UBC Theses and Dissertations

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UBC Theses and Dissertations

Some fundamental aspects of static friction Green, Marjorie Ann 1971

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SOME FUNDAMENTAL ASPECTS OF ST A T I C FRICTION b y MARJORIE ANN GREEN B.A.Sc., U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B r i t i s h C o l u m b i a , 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1971 I n p r e s e n t i n g 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 .of t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t p u b l i c a t i o n , i n p a r t o r i n w h o l e , o r t h e c o p y i n g o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . MARJORIE ANN GREEN D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a D a t e ^ V V W j k i°i , \<\"11  ABSTRACT The p r e s e n t r e p o r t s u m m a r i z e s t h e r e s u l t s o f an e x p e r i m e n t a l s t u d y o f s t a t i c f r i c t i o n . S t i c k - s l i p t y p e v i b r a t i o n was p r o d u c e d i n a p i n on d i s k f r i c t i o n s y s t e m i n o r d e r t o d e t e r m i n e t h e e f f e c t o f v a r i o u s p a r a m e t e r s on t h e s t a t i c f r i c t i o n f o r c e . I n t h e f i r s t p a r t o f t h e s t u d y i t was f o u n d t h a t two d i s t i n c t t y p e s o f s l i d i n g b e h a v i o u r c o u l d be p r o d u c e d by c o n t r o l l i n g t h e p r e p a r a t i o n o f t h e s u r f a c e s p r i o r t o s l i d i n g . I f t h e s u r f a c e s were f r e s h l y p o l i s h e d a n d k e p t r e l a t i v e l y f r e e o f o r g a n i c c o n t a m i n a n t s t h e n t h e s l i d i n g b e h a v i o u r was c h a r a c t e r i z e d b y h i g h f r i c t i o n c o e f f i c i e n t s a n d e x t e n s i v e s u r f a c e damage. U n d e r l u b r i c a t e d c o n d i t i o n s h o w e v e r , s t i c k - s l i p v i b r a t i o n was p o s s i b l e a t l o w d r i v e n s u r f a c e v e l o c i t i e s . T h e s e r e s u l t s show t h e i m p o r t a n c e o f s u r f a c e h i s t o r y w i t h r e g a r d t o f r i c t i o n phenomena a n d a i d i n t h e i n t e r p r e t a t i o n o f s u b s e q u e n t e x p e r i m e n t a l r e s u l t s . By m e a s u r i n g t h e e l e c t r i c a l r e s i s t a n c e o f t h e s l i d e r - d i s k i n t e r f a c e i t was p o s s i b l e t o m o n i t o r c h a n g e s i n t h e a r e a o f c o n t a c t d u r i n g s t i c k - s l i p . I t was o b s e r v e d t h a t t h e r e was m e t a l l i c c o n t a c t t h r o u g h o u t t h e c o m p l e t e c y c l e a l t h o u g h t h e amount o f m e t a l l i c c o n t a c t i i i v a r i e d . The s t i c k p o r t i o n o f t h e c y c l e was f o u n d t o be a r e g i o n o f i n c r e a s i n g m e t a l l i c c o n t a c t . The amount o f m e t a l l i c c o n t a c t a r e a a t s l i p was a f u n c t i o n o f t h e r a t e a t w h i c h t h e t a n g e n t i a l f o r c e was a p p l i e d . D u r i n g s l i p , t h e a r e a i n m e t a l l i c c o n t a c t d e c r e a s e d r a p i d l y and t h e r e was some e v i d e n c e t h a t t h e n o r m a l l o a d o n t h e s l i d e r was p a r t i a l l y s u p p o r t e d b y a l u b r i c a n t f i l m i n t h i s p a r t o f t h e c y c l e . The amount o f c o n t a c t d u r i n g s l i p was d e t e r m i n e d by t h e r e l a t i v e v e l o c i t y d u r i n g s l i p . By m o n i t o r i n g t h e r e s i s t a n c e o f t h e i n t e r f a c e d u r i n g a " d e l a y e d " s t i c k c y c l e i t was p o s s i b l e t o show t h a t t h e a r e a i n c o n t a c t d i d n o t i n c r e a s e w i t h t i m e u n d e r a s t a t i o n a r y l o a d i n g c o n d i t i o n . I n s t e a d t h e a r e a o f c o n t a c t a t s l i p a n d a l s o t h e s t a t i c f r i c t i o n f o r c e were f o u n d t o be d e p e n d e n t on t h e r a t e o f a p p l i c a t i o n o f t h e t a n g e n t i a l f o r c e . T h e s e f i n d i n g s c o n t r a d i c t e a r l i e r work o n t i m e - d e p e n d e n t c r e e p m o d e l s f o r s t a t i c f r i c t i o n a n d p r o v i d e a d d i t i o n a l e v i d e n c e i n s u p p o r t o f t h e v i s c o -e l a s t i c m o d e l p r o p o s e d b y J o h a n n e s [ 2 7 ] , TABLE OF CONTENTS Chapter Page 1 I n t r o d u c t i o n . . . . 1 2 L i t e r a t u r e Survey . . . . . . . 4 2.1 G e n e r a l B a c k g r o u n d — F r i c t i o n and Wear . 4 2.2 R e l a x a t i o n O s c i l l a t i o n s and the Adhesion Theory • 7 2.3 F a c t o r s I n f l u e n c i n g S t i c k - S l i p and S t a t i c F r i c t i o n 10 2.3.1 Time o f s t a t i c c o n t a c t 10 2.3.2 Role o f t a n g e n t i a l f o r c e 12 2.3.3 The e f f e c t of s u r f a c e f i l m s on s t a t i c f r i c t i o n 14 2.3.4 The e f f e c t of s u r f a c e temperature on s t a t i c f r i c t i o n 16 3 E x p e r i m e n t a l 18 3.1 Apparatus 18 3.1.1 T u r n t a b l e - d i s k assembly . . . . . 18 3.1.2 S l i d e r s u s p e n s i o n and l o a d i n g assembly 19 3.1.3 D e t a i l s o f the i n s t r u m e n t a t i o n . • 20 3.1.4 M a t e r i a l s f o r the d i s k and s l i d e r . 20 3.1.5 C o n t r o l o f the s u r f a c e temperature of the d i s k . 21 3.1.6 Humidity c o n t r o l system 22 3.1.7 Measurement o f the e l e c t r i c a l r e s i s t a n c e of the s l i d e r - d i s k i n t e r f a c e . 22 3.2 I n i t i a l C a l i b r a t i o n of the Apparatus . . 24 3.2.1 C a l i b r a t i o n of the d i s p l a c e m e n t system 24 3.2.2 Disk v e l o c i t y measurement . . . . 25 3.3 P o l i s h i n g Procedure 25 3.3.1 G o l d 25 3.3.2 S t e e l 27 3.3.3 Vapor d e g r e a s i n g 28 3.3.4 S u r f a c e f i n i s h . . . . . . . . . . 28 3.4 P r e l i m i n a r y T e s t s 29 3.5 Humidity T e s t s 29 3.6 Load, V e l o c i t y and Run-in T e s t s . . . . 30 3.7 Temperature T e s t s 31 3.8 Measurement of the E l e c t r i c a l R e s i s t a n c e of the S l i d e r - T r a c k I n t e r f a c e D u r i n g S t i c k - S l i p . . . 31 4 R e s u l t s and D i s c u s s i o n 32 4.1 E f f e c t o f S u r f a c e C o n d i t i o n s and Environment on S t i c k - S l i p V i b r a t i o n . • 32 4.1.1 Dry ( a s - p o l i s h e d ) s u r f a c e s . . . . 32 4.1.2 I n f l u e n c e o f h u m i d i t y . . . . . . 35 4.1.3 E f f e c t of water f i l m s . . . . . . 36 4.1.4 E f f e c t o f p e t r o l a t u m o i l . . . . . 36 4.1.5 E f f e c t o f vapor d e g r e a s i n g . . . . 37 4.2 R e s u l t s o f Run-in 39 4.3 Load and V e l o c i t y T e s t s 41 4.4 Temperature T e s t s . . . . . . 42 4.5 E l e c t r i c a l R e s i s t a n c e o f the T r a c k -S l i d e r I n t e r f a c e During S t i c k - S l i p . . . 43 4.5.1 O v e r a l l b e h a v i o u r o f i n t e r f a c e r e s i s t a n c e d u r i n g a s t i c k - s l i p c y c l e 44 4.5.2 A c t u a l r e s i s t a n c e o f i n t e r f a c e d u r i n g s t i c k - s l i p . . . 44 4.5.3 R e s i s t a n c e - t i m e c u r v e s d u r i n g s l i p 47 4.5.4 R e s i s t a n c e - d i s p l a c e m e n t c u r v e s d u r i n g s t i c k - s l i p 48 4.6 The E f f e c t o f T a n g e n t i a l L o a d on S t i c k -S l i p . . . . . 49 4.7 D i s c u s s i o n . . . . . 49 4.7.1 The f o r m a t i o n o f a f u l l o i l f i l m . 49 4.7.2 The r o l e o f t a n g e n t i a l l o a d . . . 54 4.7.3 The e f f e c t o f t h e r a t e o f t a n g e n -t i a l f o r c e a p p l i c a t i o n on s t a t i c f r i c t i o n f o r c e , t h e a r e a o f c o n -t a c t a t s l i p and d u r i n g s t i c k . . 62 5 C o n c l u s i o n s © © © © • a • © e • « « © • • » 65 6 S u g g e s t i o n s f o r F u r t h e r R e s e a r c h . . . . 71 R e f e r e n c e s 73 A p p e n d i x A M e a s u r i n g t h e R e s i s t a n c e o f t h e S l i d e r -D i s k I n t e r f a c e D u r i n g S t i c k - S l i p . . . . 77 A p p e n d i x B I n t e r f a c e R e s i s t a n c e a n d t h e A r e a o f C o n t a c t 81 LIST OF FIGURES F i g u r e Page 1(a) T y p i c a l Time-Displacement Records f o r S t i c k - S l i p 85 (b) Model of a System S u b j e c t t o R e l a x a t i o n O s c i l l a t i o n s 85 2 E x p e r i m e n t a l Apparatus 86(a) 3 E s s e n t i a l Components of the S l i d e r - T r a c k Assembly , 86(b) 4 Comparison of Two Modes of S l i d i n g 87 5 S u r f a c e of the Gold Track 88 6 Removing the L u b r i c a n t Decreases the Amplitude of S t i c k - S l i p 89 7 Frequency o f Occurrence of Values of Maximum S l i d e r Displacement During S t i c k f o r One Complete Track T r a v e r s e 90 8 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 s as a F u n c t i o n of Run-in f o r Gold S l i d e r on Gold Track 91 9 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 s , |Jg , as a F u n c t i o n of T a n g e n t i a l Load Rate, e , f o r G o l d on Gold and f o r S t e e l on S t e e l 92 10 D i f f e r e n t i a l V o l t a g e as a F u n c t i o n of Time During Three Complete S t i c k - S l i p C y c l e s 93 11 D i f f e r e n t i a l Voltage-Time T r a c e s f o r S t i c k - S l i p 94 12 I n t e r f a c e R e s i s t a n c e - T i m e Curve f o r S t i c k - S l i p C y c l e , S t e e l on S t e e l 95 13 I n t e r f a c e R e s i s t a n c e - T i m e Curve During S l i p 96 14 D i f f e r e n t i a l V o l t a g e vs Time and D i s p l a c e -ment vs Time T r a c e s f o r S t e e l on S t e e l 97 15 D i f f e r e n t i a l V o l t a g e Changes During S t i c k -S l i p as a F u n c t i o n of S l i d e r Displacement During S t i c k - S l i p . S t e e l on S t e e l . 98 16(a) Displacement-Time and D i f f e r e n t i a l V o l t a g e -Time T r a c e s f o r Delayed S t i c k 99 16(b) Displacement-Time and D i f f e r e n t i a l V o l t a g e -Time Records f o r Three D i f f e r e n t Disk V e l o c i t i e s 100 17 Delayed S t i c k 101 18 D i f f e r e n t i a l Voltage-Time T r a c e s f o r Gold on Gold 102 19 The E f f e c t of T a n g e n t i a l Load Rate on I n t e r f a c e R e s i s t a n c e During the S l i p P o r t i o n of the C y c l e . 103 20 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 as a F u n c t i o n of the T a n g e n t i a l Load Rate, e , f o r S t e e l on S t e e l • 104 21 I n t e r f a c e R e s i s t a n c e as a F u n c t i o n of T a n g e n t i a l Load Rate, e, f o r S t e e l on S t e e l 105 22 Change i n S t a t i c F r i c t i o n F o r c e and C o n t a c t Area as a F u n c t i o n o f T a n g e n t i a l Load Rate, G , f o r S t e e l on S t e e l 106 23(a) C i r c u i t Diagram of B r i d g e 107 23(b) R e s i s t a n c e of I n t e r f a c e vs D i f f e r e n t i a l V o l t a g e f o r 3.0 Amps 108 24 D i s p l a c e m e n t - V e l o c i t y and D i f f e r e n t i a l V o l -t a g e - V e l o c i t y Curves f o r Quasi-harmonic Type V i b r a t i o n 109 B - l Model of a S i n g l e A rea o f C o n t a c t B e f o r e and A f t e r A p p l i c a t i o n of T a n g e n t i a l F o r c e 110 ACKNOWLEDGEMENT The e x p e r i m e n t a l p a r t o f t h i s p r o g r a m was c a r r i e d o u t i n t h e T r i b o l o g y L a b o r a t o r y o f t h e D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . T he a u t h o r w i s h e s t o t h a n k D r . C. A. B r o c k l e y f o r h i s a d v i c e and e n c o u r a g e m e n t d u r i n g t h e p r o g r a m . S p e c i a l t h a n k s a r e due Mr. E . J o n e s whose a s s i s t a n c e w i t h t h e e x p e r i m e n t a l e q u i p m e n t was i n v a l u a b l e . 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 t h r o u g h D. R.B. G r a n t No. 7510-31 and i s g r a t e f u l l y a c k n o w l e d g e d . CHAPTER 1 INTRODUCTION I n t h i s s t u d y r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k - s l i p t y p e a r e u s e d a s a means o f i n v e s t i g a t i n g f u n d a m e n t a l a s p e c t s o f s t a t i c f r i c t i o n . B a s i c a l l y t h e p r o b l e m c o n s i s t s o f d e t e r m i n i n g t h e e f f e c t o f v a r i o u s p a r a m e t e r s on t h e f o r c e r e q u i r e d t o s t a r t s l i d i n g i n a s y s t e m w h i c h c o n s i s t e d o f two s o l i d s s u b j e c t e d t o a c o n s t a n t n o r m a l l o a d a n d a l i n e a r l y i n c r e a s i n g t a n g e n t i a l l o a d . The p r o b l e m i s o f c l a s s i c a l i n t e r e s t a n d a com-p l e t e u n d e r s t a n d i n g o f s t a t i c f r i c t i o n i s o f c o n s i d e r a b l e i m p o r t a n c e i n t h e c o n t e x t o f p r a c t i c a l e n g i n e e r i n g . I n t h i s s t u d y t h e f r i c t i o n s y s t e m h a d a p i n o n d i s k c o n f i g u r a t i o n : t h a t i s , a n e l a s t i c a l l y s u p p o r t e d s l i d e r was p r e s s e d a g a i n s t a r o t a t i n g s u r f a c e b y a n o r m a l l o a d . I n i t i a l l y , t h e s l i d e r was s t a t i o n a r y w i t h r e s p e c t t o t h e d i s k . The t a n g e n t i a l f o r c e was a p p l i e d t o t h e s l i d e r - d i s k i n t e r f a c e b y t h e e x t e n s i o n , a s t h e d i s k r o -t a t e d , o f t h e e l a s t i c member o f t h e s l i d e r s u s p e n s i o n . A t some p o i n t s l i d i n g b e g i n s a n d t h e s t a t i c . f r i c t i o n f o r c e i s d e f i n e d a s t h e t a n g e n t i a l f o r c e r e q u i r e d t o i n i t i a t e s l i d i n g . T he 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 i s 2 d e f i n e d a s t h e r a t i o o f t h e s t a t i c f r i c t i o n f o r c e t o t h e a p p l i e d n o r m a l f o r c e . The s u b s e q u e n t m o t i o n o f t h e s l i d e r d u r i n g t h e " s l i p " o r s l i d i n g p o r t i o n o f t h e s t i c k - s l i p c y c l e i s d e t e r m i n e d by t h e e l a s t i c , d a m p i n g and o t h e r m e c h a n i c a l p a r a m e t e r s o f t h e s y s t e m as w e l l a s t h e f r i c t i o n f o r c e s a t t h e s l i d e r - d i s k i n t e r f a c e . A f t e r a s h o r t p e r i o d o f s l i d i n g t h e s l i d e r comes t o r e s t on t h e d i s k s u r f a c e a n d t h e c y c l e i s r e p e a t e d . The m a j o r i t y o f e a r l i e r f r i c t i o n and wear s t u d i e s u s i n g r e l a x a t i o n o s c i l l a t i o n s h a v e b e e n c o n c e r n e d w i t h m e a s u r i n g s t a t i c f r i c t i o n f o r c e s a s f u n c t i o n s o f n o r m a l l o a d , d i s k v e l o c i t y , m a t e r i a l p r o p e r t i e s and w i t h d e t e r -m i n i n g t h e e f f e c t o f t h e e l a s t i c and d a m p i n g p a r a m e t e r s o f t h e s y s t e m . I n t h e p r e s e n t s t u d y , s i n c e r e l a x a t i o n o s c i l l a -t i o n s o f t h e s t i c k - s l i p t y p e a r e u s e d t o s t u d y f u n d a m e n t a l a s p e c t s o f s t a t i c f r i c t i o n , e m p h a s i s i s p l a c e d o n t h e s t a t i c p o r t i o n o f t h e s t i c k - s l i p c y c l e . I n t h i s r e g i o n t h e s l i d e r - d i s k i n t e r f a c e i s l o a d e d b y a c o n s t a n t n o r m a l and a s t e a d i l y i n c r e a s i n g t a n g e n t i a l l o a d . The m e a s u r e -ment v a r i a b l e i s t h e t a n g e n t i a l f o r c e a t s l i p ( t h e s t a t i c f r i c t i o n f o r c e ) . I t i s i n f l u e n c e d by s e v e r a l f a c t o r s s u c h a s d i s k v e l o c i t y a n d n o r m a l l o a d . T h i s s t u d y o f s t a t i c f r i c t i o n was d i v i d e d i n t o t h r e e s e c t i o n s : 1. an i n v e s t i g a t i o n o f s o u r c e s o f v a r i a t i o n i n s t a t i c f r i c t i o n v a l u e s w h i c h ha d b e e n r e p o r t e d b y p r e v i o u s i n v e s t i g a t o r s , n a m e l y , (a) r e l a t i v e h u m i d i t y o f t h e e n v i r o n m e n t (b) s u r f a c e c o n d i t i o n s ( l u b r i c a t e d and u n l u b r i c a t e d c o n t a c t ) 2. an i n v e s t i g a t i o n o f a model w h i c h ha d b e e n p r o -p o s e d by s e v e r a l a u t h o r s [ 1 8 ] , [ 4 5 ] as a p o s s i b l e e x p l a n a -t i o n f o r t h e o b s e r v e d t i m e - d e p e n d e n c e o f 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 s . 3. a n i n v e s t i g a t i o n o f v a r i a t i o n s i n m e t a l l i c c o n t a c t a r e a ( a ) d u r i n g t h e s t i c k - s l i p c y c l e a n d (b) a s a f u n c t i o n o f t h e r a t e o f i n c r e a s e i n t h e t a n g e n t i a l l o a d d u r i n g s t i c k . CHAPTER 2 LITERATURE SURVEY The f i r s t p a r t o f t h i s s u r v e y p r o v i d e s t h e b a c k -g r o u n d t o t h e p r o b l e m i n t h e f o r m o f a b r i e f r e v i e w o f f r i c t i o n and wear i n t e r m s o f t h e a d h e s i o n t h e o r y o f f r i c t i o n . T h e r e i s a f a i r amount o f c o n t r o v e r s y a b o u t s o l i d - s o l i d f r i c t i o n b u t t h e a d h e s i o n t h e o r y i s t h e most w i d e l y a c c e p t e d e x p l a n a t i o n o f t h e o r i g i n o f f r i c t i o n f o r c e s . A summary o f r e l e v a n t i n v e s t i g a t i o n s o f r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k - s l i p t y p e i s p r e s e n t e d i n t h e s e c o n d s e c t i o n . The summary a l s o i n c l u d e s an a s s e s s m e n t o f t h e c u r r e n t k n o w l e d g e c o n c e r n i n g s t a t i c f r i c t i o n . The l a s t s e c t i o n o f t h e s u r v e y i s c o n c e r n e d w i t h t h e e f f e c t s o f t e m p e r a t u r e and h u m i d i t y on f r i c t i o n a s m e a s u r e d i n s l i d i n g f r i c t i o n t e s t s . 2.1 G e n e r a l B a c k g r o u n d — F r i c t i o n and Wear S e v e r a l s u r v e y s o f f r i c t i o n a nd wear l i t e r a t u r e a r e a l r e a d y a v a i l a b l e : R a b i n o w i c z [ 1 ] , K r a g e l s k i i [ 2 ] , Cameron [ 3 ] , Bowden and T a b o r [ 4 ] , F i n i k i n [ 5 ] , a n d 5 S a l o m o n [ 6 ] . K r a g e l s k i i ' s book c o n t a i n s a r e c e n t summary o f i m p o r t a n t S o v i e t c o n t r i b u t i o n s i n t h e f i e l d o f f r i c t i o n a n d wear, as w e l l a s some c r i t i c a l r e v i e w s o f o l d e r t h e o r i e s o f f r i c t i o n . L i t e r a t u r e o f t h e d e c a d e 1956-66 h a s b e e n r e v i e w e d b y Bowden a n d T a b o r [ 4 ] . T h i s s u r v e y i s s i g n i f i c a n t b e c a u s e i t c o n t a i n s a d i s c u s s i o n o f t h e a d h e s i o n t h e o r y o f f r i c t i o n , f i r s t p r o p o s e d b y Bowden and T a b o r i n 1950, a n d now t h e most w i d e l y a c c e p t e d e x p l a n a t i o n o f t h e o r i g i n o f f r i c t i o n f o r c e s . T h i s e x p l a n a t i o n o f f r i c t i o n r e s t s o n a d e t a i l e d k n o w l e d g e o f t h e m i c r o s c o p i c s t r u c t u r e o f s o l i d s u r f a c e s and how c o n t a c t s b e t w e e n them a r e e s t a b l i s h e d d u r i n g s l i d i n g . I t h a s b e e n p a r t i c u l a r l y u s e f u l when a p p l i e d t o t h e f r i c t i o n a n d wear o f m e t a l s . The s i m p l e a d h e s i o n t h e o r y i s b a s e d o n two a s s u m p t i o n s (1) t h a t m e t a l s u r f a c e s a r e n e v e r smooth b u t c o n s i s t o f m i c r o s c o p i c p e a k s and v a l l e y s ( t h e p e a k s a r e c a l l e d a s p e r i t i e s ) a n d (2) t h a t a d h e s i o n o c c u r s b e t w e e n t h e a s p e r i t i e s i n c o n t a c t . The a c t u a l a r e a o f c o n t a c t b e t w e e n two s o l i d s u r f a c e s i s t h u s l i m i t e d t o t h e a r e a o f t h e a s p e r i t i e s i n c o n t a c t . T h e r e f o r e a s a r e s u l t o f t h e i r r e g u l a r n a t u r e o f s u r f a c e s t h e a c t u a l a r e a o f c o n t a c t i s much s m a l l e r t h a n , p e r h a p s 1/1000 o f , t h e n o m i n a l a r e a o f c o n t a c t . The r e s i s t a n c e t o m o t i o n , F . , i s c o n -' a d h e s i o n ' s i d e r e d t o be due t o t h e s h e a r i n g o f t h e w e l d e d a r e a s ( j u n c t i o n s ) , e i t h e r a t t h e o r i g i n a l i n t e r f a c e o r i n t h e a s p e r i t i e s t h e m s e l v e s . I n t h e r e v i s e d t h e o r y a n o t h e r t e r m , F , , , . , h a s b e e n a d d e d . T h i s t e r m a c c o u n t s f o r a n y d e f o r m a t x o n ' •* a d d i t i o n a l r e s i s t a n c e due t o p l a s t i c d e f o r m a t i o n and e l a s t i c h y s t e r e s e s i n t h e b u l k m a t e r i a l d u r i n g s l i d i n g . U s i n g t h e a d h e s i o n t h e o r y o f f r i c t i o n , Bowden a n d T a b o r h a v e b e e n a b l e t o q u a l i t a t i v e l y e x p l a i n m e t a l t r a n s f e r , wear d e b r i s , low f r i c t i o n c o e f f i c i e n t s i n some s y s t e m s a n d s e i z u r e d u r i n g h i g h vacuum t e s t s . A r e c e n t s t u d y o f t h e a d h e s i o n a n d f r i c t i o n o f f . c . c . m e t a l s b y S i k o r s k i [8] showed t h a t h i g h f r i c t i o n b e t w e e n m e t a l s was u s u a l l y a c c o m p a n i e d b y a l a r g e amount o f a d h e s i o n , an o b s e r v a t i o n t h a t s u p p o r t s t h e a d h e s i o n t h e o r y o f f r i c t i o n f o r t h e c l a s s o f m e t a l s t e s t e d . He a l s o o b s e r v e d t h a t t h e p r e s e n c e o f o x i d e s and o t h e r s u r f a c e c o n -t a m i n a n t s on m e t a l s i n h i b i t s a d h e s i o n a n d t h a t t h e r e m o v a l o f t h e s e f i l m s w i l l g e n e r a l l y i m p r o v e a d h e s i o n . Good a d h e s i o n f o r two s a m p l e s o f t h e same m e t a l was o b s e r v e d i f t h e s u r f a c e f i l m s were d i s r u p t e d and t h e s u r f a c e s were f o r c e d t o c o n f o r m . T h e r e i s a b u n d a n t e x p e r i m e n t a l e v i d e n c e t h a t s u r f a c e i r r e g u l a r i t i e s e x i s t e v e n on s u r f a c e s w h i c h a p p e a r t o be v e r y s m o o t h . S u r f a c e r o u g h n e s s c a n be o b s e r v e d f r o m t h e m o t i o n o f a d i a m o n d t i p p e d s t y l u s p a s s e d s l o w l y o v e r t h e s u r f a c e , [ 4 7 ] o r on a f i n e r s c a l e , b y e l e c t r o n m i c r o s c o p y . Some o p p o s i t i o n t o t h e a d h e s i o n t h e o r y h a s b e e n e x p r e s s e d by s e v e r a l a u t h o r s . B i k e r m a n [ 7 ] , f o r e x a m p l e , a r g u e s i n f a v o u r o f t h e r o u g h n e s s t h e o r y : f r i c t i o n l o s s e s a r e due t o t h e movement o f t h e a s p e r i t i e s o f one s u r f a c e o v e r t h e a s p e r i t i e s o f t h e o t h e r . The a d h e s i o n t h e o r y i s c e r t a i n l y weak i n p r e d i c t i n g q u a n t i t a t i v e r e s u l t s f o r f r i c t i o n and wear t e s t s , b u t a more e x a c t e x p l a n a t i o n o f s o l i d - s o l i d f r i c t i o n h a s n o t b e e n p r o p o s e d . 