Tribology: a systems approach to the science and technology of friction, lubrication, and wear (Tribology series)

TRIBOLOGY a systems approach to the science and technology of friction lubrication and wear TR IBO LOGY SERIES Vol. 1...

Author: Horst Czichos

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TRIBOLOGY a systems approach to the science and technology of friction lubrication and wear

TR IBO LOGY SERIES Vol. 1

Tribology - a systems approach to the science and technology of friction, lubrication and wear (Czichos)

TRIBOLOGY SERIESJ

TRIBOLOGY a systems approach to the science and technology of friction, lubrication and wear

HBRST CZICHOS Bundesanstalt fur Materiaiprufung (BAMl (Federal institute for Testing Materials) Berlin - Dahlern and Technixhe Fachhochschule Berlin

ELSEVIER SCIENTIFIC PUBLISHING COMPANY 1978 AMSTERDAM OXFORD - NEW YORK

-

ELSEVIER SCIENTIFIC PUBLISHING COMPANY 336 Jan van Galenstraat P.O. Box 211,Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

164 figures, 36 tables, 430 references

Lihrar, 01 Congrr*\ Cataloging in Publication Data

Czichos , Horst. Tribology. (Tribology s e r i e s ; v. 1) Bibliographv: p. Includes indexes. 1. Tribology. 2. SyEitem analysis. 11. S e r i e s . mJ1075.C94 621.8'9 77-28510 ISBN 0-444-41676-5

T.

Title.

ISBN 0-444-41676-6 (Vol. 1) ISBN 0-444-41677-3 (Series) Eleevier Scientific Publishing Company, 1978 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permieoion of the publisher, Eleevier Scientific Publiahing Company, P.O. Box 380,Amsterdam, The Netherlands 0

Printed in The Netherlands

V

Preface

T h i s volume g i v e s a s y s t e m a t i c u n i f i e d a p p r o a c h t o t r i b o l o g y : t h e fundamentals o f friction,

l u b r i c a t i o n and wear and t h e i r i n f l u e n c e s o n t h e s t r u c t u r e

and f u n c t i o n o f dynamic m e c h a n i c a l s y s t e m s . S i n c e f r i c t i o n i s r e s p o n s i b l e f u r a m a j o r l o s s o f u s e f u l m e c h a n i c a l e n e r g y , and wear i s a m a j o r r e a s o n f o r r e p l a c i n g e q u i p m e n t , a b e t t e r u n d e r s t a n d i n g and u t i l i z a t i o n o f t h e p r i n c i p l e s o f t r i b o l o g y i s p a r t i c u l a r l y important f o r t h e conservation o f energy and m a t e r i a l s i n e n g i n e e r i n g d e s i g n . The p l a n t o w r i t e t h i s book grew f r o m t h e p a r t i c i p a t i o n i n

co-opera-

t i v e work o f t h e " I n t e r n a t i o n a l Research Group ( I R G ) o n Wear o f E n g i n e e r i n g M a t e r i a l s " o p e r a t i n g u n d e r t h e a u s p i c e s o f t h e " O r g a n i z a t i o n f o r Economic C o - o p e r a t i o n and Development" (OECD) i n w h i c h I have been t a k i n g p a r t s i n c e t h e b e g i n n i n g o f t h e 1 9 7 0 ' s . T h e o r e t i c a l c o n s i d e r a t i o n s and p r a c t i c a l e x p e r i e n c e have shown t h a t t h e r e i s an u r g e n t need f o r a g e n e r a l , y e t p r a c t i c a l l y u s e f u l , framework i n o r d e r t o l i n k t h e many i n t e r d i s c i p l i n a r y a s p e c t s o f t r i b o l o g y , r a n g i n g froiii c o n t a c t mechanics, s u r f a c e p h y s i c s and h y d r o d y n a m i c s t o b e a r i n g t e c h n o l o g y and q u e s t i o n s o f m a i n t e n a n c e and r e l i a b i l i t y o f m e c h a n i c a l e q u i p m e n t . Moreover, i t became o b v i o u s i n r e c e n t y e a r s , t h a t spec i f i c a n a l y t i c a l methods o f i s o l a t i n g and s t u d y i n g s i n g l e e v e n t s a n d t r e a t i n g f r i c t i o n and wear i n a n a l o g y t o o t h e r ( b u l k ) m e c h a n i c a l m a t e r i a l p r o p e r t i e s a r e o n l y p a r t l y u s e f u l t o t h e s t u d y o f complex t r i b o l o g i c a l p r o b l e m s . I n d e e d , t h e o r i g i n a l d e f i n i t i o n o f t r i b o l o g y : " t h e s c i e n c e and t e c h n o l o g y o f i n t e r a c t i n g s u r f a c e s i n r e l a t i v e m o t i o n and t h e p r a c t i c e s r e l a t e d t h e r e t o " i s obv i o u s l y t h a t o f a dynamic m e c h a n i c a l system. Thus, f r i c t i o n , wear and t h e many r e l a t e d pheeomena a r e e s s e n t i a l l y due t o dynamic i n t e r a c t i o n s between t h e m o v i n g components o f s y s t e m s . ( A c o m p i l a t i o n o f m e c h a n i c a l systems i n

vi

which f r i c t i o n and wear processes o c c u r i s g i v e n i n t h e Appendix A.)

I t was

concluded t h a t t h e a p p l i c a t i o n o f systems t h i n k i n g and general systems t h e o r y a r e e s p e c i a l l y s u i t e d f o r d e v e l o p i n g a c o n v e n i e n t framework o f t r i b o l o gy, b r i n g i n g t o g e t h e r i t s many aspects c u r r e n t l y s c a t t e r e d t h r o u g h o u t t h e s c i e n t i f i c and t e c h n i c a l l i t e r a t u r e . I t f o l l o w s t h a t a t r i b o - m e c h a n i c a l system s h o u l d be analyzed and d e s c r i b e d i n terms o f i t s " s t r u c t u r e " (elements o f t h e system, p r o p e r t i e s o f elements, i n t e r r e l a t i o n s between elements) as w e l l as i n terms o f i t s " f u n c t i o n " ( i n p u t s , o u t p u t s , t r a n s f e r f u n c t i o n s ) . Whereas i n t h e a n a l y s i s o f e l e c t r i c a l systems t h e i n t e r e s t i s c o n c e n t r a t e d m a i n l y on t h e f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s , i n t r i b o l o g y t h e a n a l y s i s and d e s c r i p t i o n o f t h e (dynamic) s y s t e m ' s s t r u c t u r e i s t h e c r u c i a l p o i n t . The o r g a n i z a t i o n o f t h e book i s s t r a i g h t f o r w a r d and i s o u t l i n e d i n S e c t i o n 1.4. I t i s suggested t h a t t h e reader who i s i n t e r e s t e d m a i n l y i n t h e p r a c t i c a l a p p l i c a t i o n o f systems techniques t o t r i b o l o g i c a l problems may t u r n t o Chapter 8 on " P r a c t i c a l Systems Methodology", a f t e r r e a d i n g t h e i n t r o d u c t o r y Chapters 1 and 2, and may f o l l o w t h e n t h e sequence o f Chapters

3,4 and s o on. Because o f t h e immense scope o f t r i b o l o g y , t h i s volume conc e n t r a t e s m a i n l y on t h e b a s i c general p r i n c i p l e s o f t h e s u b j e c t m a t t e r i n o r d e r t o f i t t h e huge amount o f m a t e r i a l i n t o t h e l e n g t h a v a i l a b l e . Thus, t h e book i s a i m i n g t o p r o v i d e u n i f i e d i n t e r d i s c i p l i n a r y background knowledge f o r engineers, p h y s i c i s t s , chemists and m a t e r i a l s c i e n t i s t s w o r k i n g i n t h e v a r i o u s s p e c i a l i z e d f i e l d s o f t r i b o l o g y . When used as a t e x t b o o k , t h e t e x t i s s u i t e d t o t h e l e v e l o f s e n i o r undergraduate o r f i r s t - y e a r graduate courses i n e n g i n e e r i n g and t h e n a t u r a l sciences. Some p a r t o f t h e m a t e r i a l o f t h i s book has been p r e s e n t e d as l e c t u r e s a t t h e IRG-OECD Meetings h e l d a t ( a ) I m p e r i a l C o l l e g e , London, J u l y 1973, ( b ) BAM, Berlin-Dahlem, October 1974, ( c ) CNRS, P a r i s , A p r i l 1976. A t t h e s e Meetings h e l p f u l comments have been made by P r o f e s s o r R. C o u r t e l , CNRS, P a r i s , and P r o f e s s o r H. Chri stensen, SINTEF, Trondheim. F u r t h e r acknowledgements a r e due t o t h e f o r m e r Chairman o f IRG-OECD,

P r o f e s s o r R.L. Johnson,

Rensselaer P o l y t e c h n i c I n s t i t u t e , Troy, New York, f o r h i s c o n t i n u i n g i n t e r e s t i n t h e a p p l i c a t i o n o f systems techniques t o t r i b o l o g i c a l problems and t o t h e p r e s e n t Chairman o f IRG-OECD,

D r . G. Salomon, The Hague, f o r f r u i t f u l j o i n t

work i n t h i s f i e l d . I n p a r t i c u l a r , I l i k e t o express my s i n c e r e thanks t o P r o f e s s o r G.W.

Rowe, U n i v e r s i t y o f Birmingham, who reviewed t h e complete

d r a f t o f t h i s book making v a r i o u s v a l u a b l e suggestions. The c e n t r a l t h e o r e t i c a l p a r t o f t h i s book, namely Chapter 3, "General Theory o f T r i b o l o g y " has been worked o u t t o g e t h e r w i t h P r o f e s s o r J . Mfilgaard,

vii

Memorial U n i v e r s i t y o f Newfoundland, d u r i n g h i s s t a y a t BAM f r o m September 1975 t o June 1976 as F e l l o w o f t h e Alexander-von-Humboldt-Foundation o f t h e Federal R e p u b l i c o f Germany. I am v e r y g r a t e f u l t o P r o f e s s o r Mdlgaard f o r t h e e x c e l l e n t c o - o p e r a t i o n and h i s c o n t r i b u t i o n t o t h i s book. Thanks a r e due a l s o t o Ir. A.W.J.

de Gee and A. B e g e l i n g e r , M e t a a l i n s t i t u u t TNO, A p e l -

doorn, f o r t h e i r c o n t r i b u t i o n o f p r a c t i c a l a p p l i c a t i o n examples p r e s e n t e d i n S e c t i o n s 8.5.3,

8.5.5,

and 8.5.7.

I n o r d e r t o make t h e r e s u l t s o f t h i s

i n t e r n a t i o n a l j o i n t work e a s i l y a c c e s s i b l e t o t h e i n t e r n a t i o n a l community, t h e book has been w r i t t e n i n t h e E n g l i s h language. The e n t i r e m a n u s c r i p t has been g r a c i o u s l y r e a d by my c o l l e a g u e D r . K.-H. Habig who a l s o c o n t r i b u t e d some u s e f u l comments. I n a d d i t i o n , my c o l l e a g u e D r . H.-U. Mittmann reviewed Chapter 6 and D r . D.H.

Buckley and D r . L.D.

Wedeven, NASA Lewis Research Center, Cleveland, reviewed S e c t i o n s 4.4 and 4.5,

r e s p e c t i v e l y , making h e l p f u l remarks. The Appendix was checked by

P.M.

Ku, Southwest Research I n s t i t u t e , San Antonio, who a l s o c o n t r i b u t e d

some supplements. F u r t h e r I am i n d e b t e d t o many a u t h o r s and p u b l i s h e r s f o r k i n d l y s u p p l y i n g i l l u s t r a t i o n s and p e r m i s s i o n t o p u b l i s h them; acknowledgements a r e p r e s e n t e d i n t h e f i g u r e c a p t i o n s and i n t h e l i s t o f r e f e r e n c e s . L a s t l y , I acknowledge t h e v a l u a b l e a s s i s t a n c e o f my c o l l e a g u e s a t BAM, i n c l u d i n g t h e e x p e r i m e n t a l h e l p o f t h e e n g i n e e r s W. Evers, M. Gienau, W. Schrag and J . Schwenzien. I n s p i t e o f a l l t h e encouraging s u p p o r t , t h e book would n e v e r have been f i n i s h e d w i t h o u t t h e c o n t i n u o u s h e l p o f my w i f e Barbara who n o t o n l y t y p e d t h e p r e l i m i n a r y d r a f t s b u t a l s o produced t h e e x c e l l e n t camera-ready manus c r i p t . I n small token f o r t h e i r patience during the time o f the preparation o f t h e m a n u s c r i p t , t h e book i s d e d i c a t e d t o my f a m i l y , my w i f e Barbara and my son Carsten.

Berlin-Dahlem May 1977

H o r s t Czi chos

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ix

Contents

1.

INTRODUCTION AND BACKGROUND

1.1 1.2

2.

1

Dynamics o f p h y s i c a l systems and t h e o c c u r r e n c e o f f r i c t i o n and w e a r

1

H i s t o r i c a l development o f t r i b o l o g y

3

1.2.1

F r i c t i o n studies

3

1.2.2

Wear s t u d i e s

6

1.2.3

Lubrication studies

8

1.3

The meaning o f t r i b o l o g y

11

1.4

The scope o f t h i s volume

12

THE SYSTEM CONCEPT

14

2.1

Introduction

14

16

2.2

D e s c r i p t i o n o f a system

2.3

Energy b a l a n c e , n e t w o r k s , a n a l o g i e s

18

2.4

Bond g r a p h methods

20

2.5

C l a s s i f i c a t i o n o f systems

’

21

X

3.

GENERAL THEORY OF TRIBOLOGY

3.1

A p p l i c a t i o n o f systems concepts t o t r i b o l o g y

24

3.2

F u n c t i o n o f t r i b o - m e c h a n i c a l systems

27

3.3 ' S t r u c t u r e o f t r i b o - m e c h a n i c a l systems

30

3.4

Tribological interactions

33

3.4.1

Functional plane

33

3.4.2

Mechanical work p l a n e

36

3.4.3

Thermal p l a n e

38

3.4.4

Material planes

40

3.5

4.

24

Conclusions

43

TRIBOLOGICAL PROCESSES

45

4.1

Role o f t r i b o - p r o c e s s e s i n mechanical systems

45

4.2

Contact processes

47

4.2.1

C o n t a c t mechanics

47

4.2.2

C o n t a c t p h y s i c s and c h e m i s t r y

4.3

4.4

F r i c t i o n processes

4.3.1

T a n g e n t i a l f o r c e s i n c o n t a c t processes

69

4.3.2

Sliding friction

73

4.3.3

Rolling f r i c t i o n

81

4.3.4

Energy t r a n s m i s s i o n and d i s s i p a t i o n

a7

Wear processes

4.4.1

4.5

56 69

General d e s c r i p t i o n

97 97

4.4.2

S u r f a c e f a t i g u e wear mechanisms

105

4.4.3

A b r a s i v e wear mechanisms

112

4.4.4

Adhesive wear mechanisms

119

4.4.5

Tribo-chemical wear mechanisms

123

4.4.6

The c o m p l e x i t y o f wear processes

126

L u b r i c a t i o n modes

130

4.5.1

S t r i b e c k c u r v e and l u b r i c a t i o n modes

130

4.5.2

Hydrodynamic 1u b r i c a t i o n

132

4.5.3

E l as t ohyd rodyn ami c 1ub r ic a t ion

146

4.5.4

Mixed l u b r i c a t i o n

154

4.5.5

Boundary l u b r i c a t i o n

156

4.5.6

The l i m i t s o f l u b r i c a t i o n

166

Xi

5.

INFLUENCE OF TRIBOLOGICAL PROCESSES ON THE STRUCTURE OF MECHANICAL SYSTEMS

5.1 5.2

6.

176

General c o n s i d e r a t i o n s

176

Changes i n s y s t e n i ' s e l e m e n t s p r o p e r t i e s

178

5.2.1

S u r f a c e t o p o g r a p h y changes

179

5.2.2

S u r f a c e c o m p o s i t i o n changes

186

5.2.3

S u r f a c e s t r e n g t h p r o p e r t i e s changes

191 195

5.3

Material losses

5.4

S o l u t i o n s f o r no-wear c o n d i t i o n s

199

5.4.1

Fluid films

200

5.4.2

Magnetic f i e l d s

202

5.4.3

In t e r f ac ia 1 e l as t o m e r s

204

5.4.4

F l e x u r a l means

205

5.4.5

Wear r e s i s t a n t c o a t i n g s

207

INFLUENCE OF TRIBOLOGICAL PROCESSES ON THE FUNCTION OF MECHANICAL SYSTEMS

211

6.1

211

General c o n s i d e r a t i o n s

6.2 T r a n s m i s s i o n o f m o t i o n and s t i c k - s l i p e f f e c t s 6.2.1

Dynamics o f t r i b o - m e c h a n i c a l systems

215 215

6.2.2 S i m u l a t i o n o f s t i c k - s l i p b e h a v i o u r

218

6.3

Mechanical e f f i c i e n c y

221

6.4

Functional f a i l u r e s

227

6.4.1

Causes o f f a i l u r e

227

6.4.2

A case s t u d y : f a i l u r e modes o f g e a r s

230

6.5

Mechanical equipment r e l i a b i l i t y

234

6.6

Requirements f o r proper f u n c t i o n a l behaviour

240

6.6.1

Study o f a l t e r n a t i v e s o l u t i o n s

240

6.6.2

Proper design o f system s t r u c t u r e

242

6.6.3

P r o p e r c h o i c e of o p e r a t i n g v a r i a b l e s

244

6.6.4

M o n i t o r i n g t h e f u n c t i o n o f t h e system

246

xii

7.

TRIBOMETRY: TEST, SIMULATION AND CONTROL METHODS

248

7.1

Introduction

248

7.2

F r i c t i o n and wear t e s t methods

250

7.2.1

Tribometer t e s t system types

252

7.2.2

Control o f operating variables

254

7.2.3

T r ibometri c c h a r a c t e r i s t i c s

257

S i m u l a t i v e tri b o - t e s t i n g

264

7.4

T e s t i n g o f t r i b o - t e c h n i c a l components

272

7.5

Machinery c o n d i t i o n m o n i t o r i n g

277

7.6

Surface i n v e s t i g a t i o n techniques

286

7.3

300

. 8.1

Introduction

300

8.2

A t r i b o l o g i c a l systems d a t a s h e e t

301

8.2.1

Technical f u n c t i o n o f t h e system

303

8.2.2

Operating variables

304

8.2.3

S t r u c t u r e o f t h e system

305

8.2.4

T r ibological characteristics

308

8.3

The d e s c r i p t i o n o f t r i b o - e n g i n e e r i n g systems

310

8.4

The p r e s e n t a t i o n o f f r i c t i o n and wear r e s e a r c h d a t a

312

8.5

A p p l i c a t i o n o f systems m e t h o d o l o g y t o t h e s o l u t i o n o f t r i b o l o g i c a l p r o b l e m s : some case s t u d i e s 8.5.1

" C o u l o m b - f r i c t i o n " f o r p o l y m e r l s t e e l s1 i d i n g p a i r s 8.5.2

315

Investigation of the validity o f 316

Characterization o f the t r i b o l o g i c a l behaviour o f wear-resistant d i f f u s i o n surface coatings

321

8.5.3

M a t e r i a l s e l e c t i o n f o r off-sh'ore bearing a p p l i c a t i o n

326

8.5.4

Lubricant selection f o r instrument p i v o t bearing

332

8.5.5

R e d u c t i o n o f s e v e r e wear o f c a m - t a p p e t d e s i g n

335

8.5.6

Reduction o f f r i c t i o n - i n d u c e d n o i s e o f w h e e l / r a i l system

338

8.5.7

F a i l u r e i n v e s t i g a t i o n o f e l e c t r i c a l contacts

341

8.5.8

Compi 1 a t i o n o f c h a r a c t e r i s t i c s o f m e t a l w o r k i n g processes

345

xiii

APPENDIX

350

(A)

A c o m p i l a t i o n o f b a s i c t r i b o - e n g i n e e r i n g systems

350

(6)

E l e m e n t s o f t r i b o - e n g i n e e r i n g systems

354

(C)

B i b l i o g r a p h i c work:

356

DOCUMENTATION TRIBOLOGY

References

360

L i s t o f symbols

382

Author index

388

Subject index

393


To B a r b a r a and C a r s t e n


1

1 Introduction and background 1,l DYNAMICS AND THE

OF

PHYSICAL SYSTEMS

OCCURRENCE

OF

FRICTION

AND

WEAR

The t e c h n i c a l f u n c t i o n o f numerous e n g i n e e r i n g systems ments, v e h i c l e s , e t c . ,

-

-

machines, i n s t r u -

depends on processes o f motion. A c c o r d i n g t o i t s

b a s i c p h y s i c a l d e f i n i t i o n , t h e t e r m m o t i o n denotes t h e change o f t h e p o s i t i o n o f an o b j e c t w i t h t i m e . I n a l a r g e r sense, t h e s t u d y o f how t h i n g s change w i t h time, and o f t h e f o r c e s t h a t cause them t o do so i s t h e o b j e c t i ve o f dynamic i n v e s t i g a t i o n .

A g r e a t many processes i n n a t u r e and t e c h n o l o g y depend on t h e m o t i o n and t h e dynamic b e h a v i o u r o f s o l i d s , l i q u i d s and gases. F o r example, p r o cesses o f m o t i o n l i k e t h e f l o w o f b l o o d i n v e i n s o r t h e t r a n s m i s s i o n o f f o r c e s by moving machine components a r e e s s e n t i a l l y necessary f o r t h e f u n c t i o n i n g o f c o u n t l e s s b i o l o g i c a l systems and mechanical e n g i n e e r i n g systems. Moreover, some o b v i o u s l y non-mechanical d i s c i p l i n e s , l i k e e l e c t r o n i c s o r o p t i c s , a r e a l s o based on m o t i o n processes, i n these cases on t h e m o t i o n o f sub-microscopic p a r t i c l e s , i .e.,

e l e c t r o n s , i o n s o r l i g h t quanta. I t appears

t h a t processes o f m o t i o n l i n k t h e d i f f e r e n t d i s c i p l i n e s as an u n d e r l y i n g i m p o r t a n t p r i n c i p l e . Consequently, t h e a n a l y s i s of dynamic b e h a v i o u r has become a keystone t o niuch contemporary s c i e n c e and t e c h n o l o g y ( R e f . 1.1).

A f e a t u r e common t o a l l processes o f m o t i o n i s t h e o c c u r r e n c e o f e f f e c t s o f "resistance t o motion", i . e . ,

t h e occurrence o f f r i c t i o n o f some

k i n d o r a n o t h e r . The e f f e c t s o f f r i c t i o n a r e due t o p h y s i c a l i n t e r a c t i o n s between b o d i e s o r o b j e c t s moving r e l a t i v e l y t o each o t h e r . A s a consequence o f f r i c t i o n , t h e process o f m o t i o n and t h e dynamic b e h a v i o u r o f t h e whole

2

system are influenced o r disturbed and some p a r t o f the energy o f motion i s dissipated. Further, i f i n a dynamic system one mo.ving component consists o f a s o l i d body, the e f f e c t o f f r i c t i o n i s accompanied i n general by wear: "the progressive l o s s o f substance from the operating surface o f a body occurring as a r e s u l t o f r e l a t i v e motion a t the surface" (Ref. 1.2). I n Figure 1.1, the basic types o f motion o f s o l i d bodies together w i t h r e l e v a n t engineering systems and types o f resistance t o motion and mechanisms o f damage are ill u s t r a t e d schematically.

-

Surface motion Tech'nical systems

Resistance t o motion Mechanism of damage

a i r bearing a i r friction

f l u i d erosion

viscous f r i c t i o n

c a v i t a t i o n erosion

solid friction

wear

t u r b i n e enaine hydraulic drives

d r y bearing wheel and r a i l brakes FSgure 1.1

Types o f surface motion and r e l a t e d subjects.

Contemporary technology has developed t o a l e v e l where the problems o f movi n g surfaces r e q u i r e careful consideration and an i n t e g r a t i o n o f a l l the knowledge relevant t o the dynamics o f multicomponent systems. For example, i n an a i r c r a f t l i t e r a l l y thousands of p a r t s are subject t o f r i c t i o n and wear, f o r example brakes, bearings, seals, gears, actuators, pumps, f l i g h t c o n t r o l systems, instruments, s p l i n e s and even " s t a t i c " j o i n t s . Whereas, i n the past, i n the design o f dynamic mechanical systems the problems o f f r i c tion-induced energy losses and wear-induced m a t e r i a l s losses have been overlooked t o some extent, the f u t u r e w i l l be s e r i o u s l y concerned w i t h the conservation o f energy and m a t e r i a l s i n engineering design. I n order t o embrace a l l aspects o f moving surfaces and the transmission and d i s s i p a t i o n o f energy and materials i n mechanical systems, the word "Tribology" was coined by a B r i t i s h committee i n 1966 from t h e word " t r i b o s " , which means "rubbing" i n c l a s s i c Greek (Ref. 1.3). The phenomena o f t r i b o l o g y

-

i t s fundamental concepts, i t s basic physi-

c a l processes and i t s influences on the f u n c t i o n and s t r u c t u r e o f mechanical engineering systems are the subject o f t h i s book.

-

3

1 2 H ISTOR I C A L DEVELOPMENTOF TRI BOLOGY I

I'

I t i s q u i t e d i f f i c u l t t o do a c c u r a t e q u a n t i t a t i v e

e x p e r i m e n t s i n f r i c t i o n , and t h e laws o f f r i c t i o n are s t i l l n o t analyzed very w e l l ,

i n spite of the

e n o r m u s e n g i n e e r i n g v a l u e o f an a c c u r a t e a n a l y s i s " . R i c h a r d P . Feynrnan

-

Nobel l a u r e a t e

Feynrnan l e c t u r e s ,

1963

I t appears i n c o m p r e h e n s i b l e t h a t such o b v i o u s l y o l d problems l i k e f r i c t i o n and wear s t i l l remain unsolved problems i n many aspects. Moreover, i n many f i e l d s o f advanced technology, t h e s e problems seem t o be more i m p o r t a n t a t p r e s e n t t h a n i n f o r m e r t i m e s . Some o f t h e reasons f o r t h i s f a c t w i l l be v i s i b l e f r o m a c o n s i d e r a t i o n o f t h e h i s t o r i c a l development o f s t u d i e s i n these f i e l d s . W i t h o u t g o i n g i n t o a l l d e t a i l s , i t may t h e r e f o r e be v a l u a b l e t o g i v e a survey o f t h e development o f o u r knowledge on t h i s s u b j e c t m a t t e r . ( F o r f u r t h e r d e t a i l s see Refs. 1.4

-

1.8.) I n c h r o n o l o g i c a l o r d e r , t h e r e -

view d e a l s f i r s t w i t h f r i c t i o n and t h e n t u r n s t o t h e s u b j e c t s of wear and lubrication.

1,2,1 FRICTION STUDIES It i s l i k e l y t h a t even i n p r e h i s t o r y man was i n t e r e s t e d i n two aspects o f f r i c t i o n . The f i r s t p r a c t i c a l a p p l i c a t i o n seems t o have been t h e use o f f r i c t i o n a l h e a t i n t h e l i g h t i n g o f f i r e s . The second p r a c t i c a l a s p e c t was t o overcome f r i c t i o n i n t h e t r a n s p o r t a t i o n o f m a t e r i a l s . I t seems p r o b a b l e t h a t man has used sledges f o r t r a n s p o r t a t i o n f o r a l m o s t 9,000 y e a r s . F o r t h e enormous e n g i n e e r i n g t r a n s p o r t a t i o n problems connected w i t h t h e e r e c t i o n o f t h e pyramids, t h e E g y p t i a n s were a l r e a d y u s i n g l i q u i d l u b r i c a n t s i n o r d e r t o m i n i m i z e t h e work r e q u i r e d t o t r a n s p o r t heavy o b j e c t s . I t has been s a i d t h a t one o f t h e g r e a t e s t i n v e n t i o n man e v e r made was

t h a t o f t h e wheel. I n f a c t , by p r o p e r use o f t h i s i n v e n t i o n i t i s p o s s i b l e t o reduce t h e work needed t o overcome f r i c t i o n c o n s i d e r a b l y . From t h e r e s u l t s o f a r c h a e l o g i c a l s t u d i e s , i t m i g h t be concluded t h a t t h e m e r i t s o f r o l l i n g m o t i o n compared w i t h s l i d i n g had been r e c o g n i z e d some 5,000 y e a r s i n Mesopotamia.

4

The s c i e n t i f i c s t u d y o f t h e dynamics o f m o t i o n and o f f r i c t i o n phenomena i s , however, much more r e c e n t t h a n these e a r l y a p p l i c a t i o n s m i g h t suggest. I t s t a r t s , as i s known, w i t h t h e work done 360 y e a r s ago by G a l i l e o . G a l i l e o made a g r e a t advance i n t h e u n d e r s t a n d i n g o f m o t i o n when he d i s c o v e r e d t h e " p r i n c i p l e o f i n e r t i a " : i f a moving o b j e c t i s u n p e r t u r b e d i s n o t d i s t u r b e d by f r i c t i o n f o r c e s

-

-

if it

i t c o n t i n u e s t o move w i t h a c o n s t a n t

v e l o c i t y i n a s t r a i g h t l i n e . The n e x t s t e p i n t h e s c i e n t i f i c development o f dynamics was done by Newton i n f o r m u l a t i n g t h e c e l e b r a t e d b a s i c laws o f c l a s s i c a l mechanics. Supplementing t h e laws o f G a l i l e o and Newton on t h e mechanics o f i d e a l motion, Amontons i n 1699 and Coulomb i n 1785 f o r m u l a t e d some r u l e s o f s o l i d f r i c t i o n based on e x t e n s i v e experiments (Ref. 1.9,

1.10). F o r t h e purpose

o f h i s f r i c t i o n experiments, Coulomb developed a s p e c i a l measuring equipment named a " t r i b o m e t e r " (see F i g u r e 1 . 2 ) .

d i r e c t i o n o f motion solid body

_t

I

/ / I/ / / / / / / / /

support

/// //

"8"

coefficient o f friction f = FF/FN = t a n 8

F i g u r e 1.2

///A / / / /

/ / /

Fweight'

FF

/ / A

T r i b o m e t e r used by Coulomb f o r f r i c t i o n measurements.

The e x p e r i m e n t a l r e s u l t s o f Amontons and Coulomb showed t h a t t h e f r i c t i o n force

FF i s p r o p o r t i o n a l t o t h e normal l o a d FN. The r a t i o o f t h e f r i c t i o n

f o r c e t o t h e normal l o a d has been termed t h e " c o e f f i c i e n t o f f r i c t i o n "

f = FF/FN. The experiments i n d i c a t e d t h a t t h e v a l u e o f t h e c o e f f i c i e n t o f f r i c t i o n i s independent o f t h e g e o m e t r i c c o n t a c t area. I n e x p l a i n i n g t h e s e r e s u l t s , i t has been h y p o t h e s i z e d t h a t t h e s u r f a c e s were f u l l o f i r r e g u l a r i t i e s and t h a t t h e f r i c t i o n o r i g i n a t e d i n t h e i n t e r l o c k i n g o f a s p e r i t i e s o f t h e c o n t a c t i n g s u r f a c e s . T h i s t h e o r y became known as t h e "roughness hyp o t h e s i s o f f r i c t i o n " . Coulomb a l s o c o n s i d e r e d t h e p o s s i b i l i t y o f adhesion processes i n f r i c t i o n as suggested by D e s a g u l i e r i n 1724. D e s a g u l i e r

5

observed s t r o n g adhesion between l e a d spheres when t h e y a r e pressed t o g e t h e r and he c o n s i d e r e d t h a t s i m i l a r f o r c e s m i g h t be i n v o l v e d i n f r i c t i o n ( R e f . 1.11). Coulomb i n h i s i n t e r p r e t a t i o n o f t h e f r i c t i o n process, however, r e j e c t e d t h i s adhesion h y p o t h e s i s . P r e c e d i n g t h e work o f Amontons and Coulomb, Leonard0 da V i n c i had a l r e a d y found, by t h e m i d d l e o f t h e f i f t e e n t h c e n t u r y , t h a t t h e f r i c t i o n f o r c e was p r o p o r t i o n a l t o t h e l o a d ( R e f . 1 . 1 2 ) . From t h e r e s u l t s o f h i s experiments, he concluded t h a t t h e f r i c t i o n f o r c e was one q u a r t e r o f t h e l o a d and c o n s t a n t f o r a l l m a t e r i a l s ( i . e . ,

f = 0.25 = con-

stant). Although these f i n d i n g s seem t o answer some b a s i c q u e s t i o n s o f mechan i c a l e n g i n e e r i n g , f r o m a p h y s i c a l p o i n t o f view t h e o r i g i n o f f r i c t i o n cannot be e x p l a i n e d i n terms o f t h e c l a s s i c a l mechanics o f r i g i d b o d i e s . I f t h e s u r f a c e a s p e r i t i e s a r e assumed t o be r i g i d , an energy b a l a n c e shows

t h a t t h e process o f m e r e l y l i f t i n g one s l i d i n g s u r f a c e o v e r t h e bumps o f t h e c o u n t e r f a c e consumes no mechanical energy whereas i n r e a l i t y energy i s d i s s i p a t e d . I t f o l l o w s t h a t t h e f i n d i n g s o f Amontons and Coulomb can be r e g a r d e d o n l y as rough e m p i r i c a l r u l e s o f l i m i t e d v a l i d i t y . However, s i n c e t h e s e r u l e s were f o r m u l a t e d a t a v e r y e a r l y s t a g e o f t h e s c i e n c e o f mechanics, t h e s e f i n d i n g s have been taken as "laws" o f f r i c t i o n . Moreover, t h e f r i c t i o n beh a v i o u r of mechanical systems had been t r e a t e d i n terms o f c o n s t a n t c o e f f i c i e n t s o f f r i c t i o n which a r e assumed t o be " i n t r i n s i c m a t e r i a l p r o p e r t i e s " . As a consequence o f : (i)

t h e development o f i d e a l i z e d t h e o r i e s o f mechanics i n which t h e e f f e c t s o f f r i c t i o n are neglected e n t i r e l y ,

( i i ) t h e m i s i n t e r p r e t a t i o n o f t h e c o e f f i c i e n t o f f r i c t i o n as " i n t r i n s i c mat e r ia 1 cons t a n t " , no a c t u a l p r o g r e s s beyond t h e roughness h y p o t h e s i s was made i n t h e f i e l d o f f r i c t i o n t h r o u g h o u t t h e n i n e t e e n t h c e n t u r y and i n t o t h e t w e n t i e t h . As an a l t e r n a t i v e e x p l a n a t i o n o f t h e o r i g i n o f s o l i d f r i c t i o n , t h e "adhesion t h e o r y " o f f r i c t i o n was p u t f o r w a r d by Hardy (Ref. 1 . 1 3 ) and Toml i n s o n ( R e f . 1.14) i n t h e 1 9 2 0 ' s . I n t h i s t h e o r y i t i s assumed t h a t t h e f r i c t i o n f o r c e i s needed t o overcome m o l e c u l a r adhesion f o r c e s a c t i n g between t h e c o n t a c t i n g s u r f a c e s . Although t h i s t h e o r y appears r a t h e r obvious, i t r e q u i r e s a f r i c t i o n f o r c e p r o p o r t i o n a l t o t h e area o f c o n t a c t . T h i s , however,

i s i n disagreement w i t h t h e r e s u l t s o f numerous f r i c t i o n experiments i n d i c a t i n g t h a t t h e f r i c t i o n f o r c e i s independent o f t h e c o n t a c t area. A t t h i s s t a g e o f t h e h i s t o r i c a l development o f t h e a n a l y s i s o f f r i c t i o n ,

i t was r e c o g n i z e d t h a t t h e p h y s i c a l o r i g i n s o f f r i c t i o n a r e a v e r y c o m p l i c a t e d

6 m a t t e r which can n o t be e x p l a i n e d by a s i m p l e t h e o r y b u t need b o t h a c c u r a t e experiments and d e t a i l e d p h y s i c a l analyses. Since, d u r i n g t h e 1920's and 1930's, p h y s i c i s t s were m a i n l y i n t e r e s t e d i n t o p i c s l i k e a t o m i c p h y s i c s and quantum mechanics i t was n o t u n t i l about 1940 t h a t t h e d i s c r e p a n c i e s des c r i b e d above were c l a r i f i e d . A t t h i s time, Holm (Ref. 1.15), E r n s t and Merchant (Ref. 1.16) and Bowden and Tabor (Ref. 1.17) found a g r e a t d i f f e r ence between t h e apparent g e o m e t r i c a l area o f c o n t a c t and t h e " r e a l " a r e a o f c o n t a c t formed b y t h e t o u c h i n g a s p e r i t i e s o f t h e two s u r f a c e s . I n u s i n g t h i s o b s e r v a t i o n , t o g e t h e r w i t h t h e assumption t h a t adhesive m o l e c u l a r f o r c e s a c t i n t h e a s p e r i t y j u n c t i o n s , Bowden and Tabor (Ref.

1.18) c o u l d e x p l a i n t h e

e m p i r i c a l r u l e s o f Amontons and Coulomb. I t f o l l o w s t h a t f r i c t i o n has a " d u a l " n a t u r e i n t h a t b o t h d e f o r m a t i o n processes and adhesion processes a r e i n v o l v e d i n f r i c t i o n . T h i s dual molecular-mechanical concept has been genera l l y accepted as a " g e n e r a l i z e d " t h e o r y o f f r i c t i o n .

1,2,2 WEAR STUDIES Some o f t h e f i r s t s y s t e m a t i c s t u d i e s on t h e wear b e h a v i o u r o f m a t e r i a l s were performed by t h e g r e a t genius Leonardo da V i n c i . I n h i s m a n u s c r i p t , found i n 1967 i n Madrid (Codex Madrid

I)

(Ref. 1.12), Leonardo d e s c r i b e d h i s s t u d i e s

on t h e wear o f s i m p l e s l i d i n g b e a r i n g s . He found t h a t wear i n c r e a s e s w i t h l o a d and t h a t t h e d i r e c t i o n o f wear i s n o t n e c e s s a r i l y i n a v e r t i c a l d i r e c t i o n b u t f o l l o w s t h e main v e c t o r o f t h e load. I n o r d e r t o m i n i m i z e wear h e developed a s l i d i n g b e a r i n g , s u g g e s t i n g an a l l o y o f 30 p e r c e n t copper and 70 p e r c e n t t i n t o be used as b e a r i n g bush. A p a r t f r o m t h e work o f Leonardo, t h e b e g i n n i n g of t h e s t u d y o f wear on a s c i e n t i f i c b a s i s i s f a r more r e c e n t . An e a r l y p e r i o d o f s y s t e m a t i c wear studies workers

-

which has passed almost u n n o t i c e d by E n g l i s h - s p e a k i n g r e s e a r c h s t a r t e d i n Germany around 1930. Fuchsel e x p l a i n e d t h e d r y wear of

metals as a process o f d e f o r m a t i o n f o l l o w e d by a process o f s e p a r a t i o n (German: " A b b l a t t e r n " ) o f t h e deformed metal p a r t s (Ref. 1 . 1 9 ) . T h i s t h e o r y has been extended b y F i n k , and M a i l a n d e r and D i e s (Ref. 1.20, 1.21). They found t h a t t h e deformed metal p a r t s may o x i d i z e d u r i n g t h e wear process, and emphasized t h e i m p o r t a n t i n f l u e n c e o f t h e environmental atmosphere on t h e wear o f metals. The s t a t e o f t h e a r t o f t h e e a r l y p e r i o d o f s y s t e m a t i c wear r e s e a r c h had been reviewed by S i e b e l i n 1938 (Ref. 1.22).

Depending on t h e

n a t u r e o f e x t e r n a l c o n d i t i o n s o f wear a t t a c k , h e d i s t i n g u i s h e d between t h e f o l l o w i n g d i f f e r e n t types o f wear:

7 1.

Wear d u r i n g s l i d i n g f r i c t i o n o f d r y s u r f a c e s

2.

Wear d u r i n g s l i d i n g f r i c t i o n o f l u b r i c a t e d s u r f a c e s

3.

Wear d u r i n g r o l l i n g f r i c t i o n o f d r y s u r f a c e s

4.

Wear d u r i n g r o l l i n g f r i c t i o n o f l u b r i c a t e d s u r f a c e s

5.

Wear d u r i n g o s c i l l a t i n g c o n t a c t

6.

Wear by moving s o l i d p a r t i c l e s ( e r o s i o n )

7.

Wear by moving f l u i d s ( c a v i t a t i o n )

S i e b e l p o i n t e d o u t t h a t as a consequence o f t h e g r e a t v a r i e t y o f d i f f e r e n t types o f wear i t seems t o be i m p o s s i b l e t o d e t e r m i n e t h e wear b e h a v i o u r o f a m a t e r i a l by one s i n g l e t e s t and t o o b t a i n unique wear v a l u e s . I n a r a t h e r modern way o f t h i n k i n g , he suggested c l o s e j o i n t r e s e a r c h work t o be done by p h y s i c i s t s , chemists, metal l u r g i s t s , t h e o r i s t s o f e l a s t i c i t y and p l a s t i c i t y , d e s i g n e r s , and p l a n t e n g i n e e r s i n o r d e r t o o b t a i n r e a l p r o g r e s s i n t h e most complex f i e l d o f wear. The f i r s t p e r i o d o f wear r e s e a r c h ended i n t h e y e a r s o f World War 11. T h e r e a f t e r , i n t h e 1 9 5 0 ' s a c e r t a i n r e p e t i t i o n and e x t e n s i o n o f t h i s work c o u l d be noted, performed m a i n l y i n USA and England. F o r t h e case o f m e t a l / metal wear, Feng, B u r w e l l and S t r a n g were p r o b a b l y t h e f i r s t t o r e c o g n i z e t h e d i f f e r e n c e between m e t a l t r a n s f e r f r o m one s u r f a c e t o a n o t h e r and t h e process o f a t t r i t i o n o f m e t a l ( R e f . 1 . 2 3 ) . K e r r i d g e showed t h a t t h e t r a n s f e r o f m e t a l may be f o l l o w e d b y o x i d a t i o n o f t h e t r a n s f e r r e d m e t a l and t h a t t h e l a s t s t a g e o f such a process o f " m i l d " wear i s g i v e n by t h e a t t r i t i o n

of m e t a l o x i d e s (Ref. 1 . 2 4 ) . I n c o n t r a s t t o m i l d wear, i n processes o f "severe" wear t h e a t t r i t i o n t a k e s p l a c e d i r e c t l y a t t h e t r a n s f e r r e d m e t a l .

