e d . Here a g a i n t h e r e q u i r e -ments o f h i g h f l o w and h i g h s c a v e n g i n g e f f i c i e n c y a r e i n c o n f l i c t and a compromise must be made. A t r e n d was o b s e r v e d when t y p i c a l v a l u e s o f power per u n i t d i s p l a c e m e n t and bmep were p l o t t e d as a f u n c t i o n o f t h e e x h a u s t p o r t a r e a / t r a n s f e r p o r t a r e a r a t i o as shown i n Graph 3.8. The graph i n d i c a t e d t h a t as t h e e x h a u s t a r e a i n c r e a s e d , t h e bmep and horsepower per c u b i c i n c h d e c r e a s e d . A s i m i l a r t r e n d was o b s e r v e d by T a y l o r [3.1] when he reduced t h e e x h a u s t a r e a r a t i o o f a l o o p - s c a v e n g e d e n g i n e from A A ~ = 1.2 to r ^ = 0.6. . A t A t Based on t h e s e o b s e r v a t i o n s , a s u i t a b l e a r e a r a t i o was assumed t o be A A t By c o m b i n i n g t h i s c h o i c e w i t h t h e p r e v i o u s e x h a u s t a r e a r a t i o , t h e t r a n s f e r a r e a / p i s t o n a r e a r a t i o becomes A t -— = 30 A ' ^ P 141 and the reduced area r a t i o becomes A r 1 A e 1 The p e r i o d of time a f t e r the exhaust p o r t s open and before the t r a n s f e r p o r t s open i s c a l l e d the exhaust blowdown. A p l o t of the blowdown/stroke r a t i o versus the square r o o t of bore i n d i c a t e d t h a t the blowdown r a t i o i s independent of the bore when the r a t i o i s v a r i e d from .094 142 to .140, Graph 3.7. This graph suggested that: ^ = .20 Combining t h i s choice with the r a t i o of the exhaust port height y i e l d s Blowdown _ In designing for the intake port area and height, a compromise must be made between a large flow and minimum amount of blowback. A large flow i s achieved by making the ports large; blowback through the carburetor i s minim-ized by making port areas small and port heights low. If the areas are too, small excessive t h r o t t l i n g w i l l take place at high speeds; i f the areas are too large, excessive blow-back through the carburetor w i l l occur at slow speeds. The optimum area and height w i l l r e s u l t i n the maximum quantity of mixture being trapped at the operating speed. The areas can be made large without s a c r i f i c i n g blowback i f a one-way reed valve i s used. But reed valves f a i l , cost money, add complexity to the engine and increase the bmep only s l i g h t l y . For a small power saw the advantage of a higher torque (bmep) probably w i l l not outweigh the disadvantages of increased engine complexity and decreased r e l i a b i l i t y . With the decision made to use ports instead of 143 reed v a l v e s , there remains the question of what i n t a k e p o r t area and height t o use. As a p l o t of s p e c i f i c power versus area i n d i c a t e d no t r e n d s , the area chosen was the same as the 1.25 i n diameter engine: A. For a bore/stroke r a t i o of 1.35, Graph 3.7 gives InHt = . 2 8 s The p o r t shape c o n t r o l s the r a t e of p o r t opening. The r a t e f o r squared p o r t s i s higher than t h a t f o r round p o r t s , but a square hole i s more d i f f i c u l t t o machine and tends to snag the ends of the p i s t o n r i n g s unless the r i n g s are pinned so t h a t the r i n g ends are always supported by the c y l i n d e r w a l l . Since round holes have the width equal to the h e i g h t , the r e q u i r e d small port height n e c e s s i t a t e s a l a r g e number of small holes which r e s u l t i n a l a r g e perimeter/ area r a t i o and a high f r i c t i o n l o s s . To reduce the perimeter/area r a t i o of round h o l e s , two techniques were considered. One technique was to expose only a p o r t i o n of a l a r g e r hole and the second technique was to d r i l l the hole at an angle. The f i r s t technique i s standard p r a c t i c e on many engines w i t h round exhaust p o r t s . The p o r t s are d r i l l e d so t h a t the top edge i s at the r e q u i r e d h e i g h t ; the d r i l l s i z e chosen i s one to give the r e q u i r e d 144 cross-sectional area (when the port i s uncovered to the sp e c i f i e d height) without exceeding the allowable portion of the cyl i n d e r circumference. The second technique, often used for the transfer port, i s to d r i l l holes at an angle so that elongated holes r e s u l t . As well as having a high perimeter-to-area r a t i o , an elongated hole imparts a d i r e c t i o n a l momentum to the charge moving through i t . This can be used to advantage i n the transfer port by d i r e c t i n g the fresh charge to the back of the c y l i n d e r . The transfer port i s so placed that the flows from two opposing holes meet and are deflected upward. When the flows meet, the horizontal v e l o c i t y components cancel and the r e s u l t i n g pressure wave aids cyli n d e r scavenging. The d i r e c t i o n a l momentum may also be created i n a square port by slanting the top edge of the port so that the port i s uncovered gradually from the back to the front, causing the charge to flow toward the back of the cy l i n d e r . Because round holes can be e a s i l y d r i l l e d i n sand-cast c y l i n d e r s , they were s p e c i f i e d for a l l ports. Had squared ports been s p e c i f i e d , the machining operation would have involved a more complex m i l l i n g procedure. Had the cyli n d e r been diecast instead of sandcast, the closer t o l e r -ances possible would have allowed any shape of port to be i n t e g r a l l y cast. D r i l l e d holes were used i n t h i s design to produce large perimeter/area r a t i o holes. Based on the s p e c i f i c a t i o n s determined e a r l i e r , the l i m i t a t i o n s of space around the circumference, and the requirement of e f f i c i e n t scavenging, the f o l l o w i n g holes were s p e c i f i e d : 1. exhaust p o r t s - two .406 i n diameter holes exposed to a height of .28 i n to g i v e an exposed area of .19 i n 2 , 2. t r a n s f e r p o r t s - two .281 i n diameter holes on each s i d e d r i l l e d 45° to the r a d i a l l i n e and exposed to a height of .18 i n t o g i v e an exposed area of .24 . 2 i n . 3. i n t a k e p o r t - e i g h t .172 i n diameter h o l e s , exposed to a height of .12 i n to g i v e an exposed area of .15 2 i n . ( I t should be pointed out t h a t the exposed height of the i n t a k e p o r t i s s m a l l because the r e l -a t i v e stroke between the mount c o n t a i n i n g the holes and the cap exposing them i s h a l f of the r e l a t i v e s t r oke between the c y l i n d e r c o n t a i n i n g the t r a n s f e r and exhaust p o r t s and the p i s t o n exposing them.) Strength and mount circumference s i z e c o n s i d e r a t i o n s i n f l u e n c e d the choice of the number of holes f o r the i n t a k e p o r t . 3.2 Automatic T h r o t t l i n g The flow of a i r and f u e l through the engine i s caused by pressure v a r i a t i o n s i n the scavenging chamber i under the p i s t o n (also c a l l e d precompression chamber). In moving towards the c y l i n d e r head on i t s compression s t r o k e , the p i s t o n expands the scavenging chamber volume, thereby l o w e r i n g the chamber p r e s s u r e . The p r e s s u r e c o n t i n u e s to decrease u n t i l the c y l i n d e r cap uncovers a row of i n t a k e h o l e s i n the c i r c u m f e r e n c e of the s t a t i o n a r y r o l l e r mount. These h o l e s connect w i t h a passageway l e a d i n g t o the c a r b u r e t o r . I f the atmospheric p r e s s u r e i s h i g h e r than the scavenging chamber p r e s s u r e , a i r rushes through the c a r b u r e t o r , mixes w i t h the f u e l , and flows i n t o the chamber The a i r c o n t i n u e s to e n t e r the chamber through the i n t a k e p o r t u n t i l e i t h e r the chamber p r e s s u r e reaches atmospheric p r e s s u r e or u n t i l the cap on the c y l i n d e r , r e t u r n i n g on the power s t r o k e , c o v e r s the p o r t . S i n c e the chamber volume decrea s e s d u r i n g the power s t r o k e , some charge may escape through the i n t a k e p o r t . See F i g u r e 3.3. On the top s i d e of the p i s t o n the c y l i n d e r volume expands d u r i n g the power s t r o k e and the c y l i n d e r p r e s s u r e drops n e a r l y i s e n t r o p i c a l l y u n t i l the p i s t o n uncovers the exhaust p o r t to s t a r t the blowdown p r o c e s s . The r a p i d drop i n c y l i n d e r p r e s s u r e a s s o c i a t e d w i t h the blowdown c o n t i n u e s u n t i l the p i s t o n uncovers the t r a n s f e r p o r t or u n t i l the p r e s s u r e reaches atmospheric p r e s s u r e . I f not enough burnt gases have escaped through the exhaust p o r t s by the time the t r a n s f e r p o r t s open, the p r e s s u r e i n the c y l i n d e r w i l l s t i l l be g r e a t e r than the p r e s s u r e i n the scavenging chambe and burnt gases w i l l flow i n t o the chamber. T h i s a c t i o n 147 reduces scavenging e f f i c i e n c y . On the other hand, i f the blowdown time i s too long so t h a t the c y l i n d e r p r e s s u r e reaches atmospheric p r e s s u r e b e f o r e the t r a n s f e r p o r t s open, p a r t of the s t r o k e remains u n u t i l i z e d and the percentage of the f r e s h charge esc a p i n g d u r i n g the subsequent compres-s i o n s t r o k e i s i n c r e a s e d . For p r o p e r l y designed p o r t i n g the f r e s h charge w i l l flow from the scavenging chamber through the t r a n s f e r p o r t s and i n t o the c y l i n d e r f o r as long as the p o r t s are open. While the t r a n s f e r p o r t s are opening, the t h r o t t l e p o r t s are c l o s i n g . Optimum s t r o k e i s reached when the t r a n s f e r p o r t area equals the t h r o t t l e p o r t a r e a . I f the p i s t o n does not stop a t the optimum s t r o k e but c o n t i n u e s to move on i t s power s t r o k e , the t h r o t t l e p o r t w i l l c o n t i n u e to c l o s e . I f the power s t r o k e i s long enough and the a u x i l i a r y b l e e d p o r t opens soon enough, the t h r o t t l e p o r t w i l l be completely c l o s e d and the b l e e d p o r t w i l l be com-p l e t e l y open. The open b l e e d p o r t a l l o w s the f r e s h charge to escape from the scavenging chamber b e f o r e the p i s t o n reaches bottom dead c e n t e r . A t the end of a v e r y long s t r o k e most of the f r e s h charge w i l l have escaped, c a u s i n g the compression s t r o k e to c r e a t e a vacuum i n the chamber. T h i s draws some of the charge which had a l r e a d y e n t e r e d the c y l i n d e r , i n t o the scavenging chamber as soon as the t h r o t t l e p o r t s are uncovered. Consequently, o n l y a s m a l l amount of charge w i l l remain i n the c y l i n d e r , so t h a t the 148 i n t a k e i s e f f e c t i v e l y and a u t o m a t i c a l l y t h r o t t l e d . Automatic t h r o t t l i n g must accomplish two t h i n g s : 1. a l l o w the maximum q u a n t i t y of f u e l - a i r mixture to enter the c y l i n d e r when the p i s t o n stroke ends a t the maximum power p o s i t i o n , 2. t h r o t t l e the mixture according to the amount of energy r e q u i r e d . The i n t a k e , exhaust, and t r a n s f e r port dimensions, t o s a t i s f y the f i r s t requirement, were obtained by s c a l i n g e x i s t i n g engines as des c r i b e d i n the previous s e c t i o n . The t h r o t t l e p o r t s i z e and shape, to s a t i s f y the second requirement, c o u l d not be obtained from e x i s t i n g engines, so a computer program was set up to p r e d i c t the engine response as the s i z e s and shapes of the t h r o t t l e p o r t were changed. In the f i r s t computer t r i a l s , a h y p o t h e t i c a l r e l a t i o n s h i p between the stroke and energy r e l e a s e d was used. This r e l a t i o n s h i p was based on the assumption t h a t t h r o t t l i n g was d i r e c t l y p r o p o r t i o n a l to the p i s t o n p o s i t i o n at the bottom dead cen t e r . No t h r o t t l i n g occurred when the dead center c o i n c i d e d w i t h the maximum power p o s i t i o n a n t^ f u l l t h r o t t l i n g occurred when the dead center reached a preset p o s i t i o n . For example, i n one s e r i e s of t e s t s no t h r o t t l i n g occurred when the dimensionless stroke (at dead center) was 1.2 and f u l l t h r o t t l i n g occurred when the stroke was 2.7. These two p o i n t s were connected by a s t r a i g h t l i n e as shown on Graph 3.9. On t h i s graph i s p l o t t e d the p o r t area-time curve based on r e c t a n g u l a r p o r t s and t h r e e b l e e d p o r t s i z e v a r i a t i o n s . The v a l u e s were ob t a i n e d by measuring the area under the c o m p u t e r - c a l c u l a t e d p o s i t i o n - t i m e curve. The computer c a l c u l a t i o n s were based on a h y p o t h e t i c a l s t r a i g h t l i n e r e l a t i o n s h i p between the amount of t h r o t t l i n g and the p i s t o n p o s i t i o n . I t i s p o s s i b l e to change the shape of the area time curve not o n l y by changing the s i z e of b l e e d p o r t 1.0 1.5 2.0 2.5 / STROKE AT BDC \ EFFECTIVE STROKE Graph 3.9 Flow-area v e r s u s s t r o k e f o r i d e a l FPS 150 a r e a s a s s h o w n , b u t a l s o b y a l t e r i n g t h e p o r t t i m i n g a n d b y m o d i f y i n g t h e p o r t s h a p e . A f t e r t h e p o r t a r e a - t i m e f a c t o r s w e r e o b t a i n e d g r a p h i c a l l y , t h e c o m p u t e r p r o g r a m was m o d i f i e d t o i n t e g r a t e t h e a r e a - t i m e d i r e c t l y . T h r o t t l i n g f o r t h e p r o g r a m was s t i l l b a s e d o n t h e h y p o t h e t i c a l s t r a i g h t l i n e r e l a t i o n s h i p . T h e i n t a k e p o r t a l s o c o n t r i b u t e s t o t h r o t t l i n g a s i s s h o w n b y t h e i n t a k e a r e a - t i m e i n t e g r a t i o n . B e c a u s e t h e p i s t o n d w e l l s n e a r t h e t o p f o r s h o r t e r p e r i o d s w h e n t h e h i g h c o m p r e s s i o n p r e s s u r e p r o d u c e s h i g h a c c e l e r a t i o n s , t h e i n t a k e p o r t , a s r e f l e c t e d i n t h e i n t e g r a t i o n , i s n o t o p e n a s l o n g . T h e s p r i n g r a t e a f f e c t s t h e i n t e g r a t e d p o r t a r e a . B e c a u s e a s t i f f e r s p r i n g r e s u l t s i n a h i g h e r a c c e l e r a t i o n n e a r b o t t o m d e a d c e n t e r , t h e i n t e g r a t e d p o r t a r e a d e c r e a s e s a s t h e s p r i n g r a t e i n c r e a s e s . T h e t o p c u r v e o n G r a p h 3.10 d e p i c t s t h e p l o t o f t h e p i s t o n s t r o k e a s a f u n c t i o n o f t i m e f o r 3 v a l u e s o f t h e s p r i n g r a t e . T h e c y c l e s b e c o m e m o r e s t a b l e a s t h e s p r i n g r a t e i n c r e a s e s . F o r t h e weak s p r i n g ( k / m = 40,000), t h e t h i r d s t r o k e i s h i g h e r t h a n t h e s e c o n d a n d t h e f o u r t h i s s h o r t e r t h a n t h e e f f e c t i v e s t r o k e . T h i s c a n b e e x p l a i n e d a s f o l l o w s : f o r t h e f i r s t s t r o k e t h e a m o u n t o f t h r o t t l i n g was l e s s t h a n t h e a m o u n t o f e n e r g y a b s o r b e d b y t h e s p r i n g s o t h a t t h e s e c o n d s t r o k e was t o o l o n g , c a u s i n g t o o much t h r o t t l i n g . T h e t h i r d s t r o k e was t o o 1 5 1 s h o r t a n d c o n s e q u e n t l y d i d n o t c a u s e e n o u g h t h r o t t l i n g . T h e u n s t a b l e c y c l e s c o n t i n u e d u n t i l t h e e n g i n e s t a l l e d . By i n c r e a s i n g t h e s p r i n g s t i f f n e s s , t h e s p r i n g a b s o r b e d m o r e e n e r g y a n d p r o d u c e d m o r e u n i f o r m c y c l e s . (The same e f f e c t c o u l d h a v e b e e n p r o d u c e d b y d e c r e a s i n g t h e r a t e o f t h r o t t l i n g . ) T h e s e c o n d * c u r v e d e p i c t s t h e p i s t o n p o s i t i o n a t t h e e n d o f t h e p o w e r s t r o k e when t h r o t t l i n g d e p e n d s o n a n i n t e g r a t e d p o r t a r e a . A g a i n c o m b u s t i o n p r e s s u r e s w e r e a s s u m e d t o v a r y a t r a n d o m b u t l e s s t h a n ±10% f r o m t h e v a l u e s c a l c u l a t e d . T h e o p e r a t i n g s p e e d d e p e n d e d o n t h e s p r i n g s t i f f n e s s ; f o r a w e a k s p r i n g , t h e p i s t o n o s c i l l a t e d a t a b o u t 4 , 2 5 0 c p m , f o r a m e d i u m s p r i n g , 5 , 1 5 0 c p m , a n d f o r a s t i f f s p r i n g , 6 , 00.0 c p m . T h e e f f e c t o f t h e p i s t o n w e i g h t o n t h e p i s t o n p o s i t i o n i s i l l u s t r a t e d b y t h e t h i r d c u r v e . T h e m e d i u m w e i g h t p i s t o n p r o d u c e s t h e m o s t s t a b l e c y c l e s . I t s h o u l d a l s o b e n o t e d t h a t t h e e n g i n e s p e e d a t f u l l l o a d i s o n l y 5% h i g h e r t h a n a t no l o a d (6 , 0 0 0 cpm v e r s u s 5 , 7 0 0 c p m ) . T h e b o t t o m c u r v e i n d i c a t e s w h a t e f f e c t t h r o t t l i n g a n d e r r a t i c c o m b u s t i o n h a v e o n s t a b i l i t y . A l t h o u g h t h e e r r a t i c c o m b u s t i o n d i d n o t a f f e c t t h e s t a b i l i t y s i g n i f i c a n t l y w h e n t h e e n g i n e was t h r o t t l e d l i n e a r l y , i t d i d c a u s e t h e e n g i n e t o s t a l l e a r l i e r w h e n t h e e n g i n e was t h r o t t l e d i n p r o p o r t i o n t o t h e i n t e g r a t e d p o r t a r e a . Graph 3.10 P i s t o n strokes as a f u n c t i o n of time f o r the i d e a l o s c i l l a t i n g power saw The next stage i n the o p t i m i z a t i o n of the t h r o t t l e p o r t s i z e was to c a l c u l a t e the flow r a t e using an i d e a l gas model. By employing the techniques used by London [3.2] i n h i s s o l u t i o n of a r e c e i v e r blowdown problem, more exact equations were obtained f o r the amount of t h r o t t l i n g the charge experiences i n f l o w i n g through the p o r t s . The temper-atures i n the c y l i n d e r and scavenging chamber depend on the amount and temperature of the gases e n t e r i n g and l e a v i n g , and on the amount of compression t a k i n g p l a c e . The r a t e of gas f l o w i n g through a p o r t was c a l c u l a t e d from the f o l l o w i n g equation suggested by Taylor [3.1]: dM W = 5Bf = AC ap 0 r P, 2 p, y + l l c dt K ' ° A — * A  , d > — , d, (p-)Y - (—) Y u u Where A i s the port area, C i s the p o r t c o e f f i c i e n t , a i s the speed of sound, P^ i s the downstream pressure, P^ i s the upstream pressure, p i s the d e n s i t y , Y 1 S the r a t i o of s p e c i f i c heats. The d e r i v e d temperature equation used an i d e a l flow r a t e equation f o r each port and assumed t h a t compression took place i s e n t r o p i c a l l y . For example, when the flow enters through the i n t a k e p o r t s and leaves through the scavenging p o r t and bleed p o r t , the scavenging chamber temperature v a r i e s Where R i s the gas c o n s t a n t , m i s the m o l e c u l a r weight, c v i s the s p e c i f i c heat a t c o n s t a n t volume, T i s the temperature o f charge e n t e r i n g through a i n t a k e , Tp i s the temperature i n scavenging chamber, Wj i s the flow r a t e through i n t a k e p o r t , w D i s the flow r a t e through b l e e d p o r t , 13 wg i s the flow r a t e through scavenging p o r t , 14^  i s the mass of gas i n s i d e scavenging volume, X i s the p i s t o n d i s p l a c e m e n t , x i s the p i s t o n v e l o c i t y , L i s the maximum e f f e c t i v e p i s t o n p o s i t i o n , Q i s heat t r a n s f e r r e d out of c y l i n d e r . When the flow r e v e r s e d through any of the p o r t s , a d i f f e r e n t though s i m i l a r equation,was used. A l s o equations f o r the flow o f f u e l and and f r e s h a i r were l a t e r added to a l l o w computation o f a i r - f u e l r a t i o s throughout the engine. When combustion o c c u r r e d , the c y l i n d e r temperature was assumed t o i n c r e a s e a c c o r d i n g t o the f o l l o w i n g e q u a t i o n : m _ m + E. A9 ,800\ ^ r c " g C y J M c 155 W h e r e i s t h e t e m p e r a t u r e i n c y l i n d e r p r i o r t o c o m b u s t i o n , F — i s t h e f u e l - a i r r a t i o o f m i x t u r e e n t e r i n g , M r i s t h e m a s s o f f r e s h m i x t u r e t r a p p e d , M i s t h e m a s s o f m i x t u r e i n c y l i n d e r . c . 2 T h e s p e c i f i c v o l u m e c a l c u l a t i o n s w e r e b a s e d o n t h e m a s s o f c h a r g e p r e s e n t i n t h e c h a m b e r a n d i t s v o l u m e . The p r e s s u r e c a l c u l a t i o n s w e r e b a s e d o n t h e s p e c i f i c v o l u m e , t h e c h a m b e r t e m p e r a t u r e , a n d a n e q u a t i o n o f s t a t e . The t h r o t t l e p o r t d i a m e t e r c h o s e n f o r t h e a c t u a l e n g i n e d e s i g n , b a s e d o n t h e f a c t o r s d i s c u s s e d a n d t h e n e e d t o e n s u r e t h a t t h e max imum a m o u n t o f t h r o t t l i n g w o u l d o c c u r , w a s t h e same a s t h e t r a n s f e r p o r t d i a m e t e r . T h e h o l e s w e r e s p a c e d s o t h a t , a t t h e o p t i m u m s t r o k e , t h e p o r t i o n o f t h e t h r o t t l e p o r t u n c o v e r e d i s t h e same a s t h e p o r t i o n o f t h e t r a n s f e r p o r t u n c o v e r e d . When t h e s t r o k e i s l o n g e r , t h e t h r o t t l e p o r t i s p a r t l y o r c o m p l e t e l y c o v e r e d , w h e r e a s t h e t r a n s f e r p o r t i s p a r t l y o r c o m p l e t e l y o p e n . B e c a u s e t h e t w o p o r t s a r e i n s e r i e s , b o t h p o r t s c o n t r o l t h e f l o w r a t e . B y s p e c i f y i n g a w i d t h o f 1 / 8 i n a n d a d e p t h o f 1 / 8 i n , t h e t o t a l c r o s s - s e c t i o n a l a r e a f o r t w o b l e e d p o r t s 2 w o u l d b e . 