2.2 R e l a x a t i o n O s c i l l a t i o n s and t h e A d h e s i o n T h e o r y R e l a x a t i o n o s c i l l a t i o n s a r e a t y p e o f i n t e r m i t t e n t s l i d i n g m o t i o n a s s o c i a t e d w i t h low s l i d i n g v e l o c i t i e s i n s y s t e m s w h i c h h a v e e l a s t i c i t y . F o r m a t h e m a t i c a l a n a l y s i s , t h e s e s y s t e m s h a v e b e e n r e p r e s e n t e d by m a s s - s p r i n g - d a m p e r s y s t e m s a s i n F i g u r e 1 ( a ) . A s l i d e r o f mass 'm' i s h e l d a g a i n s t a s u r f a c e w h i c h i s m o v i n g w i t h a v e l o c i t y * v ' . The s l i d e r i s r e s t r a i n e d b y a s p r i n g , o f s p r i n g c o n s t a n t •k'. A v i s c o u s damper w i t h a damping c o e f f i c i e n t ' r ' i s a l s o i n c l u d e d . I f t h e t a n g e n t i a l d i s p l a c e m e n t s o f t h e e l a s t i — c a l l y s u s p e n d e d member o f t h e s y s t e m a r e r e c o r d e d a s a f u n c t i o n o f t i m e as i n F i g u r e 1 (b) t h e n i t c a n be s e e n t h a t r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k - s l i p t y p e h a v e a s a w - t o o t h t y p e w a v e f o r m . D u r i n g t h e f i r s t p a r t o f t h e c y c l e , when t h e s u r f a c e s i n c o n t a c t ( a n e l a s t i c a l l y s u s p e n d e d s l i d e r l o a d e d a g a i n s t a d r i v e n s u r f a c e ) a p p e a r t o h a v e no r e l a t i v e movement, t h e t a n g e n t i a l f o r c e a p p l i e d t o t h e i r i n t e r f a c e b y t h e e x t e n s i o n o f t h e e l a s t i c member i s i n c r e a s i n g . A t some t a n g e n t i a l f o r c e t h i s s t i c k p o r t i o n o f t h e c y c l e i s i n t e r r u p t e d b y s l i p , a s h o r t p e r i o d o f r e l a t i v e movement. D u r i n g s l i p , t h e r e l a t i v e v e l o c i t y may be 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 v e l o c i t y o f t h e d r i v e n s u r f a c e d u r i n g t h e s t i c k p o r t i o n o f t h e c y c l e . T h u s i n s t e a d o f s l i d i n g s m o o t h l y o v e r t h e d r i v e n s u r f a c e , t h e s l i d e r moves i n a s e r i e s o f jumps. B e c a u s e o f t h i s c h a r a c t e r i s t i c m o t i o n t h i s t y p e o f r e l a x a t i o n o s c i l l a t i o n i s known a s ' s t i c k - s l i p ' v i b r a t i o n . S t i c k - s l i p i s g e n e r a l l y c o n s i d e r e d t o be t h e r e s u l t o f f r i c t i o n f o r c e s a t t h e s l i d e r d i s k i n t e r f a c e . D u r i n g t h e ' s t i c k ' o r s t a t i c p a r t o f t h e c y c l e t h e s l i d e r a n d t h e d i s k a r e s u b j e c t e d t o c o m b i n e d n o r m a l a n d t a n g e n -t i a l l o a d i n g . T he t a n g e n t i a l f o r c e a s m e a s u r e d a t t h e e n d o f s t i c k , when t h e p i n b e g i n s t o s l i d e o n t h e d i s k , i s c a l l e d t h e s t a t i c f r i c t i o n f o r c e . D u r i n g t h e s t i c k p e r i o d , t h e f o r c e r e l a t i o n s h i p s f o r t h e f r i c t i o n s y s t e m i n F i g u r e 1 ( a ) may be w r i t t e n a s r V + Kx = N|J s where 'N(J S' i s t h e s t a t i c f r i c t i o n f o r c e . The f r i c t i o n f o r c e m e a s u r e d d u r i n g t h e s l i p p o r t i o n i s c a l l e d t h e k i n e t i c f r i c t i o n f o r c e 'N|J '. D u r i n g s l i p , t h e m o t i o n o f t h e s l i d e r c a n be d e s c r i b e d b y Mx + r x + Kx = N|J K where • N[J K* i s t h e k i n e t i c f r i c t i o n f o r c e a t a g i v e n s l i d e r v e l o c i t y , x. W i t h some e x c e p t i o n s ( r e l a x a t i o n o s c i l l a t i o n s h a v e b e e n o b s e r v e d i n s y s t e m s s u c h a s wood o n s t e e l [ 2 ] ) , t h e a d h e s i o n t h e o r y h a s b e e n a p p l i e d w i t h some s u c c e s s t o q u a l i t a t i v e l y e x p l a i n f r i c t i o n a l r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k - s l i p t y p e i n m e t a l l i c s y s t e m s * R e l a x a t i o n o s c i l l a t i o n s were r e p o r t e d b y W e l l s [ 4 8 ] i n 1929. He o b s e r v e d a d i s c o n t i n u o u s s l i d i n g m o t i o n w h i l e m e a s u r i n g f r i c t i o n c o e f f i c i e n t s a t l o w s l i d i n g s p e e d s . B e f o r e t h e c l a s s i c a l s t u d y by Bowden a n d L e b e n [ 9 ] s e v e r a l i n v e s t i g a t i o n s h a d b e e n c o n d u c t e d . D i s c o n -t i n u o u s m o t i o n d u r i n g s l i d i n g was e x p l a i n e d b y p r o p o s i n g an i n v e r s e r e l a t i o n s h i p b e t w e e n k i n e t i c f r i c t i o n a nd v e l o c i t y . K r a g e l s k i i [ 2 ] p r o v i d e s a r e v i e w o f S o v i e t l i t e r a t u r e i n t h i s a r e a . The Bowden and L e b e n e x p l a n a t i o n o f s t i c k - s l i p t y p e v i b r a t i o n i s f u n d a m e n t a l l y d i f f e r e n t f r o m e a r l i e r e x p l a n a t i o n s . T h e y c o n c l u d e d , f r o m a q u a l i -t a t i v e s t u d y o f m e t a l l i c s l i d i n g s y s t e m s w h i c h showed s t i c k - s l i p t y p e b e h a v i o u r t h a t t h e a c t u a l a r e a o f c o n t a c t i s v e r y s m a l l c o m p a r e d t o t h e n o m i n a l a r e a a n d t h a t t h e c o n t a c t a r e a i n c r e a s e s w i t h t i m e d u r i n g t h e s t i c k p o r t i o n 10 o f t h e c y c l e . I n a d d i t i o n , t h e y c o n c l u d e d t h a t s l i d i n g o r ' s l i p ' , r e s u l t s when t h e j u n c t i o n s f o r m e d b e t w e e n t h e a s p e r i t i e s o f t h e s u r f a c e s a r e s h e a r e d by t h e a p p l i e d t a n -g e n t i a l f o r c e . S u b s e q u e n t s t u d i e s o f r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k - s l i p t y p e e m p h a s i z e d t h e e x i s t e n c e o f two d i s t i n c t f r i c t i o n c o e f f i c i e n t s , n a m e l y , s t a t i c and k i n e t i c ( R a b i n o w i c z [ 1 0 ] , Sampson, M o r g a n , Reed a n d M u s k a t [ 1 1 ] , M o r g a n , Reed an d M u s k a t [ 1 2 ] , B r i s t o w [ 1 3 ] , [ 1 4 ] ) . I n a d d i t i o n t h e s e and l a t e r s t u d i e s b y D e r j a g u i n , P u s h a n d T o l s t o i [ 1 5 ] , K o s t e r i n a n d K r a g e l s k i i [ 1 6 ] , * B r o c k l e y , C ameron and P o t t e r [ 1 7 ] and D a v i s [ 4 5 ] , r e c o g n i z e d t h a t n o r m a l l o a d , t i m e o f s t a t i c c o n t a c t , v e l o c i t y o f t h e d r i v e n s u r f a c e a n d s y s t e m d a m ping an d e l a s t i c p a r a m e t e r s a f f e c t t h e o c c u r r e n c e and a m p l i t u d e o f t h e o s c i l l a t i o n s . The r e s u l t s o f t h e s e s t u d i e s h a v e e n c o u r a g e d a d d i t i o n a l i n v e s t i g a t i o n s o f s t a t i c a n d k i n e t i c f r i c t i o n a s w e l l a s r e l a x a t i o n o s c i l l a t i o n s . 2.3 F a c t o r s I n f l u e n c i n g S t i c k - s l i p and S t a t i c F r i c t i o n 2.3.1 T ime o f s t a t i c c o n t a c t When t h e v e l o c i t y o f t h e d r i v e n s u r f a c e i s d e c r e a s e d , t h e s l i d e r and t h e s u r f a c e a p p e a r t o r e m a i n " i n s t a t i c c o n t a c t f o r a l o n g e r t i m e ( t h e t i m e o f s t a t i c c o n -t a c t i s i n c r e a s e d ) and t h e a m p l i t u d e o f t h e o s c i l l a t i o n i n c r e a s e s (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 i n c r e a s e s ) . At l e a s t f i v e d i f f e r e n t groups have i n v e s t i g a t e d t h i s pheno-menon and t h r e e d i f f e r e n t r e l a t i o n s h i p s have been proposed: 1» U = (J, +• Ct s D e r j a g u i n , Push and T o l s t o i S /TTT (1957) d + t, 2* Ms= Mk + [u s-u|i-eC t sj Howe e t a l (1955) and K o s t e r i n and K r a g e l s k i i (1962) b 3. U = U + at Rabinowicz (1940) and B r o c k l e y k and Davis (1965) These s t u d i e s share two assumptions: (1) t h a t a t zer o time of s t i c k ( t = 0) 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 |J s i s e q u i v a l e n t to the k i n e t i c c o e f f i c i e n t , \i^t and (2) most i m p o r t a n t — t h a t the normal f o r c e , not the tangen-t i a l l o a d i n g f o r c e , i s the c o n t r o l l i n g f a c t o r i n i n c r e a s i n g 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 . A l a t e r study (1967) by Jones [ 4 9 ] , used i n t e r -f e r e n c e p r e s s - f i t specimens w i t h a f i l m of MoSp as a l u b r i c a n t . Under the t e s t c o n d i t i o n s ( s t a t i c c o n t a c t times v a r i e d from one second t o s e v e r a l months) the s t a t i c c o e f f i c i e n t i n c r e a s e d w i t h t ime. R e s u l t s o f model s t u d i e s by Spurr (18] and Moore and Tabor [19] supported a ' j u n c t i o n growth by c r e e p ' e x p l a n a t i o n o f i n c r e a s e d s t a t i c f r i c t i o n w i t h i n c r e a s i n g s t a t i c c o n t a c t time. I t was proposed t h a t the 12 j u n c t i o n a r e a i n c r e a s e d w i t h t i m e u n d e r t h e a c t i o n o f t h e n o r m a l l o a d . H a r d n e s s - t i m e ( t h e g e o m e t r y o f t h e i n d e n t e r -s u r f a c e i n t e r a c t i o n i s s i m i l a r t o t h e a s p e r i t y - s u r f a c e i n t e r a c t i o n ) a n d h a r d n e s s - t e m p e r a t u r e e x p e r i m e n t s a l s o s u p p o r t e d a j u n c t i o n g r o w t h m e c h a n i s m due t o c r e e p : A t k i n s , S i l v e r i o a n d T a b o r [ 2 0 ] , M u l h e a r n and T a b o r [ 2 1 ] , However, t h e s e s t a t i c f r i c t i o n s t u d i e s n e g l e c t e d t h e i n f l u e n c e o f t h e t a n g e n t i a l l o a d i n g f o r c e o n t h e s t a t i c f r i c t i o n b e h a v i o u r . 2.3.2 R o l e o f t a n g e n t i a l f o r c e One o f t h e e a r l i e s t s t u d i e s o f t h e * r o l e o f t a n g e n -t i a l f o r c e i n s o l i d f r i c t i o n s t u d i e s was c a r r i e d o u t b y P a r k e r , F a r n w o r t h and M i l n e [ 2 2 ] who r e p o r t e d t h a t , u n d e r i m p a c t c o n d i t i o n s , t h e c o e f f i c i e n t o f s t a t i c f r i c t i o n i n c r e a s e d w i t h i n c r e a s i n g r a t e o f a p p l i e d f o r c e . The t e s t s y s t e m c o n s i s t e d o f c l a m p e d p l a t e s s u b j e c t e d t o t a n g e n t i a l i m p a c t l o a d s . R e l a x a t i o n o s c i l l a t i o n s were n o t p r e s e n t and t h e l o a d i n g r a t e s were v e r y h i g h . I n 1954, G r e e n [ 2 3 ] p r o v i d e d an a n a l y s i s o f a j u n c t i o n m o d e l . T h i s a n a l y s i s l e a d s t o a d i f f e r e n t a p p r o a c h i n t h e s e a r c h t o q u a n t i t a t i v e l y e x p l a i n f r i c t i o n : t h e f r i c t i o n f o r c e b e t w e e n s u r f a c e s c a n be e s t i m a t e d by c o n s i d e r i n g t h e d e f o r m a t i o n o f t h e a s p e r i t i e s b y t h e c o m b i n e d e f f e c t s o f t h e n o r m a l a n d t a n g e n t i a l l o a d s . An e x p e r i m e n t a l s t u d y by Greenwood and T a b o r [ 2 4 ] u s e d l a r g e s c a l e m o d e l s o f f r i c t i o n j u n c t i o n s 13 t o e x p e r i m e n t a l l y i n v e s t i g a t e t h e j u n c t i o n g r o w t h m echanism o f f r i c t i o n . T h e i r r e s u l t s s u p p o r t e d G r e e n ' s t h e o r e t i c a l s t u d y . I n an e x p e r i m e n t a l s t u d y u s i n g e l e c t r i c a l r e s i s -t a n c e m e a s u r e m e n t s and t a n g e n t i a l l o a d s t o o s m a l l t o c a u s e s l i p , C o u r t n e y - P r a t t and E i s n e r [25] showed t h a t t h e a r e a o f c o n t a c t i n c r e a s e s a s t h e t a n g e n t i a l f o r c e i n c r e a s e s ; t h e t a n g e n t i a l f o r c e t e n d i n g a s y m p t o t i c a l l y t o t h e s t a t i c f r i c t i o n f o r c e . T h e y a l s o f o u n d t h a t t h e a d d i t i o n o f a l u b r i c a n t d o e s n o t a f f e c t t h e n a t u r e o f t h e d e f o r m a t i o n p r o c e s s b u t i t may r e d u c e t h e t a n g e n t i a l f d r c e r e q u i r e d t o c a u s e s l i p . The r e s u l t s o f t h i s s t u d y were i n t e r p r e t e d a s s u p p o r t i n g b o t h t h e a d h e s i o n t h e o r y o f f r i c t i o n a n d s e v e r a l a n a l y t i c a l s t u d i e s o f d e f o r m a t i o n u n d e r c o m b i n e d n o r m a l an d t a n g e n t i a l l o a d i n g . However, i n t h e i r e x p e r i -m e n t s , t h e a u t h o r s made no a t t e m p t t o i n s u r e t h a t t h e r a t e o f t a n g e n t i a l l o a d i n g was c o n s t a n t . J o h n s o n [ 2 6 ] h a s p r e s e n t e d r e s u l t s o f a s t u d y o n t h e d e f o r m a t i o n o f a p l a s t i c wedge u n d e r n o r m a l an d t a n -g e n t i a l f o r c e s . H i s r e s u l t s a l s o s u p p o r t t h e j u n c t i o n g r o w t h m e c h a n i s m a s an e x p l a n a t i o n o f t h e o b s e r v e d s t a t i c f r i c t i o n phenomena b u t do n o t i n c o r p o r a t e any r a t e e f f e c t s . More r e c e n t l y a v i s c o - e l a s t i c m odel h a s b e e n p r o -p o s e d by J o h a n n e s [ 2 7 ] t o q u a n t i t a t i v e l y e x p l a i n t h e o b s e r v e d s t a t i c f r i c t i o n - t i m e r e l a t i o n s h i p a s a f u n c t i o n o f t h e r a t e o f t a n g e n t i a l l o a d i n g . 14 2.3.3 The e f f e c t o f s u r f a c e f i l m s o n s t a t i c f r i c t i o n M e t a l s u r f a c e s e x p o s e d t o t h e a t m o s p h e r e a r e g e n e r a l l y c o v e r e d w i t h o x i d e s and a d s o r b e d c o n t a m i n a n t f i l m s o f u n d e t e r m i n e d c o m p o s i t i o n . The i m p o r t a n c e o f f i l m s and e n v i r o n m e n t i n f r i c t i o n a n d wear s t u d i e s i s i l l u s t r a t e d b y t h e r e s u l t s o f a n e a r l y s t u d y b y Bowden and Young [ 2 8 ] c o n d u c t e d a t t h e e x t r e m e s o f s u r f a c e c o n d i t i o n s : (1) h i g h vacuum c o n d i t i o n s w i t h s p e c i a l l y p r e -p a r e d s u r f a c e s (2) s u r f a c e s c o n t a m i n a t e d w i t h f i l m s o f known o r i g i n . U n d e r h i g h vacuum c o n d i t i o n s s e i z u r e o f t h e m e t a l s u r f a c e s i n c o n t a c t o c c u r r e d e v e n a t room t e m p e r a t u r e . When known amounts o f s u r f a c e - a c t i v e v a p o u r s were f e d i n t o t h e t e s t chamber, t h e a d h e s i o n b e t w e e n t h e s u r f a c e s was r e d u c e d and f r i c t i o n c o e f f i c i e n t s were l o w e r . The i n f l u e n c e o f s u r f a c e f i l m s was a l s o demon-s t r a t e d by N i c h o l a s [ 2 9 ] , who s u b j e c t e d h e m i s p h e r i c a l c o p p e r s u r f a c e s f i r s t t o n o r m a l l o a d i n g t h e n t o s i m u l -t a n e o u s n o r m a l and t a n g e n t i a l l o a d i n g . He f o u n d t h a t a d h e s i o n d i d n o t o c c u r i f t h e t a n g e n t i a l f o r c e was n o t a p p l i e d and i n t e r p r e t e d t h e s e r e s u l t s t o mean t h a t t h e t a n g e n t i a l f o r c e c a u s e d t h e d i s r u p t i o n o f p r o t e c t i v e s u r f a c e f i l m s . S i k o r s k i [ 8 ] h a s a l s o r e p o r t e d g o o d a d h e s i o n b e t w e e n s a m p l e s o f t h e same m e t a l i f t h e s u r f a c e 15 f i l m s were d i s r u p t e d a n d t h e s u r f a c e s were f o r c e d t o c o n f o r m . R e c e n t l y an e x p e r i m e n t a l s t u d y , d e s i g n e d t o s i m u l a t e t h e d e f o r m a t i o n b e h a v i o u r o f a p l a s t i c a s p e r i t y c o v e r e d w i t h a b r i t t l e f i l m and l o a d e d o n l y i n t h e n o r m a l d i r e c t i o n , h a s b e e n r e p o r t e d b y O s i a s a n d T r i p p [ 3 0 ] . T h i s s t u d y p r o v i d e s v i s u a l e v i d e n c e o f t h e b r e a k - u p o f b r i t t l e s u r f a c e f i l m s u n d e r l o a d . The a u t h o r s r e p o r t t h r e e d i s t i n c t t y p e s o f c r a c k p a t t e r n s . W i t h r e g a r d t o t h e p r e s e n t s t u d y t h i s f i l m s t u d y i s s i g n i f i c a n t a s i t i m p l i e s t h a t m e t a l - m e t a l a d h e s i o n u n d e r n o r m a l l o a d i n g w o u l d o c c u r o n l y where t h e o x i d e f i l m c r a c k s c o i n c i d e d . T h u s t h e a d h e r i n g m e t a l l i c a r e a w o u l d be s m a l l e r t h a n t h e a c t u a l c o n t a c t a r e a . S t u d i e s b y C o c k s [ 3 1 ] and A i n b i n d e r and P r a n c s [ 3 2 ] u s i n g u n l u b r i c a t e d m e t a l s u r f a c e s u n d e r s l i d i n g c o n -d i t i o n s i l l u s t r a t e t h a t a d h e s i o n o n a f a i r l y l a r g e s c a l e may be p r e s e n t u n d e r some s u r f a c e c o n d i t i o n s . T h e s e s t u d i e s d e s c r i b e t h e g r a d u a l f o r m a t i o n o f c l u m p s o f d i s -t u r b e d m a t e r i a l ("prows") d u r i n g s l i d i n g a n d a l s o e x p l a i n t h e o r i g i n o f wear d e b r i s . C o u r t n e y - P r a t t and E i s n e r [ 2 5 ] o b s e r v e d t h a t t h e p r e s e n c e o f a l u b r i c a n t d i d n o t s u b s t a n t i a l l y a f f e c t t h e g e n e r a l b e h a v i o u r o f t h e s y s t e m b u t d i d lower t h e s t a t i c f r i c t i o n f o r c e . T h i s e f f e c t was a t t r i b u t e d t o t h e r e d u c e d s t r e n g t h o f a d h e s i o n a t t h e s l i d e r - s u r f a c e i n t e r f a c e , a n e f f e c t w h i c h c o u l d h a v e b e e n a n t i c i p a t e d f r o m t h e r e s u l t s 16 o b t a i n e d f r o m t h e vacuum s t u d i e s by Bowden an d Young [ 2 8 ] . I t i s i n t e r e s t i n g to. n o t e t h a t r e l a x a t i o n o s c i l l a -t i o n s t u d i e s h a v e b e e n u s u a l l y c o n d u c t e d u n d e r ' d r y ' f r i c t i o n c o n d i t i o n s (no s p e c i f i c l u b r i c a n t s have b e e n a d d e d t o t h e s y s t e m ) b u t v e r y l i t t l e e f f o r t t o p r o t e c t t h e s u r f a c e s f r o m c o n t a m i n a n t f i l m s h a s b e e n made. 2.3.4 The e f f e c t o f s u r f a c e t e m p e r a t u r e on s t a t i c f r i c t i o n One o f t h e f i r s t s t u d i e s o f t e m p e r a t u r e a n d i t s e f f e c t o n s t a t i c f r i c t i o n was t h a t o f S i mon, McMahon, and Bowen [ 3 3 ] . U s i n g t h e s l i d e r - o n - a n - i n c l i n e d - p l a n e a p p a r a t u s t h e y m e a s u r e d t h e 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 f o r a number o f m e t a l s a t t e m p e r a t u r e s r a n g i n g f r o m 4.2°K t o 6 0 0 ° K . The m e t a l s a m p l e s were p r e p a r e d and h e l d u n d e r r e l a t i v e l y h i g h vacuum c o n d i t i o n s . They o b s e r v e d t h a t t e m p e r a t u r e c o e f f i c i e n t s o f s t a t i c f r i c t i o n a r e s m a l l and p o s i t i v e f o r t h e m e t a l s t e s t e d . T h e y c o n c l u d e d t h a t t h e s e r e s u l t s s u b s t a n t i a t e d t h e a d h e s i o n t h e o r y o f f r i c t i o n and c o n t r a d i c t e d t h e r o u g h n e s s t h e o r y o f f r i c t i o n . A l a t e r s t u d y o f f r i c t i o n and wear by P e t e r s o n , F l o r e k a n d L e e [ 3 4 ] was d i r e c t e d a t d e t e r m i n i n g t h e r e l a t i o n s h i p b e t w e e n s l i d i n g f r i c t i o n ( w i t h o u t r e l a x a t i o n o s c i l l a t i o n s ) and t e m p e r a t u r e . The a u t h o r s c o n c l u d e d t h a t t h e g e n e r a t i o n o f o x i d e s i n t h e s l i d i n g t r a c k a b o v e a p a r t i c u l a r t r a n s i t i o n t e m p e r a t u r e c o n t r i b u t e d t o i m p r o v e d s l i d i n g c h a r a c t e r i s t i c s . No r e l a x a t i o n o s c i l l a t i o n s were r e p o r t e d . 17 T h i s b a c k g r o u n d s u r v e y on s t a t i c f r i c t i o n i n d i c a t e s t h a t d u r i n g t h e s t a t i c p a r t o f t h e s t i c k - s l i p c y c l e t h e m e t a l l i c c o n t a c t a r e a i s i n c r e a s i n g , e i t h e r b y j u n c t i o n g r o w t h ( a c r e e p c o n t r o l l e d mechanism) o r by t h e r e m o v a l o f c o n t a m i n a n t f i l m s . P r e v i o u s s t u d i e s a l s o i n d i c a t e t h a t t h e e f f e c t o f t e m p e r a t u r e a l o n e s h o u l d be t o i n c r e a s e s t a t i c f r i c t i o n b u t a t h i g h e r t e m p e r a t u r e s t h e f o r m a t i o n o f o x i d e f i l m s c o u l d d e c r e a s e t h e 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 . I n a d d i t i o n , r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k -s l i p t y p e c a n be e x p e c t e d u n d e r d r y c o n d i t i o n s a n d t h e a d d i t i o n o f a l u b r i c a n t t o t h e s y s t e m w i l l ,not a p p r e c i a b l y a f f e c t t h e o c c u r r e n c e o f s t i c k - s l i p o r j u n c t i o n g r o w t h d u r i n g s t i c k . CHAPTER 3 EXPERIMENTAL I n t h i s c h a p t e r a d e s c r i p t i o n o f t h e a p p a r a t u s u s e d i n t h e e x p e r i m e n t a l p a r t o f t h e p r o g r a m a s w e l l a s a summary o f t h e e x p e r i m e n t a l p r o c e d u r e i s g i v e n . 3.1 A p p a r a t u s The a p p a r a t u s was d e s i g n e d and d e v e l o p e d i n t h e U.B.C. T r i b o l o g y L a b o r a t o r y . I t c o n s i s t e d o f t h e f o l l o w i n g m a i n c o m p o n e n t s : 1. a n e l a s t i c a l l y s u p p o r t e d s l i d e r w h i c h was l o a d e d a g a i n s t a v a r i a b l e s p e e d t u r n t a b l e ; 2. a h e a t i n g e l e m e n t i n t h e b a s e o f t h e t u r n t a b l e ; 3. a h u m i d i t y c o n t r o l s y s t e m . An o v e r a l l v i e w o f t h e a p p a r a t u s i s shown i n t h e p h o t o g r a p h i n F i g u r e 2. The e s s e n t i a l f e a t u r e s o f t h e a p p a r a t u s a r e : 3.1.1 T u r n t a b l e - d i s k a s s e m b l y The t u r n t a b l e d i s k a s s e m b l y was d r i v e n , t h r o u g h a P I C v a r i a b l e r a t i o g e a r b o x a n d a s e r i e s o f s p e e d -r e d u c i n g g e a r s , b y a v a r i a b l e s p e e d m o t o r . T u r n t a b l e 19 speeds from .0063 t o .146 rpm were p o s s i b l e w i t h t h i s arrangement. The c o r r e s p o n d i n g s u r f a c e v e l o c i t i e s c o v e r e d a range of .001 t o .2 in-sec""^". I n a d d i t i o n the t r a c k r a d i u s c o u l d be a d j u s t e d by v a r y i n g the p i n p o s i t i o n on the support beam. V a r y i n g the t r a c k r a d i u s changed b o t h the s u r f a c e v e l o c i t y and the l o a d on the p i n . 