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Dependence of the static coefficient of friction on the time of stationary contact Davis, Harold Robert 1966

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THE DEPENDENCE OF THE STATIC COEFFICIENT OF FRICTION ON THE TIME OF STATIONARY CONTACT  by  HAROLD ROBERT DAVIS B A S c , The U n i v e r s i t y of B r i t i s h Columbia, 1964  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n the Department of MECHANICAL ENGINEERING  We accept t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1966  In presenting  t h i s thesis in p a r t i a l  f u l f i l m e n t of  the  requirements for 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 that the L i b r a r y s h a l l make i t f r e e l y for reference and study.  I further agree that permission  available for  extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the Head of my Department or by h i s  representatives.  It is understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission  Department  of  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada  ii ABSTRACT The  dependence of the s t a t i c c o e f f i c i e n t of f r i c t i o n on the time of  s t a t i o n a r y c o n t a c t has been determined  u s i n g s t i c k - s l i p v i b r a t i o n to p r o v i d e  a p e r i o d i c time of s t a t i o n a r y c o n t a c t between two m e t a l l i c To d e s c r i b e t h i s time dependence a t h e o r y based d i f f u s i o n f o r metals  i n c o n t a c t has been developed.  bodies.  on the creep by  T h i s approach i s  s i m i l a r to the adhesion t h e o r y p r e s e n t e d by many authors as r e p r e s e n t a t i v e of j u n c t i o n s t r e n g t h i n f r i c t i o n . E l e v e n f r i c t i o n - c o u p l e s were s t u d i e d ; t e n c o u p l e s b e i n g v e r y pure metals r u n a g a i n s t an annealed  steel disk.  The  a hardened s t e e l s l i d e r a g a i n s t t h e annealed i n d i c a t e d t h a t , fundamentally, v e r y l i t t l e v a l u e s was  apparent  e l e v e n t h couple c o n s i s t e d of  steel disk.  difficulty  not p o s s i b l e t o compare the e x p e r i However, w i t h i n  a c c u r a c y , the shape of the f r i c t i o n - t i m e  agreed w i t h those p r e d i c t e d by  curves  theory.  By v a r y i n g the system parameters i t was the s t a t i c  friction  Because of the  mental r e s u l t s w i t h p u r e l y t h e o r e t i c a l p r e d i c t i o n s . r e a s o n a b l e experimental  results  difference i n static  between the f r i c t i o n - c o u p l e s .  i n o b t a i n i n g m a t e r i a l p r o p e r t i e s i t was  The  c o e f f i c i e n t of f r i c t i o n was  found  that, i n general,  l o a d and a r e a independent  b u t seemed  to be v e r y dependent on s u r f a c e f i n i s h and the m i c r o — s t r u c t u r e of friction-couples.  Notable  the  exceptions to t h i s r u l e were indium and  silver  which showed e x c e s s i v e creep under l o a d thus d i r e c t l y a f f e c t i n g the c o e f f i c i e n t s of  friction.  I t i s important t o s t r e s s t h a t q u a n t i t a t i v e r e s u l t s f o r the growth curves are not a p p l i c a b l e s i n c e the system parameters a f f e c t results greatly.  static  frictionthe  However, a q u a l i t a t i v e i d e a of the fundamental problems  t h a t e x i s t a l l o w s a r e a s o n a b l e p r e d i c t i o n of f r i c t i o n v a l u e s to be made.  iv  TABLE OF CONTENTS  Page No.  CHAPTER I 1.1  Introduction  1  1.2  Background  2  Theory  6  CHAPTER I I II. 1 CHAPTER I I I III.l  Apparatus  14  III. 2  Instrumentation  16  111.3  Specimens  111.4  Test Procedure  18  rV.l  Results  21  rV.2  D i s c u s s i o n of R e s u l t s  27  V.l  Conclusions  36  V.2  Recommendations f o r F u t u r e Work  37  •• 17  CHAPTER IV ,  CHAPTER V  APPENDIX I  39  LIST OF FIGURES FIG.  Page No.  1  Diagram of an A s p e r i t y  2  Diagram of Apparatus  15a  3  Graph of S l i d e r D i s p l a c e m e n t V e r s u s Time  25  4  Variation  of Y i e l d P r e s s u r e w i t h L o a d i n g Time f o r Indium ...  32  5  Variation  of Y i e l d P r e s s u r e w i t h L o a d i n g Time f o r G o l d  33  6  G e n e r a l View of A p p a r a t u s and I n s t r u m e n t a t i o n  43  7  Details  44  8  Change of S t a t i c C o e f f i c i e n t w i t h Run-in, A n n e a l e d S t e e l Specimen on Annealed S t e e l D i s k  45  Change of S t a t i c C o e f f i c i e n t w i t h Run-in, Hardened Specimen on A n n e a l e d S t e e l D i s k  45  9  10  8  of A p p a r a t u s  Steel  K i n e t i c C o e f f i c i e n t Versus S l i d i n g V e l o c i t y , A t l a s Nutherm S t e e l  46  11  Graph of u,  f o r Hardened S t e e l , One Rev. R u n - i n  47  12  Graph of u,  f o r Hardened S t e e l , Ten Rev. R u n - i n  48  13  14  S S  - t - t  Graph of u, Lubricated  - t  Graph of u, Lubricated  - t  16  Graph of u, Lubricated  - t  Graph of |x  - t  18  f o r Hardened S t e e l , One Rev. Run-in,  f o r Hardened S t e e l , Ten Rev. Run-in, 50  Graph of ^  K/W  S  49  15  17  S  S  - t  S  f o r Copper Showing the E f f e c t of Run-in ... f o r Copper Showing t h e E f f e c t of Run-in,  52 f o r I r o n Showing the E f f e c t of R u n - i n f o r  = 7.4/1.1 .!  Graph of fi - t K/W = 4 2 . 2 7 5 . 0 5  19  Graph of u,  20  Graph of u,  51  f o r I r o n Showing the E f f e c t of Run-in f o r  - t  54  S  - t  S  53  S  f o r Cadmium Showing the E f f e c t of Run-in ..  55  f o r Lead Showing the E f f e c t of Run-in  56  VI  Page No.  FIG. 21 22  Graph of U, - t f o r Z i n c Showing t h e E f f e c t s s Graph of n  o  - t  f o r N i c k e l Showing the E f f e c t  a  57  of Run-in of Run-in ...  58  23  Graph of u, - t s s f o r S i l v e r Showing t h e E f f e c t of Run-in ...  59  24  Graph of u. - t  60  25  Graph of u, - t s s f o r Indium Showing the E f f e c t  26  Graph o f l o g (u, - u. ) V e r s u s l o g ( t s  27  Graph of l o g (u, - u-) V e r s u s l o g ( t Lubricated  28 29  30  3  k  g  33 34 35 36 37 38 39  of R u n - i n ...  f  f o r Hardened S t e e l  ;  f o r Hardened  - u,^) V e r s u s l o g ( t  Graph of l o g (u,  .  61 62  Steel, 63  - u,^) V e r s u s l o g ( t ^ f o r Copper , s Graph of l o g (u. - u. ) V e r s u s l o g ( t f o r Copper, Lubricated £  for  64  65  Iron, 66  - 7.4/2.1  Graph of l o g (u^ - u-) V e r s u s l o g ( t k  K/W 32  k  of Run-in  Graph of l o g (u-  K/W 31  S f o r G o l d Showing the E f f e c t  £  for  Iron, 67  = 42.2/5.05  Graph of l o g (u. - ( i ) V e r s u s l o g ( t s k  - |i ) Versus l o g ( t k  Graph of l o g (u.  g  Graph of l o g ( | i  g  - u,^) V e r s u s l o g ( t  - (a, ) V e r s u s l o g ( t Graph of l o g (u. s - u. ) V e r s u s l o g ( t k  k  Graph o f l o g (u,  g  - u,) V e r s u s l o g ( t k  Graph of l o g ((J, - u,) V e r s u s l o g ( t s Graph of l o g (u. Graph of l o g (u. - u- ) V e r s u s l o g ( t Data , k  g  k  f o r Cadmium  68  f o r Lead  69  for Zinc  70  for Nickel  ......  71  for Silver  72  f o r Gold  73  f o r Indium ......  74  from Independent 75  LIST OF TABLES 1  L i s t of Formulae O b t a i n e d from E x p e r i m e n t a l D a t a  28  vii LIST OF SYMBOLS SYMBOL  UNITS  K  S p r i n g constant  W  Normal Load  lb  Time of s t i c k  sec  Initial  in  t  s  A  Q  A  Final  A  &  p  Q  lb/in  area of contact of a s p e r i t y  a r e a of c o n t a c t o f a s p e r i t y  Apparent  area of contact  I n i t i a l y i e l d pressure  in  2 2  in^ lb/in  / 2 p 8 0  F i n a l y i e l d pressure  lb/in  I n i t i a l y i e l d s t r e n g t h i n shear  lb/in  2 s  Final  Q  A c t i v a t i o n energy f o r s e l f d i f f u s i o n  cal/mole  R  U n i v e r s a l gas c o n s t a n t  cal/deg-mole  T  Temperature  k,n C,K^,Kg u, s u s  y i e l d s t r e n g t h i n shear  Constants Static coefficient Kinetic  coefficient  lb/in  o^  of f r i c t i o n of f r i c t i o n  6  Maximum d i s p l a c e m e n t of s l i d e r  in  6min  Minimum d i s p l a c e m e n t of s l i d e r  in  2 o  Tensile  e  Apparent  a,V  Constants  g  (n  +  stress strain  V^)"  1  lb/in in/in  VI11  ACKNOWLEDGEMENT The  author i s g r a t e f u l f o r t h e many:helpful  f a c u l t y and graduate  s u g g e s t i o n s from t h e  s t u d e n t s i n t h e Department of M e c h a n i c a l E n g i n e e r i n g  and f o r the p a t i e n c e of t h e t e c h n i c i a n s who c o n s t r u c t e d the experimental apparatus. S p e c i a l thanks a r e due to Dr. C.A. B r o c k l e y f o r h i s guidance and encouragement throughout The  t h e r e s e a r c h program.  experimental work was c a r r i e d out i n t h e L u b r i c a t i o n L a b o r a t o r y  of the department of M e c h a n i c a l E n g i n e e r i n g , U n i v e r s i t y of B r i t i s h F i n a n c i a l a s s i s t a n c e was r e c e i v e d from the Defence R e s e a r c h Board under G r a n t Number 7510-31.  Columbia. of Canada  1  CHAPTER I  1.1 INTRODUCTION  In the t h e o r y of s t i c k - s l i p v i b r a t i o n the importance o f the dependence  of the s t a t i c  c o e f f i c i e n t on t h e time of s t a t i o n a r y c o n t a c t has been  r e a l i z e d and s e v e r a l mathematical r e l a t i o n s have been proposed t o p r e d i c t the shape o f t h i s c u r v e , y e t no c l e a r e x p l a n a t i o n o f t h i s phenomenon has been p r e s e n t e d a l t h o u g h s e v e r a l attempts have been made by v a r i o u s a u t h o r s . The f a c t t h a t the v a r i a t i o n of s t a t i c the c r i t i c a l v e l o c i t y p o i n t a t which  f r i c t i o n w i t h time of s t i c k determines s t i c k - s l i p v i b r a t i o n ceases and pure  s l i d i n g commences suggests t h a t a study o f the mechanism o f t h i s phenomenon i s important.  Hence an e x p e r i m e n t a l apparatus was b u i l t which  s t i c k - s l i p v i b r a t i o n t o determine the time dependence o f s t a t i c  utilizes friction.  