For c e r t a i n c o n d i t i o n s o f s l i d i n g d r y m e t a l s u r f a c e s i n a regime o f m i l d wear, A r c h a r d found t h e e m p i r i c a l r u l e t h a t t h e wear volume i s d i r e c t l y p r o p o r t i o n a l t o t h e l o a d and t h e s l i d i n g d i s t a n c e and i n v e r s e l y p r o p o r t i o n a l t o t h e hardness o f t h e s o f t e r o f t h e two i n t e r a c t i n g m e t a l s ( R e f .

1 . 2 5 ) . A t about t h e same t i m e a t which A r c h a r d p u b l i s h e d t h e e m p i r i c a l r u l e o f d r y wear, t h e main p h y s i c a l mechanisms o f wear were c l a s s i f i e d by B u r w e l l (Ref. 1 . 2 6 ) . A c c o r d i n g t o t h i s c l a s s i f i c a t i o n , a t l e a s t f o u r d i f f e r e n t main p h y s i c a l mechanisms must be d i s t i n g u i s h e d , namely:

1.

adhesive wear

2.

a b r a s i v e wear

3.

c o r r o s i v e wear

4.

s u r f a c e f a t i g u e wear.

Having b r i e f l y r e v i e w e d t h e h i s t o r i c a l development o f t h e s t u d i e s o f f r i c t i o n and wear up t o t h e end o f t h e 1950's, i n r e t r o s p e c t i t appears t h a t a t

8

t h a t time these subjects were p a i d i n c r e a s i n g l y more a t t e n t i o n by most o f the h i g h l y i n d u s t r i a l i z e d nations, mainly f o r economic reasons. Before cont i n u i n g the chronological review, as a f u r t h e r aspect the science and technology o f l u b r i c a t i o n

-

the most important means o f reducing f r i c t i o n and

wear-induced energy and material losses

12 3 I

I

- should be taken

i n t o consideration.

LUBRICATION STUD1 E S

The purpose o f l u b r i c a t i o n i s t o separate t w o surfaces moving r e l a t i v e t o each other by a f l u i d f i l m which can e a s i l y be sheared w i t h o u t causing any damage t o the surfaces.

As mentioned above, l u b r i c a n t s were already i n use

about 5,000 years ago by the Assyrians and Egyptians i n f a c i l i t a t i n g the movement o f sledges c a r r y i n g l a r g e statues o r b u i l d i n g s blocks o f stone. Apart from t h i s ancient use o f the l u b r i c a n t s and the l u b r i c a t i o n stud-

i e s o f Leonard0 da Vinci, i t was only w i t h the advent o f accurately made m e t a l l i c machine p a r t s during the so-called I n d u s t r i a l Revolution t h a t the s c i e n t i f i c and engineering aspects o f l u b r i c a t i o n were consequently studied. Before t h i s period, the s c i e n t i f i c i n t e r e s t was concentrated mainly on the development o f "pure" theories o f f l u i d mechanics.

In t h i s connection an

i n t e r e s t i n g remark o f the mathematician John v. Neumann should be quoted (Ref. 1.27). He pointed o u t t h a t during most o f the development o f hydromechanics u n t i l about 1900, the main i n t e r e s t was v i r t u a l l y the s o l v i n g o f b e a u t i f u l mathematical problems neglecting terms o f i n t e r n a l f l u i d f r i c t i o n . These approximations, however, had almost nothing t o do with r e a l f l u i d s . John v . Neumann characterized the t h e o r i s t making such analyses as a man who studied the flow o f "dry" water.

M o s t e a r l y work on the motion o f l u b r i c a t e d machine p a r t s was devoted t o j o u r n a l bearings. I n 1883 P e t r o f f proposed the f o l l o w i n g formula f o r the f r i c t i o n a l force

FF between two coaxial c y l i n d e r s FF =

where

x

(wetted area)

7 i s the v i s c o s i t y , v the surface v e l o c i t y o f the s h a f t and ha, the

mean e f f e c t i v e f i l m thickness. This was the f i r s t expression derived f o r t h e f u l l - f l u i d - t y p e o f l u b r i c a t i o n . (The work o f P e t r o f f i s discussed i n d e t a i l i n Ref. 1.7.)

9 The mathematical f o u n d a t i o n s o f a l l hydrodynamic l u b r i c a t i o n t h e o r y were l a i d i n 1886 by Reynolds i n d e r i v i n g t h e famous e q u a t i o n s named a f t e r him which a r e t h e b a s i s on which a l l subsequent l u b r i c a t i o n t h e o r y has been based ( R e f . 1 . 2 8 ) . Fundamental e x p e r i m e n t a l work i n t h i s f i e l d was performed around t h e t u r n o f t h e 2 0 t h c e n t u r y by S t r i b e c k a t a predecessor i n s t i t u t e o f t h e B u n d e s a n s t a l t f u r M a t e r i a l p r u f u n g (BAM), Berlin-Dahlem.

Stribeck

studied i n d e t a i l the influence o f the d i f f e r e n t operating variables, l i k e l o a d and v e l o c i t y , on t h e l u b r i c a t i o n and f r i c t i o n o f s l i d i n g and r o l l i n g b e a r i n g s ( R e f . 1 . 2 9 ) . The e x p e r i m e n t a l r e s u l t s o f S t r i b e c k were compared by Sommerfeld w i t h h i s own t h e o r e t i c a l f r i c t i o n r e s u l t s which he had d e r i v e d i n i n t e g r a t i n g Reynolds e q u a t i o n u s i n g an i n g e n i o u s s u b s t i t u t i o n ( R e f . 1.30). B i e l i n 1920 was t h e f i r s t t o p o i n t o u t t h a t t h e t y p e o f f r i c t i o n c u r v e meas u r e d by S t r i b e c k

-

the generalized S t r i b e c k curve

-

i s l i k e l y t o describe

t h e general b e h a v i o u r o f l u b r i c a t e d s u r f a c e s as a f u n c t i o n o f l u b r i c a n t v i s c o s i t y , s l i d i n g v e l o c i t y and l o a d ( R e f . 1 . 3 1 ) . Based on these fundamentals o f l u b r i c a t i o n t h e o r y , c r i t e r i a f o r t h e e n g i n e e r i n g d e s i g n o f hydrodynamical l u b r i c a t e d b e a r i n g s have t h e n been developed ( R e f . 1.32). One i m p o r t a n t q u e s t i o n , however, which i s l e f t open by t h e hydrodynamic l u b r i c a t i o n t h e o r y concerns t h e l i m i t s o f f u l l - f l u i d l u b r i c a t i o n . I f , f o r i n s t a n c e , t h e s p e c i f i c l o a d i s v e r y h i g h and t h e r e l a t i v e v e l o c i t y i s low,

i t i s d i f f i c u l t t o b u i l d up a s u f f i c i e n t l y t h i c k f i l m even w i t h v e r y v i s cous l u b r i c a n t s . I n t h i s l u b r i c a t i o n regime, some p a r t s o f t h e s l i d i n g s u r faces may be covered by l u b r i c a n t f i l m s o n l y one o r two m o l e c u l a r dimensions t h i c k . Hardy i n 1922 was t h e f i r s t t o s t u d y i n d e t a i l t h i s regime o f "bounda r y " l u b r i c a t i o n , where t h e l u b r i c a n t a c t i o n i s determined by t h e chemical c o n s t i t u t i o n o f t h e l u b r i c a n t r a t h e r t h a n by i t s v i s c o s i t y ( R e f . 1 . 3 3 ) . S i n c e t h e work o f Hardy, t h e non-hydrodynamic regimes o f l u b r i c a t i o n have been s t u d i e d i n t e n s e l y under d i f f e r e n t aspects. F u r t h e r , d i f f e r e n t chemically active lubricant additives

-

l i k e extreme p r e s s u r e a d d i t i v e s o r a n t i -

wear a d d i t i v e s - were developed. The development o f l u b r i c a n t s w i t h chemic a l l y a c t i v e a d d i t i v e s a l l o w e d t h e e n g i n e e r i n g a p p l i c a t i o n o f machine e l e ments under c o n d i t i o n s which had l e d t o c a t a s t r o p h i c f a i l u r e s i f l u b r i c a t e d w i t h pure mineral o i l s . (For instance, the technical a p p l i c a t i o n o f hypoid gears f o r r e a r - a x l e d r i v e , i n t r o d u c e d i n 1927 by t h e Packard M o t o r Car Company was p o s s i b l e o n l y by u s i n g l u b r i c a n t s w i t h chemical a d d i t i v e s . ) A f t e r World War 11, a general t r e n d i n mechanical e n g i n e e r i n g towards h i g h e r loads, h i g h e r v e l o c i t i e s and h i g h e r o p e r a t i n g temperatures was observed i n c o n n e c t i o n w i t h a t t e m p t s t o reduce t h e w e i g h t s o f t h e moving p a r t s i n machinery. S i n c e t h a t t i m e t h e r e has been a s t e a d y i n c r e a s e o f i n t e r e s t

10

i n t h e problems of f r i c t i o n , l u b r i c a t i o n and wear. Tokens o f t h i s i n c r e a s i n g i n t e r e s t were, among o t h e r t h i n g s , t h e appearance o f t h e f i r s t i n t e r n a t i o n a l j o u r n a l e n t i t l e d WEAR ( s i n c e 1957) e n t i r e l y devoted t o t h e s c i e n c e and t e c h n o l o g y o f f r i c t i o n , wear and l u b r i c a t i o n . A f u r t h e r new j o u r n a l , t h e TRANSACTIONS o f ASLE, has been p u b l i s h e d ( s i n c e 1958) by t h e American S o c i e t y o f L u b r i c a t i o n Engineers. I n t h e Federal R e p u b l i c o f Germany a r e s e a r c h programme ("Schwerpunkt-Programm") had been 1 aunched i n 1961 sponsored by t h e Deutsche Forschungsgemeinschaft ( R e f . 1.34). About t h e same t i m e i n England, a Working Group was s e t up t o i n v e s t i g a t e t h e p r e s e n t s t a t e o f l u b r i c a t i o n and r e s e a r c h and t o g i v e an o p i n i o n on t h e needs o f i n d u s t r y t h e r e o f . I n 1966 t h i s Working Group p u b l i s h e d a r e p o r t i n w h i c h f o r t h e f i r s t t i m e t h e t e r m " t r i b o l o g y " appeared ( R e f . 1 . 3 ) . The o r i g i n o f t r i b o l o g y was d e s c r i b e d i n t h e r e p o r t "The i n t r o d u c t i o n o f a new technology" (1973) as f o l l o w s (Ref. 1 . 3 5 ) .

I n t h e e a r l y 1960's t h e r e was a steep i n c r e a s e i n t h e r e p o r t e d f a i l u r e o f p l a n t and machinery due t o wear and a s s o c i a t e d causes. A t t h e same t i m e , i n c r e a s e d technology and i n c r e a s e d c a p i t a l i n t e n s i t y o f p l a n t , and t h e use o f more continuous processes, made breakdowns o f such p l a n t and machinery more c o s t l y , c o m p e t i t i v e l y more s e r i o u s , and t h e r e f o r e even l e s s d e s i r a b l e t h a n b e f o r e . T h i s t r e n d was r e c o g n i z e d by s p e c i a l i s t s i n v o l v e d i n t h e subj e c t s o f wear, f r i c t i o n and l u b r i c a t i o n . The s i t u a t i o n seemed t o c a l l f o r more and b e t t e r e d u c a t i o n i n t h e s u b j e c t s and f o r more and b e t t e r c o - o r d i n a t e d research. While t r y i n g t o e s t a b l i s h t h e reasons f o r t h e wide n e g l e c t o f t h e subj e c t i n t h e p a s t , d e s p i t e i t s t e c h n o l o g i c a l and economic importance, t h r e e p r i n c i p a l reasons f o r t h i s n e g l e c t may be mentioned: (i)

The i n t e r - d i s c i p l i n a r y n a t u r e o f t h e s u b j e c t which i n c l u d e d t h e d i s c i p l i n e s o f mechanical e n g i n e e r i n g , p h y s i c s , m e t a l l u r g y and c h emi s t r y .

(ii)

The f a c t t h a t o n l y w i t h t h e advances i n t e c h n o l o g i c a l development

i n p r o d u c t i o n methods o f r e c e n t y e a r s had a t t e n t i o n been focused on t h e importance and inter-dependence o f t h e c o n s t i t u e n t s o f t h i s i n t e r d i s c i p l i n a r y subject. ( i i i ) The term " l u b r i c a t i o n " , used i n i t s n a r r o w e r sense, had n o t o n l y p r e vented many p e o p l e f r o m f u l l y a p p r e c i a t i n g t h e economic s i g n i f i c a n c e o f t h e s u b j e c t m a t t e r , b u t i t was a l s o a hisnomer f o r t h e d e s c r i p t i o n o f t h e sphere o f " t r a n s f e r e n c e o f f o r c e f r o m one moving s u r f a c e t o a n o t h e r " (whether t h e purpose o f t h e t r a n s f e r o f such f o r c e s was

11 associated w i t h high f r i c t i o n ,

e.g.,

on b r a k e s , c l u t c h e s , conveyors

o r a l t e r n a t i v e l y w i t h low f r i c t i o n , e.g.,

bearings, s l i d e s , e t c . )

A f t e r c o n s u l t a t i o n w i t h t h e E d i t o r s of t h e Supplement o f t h e O x f o r d E n g l i s h D i c t i o n a r y , t h e t e r m " T r i b o l o g y " ( T r i b o s c i e n c e o r T r i b o t e c h n o l o g y ) was recommended f o r d e s c r i b i n g t h e s u b j e c t m a t t e r . T r i b o l o g y i s d e f i n e d as: "The s c i e n c e and t e c h n o l o g y o f i n t e r a c t i n g s u r f a c e s i n r e l a t i v e m o t i o n and o f r e l a t e d s u b j e c t s and p r a c t i c e s " .

1 , 3 THE M E A N I N G OF TRIBOLOGY S i n c e i t s d e f i n i t i o n i n 1966, t h e t e r m t r i b o l o g y has been w i d e l y r e c o g n i z e d as a new g e n e r a l concept embracing a l l aspects o f t h e t r a n s m i s s i o n and d i s s i p a t i o n o f energy and m a t e r i a l s i n mechanical equipment i n c l u d i n g t h e v a r i o u s t o p i c s o f f r i c t i o n , wear, l u b r i c a t i o n and r e l a t e d f i e l d s o f s c i e n c e and technology. I n o r d e r t o c h a r a c t e r i z e t h e s i g n i f i c a n c e o f t r i b o l o g y , among o t h e r t h i n g s , t h r e e p o i n t s have been emphasized (Ref. 1.36): (i)

The economic a s p e c t o f t r i b o l o g y :

I t has been e s t i m a t e d t h a t about 30% of t h e energy generated i n t h e i n d u s t r i a l p a r t s o f t h e w o r l d i s consumed u l t i m a t e l y i n f r i c t i o n p r o cesses and t h a t i n h i g h l y i n d u s t r i a l i z e d c o u n t r i e s , l i k e England, Japan o r t h e Federal R e p u b l i c o f Germany, some

$ 2,000 m i l l i o n p e r

annum a r e l o s t as a r e s u l t o f wear processes ( R e f . 1 . 3 7 ) . Even i f these f i g u r e s a r e t a k e n as rough e s t i m a t e s o n l y , ( R e f . 1 . 3 8 ) , t h e y c l e a r l y i n d i c a t e t h e importance o f t r i b o l o g y f o r t h e c o n s e r v a t i o n o f energy and m a t e r i a l s . (ii)

The s c i e n t i f i c aspect o f t r i b o l o g y : I t i s w e l l known t h a t a l l macroscopic processes i n n a t u r e a r e i r r e v e r s i b l e . Science i n i t s "pure" t h e o r i e s has l a r g e l y o m i t t e d t h i s i r r e v e r s i b i l i t y s i n c e t h e laws o f " i d e a l " processes were much e a s i e r t o develop. T r i b o l o g y s h o u l d a t t e m p t t o i n v e s t i g a t e t h e i r r e v e r s i b l e processes o f mechanics i n d e t a i l and t o e x p l a i n t h e complex e f f e c t s o f energy and m a t e r i a l s d i s s i p a t i o n .

( i i i ) The m u l t i d i s c i p l i n a r y a s p e c t o f t r i b o l o g y : S i n c e t r i b o l o g y i s d e f i n e d as "Science and t e c h n o l o g y o f i n t e r a c t i n g s u r f a c e s i n r e l a t i v e m o t i o n " , i t i n c l u d e s n o t o n l y t h e work o f p h y s i c i s t s , chemists and m a t e r i a l s s c i e n t i s t s i n t e r e s t e d i n t h e s u r f a c e

12 p r o p e r t i e s o f m a t e r i a l s b u t a l s o t h e work o f e n g i n e e r s who use " i n t e r a c t i n g s u r f a c e s " f o r t h e t r a n s m i s s i o n o f motion, f o r c e s , work, e t c . , i n v a r i o u s t y p e s o f machinery. T h e r e f o r e , t r i b o l o g y i s connected w i t h s e v e r a l branches of s c i e n c e and technology, l i k e p h y s i c s , c h e m i s t r y , m a t e r i a1 s science, mechanical e n g i n e e r i n g , 1u b r i c a t i o n e n g i n e e r i n g , etc. The v a r i e t y o f economic, s c i e n t i f i c and t e c h n o l o g i c a l aspects o f t r i b o l o g y i s a l s o e v i d e n t when c o n s i d e r i n g t h e l i t e r a t u r e . I n t h e e l e v e n y e a r s t h a t have passed s i n c e t h e c r e a t i o n o f t h e term t r i b o l o g y i n 1966, t h e huge numb e r o f some 55,000 papers have been p u b l i s h e d i n t h e f i e l d o f t r i b o l o g y . According t o t h e BAM T r i b o l o g y Documentation S e r v i c e , which a n n u a l l y publ i s h e s a c o m p i l a t i o n ( t i t l e c o l l e c t i o n ) o f t r i b o l o g y papers appearing t h r o u g h o u t t h e w o r l d , a t p r e s e n t about 8,000 papers a r e p u b l i s h e d e v e r y y e a r i n t h i s f i e l d (Ref. 1.39).

Due t o t h e m u l t i d i s c i p l i n a r y n a t u r e o f

t r i b o l o g y , t h e papers s c a t t e r b r o a d l y i n purpose and c o n t e n t . T h e r e f o r e , a1 though some p r o g r e s s i n t h e d i f f e r e n t s p e c i a l i z e d s u b t o p i c s o f t r i b o l o g y were obtained, s u i t a b l e t o o l s a r e needed i n o r d e r t o l i n k t h e s e r e s u l t s and t o p r e p a r e t h e way f o r c o o p e r a t i o n between people o f w i d e l y d i f f e r i n g d i s c i p l ines.

1,4 THE SCOPE OF

THIS

VOLUME

The i n t r o d u c t o r y remarks have focussed a t t e n t i o n on t h e problem t h a t t r i b o l o g y , l i k e any m u l t i d i s c i p l i n a r y branch of s c i e n c e and technology, poses s e r i o u s d i f f i c u l t i e s of communication. The v e r y d e f i n i t i o n o f t r i b o l o g y " i n t e r a c t i n g s u r f a c e s i n r e l a t i v e motion"

-

-

i n d i c a t e s a l r e a d y t h a t t h e be-

h a v i o u r o f t r i b o - t e c h n i c a l c o n s t r u c t i o n s cannot be p r e d i c t e d f r o m a mere knowledge o f s i n g l e components and t h e i r f e a t u r e s . Whenever t h e i n t e r p l a y and interdependence between components i s s t r o n g e r and more c o m p l i c a t e d than t h e a c t i o n o f t h e i n d i v i d u a l components, a "systems approach" i s needed. An u n d e r s t a n d i n g o f t h i s new o u t l o o k i s r a p i d l y growing i n many areas o f contemporary s c i e n c e and technology. I n r e t r o s p e c t , i t appears t h a t t h e o v e r l o o k i n g of t h e systems aspects o f f r i c t i o n , l u b r i c a t i o n and wear problems has been o b v i o u s l y one o f t h e m a j o r reasons f o r t h e many m i s i n t e r p r e t a t i o n s and t h e slowness o f p r o g r e s s i n these f i e l d s i n t h e past.

13 I n t h i s volume, we a t t e m p t t o p r e s e n t a s y s t e m a t i c u n i f i e d approach t o t r i b o l o g y based on systems t h i n k i n g . The book has been w r i t t e n b e a r i n g i n mind b o t h t h e s p e c i a l i s t who seeks t o i n c o r p o r a t e h i s knowledge and p r a c t i c a l e x p e r i e n c e i n a g e n e r a l framework, and t h e g e n e r a l s c i e n t i s t who seeks a s y s t e m a t i c o v e r a l l view o f t h e whole s u b j e c t . As a r e s u l t o f t h e u n i f y i n g a t t e m p t , t h e s p e c i a l i s t may f i n d t h a t h i s s p e c i a l t o p i c i s t r e a t e d i n a somewhat unusual manner. I t must be borne i n mind, however, t h a t i n a u n i f y i n g i n t e r d i s c i p l i n a r y t r e a t i s e a u n i f o r m nomenclature and d e s c r i p t i o n i s necessary which i s e q u a l l y u s e f u l f o r t h e v a r i o u s s p e c i a l i s t s i n t h e f i e l d , i.e.,

p h y s i c i s t s , chemists, m a t e r i a l s c i e n t i s t s , l u b r i c a t i o n e n g i n e e r s and

mechanical e n g i n e e r s . I n o r d e r t o ease t h e c l a s s i f i c a t i o n o f t h e v a r i o u s aspects o f t r i b o l o g y i n t o a g e n e r a l framework, some o f t h e g e n e r a l systems d e f i n i t i o n s are repeated i n almost every chapter. As a s t a r t i n g p o i n t , i n Chapter 2, t h e b a s i c aspects o f t h e system concept a r e compiled. I n a p p l y i n g t h e system concept, a general t h e o r y o f t r i b o l o g y i n t h e f o r m o f a conceptual framework i s o u t l i n e d i n Chapter 3. The t h e o r y shows t h a t a complete d e s c r i p t i o n o f a t r i b o - m e c h a n i c a l system r e q u i r e s t h e c h a r a c t e r i z a t i o n o f t h e " s t r u c t u r e " o f t h e system ( s y s t e m e l e ments, p r o p e r t i e s o f elements, i n t e r a c t i o n s o f elements) as w e l l as t h e c h a r a c t e r i z a t i o n o f t h e " f u n c t i o n " o f t h e system ( i n p u t s , o u t p u t s , t r a n s f e r f u n c t i o n s ) . The t h e o r e t i c a l framework o f t r i b o l o g y i s supplemented i n Chapt e r 4 by a d e t a i I e d t r e a t i s e o f t r i b o l o g i c a l processes, i . e . ,

contact, f r i c -

t i o n and wear processes and l u b r i c a t i o n modes. The system approach i s t h e n used i n s t u d y i n g i n Chapters 5 and 6 t h e i n f l u e n c e o f t r i b o l o g i c a l processes on t h e s t r u c t u r e and f u n c t i o n o f mechanical systems i n c o n n e c t i o n w i t h t r i b o - i n d u c e d changes of t h e p r o p e r t i e s o f t h e system elements and m a t e r i a l l o s s e s as w e l l as s t i c k - s l i p e f f e c t s , mechanical e f f i c i e n c y , f u n c t i o n a l f a i l u r e s and r e l i a b i l i t y . From these d i s c u s s i o n s , c o n c l u s i o n s f o r s o l u t i o n s o f no-wear c o n d i t i o n s and t h e r e q u i r e m e n t s f o r a p r o p e r f u n c t i o n a l b e h a v i o u r o f mechanical systems a r e drawn. I n Chapter 7, t h e v a r i o u s methods o f t r i b o metry, i . e .

t h e t e s t , s i m u l a t i o n and c o n t r o l methods a r e d e s c r i b e d , r a n g i n g

f r o m l a b o r a t o r y f r i c t i o n and wear t e s t s and s i m u l a t i v e t r i b o - t e s t i n g t o mac h i n e r y c o n d i t i o n m o n i t o r i n g . F i n a l l y , i n Chapter 8 a t r i b o l o g i c a l systems d a t a sheet s u i t e d f o r a comprehensive d a t a r e p r e s e n t a t i o n i s developed and t h e a p p l i c a t i o n o f "systems methodology" t o p r a c t i c a l f r i c t i o n and wear problems i s o u t l i n e d . The Appendix g i v e s a c o m p i l a t i o n o f b a s i c t r i b o - e n g i n e e r i n g systems and i t s components and r e f e r s t o b i b l i o g r a p h i c work i n t h e f i e l d o f t r i b o l o g y p r o v i d e d by t h e DOCUMENTATION TRIBOLOGY.

14

2 The system concept 2 1 I

INTRODUCTION

The problem o f d e a l i n g w i t h complex m u l t i d i s c i p l i n a r y s u b j e c t s l i k e t r i b o l o g y appears t o b e e s s e n t i a l l y one o f t h e 1 i m i t a t i o n s o f " a n a l y t i c a l procedures" i n s c i e n c e and technology. The t h e o r e t i c a l b i o p h y s i c i s t Ludwig von B e r t a l a n f f y , t h e founder o f "General Systems Theory",

has g i v e n t h e

f o l l o w i n g d e f i n i t i o n o f meaning o f a n a l y t i c a l procedure ( R e f . 2.1): An entity; i.e.,

t h e o b j e c t o f an i n v e s t i g a t i o n , s h o u l d be r e s o l v e d i n t o t h e

P a r t s from which i t i s combined; hence i t c o u l d be c o n s t i t u t e d o r recons t i t u t e d from t h e same P a r t s . These procedures s h o u l d b e understood b o t h i n t h e i r m a t e r i a l and conceptual sense. T h i s b a s i c p r i n c i p l e o f " c l a s s i c a l " s c i e n c e can be a p p l i e d a n a l y t i c a l l y i n a v a r i e t y o f d i r e c t i o n s , e.g.,

reso-

l u t i o n o f causal r e l a t i o n s i n t o s e p a r a t e P a r t s , s e a r c h i n g f o r " a t o m i c u n i t s " i n science o r f o r "material constants" i n engineering. A p p l i c a t i o n o f t h e a n a l y t i c a l procedure t o any o f these areas depends on two c o n d i t i o n s (Ref. 2.1): (i)

The i n t e r a c t i o n s between P a r t s must be n o n - e x i s t e n t o r , a t l e a s t , weak enough t o be n e g l e c t e d f o r c e r t a i n r e s e a r c h purposes. Only under t h e s e c o n d i t i o n s can t h e P a r t s be f i r s t s i n g l e d o u t a c t u a l l y , l o g i c a l l y , and m a t h e m a t i c a l l y , and then reassembled.

( i i ) The r e l a t i o n s d e s c r i b i n g t h e b e h a v i o u r o f P a r t s must be l i n e a r ; o n l y then i s the condition o f summativity given, i . e . ,

an e q u a t i o n d e s c r i b i n g

t h e b e h a v i o u r o f t h e Whole has t h e same f o r m as t h e e q u a t i o n s d e s c r i b i n g t h e b e h a v i o u r o f t h e P a r t s ; p a r t i a l processes can t h e n be superimposed t o o b t a i n t h e t o t a l process, and so on.

15 These c o n d i t i o n s a r e n o t met i n t h e e n t i t i e s c a l l e d systems, t h e y cons i s t o f " P a r t s i n i n t e r a c t i o n " . A system o f " o r g a n i z e d c o m p l e x i t y " may be c i r c u m s c r i b e d as one i n which s t r o n g i n t e r a c t i o n s , which a r e " n o n - t r i v i a l " , i.e.,

non-linear,

prevail.

To deal w i t h complex, n o n - l i n e a r systems, a d d i t i o n a l r e s t r a i n i n g p r i n c i p l e s have t o be i n t r o d u c e d . The economist Kenneth B o u l d i n g has suggested a h i e r a r c h y o f systems based on t h e f o l l o w i n g t h r e e r u l e s ( R e f . 2 . 2 ) : (i) (ii)

Systems b e l o n g t o c l a s s e s o f d i f f e r e n t l e v e l s o f c o m p l e x i t y . A l l l o g i c a l and e m p i r i c a l laws, v a l i d a t a low l e v e l (system) a r e a l s o a p p l i c a b l e t o any o f t h e h i g h e r l e v e l systems.

( i i i ) The h i g h e r t h e l e v e l , t h e l a r g e r t h e number o f unknown elements and u n d i s c o v e r e d laws t h a t make a p a r t i c u l a r system work. To i l l u s t r a t e t h e system concept and t h e p r i n c i p l e o f t h e h i e r a r c h i c a l o r d e r

o f systems c o n s i d e r , f o r example, a t r a f f i c system shown s c h e m a t i c a l l y i n F i g u r e 2.1.

rank

b t 4

rank

b + 3

rank

b t 2

rank

b + l

rank

b

Figure 2.1

Example o f a h i e r a r c h y o f systems.

Depending on t h e l o c a t i o n o f a s o - c a l l e d "systems envelope", s e p a r a t i n g h y p o t h e t i c a l l y t h e s u b j e c t s under c o n s i d e r a t i o n f r o m t h e i r "environment", d i f f e r e n t l e v e l s o f c o m p l e x i t y o r d i f f e r e n t " r a n k s " o f t h e system under c o n s i d e r a t i o n can be d i s t i n g u i s h e d ( R e f . 2 . 3 ) . The systems o f t h e l o w e s t rank a r e i n general g i v e n by t h e elementary s i n g l e t e c h n i c a l components. ( I f these elementary p a r t s o f t e c h n i c a l systems a r e r e s o l v e d f u r t h e r , t h e

16 m i c r o - p h y s i c a l and chemical c o n s t i t u e n t s o f t h e t e c h n i c a l systems components a r e o b t a i n e d . ) T e c h n i c a l systems o f t h e n e x t r a n k up a r e o b t a i n e d i n p u t t i n g t o g e t h e r systems o f a l o w e r rank by c e r t a i n t e c h n i c a l means o r t h r o u g h i n t e r a c t i o n s o f l o w e r r a n k i n g systems. I n t h e example shown i n F i g u r e 2.1,

t h e elements o f t h e l o w e s t rank,

denoted by t h e symbol " b " , are, f o r i n s t a n c e , t e c h n i c a l components l i k e gears, s h a f t s , e t c . Through t h e dynamic i n t e r a c t i o n s o f t h e s e c o i p o n e n t s , a gear t r a i n system o f rank b t 1 i s formed. T h i s system t o g e t h e r w i t h o t h e r systems o f t h e r a n k b t 1 ( i . e . ,

t h e engine system, t h e c l u t c h system and

t h e power t r a n s m i s s i o n system) f o r m a system o f r a n k b t 2, t h e d r i v e system. A t t h e n e x t rank up, b t 3, c h a r a c t e r i z i n g t h e whole v e h i c l e , t h e topmost

l e v e l o f t h i s t e c h n i c a l system i s reached. A t t h e f o l l o w i n g l e v e l b

t

4

man-machine i n t e r a c t i o n s must be taken i n t o c o n s i d e r a t i o n . I n f a c t , t h e whole t r a f f i c system o f rank b t 4 r e s u l t s t h r o u g h dynamic i n t e r a c t i o n s o f v e h i c l e t d r i v e r t r o a d t atmospheric c o n d i t i o n s .

2,2

DESCRIPTIONOF

A

SYSTEM

A f t e r t h e general s u r v e y o f t h e systems concept, a b r i e f s i m p l i f i e d compil a t i o n o f r e l e v a n t systems d e f i n i t i o n s and c h a r a c t e r i s t i c s s u i t e d f o r t h e purpose o f t h i s book i s g i v e n i n t h i s s e c t i o n . ( F o r f u r t h e r d e t a i l s see Refs. 2.4 t o 2 . 7 . ) The general d e f i n i t i o n o f a system i s c o n t a i n e d i n t h e sentence: " A system i s a s e t o f elements i n t e r c o n n e c t e d b y s t r u c t u r e and f u n c t i o n " . A system i s termed open when i n t e r c h a n g e s o f mass and energy w i t h t h e " o u t e r w o r l d " o c c u r , w h i l e such i n t e r c h a n g e s a r e assumed t o be n e g l i g i b l e i n a " c l o s e d " system. I n t h e f i r s t case, f o r example, t h e t r a n s f o r m a t i o n o f k i n e t i c energy i n t o h e a t o r o t h e r forms o f energy t h r o u g h i r r e v e r s i b l e p r o cesses l e a d s t o " d i s s i p a t i v e systems". The main c h a r a c t e r i s t i c s o f a system a r e summarized i n F i g u r e 2.2, symbols used have t h e f o l l o w i n g meaning.

( I ) Structure The s t r u c t u r e o f a system i s d e f i n e d by ( a ) t h e s e t o f i t s elements ( A ) , ( b ) t h e r e l e v a n t p r o p e r t i e s o f t h e elements ( P ) , ( c ) t h e c o u p l i n g o f elements, s p e c i f i e d as r e l a t i o n s between t h e elements ( R )

.

the

17

With these definitions the structure of a system i s represented by the s e t : S

=

{A,P,R}

(11) Inputs , Outputs Each system can be separated schematically by a hypothetical system envelope (or control surface) from i t s "environment". The connections between the system and i t s environment, which are cut by the envelope may be classified as: ( a ) Inputs {X} and ( b ) Outputs (Y)

(111) Function

The function o f a system - utilized f o r a certain (technical) purpose - i s t o transform the inputs ( X ) i n t o the outputs \ Y ) . The transformation ( T ) of the inputs into the outputs may be described e i t h e r i n terms of mathematical equations or as a physical a n a l o g , o r as a verbal description, e t c .

Definition:

A system i s a s e t of elements

interconnected by structure and function ( I ) Structure

S = ( A , P , R)

( a ) Elements A = ( a l Y a2,

...

, an}

(n: number of elements)

( b ) Properties

P

IP(ai)l

( c ) Relations

R = IR(ai, aj)l

(11) Inputs ( x )

Outputs(Y1 outputs

Inputs S =(A,

(XI

P, R ) systems envelope

(111) Function

T

(XI Figure 2.2

4 Y )

General description of a system.

18

F o r t h e c h a r a c t e r i z a t i o n o f t h e f u n c t i o n o f a system, m a i n l y t h r e e d i f f e r e n t methods may be d i s t i n g u i s h e d ( f o r f u r t h e r d e t a i l s , see Ref. 2.7): ( a ) Dynamic S t a t e , D i f f e r e n t i a l Equations I f t h e i n p u t s and o u t p u t s v a r y w i t h t i m e , t h e system i s s a i d t o be i n

a "dynamic s t a t e " . T h i s dynamic s t a t e may be r e p r e s e n t e d by a s e t of d i f f e r e n t i a l e q u a t i o n s , named " e q u a t i o n s o f m o t i o n " . ( b ) Steady S t a t e , L i n e a r i t y

In c e r t a i n cases a system may be i n dynamic e q u i l i b r i u m , i . e . , " s t e a d y s t a t e " . F u r t h e r , t h e o u t p u t s { Y ) can o f t e n be d e s c r i b e d as l i n e a r superpositions o f the inputs {

XI

t h r o u g h an a l g e b r a i c r e p r e s e n t a t i o n .

( c ) S t o c h a s t i c Processes, "Noise" I n r e a l systems t h e f u n c t i o n a l i n p u t - o u t p u t - r e l a t i o n s may be i n f l u e n c e d b y s t o c h a s t i c processes, i . e . ,

dynamic e f f e c t s o f u n c e r t a i n t y and r a n -

dom d i s t u r b a n c e s , " n o i s e " . I n such cases, an e s t i m a t e o f t h e l i m i t s o f p r o p e r f u n c t i o n b e h a v i o u r by means o f t h e t h e o r y o f p r o b a b i l i t i e s can be attempted. I n d e s c r i b i n g t h e b e h a v i o u r o f a system by t h e terms " s t r u c t u r e " and " f u n c t i o n " a fundamental d i f f e r e n c e s h o u l d be noted:

-

A " s t r u c t u r a l " d e s c r i p t i o n o f a system i s e s s e n t i a l l y an " i n t e r n a l " one, v i z . , an a t t e m p t t o u n d e r s t a n d t h e s y s t e m ' s b e h a v i o u r i n terms o f i t s

-

elements ( t h e P a r t s ) and t h e i r interdependence.

A " f u n c t i o n a l " d e s c r i p t i o n o f a system i s " e x t e r n a l " , c h a r a c t e r i z i n g t h e s y s t e m ' s b e h a v i o u r by i t s i n t e r a c t i o n s w i t h t h e environment t h r o u g h i t s input-output relations.

2 , 3 ENERGY BALANCE, NETWORKS, ANALOGIES I n c h a r a c t e r i z i n g t h e dynamical b e h a v i o u r o f systems, t h e concept o f a genera l i z e d energy b a l a n c e has t o be i n t r o d u c e d . T h i s means t h a t t h e s y s t e m ' s n e t power e q u a l s - z e r o i f we summarize a l l i m p o r t a n t processes o f s t o r a g e and t r a n s f o r m a t i o n o f energy:

AE

=

0

I n t h i s c o n n e c t i o n i t i s i m p o r t a n t t o c o n s i d e r a n a l o g i e s between p h y s i c a l systems (Ref. 2.8),

T a b l e 2.1.

The p h y s i c a l v a r i a b l e s of a system ( i n p u t s and o u t p u t s ) may be c l a s s i f i e d c o n v e n i e n t l y a s e i t h e r " t h r o u g h " o r " a c r o s s " v a r i a b l e s . Through v a r i -

19 ables measure t h e t r a n s m i s s i o n o f something t h r o u g h an element, e i t h e r an e l e c t r i c c u r r e n t t h r o u g h a r e s i s t o r o r a f o r c e t h r o u g h a dashpot. Across v a r i a b l e s measure a d i f f e r e n c e i n s t a t e between t h e ends o f an element, as t h e v o l t a g e drop across a r e s i s t o r o r t h e d i f f e r e n c e i n v e l o c i t y between t h e ends o f a dashpot. O f s p e c i a l importance i s t h e e l e c t r i c analogy o f mec h a n i c a l systems d e s c r i b e d by t h e two g e n e r a l i z e d K i r c h h o f f ' s laws:

I

K i r c h h o f f ' s node law. The sum o f a l l " t h r o u g h v a r i a b l e s " i n t o any node o f a system must be zero. ( I n t h e case o f mechanical systems t h i s i s r e p r e s e n t e d by f o r c e e q u i l i b r i u m r e l a t i o n s according t o D'Alembert).

I 1 K i r c h h o f f ' s mesh law. The sum o f a l l " a c r o s s v a r i a b l e s " around a complete l o o p o f t h e system i s equal t o zero. These e q u i l i b r i u m and c o m p a t i b i l i t y r e l a t i o n s a r e v a l i d f o r t h r o u g h and across v a r i a b l e s o f e l e c t r i c a l systems, mechanical systems, thermodynamic systems, and f l u i d systems. I n many a p p l i c a t i o n s one s t a r t s d i r e c t l y f r o m K i r c h h o f f ' s laws i n o r d e r t o o b t a i n t h e r u l e s d e s c r i b i n g t h e f u n c t i o n a l b e h a v i o u r o f t e c h n i c a l systems.

D i s c i p l ine

Electrotechnics

Mechanics

Across v a r i a b l e

Through v a r i a b l e

(effort)

(flow)

electric

electric

voltage

u

current

i

velocity

v

force

F

torque

M

(displacement) Mechanics

angular

(rotation)

velocity

Thermodynamics

absolute

entropy

temperature T

flow

F1 u i d i cs

pressure

J,(

P

vo 1ume flow

Table 2 . 1

s

A n a l o g i e s between v a r i a b l e s o f p h y s i c a l systems.

P

20

I t should be mentioned t h a t i n t h e bondgraph technique described below, i n s t e a d o f the f o r c e - f l o w , v e l o c i t y - e f f o r t analogy shown i n Table 2.1, reverse analogy, i . e .

,a

force-effort,

a

v e l o c i t y - f l o w analogy i s o f t e n used.

Although mathematically i t i s o f no consequence which analogy i s taken, t h e d i f f e r e n c e i n analogy i s i m p o r t a n t f o r t h e comparison o f s p e c i f i c r e s u l t s .

A comparison o f b o t h analogies can be found i n Ref. 2.9.

2,4

BOND GRAPH METHODS

The bond graph method, i n i t i a t e d by H. Paynter i s a f u r t h e r g e n e r a l i z a t i o n o f t h e m o d e l l i n g o f engineering systems (Ref. 2.10). The o r i g i n a l concept c e n t r a l t o t h e bond graph method i s t h a t o f a multi-energy p o r t represent a t i o n associated w i t h a " r e t i c u l a t i o n " , i . e . ,

t h e making o f a network o f

t h e system ( r e t i , L a t i n : f i s h n e t ) . Paynter considered t h a t p h y s i c a l o r e n g i n e e r i n g systems c o u l d be represented by a m u l t i - p o r t r e t i c u l a t i o n i n a g i v e n r e g i o n o f space, n o t u n l i k e t h a t used t o represent t h e bonding between atoms i n complex chemical molecules. The graphical symbolism o f t h e bond graph method i s economical and e f f i c i e n t . The bond graph elements can be represented i n i t i a l l y by words and t h e bonds f o r power exchange between them as simple l i n e s . For example, F i g u r e 2.3 c o n t a i n s a v a r i a b l e d r i v e , e.g.,

a

Diesel engine w i t h a pump t h a t s u p p l i e s f l u i d t o a consumer (Ref. 2.9). energy f l u x o r power i n a bond i s always t h e p r o d u c t o f two v a r i a b l e s

The

-

the

p o t e n t i a l v a r i a b l e c a l l e d e f f o r t and t h e f l o w o r c u r r e n t v a r i a b l e , s i m p l y r e f e r r e d t o as f l o w . Controller

-D r i v e V

F i g u r e 2.3

Pump W

Consumer V

Word bond graph f o r a pump d r i v e .