3.1.2 S l i d e r s u s p e n s i o n and l o a d i n g assembly The s l i d e r was h e l d i n a h e m i s p h e r i c a l h o l d e r , d e s i g n e d t o f i t a c o n i c a l cup i n the sample h o l d e r . The sample h o l d e r was then p o s i t i o n e d on an aluminum beam. T h i s h e m i s p h e r i c a l h o l d e r - c o n i c a l cup system a l l o w e d the s l i d e r t o r i d e f l a t a g a i n s t the s u r f a c e of the d i s k and minimized edge l o a d i n g o f the s l i d e r . F i g u r e 3 shows the e s s e n t i a l f e a t u r e s of the s l i d e r s u s p e n s i o n and l o a d i n g assembly. The s l i d e r , A , ( i n i t s h o l d e r ) was e l a s t i c a l l y s upported by a 3.25 i n . diameter c i r c u l a r s t e e l s p r i n g , B, which had a t h i c k n e s s o f 0.025 i n . and a width of 0.5 i n . The s l i d e r was l o a d e d a g a i n s t the d i s k , D, by a p p l y i n g a dead l o a d through a c a b l e which a t t a c h e d t o the l o a d frame a t C. The l o a d a t C was t r a n s m i t t e d t o the frame, E, and thus the s l i d e r was f o r c e d a g a i n s t the d i s k . The frame, E, was hinged t o the s u p p o r t p o s t s by c r o s s e d c o p p e r - b e r y l l i u m s t r i p s . The c r o s s e d s t r i p s gave low f r i c t i o n l o s s a t the s u s p e n s i o n p o i n t s . 20 The s u s p e n s i o n a n d l o a d i n g a s s e m b l y was d e s i g n e d s o t h a t (1) t h e v i b r a t i n g mass was c o n s t a n t , a l t h o u g h t h e l o a d o n t h e s l i d e r was v a r i a b l e a n d (2) t h e s l i d e r was a r r a n g e d s o t h a t i t d e s c r i b e d a t r a c k o f c o n s t a n t r a d i u s on t h e s u r f a c e o f t h e d i s k a s t h e t u r n t a b l e r o t a t e d . 3.1.3 D e t a i l s o f t h e i n s t r u m e n t a t i o n D u r i n g t h e s t i c k - s l i p c y c l e t h e s l i d e r was d i s -p l a c e d f r o m i t s e q u i l i b r i u m p o s i t i o n and t h e s p r i n g was d e f l e c t e d . A l i n e a r d i s p l a c e m e n t t r a n s d u c e r , D a y t r o n i c M o d e l DF160, was u s e d t o m e a s u r e t h e d e f l e c t i o n o f t h e s p r i n g - m a s s s y s t e m . The t r a n s d u c e r , G, was mounted on t h e f r a m e , E , and m e a s u r e d t h e d e f l e c t i o n o f t h e a l u m i n u m beam, F, on w h i c h t h e s l i d e r was p o s i t i o n e d . T h i s d e f l e c -t i o n was a m e a s u r e 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 t h e s l i d e r a n d t h e d i s k a s t h e beam r e s p o n d e d t o t h e e x t e n s i o n o f t h e s p r i n g . The m a g n i t u d e o f t h e f r i c t i o n f o r c e was t h e n f o u n d f r o m a s t a t i c l o a d - d e f l e c t i o n c a l i b r a t i o n o f t h e m a s s - s p r i n g s y s t e m . The o u t p u t f r o m t h e t r a n s d u c e r was t h e n f e d t o a D a y t r o n i c t r a n s d u c e r A m p l i f i e r - I n d i c a t o r ( M o d e l 3 0 0 D - F - 7 0 ) . The o u t p u t f r o m t h i s i n s t r u m e n t was d i s p l a y e d o n a n o s c i l l o s c o p e o r c h a r t r e c o r d e r . 3.1.4 M a t e r i a l s f o r t h e d i s k a n d s l i d e r Two s e t s o f d i s k s and s l i d e r s were r e q u i r e d f o r 21 t h i s s t u d y . The d i s k u s e d f o r t h e s t e e l on s t e e l s t u d y was f a b r i c a t e d f r o m C1020 s t e e l . The s u r f a c e was g r o u n d and l a p p e d b e f o r e p o l i s h i n g . I t s d i m e n s i o n s w e r e : o u t e r d i a m e t e r 4.875 i n . , t h i c k n e s s .375 i n . F o r t h e g o l d o n g o l d s t u d y , a g o l d t r a c k was f a b r i c a t e d a n d mounted on a m i l d s t e e l d i s k . To do t h i s , t h r e e g o l d i n g o t s were r e c a s t i n t o one l a r g e i n g o t w h i c h was r o l l e d t o a s t r i p 0.75 i n . w i d e a n d 0.125 i n . t h i c k , a n n e a l e d , t h e n b e n t t o a c i r c u l a r t r a c k . The g o l d t r a c k was t h e n p i n n e d t o a m i l d s t e e l d i s k , m a c h i n e d a n d p o l i s h e d . The d i m e n s i o n s o f t h e f i n i s h e d d i s k w e r e : o u t e r d i a m e t e r 3.75 i n . , w i d t h 0.75 i n . , a n d t h i c k n e s s 0.94 i n . The s t e e l s l i d e r was a 0.375 d i a m e t e r s t e e l p i n w h i c h was g r o u n d t h e n l a p p e d b e f o r e p o l i s h i n g . The g o l d s l i d e r c o n s i s t e d o f a 0.25 i n . d i a m e t e r , 0.125 i n . t h i c k , g o l d p e l l e t s o l d e r e d t o a 0.375 i n . d i a m e t e r s t e e l p i n . 3.1.5 C o n t r o l o f t h e s u r f a c e t e m p e r a t u r e o f t h e d i s k A h e a t i n g e l e m e n t , i n s t a l l e d i n t h e b a s e o f t h e t u r n t a b l e a l l o w e d t h e s u r f a c e o f t h e d i s k t o be k e p t a t a d e s i r e d b u l k t e m p e r a t u r e . The h e a t i n g e l e m e n t was c a p a b l e o f m a i n t a i n i n g t h e s u r f a c e o f t h e d i s k a t t e m p e r -a t u r e s up t o 1 4 0 ° C . S u r f a c e t e m p e r a t u r e s were m o n i t o r e d u s i n g a t h e r m i s t o r p r o b e i n c o n j u n c t i o n w i t h a Y S I T e l e t h e r -mometer ( M o d e l 4 2 S C ) . The p r o b e was s p e c i f i c a l l y 22 d e s i g n e d f o r s u r f a c e temperature measurements. The u s e f u l range of the d e v i c e was -20°C to 150°C. 3.1.6 Humidity c o n t r o l system The h u m i d i t y c o n t r o l system was c a p a b l e o f main-t a i n i n g the t e s t environment a t a c o n s t a n t water-vapor c o n t e n t from a p p r o x i m a t e l y 10% r e l a t i v e h u m i d i t y t o 100% r e l a t i v e h u m i d i t y a t 24°C. The f r i c t i o n couple was s e p a r a t e d from the atmo-sphere by a P l e x i g l a s s c o v e r d u r i n g the c o n s t a n t h u m i d i t y t e s t s . The a i r i n p u t t o the t e s t atmosphere c o u l d be a d j u s t e d by v a r y i n g the volumes of wet and d r y a i r so as t o p r o v i d e the h u m i d i t y l e v e l d e s i r e d . The a i r f l o w through the system was as f o l l o w s : The a i r was drawn from the t e s t atmosphere, p a r t o f the a i r f l o w was passed through a water spray and the r e s t passed through a d r y i n g agent ( s i l i c a g e l ) . The two streams then mixed and were blown i n t o the t e s t chamber by a s m a l l f a n . 3.1.7 Measurement of the e l e c t r i c a l r e s i s t a n c e of the  s l i d e r - d i s k i n t e r f a c e Because the r e s i s t a n c e o f a f u l l y formed o x i d e f i l m o r o i l f i l m i s much h i g h e r than ( o f the o r d e r o f 10^ times) the r e s i s t a n c e of a-pure m e t a l l i c c o n t a c t , e l e c t r i -c a l r e s i s t a n c e measurements are o f t e n used i n f r i c t i o n and 23 l u b r i c a t i o n studies., S e v e r a l r e f e r e n c e s d e s c r i b i n g the use of e l e c t r i c a l r e s i s t a n c e measurements i n v a r i o u s k i n d s of f r i c t i o n s t u d i e s are a v a i l a b l e : Furey [ 3 5 ] , W i l s o n [ 3 6 ] , C o u r t n e y - P r a t t and E i s n e r [ 2 5 ] . E l e c t r i c a l r e s i s t a n c e methods have a l s o been a p p l i e d t o the s t a t i c f r i c t i o n problem (Bowden and Leben [9]) and to the measurement of a c t u a l c o n t a c t a r e a under s i n g l e c o n t a c t c o n d i t i o n s [ 3 7 ] . Measurements of c o n t a c t r e s i s t a n c e are hampered by the low r e s i s t a n c e l e v e l s of m e t a l l i c c o n t a c t . The most s e r i o u s d i s a d v a n t a g e i s t h a t i n t e r p r e t a t i o n of r e s u l t s w i t h r e s p e c t t o the a c t u a l a r e a i n c o n t a c t i s d i f f i c u l t . An e x c e l l e n t review o f l i t e r a t u r e c o n c e r n i n g e l e c t r i c a l r e s i s t a n c e measurements and s o l i d s i n s t a t i c c o n t a c t has been p r o v i d e d by Jones, Howells and P r o b e r t [ 3 8 ] . In the p r e s e n t s t u d y the e l e c t r i c a l r e s i s t a n c e of the i n t e r f a c e was monitored throughout the s t i c k - s l i p c y c l e . Thus i t was p o s s i b l e t o o b t a i n i n f o r m a t i o n on the e x t e n t o f m e t a l l i c c o n t a c t d u r i n g s t i c k - s l i p and to i n v e s -t i g a t e the v a r i a t i o n s i n c o n t a c t d u r i n g both p a r t s of the s t i c k - s l i p c y c l e . Appendix A c o n t a i n s a f u l l d e s c r i p t i o n of the t e c h n i q u e . 24 3.2 I n i t i a l C a l i b r a t i o n o f t h e A p p a r a t u s 3.2.1 C a l i b r a t i o n o f t h e d i s p l a c e m e n t s y s t e m D u r i n g t h e s t i c k - s l i p c y c l e t h e s l i d e r - b e a m a s s e m b l y was d i s p l a c e d f r o m i t s e q u i l i b r i u m p o s i t i o n . The movement p r o d u c e d an e x t e n s i o n o f t h e c i r c u l a r s p r i n g w h i c h was f i x e d t o t h e beam. The beam d i s p l a c e m e n t was m e a s u r e d a t t h e e n d o f t h e beam b y t h e d i s p l a c e m e n t t r a n s -d u c e r and i n d i c a t e d t h e f o r c e e x e r t e d on t h e s l i d e r - d i s k i n t e r f a c e b y t h e s p r i n g . To c a l i b r a t e t h e s y s t e m , known s t a t i c l o a d s were a p p l i e d t r a n s v e r s e l y t o t h e beam a t t h e v a r i o u s s l i d e r p o s i t i o n s . The h o r i z o n t a l beam d i s p l a c e m e n t s were t h e n m e a s u r e d . A l t h o u g h t h e s l i d e r was n o t i n c o n t a c t w i t h t h e s u r f a c e d u r i n g c a l i b r a t i o n , t h e beam was i n t h e t e s t p o s i t i o n . The s t a t i c l o a d - d i s p l a c e m e n t r e l a t i o n s h i p f o r t h e m a s s - s p r i n g s y s t e m was f o u n d t o be l i n e a r t h r o u g h o u t t h e r a n g e o f s l i d e r p o s i t i o n s and l o a d s u s e d . The t r a n s d u c e r - a m p l i f i e r s y s t e m was t h e n a d j u s t e d a n d i t s o u t -p u t c h e c k e d f o r l i n e a r i t y b y a p p l y i n g known d i s p l a c e m e n t s t o t h e beam and n o t i n g t h e r e s u l t i n g i n s t r u m e n t i n d i c a t i o n . F o r t h e m a j o r i t y o f t h e t e s t s c o n d u c t e d , t h e d i s p l a c e m e n t was r e c o r d e d b y a c h a r t r e c o r d e r . T h e . o u t p u t o f t h e t r a n s d u c e r - a m p l i f i e r - c h a r t r e c o r d e r s y s t e m was a l s o t e s t e d and f o u n d t o be l i n e a r t h r o u g h o u t t h e r a n g e u s e d . 25 3.2.2 D i s k v e l o c i t y m e a s u r e m e n t s S i n c e t h e v a r i a b l e s p e e d m o t o r d r i v e s t h e t u r n -t a b l e t h r o u g h s e v e r a l s e t s o f s p e e d r e d u c i n g g e a r s , a n d t h e t u r n t a b l e v e l o c i t y i s v e r y low, t h e d i s k v e l o c i t y was d e t e r m i n e d by m e a s u r i n g t h e t i m e e l a p s e d d u r i n g a known number o f r e v o l u t i o n s . The v e l o c i t y o f t h e d i s k a t t h e s l i d e r - t r a c k i n t e r f a c e was t h e n c a l c u l a t e d . 3.3 P o l i s h i n g P r o c e d u r e The g o a l o f t h e s u r f a c e f i n i s h i n g t e c h n i q u e s was t o d e v e l o p a s i m p l e p o l i s h i n g p r o c e d u r e t h a t p r o d u c e d a r e p r o d u c i b l e s u r f a c e f i n i s h and r e p r o d u c i b l e f r i c t i o n b e h a v i o u r . The s u r f a c e s were a l s o r e q u i r e d t o be f r e e o f embedded m a t e r i a l o r o i l y r e s i d u e . 3.3.1 G o l d T h r e e methods o f p r e p a r i n g t h e g o l d s u r f a c e s were t e s t e d . D u r i n g t h e p r e l i m i n a r y t e s t s t h e g o l d d i s k a n d t h e g o l d s l i d e r were u s e d i n t h e a s - r e c e i v e d c o n d i t i o n . The s l i d e r and t h e t r a c k h a d b e e n m a c h i n e d b u t n o t p o l i s h e d , a n d v i s i b l e d i r t and o i l h a d b e e n r e m o v e d b y r i n s i n g t h e d i s k a n d t h e s l i d e r w i t h h e x a n e s . U n d e r t h e s e c o n d i t i o n s s t i c k - s l i p o c c u r r e d b u t i t was n o t u n i f o r m o r r e p r o d u c i b l e . The s e c o n d t e c h n i q u e i n v o l v e d p o l i s h i n g w i t h t r i p o l i , f o l l o w e d b y j e w e l e r s r o u g e . T r i p o l i a n d j e w e l e r s 26 r o u g e a r e compounds u s e d t o p o l i s h g o l d a l l o y s c o m m e r c i a l l y . The s l i d e r a n d t h e d i s k were p o l i s h e d b y p r e s s i n g them a g a i n s t r o t a t i n g s o f t w o o d d i s k s w h i c h had b e e n c h a r g e d w i t h t h e p o l i s h i n g compound. M e d i o c r e r e s u l t s were o b t a i n e d . The s u r f a c e s were s h i n y b u t s c r a t c h e s were f i l l e d w i t h p o l i s h i n g d e b r i s and s m e a r e d g o l d . I n a d d i -t i o n t h e a b r a s i v e s i n t h e p o l i s h i n g compounds were c a r r i e d i n a wax b a s e w h i c h i m m e d i a t e l y e x c l u d e d t h e p o s s i b i l i t y o f o b t a i n i n g a c l e a n s u r f a c e . The most e f f e c t i v e p r e p a r a t i o n i n v o l v e d g r i n d i n g t h e s u r f a c e s w i t h d r y emery p a p e r . The d i s k and t h e s l i d e r were c l e a n e d w i t h s o l v e n t , t h e n g r o u n d w i t h a s e r i e s o f c l e a n , d r y , 320 and 400 g r a d e emery p a p e r s . A f t e r g r i n d i n g t h e d i s k a n d s l i d e r s were w i p e d f r e e o f p o l i s h i n g d e b r i s w i t h c l e a n d r y c o t t o n and t e s t e d i m m e d i a t e l y . U s i n g t h i s t e c h n i q u e i t was f o u n d t h a t t h e f r i c t i o n b e h a v i o u r a n d t h e s u r f a c e f i n i s h were r e p r o d u c i b l e . L a p p i n g h a s b e e n a f a v o u r i t e t e c h n i q u e i n many f r i c t i o n s t u d i e s . B e c a u s e p u r e g o l d i s s o f t a n d e a s i l y damaged a n d a l s o s u s c e p t i b l e t o embedded a b r a s i v e , l a p p i n g was r e j e c t e d a s a s u i t a b l e t e c h n i q u e . E l e c t r o l y t i c p o l i s h i n g was r e j e c t e d a s a s u i t a b l e p o l i s h i n g t e c h n i q u e b e c a u s e o f t h e s i z e o f t h e d i s k , a n d t h e t o x i c i t y o f t h e c y a n i d e e l e c t r o l y t e . 3.3.2 S t e e l Two p o l i s h i n g methods were u s e d on t h e s t e e l s a m p l e s . The f i r s t method i n v o l v e d l a p p i n g f o r a f i n a l f i n i s h . T he s u r f a c e s o f t h e d i s k and s l i d e r h a d b e e n g r o u n d a f t e r m a c h i n i n g and t h e n l a p p e d . The l a p p i n g com-po u n d u s e d was f i n e emery powder w i t h h e a v y p e t r o l a t u m o i l a s an a b r a s i v e c a r r i e r . The s u r f a c e s were l a p p e d u n t i l a l l s i g n s o f p r e v i o u s wear h a d b e e n r e m o v e d . The p o l i s h i n g compound a n d d e b r i s was t h e n r i n s e d o f f t h e s u r f a c e s w i t h h e x a n e s . The p r o b l e m w i t h t h i s t e c h n i q u e was t h a t t h e s u r f a c e s h a d b e e n e x p o s e d t o o i l d u r i n g p o l i s h i n g and s u b s e q u e n t r e m o v a l o f r e s i d u a l p e t r o l a t u m o i l was d i f f i c u l t . More r e p r o d u c i b l e r e s u l t s were o b t a i n e d b y l a p p i n g t h e s t e e l d i s k and s l i d e r , t h e n c l e a n i n g w i t h h e x a n e s , f o l l o w e d b y g r i n d i n g w i t h a s u c c e s s i o n o f emery p a p e r s , s t a r t i n g w i t h 180 g r a d e and e n d i n g w i t h 400 g r a d e . When t h i s was done i t was f o u n d t h a t t h e s t e e l s u r f a c e s were r e l a t i v e l y f r e e f r o m embedded a b r a s i v e and s c r a t c h e s . The s u r f a c e s were w i p e d w i t h c l e a n , d r y c o t t o n and t e s t e d i m m e d i a t e l y a f t e r p o l i s h i n g . B o t h t h e g o l d a n d t h e s t e e l s u r f a c e s were t e s t e d f o r c l e a n l i n e s s u s i n g t h e w a t e r d r o p t e c h n i q u e . I f a d r o p o f d i s t i l l e d w a t e r i s p l a c e d on a c l e a n m e t a l s u r f a c e i t s h o u l d s p r e a d e v e n l y on t h e s u r f a c e ; i f t h e s u r f a c e i s c o n t a m i n a t e d w i t h o i l , t h e w a t e r d r o p w i l l n o t s p r e a d [!•]• 28 I f t h e g o l d and s t e e l s u r f a c e s were p o l i s h e d u s i n g emery p a p e r t h e a n g l e o f c o n t a c t o f t h e w a t e r d r o p l e t was v e r y s m a l l ( s p r e a d i n g ) , b u t i f t h e l a p p i n g o r t r i p o l i p o l i s h i n g t e c h n i q u e were u s e d , t h e n t h e w a t e r r e m a i n e d on t h e s u r f a c e a s d e f i n i t e d r o p s w i t h l a r g e a n g l e s o f c o n t a c t . 3.3.3 V a p o r d e g r e a s i n g I n some o f t h e s t i c k - s l i p t e s t s , o i l o r g r e a s e was u s e d as a l u b r i c a n t . V a p o r d e g r e a s i n g i s one t e c h -n i q u e u s e d t o remove u n b o n d e d o r g a n i c compounds f r o m a m e t a l s u r f a c e . The s u r f a c e t o be c l e a n e d i s p l a c e d i n t h e v a p o r a b o v e a b a t h o f b o i l i n g s o l v e n t ( t r i c h l o r o -e t h l y e n e ) . The s o l v e n t v a p o r c o n d e n s e s o n t h e s u r f a c e , d i s s o l v e s t h e o r g a n i c c o n t a m i n a n t , t h e n r u n s o f f t h e s u r f a c e a n d f a l l s b a c k i n t o t h e b a t h . I n t h i s way f r e s h , s o l v e n t c o n t i n u o u s l y r i n s e s t h e s u r f a c e f r e e o f e x c e s s h y d r o c a r b o n s . 3.3.4 S u r f a c e f i n i s h The s u r f a c e f i n i s h o f t h e d i s k s was m e a s u r e d u s i n g a B r u s h " S u r f i n d i c a t o r " . The s u r f a c e s p r e p a r e d b y t h e emery p a p e r t e c h n i q u e h a d a d i r e c t i o n a l f i n i s h a n d a v e r a g e s u r f a c e r o u g h n e s s o f 5/xin. rms. a c r o s s t h e t r a c k and 3 M i n . rms. a l o n g t h e t r a c k . 3.4 P r e l i m i n a r y T e s t s P r e l i m i n a r y t e s t s were c o n d u c t e d t o d e t e r m i n e w h e t h e r t h e s l i d i n g v e l o c i t i e s , l o a d s , damping a n d e l a s t i c i t y o f t h e s y s t e m were s u c h t h a t s t i c k - s l i p w o u l d o c c u r . T e s t s t o i n d i c a t e t h e e f f e c t o f t h e v a r i o u s p o l i s h i n g a n d c l e a n i n g t e c h n i q u e s were a l s o c o n d u c t e d . P r e l i m i n a r y t e s t s were c o n d u c t e d o n g o l d s l i d i n g o n g o l d , C1020 s t e e l s l i d i n g o n C1020 s t e e l a n d g o l d s l i d i n g o n C1020 s t e e l . As a r e s u l t o f t h e s e t e s t s t h e a p p a r a t u s was m o d i f i e d s l i g h t l y t o a l l o w a l o w e r r a n g e o f d i s k v e l o c i t i e s a n d t h u s l a r g e r s t i c k - s l i p a m p l i t u d e s . The p r e l i m i n a r y t e s t s i n d i c a t e d t h a t t h e i n i t i a l s u r f a c e p r e p a r a t i o n was c r i t i c a l a n d h a d a l a r g e e f f e c t on s t a t i c f r i c t i o n v a l u e s . 3.5 H u m i d i t y T e s t s A f t e r p o l i s h i n g , t h e s u r f a c e s were e i t h e r r u n i m m e d i a t e l y o r s u b j e c t e d t o a t r e a t m e n t i n t h e h u m i d i t y c h a m b e r . F i f t e e n m i n u t e s were a l l o w e d f o r t h e t e s t c hamber t o r e a c h s t a b i l i z a t i o n a t a p a r t i c u l a r r e l a t i v e h u m i d i t y w h i c h was a l w a y s a b o v e t h e h u m i d i t y o f p o l i s h i n g The t e m p e r a t u r e o f t h e e n v i r o n m e n t was m e a s u r e d , i n a d d i t i o n t o t h e s u r f a c e t e m p e r a t u r e o f t h e d i s k . 30 3.6 Load, V e l o c i t y and Run-in T e s t s A f t e r the s u r f a c e c o n d i t i o n s which permit s t i c k -s l i p t o occur were d e f i n e d , l o a d , v e l o c i t y and r u n - i n t e s t s were conducted. The l o a d and v e l o c i t y t e s t s d e f i n e the g e n e r a l b e h a v i o u r of the g o l d on g o l d system under s t i c k - s l i p v i b r a t i o n . The amplitude of v i b r a t i o n was observed t o i n c r e a s e w i t h r e p e a t e d t r a c k t r a v e r s e s . S i n c e i n c r e a s e d amplitude was a l s o e x p e c t e d d u r i n g the s u r f a c e temperature t e s t s , r u n - i n t e s t s were n e c e s s a r y to s e p a r a t e these e f f e c t s . D u r i n g the r u n - i n t e s t s the g o l d t r a c k and g o l d s l i d e r were r u n t o g e t h e r under c o n s t a n t l o a d and a t c o n s t a n t speed f o r s e v e r a l r e v o l u t i o n s . The s t i c k - s l i p c y c l e s f o r each d i s k r e v o l u t i o n were r e c o r d e d and an average s t a t i c f r i c t i o n v a l u e f o r each r e v o l u t i o n was c a l c u l a t e d . B e f o r e the l o a d arid v e l o c i t y t e s t s were c a r r i e d out, the s u r f a c e s were r u n t o g e t h e r f o r 20 r e v o l u t i o n s under a c o n s t a n t l o a d and a t a c o n s t a n t d i s k speed. F o r each l o a d - v e l o c i t y t e s t the l o a d was h e l d c o n s t a n t and the d i s k v e l o c i t y was changed a f t e r each f u l l r e v o l u t i o n of the d i s k . The s t i c k - s l i p c y c l e s f o r each r e v o l u t i o n were r e c o r d e d and an average s t a t i c f r i c t i o n v a l u e f o r each r e v o l u t i o n was c a l c u l a t e d . 31 3.7 Temperature T e s t s The temperature t e s t s were conducted u s i n g heavy p e t r o l a t u m o i l (a n a p t h e n i c hydrocarbon) as a l u b r i c a n t . O i l was a p p l i e d t o the d i s k a t the b e g i n n i n g and 20 r e v o l u t i o n s o f the d i s k were a l l o w e d b e f o r e the tempera-t u r e was i n c r e a s e d . The temperature of the d i s k was then i n c r e a s e d t o 130°C a t 10°C i n t e r v a l s , and the r e s u l t s were r e c o r d e d f o r a f u l l r e v o l u t i o n o f the d i s k . Both g o l d on g o l d and s t e e l on s t e e l were t e s t e d . 