S i n c e s t i c k - s l i p v i b r a t i o n i s a p e r i o d i c f u n c t i o n of saw-tooth form where the i n c r e a s i n g s l o p e i s the s t i c k p o r t i o n o f the c y c l e and the v e r t i c a l  s l o p e i s the s l i p p o r t i o n of the c y c l e , a d e f i n i t e time of s t i c k , even of very short duration,  can be d u p l i c a t e d r e a d i l y and c o n t r o l l e d e a s i l y s i m p l y  by changing t h e parameters of the system such as the s u r f a c e v e l o c i t y o r the s t i f f n e s s of the s p r i n g . A g e n e r a l t h e o r y of f r i c t i o n induced v i b r a t i o n has been p r e s e n t e d by Cameron ( 1 2 ) .  The s o l u t i o n of the d i f f e r e n t i a l equations i n v o l v e d i n  s t i c k - s l i p v i b r a t i o n was  accomplished by phase p l a n e methods.  experiment conducted by the a u t h o r the s t a t i c  F o r the  c o e f f i c i e n t of f r i c t i o n  was  determined by:  ^s where K i s the s p r i n g c o n s t a n t , ¥  ~  T  the normal  l o a d and 6 the maximum d i s t a n c e  t r a v e l l e d by the specimen i n the s t i c k c y c l e from the e q u i l i b r i u m p o s i t i o n . A l s o the k i n e t i c c o e f f i c i e n t of f r i c t i o n c o u l d be o b t a i n e d i n the  stick-slip  regime by the e q u a t i o n :  ^ k where $ ^ m  n  =  2 W  i s the minimum d i s t a n c e  m  i  n  +  r  t r a v e l l e d by the specimen from the  equil-  i b r i u m p o s i t i o n of the s p r i n g .  1.2  From the time t h a t two  BACKGROUND  s u r f a c e s were f i r s t moved a t some r e l a t i v e  v e l o c i t y i t has been n o t i c e d t h a t o f t e n o t h e r than smooth s l i d i n g This  resulted.  i n t e r m i t t e n t motion, when the r e l a t i v e speeds are low, has been termed  " s t i c k - s l i p " v i b r a t i o n or r e l a x a t i o n o s c i l l a t i o n . v i b r a t i o n was  Although  stick-slip  common no attempt t o g i v e a good t h e o r e t i c a l reason f o r i t s  3 e x i s t e n c e was  made u n t i l the e a r l y  1900 s. f  In 1929 W e l l s ( l ) observed s t i c k - s l i p w h i l e a t t e m p t i n g to measure the k i n e t i c  c o e f f i c i e n t of f r i c t i o n a t low s l i d i n g v e l o c i t i e s and  proposed  t h a t t h i s phenomenon c o u l d occur o n l y i f the s t a t i c c o e f f i c i e n t were l a r g e r than the dynamic c o e f f i c i e n t of f r i c t i o n .  V a r i o u s authors attempted  e x p l a i n s t i c k - s l i p v i b r a t i o n by c o r r e l a t i n g  the system parameters,  l o a d , s p r i n g f o r c e , damping e t c . , t o the observed magnitude and of  stick-slip.  S i n c e the two  such as  frequency  s u r f a c e s i n c o n t a c t were s t a t i o n a r y f o r some  l e n g t h of time d u r i n g the s t i c k p o r t i o n of the c y c l e i t was static  to  e v i d e n t t h a t the  c o e f f i c i e n t o f f r i c t i o n would i n f l u e n c e the s t i c k - s l i p v i b r a t i o n  especially  i f i t were time dependent.  I n 1939 Bowden and Leben ( l l ) s t a t e d  t h a t the s t a t i c c o e f f i c i e n t o f f r i c t i o n depended on the breakdown of the welded j u n c t i o n s of the a s p e r i t i e s  i n c o n t a c t between the two  rubbing sur-  f a c e s and t h i s w e l d i n g process would be time dependent. Dokos (3) found t h a t the s t a t i c c o e f f i c i e n t v a r i e d i n v e r s e l y w i t h the frequency of s t i c k - s l i p and h i s d a t a i n d i c a t e d t h a t the |i - t  curve  was  l i n e a r when p l o t t e d l o g a r i t h m i c a l l y a l t h o u g h he n e v e r p o s t u l a t e d e x a c t l y how  t h i s occurred. L a t e r work by Rabinowicz  metallic asperities.  Rabinowicz  t i e s b u i l t up as a r e s u l t  (2) supported t h i s t h e o r y of a d h e s i o n of found t h a t the shear f o r c e s at the  asperi-  of imposed t a n g e n t i a l m i c r o - d i s p l a c e m e n t and  this  i n d i c a t e d t h a t the s t a t i c f r i c t i o n c o e f f i c i e n t would b u i l d up as a r e s u l t the time of s t a t i o n a r y c o n t a c t . Howe, Puddington  ^s where |i  and Benton (9) suggested t h a t the r e l a t i o n ,  =  V  +  K--^^  1  "  i s the s t a t i c c o e f f i c i e n t of f r i c t i o n f o r a v e r y l o n g time of  of  c o n t a c t and C i s some a r b i t r a r y c o n s t a n t u. - -t curve« s s  would be r e p r e s e n t a t i v e o f the  t  However t h i s curve was d e r i v e d f o r g l a s s i n c o n t a c t w i t h  g l a s s and t h e t h e o r y was based  on V a n der Waal's e l e c t r o s t a t i c f o r c e s and  hence i s not s t r i c t l y a p p l i c a b l e t o m e t a l s .  A t t h i s time an experimental  study of the problem was p r e s e n t e d by S p u r r (6) and h i s d a t a c o n f l i c t e d w i t h the p r e d i c t e d t h e o r e t i c a l curve by Howe e t a l . Whereas Howe's t h e o r y p r e d i c t s an asymptotic curve as ...the-time o f s t a t i o n a r y c o n t a c t i n c r e a s e s S p u r r ' s d a t a shows no such f l a t t e n i n g of t h e s Another  — t curve. s  p o s s i b l e curve f o r t h e time dependence o f t h e s t a t i c c o -  e f f i c i e n t o f f r i c t i o n was p r e s e n t e d by D e r j a g i n , Push and T o l s t o i ( 1 3 ) . They proposed  that: Ct ^s = h c  where k was  i s some a r b i t r a r y c o n s t a n t .  based  +  kTT  s.  ••:  The argument f o r t h i s shape of curve  on t h e i d e a t h a t as the s l i d i n g v e l o c i t y f a l l s t o zero j u s t b e f o r e  s t i c k i s imminent,, the time o f i n t e r a c t i o n between opposing i n c r e a s e s , which l e a d s t o an i n c r e a s e i n c o n t a c t a r e a * t o the above p r e s e n t a t i o n Rabinowicz  . ^  = s  \  + K  proposed  asperities  However, i n a r e p l y  that:  2 ^  where Kgand 3 a r e c o n s t a n t s and 3 i s l e s s than u n i t y , based  on t h e d a t a from  D'okos and from h i s own e x p e r i m e n t a l work. K o s t e r i n and K r a g h e l s k y ( l O ) , a f t e r o b s e r v i n g t h a t t h e s t a t i c f r i c t i o n f o r c e grew i n t e n s i v e l y i n t h e f i r s t moments of s t a t i o n a r y c o n t a c t , agreed t h a t t h e u. - t curve would resemble s s et a l .  i n form t h a t p r e s e n t e d by Howe  I n a l a t e r a r t i c l e by K o s t e r i n and K r a g h e l s k y (7) an e x t e n s i v e  t h e o r e t i c a l a n a l y s i s based  on t h e t h e o r y o f v i s c o - e l a s t i c i t y and p l a s t i c  5  deformation  and u s i n g the r h e o l o g i c a l p r o p e r t i e s of the m a t e r i a l s i n c o n t a c t ,  showed t h a t the e x p o n e n t i a l form o f the experimental  — t  g  curve was c o r r e c t .  d a t a , however, was n o t c o n c l u s i v e s i n c e i t d i d n o t f o l l o w the  form of the p r e d i c t e d c u r v e .  F u r t h e r agreement w i t h the e x p o n e n t i a l |x  curve as p r e d i c t e d f i r s t by Howe was g i v e n by Cameron (12), experimental  time  Their  evidence  - t  In a l l of the  g i v e n t o support t h e e x p o n e n t i a l |J. - t curve the s s  of s t a t i o n a r y c o n t a c t was r e l a t i v e l y small so t h a t p r e d i c t i n g the exact  form of the curve tended  t o be hazardous*  6  CHAPTER I I  I I . 1 THEORY  A d i s c u s s i o n o f the mechanism of f r i c t i o n must i n e v i t a b l y w i t h t h e f a c t t h a t i n r e a l i t y even t h e most c a r e f u l l y prepared a roughness which, compared t o m o l e c u l a r  start  s u r f a c e has  d i s t a n c e s , makes the s u r f a c e appear  as a mountainous t e r r a i n and when the s u r f a c e s a r e p l a c e d i n c o n t a c t the r e g i o n s which a c t u a l l y  touch make up an e x t r e m e l y s m a l l p r o p o r t i o n of t h e  apparent a r e a o f c o n t a c t . the o t h e r w i l l  Hence t o move one o f these s u r f a c e s r e l a t i v e to  o b v i o u s l y r e q u i r e some d i s t o r t i o n of the a s p e r i t i e s  t a c t e i t h e r by s h e a r i n g or by a ploughing  action.  i n con-  The requirements f o r  motion a r e t h e same whether t h e s u r f a c e s are moving r e l a t i v e t o one another c o n t i n o u s l y or a r e s t a r t i n g from r e s t . d i f f e r e n c e between the s t a t i c  I t would appear then t h a t the  c o e f f i c i e n t and the dynamic c o e f f i c i e n t of  f r i c t i o n i s one of magnitude o f f o r c e s and n o t of mechanism o f  deformation.  7 Since  the a s p e r i t y seems to be  the dominating f a c t o r i n f r i c t i o n i t  becomes obvious t h a t c e r t a i n p h y s i c a l f a c t o r s w i l l a f f e c t the  type and  of the a s p e r i t i e s .  contaminants,  Such v a r i a b l e s as hardness of s u r f a c e and  size  atmospheric c o n d i t i o n s , and  r e l a t i v e a c t i v i t i e s of the f r i c t i o n couples w i l l  a f f e c t the f r i c t i o n  K o s t e r i n and.Kraghelsky (7) attempted to p r e d i c t  force.  the magnitude of the f r i c t i o n f o r c e u s i n g materials  i n c o n t a c t , but  the r h e o l o g i c a l p r o p e r t i e s of  t h e i r r e s u l t s i n d i c a t e d t h a t the a n a l y s i s was  comprehensive enough f o r g e n e r a l u s e . (4) have p r e s e n t e d an e x t e n s i v e  list  Bowden and Tabor ( 5 ) and  the not  Rabinowicz  of f a c t o r s which i n f l u e n c e f r i c t i o n i n  a d d i t i o n to those p r e v i o u s l y mentioned. The 1699,  classical  laws of f r i c t i o n ,  as f i r s t proposed by Amontons i n  s t a t e d t h a t the f r i c t i o n f o r c e i s e s s e n t i a l l y p r o p o r t i o n a l to  l o a d and  i s independent of the area i n c o n t a c t .  laws was  t h a t f r i c t i o n i s independent of v e l o c i t y .  