I n r e c e n t years, t h e bond graph methods have been developed f u r t h e r , t a k i n g i n t o account the e f f e c t s o f energy conversion and d i s s i p a t i o n and p r o v i d i n g methods f o r t h e s i m u l a t i o n and e l e c t r o n i c d a t a processing d i r e c t l y from a bond graph w i t h t h e ENPORT program (Ref. 2.11). The ENPORT computer program can p r o v i d e dynamic responses d i r e c t l y from a s u i t a b l e bond graph model and specified excitations, without r e q u i r i n g the e x p l i c i t p r i o r formulation o f s t a t e equations. Thus bond graph methods o f f e r a u n i f i e d way t o proceed f r o m t h e b a s i c p h y s i c a l m o d e l l i n g o f components, devices, and t h e i r connections t o

21 a n a l y t i c a l and c o m p u t a t i o n a l r e s u l t s f o r complex systems i n v o l v i n g a v a r i e t y o f types o f energy f l o w .

2,5

CLASSIFICATIONO F SYSTEMS

The a b s t r a c t f o r m a l i s m o f t h e d e s c r i p t i o n o f a system reviewed i n b r i e f i n t h e f o r e g o i n g s e c t i o n s s h o u l d be supplemented by a c l a s s i f i c a t i o n scheme i n d i c a t i n g t h e " t y p e " o f system under s t u d y . C l e a r l y , p h y s i c a l o r e n g i n e e r i n g systems a r e composed o f m a t e r i a l s components whose p r o p e r t i e s , i n t e r r e l a t i o n s , e t c . , may change w i t h t i m e . T h e r e f o r e , parameter t i m e i s an i n d e pendent a t t r i b u t e o f any o f these systems. Systems can be c l a s s i f i e d f r o m many d i f f e r e n t p o i n t s o f view. No c l a s s i f i c a t i o n i s complete and p e r f e c t f o r a l l purposes. The d i f f e r e n t methods o f c l a s s i f i c a t i o n a r e d i s c u s s e d i n d e t a i l i n Ref. 2.5. Wiener, t h e f o u n d e r o f " c y b e r n e t i c s " ,

According t o Norbert

t h e i n p u t s and o u t p u t s o f systems may

be b r o a d l y c l a s s i f i e d i n t o t h e t h r e e c a t e g o r i e s " m a t t e r " , " i n f o r m a t i o n " ( R e f . 2.12).

(See a l s o Ref. 2.13,

"energy", and

p. 99 f . ) W i t h o u t s p e c i -

f y i n g t h e i n t e r n a l s t r u c t u r e o f a system, t h e most g e n e r a l c h a r a c t e r i z a t i o n o f a system i s then g i v e n by a "black-box'' diagram as shown i n F i g u r e 2.4.

System's f u n c t i o n :

f

t

matter

in f o rma t i on

F i g u r e 2.4

(X)

-

(Y)

matter

* c

energy S = ( A , P, R }

information

General b l a c k - b o x diagram r e p r e s e n t a t i o n o f a system.

I n u s i n g t h e b r o a d c l a s s i f i c a t i o n o f t h e i n p u t s and o u t p u t s o f a system, from a f u n c t i o n a l p o i n t o f view t h e e n t i t y o f p h y s i c a l and e n g i n e e r i n g systems can be f o r m a l l y d e s c r i b e d b y a m a t r i x r e p r e s e n t a t i o n as shown i n Table 2.2.

I n t h i s scheme t h e t h r e e b a s i c c a t e g o r i e s o f i n p u t s and o u t p u t s

a r e s u b - d i v i d e d i n t o some o f t h e i r s u b - q u a n t i t i e s .

Every p o i n t o f i n t e r -

s e c t i o n o f i n p u t s and o u t p u t s r e p r e s e n t s a c e r t a i n c l a s s o f systems and, c o r r e s p o n d i n g l y , a c e r t a i n f i e l d o f s c i e n c e o r t e c h n o l o g y . The systems and

1

22

t o p i c s characterized by Table 2 . 2 range from the c l a s s a t the upper l e f t :

(corresponding f i e l d s of science and technology a r e transportation technology and manufacturing)

t o the c l a s s a t the lower r i g h t :

information ( d i g i t a l )

information ( d i g i t a l )

(corresponding f i e l d s of science and technology are the many branches o f computer science)

outputs Inputs

Table 2.2

Matrix c l a s s i f i c a t i o n scheme. o f systems.

23 I n r e f i n i n g t h e m a t r i x r e p r e s e n t a t i o n as i l l u s t r a t e d i n T a b l e 2.2 s t i l l f u r t h e r , i t i s a l s o p o s s i b l e t o o b t a i n s u b - c l a s s i f i c a t i o n schemes f o r t h e v a r i o u s groups o f systems. The system concept as reviewed i n t h i s Chapter i s used i n t h e n e x t Chapter as b a s i s f o r t h e development o f a u n i f i e d g e n e r a l t h e o r y o f t r i b o l o g y

i n t h e f o r m o f a c o n c e p t u a l framework. The r e a d e r who i s m a i n l y i n t e r e s t e d i n t h e p r a c t i c a l a p p l i c a t i o n o f systems t e c h n i q u e s may f i r s t r e a d Chapter 8 on " P r a c t i c a l Systems Methodology" and may t h e n t u r n back t o Chapter 3.

24

3 General theory of tribology 3,l APPLICATION

OF

SYSTEMS CONCEPTS

TO

TRIBOLOGY

The review o f the system concept given i n Chapter 2 shows t h a t a system should be analyzed i n terms o f i t s " s t r u c t u r e " (elements, p r o p e r t i e s o f elements, i n t e r r e l a t i o n s between elements) as w e l l as i n terms o f i t s "function" (inputs, outputs, t r a n s f e r f u n c t i o n s ) . In developing f u r t h e r the methods o f the a p p l i c a t i o n of the system concept t o t r i b o l o g y (see Refs. 3.1 t o 3.4) we w i l l attempt i n the f o l l o w i n g t o o u t l i n e a s i m p l i f i e d general theory o f t r i b o l o g y (Ref. 3.5). The systems approach t o t r i b o l o g y i s n o t intended t o replace more t r a d i t i o n a l analyses o f f r i c t i o n and wear processes. Much o f the information required f o r the p o r t r a y a l of t r i b o l o g i c a l phenomena from a systems standp o i n t can be obtained through conventional procedures o f analysis. For i n stance, important variables such as force, v e l o c i t y , temperature, chemical p o t e n t i a l and the r e l a t e d variables stress, s t r a i n , work, power, heat f l o w and r e a c t i o n rates can o n l y be determined by standard methods. I n the a p p l i c a t i o n o f systemanalytical methods t o a c e r t a i n complex subject, systems analysis o f t e n takes the form o f "model b u i l d i n g " , i.e.,

the representation

o f a system g r a p h i c a l l y o r a n a l y t i c a l l y i n a manner which may permit the model t o be used f o r a mathematical study o f the systems performance. This i s n o t i n t e n t e d here, nor generally possible a t the present l e v e l o f our understanding o f the t r i b o l o g y of mechanical systems. The purpose o f t h i s chapter i s the development o f a l o g i c a l systemanalytical framework, whereby c u r r e n t t r i b o l o g i c a l knowledge can be b e t t e r organized, t a k i n g i n t o account the various aspects and influencing factors. In t h i s general theory, a

26

d e t a i l e d mathematical a n a l y s i s i s n o t necessary f o r a d i s c u s s i o n o f t h e p e r t i n e n t b a s i c concepts. Thus, i n t h e f o l l o w i n g , systems t h i n k i n g i s app l i e d r a t h e r t h a n a f o r m a l systems a n a l y s i s . I n a t t e m p t i n g t o a p p l y t h e system concept t o t h e s u b j e c t o f t r i b o l o g y , a fundamental d i f f e r e n c e between t h e b e h a v i o u r and t h e d e s c r i p t i o n o f e l e c t r i c a l systems and mechanical systems i n which f r i c t i o n and wear processes o c c u r must f i r s t be emphasized. Consider, f o r example, an e l e c t r i c a l t r a n s f o r m e r and a mechanical gear box, i l l u s t r a t e d i n F i g u r e 3 . 1 as b l o c k diagrams. The t e c h n i c a l d e s i g n o f b o t h systems i s t o t r a n s f o r m c e r t a i n i n p u t s

-

v o l t a g e u and c u r r e n t i i n t h e

e l e c t r i c a l system and a n g u l a r v e l o c i t y w and t o r q u e tem r e s p e c t i v e l y

-

M i n t h e mechanical sys-

i n t o o u t p u t s used f o r t h e t e c h n i c a l purposes. The t e c h n i -

c a l f u n c t i o n o f b o t h systems can be d e s c r i b e d f o r m a l l y as a t r a n s f o r m a t i o n o f the inputs i n t o the outputs v i a a c e r t a i n t r a n s f e r f u n c t i o n (T). The dynamic performance o f b o t h systems i s accompanied by p e r t u r b a t i o n s on t h e i r f u n c t i o n and s t r u c t u r e . I n b o t h systems, energy l o s s e s due t o e l e c t r o - m a g n e t i c o r f r i c t i o n r e s i s t a n c e s , r e s p e c t i v e l y , o c c u r . The fundament a l d i f f e r e n c e between t h e b e h a v i o u r o f t h e e l e c t r i c a l and mechanical systems i s t h a t i n t h e e l e c t r i c a l case t h e s t r u c t u r e o f t h e system g e n e r a l l y remains c o n s t a n t w i t h t i m e . I n t h i s case, t h e t r a n s f e r f u n c t i o n ( T ) can be worked o u t m a t h e m a t i c a l l y . T h i s has l e d t o v a r i o u s a p p l i c a t i o n s o f t h e p o w e r f u l systems e n g i n e e r i n g methods o f network t h e o r y and r e l a t e d methods c h a r a c t e r i z i n g t h e f u n c t i o n a l b e h a v i o u r o f e l e c t r i c a l systems o r r e l a t e d models. I n t h e mechanic a l case, however, t h e s t r u c t u r e o f t h e system g e n e r a l l y changes w i t h t i m e t h r o u g h t h e a c t i o n o f t h e t r i b o l o g i c a l processes o f f r i c t i o n and wear. Theref o r e , f o r mechanical systems a systems d e s c r i p t i o n i n mere terms o f i n p u t o u t p u t r e l a t i o n s i s n o t s u f f i c i e n t : t h e f u n c t i o n a l d e s c r i p t i o n o f t h e system must be supplemented b y a d e t a i l e d s t u d y o f t h e s t r u c t u r e o f t h e system and t h e i n f l u e n c e s o f t r i b o - i n d u c e d s t r u c t u r a l changes on t h e f u n c t i o n a l behavi o u r o f t h e system. I n o r d e r t o d e v e l o p a c o n v e n i e n t framework f o r t h e d e s c r i p t i o n o f systems w i t h b o t h a dynamic f u n c t i o n a l b e h a v i o u r and a dynamic s t r u c t u r e s t a t e , some s i m p l i f i c a t i o n s must be i n t r o d u c e d : a f i r s t s i m p l i f i c a t i o n s h o u l d b e made b y a p p l y i n g t h e methods o f "black-box c u t t i n g " o r "systems t e a r i n g " . Black-box c u t t i n g has worked e x c e e d i n g l y w e l l i n p h y s i c s and c h e m i s t r y : a model i s c u t down t o s m a l l e r boxes u n t i l f i r s t p r i n c i p l e s can be a p p l i e d . Systems t e a r i n g can be a c h i e v e d b y l o c a t i n g t h e h y p o t h e t i c a l systems envel o p e i n a c o n v e n i e n t manner. I n t h e f o l l o w i n g t r e a t m e n t t h e systems envelope i s l o c a t e d , as narrow as p o s s i b l e , around t h e c e n t r a l p a r t s o f t h e mechanical

26

Inputs

System's s t r u c t u r e ~

voltage ux current i

*.

71Il c

outputs voltage u Y current i Y

w

Influences on f u n c t i o n and s t r u c t u r e

(111)

~~

F e r w losses due t o

I electro-magnetic

resistance

constant w i t h time

System's s t r u c t u r e

Inputs v e l o c i t y wx toque

I

Mx

outputs

- % - > velocity

torque

energy losses due t o

system's s t r u c t u r e changes

f r i c t i o n processes

due t o wear processes

Figure 3.1

w

Y

MY

Comparison o f t h e c h a r a c t e r i s t i c s o f an e l e c t r i c a l and a mechanical system.

27

system, forming the well-known " i n t e r a c t i n g surfaces i n r e l a t i v e motion". With these reservations i n mind, a d e t a i l e d systems d e s c r i p t i o n must i n v o l v e the f o l l o w i n g steps:

( I ) System's f u n c t i o n (i)

Separate the system from i t s environment by the choice of a system's envelope,

(ii)Compile a l l inputs and outputs ( i i i ) Describe the f u n c t i o n a l input-output r e l a t i o n s (11) System's s t r u c t u r e (i)

I d e n t i f y the "elements" o f t h e system,

(ii)

Characterize the i n t e r r e l a t i o n s and i n t e r a c t i o n s between the elements,

( i i i ) Specify t h e r e l e v a n t p r o p e r t i e s o f t h e elements. Based on t h i s systemanalytical procedure, i n t h e f o l l o w i n g sections we w i l l attempt t o study and compile the basic i n f l u e n c i n g f a c t o r s and mechanisms r e l e v a n t t o the f u n c t i o n and s t r u c t u r e o f mechanical systems i n which f r i c t i o n and wear processes occur. The t h e o r e t i c a l framework obtained w i l l then be used f o r various analyses and a p p l i c a t i o n s i n the f o l l o w i n g chapters o f t h i s book.

3 , 2 FUNCTION

OF

TRIBO-MECHANICAL SYSTEMS

I n t h e attempt t o apply the system concept t o the phenomena o f f r i c t i o n , l u b r i c a t i o n and wear, the question o f the f u n c t i o n a l , t e c h n i c a l purpose o f the system under consideration has f i r s t t o be answered. A tribo-mechanical system i s defined as an e n t i t y whose f u n c t i o n a l behaviour i s connected with i n t e r a c t i n g surfaces i n r e l a t i v e motion. (The words " t r i b o l o g i c a l system" o r "tribo-system" may be used synonymously t o the word "tribo-mechanical system".) The technical aims r e a l i z e d through moving surfaces may range from aerospace a p p l i c a t i o n s t o biomechanical j o i n t s . However, from a physical p o i n t

of view, f o u r b a s i c a l l y d i f f e r e n t groups o f techni-cal purposes can be d i s t i n guished as i l l u s t r a t e d by the examples shown i n Figure 3.2. The most general technical purpose o f a tribo-mechanical system i s the r e a l i z a t i o n o f motion through various types o f "bearings". The o t h e r basic groups are the transmission o f mechanical work, the transmission o f i n f o r -

-

-

mation f o r instance the c o n t r o l o f machine functions w i t h cams and the forming o f m a t e r i a l s . As a supplement t o the b a s i c c l a s s i f i c a t i o n o f t r i b o -

28

mechanical systems into four different groups, illustrated in Figure 3.2, a detailed function-oriented compilation of tribo-mechanical systems is given in the Appendix (A).

1

Guidance of mofion

I Jransmission

of work

I

ITransmission Figure 3.2

of information

i Forming of materials

Types o f tribo-mechanical systems.

In an abstract and highly simplified description, the function of the different tribo-mechanical systems consists, basically, In converting the inputs for instance, motion, mechanical energy and materials into outputs, which are used technically, The functional cause-and-effect relations between inputs and outputs are accompanied by loss-outputs o f mechanical energy and of materials, denoted sumnarily by the terns friction and wear

-

-

29

losses. From a point of view external t o the system, the system may be treated as a black-box with inputs and outputs, as shown schematically i n Figure 3.3.

l r n 1

-

A

(LOSS-OUTPUTS] Frictional losses (entropy,noise, vibration) Wear products

[USE-OUTPUTSI Motion Work {y) Information Materials

{XI Motion Work Information Mater ia Is

+ ~ I S T U R B A N Cs] E En tropy(Heat1 Vibration Materials (including dirt)

Figure 3.3

Black-box description of tribo-mechanical systems.

The technical function can often be expressed as a relationship between an input and a useful output. Not a l l the inputs may be considered desirable, some may be regarded as disturbances. Not a l l the outputs may be desired: such o u t p u t s may, from the practical point of view, be considered as losses. In general, part of a functional input may be l o s t , appearing as a loss output. However, the loss output need not be quite the same type of quantity as the input or useful outputs. In relating a system to i t s function, we are concerned with operational variables which can be controlled by a designer or an operator, i . e . , variables which we can a l t e r before o r during the operation of a system without altering the physical composition of the system in terms of the materials o r shapes of the elements. Table 3.1 l i s t s some operational parameters t h a t we may be concerned with, and which we may also refer to as operational variables in the environment. The actual variables used to describe the relation-

30 s h i p between a system and i t s environment w i l l depend t o some e x t e n t on t h e system under c o n s i d e r a t i o n , b u t w i l l g e n e r a l l y be r e l a t e d t o , o r d e r i v e d from,

the variables l i s t e d .

~~

~

I n p u t and Primary variables

Re1a t e d and d e r i ved v a r i a b l e s

Work

Fo rce/To r q ue

Work r a t e (Power)

(Motion)

Position/Dimension

Rotational velocity

output quantities

Linear velocity

Therma 1 (Heat t r a n s f e r )

Temperature

Heat t r a n s f e r r a t e

S p e c i f i c heat

Entropy t r a n s f e r r a t e

S p e c i f i c entropy Mass

Composition

Rate o f mass t r a n s f e r

(Mass t r a n s f e r )

Free energy

Rate o f free-energy t r a n s f e r

Information

Position

Fr e qu en cy

Force/Torque

Phase

Table 3 . 1

O p e r a t i o n a l i n p u t s and o u t p u t s o f mechanical systems.

3,3 STRUCTURE OF TR IBO-MECHAN

I CAL

SYSTEMS

According t o systems t h e o r y , t h e s t r u c t u r e o f a system i s c h a r a c t e r i z e d b y t h e elements o r components o f t h e system, t h e i r r e l e v a n t p r o p e r t i e s and t h e i r i n t e r r e l a t i o n s . The s i m p l e s t s t r u c t u r e o f a t r i b o - m e c h a n i c a l system i s g i v e n by two s o l i d s (1) and ( 2 ) exchanging mechanical i n p u t s and o u t p u t s through t h e i r c o n t a c t i n t e r f a c e . A c o m p i l a t i o n o f examples o f t h e elements o r components o f t r i b o - m e c h a n i c a l systems i s p r o v i d e d i n t h e Appendix ( 6 ) .

A few words may be a p p r o p r i a t e h e r e on t h e f l o w o f one o r more q u a n t i t i e s through a system, i m p l i e d b y t h e use o f t h e terms " i n p u t " and " o u t p u t " , e.g.,

work o r mass. A mass f l o w i s o b v i o u s l y a f l o w o f a m a t e r i a l q u a n t i t y .

However, t h e " f l o w " o f o t h e r q u a n t i t i e s , such as work, can perhaps be r e garded more c o r r e c t l y as an i n f l u e n c e o f one element upon another. The not i o n t h a t a q u a n t i t y " f l o w s " i s t h e r e f o r e m e r e l y a u s e f u l convention, which

31 i n c i d e n t a l l y helps us t o d i s t i n g u i s h between t h e d i f f e r e n t k i n d s o f process which can occur i n a system. The most s e n s i b l e manner, i n which t o handle t h e d i f f e r e n t types o f q u a n t i t y i s t o t r e a t each f o r m a l l y on a plane o f i t s own, l i n k e d t o t h e o t h e r q u a n t i t i e s by transformations between the planes. T h i s leads t o a conceptual three-dimensional i n t e r n a l view o f a tribo-mechanical system, shown i n F i g u r e 3.4. The p i c t u r e can be understood as a r e s o l u t i o n o f the systems s t r u c t u r e ( t h e c e n t r a l box o f F i g u r e 3.3) i n t o g r e a t e r d e t a i l , see a l s o F i g u r e 2.4.

I t i s l i k e l y t h a t a l l the parameters, i d e n t i f i e d i n a study

o f the f u n c t i o n o f the system, w i l l be represented on planes f o r the, funct i o n , work and thermal processes. Separate planes may be used f o r each o f the chemical species t a k i n g p a r t i n t r i b o l o g i c a l processes. This i n c l u d e s chemical r e a c t i o n products. F i g u r e 3.4 might be taken t o represent a very "simple" system o f j u s t two s o l i d mechanical elements o f the same m a t e r i a l i n contact, so t h a t the i n t e r f a c i a l space a t the r e g i o n o f c o n t a c t i s t h e t h i r d element, i.e., Element (1)

F i r s t machine element

Element ( 2 )

Second machine element

Element ( 3 )

The i n t e r f a c i a l volume

The p o s s i b l e t r a n s a c t i o n s and processes between three such elements are, i n f a c t , q u i t e complex even f o r t h i s elementary system (Ref. 3.6).

We do n o t

attempt here t o represent a l l the p o s s i b l e processes i n F i g u r e 3.4,

but

r a t h e r t o i l l u s t r a t e and c l a s s i f y the various types o f processes which may occur. Consider f i r s t the t r a n s f e r of the t e c h n i c a l l y used i n p u t s ( X I and outputs ( Y ) o f the system. On each conceptual plane, the t r a n s f e r o f such a q u a n t i t y from one element t o another may occur i n d i c a t e d by h o r i z o n t a l arrows. The term " t r a n s l a t i o n " i s chosen f o r these t r a n s f e r s . Consider now the processes o f t r a n s f e r s between d i f f e r e n t planes, r e f e r r e d t o as " t r a n s formations". The v e r t i c a l s o l i d arrows i n F i g u r e 3.4 represent a t r a n s f o r mation i n m a t e r i a l o r chemical species, occurring, f o r instance, as a r e s u l t o f wear processes w i t h i n the system. The v e r t i c a l d o t t e d arrows represent the t r a n s f o r m a t i o n o f work o r mechanical energy t o heat o r entropy, o c c u r r i n g as a r e s u l t o f f r i c t i o n processes w i t h i n t h e system. Both t r a n s l a t i o n s o f mass, e.g.,

the f l o w o f l u b r i c a n t through the system and t r a n s -

formations o f mass i n w e a r processes are l i k e l y t o i n v o l v e work, accompanied by the simultaneous t r a n s f o r m a t i o n of the work i n t o heat o r entropy which appears on the thermal plane.

32

FUNCTIONAL PLANE

WORK PLANE

THERMAL PLANE

I MATERIAL

PLANES

1

I APJ

I

I

MATERIAL 1 (solid)

MATERIAL n (fluid)

MATERIAL m (Reaction products) Figure 3.4

The Tribo-process diagram: Conceptual planes o f parameters and Processes i n a tribo-mechanical system.

33 The a b s t r a c t i o n s o f t h e t r i b o - p r o c e s s diagram, F i g u r e 3.4,

clearly

demonstrate t h e s i g n i f i c a n c e o f the systems approach t o t h e a n a l y s i s and d e s c r i p t i o n o f mechanical systems i n which f r i c t i o n and wear processes occur: The c h a r a c t e r i s t i c f e a t u r e o f t r i b o l o g y i s t h e i n t e r a c t i o n between t h e d i f f e r e n t planes o f F i g u r e 3.4,

w h i l e t h e conceptual a n a l y s i s o f s i n g l e se-

p a r a t e planes r e v e r t s t o more conventional a n a l y t i c a l s i m p l i f i c a t i o n .

A t t h i s p o i n t i t i s r e l e v a n t t o i n d i c a t e t h e aspect o f l u b r i c a t i o n i n r e l a t i o n t o t h e general framework of t r i b o l o g y . L u b r i c a t i o n represents a d e l i b e r a t e attempt t o a v o i d o r reduce t h e e f f e c t o f f r i c t i o n and wear upon a mechanical system. A l u b r i c a n t can a l s o a c t , as i t f l o w s away, as a c o o l i n g agent removing h e a t from t h e l o c a t i o n o f t h e f r i c t i o n process. I f t h e s l i d i n g o r r o l l i n g surfaces, i . e . ,

elements (1) and ( 2 ) i n F i g u r e 3.4,

a r e completely

separated by t h e a c t i o n o f the element ( 3 ) a t a l l times, t h e r e may be no wear process. I n t h i s event, t h e a n a l y s i s i s s i m p l i f i e d , s i n c e a m a t e r i a l s t r a n s f e r between t h e m a t e r i a l s planes shown i n F i g u r e 3.4 w i l l be o f no concern ("no-wear model"). However, i f i n a l u b r i c a t e d s t a t e t h e r e i s some c o n t a c t between t h e surfaces o f t h e elements (1) and ( 2 ) , o r between boundary l u b r i cants on t h e surfaces, t h e processes represented on and between t h e m a t e r i a l s planes a r e o f paramount concern. I n such cases, t h e presence o f a l u b r i c a n t may complicate t h e a n a l y s i s r e l a t i v e t o t h e u n l u b r i c a t e d system, p a r t l y because t h e r e a c t i o n products present may be complex and d i f f i c u l t t o charact e r i z e , and p a r t l y because t r a n s i e n t c o n d i t i o n s may be t h e major concern.

3 4 TRIBOLOG I CAL INTERACTIONS The s e p a r a t i o n and r e p r e s e n t a t i o n o f t h e processes w i t h i n a mechanical system, onto conceptual planes shown i n F i g u r e 3.4,

a l l o w s us t o c o n c e n t r a t e

on one aspect o f t h e system a t a time.

3 , 4 , 1 FUNCTIONALPLANE The emphasis on t h e f u n c t i o n a l plane, " e x t r a c t e d " from F i g u r e 3.4 and shown i n F i g u r e 3.5,

must be on a r e p r e s e n t a t i o n o f t h e t e c h n i c a l purpose o f t h e

system and t h e e v a l u t i o n and r e p r e s e n t a t i o n o f t h e parameters which have most imnediate relevance t o t h i s t e c h n i c a l purpose.

34

(11 First machine element ( 2 ) Second machine element

( 3 ) The interfacial volume F i g u r e 3.5

The f u n c t i o n a l q l a q e o f t h e T r i b o - p r o c e s s diagram: F u n c t i o n a l t r a n s a c t i o n s i n a t r i b o - m e c h a n i c a l system.

We may w i s h t o c l a s s i f y mechanical systems a c c o r d i n g t o t h e i r f u n c t i o n . I n v a r i a b l y , m o t i o n i s a c h a r a c t e r i s t i c of a t r i b o - m e c h a n i c a l system. T h i s m o t i o n may c o n s t i t u t e a t r a n s f e r o f work, m a t e r i a l s o r i n f o r m a t i o n . I n some i n s t a n c e s , t h e purpose o f a system may be t o change a r a t e o f m o t i o n o r t o e l i m i n a t e i t altogether. It i s also o f t e n desired t o r e s t r i c t motion, i.e., t o reduce t h e number o f degrees o f freedom a machine element may possess. I n o t h e r i n s t a n c e s , m a t e r i a l s a r e n o t m e r e l y moved, b u t a l s o changed i n s t a t e o r form. Mechanical d e v i c e s which produce o r t r a n s f e r i n f o r m a t i o n a r e s t i l l common, b u t a r e b e i n g s t e a d i l y r e p l a c e d by devices i n which t h e r e i s l i t t l e o r no mechanical m o t i o n ( v i z . t h e replacement o f t h e mechanical c l o c k by d i g i t a l e l e c t r o n i c c l o c k s . ) These main aspects o f t h e f u n c t i o n o f mechan i c a l systems a r e l i s t e d i n T a b l e 3.2. I n o r d e r t o r e p r e s e n t t h e f u n c t i o n o f t h e system i n terms of ( X ) - { Y ] i n p u t - o u t p u t r e l a t i o n s , e l e c t r i c a l network a n a l o g i e s have been a p p l i e d t o mechanical systems ( R e f . 3.7). As e x p l a i n e d i n Chapter 2, t h e s e approaches a r e based on a c l a s s i f i c a t i o n o f t h e o p e r a t i n g v a r i a b l e s i n t o " t h r o u g h and across" v a r i a b l e s o r . " f l o w and e f f o r t " v a r i a b l e s and t h e a p p l i c a t i o n o f t h e we1 1 known K i r c h h o f f ' s node and mesh laws. Recently, the. bondgraph methods have a l s o been a p p l i e d t o t r i b o l o g i c a l s u b j e c t s (Ref. 3.8). As i n d i c a t e d above, these appl i c a t i o n S o f t h e o r i e s o f e l e c t r i c a l a n a l o g i e s a r e r e s t r i c t e d , however, t o no-wear, steady s t a t e models. Therefore, f r o m a t r i b o l o g i c a l p o i n t o f view, a d d i t i o n a l aspects must be t a k e n i n t o account. P a r t i c u l a r c h a r a c t e r i s t i c s i n f r i c t i o n and wear a r e g e n e r a l l y be d e s i r able. These c h a r a c t e r i s t i c s may be dependent on t h e o p e r a t i n g parameters.

I n a d d i t i o n , and perhaps more important, t h e r e may be c e r t a i n l i m i t s t o be

i d e n t i f i e d f o r these c h a r a c t e r i s t i c s , o u t s i d e which l i m i t s the system w i l l n o t perform i t s f u n c t i o n s a t i s f a c t o r i l y . The i d e n t i f i c a t i o n o f p r o p e r t i e s which a r e c r i t i c a l t o the f u n c t i o n o f each element concerned w i l l serve as a guide f o r the analyses c a r r i e d o u t on work, thermal and mass planes, t o ensure t h a t such analyses are r e l e v a n t t o t h e f u n c t i o n o f t h e system. The r e l a t i o n s h i p between t h e values o f these p r o p e r t i e s and the f u n c t i o n o f t h e system and t h e manner i n which the o p e r a t i o n o f t h e system a f f e c t s these p r o p e r t i e s , i s , from a p r a c t i c a l p o i n t o f view, t h e c r u x o f a t r i b o l o g i c a l study. I n p u t s and outputs needed f o r t e c h n i c a l

L

I

Primary t e c h n i c a l

Examples

function o f the system

function

Main i n p u t s

Main outputs

(XI

IY) Motion

Motion Work

Guidance o f motion Coupling o f motion

Clutches

A n n i h i l a t i o n o f motion

Brakes

Power transmission

Gears

(mech.,

+ Information

Work

Bearings

hydr.,

pneum. )

Generation o f

Clocks; Cams

informa t ion

and f o l l o w e r s

Reproduction o f

ffata transducer

information

(audio, video; tape

Motion

Materi a1 s

Transportation

br

record)

Wheel/rai 1

P i pel ine Forming o f m a t e r i a l s Table 3.2

Wiredrawing

Technical f u n c t i o n s o f mechanical systems.

A l l t h i s can be seen on t h e f u n c t i o n a l plane i n a systems a n a l y s i s . We-may

then imagine ourselves l o o k i n g down i n t o the t r i b o l o g i c a l s t r u c t u r e d e p i c t e d

36

below the functional plane i n Figure 3.4, in order t o ascertain the physical and chemical relationship which determine the functional characteristics.

3,4,2 MECHANICAL WORK

PLANE

In Figure 3.6, we concentrate our attention on the prL?esses involving mechanical work i n the system. I t may be that one function of the system i s , i n f a c t , t o transmit and transform work, in which case this analysis will duplicate to a large extent the analysis on the functional plane. Although this does occur quite often, i t i s nevertheless a special case. A system or element may perform mechanical work upon another system or element. Such mechanical work may be measured as the product of a force times a distance ( o r the product o f related variables). Work may also be transferred between elements by the transfer of material i n which work i s stored. The transfer of work i n either manner is referred t o as a translation work. Work may also be transmitted from an element or a system as mechanical vibration, or work m a y be transformed through the tribological interactions i n other forms of energy and elther storedr emitted or passed t o other conceptual planes of the system.

[LOSS-OUT PUTS^

+

I I

1

Power to thermal lane (due to friction

Figure 3.6

P

The work plane of the Tribo-process diagram: Work transactions i n a tribo-machanical system.

37 From a generalized energy balance- consideration o f Figure 3.6,

i t follows

t h a t the i n p u t work must be equal t o the use-output work t t h e loss-output energy

+

the energy stored i n the system t the energy transformed t o o t h e r

conceptual planes o f t h e system. The r a t e o f performance o f mechanical work i s power. I n summarizing the various p o r t i o n s o f power, f o r a system as a whole, a power balance equation i s

where

i!

:

i!

: use-output power

EZ

: loss-output energy r a t e

i n p u t power

A Es : stored energy EwT : thermal energy transformed from mechanical work

Viewing o n l y one element, j:

where t h e s u b s c r i p t i r e f e r s t o a l l elements w i t h which the element j has work transactions and

kWMt o

the absorption o f mechanical power, as discussed

-

below i n t h e s e c t i o n on m a t e r i a l s planes. The transmission o f power k, ,!i i n a mechanical system i s u s u a l l y a r e l a t i v e l y simple a p p l i c a t i o n o f mechanics. The question which i s l e s s w e l l understood and which o f t e n c o n s t i t u t e s a basic problem i n mechanical systems i s the manner i n which mechanical power i s n o t transmitted, i.e., “absorbed” by f r i c t i o n o r v i b r a t i o n . Thus, the energy o r power balance cons i d e r a t i o n s should be supplemented by a discussion o f the t r i b o l o g i c a l processes involved i n the storage, transformation, emission and d i s s i p a t i o n o f mechanical work. Clearly, a1 1 these phenomena a r e c l o s e l y connected w i t h the contact, deformation and f r i c t i o n processes o c c u r r i n g a t t h e i n t e r f a c e be-

tween elements (1) and ( 2 ) o f a tribo-mechanical system. I n Table 3.3 some o f t h e b a s i c processes a r e l i s t e d . A d e t a i l e d d i s c u s s i o n o f t h e r e l e v a n t t r i b o l o g i c a l processes i s g i v e n i n Chapter 4. Work t r a n s a c t i o n s

Processes

Trans1 a t i o n o f work

E l a s t i c deformation

Transformation o f work

F r i c t i o n mechanisms:

(

I

e l a s t i c hysteresis

1

p l a s t i c deformation

Emission o f energy Conduction t o o t h e r

I Table 3.3

(

conceptual planes

1

Mechanisms and processes o f work t r a n s a c t i o n s .

F i g u r e 3.7 shows t h e p r i n c i p l e s o f an a n a l y s i s on a thermal p l a n e o f a tribo-mechanical system. We have a l r e a d y r e f e r r e d t o t h e t r a n s f o r m a t i o n of mechanical work t o entropy, i.e., mechanical power t o thermal power, which proceeds according t o t h e e q u a t i o n

where

i J. i s

t h e r a t e o f g e n e r a t i o n o f e n t r o p y i n element j and T . i s t h e

absol Ute temperature.

J

The thermal power g e n e r a t i o n w i l l u s u a l l y r e s u l t i n t h e temperature of locations o f entropy generation being appreciably higher than t h e i r surroundings, r e s u l t i n g i n t h e t r a n s f e r o f t h e thermal power, b y conduction o r r a d i a t i o n away f r o m t h e l o c a t i o n s o f f r i c t i o n . Heat and e n t r o p y can be t r a n s f e r r e d between systems elements. The t r a n s f e r o f thermal power down a temp e r a t u r e g r a d i e n t i s a unique work process i n t h a t t h e work i n v o l v e d appears as thermal power, i . e . ,

a f l o w o f t h e same t y p e o f q u a n t i t y as t h e one b e i n g

t r a n s f e r r e d . The n e t r e s u l t i s t h a t i n thermal conduction o r r a d i a t i o n , t h e

39 t o t a l t h e r m a l - p o w e r - f l o w r a t e remains c o n s t a n t , i. e . ,

where

iri s

t h e t o t a l f l o w r a t e o f e n t r o p y across a s u r f a c e a t a d i s t a n c e r

from a s o u r c e o f e n t r o p y and a t an a b s o l u t e t e m p e r a t u r e source o f e n t r o p y S . a t an a b s o l u t e temperature T J j' h e a t - f l ow-generati on r a t e .

I

T-

surrounding a

6. is'the J

associated

Thermal energy from work plane

[LOSS- OUTPUT^

I

I

I

Thermal energy produced by processes on the materials planes

F i g u r e 3.7

The t h e r m a l p l a n e o f t h e T r i b o - P r o c e s s diagram: Thermal t r a n s a c t i o n s i n a t r i b o - m e c h a n i c a l system.

Work may a l s o be performed when t h e p o t e n t i a l o f a system o r an element i s changed. T h i s concept can be a p p l i e d n o t o n l y t o mechanical work, b u t a l s o t o chemical work (change o f chemical p o t e n t i a l ) , e l e c t r i c a l work (change o f e l e c t r i c a l p o t e n t i a l ) and thermal work (change o f t e m p e r a t u r e ) . A1 1 t h e s e d i f f e r e n t forms o f work w i l l g e n e r a l l y l e a d t o t h e f o r m a t i o n o f e n t r o p y (Ref. 3 . 9 ) . Thermal power may be s t o r e d , i n w h i c h case t h e l o c a t i o n o f t h e s t o r a g e i n c r e a s e s i n temperature. V i c e versa, t h e t e m p e r a t u r e drops when s t o r e d thermal power i s g i v e n up. I n g e n e r a l , thermal processes a r e o f i n t e r e s t i n t r i b o l o g y i n so f a r as t h e temperature changes i n v o l v e d a f f e c t f r i c t i o n and wear processes.

40

That i s , we are concerned w i t h the r e l a t i o n s h i p between temperature and the mechanical f u n c t i o n o f the system. This amounts t o a concern f o r the e f f e c t o f temperature on p r o p e r t i e s which determine the processes o f v i b r a t i o n , f r i c t i o n and wear. These aspects are also discussed i n some d e t a i l i n Chapter 4.

3 4 4 MATERIAL PLANES I

I

A p r i n c i p l e purpose o f a representation on t h e material planes as shown i n Figure 3.8 i s t o f a c i l i t a t e i n s i g h t i n t o the mass t r a n s f e r and mass transformation processes which are i n v a r i a b l y p a r t o f the wear o f a mechanical system.

Reaction energy t o thermal plane

-

‘t

+LOSS OUTPUTS I Materials

I

Figure 3.8

Material planes o f the Tribo-process diagram: Material transactions i n a tribo-mechanical system,

41

I n some cases. t h e purpose o f t h e mechanical system may be t o t r a n s p o r t some m a t e r i a l , i n which case an e v a l u a t i o n o f aspects o f t h e t r a n s p o r t o f t h e m a t e r i a l w i l l be d u p l i c a t e d on t h e f u n c t i o n a l p l a n e and on a m a t e r i a l p l ane. The b a s i c c h a r a c t e r i s t i c o f wear i s t h e removal o f m a t e r i a l f r o m one o r more machine elements. I n some i n s t a n c e s , m e r e l y a permanent change i n shape, t h r o u g h d e f o r m a t i o n , o f a machine element i s c o n s i d e r e d t o c o n s t i s t u t e wear. I t may be p r e f e r a b l e t o c a l l t h e a c t u a l process o f t h e removal o f m a t e r i a l a process o f " a t t r i t i o n " , and t o a p p l y t h e t e r m "wear" t o c o v e r a l l t h e processes i n a system which combine t o cause a t t r i t i o n . I n wear, m a t e r i a l may be deformed w i t h i n an element. I t may a l s o be t r a n s f e r r e d f r o m one element t o a n o t h e r . T h i s process i s c a l l e d t r a n s l a t i o n , which i n c l u d e s n o t o n l y t r a n s f e r f r o m one s o l i d element t o a n o t h e r , b u t a l s o a t t r i t i o n , i n which case m a t e r i a l becomes, as d e b r i s , p a r t o f t h e i n t e r f a c i a l volume. Furthermore, a m a t e r i a l may, t h r o u g h chemical r e a c t i o n , be t r a n s f o r m e d t o a n o t h e r m a t e r i a l . U s i n g i a . as t h e symbol f o r t h e f l o w r a t e o f a mass s p e c i e s a f r o m 1J

element i t o element j , l e t t i n g i a b r e f e r t o a t r a n s f o r m a t i o n o f a mass J s p e c i e s a t o mass s p e c i e s b w i t h i n element j, and l e t t i n g m? be t h e mass

J

o f s p e c i e s a i n element j , t h e n a mass b a l a n c e e q u a t i o n f o r s p e c i e s a i n element j would be

where i r e f e r s t o a l l elements f r o m which t h e m a t e r i a l i s t r a n s l a t e d t o j ,

k t o a l l elements t o w h i c h t h e m a t e r i a l i s t r a n s l a t e d f r o m j , c a l l t h e chemical s p e c i e s which i n chemical r e a c t i o n become p a r t o f m a t e r i a l a, and b r e p r e s e n t s a l l t h e chemical s p e c i e s t o w h i c h t h e m a t e r i a l i s t r a n s f o r m e d . ( I n o r d e r t o a l s o d i s t i n g u i s h g r a p h i c a l l y between t h e d i f f e r e n t m a t e r i a l species, i t may be a p p r o p r i a t e i n c e r t a i n cases t o s p l i t up t h e m a t e r i a l planes shown i n F i g u r e 3.8 i n t o m a t e r i a l sub-planes.) I n a t t r i t i o n , we w i l l e x p e c t ma t o be n e g a t i v e f o r elements which l o s e J mass b y a t t r i t i o n . However, t h e e q u a t i o n i l l u s t r a t e s t h a t c e r t a i n elements .a may r e t a i n a more o r l e s s s t e a d y mass, i . e . , mj = 0, w h i l e s i g n i f i c a n t t r a n s l a t i o n and t r a n s f o r m a t i o n processes o c c u r on t h e element. T h i s i s o f t e n t h e case i n p r a c t i c e .

42

F o r a system as a whole, we may w r i t e

where X and Y,Z

r e f e r t o i n p u t s and o u t p u t s r e s p e c t i v e l y .