3.8 Measurement of the E l e c t r i c a l R e s i s t a n c e of the  S l i d e r - T r a c k I n t e r f a c e d u r i n g S t i c k - S l i p The changes i n the r e s i s t a n c e of the s l i d e r - t r a c k i n t e r f a c e d u r i n g s t i c k - s l i p were monitored u s i n g the b r i d g e d e s c r i b e d i n Appendix A. CHAPTER 4 RESULTS AND DISCUSSION 4.1 E f f e c t of Surface Conditions and Environment on  S t i c k - S l i p V i b r a t i o n The behaviour of the gold on gold system was tested at humidities ranging from 10% to 90% r e l a t i v e humidity at room temperature and also under four d i f f e r -ent surface conditions: (1) dry (as polished); (2) water f i l m on the surface; (3) napthenic petrolatum o i l and (4) vapor-degreased surfaces. The preparation of the surfaces has been described i n a previous s e c t i o n . B a s i c a l l y i t consisted of generating new, uncontaminated surfaces by abrading the disk and s l i d e r with dry emery paper. In the tests under consideration, the temperature of the environment was 24°C; the s l i d i n g v e l o c i t i e s ranged from 0.001 in-sec to 0.2 in-sec"*'*", and the loads applied to the s l i d e r ranged from 2.1 to 5.2 l b s . 4.1.1 Dry (as-polished) surfaces When the s l i d e r and the track were run together immediately a f t e r p o l i s h i n g , s t i c k - s l i p v i b r a t i o n would not occur. The displacement-time record of a t y p i c a l run i s shown i n Figure 4 ( a ) . In t h i s case the f r i c t i o n c o e f f i c i e n t s are greater than 1. The displacement-time record also shows that the motion of the s l i d e r can be in t e r m i t t e n t , as i n s t i c k - s l i p type v i b r a t i o n . However, the displacement-time records d i f f e r from those observed i n a s t i c k - s l i p type of motion (see Figure 4(b) ) i n two ways: (1) the f r i c t i o n c o e f f i c i e n t s are much lower when s t i c k - s l i p v i b r a t i o n occurs and (2) the ta n g e n t i a l force increases l i n e a r l y with respect to time during the s t i c k part of the cycl e i n true s t i c k - s l i p type v i b r a t i o n and s l i p occurs at regular i n t e r v a l s . Microscopic i n v e s t i g a t i o n s of the s l i d e r and the track before and a f t e r the dry te s t s showed that running the clean, dry gold surfaces together r e s u l t e d i n a heavy scoring of both the s l i d e r and the track. Figures 5(a) and 5(b) are photographs of the track before and a f t e r the t e s t s . The part of the wear track shown i n Figure 5(b) i s t y p i c a l of the damage observed. The wear tracks begin with a narrow shallow area that widens and deepens. They end with a deposit of disturbed metal which l i e s above the surface. The wear tracks may be continuous or they may be interrupted at i r r e g u l a r i n t e r -v a l s . At the lower of the applied normal loads, 2.1 l b s . the damage was usually observed to c o n s i s t of a s i n g l e track. With higher loads, two or three simultaneous tracks were observed. Under the low load conditions, a 34 t y p i c a l t r a c k was about 0.01 i n . wide and .005 i n . i n depth. The s u r f a c e of the s l i d e r was a l s o damaged d u r i n g s l i d i n g . The damage c o n s i s t e d both of areas of heavy wear s i m i l a r t o those found on the t r a c k and clumps of d i s t u r b e d metal c a l l e d "prows". In some c a s e s , these prows c o u l d be observed a t the s l i d e r d i s k i n t e r f a c e as the s l i d e r t r a v e r s e d the d i s k . T h i s type of s l i d i n g b e h a v i o u r was found to be c h a r a c t e r i s t i c of both s t e e l s l i d i n g on s t e e l and g o l d s l i d i n g on g o l d under d r y , f r e s h l y p o l i s h e d c o n d i t i o n s . The r e s u l t s of these t e s t s can be i n t e r p r e t e d i n terms of the r e s u l t s o f some of the h i g h vacuum s t u d i e s of metal s l i d i n g systems conducted by K e l l o g g [39] and by Bowden and Young [ 2 8 ] , In the h i g h vacuum t e s t s , the s u r f a c e s are c l e a n e d o f s u r f a c e f i l m s and then kept f r e e o f adsorbed contaminants by the h i g h vacuum environment. Even a t room temperature the metal specimens s e i z e t o g e t h e r , and v e r y h i g h f r i c t i o n c o e f f i c i e n t s r e s u l t . I n the p r e s e n t study, p r o t e c t i v e o x i d e or o r g a n i c f i l m coverage of the s u r f a c e s was l i m i t e d by u s i n g d r y g r i n d i n g (no o r g a n i c a b r a s i v e c a r r i e r s were used) t e c h -n i q u e s and by u s i n g g o l d which r e s i s t s o x i d a t i o n . The h i g h f r i c t i o n v a l u e s o b t a i n e d and the severe wear of the c o n t a c t i n g s u r f a c e s i s due t o adhesion o f the s u r f a c e s over the a r e a o f c o n t a c t . S i m i l a r adhesion has been ob s e r v e d i n h i g h vacuum environments, or i n s i t u a t i o n s 35 i n which pro t e c t i v e surface f i l m s are disrupted by normal and tangential loads as i n r o l l - b o n d i n g . Studies on the geometry of the "prow" formed during scoring and the h o r i z o n t a l forces involved i n s l i d -ing have been reported by Antler [40], Ainbinder and Prancs [32] and Cocks [31]. The exact d e t a i l s of the surface damage were not considered relevant to the present study. The most important r e s u l t i s that the observed d i s r u p t i o n of the surfaces and the i r r e g u l a r displacement-time records demonstrate that under these dry conditions, with gold on gold and s t e e l on s t e e l systems, r e l a x a t i o n o s c i l l a t i o n s of the s t i c k - s l i p type w i l l not occur. This i n d i c a t e s that surface contamination may be a very s i g n i -f i c a n t parameter i n subsequent i n v e s t i g a t i o n s of 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 s . 4.1.2 Influence of humidity In the humidity t e s t s , f r e s h l y polished gold surfaces were exposed to the environment i n the humidity chamber f o r 15 minutes, then tested i n the constant humid-i t y environment. In the range of humidities tested, from 10% to 90% r e l a t i v e humidity at 24°C, no e f f e c t was n o t i c e a b l e . In a l l of the tests i n t h i s range, seizure of the s l i d i n g surface's s i m i l a r to the seizure encountered i n the dry t e s t s occurred. I f humidity had any e f f e c t on the magnitude of the t a n g e n t i a l forces required to cause r e l a t i v e movement of the s l i d e r , then the s c a t t e r normally 36 a s s o c i a t e d w i t h t e s t s i n w h i c h s e i z u r e o c c u r s h a s o b s c u r e d t h a t e f f e c t . The r e l a t i v e h u m i d i t y o f t h e t e s t e n v i r o n m e n t was i n c r e a s e d u n t i l c o n d e n s a t i o n o c c u r r e d o n t h e g o l d s u r f a c e s . T h e n when t h e s l i d e r a n d t r a c k were r u n t o g e t h e r s t i c k -s l i p v i b r a t i o n s o c c u r r e d . 4.1.3 E f f e c t o f w a t e r f i l m s I n o r d e r t o e l i m i n a t e t h e p o s s i b i l i t y o f w a t e r -b o r n e c o n t a m i n a t i o n , s i n g l e - d i s t i l l e d w a t e r was c o n d e n s e d on t h e s u r f a c e s . When t e s t e d , s t i c k - s l i p v i b r a t i o n s o c c u r r e d a t low s l i d i n g v e l o c i t i e s ( i n t h e r e g i o n o f 0.001 i n - s e c " " ^ ) . A b o u t o n e - h a l f i n c h o f t h e t r a c k p e r i m e t e r was c o v e r e d i n a s i n g l e t e s t . I f t h e c o n d e n s e d w a t e r was r e m o v e d f r o m b e t w e e n t h e s l i d e r a n d t h e t r a c k , and t h e a r e a r e t e s t e d , t h e s u r f a c e s s e i z e d t o g e t h e r and were a s h e a v i l y damaged a s b e f o r e . The r e s u l t s o f t h e s e t e s t s i n d i c a t e d t h a t t h e p r e s e n c e o f w a t e r was s u f f i c i e n t t o s t o p s e i z u r e a t t h e s e v e l o c i t i e s and t h a t t h e e f f e c t was due t o t h e w a t e r i t s e l f , n o t w a t e r - b o r n e o i l o r g r e a s e c o n t a m i n a n t s . 4.1.4 E f f e c t o f p e t r o l a t u m o i l The g o l d s l i d i n g on g o l d s y s t e m was a l s o t e s t e d u s i n g h e a v y p e t r o l a t u m o i l as a l u b r i c a n t . T h i s o i l i s 37 a n a p t h e n i c h y d r o c a r b o n and d o e s n o t , i n i t s p u r e f o r m , c o n t a i n any p o l a r g r o u p s . I n t r o d u c i n g t h e p e t r o l a t u m o i l c a u s e d r e l a x a t i o n o s c i l l a t i o n s a t l o w s l i d i n g s p e e d s ( l e s s t h a n 0.4 i n - s e c - " 1 " ) i n b o t h t h e g o l d on g o l d and t h e s t e e l on s t e e l s y s t e m s . I n t h e l o n g t e r m t e s t s t h e p e t r o l a t u m o i l d e c r e a s e d , b u t d i d n o t a l w a y s e l i m i n a t e , s c o r i n g i n t h e two s y s t e m s . M i c r o s c o p i c e x a m i n a t i o n s o f t h e s u r f a c e s u n d e r -g o i n g s t i c k - s l i p t y p e v i b r a t i o n showed t h a t v e r y l i t t l e s u r f a c e damage h a d o c c u r r e d . The t r a c k s u r f a c e ( s e e F i g u r e 5 ( c ) ) showed v e r y m i l d w ear. The s u r f a c e o f t h e s l i d e r was undamaged, e x c e p t f o r a s m a l l r e g i o n n e a r t h e c e n t r e o f t h e s l i d e r w h i c h was smooth a n d w o r n . A l t h o u g h m e t a l l i c c o n t a c t c a n o c c u r , t h e low f r i c t i o n v a l u e s a n d t h e a b s e n c e o f e x t e n s i v e s u r f a c e damage d u r i n g s t i c k - s l i p i n d i c a t e t h a t t h e r e i s much l e s s a d h e s i o n d u r i n g s t i c k - s l i p t h a n d u r i n g t h e i n t e r m i t t e n t s l i d i n g m o t i o n . T h e s e t e s t s w i t h p e t r o l a t u m o i l and w i t h a w a t e r f i l m a l s o i n d i c a t e t h a t one o f t h e i m p o r t a n t p a r a -m e t e r s i n d e t e r m i n i n g w h e t h e r s t i c k - s l i p t y p e v i b r a t i o n w i l l o c c u r i n a p a r t i c u l a r s y s t e m i s t h e p r e s e n c e o f some medium t h a t w i l l p r e v e n t g r o s s a d h e s i o n . 4.1.5 E f f e c t o f v a p o r d e g r e a s i n g F r o m t h e i n i t i a l t e s t s i t was. n o t a p p a r e n t w h e t h e r t h e e f f e c t o f p e t r o l a t u m o i l on t h e f r i c t i o n b e h a v i o u r was 38 o f c h e m i c a l o r p h y s i c a l o r i g i n . U s i n g t h e v a p o r d e g r e a s i n g t e c h n i q u e i t was p o s s i b l e t o remove e x c e s s l u b r i c a n t f r o m t h e s u r f a c e s . Any c h e m i c a l c o n t a m i n a t i o n ( s u r f a c e - a c t i v e s o l u t e s t h a t c o u l d h a v e c o n t a m i n a t e d t h e p e t r o l a t u m o i l ) w o u l d n o t be r e m o v e d . The p o s s i b i l i t y t h a t s u f f i c i e n t a mounts o f s u r f a c e a c t i v e s p e c i e s were p r e s e n t i n t h e p e t r o l a t u m o i l c o u l d n o t be i g n o r e d a s t h e p e t r o l a t u m o i l w o u l d h a v e a t e n d e n c y t o o x i d i z e o v e r a p e r i o d o f t i m e , and c o u l d a l s o be c o n t a m i n a t e d b y e x p o s u r e t o o t h e r l u b r i -c a n t s i n g e n e r a l u s e i n t h e l a b o r a t o r y . On t h e d e g r e a s e d g o l d s u r f a c e s , . s e i z u r e o c c u r r e d i n a r e a s w h i c h h a d p r e v i o u s l y shown g o o d s t i c k - s l i p v i b r a t i o n . I n t h e c a s e o f s t e e l o n s t e e l a few c y c l e s o f s t i c k - s l i p w o u l d be f o l l o w e d b y s e i z u r e and p l o u g h i n g . The e f f e c t o f t h e p e t r o l a t u m o i l c a n a l s o be shown by d e l i b e r a t e l y d i s r u p t i n g t h e o i l f i l m o n t h e s u r f a c e . I n F i g u r e 6(a) t h e s t i c k - s l i p v i b r a t i o n i s w e l l e s t a b l i s h e d ; i n F i g u r e 6(b) t h e o i l h a s b e e n r e m o v e d f r o m a s e c t i o n o f t h e t r a c k ( w i t h o u t d i s t u r b i n g t h e s l i d e r ) a n d t h e a m p l i -t u d e o f v i b r a t i o n h a s d e c r e a s e d . T h i s s e r i e s o f t e s t s on s u r f a c e c o n d i t i o n s a n d r e l a x a t i o n o s c i l l a t i o n s was i m p o r t a n t t o t h i s s t u d y i n s e v e r a l r e s p e c t s . F i r s t o f a l l i n t h e g o l d on g o l d s l i d i n g s y s t e m r e l a t i v e h u m i d i t y d o e s n o t seem t o a f f e c t t h e b e h a v i o u r u n t i l v e r y h i g h h u m i d i t i e s a r e r e a c h e d . S e c o n d l y , s t i c k - s l i p t y p e o s c i l l a t i o n s c a n n o t be e x p e c t e d 39 u n d e r d r y f r i c t i o n c o n d i t i o n s . I n s t e a d , an i n t e r m i t t e n t s l i d i n g m o t i o n w i l l be p r o d u c e d . S e v e r e s u r f a c e damage and h i g h f r i c t i o n c o e f f i c i e n t s accompany t h i s t y p e o f s l i d i n g . The i n t r o d u c t i o n o f p e t r o l a t u m o i l b e t w e e n t h e s l i d e r and t h e d i s k r e d u c e s t h e damage and a l s o p e r m i t s s t i c k - s l i p t y p e v i b r a t i o n a t low s p e e d s . S i n c e one'-of t h e g o a l s o f t h e r e s e a r c h was t o e x p l o r e t h e e f f e c t o f t e m p e r a t u r e o n t h e s t a t i c f r i c t i o n f o r c e ( t a n g e n t i a l f o r c e a t s l i p ) u s i n g s t i c k - s l i p t y p e v i b r a t i o n s , i t was d e c i d e d t o u s e t h e p e t r o l a t u m o i l i n t h e s u b s e q u e n t t e s t s . The r e s u l t s o f t h e s e t e s t s on s u r f a c e p r e p a r a t i o n , and some o t h e r s t u d i e s on n o r m a l v i b r a t i o n s d u r i n g r e l a x -a t i o n o s c i l l a t i o n s b y T o l s t o i [ 4 1 ] a l s o r a i s e d some i n t e r e s t i n g q u e s t i o n s a s t o t h e r o l e o f t h e l u b r i c a n t i n s t i c k - s l i p . B e f o r e t h e t e m p e r a t u r e t e s t s c o u l d be c o n d u c t e d i t was n e c e s s a r y t o d e t e r m i n e how o t h e r f a c t o r s s u c h a s r u n - i n a n d d i s k v e l o c i t y a f f e c t e d t h e s t a t i c f r i c t i o n f o r c e s f o r t h e g o l d a n d g o l d s y s t e m . S i n c e t h i s i n f o r m a -t i o n was n o t a v a i l a b l e r u n - i n , v e l o c i t y a n d n o r m a l l o a d i n g t e s t s were c o n d u c t e d a t room t e m p e r a t u r e a n d h u m i d i t y , u s i n g t h e p e t r o l a t u m o i l a s a l u b r i c a n t . 4 . 2 R e s u l t s o f R u n - I n The r u n - i n t e s t s were c a r r i e d o u t a t a f i x e d d i s k v e l o c i t y and n o r m a l l o a d . The d i s p l a c e m e n t - t i m e r e c o r d o f 40 t h e s l i d e r m o t i o n was r e c o r d e d f o r t h e f u l l r e v o l u t i o n o f t h e d i s k . A f u l l r e v o l u t i o n o f t h e d i s k w o u l d y i e l d up t o 300 s e p a r a t e s t i c k - s l i p c y c l e s . The s t a t i c f r i c t i o n f o r c e was n o t a c o n s t a n t v a l u e i n any o f t h e s e r u n - i n t e s t s and some method o f j u d g i n g w h i c h v a l u e was r e p r e s e n t a t i v e was n e e d e d . I t was d e c i d e d t h a t one method c o u l d be t o p l o t a f r e q u e n c y d i s t r i b u t i o n c u r v e o f a l l t h e s t a t i c f r i c t i o n v a l u e s o b t a i n e d i n e a c h r e v o l u t i o n o f t h e d i s k a n d s e l e c t t h e mode o r most r e p e t i t i v e v a l u e . I n some c a s e s ( s e e F i g u r e 7) t h i s method was a d e q u a t e : t h e s t a t i c f r i c t i o n v a l u e s f o r a p a r t i c u l a r r u n a r e g r o u p e d a b o u t a s i n g l e v a l u e w h i c h w o u l d i n d i c a t e t h a t t h e f r i c t i o n c o e f f i c i e n t h a d a c o n s t a n t v a l u e a r o u n d t h e t r a c k . However, i n o t h e r c a s e s t h e r e were t h r e e o r f o u r s t a t i c f r i c t i o n v a l u e s w h i c h o c c u r r e d w i t h e q u a l f r e q u e n c y . T h i s was e s p e c i a l l y t r u e o f t h e i n i t i a l r u n s . B e c a u s e o f t h e d i f f i c u l t y i n s e l e c t i n g a r e p r e s e n t a t i v e v a l u e f o r t h e i n i t i a l r u n s t h e s t a t i c f r i c t i o n f o r c e v a l u e f o r a p a r t i c u l a r t e s t was d e t e r m i n e d b y t a k i n g t h e a v e r a g e o f t h e s t a t i c f r i c t i o n f o r c e s f o r e a c h o f t h e s t i c k - s l i p c y c l e s . T h i s a v e r a g e s t a t i c f r i c t i o n f o r c e v a l u e was t h e n u s e d i n c a l c u l a t i n g t h e 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 s . 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 was f o u n d t o be s e n s i t i v e t o r u n - i n f o r t h e f i r s t 10 t o 15 r e v o l u t i o n s o f t h e d i s k . The r e s u l t s o f f o u r r u n - i n t e s t s , c o n d u c t e d a t v a r i o u s l o a d i n g r a t e s and n o r m a l l o a d s a r e shown i n 41 F i g u r e 8. A f t e r t h e t e n t h r e v o l u t i o n , t h e s t a t i c f r i c t i o n v a l u e s were s t i l l i n c r e a s i n g , b u t a t a r e d u c e d r a t e . The e f f e c t o f r u n - i n d u r i n g s u b s e q u e n t l o a d , v e l o c i t y o r t e m p e r a t u r e t e s t was m i n i m i z e d by r u n n i n g t h e s l i d e r and t r a c k t o g e t h e r f o r 20 r e v o l u t i o n s b e f o r e v a r y i n g any o t h e r p a r a m e t e r s . 4.3 L o a d and V e l o c i t y T e s t s 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 o f t h e g o l d - g o l d s y s t e m was s e n s i t i v e b o t h t o t h e a p p l i e d n o r m a l l o a d and t h e d i s k v e l o c i t y . I n F i g u r e 9 t h e r e s u l t s o f l o a d -v e l o c i t y t e s t s f o r g o l d and v e l o c i t y t e s t s f o r s t e e l a r e p r e s e n t e d . 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 f o r g o l d o n g o l d i s h i g h e r t h a n t h e 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 f o r s t e e l on s t e e l . I n F i g u r e 9, 9 i s u s e d a s t h e a b s c i s s a , i n s t e a d o f t r a c k v e l o c i t y . The t r a c k v e l o c i t y c o n t r o l s F t h e r a t e o f a p p l i c a t i o n o f t h e t a n g e n t i a l f o r c e , F, f r o m t h e i n i t i a l t a n g e n t i a l l o a d , F Q . T h u s a t any t i m e F = F + F t . The r a t i o o f t h e r a t e o f a p p l i c a t i o n o f t h e o t a n g e n t i a l f o r c e t o t h e n o r m a l l o a d , F/N i s 9 . From t h e e x p e r i m e n t a l d a t a o f F i g u r e 9, i t c a n be s e e n t h a t i n b o t h t h e g o l d o n g o l d a n d s t e e l on s t e e l c a s e s , t h e 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 d e c r e a s e s a s t h e t a n g e n t i a l l o a d i n g r a t e i n c r e a s e s . T h e s t a t i c f r i c t i o n v a l u e s f o r s t e e l f r o m t h e p r e s e n t work and t h o s e o f J o h a n n e s [ 2 7 ] a r e i n g o o d a g r e e m e n t e v e n t h o u g h t h e f r i c t i o n s y s t e m s . 42 h a d d i f f e r e n t c o n f i g u r a t i o n s . The o r i g i n o f t h e e f f e c t o f t a n g e n t i a l l o a d i n g r a t e o n s t a t i c f r i c t i o n w i l l be i n v e s t i g a t e d f u r t h e r , a s one p a r t o f t h e i n v e s t i g a t i o n o f c h a n g e s i n e l e c t r i c a l r e s i s t a n c e o f t h e s l i d e r - t r a c k i n t e r f a c e d u r i n g s t i c k - s l i p . 4.4 T e m p e r a t u r e T e s t s F rom t h e i n i t i a l s t u d i e s on t h e i n i t i a t i o n o f s t i c k - s l i p i n a g o l d o n g o l d s y s t e m , i t was c o n c l u d e d t h a t s t i c k - s l i p i s n o t p o s s i b l e o n v e r y c l e a n g o l d o r s t e e l s u r f a c e s and t h a t n a p t h e n i c p e t r o l a t u m o i l c o u l d be u s e d t o o b t a i n c o n s i s t e n t s t i c k - s l i p . O r i g i n a l l y i t was p r o p o s e d t h a t t h e o b s e r v e d i n c r e a s e i n s t a t i c f r i c t i o n f o r c e a s t h e d i s k v e l o c i t y was d e c r e a s e d was due t o c r e e p u n d e r t h e a c t i o n o f t h e n o r m a l l o a d . I n c r e a s i n g t h e t e m p e r a t u r e o f t h e g o l d s h o u l d a l l o w more c r e e p p e r u n i t o f t i m e o f s t i c k a n d t h u s a c o r r e s p o n d i n g i n c r e a s e i n s t a t i c f r i c t i o n . I n t r o d u c i n g a l u b r i c a n t i n t o t h e f r i c t i o n s y s t e m c o m p l i c a t e d t h e i n t e r p r e t a t i o n o f t h e t e m p e r a t u r e t e s t s . The o i l c o u l d d e compose, v a p o r i z e o r o x i d i z e as w e l l a s c h a n g e v i s c o s i t y as t h e t e m p e r a t u r e was i n c r e a s e d . I n i t i a l l y t h e r e s u l t o f i n c r e a s i n g t h e b u l k tem-p e r a t u r e o f t h e s t e e l a n d t h e g o l d s y s t e m s was t o i n c r e a s e t h e 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 . T h e n a t a p p r o x i m a t e l y 43 1 0 0 ° C s t i c k - s l i p c e a s e d a n d p l o u g h i n g b e g a n . T h i s t e m p e r -a t u r e v a r i e d f r o m t e s t t o t e s t b u t f o r t h e e i g h t t e s t s o f t h e two s y s t e m s , t h e r a n g e was 1 0 5 ° C t o 1 2 0 ° C . The t e m p e r -a t u r e was m e a s u r e d on t h e s u r f a c e o f t h e d i s k , a n d t h u s d o e s n o t r e p r e s e n t t h e i n t e r f a c e t e m p e r a t u r e . The t e m p e r -a t u r e a t w h i c h p l o u g h i n g o c c u r r e d was much l o w e r t h a n t h e d e c o m p o s i t i o n t e m p e r a t u r e o f m i n e r a l o i l s ( a b o u t 2 5 0 ° C ) and t o o low f o r a p p r e c i a b l e c r e e p t o h a v e o c c u r r e d . I t i s p o s s i b l e t h a t t h i s t e m p e r a t u r e r e p r e s e n t s t h e t e m p e r a t u r e a t w h i c h t h e s t r u c t u r e o f t h e a d s o r b e d o i l l a y e r s i s d e s t r o y e d . T h u s i t c a n be c o n c l u d e d t h a t s i n c e i n i t i a t i n g s t i c k - s l i p t y p e v i b r a t i o n s r e q u i r e s a l u b r i c a n t , t h e e f f e c t o f t e m p e r a t u r e on 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 s w i l l be d e p e n d e n t on t h e l u b r i c a n t u s e d a n d t h a t d i s c e r n i n g t h e c h a n g e s t h a t a r e due t o t h e e f f e c t o f t e m p e r a t u r e on m a t e r i a l p r o p e r t i e s may be d i f f i c u l t . 