f a c t t h a t the f r i c t i o n required  t h a t these c l a s s i c a l understand the  and  Also  recognized  However, i t i s w i d e l y r e c o g n i z e d  l i m i t a t i o n s of these laws and  being  e x i s t but  surfaces  sheared i t  I t seems  experiments  Tabor (5) show t h a t i n f a c t a d h e s i o n i s the main  method of forming j u n c t i o n s between a s p e r i t i e s f o r m e t a l s . j u n c t i o n between two  to  adhesion,  ploughed or t o r n .  r e a s o n a b l e t h a t a l l of these modes of s h e a r i n g p r e s e n t e d i n Bowden and  today  formulated.  i s n e c e s s a r y to d e c i d e whether the a s p e r i t i e s have j o i n e d by s e l f - d i f f u s i o n or are simply  the  to p r e d i c t the f r i c t i o n pheno-  Assuming t h a t f r i c t i o n f o r c e s r e s u l t when a s p e r i t i e s are  cohesion,  was  In order  dependent on the a s p e r i t i e s of two  t h e i r i n t e r a c t i o n must be  these  greater than that  laws are a g r o s s o v e r - s i m p l i f i c a t i o n .  menon i n some manner, a t h e o r y i n contact  A l a t e r a d d i t i o n to  f o r c e r e q u i r e d to s t a r t motion was  t o m a i n t a i n the motion.  the  Hence  a s p e r i t i e s i n c o n t a c t w i l l have some shear  the  strength  8 dependent on the c o n d i t i o n s of f o r m a t i o n and on the p h y s i c a l p r o p e r t i e s of the metals* A typical  j u n c t i o n may  resemble  s c a l e has been m a g n i f i e d g r e a t l y .  F i g . 1 except t h a t the  vertical  When m e t a l s , a r e p l a c e d i n c o n t a c t they  touch o n l y a t the t i p s of the a s p e r i t i e s  Fig.  1  Diagram o f an A s p e r i t y where the p r e s s u r e i s always h i g h enough t o cause p l a s t i c metal f l o w s p l a s t i c a l l y u n t i l a s u f f i c i e n t normal l o a d * is p  Q  I f the normal l o a d i s W  , assuming two  deformation.  The  a r e a i s formed to support the  and the y i e l d p r e s s u r e of the metal  s i m i l a r metals are i n c o n t a c t , the t r u e a r e a of  contact i s :  Also  i f the b u l k shear s t r e n g t h of the adhered j u n c t i o n i s s t h e n the f o r c e Q  r e q u i r e d to shear the j u n c t i o n becomes; s  F = s. A =  ooo  W  'lSp  o  9 Noting that the c o e f f i c i e n t of f r i c t i o n i s defined as;  I t i s obvious that the c o e f f i c i e n t of f r i c t i o n i s independent of load and area of contact and i s simply the r a t i o of two p h y s i c a l properties of the metals i n contact, the shear strength and y i e l d pressure.  This simple model  also demonstrates Amontons law that the f r i c t i o n force i s proportional to the load and independent of the area of contact.  No statement has been made  as to whether the model demonstrates the s t a t i c or dynamic c o e f f i c i e n t of friction. The problems of such a model are obvious i n that the shear strength and y i e l d pressure are r e l a t e d to one another and are not too much d i f f e r e n t and yet c o e f f i c i e n t s of f r i c t i o n have a large range, some being greater than u n i t y , depending on the p h y s i c a l conditions.  The f i r s t m o d i f i c a t i o n would  be that surface contaminants tend to give a lower shear stress value. Secondly, and most important, the a n a l y s i s does not include the e f f e c t of the applied shear stress on the p l a s t i c deformation. To consider the e f f e c t of the shear s t r e s s apply Von Mises y i e l d c r i t e r i o n to a two-dimensional case as done by Bowden and Tabor ( 5 ) i n t h e i r j u n c t i o n growth theory.  < T " T22>2 + (T22 - T33)2 U  (T33 - T N ) 2  +  6(T 1 2 2 + T132  +  T^2) = 6k  2  = p (the normal pressure) and T^ = s (the applied shear stress)  where and k = s  +  2  Q  (the y i e l d strength i n shear).  Hence: For a three-dimensional  p  2  +  OS  2  The other stresses are zero.  „ 2 = ds_o  case no exact s o l u t i o n e x i s t s but the form remains  the same as the two—dimensional case. (Ref. 5)  10  p  2  2  + as  r  = as  2  0  Under combined s t r e s s the a r e a i n c r e a s e s from the i n i t i a l A v a l u e A and the f o l l o w i n g r e l a t i o n s now  o  t o some  new  hold.  W " A  P  8  I f the a s p e r i t y i n t e r f a c e has  =  F A  a shear s t r e n g t h s^ which i s lower than the  b u l k shear s t r e n g t h of the m a t e r i a l S  then:  q  s. = ks 1 The  c r i t e r i o n which determines  s t r e n g t h s^.  o p l a s t i c y i e l d i n g w i l l be the i n t e r f a c e  F o r lower v a l u e s of shear s t r e s s than s^ the combined  c o n t r i b u t e s t o j u n c t i o n growth. mined by: p  2  r  Rearranging  k<l  and  The  shear  stress  c o n d i t i o n of gross s l i d i n g i s d e t e r -  + as. 1  2  = as  2  o  substituting: P  2  =  2 /l  (-£ -  ota  s. I  , k  P  /a  ,x  1)  \L  1  / H P s.  From t h i s e x p r e s s i o n i t i s obvious t h a t the r a t i o — the v a l u e of k.  N o t i n g t h a t the f r i c t i o n f o r c e i s : F =  s.A l  and the normal p r e s s u r e :  W P  then:  =  A  i s v e r y s e n s i t i v e to  11  ^ The  _ F _  W ~p  1  _ k  Tot Tl^kS  above e x p r e s s i o n f o r the c o e f f i c i e n t of f r i c t i o n i s v e r y dependent on  the s u r f a c e  shear s t r e s s of t h e metals i n c o n t a c t .  ( R e f . 5)  I f the a s p e r i t i e s i n c o n t a c t are p l a s t i c a l l y deformed then i t i s reasonable  t o assume t h a t the m a t e r i a l s w i l l  creep under l o a d .  E v i d e n c e to  t h i s e f f e c t has been r e p o r t e d by Bowden and Tabor ( 5 ) , and Pomey e t a l . , (8) where hardness t e s t s showed t h a t the i n d e n t a t i o n hardness of metals decreased  i f the l o a d i n g time i n c r e a s e d .  The p r o c e s s was d e s c r i b e d by Bowden  and Tabor as obeying the v i s c o u s creep phenomenon i n t e n s i l e t e s t s where the following relation  holds.  i f - CcAT IV dt  Here C and n a r e c o n s t a n t s , Q i s the a c t i v a t i o n energy f o r s e l f - d i f f u s i o n , R i s the u n i v e r s a l gas c o n s t a n t The  and T i s the temperature.  r e a l a r e a of c o n t a c t f o r a j u n c t i o n may be e s t i m a t e d  of s t r a i n by assuming t h a t the a s p e r i t i e s a r e t r u n c a t e d cones.  i n terms  The area  would be: AA  = nr  2  r where r i s the r a d i u s of the t r u n c a t e d i s 2a and the v e r t i c a l  I f the apex angle  of the cone  s t r a i n i s e the a r e a becomes: A  where h  cone.  r  '  = n(hetana) N  i s the a s p e r i t y h e i g h t K r a g h e l s k y  2  = k e  2  0  3  and K o s t e r i n ( 7 )  suggest t h a t the  r e a l a r e a of c o n t a c t obeys the r e l a t i o n : A  = A be ' a 1  r  where b and V are c o n s t a n t s , which i s the same form as t h a t o b t a i n e d  from  the  simple model. The  The  apparent a r e a of  normal s t r e s s  a t the a  contact i s  Aa.  junction interface W  =  becomes;  W r  A  be  a  •^•.CA'^V)^", a  Differentiating:  '•  dt Substituting into  the  =  ^  VA  b / a  v i s c o u s creep  n  r  BT  "C  l/v V'vV  1+i  .) dt  CT  relation:  /  W  /- 1"\  "\  „  da  W  V  a S e p a r a t i n g the  v a r i a b l e s and -(  integrating  n+f  )  w i t h r e s p e c t to  f n+i")  ^e"^  T A T  1  ft  The  stress  a is identical  to  the  time:  7 •  "  •  p r e s s u r e o b t a i n e d i n the  static  friction  relation. s.  V  8  Substituting:  1  = i 1 ^ jTy/v / s  *  1 +  c  2  a N o t i n g the  fact  t h a t a t zero time of  f r i c t i o n i s e q u i v a l e n t to the  u.  The  s  -  u,.  above e q u a t i o n r e l a t e s  k  kinetic  = K, e 1  the  s t i c k the  static coefficient  coefficient, ^  n+1 -  n +  x  v  J t+  of  hence:  -n + i  static coefficient  V  of f r i c t i o n to the  time  13  of s t a t i o n a r y contact of the a s p e r i t i e s and includes a s e l f - d i f f u s i o n mechanism to give temperature dependence along with basic viscous creep.  14  CHAPTER I I I  I I I . l APPARATUS  I n t h e i n t e r e s t s of h a v i n g compact equipment and to f a c i l i t a t e the study of t h e v a r i a t i o n i n f r i c t i o n w i t h l e n g t h of r u n - i n the apparatus was d e s i g n e d w i t h a r o t a t i n g d i s k as the moving s u r f a c e . system parameters  A wide range o f  such as s u r f a c e v e l o c i t y , normal l o a d , s p r i n g c o n s t a n t s  and atmospheric c o n d i t i o n s were g e n e r a l r e q u i r e m e n t s .  Hence the apparatus  was d e s i g n e d w i t h t h r e e main s e c t i o n s ; a v a r i a b l e speed t u r n t a b l e , a c a n t i l e v e r beam t o p r o v i d e b o t h normal l o a d and s p r i n g f o r c e , and a d e f l e c t i o n measuring  d e v i c e t o determine the f r i c t i o n f o r c e . ( F i g . 2) The  r o t a t i n g d i s k was supported by b a l l b e a r i n g s and was d r i v e n  by a D.C. servo-feedback motor through a s e r i e s o f spur r e d u c t i o n gears and a b e v e l gear. load to f u l l - l o a d  T h i s motor had speed r e g u l a t i o n b e t t e r than 5 $ from noc o n d i t i o n s and the response was n e a r l y i n s t a n t a n e o u s so  that  the  city. rpm,  s t i c k - s l i p v i b r a t i o n would not  The t u r n t a b l e thus  in/sec.  speed  c o u l d be v a r i e d  providing a typical The t u r n t a b l e  one  cantilever  e n d a n d was  overhung the  i n the  so  i n the  make  made  so  ball  specimen h o l d e r .  beam was that  the  w h i c h i m p o s e d a moment  compact  cover  c o u l d be  were m a n u f a c t u r e d  force  per u n i t  various  from 0  one  the  on t h e  velo-  in/sec  studs  to  mounted on trace  of  the  to  give  or  joint  all  5 1 the  on a  5 lb.  running tracks  on t h e  specimen  rotating  disk. and  retaining  specimens  to  of  the  interchangeability  of  beams  was v a r i a b l e .  