The processes on and between t h e m a t e r i a l planes a r e l i k e l y t o i n v o l v e e n t r o p y changes, g e n e r a l l y t h e p r o d u c t i o n o f e n t r o p y which w i l l appear as sources o f e n t r o p y i n t h e thermal p l a n e o f t h e same element. I t i s p o s s i b l e t h a t work may be performed i n c e r t a i n aspects o f m a s s - t r a n s l a t i o n processes, n o t a b l y t h e f o r m a t i o n o f new f r e e s u r f a c e s as i n f r a c t u r e o r o t h e r forms o f t h e s e p a r a t i o n o f m a t e r i a l . The o p p o s i t e process, t h e j o i n i n g o f two s u r faces, e l i m i n a t i n g some f r e e s u r f a c e , i s l i k e l y t o be accompanied by t h e f o r m a t i o n o f e n t r o p y . Thus, a r e p e a t e d sequence o f s e p a r a t i o n - j o i n i n g s e p a r a t i o n and so on w i l l , i n e f f e c t , c o n v e r t mechanical power i n t o thermal power and appear as a mechanisms o f f r i c t i o n . L i m i t i n g o u r concern t o t h e m a t e r i a l planes, we can l i s t some p e r t i n e n t processes i n T a b l e 3.4. The wear mechanisms a r e d i s c u s s e d i n d e t a i l i n S e c t i o n 4.4.

Wear mechanism

Processes W i t h i n element

Translation

Transformation

and p l a n e Surface f a t i g u e

Cycl ic

Fracture

-

de f o rma t ion Abrasion

Deformation

Fracture

-

Adhesion t

Deformation

Transfer

-

fracture T r i bochemical reactions

Table 3.4

Fracture Deforma t ion

Adsorption

Chemical

Fracture

reactions

Wear mechanisms and processes.

43

3 , 5 CONCLUSIONS The a n a l y s i s o f a t r i b o - m e c h a n i c a l system f r o m t h e systems v i e w p o i n t as i l l u s t r a t e d i n t h e t r i b o - p r o c e s s diagram, F i g u r e 3.4, c l e a r l y shows t h a t t h e c h a r a c t e r i s t i c f e a t u r e o f t r i b o l o g y i s t h e i n t e r a c t i o n between t h e d i f f e r e n t conceptual p l a n e s o f F i g u r e 3.4. Concluding t h e d i s c u s s i o n on t h e processes w i t h r e s p e c t t o t h e d i f f e r e n t p l a n e s o f t h e conceptual framework o f F i g u r e 3.4, some remarks on t h e c o r r e l a t i o n s o f p r o p e r t i e s s h o u l d be made. We have a l r e a d y n o t e d above t h a t each o f t h e p r o p e r t i e s o f concern on t h e work p l a n e i s l i k e l y t o be a f f e c t e d by t e m p e r a t u r e and a l s o p o s s i b l e by mechanical s t r e s s o r s t r a i n . The same a p p l i e s t o t h e p r o p e r t i e s o f concern

on t h e m a t e r i a l planes. As a general p r i n c i p l e , c e r t a i n p r o p e r t i e s o f t h e elements may be regarded as dependent p r o p e r t i e s on c e r t a i n p l a n e s and independent p r o p e r t i e s on o t h e r p l a n e s . F o r example, temperatures a r e c l e a r l y dependent on t h e processes r e p r e s e n t e d on t h e thermal p l a n e , b u t may be regarded as independent p r o p e r t i e s i n f l u e n c i n g processes on o t h e r planes. A complete a n a l y s i s must t h e r e f o r e i n c l u d e a c o r r e l a t i o n o f t h e p r o p e r t i e s on t h e d i f f e r e n t planes f o r each l o c a t i o n o f i n t e r e s t i n t h e system. Temperatures c o n s i s t e n t w i t h t h e process on t h e thermal p l a n e must e n t e r i n t o o u r c o n s i d e r a t i o n o f t h e processes on t h e o t h e r p l a n e s . L i k e w i s e , s t r e s s e s , s t r a i n s and v e l o c i t i e s c o n s i s t e n t w i t h t h e processes on t h e mec h a n i c a l work p l a n e must e n t e r i n t o o u r c o n s i d e r a t i o n s o f t h e processes on t h e thermal and m a t e r i a l s p l a n e s . This analysis n o t o n l y i l l u s t r a t e s the complexity o f the t r i b o l o g y o f mechanical systems, b u t a l s o t h e i n e v i t a b l e i n t e r d i s c i p l i n a r y n a t u r e o f e f f o r t s made t o deal w i t h such systems. Thus t h e work o f a mechanical d e s i g n e r o r t h e p r o d u c t i o n e n g i n e e r takes p l a c e , s o t o speak, on t h e " f u n c t i o n a l p l a n e " o f F i g u r e 3.4. The mechanical e n g i n e e r w i l l a l s o be concerned w i t h t h e analyses on t h e work and thermal p l a n e s . These analyses a r e a l s o i n t h e p r o v i n c e o f t h e p h y s i c i s t . P h y s i c i s t s , a l o n g w i t h m a t e r i a l s s c i e n t i s t s , w i l l be q u a l i f i e d t o i n v e s t i g a t e t h e processes on t h e m a t e r i a l planes, w h i l e chemists and chem i c a l e n g i n e e r s w i l l be c l o s e l y concerned w i t h t h e i n t e r p l a y between t h e m a t e r i a l planes, i.e.,

t h e chemical r e a c t i o n s c a u s i n g t h e t r a n s f o r m a t i o n

of material. The s p e c i a l i s t s , however, i n e v i t a b l e seeks t o i n c o r p o r a t e h i s knowl e d g e and p r a c t i c a l e x p e r i e n c e i n some k i n d o f conceptual framework. Given

44

t h e complexity o f t r i b o l o g i c a l processes, a t h e o r y o f t r i b o l o g y based on systems t h i n k i n g i s l i k e l y t o p r o v i d e the b e s t type o f framework a v a i l a b l e . The a n a l y s i s shows t h a t a s a t i s f a c t o r y d e s c r i p t i o n o f a tribo-mechanic a l system would be one which c l e a r l y r e l a t e s t h e elements o f a system, t h e I

processes between t h e elements and t h e i r r e l e v a n t p r o p e r t i e s , t o t h e operat i o n a l v a r i a b l e s and t h e i n p u t s and outputs, i n p a r t i c u l a r i n r e l a t i o n t o a p a r t i c u l a r f u n c t i o n f o r t h e system. The i n f o r m a t i o n compiled i n t h e various Figures and Tables o f t h i s chapter w i l l be used as a convenient g u i d e - l i n e f o r t h e discussions o f these aspects i n the f o l l o w i n g chapters.

45

4 Tr ibological processes 4 , l ROLE

OF

TRIBO-PROCESSESI N MECHANICAL SYSTEMS

The general theory o f t r i b o l o g y as o u t l i n e d i n Chapter 3 can be regarded as a general framework l i n k i n g t h e v a r i o u s processes and v a r i a b l e s connected w i t h f r i c t i o n and wear o f mechanical systems. I t has been shown t h a t i n an a b s t r a c t manner a tribo-mechanical device can be c h a r a c t e r i z e d as a system i n which c e r t a i n i n t e r f a c i a l processes o f " t r a n s l a t i o n " and " t r a n s f o r m a t i o n " o f f u n c t i o n a l q u a n t i t i e s , e.g.,

motion, work, m a t e r i a l s , occur. The i n t e r -

f a c i a l processes connected w i t h t h e i n t e r a c t i o n o f m a t e r i a l surfaces i n r e l a t i v e motion a r e termed " t r i b o l o g i c a l processes" o r , b r i e f l y , " t r i b o processes': I n t h i s connection t h e f o l l o w i n g questions a r i s e : ( a ) What a r e t h e mechanisms by which t h e u s e - q u a n t i t i e s o f a mechanical system a r e t r a n s m i t t e d through t h e system, i.e.,

what a r e t h e a c t u a l

p h y s i c a l processes by which, f o r instance, work i s t r a n s m i t t e d through t h e system as described on t h e conceptual f u n c t i o n a l plane (see F i g u r e

3.5)? ( b ) What a r e t h e t r i b o l o g i c a l processes which l e a d t o t h e g e n e r a t i o n o f loss-outputs,

i.e.,

what a r e t h e a c t u a l p h y s i c a l mechanisms o f power

d i s s i p a t i o n due t o f r i c t i o n (see F i g u r e 3.6) and t h e g e n e r a t i o n o f wear products (see F i g u r e 3.8)? ( c ) How can t h e d i s s i p a t i v e loss-mechanisms ( b ) be i n f l u e n c e d o r minimized? Since t h e general t h e o r y o f t r i b o l o g y as developed i n Chapter 3 i s a conceptual framework o n l y , t h e answers o r s o l u t i o n s t o these questions must be worked o u t by conventional methods o f a n a l y s i s . These d e t a i l s must then be i n t e g r a t e d i n t o t h e framework of t h e general theory.

46

Obviously, t h e answers t o t h e above q u e s t i o n s ( a ) , ( b ) , ( c ) depend on t h e t y p e o f system under c o n s i d e r a t i o n . I t has been shown above t h a t t h e d i f f e r e n t t r i b o - m e c h a n i c a l systems can be c l a s s i f i e d a c c o r d i n g t o t h e i r f u n c t i o n i n t o d i f f e r e n t groups (see T a b l e 3 . 2 ) . F o r any o f t h e s e d i f f e r e n t groups, d i f f e r e n t mechanisms o f t r a n s l a t i o n and t r a n s f o r m a t on o f t h e systems q u a n t i t i e s a r e r e l e v a n t , f o r i n s t a n c e : (I)

I f t h e t e c h n i c a l f u n c t i o n o f a mechanical system cons s t s i n t h e

t r a n s m i s s i o n o f m o t i o n o r mechanical power, as i n t h e t r a n s m i s s i o n o f a t o r q u e t h r o u g h a b e a r i n g s h a f t , t h e a c t u a l t r a n s i s s i o n process ( a ) i s g i v e n by a b u l k e l a s t i c d e f o r m a t i o n o f t h e s h a f t . No p r a c t i c a l devices e x i s t , however, which can t r a n s m i t power w i t h o u t c o r r e s p o n d i n g p a r a s i t i c "guidance"

-

o r "support-losses"

( b ) . These l o s s e s can be

m i n i m i z e d ( c ) t h r o u g h p r o p e r l u b r i c a t i o n , as i n a h y d r o s t a t i c o r hydrodynamic b e a r i n g , f o r example. (11)

I f t h e t e c h n i c a l f u n c t i o n o f a mechanical system c o n s i s t s i n t h e i n t e r f a c i a l t r a n s m i s s i o n o f mechanical power, as i n a gear t r a i n f o r i n s t a n c e , t h e t r a n s m i s s i o n o f mechanical work ( a ) i s o b t a i n e d t h r o u g h c o n t a c t d e f o r m a t i o n processes. The c o n t a c t d e f o r m a t i o n i n e v i t a b l y i n v o l v e s some f r i c t i o n processes ( b ) which can be i n f l u e n c e d ( c ) by l u b r i c a t i o n o f an elastohydrodynamic o r boundary l u b r i c a t i o n mode.

(111) I f t h e t e c h n i c a l f u n c t i o n o f a mechanical system c o n s i s t s o f f o r m i n g m a t e r i a l s , as i n w i r e d r a w i n g f o r i n s t a n c e , an e s s e n t i a l p a r t o f t h e m a t e r i a l s t r a n s m i s s i o n mechanism ( a ) c o n s i s t s o f p l a s t i c d e f o r m a t i o n processes. I n t h i s case, some energy-loss-processes

( b ) may r e s u l t

through d i s l o c a t i o n damping. A l s o these processes may be i n f l u e n c e d c o n s i d e r a b l y by p r o p e r l u b r i c a t i o n ( c ) . The i n s p e c t i o n o f t h e p o s s i b l e t r i b o l o g i c a l processes o f " t r a n s l a t i o n " and " t r a n s f o r m a t i o n " o f q u a n t i t i e s w i t h i n a mechanical system i n d i c a t e s t h a t t h e f o l l o w i n g main e f f e c t s s h o u l d be s t u d i e d : (i)

b u l k e l a s t i c d e f o r m a t i o n and i n t e r f a c i a l c o n t a c t d e f o r m a t i o n p r o cesses,

(ii)

t h e mechanisms o f energy and m a t e r i a l d i s s i p a t i o n t h r o u g h i n t e r f a c i a l f r i c t i o n and wear processes,

( i i i ) t h e processes and modes o f l u b r i c a t i o n as t h e most e f f e c t i v e means o f i n f l u e n c i n g t h e d i s s i p a t i o n mechanisms. I n o r d e r t o complete t h e general framework d e r i v e d i n Chapter 3, a s u r v e y o f t h e main t r i b o l o g i c a l processes g e n e r a l l y r e c o g n i z e d as b e i n g r e l e v a n t

47

t o mechanical systems i s g i v e n i n t h i s c h a p t e r . The t r e a t m e n t does n o t attempt t o e n t e r i n t o s p e c i f i c d e t a i l s o f the t r i b o l o g i c a l behaviour o f materials b u t t r i e s t o present a u n i f i e d p i c t u r e o f t h e important basic phenomena. Since t h e t r e a t m e n t i n t h i s c h a p t e r i s based on c o n v e n t i o n a l analyses, t h e s u r v e y can be regarded

-

b e s i d e s t h e systems a s p e c t s

-

as

a r e v i e w o f t h e p r e s e n t knowledge o f t h e mechanisms o f f r i c t i o n , l u b r i c a t i o n and wear f r o m a p h y s i c a l p o i n t o f view. The i n t e g r a t i o n o f t h e r e s u l t s o f t h i s c h a p t e r t o t h e general systems concepts i s g i v e n i n Chapter 5 and 6.

4,2

CONTACT PROCESSES

I n a g r e a t deal o f t r i b o l o g i c a l systems, t h e t r a n s a c t i o n s o f t h e r e l e v a n t i n p u t s and o u t p u t s o c c u r t h r o u g h t h e c o n t a c t i n t e r f a c e between t r i b o element (1) and t r i b o - e l e m e n t ( 2 ) . I n t h e s e i n t e r f a c i a l c o n t a c t processes, t h e f o r c e s and displacements o f t h e i n t e r a c t i n g b o d i e s , i . e . , mechanics", as w e l l as t h e m a t e r i a l s i n t e r a c t i o n s i . e . ,

the "contact

the "contact physics

and c h e m i s t r y " must be t a k e n i n t o account. I n t h i s s e c t i o n t h e d i s c u s s i o n i s r e s t r i c t e d t o t h e c o n t a c t processes between d r y s u r f a c e s ; t h e c o n t a c t p r o cesses between l u b r i c a t e d s u r f a c e s a r e t r e a t e d s e p a r a t e l y ( s e e S e c t i o n 4.5).

4 2 , 1 CONTACT

MECHAN I c s

I n c o n t a c t mechanics, a g r e a t v a r i e t y o f s i t u a t i o n s can be c o n s i d e r e d depending on: ( a ) t h e number o f b o d i e s t a k i n g p a r t i n t h e c o n t a c t process, ( b ) t h e macro-geometry o f t h e b o d i e s ( t w o - o r t h r e e - d i m e n s i o n a l p r o b l e m s ) , ( c ) t h e s u r f a c e topography (smooth o r rough s u r f a c e s ) , ( d ) t h e mechanical p r o p e r t i e s o f t h e b o d i e s (modules, hardness, e t c . ) , ( e ) t h e d e f o r m a t i o n mode ( e l a s t i c , p l a s t i c , e l a s t o - p l a s t i c ) , ( f ) t h e c o n t a c t f o r c e s (normal f o r c e s FN, t a n g e n t i a l f o r c e s F T ) , (9) the type o f r e l a t i v e motion ( s t a t i c contact, r o l l i n g , s l i d i n g , spinning, r o l l i n g with slip, etc.), ( h ) the v e l o c i t y o f r e l a t i v e motion. I t i s n o t t h e i n t e n t i o n here, n o r i s i t p o s s i b l e w i t h i n t h e scope o f t h i s

volume, t o d e a l w i t h a l l these s i t u a t i o n s . ( E x c e l l e n t r e v i e w a r t i c l e s on

various aspects o f contact mechanics can be found i n the proceedings o f a symposium on "The mechanics o f the contact between deformable bodies", see Ref. 4.1.) The purpose o f t h i s section i s t o gain a general physical p i c t u r e o f the contact-deformation process and t h e mechanisms o f the t r a n s f e r o f mechanical work through a contacting i n t e r f a c e . Obviously, a work transf e r can be obtained only through e l a s t i c contact-deformation processes. I t t h e r e f o r e seems appropriate t o consider f i r s t the e l a s t i c contact o f smooth s o l i d bodies under the a p p l i c a t i o n of a pure normal load

FN ( e l a s t o s t a t i c s )

and then t o study t h e i n f l u e n c e o f the e f f e c t s o f surface roughness, impuls i v e loading and e l a s t o - p l a s t i c conditions. Consider as a s t a r t i n g p o i n t a s e m i - i n f i n i t e e l a s t i c s o l i d under an a r b i t r a r y load d i s t r i b u t i o n p (xl,

Inw i l l be recognized t h a t load FN

x2), as i l l u s t r a t e d i n Figure 4.1.

t e g r a t i n g over the contact region A,,

it

i s given by

The c l a s s i c a l problem o f e l a s t o s t a t i c s , shown i n Figure 4.1, which was f i r s t solved by Boussinesq, can be t r e a t e d by the Fourier-transform method. ( F o r d e t a i l s , see Ref. 4.2.)

Figure 4.1

Load d i s t r i b u t i o n a c t i n g on a s e m i - i n f i n i t e body.

I n t r i b o l o g y , i n a great many contact problems we are concerned w i t h the contact o f curved bodies such as cylinders, spheres, as i n rolling-elementtype bearings, gear-teeth contacts, etc. The c l a s s i c basis f o r a l l o f these

49

c o n t a c t problems o f " c o n t r a f o r m a l s u r f a c e s " i s g i v e n by t h e famous H e r t z theory (Ref. 4.3). T h i s t h e o r y t r e a t s t h e c o n t a c t o f e l a s t i c b o d i e s as an e l a s t o - s t a t i c a l problem under t h e f o l l o w i n g r e s t r i c t i o n s : (i)

perfectly e l a s t i c materials, b o t h b o d i e s have t h e same e l a s t i c c o n s t a n t s ,

(ii) ( i ii ) t o p o g r a p h i c a l l y smooth s u r f a c e s , (iv)

t h e two s u r f a c e s a r e n o t c l o s e l y conforming i n t h e c o n t a c t r e g i o n ,

(v)

no r e l a t i v e a n g u l a r v e l o c i t y o f " s p i n " about t h e common normal t o

(vi)

no t a n g e n t i a l ( t r a c t i v e ) f o r c e i s t r a n s m i t t e d .

the contact surface,

However, t h e r e s u l t s o f t h e H e r t z i a n t h e o r y have a l s o been w i d e l y a p p l i e d s u c c e s s f u l l y t o many s i t u a t i o n s i n which t h e b o d i e s under q u e s t i o n a r e moving. Owing t o t h e g r e a t importance o f t h e H e r t z e q u a t i o n s i n t r i b o l o g y , some o f t h e r e s u l t s o f t h e H e r t z t h e o r y w i l l be reproduced h e r e . F o r t h e purpose o f t h i s t r e a t m e n t , i t i s c o n v e n i e n t t o r e s t r i c t o u r a t t e n t i o n t o t h e case o f t h e e l a s t i c c o n t a c t of two s p h e r i c a l b o d i e s under a p u r e normal l o a d FN. The c o n t a c t s i t u a t i o n i s i l l u s t r a t e d i n F i g u r e 4.2,

where rl and r 2

a r e t h e r a d i i o f c u r v a t u r e o f t h e two b o d i e s and E l , E2 and vl,

v2 t h e i r

e l a s t i c moduli and t h e i r P o i s s o n ' s r a t i o s , r e s p e c t i v e l y . U s i n g t h e abbrev i a t ions :

r: e q u i v a l e n t r a d i u s

o f curvature

E: L

4

composite e l a s t i c modulus

t h e c o n t a c t p r e s s u r e p a t a l o c a t i o n 1 w i t h i n t h e c o n t a c t area, and t h e r a d i u s o f c o n t a c t aH under t h e a c t i o n o f a normal l o a d ,,F,

F o r t h e c o n t a c t area AH, i t f o l l o w s t h a t

i s g i v e n by

50

AH

[ g] F3I: 2/3

= n a Z H = TC

FN = 0

pressure distribution, P

area, A, FN = 0

F i g u r e 4.2

Hertzi

n t c t betwe n two spheres.

C o n s i d e r i n g now t h e process o f a t r a n s f e r o f work p e r p e n d i c u l a r through t h e i n t e r f a c e , i t i s necessary t o c a l c u l a t e t h e v a l u e o f approach z o f t h e two b o d i e s as a consequence of t h e i r e l a s t i c d e f o r m a t i o n . From H e r t z i a n t h e o r y it follows that

Using t h e e x p r e s s i o n i t i s p o s s i b l e t o determine t h e p o t e n t i a l e l a s t i c e n e r g y A U o f t h e two c o n t a c t i n g b o d i e s . Since FN = g i v e n by

az

the p o t e n t i a l i s

51

I f t h e c o n t a c t s i t u a t i o n i s e n t i r e l y e l a s t i c , t h e p o t e n t i a l energy can

be t r a n s f o r m e d i n t o k i n e t i c energy i n r e l e a s i n g t h e c o n t a c t . I n t h i s case, t h e system o f t h e e l a s t i c b o d i e s p e r f o r m s work a g a i n s t i t s environment. I n c o n s i d e r i n g t h e whole process o f c o n t a c t f o r m a t i o n and c o n t a c t r e l e a s e , i t t u r n s o u t t h a t t h e q u a s i - s t a t i c H e r t z i a n c o n t a c t s i t u a t i o n can be r e g a r d e d as model o f t h e i n t e r f a c i a l t r a n s f e r o f mechanical energy t h r o u g h a system o f contacting bodies. A l t h o u g h t h e main f e a t u r e s o f an " i d e a l " t r a n s m i s s i o n o f mechanical energy t h r o u g h an e l a s t i c c o n t a c t i n t e r f a c e can be understood on t h e b a s i s o f H e r t z i a n t h e o r y , i n any c o n t a c t s i t u a t i o n o f " r e a l s u r f a c e s " t h e e f f e c t o f s u r f a c e topography must be t a k e n i n t o account ( R e f s . 4.4, 4 . 5 ) . A c c o r d i n g t o t h e German s t a n d a r d D I N 4760, t h e d e v i a t i o n s f r o m an i d e a l smooth s u r f a c e can be c l a s s i f i e d i n t o d i f f e r e n t groups: ( a ) d e v i a t i o n s i n shape ( b ) waviness ( l a r g e - s c a l e s u r f a c e d e v i a t i o n s ) ( c ) roughness ( s m a l l - s c a l e d e v i a t i o n s ) (d) l a t t i c e structure I n o r d e r t o d e s c r i b e t h e roughness o f s u r f a c e , a c o u p l e o f parameters have been d e f i n e d i n r e l a t i o n t o a c r o s s - s e c t i o n o f t h e s u r f a c e , see F i g u r e 4.3.

s u r f a c e topography (3-dim.) (a) height distribution ( b ) bearing-area curve

/

surface p r o f i l e (2-dim.)

w /

(b)

0

sample l e n g t h 1

mean l i n e : area o f s o l i d = area of. v o i d

F i g u r e 4.3

(a)

sol i d void

C h a r a c t e r i s t i c s o f s u r f a c e roughness.

100 %

62

The most commonly used h e i g h t parameter i n s u r f a c e p r o f i l o m e t r y i s t h e Ra v a l u e o r c e n t e r - l i n e - a v e r a g e v a l u e ( c . 1 . a . ) .

I t i s s i m p l y t h e average de-

v i a t i o n o f t h e p r o f i l e f r o m t h e r e f e r e n c e mean l i n e . Other h e i g h t parameters i n c l u d e t h e maximum p e a k - t o - v a l l e y h e i g h t Rt w i t h i n t h e sample l e n g t h 1, t h e average d e v i a t i o n o f t h e f i v e h i g h e s t peaks and f i v e l o w e s t v a l l e y s , R,,

and

many more, a l l o f which a r e w e l l documented i n t h e l i t e r a t u r e (Refs. 4.6,

4.7). Another approach t o d e s c r i b e t h e topography o f s u r f a c e s i s t o r e g a r d t h e p r o f i l e , as d e t e c t e d by a p r o f i l e m e t e r , as an e l e c t r i c a l s i g n a l and t o a n a l y z e i t s t a t i s t i c a l l y (Ref. 4.8). I t i s t h e n p o s s i b l e t o c l a s s i f y t h e p r o f i l e i n terms o f t h e f o l l o w i n g f u n c t i o n s :

( I ) The p r o b a b i l i t y d i s t r i b u t i o n o f o r d i n a t e h e i g h t s . F o r many e n g i n e e r i n g surfaces f i n i s h e d b y g r i n d i n g o r a b r a s i o n processes i t was found t h a t t h e h e i g h t s o f t h e p r o f i l e s were d i s t r i b u t e d i n a Gaussian manner. (11) The a u t o - c o r r e l a t i o n f u n c t i o n o f t h e p r o f i l e d e f i n e d as:

+y1 Z (A)

'i*

limT

=

1-00

y(x)

y ( x + A ) dx

-% 7

where y ( x ) i s t h e h e i g h t o f t h e p r o f i l e a t a g i v e n c o - o r d i n a t e x and y ( x t A ) i s t h e h e i g h t a t an a d j a c e n t c o - o r d i n a t e ( x

+ A ) . Peklenik

has analyzed t h e s u r f a c e s produced by many d i f f e r e n t techniques and has proposed a system o f c l a s s i f y i n g s u r f a c e s based upon t h e n a t u r e of t h e a u t o - c o r r e l a t i o n f u n c t i o n s o f t h e i r p r o f i l e (Ref. 4.9).

/

a

4 / rI

n

A,

F i g u r e 4.4

= a - b >> A

r

.

A:

=

(n: number o f c o n t a c t s )

i=1

Nominal and r e a l a r e a o f c o n t a c t .

53 Now, r e t u r n i n g t o c o n t a c t mechanics, i n o r d e r t o a v o i d a m b i g u i t y , f o r t h e c o n t a c t o f rough s u r f a c e s two terms must be d i s t i n g u i s h e d , as i l l u s t r a t ed i n F i g u r e 4.4:

(i)t h e nominal area o f c o n t a c t Ao, the contacting solids, ( i i ) t h e r e a l area o f c o n t a c t A,,

i .e.,

i.e.,

t h e apparent area o f o v e r l a p o f

t h e sum o f t h e s e p a r a t e m i c r o s c o p i c

areas a t which t h e a s p e r i t i e s a r e i n c o n t a c t . S i n c e i t i s obvious t h a t t h e r e a l area o f c o n t a c t , r a t h e r t h a n t h e nominal area, i s c r u c i a l f o r t h e i n t e r f a c i a l t r a n s m i s s i o n o f work, a g r e a t many s t u d i e s have been devoted t o t h e e s t i m a t i o n and e x p e r i m e n t a l d e t e r m i n a t i o n o f t h e r e a l area o f c o n t a c t Ar ( R e f s . 4.10, 4.11). A comprehensive s t u d y o f e l a s t i c d e f o r m a t i o n u s i n g model arrangements

was made by Archard ( R e f s . 4.12, simplifications,

4.13).

A l t h o u g h t h e s e models a r e o v e r -

t h e y i l l u s t r a t e t h a t m u l t i p l e - p o i n t c o n t a c t under e l a s t i c

d e f o r m a t i o n can g i v e a r e a l a r e a o f c o n t a c t almost l i n e a r l y p r o p o r t i o n a l t o FN, i . e . ,

Ar

=

constant

[]:

C 4/5 s C s 44/45 (depending on t h e model )

Another e x t e n s i o n o f t h e H e r t z i a n t h e o r y o f e l a s t i c c o n t a c t between spheres t o t h e case o f rough s u r f a c e s w i t h a Gaussian h e i g h t d i s t r i b u t i o n was made by Greenwood and T r i p p ( R e f . 4 . 1 4 ) . T h e i r model i s d e f i n e d by t h r e e parameters

U*

:

mean d e v i a t i o n o f t h e a s p e r i t y ,

p

:

mean r a d i u s o f t h e c u r v a t u r e o f t h e a s p e r i t y - t i p s assumed t o be c o n s t a n t f o r a1 1 a s p e r i t i e s ,

n

d e n s i t y o f a s p e r i t i e s p e r u n i t area.

They showed m a t h e m a t i c a l l y : (i1

t h e t o t a l number o f m i c r o c o n t a c t s i s a l m o s t p r o p o r t i o n a l t o t h e l o a d FN,

(ii)

t h e average s i z e o f a m i c r o c o n t a c t i s almost l o a d independent,

( i i i ) t h e r e a l a r e a o f c o n t a c t Ar i s p r o p o r t i o n a l t o t h e number o f contacts, thus t h e r e a l area o f c o n t a c t Ar,

i.e.,

t h e sum o f t h e m i c r o - c o n t a c t areas,

i s p r o p o r t i o n a l t o t h e l o a d FN. While a t low l o a d s t h e r e a r e c o n s i d e r a b l e

64

differences between the contact areas A,

and Ao(Hertz), a t higher loads i n

the rough surfaces contact s i t u a t i o n an e f f e c t i v e radius can be defined which approaches the H e r t r i a n radius and l i k e i t varies as the one-third power o f the load. I n the discussion so far, mainly r e v e r s i b l e q u a s i - s t a t i c e l a s t i c cont a c t deformations have been considered which can be regarded as models f o r the transmission of work i n a tribo-mechanical system. However, i n contact s i t u a t i o n s under pure normal loads some i r r e v e r s i b l e i n t e r f a c i a l processes already e x i s t which lead t o a d i s s i p a t i o n o f mechanical energy. Unfortunatel y , f o r the i r r e v e r s i b l e processes i n contact deformation t h e r e e x i s t s no

theory as there i s f o r the r e v e r s i b l e e l a s t i c case. Therefore, i n the f o l lowing o n l y some s h o r t remarks on d i s s i p a t i v e processes i n contact mechanics w i l l be made (a physical t r e a t i s e on the o r i g i n s o f energy d i s s i p a t i o n i s given i n Section 4.3). The f o l l o w i n g processes may c o n t r i b u t e t o an energy d i s s i p a t i o n i n contact mechanics: (a)

INTERFACIAL SLIP, I.E.,

PARTIAL MOTION OF THE CONTACTING SURFACES

OF THE BODIES I N THE INTERFACE I f i n a H e r t t i a n contact the two contacting bodies have d i f f e r e n t e l a s t i c

properties, an i n t e r f a c i a l shear s t r e s s r e s u l t s which i n t u r n influences the pressure d i s t r i b u t i o n . Depending on the physical nature o f the surfaces, the i n t e r f a c i a l t a n g e n t i a l shear may cancel o u t through l o c a l micro-sl i p processes, thus d i s s i p a t i n g energy (see also Section 4.3.4). Also i f the tang e n t i a l stresses are "frozen i n " d u r i n g the d u r a t i o n o f the contact as a consequence o f i n t e r f a c i a l adhesion forces (see Section 4.2.2),

i t i s like-

l y t h a t i n the release o f contact, energy i s dissipated.

(b)

THE GENERATION OF ELASTIC WAVES

IN THE INTERFACE

I n any contact s i t u a t i o n a t l e a s t two t r a n s i e n t s t a t e s are involved: the formation o f the contact and the separation o f the contact. I n these t r a n s i e n t states due t o changes i n t h e load o r t h e pressure d i s t r i b u t i o n , t h e r e may be a pronounced e f f e c t o f m i c r o - s l i p and a generation o f e l a s t i c waves. I t has been shown experimentally t h a t under impulsive loading o f Hertzian

contacts, gross s l i p e f f e c t s occur and energy applied d u r i n g gross s l i p i s d i s s i p a t e d (Ref. 4.15).

55

(c)

VISCOELASTIC DAMPING

The above d i s c u s s i o n s o f c o n t a c t - d e f o r m a t i o n processes on t h e b a s i s o f t h e H e r t z i a n t h e o r y r e f e r t o e l a s t i c s o l i d s as g i v e n a p p r o x i m a t e l y by hardened b a l l - b e a r i n g s t e e l . There a r e , however, o t h e r groups o f t e c h n i c a l l y import a n t m a t e r i a l s , f o r i n s t a n c e e l a s t o m e r s , which cannot be t r e a t e d i n t h i s manner. U n l i k e a h a r d m a t e r i a l l i k e s t e e l , t h e e l a s t o m e r s t r u c t u r e i s composed o f f l e x i b l e c h a i n s which a r e i n a c o n s t a n t s t a t e o f thermal motion. The t e r m " v i s c o e l a s t i c i t y "

i s commonly a p p l i e d t o m a t e r i a l s which a r e n e i t h e r

i d e a l e l a s t i c s o l i d s n o r v i s c o u s l i q u i d s ( s e e S e c t i o n 4.5.2),

but i n fact

possess c h a r a c t e r i s t i c s which a r e t y p i c a l o f b o t h . The e l a s t i c b e h a v i o u r may be r e p r e s e n t e d by an i d e a l s p r i n g and v i s c o s i t y by an i d e a l dashpot. Combini n g two b a s i c mechanical models, known as t h e V o i g t and Maxwell models cons i s t i n g s i m p l y o f s p r i n g and dashpot i n p a r a l l e l and s e r i e s r e s p e c t i v e l y , t h e c o n t a c t - d e f o r m a t i o n b e h a v i o u r o f v i s c o e l a s t i c m a t e r i a l s may be modelled. As a general feature,

i n t h e sequence o f c o n t a c t f o r m a t i o n and s e p a r a t i o n o f

such m a t e r i a l s , mechanical work i s d i s s i p a t e d t h r o u g h h y s t e r e s i s damping e f f e c t s (Ref. 4 . 1 6 ) . (d)

PLASTIC CONTACT PROCESSES

As e a r l y as 1901, S t r i b e c k p o i n t e d t o t h e l i m i t s o f t h e H e r t z i a n t h e o r y s e t by p l a s t i c d e f o r m a t i o n processes a t h i g h e r l o a d s ( R e f . 4 . 1 7 ) . An e l a s t i c plastic transition criterion, i.e.,

the so-called p l a s t i c i t y index

+ is

g i v e n by Greenwood and W i l l i a m s o n ( R e f . 4.18) as

E H

: composite e l a s t i c modulus

*

: hardness

6

: mean d e v i a t i o n o f s u r f a c e asperity height

p

: mean a s p e r i t y r a d i u s

A s i m i l a r e x p r e s s i o n has been d e r i v e d by Whitehouse and Archard (Ref. 4.19). ( F o r a comparison o f b o t h models see Ref. 4.20.) s h o u l d be e l a s t i c under a l l p r a c t i c a l l o a d s . I f

I f Q1, a p a r t o f the contact

w i l l i n v o l v e p l a s t i c f l o w . As most s u r f a c e s have values

+ i n excess

o f unity,

t h e r e w i l l be some p l a s t i c c o n t a c t d e f o r m a t i o n o f a s p e r i t i e s i n a l m o s t any c o n t a c t s i t u a t i o n . T h i s i s i n l i n e w i t h t h e view o f Bowden and Tabor (Ref. 1 . 4 ) who argued t h a t , because s u r f a c e s c o n t a i n a s p e r i t i e s o f s m a l l - r a d i u s of-curvature,

p l a s t i c f l o w would o c c u r a t t h e t r u e areas o f c o n t a c t even

66

under v e r y small l o a d s . They expressed t h e r e a l area of c o n t a c t by t h e relation

where p i s t h e y i e l d p r e s s u r e f o r t h e weaker m a t e r i a l . I t i s t h e r e f o r e Y l i k e l y t h a t i n a l m o s t any c o n t a c t s i t u a t i o n t h e r e i s some d i s s i p a t i o n o f mechanical energy due t o p l a s t i c a s p e r i t y - d e f o r m a t i o n processes. A c c o r d i n g t o N i c h o l a s (Ref. 4.21),

i n g e n e r a l , f o u r main mechanisms o f energy d i s s i -

p a t i o n i n p l a s t i c d e f o r m a t i o n can be named: (i)

The moving d i s l o c a t i o n s r e q u i r e a h i g h k i n e t i c energy, which i s s e t f r e e i f t h e d i s l o c a t i o n s a r e locked.

(ii)

The d i s l o c a t i o n s d i s s i p a t e energy c o n t i n u o u s l y t h r o u g h t h e thermoe l a s t i c damping and s c a t t e r i n g o f a c o u s t i c waves.

(iii)D i s l o c a t i o n s a r e generated and a n n i h i l a t e d d u r i n g t h e d e f o r m a t i o n . (iv)

P o i n t d e f e c t s a r e generated and a n n i h i l a t e d d u r i n g t h e d e f o r m a t i o n .

4 2,2 CONTACT I

PHYS Ics

AND CHEMI

STRY

I n t h e c o n t a c t o f p h y s i c a l bodies, besides t h e c o n t a c t nmechanicsn, i n t e r f a c i a l m o l e c u l a r m a t e r i a l i n t e r a c t i o n s and " s u r f a c e f o r c e s " must be t a k e n i n t o account. S i n c e these processes depend on t h e p h y s i c a l and chemical nature o f the surfaces i n contact, a d e s c r i p t i o n o f the surface characteri s t i c s i s needed. From t h e view o f s o l i d s t a t e p h y s i c s , s u r f a c e s o f c r y s t a l l i n e b o d i e s r e p r e s e n t an a b r u p t t e r m i n a t i o n o f t h e p e r i o d i c i t y o f t h e c r y s t a l l i n e l a t t i c e . Compared w i t h t h e b u l k p r o p e r t i e s o f a c r y s t a l l i n e s o l i d , t h e i m p l i c a t i o n s o f such an a b r u p t t e r m i n a t i o n o f l a t t i c e a r e (Ref. 4.22): ( a ) s t r u c t u r a l r e o r i e n t a t i o n s ( c r y s t a l 1i n i t y and e n e r g e t i c s ) ( b ) surface/environment i n t e r a c t i o n s (physical adsorption, chemisorption, o x i d a t i o n o r f i l m formation) ( c ) changes i n p h y s i c a l p r o p e r t i e s F o r t e c h n i c a l s u r f a c e s , due t o t h e m a n u f a c t u r i n g process, a d d i t i o n a l aspects must be t a k e n i n t o account l i k e : ( d ) a work-hardened l a y e r

57 ( e ) t e x t u r i n g o f t h e surface ( f ) local internal stress f i e l d s I n o r d e r t o d e s c r i b e t h e c o m p o s i t i o n o f r e a l s u r f a c e s , Schmaltz as e a r l y as

1936 d i s t i n g u i s h e d between an " i n n e r s u r f a c e l a y e r " ,

b u l k m a t e r i a l and

worked l a y e r , and an " o u t e r s u r f a c e l a y e r " , contaminants, adsorbed l a y e r s , oxide l a y e r s (Ref. 4.23).

The c o m p o s i t i o n o f a s u r f a c e i n a c r o s s - s e c t i o n a l

view i s shown s c h e m a t i c a l l y i n F i g u r e 4 . 5 . C l e a r l y , t h e a c t u a l c o m p o s i t i o n o f a g i v e n s u r f a c e and t h e s t r u c t u r e and t h i c k n e s s o f t h e d i f f e r e n t s u r f a c e l a y e r s , as shown s c h e m a t i c a l l y i n F i g u r e 4.5,

depends on 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 and on t h e environment, a p a r t f r o m t h e b u l k m a t e r i a l p r o p e r t i e s .

contaminant l a y e r outer surface layers

inner

adsorbed gas l a y e r 10

nm

oxide l a y e r

>5

pm

work-hardened 1a y e r

surface 1ayers metal s u b s t r a t e

F i g u r e 4.5

Schematic r e p r e s e n t a t i o n o f t h e l a y e r e d c o m p o s i t i o n of a m e t a l l i c surface.

Consider now t h e c o n t a c t process o f two s o l i d b o d i e s under a p u r e normal l o a d FN. As d e s c r i b e d i n t h e f o r e g o i n g s e c t i o n , t h e c o n t a c t i n g s u r f a c e s

w i l l t o u c h o n l y w i t h i n d i s c r e t e m i c r o - s p o t s whose sum forms t h e r e a l a r e a o f c o n t a c t Ar.

I n t h e process o f c o n t a c t f o r m a t i o n , b e s i d e s an e l a s t i c de-

f o r m a t i o n process t h e a s p e r i t i e s undergo some p l a s t i c d e f o r m a t i o n . Due t o t h i s d e f o r m a t i o n processes, i n t i m a t e c o n t a c t between t h e p a r t n e r s occurs so t h a t m o l e c u l a r s u r f a c e f o r c e s may a c t t h r o u g h t h e i n t e r f a c e , w h i c h r e s u l t s i n " i n t e r f a c i a l bonding" and t h e g e n e r a t i o n o f adhesive " j u n c t i o n s " . Thus t h e d i f f e r e n t types o f m o l e c u l a r f o r c e s t h a t can a c t w i t h i n t h e i n t e r f a c e o f two c o n t a c t i n g b o d i e s t o produce "adhesion" and t h e energy o f i n t e r f a c i a l adhesion b o n d i n g must be considered.