4.5 E l e c t r i c a l R e s i s t a n c e o f T r a c k - S l i d e r I n t e r f a c e  D u r i n g S t i c k - S l i p The e l e c t r i c a l r e s i s t a n c e o f t h e t r a c k - s l i d e r i n t e r f a c e d u r i n g s t i c k - s l i p was i n v e s t i g a t e d i n t h r e e s t a g e s : 1. o v e r a l l b e h a v i o u r o f i n t e r f a c e r e s i s t a n c e d u r i n g s t i c k - s l i p c y c l e f o r g o l d on g o l d and s t e e l - s t e e l f r i c t i o n c o u p l e s ; 2. r o l e o f t a n g e n t i a l l o a d i n g r a t e on m e t a l l i c 44 c o n t a c t a r e a d u r i n g s t i c k ; 3. e f f e c t o f t a n g e n t i a l l o a d i n g r a t e on i n t e r f a c e r e s i s t a n c e d u r i n g s l i p . 4.5.1 O v e r a l l b e h a v i o u r o f i n t e r f a c e r e s i s t a n c e d u r i n g  s t i c k - s l i p c y c l e I n i t i a l l y i t was t h o u g h t t h a t d u r i n g s l i p a f u l l o i l f i l m c o u l d be d e v e l o p e d b e t w e e n t h e s l i d e r a n d t h e d i s k . T h u s i t was n e c e s s a r y t o d e t e r m i n e : ( a ) t h e a c t u a l r e s i s t a n c e o f t h e i n t e r f a c e ; ( b ) t h e d u r a t i o n and m a g n i t u d e o f t h e o b s e r v e d r e s i s t a n c e i n c r e a s e d u r i n g s l i p a nd ( c ) t h e e f f e c t o f t a n g e n t i a l f o r c e on s t i c k - s l i p . U s i n g t h e r e s u l t s o f t h e s e t e s t s i t was p o s s i b l e t o i n v e s t i g a t e s t i c k - s l i p i t s e l f a s w e l l a s p r o v i d e a b a c k g r o u n d f o r t h e s u b s e q u e n t i n v e s t i g a t i o n o f t h e e f f e c t s o f t a n g e n t i a l l o a d i n g r a t e . 4.5.2 A c t u a l r e s i s t a n c e o f i n t e r f a c e d u r i n g s t i c k - s l i p ( a ) The f o r m a t i o n o f a f u l l o i l f i l m The f i r s t s e t o f e l e c t r i c a l r e s i s t a n c e m e a s u r e -ments o f t h e s l i d e r - t r a c k s u r f a c e were c o n d u c t e d t o mea-s u r e t h e a c t u a l r e s i s t a n c e o f t h e i n t e r f a c e and t h u s t o d e t e r m i n e i f a f u l l o i l f i l m was f o r m e d d u r i n g a ny s e c t i o n o f t h e s t i c k - s l i p c y c l e . B o t h t h e g o l d and s t e e l on s t e e l s y s t e m s were t e s t e d . The i n i t i a l r e s i s t a n c e m e asurement, u s i n g a b r i d g e w h i c h was d e s i g n e d t o d e t e c t c h a n g e s o f s e v e r a l ohms, showed t h a t t h e r e were no 45 d e t e c t a b l e c h a n g e s i n t h e i n t e r f a c e r e s i s t a n c e d u r i n g s t i c k - s l i p . An a . c . s i g n a l ( o f v a r i a b l e f r e q u e n c y ) was u s e d and t h e o s c i l l o s c o p e t r a c e s o f t h e d i f f e r e n t i a l v o l t a g e i n t h e b r i d g e showed t h a t t h e r e was no d i s c h a r g e t h r o u g h a f i l m . S u b s e q u e n t l y t r a n s f o r m e r o i l was u s e d a s a l u b r i c a n t . T h e s e t e s t s y i e l d e d t h e same r e s u l t : t h e r e s i s t a n c e o f t h e i n t e r f a c e was l e s s t h a n 1 ohm; and t h e r e was no a r c i n g t h r o u g h t h e f i l m . The b r i d g e s e n s i t i v i t y was t h e n i n c r e a s e d t o m o n i t o r t h e low i n t e r f a c i a l r e s i s t a n c e d u r i n g s t i c k - s l i p . The b r i d g e was m o d i f i e d by d e c r e a s i n g t h e b r i d g e r e s i s -t a n c e s so t h a t t h e a d d i t i o n o f t h e s m a l l c o n t a c t r e s i s -t a n c e i n s e r i e s w i t h one s i d e o f t h e b r i d g e w o u l d p r o d u c e a s i g n i f i c a n t d i f f e r e n t i a l v o l t a g e b e t w e e n t h e two s e c -t i o n s o f t h e b r i d g e . When t h i s more s e n s i t i v e b r i d g e was u s e d i t was f o u n d t h a t t h e r e s i s t a n c e o f t h e g o l d -g o l d i n t e r f a c e was i n t h e r a n g e o f .0005 ohms and t h e s t e e l - s t e e l i n t e r f a c e was i n t h e .001 ohm r a n g e . The c o n t a c t r e s i s t a n c e d i d n o t r e m a i n c o n s t a n t t h r o u g h o u t t h e s t i c k - s l i p c y c l e . The c h a n g e s were m o n i t o r e d b y r e c o r d i n g t h e d i f f e r e n t i a l v o l t a g e o f t h e b r i d g e on a n o s c i l l o s c o p e . F i g u r e 10 i s a p h o t o g r a p h o f an o s c i l l o -s c o p e t r a c e p r o d u c e d d u r i n g s t i c k - s l i p w i t h a n a . c . s i g n a l a p p l i e d t o t h e b r i d g e . The u p p e r o s c i l l o s c o p e t r a c e i s d i f f e r e n t i a l v o l t a g e v s . t i m e , t h e l o w e r t r a c e i s s l i d e r d i s p l a c e m e n t v s . t i m e . T h i s p a t t e r n i s t y p i c a l 46 o f t h e d i f f e r e n t i a l v o l t a g e - t i m e p l o t s r e c o r d e d d u r i n g s t i c k - s l i p v i b r a t i o n o f s t e e l on s t e e l w i t h p e t r o l a t u m o i l a s a l u b r i c a n t . As t h e beam i s d i s p l a c e d f r o m i t s e q u i -l i b r i u m p o s i t i o n d u r i n g s t i c k , t h e e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e d e c r e a s e s u n t i l s l i p . D u r i n g s l i p t h e c o n t a c t r e s i s t a n c e i n c r e a s e s v e r y r a p i d l y a n d t h i s s u g g e s t e d t h a t f l u i d f i l m f o r m a t i o n c o u l d be o c c u r r i n g d u r i n g s l i p . To t e s t t h e v a l i d i t y o f t h i s a s s u m p t i o n i t was n e c e s s a r y t o d e t e r m i n e t h e r e s i s t a n c e o f t h e i n t e r -f a c e a n d t h e m a g n i t u d e o f r e s i s t a n c e peak d u r i n g s l i p . (b) A c t u a l r e s i s t a n c e o f t h e i n t e r f a c e d u r i n g s t i c k The r e s i s t a n c e o f t h e i n t e r f a c e d u r i n g s t i c k - s l i p was d e t e r m i n e d b y a p p l y i n g a d . c . s i g n a l t o t h e b r i d g e and m e a s u r i n g t h e d i f f e r e n t i a l v o l t a g e o n t h e o s c i l l o s c o p e . F i g u r e 1 1 ( a ) shows c o n t a c t r e s i s t a n c e c h a n g e s d u r i n g f i v e s l i p c y c l e s . T he u p p e r t r a c e i s d i f f e r e n t i a l v o l t a g e v s . t i m e ; t h e l o w e r t r a c e i s beam d i s p l a c e m e n t v s . t i m e . I n F i g u r e 12 t h e c o r r e s p o n d i n g i n t e r f a c e r e s i s t a n c e h a s b e e n p l o t t e d f o r t h e 4 t h s t i c k - s l i p c y c l e o f t h e s e r i e s . T he r e s i s t a n c e j u s t b e f o r e s l i p i s 1.05 m i l l i o h m s a n d d u r i n g s l i p 6.5 m i l l i o h m s . T h e s e r e s u l t s d e m o n s t r a t e t h e r e l a t i v e l y l a r g e i n c r e a s e i n r e s i s t a n c e d u r i n g s l i p . T h e s e v a l u e s o f r e s i s t a n c e , w h i c h a r e t y p i c a l v a l u e s f o r s t e e l on s t e e l d u r i n g s t i c k - s l i p , s u g g e s t t h a t d u r i n g t h e w h o l e s t i c k - s l i p p r o c e s s , t h e s l i d e r i s i n e s s e n t i a l l y m e t a l l i c c o n t a c t w i t h t h e d i s k . F u r t h e r m o r e , t h e r e g i o n o f s t i c k i s a r e g i o n i n w h i c h m e t a l l i c c o n t a c t i s i n c r e a s i n g , w h i l e 47 t h e s l i p r e g i o n i s a r e g i o n o f d e c r e a s i n g t h e n i n c r e a s i n g m e t a l l i c c o n t a c t . 4.5.3 R e s i s t a n c e - t i m e c u r v e s d u r i n g s l i p I n o r d e r t o o b s e r v e t h e d u r a t i o n a n d e x t e n t o f t h e r e s i s t a n c e c h a n g e d u r i n g s l i p , t h e t i m e s c a l e was e x p a n d e d a n d t h e d i f f e r e n t i a l v o l t a g e o f t h e b r i d g e m o n i -t o r e d ( a l s o u s i n g a d . c . s o u r c e ) . The r e s u l t i s shown i n F i g u r e 1 K b ) . I n F i g u r e 13 t h e r e s i s t a n c e o f t h e i n t e r -f a c e d u r i n g s l i p h a s b e e n p l o t t e d . I t i s o b v i o u s t h a t d u r i n g s l i p t h a t t h e i n t e r f a c i a l r e s i s t a n c e n e v e r r e a c h e s t h e u p p e r l i m i t t h a t c a n be m e a s u r e d b y t h e b r i d g e , s o t h a t t h e r e i s no p o s s i b i l i t y o f f u l l f i l m f o r m a t i o n b e t w e e n t h e s l i d e r a n d t h e d i s k a t any t i m e d u r i n g s l i p . No d i f f e r e n t i a l v o l t a g e p e a k s o f s u f f i c i e n t m a g n i t u d e t o i n d i c a t e r e s i s t a n c e s g r e a t e r t h a n 10 m i l l i -ohms were o b s e r v e d i n e i t h e r t h e g o l d on g o l d o r s t e e l on s t e e l s y s t e m s . From t h e d i f f e r e n t i a l v o l t a g e - t i m e t r a c e i n F i g u r e 1 K b ) , s l i p l a s t s a b o u t .040 s e c o n d s , and t h e r e s i s t a n c e i s maximum a t a p p r o x i m a t e l y h a l f t i m e . F r o m F i g u r e 13, i t c a n b e s e e n t h a t t h e r e s i s t a n c e j u s t b e f o r e s l i p ( l i n e ab) i s l e s s t h a n t h e i n t e r f a c i a l r e s i s t a n c e a t t h e e n d o f s l i p ( l i n e c d ) . A l t h o u g h t h e r e s i s t a n c e o f t h e i n t e r f a c e i s a l w a y s l e s s t h a n t h a t o f a f u l l y d e v e l o p e d o i l f i l m , t h e r e s i s t a n c e 48 d u r i n g s l i p c a n be g r e a t e r t h a n t h e r e s i s t a n c e o f t h e i n t e r f a c e u n d e r p u r e n o r m a l l o a d i n g c o n d i t i o n s . I n F i g u r e 14 t h e r e s i s t a n c e - t i m e and d i s p l a c e m e n t - t i m e c u r v e s f o r t h e f i r s t s i x c y c l e s o f s t i c k - s l i p a r e p r e s e n t e d . The s l i d e r was l i f t e d c l e a r o f t h e t r a c k , t h e n r e p l a c e d o n t h e t r a c k u n d e r t h e n o r m a l l o a d o n l y . C a r e was t a k e n t o s e e t h a t t h e s l i d e r was s i t t i n g f l a t o n t h e d i s k . The d i s k - s l i d e r i n t e r f a c e r e s i s t a n c e was r e c o r d e d ( l i n e a b ) . The d i s k was t h e n s t a r t e d a t p o i n t c . The f i r s t s l i p o c c u r r e d a t d, a n d t h e r e s i s t a n c e d u r i n g t h i s s l i p e x c e e d e d t h e r e s i s t a n c e o f t h e i n t e r f a c e u n d e r s i m p l e n o r m a l l o a d i n g . T h e s e r e s u l t s a r e t y p i c a l a l t h o u g h some r e s i s t a n c e p e a k s ( d u r i n g s l i p ) l e s s t h a n t h e n o r m a l l o a d -i n g r e s i s t a n c e were a l s o o b s e r v e d . T h e s e o b s e r v a t i o n s l e n d s u p p o r t t o t h e h y p o t h e s i s t h a t t h e n o r m a l l o a d o n t h e s l i d e r may be s u p p o r t e d b y a p a r t i a l l u b r i c a n t f i l m d u r i n g s l i p . 4.5.4 R e s i s t a n c e - d i s p l a c e m e n t c u r v e s d u r i n g s t i c k - s l i p I n F i g u r e 15 a t y p i c a l d i f f e r e n t i a l - v o l t a g e d i s -p l a c e m e n t p l o t i s shown. F r o m t h i s t r a c e i t i s o b v i o u s t h a t t h e r e s i s t a n c e v a r i e s a s t h e s l i d e r moves d u r i n g s l i p . S i n c e c h a n g i n g r e s i s t a n c e r e f l e c t s t h e c h a n g e s i n m e t a l l i c c o n t a c t a r e a , i t i s o b v i o u s t h a t t h e c o n t a c t a r e a d e c r e a s e s t o a minimum l e v e l p a r t w a y t h r o u g h t h e s l i p c y c l e b u t t h e n i n c r e a s e s a s t h e s l i d e r r e a c h e s t h e p o s i t i o n where s t i c k b e g i n s . 49 4.6 The E f f e c t o f T a n g e n t i a l L o a d on S t i c k - S l i p The i m p o r t a n c e o f t h e t a n g e n t i a l l o a d i n i n c r e a s i n g m e t a l l i c c o n t a c t i s shown i n F i g u r e 17. I n t h i s c a s e t h e d r i v e n s u r f a c e was s t o p p e d f o r s e v e r a l s e c o n d s , t h e n r e - s t a r t e d . The r e s u l t s show t h a t t h e c o n t a c t a r e a d o e s n o t i n c r e a s e w i t h t i m e b u t w i t h i n c r e a s e d t a n g e n t i a l l o a d . 4.7 D i s c u s s i o n 4.7.1 The f o r m a t i o n o f a f u l l o i l f i l m The r e s u l t s o f t h e s u r f a c e c o n d i t i o n s study-i n d i c a t e d t h a t t h e p r e s e n c e o f a l u b r i c a n t was n e c e s s a r y f o r s t i c k - s l i p v i b r a t i o n t o o c c u r i n t h i s s y t e m when g o l d - g o l d and s t e e l - s t e e l f r i c t i o n c o u p l e s were t e s t e d . T h i s o b s e r v a t i o n l e n t some s u p p o r t t o a n a l t e r n a t e t h e o r y o f r e l a x a t i o n o s c i l l a t i o n s p r o p o s e d b y K o o d i n o v . A c c o r d i n g t o T o l s t o i [ 4 1 ] , K o o d i n o v h a s d e v e l o p e d a t h e o r y o f s e l f - e x c i t e d f r i c t i o n a l v i b r a t i o n s b a s e d o n t h e p r e m i s e t h a t h y d r o d y n a m i c o r s e m i - h y d r o d y n a m i c l u b r i c a t i o n c o n d i t i o n s e x i s t . R e c e n t ( 1 9 6 8 ) m e a s u r e m e n t s by T o l s t o i [ 4 1 ] o f n o r m a l d i s p l a c e m e n t s o c c u r r i n g d u r i n g s l i p l e n d some s u p p o r t t o K o o d i n o v ' s i d e a s . The r e s u l t s o f t h r e e o t h e r s t u d i e s a l s o s u g g e s t t h a t t h e r e c o u l d be f i l m f o r m a -t i o n d u r i n g s l i p . A r e p o r t o f a n e a r l y ( 1 9 3 9 ) s t u d y o f v a r i o u s m e t a l l i c f r i c t i o n c o u p l e s by Bowden and L e b e n [ 9 ] w h i c h was a l s o c o n c e r n e d w i t h i n t e r f a c e e l e c t r i c a l 50 r e s i s t a n c e d u r i n g s t i c k - s l i p c o n t a i n s an o b s e r v a t i o n t h a t d u r i n g s l i p , t h e c o n d u c t a n c e w o u l d f a l l a l m o s t t o z e r o i n d i c a t i n g t h a t a f u l l f i l m h a d f o r m e d . S e c o n d l y , i n d e p e n d e n t s t u d i e s by R o b e r t s o n a n d S p i l l m a n [ 4 2 ] u s i n g a p i n - d i s k c o n f i g u r a t i o n i n d i c a t e t h a t a p p r e c i a b l e l i f t c a n o c c u r f r o m s e v e r a l p o s s i b l e s o u r c e s i n n o m i n a l l y f l a t c o n t a c t s d u r i n g s l i d i n g . H a m i l t o n , W a l o w i t a n d A l l e n [ 4 3 ] h a v e o u t l i n e d a t h e o r y o f l i q u i d l u b r i c a t i o n o f p a r a l l e l s u r f a c e s i n w h i c h l o a d c a r r y i n g c a p a c i t y i s d e v e l o p e d b e c a u s e o f t h e s u r f a c e m i c r o - i r r e g u l a r i t i e s ( a s p e r i t i e s ) and a s s o c i a t e d f i l m c a v i t i e s . T h e y a l s o p r e s e n t a n a l y t i c a l s o l u t i o n s g i v i n g l o a d c a p a c i t y a s a f u n c t i o n o f s p e e d , v i s c o s i t y a n d s u r f a c e - a s p e r i t y d i m e n s i o n s . T h e r e a r e s e v e r a l r e a s o n s i n f a v o u r o f f i l m f o r m a t i o n d u r i n g s l i p . F i r s t , f r o m t h e p r e c e d i n g s u r f a c e c o n d i t i o n s t u d i e s i t i s o b v i o u s t h a t t h e p r e s e n c e o f a l u b r i c a n t i s an i m p o r t a n t f a c t o r i n s t i c k - s l i p i n i t i a t i o n i n t h e s e s y s t e m s . S e c o n d , t h e g e o m e t r y o f t h e s l i d e r h o l d e r and c o n i c a l c u p s y s t e m a l l o w s t h e s l i d e r t o be s e l f - p o s i t i o n i n g d u r i n g s l i p , so t h a t i t w o u l d be p o s s i b l e f o r a n o i l wedge t o f o r m b e t w e e n t h e s l i d e r and t h e t r a c k d u r i n g s l i p . T h i r d , a l t h o u g h t h e d r i v e n s u r f a c e v e l o c i t y i s v e r y low a n d i n t h e r e g i o n u s u a l l y r e g a r d e d as " b o u n d a r y " l u b r i c a t i o n , t h e r e l a t i v e v e l o c i t y d u r i n g s l i p may be a n o r d e r o f m a g n i t u d e h i g h e r t h a n t h e d r i v e n 51 s u r f a c e v e l o c i t y f o r a s h o r t p e r i o d o f t i m e . A l t h o u g h t h e maximum r e l a t i v e v e l o c i t y was n o t m e a s u r e d i n t h i s s t u d y i t c a n be e s t i m a t e d by c o n s i d e r i n g t h e m o t i o n t o be s i m p l e h a r m o n i c d u r i n g s l i p . T h e n x = A s i n wt ( 4 . 7 . 1 ) and x = Aw c o s w t ( 4 . 7 . 2 ) The r e l a t i v e v e l o c i t y o f t h e s l i d e r d u r i n g s l i p i s x + V,. , . The maximum r e l a t i v e v e l o c i t y , V , i s OX SiC TU3.X Aw + v d ^ s k > where A i s 1/2 o f A t o t a i t h e a m p l i t u d e o f s t i c k . I n t h e a p p a r a t u s u s e d , w = 62.8 radians-sec"""*". F o r a d i s k v e l o c i t y o f 0.016 i n - s e c - " * " , t h e t o t a l a m p l i t u d e was 0.02 i n . T h e r e f o r e V = Aw + V,. . = 0.948 i n - s e c - 1 . max d i s k The e x i s t e n c e o f h y d r o d y n a m i c l i f t a t low v e l o c i t i e s i n s y s t e m s w i t h a p i n on d i s k c o n f i g u r a t i o n h a s b e e n e x a m i n e d b y R o b e r t s o n and S p i l l m a n [ 4 2 ] , T h e i r r e s u l t s , o b t a i n e d b y t e s t i n g t h e e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e d u r i n g p u r e s l i d i n g , show t h a t a f u l l f i l m c o u l d e x i s t when s p e e d s were a s l o w a s 5 i n - s e c - 1 . H a m i l t o n , W a l o w i t and A l l e n [ 4 3 ] p r e s e n t e x p e r i m e n t a l r e s u l t s s h o w i n g f u l l f i l m f o r m a t i o n a t 20 i n - s e c - 1 . T h e y showed t h a t t h e l o a d - c a r r y i n g c a p a c i t y o f t h e i r s y s t e m ( a r o t o r - s t a t o r s y s t e m u s i n g m i n e r a l o i l a s a l u b r i c a n t ) was d e p e n d e n t o n t h e p a t t e r n o f i n t e r f a c i a l a s p e r i t i e s a s w e l l a s v e l o c i t y . 52 The r e s u l t s o f t h e p r e s e n t s t u d y on t h e e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e d u r i n g s t i c k - s l i p s u g g e s t , h o w e v e r , t h a t s i n c e t h e i n t e r f a c i a l r e s i s t a n c e i s a l w a y s i n t h e m e t a l l i c r a n g e , f u l l f l u i d f i l m f o r m a t i o n i s n o t a p r e r e q u i s i t e t o s t i c k - s l i p . The r e s i s t a n c e p e a k s d u r i n g s l i p were n e v e r o b s e r v e d t o r e a c h t h e r e s i s t a n c e l e v e l o f a l u b r i c a n t f i l m ; h o w ever t h e r e s i s t a n c e p e a k s d i d e x c e e d t h e r e s i s t a n c e o f t h e i n t e r f a c e when t h e s l i d e r a n d d i s k were i n c o n t a c t u n d e r p u r e n o r m a l l o a d i n g (no t a n g e n t i a l l o a d o n t h e i n t e r f a c e ) . S i n c e t h e amount o f m e t a l l i c c o n t a c t d u r i n g s l i p was l e s s t h a n t h e a r e a o f m e t a l l i c c o n t a c t u n d e r p u r e l y n o r m a l l o a d i n g , i t c a n be s u p p o s e d t h a t p a r t o f t h e n o r m a l l o a d was b e i n g s u p p o r t e d d u r i n g . s l i p . By a p p l y i n g t h e r e s u l t s o f t h e s t u d i e s by R o b e r t s o n and S p i l l m a n [ 4 2 ] and H a m i l t o n , W a l o w i t and A l l e n [ 4 3 ] o n s o u r c e s o f h y d r o d y n a m i c l i f t i t s h o u l d be p o s s i b l e t o e s t i m a t e t h e t h e o r e t i c a l l o a d - c a r r y i n g c a p a c i t y o f t h e s l i d e r - d i s k s y s t e m f o r t h e v a r i o u s m e c h a n i s m s t h e y p r o -p o s e d . T h i s a s p e c t was n o t e x p l o r e d f u r t h e r . The s u d d e n i n c r e a s e i n i n t e r f a c i a l r e s i s t a n c e a g r e e s r a t h e r w e l l w i t h t h e s u d d e n i n c r e a s e i n n o r m a l s e p a r a t i o n o f t h e s u r f a c e s r e p o r t e d b y T o l s t o i [ 4 1 ] . T h i s d e c r e a s e i n m e t a l l i c c o n t a c t w o u l d seem t o be a d e q u a t e l y e x p l a i n e d b y t h e f o r m a t i o n o f a p a r t i a l f i l m d u r i n g s l i p , b a s e d o n t h e o b s e r v a t i o n s o f e l e c t r i c a l r e s i s t a n c e p e a k s d u r i n g s l i p . However C o u r t e l [ 4 4 ] h a s 53 o b s e r v e d t h e f o r m a t i o n o f a " f r o n t a l b u l g e " due t o p l a s t i c d e f o r m a t i o n d u r i n g s t i c k , a n d he a t t r i b u t e s n o r m a l v i b r a -t i o n s a s due t o t h e s l i d e r s u r m o u n t i n g t h i s v e r t i c a l b a r r i e r . T h i s i s a l s o a p l a u s i b l e e x p l a n a t i o n a n d t h e s h a r p r i s e i n r e s i s t a n c e a t t h e b e g i n n i n g o f s l i p ( F i g u r e 1 1 ( a ) ) w o u l d s u p p o r t t h i s a r g u m e n t . On f u r t h e r e x a m i n a t i o n o f t h e r e s i s t a n c e - d i s p l a c e m e n t c u r v e s , F i g u r e 15, t h e s e p a r a t i o n o f t h e s u r f a c e s d u r i n g s l i p a s m e a s u r e d b y t h e r e s i s t a n c e , i s e q u a l t o o r l a r g e r t h a n t h e i n i t i a l s e p a r a -t i o n o v e r t h e m a j o r i t y o f t h e d i s p l a c e m e n t CO.020 i n . ) w h i c h w o u l d i n d i c a t e t h a t a ny " f r o n t a l b u l g e " w o u l d be much w i d e r t h a n t h a t m e a s u r e d by C o u r t e l . The r e s u l t s o f t h e p r e s e n t s t u d y t e n d t o a g r e e most c l o s e l y w i t h t h e r e s u l t s p u b l i s h e d b y Bowden and L e b e n o f t h e i r s t u d y on " u n l u b r i c a t e d " m e t a l p a i r s . The r e s i s t a n c e - t i m e c u r v e s f o r s t e e l on s t e e l d u r i n g s t i c k d i f f e r i n s h a p e i n a m i n o r way, as d o e s t h e e x p a n d e d t i m e -r e s i s t a n c e c u r v e d u r i n g s l i p . W i t h t h e g o l d on g o l d s y s t e m w i t h p e t r o l a t u m a s a l u b r i c a n t t h e d i f f e r e n t i a l -v o l t a g e t i m e c u r v e s were s i m i l a r i n s h a p e t o t h o s e o f t h e s t e e l o n s t e e l . Bowden and L e b e n d i d n o t t e s t g o l d on g o l d , b u t u s e d p l a t i n u m a s t h e i r n o b l e s t m e t a l . However, t h e r e s i s t a n c e - t i m e c u r v e s t h e y o b t a i n e d f o r c l e a n p l a t i n u m d i f f e r f r o m t h o s e o b t a i n e d f o r t h e l u b r i -c a t e d g o l d on g o l d c a s e . I t i s p o s s i b l e , t h a t i n t h e c a s e o f p l a t i n u m t h e y were n o t o b s e r v i n g t r u e s t i c k - s l i p , 54 b u t t h e i n t e r m i t t e n t s l i d i n g m o t i o n w h i c h i s c h a r a c t e r i z e d b y e x t e n s i v e s u r f a c e damage. I n F i g u r e s 1 8 ( a ) a n d (b) t h e r e s u l t s o f t h e g o l d on g o l d r e s i s t a n c e m e a s u r e m e n t s a r e shown. B e c a u s e t h e r e s i s t a n c e o f t h e i n t e r f a c e i s v e r y low i t i s e x p e r i m e n t a l l y d i f f i c u l t t o d e t e c t r e s i s t a n c e c h a n g e s d u r i n g t h e s t i c k p o r t i o n o f t h e c y c l e . T h e r e f o r e , s t e e l on s t e e l w h i c h showed a s i m i l a r r e s i s t a n c e - t i m e p a t t e r n was u s e d i n t h e s u b s e q u e n t s t u d i e s o f t h e r e s i s t a n c e c h a n g e s d u r i n g s t i c k . 