0 3 i n ( o r 1 / 6 o f t h e t r a n s f e r p o r t a r e a ) . By s p e c i f y i n g a h e i g h t / s t r o k e r a t i o o f 1 . 8 , t h e e f f e c t o f t h e b l e e d h o l e s h o u l d b e s i m i l a r t o t h a t s h o w n o n G r a p h 3 . 9 . 156 3.3 Design of Components 3.3.1 General Considerations In the preceding step, concept f e a s i b i l i t y and performance optimization were design considerations. In the present step strength, cost, material a v a i l a b i l i t y and manufacturing c a p a b i l i t y were general considerations. More s p e c i f i c a l l y , the following practices were followed i n designing the parts constituting the free piston r e c i p r o -cating blade power saw: 1. r i g h t and l e f t hand parts were eliminated wherever possible, 2. as few parts as possible were used, 3. size and weight of parts were kept at a minimum, except for the piston which had to have the same mass as the cylinder, 4. wherever p r a c t i c a l , the machine shop f a c i l i t i e s at the University of B r i t i s h Columbia were used, 5. ease of assembly and appearance determined the shape of the parts where strength was not important. A 1 hp engine o s c i l l a t i n g at 6,000 cpm with a .93 i n stroke w i l l produce about 65 i n - l b of work per cycle. A 1.25 i n diameter piston and cylinder (bmep = 57 psi) exert a combined cutting force of 140 lbs on the blade. This f o r c e must be matched by an equal f o r c e on the handle. The operator applying t h i s f o r c e a l s o e x e r t s a feeding f o r c e whose magnitude depends on the shape and c o n d i t i o n of the te e t h (assumed to be 40 l b s as shown on Fi g u r e 3.1), and a t w i s t i n g moment. I f the f o r c e a p p l i e d i s 2.3 i n (X 2) above the s p e c i f i e d c u t t i n g f o r c e and 8 i n (X^) back from the feeding force,no bending moment i s r e q u i r e d . I f fo r c e s are ap p l i e d on the bottom handle (X 2 = -3.5 i n and X^ - -4.0 in) then the r e q u i r e d t w i s t i n g moment equals 950 i n - l b ) . Because the t w i s t i n g moment i s s m a l l e s t when the top handle i s used to load the saw, the bottom handle w i l l be used mainly to c o n t r o l the cut. Fi g u r e 3.1 Free body diagram of the r e c i p r o c a t i n g power saw T h e b e n d i n g moment a c t i n g i n t h e b l a d e d e p e n d s o n t h e m a g n i t u d e o f t h e f o r c e s , t h e p r e s e t d i s t a n c e f r o m t h e s a w i n g f o r c e t o t h e b l a d e c e n t r o i d ( X ^ ) , a n d t h e c o n s t a n t l y c h a n g i n g d i s t a n c e f r o m t h e f e e d i n g f o r c e t o t h e f r a m e ( X ^ ) . ( I f X ^ v a r i e s 1 -7 i n a n d a v e r a g e s 4 i n , X ^ s h o u l d b e . 8 6 i n , s o t h a t t h e b e n d i n g moment d u r i n g t h e c u t t i n g s t r o k e w i l l b e l e s s t h a n ± 120 i n - l b a n d t h e s t r e s s i n a . 1 2 x . 6 4 i n b l a d e w i l l b e l e s s t h a n 1 6 , 0 0 0 p s i . ) B u t t h e max imum s t r e s s o c c u r s n o t a s c a l c u l a t e d a b o v e b u t d u r i n g t h e r e t u r n s t r o k e . I f t h e f e e d i n g f o r c e r e m a i n s a t 40 l b s a n d f r i c t i o n i s 20% o f t h e f e e d i n g f o r c e , t h e s t r e s s e q u a l s 2 9 , 0 0 0 i n - l b d u r i n g t h e r e t u r n s t r o k e , g i v i n g a f a c t o r o f s a f e t y , w i t h A I S I 1040 s t e e l , o f 2 . 7 . T h e s h e a r s t r e s s i n t h e l u g a n d t h e b e n d i n g s t r e s s a t t h e p i n c r o s s - s e c t i o n a r e s l i g h t l y l o w e r a t 2 8 , 0 0 0 a n d 2 7 , 0 0 0 p s i r e s p e c t i v e l y . 3 . 3 . 2 B o u n c e S p r i n g O n c e i t was d e t e r m i n e d t h a t t h e o v e r a l l f o r c e s w e r e r e a s o n a b l e , a n a n a l y s i s w a s made o f t h e r e q u i r e m e n t s o f t h e p o w e r s p r i n g . I t s p u r p o s e was t o c o m p r e s s t h e c h a r g e a n d t o p r o v i d e a means o f r e l a t i n g t h e a m o u n t o f t h e t h r o t -t l i n g t o t h e a m o u n t o f w o r k . T h e i d e a l r e l a t i o n s h i p r e q u i r e d a d i r e c t c o r r e l a t i o n b e t w e e n t h e a m o u n t o f e n e r g y r e l e a s e d i n c o m b u s t i o n ( c o n t r o l l e d b y t h e t h r o t t l e ) a n d t h e a m o u n t o f e n e r g y c o n v e r t e d t o w o r k ( c o n t r o l l e d b y l o a d a n d s t r o k e l e n g t h ) . When t h e a m o u n t o f w o r k i s r e d u c e d b y r e m o v i n g 159 some of the load from the blade, the stroke l e n g t h increases to absorb more energy. The increased stroke must t h r o t t l e the i n t a k e more, so t h a t the subsequent power strokes w i l l r e l e a s e l e s s energy. The c o r r e c t amount of t h r o t t l i n g w i l l r e l e a s e j u s t as much energy as i s r e q u i r e d by the work taken out so th a t the len g t h of subsequent strokes w i l l not change. I f the amount of t h r o t t l i n g i s not c o r r e c t , the stroke l e n g t h w i l l continue to change u n t i l the q u a n t i t y of energy r e l e a s e d and the amount of work performed i s balanced. The equation governing the len g t h of s t r o k e , d e r i v e d from an energy balance taken over one c y c l e , i s as f o l l o w s : N 1 ( x ± ) + f ( x i ) = Wk + f ( x ) + E f Where N 1(x^) i s the energy r e l e a s e d i n combustion, f( x ) i s the energy stored i n the s t o r i n g d e v i c e , W. i s the work removed, and k i s the energy l o s t i n f r i c t i o n . When a mechanical s p r i n g w i t h a l i n e a r t h r o t t l e r a t e i s used, the equation can be solved f o r x and expressed as: { 160 - F + ! / F 2 + N + X ± 2 Where X i s the piston p o s i t i o n at BDC (= — ) , x o X1. i s the i n i t i a l p o s i t i o n at BDC (= ——) 1 X Q i s a reference p o s i t i o n , F 1 F i s the load on blade (= ) k i s the spring rate, N i s the work released during the power stroke minus energy l o s t i n f r i c t i o n i n dimension-(N 1 (x. )-E f) less units (N = 2N* = 2 - ) kx z o This equation can be used to study the e f f e c t of t h r o t t l i n g on the s t a b i l i t y of the cyc l e s . A general require-ment for s t a b i l i t y i s that a suddenly applied f u l l load or a suddenly removed f u l l load should not s t a l l the engine. For example; consider a t y p i c a l engine: i t reciprocates with a stroke of 1 i n , releases 100 i n - l b s during the power stroke, performs 60 i n - l b s of work and stores 40 i n - l b s of energy i n the spring (k=80 p p i ) . When the load i s suddenly removed the spring w i l l d e f l e c t 1.6 i n to absorb a l l the energy released (e.g., 100 i n - l b s less 5% f r i c t i o n ) and the t h r o t t l e should allow no more charge to enter. In t h i s example the equation for the energy released i s given by: * Assumptions: 1. amount of t h r o t t l i n g varies l i n e a r l y with the stroke and releases 60 i n - l b s of energy when Xj_=l and releases no energy when the spring has absorbed 60 i n - l b s of energy, 2. a lin e a r spring i s used, 3. work out varies with force and distance, 4. f r i c t i o n loss i s proportional to maximum energy released, 5. e f f e c t i v e stroke does not change. 161 N * = 2.04 - 1.25 X . l a n d t h e e q u a t i o n f o r t h e p i s t o n p o s i t i o n i s ^ F 2 + X ± X = - F + "V "  X , 2 + 4 .08 - 1.25 X ± 2 T h e e q u a t i o n g i v i n g t h e s t r o k e l e n g t h when t h e l o a d i s s u d d e n l y r e m o v e d i s o b t a i n e d f r o m t h e l a t t e r e q u a t i o n b y s e t t i n g t h e l o a d (F) e q u a l t o z e r o : X = J x . 2 - 2.5 X . + 4.08 n i i i T h e e q u a t i o n g i v i n g t h e s t r o k e l e n g t h w h e n t h e e n g i n e i s s u d d e n l y l o a d e d t o c a p a c i t y i s o b t a i n e d b y s e t t i n g F=.75 a n d c a n b e r e p r e s e n t e d b y X „ = - .75 + Jx.2 - 2.5 X . + 4.64 T h e s e c o n d e q u a t i o n o n G r a p h 3.11 i s a m o r e a c c u r a t e r e p r e s e n t a t i o n o f t h r o t t l i n g b e c a u s e i t a p p r o x i m a t e s t h e i n -t e g r a t e d p o r t a r e a m o r e c l o s e l y . I f t h i s e q u a t i o n , N = 1.94 - 1.19 X . - - 0 0 0 7 5 1 ( X i - . 9 ) 3 i s s u b s t i t u t e d i n t o t h e s t r o k e e q u a t i o n a n d t h e l o a d s u d d e n l y r e m o v e d , t h e p i s t o n s t r o k e i s g i v e n b y X = W X . 2 + N n 1 l and when the load i s suddenly applied (F=.49) the piston stroke i s : 162 X £ = - .49 + ^ ( . 4 9 ) 2 + X i 2 + N~ Note on t h i s graph what happens to the piston when the load i s suddenly removed. Assume that during the previous cycle the piston had stopped when Xj_=1.30. This means that .41 uni t of energy i s added to the engine when combustion occurs ( t h r o t t l i n g follows the N=2 .04-1.25X^ curve, on Graph 3.11). I f the load i s then removed so that no work i s taken out of the engine during the next power stroke, the spring w i l l d e f l e c t 1.56. The next combustion cycle w i l l release .07 units of energy, and d e f l e c t the spring to 1.62. No energy w i l l be released during subsequent cycles u n t i l f r i c t i o n reduces the stroke to i t s steady state, no-load value of 1.6. If the load i s suddenly increased from F=.31 to F=.75 the stroke w i l l decrease to 1.0, on the curve. The next combustion cycle w i l l release the maximum energy of .78 units and the engine w i l l be s t a b i l i z e d at X=l . o . If the t h r o t t l i n g follows the N=l. 94-1. 19x±- . 00075/ ( X ^ . 9 ) 3 curve and the load i s suddenly increased to F=.49, the strokes w i l l gradually decrease u n t i l steady state conditions are reached at X = l . l l . A t y p i c a l c o i l e d s p r i n g w i t h a s p r i n g r a t e of 87 pp i absorbs 45 i n - l b when compressed to 1.03 i n , 105 i n - l b when compressed to 1.56 i n , and 175 i n - l b when compressed to 2.0 0 i n . The r a t e of t h r o t t l i n g must t h e r e f o r e vary l i n e a r l y from no t h r o t t l i n g a t a stroke of 1.03 i n to f u l l t h r o t t l i n g at a stroke of 1.56 i n . REGION OF FULL THROTTLING IN IT IAL DEFLECTION IN IT IAL DEFLECTION Graph 3.11 Stroke when load suddenly changed High carbon s p r i n g s t e e l wire (.156 i n diameter), when made i n t o a 1.0 i n mean diameter c o i l e d s p r i n g , w i l l r e q u i r e 10 a c t i v e c o i l s to stor e 175 i n - l b of energy d u r i n g a 2 i n d e f l e c t i o n . I t w i l l compress to a s o l i d height of 3 1.56 i n , occupy a .80 i n , and weigh .17 l b s . This s p r i n g c a n s t o r e 1 , 0 0 0 i n - l b / l b m a s s o r 220 i n - l b / c u i n . The g a s u n d e r t h e p i s t o n c a n b e u s e d a s a n e n e r g y a b s o r b e r a n d p i s t o n b o u n c e . T h e e q u a t i o n f o r t h e a m o u n t o f w o r k r e q u i r e d t o c o m p r e s s a n i d e a l g a s i s e n t r o p i c a l l y s u g g e s t s t h a t t h e e n e r g y a b s o r b i n g a b i l i t y o f t h e g a s i n -c r e a s e s r a p i d l y w i t h a d e c r e a s e i n v o l u m e . F o r e x a m p l e , w h e n t h e max imum p o s s i b l e s t r o k e o f t h e e n g i n e i s . 7 5 0 i n , a s t r o k e o f . 6 5 2 i n s t o r e s 45 i n - l b o f e n e r g y a t a c o m p r e s -s i o n r a t i o o f 7 . 6 , a s t r o k e o f . 7 3 4 i n s t o r e s 105 i n - l b a t a c o m p r e s s i o n r a t i o o f 5 4 , a n d a s t r o k e o f . 7 4 6 i n s t o r e s 175 i n - l b a t a c o m p r e s s i o n r a t i o o f 1 9 5 . F o r t h i s e x a m p l e t h e t h r o t t l e m u s t a c c o m p l i s h t h r e e t h i n g s : 1 . n o t r e s t r i c t t h e f l o w when t h e s t r o k e i s . 6 5 2 i n , 2 . s t o p t h e f l o w c o m p l e t e l y when t h e s t r o k e i s . 7 3 4 i n o r l o n g e r , 3 . v a r y t h e f l o w i n a n i s e n t r o p i c f a s h i o n b e t w e e n t h e two l i m i t s . B e c a u s e t h i s i s v e r y d i f f i c u l t t o a c c o m p l i s h , g a s i s n o t a g o o d m e a n s o f s t o r i n g e n e r g y . F l a t s p r i n g s * R e f e r e n c e [ 3 . 3 ] g i v e s t h e f o l l o w i n g s p e c i f i c a t i o n s f o r o i l t e m p e r e d w i r e (ASTM A 2 2 9 - 4 1 ) : S = E l a s t i c l i m i t 1 2 0 , 0 0 0 - 2 5 0 , 0 0 0 p s i , E = M o d u l u s o f E l a s t i c i t y - 3 0 , 0 0 0 , 0 0 0 p s i , p = D e n s i t y - . 2 8 2 l b / c u i n . or bands can be used as an energy absorber and bounce. They can also be used to synchronize the c y l i n d e r with the piston, thereby serving a dual purpose. Steel bands are more e f f i c i e n t on a weight basis than a c o i l spring, and make possible a variable spring rate that corresponds more c l o s e l y to actual t h r o t t l e requirements. Bands are usually long (25 i n when the 2 cross-sectional area i s .010 i n ) and must be securely attached to the c y l i n d e r and piston. (The attachment force required i s 2,000 lbs when the length i s 25 i n ) . Storing 175 i n - l b of energy (W^ ) i n a band requires a band volume of .25 i n 3 (Volume = 2 E ^ ) and a weight of .07 0 l b . S Bands of rubber and nylon can be used to store the required energy and bounce the piston. For evaluation of rubber as a spring material, s i l a s t i c rubber was chosen because i t i s exceptionally r e s i s t a n t to solvents, j e t fuels and o i l s and i s r e l a t i v e l y strong as compared with other f l u o r o s i l i c o n e rubber stocks. I t i s easy to handle i n the unvulcanized state and may be processed by m i l l i n g , calender ing, extruding or moulding [3.4]. For a 2 i n stroke and 175 l b force, the rubber band must be .53 i n long and have a cross-sectional area 2 3 of .13 i n . I t w i l l occupy .069 i n and weigh .0036 l b . 3 * (It can store 50,000 i n - l b / l b mass and 2,500 i n - l b / i n ) * Reference [3.4] gives the t y p i c a l physical properties of S i l a s t i c LS-2249V f l u o r o s i l i c o n e rubber as follows: Tensile strength - 1370 p s i Tear strength - 165 p s i Elongation - 480% S p e c i f i c gravity - 1.46 166 Its e l a s t i c i t y and high strength make nylon a suitable material for absorbing or storing energy. In 3 stretching 2 i n , a piece of nylon 5.7 i n long (.035 i n * volume) can store 175 i n - l b and w i l l weigh .0012 l b . (It stores 150,000 i n - l b / l b mass and 5,000 i n - l b / i n 3 ) . Table IV summarizes the energy storing a b i l i t y of the four materials considered,by l i s t i n g the volume and weights required to store 175 i n - l b of energy. Table IV Size of Material Required to Store 175 i n - l b s of Energy Volume Occupied (i n 3 ) Weight (lb). C o i l spring .80 .17 Steel band .25 .070 S i l a s t i c rubber .069 .0036 Nylon .035 .0012 A comparison shows that on a per pound basis, the energy storing capacity of nylon i s 140 times greater than a c o i l e d Reference [3.5] gives the following s p e c i f i c a t i o n s for Extremultus b e l t i n g : Tensile strength - 28,500 p s i at 35% stretch E - 78,230 p s i 3 Density - 30 i n / l b Heat resistance to +160°F Cold resistance to -20°F 167 s p r i n g , rubber i s 47 times g r e a t e r , and a s t e e l band i s 2 1/2 times g r e a t e r . But i n s p i t e of i t s poor r a t i n g , a s t e e l c o i l e d s p r i n g was chosen to bounce the p i s t o n f o r these reasons: 1. the d i f f e r e n c e i n weight between any of the m a t e r i a l s i s l e s s than 3 ounces, 2. s p r i n g d e f l e c t i o n s are p r o p o r t i o n a l t o the l o a d , 3. the f a t i g u e l i f e i s very high f o r low s t r e s s e s (nylon and rubber have a short l i f e i f com-pres s i o n s are h i g h ) , 4. springs are easy to design. Even though they are more e f f i c i e n t than round wire i n the use of space, r e c t a n g u l a r w i r e c o i l e d s prings r e q u i r e more expensive m a t e r i a l s and more complex manufacturing techniques. Because i t . i s not produced i n tonnage,rectangular w i r e has not had the r e f i n i n g development given to round w i r e , so t h a t the a v a i l a b l e q u a l i t y i s not equal to t h a t of good grades of round w i r e . Because they must not f a i l under an i n f i n i t e number of l o a d i n g s , the springs must be given the best i n desi g n , m a t e r i a l and manufacture. Consequently round wire springs were chosen. The choice of m a t e r i a l f o r springs i s u s u a l l y between s t r a i g h t carbon (ASTM A230-47) and a l l o y s t e e l s . 168 Carbon v a l v e s p r i n g m a t e r i a l i s p r e f e r r e d because i t s u l t i m a t e s t r e n g t h equals t h a t of a l l o y s t e e l s and i t s d e p e n d a b i l i t y at o r d i n a r y temperatures i s g r e a t e r . Exposing carbon s t e e l to temperatures i n excess of 350°F w i l l cause heat s e t t i n g and l o s s of lo a d . A l l o y s t e e l s , on the other hand, u s u a l l y are more su b j e c t to seams and have a g r e a t e r tendency t o quench-crack. Carbon v a l v e s p r i n g wire (ASTM A230-47) has an u l t i m a t e s t r e n g t h of 200,000-230,000 p s i , chrome vanadium a l l o y s t e e l (SAE 6150) has an u l t i m a t e s t r e n g t h of 200,000-250,000 p s i ( e l a s t i c l i m i t i s 180,000-230,000 p s i ) , chrome s i l i c o n a l l o y s t e e l (SAE 9254) has an u l t i m a t e s t r e n g t h of 250,000-325,000 p s i ( e l a s t i c l i m i t i s 220,000-300,000 p s i ) , and oil-tempered s p r i n g wire (ASTM A229-41) which i s most g e n e r a l l y used, has an e l a s t i c l i m i t of 120,000-250,000 p s i . In s p e c i f y i n g a m a t e r i a l f o r a p a r t i c u l a r p a r t , a v a i l a b i l i t y , performance and cost are always connected. In research and development, co s t i s o f t e n of secondary importance to per-formance and a v a i l a b i l i t y . The d e s i r e f o r quick d e l i v e r y l i m i t e d the choice of wire m a t e r i a l s to oil-tempered wire a v a i l a b l e l o c a l l y and chrome s i l i c o n a l l o y s t e e l a v a i l a b l e on a short order b a s i s . Because i t r e s i s t s heat up to 450°F w e l l , chrome s i l i c o n wire was chosen. Shot b l a s t i n g was s p e c i f i e d because the impact of the s t e e l or g l a s s b a l l s p r e s t r e s s e s and c o l d works the surface and so r a i s e s the p h y s i c a l p r o p e r t i e s of the m a t e r i a l on the surface where the s t r e s s i s the highest and where f a t i g u e f r a c t u r e s w i l l s t a r t . 169 When t h e i n i t i a l d e s i g n u s i n g a s i n g l e s p r i n g was m o d i f i e d t o two s p r i n g s , a b e t t e r a r r a n g e m e n t r e s u l t e d . T h e d i a m e t e r o f t h e s c a v e n g i n g c h a m b e r e n c l o s i n g t h e c y l i n d e r s p r i n g w a s made l a r g e r t h a n t h e p i s t o n d i a m e t e r s o t h a t a s h o r t e r m a c h i n e was p o s s i b l e . T h i s a d d e d c o m p l e x i t y t o t h e d e s i g n . T h e c h o i c e o f d i m e n s i o n s was r e s t r i c t e d b y t h e f a c t t h a t t h e s p r i n g s (a) o p e r a t e d w i t h i n p r e s e t o u t s i d e d i a m e t e r s , (b) o p e r a t e d o v e r p r e s e t s h a f t d i a m e t e r s , (c ) h a d s p e c i f i e d max imum s o l i d h e i g h t s , (d) h a d t h e same s p e c i f i e d d e f l e c t i o n s , a n d (e) r e q u i r e d t h e same s p r i n g r a t e . B e c a u s e a l l t h e s e c o n d i t i o n s w e r e n e c e s s a r y a n d c o n d i t i o n s c h a n g e d w h e n e v e r e n g i n e s i z e s w e r e c h a n g e d , w h e n e v e r new s p r i n g m a t e r i a l s w e r e c o n s i d e r e d , a n d w h e n e v e r new c h a r a c t e r -i s t i c s w e r e d e s i r e d , a l a r g e n u m b e r o f c a l c u l a t i o n s w e r e p e r f o r m e d b e f o r e t h e f i n a l s i z e s w e r e s e l e c t e d . A s l i d e r u l e d e s i g n e d b y A s s o c i a t e d S p r i n g C o r p o r a t i o n [ 3 . 6 ] t o a i d s i z e s e l e c t i o n r e d u c e d t h e t i m e r e q u i r e d f o r c a l c u l a t i o n s s o t h a t a c o m p u t e r p r o g r a m f o r o p t i m i z i n g t h e s i z e was n o t r e q u i r e d . The s l i d e r u l e w a s b a s e d o n t h e f o l l o w i n g t w o f o r m u l a s : 8 PDK 170 Gd 4 P = 8D3N p i s the load on s p r i n g , D i s the mean diameter of c o i l , d i s the diameter of w i r e , S i s the t o r s i o n a l s t r e s s , K i s the Wahl c o r r e c t i o n formula f o r s t r e s s caused by curvature of wire l o a d , G i s the t o r s i o n a l modulus, N i s the number of a c t i v e c o i l s , 6 i s the d e f l e c t i o n . When subjected to above normal temperatures, sp r i n g s o f t e n shorten ( or "set" ) and l o s e l o a d . This l o s s of load can be p r e d i c t e d and allowances can be made i n * cases where the load i s steady. Where the load i s unpre-d i c t a b l e and the s p r i n g design i s not f l e x i b l e enough, the spri n g s may be preset by' exposing them to temperatures and s t r e s s e s above those encountered i n o p e r a t i o n . Since the s p r i n g design i s f l e x i b l e i n the present design,no c o r r e c -t i o n f a c t o r f o r set was s p e c i f i e d . On page 25, reference [3.6] s t a t e s t h a t SAE 6150 l o s e s 4% load when s t r e s s e d to 80,000 p s i at 350°F, 7% at 100,000 p s i and 13% at 120,000 p s i . 