Adhesion mechanism

Bonding through:

Val idi ty

electromagnetic fluctuation fields

z > atomic

I van der Waals 1 '1 id

solid (*)

dime ns ions

electrostatic fields

zc tunnel distance (localized charges)

mobile interfacial electrons

z = atomic dimensions (grain boundary analogy)

1 metallic J

F

l z E atomic overlap o f electron distributions

Fiaure - 4.6

Types of adhesion bonding mechanisms.

dimensions (dangl ing bonds)

59

T h e o r e t i c a l l y , t h e a t t r a c t i v e i n t e r a c t i o n f o r c e s between two c o n t a c t i n g s o l i d s include, a t l e a s t i n p r i n c i p l e , a l l those types o f i n t e r a c t i o n t h a t c o n t r i b u t e t o t h e cohesion o f s o l i d s , such as m e t a l l i c , c o v a l e n t and i o n i c , i.e.,

p r i m a r y chemical bonds ( s h o r t - r a n g e f o r c e s ) , as w e l l as secondary van

d e r Waals bonds ( l o n g - r a n g e f o r c e s ) . F o r example, two p i e c e s o f c l e a n g o l d p l a c e d i n c o n t a c t w i l l f o r m m e t a l l i c bonds o v e r t h e r e g i o n s o f a t o m i c cont a c t and t h e i n t e r f a c e w i l l have t h e s t r e n g t h o f b u l k g o l d . W i t h c l e a n d i a mond, t h e s u r f a c e f o r c e s w i l l resemble v a l e n c y f o r c e s ; w i t h r o c k s a l t t h e s u r f a c e f o r c e s w i l l be p a r t l y i o n i c . A l l these a r e e s s e n t i a l l y s h o r t - r a n g e f o r c e s . Long-range van d e r Waals f o r c e s a c t i n t h e adhesion between s o f t r u b b e r - l i k e m a t e r i a l s and between p o l y m e r i c s o l i d s . I n F i g u r e 4.6 some char a c t e r i s t i c s o f t h e adhesion bonding mechanisms a r e shown. Due t o t h e g r e a t importance o f adhesion i n t r i b o l o g i c a l processes, some f e a t u r e s o f t h e a c t i o n o f van d e r Waals f o r c e s and m e t a l l i c bonds reasons f o r an adhesion o f polymers and m e t a l s

-

-

t h e main

w i l l be d e s c r i b e d i n some

detail.

I f two s o l i d s a r e b r o u g h t t o g e t h e r t h e y w i l l f i r s t e x p e r i e n c e a t t r a c t i v e f o r c e s due t o van d e r Waals i n t e r a c t i o n s . These f o r c e s a r i s e f r o m t h e f l u c t u a t i n g charge d i s t r i b u t i o n s i n t h e atoms o r molecules o f t h e two b o d i e s , c r e a t i n g momentary and c o n t i n u o u s l y s h i f t i n g d i p o l e s and c o r r e s p o n d i n g l y induced d i p o l e s i n n e i g h b o u r i n g atoms o r molecules. As a f i r s t approximat i o n f o r a s o l i d body, i t may be assumed t h a t t h e van d e r Waals f o r c e between any p a i r o f atoms o r molecules i s a d d i t i v e so t h a t t h e t o t a l f o r c e may be c a l c u l a t e d by summation f o r a l l p a i r s o f atoms i n t h e two b o d i e s . On t h e b a s i s o f t h i s assumption, C a s i m i r was t h e f i r s t t o d e r i v e t h e f o l l o w i n g formula f o r t h e f o r c e o f adhesion FA i n t h e i n t e r f a c e A o f two m i r r o r p l a n e s (Ref. 4.24):

h tl

FA

cr2

240

A

7

=

h

(h

:

Planck's constant)

c

:

speed o f l i g h t

z

:

d i s t a n c e between the surfaces

I n t h e c a l c u l a t i o n o f t h e van d e r Waals f o r c e s , two cases must be d i s t i n guished: ( a ) non r e t a r d e d f o r c e s o c c u r r i n g between i n t e r a c t i n g d i p o l e s which a r e

i n phase,

60

(b) retarded forces occurring i f the i n i t i a l d i p o l e and t h e induced d i p o l e are no longer i n phase. For these two cases the f o l l o w i n g expressions f o r the adhesion f o r c e FA between a sphere o f radius r a t a distance o f nearest approach z from a f l a t surface can be derived (a) non-retarded forces

( b ) retarded forces J

L

where kl and k2, a r e the Hamaker constants f o r non-retarded and retarded forces respectively. The v a l i d i t y o f these formulae has been proved i n experiments w i t h clean smooth mica surfaces. It was found t h a t a t

z>

100 nm,

the formulae f o r t h e retarded forces i s v a l i d whereas a t z < 20 nm the measured van der Waals a t t r a c t i v e f o r c e FA agrees w e l l w i t h t h e theory f o r nonretarded i n t e r a c t i o n s (Ref. 4.25). I f the van der Waals surface forces are described i n terms o f surface e n e r g y y , t y p i c a l values o f about 0.02 t o 0.04

Jm"

are found.

These r e s u l t s lead t o an important generalization: since van der Waals i n t e r a c t i o n s occur between any type o f atoms o r molecules, i t can be assumed t h a t the van der Waals adhesion forces a c t between a l l m a t e r i a l s t h a t are brought i n t o contact down t o distances o f a few nm. Below 1 nm, a t atomic dimensions, s h o r t range surface forces o f d i f f e r e n t type come i n t o a c t i o n which depend on t h e nature o f t h e m a t e r i a l s i n contact. As an important example o f the a c t i o n o f short-range surface forces, the adhesion o f clean metals w i l l be discussed. I n order t o estimate the strength o f m e t a l l i c adhesion bonding, cons i d e r f i r s t the b u l k cohesion o f metals. Due t o the complicated e l e c t r o n i c s t r u c t u r e o f most metals, a t present i t i s n o t y e t possible t o c a l c u l a t e the cohesion strength o f metals from f i r s t p r i n c i p l e s . Estimations o f the cohesion bond strength o f simple metals can be attempted using the so-called " j e l l i u m model". According t o Ziman (Ref. 4.26), i t can be seen t h a t i n t h e simple p i c t u r e o f a j e l l i u m model cohesion depends, b a s i c a l l y , on having an " e l e c t r o n gas" o f f a i r l y high density, n o t on t h e d e t a i l s o f the c r y s t a l structure. The e l e c t r o n gas behaves l i k e a ,ubiquitous l i q u i d glue t h a t w i l l b i n d together more o r l e s s any arrangement o f ions t h a t i s s u f f i c i e n t l y densely packed.

61 The a p p l i c a t i o n o f t h e j e l l i u m model t o t h e case o f adhesion a t a b i m e t a l l i c i n t e r f a c e i s i l l u s t r a t e d i n F i g u r e 4.7.

I n t h i s model, j u s t t h e

o v e r l a p o f t h e metal-vacuum electron-number d e n s i t i e s nl and n 2 o f t h e two c o n t a c t i n g p a r t n e r s w i t h i n t h e t r u e a r e a o f c o n t a c t i s considered.

metal 1

-.---

?.? .A

*\

. I

.--metal 2

-Lo IF i g u r e 4.7

J e l l i u m model o f a b i m e t a l l i c adhesion i n t e r f a c e .

A f i r s t p r e l i m i n a r y c a l c u l a t i o n o f t h e adhesive i n t e r a c t i o n o f a b i m e t a l l i c

i n t e r f a c e energy was performed by F e r r a n t e and Smith (Ref. 4.27),

which has

r e c e n t l y been extended (Ref. 4.28). The t h e o r y proceeds f r o m an e x p r e s s i o n f o r t h e t o t a l energy o f t h e system i n terms o f e l e c t r o n number d e n s i t y , i n c l u d i n g exchange and c o r r e l a t i o n e n e r g i e s , and i s a p p l i e d t o t h e c l o s e packed planes o f s i m p l e m e t a l s . I n t h i s t h e o r y t h e s t r e n g t h o f adhesion bonding depends, b a s i c a l l y , on t h e f r e e - e l e c t r o n d e n s i t y . As i n t e r f a c i a l f r e e - e l e c t r o n d e n s i t y i n t u r n depends on how s t r o n g l y t h e e l e c t r o n s a r e l o c a l i z e d i n s i d e the contacting partners, i n a d d i t i o n t o the free-electron j e l l i u m formalism,

t h e e l e c t r o n i c s t r u c t u r e o f m e t a l s and t h e c h a r a c t e r

( s , p, d) o f e l e c t r o n s f r e e f o r i n t e r f a c i a l adhesion bonding must be cons i d e r e d . T h i s has l e d t o t h e h y p o t h e s i s t h a t f o r l i k e m e t a l s t h e s t r e n g t h o f adhesion bonding s h o u l d i n c r e a s e w i t h i n t h e p e r i o d i c t a b l e f r o m l e f t t o r i g h t i n t h e o r d e r o f t r a n s i t i o n m e t a l s , n o b l e metals, 6-subgroup m e t a l s (Ref. 4.29).

F o r t h e adhesion bonding o f u n l i k e m e t a l s , f u r t h e r a s p e c t s

such as t h e d i f f e r e n c e s i n Fermi l e v e l s , e l e c t r o n work f u n c t i o n s and s t r u c t u r e and d e n s i t y o f e l e c t r o n s t a t e s o f b o t h p a r t n e r s must be c o n s i d e r e d . Here, t h e d e n s i t y o f s t a t e s i n t h e metal on one s i d e o f t h e i n t e r f a c e may determine t h e t o t a l number o f e l e c t r o n s i m p i n g i n g on t h e j u n c t i o n , and t h e d e n s i t y o f s t a t e s i n t h e o t h e r metal may determine t h e number o f f i n a l s t a t e s a v a i l a b l e f o r t h e passed adhesive bonding e l e c t r o n s . I t may be h y p o t h e s i z e d t h a t s t r o n g adhesion bonds w i l l o c c u r i f one p a r t n e r can a c t

62

as an "electron donor'' and the other as an "electron acceptor" (Refs. 4.29, 4.30). These considerations are, however, rather speculative because a t present there i s no d i r e c t way of studying the actual interfacial electron densities o r determining the interfacial bond strength. Although adhesion i s essentially the r e s u l t of interfacial molecular bonding forces, i t should be borne i n mind t h a t the net adhesion e f f e c t between solids i s influenced by a t l e a s t three further important factors: The elasto-plastic contact behaviour of the partners, determining the size of the real area of contact in which the actual surface forces are able t o act. ( i i ) The influence of e l a s t i c stresses in contact separation, eventually peeling junctions apart, particularly i f the contacting partners a r e lacking in d u c t i l i t y . ( i i i ) The presence of surface films and surface asperities which may reduce the adhesion forces.

(i)

I

20

Figure 4.8

SEM micrograph of an adhesive junction a f t e r contact separation (copper surface).

63 Experimentally, t h e o n l y way o f s t u d y i n g adhesive i n t e r a c t i o n s between two s o l i d bodies which contact under a pure normal l o a d FN i s t o destroy the bonding and t o measure the f o r c e FA necessary f o r the separation o f t h e surfaces. According t o Bowden the r a t i o

i s termed the c o e f f i c i e n t o f adhesion. The t y p i c a l appearance o f a broken m e t a l h e t a l adhesion j u n c t i o n can be seen i n F i g u r e 4.8 i n a scanning e l e c t r o n microscope (SEN) micrograph, having the appearance o f d u c t i l e f r a c t u r e . The e a r l y experimental work o f Bowden and Rowe (Ref. 4.31) showed c l e a r l y t h a t very s t r o n g adhesion c o u l d be obtained between metal surfaces t h a t had f i r s t been cleaned by h e a t i n g t o a h i g h temperature i n a vacuum o f 130 pPa (10-6Torr).

I n these experiments, r e l a t i v e l y heavy j o i n i n g loads had

been used so t h a t t h e surfaces underwent p l a s t i c deformation.

Likewise

under p l a s t i c c o n t a c t c o n d i t i o n s combined w i t h a d i s r u p t i o n o f surface contaminant l a y e r s , S i k o r s k i s t u d i e d t h e c o r r e l a t i o n o f t h e c o e f f i c i e n t o f adhesion w i t h various b u l k p r o p e r t i e s o f metals i n a p p l y i n g the twist-compression bonding method under normal atmospheric c o n d i t i o n s (Ref. 4.32).

In

F i g u r e 4.9 the r e s u l t s o f S i k o r s k i a r e represented showing t h e mean c o e f f i c i e n t o f various metals as a f u n c t i o n o f i t s Vickers hardness. These r e s u l t s i n d i c a t e two b a s i c features: (i)

The adhesion c o e f f i c i e n t decreases w i t h i n c r e a s i n g hardness (and a l s o w i t h i n c r e a s i n g e l a s t i c moduli and surface energy).

( i i ) The values o f the adhesion c o e f f i c i e n t are s p l i t up f o r t h e d i f f e r e n t types o f c r y s t a l s t r u c t u r e ; t h e adhesion i s lowest f o r hexagonal close-packed metals. This general feature o f the adhesion o f metals has a l s o been observed f o r clean pure metals under c o n d i t i o n s o f u l t r a h i g h vacuum i n extensive e x p e r i ments by D. Buckley (Refs. 4.33,

4.34).

I t was a l s o found t h a t , c o n t r a r y t o

a p r e v i o u s l y h e l d view, s t r o n g adhesion c o u l d be obtained between u n l i k e metals which had no mutual s o l u b i l i t y (Refs. 4.35,

4.36).

F u r t h e r , on sepa-

r a t i o n of the surfaces the cohesively weaker metal has g e n e r a l l y been observed t o t r a n s f e r t o the cohesively stronger.

64

0

fcc

x

bcc

tl

0 .I-

4-

VI

01

+ tetragonal

r

U 4

+ 0

3-

c, E

aJ

.r

:.Y- 2 Lc

aJ 0 u

s ..Q W z

Pt

I0 I

1

0.03 0.05

0.01

1

0.1

0.3

0.5

V i c k e r s hardness

F i g u r e 4.9

1

3

5

(GN/m2)

C o r r e l a t i o n between t h e median c o e f f i c i e n t s o f adhesion and V i c k e r s hardness f o r m e t a l s o f v a r i o u s 1 a t t i c e s t r u c t u r e s (Ref. 4.32).

I n t r y i n g t o e x p l a i n t h e s e e x p e r i m e n t a l o b s e r v a t i o n s i n terms of p h y s i c a l p r o p e r t i e s o f metals, two aspects have been emphasized: ( a ) The a b i l i t y o f s u r f a c e s t o deform p l a s t i c a l l y o b v i o u s l y e x h i b i t s a marked i n f l u e n c e on adhesion s i n c e i t i n f l u e n c e s t h e t r u e area o f cont a c t . As i l l u s t r a t e d i n F i g u r e 4.10 w i t h f a c e - c e n t r e d - c u b i c

( f c c ) me-

t a l s t h e r e a r e 12 p o s s i b l e s l i p systems. Body-centred-cubic ( b c c ) met a l s have 12 main o p e r a b l e s l i p systems and 36 secondary s l i p systems which r e q u i r e h i g h e r shear s t r e s s e s t o produce s l i p . W i t h hexagonal m e t a l s ( h c p ) , however, a t room temperature t h e r e a r e o n l y 3 o p e r a b l e basal s l i p systems. The l i m i t e d s l i p b e h a v i o u r i n t h e hexagonal m e t a l s , t h e r e f o r e , seems t o i n d i c a t e t h a t t h e hexagonal m e t a l s m i g h t w e l l exh i b i t l o w e r adhesion b e h a v i o u r than e i t h e r bcc (Refs. 4.37,

-

o r fcc

- metals

4.38).

( b ) The e l e c t r o n i c s t r u c t u r e o f t h e m e t a l s and t h e i n t e r f a c i a l f r e e e l e c t r o n d e n s i t y i s assumed t o determine t h e i n t e r f a c i a l bond s t r e n g t h (Refs. 4.27 t o 4.29). F o r example, i n c a l c u l a t i n g t h e b i n d i n g e n e r g i e s

66

f o r a couple o f u n l i k e fcc metals using the e l e c t r o n theory o f m e t a l l i c binding, an ordering of b i n d i n g energies was obtained as shown i n Table 4.1. As i n d i c a t e d i n Table 4 . 1 the t h e o r e t i c a l f i n d i n g s have been exp e r i m e n t a l l y v e r i f i e d (Ref. 4.39). Besides the extensive experimental work on the adhesion o f metals, r e l a t i v e l y few studies have been reported o f adhesion between o t h e r types o f s o l i d such as covalent o r i o n i c m a t e r i a l s o r van der Waals bonded s o l i d s . I n addit i o n , l i t t l e work appears t o have been c a r r i e d o u t between such s o l i d s and clean metals. (Examples o f polymer-metal adhesion as studied by o p t i c a l microscopy and f i e l d i o n microscopy can be found i n Section 7.6.)

Tabor

and co-workers described a study o f the adhesion between s o l i d s o f d i f f e r e n t type performed i n a vacuum o f 13 nPa (lO-loTorr)

(Ref. 4.40).

They found

t h a t adhesion o f s o f t metals t o a hard s o l i d such as t i t a n i u m carbide can be high and when the surfaces are separated fragments o f metal are found a t tached t o the harder surface. With o t h e r hard s o l i d s such as saphire o r diamond the adhesion o f copper i s appreciably less, i n d i c a t i n g t h a t the bonding between copper and these covalent m a t e r i a l s i s i n t r i n s i c a l l y weak. From the study o f the adhesion bonding mechanisms an important general conclusion can be drawn: Since both partners c o n t r i b u t e t o t h e adhesion bonding, the bond strength i s e s s e n t i a l l y an i n t e r a c t i o n c h a r a c t e r i s t i c . Therefore, any measure o r c h a r a c t e r i s t i c o f adhesion cannot be handled i n engineering a p p l i c a t i o n s l i k e a m a t e r i a l s property (as f o r instance the e l a s t i c modulus) b u t r a t h e r as a q u a n t i t y r e l a t e d t o the whole system o f contacting partners under consideration. I n c o n t r a s t t o m a t e r i a l p r o p e r t i e s l i k e the e l a s t i c modulus which can be regarded as a "system-independent" parameter, the adhesion behaviour o f a material p a i r i s a s t r o n g l y "system-dependent" characteristic. I n the discussion o f contact processes so f a r , the contact mechanics as based on Hertzian theory and the i n t e r f a c i a l adhesion surface forces have been t r e a t e d separately. An analysis o f the e l a s t i c contact between a smooth e l a s t i c sphere and a smooth f l a t surface t a k i n g i n t o account the e f f e c t o f i n t e r f a c i a l a t t r a c t i v e adhesion forces was made by Johnson, Kendall and Roberts (Ref. 4.41). They showed t h a t the area o f contact i s always greater than t h a t given by c l a s s i c a l Hertzian theory. This i s obviously due t o a n e t release o f surface energy r e s u l t i n g from the replacement o f two surfaces by one s o l i d / s o l i d i n t e r f a c e o f lower surface energy. The change i n surface

66

Slip plane

Structure

Slip direction

Number o f s l i p systems

FCC Cu, A l , N i , Pb, Au, Ag, y Fe,

...

(111) 6x 2 =1 2 secondary s l ip sys tems : 12 x 1 12 (111) 24 x 1 = 24 (111)

BCC W, Mo, aFe,

..

p brass,.

(1120)

HCP

(basal s l i p )

Cd, Zn, Mg, co,

...

Figure 4.10

1 x 3 = 3

Observed s l i p systems i n c r y s t a l s .

~

Theoretical

A1 A1 A1 A1 cu AU CU

Ag

Table 4.1

Ordering binding energy, ergs/cm21

-

A1

525

AU

- CU

465 455

-

Ag

385

cu

- AU

375 345

-

Ag

335

Ag

290

Experimental ordering

Ordering o f adhesive binding energies (Ref. 4.39).

67 energy p e r u n i t area of c o n t a c t , A y

where

,

may be w r i t t e n as

y1 i s t h e s u r f a c e energy o f t h e sphere,

y 2 o f t h e f l a t and y12 o f

t h e i n t e r f a c e . The a n a l y s i s shows t h a t t h e r e i s a f i n i t e t e n s i l e f o r c e F*N r e q u i r e d t o p u l l t h e sphere o f f t h e f l a t . The v a l u e o f F*N i s t h e same whether o r n o t t h e s u r f a c e s a r e i n i t i a l l y pressed t o g e t h e r w i t h an e x t e r n a l f o r c e , and i s g i v e n by F*,

=

3

IT

ray

The r e s u l t s o f t h e a n a l y s i s o f Johnson, K e n d a l l and Roberts f o r t h e case o f a r u b b e r / r u b b e r c o n t a c t a r e shown i n F i g u r e 4.11. F o r s o f t e l a s t i c van d e r

y

Waals s o l i d s , ( r = 22 mm,

= 30 mJm-2)

t h e adhesion observed i s s e v e r a l mN.

F o r t h o r o u g h l y c l e a n c r y s t a l l i n e s o l i d s where y i s a t l e a s t an o r d e r o f niagnitude g r e a t e r one would e x p e c t adhesive f o r c e s , independent o f t h e j o i n i n g l o a d , o f o r d e r o f 10-2N.

1.5

I

1.0

.

0.5

.-

E

v

I

m

s!

He rt z t h e o ry , w i t h adhesion

.r

-0

m L

+J

V rc( +J

K

/

0 V

/

"aH

Hertz theory, w i t h o u t adhesion

/ 0 1 2 3 4

-1

Load FN

Figure 4.11

(10-2N)

H e r t z i a n e l a s t i c c o n t a c t w i t h o u t and w i t h i n t e r f a c i a l adhesion ( R e f . 4.41).

68

The a n a l y s i s i l l u s t r a t e d i n F i g u r e 4.11 i s v a l i d f o r o p t i c a l l y smooth r u b b e r - l i k e m a t e r i a l s where o v e r a l l d e f o r m a t i o n s a r e l a r g e and l o c a l m i c r o a s p e r i t i e s a r e e a s i l y accommodated. As a c r i t e r i o n f o r t h e i n f l u e n c e o f s u r f a c e roughness on t h e adhesion o f e l a s t i c s o l i d s , F u l l e r and Tabor (Ref. 4.42) have d e f i n e d an "adhesion parameter" g i v e n by

where

p

i s t h e average r a d i u s o f c u r v a t u r e o f i n d i v i d u a l a s p e r i t i e s , z t h e

d e v i a t i o n f r o m t h e mean h e i g h t , E t h e reduced e l a s t i c modulus and b y t h e surface-energy change d e f i n e d above. P h y s i c a l l y , t h e q u a n t i t y measure o f t h e adhesive f o r c e , t h e q u a n t i t y E

z3/'

pl/'

is a

a measure o f t h e

f o r c e e x e r t e d b y t h e a s p e r i t i e s i n pushing t h e s u r f a c e s a p a r t . I f 0 i s s m a l l , t h i s i m p l i e s t h a t t h e adhesion i s ' d o m i n a n t , i f 0 i s l a r g e t h e asperi t i e s dominate and t h e adhesion i s s m a l l . I t i s assumed t h a t t h e t r a n s i t i o n f r o m s t r o n g t o weak adhesion accurs i f i r r e g u l a r i t i e s o f dimensions z and z

E

=

0 > l o . T h i s corresponds t o s u r f a c e

1 pm f o r van d e r Waals s o l i d s , l i k e rubber,

5nm f o r h a r d m a t e r i a l s such as diamond. T h i s a n a l y s i s shows t h a t

w i t h h a r d e l a s t i c s o l i d s , v e r y small s u r f a c e i r r e g u l a r i t i e s a r e s u f f i c i e n t t o reduce adhesion t o a v e r y l o w value. I f , on t h e o t h e r hand, t h e j u n c t i o n s can deform p l a s t i c a l l y , then adhesion d o m i n a t i n g o v e r roughness i s more

1i k e l y t o occur. I n summary, i n any c o n t a c t s i t u a t i o y t h e combined i n f l u e n c e s of c o n t a c t mechanics and c o n t a c t p h y s i c s and c h e m i s t r y must be t a k e n i n t o account. The analyses, performed f o r t h e case o f two s o l i d bodies c o n t a c t i n g under t h e a c t i o n o f a pure normal l o a d FN, show t h a t t h e f o l l o w i n g main c h a r a c t e r i s t i c s and processes must be considered: (I)

Surface c h a r a c t e r i s t i c s ( a ) S u r f a c e topography

-

s u r f a c e roughness parameters p r o f i l e d i s t r i b u t i o n curve p r o f i l e auto-correlation function s t a t i s t i c a l s u r f a c e parameters

( b ) Surface composition

-

contaminants

- phys isorbed 1ayers - chemi sorbed 1ayers

69

- oxide l a y e r s - worked l a y e r s (11) Contact formation ( a ) Contact mechanics - Hertz theory apparent and real area of contact - deformation mode ( p l a s t i c i t y index) - e l a s t i c - a s p e r i ty-contact deformation plastic-asperity-contact deformation ( b ) Contact physics and chemistry - van d e r Waals forces m e t a l l i c bonding e f f e c t of o t h e r short-range forces - e f f e c t of surface films (111) Contact separation - interfacial s l i p - generation of e l a s t i c waves e l a s t i c recovery - t r a n s f e r of adherent material - fracture

-

-

-

4,3 FRICTIONPROCESSES 4,3,1 TANGENTIAL FORCES

I N CONTACT PROCESSES

In t h i s s e c t i o n , t h e o r i g i n s and mechanisms of dry f r i c t i o n w i l l be considered i n order t o explain the d i s s i p a t i o n processes t h a t occur on the conceptual work plane i n a t r i b o l o g i c a l system a s i l l u s t r a t e d in Figure 3.6. Consider as a s t a r t i n g point the s t a t i c contact o f two bodies under a pure normal force FN on which a tangential f o r c e FT i s superimposed without causing a macroscopic r e l a t i v e motion between the two bodies. In t h i s case, the addition o f FT t o FN modifies the i n t e r f a c i a l e l a s t i c - and p l a s t i c contact-deformation s i t u a t i o n as described in the foregoing s e c t i o n . There a r e four main aspects t h a t must now be considered:

( a ) ELASTIC STRESSES AND DISPLACEMENTS Mindlin made a detailed study of the idealized case of e l a s t i c Hertzian contact under the additional action of a small tangential force (Ref. 4.43). In the case of a tangential force across a c i r c u l a r Hertzian contact area, i . e . , the case of two spherical bodies in contact, the tangential traction i s everywhere parallel to the direction of the applied force. The contours of constant tangential traction are concentric circles. The magnitude o f the traction rises from one-half the average a t the centre to i n f i n i t y a t the edge. Obviously, the high traction stresses in some way cause micros l i p between the two contacting materials depending on the shear strength o f adhesion bonding between the materials in contact. If the resistance against motion i s expressed formally'by the coefficient of f r i c t i o n f, presumably the tangential component of traction cannot exceed the product of the coefficient of f r i c t i o n and the normal component of traction. If aH denotes the radius of the Hertzian contact c i r c l e , i t follows that no s l i p occurs within a c i r c l e of radius I/ 3

a'

=

aH ]:-I[

whereas i n t h a t p a r t o'f the Hertzian contact zone i n which the radius i s between a ' and a,, s l i p occurs. The situation i s i l l u s t r a t e d in Figure 4.12.

Figure 4.12

S l i p and no-slip regions o f a Hertzian contact under combined normal and tangential forces.

71 ( b ) JUNCTION GROWTH Consider now t h e p o s s i b i l i t y o f p l a s t i c d e f o r m a t i o n o f a s t a t i c c o n t a c t under t h e a c t i o n o f a normal f o r c e FN and a superimposed s m a l l t a n g e n t i a l f o r c e FT. A c c o r d i n g t o t h e p l a s t i c i t y t h e o r y o f b u l k m a t e r i a l s , i n t h e twodimensional case t h e von Mises y i e l d c r i t e r i o n i s g i v e n by

p2 t 3 T 2

py 2

=

p

:

‘I:

:

py

:

normal p r e s s u r e shear s t r e s s y i e l d pressure

I t has been shown i n S e c t i o n 4.2 t h a t i n t h e c o n t a c t o f c l e a n rough m e t a l l i c s u r f a c e s under a p u r e normal load, p l a s t i c d e f o r m a t i o n o f t h e t o u c h i n g asp e r i t i e s o c c u r s and adhesive j u n c t i o n s a r e formed. F o r an i d e a l two-dimens i o n a l model o f an i n t e r m e t a l l i c j u n c t i o n , by analogy t h e y i e l d c r i t e r i o n may be expected t o have t h e f o r m ( R e f . 4 . 4 4 ) : p

2

t C T 2

Po 2

=

where C i s a c o n s t a n t w i t h a v a l u e o f about 10, and po i s t h e s t a t i c c o n t a c t pressure. Since

it follows that

which l e a d s t o

Ar

=

[$

t

C

.T’ 2

PO

1

1’2

or

A p l o t of t h i s e x p r e s s i o n i s shown i n F i g u r e 4.13.

12

Ratio

0.1

0.2

0.3

R a t i o FT/FN

F i g u r e 4.13

J u n c t i o n growth under combined normal and t a n g e n t i a l f o r c e s .

I t can be seen t h a t t h e r e may be a c o n s i d e r a b l e i n c r e a s e i n t h e c o n t a c t

area due t o t h e combined a c t i o n o f FN and FT. The v a l i d i t y o f t h i s r e s u l t s has been proved e x p e r i m e n t a l l y f o r c l e a n m e t a l s , i . e . ,

high interfacial

adhesion bonding. I t i s p o s s i b l e t h a t i n t h i s case t h e r e a l area o f c o n t a c t Ar i n c r e a s e s u n t i l i t i s equal t o t h e nominal geometric a r e a o f c o n t a c t A,. I f t h e i n t e r f a c i a l adhesion bonding i s lowered, f o r i n s t a n c e t h r o u g h l u b r i -

c a t i o n o f t h e s u r f a c e s , s i m i l a r j u n c t i o n growth i s observed u n t i l gross t a n g e n t i a l s l i d i n g occurs as i n d i c a t e d i n F i g u r e 4.13. ( c ) DISPERSAL OF CONTAMINANTS Most s u r f a c e s under normal atmospheric c o n d i t i o n s possess a s u r f a c e compos i t i o n as shown i n F i g u r e 4.5. The topmost, i.e.,

the "outer" surface l a y e r s

a r e formed by contaminants, l i k e o x i d e s and m o i s t u r e . Through these contaminants, t h e s h o r t - r a n g e s u r f a c e f o r c e s e x i s t i n g a t a s o l i d s u r f a c e a r e sat u r a t e d under atmospheric c o n d i t i o n s . I f two s u r f a c e s a r e b r o u g h t i n t o cont a c t i n t h e d i r e c t i o n normal t o t h e i r i n t e r f a c e , i n general o n l y (week) long-range f o r c e s o f t h e van d e r Waals t y p e can a c t a d h e s i v e l y , s i n c e t h e ( s t r o n g ) s h o r t - r a n g e f o r c e s a r e a l r e a d y s a t u r a t e d and t h e t h i c k n e s s o f t h e contaminant l a y e r s o f b o t h s u r f a c e s i s i n g e n e r a l l a r g e r t h a n t h e range o f t h e s h o r t - r a n g e s u r f a c e f o r c e s . I f , however, a t a n g e n t i a l f o r c e i s superimposed t h e r e may be a d i s p e r s a l o f t h e contaminant f i l m s t h r o u g h t h e comb i n e d a c t i o n o f j u n c t i o n growth and m i c r o s c o p i c s h e a r i n g o f contaminants. Consequently, s h o r t - r a n g e f o r c e s come i n t o a c t i o n and l e a d t o s t r o n g l o c a l

73 adhesive bonds. F o r m e t a l s i t has been proved e x p e r i m e n t a l l y t h a t t h r o u g h t h e s u p e r i m p o s i t i o n o f t a n g e n t i a l f o r c e s and a r e l a t i v e m o t i o n a t t h e i n t e r face, adhesion may i n c r e a s e more than t e n f o l d . ( d ) MICRODISPLACEMENTS BEFORE SLIDING I t has been observed t h a t when a t a n g e n t i a l f o r c e FT i s a p p l i e d t o a s t a t i c

c o n t a c t , a s m a l l r e l a t i v e displacement o f about 0.1 t o 1 pm between t h e components i n c o n t a c t i n t h e d i r e c t i o n o f FT occurs almost i n s t a n t a n e o u s l y (Ref. 4.45).

These m i c r o d i s p l a c e m e n t s b e f o r e g r o s s s l i d i n g a r e i n some cases

r e v e r s i b l e and i n o t h e r s i r r e v e r s i b l e . T h i s i n d i c a t e s t h a t e l a s t i c o r p l a s t i c processes on a s m a l l s c a l e t a k e p l a c e b e f o r e gross s l i d i n g occurs.

4 , 3 , 2 SLIDING

FRICTION

If, i n a dry s t a t i c contact situation, the load applied tangential t o the c o n t a c t s u r f a c e exceeds a c e r t a i n value, gross s l i d i n g between t h e compon e n t s i n c o n t a c t occurs, F i g u r e 4.14.

I n t h i s situation, the following

macroscopic r u l e s have i n g e n e r a l been observed e x p e r i m e n t a l l y : (i)

When t a n g e n t i a l m o t i o n between two c o n t a c t i n g b o d i e s occurs, t h e f r i c t i o n f o r c e FF always a c t s i n a d i r e c t i o n o p p o s i t e t o t h a t o f t h e r e 1 a t i ve v e l o c i t y o f t h e s u r f a c e s .

(ii)

The f r i c t i o n f o r c e FF i s p r o p o r t i o n a FF

=

f

t o t h e normal f o r c e FN

' FN

Through t h i s r e l a t i o n s h i p i t i s poss 3 l e t o d e f i n e a c o e f f i c i e n t o f friction

( i i i ) The f r i c t i o n f o r c e i s independent o f t h e apparent g e o m e t r i c a r e a of contact. These r u l e s , known as t h e "Amontons-Coulomb laws" o f d r y s l i d i n g f r i c t i o n have been used so f a r as g u i d i n g r u l e s i n e n g i n e e r i n g a p p l i c a t i o n s .

74

d i r e c t i o n o f motion _cc

/ / / / I / / /// /

asperity interactions (see F i g . 4.15)

F i g u r e 4.14

A s o l i d body i n s l i d i n g motion.

In S e c t i o n 1.2.1 t h e danger o f m i s i n t e r p r e t a t i o n s of t h e s e "laws" was emphasized. T h e r e f o r e , a p h y s i c a l p i c t u r e o f t h e mechanisms o f s o l i d f r i c t i o n i s needed, f r o m which t h e i n f l u e n c i n g f a c t o r s and t h e r e l e v a n t p r o p e r t i e s o f t h e s l i d i n g components can be compiled. As e x p l a i n e d above, a gen e r a l t r e a t m e n t must i n c l u d e b o t h an e x p l a n a t i o n o f t h e f o r c e s necessary t o overcome f r i c t i o n and a p h y s i c a l p i c t u r e o f t h e processes o f energy d i s s i pation, i.e.,

t h e mechanisms o f t h e t r a n s f o r m a t i o n o f mechanical work t o

o t h e r forms o f energy as d e s c r i b e d s c h e m a t i c a l l y i n F i g u r e 3.6. To b e g i n w i t h , l e t us summarize t h e b a s i c r e s u l t s o f t h e c o n t a c t p r o cess w h i c h may a l s o be r e l e v a n t t o d r y s l i d i n g f r i c t i o n . The r e s u l t s o f S e c t i o n 4.2 show t h a t t h e f o l l o w i n g p o i n t s a r e r e l e v a n t i n any s t a t i c c o n t a c t s i t u a t i o n : (a)

Two s o l i d s u r f a c e s i n c o n t a c t o v e r a nominal geometric area A, a r e a c t u a l l y t o u c h i n g o n l y i n d i s c r e t e spots, c a l l e d m i c r o - c o n t a c t s .

(b)

The sum o f t h e m i c r o - c o n t a c t s forms t h e r e a l a r e a o f c o n t a c t Ar which c a r r i e s t h e normal l o a d FN.

(c)

Depending on t h e d e f o r m a t i o n mode, t h e f o l l o w i n g r e l a t i o n s between t h e r e a l area o f c o n t a c t A, and t h e normal l o a d ,,F, e x i s t :

-

e l a s t i c d e f o r m a t i o n ( p l a s t i c i t y i n d e x JIe0.6) FN

-

E


p l a s t i c deformation ( p l a s t i c i t y index $ 4 1 )

A,

oc

FN PY

py

: y i e l d pressure

75 (d)

I n the micro-contacts,

adhesive j u n c t i o n s a r e formed t h r o u g h t h e

a c t i o n o f surface forces:

-

long-range f o r c e s , a c t i n g between any c o m b i n a t i o n o f m a t e r i a l s down t o s e p a r a t i o n o f about Inrn,

-

s h o r t - r a n g e f o r c e s o f m e t a l l i c , i o n i c o r c o v a l e n t t y p e , depending

on t h e n a t u r e o f t h e m a t e r i a l s i n c o n t a c t , a c t i n g a t s e p a r a t i o n s .c lnm.

F o r t h e case o f a s l i d i n g c o n t a c t , based on t h e e x i s t i n g knowledge o f t h e topography and c o m p o s i t i o n o f s o l i d s u r f a c e s , we may p o s t u l a t e t h e f o l l o w i n g m i c r o s c o p i c view o f s l i d i n g f r i c t i o n : f r i c t i o n occurs t h r o u g h a s p e r i t y i n t e r a c t i o n s , i.e.,

t h r o u g h d i s s i p a t i v e processes i n v o l v e d i n t h e j o i n i n g

and s e p a r a t i o n o f m i c r o c o n t a c t s .

stage I: e l a s t i c deformation p l a s t i c deformation ploughing

s t a g e 11: adhesion b o n d i n g

s t a g e 111: shearing o f j u n c t i o n s e l a s t i c recovery

F i g u r e 4.15

Schematic r e p r e s e n t a t i o n o f a u n i t e v e n t i n t h e f r i c t i o n process.

I n t h i s model

, the

macroscopic f r i c t i o n f o r c e can be expressed as t h e

sum o f m i c r o s c o p i c f r i c t i o n f o r c e s a t t h e i n d i v i d u a l m i c r o - c o n t a c t s , and t h e energy d i s s i p a t e d may be expressed as t h e sum o f c o r r e s p o n d i n g element a r y d i s s i p a t i o n processes. The elementary processes t h a t o c c u r d u r i n g t h e j o i n i n g and s e p a r a t i o n o f a m i c r o - c o n t a c t formed between two a s p e r i t i e s i n t e r p e n e t r a t i n g t o a c e r t a i n depth are i l l u s t r a t e d schematically i n F i gure 4.15. Obviously, i n t h e d i f f e r e n t stages o f t h e f o r m a t i o n and s e p a r a t i o n o f a m i c r o - c o n t a c t , t h e f o l l o w i n g main processes a r e i n v o l v e d : (i)

e l a s t i c a s p e r i t y deformation,

(ii)

p l a s t i c a s p e r i t y deformation,

( i i i ) ploughing, (iv)

s h e a r i n g o f adhesive j u n c t i o n s .

Each o f t h e p a r t i a l processes i n v o l v e s a t a n g e n t i a l f o r c e necessary t o m a i n t a i n t h e r e l a t i v e m o t i o n as w e l l as a p a r t i a l process o f energy d i s s i p a t i o n . K r a g e l s k i (Ref. 1.6) i n a d e t a i l e d a n a l y s i s s t u d i e d t h e d i f f e r e n t causes o f f r i c t i o n t a k i n g p l a c e i n t h e m i c r o - c o n t a c t s and expressed t h e t o t a l macroscopic f r i c t i o n f o r c e FF as

where

F1 : r e s i s t a n c e caused by e l a s t i c displacement o f t h e m a t e r i a l F2

: r e s i s t a n c e caused by p l a s t i c displacement

Fg

:

r e s i s t a n c e due t o s h e a r i n g ( p l o u g h i n g ) o f t h e m a t e r i a l

F4

:

r e s i s t a n c e due t o s h e a r i n g o f t h e ( a d h e s i v e ) f i l m

With t h i s model, f r o m a p h y s i c a l p o i n t o f view t h e causes o f t h e f r i c t i o n force can be understood q u a l i t a t i v e l y (Ref. 4.46).

A q u a n t i t a t i v e calcu-

l a t i o n o f f r i c t i o n f o r c e s or f r i c t i o n c o e f f i c i e n t s i s , however, o n l y p o s s i b l e t o v e r y rough approximations under s p e c i a l s i m p l i f i e d c o n d i t i o n s . T h i s i s due m a i n l y t o o u r i n c o m p l e t e knowledge o f t h e s u r f a c e p r o p e r t i e s o f s o l i d s . I n o r d e r t o compare t h e i m p l i c a t i o n s o f t h e m i c r o s c o p i c model o f f r i c t i o n w i t h macroscopic e x p e r i m e n t a l besul t s , some e s t i m a t i o n s o f t h e magnitude o f t h e f r i c t i o n c o e f f i c i e n t f o r m e t a l s i n s l i d i n g c o n t a c t w i l l be made i n t h e f o l l o w i n g based on t h e t h e o r y o f Bowden and Tabor (Ref. 1.4). I t s h o u l d be emphasized t h a t these can be regarded o n l y as rough a p p r o x i -

mations.

According t o t h e m i c r o s c o p i c model o f f r i c t i o n , t h e d i f f e r e n t c o n t r i b u t i o n s t o f r i c t i o n may be c l a s s i f i e d b r o a d l y i n t o two groups: ( a ) deformat i o n processes and ( b ) adhesion processes. I n g e n e r a l , t h e processes bel o n g i n g t o t h e s e two groups a r e n o t independent o f each o t h e r (Ref. 4 . 4 7 ) . Under c e r t a i n s p e c i a l c o n d i t i o n s , however, one process may dominate so t h a t t h e o t h e r c o n t r i b u t i o n s a r e comparative s m a l l and may be n e g l e c t e d t o a f i r s t a p p r o x i m a t i o n . Consider, f o r example, two s p e c i a l cases o f t h e f r i c t i o n o f metals: ( a ) PLOUGHING COMPONENT OF FRICTION T h i s case may be a p p r o x i m a t e l y g i v e n i f a v e r y h a r d rough s u r f a c e s l i d e s o v e r a s o f t one. The f r i c t i o n a l r e s i s t a n c e i s t h e n m a i n l y caused by t h e a s p e r i t i e s o f t h e h a r d e r s u r f a c e p l o u g h i n g t h r o u g h t h e s o f t e r , and t h e c o e f f i c i e n t o f f r i c t i o n may be e s t i m a t e d f r o m t h e f o r c e s r e q u i r e d f o r p l a s t i c f l o w o f t h e s o f t e r m e t a l . The normal l o a d FN i s balanced by t h e y i e l d o f t h e metal a c t i n g v i a t h e r e a l a r e a o f c o n t a c t Ar: pressure p YN

The r e s i s t a n c e FT t o t a n g e n t i a l m o t i o n i s balanced b y t h e y i e l d p r e s s u r e pYg

o f t h e m e t a l a c t i n g o v e r t h e c r o s s - s e c t i o n a l a r e a o f t h e groove A

Assuming t h a t t h e p l a s t i c - y i e l d i n g metal i s i s o t r o p i c , i . e . ,

*

g'

pyN = pyT,

t h e " f r i c t i o n c o e f f i c i e n t " i s g i v e n by

I n t h i s model t h e v a l u e o f f i s determined by t h e r a t i o o f t h e areas A / A g rs depending on t h e a s p e r i t y shape model. F o r t h e case o f a c o n i c a l i n d e n t e r , as i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 4.16,

i t f o l l o w s f r o m s i m p l e geomet-

r i c consideration t h a t

f

2

= -cot9 TI;

9 : semiapex a n g l e o f the conical identer

__t

-t lo

Ag, \

F i g u r e 4.16

\

P l o u g h i n g component f o r a h a r d c o n i c a l i d e n t e r s l i d i n g o v e r a s o f t metal.