This  loading  normal  awkward,  specimen. entire  the Also,  lb/in  changed.  a  remove-  control. to  The normal  cantilever-load  obtained.  of  apparatus  atmospheric  from 4  was  arrangement  l o a d was  kept  canti-  T h e beam  a p p l i e d b y means  requirements.  d i s k c o u l d be  holder  i n diameter  a l l o w e d the  spring constants  By s h i f t i n g the  in.  mounted  The l e n g t h  system.  the  the  i n a conical  a n d l o a d was  initial  for  on t h e  3/8  times.  system  appearing  at  The specimen  curvature  even though the  d e f l e c t i o n measured to  end.  provided which would allow f o r  Beams  variable  of  although  satisfying  of  -3- i n .  of  d i s k at  v i b r a t i n g mass c o n s t a n t  thus  type  low f r i c t i o n b e a r i n g s  l o a d i n g arrangement,  able  0.001  specimen h o l d e r  running track  either  spring constant  weights the  the  other  and p r o v i s i o n f o r  on two  The  of  rigid  b e a r i n g which rode  c o n t a c t w i t h the adjustable  the  radius  as  This  pivoted  kept  the  surface  in a drilled  excellent  lever  that  same s e n s e  specimens, had a f l a t  were mounted cup  of  providing a continuous  beam h a d a d e t a c h a b l e  clamped s o l i d l y at  turntable  v i b r a t i o n was The  surface  i n f i n i t e l y f r o m 0 . 0 0 5 rpm t o  s p e e d was m o n i t o r e d b y means thus  the  recorder. The  at  adversely  running track v e l o c i t y  disk which tripped a micro-switch chart  affect  42  lb/in  load  was  mechanism  Balance Weight Low F r i c t i o n P i v o t Bearings  Weights  C a n t i l e v e r Beam  Specimen Holde Turntable  Speed C o n t r o l U n i t  F i g . 2—Diagram of Apparatus  16 Of the many devices a v a i l a b l e to measure the d e f l e c t i o n of the beam i n order to determine the f r i c t i o n f o r c e , a modified M e t r i s i t e displacement transducer provided the greatest f l e x i b i l i t y and accuracy of measurement. In order to reduce the moving mass and eliminate  f r i c t i o n i n the transducer  so as not to a f f e c t the motion of the beam, a t e f l o n s l i d e r was manufactured to replace the o r i g i n a l s t e e l one. The M e t r i s i t e transducer, of the moving E - c o i l design, provided a useable range of solved displacements accurately  in» beam d e f l e c t i o n and r e -  to 0.0001 i n .  I I I . 2 INSTRUMENTATION  The M e t r i s i t e displacement transducer was mounted on a s l i d e r so that the u n i t could be mechanically zeroed i n the e l e c t r i c a l n u l l p o s i t i o n before a t e s t was begun.  I t was found that w i t h a l l beams the output from  the transducer was proportional  to the displacement of the specimen. The  d e t a i l s of the c a l i b r a t i o n of the u n i t are contained i n Appendix I . The transducer was excited by a Daytronic d i f f e r e n t i a l transformer i n d i c a t o r (Model 300 BF) which also analyzed the output and provided a v i s u a l reading.  The analyzed s i g n a l from the Daytronic was f e d to an  oscilloscope f o r quick analysis of the r e s u l t s and t o an E d i n modulator a m p l i f i e r (Model 8108 A) which provided e x c i t a t i o n f o r a Brush dual channel oscillograph.  One channel of the o s c i l l o g r a p h displayed  a displacement-  time graph of the specimen motion while the other channel monitored the turntable v e l o c i t y .  17 I I I .3  Initially the  effect  curves  of  surface  as w e l l as  phere.  steel-on-steel  Hence  to  the  consistent metals.  was  study  first  the  a disk  results was  It  was  would be  properties  the  the  appeared  results  reported  for  of  became  annealed.  it  if a  also  the  this  and t h i s that  less  the  workers  Where  zinc,  of  (^77).  determine  samples  the  field  the  were  to R  of  53.5  the  and  c friction  reversed,better  steel  hardened  was v e r y  try  factor  for  to  R  55 c  friction  important  properties  specimens of  comparison  gold,  silver,  fabricated  o b t a i n e d were  and of  made  alloying  invariably dealt  iron,  metals  in-  non-homogenity  fundamental  a n d cadmium w e r e  applicable  1020)  used.  Also,  of  atmos-  (C  The r e s u l t a n t  was d e c i d e d t o elements  stick  ground and l a p p e d .  the  friction-couple  i n the  steel  and a n n e a l e d  s y s t e m was  it  of  combination yielded very  of Keewatin  important.  Hence h i g h p u r i t y  a mild  yielded inconsistent  d i s k o f C 1020  determine  and c o n t r o l l e d  f r i c t i o n couple  specimen  friction  by other  purposes.  t r i e d was  to  friction-time  lubricants  probably because  designed to  aluminium, copper,  test  that  By using m e t a l l i c  hardness  pure m e t a l s . indium,  was  coefficient  from pure m e t a l s . material  so  annealed  experiment  static  that  obtained  it  on t h e  d i s k which had been  tried,, yet  w e r e much b e t t e r  Since since  steel  were r u n i n o r d e r  of A t l a s N u t h e r m h a r d e n e d  thought  r u n on a f u l l y  of  friction-couple  immediately obvious  g r o u n d a n d l a p p e d was results.  and wear  effect  f r i c t i o n properties  Next  experiments  contamination  specimen r u n n i n g on a m i l d It  SPECIMENS  and  purposes, with nickel,  into  the lead,  specimens  fully  18 I I I . 4 T E S T PROCEDURE  A to  standard  o b t a i n the  specimens. the  test  most  consistent  Experiments  turntable  procedure,  s h o u l d be  f i n i s h was  were  also  10-12  ground f l a t  finishing  ethyl  A t the  alcohol  and c l e a n e d  possible  ensure  that  Even w i t h the was  slip  found  that  the  the  a u  — t s  curve.  d i s k and r e f i n i s h i t , and so  on.  one r e v o l u t i o n w i t h o u t values the  to  for  run the run.  ensure  d i s k v a r i e d by too  results  lapping  agent.  cleaned with  static  plate  The  The  specimens  the  lapped  way i t  was  be u s e f u l average  runs.  surfaces  f r i c t i o n d u r i n g the  to  to  experimental  u n i f o r m i t y of  much t o  result-  tri-  d i s k was  In t h i s  m e t h o d t r i e d was  |J. G -  t  section  g  the  It  one  constant  average  the  static  was n o t p o s s i b l e  extent.  curve changed  After a trial of  then  d i s k at  r e f i n i s h i n g because  a great  p a r a m e t e r s were  conclusive. small  obtained  f r i c t i o n around the  second v e l o c i t y  system  best  finish.  u n i f o r m between to  all  immediately run a f t e r  next  were  methods  in  stick-  pre-  the  values  s  the  for  for  a cutting  were  every  the  taken  The f i r s t  static  results  surfaces  values  for  friction  before  precautions  phenomenon a r o u n d t h e  dicting  showed t h a t  and w e r e  completion of  debris  it  followed for  a n d l a p p e d on a s p e c i a l  The s u r f a c e s  remove w e a r to  trying various  ( j , i n . RMS a n d h a d no d i r e c t i o n a l  and t h e n  process.  was  and a l u m powder as  g r o u n d and l a p p e d .  chlorethylene  after  friction results,  with steel-on-steel  with medicinal petroleum o i l ant  determined  the wear  p r i m a r i l y because enough to  and e r r o r  running track  were u s e d t o  remove for  r u n the  d i s k more  track  influenced  method gave v e r y  it  was  runs  found that  o b t a i n the  (-1  -  if t  a than the  poor  i n r e f i n i s h i n g the  make a c o m p a r i s o n o f  procedure  then  f r i c t i o n values  to  However t h i s  velocity,  disk  the  ina  very  curve  19 the r e s u l t s were r e a s o n a b l e .  Hence the procedure was  t o take two or t h r e e  s t i c k - s l i p c y c l e s a t one v e l o c i t y , t h e n change the v e l o c i t y and take t h r e e more s t i c k - s l i p c y c l e s and so on u n t i l a f u l l range of v e l o c i t i e s had been c o v e r e d so t h a t the r e s u l t s o b t a i n e d i n c l u d e d times of s t i c k from i n the o r d e r of f i f t y  seconds  to pure s l i d i n g .  T h i s method gave a u. s  t  curve s  o b t a i n e d from l e s s t h a n o n e - s i x t h of a t u r n t a b l e r e v o l u t i o n and a l l o w e d t h r e e o r f o u r d i f f e r e n t c u r v e s to be taken f o r one r e v o l u t i o n o f the t u r n t a b l e thus e l i m i n a t i n g r u n n i n g more than once over the wear t r a c k . v a l u e f o r the k i n e t i c c o e f f i c i e n t of f r i c t i o n was t a b l e v e l o c i t y when the specimen was  The  taken a t the lowest t u r n -  s l i d i n g without v i b r a t i o n .  To study the e f f e c t of r u n - i n on the s t a t i c f r i c t i o n v a l u e s , u. - t curves were o b t a i n e d from the f i r s t , second and t e n t h c o n s e c u t i v e s s ' r e v o l u t i o n o f the t u r n t a b l e . little  I t was  change i n f r i c t i o n v a l u e s was  specimens i t was  found t h a t a f t e r t e n r e v o l u t i o n s v e r y apparent.  F o r the s t e e l and  copper  d e c i d e d t o t r y v a r i o u s runs u s i n g e t h y l a l c o h o l as a p r o -  t e c t i v e f i l m f o r the running t r a c k t o i n h i b i t o x i d a t i o n of the s u r f a c e s and wear d e b r i s .  The  e f f e c t of e t h y l a l c o h o l as an a c t i v e c h e m i c a l o r h y d r o -  dynamic l u b r i c a n t was The  thought to be  e f f e c t of d i f f e r e n t l o a d s and s p r i n g c o n s t a n t s was  the copper and s t e e l specimens. system was  negligible.  a s p r i n g of 42,2  studied for  F o r a l l o t h e r specimens t h e standard  l b / i n s t i f f n e s s and a l o a d of 5.05  l b . , except  indium where the f r i c t i o n a l v a l u e s were so h i g h t h a t t h e l o a d had to be reduced t o 3.55  l b . t o ensure l i n e a r i t y of r e s u l t s .  