171 A c h a r a c t e r i s t i c s o m e t i m e s c r i t i c a l i s t h e n a t u r a l v i b r a t i o n f r e q u e n c y o f t h e s p r i n g . I f i t i s t o o l o w t h e s p r i n g w i l l s u r g e a n d s t r e s s e s w i l l b e g r e a t l y a u g m e n t e d . S i n c e t h e n a t u r a l f r e q u e n c y o f t h e d e s i g n e d s p r i n g i s 3 . 5 t i m e s t h e o p e r a t i n g f r e q u e n c y , t h e e f f e c t o f s p r i n g s u r g i n g w i l l h a v e t o b e o b s e r v e d i f p r o b l e m s a r i s e . C o m p r e s s i o n s p r i n g s i n w h i c h t h e f r e e l e n g t h i s m o r e t h a n f o u r t i m e s t h e mean d i a m e t e r c a n b u c k l e . A c a l c u l a -t i o n s h o w e d t h a t t h e r a t i o o f f r e e l e n g t h t o mean d i a m e t e r i s w e l l b e l o w 4 a n d t h e r e f o r e t h e d e s i g n e d s p r i n g s s h o u l d n o t f a i l d u e t o b u c k l i n g . T h i s was c o n f i r m e d b y c h e c k i n g t h e d e f l e c t i o n / f r e e l e n g t h r a t i o w i t h t h e l i m i t s e t b y T h e A s s o c i a t e d S p r i n g C o r p o r a t i o n . D e f l e c t i o n / f r e e l e n g t h r a t i o f o r t h e p i s t o n s p r i n g i s . 4 ( l i m i t i s . 7 0 ) a n d f o r t h e c y l i n d e r s p r i n g i t i s . 5 ( l i m i t i s . 7 2 ) [ 3 . 6 , p . 2 4 ] . T h e i n c r e a s e i n d i a m e t e r a s t h e s p r i n g i s c o m p r e s s e d was c a l c u l a t e d a n d f o u n d t o be s m a l l . T h e max imum i n c r e a s e i n d i a m e t e r f o r t h e c y l i n d e r s p r i n g i s . 0 2 5 i n a n d f o r t h e p i s t o n s p r i n g i t i s . 0 1 1 i n . * R e f e r e n c e [ 3 . 6 ] , p a g e 2 2 , s u g g e s t s t h a t t h e v i b r a t i o n s p e r m i n o f a s p r i n g v i b r a t i n g b e t w e e n i t s own e n d s c a n b e g i v e n b y : N = . 2 1 S w h e r e S i s t h e u n c o r r e c t e d s t r e s s ( n o t i n c l u d i n g t h e W a h l c o r r e c t i o n f a c t o r ) f o r a d e f l e c t i o n o f 1 i n . F o r o u r c a s e S w a s a p p r o x i m a t e l y 1 0 0 , 0 0 0 p s i s o t h a t N i s 2 1 , 0 0 0 c p m . 3 . 3 . 3 S y n c h r o n i z i n g M e c h a n i s m T h e p i s t o n a n d c y l i n d e r c a n b e s y n c h r o n i z e d w i t h c o n n e c t i n g r o d s a n d c r a n k s h a f t s w h i c h a r e s i m p l e t o d e s i g n a n d i n e x p e n s i v e t o f a b r i c a t e . T h e r a t i o o f p i s t o n s t r o k e t o c y l i n d e r s t r o k e c a n b e e a s i l y c h a n g e d a n d s u i t a b l e t o l e r a n c e s f o r t h e b e a r i n g s c a n b e e a s i l y h e l d . E i t h e r s t a n d a r d r o l l e r b e a r i n g s r e q u i r i n g o i l t o m i n i m i z e h e a t g e n e r a t i o n a n d w e a r , o r t e f l o n i m p r e g n a t e d s e l f - l u b r i c a t e d b e a r i n g s c a n b e u s e d . A t y p i c a l s e l f - l u b r i c a t e d b e a r i n g c o n s i s t s o f a t h i n p o r o u s l a y e r o f s p h e r i c a l b r o n z e i m p r e g -n a t e d w i t h a m i x t u r e o f T F E f l u o r o c a r b o n r e s i n a n d l e a d p o w e r [ 3 . 7 ] . T h e F r e e - P i s t o n C o m p a n y o f K i n g s t o n f o u n d t h a t f o r o s c i l l a t i n g s h a f t s , t e f l o n i m p r e g n a t e d b e a r i n g s w e r e * b e t t e r t h a n r o l l e r b e a r i n g s . D e s i g n c a l c u l a t i o n s s h o w e d t h a t a 1 i n d i a m e t e r b y . 5 l o n g b e a r i n g c a n s a f e l y c a r r y a s h o c k l o a d o f 1 , 0 0 0 l b s w i t h o u t e x c e e d i n g G a r l o c k ' s [ 3 . 7 ] s u g g e s t e d l i m i t o f 2 , 0 0 0 p s i . T h e s e r v i c e f a c t o r f o r 1 0 , 0 0 0 h o u r s a t a n a v e r a g e o p e r a t i n g l o a d o f 25 l b s i s 9 , 5 0 0 a n d w e l l b e l o w t h e s u g g e s t e d l i m i t o f 2 4 , 0 0 0 . E v e n t h o u g h t h e r e q u i r e d c r o s s - s e c t i o n a r e a f o r t h e c o n n e c t i n g r o d i s q u i t e s m a l l 2 ( . 0 4 i n f o r a s t r e s s o f 2 5 , 0 0 0 p s i ) , t h e r e q u i r e d s p a c e t o a l l o w o s c i l l a t i o n i s n o t . T h e c y l i n d e r c o n n e c t i n g r o d s , i n o r d e r t o o s c i l l a t e f r e e l y , r e q u i r e a s p a c e 2 1 / 2 x 1 * U n o f f i c i a l d i s c u s s i o n s , 1 9 6 5 . 173 x 5 i n , a n d t h e p i s t o n c o n n e c t i n g r o d s r e q u i r e a s p a c e 2 1 / 2 x 1 x 1 1 / 2 i n . I n a r a c k a n d p i n i o n a r r a n g e m e n t , t h e r a c k s move o v e r o r i n t o t h e c o i l o f t h e s p r i n g s o t h e a r r a n g e m e n t r e -q u i r e s l e s s v o l u m e t h a n a c o n n e c t i n g r o d a r r a n g e m e n t . T h e g e a r s e r v i c e f a c t o r r e s t r i c t s t h e a v e r a g e s t r e s s t o o n l y o n e - t e n t h o f t h e max imum s t r e s s , b u t s i g n i f i c a n t l y , t h e f o r c e s i n v o l v e d d u r i n g s t a r t i n g a n d s t o p p i n g a r e t e n t i m e s h i g h e r t h a n t h e a v e r a g e o p e r a t i n g f o r c e s , s o t h e g e a r m a t e r i a l i s u s e d e f f i c i e n t l y . A r a c k a n d p i n i o n a r r a n g e m e n t was u s e d i n t h e f i r s t d e s i g n . T h e p i n i o n s m a t e d w i t h t e e t h o n t h e p i s t o n s k i r t a n d o n t h e c y l i n d e r , a n d a s i n g l e s p r i n g f i t t e d i n s i d e t h e p i s t o n . A f t e r t h e l a y o u t d r a w i n g s o f t h e a s s e m b l y a n d p a r t s h a d b e e n c o m p l e t e d , t h e c o n c e p t o f p l a c i n g t h e p i n i o n g e a r s b e t w e e n a d i v i d e d s p r i n g was f o r m a l i z e d . I n s p i t e o f a l l t h e w o r k p e r f o r m e d o n t h e f i r s t d e s i g n , t h e o r i g i n a l d r a w i n g s w e r e s c r a p p e d a n d a new d e s i g n u n d e r t a k e n when t h e d i v i d e d s p r i n g a r r a n g e m e n t s h o w e d t h a t a m o r e c o m p a c t e n g i n e w a s p o s s i b l e . I n t h e new a r r a n g e m e n t d e l i n e a t e d , t h e g e a r m a t e d w i t h t e e t h o n t h e p i s t o n r o d a n d r o t a t e d i n a s t a t i o n a r y m o u n t . I n t h i s a r r a n g e m e n t t h e l a t c h p i v o t e d o n t h e f r a m e s o t h a t t h e f o r c e a c t i n g i n t h e l a t c h when t h e e n g i n e was s t o p p e d , i s t r a n s m i t t e d t h r o u g h t h e g e a r . T h e f o r c e i s l a r g e s t w h e n t h e t e e t h o n t h e l a t c h e n g a g e t h e t e e t h o n t h e b l a d e . 174 When compared to the s l i d i n g action of the connect-ing rod bearing, the r o l l i n g action of a gear on a rack generates less heat and requires less l u b r i c a t i o n . Because the load changes continually from one tooth to another and reverses at the end of each stroke, the gears would be noisy unless close tolerances were maintained. The gears designed for the rack and pinion took into account tolerances, geometry, load d i s t r i b u t i o n , s i z e , dynamic overload, service l i f e , temperature e f f e c t s and p i t t i n g d u r a b i l i t y . The analysis followed the American Gear Manufacturers' Associa-t i o n standards [3.8, 3.9]. The r e s u l t i n g gears (24 p i t c h , 20° spur with a p i t c h diameter of 3/4 i n and a face width of 3/8 i n ) , occupy a volume 3/4 x 2 x 7/8 i n . On completion of the design and de l i n e a t i o n , a manufacturer for the small rack and pinion gears was sought. None of the l o c a l companies v i s i t e d had the proper f a c i l i t i e s and most of the outside companies contacted by mail were not interested i n the small job. The synchronizing mechanism was therefore reappraised and a new arrangement sought. Again the continuous quest for a compact, low-stressed design resulted i n a new and valuable idea. This idea was adopted even though again i t meant scrapping the old mechanism and i n i t i a t i n g a new arrangement. In the new arrangement the stop l a t c h was mounted on the cylinder so that i t transmitted the stopping force d i r e c t l y to the cylin d e r and the i n i t i a l spring compressing mechanism was 175 m o u n t e d o n t h e p i s t o n s o t h a t i t t r a n s m i t t e d t h e s t a r t i n g l o a d d i r e c t l y t o t h e c y l i n d e r . T h e s e m o d i f i c a t i o n s r e d u c e d t h e f o r c e a c t i n g i n t h e s y n c h r o n i z i n g m e c h a n i s m b y a f a c t o r o f 1 0 . N e v e r t h e l e s s , t h e s i z e o f g e a r s c o u l d n o t b e r e d u c e d b e c a u s e t h e s e r v i c e l o a d h a d c h a n g e d v e r y l i t t l e . B u t c a l -c u l a t i o n s now b a s e d o n t h e s m a l l e r f o r c e s s h o w e d t h a t t h e c o n n e c t i n g r o d a r r a n g e m e n t c o u l d f i t i n t o s p a c e a l r e a d y d e s i g n e d f o r t h e r a c k a n d p i n i o n a r r a n g e m e n t . A 3 / 1 6 i n d i a m e t e r c o n n e c t i n g r o d b e a r i n g ( T e f l o n i m p r e g n a t e d ) w o u l d h a v e t o b e o n l y 3 / 1 6 i n w i d e f o r a s e r v i c e l i f e o f 1 0 , 0 0 0 h o u r s a n d a u n i t l o a d o f 700 p s i , [ 3 . 7 ] . T h e s m a l l e r f o r c e s a l s o made c h a i n s , t i m i n g b e l t s a n d b a n d s f e a s i b l e . F o r e x a m p l e , a M o r s e 1 /4 p i t c h r o l l e r c h a i n w i t h a n a v e r a g e t e n s i l e s t r e n g t h o f 875 l b s t r a n s -m i t t i n g 1.4 ' h p a t 4 , 0 0 0 r p m a n d . 5 h p a t 8 , 0 00 r p m c o u l d b e u s e d [ 3 . 1 0 ] . J o i n t g a l l i n g c a u s e d b y f r i c t i o n b e t w e e n t h e p i n a n d b u s h i n g a s t h e j o i n t a r t i c u l a t e s a t h i g h s p e e d s , l i m i t s t h e s p e e d o f t h i s c h a i n t o 1 0 , 0 0 0 r p m . T h i s l i m i t i s h i g h e r f o r a c h a i n i n w h i c h t h e m o t i o n b e t w e e n m e t a l p a r t s d u r i n g a r t i c u l a t i o n i s a r o l l i n g a c t i o n r a t h e r t h a n a s l i d i n g a c t i o n . The M o r s e s i l e n t c h a i n u s e s s u c h a r o c k e r -p i n j o i n t . A 3 / 1 6 i n p i t c h 1 1 / 3 2 i n w i d e s i l e n t c h a i n h a s a n u l t i m a t e t e n s i l e s t r e n g t h o f 1 , 2 5 0 l b s a n d a l o a d c a r r y -i n g c a p a c i t y o f 0 . 7 h p a t 7 , 0 0 0 - 9 , 0 0 0 r p m . T i m i n g b e l t s a r e q u i e t e r t h a n c h a i n s o r g e a r s b e c a u s e t h e h e l i c a l l y wound l o a d - c a r r y i n g c a b l e s a r e i m b e d d e d 1 7 6 i n a rubber o r a p l a s t i c c o v e r i n g . The t e e t h , an i n t e g r a l p a r t of the c o v e r i n g , engage a mating sp r o c k e t and f u n c t i o n l i k e the t e e t h i n a rack. The Morse 1/5 i n p i t c h , 3/8 i n wide, "XL" t i m i n g b e l t , when used w i t h a 12 t o o t h , .764 p i t c h diameter s p r o c k e t , t r a n s m i t s .34 hp a t a maximum recommended speed of 5,000 rpm, and oc c u p i e s the same volume as a r a c k and p i n i o n assembly. When used w i t h an 18 t o o t h , 1.15 p i t c h diameter s p r o c k e t , the b e l t t r a n s m i t s .95 hp a t 10,000 rpm. A h e l i c a l l y wound wire rope t u r n i n g over a p u l l e y can be used t o c a r r y the l o a d . Because the s t r a n d s c r o s s the r o l l e r a t an angle, the diameter of the st r a n d s can be l a r g e r than the a l l o w a b l e band t h i c k n e s s . For example 40 s t r a n d s o f .007 i n diameter wire wound i n a .060 i n diameter rope can t r a n s m i t a 35 l b f o r c e . s y n c h r o n i z e the p i s t o n and c y l i n d e r w h i l e t r a n s m i t t i n g o n l y a . t e n s i o n l o a d . The t o t a l s t r e s s i n the band w i l l be the sum of the f l e x u r e s t r e s s due to bending over the r o l l e r , p l u s the t e n s i l e s t r e s s due to the l o a d . The d e r i v e d e q u a t i o n of f o r c e i s : S t e e l o r p l a s t i c bands f l e x i n g over a . r o l l e r can F=S Wt — Where t i s band t h i c k n e s s W i s band width, 177 F i s t e n s i l e l o a d , d i s r o l l e r diameter, E i s the modulus of e l a s t i c i t y , S i s y i e l d s t r e s s . The equations f o r maximum l o a d c a p a c i t y and optimum band t h i c k n e s s can be found by d i f f e r e n t i a t i n g t h i s e q u a t i o n and e q u a t i n g the r e s u l t to zero: These equations show t h a t the band can c a r r y i t s maximum loa d when the t h i c k n e s s i s such t h a t the bending s t r e s s i s equal t o h a l f of the y i e l d s t r e s s , and t h a t the b e s t band m a t e r i a l w i l l be the one w i t h the h i g h e s t s t r e n g t h - t o - s t i f f n e s s S 2 r a t i o (=—) • The m a t e r i a l s which be s t meet t h i s c r i t e r i o n i n -elude some p l a s t i c s and the metals commonly used i n s p r i n g s . The s p r i n g s t e e l s have a h i g h y i e l d s t r e s s and a h i g h modulus of e l a s t i c i t y w h i l e the p l a s t i c s have a low y i e l d s t r e s s but a l s o a low modulus. Consequently some p l a s t i c s can c a r r y more l o a d than the s t e e l s . The p l a s t i c s do have the d i s -advantage of p l a s t i c "creep", u n d e s i r a b l e aging c h a r a c t e r -i s t i c s , poor s t a b i l i t y under changing temperatures and o f t e n a l a r g e h y s t e r e s i s l o s s . t F max 178 To f i t i n t o t h e e x i s t i n g s p a c e , t h e r o l l e r d i a m e t e r was r e s t r i c t e d t o a b o u t 3/4 i n a n d t h e p o w e r b a n d w i d t h was l i m i t e d t o 1/4 i n ( t h e p o w e r b a n d was t o b e t w i c e a s w i d e a s t h e r e t u r n b a n d ) . When t h e s e l i m i t i n g d i m e n s i o n s a r e s u b -s t i t u t e d i n t o t h e a b o v e e q u a t i o n s t h e max imum f o r c e a n d o p t i m u m b a n d t h i c k n e s s i s g i v e n b y : S 2 F = .0469 £-max E t = .375 | T a b l e V l i s t s , f o r a n u m b e r o f m a t e r i a l s , t h e v a l u e s o f max imum l o a d a n d o p t i m u m b a n d t h i c k n e s s b a s e d o n t h e s e t w o e q u a t i o n s . T h e t a b l e s u g g e s t s t h a t s p r i n g s t e e l i s p r e f e r -a b l e f o r r e l i a b i l i t y a n d h i g h t h e r m a l s t a b i l i t y a n d n y l o n i s p r e f e r a b l e f o r h i g h l o a d c a r r y i n g c a p a c i t y . B e c a u s e o f i t s a v a i l a b i l i t y a s w e l l a s i t s l o a d c a p a c i t y , n y l o n was t h e f i r s t m a t e r i a l u s e d i n t h e d e s i g n e v e n t h o u g h i t s m e l t i n g t e m p e r a t u r e w a s o n l y 400 ° F . T h e n y l o n b a n d s w e r e t o b e p r e l o a d e d s o t h a t t h e y w o u l d r e m a i n i n c o n t a c t w i t h t h e r o l l e r s d u r i n g a l l l o a d c o n d i t i o n s . F o r e x a m p l e , b y p r e l o a d i n g t h e " H a b a s i t F - l " n y l o n p o w e r a n d r e t u r n b a n d s t o 3.8 l b s , t h e p o w e r b a n d l o a d i n c r e a s e d t o 16 l b s (2.8% s t r e t c h ) a n d t h e r e t u r n b a n d l o a d d e c r e a s e d t o z e r o (2.8% c o n t r a c t i o n ) w h e n 64 l b s w e r e a p p l i e d t o t h e b l a d e . Table V Capacity and Optimum Size of Bands M a t e r i a l $7 E Fmax & t Kesurics Preformed H^var 320,000 30 x l 0 6 3*0 .0^ .1 .008 Winter* mainspring steul 2. n Havtir<80% CW. t aged) 320,000 30 x l 0 6 160 .0107 .0040 Watch mainspring steel 3.1 1 Spring s t e e l e.g. SAE 1074 200,000 30 x l 0 6 62 .0067 .0025 S p e c i t l mold for 950° 3.3 Fiberglass r e i n f o r c e d epoxy ; 200,000 7.5xl0 6 350 .0100 Vibration dumper 3.27 Nylon type 8 57,000 160,000 950 .134 Melts at 400°F 3.29 Preformed sprir-2 s t e e l 200,000 3 0 x l 0 6 124 .005 Preformed to l j inch ait-. 3.3 Extremultus nylon <:8,000 78,000 490 .136 Temp -20 to 160°F 3.5 Habasit nylon 57,000 45,000 3400 Temp -4 to 300°F 3.29 Mylar 4 77°F 12,000 550,000 12 .0081 s.2e J 392°F 1,000 50,000 . 1 .007 3.2a Kupton S 77°F 14,000 430,000 28 .012 3.28 d 392°F 9,000 260,000 14 .013 High thermal s t a b i l i t y '3.28 Nylon 6/6 glass r e i n f o r c e d 30,000 1.8xl0 6 24 .017 .0063 Heat d i s t o r t i o n * 500°K 3.30 Unlike nylon which has an upper temperature l i m i t a t i o n of about 300°F, some s t e e l a l l o y s such as SAE 1074 are suitable as bands even up to 950°F, although the usual spring materials are r e l i a b l e only up to 400°F. SAE 1074 s t e e l with a y i e l d stress of 200,000 p s i requires a band thickness of .0025 i n to carry the maximum load of 250 l b s / i n width when f l e x i n g over a 3/4 i n diameter r o l l e r . The f l a t portion of the band w i l l experience a d i s t r i b u t e d stress of 100,000 p s i and the portion i n contact with the r o l l e r w i l l experience a bending stress of 100,000 p s i superimposed on the d i s t r i b u t e d stress. This i n t e r e s t i n g f a c t led to the discovery that by prebending the band to twice the diameter of the r o l l e r , the band thickness and load could be doubled 180 without exceeding the y i e l d stress because i n being s t r a i g h t -ened out the f l a t portion of the band was stressed i n one d i r e c t i o n and by being bent to conform with the r o l l e r diameter, the bent portion was stressed i n the opposite d i r e c t i o n . Because the stress alternates from compression to tension, early fatigue f a i l u r e may r e s u l t . Because the f l e x i n g action of the band resembles the stressing action of a watch mainspring,the materials used as watch springs could probably be used as bands. In t h i s regard i t i s s i g n i f i c a n t to note that not u n t i l the develop-ment of the high strength cobalt base a l l o y s such as Havar did unbreakable mainsprings become av a i l a b l e . It i s possible that Havar may prove to be the a l l o y best suited for band material not only because of i t s high strength (300,000 psi) and high temperature s t a b i l i t y (strength remains high even above 1,000°F,) but also because of i t s resistance to "set" and stress corrosion [3.11]. The bands most e a s i l y a v a i l a b l e were high strength automotive f e e l e r gauges. For a quick check as to the y i e l d s t r e s s , a .005 i n f e e l e r gauge was bent over a 3/4 i n diameter mandrel. Since the band did not deform p l a s t i c a l l y , the y i e l d stress was i n excess of 200,000 p s i and therefore suitable as a band. Before the band thickness of .004 i n was chosen, the load c a r r i e d by the band was plotted as a function of band thickness, Graph 3.12. The graph shows that the f l a t band (.004 in) can carry 150 lbs without 181 exceeding the y i e l d stress of 200,000 p s i . A higher load w i l l permanently deform the band, but not u n t i l the load reaches 480 lbs i s there danger of f a i l u r e . A .005 i n band would permanently deform with any load but the load at f a i l u r e i s higher (700 l b s ) . 0 .004 .008 .012 BAND T H I C K N E S S ( i N ) Graph 3.12 Maximum load transmitted by bands The load carrying capacity of the bands can be increased by combining several f l a t bands into a composite band. The equation governing the load c a r r i e d by the com-posit e , derived from a force analysis, i s given by: 182 F = | (Wt) + N " 2 2 v ' l+3y l+6y Where N i s number of bands, y i s the c o e f f i c i e n t of f r i c t i o n , W i s the band wid t h , -t i s the band t h i c k n e s s , S i s the y i e l d s t r e n g t h of band. I f each band i s separated by a l a y e r of l o w - f r i c t i o n m a t e r i a l such as t e f l o n or grease, the maximum load i s n e a r l y d i r e c t l y p r o p o r t i o n a l t o the number of bands because the low c o e f f i c -i e n t of f r i c t i o n allows each band to act n e a r l y independently of the other bands. But i f the f r i c t i o n i s high, the com-p o s i t e band ac t s as a s i n g l e t h i c k band and the load c a p a c i t y may even be l e s s than a s i n g l e t h i n n e r band. The r a t i o of the r a t e of heat generated by f r i c t i o n t o the maximum power i s given by: F' Q' = (4 F' + ) (£) s' y (J-1) P 6 D Where F ' i s the load on blade/maximum a l l o w a b l e load P on blade, F^ i s the band pretension/maximum load on blade, s' i s the s t r o k e / s t r o k e at maximum l o a d , t/D i s the band t h i c k n e s s / r o l l e r diameter, y i s the c o e f f i c i e n t of f r i c t i o n , J i s the number of bands. 