Normal s u r f a c e a s p e r i t i e s seldom have an e f f e c t i v e s l o p e exceeding 5' o r 6' (i.e.,

q) = 85' o r 84').

It follows that f

=

0.05

T h i s v a l u e may be regarded, however, o n l y as a l o w e r f r i c t i o n - c o e f f i c i e n t

l i m i t f o r t h e d e f o r m a t i o n component o f f r i c t i o n due t o t h e n e g l e c t i o n s d e s c r i b e d above and t h e e x p e r i m e n t a l l y observed f a c t t h a t a p i l e - u p of m a t e r i a l ahead o f t h e g r o o v i n g p a t h ( " b o u r r e l e t f r o n t a l " ) occurs i n most cases o f p l a s t i c d e f o r m a t i o n s d u r i n g s l i d i n g ( R e f . 4.48). ( b ) ADHESION COMPONENT OF FRICTION T h i s case may be a p p r o x i m a t e l y g i v e n f o r a s l i d i n g c o n t a c t o f two r e l a t i v e l y s o f t c l e a n metals. Depending on t h e degree o f i n t e r p e n e t r a t i o n o f a s p e r i t i e s and on t h e s u r f a c e composition, adhesion bonding i n t h e m i c r o c o n t a c t s occurs. I f s l i d i n g i s t o t a k e p l a c e , t h e f r i c t i o n f o r c e i s needed t o shear t h e weakest t a n g e n t i a l p l a n e s a t t h e areas o f a c t u a l c o n t a c t . I f t h e mean shear s t r e n g t h o f t h e weakest planes a t t h e c o n t a c t areas i s den o t e d by z s (assumed t o be o f equal v a l u e i n a l l m i c r o - c o n t a c t s ) and t h e i r t o t a l a r e a i s assumed t o be a p p r o x i m a t e l y equal t o t h e r e a l area o f c o n t a c t ,

I9 n e g l e c t i n g t h e e f f e c t o f j u n c t i o n growth, we may w r i t e

( F o r an e x t e n s i o n o f t h i s a p p r o x i m a t i o n see Ref. 4.49.)

Since f o r the plas-

t i c c o n t a c t c o n d i t i o n ( p l a s t i c i t y index (0 > 1) t h e r e a l area o f c o n t a c t i s given by py : y i e l d p r e s s u r e

i t f o l l o w s t h a t t h e c o e f f i c i e n t o f f r i c t i o n i s g i v e n by = - FF _ --

f

FN F o r m e t a l s which a r e n o t work-hardened,

ts py

t h e shear s t r e n g t h

t S o f the i n t e r -

f a c e i s a p p r o x i m a t e l y equal t o t h e c r i t i c a l shear s t r e s s o f t h e m e t a l t

.

The y i e l d p r e s s u r e p has been shown t o be a p p r o x i m a t e l y 5 t . I t f o l l o w s Y that f

0.2

z

F u r t h e r , t h i s v a l u e can o n l y be regarded as a l o w e r f r i c t i o n - c o e f f i c i e n t

l i m i t f o r t h e adhesion component o f f r i c t i o n o f ( t e c h n i c a l l y ) c l e a n m e t a l s , s i n c e f o r r e a l l y c l e a n m e t a l s w i t h t h e h e l p o f j u n c t i o n growth, f r i c t i o n c o e f f i c i e n t s as h i g h as f z 40 t o 100 have been measured. On t h e o t h e r hand, i t i s p o s s i b l e t o l o w e r t h e f r i c t i o n c o e f f i c i e n t down t o v a l u e s o f f

=

0.02 w i t h boundary l u b r i c a n t s . From t h e m i c r o s c o p i c model o f f r i c t i o n and t h e s i m p l e e s t i m a t i o n s

based on t h i s model, i t i s p o s s i b l e t o v e r i f y t h e f o r m o f t h e e m p i r i c a l Amontons-Coulomb l a w o f s l i d i n g f r i c t i o n . I t has been d e s c r i b e d t h a t t h e f r i c t i o n processes o c c u r w i t h i n t h e r e a l a r e a o f c o n t a c t Ar,

and t h a t f o r

b o t h t h e d e f o r m a t i o n component and t h e adhesion component

FF

oc

Ar.

The r e s u l t s o f t h e c o n t a c t mechanics o f rough s u r f a c e s f o r b o t h e l a s t i c -

80

and p l a s t i c - c o n t a c t conditions show t h a t

I f i t i s assumed t h a t these r e s u l t s also hold f o r s l i d i n g contact conditions, i t follows t h a t

Thus, the f r i c t i o n f o r c e i s proportional t o t h e load and independent o f t h e geometric contact area, i n agreement w i t h the empirical Amontons-Coulomb law of sliding friction. However, t h e microscopic model o f f r i c t i o n as i l l u s t r a t e d i n Figure 4.15 i n d i c a t e s t h a t f r i c t i o n i s n o t o n l y a composite process b u t i s also s e n s i t i v e t o changes i n the deformation and adhesion c h a r a c t e r i s t i c s o f the contacting surfaces. Depending on the operating conditions and t h e a t mospheric environment, i.e., t h e " t h i r d body", i n t e r a c t i n g w i t h t h e two s l i d i n g partners , i n general, changes i n the surface topography as w e l l as i n the surface composition and the surface strength p r o p e r t i e s w i l l take place, see Section 5.2. These changes may i n f l u e n c e the f r i c t i o n c o e f f i c i e n t markedly, see Section 8.5.2. Thus, as discussed already i n Section 4.2 f o r the s t a t i c contact s i t u ation, there are many properties o f m a t e r i a l s which i n f l u e n c e t h e nature o f the i n t e r f a c e i n s l i d i n g f r i c t i o n . For example, f o r metals these include surface o r i e n t a t i o n , l a t t i c e spacing, g r a i n boundaries, c r y s t a l s t r u c t u r e , nature o f adhesion bond character and a l l o y i n g elements. The e f f e c t o f a l l o y i n g elements can a1 t e r i n t e r f a c i a l behaviour by segregation t o the surface o f metals o r by a l t e r i n g b u l k p r o p e r t i e s through c r y s t a l t r a n s f o r mation k i n e t i c s (Ref. 4.50). Since i t i s n o t possible t o deal w i t h the f r i c t i o n behaviour o f the various m a t e r i a l s w i t h i n the scope o f t h i s volume, t h i s section may be closed b e s t i n quoting t h e summarizing remarks from t h e recent e x c e l l e n t review o f D. Tabor on the general mechanisms o f s l i d i n g f r i c t i o n (Ref. 4.51): "The f r i c t i o n between unlubricated s o l i d s i s due t o two main factors. The f i r s t i s the adhesion occurring a t the regions o f r e a l contact. The second a r i s e s i f t h e a s p e r i t i e s on a hard surface produce grooving o r c u t t i n g i n the other. With metals t h e ploughing a c t i o n involves p l a s t i c d i s -

81 placement, w i t h b r i t t l e s o l i d s some c r a c k i n g o r f r a g m e n t a t i o n , w i t h r u b b e r s and polymers h y s t e r e s i s l o s s e s . O t h e r f a c t o r s may a l s o p l a y a p a r t i n t h e f r i c t i o n a l process, b u t e x c e p t i n s p e c i a l circumstances t h e s e a r e g e n e r a l l y o f only t e r t i a r y significance. S o l i d s t h a t deform e a s i l y and i s o t r o p i c a l l y w i l l t e n d t o g i v e v e r y h i g h c o e f f i c i e n t s o f f r i c t i o n , On t h e o t h e r hand, b r i t t l e s o l i d s w i l l g i v e r e s t r i c t e d j u n c t i o n growth and l o w e r c o e f f i c i e n t s o f f r i c t i o n . Again, s o l i d s

with w e l l - d e f i n e d a n i s o t r o p y may show a n i s o t r o p i c f r i c t i o n a l p r o p e r t i e s . T h i s i s most marked w i t h l a m e l l a r s o l i d s t h a t a r e o f t e n l o w f r i c t i o n mat e r i a l s , though t h i s i s by no

means always t h e case. W i t h v i s c o e l a s t i c

s o l i d s t h e d e f o r m a t i o n p r o p e r t i e s a r e r a t e - and temperature-dependent,

and

t h e r e i s a c o r r e s p o n d i n g v a r i a t i o n o f f r i c t i o n w i t h s l i d i n g speed and temp e r at u r e

.

A l t h o u g h d e f o r m a t i o n p r o p e r t i e s a r e i m p o r t a n t , t h e f a c t o r t h a t has t h e l a r g e s t o v e r a l l i n f l u e n c e on f r i c t i o n i s t h e c l e a n l i n e s s o f t h e s u r f a c e s .

A s m a l l t r a c e o f oxygen o r some o t h e r contaminant can r a d i c a l l y reduce t h e adhesion and f r i c t i o n . I t i s p r o b a b l e t h a t i n p r a c t i c a l a f f a i r s i n v o l v i n g t h e s l i d i n g o f u n l u b r i c a t e d metals, atmospheric c o n t a m i n a t i o n i s t h e main f a c t o r r e s p o n s i b l e f o r r e d u c i n g f r i c t i o n and wear and f o r p r e v e n t i n g t o t a l s e i z u r e . W i t h polymers and b r i t t l e m a t e r i a l s t h e s i t u a t i o n i s n o t as c l e a r l y d e f i n e d , b u t , i n g e n e r a l , s u r f a c e c o n t a m i n a t i o n has l e s s e f f e c t t h a n w i t h metals" . I n a d d i t i o n t o the discussion o f t h e f r i c t i o n force, i.e.,

the re-

s i s t a n c e t o s l i d i n g m o t i o n as d i s c u s s e d i n t h i s s e c t i o n , t h e q u e s t i o n on t h e f r i c t i o n a l energy d i s s i p a t i o n must be s t u d i e d . B e f o r e d i s c u s s i n g t h e f r i c t i o n - i n d u c e d energy d i s s i p a t i o n processes ( s e e S e c t i o n 4 . 3 . 4 ) ,

t h e me-

chanisms o f r o l l i n g f r i c t i o n f o r c e , i . e . t h e causes o f t h e r e s i s t a n c e t o r o l l i n g m o t i o n a r e reviewed i n t h e n e x t s e c t i o n .

4 , 3 , 3 ROLLING

FRICTION

R o l l i n g f r i c t i o n , a l t h o u g h i n general much s m a l l e r t h a n s l i d i n g f r i c t i o n , i s a l s o a v e r y complex phenomenon because o f i t s dependence upon so many f a c t o r s (Ref. 4.52).

C l e a r l y , t h e c o n t a c t processes, i . e . ,

t h e c o n t a c t me-

chanics and c o n t a c t p h y s i c s and c h e m i s t r y , as d i s c u s s e d i n S e c t i o n 4.2, a r e adequately v a l i d i n r o l l i n g - c o n t a c t s i t u a t i o n s . The c o n t a c t d e f o r m a t i o n i n steady r o l l i n g i s c o n v e n i e n t l y approached f r o m t h e E u l e r i a n p o i n t o f view.

82

The nominal p o i n t o f c o n t a c t i s taken as t h e o r i g i n o f c o o r d i n a t e s ; m a t e r i a l o f b o t h s o l i d s " f l o w s " s t e a d i l y through a t i m e - i n v a r i a n t s t r a i n f i e l d i n the contact region. Comparing t h e i n t e r f a c i a l k i n e m a t i c s and s t r e s s c o n d i t i o n s o f s l i d i n g f r i c t i o n , i t i s obvious t h a t t h e main reasons f o r s l i d i n g f r i c t i o n p l o u g h i n g and s h e a r i n g o f adhesive j u n c t i o n s

-

-

like

a r e n o t met i n a r o l l i n g

s i t u a t i o n . T h e r e f o r e , t h e m i c r o s c o p i c model o f s l i d i n g f r i c t i o n cannot be a p p l i e d i n o r d e r t o e x p l a i n t h e occurrence o f r e s i s t a n c e t o r o l l i n g , so t h a t o t h e r e x p l a n a t i o n s a r e needed. As i n t h e case o f s l i d i n g , any model of r o l l i n g f r i c t i o n must e x p l a i n b o t h t h e r o l l i n g f r i c t i o n f o r c e and t h e r o l l i n g - f r i c t i o n energy d i s s i p a t i o n . R o l l i n g f r i c t i o n may be c l a s s i f i e d i n t o a type, where l a r g e t a n g e n t i a l f o r c e s a r e t r a n s m i t t e d , e.g., t h e d r i v i n g wheels o f a l o c o m o t i v e , o r i n a n o t h e r t y p e where s m a l l t a n g e n t i a l f o r c e s a r e t r a n s m i t t e d , o f t e n c a l l e d " f r e e r o l l i n g " . Consider, as a s t a r t i n g p o i n t a H e r t z i a n c o n t a c t . I f a t o r q u e i s i n t r o d u c e d which causes a r o l l i f l g motion, t h e n i n a d d i t i o n t o t h e H e r t z i a n normal s t r e s s e s , t a n g e n t i a l s t r e s s e s occur, see M i n d l i n ' s t h e o r y , S e c t i o n 4.3.1.

T h i s r e s u l t s i n t h e d i v i s i o n o f t h e c o n t a c t area i n t o a

r e g i o n o f m i c r o - s l i d i n g , and r e g i o n s o f adhesion w i t h i n which t h e surfaces r o l l w i t h o u t r e l a t i v e ( s l i d i n g ) motion. As main c o n t r i b u t i o n s t o r o l l i n g r e s j s t a n c e , t h e f o l l o w i n g e f f e c t s can be l i s t e d : (a)

micro-slip (i-e., micro-sliding)

(b)

e l a s t i c hysteresis

(c)

p l a s t i c deformation

(d)

adhesion e f f e c t s

I n the following,

these d i f f e r e n t components o f f r e e - r o l l i n g f r i c t i o n w i l l

be discussed i n b r i e f . ( a ) MICRO-SLIP EFFECTS I n t h e t h e o r i e s o f m i c r o - s l i p , d i f f e r e n t cases a r e d i s t i n g u i s h e d i n t h e l i t e r a t u r e , t h e most i m p o r t a n t o f which a r e : (i)

Reynolds s l i p (Ref. 4.53) Consider a H e r t z i a n c o n t a c t o f two b o d i e s h a v i n g d i f f e r e n t e l a s t i c c o n s t a n t s . I f t h e two bodies r o l l f r e e l y t o g e t h e r t h e p r e s s u r e which a c t s on each g i v e s r i s e , i n g e n e r a l , t o unequal t a n g e n t i a l d i s p l a c e ments o f t h e s u r f a c e s l e a d i n g t o i n t e r f a c i a l s l i p processes.

83 (ii)

Heathcote s l i p ( R e f . 4.54) Consider a r o l l i n g c o n t a c t where t h e r o l l i n g element i s a b a l l which r o l l s i n s i d e a grooved t r a c k . I n t h i s case t h e p r o f i l e s may conform c l o s e l y i n t h e t r a n s v e r s e d i r e c t i o n t o t h e t r a c k on which t h e y r o l l . Due t o s u r f a c e p o i n t s l y i n g a t a p p r e c i a b l y d i f f e r e n t d i s t a n c e s f r o m t h e a x i s o f r o t a t i o n , t a n g e n t i a l t r a c t i o n s a r e i n t r o d u c e d and m i c r o s l i p e f f e c t s occur.

( i i i ) Carter-Poritsky-Foppl

s l i p (Refs. 4.55.

F o r t h e two-dimensional case (e.g.,

4.56,

4.57)

two c y l i n d e r s r o l l i n g on each

o t h e r ) w i t h a tangential force i n the d i r e c t i o n o f r o l l i n g , the m i c r o - s l i p a r e a c o u l d be c a l c u l a t e d . T h i s work l e d t o t h e i m p o r t a n t conclusion that, i n r o l l i n g ,

t h e adhesion zone i s a d j a c e n t t o t h e

l e a d i n g edge o f t h e c o n t a c t area; i n c o n t r a s t t o t h e s t a t i c problem where t h e adhesion zone i s c e n t r a l l y p l a c e d , see F i g u r e 4.17.

-driving torque

sl

F i g u r e 4.17

. s l ip

S l i p and n o - s l i p r e g i o n s i n a r o l l i n g c o n t a c t .

Tabor s t u d i e d e x p e r i m e n t a l l y t h e s l i p e f f e c t s o f t h e Reynolds and Heathcote t y p e u s i n g s t e e l b a l l s r o l l i n g i n grooved r u b b e r t r a c k s ( R e f . 4.58).

He

showed t h a t u n l e s s t h e r e i s a h i g h degree o f g e o m e t r i c a l c o n f o r m i t y , b o t h m i c r o - s l i p e f f e c t s c o n t r i b u t e o n l y v e r y l i t t l e t o t h e observed r o l l i n g f r i c t i o n f o r c e . R e c e n t l y i t was shown e x p e r i m e n t a l l y t h a t above a c r i t i c a l v a l u e o f t h e r a t i o b a l l r a d i u s rg t o groove r a d i u s rG( r g / r G

> 0.8 s a y ) ,

r o l l i n g f r i c t i o n i s p r i m a r i l y due t o a s l i d i n g mechanism ( R e f . 4 . 5 9 ) .

In

genera?, however, a c c o r d i n g t o Bowden and Tabor, r o l l i n g f r i c t i o n cannot b e t r a c e d back t o s l i d i n g f r i c t i o n v i a t h e e f f e c t o f m i c r o - s l i p s i n c e t h e r o l l i n g - f r i c t i o n c o e f f i c i e n t i s n o t reduced by l u b r i c a t i o n as i s t h e case

84

f o r t h e s l i d i n g f r i c t i o n c o e f f i c i e n t . These experiments i n d i c a t e t h a t m i c r o - s l i p may c o n t r i b u t e o n l y v e r y l i t t l e t o t h e r o l l i n g - f r i c t i o n c o e f f i c i e n t . On t h e o t h e r hand, i t i s g e n e r a l l y r e c o g n i z e d t h a t t h e e x i s t e n c e o f f r i c t i o n f o r c e s a t t h e i n t e r f a c e between r o l l i n g e l a s t i c b o d i e s r e s u l t s i n t h e d i v i s i o n o f t h e c o n t a c t area i n t o r e g i o n s o f m i c r o - s l i p , and r e g i o n s w i t h i n t h e s u r f a c e s r o l l w i t h o u t r e l a t i v e m o t i o n . Obviously, these e f f e c t s have i m p o r t a n t e n g i n e e r i n g i m p l i c a t i o n s f o r t h e t r a n s m i s s i o n o f mechanical work through a r o l l i n g c o n t a c t , as i n a f r i c t i o n d r i v e f o r example. ( b ) ELASTIC HYSTERESIS The e l a s t i c h y s t e r e s i s t h e o r y o f r o l l i n g f r i c t i o n , proposed i n 1952 by Tabor (Ref. 4.60),

assumes t h a t t h e r o l l i n g r e s i s t a n c e i s due t o t h e e l a s -

t i c h y s t e r e s i s l o s s e s i n t h e m a t e r i a l o f t h e t r a c k . I n S e c t i o n 4.2.1 i t has been shown t h a t i n t h e case o f an i d e a l H e r t z i a n c o n t a c t , a c e r t a i n amount o f energy i s needed t o b u i l d up t h e c o n t a c t zone. F o r t h e f o r m a t i o n o f an e l a s t i c a l l y deformed r o l l i n g t r a c k a c e r t a i n mechanical power i s needed. I n t h e d e f o r m a t i o n process t h e s u r f a c e s undergo c o m p l i c a t e d combined compress i o n s and t o r s i o n s . The e l a s t i c d e f o r m a t i o n energy i s r e c o v e r e d m a i n l y i n t h e c o n t a c t r e l e a s e . As a consequence o f r e l a x a t i o n e f f e c t s , however, t h e r e l e a s e d f o r c e s may be s m a l l e r t h a n t h e p r e v i o u s ones; t h e d i f f e r e n c e may be i n t e r p r e t e d as r o l l i n g - f r i c t i o n loss. The e l a s t i c h y s t e r e s i s l o s s e s o f m a t e r i a l s , b e i n g r e l a t e d t o t h e damping and r e l a x a t i o n p r o p e r t i e s o f t h e m a t e r i a l s , a r e o b v i o u s l y more pronounced f o r v i s c o e l a s t i c m a t e r i a l s t h a n f o r m e t a l s . I t has been found f o r v i s c o e l a s t i c m a t e r i a l s t h a t t h e r o l l i n g - f r i c t i o n

c o e f f i c i e n t can be r e l a t e d t o t h e r e l a x a t i o n t i m e ( o r t h e r e l a x a t i o n spectrum) o f t h e m a t e r i a l . Representing a v i s c o e l a s t i c m a t e r i a l by a s e r i e s o f para1 l e l l i n e a r Maxwell elements which undergo compression and r e c o v e r y d u r i n g r o l l i n g , i t f o l l o w s t h a t i n a s i m p l e model a t a c e r t a i n r o l l i n g vel o c i t y , which corresponds t o t h e r e t a r d a t i o n t i m e , t h e r o l l i n g - f r i c t i o n c o e f f i c i e n t e x h i b i t s a maximum ( R e f . 4.61). A t low r o l l i n g v e l o c i t i e s t h e v i s c o e l a s t i c m a t e r i a l w i l l r e c o v e r a t

the t r a i l i n g side o f the contact s u f f i c i e n t l y q u i c k l y t o maintain a f a i r l y symmetrical p r e s s u r e d i s t r i b u t i o n , so t h a t t h e r o l l i n g r e s i s t a n c e w i l l be small. A t high r o l l i n g v e l o c i t i e s the material w i l l n o t recover s u f f i c i e n t l y q u i c k l y t o even make c o n t a c t on t h e t r a i l i n g s i d e . The i n c r e a s e o f p r e s -

s u r e asymmetries w i t h i n c r e a s i n g r o l l i n g v e l o c i t i e s have been checked exp e r i m e n t a l l y w i t h o p t o - e l a s t i c techniques ( R e f . 4.62).

85

(c)

PLASTIC DEFORMATION

I t i s w e l l known t h a t i f i n a r o l l i n g c o n t a c t o f m e t a l l i c b o d i e s t h e con-

t a c t p r e s s u r e exceeds a c e r t a i n value, gross y i e l d i n g w i l l o c c u r . F o r f r e e l y r o l l i n g c y l i n d e r s y i e l d o c c u r s f i r s t a t a p o i n t beneath t h e s u r f a c e when

where pH i s t h e maximum H e r t z p r e s s u r e and p i s t h e y i e l d s t r e s s o f t h e Y m a t e r i a l i n s i m p l e shear. I n t h i s case energy i s needed t o f o r m p l a s t i c deformed r o l l i n g t r a c k . An e x a c t a n a l y s i s o f t h e p l a s t i c d e f o r m a t i o n processes i n t h e r o l l i n g o f a b a l l o v e r a p l a n e i s v e r y complicated. An approximate s o l u t i o n i s due t o Eldredge and Tabor (Ref, 4.63).

They observed t h a t i n t h e f i r s t t r a v e r s a l

a p l a s t i c deformed r o l l i n g t r a c k i s formed, and f o u n d f o r t h e r o l l i n g - f r i c t i o n f o r c e an e m p i r i c a l e x p r e s s i o n o f t h e f o r m

FN

FFoc

2/ 3

7

FN : normal l o a d

r

: b a l l radius

They e x p l a i n e d t h i s r e l a t i o n by assuming t h a t r o l l i n g r e s i s t a n c e i s m a i n l y due t o t h e p l a s t i c d e f o r m a t i o n i n f r o n t o f t h e r o l l i n g b a l l . Under w e l l defined metallographic conditions, i.e.,

i n t h e case o f r o l l i n g d e f o r m a t i o n

o f metal s i n g l e c r y s t a l s , t h e p l a s t i c d e f o r m a t i o n s can be e x p l a i n e d on t h e b a s i s o f c r y s t a l l o g r a p h i c data, such as c r y s t a l l o g r a p h i c o r i e n t a t i o n and s l i p systems ( R e f . 4 . 6 4 ) . I n r e p e a t e d r o l l i n g - c o n t a c t c y c l e s , however, t h e above y i e l d c r i t e r i o n does n o t h o l d (Ref. 4.65).

D u r i n g t h e f i r s t c o n t a c t c y c l e t h e s u r f a c e ma-

t e r i a l i s p l a s t i c a l l y compressed and r e s i d u a l compressive s t r e s s e s a c t i n g p a r a l l e l t o t h e s u r f a c e a r e i n t r o d u c e d . D u r i n g subsequent r o l l i n g c y c l e s t h e m a t e r i a l i s s u b j e c t t o t h e combined a c t i o n o f r e s i d u a l and c o n t a c t s t r e s s e s , F u r t h e r y i e l d i n g i s l e s s l i k e l y and a s t e a d y - s t a t e may be reached i n which t h e m a t e r i a l i s no l o n g e r s t r e s s e d beyond i t s e l a s t i c l i m i t . T h i s process i s known as "shakedown" and t h e maximum l o a d f o r which i t occurs

w i l l be c a l l e d t h e shakedown l i m i t , g i v e n i n p u r e r o l l i n g by

P

=

4Py

86

I f r o l l i n g c y l i n d e r s are subjected t o loads i n excess o f the shakedown

l i m i t a new type o f p l a s t i c deformation occurs. This mode o f p l a s t i c deformation i n r o l l i n g contact was f i r s t observed by Crook (Ref. 4.66) and studi e d experimentally by Hamilton (Ref. 4.61) and t h e o r e t i c a l l y by Merwin and I t consists o f forward shearing o f the surface o f each

Johnson (Ref. 4.68).

c y l i n d e r r e l a t i v e t o i t s core. The deformation i s cumulative i n the sense t h a t an equal increment o f p l a s t i c s t r a i n i s acquired w i t h each r e v o l u t i o n , I t f o l l o w s that, a t loads above the shakedown l i m i t , continuous and cumula-

t i v e p l a s t i c deformation i s observed, whereas a t loads below i t , even though some y i e l d i n g i s caused i n i t j a l l y , a f t e r a few t r a v e r s a l s the system shakes down t o an e l a s t i c cycle o f stress. Accordingly, the f r i c t i o n mechanism i s changed. (d) ADHESION EFFECTS According t o Section 4.2.2, i n r o l l i n g - c o n t a c t conditions surface forces may a c t i n the i n t e r f a c e between t h e r o l l i n g bodies. Comparing the j o i n i n g and separation o f surface elements i n r o l l i n g contacts and s l i d i n g contacts some important d i f f e r e n c e s should be noted. Due t o the d i f f e r e n c e s i n kinematics, i n r o l l i n g contact the surface elements approach and separate i n a d i r e c t i o n "normal" t o the i n t e r f a c e r a t h e r than i n a tangential d i r e c t i o n . Therefore, as described i n Section 4.3.1,

j u n c t i o n growth and dispersal o f

surface contaminants i s u n l i k e l y i n the main p a r t o f the contact area. Consequently, a t the regions w i t h i n the r o l l i n g - c o n t a c t i n t e r f a c e where no r e l a t i v e motion i n a tangential d i r e c t i o n occurs, adhesion forces may be mainl y o f the (weak) van der Waals type. Short-range forces such as strong me-

t a l l i c bonds may a c t o n l y i n micro-contacts w i t h i n the m i c r o - s l i p area. I f adhesion bonds are formed they are separated a t the t r a i l i n g end o f the r o l l i n g contact i n tension r a t h e r than i n shear as i n a s l i d i n g contact. Therefore, i n general the adhesion component o f r o l l i n g f r i c t i o n may be only a small p o r t i o n o f the f r i c t i o n resis;tance. For t h e r o l l i n g o f metals under s p e c i f i c experimental s i t u a t i o n s , however (e.g.,

d i f f e r e n t t h i n me-

t a l l i c layers on hard b a l l s ) an adhesion component can nevertheless be the dominant f a c t o r i n determining t h e order o f r o l l i n g - f r i c t i o n c o e f f i c i e n t s f o r d i f f e r e n t metal p a i r s (Ref. 4.69). A l s o the r o l l i n g contact between a glass c y l i n d e r and a smooth rubber f l a t has been successfully t r e a t e d as an adhesive j o i n t through which two cracks propagate a t the same speed, one crack continuously opening t o break the i n t e r f a c i a l j o i n t and the o t h e r c l o s i n g t o reform i t (4.70). see Figure

87

R o l l i n g f r i c t i o n on t h i s b a s i s i s t h e consequence o f adhesive h y s t e r -

4.18. esis

-

t h e energy l o s s a s s o c i a t e d w i t h f o r m i n g and b r e a k i n g an adhesive

bond.

adhesive j o i n t

F i g u r e 4.18

The c o n t a c t between a r i g i d c y l i n d e r and an e l a s t i c p l a n e c o n s i d e r e d as an adhesive j o i n t c o n t a i n i n g two c r a c k s .

Another t y p e o f adhesion t h e o r y f o r r o l l i n g f r i c t i o n was proposed b y D e r j a g u i n and Smilga (Ref. 4.71).

According t o t h i s theory, contact partners o f

d i f f e r e n t e l e c t r o n i c a f f i n i t y undergo an e l e c t r o - s t a t i c c h a r g i n g . D u r i n g r o l l i n g t h e r e i s a f l o w a charge l e a d i n g t o energy d i s s i p a t i o n . The d i s c u s s i o n o f t h e cause o f t h e r o l l i n g f r i c t i o n r e s i s t a n c e shows t h a t r o l l i n g f r i c t i o n i s a l s o a complex composite process d e t e r m i n e d b y a c o u p l e o f p r o p e r t i e s o f t h e r o l l i n g - c o n t a c t p a r t n e r s and o p e r a t i n g v a r i a b l e s . I n s p e c i a l cases, i . e . ,

under s p e c i f i c e x p e r i m e n t a l s i t u a t i o n s , i t i s pos-

s i b l e f o r one mechanism t o predominate. I t may t h e n be p e r m i t t e d t o r e l a t e the r o l l i n g - f r i c t i o n data with s p e c i f i c p r o p e r t i e s o f t h e r o l l i n g partners. I n t h e g e n e r a l case, however, t h e d i f f e r e n t mechanisms a r e superimposed. Therefore, a l l i n f l u e n c i n g parameters must be t a k e n i n t o account s y s t e m a t i c a l l y on c o n s i d e r i n g t h e whole process o f energy t r a n s m i s s i o n s and energy dissipations.

4 , 3 , 4 ENERGYTRANSMISSION

AND ENERGY DISSIPATION

Having d i s c u s s e d t h e main f r i c t i o n processes, i t i s now p o s s i b l e t o complete t h e g e n e r a l framework o f t h e processes on t h e conceptual "work p l a n e " o f a t r i b o - m e c h a n i c a l system ( s e e S e c t i o n 3 . 4 . 2 ) .

A c c o r d i n g t o F i g u r e 3.6, t h e

88

i n p u t work o f a tribo-mechanical system can o n l y be p a r t l y used as useoutput; some p a r t o f the work i s e i t h e r stored w i t h i n the system o r emitted as l o s s i n t o the environment o r t r a n s f e r r e d t o the thermal plane. I t was explained above (see Section 4.1) t h a t a transmission o f work

througH a mechanical system can be obtained o n l y through processes o f e l a s t i c deformation e i t h e r o f a bulk machine element, l i k e the s h a f t o f a s l i d i n g bearing, o r through the i n t e r f a c e o f two contacting machine elements, as i n the case o f contacting gear-teeth. These e l a s t i c deformation processes a r e r e v e r s i b l e . I n i d e a l i z e d cases, the transmission o f work through a mechanical system can be c a l c u l a t e d o r estimated using conventional techniques o f the mechanics o f s o l i d bodies. The processes by which mechanical work i s n o t transmitted through a mechanical system are, o f course, e s s e n t i a l l y i r r e v e r s i b l e . Since they are the u l t i m a t e o r i g i n o f f r i c t i o n , these processes w i l l be discussed i n the f o l l o w i n g i n order t o gain a physical p i c t u r e o f the e f f e c t s t h a t take p a r t i n the d i s s i p a t i o n o f mechanical energy i n a tribo-mechanical system. Owing t o the great complexity o f these i r r e v e r s i b l e processes i t i s only possible

so f a r t o o u t l i n e a q u a l i t a t i v e p i c t u r e o f t h e main features o f these processes. The whole course o f the " l o s s " process o f mechanical energy i n a t r i b o mechanical system can be f o r m a l l y divided i n t o three phases:

I.

I n t r o d u c t i o n o f work i n t o t h e contact zone

11.

Transformation o f work w i t h i n the contact zone --c e l as t ic de f o rma t ion

-formation

-plastic

o f r e a l area o f contact

deformation

-adhesion

111. D i s s i p a t i o n o f energy (a) Storage -generation -strain (b) Emission -phonons --c photons

o f p o i n t defects and d i s l o c a t i o n s energy storage (acoustic waves, sound) ( t r ibo-1 umi nescence)

-electrons (exo-electrons, Kramer e f f e c t ) (c) Transformation t o thermal plane -generation

o f heat and entropy

89

Phases ( I ) and ( 1 1 ) have been d e s c r i b e d i n some d e t a i l i n t h e f o r e going section i n connection w i t h the discussion o f f r i c t i o n forces. I n t h e f o l l o w i n g , t h e main processes o f t h e d i s s i p a t i o n phase (111) w i l l be considered. ( a ) STORAGE OF ENERGY I n t h e m i d d l e o f t h e 1 9 5 0 ' s i t became p o s s i b l e t o s t u d y t h e m o l e c u l a r a r r a y o f c r y s t a l l i n e b o d i e s and t h e d i s l o c a t i o n s and i m p e r f e c t i o n s i n t h i s a r r a y by u s i n g o f t h e M o i r e t e c h n i q u e i n c o n j u n c t i o n w i t h an e l e c t r o n microscope. Since on one hand, t h e p l a s t i c d e f o r m a t i o n and s h e a r i n g o f s o l i d s i s governed by i m p e r f e c t i o n s and d i s l o c a t i o n s and, on t h e o t h e r hand, most f r i c t i o n p r o cesses i n v o l v e p l a s t i c d e f o r m a t i o n processes, i t appeared obvious t o r e l a t e t h e f r i c t i o n process d i r e c t l y t o t h e d i s l o c a t i o n e f f e c t s ( 4 . 7 2 ) .

I n 1965

K o s t e t s k i and Nazarenko t r i e d t o e x p l a i n t h e Coulomb-Amontons l a w o f s l i d i n g f r i c t i o n t h r o u g h a r e l a t i o n between normal f o r c e s , f r i c t i o n f o r c e s and t h e d i s l o c a t i o n s t r u c t u r e o f t h e s o l i d s (Ref. 4.73).

They o b t a i n e d e x p e r i m e n t a l l y

f o r t h e s l i d i n g o f armco i r o n p a r a l l e l curves f o r t h e i n c r e a s e o f f r i c t i o n f o r c e and t h e l o g a r i t h m o f d i s l o c a t i o n d e n s i t y w i t h i n c r e a s i n g normal l o a d as shown i n F i g u r e 4.19. I t has now been w e l l e s t a b l i s h e d t h r o u g h d i r e c t obs e r v a t i o n s w i t h t h e t r a n s m i s s i o n e l e c t r o n microscope t h a t i n s l i d i n g c o n t a c t o f m e t a l s d i s l o c a t i o n s a r e generated ( R e f . 4.74).

h

N

200 100 60 20

'\N I

2

I

I

4

8

= f ( FN )

6

I

I

8

1

I

4

0

Load FN (kN)

F i g u r e 4.19

F r i c t i o n f o r c e and d i s l o c a t i o n d e n s i t y ( R e f . 4.73).

From t h e t h e o r y o f d i s l o c a t i o n s i t f o l l o w s t h a t t h e work p e r u n i t l e n g t h t o c r e a t e a d i s l o c a t i o n i n an i s o t r o p i c u n d i s t u r b e d medium i s g i v e n by (Ref. 4.75)

90

(edge d i s l o c a t i o n )

Gb2 AES

where

==

In

rl -

shear modulus

G

:

b

: Burgers v e c t o r

rl

:

ro : :

v

(screw d i s l o c a t i o n )

rO

core radius radius o f influence Poisson number

As an example, w i t h t h e d a t a o f copper

(G = 4 * 1010N/m 2.,

V = 0.34;

b = 2.5

- 10-lom;

r = lO-’m; 0

rl = lO-‘m)

i t follows that

A Ee

=

4.8 . lo-’ Jm-I

I f t h i s v a l u e i s compared w i t h t h e f r i c t i o n a l energy measured under e x p e r i mental c o n d i t i o n s which a r e comparable w i t h t h e c o n d i t i o n s o f t h e estimat i o n o f AEe, i t was found t h a t t h e s t o r e d e l a s t i c energy i n a c o n d i t i o n o f i n c i p i e n t p l a s t i c i t y can o n l y account f o r l e s s t h a n 1%o f t h e energy expended i n f r i c t i o n (Ref. 4.76). A s i m i l a r r e s u l t was a l s o found i n c o n d i t i o n s o f more severe p l a s t i c - d e f o r m a t i o n c o n d i t i o n s o f s l i d i n g (Ref. 4.77). T h i s may be due t o t h e f a c t t h a t i n t h e p l a s t i c - d e f o r m a t i o n mode t h e d i s l o c a t i o n s generated would n o t have remained i n t h e s u r f a c e a f t e r t h e passage o f t h e s l i d i n g c o u n t e r f a c e and t h e energy would appear as h e a t ( i . e . , t r a n s f o r m e d t o t h e thermal p l a n e o f t h e t r i b o l o g i c a l system). These r e s u l t s i n d i c a t e t h a t some p a r t o f t h e f r i c t i o n a l energy i s indeed s t o r e d w i t h i n t h e s l i d i n g p a r t n e r v i a a d i s l o c a t i o n mechanism. Since t h i s s t o r e d energy i s o b v i o u s l y o n l y a small p a r t o f t h e whole f r i c t i o n a l energy, i n general o t h e r d i s s i p a t i o n mechanisms must a l s o be considered.

91

(b)

EMISSION OF ENERGY (OTHER THAN THERMAL)

I n the microscopic model of f r i c t i o n i t has been explained t h a t during s l i d i n g o r r o l l i n g , micro-contacts are formed and destroyed. These processes are s t a t i s t i c a l l y d i s t r i b u t e d i n time and l o c a t i o n w i t h i n the geometric area o f contact. I t i s l i k e l y t h a t i n the process o f j u n c t i o n formation some o f the a s p e r i t i e s o r some p a r t o f them are deformed e l a s t i c a l l y . I f then the j u n c t i o n s are destroyed and the adhesion bonds are broken, the e l a s t i c deformed p a r t s of the a s p e r i t i e s snap a p a r t thus generating v i b r a t i o n s and o t h e r l a t t i c e s t i m u l a t i o n s which lead t o the emission o f energy i n d i f f e r e n t forms. I n s o l i d s t a t e physics, d i f f e r e n t processes o f the transformation o f energy i n t o apparently o t h e r forms are known (e.g.,

the

p h o t o e l e c t r i c e f f e c t o r thermoionic emission). I n analogy, the main " t r i b o induced" energy emission e f f e c t s which have been observed experimentally are sketched i n b r i e f ( t h e effect o f heat generation i s t r e a t e d separately be1ow). ( i ) Emission o f phonons (acoustic waves, sound) The generation of f r i c t i o n - i n d u c e d acoustic waves ( c o n s i s t i n g o f phonons) and the emission of sound i s a common f e a t u r e o f most t r i b o l o g i c a l processes. Since noise i s considered as an "acoustic p o l l u t a n t " the reduction o f noise emission i s an important task i n today's i n d u s t r y (Ref. 4.78). Physically, the generation of sound i n tribo-mechanical systems i s connected w i t h processes o f e l a s t i c deformation and release o f a s p e r i t i e s . A theory o f n a t u r a l normal micro-vibrations i n s l i d i n g c o n t a c t was p u t forward by T o l s t o i (Ref. 4.79).

He showed t h a t the s e l f - e x c i t e d micro-vibrations d u r i n g

s l i d i n g are i n v a r i a b l y accompanied by simultaneous upward jumps o f asperit i e s . The frequency o f the n a t u r a l micro-vibrations i s determined by the contact s t i f f n e s s and the mass o f the s l i d i n g surface. These micro-vibrations vanish o n l y when the normal v i b r a t i o n s are damped by external means o r when the v e l o c i t y i s lower than a c e r t a i n l i m i t . The value o f the c r i t i c a l veloc i t y , vcr,

may be roughly estimated i n terms o f the creep v i s c o s i t y , q ,

the rubbing s o l i d s , t h e i r y i e l d strength, d and both the height, y, and spacing 1,

the f r i c t i o n c o e f f i c i e n t , f, Y' o f the surface a s p e r i t i e s :

For the s l i d i n g of conventional s t e e l surfaces i t f o l l o w s t h a t vcr = 5

*

'cm/s.

of

This very low value i n d i c a t e s t h a t i n almost any

92

s l i d i n g s i t u a t i o n a c e r t a i n amount o f t h e mechanical energy i s d i s s i p a t e d through t h e g e n e r a t i o n o f v i b r a t i o n and t h e f o l l o w i n g e m i s s i o n o f a c o u s t i c waves. The a b s o l u t e amount o f energy e m i t t e d i s , however, u s u a l l y o n l y a v e r y small p a r t o f t h e whole f r i c t i o n a l energy. ( i i ) Emission o f photons ( t r i b o - l u m i n e s c e n c e ) The e f f e c t o f tribolurninescence i s w e l l known i n p h y s i c s . I t occurs i f c e r t a i n s o l i d bodies, such as u r a n - n i t r a t e o r ZnSMn, a r e rubbed a g a i n s t each o t h e r . I n t h i s case, t h e mechanical work which separates adhesion bonds a c t i v a t e s photons which a r e e m i t t e d as v i s i b l e l i g h t . T h i s e f f e c t i s n o t r a r e : so f a r i t has been observed i n more t h a n a thousand m a t e r i a l s (Ref. 4.80). A complete t h e o r e t i c a l e x p l a n a t i o n o f t h i s e f f e c t i s s t i l l needed.