The s t a n d a r d u n i v e r s a l  j o i n t t h a t p r o v i d e d i n t i m a t e specimen c o n t a c t w i t h the d i s k proved u s e l e s s w i t h l e a d , g o l d and indium because  these m e t a l s deformed so r e a d i l y  f l a t edges r e s u l t e d d u r i n g t h e e x p e r i m e n t a l r u n s . specimen h o l d e r was  Thus a s p e c i a l  made t o ensure t h a t t h e s e specimens would  that  rigid  remain  20  perpendicular to the running surface. A l l tests were conducted at 80 °F room temperature.  The magnitude  of s t r u c t u r a l damping was checked by means of free v i b r a t i o n of the beam. The damping was found to be of a combined coulomb and viscous nature and was negligible.  Typical values of the damping c o e f f i c i e n t s were 0.005 l b - s e c / i n  f o r the 7.4 l b / i n beam and 0.01 l b - s e c / i n f o r the 42.2 l b / i n beam. The equivalent v i b r a t i n g weight was determined t o be 0.24 l b . A l l u, - t S  S  curves presented i n the r e s u l t s are t y p i c a l of a s e r i e s of experimental runs and i n most cases only one curve i s given f o r each p a r t i c u l a r system i n order to preserve c l a r i t y of the data.  21  CHAPTER IV  IV. 1 RESULTS  Steel  specimen The  the  first  step i n d e t e r m i n i n g t h e f r i c t i o n parameters was t o r u n  s t e e l specimens f o r as many c o n s e c u t i v e  found n e c e s s a r y t o determine a s t a b l e v a l u e f r i c t i o n w i t h a f u l l y r u n - i n wear t r a c k .  t u r n t a b l e r e v o l u t i o n s as was f o r the s t a t i c  c o e f f i c i e n t of  F o r a specimen o f annealed C 1020  the v e l o c i t y was 0.03 i n / s e c and the t u r n t a b l e f i n i s h was 13|xin. s t a r t of r u n - i n .  RMS  a t the  A f t e r t e n r e v o l u t i o n s the s t a t i c f r i c t i o n v a l u e had  s t a b i l i z e d and the wear t r a c k was 15-18p,in. a c r o s s  the t r a c k . ( F i g . 8)  For  the hard specimen of A t l a s Keewatin, a l s o r u n a t 0.03 i n / s e c , the s t a t i c c o e f f i c i e n t of f r i c t i o n s t a b i l i z e d a f t e r t h r e e r e v o l u t i o n s .  ( F i g . 9)  f r i c t i o n - v e l o c i t y curve i n t h e s t i c k - s l i p r e g i o n f o r t h e hardened specimen on the f u l l y annealed t u r n t a b l e was a l s o c o n s i d e r e d .  The  steel  The k i n e t i c  22 friction  coefficient  was  calculated  from Cameron s 1  K  Pure  sliding  of 42,2  resulted  lb/in The  static  time  hardened The  of  was  annealed turntable  of  5.05  The  and 7 . 4  of  constants  The lubricated  in/sec  with a  soft  s p e c i m e n were  so  erratic  any i n f o r m a t i o n o b t a i n e d  track  (J,  G  -  t  curves  concerning  for  RMS a f t e r  Copper  specimen The  p,  s  across run-in  -  t  system  a lubricant  to  g  hardened  of  For  obtain  the for  7.4  a  one r e v o l u t i o n a n d  on t h e  static  specimen by experimental  determined.  b o t h the  for  of  specimens  the  i n the  revolutions,was  track  lubricated  copper  run-in  of  the  lb/in,  fricwith  3.55  (Figs.  b y not  more  and u n l u b r i c a t e d  The e f f e c t surfaces  of 42,2  of  runs  lubricated  s p e c i m e n was  lb.  s p r i n g - l o a d system  run-in  lb  .13 &  14)  and u n -  barely noticeable.  had i n c r e a s e d  and 3.55  of  another  coefficient  also  ten  at  12)  r u n - i n were steel  easily.  The e f f e c t  l b and 7.4  lb/in  stable  at  ll)  5.05  wear  effect  (Fig.  lb/in,  the  relation  and the  15 & 16)  impossible  for  lb.  (Fig.  the  determined by running t e s t s  results  alcohol  c o n d i t i o n s , even a f t e r  roughness  spring-load  of  of 42.2 of  was  3.55  spring  10)  However the  disk.  f o r the  and l o a d s  wear  set  ethyl  The e f f e c t s  lOpdn.  (Figs,  than 0,12  the  that  lb/in,  the  i n f l u e n c e of  respectively.  as  lb  was d e m o n s t r a t e d  average  for  l o a d and s p r i n g c o n s t a n t  ten revolutions  spring  (Fig.  f r i c t i o n values  d e t e r m i n e d b y t a k i n g one  tion  greater  s t i c k was m e a n i n g l e s s .  lb/in,  after  lb.  +  s p e c i m e n were u n i f o r m and c o u l d be d u p l i c a t e d r e l a t i v e l y  effect  42.2  5.05  ^s  min  velocities  a n d l o a d of  when r u n o n t h e the  at  T  c  W  =  formula:  lb/in  s t i c k - s l i p v i b r a t i o n since  than cases.  obtained for of  was  ethyl  a  alcohol  demonstrated.  and 5.05 after  The  lb i t  a very  few  was  23 c y c l e s the s t i c k - s l i p d e t e r i o r a t e d i n t o pure s l i d i n g even f o r s u r f a c e v e l o c i t i e s of 0.0005 i n / s e c .  The k i n e t i c c o e f f i c i e n t of f r i c t i o n was  determined t o be v e l o c i t y independent f o r a l l c o n f i g u r a t i o n s . was e v i d e n t Iron  A wear t r a c k  and c o n s i s t e d p r i m a r i l y o f copper d e b r i s on the running  surface.  specimen A n i r o n specimen, F e r r o v a c  t i o n s , 7.4 l b / i n ,  E , was r u n f o r two s p r i n g l o a d  2.1 l b and 42,2 l b / i n , 5.05 l b .  configura-  The c o r r e s p o n d i n g JJ,  - t  curves were o b t a i n e d  f o r each s p r i n g l o a d combination i n c l u d i n g one arid t e n  revolutions run-in,  ( F i g s . 17 & 18)  oxide.  The wear t r a c k c o n s i s t e d of b l a c k  iron  The k i n e t i c c o e f f i c i e n t of f r i c t i o n was v e l o c i t y independent.  Cadmium specimen F o r a s p r i n g - l o a d c o n f i g u r a t i o n of 42.2 l b / i n and 5.05 l b the u,  - t s  curves were o b t a i n e d  f o r one and t e n r e v o l u t i o n o f r u n - i n .  (Fig.19)  s  A wear t r a c k o f cadmium p a r t i c l e s was e v i d e n t kinetic given  after f u l l  run-in.  The  c o e f f i c i e n t o f f r i c t i o n appeared t o be v e l o c i t y independent.  For a  s u r f a c e v e l o c i t y the magnitude o f t h e s t a t i c c o e f f i c i e n t of f r i c t i o n  decreased s l i g h t l y d u r i n g about f i v e  s t i c k - s l i p u n t i l a stable value  was reached a f t e r  cycles.  Lead specimen A r i g i d specimen h o l d e r was n e c e s s a r y t o p r e v e n t e x c e s s i v e mation of the edges of t h e l e a d specimen d u r i n g s o f t t h a t any p r e s s u r e  the t e s t .  a spring-load  obtained  The l e a d was so  on an edge caused immediate p l a s t i c d e f o r m a t i o n thus  changing the o r i e n t a t i o n of t h e specimen w i t h r e s p e c t For  defor-  to.the  running  track.  system o f 42.2 l b / i n and 5.05 l b the U. - t curves were s s  f o r one and t e n r e v o l u t i o n s of r u n - i n .  cadmium r e s u l t s the v a l u e s  ( F i g . 20)  S i m i l a r t o the  o f t h e s t a t i c c o e f f i c i e n t ' d e c r e a s e d with an  24 i n c r e a s i n g number of c y c l e s of s t i c k - s l i p a t c o n s t a n t  velocity.  However, t o  reach a s t a b l e l i m i t took u s u a l l y t e n t o twenty c y c l e s and i n some cases the s t i c k - s l i p phenomena d i e d out c o m p l e t e l y and pure s l i d i n g r e s u l t e d .  The  k i n e t i c c o e f f i c i e n t o f f r i c t i o n a l s o appeared v e r y v e l o c i t y s e n s i t i v e ; i n f a c t , the f r i c t i o n v a l u e  rose p r o g r e s s i v e l y w i t h s l i d i n g speed u n t i l a  l i m i t i n g v e l o c i t y of 1 i n / s e c was reached by the a p p a r a t u s . p o s s i b l e t o o b t a i n an a c c u r a t e value  I t was im-  u.^ - V curve because the k i n e t i c f r i c t i o n  changed e r r a t i c a l l y depending on the p o s i t i o n on the t u r n t a b l e .  A  very  heavy wear t r a c k was composed o f pure l e a d . Aluminium specimen The  aluminium specimen was unusual i n t h a t s l i p - s t i c k v i b r a t i o n  c o u l d not be induced f o r a s p r i n g o f 7.4 l b / i n and l o a d s  of 2.1 l b or 3.55  l b or f o r a s p r i n g o f 42.4 l b / i n and a l o a d of 5.05 l b .  The specimen  slid  smoothly f o r over t e n r e v o l u t i o n s even though a v e r y prominent wear t r a c k of white aluminium oxide d e p o s i t e d  itself  on the t u r n t a b l e .  The k i n e t i c c o -  e f f i c i e n t of f r i c t i o n averaged 0.30 around t h e d i s k and d i d n o t change w i t h run-in. not  Even manually induced v i b r a t i o n a t t h e s l o w e s t s u r f a c e v e l o c i t y d i d  cause any s t i c k - s l i p v i b r a t i o n i n d i c a t i n g t h a t the specimen was i n a  stable c o n f i g u r a t i o n while Zinc  sliding.  specimen F o r a s p r i n g - l o a d c o m b i n a t i o n o f 42.2 l b / i n and 5.05 l b the u  curves were determined f o r t h e z i n c specimen.  ( F i g . 2 l ) No  s  - t  s  noticeable  d i f f e r e n c e i n t h e curves was obvious even a f t e r t e n r e v o l u t i o n s o f the t u r n t a b l e and t h e k i n e t i c c o e f f i c i e n t of f r i c t i o n remained f a i r l y through a wide v e l o c i t y range. on the wear t r a c k a f t e r r u n - i n .  constant  A s l i g h t amount of z i n c i d e b r i s was  evident  25 Nickel  specimen The (J,  s  - t  s  curves f o r n i c k e l were determined a f t e r one and t e n  t u r n t a b l e r e v o l u t i o n s f o r a s p r i n g - l o a d system of 42.2 l b / i n and 5.05 l b . ( F i g . 22) itself  There was no n o t i c e a b l e wear t r a c k a f t e r r u n - i n and the specimen  showed v e r y l i t t l e wear.  The k i n e t i c  c o e f f i c i e n t of f r i c t i o n r e -  mained c o n s t a n t . Silver  specimen I t was d i f f i c u l t to determine s t a t i c f r i c t i o n v a l u e s f o r the s i l v e r  specimen because i t e x h i b i t e d an unusual phenomenon which might be termed rapid creep.  D u r i n g the s t i c k regime the specimen d i s p l a c e m e n t - t i m e curve  should have had a c o n s t a n t s l o p e ( t h e s u r f a c e v e l o c i t y ) but f o r s i l v e r t h e slope changed r a p i d l y i n a p o s i t i v e d i r e c t i o n j u s t b e f o r e s l i p (Fig.  commenced.  