183 When the bands are p r e s t r e s s e d so t h a t at maximum load the r e t u r n band c a r r i e s no l o a d , then: F 1 = i P 8 The amount of heat generated v a r i e s from .1% to .2% of r a t e d power. Up to now only the f o r c e s a c t i n g on the blade were considered. The question of what f o r c e s are present when the c y l i n d e r assembly mass does not equal the p i s t o n assembly mass was answered a f t e r the a c c e l e r a t i o n of the p i s t o n was equated to the a c c e l e r a t i o n s of the c y l i n d e r . This y i e l d e d the f o l l o w i n g equation f o r the f o r c e i n the band: (A ) F = — 2 - PAm 2 Where A i s the p i s t o n area, P P i s the c y l i n d e r pressure, Am i s the r a t i o of weight d i f f e r e n c e to sum of M -M p i s t o n and c y l i n d e r weights (Am = P + M c ) p c The equation showed t h a t a 3% d i f f e r e n c e i n weight between the p i s t o n and c y l i n d e r assemblies would cause a 36 l b f o r c e t o a c t i n the band when the c y l i n d e r pressure was 2,000 p s i . T h i s d i f f e r e n c e i n weight can occur as the r e s u l t of sharpening the t e e t h (shortening them by 1/4 i n ) . The r e s u l t -i n g f o r c e w i l l be c a r r i e d by the s i n g l e r e t u r n band because the p i s t o n i s l i g h t e r than the c y l i n d e r . 184 The bands can be fastened to the cylind e r by form-ing hooks on each end of the band. The minimum radius for a cold worked hook i s about 1/32 i n so the maximum force the hook can carry i s 6.7 lbs . To carry a larger force, the band can be heated and a smaller hook formed, or the hook can be clamped. Altern a t i v e s to the hook are d r i l l e d holes or welded brackets. Among the methods of adjusting band tension con-sidered, one required attaching the s t e e l band to a f l e x i b l e material such as nylon, another required adding some f l e x i b l e material on the r o l l e r s or under the hooks, and a t h i r d required adding a setscrew-adjusted l i n k on the end of the band. Because of i t s p o s i t i v e fastening and adjustment p o s s i b i l i t i e s even under high temperature operation, the adjustable l i n k was chosen. 3.3.4 Arresting Mechanism In designing a suitable device to stop and lock the piston and cylinder, i t was necessary to consider the magni-tude of the forces involved i n stopping the assemblies. For t h i s purpose the energy absorbed by the device was equated to the energy released by the spring i n expanding from the end of the stroke to the stopped p o s i t i o n . The force equation became: = 2Kx 1 +^~r_-2— n 185 Where K i s the s p r i n g r a t e , x i s the s p r i n g d e f l e c t i o n , 6 i s the displacement from BDC to p o i n t l a t c h engages, Z i s the d e f l e c t i o n of nth member, n ' F i s the l o a d on d e v i c e . The f o r c e i s s m a l l e s t when the d e v i c e l o c k s the p i s t o n a t the end of the s t r o k e (6=0). But because of impact, the magnitude of the instantaneous f o r c e i s twice the steady s t a t e magnitude. A p o s s i b l e l o c k i n g d e v i c e i s a one-way c l u t c h . I t allo w s v e r y l i t t l e motion b e f o r e l o c k i n g but i t r e q u i r e s a very l a r g e f o r c e to unlock and a mechanism t h a t w i l l - a l l o w the c l u t c h t o engage o n l y a t the end of a s e l e c t e d s t r o k e . A l a t c h o r r a t c h e t allows some movement b e f o r e the t e e t h lock, so the f o r c e i n v o l v e d i n st o p p i n g the assemblies i s h i g h e r than f o r a one-way c l u t c h . I f the energy absorbing member i s f l e x i b l e (Z >>0). the f o r c e s i n v o l v e d are not e x c e s s i v e , n i By c a l c u l a t i n g the d e f l e c t i o n o f each member i n terms of s t r e s s (assuming a con s t a n t s t r e s s - s t r a i n r e l a t i o n s h i p ) , the f o r c e e q u a t i o n becomes: F = KX + / ( K X ) 2 + 2 ( K X ) S -—-A E n n 186 Where L n i s the l e n g t h of nth member, A n i s the area of nth member, E n i s Young's modulus f o r nth member. This equation can be used when the s i z e of members i s known but the s t r e s s e s are not. For example, when a 3/16 i n diameter s t e e l r o d , 2.8 i n long stops the p i s t o n i n .10 i n (Kx=175), the rod w i l l d e f l e c t .005 i n , be loaded to 1,380 l b s , and experience a s t r e s s of 50,000 p s i . But i f the s t e e l rod r e s t s on a 3/16 i n diameter nylon rod, .25 i n l o n g , the assembly w i l l d e f l e c t .054 i n and each member w i l l be loaded t o only 990 l b s and experience a s t r e s s of 36,000 p s i . the maximum a l l o w a b l e s t r e s s e s are, then the f o l l o w i n g r e -arranged equation can be used to c a l c u l a t e the unknown dimension: For example, when used to c a l c u l a t e the l e n g t h of a nylon rod so t h a t the s t r e s s i n the 3/16 i n diameter by 2.8 i n long s t e e l rod w i l l not exceed 30,000 psi,and the s t r e s s i n the nylon rod w i l l not exceed 20,000 p s i , the equation gave the l e n g t h as 5/8 i n and the diameter as 1/4 i n . In t h i s example the rods w i l l t r a n s m i t a f o r c e of 830 l b s . When the s i z e of a l l members i s not known but a l l n - 1 2Kx In the design of the t e e t h on the l a t c h , t h e f a c t t h a t the c o e f f i c i e n t of s l i d i n g f r i c t i o n i s l e s s than the c o e f f i c i e n t of s t a t i c f r i c t i o n was used to advantage. The angles of the t e e t h were chosen so t h a t the f o r c e of f r i c -t i o n holds the l a t c h i n the locked p o s i t i o n when the l a t c h i s s t a t i o n a r y and helps to open the l a t c h when i t i s already s t a r t i n g t o open. The fo r c e of f r i c t i o n w i l l hold or r e l e a s e the l a t c h as r e q u i r e d when tangent of the tooth angle i s between the s t a t i c and s l i d i n g c o e f f i c i e n t of f r i c t i o n : y -, . • < tan 8 > y . . . s l i d i n g s t a t i c But the c o e f f i c i e n t of f r i c t i o n depends on the type and q u a n t i t y of l u b r i c a t i o n used and on the surface f i n i s h . The c o e f f i c i e n t of s t a t i c f r i c t i o n of s t e e l - o n -s t e e l i s .78 when dry and .23 when l u b r i c a t e d w i t h a l i g h t m i n e r a l o i l ; the c o e f f i c i e n t of s l i d i n g f r i c t i o n of s t e e l -o n - s t e e l i s .42 when dry and .080 when l u b r i c a t e d w i t h a ca s t o r o i l or grease [3.12]. Therefore, the toot h angle should be between 23° and 38° when the t e e t h are dry and between 4 1/2° and 13° when the t e e t h are l u b r i c a t e d w i t h o i l . Consequently,the l a t c h e s designed f o r op e r a t i o n w i t h l u b r i c a t i o n w i l l r e q u i r e a l a r g e f o r c e to open them when the te e t h are not l u b r i c a t e d , a n d l a t c h e s designed f o r oper a t i o n w i t h no l u b r i c a t i o n w i l l f l y open by themselves when the te e t h r e c e i v e l u b r i c a t i o n . 188 A f o r c e o f 10 l b s i s r e q u i r e d t o b r e a k a n o i l e d l a t c h w i t h 1 0 ° t e e t h f r e e f r o m t h e l o c k e d p o s i t i o n a n d no f o r c e i s n e c e s s a r y t o k e e p i t m o v i n g . A f o r c e o f 107 l b s i s r e q u i r e d t o b r e a k f r e e a d r y l a t c h w i t h t h e same t o o t h a n g l e a n d a 44 l b f o r c e i s n e e d e d t o k e e p i t m o v i n g . A s i t o p e n s , t h e d r y l a t c h w i l l d i s s i p a t e 2 . 2 i n - l b o f e n e r g y . T h e l a r g e f o r c e r e q u i r e d t o o p e n t h e l a t c h ( e . g . 107 l b s w h e n d r y ) c o u l d make s t a r t i n g t h e e n g i n e d i f f i c u l t . T h i s d i f f i c u l t y was a v o i d e d b y u s i n g a c o i l s p r i n g , p r e -t e n s i o n e d b y t h e m o t i o n o f t h e c y l i n d e r s , t o o p e n t h e l a t c h when t h e t r i g g e r r e l e a s e d t h e e x t e n d e d s p r i n g , F i g u r e 3 . 3 . The o p e r a t o r s t a r t s t h e e n g i n e b y p u l l i n g -a s m a l l f l a t s p r i n g o u t o f a s l o t ; o n c e i t i s n o l o n g e r l o c k e d b y t h e f l a t s p r i n g , t h e c o i l s p r i n g c o n t r a c t s , p u l l s t h e l e v e l , s l i d e s t h r o u g h a n a r c , a n d p u l l s t h e l a t c h away f r o m t h e p i s t o n r o d , t h e r e b y f r e e i n g t h e p i s t o n r o d a n d c y l i n d e r . T h e o p e r a t o r i n i t i a t e s t h e s t o p p i n g a c t i o n b y r e l e a s i n g t h e f l a t s p r i n g ; o n c e t h e f l a t s p r i n g l o c k s i n t h e s l o t , t h e m o t i o n o f t h e c y l i n d e r l a t c h a s s e m b l y e x t e n d s t h e c o i l e d s p r i n g , p u l l s t h e l e v e r t h r o u g h a n a r c , f o r c e s t h e l a t c h t o s l i d e o v e r t h e t e e t h o n t h e p i s t o n r o d , a n d e n g a g e s t h e t e e t h w h e n t h e m o t i o n r e v e r s e s . To a l l o w t h e l a t c h t e e t h t o f o l l o w t h e c o n t o u r o f t h e r o d t e e t h a n d t o i m p a r t a n i m p a c t l o a d t o t h e s l i d e r , t h e l e v e r was h i n g e d . T h e c o i l s p r i n g a t t a c h e d t o t h e h i n g e m u s t s u p p l y t h e f o r c e r e q u i r e d t o o v e r c o m e t h e l o c k i n g f o r c e a n d k e e p 189 t h e l a t c h i n c o n t a c t w i t h t h e r o d t e e t h . The f o r c e o n t h e l a t c h , t h e i n e r t i a o f t h e l a t c h - s l i d e r a s s e m b l y , a n d t h e g e o m e t r y w i l l d e t e r m i n e t h e d i s t a n c e t h e p i s t o n a n d c y l i n d e r t r a v e l f r o m t h e t i m e t h e t e e t h t o p s s e p a r a t e u n t i l t h e t e e t h f l a t s t o u c h . F o r t h e s i z e o f l a t c h u s e d , t h e d i s t a n c e (Z) d e p e n d s o n t h e s p r i n g f o r c e (F) a c c o r d i n g t o t h e e q u a t i o n : I = [ i n ] A 1 l b f o r c e w i l l c a u s e t h e t e e t h t o e n g a g e f u l l y when t h e c y l i n d e r - p i s t o n a s s e m b l y t r a v e l s a t l e a s t ' .022 i n a f t e r t h e t e e t h t o p s h a v e s e p a r a t e d . I f t h e c y l i n d e r - p i s t o n r e a c h e s b o t t o m d e a d c e n t e r b e f o r e i t h a s t r a v e l l e d . 0 2 2 i n , t h e t e e t h w i l l n o t b e f u l l y e n g a g e d . A c o i l s p r i n g w i t h a r a t e o f 6 p p i , w i l l r e l e a s e 2 . 2 i n - l b o f e n e r g y a s i t s h o r t e n s f r o m 1 i n t o 1 /2 i n , t h u s g i v i n g t h e r e q u i r e d f o r c e a n d r e l e a s i n g t h e r e q u i r e d e n e r g y . T h e c a l c u l a t e d s t r e s s e s i n t h e s l i d e r a n d p i s t o n r o d d u r i n g i m p a c t s h o w e d t h e n e c e s s i t y o f s p e c i f y i n g s t e e l a s t h e r e q u i r e d m a t e r i a l . T h e max imum s t r e s s i n t h e s l i d e r i s 3 1 , 0 0 0 p s i a n d i n t h e p i s t o n r o d i t i s 5 0 , 7 0 0 p s i . (The r o d s t r e s s i n t h e same l o c a t i o n d u r i n g f u l l l o a d i s 2 9 , 3 0 0 p s i ) . T h e t e f l o n b e a r i n g i n s i d e t h e s l i d e r m u s t b e 3 / 1 6 i n l o n g t o s a f e l y t r a n s m i t t h e 109 l b s h o c k l o a d . 190 3.3.5 C o o l i n g System In d e s i g n i n g e f f i c i e n t c o o l i n g f i n s , no mechanism i s as important as the heat exchange between a s o l i d body and a i r . The heat t r a n s f e r , a c c o r d i n g t o Mackerle [3.13], v a r i e s d i r e c t l y w i t h the t a n g e n t i a l s u r f a c e f r i c t i o n f o r c e and i n v e r s e l y w i t h the v e l o c i t y . I f the s u r f a c e f r i c t i o n f o r c e i s expressed i n terms of a i r v e l o c i t y , the heat t r a n s f e r v a r i e s d i r e c t l y w i t h the a i r v e l o c i t y when flow i s t u r b u l e n t , and w i t h the square r o o t o f the v e l o c i t y when the flow i s la m i n a r : Q = K V n _ 1 Where n =1.5 f o r laminar flow, n =2.0 f o r t u r b u l e n t flow, n = 1.73 f o r p a r t t u r b u l e n t and p a r t laminar, K i s a c o n s t a n t , V i s the mean v e l o c i t y of flow. Since the heat t r a n s f e r i s most i n t e n s e through a t u r b u l e n t boundary l a y e r , the sooner the t r a n s i t i o n from laminar t o t u r b u l e n t flow takes p l a c e , the b e t t e r the average heat t r a n s f e r per u n i t heat w i l l be. Twenty to twenty f i v e p e r c e n t o f the heat r e l e a s e d i n the c y l i n d e r i n a high-speed two-stroke engine i s removed by the c o o l i n g a i r . The purpose of c o o l i n g i s t o secure a s l i d i n g s u r f a c e f o r the p i s t o n which i s moving a t an average speed of 40 f p s . T h i s s u r f a c e i s f l u s h e d by hot gases whose 191 maximum temperature a t the onset of expansion may reach 4,000°F. The c o n d i t i o n s f o r the fo r m a t i o n of a l u b r i c a t i n g f i l m a re adverse/ so t h a t the temperature o f the w a l l s must be maintained below 400°F f o r normal o p e r a t i o n . A t e l e v a t e d temperatures l u b r i c a t i o n becomes i r r e g u l a r and the p i s t o n r i n g s s u f f e r from e x c e s s i v e wear. I t i s a common p r a c t i c e to supply power saws w i t h a r i c h f u e l - a i r mixture t o c o o l the engine i n t e r n a l l y and to p r o v i d e adequate l u b r i c a t i o n . Some of M a c k e r l e 1 s c o n c l u s i o n s from the r e s u l t s of h i s t e s t s on the heat t r a n s m i s s i o n from a i r c o o l e d engines concern the s u r f a c e c o e f f i c i e n t of heat t r a n s f e r (h) and are l i s t e d below: 1. The h e i g h t of f i n s normally used has no i n f l u e n c e on the s u r f a c e heat t r a n s f e r c o e f f i c i e n t . 2. The f i n t h i c k n e s s has no s i g n i f i c a n t i n f l u e n c e . 3. The f i n s p a c i n g (Z) i n f l u e n c e s the c o e f f i c i e n t , a c c o r d i n g t o the r e l a t i o n : h a Z but the c o e f f i c i e n t d e t e r i o r a t e s c o n s i d e r a b l y a t spacings below .060 i n . 4. The a i r v e l o c i t y (V) i n f l u e n c e s the c o e f f i c i e n t a c c o r d i n g t o the approximate r e l a t i o n : V, w 7 3 h a V 5. A matte s u r f a c e has d e f i n i t e advantages over a g l o s s y one whereas a punch marked s u r f a c e (.020 i n deep, 192 . 0 7 0 i n a p a r t ) h a s n o a d v a n t a g e o v e r a n u n p u n c h e d o n e . A l t h o u g h t h e s u r f a c e q u a l i t y i n f l u e n c e s t h e c o e f f i c i e n t , i t i s n o t t r u e t h a t h e a t i s a l w a y s b e t t e r t r a n s m i t t e d b y a r o u g h l y c a s t s u r f a c e t h a n b y a m a c h i n e d o n e . I n t h e c a s e o f l a r g e p r o -j e c t i o n s o n t h e s u r f a c e , i n c r e a s e d r e s i s t a n c e t o a i r f l o w i s n o t c a u s e d b y s u r f a c e f r i c t i o n b u t b y p r e s s u r e h e a d d i f f e r e n c e s . T h i s t y p e o f r e s i s t a n c e i m p e d e s h e a t t r a n s f e r . 6 . T h e c y l i n d e r d i a m e t e r i n f l u e n c e s t h e c o e f f i c i e n t b e c a u s e t h e r a t i o o f s u r f a c e a r e a s e x p o s e d t o l a m i n a r a n d t u r b u l e n t f l o w v a r i e s w i t h t h e d i a m e t e r . 7 . T h e a i r s t r e a m d i r e c t i o n i n f l u e n c e s t h e c o e f f i c i e n t b e c a u s e i f t h e a i r f l o w b e t w e e n t h e f i n s i s d i s -r u p t e d a n d i n t e n s i v e t u r b u l e n c e i n t h e f i n i n t e r -s t i c e r e s u l t s , h e a t t r a n s f e r i s c o n s i d e r a b l y a u g m e n t e d . 8 . R a p i d v i b r a t i o n o f f i n s h a s l i t t l e i n f l u e n c e o n t h e c o e f f i c i e n t . T h e e x t e n t t o w h i c h M a c k e r l e ' s o b s e r v a t i o n s o n s t e a d y a i r f l o w s o v e r s t a t i o n a r y c y l i n d e r s a l s o a p p l y t o r e c i p r o c a t i n g c y l i n d e r s m o v i n g i n s t a t i o n a r y a i r i s y e t t o b e d e t e r m i n e d . E v e n t h o u g h t h e t h e o r e t i c a l l y i d e a l f i n h a s s i d e s i n a p a r a b o l i c s h a p e t e r m i n a t i n g i n a s h a r p e d g e , t h e b e s t p r a c t i c a l c o m p r o m i s e , a c c o r d i n g t o J u d g e [ 3 . 1 4 ] i s a t r u n -c a t e d c o n i c a l f i n w i t h r o u n d e d e d g e s . I n p r a c t i c e , t h e f i n 193 t h i c k n e s s i s chosen as s m a l l as p r o d u c t i o n processes permit. There should be as many f i n s as p o s s i b l e but the i n t e r s t i c e s must be l a r g e enough t o ensure a s a t i s f a c t o r y flow of c o o l -i n g a i r . For s m a l l a i r v e l o c i t i e s Mackerle recommends a s p a c i n g of .31 to .47 i n f o r a f r e e l y exposed c y l i n d e r having no c o w l i n g . I f a s t r o n g e r a i r flow i s a v a i l a b l e f o r c o o l i n g , f i n s are more d e n s e l y spaced. But i f the i n t e r s t i c e s are s m a l l e r than twice the laminar boundary l a y e r t h i c k n e s s , a r a p i d d e t e r i o r a t i o n of flow c o n d i t i o n s and f i n e f f i c i e n c i e s o c c u r s . At an a i r speed of 127 f p s , Mackerle found t h a t e f f i c i e n c y drops o f f r a p i d l y a t i n t e r s t i c e s below .10 i n . T h e -simplest method of c o o l i n g the c y l i n d e r uses the i n h e r e n t r e c i p r o c a t i n g motion of the c y l i n d e r . A l i t e r -a t u r e search r e v e a l e d v e r y l i t t l e v a l u a b l e i n f o r m a t i o n on t h i s type of heat t r a n s f e r . In a survey a r t i c l e on the e f f e c t s of v i b r a t i o n and sound on heat t r a n s f e r , R i c h a r d s o n [3.15] surmised t h a t under some circumstances ^ heat t r a n s f e r by o s c i l l a t i o n s would exceed t h a t by f o r c e d c o n v e c t i o n when compared on a mean v e l o c i t y b a s i s . But the r e q u i r e d a m p l i -tudes of o s c i l l a t i o n s are so l a r g e t h a t they may not be o b t a i n e d i n p r a c t i c e and on a c o s t and weight b a s i s , f o r c e d c o n v e c t i o n i s an o u t r i g h t winner. To gener'ate enough in f o r m a t i o n , f o r a v a l i d e v a l u -a t i o n of t h i s type of heat t r a n s f e r and t o determine the amount of heat t r a n s f e r r e d from a r e c i p r o c a t i n g c y l i n d e r head, an experiment was set up and tests were performed. The apparatus consisted of a heater element, thermocouples, standard and sp e c i a l c y l i n d e r heads, and a mechanism to reciprocate the head at varying speeds and through several amplitudes. Photographs of the t e s t apparatus are shown on Figure 3.2 and the data i s given i n Appendix VI. Calculations for the heat transfer c o e f f i c i e n t (h) were based on the measured values of the power supplied to the heater, the f i n temperature, the a i r temperature, and the f i n area. The data i s plotted on Graph 3.13. Of a l l the co-ordinates t r i e d , the ones used on the graph (Nusselt number (Nu) versus the product of the Reynolds number (Re) and the square root of the f i n height-to-stroke r a t i o (£/s)),best correlated a l l the available data. The equation obtained from the p l o t i s given by: ,,.986 Nu = 10.8 + .0862 Where Nu Re hi K Ns£ K = conductivity of a i r , v = kinematic v i s c o s i t y of cooling a i r . The graph was then used to calc u l a t e the expected temperature of the designed c y l i n d e r . For an ambient temperature 70°F, (frequency (N)=6,000 cpm, stroke (s)=.75 i n , f i n height (£)= 195 •Figure 3.2 Photograph of heat transfer test apparatus: (A) Model 210 head with heating element and spacer, (B) Model 275 head, (C) 275 head and block with heating element (D) 210 head assembled on scotch yolk, (E) test set-up (F) special cylinder head and mating station-ary fins assembled on scotch yolk 196 2 1.30 i n , f i n area 100 i n ) the f i n temperature may go up t o 430°F. This means t h a t the f i n temperature i n the f r e e -p i s t o n engine w i l l be approximately the same as i n the con-v e n t i o n a l power saw. Graph 3.13 Heat t r a n s f e r data f o r r e c i p r o c a t i n g c y l i n d e r 197 3.3.6 Combustion System The need f o r a l i g h t w e i g h t c y l i n d e r assembly to keep o v e r a l l weight low and ope r a t i n g speed h i g h , l i m i t e d the choice of the c y l i n d e r and f i n m a t e r i a l to the aluminum a l l o y s shown on Table VI. The f i n a l choice was Mean 135 as i t was a v a i l a b l e l o c a l l y and gives s a t i s f a c t o r y s e r v i c e i n c o n v e n t i o n a l power saws. Table VI M a t e r i a l s S u i t a b l e f o r C y l i n d e r Heads and Blocks Alcan 135 Alcan 225 ivlcan 250 «lcan 385 Aican 125 Alcur. <13 ASTH SU70JI ASTi-1 C4A iiSTM CG100A ASTM 4032 ASTM SC5L, AaTK C.V.... Form Sand & P.Mold Sand Sand & P.Hold Forced Sand 4 P.fioi.^ Heat treatment T5 T6 T6 T5B T5C T6 T6 T5 T6 T t l T571 —3 T e n s i l e strength (xlO ) 26 35 39 25 37 36 23 29 —3 Compressive strength (xlO ) 22 22 £5 40 24 13 ii. X l e l d strength ( x l 0 ~ 3 ) 19 27 28 20 35 30 23 18 >0 Hardness ( B r i n e l l ) 60 70 80 75 115 110 65 70 85 —3 Shear strength <xtO ) 18 27 30 i l 30 29 22 ^1 .6 Fatique l i m i t U:o"3) 7.5 8 6.5 9.5 8.5 8 8 i l l i e l d a t 400°F ( x l O - 3 ) 10.5 9.5 16.5 10.0 1<:.C ..1 Keference (3.18, 3.19) (3.18, 3.19) (3.18, 3.19) (3.18, 3.19) (3.18, 3.19) U.17, (3.19) Uses c y l i n d e r heat r e c i p r o c a t i n g c y l i n d e r head pistons cylinder head r.euvy juty and bio cit, parts i n en- pi s t o n , bush- timing gear3 axles, wheels gines, cranjc case ings j/ l i r . - e r neiidj Because the r i n g s r e q u i r e a s p e c i a l s l i d i n g s u r f a c e , the c y l i n d e r bore had t o be anodized, chrome p l a t e d , metal sprayed or l i n e d w i t h a c a s t i r o n sleeve. To minimize 198 w e i g h t a n d m a x i m i z e r e l i a b i l i t y , c h r o m e p l a t i n g t o a d e p t h o f . 