4.7.2 The r o l e o f t a n g e n t i a l l o a d ( a ) d u r i n g s t i c k S e v e r a l i n v e s t i g a t o r s o f t h e s t i c k - s l i p p h e n o -menon ( D a v i s [ 4 5 ] , R a b i n o w i c z [ 1 ] ) h a v e o b s e r v e d t h a t i n c r e a s i n g t h e t i m e t h a t t h e s u r f a c e s were i n c o n t a c t d u r i n g s t i c k i n c r e a s e d 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 . I t was p o s t u l a t e d t h a t t h i s e f f e c t was t h e r e s u l t o f c r e e p due t o t h e n o r m a l l o a d . The t i m e o f s t i c k was v a r i e d b y c h a n g i n g t h e s p e e d o f t h e d r i v e n s u r f a c e . I n t h e p r e s e n t s t u d y t h e e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e and t h e s t a t i c f r i c t i o n f o r c e were m e a s u r e d f o r v a r i o u s t i m e s o f s t i c k . L o n g e r s t i c k t i m e s were o b t a i n e d b y r e d u c i n g t h e d r i v e n s u r f a c e v e l o c i t y . As s t i c k t i m e was i n c r e a s e d t h e s t a t i c f r i c t i o n f o r c e i n c r e a s e d f o r b o t h g o l d o n g o l d and s t e e l o n s t e e l s y s t e m s . The e l e c t r i c a l r e s i s t a n c e m e a s u r e m e n t s o f t h e 55 s t e e l i n t e r f a c e showed t h a t t h e r e s i s t a n c e o f t h e i n t e r -f a c e a t s l i p was a l s o s e n s i t i v e t o t h e amount o f t i m e t h a t t h e s u r f a c e s were i n c o n t a c t d u r i n g s t i c k . I n F i g u r e 1 6 ( b ) t h r e e d i f f e r e n t t i m e s o f s t i c k and t h e c o r r e s p o n d i n g d i f f e r e n t i a l v o l t a g e d r o p s a c r o s s t h e i n t e r f a c e f o r t h e c y c l e s a r e shown. T h r e e d i f f e r e n t l o a d i n g r a t e s were u s e d t o o b t a i n t h e d i f f e r e n t t i m e s o f s t i c k . The d e c r e a s i n g r e s i s t a n c e a t s l i p f o r l o n g e r t i m e s o f c o n t a c t s u g g e s t s t h a t t h e a r e a o f m e t a l l i c c o n t a c t a t s l i p i n c r e a s e s f o r l o n g e r t i m e s o f s t a t i o n a r y c o n t a c t . T h e r e a r e a t l e a s t t h r e e ways t h a t t h i s e f f e c t c a n b e e x p l a i n e d : 1. t h e c o n t a c t a r e a i s i n c r e a s i n g w i t h t i m e , b e c a u s e o f c r e e p , u n d e r t h e a c t i o n o f t h e n o r m a l l o a d . S i n c e t h e s i z e o f t h e j u n c t i o n s w i l l i n c r e a s e w i t h t i m e , t h e amount o f m e t a l l i c c o n t a c t i n c r e a s e s . T h i s d e c r e a s e s t h e e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e b u t i n c r e a s e s t h e amount o f t a n g e n t i a l f o r c e ( s t a t i c f r i c t i o n f o r c e ) n e c e s s a r y t o s h e a r t h e i n t e r f a c e and i n i t i a t e g r o s s s l i d i n g ( s l i p ) . T h i s a p p r o a c h a g r e e s w i t h t h a t o f D a v i s [ 3 9 ] and R a b i n o w i c z [ 1 ] . 2. an o i l f i l m i s s q u e e z e d f r o m u n d e r t h e s l i d e r d u r i n g s t i c k . T h i s w o u l d p e r m i t t h e s u r f a c e s t o a p p r o a c h more c l o s e l y ( b y t h e f o r m a t i o n o f new c o n t a c t s a n d / o r • i n c r e a s e d d e f o r m a t i o n o f t h e o l d ) a s t h e l o a d - s u p p o r t i n g o i l . i s s q u e e z e d f r o m t h e i n t e r f a c e a r e a . I n c r e a s i n g 56 m e t a l l i c c o n t a c t means t h a t t h e r e s i s t a n c e w o u l d d e c r e a s e , w h i c h i s o b s e r v e d . 3. t h e amount o f f o r c e n e c e s s a r y t o s h e a r t h e i n t e r f a c e ( t h e s t a t i c f r i c t i o n f o r c e ) i s s e n s i t i v e t o t h e r a t e a t w h i c h t h e t a n g e n t i a l l o a d i s a p p l i e d . The f o r c e w o u l d t h e n a p p e a r t o be a f u n c t i o n o f t i m e o f c o n t a c t . The s e n s i t i v i t y o f t h e r e s i s t a n c e ( m e t a l l i c c o n t a c t a r e a ) t o t a n g e n t i a l l o a d i n g r a t e c o u l d be e x p l a i n e d i n two ways: a . t h e j u n c t i o n s f o r m e d by t h e c o n t a c t i n g a s p e r i t i e s d e f o r m u n d e r t h e c o m b i n e d a c t i o n o f t h e n o r m a l and t a n g e n t i a l l o a d s , t h u s i n c r e a s i n g t h e m e t a l l i c c o n t a c t a r e a . T h i s d e f o r m a t i o n w o u l d h a v e t o be r a t e d e p e n d e n t t o e x p l a i n t h e i n c r e a s e i n m e t a l l i c a r e a w i t h d e c r e a s i n g l o a d r a t e ; b . t h e t a n g e n t i a l l o a d c a u s e s i n s u l a t i n g f i l m s ( o x i d e s , l u b r i c a n t f i l m s ) t o be r e m o v e d f r o m t h e i n t e r f a c e , t h u s i n c r e a s i n g t h e m e t a l l i c c o n t a c t . I f t h e e x t e n t o f r e m o v a l was s e n s i t i v e t o r a t e o f s h e a r , i t i s p o s s i b l e t h a t t h e amount o f m e t a l l i c c o n t a c t c o u l d i n c r e a s e w i t h d e c r e a s i n g r a t e s o f t a n g e n t i a l l o a d a p p l i c a t i o n . I n o r d e r t o s e p a r a t e t h e t i m e - d e p e n d e n t a n d t h e l o a d - r a t e d e p e n d e n t p o s s i b i l i t i e s , t h e r e s i s t a n c e o f t h e i n t e r f a c e was m e a s u r e d a s a f u n c t i o n o f t h e t i m e o f a p p l i -c a t i o n o f a p a r t i c u l a r t a n g e n t i a l and n o r m a l l o a d o n l y ; i . e . t h e d r i v e n s u r f a c e was s t o p p e d p a r t w a y t h r o u g h t h e s t i c k c y c l e . I n F i g u r e s 1 6 ( a ) and 17 t h e r e s u l t s o f 57 s t o p p i n g t h e d r i v e n s u r f a c e f o r a b o u t 15 s e c o n d s a r e shown. I f t h e t i m e o f s t i c k i s d e l a y e d a s i n t h e s e c t i o n 'ab* o f t h e c y c l e i n F i g u r e 1 6 ( a ) , i t i s a p p a r e n t t h a t t h e c o n t a c t r e s i s t a n c e d o e s n o t c h a n g e . I f t h e s t a t i c f r i c t i o n f o r c e was a s t r o n g f u n c t i o n o f t h e t i m e o f c o n t a c t o n l y ( t h e r e s u l t o f i n c r e a s i n g c o n t a c t a r e a b e c a u s e o f c r e e p o r b e c a u s e o f t h e d i s s i p a t i o n o f a s q u e e z e f i l m ) t h e n t h e r e s i s t a n c e o f t h e i n t e r f a c e c o u l d be e x p e c t e d t o i n c r e a s e a s a f u n c t i o n o f t i m e . The r e s u l t s o f t h e s e d e l a y e d s t i c k t e s t s i n d i c a t e t h a t t h e m e t a l l i c c o n t a c t a r e a i s s e n s i t i v e t o t h e t a n g e n t i a l l o a d . A s e n s i t i v i t y t o t a n -g e n t i a l l o a d w o u l d a l s o e x p l a i n b o t h o b s e r v a t i o n s i n F i g u r e s 1 6 ( a ) and (b) and t h e g e n e r a l o b s e r v a t i o n s a b o u t c o n t a c t t i m e s and t h e s t a t i c f r i c t i o n v a l u e s . A t h i g h e r d r i v e n s u r f a c e v e l o c i t i e s t h e r a t e o f a p p l i c a t i o n o f t h e t a n g e n t i a l f o r c e i n c r e a s e s . F r o m F i g u r e 1 6 ( b ) i t i s o b v i o u s t h a t a t a h i g h s u r f a c e v e l o c i t y t h e m e t a l l i c c o n t a c t a r e a a t s l i p i s s m a l l e r t h a n t h e a r e a a t s l i p a t a low s u r f a c e v e l o c i t y . T h u s t h e a r e a o f c o n -t a c t a t s l i p w o u l d a p p e a r t o be i n f l u e n c e d b y t h e r a t e o f t a n g e n t i a l l o a d a p p l i c a t i o n a n d n o t g r o s s l y a f f e c t e d b y t h e t i m e o f s t a t i o n a r y c o n t a c t . The o b s e r v a t i o n t h a t t h e amount o f m e t a l l i c c o n -t a c t a t s l i p i s d e t e r m i n e d by t h e r a t e o f a p p l i c a t i o n o f t h e t a n g e n t i a l l o a d r a t h e r t h a n t i m e o f s t a t i o n a r y c o n t a c t a g r e e s w i t h t h e o b s e r v a t i o n s o f s t a t i c f r i c t i o n and l o a d 58 r a t e w i t h J o h a n n e s [ 2 7 ] . He o b s e r v e d , w h i l e t r y i n g t o m e a s u r e t h e 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 s f o r v e r y l o n g p e r i o d s o f c o n t a c t t i m e , t h a t i f t h e d r i v e n s u r f a c e was s t o p p e d f o r a p e r i o d o f t i m e d u r i n g t h e s t i c k . p o r t i o n o f t h e c y c l e , no i n c r e a s e i n s t a t i c f r i c t i o n f o r c e o c c u r r e d , e v e n t h o u g h t h e t i m e o f s t a t i o n a r y c o n t a c t h a d i n c r e a s e d . He a p p l i e d a v i s c o - e l a s t i c model f o r j u n c t i o n g r o w t h d u r i n g s t i c k t o e x p l a i n h i s o b s e r v a t i o n s . (b) d u r i n g s l i p I t was o b s e r v e d t h a t i n c r e a s i n g t h e t a n g e n t i a l l o a d i n g r a t e d u r i n g s t i c k i n c r e a s e d t h e amount o f c o n t a c t d u r i n g s l i p . T h i s c a n be e x p l a i n e d b y c o n s i d e r i n g t h e r e l a t i v e v e l o c i t i e s o f t h e s l i d e r - t r a c k s y s t e m . I t i s t h e r e l a t i v e v e l o c i t y o f t h e s l i d e r - t r a c k s u r f a c e w h i c h c o n t r o l s t h e amount o f c o n t a c t d u r i n g s l i p . A t a h i g h e r r e l a t i v e v e l o c i t y t h e c o n t a c t w i l l be l e s s , p r o b a b l y due t o i n c r e a s e d f i l m f o r m a t i o n a t h i g h e r r e l a t i v e s p e e d s . T h u s i n t h e c a s e i l l u s t r a t e d b y F i g u r e 19 t h e r e l a t i v e v e l o c i t y s h o u l d be h i g h e r i n t h e o u t e r t r a c e e v e n t h o u g h t h e d i s k v e l o c i t y i s e l e v e n t i m e s l o w e r . I t i s n o t p o s s i b l e t o m e a s u r e t h e r e l a t i v e v e l o -c i t y i n t h e p r e s e n t s y s t e m , b u t i t i s p o s s i b l e t o e s t i m a t e i t i f t h e a m p l i t u d e o f v i b r a t i o n and t h e n a t u r a l f r e q u e n c y o f t h e s y s t e m i s known u s i n g e q u a t i o n 4.7.1. In the case of the inner trace A. . , =?.' .0063 i n t o t a l V ,. . = .011 i n - s e c - 1 d i s k then V = 0.209 i n - s e c - 1 . In the case o f the max o u t e r t r a c e A . , , = .015 i n t o t a l V J. , = .001 i n - s e c - 1 d i s k then V = 0.472 i n - s e c " " 1 , max V ,. . a f f e c t s V by d e t e r m i n i n g A, the amplitude of v i b r a t i o n . The f i n d i n g s of Cameron demonstrated t h a t the amplitude o f v i b r a t i o n has a l a r g e e f f e c t on the r e l a t i v e v e l o c i t y because i t c o n t r o l s the maximum v e l o c i t y of the s l i d e r d u r i n g s l i p . T h e r e f o r e t a n g e n t i a l l o a d i n g r a t e does a f f e c t the amount of m e t a l l i c c o n t a c t d u r i n g the s l i p p a r t o f the c y c l e . I n g e n e r a l , low t a n g e n t i a l l o a d -i n g r a t e s g i v e l a r g e r s l i p v e l o c i t i e s than h i g h l o a d i n g r a t e s . I f the d i s k v e l o c i t y i s i n c r e a s e d u n t i l s l i d i n g j u s t b e g i n s , the r e s i s t a n c e - d i s p l a c e m e n t t r a c e s c o n t i n u e to d ecrease i n diameter u n t i l they c o l l a p s e to a p o i n t . The r e s i s t a n c e o f the i n t e r f a c e a t t h i s p o i n t i s l e s s (hence more m e t a l l i c c o n t a c t ) than the maximum r e s i s t a n c e d u r i n g s l i p but h i g h e r ( l e s s m e t a l l i c c o n t a c t ) than the 60 minimum r e s i s t a n c e d u r i n g s t i c k . I n a d d i t i o n t o s h o w i n g t h e e f f e c t s o f t a n g e n t i a l l o a d r a t e on a r e a i n m e t a l l i c c o n t a c t d u r i n g s l i p , t h e d i s p l a c e m e n t - r e s i s t a n c e t r a c e s show q u i t e c l e a r l y t h a t b o t h m e t a l l i c c o n t a c t a r e a a n d t h e t a n g e n t i a l f o r c e o n t h e i n t e r f a c e a f t e r s l i p a r e l e s s f o r t h e s l o w e r d i s k v e l o c i t y , w h i l e t h e s t a t i c f r i c t i o n f o r c e and t h e a r e a a t s l i p a r e g r e a t e r f o r t h e s l o w e r d i s k v e l o c i t y . I n t h i s c a s e i t a l s o a p p e a r s t h a t t h e r e s i s t a n c e - d i s p l a c e m e n t s l o p e i s n e a r l y c o n s t a n t , and n e a r l y t h e same f o r b o t h l o a d i n g r a t e s . I t w o u l d a l s o a p p e a r t h a t a t a c o n s t a n t f o r c e ( d i s p l a c e m e n t ) t h e d i f f e r e n t i a l v o l t a g e ( h e n c e t h e a r e a ) o f t h e c o n t a c t s a r e a p p r o x i m a t e l y t h e same, r e g a r d -l e s s o f t h e i n i t i a l s t a r t i n g p o i n t , o r t h e r a t e . Summary I n t h i s p a r t o f t h e s t u d y on s t a t i c f r i c t i o n , t h e e l e c t r i c a l r e s i s t a n c e o f t h e s l i d e r - t r a c k i n t e r f a c e was m o n i t o r e d d u r i n g s t i c k - s l i p . T h r e e i m p o r t a n t o b s e r v a t i o n s were made. T h e s e o b s e r v a t i o n s f o r m t h e b a c k g r o u n d o f a s u b s e q u e n t s t u d y o n t h e s e n s i t i v i t y o f t h e c o n t a c t a r e a t o t h e r a t e o f a p p l i c a t i o n o f t h e t a n g e n t i a l s h e a r i n g f o r c e . 61 1. I t was f o u n d t h a t t h e s u r f a c e s were i n m e t a l l i c c o n t a c t t h r o u g h o u t t h e e n t i r e s t i c k - s l i p c y c l e , b u t t h a t t h e amount o f c o n t a c t v a r i e d , b e i n g l e s s d u r i n g s l i p t h a n d u r i n g s t i c k . F o r t h e c o n d i t i o n s o f t h e p r e s e n t e x p e r i -ments t h e r e was l i t t l e p o s s i b i l i t y t h a t a f u l l f l u i d f i l m f o r m s b e t w e e n t h e s l i d e r and t h e d i s k d u r i n g s l i p , b u t t h e r e i s some e v i d e n c e t h a t t h e n o r m a l l o a d o n t h e s l i d e r was p a r t i a l l y s u p p o r t e d d u r i n g s l i p . 2. The s t i c k p o r t i o n o f t h e c y c l e was f o u n d t o be a r e g i o n o f i n c r e a s i n g m e t a l l i c c o n t a c t . T h i s o b s e r -v a t i o n a g r e e s w i t h t h e r e s u l t s o f m odel s t u d i e s b y J o h n s o n [ 2 6 ] and c o n t a c t a r e a s t u d i e s b y C o u r t n e y - P r a t t and E i s n e r [ 2 5 ] . T h e y o b s e r v e d t h a t a s t h e t a n g e n t i a l f o r c e i s i n c r e a s e d t h e a r e a o f c o n t a c t b e t w e e n two s u r f a c e s a l s o i n c r e a s e s . By s t o p p i n g t h e d r i v e n s u r f a c e and t h u s s u b m i t t i n g t h e i n t e r f a c e t o i n c r e a s e d c o n t a c t t i m e u n d e r c o n s t a n t n o r m a l an d t a n g e n t i a l l o a d i n g , i t was p o s s i b l e t o show t h a t t h e " j u n c t i o n g r o w t h by c r e e p " m o d e l d o e s n o t a d e q u a t e l y d e s c r i b e t h e b e h a v i o u r o f t h e c o n t a c t a r e a d u r i n g s t i c k . A s i m i l a r o b s e r v a t i o n b a s e d o n s t a t i c f r i c t i o n v a l u e s h a s b e e n made b y J o h a n n e s [ 2 7 ] , He o b s e r v e d t h a t t h e 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 d i d n o t i n c r e a s e w i t h s t a t i o n a r y c o n t a c t t i m e . 3. I t h a s b e e n p o s s i b l e t o show t h a t t h e r e s i s t a n c e o f t h e i n t e r f a c e d u r i n g s l i p i s s e n s i t i v e t o 62 t h e r a t e a t w h i c h t h e t a n g e n t i a l l o a d i s a p p l i e d . The i n t e r f a c e r e s i s t a n c e d u r i n g s l i p i s d e t e r m i n e d by t h e r e l a t i v e v e l o c i t y d u r i n g s l i p , w h i c h i n t u r n i s c o n t r o l l e d b y t h e r a t e a t w h i c h t h e t a n g e n t i a l l o a d i s a p p l i e d . The f i n a l s e c t i o n o f t h i s s t u d y i s an i n v e s t i g a -t i o n o f t h e r o l e o f t a n g e n t i a l f o r c e i n d e t e r m i n i n g t h e f i n a l c o n t a c t a r e a a t s l i p a n d t h e s t a t i c f r i c t i o n f o r c e . 4.7.3 The e f f e c t o f t h e r a t e o f t a n g e n t i a l f o r c e a p p l i c a t i o n on s t a t i c f r i c t i o n f o r c e , t h e a r e a  o f c o n t a c t a t s l i p a n d d u r i n g s t i c k . J o h a n n e s d e m o n s t r a t e d t h a t t h e t i m e o f s t a t i o n a r y c o n t a c t was n o t t h e c o n t r o l l i n g f a c t o r i n d e t e r m i n i n g t h e s t a t i c f r i c t i o n f o r c e . I n s t e a d t h e f r i c t i o n f o r c e a t s l i p was d e t e r m i n e d by t h e r a t e a t w h i c h t h e t a n g e n t i a l l o a d was a p p l i e d d u r i n g s t i c k . The a i m o f t h i s p a r t o f t h e s t u d y on s t a t i c f r i c t i o n was t o d e t e r m i n e i f t h e r a t e o f t a n g e n t i a l l o a d i n g a f f e c t e d t h e c o n t a c t a r e a a t s l i p . The e f f e c t o f t a n g e n t i a l f o r c e r a t e on t h e s t a t i c f r i c t i o n f o r c e was d e m o n s t r a t e d by r e c o r d i n g t y p i c a l r e s i s t a n c e - t i m e and t h e c o r r e s p o n d i n g d i s p l a c e m e n t - t i m e o u t p u t s on t h e o s c i l l o s c o p e f o r a s u c c e s s i o n o f d i s k s p e e d s . T h u s i t was p o s s i b l e t o m e a s u r e : 1. t h e c o n t a c t r e s i s t a n c e and t h e t a n g e n t i a l f o r c e on t h e i n t e r f a c e a t t h e b e g i n n i n g o f s t i c k 2. t h e l e n g t h o f s t i c k 3. t h e t a n g e n t i a l l o a d i n g r a t e 63 4. t h e c o n t a c t r e s i s t a n c e and t h e t a n g e n t i a l f o r c e o n t h e i n t e r f a c e ( t h e s t a t i c f r i c t i o n f o r c e ) a t s l i p . F r o m t h e s e m e a s u r e m e n t s i t was p o s s i b l e t o d e t e r m i n e how t h e c h a n g i n g t a n g e n t i a l l o a d r a t e a f f e c t s t h e . i n i t i a l c o n -t a c t a r e a , t h e f r a c t u r e a r e a (when s l i p o c c u r s ) and t h e r a t e o f i n c r e a s e i n a r e a d u r i n g s t i c k . The r e s u l t s o f two t y p i c a l t e s t r u n s a r e p l o t t e d i n F i g u r e s 20 a n d 21. I n F i g u r e 20 t h e f r i c t i o n c o e f f i -c i e n t a t s l i p ( t h e 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 ) i s p l o t t e d a s a f u n c t i o n o f l o a d i n g r a t e . .The c u r v e s a r e s l i g h t l y d i f f e r e n t f o r e a c h r u n , b u t t h e g e n e r a l b e h a v i o u r i s t h e same: a s t h e l o a d r a t e i s d e c r e a s e d t h e 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 i n c r e a s e s . T h i s was o b s e r v e d i n t h e t e s t s o n g o l d and o n s t e e l ( F i g u r e 9 ) . I n F i g u r e 21 t h e r e s i s t a n c e o f t h e i n t e r f a c e a t t h e i n c e p t i o n o f s l i p i s a l s o p l o t t e d as a f u n c t i o n o f l o a d r a t e . From t h e s e two c u r v e s i t i s a p p a r e n t t h a t t h e i n t e r f a c e r e s i s t a n c e i n c r e a s e s as t h e t a n g e n t i a l l o a d r a t e i n c r e a s e s . T h u s t h e a r e a o f c o n t a c t d e p e n d s i n some way on t h e t a n g e n t i a l l o a d i n g r a t e , 0 . The q u a n t i t y o f i n t e r e s t i n t h e s e s t u d i e s i s t h e m e t a l l i c c o n t a c t a r e a . S i n c e t h e a r e a i n c o n t a c t i s made up o f numerous s m a l l a r e a s o f c o n t a c t o f v a r i o u s s i z e s , i t i s d i f f i c u l t t o q u a n t i t a t i v e l y d e t e r m i n e t h e a c t u a l . a r e a i n c o n t a c t f r o m m e a s u r e m e n t s o f t h e o v e r a l l e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e . I t was p o s s i b l e , 64 h o w e v e r , t o e s t i m a t e t h e r e l a t i v e m a g n i t u d e o f c h a n g e s i n t h e c o n t a c t a r e a t h a t o c c u r i n t h e s t i c k p o r t i o n o f a c y c l e . An a p p r o x i m a t e a n a l y s i s t o d e t e r m i n e t h e c h a n g e i n c o n t a c t a r e a i s g i v e n i n A p p e n d i x B. U s i n g t h a t a n a l y s i s , p e r c e n t a g e c h a n g e s i n c o n t a c t a r e a and t h e p e r c e n t a g e c h a n g e i n t a n g e n t i a l f o r c e a p p l i e d t o t h e i n t e r f a c e d u r i n g s t i c k were c a l c u l a t e d f o r a r a n g e o f t a n -g e n t i a l l o a d i n g r a t e s . From F i g u r e 22 i t c a n be s e e n t h a t t h e amount o f i n c r e a s e i n c o n t a c t a r e a i s a d e c r e a s -i n g f u n c t i o n o f t h e l o a d i n g r a t e . The a m p l i t u d e o f s t i c k - s l i p v i b r a t i o n a l s o d e c r e a s e s as t h e l o a d i n g r a t e , 6, i n c r e a s e s . A t some p o i n t , Qc , on t h e l o a d i n g r a t e a x i s t h e s t i c k - s l i p v i b r a t i o n w i l l c e a s e a n d t h e p u r e s l i d i n g b e g i n s . A t t h i s p o i n t t h e r e w o u l d be no a r e a g r o w t h . T h i s p o i n t , when t h e l o a d r a t e i s t o o h i g h f o r t h e a r e a g r o w t h t o o c c u r , r e f l e c t s t h e t r a n s i t i o n f r o m s t a t i c t o k i n e t i c f r i c t i o n r e g i m e s . I f t h e l o a d i n g r a t e s a r e l o w t h e r e c a n be a p p r e c i a b l e a r e a g r o w t h as t h e t a n -g e n t i a l f o r c e i s a p p l i e d t o t h e i n t e r f a c e ; a t t h e h i g h e r l o a d i n g r a t e s t h e r e i s no a r e a g r o w t h s o t h a t t h e s t a t i c f r i c t i o n phenomena a r e n o t o b s e r v e d . CHAPTER 5 CONCLUSIONS I n t h i s s t u d y r e l a x a t i o n o s c i l l a t i o n s o f t h e s t i c k -s l i p t y p e were u s e d a s a means o f i n v e s t i g a t i n g f u n d a m e n t a l a s p e c t s o f s t a t i c f r i c t i o n . B a s i c a l l y t h e f r i c t i o n s y s t e m c o n s i s t e d o f two s u r f a c e s s u b j e c t e d t o a c o n s t a n t n o r m a l and a l i n e a r l y i n c r e a s i n g t a n g e n t i a l l o a d . 1. The f i r s t p a r t o f t h e s t u d y was c o n c e r n e d w i t h d e f i n i n g t h e c o n d i t i o n s u n d e r w h i c h s t i c k - s l i p v i b r a t i o n w i l l o c c u r and a l s o w i t h i n v e s t i g a t i n g t h e e f f e c t o f t h e h u m i d i t y o f t h e t e s t e n v i r o n m e n t . G o l d s p e c i m e n s were u s e d a n d i t was p o s s i b l e t o e x a m i n e t h e f r i c t i o n b e h a v i o u r o f a s y s t e m b o t h u n d e r n e a r l y p u r e m e t a l l i c c o n t a c t c o n d i -t i o n s and l u b r i c a t e d c o n d i t i o n s . Two d i s t i n c t t y p e s o f b e h a v i o u r were o b s e r v e d . I f t h e g o l d s u r f a c e s were r u n t o g e t h e r i m m e d i a t e l y a f t e r p o l i s h i n g , s t i c k - s l i p v i b r a t i o n w o u l d n o t o c c u r . The m o t i o n o f t h e s l i d e r was i r r e g u l a r and t h e f r i c t i o n c o e f f i c i e n t s were v e r y h i g h . E x a m i n a t i o n o f t h e s u r f a c e s showed t h a t b o t h t h e s l i d e r and t h e t r a c k were h e a v i l y damaged. 