3)  6  Fig. 3 Graph of S l i d e r D i s p l a c e m e n t V e r s u s Time  T a k i n g the s t a t i c  c o e f f i c i e n t a t the p o i n t where s l i d i n g commenced, the  u, - t c u r v e s f o r one and t e n r e v o l u t i o n s o f the t u r n - t a b l e were o b t a i n e d s s f o r a s p r i n g - l o a d combination of 42.2 l b / i n and 5.05 l b . ( F i g . 23) wear t r a c k was  evident.  A heavy  26  Gold  specimen S i m i l a r to the l e a d specimen a r i g i d specimen h o l d e r was  f o r the g o l d specimen i n order corners.  The  to p r e v e n t e x c e s s i v e  u, - t curves were o b t a i n e d "s s  f o r one  system of 4 2 . 2  the t u r n t a b l e w i t h a s p r i n g - l o a d  A v e r y prominent wear t r a c k r e s u l t e d a f t e r  necessary  deformation of and  the  ten r e v o l u t i o n s  l b / i n and  5.05  of  (Fig.24)  lb.  run-in.  Indium specimen The  r i g i d specimen h o l d e r  was  a l s o used f o r the indium specimen  because indium deformed even more r e a d i l y than l e a d . combination of 4 2 . 2 efficients  l b / i n and  3.55  were extremely h i g h ,  i n the  s u r f a c e v e l o c i t i e s , around 0 . 0 0 1 The  l b the  static  order  For  and  a  spring-load  dynamic f r i c t i o n  of u n i t y .  ( F i g . 25)  the d i s p l a c e m e n t would reach some s t a b l e v a l u e s l i p would d i s a p p e a r .  By  c o u l d be  a sufficient  sliding  commenced.  At  i n c r e a s i n g the  surface v e l o c i t y ,  v e l o c i t y was  tude of s t i c k - s l i p would d i m i n i s h u n t i l  except t h a t  at low v e l o c i t i e s and stable  stick-slip  a stable value  v e l o c i t y , the was  ampli-  obtained.  The  wear t r a c k , a f t e r t e n r e v o l u t i o n s of the t u r n - t a b l e , c o n s i s t e d of a  f r i c t i o n d i d not  change by any  during  form a t c o n s t a n t  the  values  of  very  static  run-in.  r e l a t i o n s h i p between the  static  time of s t a t i o n a r y c o n t a c t would have  cothe  temperature: ^ s " ^k  where |3 = " " j y  The  l a r g e amount d u r i n g  T h e o r y p r e d i c t e d t h a t the e f f i c i e n t of f r i c t i o n and  run-in.  stick-  r e a c h e d a t which pure  S i m i l a r to l e a d , a t some constant  heavy l a y e r of indium d e p o s i t e d  slow  i n / s e c , indium e x h i b i t e d phenomenal c r e e p .  r e s u l t a n t d i s p l a c e m e n t - t i m e curve resembled s i l v e r ( F i g . 3 )  induced u n t i l  co-  a n  d  Kg  are  "  V.  some c o n s t a n t s  P  dependent on the r a t e e f f e c t s  of  27  plastic trend  deformation  of  theory.  the  of  the  experimental  T h e (J,  -  t  asperities p, s  curves  s  t  curves  agreed  contact.  w i t h the  The  shape  general predicted  by  s  for  the  various  metals  tested  showed t h a t  for  s  any p a r t i c u l a r  f r i c t i o n couple  were  displaced vertically  generally  i n physical  the  curves  were  of  p,  axis  on the  the  same b a s i c  shape  f r o m one a n o t h e r .  but Hence  s by taking  the  difference  Replotting  perimental  results - l o g (t  )  - p,. )  the  c o n s t a n t K g was 26  -  p. s  t  the  curves  curves  collapsed  plot  onto  on l o g - l o g a x e s  a  single  showed t h a t  plot.  the  ex-  s  the  slope  determined  at  of  the  linear  u n i t y time  of  by theory. l i n e was  stick  On a  log  |3 a n d t h e  value  w h e r e K g = p,  -  g  of  p.^*  38)  The are  - p.,,  d i d agree w i t h those p r e d i c t e d  (p,  (Figs.  the  p.  equations  from the  summarized i n T a b l e  l o g - l o g graphs  for  the  various, metals  tested  1,  I V . 2 D I S C U S S I O N OF RESULTS  An  examination  of  the  p,  -  t  s specimen  showed t h a t  slight.  S i m i l a r l y zinc  coefficient and s i l v e r specimens  of  wear  debris.  that  effect  final  phase  decreased  whereas  it  the  as  all  or  no  of  for  these  the  hardened  steel  the  for  the  the  zinc,  specimen  annealed  l e a d and z i n c  copper,  The  a wear  on p u r e  specimens  disk.  dynamic lead  gold  track, specimen  r u n - i n was much steel  was  cadmium,  n i c k e l and  left  sliding  after  and r u n - i n  with run-in.  specimens  friction-couple  cadmium,  change  with run-in  specimen r u n n i n g on the  steel,  for  s p r i n g - l o a d system  increased  r u n - i n was  The r e s u l t i n g  original the  of  of  showed l i t t l e  which i n d i c a t e d ,  the  seen  friction  specimens  that  from the  the  curves s  It  gave a c u r v e  different can  be  which,  RESULTS  DESCRIPTION  SPECIMEN Fig.  21  A t l a s Nutherm  One to Ten R e v o l u t i o n s , D r y  Fig.  22  A t l a s Nutherm  One t o Ten R e v o l u t i o n s ,  Fig.  23  Copper  One Rev, Run-in, D r y  Fig.  23  Copper  Ten Rev. R u n - i n , D r y  |i> — (Ji. = 0.030t ° ' s k 8 ji - ji, = 0,028t ° ' ji s - jik = 0.040t s ' ^ s ^k s ji - ji = 0.040t  Fig.  24  Copper  One Rev. Run-in, L u b r i c a t e d  ji  Fig.  24  Copper  Ten Rev. Run-in, L u b r i c a t e d  Ji  Fig.  25  Iron  One Rev. Run-in,  Fig.  25  Iron  Ten Rev. Run-in, /  Fig.  26  Iron  One to Ten Rev. Run-in,  Fig.  27  Cadmium  One to Ten Rev. Run-in, D r y  Fig,  28  Lead  One to Ten Rev. Run-in, D r y  Fig.  29  Zinc  One t o Ten Rev, Run-in, D r y  Fig.  30  Nickel  One Rev. Run-in, D r y  Fig.  30  Nickel  Ten Rev, Run-in, D r y  ji  - ji  = 0.025t  u  '  3 b  Fig.  31  Silver  One Rev. Run-in, D r y  ji  - ji  = 0.039t  U  '  1 Y  Fig.  31  Silver  Ten Rev. Run-in, D r y  ji  Fig.  32  Gold  One Rev. Run-in, D r y  - ji. = 0.042t O*^ s k s . j i - j i = 0.046t 0.25  Fig.  32  Gold  Ten Rev, Run-in, D r y  ji  Fig.  33  Indium  Ten Rev. Run-in, D r y  JI  Note;  K  K  /W w  Lubricated  u  7 4 = - ~ - , Dry = 7TT  »  K/ /W  D l  Q  5  , Dry  ji (i  3 i  u  = 0.038t  - Jl, a 0.018t k s = 0.043t  k  0  ,  1  6  s  p, - n, = 0.036t ° » s k s  42.2 &  s  [i. s  T  =  - ji  3 4  3 5  - H, = 0.029t ° ' s k s  4 1  - H, = 0.023t ° « k s ji - ji, = 0.030t ° ' s k s ji - ji = 0.065t s k s s  3 4  4 i i  = o.out.»-«  5  s  s b  k  g  - H, = 0.112t 0.086 k s - J i = 0.153t 0.061 k  g  I n A l l T e s t s the Running S u r f a c e was A n n e a l e d C1020 TABLE 1  to co  29 d i s r e g a r d i n g the dynamic c o e f f i c i e n t of f r i c t i o n , was independent of r u n - i n . T h i s i n d i c a t e d t h a t i f one of these pure metals were r u n t o g e t h e r  as a  f r i c t i o n - c o u p l e the r e s u l t a n t f r i c t i o n curves would be s i m i l a r to those were o b t a i n e d  when the metal was r u n on annealed s t e e l .  that  I r o n was the o n l y  m a t e r i a l which showed a dependence on the normal l o a d a l t h o u g h an e x p l a n a t i o n f o r t h i s e f f e c t i s not immediately a v a i l a b l e . The  e f f e c t of e t h y l a l c o h o l as a l u b r i c a n t was dubious and i t s  i n c l u s i o n i n the t e s t program was to determine the e f f e c t of removing the atmosphere from the wear t r a c k i n o r d e r  to p r e v e n t o x i d a t i o n of the s u r f a c e .  Thus t h e e f f e c t of r u n n i n g i n an oxygen-free environment c o u l d be determined. F o r the s t e e l specimen t h e r e was no d i f f e r e n t i n the u. - t curves w i t h s s r u n - i n and t h e u l t i m a t e v a l u e s obtained  f o r dry f r i c t i o n .  of f r i c t i o n c l o s e l y resembled the r e s u l t s  However, the copper specimen showed a marked  decrease i n k i n e t i c f r i c t i o n w i t h r u n - i n f o r the l u b r i c a t e d c o n d i t i o n y e t the i n i t i a l  s t a t i c f r i c t i o n values  than i n the u n l u b r i c a t e d  state.  were much h i g h e r  Oxidation  i n the l u b r i c a t e d s t a t e  of the s t e e l was p r o b a b l y un-  a f f e c t e d by the e t h y l a l c o h o l because s u f f i c i e n t oxygen was trapped i n the f l u i d to e f f e c t f u l l  o x i d a t i o n of the wear d e b r i s .  Hence t h e r e was no  n o t i c e a b l e d i f f e r e n c e i n t h e u, - t c u r v e s f o r the l u b r i c a t e d and uns s lubricated conditions. requirements f o r f u l l contact  from suspended a i r i n the l u b r i c a n t and, as a  t u r n t a b l e r e v o l u t i o n showed a marked i n c r e a s e i n f r i c t i o n  over the u n l u b r i c a t e d  c o n d i t i o n because metals i n c o n t a c t w i t h o u t an  oxide s u r f a c e f i l m tend to c o l d weld. creased,  oxygen  o x i d a t i o n of the wear p a r t i c l e s and a s p e r i t i e s i n  c o u l d n o t be o b t a i n e d  r e s u l t , the f i r s t values  However, f o r the copper specimen, the i n i t i a l  As the number o f r e v o l u t i o n s i n -  g r a d u a l l y the wear d e b r i s became o x i d i z e d and t h e s t a t i c  c o e f f i c i e n t s f e l l to a v a l u e  equal to f u l l  friction  r u n - i n f o r the u n l u b r i c a t e d  case.  30 A l u m i n i u m was stick-slip which  phenomenon.  surrounded  the  were p r o b a b l y o x i d e the  same manner  dependence the  of  coefficient  slip  as  the  conditions  efficient  Because  particles the  other  hardness  of  of  f r i c t i o n was  of  the  t e s t e d which would not  a very  the  and s t r o n g  exhibit  Further  measurably  immediately  oxide  plastic  H e n c e t h e r e was  aluminium and i t  test.  exhibit  i n contact with the  which would not  not  criterion  coherent  asperities  specimens.  imposed by the  and t h i s  tests  larger  eliminated  the  the  disk  deformation  determining the  higher  than  would be  the  the  to  the  any |i  the  under  static  kinetic  co-  p o s s i b i l i t y of  stick-  t  to  the  which,  curves  results  fact as  that  stick-slip  velocity  of  graphic  faces with different  kinetic  coefficients  sliding.  resisting  from v e l o c i t y obtained  This higher to  Thus,  of  for  force  sensitive  specimen  Hence be  shape  from  materials.  