0 0 1 i n was o r i g i n a l l y s p e c i f i e d b u t w h e n , d u r i n g f a b r i c a t i o n , a m a c h i n i n g e r r o r d e s t r o y e d t h e s u r f a c e t o b e p l a t e d , a . 0 4 0 i n w a l l c a s t i r o n s l e e v e was s p e c i f i e d . F o r a r o o m t e m p e r a t u r e i n t e r f e r e n c e f i t o f . 0 0 3 i n o n t h e o u t -s i d e d i a m e t e r ( s p e c i f i e d t o p r e v e n t t h e l i n e r a n d c y l i n d e r b l o c k f r o m s e p a r a t i n g e v e n when t h e c y l i n d e r t e m p e r a t u r e r e a c h e s 5 0 0 ° F ) t h e c o n t a c t p r e s s u r e i s 1 , 1 5 0 p s i a n d t h e l i n e r b o r e i s . 0 0 1 7 i n s m a l l e r . To a l l o w f o r t h e r e m o v a l o f . 0 0 1 0 - . 0 0 1 5 i n t h i c k m a t e r i a l i n t h e f i n a l h o n i n g p r o c e s s , t h e m a c h i n e d b o r e d i a m e t e r w a s s p e c i f i e d . 0 0 1 i n u n d e r s i z e . To e s t i m a t e t h e max imum s t r e s s i n t h e c y l i n d e r w a l l s , t h e c y l i n d e r h e a d was a s s u m e d t o a c t a s a f l a t c i r c u l a r p l a t e , s u b j e c t e d t o a u n i f o r m 2 , 0 0 0 p s i p r e s s u r e a n d s i m p l y s u p p o r t e d a r o u n d t h e e d g e . T h e c a l c u l a t e d s t r e s s , n e g l e c t i n g t h e s t i f f e n i n g e f f e c t o f t h e f i n s a n d w a l l s , was 1 2 , 0 0 0 p s i . The s h e a r s t r e s s a r o u n d t h e c y l i n d e r h e a d was 2 , 5 0 0 p s i a n d t h e t e n s i l e s t r e s s i n t h e w a l l s w a s 5 , 0 0 0 p s i . T h e t e n s i l e s t r e s s w a s h i g h e r a t p o i n t s o f s t r e s s c o n c e n -t r a t i o n , a n d b e c a u s e t h e a c c e l e r a t e d m a s s d e c r e a s e d , t h e s t r e s s was l o w e r f a r t h e r away f r o m t h e h e a d . T h e s t r e s s d u e t o t h e l o a d o n t h e b l a d e (140 l b s ) w a s 560 p s i a n d d u e t o t h e s p r i n g l o a d i t w a s 800 p s i . To a c h i e v e a v e r y h i g h c o m p r e s s i o n r a t i o b e f o r e t h e p i s t o n r e a c h e s t h e t o p m e c h a n i c a l l i m i t , t h e c o m b u s t i o n c h a m b e r a n d p i s t o n f a c e m u s t r e m a i n f l a t . I n a n a t t e m p t t o determine how adversely t h i s requirement would a f f e c t the heat t r a n s m i s s i o n , the product of the exposed area and the c a l c u l a t e d temperature d i f f e r e n c e between the w a l l and the gas was p l o t t e d as a f u n c t i o n of time f o r a conventional power saw w i t h a c o n i c a l combustion chamber and a f r e e -p i s t o n saw w i t h a f l a t combustion chamber. Although com-b u s t i o n was assumed to occur i n s t a n t a n e o u s l y at a compression r a t i o of 7.4 i n both engines, the maximum compression r a t i o i n the f r e e - p i s t o n engine i s a f u n c t i o n of l o a d . Temperatures were taken from Taylor's [3.1] graphs of thermodynamic prop-e r t i e s of g a s o l i n e - a i r mixtures or products of combustion at r e a l i s t i c a i r - f u e l r a t i o s and p r o p o r t i o n s of unburned f u e l . The r e s u l t , p l o t t e d on Graph 3.14, i n d i c a t e s t h a t because of higher p i s t o n speeds i n the f r e e - p i s t o n engine, l e s s heat t r a n s f e r w i l l take place i n the f r e e - p i s t o n engine as the compression r a t i o goes up. For example, i f the heat t r a n s f e r c o e f f i c i e n t remains constant, then at a compression r a t i o of 7.4 the heat t r a n s m i s s i o n from the f r e e - p i s t o n engine w i l l be about the same as from the con v e n t i o n a l engine, but at a compression r a t i o of 22.4 the t r a n s m i s s i o n i n the f r e e - p i s t o n engine w i l l be halved because the power stroke w i l l be completed i n much l e s s time. So at p a r t l o a d , the heat t r a n s f e r from the f r e e - p i s t o n engine should be c o n s i d e r -a b l y l e s s than from the conventional engine. 20.0 TIME AFTER IGNITION ( M I L L I S E C . ) Graph 3.14 C a l c u l a t e d thermal l o s s e s from the combustion chambers Tests performed by the author [3.16] on the conven-t i o n a l engine y i e l d e d the f o l l o w i n g observations when the c o n i c a l combustion chamber was rep l a c e d w i t h a f l a t one: 1. power went down 5-12%, 2. exhaust temperature dropped, 201 3 . c y l i n d e r h e a d t e m p e r a t u r e w e n t u p ( l e d t o d e t o n a t i o n a t h i g h s p e e d s ) , 4 . s c a v e n g i n g e f f i c i e n c y w e n t d o w n . F r o m t h e r e s u l t s i t w a s c o n c l u d e d t h a t o n s t a n d a r d e n g i n e s t h e h e a t t r a n s m i s s i o n f r o m a f l a t h e a d i s h i g h e r t h a n f r o m a c o n i c a l h e a d . S i n c e t h e p i s t o n a s s e m b l y was t o w e i g h t h e same a s t h e c y l i n d e r a s s e m b l y ( s o t h a t t h e p i s t o n s t r o k e w o u l d e q u a l t h e c y l i n d e r s t r o k e ) , t h e c h o i c e o f a m a t e r i a l f o r t h e p i s t o n was l i m i t e d t o h e a v y m e t a l s s u c h a s n o d u l a r c a s t i r o n (ASTM 1 0 0 - 7 5 - 0 4 ) , m a l l e a b l e c a s t i r o n (ASTM 8 0 - 0 0 2 ) , n i t r i d i n g s t e e l s ( c l a s s N) o r h i g h s t r e n g t h a l l o y s t e e l s . T h e c h a r a c t e r i s t i c s o f t h e s e m e t a l s a r e d e s c r i b e d o n T a b l e V I I . When t h e d e c i s i o n w a s made t o f a b r i c a t e t h e p i s t o n a n d r o d i n o n e p i e c e , t h e s t r e n g t h r e q u i r e m e n t o f t h e r o d l i m i t e d t h e c h o i c e o f m e t a l s t o h i g h s t r e n g t h a l l o y s . T h e f i n a l c h o i c e was A I S I 6 1 5 0 , a t o u g h m a t e r i a l c o m m o n l y u s e d f o r s h a f t s , g e a r s , l i n e r s a n d p i s t o n s . I n e x i s t i n g f r e e p i s t o n e n g i n e s t h e e x t r e m e l y h i g h a c c e l e r a t i o n s a n d r a p i d p r e s s u r e c h a n g e s n e a r t o p d e a d p o i n t l e a d s t o i n s u f f i c i e n t g a s p r e s s u r e u n d e r t h e r i n g s . T h i s r e s u l t s i n e r r a t i c " f l u t t e r " a n d e v e n t u a l b r e a k a g e o f t h e r i n g s [ 3 . 2 1 ] . H i g h t h e r m a l l o a d i n g a n d m a r g i n a l l u b r i -c a t i o n a l s o s h o r t e n r i n g l i f e . T h e F o r d M o t o r C o m p a n y 202 Table V I I M a t e r i a l s S u i t a b l e f o r P i s t o n s C^st. n l . ,-.lcn 14* Foiled ..1. ..dTn i u 3 t-Toi Heriii. 1-IOJ.G ..lean 162 Diecast ftlcan I O U A .oTri ai«.«,B i'JOOUiar 100-75-04 .•iaile-ble C . i . dOOOi hi tricing N . l i d t i i O TensiLe -.U:i:ngth (xio* 3) ( U ) - 3 5 35 100-1^0 100 190 3 1 5 - - 8 s t r e n 6 t i i (x10~ ) - 200-240 197-290 lifeld strength <xl0~3) HarullC:S3 (lirir.ell) 8 .=. 500°F 5.5 <i 500°F 95 16 75-90 200-^40 80 24I-269 180 U5 «.70-108 6 C i - i v l 149 Density ( l b / i n 3 ) .098 096 .257 .265 . 2 8 3 Uses heavy uuty pistons & a i r cooled cylinder heads pistons pistons & cylinders pistons con rods cylinders gears, pistons gears, diesel pistons cylinder liners, bushings gears shaf t i , r i j tv 1!' J > liners »::..!'t», b ' - i : _ i : . b ! i References 3.17 3.19 3.18 3.18 3.19 3-19 3.19 [3.22] overcame t h i s problem of r i n g f r a c t u r e and burning by reducing the pressure ( o r i g i n a l l y 4,000 p s i ) , changing f u e l i n j e c t i o n t i m i n g , employing porous-chrome p l a t e d c y l i n d e r bores, and using s t e e l i n s t e a d of c a s t i r o n r i n g s . Rings can be made of ca s t i r o n , s t e e l a l l o y s and compounded forms of TFE fl u o r o c a r b o n . Cast i r o n r i n g s , used e x t e n s i v e l y i n conv e n t i o n a l p i s t o n engines, are inexpensive and i f p r o p e r l y l u b r i c a t e d , g i v e long t r o u b l e - f r e e s e r v i c e . In the manufacturing process the r i n g can be covered w i t h an o i l a b s o r p t i v e c o a t i n g t h a t f a c i l i t a t e s r a p i d s e a t i n g and 203 r e t a r d s s c o r i n g a n d s c u f f i n g . A l t e r n a t e l y , t h e c y l i n d e r c a n be p l a t e d w i t h t i n o r c a d m i u m t o i n d u c e s e a t i n g a n d r e t a r d s c o r i n g a n d s c u f f i n g . F o r a d d e d p r o t e c t i o n a g a i n s t a b r a s i o n , t h e r i n g f a c e s c a n b e p l a t e d w i t h c h r o m i u m a n d f o r p r o -t e c t i o n a g a i n s t s c u f f i n g t h e y c a n b e s p r a y e d w i t h m o l y b d e n u m R i n g s made o f a T F E f l u o r o c a r b o n ( t e f l o n ) c o m p o u n d e d w i t h s p e c i a l w e a r r e s i s t a n t m a t e r i a l s f o r l o n g l i f e , a r e e x p e n s i v e , h a v e a l o w c o e f f i c i e n t o f f r i c t i o n ( 0 . 4 d r y ) a n d r e q u i r e n o l u b r i c a t i o n . B e c a u s e i t c o n f o r m s t o t h e e c c e n -t r i c i t i e s o f t h e b o r e a n d i s f o r c e d a g a i n s t i t b y a m e t a l e x p a n d e r , t e f l o n m a k e s a g o o d s e a l u p t o 5 0 0 ° F a n d r e d u c e s g a s l e a k a g e t o a n e g l i g i b l e a m o u n t . I f t h e r i n g c a n b e made w i t h o u t a g a p ( n e c e s s a r y i n c a s t i r o n r i n g s t o a l l o w f o r t h e r m a l e x p a n s i o n ) , t h e n t h e c o n t i n u o u s s e a l w i l l r e d u c e b l o w b y . T h i s w i l l r e d u c e t h e d i s c h a r g e o f p o l l u t a n t s i n t o t h e a i r a n d i n c r e a s e t h e c o m p r e s s i o n r a t i o b e f o r e m e t a l - t o -m e t a l c o n t a c t o c c u r s . A n u m b e r o f 100 h o u r t e s t s a t 1 , 8 0 0 t o 4 , 2 0 0 r p m p e r f o r m e d a t t h e Du P o n t L a b o r a t o r y [ 3 . 2 3 ] s h o w e d t h a t t e f l o n r i n g s i n g a s o l i n e e n g i n e s w e r e p r a c t i c a l . S e a l i n g w i t h c a s t i r o n r i n g s c a n b e i m p r o v e d b y m a k i n g t h e h e a d l a n d ( t h e a r e a b e t w e e n t h e p i s t o n h e a d a n d t h e c o n v e n t i o n a l t o p r i n g ) , p a r t o f t h e t o p p i s t o n r i n g . W i t h t h i s c h a n g e t h e S e a l e d P o w e r C o r p o r a t i o n [ 3 . 2 4 ] c l a i m s t o h a v e d e c r e a s e d b l o w b y b y 50%. E x t e n d i n g t h e r i n g u p t o t h e p i s t o n h e a d s e a l s t h e a n n u l u s b e t w e e n t h e p i s t o n a n d c y l i n d e r w a l l . A l t h o u g h t h e L - s h a p e p e r m i t s t h e c o m p r e s s i o n -204 gas p r e s s u r e t o e f f e c t a b e t t e r s e a l , the l a r g e r area over which the pr e s s u r e a c t s i n c r e a s e s the f r i c t i o n f o r c e , and the d i r e c t c o n t a c t w i t h h i g h temperature gases r a i s e s the r i n g temperature. The gas pr e s s u r e under the r i n g and the i n t e r n a l p r e - t e n s i o n combine t o e f f e c t a good s e a l i n the c o n v e n t i o n a l d e s i g n . To keep the r i n g temperature low so t h a t s e t does not remove the p r e t e n s i o n , the c o n v e n t i o n a l r i n g i s p l a c e d some d i s t a n c e away from the hot gas and to get an equal p r e s s u r e drop a c r o s s each r i n g , the l a n d diameter i s made s m a l l e r than the s k i r t diameter. These c o n v e n t i o n a l p r a c t i c e s were f o l l o w e d i n d e s i g n i n g the f r e e - p i s t o n power saw. For s a t i s f a c t o r y combustion t o oc c u r , the a i r - f u e l charge must be w e l l mixed, i n the c o r r e c t r a t i o (14.6 f o r a s t o i c h i o m e t r i c c h a r g e ) , and brought up t o i g n i t i o n temper-a t u r e by a flame, a spark, a hot spot, or a hig h compression p r e s s u r e . A l e a n mixture r e q u i r e s a h i g h e r i g n i t i o n temper-a t u r e . When the i n t a k e i s t h r o t t l e d , the a i r - f u e l charge e n t e r i n g the c y l i n d e r mixes w i t h the r e s i d u a l exhaust gases and i s d i l u t e d . F or r a p i d and complete combustion, the charge e n t e r i n g must be r i c h o r the i g n i t i o n energy must be hi g h . In the c o n v e n t i o n a l engine the o v e r a l l mixture i s e n r i c h e d , i n the s t r a t i f i e d charge engine the p o r t i o n of the charge i n the v i c i n i t y o f the spark p l u g i s e n r i c h e d [3.25], and i n the f r e e - p i s t o n engine the compression r a t i o i s a u t o m a t i c a l l y i n c r e a s e d . 205 The c a r b u r e t o r s p e c i f i e d was a c o n v e n t i o n a l diaphragm type w i t h a 3/8 i n diameter v e n t u r i . The c a r b u r e t o r r e c e i v e s i t s p r e s s u r e p u l s e s from the scavenging chamber through a tube i n the mount,and i t s f u e l from the tank i n the handle-through a tube i n the frame. To l i m i t the magnitude of the p u l s e s d u r i n g p a r t - l o a d o p e r a t i o n , the h o l e opening t o the chamber was l o c a t e d so t h a t i t would be c l o s e d by the c y l i n d e r cap when the s t r o k e i n c r e a s e d to about 3/4 i n . C o n s i d e r a t i o n was g i v e n to d e s i g n i n g a s p e c i a l c a r b u r e t o r f i t t i n g i n s i d e the engine. In t h i s c a r b u r e t o r a f l u i d i c d e v i c e c o u l d meter the f u e l [3.26]. But f o r r e l i a b i l i t y d u r i n g the i n i t i a l t e s t s a standard c a r b u r e t o r was thought to be b e s t . The f e l t pick-up i n the tank draws f u e l i n t o the l i n e s from where i t i s pumped i n t o the c a r b u r e t o r by the diaphragm. An i n s u l a t o r b l o c k p l a c e d between the c a r b u r e t o r and frame reduces heat t r a n s f e r to c a r b u r e t o r and r e t a r d s the v a p o u r - l o c k . An a i r f i l t e r made of wire s c r e e n covered w i t h a rayon f l o c k i n g r e s t r i c t s the entrance of d i r t and f o r e i g n m a t e r i a l ; a i r e n t e r i n g the f i l t e r cap must flow h o r i z o n t a l l y , so m a t e r i a l cannot f a l l onto the f i l t e r . A lthough designed f o r an AISI 1010/1015 s t e e l sheet, the m u f f l e r was made o f aluminum, to f a c i l i t a t e machining i n the shop. The r e c i p r o c a t i n g motion moves c o o l i n g a i r over the exposed p a r t s and prevents twigs and l e a v e s from s e t t l i n g on the hot s u r f a c e . As a purpose of the m u f f l e r i s to break up the l a r g e carbon p a r t i c l e s , the m u f f l e r was c o n s t r u c t e d so that the escape ou t l e t was at r i g h t angles to the exhaust port opening. Carbon sparks impinge d i r e c t l y against the side and top wall of the muffler and then work through the perforations i n the screen to the second chamber where they again impinge on the wall of the muffler before working through the second group of perforations. These impinge-ments break the carbon p a r t i c l e s into sizes that w i l l not s t a r t a f i r e . T h i r t y - s i x holes (3/32 i n diameter) gave a 2 per f o r a t i o n area of .25 i n . This completed the design of the important com-ponents. I t was of course necessary to design the small elements but t h e i r delineation was straight-forward and w i l l not be described. Figure 3.3 shows the f i n a l assembly layout. 3.4 F a b r i c a t i o n of Parts In the development of a new concept as complex as a two-stroke engine, modifications are not limi t e d to the t h e o r e t i c a l design stages. Even during the f a b r i c a t i o n process many v a l i d modifications suggest themselves, some to be incorporated immediately and others to be incorporated i n future models. The modifications can be grouped as follows: R - re v i s i o n s that simplify f a b r i c a t i o n or improve performance, C - corrections to design or drawings, T - temporary changes to make revised parts f i t e x i s t i n g components, to accept machining and 208 c a s t i n g e r r o r s , and to a l l o w f o r the in s t r u m e n t a t i o n of the u n i t . 1. (T) To g i v e the r i n g s a good bearing surface w h i l e keep-in g the weight low, the i n i t i a l design s p e c i f i e d chrome p l a t i n g on the c y l i n d e r bore. When an under-cut was a c c i d e n t a l l y made i n the bore so t h a t p l a t i n g was no longer p o s s i b l e , the c y l i n d e r was modified to accept a c a s t i r o n s l e e v e . 2. (T) The d i s t a n c e s from the tops of the exhaust holes to the tops of the t r a n s f e r holes (blowdown) were machined .050 and .085 i n i n s t e a d of .100 i n . Be-cause the t r a n s f e r p o r t s opened too soon, the- exhaust gases flowed i n t o the scavenging volume and prevented e f f i c i e n t scavenging. To c o r r e c t t h i s machining e r r o r , the low t r a n s f e r p o r t heights and the exhaust p o r t s were r a i s e d .080 t o giv e a .100 blowdown. The machining o p e r a t i o n i s shown on F i g u r e 3.4. 3. (T) Because the p i s t o n s k i r t was the same width as the exhaust p o r t width, a small misalignment i n the angular l o c a t i o n of the s k i r t r e s u l t e d i n a hole between the scavenging chamber and m u f f l e r . P l a s t i c s t e e l was used to f i l l the h o l e . 4. (T) Because they allowed the i n s p e c t i o n of the t r a n s f e r p o r t s , temporary removable p l a t e s were s u b s t i t u t e d f o r expansion plugs i n the t r a n s f e r p o r t h o l e s . In the process of d r i l l i n g the t r a n s f e r holes the d r i l l came through the m a t e r i a l so the area was b u i l t up w i t h weld m a t e r i a l . A comparison of the wooden p a t t e r n w i t h the drawing revealed an e r r o r i n the p a t t e r n . F i g u r e 3.4 Photograph of t r a n s f e r p o r t machining o p e r a t i o n (C) When the mount was lengthened by .050 i n during a design change,the corresponding rod l e n g t h was i n a d v e r t e n t l y l e f t unchanged. This e r r o r r e q u i r e d machining clearance s l o t s f o r the blade. (T) Because proper surface g r i n d i n g f a c i l i t i e s f o r c o r r e c t i n g heat treatment d i s t o r t i o n were not a v a i l -a b l e , the p i s t o n rod was accepted unhardened ( y i e l d s t r e s s 100,000 p s i i n s t e a d of 200,000 p s i when hardened t o Rc 40). The blade s l o t was machined 210 .132-.140 i n wide i n s t e a d of the s p e c i f i e d .125 i n , the screw l o c a t i o n was o f f by about .020 i n , and the blade s p i g o t was .120 i n diameter and tapered i n s t e a d of .125 i n and p a r a l l e l to the blade. Con-sequently, the saw blade was not p a r a l l e l t o the p i s t o n rod (varied 1/2° to 3°). The blade was made from an e x i s t i n g saw blade and screwed t o a l a r g e backing p l a t e (made l a r g e to balance the weight of the c y l i n d e r ) . 7. (R) The o r i g i n a l design f o r a t t a c h i n g the band t o the p i s t o n rod c a l l e d f o r a m i l l e d s l o t on the rod. An i n s p e c t i o n of the completed rod revealed t h a t the s l o t s had not been machined per p e n d i c u l a r to the r o d , the i n s i d e edge of the s l o t had been machined convex and i r r e g u l a r , and the s l o t s were not cut d i r e c t l y opposite each other as s p e c i f i e d on the drawing. An attempt was made t o manually square the s l o t s but an i n s t a l l e d band f a i l e d a f t e r a few c y c l e s . To r e c t i f y the problem a new s l o t was m i l l e d across the rod but again the edge was not smooth, p e r p e n d i c u l a r nor round. Even an undercut d i d not prevent another band from f a i l i n g . For the next attempt, spot faces f o r dowels were end-milled at the center of the s l o t . Even though the drawings had s p e c i f i e d c l o s e t o l e r -ances f o r the important surfaces t o prevent the previous problem from r e - o c c u r i n g , when completed, one spot 211 face was machined i n a c c u r a t e l y . The l o c a t i o n was o f f by .014 i n , the diameter of the same spot face was l a r g e r by about .005 i n and the edge of the spotface was 1° from the p e r p e n d i c u l a r . To salvage the p i s t o n , the diameter of the of f e n d i n g spot-face was enlarged to take a shim. With t h i s m o d i f i -c a t i o n , the attachment as shown on Figu r e 3.5, per-formed s a t i s f a c t o r i l y but the p i s t o n rod had a number of sharp edges and t h i n s e c t i o n s , s o i t f a i l e d when d r i v e n by a fixed-throw c r a n k s h a f t . 8. (R) Although the ends of the f i r s t bands were bent i n t o hooks which clamped over the attachment p l a t e , most of the load was t o be c a r r i e d by f r i c t i o n when the band was squeezed between the attachment p l a t e and the c y l i n d e r . The r i v e t s l o c a t i n g the bands were repl a c e d w i t h screws t o a l l o w d i s m a n t l i n g and t o incr e a s e clearance under the attachment p l a t e . 9. (R) When the nylon band was repl a c e d w i t h a s t e e l band, the r o l l e r diameter was increased t o g i v e a sm a l l clearance between the p i s t o n rod and r o l l e r (to stop a p i s t o n from t w i s t i n g ) and to keep band t e n s i o n constant throughout the s t r o k e . 