66 The h i g h f r i c t i o n v a l u e s and t h e s e v e r e wear o f t h e s u r f a c e s c a n be e x p l a i n e d i n t e r m s o f t h e a d h e s i o n o f t h e s u r f a c e s . S i m i l a r r e s u l t s h a v e b e e n o b s e r v e d d u r i n g s l i d i n g t e s t s u n d e r h i g h vacuum c o n d i t i o n s . M e t a l l i c s u r f a c e s w h i c h h a v e b e e n c l e a n e d p r i o r t o t e s t i n g and m a i n t a i n e d i n a c o n t a m i n a n t - f r e e c o n d i t i o n b y t h e h i g h vacuum e n v i r o n m e n t s e i z e t o g e t h e r when p l a c e d i n c o n t a c t . V e r y h i g h f r i c t i o n c o e f f i c i e n t s r e s u l t . The s e c o n d t y p e o f f r i c t i o n b e h a v i o u r c o u l d be p r o d u c e d b y a d d i n g n a p t h e n i c m i n e r a l o i l t o t h e f r i c t i o n s y s t e m p r i o r t o s l i d i n g . I n t h i s c a s e , s t i c k - s l i p v i b r a -t i o n was o b s e r v e d and t h e f r i c t i o n c o e f f i c i e n t s were r e d u c e d . The damage t o t h e s u r f a c e s d u r i n g s t i c k - s l i p was n e g l i g i b l e . T h e s e t e s t s were r e p e a t e d u s i n g f r e s h l y p o l i s h e d s t e e l s a m p l e s . S i m i l a r r e s u l t s w e r e o b t a i n e d . I n t h e h u m i d i t y t e s t s , c l e a n g o l d s u r f a c e s were e x p o s e d t o a c o n s t a n t h u m i d i t y e n v i r o n m e n t f o r 15 m i n u t e s t h e n t e s t e d . I n a l l o f t h e t e s t s c o n d u c t e d ( h u m i d i t y r a n g e : 10% t o 90% r e l a t i v e h u m i d i t y a t 2 4 ° C ) t h e s e i z u r e o f t h e s l i d i n g s u r f a c e s o c c u r r e d . The h u m i d i t y h a d no d i s c e r n i b l e e f f e c t o n t h e f o r c e n e c e s s a r y t o p r o d u c e s l i d i n g . I f t h e r e l a t i v e h u m i d i t y was i n c r e a s e d u n t i l t h e w a t e r v a p o r c o n d e n s e d on t h e s u r f a c e o f t h e d i s k , t h e s y s t e m w o u l d u n d e r g o s t i c k - s l i p v i b r a t i o n f o r a s h o r t p e r i o d o f t i m e . The l o n g t e r m e f f e c t o f h u m i d i t y on t h e s t e e l on s t e e l s y s t e m was n o t e x a m i n e d . 67 T h e s e r e s u l t s f o r m e d an i m p o r t a n t p a r t o f t h e s t u d y . T h e y d e m o n s t r a t e d t h a t s t i c k - s l i p t y p e o s c i l l a t i o n s c a n n o t be e x p e c t e d u n d e r d r y f r i c t i o n c o n d i t i o n s , t h e r e b y i n d i c a t i n g t h a t t h e a u x i l i a r y s t u d y on t h e e f f e c t o f s u r f a c e t e m p e r a t u r e on s t a t i c f r i c t i o n would h a v e t o be c a r r i e d o u t u n d e r l u b r i c a t e d c o n d i t i o n s . T h u s t h e r e s u l t s o b t a i n e d c o u l d r e f l e c t t h e t e m p e r a t u r e - s e n s i t i v e p r o p e r t i e s o f t h e o i l ( v i s c o s i t y , c o m p o s i t i o n ) a s w e l l a s t h e m a t e r i a l . A t t h i s t i m e t h e e f f e c t s o f n o r m a l l o a d , d i s k v e l o c i t y and r u n - i n o n s t a t i c f r i c t i o n i n t h e g o l d - g o l d s y s t e m were a l s o d e t e r m i n e d as i n f o r m a t i o n on s l i p - s l i p t y p e v i b r a t i o n i n a g o l d o n g o l d s y s t e m was n o t a v a i l a b l e . The r e s u l t s o f t h e s t u d y o n t h e e f f e c t o f d i s k v e l o c i t y o n s t a t i c f r i c t i o n v a l u e s f o r s t e e l o n s t e e l , a g r e e d w i t h t h o s e o f J o h a n n e s [ 2 7 ] , e v e n t h o u g h t h e g e o m e t r y o f t h e t e s t a p p a r a t u s was somewhat d i f f e r e n t . T h i s a g r e e m e n t i n d i c a t e s t h a t t h e u s e o f t h e p a r a m e t e r © (where © = F_) may be s i g n i f i c a n t b o t h p r e d i c t i n g t h e s t a t i c N f r i c t i o n c o e f f i c i e n t s f o r s t e e l o n s t e e l f o r o t h e r s y s t e m s i n w h i c h r e l a x a t i o n o s c i l l a t i o n s a r e u s e d t o e x a m i n e s t a t i c f r i c t i o n * a n d i n t e s t i n g t h e o r e t i c a l m o d e l s o f s t a t i c f r i c t i o n . 2. The s e c o n d p a r t o f t h e s t u d y was c o n c e r n e d w i t h t h e e f f e c t o f t e m p e r a t u r e o n s t a t i c f r i c t i o n . One o f t h e m o d e l s p r o p o s e d t o e x p l a i n t h e o b s e r v e d t i m e -d e p e n d e n c e o f s t a t i c f r i c t i o n [ 1 8 ] , [ 4 5 ] i n v o l v e s a 68 p r o c e s s o f j u n c t i o n g r o w t h due t o c r e e p . U n d e r t h e a c t i o n o f t h e n o r m a l f o r c e t h e a r e a s o f c o n t a c t ( j u n c t i o n s ) w o u l d i n c r e a s e w i t h t i m e t h u s t h e t a n g e n t i a l f o r c e n e e d e d t o s h e a r t h e s e j u n c t i o n s a n d c a u s e s l i p ( t h e s t a t i c f r i c t i o n f o r c e ) w o u l d a l s o be i n c r e a s i n g a s a f u n c t i o n o f t h e t i m e t h e s u r f a c e s were i n c o n t a c t . T h e r e i s some e x p e r i m e n t a l j u s t i f i c a t i o n f o r t h i s m o d e l . I t i s o b s e r v e d t h a t i f t h e v e l o c i t y o f t h e d i s k i s i n c r e a s e d , t h e n t h e t i m e o f c o n -t a c t o f t h e s u r f a c e s d e c r e a s e s and t h e s t a t i c f r i c t i o n f o r c e , a l s o d e c r e a s e s . I f t h i s a r e a g r o w t h was c o n t r o l l e d b y a t e m p e r a t u r e - s e n s i t i v e c r e e p p r o c e s s t h e n , by i n c r e a s -i n g t h e s u r f a c e t e m p e r a t u r e , i t s h o u l d be p o s s i b l e t o p r o d u c e a c o r r e s p o n d i n g i n c r e a s e i n t h e c o n t a c t a r e a a n d t h e r e f o r e an i n c r e a s e i n t h e s t a t i c f r i c t i o n f o r c e . T h i s m o d e l o f s t a t i c f r i c t i o n was t e s t e d u s i n g b o t h g o l d on g o l d and s t e e l o n s t e e l f r i c t i o n s y s t e m s . S t a b l e s t i c k - s l i p v i b r a t i o n was p r o d u c e d i n e a c h o f t h e s y s t e m s u s i n g m i n e r a l o i l a s a l u b r i c a n t . The s u r f a c e t e m p e r a t u r e o f t h e d i s k s e c t i o n o f t h e f r i c t i o n c o u p l e was i n c r e a s e d i n 10°C i n c r e m e n t s . I n b o t h c a s e s , when t h e s u r f a c e t e m p e r a t u r e o f t h e d i s k a p p r o a c h e d t h e 1 Q 5 ° C -1 2 0 ° C r a n g e , t h e s t i c k - s l i p v i b r a t i o n c e a s e d , t h e m o t i o n o f t h e s l i d e r became i r r e g u l a r and t h e f r i c t i o n c o e f f i -c i e n t s i n c r e a s e d . E x a m i n a t i o n o f t h e s u r f a c e s r e v e a l e d t h a t b o t h t h e s l i d e r a n d t h e t r a c k were h e a v i l y damaged. T h i s t e m p e r a t u r e r a n g e i s b e l o w t h e d e c o m p o s i t i o n t e m p e r -a t u r e o f t h e m i n e r a l o i l , and t o o low t o p r o d u c e a p p r e c i a b l e c r e e p o f e i t h e r m a t e r i a l . The e x t e n t o f t h e s u r f a c e damage and t h e l o w s u r f a c e t e m p e r a t u r e s u g g e s t t h a t t h e f r i c t i o n b e h a v i o u r c h a n g e d b e c a u s e t h e p r o t e c t i v e s u r f a c e f i l m ( e i t h e r a m e t a l l i c s o ap f i l m o r a n a d s o r b e d h y d r o c a r b o n l a y e r ) was a d v e r s e l y a f f e c t e d by t h e i n c r e a s e d s u r f a c e t e m p e r a t u r e . The c r e e p m o d e l o f s t a t i c f r i c t i o n was e x a m i n e d f u r t h e r b y m e a s u r i n g t h e c o n t a c t r e s i s t a n c e o f t h e s l i d e r - d i s k i n t e r f a c e a s a f u n c t i o n o f t i m e . By m o n i t o r i n g t h e e l e c t r i c a l r e s i s t a n c e o f t h e i n t e r f a c e i t was p o s s i b l e t o f o l l o w c h a n g e s i n c o n t a c t a r e a s a s a f u n c t i o n o f t i m e o f c o n t a c t . From t h e s e r e s u l t s i t was p o s s i b l e t o show t h a t t h e " j u n c t i o n g r o w t h by c r e e p " m o d e l f o r s t a t i c f r i c t i o n d o e s n o t a d e q u a t e l y d e s c r i b e t h e o b s e r v e d phenomena. 3. I n t h e t h i r d p a r t o f t h i s s t u d y on s t a t i c f r i c t i o n t h e e l e c t r i c a l r e s i s t a n c e o f t h e s l i d e r - t r a c k i n t e r f a c e was m o n i t o r e d d u r i n g s t i c k - s l i p . I t was f o u n d t h a t t h e s u r f a c e s were i n m e t a l l i c c o n t a c t t h r o u g h o u t t h e e n t i r e s t i c k - s l i p c y c l e b u t t h a t t h e amount o f c o n t a c t v a r i e d . I t was o b s e r v e d t h a t t h e c o n t a c t t h r o u g h o u t t h e c o m p l e t e c y c l e was m e t a l l i c a l t h o u g h t h e amount o f m e t a l l i c c o n t a c t v a r i e d d u r i n g t h e c y c l e . The s t i c k p o r t i o n o f t h e c y c l e was f o u n d t o be a r e g i o n o f i n c r e a s i n g m e t a l l i c c o n t a c t . The amount o f m e t a l l i c c o n -t a c t a r e a a t s l i p was f o u n d t o be a f u n c t i o n o f t h e r a t e a t w h i c h t h e t a n g e n t i a l f o r c e was a p p l i e d . 70 D u r i n g s l i p , t h e a r e a i n m e t a l l i c c o n t a c t d e c r e a s e d r a p i d l y and t h e r e was some e v i d e n c e t h a t the_ n o r m a l l o a d on t h e s l i d e r was p a r t i a l l y s u p p o r t e d b y a l u b r i c a n t f i l m i n t h i s p a r t o f t h e c y c l e . The amount o f c o n t a c t d u r i n g s l i p was d e t e r m i n e d by t h e r e l a t i v e v e l o c i t y d u r i n g s l i p . A d d i t i o n a l m e a s u r e m e n t s o f t h e i n t e r f a c e r e s i s -t a n c e and s u b s e q u e n t c a l c u l a t i o n s o f c o n t a c t a r e a i n c r e a s e d u r i n g s l i p i n d i c a t e t h a t t h e most i m p o r t a n t v a r i a b l e i n d e t e r m i n i n g t h e c o n t a c t a r e a a t s l i p i s t h e r a t e o f a p p l i -c a t i o n o f t h e t a n g e n t i a l l o a d . T h i s v a r i a b l e a l s o a f f e c t e d t h e 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 o f b o t h t h e g o l d and t h e s t e e l s y s t e m s . A v i s c o - e l a s t i c m o d e l w h i c h e x p l a i n s t h i s t y p e o f b e h a v i o u r h a s b e e n p r o p o s e d b y K o s t e r i n a n d K r a g e l s k i i [ 1 6 ] and b y J o h a n n e s [ 2 7 ] . A t t h i s t i m e , h o w e v e r , i t i s n o t c l e a r w h e t h e r t h e i n c r e a s e i n c o n t a c t a r e a i s due t o ( a ) an i n c r e a s e i n t h e o v e r a l l a r e a o f t h e j u n c t i o n and w i t h i t a n i n c r e a s e i n t h e m e t a l l i c p o r t i o n o f t h e a r e a o f c o n t a c t o r (b) g r o w t h i n t h e a r e a o f m e t a l l i c c o n t a c t a t t h e e x p e n s e o f t h e n o n - m e t a l l i c c o n -t a c t , o r some c o m b i n a t i o n o f t h e s e two p o s s i b i l i t i e s . More r e s e a r c h a l o n g t h e s e l i n e s i s s u g g e s t e d . CHAPTER 6 SUGGESTIONS FOR FURTHER RESEARCH The p r e s e n t work c a n be e x t e n d e d i n two d i r e c -t i o n s . By u s i n g a n u l t r a - h i g h vacuum e n v i r o n m e n t i n c o n -j u n c t i o n w i t h e n v i r o n m e n t s o f known c o m p o s i t i o n i t s h o u l d be p o s s i b l e t o d e t e r m i n e t h e e f f e c t o f r a t e o f a p p l i c a t i o n o f t a n g e n t i a l l o a d i n g on t h e d e g r e e o f a d h e s i o n o f two s i m i l a r m e t a l s w h i c h a r e s u b j e c t e d t o s i m u l t a n e o u s n o r m a l and t a n g e n t i a l l o a d i n g . The r e s u l t s o f t h e i n v e s t i g a t i o n s b y J o h a n n e s a n d t h i s s t u d y i n d i c a t e t h a t i t s h o u l d be p o s s i b l e t o a c h i e v e more e x t e n s i v e c o l d - w e l d i n g i f a c o n -t r o l l e d - r a t e t a n g e n t i a l l o a d i s a p p l i e d t o t h e i n t e r f a c e o f two m e t a l s , i n a d d i t i o n t o t h e c o n s t a n t n o r m a l l o a d . S e c o n d l y , b y a p p l y i n g t h e r e s i s t a n c e m e a s u r i n g t e c h n i q u e t o more e x t e n s i v e s t u d i e s o f s t i c k - s l i p a n d q u a s i - h a r m o n i c v i b r a t i o n i t may be p o s s i b l e t o e x p l a i n some o f t h e o b s e r v e d f r i c t i o n phenomena s u c h as t h e " h y s t e r e s e s " i n t h e f r i c t i o n - v e l o c i t y c u r v e s d u r i n g s l i p . A v e r y l i m i t e d amount o f work o n t h i s a s p e c t was c a r r i e d o u t i n c o n j u n c t i o n w i t h D r . P. L . Ko. Some r e s u l t s o f t h i s work a r e i n c l u d e d i n F i g u r e 24. I t i s o b v i o u s (1) t h a t t h e amount o f m e t a l l i c c o n t a c t i s n o t c o n s t a n t 72 d u r i n g t h e c y c l e , (2) t h a t t h e g r e a t e s t s e p a r a t i o n o c c u r s a t t h e r e g i o n o f maximum r e l a t i v e v e l o c i t y and (3) t h a t f o r a g i v e n r e l a t i v e v e l o c i t y o f s l i p t h e c o n t a c t a r e a c a n have two v a l u e s . REFERENCES 1. R a b i n o w i c z , R., F r i c t i o n and Wear o f M a t e r i a l s , J o h n W i l e y and S o n s , New Y o r k , 1965. 2. K r a g e l s k i i , I . V., F r i c t i o n and Wear, B u t t e r w o r t h s , 1965. 3. Cameron, A. C , L u b r i c a t i o n , J o h n W i l e y and S o n s , New Y o r k , 1965. 4. Bowden, F . P. and T a b o r , D., " F r i c t i o n , L u b r i c a t i o n a n d Wear: A S u r v e y o f Work D u r i n g t h e L a s t D e c a d e " , B r i t i s h J o u r n a l o f A p p l i e d P h y s i c s , v o l . 17, p p . 1321-44, 1966. 5. F i n i k i n , E . , " F r i c t i o n , A d h e s i v e Wear and A b r a s i v e Wear, P r i n c i p a l l y i n M e t a l s : A Review"ASME P a p e r No. 63-WA-89, 1963. 6. Houwink, R. and S a l o m o n , G., e d . , " A d h e s i o n a n d  A d h e s i v e s " , V o l . 1, E l s e v i e r , Amsterdam, 1965. 7. B i k e r m a n , J . J . , " T h e r m o d y n a m i c s , A d h e s i o n and S l i d i n g F r i c t i o n " ASME P a p e r No. 69-LUB-4, 1969. 8. S i k o r s k i , M. E . , "The A d h e s i o n o f M e t a l s " , M e c h a n i s m s  o f S o l i d F r i c t i o n . P. J . B r y a n t , M. L a v i k and G. S a l o m o n , e d . , E l s e v i e r , 1964, p.144. 9. Bowden, F . P. and L e b e n , L . , "The N a t u r e o f S l i d i n g a n d t h e A n a l y s i s o f F r i c t i o n " P r o c e e d i n g s o f t h e R o y a l S o c i e t y , A, V o l . 169, p p . 371-413, 1938. 10. R a b i n o w i c z , E . , "The N a t u r e o f t h e 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 o f A p p l i e d P h y s i c s , V o l . 22. No. 11, pp. 1373-1379, 1951. 11. Sampson, J . B., Morgan, F., Reed, D. W. a n d M u s k a t , M . , " F r i c t i o n B e h a v i o u r D u r i n g t h e S l i p P o r t i o n o f t h e S t i c k - S l i p P r o c e s s " , J o u r n a l o f A p p l i e d P h y s i c s , v o l . 14, p . 689, 1943-. 12. M o r g a n , F., M u s k a t , M. and Reed, D. W., " F r i c t i o n Phenomena and t h e S t i c k - S l i p P r o c e s s " , J o u r n a l o f " A p p l i e d P h y s i c s , V o l . 12, p. 743, 1941. 74 13. B r i s t o w , J . R., " K i n e t i c B o u n d a r y F r i c t i o n " , P r o c e e d i n g s o f t h e R o y a l S o c i e t y , A, V o l . 189, pp. 88-102, 1945. 14. B r i s t o w , J . R., "The M e a s u r e m e n t o f K i n e t i c B o u n d a r y F r i c t i o n " , P r o c e e d i n g s o f t h e I n s t i t u t i o n o f M e c h a n i c a l E n g i n e e r s , V o l . 160, p . 259, 1949. 15. D e r j a g u i n , B. V., P u s h , V. E . and T o l s t o i , D. M., "A T h e o r y o f S t i c k - S l i p S l i d i n g o f S o l i d s " , P r o c e e d i n g s o f t h e C o n f e r e n c e on L u b r i c a t i o n a n d Wear, O c t . 1957, p . 257. 16. K o s t e r i n , J . I . and K r a g e l s k i i , I . V., " R h e o l o g i c a l Phenomena i n D r y F r i c t i o n " , Wear, 5 ( 1 9 6 2 ) , 190-197. 17. B r o c k l e y , C. A., Cameron, R. and P o t t e r , A. F . , " F r i c t i o n I n d u c e d V i b r a t i o n " , J o u r n a l o f L u b r i c a t i o n T e c h n o l o g y , S e r i e s F . , V o l . 90, p . 35, 1968. 18. S p u r r , R. T., " C r e e p a n d 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 o f A p p l i e d P h y s i c s , V o l . 6 , pp. 402-3, 1955. 19. M o o r e , A. C. a n d T a b o r , D., B r i t i s h J o u r n a l o f A p p l i e d P h y s i c s , V o l . 3, p . 299, 1952. 20. A t k i n s , A. G., S i l v e r i o , A. a n d T a b o r , D., " I n d e n t a t i o n H a r d n e s s and t h e C r e e p o f S o l i d s " , J o u r n a l o f t h e I n s t i t u t e o f M e t a l s , V o l . 9 4 ( 1 9 6 6 ) , pp. 369-378. 21. M u l h e a r n , T. O. and T a b o r , D., " C r e e p a n d t h e H a r d n e s s o f M e t a l s : A P h y s i c a l S t u d y " , J o u r n a l o f t h e I n s t i t u t e o f M e t a l s , V o l . 89, pp. 7-12, 1966. 22. P a r k e r , R. C , F a r n w o r t h , W. and M i l n e , R., "The V a r i a t i o n o f t h e C o e f f i c i e n t o f S t a t i c F r i c t i o n w i t h t h e R a t e o f A p p l i c a t i o n o f t h e T a n g e n t i a l F o r c e " , P r o c e e d i n g s o f t h e I n s t i t u t i o n o f M e c h a n i c a l E n g i n e e r s , V o l . 160, pp. 176-184, 1949. 23. G r e e n , A. P., "The P l a s t i c Y i e l d i n g o f J u n c t i o n s due t o Combined S h e a r a n d P r e s s u r e " , J o u r n a l o f t h e M e c h a n i c s a n d P h y s i c s o f S o l i d s , V o l . 2, pp. 197-211, 1954. 24. Greenwood, J . A. and T a b o r , D., " D e f o r m a t i o n P r o p e r t i e s o f F r i c t i o n J u n c t i o n s " , P r o c e e d i n g s o f P h y s i c a l S o c i e t y L X V I I I , V o l . 9-B, pp. 609-619, 1955. 25. C o u r t n e y - P r a t t , J . S. and E i s n e r , E . , "The E f f e c t o f a T a n g e n t i a l F o r c e on t h e C o n t a c t o f M e t a l l i c B o d i e s " , P r o c e e d i n g s o f t h e R o y a l S o c i e t y ( L o n d o n ) , A 2 3 8 ( 1 9 5 7 ) , p . 529. 75 26. J o h n s o n , K. L . , " D e f o r m a t i o n o f a P l a s t i c Wedge by a R i g i d F l a t D i e U n d e r t h e A c t i o n o f a T a n g e n t i a l F o r c e " , J o u r n a l o f t h e M e c h a n i c s and P h y s i c s o f S o l i d s , V o l . 1 6 ( 1 9 6 8 ) , pp. 395-402. 27. J o h a n n e s , V. I . , " F r i c t i o n I n d u c e d V i b r a t i o n s i n a H y d r a u l -i c a l l y D r i v e n S y s t e m " , Ph.D. T h e s i s , D e p a r t m e n t o f 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 o f B r i t i s h C o l u m b i a , 1969. 28. Bowden, F . P. a n d Y o u n g , J . E . , "The F r i c t i o n o f C l e a n M e t a l s a n d t h e I n f l u e n c e o f A d s o r b e d F i l m s " , P r o c e e d i n g s o f t h e R o y a l S o c i e t y ( L o n d o n ) , A, V o l . 2 0 8 ( 1 9 5 1 ) , pp. 311-325. 29. N i c h o l a s , M. G., " C o l d B o n d i n g Between H e m i s p h e r i c a l C o p p e r S u r f a c e s " , T r a n s , o f M e t a l l u r g i c a l S o c i e t y o f AIME, V o l . 2 2 7 ( 1 9 6 3 ) , pp. 250-256. 30. O s a i s , J . R. and T r i p p , J . H., " M e c h a n i c a l D i s r u p t i o n o f S u r f a c e F i l m s o n M e t a l s " , Wear, 9 ( 1 9 6 6 ) , p p . 388-397. 31. C o c k s , M. ( a ) " I n t e r a c t i o n o f S l i d i n g M e t a l S u r f a c e s " , J o u r n a l o f A p p l i e d P h y s i c s , V o l . 33, No. 7, pp. 2152-2161, 1962. (b) " S h e a r i n g o f J u n c t i o n s B e t w e e n M e t a l S u r f a c e s " , Wear, 9 ( 1 9 6 6 ) , p p . 320-328. 32. A i n b i n d e r , S. B. and P r a n c s , A. S., "On t h e M e c h a n i s m o f t h e F o r m a t i o n a n d D e s t r u c t i o n o f A d h e s i o n J u n c t i o n s B e t w e e n B o d i e s i n F r i c t i o n a l C o n t a c t " , Wear, 9 ( 1 9 6 6 ) , pp. 209-227. 33. S i m o n , I . , McMahon, H. O. a n d Bowen, R. J . , " D r y M e t a l l i c F r i c t i o n a s a F u n c t i o n o f T e m p e r a t u r e B e t w e e n 4.2°K and 6 0 0 ° K " , J o u r n a l o f A p p l i e d P h y s i c s , V o l . 22, No. 2, pp. 177-184, 1951. 34. P e t e r s o n , M. B., F l o r e k , J . J . a n d L e e , R. E . , " S l i d i n g C h a r a c t e r i s t i c s o f M e t a l s a t H i g h T e m p e r a t u r e s " , ASLE T r a n s a c t i o n s , V o l . 3 ( 1 9 6 0 ) , pp. 101-107. 35. F u r e y , M. J . , " M e t a l l i c C o n t a c t and F r i c t i o n B e t w e e n S l i d i n g S u r f a c e s " , A S L E T r a n s a c t i o n s V o l . 4 ( 1 9 6 1 ) , pp. 1-11. 36. W i l s o n , W. R., "The C o n t a c t R e s i s t a n c e a n d M e c h a n i c a l P r o p e r t i e s o f S u r f a c e F i l m s on M e t a l s " , P r o c e e d i n g s o f t h e P h y s i c a l S o c i e t y , L X V I I I , 9-B, pp. 625-621, 1955. 37. M c N i c h o l a s , T. a n d K e l l e r , D. V., " U t i l i z a t i o n o f C o n -t a c t R e s i s t a n c e M e a s u r e m e n t s i n t h e I n v e s t i g a t i o n o f t h e M e t a l l i c A d h e s i o n o f I r o n " , J o u r n a l o f A d h e s i o n , V o l . 1 ( 1 9 6 9 ) , pp. 164-179. 76 38. J o n e s , M. H. and H o w e l l s , R. I . L . , and P r o b e r t , S. D., " S o l i d s i n S t a t i c C o n t a c t " , Wear, 1 2 ( 1 9 6 8 ) , pp. 225-240. 39. K e l l o g g , L . G., " D e v e l o p m e n t s i n H i g h T e m p e r a t u r e , U l t r a - h i g h Vacuum S t u d i e s " , J o u r n a l o f A m e r i c a n S o c i e t y o f L u b r i c a t i o n E n g i n e e r s , V o l . 22, No. 2, pp. 141-150. 40. A n t l e r , M., "Wear and F r i c t i o n o f t h e P l a t i n u m M e t a l s " , P l a t i n u m M e t a l s R e v i e w , v o l . 1 0 ( 1 9 6 6 ) , pp. 2-8. 41. T o l s t o i , D. M., " S i g n i f i c a n c e o f t h e N o r m a l D e g r e e o f F r e e d o m and N a t u r a l N o r m a l V i b r a t i o n s i n C o n t a c t F r i c t i o n " , Wear, 1 0 ( 1 9 6 7 ) , pp. 199-213. 