f a i r l y large  could not  than  for velocity  could  be  crystals  of  would p r e s e n t - d i f f e r e n t  lead  greater  amplitude  a different  lead  much  the  independent  from the  consists  decrease  f r i c t i o n properties.  friction  s p e c i m e n was force  p r o b a b l y w o u l d have  lead  the  role  phenomenon.  providing a resisting  wear p r o c e e d e d ,  of  the  from the  surface v e l o c i t y .  obtained  erratic  and i n d i u m p l a y e d an i m p o r t a n t  d a m p i n g and w o u l d t e n d  given  -  thus  d u r i n g normal  non-linear at  The  orientation  lead  f r i c t i o n values  disk velocity  t h a t w h i c h would be  attributed  of  s l i p p o r t i o n Of s t i c k - s l i p  of v i b r a t i o n materials,  dependence  static  encountered  similar  the  random  crystallostatic  predicted  and  with  great  accuracy. The r a p i d could  in  time  stick-slip  showed t h a t than  layer  steel  little  would not  the  occurring.  During  is  only material  specimen  The v e l o c i t y in  the  o n l y be  creep e f f e c t  expected from very  evident  i n the  silver  ductile materials.  and i n d i u m However,  the  specimens gold  and  31 lead  specimens d i d n o t e x h i b i t  a factor. for at  E x a c t l y why t h e r e  this  phenomenon t h u s  s h o u l d be a sudden r e l a x a t i o n  s i l v e r and i n d i u m i s n o t known. which  was  sliding  so g r e a t  s h o u l d have  that  plastic  t i o n broke the surface  e l i m i n a t i n g d u c t i l i t y as  Perhaps  i s shear  the m a t e r i a l s  reached  commenced y e t a d h e s i o n b e t w e e n t h e  flow  strength the point  asperities  commenced i n t h e b u l k m a t e r i a l u n t i l  bonds.  This  mechanism reseumbles  large  scale  deformajunction  growth. I n p r e v i o u s work s e v e r a l agreed  fairly  well  with  authors  the values  obtained experimental  f o r t h e \i -  t  curves  s thesis,  ( F i g . 39) D o k o s ( 3 )  high load  on a s o f t  steel  results  presented  which  i n this  s  obtained f o r a soft  steel  specimen running under  disk:  0 24 M,  s  Similarly  i n a study o f the time  gave r e s u l t s  11, = k  0.092t s  dependence o f s t a t i c  f r i c t i o n Spurr  (6)  f o r i n d i u m on g l a s s ,  n ^1 .ji  a  -  ^  =  -  n, = k  0.049t  s  -  U  d l  and f o r z i n c o n g l a s s : U. s However S p u r r d e t e r m i n e d the s t a t i c loading load  0 "SI  0.012t s  coefficients  of f r i c t i o n f o r indium by  the specimen f o r a predetermined l e n g t h of time,  and a p p l y i n g  a tangential  force.  then removing the  P r o b a b l y the v a l u e s  s h o u l d have  been  much h i g h e r . From d a t a at  high  p r e s e n t e d b y Pomey e t a l , ( 8 )  f o r hardness  tests  temperatures: o  where a i s t h e y i e l d  strength  = 54.7t ~ s  of t h e m e t a l .  0  ,  1  6  ( K i p s / . 2) xn '  v  r  1  Combining  t h i s with the  of  steel  32 relation: ^  »*8  * a"  from the theory and taking an i n t e r f a c e shear s t r e s s value of approximately 5 K i p s / . 2. xn r  1  A  >*. - he -  i ° '  A  .  U  0.16  This compares reasonably w e l l w i t h r e s u l t s obtained experimentally i n t h i s thesis: H  - n  g  n  04.  = 0.030t *^ U  k  8  S i m i l a r data from Bowden and Tabor (5) taken from i n d e n t a t i o n hardness t e s t s on indium ( F i g . 4) y i e l d e d the r e l a t i o n . 0.83t -°s  095  a  x  (Kg/ 2) mm mm  2 Assuming an i n t e r f a c e shear stress of approximately 0.11 Kg/mm" then: ^  8  - ^k  =  0  * £  0.1  l t  0 1.8  1.6  log p (Kg/mm )  T T.4_ 4  100°C  1.2 0  1 log t  2  (sees)  F i g . 4 - V a r i a t i o n i n y i e l d pressure with loading time f o r indium  33 The experimental r e s u l t s f o r indium gave: U  s  - u- - 0.153t °k  061  s  Data by Williamson (14) taken from i n d e n t a t i o n hardness t e s t s on workhardened gold y i e l d e d the r e l a t i o n , ( F i g . 5) a = 83.7t "°-'  074  B  (Kg/mm ) 2  Assuming an i n t e r f a c e shear strength of approximately 10 Kg/mm f o r the workhardened m a t e r i a l then:  The experimental r e s u l t s f o r gold i n the f u l l y r u n - i n c o n d i t i o n yielded: n  1 1 0  »*• - *k * ° -  1.60 I 1.0  1  1 2.0  1  . 0.086 s  112t  I  I  3.0 log t  '  •  4.0 (sees)  Fig.5 - V a r i a t i o n i n y i e l d pressure with loading time f o r work-hardened g o l d .  34  T h e r e f o r e the r e s u l t s  o b t a i n e d by independent a u t h o r s i n t h i s  field  of r e s e a r c h tend to support the t h e o r y t h a t the s t a t i c c o e f f i c i e n t o f f r i c t i o n v a r i e s w i t h the time of s t i c k i n the manner:  ^s  =  K  2  t  s  P  The e f f e c t of ambient temperature on the u,  - t  curves as p r e d i c -  t e d by t h e o r y can be determined from the f o r m u l a .  V - ^ k -  K  i  R  T  *  B  Rearranging:  In  = ja  ^ k K|t . I s P  Taking two  RT  temperatures Tg-^^ and s u b t r a c t i n g  gives:  SSL  Evaluating:  To determine the magnitude  of t h i s v a r i a t i o n ,  indium were used. Q=16 kcal/mole R=2 c a l / d e g mole 3=0.061 Assuming T^ i s the ambient  temperature (20°C) where =  1.00  IJ..  =  0.80  T  = 100°C  Ui s  k 2  l  t y p i c a l values f o r  Hence: P 1  0.061(16,000) H  = 0.80 + 0.20 e  2  L  2  9  3  _ _1_] 3  9  a  ^  V (i  = S  1.086  2  The change i s a p p r o x i m a t e l y 9$ f o r a 27$ change i n a b s o l u t e temperature  36  CHAPTER V  V.l  The  CONCLUSIONS  e x p e r i m e n t a l evidence v e r i f i e d the t h e o r e t i c a l p r e d i c t i o n  that  the v a r i a t i o n of the s t a t i c c o e f f i c i e n t of f r i c t i o n w i t h time of s t a t i o n a r y contact followed the general r e l a t i o n :  .  ^  "  "  where i n u s u a l p r a c t i c e f o r m e t a l s b o t h c o n s t a n t s K and j3 were l e s s than unity.  The e x p e r i m e n t a l v e r i f i c a t i o n was o b t a i n e d u s i n g the s t i c k - s l i p  phenomenon i n which the time dependence of s t a t i c f r i c t i o n p l a y s an i m p o r t ant r o l e .  F o r the v a r i o u s metals t e s t e d i t was noted t h a t except f o r the  v e r y d u c t i l e metals such as g o l d and indium the v a l u e s o f the c o n s t a n t s K and P were remarkably s i m i l a r when the r u n n i n g s u r f a c e was annealed In f a c t l i t t l e  e r r o r would r e s u l t i f ,  a g e n e r a l curve were used:  f o r unknown f r i c t i o n  steel.  characteristics,  The  e f f e c t of r u n - i n f o r the pure metals was  t h a t e v e n t u a l l y the  running t r a c k became coated w i t h wear d e b r i s and the f r i c t i o n - c o u p l e changed from a pure metal metal.  The u-  r u n on annealed  - t  f r i c t i o n parameters.  s t e e l to a pure metal running on a pure  curve changed a c c o r d i n g l y depending on the G e n e r a l l y , however, the s t a t i c  metal's  friction coefficients  decreased with r u n - i n . S i n c e e t h y l a l c o h o l f a i l e d to decrease  the s t i c k - s l i p phenomenon by  any a p p r e c i a b l e amount i t s e f f e c t as a l u b r i c a n t was gible. static  negli-  A l s o i t d i d n o t seem to have a pronounced e f f e c t on the v a l u e s of f r i c t i o n as r u n - i n p r o g r e s s e d i n d i c a t i n g t h a t oxide f o r m a t i o n  t i n u e s r e g a r d l e s s of atmospheric form.  c o n s i d e r e d t o be  con-  i n h i b i t o r s a l t h o u g h perhaps i n a m o d i f i e d  To prevent o x i d a t i o n would p r o b a b l y r e q u i r e the e l i m i n a t i o n of the  s u r r o u n d i n g atmosphere. The  static  pendent of l o a d and  c o e f f i c i e n t of f r i c t i o n g e n e r a l l y appeared  t o be  inde-  s h e a r i n g f o r c e but showed a s t r o n g dependence on the  r a t e of a p p l i e d shear f o r c e which agreed w i t h the t h e o r e t i c a l p r e d i c t i o n of j u n c t i o n area growth as a time dependent f u n c t i o n .  T h i s e f f e c t was  also  m a n i f e s t i n the r a p i d creep phenomenon i n shear e x h i b i t e d by some of the more d u c t i l e and c o h e s i v e m e t a l s . aluminium-steel  The  anomaly i n the t e s t s was  f r i c t i o n - c o u p l e which d i d not show any  the  form of r e l a x a t i o n  oscillation.  V.2  RECOMMENDATIONS FOR  FUTURE WORK  F u r t h e r r e s e a r c h should be c a r r i e d out i n t h r e e main a r e a s .  First,  38 a check on the e f f e c t s of humidity could be attempted.  The p l e x i g l a s s cover  constructed f o r the apparatus would provide an easy method of c o n t r o l l i n g the humidity.  A t the same time the temperature  could be v a r i e d to check the  t h e o r e t i c a l p r e d i c t i o n s f o r the change i n the s t a t i c c o e f f i c i e n t of f r i c t i o n values by using an e l e c t r i c a l l y heated t u r n t a b l e . Secondly, some attempt should be made to determine the e f f e c t s of surface f i n i s h and active chemical lubricants.  From the experimental r e s u l t s i n t h i s t h e s i s i t seems that the  surface f i n i s h d i r e c t l y a f f e c t s the s t a t i c f r i c t i o n v a l u e s .  T h i r d l y , there  seems t o be experimental v e r i f i c a t i o n that the determining f a c t o r i n the v a r i a t i o n of the s t a t i c c o e f f i c i n n t of f r i c t i o n i s not n e c e s s a r i l y the time of s t a t i o n a r y contact but rather the r a t e of a p p l i e d shear s t r e s s .  It is  suggested that f u r t h e r experimental work be conducted wherein the shear s t r e s s rate i s c o r r e l a t e d t o the s t a t i c f r i c t i o n v a l u e s .  