10. (T) When the f i r s t s p r ings were tested,the s p r i n g r a t e s , i n s t e a d of being 175 p p i as s p e c i f i e d , were only 147 to 150 p p i and o v e r s i z e . When the spr i n g s were ground down to the s p e c i f i e d s i z e , the r a t e had 212 Figure 3.5 Photographs o f the synchronizing and a r r e s t i n g mechanism assemblies 213 decreased to 140 ppi. Consequently two back-up springs were designed to f i t inside the o r i g i n a l ones and a new set of springs were ordered. The sharp edges of the spring ends were rounded so that the bands would not be cut and the flow path would be smoother. The f i n a l t e s t engine used a double spring under the piston (K=158 and K=32 ppi) and a single spring i n the cylinder (K=190 p p i ) . 11. (R) The new arresting mechanism, devised when the rack and pinion arrangement was replaced by the band and r o l l e r arrangement a f t e r the cover had already been cast, required a new t r i g g e r assembly which pushed instead of pulled,and some minor modifications to the e x i s t i n g cover so the mechanism would f i t . 12. (T) Not u n t i l the arresting mechanism had been assembled and t r i e d out was i t established that the lever arms to the s l i d e r were .100 i n shorter than the drawing c a l l e d f o r , so new ones were made. When i t became obvious that the t e f l o n tape could not be bonded to the s l i d e r with the available epoxy, a bronze bushing was brazed into the s l i d e r . The springs which pulled the s l i d e r were doubled one inside the other to conserve space. A guide for the levers was added so that the l a t c h remained p a r a l l e l to the piston rod while the engine was running. 214 13. (T) Because the cover as r e c e i v e d from the foundry d i d not have s u f f i c i e n t m a t e r i a l on the bar f o r the mount, the r e q u i r e d m a t e r i a l was added by welding and a hole was d r i l l e d through t h i s welded m a t e r i a l t o connect the f u e l l i n e w i t h the c a r b u r e t o r . A f t e r the f a b r i c a t i o n and m o d i f i c a t i o n s had been completed, the p a r t s were assembled i n t o the complete f r e e -p i s t o n power saw. Figures 3.6 and 3.7 show the f i n i s h e d p a r t s and t h e i r r e l a t i o n s h i p s t o each other. The completed saw was instrumented and put on a t e s t bench f o r concept e v a l u a t i o n , as described i n the next chapter. F i g u r e 3.6 Photograph of a l l FPS p a r t s 215 Figure 3.7 Photographs of FPS components 216 4. EVALUATION 4.1 Performance C h a r a c t e r i s t i c s of the F r e e - P i s t o n Power Saw While the engine was being f a b r i c a t e d and the t e s t s were being performed, the computer program was being r e f i n e d to a l l o w more accurate r e p r e s e n t a t i o n of engine thermodynamics and to permit more c o n d i t i o n s to be i n v e s t i g a t e d . The r e f i n e -ments l e d t o the fol3owing assumptions: 1. The pressure i n the f i r s t r i n g groove i s equal to the c y l i n d e r pressure and i n the second r i n g groove the pressure i s equal to h a l f of the c y l i n d e r pressure, [3.1]. In a d d i t i o n to the pressure f o r c e s , a constant r i n g p r e - t e n s i o n f o r c e a c t s on the r i n g s 2. The combustion e f f i c i e n c y below a f u e l / a i r r a t i o of .068 i s constant at 95% and above .068 i t decreases l i n e a r l y w i t h the f u e l / a i r r a t i o to 54% at a r a t i o of .100. No combustion takes place when the mixture r a t i o i s below .05 and above .143 [4.1]. 3. The c o e f f i c i e n t ' o f f r i c t i o n doubles when the v e l o c i t y drops below 10 i p s . 4. The minimum volume at the top end of the stroke when the p i s t o n touches the c y l i n d e r head i n c l u d e s the volume under the f i r s t r i n g , h a l f of the volume under the second r i n g , the annular volume between the p i s t o n head-land and c y l i n d e r , h a l f of the volume between the r i n g s , and the volume i n s i d e the glow p l u g . The damping c o e f f i c i e n t v a r i e s i n v e r s e l y w i t h the temperature according to the f o l l o w i n g r e l a t i o n s h i p : (T^ p f-T^. ).00356 = e r e r txn r r e f (- changed from 2. at 100°F to .5 a t 500°F) r e f Where T r e f = reference temperature, T^^n = f i n temperature. The o v e r a l l e f f e c t i v e r i n g gap area v a r i e s i n d i r e c t p r o p o r t i o n t o the thermal expansion: A n = (GAP + .28 x 10~ 4 (T £. -T ,))-'x 1 f i n r e f (DDI + .89 x 10~ 5 (T... -T .)) f i n r e f A A 1 A 2 e f f e c t i v e = . . f o r the two r i n g s . A l + A 2 ( I f an aluminum p i s t o n and an aluminum c y l i n d e r i s used,the clearance between the p i s t o n and c y l i n d e r . (DDI) does not change.) Combustion s t a r t s when the gas temperature i n the c y l i n d e r reaches a pre-set value or when the p i s t o n comes w i t h i n a pre-set d i s t a n c e from the head, and continues at a pre-set r a t e (based on the speed and 218 the amount of combustible mixture present) u n t i l a l l a v a i l a b l e f u e l has i g n i t e d or u n t i l the pre-set detonation temperature i s reached. As soon as the detonation temperature i s exceeded, the temperature increases very r a p i d l y . The r a t e of temperature increase during detonation was chosen to g i v e complete combustion i n the co n v e n t i o n a l engine during a 3° crank r o t a t i o n [4.1]. 8. J a k l i s h ' s heat t r a n s f e r equations represent the . amount of heat t r a n s f e r r e d from the gas to the c y l i n d e r , [4.2, 3.13], (1 + .0063 C ) a = 3r P 2 T .0001685 ) ] C * C ^ Q = a (2rr (52^1) + T T B O R E X ) (T -T _. )/144 [Btu/hr] « \ 2 cy f i n Where C = mean p i s t o n speed (fpm), mean BORE = p i s t o n diameter ( i n c h ) , x = p i s t o n p o s i t i o n ( i n c h ) , = c y l i n d e r pressure ( p s i ) , T = c y l i n d e r gas temperature (°F). 9. The amount of heat t r a n s f e r r e d from the c y l i n d e r to the c o o l i n g a i r i s given by the f o l l o w i n g formula which had been determined e x p e r i m e n t a l l y : Q = A f . n (1.48 + .00257 ( S p e e d ) * 9 8 5 i ^ ^ ) 1 ' 4 7 1 ) (Tf. -T ) [Btu/hr] t i n atm 219 2 Where A f = f i n area ( f t ), Speed = engine speed (cpm), X„ = p i s t o n p o s i t i o n at BDC ( i n c h ) , max c c Tatm = ^ k i e n t temperature (°F), T f i n = f i n temperature (°F). 10. The f i n temperature i s based on an energy balance between the heat t r a n s f e r from the gases ( i n c l u d i n g the heat produced by f r i c t i o n ) and the heat t r a n s -f e r r e d to the c o o l i n g a i r . 11. Mackerle's [3.13] e x p e r i m e n t a l l y d e r i v e d flow coef-f i c i e n t s are v a l i d f o r the flow through the p o r t s , (C=0.5). P e r f e c t mixing occurs and the flow i s gi v e n by the f o l l o w i n g equations: (a) f o r s u b - c r i t i c a l flow Wf = .923 C Area (b) f o r c r i t i c a l flow 44 Wf = .923 C Area I .58 up, Where s u b s c r i p t s "up" and "dn" r e f e r to upstream and downstream 12. The f o l l o w i n g f o r c e s act on the p i s t o n and c y l i n d e r : (a) Gas f o r c e s due to pressures i n the c y l i n d e r and i n the precompression chamber (= A^ ^ cy~^pc^ ^ * 220 (b) Ring f r i c t i o n f o r c e due to r i n g p r e t e n s i o n and gas pressure under the r i n g s (= y £ p C y A r + {-^ p~} K}+Fr]>-(c) Load on the blade (= F ^ ) . F l (d) F r i c t i o n f o r c e due to lo a d i n g f o r c e , (= yy-) • (e) Spring f o r c e (= kX). The f o r c e equation i s : ( P - P ) A - y ( J P A + F + I- F J - kx cy pc p 2 cy r r 2 1 A — p i s t o n area ( i n ^ ) , P P cy c y l i n d e r gas pressure ( p s i ) , p pc = precompression gas pressure ( p s i ) , y = c o e f f i c i e n t of f r i c t i o n , A r = p i s t o n r i n g area ( i n ^ ) , F r = r i n g p r e t e n s i o n f o r c e ( l b ) , F l = load on blade ( l b ) , k = s p r i n g r a t e ( p p i ) , X = p i s t o n s t r o k e ( i n ) . Performance c h a r a c t e r i s t i c s d u r i n g p r e l i m i n a r y t e s t s were obtained from the prototype which was instrumented w i t h a crankcase pressure transducer, a c y l i n d e r head accelerometer, a c y l i n d e r head thermocouple, and a p h o t o - e l e c t r i c p o s i t i o n i n d i c a t i n g mechanism. This mechanism c o n s i s t e d of a l i g h t source and a p h o t o - e l e c t r i c c e l l and was mounted so t h a t the blade p o s i t i o n determined the amount of l i g h t reaching the 221 c e l l . When the s t a r t - s t o p t r i g g e r was pressed, a contact s w i t c h t r i g g e r e d an o s c i l l o s c o p e which d i s p l a y e d the p i s t o n p o s i t i o n as a f u n c t i o n of time. Photographs of the i n s t r u -mented assembly are shown on Fi g u r e 4.1. Tests without f u e l but w i t h o i l on the c y l i n d e r w a l l i n d i c a t e d t h a t the c o e f f i c i e n t of f r i c t i o n and r i n g leakage was high. Experimental p i s t o n p o s i t i o n s and crank-case pressure t r a c e s shown on Graph 4.1 were compared w i t h the computer c a l c u l a t e d r e s u l t s shown on Graph 4.2. Computed r e s u l t s were obtained by using measured engine parameters whenever p o s s i b l e . Parameters not e a s i l y measured were determined by repeatedly comparing the computed r e s u l t w i t h the t e s t r e s u l t s . Some of the parameter v a r i a t i o n s are shown on Graph 4.3. The procedure l e d to the f o l l o w i n g important o b s e r v a t i o n s : 1. The amount of leakage from the c y l i n d e r i n f l u e n c e d the f i n a l stopped p i s t o n p o s i t i o n . (An e f f e c t i v e 2 gap area of . 0005y i n c o r r e l a t e d the computed p i s t o n p o s i t i o n s w i t h the f i r s t t e s t data. Since the 2 c a l c u l a t e d r i n g gap area was .0001 i n the amount of leakage over the r i n g s was four times higher than the amount of leakage through the r i n g gaps. As the r i n g s wore i n , the e f f e c t i v e gap area decreased). 2. The c o e f f i c i e n t of f r i c t i o n i n f l u e n c e d the number of c y c l e s before the p i s t o n motion stopped. (A f r i c t i o n c o e f f i c i e n t of .55 c o r r e l a t e d the computed v a l u e s " w i t h the t e s t observation.) 222 Figure 4.2 Photograph of the FPS with a fixed-throw crankshaft 223 ( T h r o t t l e o p en, t o p c u r v e - p o s i t i o n b o t t o m - c y l . a c c . ( r e f . - 2 0 g / d i v ) DThr. p a r t l y open c y l i n d e r greased b o t . - c y l . a c c e l . (lOOg/div) G T h r . p a r t l y open c y l i n d e r g r e a s e d b o t . - s c a v . p r e s s B T h r o t t l e open b o t . - s c a v . p r e s s ( r e f . = 5 p s i ) E T h r . p a r t l y o p e n c y l i n d e r g r e a s e d b o t . - c y l . a c c e l . ( l O O g / d i v )  P| H T h r o t t l e c l o s e d b o t . - c y l . a c c e l . • C T h r o t t l e c l o s e d b o t . - s c a v . p r e s s . r e f . = 5 p s i ) p T h r o t t l e c l o s e d b o t . - c y l . a c c e l ( l O O g / d i v ) IilNllll JBMH IWill fUf. | T h r . p a r t l y open b o t . - c y l . a c c e l . ( l O O g / d i v ) N o t e : R e f e r e n c e l i n e s fot p o s i t i o n t r a c e s a r e i n 1/4 i n i n c r e m e n t s . Time = 20 m i l l s e c / d i v G r a p h 4.1 P r o t o t y p e e n g i n e t e s t t r a c e s 224 Of co o o CO CO LU < DC U ZD ^ CO Z CO < LU DC (X O CL .58—f iv i \ i \ f \ i i * °I 1 r o a. o 20 40 60 TIME (MILLISEC) Graph 4.2 Prototype engine t r a c e s (computed) without combustion Graph 4.3 E f f e c t of leakage, f r i c t i o n and damping on t r a c e s (computed) .Of • TEST TRACE (GRAPH 4 • TEST TRACE (GRAPH 4 .1-G) .1-E) AIR-•FUEL IN CYLINDER ( A F C ) = 18 .8 AIR- FUEL IN PRECOMP. CH. ( A F p ) = 500 AIR- FUEL MIXTURE SUPPLIED ( A F S ) = 8.5 u r =.05 Agap =.0001 A l e a k = . 0 0 3 -TRANSFER EXHAUST 4 P r o t o t y p e e n g i n e p o s i t i o n t r a c e s (computed) w i t h c o m b u s t i o n 227 3. The amount of leakage from the precompression chamber i n f l u e n c e d the chamber pressure and the r a t e of 2 decay. (The deduced leakage area was .006 i n which was e q u i v a l e n t to a clearance of .001 i n on a l l s l i d -i n g surfaces.) 4. The amount of damping i n f l u e n c e d the shape of the stroke-time curve. (The deduced damping c o e f f i c i e n t 2 2 was .05 sec - l b / i n ). O r i g i n a l l y o n l y a few combustion c y c l e s could be obtained from the t e s t engine,as shown e a r l i e r on Graph 4.1, and then only when s t a r t i n g f l u i d was i n j e c t e d i n t o the c y l i n d e r p r i o r to a s t a r t . Nevertheless,important deductions were made by comparing the engine t r a c e s w i t h the computed r e s u l t s , as shown on Graph 4.4. Some of the deductions are as f o l l o w s : 1. When the i g n i t e d a i r - f u e l r a t i o was approximately s t o i c h i o m e t r i c or when too much energy was put i n t o the s p r i n g , the p i s t o n h i t the top of the c y l i n d e r head, Graph 4.1 E. 2. When the c y l i n d e r mixture was r i c h , two combustion c y c l e s occurred; when the mixture was very r i c h , the second c y c l e r e l e a s e d more energy than the f i r s t , Graph 4.1 H. 3. When the crankcase contained a lean mixture and the c y l i n d e r contained a r i c h mixture, three combustion c y c l e s occurred. 228 4. When the crankcase contained a r i c h mixture and the c y l i n d e r a l s o contained a r i c h mixture, four or f i v e combustion c y c l e s occurred. When i t became obvious t h a t i n order t o f i n d the c o r r e c t a i r - f u e l r a t i o the engine had to be r e c i p r o c a t e d c o n t i n u a l l y , a three-throw'crankshaft was designed and f a b r i c a t e d . The cran k s h a f t allowed the engine to be d r i v e n w i t h an e l e c t r i c motor at a f i x e d s t r o k e so t h a t the carbur-e t o r could be adjusted and the r i n g s could be worn i n . The mechanism i s shown on Fi g u r e 4.2. A f t e r the carburetor had been adjusted t o produce a combustible mixture, combustion took place c o n t i n u a l l y but not u n t i l the engine was cooled w i t h an e x t e r n a l blower d i d the engine become s e l f - s u s t a i n i n g i n d e f i n i t e l y . The use of the e x t e r n a l blower to keep the f i n temperature low came about because the computer r e s u l t s had shown t h a t the uncooled engine would a t t a i n a f i n temperature of 567°F i f d r i v e n e x t e r n a l l y . The high f i n temperature caused a l a r g e r i n g gap, a low charge d e n s i t y and e a r l y i g n i t i o n . Above a f i n temperature of 250°F the i n d i c a t e d horsepower was l e s s than the f r i c t i o n horsepower so t h a t the engine would not run by i t s e l f . The d i s t r i b u t i o n of energy as the f i n temperature changes i s shown on Graph 4.5. The computed charge flow was v e r i f i e d e x p e r i m e n t a l l y by measuring the a i r flows and e s t i m a t i n g c y l i n d e r tempera-229 .50 r -< DC CD .^40 CD LU > < CJ CO — 1 1 • FIRING-TEST DATA O NOT FIRING-TEST DATA Tc^ j P • COMPUTED NOT FIRING ., "~ ™" ^» "» O • """"""a—ff , I . 1 CYLINDER TEMPERATURE ( ° F ) Graph 4.5 Crank engine t e s t r e s u l t s t u r e s . The d a t a i s g i v e n i n Appendix V I I I and the r e s u l t s are i n c l u d e d on the graph. A f t e r the c a r b u r e t o r had been a d j u s t e d to produce a combustible mixture, the s p e c i a l c r a n k s h a f t was moved and r e p l a c e d w i t h an o s c i l l a t i n g c r a n k s h a f t . The new c r a n k s h a f t s y n c h r o n i z e d the p i s t o n t o the c y l i n d e r and l a t e r allowed 230 Figure 4.3 Photographs of FPS with an o s c i l l a t i n g crank-shaft (A) with a fixed-throw drive crankshaft (B) details of connecting rod (C) Prony brake free from crankshaft flywheel (D) Prony brake loaded (E) general view i n free-piston configura-tion (F) manual starting with wrench the spring to be pre-compressed manually. A side e f f e c t of the crankshaft and connecting rod masses was to reduce the operating frequency from 4,200 cpm to 2,500 cpm. The new crankshaft was o s c i l l a t e d with the o r i g i n a l crankshaft-motor mechanism or precompressed manually with a wrench (Figure 4.3). When the wrench was suddenly removed the spring was free to drive the piston through i t s compres-sion strokes. Because the strokes were no longer controlled by a crankshaft,the engine o s c i l l a t e d on the free-piston p r i n c i p l e as o r i g i n a l l y designed, although at a lower f r e -quency because the crankshaft and connecting rods increased the o s c i l l a t i n g masses. A Prony brake with a leather f r i c t i o n surface was added to the frame so that the o s c i l l a t i n g crankshaft could be loaded for power t e s t , as shown on Figure 4.3. Although the blade i n an actual saw would be loaded only during i t s outstroke, the Prony brake applied a load to the crankshaft flywheel (diameter = 2.5 i n , crank throw = .75 in) during the instroke as well as during the outstroke. Experimental p o s i t i o n traces during load and no-load conditions are shown on Graph 4.6. Several t y p i c a l piston positions at the end of the stroke and the computed traces are shown on Graph 4.7. The lower curve on the graph shows what e f f e c t a i r - f u e l r a t i o v a r i a t i o n has on the piston p o s i t i o n . The t e s t engine traces of Graph 4.6 indicate that the engine started and ran when the equivalent of a 7.4 lb 232 A,NO LOAD B. LOAD = 1.6 LB C. LOAD = 13.7 LB D. NO LOAD E . LOAD = 1.6 LB F. LOAD = 4.2 LB G. LOAD = 4.5 LB H. LOAD = 7.4 LB I . LOAD = 13.7 LB J . NO LOAD K. NO LOAD L. NO LOAD N o t e : R e f e r e n c e l i n e s a r e i n 1/4 i n i n c r e m e n t s . Time b a s e = 50 m i l l i s e c / d i v G r a p h 4.6 E x p e r i m e n t a l e n g i n e t e s t p o s i t i o n t r a c e s 233 co o O r — CO I—I o y->—« CO o a . o r -CO r ^ ^ ^ A ^ TEST TRACE (GRAPH 4.6-j]f/\ j p O LOAD IIAIR-FUE L~ C YL~  IAIR-  . " ( A F T = 7 . 6 / 1 | . | _/ AIR-FUEL P.C. ( A F C ) = 7.6 I \ / J / • » M R -FUEL CARB ( A F P ) = 1 3 . 2 / I | » / \ : ',/ \ ; w './ W H-Ei.HA,USTt "" .6  13.2 ^ HEAD-J INTAKE r to o I— I—t co o CL —\ o r — CO 1—4 CL y .30 r = .09 Agap = .0001 A l e a k = .007 \ i a I I 1.0fr-0.1 TIME (SEC) G r a p h 4.7 E x p e r i m e n t a l e n g i n e p o s i t i o n t r a c e s (computed) 234 load (.05 bhp) was acting on the saw blade but s t a l l e d when a 13.7 lb load (.10 bhp) was acting. These r e s u l t s were v e r i f i e d by the computed r e s u l t s . What the computed r e s u l t s do not show i s the sporadic type of combustion tak-ing place during the slow speed o s c i l l a t i o n . The computer program assumed i d e a l carburetion. The sporadic engine operation can be explained as follows: 1. The operating speed was just above i d l i n g so that, with the e x i s t i n g large-throat carburetor, carbur-etion was poor: a i r - f u e l fluctuated and vapor-i z a t i o n was incomplete. Typical power saw engines 3 at t h i s speed have s i m i l a r problems (A 4.2 i n engine produced only .1 bhp at 2,300 rpm, [2.47]). 2. A good combustion cycle released enough energy to force the piston against the cylinder head. The impact often absorbed enough energy to stop the engine. 3. The f r i c t i o n and damping c o e f f i c i e n t s were high. 4. The amount of leakage past the rings was very high; 2 (the gap area at room temperature was .0001 i n 2 whereas the designed area was .00001 in ). 5. I g n i t i o n did not s t a r t at the optimum piston p o s i t i o n . The point at which i g n i t i o n started depended on the cyli n d e r head temperature, on the composition of the f u e l (mainly on the amount of s t a r t i n g f l u i d 235 present and what f u e l was u s e d — e n g i n e ran on d i e s e l f u e l , white gas, r e g u l a r gas and glow-plug engine f u e l ) , and on the amount of energy s u p p l i e d t o the glow-plug. Consequently the i n d i c a t e d horsepower v a r i e d from c y c l e to c y c l e and from t e s t to t e s t . Some of the aforementioned drawbacks t o good engine performance w i l l a l s o be present i n the redesigned engine. I t w i l l be d i f f i c u l t to know what mixture the carburetor i s producing unless the engine i s already running. U n l i k e the co n v e n t i o n a l engine where q u i t e a few r e v o l u t i o n s occur when the engine i s s t a r t e d , the present f r e e - p i s t o n engine has a maximum of seven charging c y c l e s per s t a r t i n g attempt (from an i n i t i a l s troke of 1.9 i n ) . For example,with an i n i t i a l a i r / f u e l r a t i o of 100:1 and w i t h the c a r b u r e t o r c o r r e c t l y a d j u s t e d , at l e a s t two s t a r t i n g attempts w i l l be r e q u i r e d before the mixture i n the c y l i n d e r i s i g n i t a b l e . But because the f r e e - p i s t o n engine always runs a t f u l l speed and the bleed p o r t charge r e c i r c u l a t e s through the c a r b u r e t o r , the a i r v e l o c i t y i n the carburetor t h r o a t w i l l always be h i g h . Consequently mixing and v a p o r i z a t i o n i n a p r o p e r l y matched car b u r e t o r w i l l be good. I n i t i a l i g n i t i o n of a combustible charge should present no problem because the i n i t i a l compression r a t i o i s very h i g h . For example, i f the engine i s s t a r t e d from an i n i t i a l s t r o ke of 1.90 i n , the f i r s t compression r a t i o w i l l be 55:1 and the gas temperature w i l l be 1,800°F. I f the a i r 236 t e m p e r a t u r e i s 4 0 ° b e l o w z e r o i n s t e a d o f 6 0 ° F , t h e c o m p r e s -s i o n t e m p e r a t u r e w i l l b e 1 2 0 0 ° F . A n o t h e r d r a w b a c k o f t h e p r o t o t y p e saw w i l l b e t h e v i b r a t i o n c a u s e d b y t h e u n i d i r e c t i o n a l c u t t i n g a c t i o n . A 3 l b u n i t o s c i l l a t i n g a t 6 , 4 00 cpm w i l l h a v e a p e a k - t o - p e a k h a n d - h e l d v i b r a t i o n a m p l i t u d e o f . 