42. R o b e r t s o n , W. G. a n d S p i l l m a n , D. T., "The H y d r o -d y n a m i c s o f F l a t C o n t a c t s : F r i c t i o n S t u d i e s i n t h e P i n a n d D i s c M a c h i n e " , P r o c e e d i n g s o f t h e I n s t i t u t i o n o f M e c h a n i c a l E n g i n e e r s , V o l . 180, P a r t 3K ( 1 9 6 5 - 6 6 ) , p p . 49-60. 43. H a m i l t o n , D. B., W a l o w i t , J . A. a n d A l l e n , C. M., "A T h e o r y o f L u b r i c a t i o n by M i c r o - i r r e g u l a r i t i e s " , ASME P a p e r No. 6 5 - L u b - l l , 1965. 44. C o u r t e l , R., " N o r m a l V i b r a t i o n s i n C o n t a c t F r i c t i o n " , Wear, 1 1 ( 1 9 6 8 ) , p . 77. 45. D a v i s , H. R., "The D e p e n d e n c e 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 on t h e T i m e o f S t a t i o n a r y C o n t a c t " , M.A.Sc., T h e s i s , D e p a r t m e n t o f 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 o f B r i t i s h C o l u m b i a , 1966. 46. Adamson, A. W., P h y s i c a l C h e m i s t r y o f S u r f a c e s , I n t e r - , s c i e n c e P u b l i s h e r s , I n c . , New Y o r k , 1967. 47. W i l l i a m s o n , J . B. P. a n d H u n t , R. T., "The M i c r o t o p o -g r a p h y o f S o l i d S u r f a c e s " , R e s e a r c h R e p o r t No. 59 ( J a n u a r y 26, 1 9 6 8 ) , B u r n d y R e s e a r c h D i v i s i o n , N o r w a l k , C o n n e c t i c u t . 48. W e l l s , J . H., " K i n e t i c B o u n d a r y F r i c t i o n " , The E n g i n e e r , ( L o n d o n ) , V o l . 1 4 7 , 1929, p . 454. 49. J o n e s , J . R., "The E f f e c t o f I d l e T ime o n S t a t i c F r i c t i o n " , J o u r n a l o f t h e ASLE ( A p r i l , 1 9 6 7 ) , p p . 154-164. APPENDIX A MEASURING THE RESISTANCE OF THE SLIDER-DISK INTERFACE DURING S T I C K - S L I P . The b a s i s o f t h e r e s i s t a n c e m e a s u r i n g t e c h n i q u e i s t h a t t h e r e s i s t a n c e o f a n o i l f i l m i s s e v e r a l o r d e r s o f m a g n i t u d e g r e a t e r t h a n t h e r e s i s t a n c e o f a m e t a l l i c c o n t a c t . The s p e c i f i c e l e c t r i c a l r e s i s t a n c e , p , f o r most. 12 o i l s i s i n t h e r a n g e o f 10 ohm-cm.;for common m e t a l s i t -4 i s i n t h e r a n g e o f 10 ohm-cm. An e s t i m a t e o f t h e e l e c -t r i c a l r e s i s t a n c e o f a t y p i c a l o i l f i l m e x p e c t e d u n d e r t h e p r e s e n t c o n d i t i o n s c a n be o b t a i n e d f r o m R = pL/A. 12 B a s e d on v a l u e s o f P ., = 10 ohm-cm., A ( a r e a o f f i l m ) o i l 7 = 1 cm., and L ( f i l m t h i c k n e s s ) = 10"^ cm., t h e r e s i s t a n c e 8 o f a f i l m , i f f o r m e d , w o u l d be 10 ohm. Compare t h i s t o t h e r e s i s t a n c e o f t h e i n t e r f a c e i f t h e r e i s a p u r e m e t a l l i c —8 2 c o n t a c t o f o n l y 1 0 " cm. a r e a . F o r a p u r e m e t a l l i c c o n -t a c t o f s m a l l d i a m e t e r , where t h e s m a l l s i z e o f t h e c o n t a c t r e s t r i c t s t h e c u r r e n t f l o w , t h e ' s p r e a d i n g r e s i s t a n c e ' o f t h e c o n t a c t i s R = P/2r. T h u s t h e s p r e a d i n g r e s i s t a n c e — 5 —8 2 o f a s i n g l e i r o n c o n t a c t ( p = 10~ ohm-cm.) o f 1 0 " cm. -1 9 a r e a w o u l d b e ^ l O ohm' o r 10 t i m e s l e s s t h a n a t h i n o i l f i l m . 7 8 I n i t i a l l y i t was assumed t h a t a f u l l o i l f i l m was d e v e l o p e d d u r i n g s l i p . T h i s a s s u m p t i o n was t e s t e d u s i n g a r e s i s t a n c e m e a s u r i n g b r i d g e , s i m i l a r t o t h a t shown i n F i g u r e 2 3 ( a ) , t o m e a s u r e t h e s l i d e r - t r a c k c o n t a c t r e s i s -t a n c e d u r i n g s t i c k - s l i p . F o r t h e s e i n i t i a l t e s t s u s i n g a l o w v o l t a g e , h i g h f r e q u e n c y A.C. s o u r c e (60 t o 6000 c p s ) i n s t e a d o f a D.C. s o u r c e t o power t h e b r i d g e h a d two a d v a n t a g e s : 1. any a r c i n g t h r o u g h t h e f i l m w i l l be v i s i b l e o n t h e o s c i l l o s c o p e ( t h e s i n u s o i d a l w a v e f o r m w i l l be b r o k e n when a r c i n g o c c u r s ) a n d i 2. t h e r e i s no p o s s i b i l i t y o f D.C. d r i f t . The i n i t i a l s t u d y showed t h a t t h e r e s i s t a n c e p f t h e s l i d e r - t r a c k i n t e r f a c e was l e s s t h a n 1 ohm d u r i n g b o t h p a r t s o f t h e s t i c k - s l i p c y c l e . To s t u d y any r e s i s t a n c e c h a n g e s b e l o w t h i s l e v e l a b r i d g e s u i t a b l e f o r m e a s u r i n g s m a l l r e s i s t a n c e s was d e v e l o p e d . The c i r c u i t d i a g r a m o f t h e b r i d g e i s g i v e n i n F i g u r e 2 3 ( a ) . On one s i d e o f t h e b r i d g e t h e unknown r e s i s t a n c e , R t o t a l ' w a s c o n n e c t e d ^ n s e r i e s w i t h a known r e s i s t a n c e , RQ. T h i s s i d e o f t h e b r i d g e was t h e n c o n n e c t e d i n p a r a l l e l t o a s i n g l e r e s i s t a n c e w h i c h i s e q u a l i n v a l u e t o R Q . I f R t o t a l l s z e r o t h e n t h e b r i d g e i s b a l a n c e d s o t h a t t h e d i f f e r e n t i a l v o l t a g e r e a d i n g o n t h e o s c i l l o s c o p e i s z e r o . I f R t 0 t a ] _ ^ s g r e a t e r t h a n z e r o t h e v o l t a g e d r o p s a c r o s s t h e b r i d g e r e s i s t a n c e s , R q , a r e u n e q u a l a n d t h e i r d i f f e r e n c e 79 i s m e a s u r e d a s d i f f e r e n t i a l v o l t a g e o n t h e o s c i l l o s c o p e . T h u s t h e d i f f e r e n t i a l v o l t a g e r e a d i n g , V, on t h e o s c i l l o -s c o p e i s a f u n c t i o n o f t h e r e s i s t a n c e o f t h e s l i d e r - t r a c k i n t e r f a c e . S i n c e t h e c u r r e n t was known and t h e b r i d g e r e s i s t o r s h a v e a known v a l u e , t h e r e s i s t a n c e o f t h e i n t e r -f a c e c a n be c a l c u l a t e d b y s o l v i n g two e q u a t i o n s : ( 1 ) I , + I 0 = I 1 d o (2) R o ( i 1 + I 2 ) = R t o t a l I 2 = V I i s r e g u l a t e d and known and R i s known. F i g u r e 2 3 ( b ) o o i s a g r a p h o f r e s i s t a n c e v s . d i f f e r e n t i a l v o l t a g e , u s e d i n t h i s s t u d y . I n i t i a l l y t h e r e s i s t a n c e m e a s u r e m e n t s were c o n d u c -t e d on t h e g o l d - g o l d i n t e r f a c e . However, b e c a u s e o f t h e low r e s i s t a n c e o f t h e i n t e r f a c e , m e asurement o f t h e e l e c t r i c a l r e s i s t a n c e c h a n g e s d u r i n g s t i c k - s l i p was d i f f i c u l t . The r e s u l t s o f some p r e l i m i n a r y t e s t s u s i n g s t e e l s l i d i n g on s t e e l were c o m p a r e d and t h e g e n e r a l b e h a v i o u r o f t h e r e s i s t a n c e d u r i n g s t i c k - s l i p was f o u n d t o be s i m i l a r . B e c a u s e t h e i n t e r f a c e r e s i s t a n c e was e a s i e r t o m easure and t h e g e n e r a l b e h a v i o u r o f t h e s y s t e m s was s i m i l a r , i t was d e c i d e d t o c o n t i n u e t h e r e s i s t a n c e m e a s u r e m e n t s u s i n g s t e e l on s t e e l . Some o f t h e g o l d o n g o l d r e s u l t s a r e a l s o i n c l u d e d f o r c o m p a r i s o n . B o t h s t u d i e s u s e d p e t r o l a t u m o i l a s a l u b r i c a n t and were c o n d u c t e d a t a m b i e n t t e m p e r a t u r e a n d h u m i d i t y . 80 The d e v e l o p m e n t o f t h e b r i d g e p e r m i t t e d t h e m o n i t o r i n g o f r e s i s t a n c e c h a n g e s i n t h e s l i d e r - t r a c k i n t e r -f a c e d u r i n g s l i d i n g and s t i c k - s l i p . T h u s i t was p o s s i b l e t o s t u d y s e v e r a l a s p e c t s o f s l i d e r - t r a c k c o n t a c t . I n t h e s t i c k p o r t i o n o f t h e s t i c k - s l i p c y c l e t h e two s o l i d s a r e i n c o n t a c t u n d e r c o m b i n e d n o r m a l and t a n g e n t i a l l o a d i n g . The t a n g e n t i a l f o r c e i s s t e a d i l y i n c r e a s i n g and t h e r e l a -t i v e movement b e t w e e n t h e s l i d e r and t h e t r a c k i s v e r y l i m i t e d . By u s i n g t h e r e s i s t a n c e m e a s u r i n g t e c h n i q u e i t was p o s s i b l e t o o b s e r v e c o n t a c t a r e a c h a n g e s u n d e r t h e s e l o a d i n g c o n d i t i o n s . The r e s i s t a n c e m e a s u r i n g t e c h n i q u e a l s o p r o v i d e d a n o t h e r method o f e x a m i n i n g t h e r o l e o f t h e r a t e o f t a n g e n t i a l f o r c e a p p l i c a t i o n on t h e s t a t i c f r i c t i o n v a l u e a n d t h e c o n t a c t a r e a . APPENDIX B INTERFACE RESISTANCE AND THE AREA OF CONTACT An a p p r o x i m a t e a n a l y s i s o f t h e r e l a t i o n s h i p b e t w e e n t h e c h a n g e i n i n t e r f a c e r e s i s t a n c e and t h e c o n -t a c t a r e a c h a n g e i s p r e s e n t e d i n t h i s s e c t i o n . A r e a o f C o n t a c t C o n s i d e r t h e s t i c k - s l i p c y c l e shown i n F i g u r e K b ) . A t t h e b e g i n n i n g o f e a c h s t i c k c y c l e , t h e s u r f a c e s t o u c h a t n p o i n t s . The number o f p o i n t s i s d e t e r m i n e d by t h e p r o f i l e o f t h e s u r f a c e s and t h e a p p l i e d n o r m a l l o a d . The s i z e d i s t r i b u t i o n o f t h e s e a r e a s o f c o n t a c t i s n o t known, n e i t h e r i s t h e i r e x a c t s h a p e . T h e s e a r e a s a r e s m a l l when c o m p a r e d t o t h e a p p a r e n t a r e a o f c o n t a c t . Assume t h a t a t y p i c a l a r e a c a n be a p p r o x i m a t e d b y an e q u i v a l e n t c i r c u l a r a r e a o f r a d i u s , r . T hus t h e t o t a l a r e a o f c o n t a c t a t t h e b e g i n n i n g o f s t i c k i s A T O T A L = ( a 2 + b 2 + c 2 + . . . + r 2 ) C l ) where a, b, e t c . d e n o t e t h e a p p r o x i m a t e r a d i i o f p a r t i c u -l a r a r e a s o f c o n t a c t . 82 The m e t a l l i c a r e a o f c o n t a c t a t t h e b e g i n n i n g o f s t i c k i s A. where A. = k A--.-,.. , where k d e n o t e s t h e f r a c t i o n o f t o t a l c o n t a c t s t h a t a r e m e t a l l i c . Assume t h a t d u r i n g s t i c k t h e a p p l i c a t i o n o f t h e t a n g e n t i a l l o a d c a u s e s a n a v e r a g e s t r a i n , e ( t ) , a c r o s s t h e i n t e r f a c e . D u r i n g s t i c k t h e number o f a r e a s i n c o n t a c t d o e s n o t i n c r e a s e a p p r e c i a b l y ( u n l i k e t h e s i t u a t i o n when t h e n o r m a l l o a d i s i n c r e a s e d ) due t o t h e a p p l i c a t i o n o f t h e t a n g e n t i a l f o r c e , b u t t h e i n d i v i d u a l c o n t a c t a r e a s i n c r e a s e i n s i z e . A c i r c u l a r c o n t a c t a r e a , o r i g i n a l l y o f r a d i u s , r , w o u l d d e f o r m t o an e l l i p t i c a l a r e a w i t h m i n o r a x i s , r , a n d m a j o r a x i s , (1 + « ) r , ( s e e F i g u r e B - l ) The new a r e a o f c o n t a c t o f t h e i n t e r f a c e i s A „ where F A^ = [ a 2 ( 1 + € ) + b 2 ( 1 + « ) + c 2 ( 1 + « ) . . . + r 2 ( 1 + f ) ] r (2) The p o r t i o n o f m e t a l l i c c o n t a c t i s A f - k A p . T h u s t h e i n i t i a l a n d f i n a l a r e a s o f c o n t a c t h a v e t h e r a t i o ( A i / A f = ( 1 + \ > C o n t a c t R e s i s t a n c e The s i z e o f t h e a r e a s i s s m a l l so t h a t t h e e l e c -t r i c a l r e s i s t a n c e o f e a c h 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 i t s r a d i u s [ 3 7 ] , T h u s t h e r e a r e n c o n t a c t s , e a c h o f d i f f e r e n t 83 r a d i u s — a, b , c , d, e t c . and e a c h h a v i n g a r e s i s t a n c e p R Some o f t h e s e c o n t a c t a r e a s a r e p u r e l y r 2r m e t a l l i c and some a r e n o n - m e t a l l i c . T h e s e n c o n t a c t s a c t as n r e s i s t o r s i n p a r a l l e l when a v o l t a g e i s a p p l i e d , a c r o s s t h e i n t e r f a c e . T h u s t h e o v e r a l l i n i t i a l r e s i s t a n c e R^ f o r a number o f m i x e d c o n t a c t s , m e t a l l i c and n o n - m e t a l l i c w o u l d b e : 1 _ 1 1 1 R. R + R K R + i a b c R_ n (3) I R; ^ m e t a l l i c (a + hm + m m ) + 2_ (anm + t>nm P n o n - m e t a l l i c a s s u m i n g t h a t P n o n - m e t a l l i c » P m e t a l l i c (4) t h e n 1 R^ P m e t a l l i c R. ~ p m e t a l l i c x * ( a + b + c . . .) (_i ) \ a + b + c . . . / ( 5 ) (6) I n o r d e r t o f i n d t h e f i n a l c o n t a c t r e s i s t a n c e we r e q u i r e an e q u i v a l e n t r a d i u s f o r t h e assumed e l l i p t i c a l c o n t a c t i n o r d e r t o a p p l y c o n s t r i c t i o n r e s i s t a n c e e q u a t i o n s . The f o l l o w i n g a n a l y s i s g i v e s t h i s r a d i u s f o r a t y p i c a l a s p e r i t y w h i c h h a d an o r i g i n a l r a d i u s o f r a t t h e b e g i n n i n g o f s t i c k av r (1 + « ) (7) 84 and t h u s r = r ( l + e ) 1 / 2 ( 8 ) av T h e r e f o r e t h e f i n a l r e s i s t a n c e o f t h e i n t e r f a c e i s g i v e n by •Rf~- P m e t a l l i c / _ 1 \ (9) 2 ( 1 + e ) 1 / 2 \ a + b + c + . . ./ From (6) a n d (9) (10) s o t h a t t h e c o n t a c t a r e a c a n be d e r i v e d f r o m t h e i n t e r f a c e r e s i s t a n c e m e a s u r e m e n t s b y 2 " i (11) ( The r e s u l t s o f t h i s a p p r o x i m a t e a n a l y s i s were u s e d t o c a l c u l a t e t h e v a r i a t i o n o f c o n t a c t a r e a w i t h r a t e o f t a n g e n t i a l f o r c e a p p l i c a t i o n i n F i g u r e 22. F i g u r e 1 ( a ) (b) T y p i c a l T i m e - D i s p l a c e m e n t R e c o r d s f o r S t i c k - S l i p M o d e l o f a S y s t e m S u b j e c t t o R e l a x a t i o n O s c i l l a t i o n s F i g u r e 2 E x p e r i m e n t a l A p p a r a t u s CO 86(b) F i g u r e 3 E s s e n t i a l Components o f t h e S l i d e r - T r a c k A s s emb l y c CD E • CD O _<n Q . C/D Q .30 Time [sec] .£ o-i60 ,90 .05-.V. S301--' • f • Trr. ;rrr r X : % -; rr . r rr.~ :-: rr. 777: ••->5.: \ - ~7- * •r \ - • •rrr r:I— 7rr~ -FT? —r? rrrrr . r : r . .rrr • r r rr Irrr •rrrrr • .==. rr?. < ~7 -J:rr> .r7r-: '-rr. .rrr - r -I a : * J r T- -V: '." 7 - '-. ----- ~r~r =z . ~_r - r • — __.. - V - - - j r . - ~-\- Irrrr > : - _-• 7-7 - r. . ..- - .--\r r r r . r r i 1 • i -..1 •1 > . l . r ~ |. -I r y C CD E CD O _rg Q . co ,30 0-.05-i60 .90 F i g u r e 4 C o m p a r i s o n o f Two Modes o f S l i d i n g ( a ) s l i d i n g u n d e r u n l u b r i c a t e d c o n d i t i o n s : h i g h f r i c t i o n c o e f f i c i e n t s a n d e x t e n s i v e s u r f a c e damage r e s u l t . ( b ) s l i d i n g u n d e r s t i c k - s l i p c o n d i t i o n s : f r i c t i o n c o e f f i c i e n t s a r e l o w e r a n d t h e r e i s v e r y l i t t l e s u r f a c e damage. CD F i g u r e 5 S u r f a c e of the Gold T r a c k . (a) i n the a s - p o l i s h e d c o n d i t i o n , (b) a f t e r d r y s l i d i n g d u r i n g which ploughing o c c u r r e d , (c) a f t e r s l i d i n g d u r i n g which s t i c k - s l i p o c c u r r e d . M a g n i f i c a t i o n : 60 x. Unetched. F i g u r e 6 Removing t h e L u b r i c a n t D e c r e a s e s t h e A m p l i t u d e o f S t i c k - S l i p . co 100. 80-60-X c <D D ' CT 40. 20-0-•030 .035 .040 .045 .050 Displacement ( in. ) F i g u r e 7 F r e q u e n c y o f O c c u r r e n c e o f V a l u e s o f Maximum S l i d e r D i s p l a c e m e n t D u r i n g S t i c k f o r One C o m p l e t e T r a c k T r a v e r s e . -1 Run 4, g o l d on g o l d ; 3 3°C, 30% r e l a t i v e h u m i d i t y , 9 =i02 s e c o .70-.60-.50- v v • v • B 9 e * .40. ' .30. Gold on Gold © e=.2 sec. -1 ; -1 • 9=.18 sec. V 9=»13 sec. A 9=.13 sec." 1 . N . 5.2 lb. .20-.10-0 100 '200 400 "300 D ( inches ) Figure 8 Static Friction Coefficient as a Function of Run-in. D is the distance that the slider travelled.} one revolution of the disk = 10 inches. 500 IB A A A • S T E E L / S T E E L N =4.1 LB. A G O L D / G O L D N = 4 . 0 L B . V G O L D / G O L D N-4.8 LB. H G O L D / G O L D N = 3.4 LB. »© :oi :i e ( secT1) 'i F i g u r e 9 ' 1 0 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 s , | J S , a s a F u n c t i o n o f T a n g e n t i a l L o a d R a t e Q , f o r G o l d on G o l d and f o r S t e e l o n S t e e l -F i g u r e 10 D i f f e r e n t i a l V o l t a g e as a F u n c t i o n of Time During Three Complete S t i c k - S l i p C y c l e s . A l s o shown i s the c o r r e s p o n d i n g d i s p l a c e m e n t - t i m e t r a c e of the s t i c k - s l i p c y c l e s . The d i f f e r e n t i a l v o l t a g e i n d i c a t e s the changes i n m e t a l l i c c o n t a c t d u r i n g s t i c k -s l i p . A.C. S i g n a l , 6000 c p s . S t e e l on S t e e l . I 94 (a) TIME (5 sec./div. ) Figure 11 D i f f e r e n t i a l Voltage-Time Traces f o r S t i c k - S l i p . (a) Five s t i c k - s l i p c y c l e s : Upper trace: d i f f e r e n t i a l voltage across s t e e l i n t e r f a c e under s t i c k - s l i p conditions. Lower trace: displacement-time trace. D.C. source. (b) D i f f e r e n t i a l voltage measured durina s l i p part of s t i c k - s l i p ; s t e e l on s t e e l . D.C. source. 2.7 amps. 95 7_ 6 J SLIP E cc 4 J 3 J 2 J 1 H STICK 5 SLIP - - - - ® . . © . . j j b 0-0 r2 r — r - 7 "^0 ^ f14 Time (seconds) Figure 12 Interface Resistance-Time Curve for S t i c k - S l i p Cycle. Steel on S t e e l . Cycle number 4 of Figure 11(a). D.C. source. 9 6 8-, 7J 6J 5J 4. c; E O f 3_| 2J 'o 10 "120 r 30 40 Time (milliseconds ) 50 "60 F i g u r e 13 I n t e r f a c e R e s i s t a n c e - T i m e C u r v e D u r i n g S l i p . D a t a was c a l c u l a t e d f r o m d i f f e r e n t i a l - v o l t a g e t i m e p l o t o f F i g u r e 1 K b ) . TIME ( sec. ) 0-1 .050-1 T 0 '20 TIME ( sec. ) <40 Figure 14 Differential Voltage vs Time and Displacement vs Time Traces for Steel on Steel. Line'ab'represents the contact resistance of the interface under normal loading only. The contact area during s l i p i s less than under pure normal loading) this suggests partial load support during s l i p . DISPLACEMENT (.01 i n . / 3 div. ) F i g u r e 15 D i f f e r e n t i a l V o l t a g e Changes During S t i c k - S l i p as a F u n c t i o n of S l i d e r Displacement During S t i c k - S l i p . S t e e l on s t e e l . cc F i g u r e 16 ( a Displacement-Time and D i f f e r e n t i a l Voltage-Time Tr a c e s f o r Delayed S t i c k . I n c r e a s i n g the time t h a t the s l i d e r and d i s k are i n c o n t a c t does not i n r ; e a s e the m e t a l l i c c o n t a c t area at s l i p . T h i s ob-s e r v a t i o n i n v a l i d a t e s the common t h e o r y t h a t the c o n t a c t a r e a i n c r e a s e s as a f u n c t i o n of time due to c r e e p . D.C. s i g n a l . Upper trace Is Lower trace i s Displacement { . 0 0 5 In. /d lv.) vs Time ( 5 sec, /div. ) D i f f e r e n t i a l voltage ( .5 mV/div. ) vs Time ( 5 sec./div. F i g u r e 16(b) Displacement-Time and D i f f e r e n t i a l Voltage-Time Records f o r Three D i f f e r e n t Disk V e l o c i t i e s , The a r e a of m e t a l l i c c o n t a c t a t s l i p i s s e n s i t i v e to the tangen-t i a l l o a d i n g r a t e , , which i s c o n t r o l l e d by the d i s k v e l o c i t y . Upper tra c e i s Displacement ( . 010 i n . / d i v . ) vs Time (2 sec. /div.) Lower trace i s D i f f e r e n t i a l Voltage (,5mV/div. ) vs Time (2 sec./div.) 101 m k ! • •1 mm 1 m\m\ i n I i f l F i g u r e 17 Delayed S t i c k . D e l a y i n g the s t i c k time has no e f f e c t on the i n t e r f a c e r e s i s t a n c e i f the d r i v e n s u r f a c e i s stopped. A.C. s i g n a l , 6000 cps . Delay time i s about 11 seconds. Upper t r a c e : D i f f e r e n t i a l v o l t a g e - t i m e . Lower t r a c e : S l i d e r d i s p l a c e m e n t - t i m e . (a) (b) F i g u r e 18 D i f f e r e n t i a l Voltage-Time T r a c e s f o r Gold on G o ld. The behaviour of a g o l d - g o l d f r i c t i o n c o u p l e d u r i n g s t i c k - s l i p i s e s s e n t i a l l y the same as a s t e e l - s t e e l f r i c t i o n c o u p l e . The amplitude of s l i p i s .015 i n ; normal l o a d i s 5.2 l b s . (a) a complete s t i c k - s l i p c y c l e ; (b) s l i p p o r t i o n c y c l e . V e r t i c a l s c a l e i s 0.1 mv/div., h o r i z o n t a l s c a l e i s (a) 5 s e c / d i v . (b) 10 m i l l i s e c / d i v . M o DISPLACEMENT ( .01 i n . / 3 div. ) F i g u r e 19 The E f f e c t of T a n g e n t i a l Load Rate on I n t e r f a c e R e s i s t a n c e During the S l i p P o r t i o n of the C y c l e . Shown are d i f f e r e n t i a l v o l t a g e - s l i d e r d i s p l a c e m e n t t r a c e s f o r two d i f f e r e n t t a n g e n t i a l l o a d i n g r a t e s . Loading r a t e of i n n e r t r a c e i s .011 i n - s e c - 1 ; o u t e r t r a c e i s .001 i n - s e c " 104 .55., .50. .45. .40. .35_ .30. .25-.20. • • • • RUN 2 B RUN 3 .02 .04 .'06 e (sec. 1 ) .10 .12 F i g u r e 20 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 as a F u n c t i o n of the T a n g e n t i a l Load Rate, © , f o r S t e e l on S t e e l . 105 1.3-. 1.2-1.1-1.0-a £ .9-.8. • • .7-O RUN 2 B RUN 3 .02 .04 .06 .08 .10 e (sec?1) .12 F i g u r e 21 I n t e r f a c e R e s i s t a n c e as a F u n c t i o n of T a n g e n t i a l Load Rate, ©, f o r S t e e l on S t e e l . 106 140. 120. 1 0 0 . 80. 0 Z < X « 60. o • 6 40. 20_ 0. • .02 .04 © CONTACT AREA T STATIC FRICTION FORCE T>6~ .08 .10 e (sec . ) .12 F i g u r e 22 Change i n S t a t i c F r i c t i o n F o r c e and C o n t a c t Area as a F u n c t i o n of T a n g e n t i a l Load R a t e , e > f o r S t e e l on S t e e l . disk&pin interface - R + R t o t a l disk + pin interface F i g u r e 23 ( C i r c u i t Diagram o f B r i d g e . 108 4.0-, F i g u r e 23(b) R e s i s t a n c e of I n t e r f a c e v s . D i f f e r e n t i a l V o l t a g e (The current applied to the bridge i s 3.° amps t o t a l . The \ section of the curve shown i s f o r d i f f e r e n t i a l voltages below 3.0 mV. ) 109 Figure 24 Displacement-Velocity and Differential Voltage -Velocity Curves for Quasi-harmonic Type Vibration. From these curves i t is found that the contact area is double-valued for a given velocity and that the contact area is a minimum at the maximum relative velocity. The disk velocity is about 2 in.-sec. j the maximum interface resistance is approximately ,ol ohm. J (1) Displacement-Velocity (2) Interface Resistance-Velocity 

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