Some o b s e r v a t i o n s s u p p o r t t h e assumption t h a t i n t h e s u r f a c e c r a c k s o f t h e c r y s t a l s , e l e c t r o s t a t i c d o u b l e - l a y e r s e x i s t w h i c h cause a k i n d o f spark d i s c h a r g i n g i f t h e s u r f a c e c r a c k s a r e c l e a v e d d u r i n g t h e f r i c t i o n process. O b v i o u s l y some p a r t o f t h e f r i c t i o n a l mechanical energy a c t s as a c t i v a t i o n energy and i s

-

v i a a m e c h a n o - e l e c t r o - o p t i c a l t r a n s f o r m a t i o n mechani sin

-

e m i t t e d as o p t i c a l r a d i a t i o n . C l e a r l y , i f i t occurs, t h i s e f f e c t a l s o consumes o n l y a s m a l l p a r t o f t h e whole f r i c t i o n a l energy. ( i i i ) Emission o f e l e c t r o n s ( e x o - e l e c t r o n emission, EEE, Kramer e f f e c t ) A t t h e end o f t h e 1 9 4 0 ' ~Kramer ~ a t t h e P h y s i k a l i s c h - T e c h n i s c h e Bundesan-

s t a l t (PTB) observed t h a t e l e c t r o n s a r e e m i t t e d f r o m f r e s h l y abraded met a l l i c s u r f a c e s . Kramer i n i t i a l l y t h o u g h t t h a t these e l e c t r o n s were due t o e x o t h e r m i c processes o c c u r r i n g a t t h e s u r f a c e . I t i s assumed t h a t t h e f r i c t i o n process a c t s as an a c t i v a t i o n process f o r t h e emission o f e x o - e l e c t r o n s and t h a t some a n a l o g i e s between EEE and o t h e r emission e f f e c t s l i k e l u m i nescence, f i e l d emission and photoemission e x i s t . However, owing t o t h e c o m p l e x i t y o f t h e sequence o f events i n v o l v e d i n t h e whole process, a comp l e t e t h e o r y o f t h e EEE e f f e c t i s n o t y e t a v a i l a b l e . Recent e x p e r i m e n t a l work on t h e EEE o f a clean, annealed magnesium s i n g l e c r y s t a l s u r f a c e , p e r formed i n UHV, v e r i f i e s t h a t e l e c t r o n e m i s s i o n occurs a l r e a d y f r o m a s t r a i n f r e e surface s i m p l y upon a d s o r p t i o n o f oxygen (Ref. 4.81).

On t h e o t h e r

hand, measurements o f EEE r a t e s d u r i n g f r i c t i o n experiments on aluminium s u r f a c e s show t h a t t h e r e a r e c l o s e connections between t h e e m i s s i o n r a t e o f e x o - e l e c t r o n s , t h e c o m p o s i t i o n o f t h e topmost s u r f a c e l a y e r s and t h e f r i c t i o n c o e f f i c i e n t ( R e f . 4.82)..An

example o f t h e c o r r e l a t i o n between t h e EEE

r a t e and t h e f r i c t i o n c o e f f i c i e n t f o r t h e s l i d i n g o f aluminium a g a i n s t aluminium i s shown i n F i g u r e 4.20.

Although i n t h e whole energy b a l a n c e of

a t r i b o - m e c h a n i c a l system t h e energy " l o s s " due t o t h e e m i s s i o n o f exo-

93 e l e c t r o n s i s o n l y a very small p a r t , i t i s obvious t h a t i f exo-electrons are generated they may p l a y an important r o l e f o r the tribo-chemical processes o c c u r r i n g i n the system.

I

Revolution o f d i s c CI

c s

I

I

40

80

I

I

120

160

S l i d i n g distance 1 Figure 4.20

(mn)

F r i c t i o n c o e f f i c i e n t and exo-electron emission r a t e (Ref. 4.82).

I n summary, discussion of the e f f e c t s (i), ( i f ) , (iii) shows t h a t t h e r e are some t r i b o - i n d u c e d emission processes t h a t must be i n c l u d e d i n t h e whole p i c t u r e o f the d i s s i p a t i o n o f energy i n a t r i b o l o g i c a l system. Although these t r i b o - i n d u c e d processes are p h y s i c a l l y very i n t e r e s t i n g and may i n c e r t a i n cases be very important f o r t h e t r i b o - c h e m i c a l processes o c c u r r i n g i n t h e system,in general, they account f o r o n l y a very small p a r t

o f the whole energy d i s s i p a t e d .

94

( c ) TRANSFORMATION

TO THERMAL PLANE

The discussion o f energy d i s s i p a t i o n mechanisms h i t h e r t o has shown t h a t there are some processes o f storage and emission o f energy ( o t h e r than thermal) t h a t c o n t r i b u t e t o the consumption o f energy i n f r i c t i o n . Since these c o n t r i b u t i o n s , i n general, are very small, t h i s r a t h e r d e t a i l e d cons i d e r a t i o n o f the various processes also leads t o the conclusion t h a t nearl y a l l the energy dissipated by f r i c t i o n appears as heat. Indeed, t h i s has

been known from ancient times and i s the basis o f the mechanical equivalent o f heat. From the microscopic model o f f r i c t i o n i t i s obvious t h a t a l l t h e processes involved i n the formation and separation o f a s p e r i t y micro-cont a c t s lead t o l a t t i c e d i s t o r s i o n s and v i b r a t i o n s which manifest as heat. I n the general theory o f t r i b o l o g y the generation o f heat i n f r i c t i o n i s expressed as a transformation o f work t o the conceptual thermal plane o f the system (see Section 3.4.3).

Clearly, the h e a t generated i n f r i c t i o n may

e i t h e r remain w i t h i n the system ( a c t i n g perhaps as a c t i v a t i o n energy f o r material changes or chemical reactions) or leave t h e system through convection, conduction o r r a d i a t i o n .

An important f e a t u r e o f the generation o f heat i s the increase o f temperature o f the m a t e r i a l elements o f a t r i b o l o g i c a l system. Since the i n creased temperature and the temperature gradients i n t u r n i n f l u e n c e the mat e r i a l properties o f the f r i c t i o n partners and a c t i v a t e t r i b o l o g i c a l processes, the knowledge o f tribo-induced temperatures i s o f paramount i m portance i n t r i b o l o g y . I n the tribo-induced temperature r i s e s we must distinguished between :

( i ) a b u l k temperature r i s e (ii) temperature gradients (ii i) l o c a l temperature r i s e s o r " f l a s h temperatures" Theoretical treatments o f the f l a s h temperature problem were performed by Carslaw and Jaeger (Ref. 4.83), Holm (Ref. 4.84) and Blok (Ref. 4.85). These theories were combined and s i m p l i f i e d by Archard (Ref. 4.86).

Owing

t o the great importance of t h i s theory t o many t r i b o l o g i c a l s i t u a t i o n s , the main r e s u l t s o f t h i s theory w i l l be sketched i n b r i e f . The model used i n Archard's treatment i s shown i n Figure 4.21. A surface a s p e r i t y o f body (1) forms a c i r c u l a r area o f contact A =

n a2, which

moves w i t h a v e l o c i t y v over the f l a t surface o f body ( 2 ) . The temperatures are c a l c u l a t e d on t h e assumption t h a t t h e heat i s generated a t the t r u e area o f contact and t h a t t h i s heat i s conducted away i n t o t h e b u l k o f the rubbing members.

95

A’

F i g u r e 4.21

Model o f a s l i d i n g a s p e r i t y

The t h e o r y f i r s t l y r e q u i r e s t h e s o l u t i o n o f t h e e q u a t i o n s f o r t h e f l o w o f h e a t i n t o each body. The d e r i v e d s u r f a c e temperatures a r e expressed i n terms o f t h e r a t e o f s u p p l y o f h e a t , t h e s i z e and speed o f t h e h e a t source, and

t h e thermal p r o p e r t i e s o f t h e m a t e r i a l . Secondly, t h e p r o p o r t i o n o f t h e t o t a l h e a t f l o w i n g i n t o each body i s t h e n determined by t h e c r i t e r i o n t h a t t h e e q u a t i o n o f h e a t f l o w f o r b o t h bodies s h a l l g i v e t h e same average t e m p e r a t u r e o v e r t h e c o n t a c t area. Depending on t h e o p e r a t i n g c o n d i t i o n s o f l o a d FN and speed v, t h e n a t u r e o f m a t e r i a l s and t h e d e f o r m a t i o n mode, d i f f e r e n t f o r m u l a e have been d e r i v e d . F o r t h e case o f p l a s t i c a s p e r i t y d e f o r m a t i o n o f b o d i e s o f t h e same m a t e r i a l u s i n g t h e a b b r e v a t i o n s f

Tw3Ppy

N =

9

J P C

:

f r i c t ion c o e f f ic i e n t

:

a c c e l e r a t i o n due t o g r a v i t y

PY :

J

:

f l o w o r y i e l d pressure mechanical e q u i v a l e n t o f h e a t

P :

density

c

s p e c i f i c heat

:

X :

thermal d i f f u s i v i t y

k

thermal c o n d u c t i v i t y

:

( x =-)k

PC

i t f o l l o w s t h a t t h e maximum f r i c t i o n - i n d u c e d temperature r i s e A T i s g i v e n by

the f o l l o w i n g expressions:

A Tmax

=

0.25 NL

A Tmax

=

0.25

CINL

for L

-= 0 . 1

f o r 0 . 1 L~ < 5 (C1

=

0.95 a t L = 0.1

C1

=

0.5 a t L = 5 )

96

A Tmax

=

0.435 C2NL 1/2

f o r 5 c L c 100 (C2 = 1/ [l

A Tmax

=

0.87 L-”‘])

f o r L > 100

0.435 NL

The a p p l i c a t i o n s o f these r e I1

+

S

0

carbon s t e e l w i t h a hardness o f V.P.N

he example o f a s l i d i n g p a i r o f p i i n

150, 250 and 850 i s shown i n F i g u r e

4.22.

lo4 T/ f

F i g u r e 4.22

Maximum a t t a i n a b l e f l a s h temperatures f o r s l i d i n g contacts o f s t e e l , ( a ) : V.P.N., 150. ( b ) : V.P.N., 250. 850. (Ref. 4.86) ( c ) : V.P.N.,

I n a d d i t i o n t o t h e temperature r i s e w i t h i n a f r i c t i o n a l i n t e r f a c e , the d i s t r i b u t i o n o f h e a t t o t h e two i n t e r a c t i n g bodies i s important. C l e a r l y , t h e d i s t r i b u t i o n depends n o t o n l y on t h e o p e r a t i n g parameters and the m a t e r i a l s p r o p e r t i e s b u t a l s o on t h e geometry o f both bodies (Ref. 4.87). For a system c o n s i s t i n g of two bodies o f equal kinematics and geometry i t has been proposed t h a t the f r i c t i o n a l heat i s d i s t r i b u t e d between t h e two bodies according t o the f a c t o r (thermal c o n d u c t i v i t y x s p e c i f i c heat x density)’I2

of b o t h bodies (Ref. 4.88).

97

The d i s c u s s i o n o f t h e whole c y c l e o f introduction-transformationd i s s i p a t i o n o f work i n a t r i b o - m e c h a n i c a l system shows t h e m a n i f o l d o f processes and e f f e c t s i n v o l v e d i n f r i c t i o n . A l t h o u g h w i t h t h e contemporary techniques o f e x p e r i m e n t a t i o n i t i s p o s s i b l e t o s t u d y a s i n g l e i s o l a t e d e f f e c t , i n g e n e r a l t h e r e i s an o v e r l a p and an i n t e r a c t i o n o f t h e d i f f e r e n t processes. The d e t a i l e d d i s c u s s i o n as performed i n t h e l a s t s e c t i o n s has provided a basis f o r the compilation o f the p r o p e r t i e s o f m a t e r i a l s r e l e v a n t t o t h e d i f f e r e n t s t e p s o f t h e t r a n s m i s s i o n and d i s s i p a t i o n o f energy. These p r o p e r t i e s b e l o n g t o d i f f e r e n t c l a s s e s a c c o r d i n g t o t h e i r r e l e v a n c e t o the d i f f e r e n t interactions occurring a t the interface i n a t r i b o l o g i c a l sys tem:

( a ) P r o p e r t i e s " p e r se"

-

volume p r o p e r t i e s : geometry, dimensions, chemical c o m p o s i t i o n s u r f a c e p r o p e r t i e s : s u r f a c e topography, s u r f a c e c o m p o s i t i o n

( b ) Properties r e l e v a n t t o tribo-mechanical i n t e r a c t i o n s

-

e l a s t i c i t y , p l a s t i c i t y , e l a s t o v i s c o s ity

( c ) Properties r e l e v a n t t o tribo-chemical i n t e r a c t i o n s

-

r e a c t i v i t y w i t h t h e environment

(d) Properties relevant t o tribo-physical

-

interactions

adhesion, t r a n s p o r t p r o p e r t i e s

A data sheet t o a s s i s t i n the compilation o f the r e l e v a n t p r o p e r t i e s o f f r i c t i o n p a i r s i s g i v e n i n Chapter 8.

4,4 WEAR PROCESSES 4,4 1 GENERAL I

DESCRIPTION

I n t h e f o r e g o i n g s e c t i o n d e a l i n g w i t h f r i c t i o n processes, t h e t r a n s a c t i o n s on t h e work p l a n e and t h e thermal p l a n e o f a t r i b o - m e c h a n i a l system have been d i s c u s s e d a c c o r d i n g t o t h e t r i b o - p r o c e s s diagram, F i g u r e 3.4.

I n order

t o complete t h e conceptual framework o f t h e t r i b o l o g y o f mechanical systems as o u t l i n e d i n F i g u r e 3.4 f u r t h e r , t h e t r a n s a c t i o n s on t h e m a t e r i a l s p l a n e s must be s t u d i e d i n c o n n e c t i o n w i t h t h e r e l e v a n t wear processes. Comparing f r i c t i o n w i t h wear, depending on t h e t e c h n i c a l f u n c t i o n o f t h e tribo-mechan i c a l system under c o n s i d e r a t i o n , b a s i c d i f f e r e n c e s between f r i c t i o n and wear processes must be n o t i c e d . According t o Table 3.2, t h e v a r i o u s t r i b o mechanical systems can be c l a s s i f i e d b r o a d l y i n t o two d i f f e r e n t groups:

98

(a)

A f i r s t group i n which t h e main i n p u t s and o u t p u t s o f t h e system a r e g i v e n by p h y s i c a l ( i . e . ,

n o n - m a t e r i a l ) q u a n t i t i e s , headed by t h e terms

motion, work and i n f o r m a t i o n . (b)

A second group i n which t h e main i n p u t s and o u t p u t s a r e g i v e n by a f l o w o f m a t e r i a l s through t h e system, as i n t h e case o f a w i r e d r a w i n g system.

According t o t h e d e f i n i t i o n o f wear as " t h e p r o g r e s s i v e l o s s o f substance from t h e o p e r a t i n g s u r f a c e o f a body o c c u r r i n g as a r e s u l t o f r e l a t i v e m o t i o n a t t h e s u r f a c e " i t f o l l o w s t h a t i n case ( b ) wear may be seen as a process which l e a d s t o a l o s s o f a m a t e r i a l i n p u t q u a n t i t y o f t h e system. I n these cases, m a t e r i a l l o s s e s due t o wear may be t r e a t e d f o r m a l l y i n analogy t o energy l o s s e s due t o f r i c t i o n . On t h e c o n t r a r y , f o r systems o f group ( a ) , which w i l l be c o n s i d e r e d m a i n l y i n t h i s s e c t i o n , t h e t e c h n i c a l l y r e l e v a n t i n p u t and use-output q u a n t i t i e s a r e e s s e n t i a l l y n o n - m a t e r i a l . Therefore, i n t h i s case wear l e a d s t o p r o p e r t y changes and l o s s e s from t h e elements o f t h e system. To r e p e a t t h i s e v i d e n t b u t i m p o r t a n t p o i n t : f r o m a systems p o i n t o f view, f r i c t i o n i s a process which l e a d s t o l o s s e s from t h e i n p u t q u a n t i t i e s o f t h e system whereas wear i s a process which l e a d s t o l o s s e s f r o m t h e elements o f t h e system. Therefore, f r i c t i o n i n f l u e n c e s p r i m a r i l y t h e i n p u t - o u t p u t r e l a t i o n s ( i .e.,

the function of the

system) whereas wear p r i m a r i l y i n f l u e n c e s o r changes t h e p r o p e r t i e s o f t h e elements o f t h e system ( i . e . ,

t h e s t r u c t u r e o f t h e system). I n t h e f o l l o w -

i n g , t h e main wear processes r e l e v a n t t o t r i b o - m e c h a n i c a l systems o f group ( a ) w i 11 be discussed. Consider, as a s t a r t i n g p o i n t , t h e d r y wear o f metals o c c u r r i n g i n a s i m p l e t r i b o - m e c h a n i c a l system c o n s i s t i n g o f t h e p a r t n e r s

(1) One machine element (2)

A second machine element

(3)

The i n t e r f a c i a l volume (gaseous atmosphere)

F o r example, such a system may be g i v e n by t h e c o n f i g u r a t i o n shown schemat i c a l l y i n F i g u r e 4.23 i n which t h e s u r f a c e s o f (1) and ( 2 ) s l i d e a g a i n s t each o t h e r i n a i r ( 3 ) under a normal l o a d FN w i t h a s l i d i n g v e l o c i t y v. Consider now t h e wear processes t h a t t a k e p l a c e on one o f t h e two p a r t n e r s , say on element (1). A c c o r d i n g t o F i g u r e 3.8 t h e m a t e r i a l l o s s e s due t o t h e wear processes may be d e s c r i b e d as: (i)

m a t e r i a l t r a n s f e r f r o m (1) t o ( 2 )

(ii)

m a t e r i a l loss f r o m (1) t o ( 3 )

( i i i ) formation o f reaction products

99

(There may be b a c k - a n d - f o r t h r e a c t i o n s between t h e elements

(l), ( 2 ) , ( 3 ) ;

these w i l l be c o n s i d e r e d below i n S e c t i o n 4 . 4 . 6 ) .

wear processes (see F i g . 4.24)

systems envelope

F i g u r e 4.23

A s i m p l e t r i b o - m e c h a n i c a l system.

Depending on t h e amount o f m a t e r i a l which i s l o s t f r o m element ( l ) , t h e wear may be b r o a d l y c l a s s i f i e d as " m i l d wear" o r " s e v e r e wear". O b v i o u s l y t h i s c l a s s i f i c a t i o n can be r e l a t e d t o t h e c o m p o s i t i o n o f t h e s u r f a c e , ( F i g u r e 4.5).

I n m i l d wear, t h e wear processes o c c u r a t t h e " o u t e r " s u r f a c e

l a y e r s . The s u r f a c e s remain r e l a t i v e l y smooth and a r e u s u a l l y p r o t e c t e d by s u r f a c e o x i d e l a y e r s generated i n r u b b i n g . The worn d e b r i s c o n s i s t s o f s m a l l p a r t i c l e s down t o some nm. I n severe wear, t h e c o n t a c t i s m e t a l l i c , t h e s u r f a c e s a r e deeply t o r n , and t h e worn d e b r i s c o n s i s t s o f m e t a l l i c p a r t i c l e s up t o some 100 pm. C l e a r l y , t h e c l a s s i f i c a t i o n o f wear i n t o " m i l d " and " s e v e r e " i s primarily a d i s t i n c t i o n i n the scale o f size.

A s i n t h e case o f s l i d i n g f r i c t i o n , t h e r e a r e some "macroscopic r u l e s " o f t h e wear o f m e t a l s under d r y s l i d i n g c o n d i t i o n s which have been e x p e r i m e n t a l l y observed i n s t e a d y - s t a t e s i t u a t i o n s , p r o v i d e d t h e " n a t u r e " o f s u r faces does n o t change:

I.

The wear r a t e w, i . e . t h e volume V o f m a t e r i a l removed p e r u n i t s l i d i n g 1 i s p r o p o r t i o n a l t o t h e normal l o a d FN

11. The wear r a t e w i s independent o f t h e apparent area o f c o n t a c t .

100

I n o r d e r t o e x p l a i n these macroscopic r u l e s , a microscopic model o f t h e wearing process s i m i l a r t o t h a t used i n t h e d i s c u s s i o n o f t h e f r i c t i o n process ( F i g u r e 4.15) may be considered. C l e a r l y , t h e processes o c c u r r i n g between i n t e r a c t i n g a s p e r i t i e s so on

-

l i k e e l a s t i c and p l a s t i c def ormat ion, and

-

as d is c us s e d i n t h e f o r e g o i n g s e c t i o n s , n u s t s i m i l a r l y be t aken i n t o account i n any m i c r o s c o p i c model o f t h e wear krocess, I n F i g u r e 4.24

a schematic r e p r e s e n t a t i o n o f a u n i t e v e n t o f t h e wea; process i s shown.

F i g u r e 4.24

Schematic r e p r e s e n t a t i o n o f a u n i t event i n t h e wear process,

There have been s e v e r a l a t t e m p t s ( s e e S e c t i o n 1.2.2)

t o d e r i v e formulae

expre s s ing t h e macroscopic obseryed wear r u l e s mentioned above. The essent i a l concept as summarized by Archard (Ref. 4.89) i s t h a t t h e worn volume V , produced i n s l i d i n g a d i s t a n c e 1, can be r e l a t e d t o t h e t r u e

-

area o f c o nt a c t , Ar.

-

I t i s u s u a l l y assumed t h a t t h e u n i t event which must

be c ons idere d i s t h e c o n t a c t o f two a s p e r i t i e s on t h e opposing surf aces.

101 As i d e a l i z e d i n F i g u r e 4.24,

t h e u n i t e v e n t i s concerned w i t h t h e e s t a b -

l i s h m e n t o f an area o f c o n t a c t c o n s i d e r e d t o be a c i r c l e o f r a d i u s , a, and 2 area A A = TC a . I f i t i s assumed t h a t i n s l i d i n g a d i s t a n c e A 1 = 2a a h e m i s p h e r i c a l p a r t i c l e o f r a d i u s a and volume A V = 2 / 3 n a 3 i s generated it follows that

Archard has suggested t h a t n o t e v e r y u n i t e v e n t r e s u l t s i n t h e f o r m a t i o n

o f a wear p a r t i c l e . I n t r o d u c i n g a f a c t o r K which r e p r e s e n t s t h e p r o b a b i l i t y t h a t any g i v e n e v e n t w i l l produce a worn p a r t i c l e and summing f o r a l l m i c r o c o n t a c t s , t h e t o t a l wear r a t e i s

!!

=

?1K A r

1 I t has been shown above t h a t , depending on t h e d e f o r m a t i o n mode, t h e f o l l o w i n g r e l a t i o n s between t h e r e a l area o f c o n t a c t , Ar,

and t h e normal l o a d FN

exist:

-

e l a s t i c deformation ( p l a s t i c i t y index $ < 0.6) Ar

-

a

FN -

E

E

:

composite e l a s t i c modulus

p l a s t i c d e f o r m a t i o n ( p l a s t i c i t y index $ >1)

Ar

DC

tN PY

py : y i e l d p r e s s u r e

From these r e l a t i o n s i t f o l l o w s t h a t t h e p r o p o r t i o n a l i t y

e x i s t s , as observed e x p e r i m e n t a l l y i n many s i t u a t i o n s o f t h e d r y wear o f m e t a l s 'under s t e a d y - s t a t e c o n d i t i o n s . I n t r y i n g t o d e s c r i b e s y s t e m a t i c a l l y t h e v a r i o u s wear processes t h a t may o c c u r i n a t r i b o - m e c h a n i c a l system a c o u p l e o f severe d i f f i c u l t i e s a r i s e These a r e n o t o n l y due t o t h e g r e a t c o m p l e x i t y o f wear processes b u t a l s o t o t h e i m p r e c i s e and ambiguous use o f t h e t e r m wear. F o r example, t h e t y p e

102 of wear o f an u n l u b r i c a t e d metal p a i r s l i d i n g i n a d u s t y atmosphere may be termed d r y wear o r m e t a l l i c wear o r s l i d i n g wear o r s c r a t c h i n g wear o r a b r a s i v e wear depending on t h e emphasis intended. Since most o f t h e i m p r e c i s e wear terms i n common use a r e connected w i t h p r a c t i c a l wear problems, a wear c l a s s i f i c a t i o n scheme i s needed which m a i n t a i n s t h e known terms b u t a v o i d s ambig u i t y . I n t h e r e v i e w o f t h e h i s t o r i c a l development o f wear s t u d i e s , S e c t i o n

1.2.2,

two wear c l a s s i f i c a t i o n schemes have been a l r e a d y mentioned:

(a)

C l a s s i f i c a t i o n i n r e l a t i o n t o t h e t y p e o f r e l a t i v e motion, suggested

(b)

C l a s s i f i c a t i o n i n r e l a t i o n t o t h e t y p e o f wear mechanism, suggested

i n 1938 by S i e b e l (Ref. 1.22). i n 1957 by B u r w e l l ( R e f . 1.26). Comparing these wear t e r m i n o l o g i e s w i t h t h e t e r m i n o l o g y used i n t h e f i e l d o f t h e b u l k s t r e n g t h o f m a t e r i a l s , t h e c l a s s i f i c a t i o n ( a ) can be seen i n analogy t o t h e t y p e o f " e x t e r n a l s t r e s s " (e.g.,

compression, t e n s i o n , bend-

ing, e t c . ) and t h e c l a s s i f i c a t i o n ( b ) can be seen i n analogy t o t h e t y p e o f t h e mechanism o f " i n t e r n a l damage" (e.g.,

d u c t i l e fracture, b r i t t l e frac-

ture, etc.). From a system's p o i n t o f view, t h e wear l o s s - o u t p u t o f a g i v e n t r i b o mechanical system should be r e l a t e d t o t h e i n p u t s o f t h e system (e.g.,

type

o f motion, work) as w e l l as t o t h e s t r u c t u r e o f t h e system ( s y s t e m ' s e l e ments, p r o p e r t i e s o f t h e elements, i n t e r r e l a t i o n s between t h e elements). Combining these requirements w i t h t h e e x i s t i n g c l a s s i f i c a t i o n s ( a ) and ( b ) , f o r an unequivocal c h a r a c t e r i z a t i o n o f wear, t h e f o l l o w i n g c h a r a c t e r i s t i c s should be s p e c i f i e d : (i) (ii)

t h e t y p e o f r e l a t i v e motion, t h e i n t e r a c t i n g elements,

( i i i ) t h e dominant wear mechanism. Obviously, t h e c o m b i n a t i o n o f t h e s e t h r e e c h a r a c t e r i s t i c s s p e c i f i e s t h e " t y p e " of wear. F o r a more q u a n t i t a t i v e c h a r a c t e r i z a t i o n , i n a d d i t i o n t h e f o l l o w i n g c h a r a c t e r i s t i c s s h o u l d be s p e c i f i e d : (iv)

t h e i n p u t work: normal l o a d , f r i c t i o n c o e f f i c i e n t , d i s t a n c e o f motion ( a t s t a t e d v e l o c i t y ) ,

103

I n t e r a c t ing elements

mechanisms

r e 1 a t ive

stress

stress

material

inter-

inter-

actions

actions

‘7

(metals, polymers,

A-

sliding

p1

minerals, etc. ) or with

0

lubricants

2%

soli d / l iquid

impact

-L

0

flow

Table 4.2

C,v

LT

s l i d i n g wear

I

I

r o l l i n g wear

I

I

i m p a c t wear

I

f r e t t i n g wear

c a v i t a t i o n wear

I flow

particles

lu

-a

I

s o l id/ f 1u i d

+

lu

n

I o s c i 11a t i o n

I\ /I

f l u i d erosion

C h a r a c t e r i z a t i o n o f wear.

I

Wear mechanisms

I

Appearance o f t h e worn s u r f a c e s

I

I

Surface f a t i g u e

I

cracks, p i t s

I

Abrasion

s c r a t c h e s , grooves, s t r i a t i o n s

Adhesion

cones, f l a k e s , p i t s

T r i bochemical

r e a c t i o n products ( f i l m s , p a r t i c l e s )

Table 4.3

Appearances o f worn s u r f a c e s .

v

8 2 .-aJ

I

7

without

lu

G -c

I rolling

I

m L

v)

LC,

7

0 .?

0

v 3 lum v- .7 z+lu m4-

solid/solid

c

S

aJw

motion

+

mainly

104 (v)

t h e m a t e r i a l p r o p e r t i e s r e l e v a n t t o wear,

(vi)

t h e wear r a t e

( v i i ) t h e appearance o f t h e worn s u r f a c e s . I n Table 4.2 a c l a s s i f i c a t i o n scheme which t r i e s t o combine t h e above c h a r a c t e r i s t i c s ( i ) , ( i i ) , ( i i i ) i s shown. I n t h i s t a b l e , t h e t y p e s of wear a r e termed a c c o r d i n g t o t h e t y p e o f r e l a t i v e m o t i o n i n analogy t o t h e c l a s s i f i c a t i o n o f f r i c t i o n modes. ( T h i s i s t h e most e v i d e n t way o f d i s t i n g u i s h i n g between d i f f e r e n t types o f wear s i n c e i n p r a c t i c a l e n g i n e e r i n g s i t u a t i o n s t h e a c t u a l i n t e r f a c i a l wear processes a r e seldom easy t o d e t e c t . )

I n mechanical e n g i n e e r i n g , t h e wear o f t h e components o f t r i b o - m e c h a n i c a l systems i s connected w i t h f o u r b a s i c t y p e s o f r e l a t i v e motion: s l i d i n g , r o l l i n g , impact, o s c i l l a t i o n . I t has been found t h a t t h e i n t e r f a c i a l wear mechanisms a c t i n g d u r i n g these motions can be c l a s s i f i e d i n t o f o u r groups under t h e headings: s u r f a c e f a t i g u e , abrasion, adhesion, t r i b o - c h e m i c a l

.

As i n d i c a t e d i n Table 4.2 i n any o f t h e d i f f e r e n t types o f r e l a t i v e m o t i o n one o r more o f t h e f o u r b a s i c wear mechanisms may a c t . I n p r a c t i c e i t i s o f t e n d i f f i c u l t t o determine what t y p e o f i n t e r f a c i a l wear mechanism ( o r what combination) a c t s i n a g i v e n s i t u a t i o n . F o r example, i n p u r e s l i d i n g o f a metal/metal p a i r t h e a b r a s i o n o r t h e adhesion wear mechanism may domin a t e , whereas d u r i n g o s c i l l a t i o n o f a m e t a l / m e t a l c o u p l e f r e t t i n g occurs e s s e n t i a l l y through t h e c o m b i n a t i o n o f a l l f o u r b a s i c wear mechanisms (see S e c t i o n 4.4.6).

A customary ( i n d i r e c t ) way o f d e t e c t i n g t h e t y p e o f wear mechanism a c t i n g i n a g i v e n wear s i t u a t i o n i s t o s t u d y t h e appearance o f t h e worn s u r f a c e s . I n Table 4.3 some t y p i c a l c h a r a c t e r i s t i c s o f s u r f a c e damage due t o t h e f o u r b a s i c wear mechanisms a r e l i s t e d . With t h e combination o f t h e c h a r a c t e r i s t i c s shown i n Tables 4.2 and 4.3 t h e b a s i s f o r an unambiguous d i s t i n c t i o n between wear o f d i f f e r e n t types may be given. A f t e r t h e general d e s c r i p t i o n o f wear and i t s e x t r e m e l y complex n a t u r e , i n t h e f o l l o w i n g t h e main aspects o f t h e f o u r b a s i c types o f wear mechanisms i n r e l a t i o n t o s l i d i n g , r o l l i n g , and o s c i l l a t i n g w i l l be s t u d i e d from a p h y s i c a l p o i n t o f view ( R e f . 4.90).

The d i s c u s s i o n i s r e s t r i c t e d t o t h e

wear mechanisms between s o l i d b o d i e s . The e f f e c t s o f c a v i t a t i o n and e r o s i o n cannot be t r e a t e d w i t h i n t h e scope o f t h i s volume. ( F o r a d i s c u s s i o n o f t h e mechanisms of impact wear t h e r e a d e r i s r e f e r r e d t o a r e c e n t book by E n g e l ) ( R e f . 4.91.)

I t s h o u l d be emphasized a g a i n t h a t t h e occurrence o f one s i n g l e

wear mechanism i s met o n l y under s p e c i f i c c o n d i t i o n s and t h a t , i n g e n e r a l , a c o m b i n a t i o n o f wear mechanisms occurs. T h i s i s discussed below i n S e c t i o n 4.4.6.

105

4,4 2 SURFACEF A T I G U E WEAR MECHAN I SMS I

A t a f i r s t glance, surface f a t i g u e seems t o be a r e l a t i v e l y simple wear mechanism since i t appears t o be based o n l y on the a c t i o n o f stresses on the surfaces w i t h o u t needing a d i r e c t physical s o l i d contact o f the surfaces under consideration. This f o l l o w s from the observation t h a t surface f a t i g u e e f f e c t s are observed t o occur i n j o u r n a l bearings where the i n t e r a c t i n g surfaces are f u l l y separated by a t h i c k l u b r i c a n t f i l m (Ref. 4.92). The e f f e c t o f f a t i g u e wear processes i s normally associated w i t h repeated stress c y c l i n g i n r o l l i n g o r s l i d i n g contact. I n f a t i g u e , f a i l u r e i n t h e material arises because o f stress-reverse e f f e c t s , i. e . ,

f r a c t u r e can

develop under a l t e r n a t i n g stresses w i t h a peak l e v e l which could be safe i f imposed i n only tension o r compression. Scanning e l e c t r o n micrographs

shown i n Figure 4.25 e x h i b i t the t y p i c a l appearance o f the surface fatigue damage a f t e r repeated u n i d i r e c t i o n a l s l i d i n g o f a p i n over a d i s c .

-20 Figure 4.25

pm

t-------l 4

pm

Appearance o f surface f a t i g u e damage.

Since surface f a t i g u e i s the c l a s s i c f a i l u r e mode o f r o l l i n g contact, as i n b a l l and r o l l e r bearings, the mechanisms o f surface f a t i g u e i n r o l l i n g cont a c t w i l l be considered f i r s t . Comparing the surface f a t i g u e o f r o l l i n g contacts w i t h the o r d i n a r y f a t i g u e o f b u l k m a t e r i a l , there are two d i f f e r e n c e s t o be noted. F i r s t , the f l u c t u a t i o n s i n the time t o f a i l u r e , the " l i f e t i m e " , are much more severe i n r o l l i n g contact. Second, there i s the important phenomena o f f a t i g u e

106

l i m i t s t r e s s which i s observed i n o r d i n a r y b u l k t e s t i n g , i . e . ,

there

e x i s t s a c e r t a i n s t r e s s l i m i t f o r a g i v e n m a t e r i a l below w h i c h t h e m a t e r i a l enjoys an i n f i n i t e f a t i g u e l i f e . Such l i m i t has n o t been d e t e c t e d i n t h e s u r f a c e f a t i g u e case (Ref. 4.93).

E m p i r i c a l l y , i t has been f o u n d i n a s e r i e s

o f experiments t h a t t h e f o l l o w i n g r e l a t i o n f o r t h e t i m e t o f a i l u r e e x i s t s : t

= - const

0m9

where

dm i s t h e maximum e l a s t i c s t r e s s . To understand how and where s u r f a c e - f a t i g u e cracks form, i t i s neces-

s a r y t o c o n s i d e r t h e n a t u r e o f t h e s t r e s s f i e l d s which e x i s t beneath t h e s u r f a c e . The H e r t z i a n t h e o r y o f s t a t i c e l a s t i c c o n t a c t shows t h a t t h e maximum compressive s t r e s s occurs a t t h e s u r f a c e and t h e maximum u n i d i r e c t i o n a l shear s t r e s s i s some d i s t a n c e , y, below i t (e.g.,

i n t h e case o f two

c o n t a c t i n g c y l i n d e r s w i t h a c o n t a c t w i d t h o f 2aH a t y = 0.78aH). Under r o l l i n g c o n t a c t c o n d i t i o n s t h e i m p o r t a n t s t r e s s parameter i s t h e maximum r e versed shear s t r e s s and t h i s can be shown t o l i e c l o s e r t o t h e s u r f a c e t h a n t h e maximum u n i d i r e c t i o n a l shear s t r e s s . If t h e c o n t a c t i s s u b j e c t e d t o c o n s i d e r a b l e s u r f a c e t r a c t i o n forces t h e n t h e p o s i t i o n s o f t h e s e shear s t r e s s maxima change and move towards t h e s u r f a c e r e g i o n . The two s i t u a t i o n s a r e i l l u s t r a t e d i n F i g u r e s 4.26 and 4.27 which r e p r e s e n t combined s t r e s s d i s t r i b u t i o n s c a l c u l a t e d f o r t h e case o f a c y l i n d e r l f l a t c o n t a c t by f i n i t e element methods (Ref. 4.94). A l t h o u g h t h e r e has been c o n s i d e r a b l e p r o g r e s s i n t h e c a l c u l a t i o n s o f r o l l i n g stress d i s t r i b u t i o n s , a couple o f a d d i t i o n a l i n f l u e n c i n g f a c t o r s must b e considered. L i t t m a n n (Ref. 4.95) has compiled t h e f o l l o w i n g l i s t o f those f a c t o r s which m o d i f y t h e nominal c o n t a c t s t r e s s d i s t r i b u t i o n f r o m t h a t computed f o r homogeneous, i s o t r o p i c , e l a s t i c , smooth-surface m a t e r i a l s i n dry r o l l i n g contact: Subsurface s t r e s s r a i s e r s Oxides and o t h e r hard, b r i t t l e i n c l u s i o n s , S u l f i d e s , c a r b i d e s , and o t h e r second phase p a r t i c l e s , G r a i n boundaries, sub-boundaries, Surface character S u r f a c e topography and t e x t u r e , Residual s t r e s s e s , S u r f a c e energy l e v e l , Microstructure, Contaminants.

t w i n s , and o t h e r d i s l o c a t i o n a r r a y s .

107

F i g u r e 4.26

6 -2 Map o f maximum shear s t r e s s e s ( x 10 Nm ) f o r c y l i n d e r / p l a n e 9 -2 c o n t a c t due t o normal l o a d a l o n e ( G H Z = 10 Nm ) ( R e f . 4.94).

F i g u r e 4.27

6 -2 Map o f maximum shear s t r e s s e s ( x 10 Nm ) f o r c y l i n d e r / p l a n e c o n t a c t due t o combined normal and t a n g e n t i a l l o a d s 9 -2 (FT/FN = 0.3; G H z = 10 Nm ) (Ref. 4 . 9 4 ) .

Surface flaws I n c l u s i o n s and second phase p a r t i c l e s , N i c k s and dents i n c l u d i n g t r u e and f a l s e b r i n e l l i n g , Grooves and s c r a t c h e s , Corrosion p i t s , rust, water etch, F r e t t i n g damage, S k i d d i n g damage. D i s c o n t i n u i t i e s i n c o n t a c t geometry End o f " 1 i n e " c o n t a c t geometry, D e b r i s p a r t i c l e s i n t h e c o n t a c t area. Load d i s t r i b u t i o n w i t h i n t h e b e a r i n g E l as t ic de f 1e c t ions , Misalignment o f b e a r i n g p a r t s , I n t e r n a l clearance

-

b e a r i n g adjustment.

E l astohydrodynamics Tangenti a1 f o r c e s W i t h o u t gross s l i d i n g , Rolling plus sliding. This compilation o f i n f l u e n c i n g f a c t o r s indicates the complexity o f surf a c e f a t i g u e e f f e c t s i n r o l l i n g c o n t a c t . An e n g i n e e r i n g model of f a t i g u e f a i l u r e i n r o l l i n g c o n t a c t which takes i n t o account t h e i n f l u e n c e o f many f a c t o r s has been proposed by T a l l i a n and co-workers (Ref. 4.96).

A

fundamental e x p e r i m e n t a l s t u d y o f t h e c o n t a c t - f a t i g u e processes

under c y c l i c v a r i a t i o n (26 kHz) o f t h e normal l o a d a p p l i e d t o t h e c o n t a c t between a b a l l and a f l a t specimen (52,100 s t e e l ) was made by T y l e r , B u r t o n and Ku (Ref. 4.97).

I n t h i s case t h e a p p l i e d c o n t a c t s t r e s s was beyond t h e

e l a s t i c range. As i l l u s t r a t e d i n F i g u r e 4.28,

t h e r e a r e two d i s t i n c t con-

t a c t c i r c l e s formed on b o t h specimens c o r r e s p o n d i n g t o t h e minimum and maximum loads. As a consequence o f t h e o s c i l l a t o r y l o a d i n g t h r e e d i s t i n g u i s h a b l e types o f s u r f a c e damage were observed: (a)

In t h e t o r o i d a l r e g i o n between t h e i n n e r and t h e o u t e r c o n t a c t c i r c l e s " f r e t t i n g " o c c u r r e d as a consequence o f shear t r a c t i o n s induced d u r i n g t h e l o a d i n g and u n l o a d i n g c y c l e s and i n f l u e n c e d by t h e d i f f e r e n c e of t h e e l a s t i c moduli o f t h e specimens. (The f r e t t i n g mode o f wear p r o cesses i s d i s c u s s e d i n S e c t i o n 4.4.6.)

(b)

The c e n t r a l p a r t o f t h e c o n t a c t area underwent a d e p r e s s i o n due t o p l a s t i c d e f o r m a t i o n which was found t o accumulate w i t h repeated loading.