0 4 i n a t f u l l l o a d (57 l b s ) . When h e l d a g a i n s t a b u c k i n g s p i k e t h e a m p l i t u d e w i l l b e c o n s i d e r a b l y l e s s . I f t w o c o u n t e r - o s c i l l a t i n g saw b l a d e s a r e u s e d , t h e a m p l i t u d e c a n b e r e d u c e d t o a n e g l i g i b l e a m o u n t . T h e l a c k o f o v e r l o a d p r o t e c t i o n w i l l b e a d e t e r r a n t t o r u n n i n g t h e e n g i n e a t max imum p o w e r . The d r a w b a c k w i l l b e l e s s c r i t i c a l i f t h e e n g i n e h a s a f l a t p o w e r - v e r s u s - s t r o k e c u r v e n e a r max imum p o w e r , o r i f t h e f r a m e o r b l a d e i s d e s i g n e d t o t r a n s m i t n o m o r e t h a n t h e max imum p e r m i s s i b l e l o a d . I f t h e b l a d e h i t s a s o l i d o b j e c t a n d t h e l o a d a p p l i e d t h r o u g h t h e h a n d l e i s l e s s t h a n t h e p e r m i s s i b l e l o a d , t h e f r a m e w i l l a c c e l e r a t e a n d s t o r e m o r e e n e r g y . T h e a c c e l e r a t i o n w i l l p r e v e n t t h e e n g i n e f r o m s t a l l i n g u n l e s s t h e f r i c t i o n o n t h e saw b l a d e i s e x c e s s i v e . M o r e d e v e l o p m e n t w o r k w i l l b e r e q u i r e d b e f o r e t h e s e d r a w b a c k s c a n b e f u l l y e v a l u a t e d , a l t h o u g h a n u m b e r o f c o n c l u s i o n s c a n b e d r a w n a b o u t t h e e n g i n e c o n c e p t . T h e s e c o n c l u s i o n s a r e g i v e n i n t h e n e x t s e c t i o n . 4.2 Conclusions The performance data of the t e s t engine, the pre-dicted values of the prototype, and the predicted values of a redesigned engine are l i s t e d i n Table VIII. The increased Table VIII Performance C h a r a c t e r i s t i c s of FPS Data Test Engine Computed Values Proto-type Redesigned Shaft horsepower (shp) .05 .50 1.00 Maximum load (lb) ±7.4 35 57 Unit weight (lb) 10 6 3 Speed (cpm) 2500 4700 6400 Fuel consumption (lb/shp-hr) - 0.95 0.90 Piston diameter (in) 1.25 1.25 1.25 Blade stroke (in) .5-1.0 .5-1.0 .7-1.3 Spring constant (ppi) 95 95 95 Overload protection none none i f required I g n i t i o n glow-plug glow-plug proximity plug Fuel gas-ether m u l t i f u e l capacity O i l with f u e l with f u e l none Throttle open none none Carburetor f l o a t -type conven-t i o n a l diaphragm integrated diaphragm Vi b r a t i o n l e v e l s below damage l e v e l Noise l e v e l s i n range of t y p i c a l saws Starting instantaneous, e f f o r t l e s s 2 3 8 power of the r e d e s i g n e d engine i s due to h i g h e r o p e r a t i n g speeds ( s m a l l e r p i s t o n mass), lower c y l i n d e r temperatures, and a l a r g e r area f o r the i n t a k e p o r t . The s i m p l i c i t y of the f r e e - p i s t o n power saw i s shown by the photographs on F i g u r e 4.4. When compared wi t h a c o n v e n t i o n a l r e c i p r o c a t i n g blade power saw, the fewer components of the FPS (no i g n i t i o n system, s t a r t e r assembly, fa n , t h r o t t l e and reed v a l v e s ) show the advantage of the f r e e p i s t o n p r i n c i p l e i n a power saw. The new saw w i l l be s a f e r to operate because of" the f o l l o w i n g c h a r a c t e r i s t i c s : 1. No t i m e - l a g occurs when s t a r t i n g and s t o p p i n g the saw. Once the t r i g g e r i s r e l e a s e d , the blade w i l l be m o t i o n l e s s i n l e s s than .01 sec. A m o t i o n l e s s b l a d e i s o b v i o u s l y s a f e r than a moving blade and much s a f e r than a moving c h a i n w i t h t r e a c h e r o u s t e e t h on the top and bottom o f the b l a d e . The i n s t a n t , e f f o r t l e s s s t a r t i n g f e a t u r e enables the o p e r a t o r t o s t a r t the saw a f t e r he has manouvered i t i n t o an awkward p o s i t i o n and so f r e e s him from the n e c e s s i t y of h a n d l i n g a dangerous weapon i n a hazardous s i t u a t i o n . 2 . T h r o t t l i n g ' i s automatic. T h i s means t h a t the o p e r a t o r w i l l not be concerned about the engine speed d u r i n g p a r t - l o a d o p e r a t i o n s . c o n v e n t i o n a l blade saw f r e e - p i s t o n power saw 239 SUB ASSEMBLIES  NOT REQUIRED reed v a l v e s t a r t e r t h r o t t l e magneto spark plug fan (crankshaft and connecting rods not shown) - REQUIRED cover c a r b u r e t o r blade, p i s t o n and c y l i n d e r assembly f u e l tank and pickup m u f f l e r i g u r e 4 . 4 Photographs of con v e n t i o n a l power saw and the FPS 3. I f the engine s t a l l s suddenly d u r i n g an o v e r l o a d , some acc i d e n t s w i l l be prevented or reduced. Although the exhaust noise l e v e l s from the f r e e -p i s t o n engine w i l l be about the same as from a conventional engine w i t h a s i m i l a r m u f f l e r , the noise caused by s t r u c t u r a l v i b r a t i o n s w i l l be lower f o r the f o l l o w i n g reasons: 1. Since the engine i s balanced, the v i b r a t i o n ampli-tude of the frame w i l l be lower. 2. Since no cran k s h a f t i s used, the amount of p i s t o n s l a p and bearing noise i s reduced. 3. Since the c y l i n d e r i s short and s t i f f and the t r a n s -m i t t e d f o r c e s are mainly l o n g i t u d i n a l , l i t t l e l a t e r a l v i b r a t i o n w i l l occur. 4. Since no fan i s r e q u i r e d , aerodynamic noise i s reduced. 5. Since a blade and not a chain i s used, the chain and sprocket noises are e l i m i n a t e d . Although the prototype engine i s s e l f - s u s t a i n i n g and has produced a p o s i t i v e output, more development work i s r e q u i r e d before i t can produce the s p e c i f i e d power. The f o l l o w i n g design steps could be f o l l o w e d : 1. Redesign p i s t o n head to reduce the clearance volume at the top of the s t r o k e . This r e d u c t i o n can be achieved by using r i n g s w i t h smaller gaps and by 241 reducing the volume under the r i n g s , between the p i s t o n headland and c y l i n d e r l i n e r , and i n the glow p l u g . 2. Design an i g n i t i o n system f o r a p r o x i m i t y - t y p e spark p l u g . 3. Redesign the s y n c h r o n i z i n g and a r r e s t i n g mechanism to s i m p l i f y the d e s i g n , to reduce the number of components, and t o permit the use of a l i g h t aluminum p i s t o n . 4. Design a f u e l metering system f o r a s m a l l propane tank and so reduce the s p e c i f i c f u e l consumption and the amount of p o l l u t a n t s i n the exhaust gases. 5. Redesign engine t o i n c o r p o r a t e spark i g n i t i o n , to i n c o r p o r a t e a gaseous f u e l metering system, to r e -duce the frame weight, and t o a l l o w f o r economical manufacture. 4.3 Summary The design envelope f o r the power saw was based on experiments, published i n f o r m a t i o n , q u e s t i o n n a i r e s , and p r a c t i c a l experience. Experiments were performed on e x i s t -i n g saws to determine optimum c u t t i n g speeds and t y p i c a l v i b r a t i o n and noise l e v e l s . These l e v e l s were compared w i t h a l l o w a b l e noise and v i b r a t i o n l e v e l s p u b l i s h e d i n medical and engineering papers. The s p e c i f i c a t i o n s f o r a spark 242 a r r e s t o r design was based on government r e g u l a t i o n s . The optimum s i z e and d e s i r e d o p e r a t i n g c h a r a c t e r i s t i c s were based on a q u e s t i o n n a i r e d i s t r i b u t e d t o power saw users and on p e r s o n a l experience gained w h i l e employed as a research engineer w i t h a chain saw company and as a chain saw operator w i t h a l o g g i n g f i r m . The c u t t i n g speed t e s t s produced data on the e f f e c t of c h a i n p i t c h , wood type, sprocket s i z e , " b i t e " depth, bar l e n g t h , gear r e d u c t i o n and speed v a r i a t i o n on the s p e c i f i c energy r e q u i r e d . C a l c u l a t i o n s based on the experimental r e s u l t s showed t h a t f o r hemlock the minimum s p e c i f i c energy 2 r e q u i r e d was 1,600 i n - l b / i n , and f o r maple the energy r e -2 q u i r e d was 3,700 i n - l b / i n . V i b r a t i o n l e v e l t e s t s showed t h a t the v i b r a t i o n amplitudes of e x i s t i n g saws v a r i e d from .013 t o .030 i n , so t h a t f o r continuous saw o p e r a t i o n the v i b r a t i o n c ould cause damage to the v a s c u l a t u r e of the hands. The noise l e v e l t e s t s a l s o showed t h a t f o r long term exposure the noise could cause h e a r i n g impairment ( t y p i c a l l e v e l s were about 105 dBA). The second design stage c o n s i s t e d of an e v a l u a t i o n of a v a i l a b l e energy sources and an a n a l y s i s of wood c u t t i n g d e v i c e s . I t was concluded t h a t of the engines considered, the i n t e r n a l combustion engine burning hydrocarbon f u e l s had one of the lowest weight/power r a t i o s , and t h a t shears had one of the lowest s p e c i f i c power requirements. Although q u i t e e f f i c i e n t , shears are nevertheless heavy so t h a t the 243 c o n v e n t i o n a l saw blade was chosen as the c u t t i n g d e v i c e . The s y n t h e s i s of new engine arrangements s t a r t e d w i t h an a n a l y s i s of problem areas i n e x i s t i n g engines and produced three new engine c o n f i g u r a t i o n s , one of which was t o produce r o t a r y motion and the other two were to produce r e c i p r o c a t i n g motion. The r o t a r y c o n f i g u r a t i o n c o n s i s t e d of a p i s t o n bouncing i n a r o t a t i n g c y l i n d e r so t h a t the weight of the p i s t o n caused the c y l i n d e r t o t u r n ; t h i s engine was not dynamically s t a b l e . The r e c i p r o c a t i n g c o n f i g u r a t i o n s c o n s i s t e d of a p i s t o n bouncing i n an o s c i l l a t i n g c y l i n d e r ; these engines were s t a b l e i f the p i s t o n and c y l i n d e r were synchronized. I t was necessary to represent the dynamics of a l l three c o n f i g u r a t i o n s by two coupled n o n - l i n e a r d i f f e r -e n t i a l equations before t h e i r s t a b i l i t y c o uld be checked w i t h the a i d of a computer. o s c i l l a t e d between gases i n one end of the c y l i n d e r and a mechanical s p r i n g i n the other. Because the c y l i n d e r was a l s o f r e e t o o s c i l l a t e , the engine was balanced and the c y l i n d e r was s e l f - c o o l i n g . To determine the amount of s e l f -c o o l i n g and the s i z e of f i n s r e q u i r e d to prevent the c y l i n d e r from ov e r h e a t i n g , i t was necessary to o b t a i n heat t r a n s f e r c o e f f i c i e n t s e x p e r i m e n t a l l y . The data i n d i c a t e d t h a t the heat t r a n s f e r from a c y l i n d e r head increased by a f a c t o r of 6 over f r e e convection when a c y l i n d e r .was r e c i p r o c a t e d w i t h a stroke of 1.375 i n a t 1 a speed of 3,000 cpm (Nu = 10.8 + In the c o n f i g u r a t i o n f i n a l l y chosen, the p i s t o n .082 (Re 244 The i n f o r m a t i o n f o r the p i s t o n s i z e and p o r t dimen-sions was obtained from an a n a l y s i s of e x i s t i n g engine performances and dimensions. The a v a i l a b l e data was assembled, c o r r e l a t e d i n terms of u s e f u l dimensionless parameters, and used i n c o n j u n c t i o n w i t h d e r i v e d s c a l i n g f a c t o r s to provide the necessary dimensions f o r the po r t s i z e s . The i n f o r m a t i o n f o r the scavenging and bleed p o r t s (for automatic t h r o t t l i n g ) was obtained from an a n a l y s i s of the dynamic and thermo-dynamic behaviour of the proposed engine i n c o n j u n c t i o n w i t h a computer program. The design of the machine components fo l l o w e d c o n v e n t i o n a l techniques and d e l i n e a t e d a prototype t h a t was evaluated t h e o r e t i c a l l y as w e l l as e x p e r i m e n t a l l y . The f i r s t attempts a t s t a r t i n g the engine, a f t e r the p a r t s had been made and assembled, produced only a maximum of 5 successive combustion c y c l e s . When the engine was d r i v e n w i t h a fixed-throw c r a n k s h a f t i t was p o s s i b l e to br e a k - i n the engine and a d j u s t the a i r - f u e l r a t i o so t h a t i t would become s e l f - s u s t a i n i n g . F o l l o w i n g t h i s adjustment i t was a simple matter to disconnect the connecting rod and run the engine i n the f r e e - p i s t o n c o n f i g u r a t i o n . The prototype of the f r e e p i s t o n power saw i n c o r -porated the f o l l o w i n g novel f e a t u r e s : 1. The engine can be a c c u r a t e l y balanced. When c o r r e c t l y synchronized, the a c c e l e r a t i o n of the p i s t o n i s balanced by the a c c e l e r a t i o n of the c y l i n d e r . 245 2. The c y l i n d e r head i s s e l f - c o o l i n g . The r e c i p r o -c a t i n g motion of the c y l i n d e r moves the c o o l i n g a i r across the f i n s . 3. The p i s t o n stroke i s c o n t r o l l e d by gas and s p r i n g f o r c e s and depends on an energy balance between the amount r e l e a s e d and the amount taken out d u r i n g the c y c l e . ,4. T h r o t t l i n g i s automatic. Because the stroke changes ^ when the load i s changed, the l e n g t h of time the t r a n s f e r and bleed p o r t s are open depends on the l o a d . 5. The compression r a t i o i n c r e a s e s when t h r o t t l i n g i n c r e a s e s . As a r e s u l t , more energy i s a v a i l a b l e f o r i g n i t i o n when the f r e s h charge i s more d i l u t e d w i t h r e s i d u a l gases. 6. The carbureted a i r - f u e l mixture i s i g n i t e d w i t h the energy of compression. 7. The s p r i n g i s a u t o m a t i c a l l y locked i n a compressed s t a t e when the engine i s stopped. This f e a t u r e r e s u l t s i n i n s t a n t , e f f o r t l e s s s t o p - s t a r t c h a r a c t e r -i s t i c s . 8. The r e c i p r o c a t i n g motion of the p i s t o n i s used d i r e c t l y s i n c e the blade of the saw i s p a r t of the p i s t o n . Once the experimental t e s t data and computed r e -s u l t s were c o r r e l a t e d , i t was p o s s i b l e to p r e d i c t engine 246 performance and t o i s o l a t e and evaluate problem areas. At t h i s stage the p r o j e c t o b j e c t i v e s had been achieved: a new p r i n c i p l e had been conceived, components had been d e l i n e a t e d and a working prototype had been evaluated. I 247 REFERENCES 1.1 Thomas T. Woodson, I n t r o d u c t i o n t o E n g i n e e r i n g Design, New York, McGraw H i l l , 1966. 1.2 M.C. De Malherbe and B.W. F i r t h , I n t e r n a t i o n a l Survey  of E n g i n e e r i n g Design E d u c a t i o n , U n i v e r s i t y of Wit-water srand, Johannesburg, Mech. Eng. Report No. 33. 1.3 Robert Matousek, E n g i n e e r i n g Design: A Systematic  Approach, London, B l a c k i e , 1963. 1.4 J.P. Duncan, E n g i n e e r i n g Design and Manufacture, I n -a u g u r a l Address, U n i v e r s i t y of S h e f f i e l d , 1958. 1.5 F. 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Mohr, V i b r a t i o n and Noise C o n t r o l o f Ourboard  Motors and Other P r o d u c t s , SAE paper No. 183B, June, 1960. 1.51 Power Saw Manufacturers A s s o c i a t i o n , Recommended  P r a c t i c e f o r Spark A r r e s t e r s Used on M u l t i p o s i t i o n  Engines (proposed d r a f t ) , Chicago, May 5, 1967. 1.52 Power Saw Manufacturers A s s o c i a t i o n ( C E . 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Johnson, "Nuclear Power i n Space", Mec h a n i c a l E n g i n e e r i n g , V o l . 89, No. 2, 1967. 2.5 W i l l i a m Tucker, "Power", R e p r i n t from Machine Design, V o l . 38, No. 16, J u l y 7, 1966. 251 2.6 R.E. Henderson, " E n e r g e t i c s 7: The Comprehensive View", Mechanical E n g i n e e r i n g , V o l . 28, No. 12, December, 1966. 2.7 "News/Trends", Machine Design, V o l . 39, No. 12, May 23, 1967. 2.8 "News/Trends", Machine Design, August 31, 1967. 2.9 P.E. G l a s e r , " S o l a r Power: R e a l i t y of V i s i o n " , Mechan-i c a l E n g i n e e r i n g , V o l . 88, No. 3, March, 1966. 2.10 A r v i n H. Smith, E n e r g e t i c s 5: P h o t o v o l t a i c Power", Me c h a n i c a l E n g i n e e r i n g , V o l . 88, No. 10, October, 1966. 2.11 John M. Houston, " E n e r g e t i c s 4: Thermionic Power", Mecha n i c a l E n g i n e e r i n g , V o l . 88, No. 9, September, 1966. 2.12 R.L. Klem and A.G.F. P i n g w a l l , " E n e r g e t i c s 3: Thermo-e l e c t r i c Power", Mech a n i c a l E n g i n e e r i n g , V o l . 88, No. 8, August, 1966. 2.13 A.C.J. Mattsson, E.L. Ducharme, E.M. Govani, I.B. Morrow J r . , and T.R. Brogen, " E n e r g e t i c s 6: Magneto-Hydrodynamic Power", Me c h a n i c a l E n g i n e e r i n g , V o l . 88, No. 11, Novem-ber, 1966 . 2.14 W i l l i a m Tucker, "Power", R e p r i n t from Machine Design, J u l y 7, 1966. 2.15 Wells M a n u f a c t u r i n g Company, The Sawing Magic of Wellsaw  400, S a l e s B u l l e t i n , Three R i v e r s , M i c h i g a n , 1962. 2.16 C a r l H. de Zeeuw, "Wood", Marks' Mechanical E n g i n e e r s  Handbook, ed. Theodore Baumeister, New York, McGraw-H i l l , 1958, Sec. 6, pp. 145-164. 2.17 Fag Company, B a l l and R o l l e r B e a r i n g E n g i n e e r i n g , Fag K u g e l f i s c h e r Georg Sc h a f e r & Co., S c h w e i n f u r t , West Germany, 1967,No. 3. 2.18 Kewi Cho Yu, The F r i c t i o n Sawing o f Wood, U n i v e r s i t y of B r i t i s h Columbia t h e s i s , 1967. 2.19 Eugene Lee Bryan, "High Energy J e t s as a New Concept i n Wood Machining", F o r e s t Products J o u r n a l , V o l . 13, No. 8, August, 1963. 2.20 V.G. Yugov and A . I . Osipov, "The Use of High Speed Wa t e r j e t s i n Wood C u t t i n g and P r o c e s s i n g " , T r a n s a c t i o n s  of the C e n t r a l S c i e n t i f i c Research I n s t i t u t e of Mechan-i z a t i o n and Energy Requirements of the F o r e s t I n d u s t r y  of U.S.S.R., ( t r a n s l a t i o n No. 149, Canada Department of F o r e s t r y , 1962), V o l . 18, No. 6, Moscow, 1960. 252 2.21 S.J. Leach and G.L. Walker, XXVI, "Some As p e c t s o f Rock C u t t i n g by High Speed Water J e t s " , P h i l . T r ans. Royal  S o c i e t y o f London, S e r i e s A, ' V o l . 260, No. 28, J u l y , 1966. 2.22 J.S. Johnston, "Cross C u t t i n g of Roundwood.by S h e a r i n g " , Canadian Department o f F o r e s t r y , Program Report on  P r o j e c t 0-209, No. 2, May, 1964. 2.23 Johnston, "Shearing", Canadian Department of F o r e s t r y , Program Report on P r o j e c t 0-209, No. 4, March, 1966. 2.24 J.S. Johnston, "An Experiment i n Shear-blade C u t t i n g o f Small Logs", R e p r i n t e d from Pulp and Paper Magazine of  Canada, V o l . 69, No. 3, February 2, 1968. 2.25 "Roanoke Tree F e l l e r L i n e " , R e p r i n t from Pulpwood  P r o d u c t i o n and Saw M i l l Logging, October, 1966. 2.26 "New World Champions Compete a t Lumberjack Bowl", Chain  Saw Age, November, 1967. 2.27 "Power M i s c e l l a n y " , Marks' M e c h a n i c a l E n g i n e e r s Handbook, ed. Theodore Baumeister, New York, McGraw-Hill, 1958, Sec. 9, pp. 228-232. 2.28 "Power Increment Borer", F o r e s t r y Equipment News, No. A-30-63, F. and A.O., U n i t e d N a t i o n s , Rome, June, 1963. 2.29 "Energy", Product Design and Value E n g i n e e r i n g , J u l y , 1965. 2.30 J.S. Johnston, "Experimental C u t - o f f Saw", R e p r i n t from F o r e s t Products J o u r n a l , Canada Department of F o r e s t r y , June, 1962. 2.31 "20 hp Gas T u r b i n e " , Gas Turbine D i v i s i o n N e w s l e t t e r , ASME, V o l . 8, No. 1, February, 19 67. 2.32 Farm Equipment News B u l l e t i n , A p r i l , 1962. 2.33 "Mercury U n i t t e s t s i t s Stamina", Machine Design, News/ Trends, June 8, 1967. 2.34 S.O. Kronogard, "Automotive Gas Tu r b i n e by V o l v o " , M e c h a n i c a l E n g i n e e r i n g , (from ASME papers, 62-G7P-8), November, 1962. 2.35 A.L. London, "Chairman, P r o f e s s o r A.L. London Comments", Gas Turbine D i v i s i o n N e w s l e t t e r , ASME, V o l . 8, No. 1, February, 1967. 253 2.36 W. Frode, Recent Developments i n the NSU Wankel Engine, advance copy of James C l a y t o n ' s l e c t u r e , February, 1966, p u b l i s h e d i n Proceedings, 1965-66, V o l . 180, P a r t 2A, I n s t . Mech. E n g i n e e r s . 2.37 Go-Power Corp., Go Power Engine A n a l y s i s Systems, Go Power Corp., San F r a n c i s c o , 1967. 2.38 R.F. Ansdale, " A i r - c o o l e d Wankel Engine", Automobile  E n g i n e e r , August, 1965. 2.39 C h a r l e s Jones, The C u r t i s s - W r i g h t R o t a t i n g Combustion  Engines Today, SAE paper No. 8 86D, August, 19 64. 2.40 R.J. M e i j e r , "The P h i l i p s Hot-gas Engine w i t h Rhombic D r i v e Mechanism", P h i l i p s T e c h n i c a l Review, V o l . 20, 1959. 2.41 D.W. K i r k l e y , A Thermodynamic A n a l y s i s of the S t i r l i n g  C y c l e and a Comparison With Experiment, SAE paper No. 949B, January, 1965. 2.42 F . A . Creswick, Thermal Design of S t i r l i n g C y c l e Machines, SAE paper No. 949C, January, 1965. 