39  APPENDIX I  Calibration  of the Beam, Transducer  and  Oscillograph  W i t h the beam i n i t s e q u i l i b r i u m displacement  p o s i t i o n and t h e s l i d e r on t h e  t r a n s d u c e r a t t a c h e d t o the beam, the n u l l p o s i t i o n  of t h e  t r a n s d u c e r was o b t a i n e d by moving the t r a n s d u c e r r e l a t i v e t o the beam. locking  After  t h e t r a n s d u c e r i n t h e n u l l p o s i t i o n a micrometer b a r r e l was a t t a c h e d  r i g i d l y t o t h e apparatus  w i t h the s p i n d l e  j u s t t o u c h i n g the specimen h o l d e r .  The micrometer was g i v e n 0.005 i n . increments  up to 0.10 i n . , i n c r e a s i n g and  d e c r e a s i n g , and t h e g a i n on the D a y t r o n i c i n d i c a t o r u n i t was a d j u s t e d u n t i l full  scale  d e f l e c t i o n was o b t a i n e d .  L i n e a r i t y of the beams was w i t h i n \f>  and h y s t e r s i s  e r r o r was i n s i g n i f i c a n t .  provided f u l l  s c a l e d e f l e c t i o n from 0.01 i n . t o 0.25 i n . specimen  ment u s i n g t h e i n i t i a l  calibration.  vided a reference f o r future  A t t e n u a t i o n of the i n d i c a t o r  unit  displace-  An i n t e r n a l c a l i b r a t i o n s i g n a l  pro-  resettings.  /With t h e t r a n s d u c e r c a l i b r a t e d f o r displacement  the s t i f f n e s s o f the  40 cantilever holder, after The to  beam was  A light  the  from the  at To  strain  was  a l i g n e d to  found to  maximum  the  were a p p l i e d t o  weights  used i n the  arms  the  loads  weight  allowed the  in  experiment  the  The modulator  unit  be  the  the  at  other  the  the  end to  specimen h o l d e r  stiffness  of  the  at  a  and,  weight-pan.  right  angles  specimen  dis-  beam was  normal  l o a d the  obtained.  maximum  error  s p e c i m e n h o l d e r was p l a c e d  analyzed by a Baldwin s t r a i n  the  weightpan.  T h e l o a d was  A q u i c k check  by c o n s i d e r i n g  the  frictionless  For  the  one beam l e n g t h u s e d i n t h e  were 0.70  lb,  system without  2,1 to  be  that  scale  3,55  the  calibrated  full  scale  deflection  balanced  load  lb. for  the  and  four  moment the  normal  experiment  the  A moveable  balance  the  two beams  used  calibration.  by a d j u s t i n g  deflection on t h e  the  v e r i f i e d that  l b and 5.05  statically  affecting  o s c i l l o g r a p h was  a m p l i f i e r so  lb,  bearings  on a  gauge a n a l y z e r  obtained for  about  corresponded-to'full  specimen  specimen h o l d e r  l i n e a r w i t h i n 2$ w i t h t h e  experiment.  were c o r r e c t .  normal  pull  end to  the  displacement.  determine  system  one  to  w e i g h t - p a n and d e t e r m i n i n g the  indicator  g a u g e r i n g w h i c h was  of  at  low f r i c t i o n p u l l e y ,  weights  loads  attached  By l o a d i n g the  stiffness  occurring  a  carefully  beam.  placement The  c o r d was  running over  c o r d was  d e t e r m i n e d b y a p p l y i n g a known f o r c e  the  on t h e  chart paper  g a i n on  the  displacement of  the  unit  oscillograph.  BIBLIOGRAPHY  W e l l s , J.H. " K i n e t i c Boundary F r i c t i o n " The E n g i n e e r (London), V o l . 147, 1929, p 454 Rabinowicz, E , "The Nature of S t a t i c and K i n e t i c C o e f f i c i e n t s o f F r i c t i o n " J o u r n a l of A p p l i e d P h y s i c s , No. 12, Vo. 222, 1951, p 1373 Dokos, S . J . " S l i d i n g F r i c t i o n under Extreme P r e s s u r e " J o u r n a l of A p p l i e d Mechanics, V o l . 13, No. 2, 1946, p A148 Rabinowicz, E . " F r i c t i o n and Wear of M a t e r i a l s " John W i l e y and Sons, New York, 1965 Bowden, F.P., Tabor, D. "The F r i c t i o n and L u b r i c a t i o n o f S o l i d s " O x f o r d , V o l . I I , 1965 S p u r r , R.T. "Creep and S t a t i c F r i c t i o n " B r i t i s h J o u r n a l of A p p l i e d P h y s i c s , Vo. 6, 1955, p 402 K o s t e r i n , J . I . , K r a g h e l s k y , T.V. " R h e o l o g i c a l Phenomina i n D r y F r i c t i o n " Wear, V o l . 5, 1962, p 190 Pomey, J . , Royez, A., Georges, J . P . "La Diirete a Chaud" Revue de M e t a l l u r g i e , L V I , No. 3, 1959, p 215 Howe, P.G., Benton, D.P., Puddington, I . E . "London-Van d e r Waal's A t t r a c t i v e F o r c e s Between G l a s s Canadian J o u r n a l of Chemistry, V o l . 33,'1955, p 1375  Surfaces  K o s t e r i n , J . I . , K r a g h e l s k y , I.V. " R e l a x a t i o n O s c i l l a t i o n i n E l a s t i c F r i c t i o n Systems" and Wear i n Machinery, V o l , 12, 1958, p 111  Friction  Bowden, F.P,, Leben, L . "The Nature o f S l i d i n g and t h e A n a l y s i s of F r i c t i o n " of the Royal S o c i e t y , V o l . 109, No. 938, 1939  Proceeding  Cameron, R. " F r i c t i o n Induced V i b r a t i o n " M.A.Sc. T h e s i s i n M e c h a n i c a l E n g i n e e r i n g U n i v e r s i t y of B r i t i s h Columbia, 1963  42 (13) D e r j a g i n , B.V., Push, V.E., T o l s t o i , D.M. "A Theory of S t i c k - S l i p S l i d i n g of S o l i d s " Proceedings of the Conference of L u b r i c a t i o n and Wear, London, October, 1957, p 265 (14) Williamson, B. P r i v a t e communication to C.A. Brockley.  F i g . 6 - General View of Apparatus  and  Instrumentation 4^ CO  2  6 8 Turntable Revolutions  4  10  F i g . 8 - Change of S t a t i c C o e f f i c i e n t w i t h Run-in-Annealed C1020 S t e e l Specimen on Annealed S t e e l D i s k .  0.3  >  o  <^  C\  r  )  0.2  0.1  2  4  6 8 10 Turntable Revolutions F i g . 9 - Change of S t a t i c C o e f f i c i e n t w i t h Run-in - Hardened A t l a s Nutherm S t e e l Specimen on Annealed S t e e l D i s k .  46  0.3  —«3  0.2  0.1  .04  .08  .12 .16 Sliding Velocity  F i g . 10 - K i n e t i c C o e f f i c i e n t as C a l c u l a t e d D u r i n g v s . S l i d i n g V e l o c i t y f o r A t l a s Nutherm.  (in./sec.)  Stick-Slip  F i g . 11 - A t l a s Nutherm Specimen Showing E f f e c t of S p r i n g - L o a d System One Rev. R u n - i n - A n n e a l e d S t e e l D i s k .  0.  0.  0.  r  A  0.  8  16  24  32  40  t  (sec.) s ' x  Fig,  13 - A t l a s Nutherm Specimen w i t h E t h y l A l c o h o l L u b r i c a n t - One Rev. - Annealed S t e e l D i s k .  Run-in  48  F i g . 15 - Copper Specimen Showing E f f e c t of Run-In - Annealed S t e e l Disk*  Legend: Q Ay  - One Rev.  Run-in  - Ten Rev. R u n - i n  0.40  0.35  0.30  0.25  0.20  8  16  24  F i g . 17 - I r o n Specimen Showing E f f e c t of R u n - i n F o r - Annealed S t e e l D i s k .  Iff  ST K/„, /W =  7.4  /2.1 y  t  (sec.)  "ft  Legend: Q  - One Rev.  Run-in  / \ - Ten Rev.  Run-in  ^^J5^^^  ii  J  i  A  6  aa  F i g . 18 - I r o n Specimen Showing E f f e c t o f Run—In f o r K/^ - Annealed S t e e l D i s k .  1  • 42.2 5.05  4 10  4*  t  (sec.) s ' x  Legend:  - One Rev,  Run-in  / \ - Ten Rev. R u n - i n 0.4C  0.35  0.30  0.251  0.20 16  24  32  40  K F i g . 20 - Lead Specimen Showing E f f e c t of R u n - i n f o r - Annealed S t e e l Disk.  /W  =  4-2 2  5.05  t  s  (sec.)  48  Legend: Q * \ V L i m i t s of D a t a  0.50  0.45  0.40  0.35  0.30  8  18  24 K  F i g . 21 - Z i n c Specimen f o r /W = - Annealed S t e e l D i s k .  Q  5  40  48 t  2  4-2  Q  32 (One t o Ten R e v o l u t i o n s )  (sec.)  Legend:Q - One Rev, Run-in / \ - Ten Rev.  Run-in  F i g . 22 - N i c k e l Specimen Showing E f f e c t o f R u n - i n f o r / W - Annealed S t e e l Disk. K  42.2 5.05  L e g e n d : © - One Rev, Run-In j\ - Ten Rev. Run-In  ————""  A  1  f •j  I /  0.4E  1  8  16  24  J  a 2"  F i g . 24 - G o l d Specimen Showing E f f e c t of R u n - i n f o r /W - Annealed S t e e l D i s k .  42.2 5.05  1.5  42.2 ©  -  5.05  (  A  R e v  *  R  u  n  _  I  n  )  7.4 A •  -  3 ^ 5 5 ( l Rev. Run-in) (10 Rev. Run-in) 3.55  1  o 0  ©  •  ^  ^  ^  ^  A 2.5  r^A  ji < - p, S  f75  6  K  = 0.0285t  0  ,  3  1  4  S  o7E  log ( t )  iTB"  g  F i g . 27 - A t l a s Nutherm L u b r i c a t e d Specimen on Annealed S t e e l D i s k . OS  co  A O"  - Ten Rev. Run-in One Rev. Run-in  (j,  S  _  u  K  =  0.04ot  °'  ^  3 7 2  {5j ^^^^^  1  log(Ug-fi )  C*3 ^ ^ ^ ^  k  , = 0.040t ° k  2 0 0  s  2.5  o  2" 1.5  0  0.5  1  1.5 log ( t ) s  F i g . 28 - Annealed Copper Specimen  on Annealed S t e e l D i s k . OS  0 -  1  A -  10 Rev, R u n - i n  Rev. R u n - i n  O  T (j, -u S  = 0.038(  s  ~  log(|i -ii ) g  K  C)  k  ^  —  ^ '  t 0 0 0  ^^  ©  '  2.5 - M, = 0.<)180t k  A  s  °'  3 8 4  si T.5  0  0.5  L  1 .5 log ( t ) g  Fig.  29 - Annealed Copper L u b r i c a t e d Specimen on A n n e a l e d S t e e l D i s k .  o  -  A -  One Rev. R u n - i n Ten Rev. Run-In  p.  a  0.352 - Li, = .0355t k s  ^  T  #\  «oi  x. = 0.043t k s  0.163  2.5  A  2  T.5  0  0.5  1  1.5 log ( t ) s  F i g . 30 - I r o n ( / f f = K  7 , 4  / 2 . l ) Specimen on A n n e a l e d S t e e l D i s k .  0  - One Rev.  A\  Run-In  - Ten Rev. Run-in  log(n -Li ) s  k  2.5  B  k  = 0.0228t  0  ,  3  4  0  s  ©  2 1.5  0  0.5  1  1. 5 log ( t ) g  F i g . 32 - Cadmium Specimen on A n n e a l e d S t e e l D i s k . C5 00  1.5  o A  - One Rev. R u n - i n - T e n Rev.  Run-in  = 0.042t  0  ,  2  5  1  s  ^  /K  log(M, -fi, ) g  k  i 2.5  M-  ©  - H  g  k  = 0.03SIt  0  ,  1  7  1  s  -==3s£—_  2SS  -  -  log ( t ) g  F i g . 36 - S i l v e r Specimen On Annealed S t e e l D i s k . to  1.5  o  --  A  -- T e n Rev. Run-in  One Rev, Run-in  u. - u. = s  k  0.3 12t ° - °  855  s  -  T  r i  n  10g(u. -+A ) s  s  - n = O.C(455t k  k  2.5  2"  0.249 ; s  o  1.5  0  0.5  ]  1.5 log ( t ) s  F i g . 37 - G o l d Specimen On A n n e a l e d S t e e l D i s k . co  5 _  o)  One to Ten Rev.  -O  A  A  1  A  0  o—  ©•  T ^ H  B  - Mfc = 0.153t°'  )614  (  lo (u. -u. ) g  g  k  2.5  2  T  0  0.5  1  1  log ( t ) s  F i g . 38 - Indium Specimen on A n n e a l e d S t e e l D i s k .  >  5  0  1.5  0.5  1.5  (•) - D o k o s -r s o f t  log(n -^ ) s  JOT  k  li,  -  s  Spurr LI  2.5  -  j*7*| -  Lt = 0 . 0 9 2 t ° ' k s  - m  = 0.049t  k  2  4  steel 4  ,  3  1  on glass _  "  0  s  Spurr ~ zinc ^s  on s o f t  i n d i u m on g l a s s  s -  steel  =  A  ° - °  1  0 1  2  . 0.505 t  s  1  1  2.5  lc5  log Fig.  I  39 -  Comparison D a t a ,  (t ) g  

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