2.43 A.A . Dros, "An I n d u s t r i a l Gas R e f r i g e r a t i n g Machine w i t h H y d r a u l i c P i s t o n D r i v e " , P h i l i p s T e c h n i c a l Review, V o l . 26, 1965. 2.44 G. Walker, "Operations C y c l e of the S t i r l i n g Engine w i t h P a r t i c u l a r Reference to the F u n c t i o n of the G e n e r a t o r " , J o u r n a l of Mechanical E n g i n e e r i n g S c i e n c e , V o l . 3, No. 4, 1961. 2.45 Gregory F l y n n J r . , Worth H. P e r c i v a l and F. E a r l H e f f n e r , "G.M.C. S t i r l i n g Thermal Engine P a r t of the S t i r l i n g Engine S t o r y , 1960 Chapter", R e p r i n t from SAE Transac-t i o n s , V o l . 68, 1960. 2.46 J . A . R i e t d i j k , , H . C . J , van Beukering, H.H.M. van der Au, and R.J. M e i j e r , "A P o s i t i v e Rod or P i s t o n S e a l f o r Large P r e s s u r e D i f f e r e n c e s " , P h i l i p s T e c h n i c a l Review, V o l . 26, No. 10, 1965. 2.47 Helmut E. F a n d r i c h , S t r a t i f i e d Charge Scavenging of a  Two-Stroke Engine a t P a r t T h r o t t l e , Masters t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, 1962. 2.48 M c C u l l o c h Corp., S a l e s B u l l e t i n , M cCulloch Corp., Los A n g e l e s . 2.49 A. Braun, "The P o t e n t i a l i n the F r e e - P i s t o n Engine P r i n c i p l e " , The E n g i n e e r i n g J o u r n a l , J u l y , 1960. 254 2.50 T.M. L e i g h , The S e l f - C o n t a i n e d D i e s e l P i l e Hammer, SAE paper No. 900B, September, 1964. 2.51 Svenska Co., Motorborr, S a l e s B u l l e t i n , Svenska Motor-b o r r A k t i e b o l a g e t , Stockholm, Sweden. 2.52 J.H. McNich, D.G. Mark and R.J. McCrory, The F u e l and  I g n i t i o n Systems of a F r e e - P i s t o n R e f r i g e r a n t Compressor, SAE paper No. 126B, February, 1960. 3.1 C h a r l e s F a y e t t e T a y l o r , The I n t e r n a l Combustion Engine  i n Theory and P r a c t i c e , New York, Wiley, 1960. 3.2 A.L. London, M.E. 233 Course notes, S t a n f o r d U n i v e r s i t y , F a l l Quarter, 1962. 3.3 A s s o c i a t e d S p r i n g Corp., S p r i n g Design and S e l e c t i o n i n B r i e f , B u l l e t i n o f A s s o c i a t e d S p r i n g Corp., B r i s t o l , C o n n e c t i c u t , 1956. 3.4 Dow Co r n i n g B u l l e t i n No. 09-081, June, 1964, M i d l a n d , M i c h i g a n . 3.5 Extremultus Inc., E x t r e m u l t u s , the U l t i m a t e i n Power  T r a n s m i s s i o n B e l t i n g , S a l e s B u l l e t i n , Extremultus T r a n s m i s s i o n s L t d . , 115 S i x t h Avenue, L a c h i n e , P.Q. 3.6 A s s o c i a t e d S p r i n g Corp., Handbook of Mec h a n i c a l S p r i n g  Design, B r i s t o l , C o n n e c t i c u t , 1950. 3.7 G a r l o c k Inc., B u l l e t i n BP-563, Camden, New J e r s e y . 3.8 AGMA, AGMA Standard f o r S u r f a c e D u r a b i l i t y ( P i t t i n g ) of  Spur Gear Teeth, AGMA 210.02, Washington, January, 1965. 3.9 AGMA, AGMA Standard f o r R a t i n g the S t r e n g t h o f Spur Gear  Teeth, AGMA 220.02, Washington, August, 1966. 3.10 Morse Chain Co., Morse Mech a n i c a l Power T r a n s m i s s i o n  Stock P r o d u c t s , SP-65, Morse Chain Co., I t h a c a , New York, 1965. 3.11 M.S. Walmer, M a t e r i a l P r o p e r t i e s and T o l e r a n c e s i n Rolamite Bands, B u l l e t i n Hamilton Watch Company, Lan-c a s t e r Pa., November, 1968. 3.12 Dudley D. F u l l e r , " F r i c t i o n " , Marks Mech a n i c a l Engineers  Handbook, ed. Theodore Baumeister, New York, McGraw-Hill, 1958, Sec. 3, pp. 31-52. 255 3.13 J u l i u s Mackerle, A i r c o o l e d Motor Engines, London, Cleaver-Hume, 1961. 3.14 A.W. Judge, Modern P e t r o l Engines, London, Chapman and H a l l , 1955. 3.15 P e t e r D. R i c h a r d s o n , " E f f e c t s o f Sound and V i b r a t i o n s on Heat T r a n s f e r " , App. Mech. Review, V o l . 20, No. 3, March 1967. 3.16 Helmut E. F a n d r i c h , E v a l u a t i o n of S e v e r a l Combustion  Chamber Shapes, Tech. Report No. 4, I n t e r n a l Report, Power Machinery, Ltd., Vancouver, February, 1966. 3.17 A l c o a , A l c o a Aluminum Handbook, Aluminum Company of America, P i t t s b u r g h , 1962. 3.18 A l c a n , Handbook of Aluminum, Second E d i t i o n , Aluminum Company of Canada, M o n t r e a l , 1961. 3.19 M a t e r i a l s i n Design E n g i n e e r i n g , M a t e r i a l s S e l e c t i o n Issue, V o l . 60, No. 5, October, 1964. 3.20 A t l a s Stees Company, T e c h n i c a l Data S e l e c t a l l o y  Machinery S t e e l s , Welland, O n t a r i o . 3.21 A.W. Judge, Small Gas T u r b i n e s and Free P i s t o n Engines, London, Chapman and H a l l , 1960. 3.22 F.A. Creswick, R.W. King and R.J. McCrory, " F r e e - P i s t o n Engines" R e p r i n t from Advances i n Petroleum Chemistry  and R e f i n i n g , ed. John J . McKetta, V o l . 7, I n t e r s c i e n c e , New York, 1963. 3.23 " T e f l o n E n g i n e - P i s t o n Rings Improve S e a l i n g " , Machine  Design, V o l . 39, No. 3, February 2, 1967, p. 32. 3.24 News/Trends, "New P i s t o n Ring Solves I.C. E n g i n e e r ' s Problems", Machine Design, V o l . 40, No. 18, August 1, 1968. 3.25 Helmut E. F a n d r i c h , A S t r a t i f i e d Charge Two-Stroke Spark I g n i t i o n Engine Performance C h a r a c t e r i s t i c s , T h e s i s , S t a n f o r d U n i v e r s i t y , 1964. 3.26 News/Trends, " F l u i d i c A m p l i f i e r Feeds Gas t o Auto Engine", Machine Design, V o l . 39, No. 2, May 25, 1967, p. 12. 3.27 F i b e r g l a s s Canada L i m i t e d , F i b e r g l a s R e i n f o r c e d P l a s t i c s , B u l l e t i n Book 1, A p r i l 1965. 3.28 N.W. Todd, F.A. W o l f f , R.S. Mallouk, J.R. C o u r t r i g h t , " P o l y i m i d e s " , Machine Design, June 16, 1966 ( P l a s t i c s Reference I s s u e ) , pp. 81-83. 256 3.29- Habasit Canada L i m i t e d , Product Information Manual PI-68-1, Habasit (Canada) L i m i t e d , O a k v i l l e , O n t a r i o , January, 1968. 3.30 D.D. C a r s w e l l , "Nylons", Machine Design, June 6, 1966, pp. 68-71. 4.1 L e s t e r C. L i c h t y , I n t e r n a l Combustion Engines, New York, McGraw-Hill, 1951. 4.2 A. Stambuleanu, " C o n t r i b u t i o n to the Study of the D i s t r i b u t i o n of Heat Transfer C o e f f i c i e n t s During the Phase of the Working Cycle of an I n t e r n a l Combustion Engine", Proceedings of the T h i r d I n t e r n a t i o n a l Heat  Tra n s f e r Conference, A.I.Ch.E., New York, V o l . I , August 1966, pp. 339-353. APPENDIX I CUTTING SPEED TESTS WITH CONVENTIONAL POWER SAW performed i n U.B.C. Endowment Lands F o r e s t Date & Jaw S/N Speed C u t t i n g Log Date & Suw S/N Speed C u t t i n g hOg Type of Sc Specs. (rpm) Time Diameter Type of & Specs. ( r . «) Time Diameter Vood (sec) ( i n ) Wood (sec) ( i n ) 24/4/67 1770140 6000 25 12 & 16 1/5/67 2711,".b9^ 6500 1 3 i d x w = maple 7 t e e t h tooo 25 ( r o t 4x7) hemlock 7 t e e t h 6500 15 14 x 12 ( f r e s h ) 26 (aemi-dry) ( c e n t e r r o t .404 p i t c h 6400 ( d i f f i c u l t -404 p i t c h 6500 12 4" x 7") .025 Joint 6400 *7 to l o a d .030 j o i n t 6500 U s 15" bar 6300 28 Saw) 15" bar 6500 12 d i r e c t 7000 28 3:1 gear 6500 12 d r i v e 5800 25 r e d u c t i o n 6300 11 d x w 2 5500 24 6200 11 1 4 i x l 2 $ 5500 24 2/5/67 ^711069^ 7000 *3 «.i d i a . 5000 26 hemlock 9 t e e t h 7000 <\ 4500 27 ( f r e s h ) •404 p i t c h 6000 2L ' 24/4/67 1770140 5000 27 12 <ic 16 .030 j o i n t 6500 21* maple 8 t e e t h 7000 32 ( r o t 4x7) 24" b a r 7500 *5 ( f r e s n ) .375 p i t c h 4500 28 3:1 gear 7500 22* .040 j o i n t 6000 28 7000 21 15" b ar 5000 28 6500 20?- 20j 7000 29 2/5/67 ^7110692 6000 *2* 20 6500 26 hemlock 9 t e e t h 6000 20 6000 24 ( f r e s h ) .404 p i t c h 7000 6000 25 .040 j o i n g 7000 22 6000 30 24" b a r 6500 21s 6000 26 3:1 gear 6500 23 7000 27 U j Sc 15 6500 22J 4500 27- ( r o t 4x6) 6500 20 24/4/67 1770140 6000 22 11* & 15 2/5/67 27110692 7000 2* 20 d i a . maple 7 t e e t h 7000 25 ( r o t 4x6) hemlock 7 t e e t h 7000 ^0* ( f r e s n ) .375 p i t c h 5000 20 ( f r e s h ) .500 p i t c h 7000 183 .040 j o i n t 5500 20 .030 j o i n t 7000 20 15" bar 6000 22 24" b a r 6500 19 5000 24 3:1 gear 6500 1 9 i 5500 23 6000 19s 6500 22 11 4 15 6000 20 7000 27 ( r o t 2x3) 7000 21* 25/4/67 1770140 6000 15 12 Sc 12; 2/5/67 1770140 6500 35* 19 & 19* hemlock 7 t e e t h 6000 14 hemlock 8 t e e t h 7000 43 (semi-dry) .375 p i t c h 5000 13j ( f r e s h ) .404 p i t c h 7000 48 .040 J o i n t 5000 13 .025 j o i n g 6000 32 15" b ar 6500 17 24" b a r 6000 30* 6500 17 d i r e c t 6000 28 j -7000 18 d r i v e 6000 30 7000 18 5000 i 9 j 4500 16 5000 31 5500 132 5000 3* 5500 5500 292 6000 1 8 j 5500 292 6000 14 7000 49* 6000 ' 14* 12* & 1 2 5 6500 31 i 1/5/67 1770140 6000 16 13« & 13 6500 34j hemlock 7 t e e t h 6000 16 6600 ift s e l f feed (3emi-dry) .375 p i t c l T^OOO I82 2/5/67 1770140 6500 44* *0 SL 24 .025 J o i n t 7000 19 cedar 8 t e e t h 6000 35* (4" d i a . 15" bar 7000 18 (3emi-6iy) .404 p i t c f t 5000 352 r o t ) 5000 13a (3mall r o t ) .025 j o i n t 6000 43 5000 12 «_4» bar 6000 46 5500 U d i r e c t 6000 38 21 d i a . 5500 H i d r i v e 5000 37* U" r o t ) 6500 14 6500 45 6500 Ui Power check S/N ±776140 6000 14 14/4/67 10/5/67 5000 12 s c a l e bhp s c a l e bhp 5000 u i 4500 6.8 3.06 7.0 3.15 7000 17* 5000 6.5 3.25 6 .4 3.-0 5000 10 d x w = 5500 6.1 3.35 • t>.0 . 3.30 0000 102 13 x 11 6000 5. 6 3.36 5.5 3.30 7000 12* 6500 5. 5 3.57 5.0 3.25 1/5/67 1770140 6000 11 G X V - 70U0 5.1 3.57 3.8 2.66 hemlock 8 t e e t h 6000 11 14 x 12 7500 4. 4 3.30 3.4 2.55 (semi-dry) .375 p i t c h 7000 13* Power check X/H ^711069* 3/5/67 .025 j o i n t 7000 13 <5/4/67 15" bar- 5000 10 6000 7.8 4.63 8.1 4.86 5000 10 5500 8.0 4.40 8.2 4.51 5500 n 5000 8. J 4.10 8.5 4.25 5500 10j- 4500 8.3 3.73 8.6 3.87 6500 13 5000 8. 1 4.05 8.5 4.25 6500 12 5500 8. 0 4.40 8.~ 4.51 5000 11 OOOO 7. 8 4.68 8.1 4.86 bOOO 11 6500 7. 3 4-74 7.3 5.00 7000 15 Vuoo o.8 4.76 7.0 4.90 A P P E N D I X I I V I B R A T I O N L E V E L T E S T DATA (Peek-to-peak vibration amplitude, inch xlO , Noremec Meter APM 201) 8 — I Horizontal! front backj m vO m H :V -V c-—j- i n (v cv -.V H o to >n oo cn rH H CV H •>t vO O cn m r i r l H H (M o -<f cn cv to \ o - t cn r-i r-i r-i r-i r-i r-i O O f > - < t O l > H O H rH H rH r-i -4 H O CV CV r l co o cn r-i r-i CV CV cn £> r-i C\l r-i r-i r-i t> o m cv r-i r-i r-i r-i r i cv cn •>4 CV .V ! •£> o o rH r l CV rH O r | 00 CV H H s f ^ O O rH H H r l r | r | H O m r-i r-i m m r l r l cn o r l r l -1 O CV O —) r l m r l —i xO r l o H '.V t> —| r-H <A O Vertical I top bot. FRONT HANDLE < •p • so fl o « -P 0) H i n c*-H m o H o m cv cv cv cv cn H o CV CV CV H O to -4- to cv o to m c- cn •X> CV H CV r-i CV rH H cv vO m r-i cn cv m to o m cv cv H cv cn '."v cv H O m cn r l sO O r-i CV m iV CV r l r l t> CV vO c^r rH CV -4" o to V o CV r l to m cn co -4 to -H r l r i <n r-i -0 -4 rv O -i H <n r | V £> r-i REAR HANDLE Rt. Vert. Long. Lat. Angle r-i r l r l -4- m cv -4 <n CV CV rH r l to o to CV rH r-i to m H cn CV CV rH r-i o to r-i cv m rH r-i r-i r-i m r- o cv to -4 CV H H CV r-i r-i cv cn cn H H r l o o o H cv m o CV r-i r-i CV H r-i CV o -4 m CV r-i rH •fl O to :V H ^ H r l r l j> r- o Cn rH CV O r-i CO tO CV CV r-i H t> CV O r-i H r-i i n cv <n o -4-cn CV CV r-i r l CV r-i r-i m cn m m m i.V CV r-i r-i to r-i CV r l r | cn rH -4/ m rH CV cv cn rH CV vO NO r l H <n CV -4 r l r | r-i O CV H r i cn O r l CV r-i CV rH 50 r-—I —i cn H —i m V r l o m -V r l CO o :v H c> cn CV H SPEED o o o o o o 7000 7000 2400 6000 6000 7200 7000 o o o o o o o o o t> I> r-o o o Q O O cv 3 1 > 7000 7000 O o o o o o V -35 o 7000 7000 7000 | 7000 7000 7000 7000II | 7000 7000 7000 o O t> DETAILS TEST DATE no bar 29/5/68 36" bar, cutting 30/5/68 no bar 29/5/68 36" bar, cut, 29/5 36" bar, cutting 30/5/68 no bar 29/5/68 36" bar, cutting 30/5/68 no bar 29/5/68 w> c -p o i n cn cn $ m o cn Xi o a 36" bar, cut, 30/5 115" bar, cutting | 15" bar, not cutting 15" bar, cutting 15" bar, not cutting 115" bar, cutting | 15" bar, not cutting 31/5/68 18" bar, cutting 10 . f l •4i •l-J CJ +> 3 m - -i cn MACHINE & S/N •P Tf ? cu - o O 0 «t to nj O io^ O X> o to to CV sO CV —• £> H 28100005 (196 gm c'wt 53% balanced) G 28100007 (207 gm c'wt 53% balanced) F 28100006 (222 gm c'wt 63% balanced) E /rubber 1128940 C 34001031 31/5/68 (23% balanced) B 18500002 (20% balanced) T ) co o d crj Q o ; n x i H o c -c^cv c n — For t y p i c a l power saws with wide open t h r o t t l e taken on May 17, 1967, at a distance of 2.5 f e e t from microphone to sprocket c e n t e r l i n e using a Bruel & Kjaer Sound Meter Type 2203 with octave f i l t e r type 1613 and microphone type 4131. Readings taken on f l a t grassy t e r r a i n i n Hew Orleans, La. Saw S/N and Speed dBA dB Linear OCTAVE BAWD NOISE LEVEL IN DECIBELS Freq. G P S (H 2) K C P S (Kflg) 63 125 250 500 1000 4-5 89 178 355 709 89 178 355 709 1410 2 4 8 16 1.41 2.82 5.63 11.2 2.82 5-63 11.2 22.4 Center Lower Upper 1760103 at 7C00 rpm A 109 109 110 110 82 97 102 107 110 73 9 6 97 103 107 103 102 94 88 100 102 94 86 36001171 at c u t t i n g rpm B 110 111 85 94 99 107 108 100 96 92 93 3100-2-194-8 at cutting rpm C 104 102 105 102 75 94- 98 93 98 97 93 90 87 78 92 9 7 9 7 98 9 5 89 88 79 1760103 at 7000 rpm on e l e c t r i c dynamometer 108 110 80 100 98 104 103 98 96 82 69 operator-absent 110 110 80 98 104 108 99 99 86 8b 72 operator present APPENDIX IV RESULTS OF QUESTIONNAIRE DISTRIBUTED TO CHAIN SAW USERS IN 1967 Extent machine characteristics bother operator Replies Received (code: V-very much, Q-quite a bit, S-somewhat, N-not at all) Professional Loggers Casual Users 1. viJbration S H s u V V Q N 2. smell S a s N Q Q S 3. nsaise Q N Q N s N s V Q 4. weight V 6 V Q V V s Q Importance of specific items (code: E-extremely important, y-quite important, S-only slightly important, H-unimportant) 5. exasy starting E Q E • E. E Q E E E E 6. reliability E ; E E E Q E E E 7. easy maintenance N W Q • H E Q Q E 8. Imt fuel consumption Q S '' S E . E :. S s 9. neat appearance $ s s ;'• ,;E • • •' s.' s s N 10. imm upkeep cost N Q k- E <i £ •". y Q 11. low o i l consumption Q 3 ' s;:. E Q Q ; s Q 12. JEW f i r s t cost price Q E • •' s E E E Q Q 13. low weight and small size Q Q E E E E E s Q E 14.. long, troublefree l i f e Q Q E E E Q Q Q E E Area saw i s used Ont. Ont. Ont. Ont. Ont. N.B. N.B. B.C. Van. Van, Average tree size cart (inch diameter) 7 8 6 6 8 7 40 18 18 Maximum tree size out (inch diameter) 16 15 15 12 26 24'.' 120 36 36 Saw used i n snow y.. y ; y y: y ; y / - y.... y no y Saw used i n rain y y y y y y y y y y Saw used where temperatures drop below 0°F • y y y y y y y .." y no .20° below y y i y y y y y no 40° below y y y y no no no Saw used where temperature goes above 110°F y y y y y y y Dumber of starts pesr day 20 20 20 5 20 50 50 25 6 15 Amount of wood cut — cords per day U 50 u 12 12 6 3 30th 1 cords per year 2800 2800 3000 1188 6H 2 2 cords per saw 4000 200 2000 1000 10M 6 Desired running tiaas on tankful of gas (minutes) 60 60 60 50 120 90 90 40 45 APPENDIX V TYPICAL POWER SAW PERFORMANCE DATA 261 SAW V MAX bhp EXHA JST TRANSFER INTAKE SZMBOL D s/b BMEP a. rpm Ht/S Ae/Ap Ht/S At/Ap Ht/S Ai/Ap 06 8.3 .60 60 .82 7000 .30 .123 .16 .108 Reed valve 75 7.4 .53 53 .79 $ 6500 .36 .143 .23 .155 .38 .183 70 5.8 .60 55 .83 3 7000 .34 .143 .23 .195 .32 • 77 5.8 .60 41 .66 «$ 7500 .35 .143 .24 .133 .32 .14 75 5.5 .61 51 .69 3 7000 • 34 .135 .24 .110 - .15 21 5.0 .55 58 .82 7000 .35 .150 .25 .092 Reed valve 00 4.5 .72 55 .78 ai 6500 .31 .20 .21 .195 Reed valve 78 4*2 .60 55 .86 & 7000 .32 .108 .22 .136 .29 .132 PP 4.2 .60 49 .81 si 7000 .38 .173 .26 .175 .45 .087 42 4.1 .80 65 .93 7000 .30 .24 .21 .23 Reed valve U 3.6 .76 51 .71 6500 .30 .25 .21 .127 Reed valve 10 3.3 .79 53 .75 6500 .31 .25 .175 .150 .27 .191 12 3.3 .79 53 .73 6000 - - - - Reed valve 10 3.3 .79 52 .73 & 6000 .28 .24 .165 .116 Reed valve 79 1.5 1.00 56 .78 & 7000 .27 .23 .175 .200 .25 .19 AS 1.3 1.00 56 .75 7000 - - - - - -OR 1.3 .83 35 .40 & 4500 .24 .20 .125 .13 Reed valve Model 0.1 jl.04 47 1.36 11,400| - -APPENDIX VI HEAT TRANSFERS FROM RECIPROCATING CYLINDER HEADS 262 Wattmeter 3/N 6E22 O s c i l l a t i n g mechanism - scotch yoke and converted c h a i n saw base VT V o l t oetor S/H 6E83 Strobotoc 3/N 6C20 D e s c r i p t i o n Teat Tims Amplitude Frequency Houter P l u g F i n Koom Head Block o f ho. s i n c e pk-to-pk Power Temp. Temp. Temp. Temp. Temp. c y l i n d e r change head (min.) ( i n . ) (cpm) (w.ats) m i l l i v o l t m i l l i v o l t 0°F m i l l i v o l t m i l l i v o l t Canadian 1 • 25 0 216 8.10 7.80 7.95 7 .85 13 /11 /67 275 block 2 .25 400 216 7.8 7 .6 7.65 7.55 and head 3 .25 800 212 7.55 7 .3 7.35 7 .15 4 .25 1600 213 6.90 6.15 .6 . 30 6.15 5 .25 2200 216 5 .85 5.50 5.65 5.95 6 .25 2550 215 4 . 85 4.45 70 4 . 4 .50 l r t ; . v i b r . prsa-svoH" n r , E x t e r n a l c o o l i n g a i r s u p p l i e a by vacuum cleaner bxower, no cover over nead. o u t l e t top | root 7 0 0 106 0 .42 0 . 10 70 0.41 l 1 away . 3 " i t O -8 0 0 106 0 . 36 0 . 02 70 0 .33 4 ' .2" . 0 5 ° 9 0 0 106 0 .35 - 70 0 .33 4- .2" .05" Canadien 10 0 0 94 6.20 0.20 23 / 1 1 / 67 210 c y l . 11 • 50 500 93 5 .40 . 5.30 bead 12 .50 1600 89 3.83 3.80 13 .50 2000 91 3.50 '.. 3.45 14 .50 2600 91 U /S . • 2 .65 p l u g t / c broke 15 .50 3000 92 2 .50 16 .25 500 92 5.80 17 .25 1600 92 . 5.60 . •-; A- • 18 ;25 2000 92 . 5.30 19 .25 . 2600 92 . 4 .80 '• / ." -20 .25 3000 92 ' 4 .40 21 .25 3600 92 4 -1 fuse blew Then&o couplet changed to Chromel-alume! 24 / 11 /67 Canadian 22 0 0 93 7 . 0 6.8 SPACER clearance a t TDC 210 c y l . 23 .25 - 500 93 6 .4 6 .2 70 4 . 5 between spacer & bead K i t h 24 .25 1600 93 : 5.4 5 . 2 69 3.9 head = .05" o a t c h i n g 25 .25 2000 93 4 . 9 , 4 . 7 . 68 3 .5 spacer 26 .25 2600 93 4 . 2 : . 4 . 0 . 68 . 2 . 7 27 .25 3000 93 . 3 .9 ,- 3 . 7 68 -' 2 . 4 28 80 0 0 90 8 .25 • 8 . 0 73 . 4 .45 29 / 11 /67 29 .50 . 500 . 92 5.90 5.76 , . 75 3 .4 30 90 0 0 . ' . 92 8 .75 8 . 5 • 7 6 4 . 8 31 5 .50 500 92 7 .20 6.95 76 4 . 1 -32 10 . .50 500 - 92 6.70 ,6 .45 76 3 .9 33 15 -50 500 92 6 .45 ^ 6 .20 7 7 • . 3 . 8 .. 34 20 .50 . 500 92 6.33 " v 6 . 0 8 78 ;*• 3 .65 35 25 . .50 500 • 92- .'. . b . 20 - - 6.00 78 3.55 36 30 .50 500 93 6.13 . 5 .14 . 78 • 3 .50 37 5 .50 . 1600 93 5.03 4.78 78 2 .93 38 10 .50 1600 93 . 4 . 5 0 -" 4.28 79 2 .60 39 15 .50 ltt» 93 4 .23 • •• 4-02 . 79 . : 2 .40 40 20 . .50 1600 93 •4-10 . . 3 .90 80 ". 2 .23 41 25 .50 . 1600 . 9 3 . 4 .02 3.82 80 2 . 1 3 ' 42 30 .50 • 1600 93 " 4.02 • 3.82 . 79 2 .15 Power o f f f o r f r a c -43 35 .50 . 1600 • . ' 92 .' 4 .00 3.80 78 2 .08 U o n o f sec. t e s t 42 44 40 • 50 • 1600 91 3.90 3 .73 77 iO.07 45 5 • 50 2000 . 90 3.60 3 .38 77 1.90 46 10 .50 2000 90 3-48 3.28 76 1.83 47 3 .50 2600 90 3.13 2 .82 76 1 .70 48 5 • 50 . 2600 '•' 90 3 .02 2 .80 76 1 .63 49 7 .50 2600 90 3 .01 • 2 . 8 0 : 76 1.61 50 3 .50 3O00 8 9 i 2 .82 .• . 2 . 5 3 76 1.50 51 7 .50 3000 8 9 j 2 . 74 2 .50 76 1.40 Voltage suddenly 52 9 .50 3000 89* 2 .74 2.51 76 1.35 decreased t o s t 51 S p e c i a l head 53 .50 0 190 8.8 - 4,'VtS and matching 54 5 .50 400 190 8.1 • - Clearance at TDC spacer to 55 5 .50 1600 190 7 .1 - between bead and squeeze a i r 56 5 .50 2000 191 6 .1 spacer = .02" 57 3 .50 2600 191 5.1 -Canadltui 58 20 1 .375 0 193 12 .6 l i . 5 IS/1/ 6U 210 head 59 5 1.375 400 193 8.45 -only 60 10 1.375 400 195 8 .48 8 .08 68 19/1/68 61 1.375 0 185 11.0 10 .9 62 5 1.375 400 195 0 /S 6 . 0 63 5 1.375 1600 194 - 3.2 64 5 1.375 2000 196 - 2 .53 65 - 1.375 2600 196 - - 23/1/66 66 5 1.375 2000 196 - 2.58 74 ' 67 2 1.375 2600 196 - 2.20 68 0 1.375 2600 193 - 2.00 69 2 1.375 3000 196 - 1.82 Spec i a l h«ad 70 50 .50 0 l o d - 10 70 una spacer 71 50 .50 50 193 10.6 clearance . 05* designed to T i 5 .50 400 193 9.85 acre* bolea on act as a i r 73 10 .50 400 196 9 .50 spacer open putsp 74 5 .50 1000 198 8 .35 Test 73 - o i l added 75 10 .50 1000 197 7.7 Teat 75 - o i l added 70 5 .50 1400 197 6.8 77 10 .50 1400 197 6 .43 Teat 78 - ecrew - .50 0 193 9 . 7 holes plugged-79 4 .50 400 193 B .5 Test 79 - heater >-atortod APPENDIX V I I 263 FPS PROTOTYPE TEST DATA A. Test Data for engine with fixed throw crankshaft- driven externally Date of Test No. Speed (rpm) Pree drop (in H20) Fin temp (°F) Combustion Fuel Flow Scavenging ratio Air/ Fuel 30/10/69 1 1 3200 2750 .010 .008 350* 100* yes no 10cc/ 2.48mii 36.5 37.5 10.2 2 2910 .010 - no 40.0 3 3600 .018 100* yes 43.0 4 3700 .016 200* yes 40.0 5 3000 .012 100* no 42.5 6 3600 .015 - yes 39.5 7 3400 .014 350* yes 40.5 8 3400 .012 450* yes 37.5 9 3430 .012 450* yes 37.0 10 2620 .007 350* no 37.5 5/1/70 1 2 3650 3700 .013 .014 130-145 149-155 yes yes 2.8cc/ .56min 7. cc/ 1,9min 36.5 37.0 8.5 12.0 6/1/70 1 4200 - self-susteining. Started to Blow down when f i n temp 230-250 F. When motion ceased, f i n temp was 270 F. 2 3600 - self-susteining. Started to slow down when fin temp 210° 3 3800 - self-susteining. Started to slow down when f i n temp 190-20O F. When motion ceased, f i n temp was 240 F. Soak temp was^260 F. 10/1/70 1 3600 - With external cooling supplied by blower, fin temp remained below 200 F and engine ran continuously •estimated temperature of piston B. Test Data for free-piston test engine. NoT Date Speed (rpm) Length (cycles) Loading (out & in) Stroke Fuel 19/1/70 28/1/70 5/2/70 5/2/70 1 2 3 4 2500 2480 2460 500 100 20 6 0# \H @ 8" i# @ 19" 1# @ 19" 1.15 1.15 1.05 while gas, o i l reg. gas, o i l reg. gas, o i l , ether reg. gas, o i l , ether Load = Load moment + lever arm moment L 1.5 where lever arm moment = .26 x 9.7 M = coefficient of f r i c t i o n , leather on C.I, = .56 

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