109 (c)

The u l t i m a t e f a i l u r e o f the contact progressed as the f o l l o w i n g succession o f events generated i n the t o r o i d a l area: crack formation, crack growth and interweaving and f l a k i n g o u t o f the crack-surrounded areas. The f a t i g u e cracks d i d n o t i n i t i a t e i n the most hardened mat e r i a l b u t i n the material adjacent t o i t . I t was found t h a t a r a p i d temperature r i s e occurred i n the i n i t i a l stage o f crack formation. The propagation o f micro-cracks tended t o f o l l o w the boundary o f the hardened region along carbide s t r i n g e r s and influenced by the p r i o r austeni t i c g r a i n boundaries.

static

1oad

I time

Figure 4.28

' I

V a r i a t i o n o f load and contact area on f a t i g u e specimens (Ref. 4.97).

The experimental observations o f surface f a t i g u e i n d i c a t e t h a t physical p o i n t o f view

-

- from a

the study o f contact f a t i g u e i s b a s i c a l l y a study

o f s t r e s s concentration e f f e c t s t h a t govern f a t i g u e crack i n i t i a t i o n coupled w i t h crack propagation behaviour. I n t h e f o l l o w i n g , the physical mechanisms o f ( i ) crack i n i t i a t i o n and (ii) crack propagation w i l l be discussed. The models described may be of s i g n i f i c a n c e n o t o n l y f o r t h e ( c l a s s i c ) surface f a t i g u e mode o f wear b u t a l s o i n a broader sense f o r the discussion o f

-

-

r e c e n t l y developed wear models r e l a t k d t o the generation and propagation o f surface cracks.

On the basis o f d i s l o c a t i o n theory, there are several p o s s i b l e mechanisms f o r crack i n i t i a t i o n . These mechanisms were o r i g i n a l l y proposed i n

110

reference t o bulk-material behaviour b u t they can be applied equally well to near-surface phenomena (Ref. 4.36). The main forms of crack i n i t i a t i o n are (Ref. 4.98): ( a ) Pile-up o f dislocations in s l i p band against grain boundary (C1. Zener). (b) Coalescence of two s l i p dislocations t o form a crack along a cleavage plane ( A . H . C o t t r e l l ) . ( c ) Crack formed a t t i l t boundary (A.N. Stroh). These mechanisms are presented schematically in Figure 4.29.

:/" 1

Figure 4.29

Mechanisms o f crack i n i t i a t i o n .

Another mechanism t h a t can i n i t i a t e subsurface cracks i s based on the eff e c t of inclusions. The mechanism o f crack i n i t i a t i o n can be started by such obstacles as oxide inclusions which are very prevalent i n the nearsurface layers of relatively s o f t metals such as copper. Further, w i t h bearing and gear s t e e l s , carbide inclusions are always present. The presence of such obstacles can give rise to dislocation coalescence and the i n i t i a t i o n o f subsurface crack nuclei. Although the described mechanisms o f crack i n i t i a t i o n a r e mostly used as s t a r t i n g points for a discussion of metal fatigue, there are some other d e t a i l s of dislocation behaviour t h a t should be considered which are beyond the scope of t h i s volume (Ref. 4.99).

111 Once an atomic crack has been formed by one o f t h e mechanisms d i s cussed above, t h e processes t h a t govern t h e crack propagation must be considered. For b r i t t l e m a t e r i a l s the w e l l known c l a s s i c continuum theory o f G r i f f i t h may be a p p l i c a b l e . Consider an e l l i p t i c a l crack o f l e n g t h 2a under 2

a t e n s i l e s t r e s s G . The s u r f a c e energy o f t h e crack i s equal t o 2 y C r E a

.

The d i s t o r s i o n s i n f r o n t o f the crack t i p are o f t h e o r d e r o f G / E and extend over dimensions o f the order o f a. Thus an opening o f the crack i n t h e d i s t o r e d m a t e r i a l leads t o an energy change

AU

=

2ycrna2

-

When t h e energy p u t i n t o t h e m a t e r i a l by t h e a p p l i e d s t r e s s exceeds t h e surface energy o f t h e m a t e r i a l , t h e crack s u r f a c e area w i l l increase. A t t h a t point

and

For example, f o r s t e e l ( G = 700 N/mm a zz

2

, ycr

= 1200 erg/cm2) i t f o l l o w s t h a t

1 pm. The above equation shows the importance o f t h e parameter Kc

=

dcr a 1/2

for the a b i l i t y o f crack propagation. Recently, t h e r e have been attempts t o r e l a t e the wear behaviour o f metals w i t h t h i s parameter (Ref. 4.100). These considerations apply t o crack propagation i n b r i t t l e m a t e r i a l s . I f t h e m a t e r i a l i s a b l e t o deform p l a s t i c a l l y , some o f t h e energy i n p u t i n t o the m a t e r i a l w i l l be absorbed i n p l a s t i c f l o w i n t h e regions o f t h e crack t i p . I n s t u d y i n g t h e p l a s t i c - e l a s t i c s t r e s s f i e l d s i n t h e subsurface regions o f s l i d i n g a s p e r i t y contacts and t h e p o s s i b l e d i s l o c a t i o n i n t e r a c t i o n , a "delamination theory o f wear" has been p u t forward by Suh (Ref. 4.101) i n which the generation o f s h e e t - l i k e p a r t i c l e s i s explained on the basis o f the f o l l o w i n g chain o f events:

112

(i)

g e n e r a t i o n o f subsurface d i s l o c a t i o n s ,

(ii)

d i s l o c a t i o n pile-up,

( i i i ) f o r m a t i o n o f voids, (iv)

coalescence o f v o i d s l e a d i n g t o cracks p a r a l l e l t o t h e s u r f a c e ,

(v)

p r o d u c t i o n o f s h e e t - l i k e p a r t i c l e s when t h e c r a c k reaches a c e r t a i n c r i t i c a l length.

I n r e f i n i n g t h i s t h e o r y , some i m p l i c a t i o n s o f c r y s t a l p l a s t i c i t y e f f e c t s have been d i s c u s s e d i n c l u d i n g a s p e c i f i c d i s l o c a t i o n model f o r hexagonal close-packed (h.c.p.)

m e t a l s under wear c o n d i t i o n s and a c o r r e l a t i o n w i t h

s t a c k i n g f a u l t energy f o r f a c e - c e n t r e d c u b i c and h.c.p.

m e t a l s ( R e f . 4.102).

I t appears t h a t , by t h e use o f d i s l o c a t i o n models, i t i s now p o s s i b l e

t o e x p l a i n t h e occurrence o f s h e e t - l i k e wear p a r t i c l e s , observed as e a r l y as 1929 by Fuchsel (Ref. 1.19) and i n t e r p r e t e d through a process o f m a t e r i a l separation.

4,4,3

ABRASIVE W E A R

MECHANISMS

As i n s u r f a c e f a t i g u e processes, t h e a t t r i t i o n o f m a t e r i a l s p a r t i c l e s i n

t h e a b r a s i v e wear mechanism i s a l s o caused m a i n l y by c o n t a c t d e f o r m a t i o n processes. The e f f e c t o f a b r a s i o n occurs i n c o n t a c t s i t u a t i o n s i n which d i r e c t p h y s i c a l c o n t a c t between two s u r f a c e s i s g i v e n where one o f t h e s u r f a c e s i s c o n s i d e r a b l y h a r d e r t h a n t h e o t h e r . The h a r d e r s u r f a c e a s p e r i t i e s press i n t o the s o f t e r surface w i t h p l a s t i c flow o f t h e s o f t e r surface occurring around t h e a s p e r i t i e s f r o m t h e h a r d e r s u r f a c e . When a t a n g e n t i a l m o t i o n i s imposed t h e h a r d e r s u r f a c e w i l l move, p l o u g h i n g and removing t h e s o f t e r m a t e r i a l . The e f f e c t o f a b r a s i o n i s comparable w i t h a " m i c r o - c u t t i n g p r o cess", as can be seen i n t h e scanning e l e c t r o n micrograph, F i g u r e 4.30, showing an A1 s u r f a c e . I n i n d u s t r i a l s i t u a t i o n s , a b r a s i v e wear processes a r e v e r y widespread; i n f a c t , i t has been e s t i m a t e d t h a t about 50% o f wear encountered i n i n d u s t r y i s due t o a b r a s i o n mechanisms (Ref. 4.103).

As a consequence o f t h e

g r e a t v a r i e t i e s o f a b r a s i v e wear s i t u a t i o n s , d i f f e r e n t t y p e s o f a b r a s i v e wear a r e d i s t i n g u i s h e d i n p r a c t i c e . As i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 4.31,

f i r s t l y we d i s t i n g u i s h

between "two-body a b r a s i o n " and "three-body a b r a s i o n " . F o r example, t h e two-body s i t u a t i o n i s most f r e q u e n t l y encountered i n t h e t r a n s p o r t o f l o o s e

113

Figure 4.30

Appearance o f surface damage due t o abrasion.

Two-body abrasion

Figure 4.31

Three-body abrasion

Two-body and three-body abrasion.

114

m i n e r a l s and t h e three-body i n m i n e r a l t r e a t m e n t and on t h e i n g r e s s o f f o r e i g n p a r t i c l e s i n t o bearings. Secondly we d i s t i n g u i s h between: (a)

Gouging a b r a s i o n Examples: Shovel d i p p e r t e e t h , Hammers i n impact p u l v e r i z e r s , e t c .

(b)

Grinding abrasion Examples: G r i n d i n g b a l l s , e t c .

(c)

Erosion abrasion Examples: A g i t a t o r i m p e l l e r s , Sandblast n o z z l e s , e t c .

Research i n t o t h e mechanism o f a b r a s i o n i n t h e l a b o r a t o r y t a k e s t h e f o r m o f examining t h e wear of s o l i d s s l i d i n g on a b r a s i v e paper. E x t e n s i v e s t u d i e s i n t h i s f i e l d have been performed by W e l l i n g e r and Uetz (Ref. 4.104,

4.105),

Khruschov (Ref. 4.106, 4.107) and Richardson (Ref. 4.108). The r e s u l t s o f t h e s e s t u d i e s may be summarized as f o l l o w s : I n a g i v e n wear regime, t h e abraded wear volume V o f m e t a l s i n c r e a s e s i n most cases l i n e a r l y w i t h l o a d FN and s l i d i n g d i s t a n c e 1

I f d e v i a t i o n s o c c u r , t h e y a r e u s u a l l y due t o a r e d u c t i o n i n p a r t i c l e s i z e

I n o r d e r t o compare t h e a b r a s i o n b e h a v i o u r o f d i f f e r e n t m a t e r i a l s , t h e f o l l o w i n g measures

o f t h e a b r a s i v e o r c l o g g i n g o f t h e s u r f a c e (Ref. 4.103). have been d e f i n e d : (a)

t h e wear volume V,

(b)

t h e wear r e s i s t a n c e E

(c)

1

-

- wear volume

t h e r e l a t i v e wear r e s i s t a n c e

'W

-

E E

(specimen (standard;

I t has been found t h a t t h e a b r a s i v e wear depends on t h e c o r r e l a t i o n between

t h e hardness o f t h e a b r a s i v e , Ha, and t h e hardness o f t h e m e t a l , ,H, t o t h r e e d i s t i n c t wear regimes, as shown i n F i g u r e 4.32:

leading

115 a low-wear regime, i f Ha

-=

Hm

a t r a n s i t i o n regime, i f

Ha z

Hm

a high-wear regime, i f Ha

’

Hm

I 7

Ri

c, W

E

+ 0 W

5

c

0 >

L

C u a, 3

Hardness o f a b r a s i v e

F i g u r e 4.32

I n f l u e n c e o f t h e hardness o f t h e a b r a s i v e on t h e wear o f m e t a l s (schematic).

T h i s l e a d s t o t h e i m p o r t a n t c o n c l u s i o n t h a t i n o r d e r t o reduce an a b r a s i v e wear component, t h e hardness o f t h e m a t e r i a l , Hm, s h o u l d be h i g h e r t h a n t h e hardness o f t h e a b r a s i v e by a f a c t o r o f about 1.3,

i.e.,

may be used as a c r i t e r i o n f o r a low-wear a b r a s i o n r a t e . ( I t i s n o t necess a r y t o i n c r e a s e t h e hardness o f t h e m a t e r i a l beyond 1.3 t i m e s t h a t o f t h e a b r a s i v e because no f u r t h e r s i g n i f i c a n t improvement i s o b t a i n e d , Ref. 4.103.)

I n o r d e r t o determine t h e r e l e v a n t m a t e r i a l p r o p e r t i e s t h a t govern t h e a b r a s i v e wear b e h a v i o u r i n t h e high-wear regime (111) o f F i g u r e 4.32, a g r e a t

116 v a r i e t y o f m a t e r i a l s has been t e s t e d . I n F i g u r e 4.33 t h e wear r e s i s t a n c e

c W o f v a r i o u s groups o f m a t e r i a l s as a f u n c t i o n o f t h e hardness o f t h e mat e r i a l s , Hm, measured under c o n d i t i o n s o f regime (111) o f F i g u r e 4.32, i s shown s c h e m a t i c a l l y (Ref. 4.107).

40 3 W

aJ u c

9

30

v)

c o r u n d y’ 0

.r v)

2 L

: 20 3

\

7

IX aJ

10

I

I

10

5

0

Hardness H, F i g u r e 4.33

I

15

I

20

(GN/m2)

Khrushov diagram: wear r e s i s t a n c e as a f u n c t i o n o f t h e hardness o f m a t e r i a l s .

The d a t a were o b t a i n e d u s i n g an e l e c t r o c a l l y produced corundum a b r a s i v e

( H = 22,900 N/m2 ) and a B a b b i t - t y p e l e a d - t i n a l l o y ( c o n t a i n i n g antimony) as t h e standard. The hardness o f t h e t e s t m a t e r i a l s was determined b e f o r e t h e t e s t by diamond i n d e n t a t i o n . The b a s i c c o n c l u s i o n s t h a t can be drawn f r o m t h e Khrushov diagram, F i g u r e 4.33, may be summarized as f o l l o w s : (a)

T e c h n i c a l l y p u r e m e t a l s i n an annealed s t a t e and annealed s t e e l s show a d i r e c t p r o p o r t i o n a l i t y between t h e r e l a t i v e wear r e s i s t a n c e , and t h e pyramid hardness, Hm:

‘w where

=

‘metal

‘ Hm

‘metal

=

13.8

N-’

mm2

cW,

117 (b)

F o r n o n - m e t a l l i c h a r d m a t e r i a l s and m i n e r a l s , a l i n e a r r e l a t i o n s h i p between wear r e s i s t a n c e and hardness i s s i m i l a r l y found: E

W

where

(c)

-

-

‘mineral s

‘minerals

d

Hm =

1.3

2

.

N - ~mm

F o r m e t a l l i c m a t e r i a l s c o l d work-hardened by p l a s t i c d e f o r m a t i o n , t h e r e l a t i v e w e a r - r e s i s t a n c e does n o t depend on t h e hardness r e s u l t i n g f r o m c o l d work hardening.

(d)

A h e a t - t r e a t m e n t o f s t r u c t u r a l s t e e l s (normal h a r d e n i n g and tempering) improves t h e a b r a s i v e wear. r e s i s t a n c e .

These r e s u l t s i n d i c a t e t h e g r e a t importance o f t h e hardness o f m a t e r i a l s and o f o t h e r m e t a l l u r g i c a l f a c t o r s on t h e a b r a s i v e wear r e s i s t a n c e o f m a t e r i a l s

(Ref. 4.109). The l i n e a r r e l a t i o n s h i p between a b r a s i v e wear r e s i s t a n c e and t h e mat e r i a l hardness can be v e r i f i e d u s i n g t h e s i m p l e model o f p l o u g h i n g shown i n F i g u r e 4.16. I n t h i s model an a b r a s i v e a s p e r i t y i s approximated by a cone t h a t ploughs o u t and removes m a t e r i a l f r o m t h e c o u n t e r f a c e . I f t h e l o a d , 5 F N , on t h e i n d e n t e r i s o n l y s u p p o r t e d o v e r t h e l e a d i n g h a l f o f t h e c o n t a c t , h FN i s balanced by t h e y i e l d pressure, py, o f t h e c o u n t e r f a c e a c t i n g v i a t h e c o n t a c t a r e a A:

A FN

=

A py

The volume o f m a t e r i a l A V removed i n s l i d i n g a d i s t a n c e A 1 i s g i v e n by the cross-sectional area o f the indenter times A 1

AV Thus, s u b s t i t u t i n g f o r d f r o m above

d2 4

= -Al.cottp

118

and assuming t h a t o n l y a p r o p o r t i o n , K , o f a l l t h e c o n t a c t s produce worn particles, i t follows t h a t

T h i s e x pre s s ion shows t h a t t h e wear volume i s p r o p o r t i o n a l t o t h e l o a d and t h e s l i d i n g dis t a nc e , and t h a t t h e o n l y m a t e r i a l p r o p e r t y i n v o l v e d i s t h e y i e l d pressure. I f t h e y i e l d p r e s s u r e i s assumed t o be equal t o t h e indent a t i o n hardness, H, f o r g i v e n values o f FN and 1, t h e l a s t e q u a t i o n can be simp1 i f i e d t o V

=

1 c o n s t -A

I n t r o d u c i n g t h e wear r e s i s t a n c e d e f i n e d above as t h e r e c i p r o c a l wear volume i t follows t h a t

Abrasive wear r e s i s t a n c e

=

c o n s t . x hardness

T his s imp le d e r i v a t i o n and t h e e x p e r i m e n t a l r e s u l t s shown i n F i g u r e 4.33 i n d i c a t e t h a t t h e a b r a s i v e wear r e s i s t a n c e i s o n l y dependent on t h e m a t e r i a l hardness. T here f o r e , t h e a b r a s i v e wear r e s i s t a n c e may be i n t e r p r e t e d v i a t h e m a t e r i a l hardness, as a k i n d o f ' t r i b o l o g i c a l m a t e r i a l p r o p e r t y " , i . e . as an appa re nt ly system-independent p r o p e r t y . I t s h o u ld be borne i n mind, however, t h a t t h e a b r a s i v e wear r e s i s t a n c e , t h a t the l i n e a r

E

-

E ~ i, s

d e f i n e d as a r e l a t i v e measure and

H r e l a t i o n s h i p i s v a l i d o n l y f o r c o n d i t i o n s o f regime

(111) o f F i g u r e 4.32,

i.e.,

f o r t h e cases i n which t h e a b r a s i o n process a c t s

m a i n l y i n t h e b u l k o f t h e m a t e r i a l under s t u d y . I f , on t h e o t h e r hand, an a b r a s i v e wear process a c t s i n t h e " o u t e r " s u r f a c e l a y e r s , t hen t h e i n f l u e n c e of s u r f a c e contaminants and t h e a c t i o n o f t h e environmental atmosphere must a d d i t i o n a l l y be t a k e n i n t o account (Ref. 4.110).

119

4 4,4 ADHESIVE I

WEAR MECHAN I SMS

Whereas t h e wear mechanisms o f s u r f a c e f a t i g u e and a b r a s i o n can be exp l a i n e d m a i n l y i n terms o f f o r c e s , s t r e s s e s and d e f o r m a t i o n processes, i n t h e adhesive wear mechanism, m a t e r i a l i n t e r a c t i o n s p l a y an i m p o r t a n t r o l e . I t was d e s c r i b e d i n S e c t i o n 4.2.2 t h a t i f two s o l i d b o d i e s a r e b r o u g h t i n t o

c o n t a c t t h e y w i l l f i r s t e x p e r i e n c e l o n g - r a n g e van d e r Waals f o r c e s . A t d i s tances o f a b o u t lnm s t r o n g s h o r t - r a n g e s u r f a c e s f o r c e s come i n t o a c t i o n a t t h e r e a l areas o f c o n t a c t , t h e t y p e o f which depends on t h e n a t u r e o f t h e s u r f a c e s i n c o n t a c t . Thus, s t r o n g adhesive j u n c t i o n s may be formed w i t h t h e a s s i s t a n c e o f t h e d i s p e r s a l o f s u r f a c e contaminants and j u n c t i o n g r o w t h (see S e c t i o n 4.3.1).

I n o r d e r t h a t adhesive wear s h o u l d t a k e p l a c e , f r a c t u r e

must o c c u r i n t h e s u b s u r f a c e o f one o r b o t h m a t e r i a l s . The s i t u a t i o n i s ill u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 4.34.

motion ____L

adhe

/

fracture

F i g u r e 4.34

Adhesive wear s i t u a t i o n .

I n c o n t r a s t t o t h e o t h e r wear mechanisms which g e n e r a l l y t a k e some t i m e t o develop o r t o reach a c r i t i c a l d e s t r u c t i v e magnitude, adhesive wear e f f e c t s o c c u r q u i t e p r e c i p i t o u s l y l e a d i n g i n t h e i r severe forms t o dangerous f a i l u r e i n t h e f o r m o f " s c u f f i n g " o r " s e i z u r e " o f moving p a r t s i n mec h a n i c a l e n g i n e e r i n g systems. I n F i g u r e 4.35 t h e t y p i c a l appearance o f t h e s u r f a c e s o f a s l i d i n g s t e e l / s t e e l p a i r a f t e r f a i l u r e due t o adhesive wear processes i s shown. I t can be seen t h a t l a r g e m a t e r i a l lumps were t r a n s f e r r e d f r o m t h e c o u n t e r p a r t n e r and adhere s t r o n g l y on one s u r f a c e i n " c o l d we1 ded" j u n c t i o n s .

120

F i g u r e 4.35

Appearance o f s u r f a c e damage due t o adhesive wear processes.

Concerning t h e p h y s i c a l mechanisms o f adhebive wear, o b v i o u s l y t h e processes and parameters o f adhesion ( S e c t i o n 4.2.2) ( S e c t i o n 4.4.2)

as w e l l as t h o s e o f f r a c t u r e

must be t a k e n i n t o account. S i n c e b o t h adhesion and f r a c t u r e

a r e i n f l u e n c e d by s u r f a c e contaminants and t h e e f f e c t o f t h e environment, i t i s q u i t e d i f f i c u l t t o r e l a t e adhesion wear r a t e s w i t h elementary b u l k p r o p e r t i e s o f m a t e r i a l s . I n vacuum where these i n f l u e n c e s a r e e l i m i n a t e d , t h e f o l l o w i n g e x p e r i m e n t a l r e s u l t s have been observed t o be g e n e r a l l y v a l i d f o r t h e adhesive wear processes o f m e t a l / m e t a l p a i r s (Ref. 4.111): (i)

I n t e r f a c i a l m e t a l l i c adhesion bonding o c c u r s between any p a i r o f metals; t h e r e i s no d i r e c t r e l a t i o n between t h e (volume) s o l u b i l i t y o f metal p a i r s and t h e i r ( s u r f a c e ) adhesion bonding.

(ii)

C r y s t a l s t r u c t u r e e x e r t s an i n f l u e n c e on adhesive wear. Hexagonal m e t a l s i n general e x h i b i t l o w e r adhesive wear c h a r a c t e r i s t i c s t h a n e i t h e r body-centred c u b i c o r f a c e - c e n t r e d c u b i c m e t a l s . T h i s d i f f e r e n c e i s assumed t o be r e l a t e d t o d i f f e r e n t p l a s t i c a s p e r i t y cont a c t d e f o r m a t i o n modes and t h e number o f o p e r a b l e s l i p systems i n t h e c r y s t a l systems.

121 ( i i i ) C r y s t a l o r i e n t a t i o n i n f l u e n c e s t h e adhesive wear behaviour. I n general h i g h atomic d e n s i t y , low surface energy g r a i n o r i e n t a t i o n s e x h i b i t l o w e r adhesion and l e s s adhesive wear than do o t h e r o r i e n t a t i o n s . (iv)

When d i s s i m i l a r metals are i n c o n t a c t the adhesive wear process w i l l g e n e r a l l y r e s u l t i n t h e t r a n s f e r o f p a r t i c l e s o f t h e cohesively weaker o f the two m a t e r i a l s t o the cohesively stronger.

(v)

Small amounts o f a l l o y i n g elements ( a few p a r t s p e r m i l l i o n ) such as carbon and s u l f u r are s u f f i c i e n t t o i n h i b i t appreciably the adhesion o f m e t a l l i c a l l o y s thereby m i n i m i z i n g t h e i r adhesive wear. ( S u l f u r and carbon w i l l , a c t i v a t e d by f r i c t i o n a l heating, d i f f u s e t o a surface and occupy a c o n c e n t r a t i o n a t the surface f a r i n excess o f t h e i r concent r a t i o n i n the bulk material. )

These r e s u l t s c l e a r l y show t h e i n f l u e n c e s o f the various c h a r a c t e r i s t i c s o f c o n t a c t adhesion and c o n t a c t deformation processes, as dicussed above, on adhesive wear. The combined e f f e c t s o f adhesion and f r a c t u r e a l s o a c t i n t h e formation o f loose adhesive wear p a r t i c l e s . I n s t u d y i n g t h e d e t a i l s o f t h e adhesive wear mechanism, Cocks (Ref. 4.112) and A n t l e r (Ref. 4.113) considered the process o f "prow" formation by which c o n t a c t i s maintained f o r a l o n g e r p e r i o d w h i l e t h e j u n c t i o n i s growing and the j u n c t i o n base i s moving along one o r both o f the running surfaces. I n r e f i n i n g t h i s model, Landheer and Zaat (Ref. 4.114) emphasized t h e f o l lowing phenomena i n the severe adhesive wear process: ( a ) a j u n c t i o n development, where under t h e i n f l u e n c e o f shear r e s i s t a n c e i n t h e i n t e r f a c e , a f i e l d o f i s o - s t r a i n l i n e s ( p l a s t i c s t r a i n ) moves through the metal o f the wearing surface i n a d i r e c t i o n opposite t o t h e s l i d i n g d i r e c t i o n , so t h a t metal accumulates i n the j u n c t i o n s and the d i s t a n c e between t h e running surfaces i s enlarged,

(b)

c r a c k i n g o f the metal a t the backside o f the j u n c t i o n , by which m a t e r i a l

detaches f o r t r a n s f e r . An i n s t r u c t i v e experimental example o f t h e generation o f an adhesive wear p a r t i c l e has been given by Buckley (Ref. 4.115). He performed s l i d i n g f r i c t i o n experiments w i t h a p o l y c r y s t a l l i n e copper r i d e r s l i d i n g across the surface o f a b i c r y s t a l o f copper. One g r a i n o f the b i c r y s t a l was o f the (111) o r i e n t a t i o n w h i l e t h e second was a (210) plane. With a s i n g l e pass o f t h e r i d e r across the surface, cracks developed i n t h e s u r f a c e o f b o t h g r a i n s o f t h e b i c r y s t a l . These surface cracks a r e shown i n t h e scanning e l e c t r o n micrograph

o f Figure 4.36. The f r a c t u r e cracks developed a t room tempera-

122

F i g u r e 4.36

Areas o f wear on (210) copper g r a i n (Ref. 4.115).

Slip-Band Format ion

FL-

J (

v=l ,4mm/mi n Fracture

-

S1 i p Bands Subsequent Passes

F i g u r e 4.37

Surface

G e n e r a t i n g Wear

Projection

Particle

O r i g i n o f s u r f a c e f r a c t u r e and f o r m a t i o n o f wear p a r t i c l e ( R e f . 4.115).

123

t u r e w i t h i n t h e copper. Close e x a m i n a t i o n o f these c r a c k s i n d i c a t e s t h a t t h e w a l l o f t h e c r a c k i s v e r y smooth. F u r t h e r , t h e m a t e r i a l a t t h e l e a d i n g edge o f t h e c r a c k has been c u r l e d up above t h e p l a n e o f t h e b i c r y s t a l s u r face. The measured a n g l e between t h e c r a c k and t h e o r i e n t a t i o n o f t h e s u r f a c e p l a n e i n d i c a t e s t h a t t h e f r a c t u r e c r a c k occurs a l o n g s l i p bands. The mechanism r e s p o n s i b l e f o r t h e c r a c k s shown i n F i g u r e 4.36 i s p r e sented i n F i g u r e 4.37. Adhesion o f t h e r i d e r t o t h e b i c r y s t a l o c c u r s . W i t h t a n g e n t i a l m o t i o n f r a c t u r e occurs a l o n g s l i p bands as t h e t a n g e n t i a l f o r c e p a r t s a t o m i c planes. A t some a p p l i e d t a n g e n t i a l f o r c e , t h e a p p l i e d f o r c e exceeds t h e adhesive b o n d i n g f o r c e and t h e r i d e r breaks away f r o m t h e b i c r y s t a l s u r f a c e l e a v i n g a c u r l o f metal p r o j e c t i n g above t h e surface. A second pass shears o f f t h e c u r l and an adhesive wear p a r t i c l e has been generated.

4,4 5 I

TRIBO-CHEMI CAL

WEAR MECHANISMS

Whereas t h e mechanism o f s u r f a c e f a t i g u e wear, a b r a s i v e wear, and adhesive wear can be understood i n terms o f d e f o r m a t i o n and adhesion i n t e r a c t i o n s between two c o n t a c t i n g s u r f a c e s , (1) and ( Z ) ,

i n t r i b o - c h e m i c a l wear as

t h i r d p a r t n e r t h e environment ( 3 ) and t h e dynamic i n t e r a c t i o n s between ( l ) ,

( 2 ) and ( 3 ) d e t e r m i n e t h e wear process ( R e f . 4.116).

I f t h e two s u r f a c e s

r e a c t a c t i v e l y w i t h t h e environment, t h e r u b b i n g o f s u r f a c e s t o g e t h e r i n such an environment r e s u l t s i n t h e c o n t i n u o u s f o r m a t i o n and removal o f r e a c t i o n products. Since the material o f the contacting surfaces are contained i n t h e r e a c t i o n p r o d u c t s , m a t e r i a l i s b e i n g removed f r o m t h e s u r f a c e s . The t y p i c a l appearance o f t r i b o - c h e m i c a l l y formed wear p a r t i c l e s i s shown i n F i g u r e 4.38 i n scanning e l e c t r o n micrographs. The d i f f e r e n c e s i n t h e mechanisms o f s u r f a c e f a t i g u e , a b r a s i o n and adhesion on one hand and t r i b o - c h e m i c a l wear e f f e c t s on t h e o t h e r can be seen i n t h e conceptual diagram o f t h e wear processes w i t h i n a t r i b o l o g i c a l system, F i g u r e 3 . 8 and F i g u r e 3.4. The f i r s t t h r e e mechanisms can e s s e n t i a l l y be d e s c r i b e d - i n t h e s i m p l e s t case

-

as i n t e r a c t i o n s between o n l y two

p a r t n e r s , namely t h e two s o l i d s u r f a c e s ( 1 ) and (2), l e a d i n g d i r e c t l y t o t h e M g e n e r a t i o n o f d e b r i s { Z ) f r o m (1) and ( 2 ) . I n t h e case o f t r i b o - c h e m i c a l wear, t h e whole mechanism c l e a r l y c o n s i s t s o f t h e i n t e r a c t i o n s o f t h r e e p a r t n e r s , namely t h e s o l i d s u r f a c e s (1) and ( 2 ) and t h e environment ( 3 ) . These i n t e r a c t i o n s may be expressed as a c y c l i c s t e p w i s e process:

124 (i)

A t t h e f i r s t stage, t h e s u r f a c e s ( I ) and ( 2 ) r e a c t w i t h t h e e n v i r o n and (2)-(3)

ment ( 3 ) . I n t h i s process, r e a c t i o n p r o d u c t s (1)-(3)

a r e formed on t h e s u r f a c e s o f (1) and ( 2 ) , shown i n F i g u r e 3.8 below. (ii)

The second s t e p c o n s i s t s o f t h e a t t r i t i o n o f t h e r e a c t i o n p r o d u c t s as a r e s u l t o f c r a c k f o r m a t i o n and a b r a s i o n i n t h e c o n t a c t process i n t e r a c t i o n s o f (1) and ( 2 ) . When t h i s occurs " f r e s h " ,

i.e.,

r e a c t i v e sur-

f a c e p a r t s , o f (1) and ( 2 ) a r e formed and stage ( i ) c o n t i n u e s . C l e a r l y , i n a t t e m p t s t o s t u d y t h e mechanisms o f t r i b o - c h e m i c a l wear, besides t h e e f f e c t s o f d e f o r m a t i o n and adhesion, t h e c h e m i s t r y o f t h e r e a c t i o n p r o d u c t f o r m a t i o n must be c o n s i d e r e d a d d i t i o n a l l y , t a k i n g i n t o account t h e cont r i b u t i o n o f f r i c t i o n a l energy i n these processes.

H50

F i g u r e 4.38

pm

H

5

Appearance o f t r i b o - c h e m i c a l wear p a r t i c l e s .

As a consequence o f thermal and mechanical a c t i v a t i o n , t h e a s p e r i t i e s undergo t h e f o l l o w i n g changes: (a)

t h e r e a c t i v i t y i s i n c r e a s e d due t o t h e i n c r e a s e d a s p e r i t y temperature;

(b)

t h e mechanical p r o p e r t i e s o f t h e s u r f a c e a s p e r i t y l a y e r s a r e changed:

therefore the formation o f surface layers i s accelerated, i n general t h e y have a tendency t o b r i t t l e f r a c t u r e . S t a r t i n g w i t h t h e assumption t h a t t r i b o - c h e m i c a l l y formed s u r f a c e a s p e r i t y l a y e r s a r e detached a t a c e r t a i n c r i t i c a l t h i c k n e s s , Q u i n n proposed an

125 o x i d a t i o n hypothesis o f the wear o f s t e e l s (Ref. 4.117).

Since t h i s theory

i n d i c a t e s the main i n f l u e n c i n g f a c t o r s of the tribo-chemical wear process, i t w i l l be reproduced here. I t was assumed t h a t , a t a given a s p e r i t y c o n t a c t ,

on average, 1 / K encounters are necessary (K: s t a t i s t i c a l wear c o e f f i c i e n t , see Section 4:4.1) f o r a c r i t i c a l oxide f i l m thickness

t o b u i l d up b e f o r e

i t becomes detached t o form a wear p a r t i c l e . I f tc i s t h e d u r a t i o n o f a

s i n g l e wearing contact, then the t o t a l time t t o produce a wear p a r t i c l e o f thickness

5

i s given by

But tc = d/v, where d i s the d i s t a n c e along which a wearing c o n t a c t i s made and v i s the speed o f s l i d i n g . Hence t

d/vK

=

Now the mass per u n i t area o f oxide growth A m depends on t h e time o f o x i d a t i o n t through t h e p a r a b o l i c r e l a t i o n

A m2

kp. t

=

i s the p a r a b o l i c o x i d a t i o n r a t e constant. I t i s reasonable t o P assume A m = s p , where p i s the d e n s i t y o f the oxide, so t h a t we g e t

where k

g2

=

k

P

.

t/p 2

E l i m i n a t i n g t we o b t a i n an expression f o r K, namely

I t i s now g e n e r a l l y accepted t h a t k temperature o f o x i d a t i o n To namely kp

=

P

is e x p o n e n t i a l l y dependent on t h e

Ac exp

-Q/RcTo)

where Ac i s the Arrhenius constant, Q i s the a c t i v a t i o n energy, and R,

is

t h e gas constant. Combining equations and w r t i n g Tc ( t h e c o n t a c t temperat u r e ) f o r To, we g e t

126

From t h e r e s u l t s o f S e c t i o n 4.4.1 i t f o l l o w s t h a t under t h e assumption o f a > 1, y i e l d p r e s s u r e

p l a s t i c a s p e r i t y d e f o r m a t i o n mode ( p l a s t i c i t y i n d e x

hardness H) t h e wear c o e f f i c i e n t K can be r e l a t e d w i t h t h e wear v o l u py =: me V v i a t h e e x p r e s s i o n V

K

= -F

N

3H

* 1

Combining t h i s r e l a t i o n w i t h t h e e x p r e s s i o n f o r K, c a l c u l a t e d on t h e b a s i s o f Quinn's theory, i t follows

v =

d

A;

exp (-Q/RcTc)

3*g2*p2-v

.H

FN * 1

T h i s e x p r e s s i o n i n d i c a t e s t h e dependence o f t h e wear volume V on t h e f o l l o w i n g groups o f parameters o f t h e t r i b o l o g i c a l system: (a)

o p e r a t i n g v a r i a b l e s (FN, v, 1, Tc)

(b)

g e n e r a l c o n s t a n t s and m a t e r i a l parameters (Ac, Q, Rc,P,

(c)

i n t e r a c t i o n c h a r a c t e r i s t i c s (d, Tc,

5

H)

)

Although i t i s q u i t e d i f f i c u l t t o p e r f o r m r e l i a b l e c a l c u l a t i o n s o f t h e wear r a t e s due t o t h e u n c e r t a i n t i e s o f some o f t h e s e q u a n t i t i e s , t h e above equat i o n s may s e r v e as a b a s i s f o r a p h y s i c a l p i c t u r e o f t h e t r i b o - c h e m i c a l wear mechanism.

4,4,6

THE

COMPLEXITY

OF WEAR PROCESSES

I n general, t h e d i f f e r e n t wear mechanisms as d i s c u s s e d s e p a r a t e l y i n t h e f o r e g o i n g s e c t i o n s , a r e superimposed. The processes o f t r i b o - c h e m i c a l r e a c t i o n s and adhesion l e a d t o changes i n t h e p r o p e r t i e s o f t h e s u r f a c e s . Thereby r e a c t i o n p r o d u c t s a r e formed o r m a t e r i a l i s t r a n s f e r r e d t o t h e o t h e r p a r t n e r . The processes a r e a c t i v a t e d by t h e mechanical and thermal energy t r a n s f e r r e d and d i s s i p a t e d i n t h e s u r f a c e a s p e r i t i e s and i n t h e b u l k m a t e r i a l . A l l t h e s e processes promote t h e f o r m a t i o n o f l o o s e wear p a r t i c l e s which, i n any case, a r e generated t h r o u g h t h e mechanisms o f s u r f a c e f a t i g u e and abrasion.

127

A w e l l known wear mode which r e s u l t s t h r o u g h t h e s u p e r p o s i t i o n o f a l l f o u r b a s i c wear mechanisms d e s c r i b e d above i s f r e t t i n g wear (Ref. 4.118,

4.119).

F r e t t i n g wear o c c u r s i f two c o n t a c t i n g s o l i d b o d i e s move r e l a t i v e l y

t o each o t h e r i n an o s c i l l a t o r y m o t i o n w i t h an a m p l i t u d e o f movement o f l e s s

than 100 pm. I n i n d u s t r y , f r e t t i n g occurs, f o r example, i n t h e f o l l o w i n g mechanical systems and components: l a p j o i n t s , s p l i n e s , p u s h - f i t t e d s h a f t wheels, metal s t a t i c s e a l s , e n g i n e mounts, c l u t c h e s , e t c . The s u r f a c e damage due t o f r e t t i n g i s c h a r a c t e r i z e d by t h e i n i t i a t i o n o f f a t i g u e c r a c k s and t h e f o r m a t i o n o f f r e t t i n g d e b r i s . As a consequence o f f r e t t i n g , f a t i g u e - s t r e n g t h r e d u c t i o n f a c t o r s o f 3 t o 6 a r e q u i t e normal ( R e f . 4.120). The c h a i n o f events t h a t l e a d s t o f r e t t i n g i s compiled s c h e m a t i c a l l y i n Table 4.4 (Ref.

4.121).

I

Initiation and propagation of surface cracks

Formation and rupture

II

Ill

Table 4.4

Schematic r e p r e s e n t a t i o n o f t h e d i f f e r e n t stages o f f r e t t i n g .

The f i r s t s t a g e ( I ) i s i n i t i a t e d by t h e o s c i l l a t o r y c o n t a c t d e f o r m a t i o n l e a d i n g t o t h e g e n e r a t i o n and p r o p a g a t i o n o f s u r f a c e c r a c k s as w e l l as t o t h e d i s p e r s a l o f s u r f a c e contaminants and t h e f o r m a t i o n and r u p t u r e o f adh e s i v e bonds. The second s t a g e ( 1 1 ) i s t h e f o r m a t i o n o f wear p a r t i c l e s e i t h e r by t h e s u r f a c e f a t i g u e mechanism o r t h e a d h e s i o n / d e f o r m a t i o n process. T h i s i s f o l l o w e d by t h e o x i d a t i o n o f wear p a r t i c l e s i n t r i b o - c h e m i c a l

re-

a c t i o n s . The t h i r d s t a g e ( 1 1 1 ) c o n s i s t s o f t h e a b r a s i v e a c t i o n o f formed wear p a r t i c l e s . T h i s i n t u r n a s s i s t s t h e processes o f stage ( I ) , and so on. The f r e t t i n g mode o f wear which occurs under o s c i l l a t o r y m o t i o n i s a v e r y pronounced example o f t h e s u p e r p o s i t i o n o f t h e d i f f e r e n t wear mechanisms

128 d e s c r i b e d s e p a r a t e l y above. From v a r i o u s wear s t u d i e s i t i s obvious t h a t under s l i d i n g and r o l l i n g c o n d i t i o n s i n most cases a s u p e r p o s i t i o n o f wear mechanisms a l s o occurs. Consider, f o r example a s i m p l e t r i b o - m e c h a n i c a l system c o n s i s t i n g o f two s o l i d b o d i e s ( l ) , ( 2 ) s l i d i n g i n a r e a c t i v e gaseous atmosphere ( 3 ) as i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 4.39 above. As i n d i c a t e d by t h e schematic diagram i n t h e c e n t r e o f F i g u r e 4.39, t h e f o l l o w i n g processes o c c u r i n general s i m u l t a n e o u s l y a t t h e i n t e r f a c e : (i)

f o r m a t i o n o f s u r f a c e l a y e r s by a d s o r p t i o n o r t r i b o - c h e m i c a l r e a c t i o n s o f t h e s l i d i n g s u r f a c e s ( 1 ) and ( 2 ) w i t h t h e gaseous environment ( 3 ) ,

( i i)

adhesive t r a n s f e r o f m a t e r i a l and r e a c t i o n p r o d u c t s f r o m (1)-(

2)

and (2)--(1), ( i i i ) g e n e r a t i o n o f wear p a r t i c l e s from t h e b u l k m a t e r i a l , t h e r e a c t i o n p r o d u c t s or t h e adhesive t r a n s f e r r e d m a t e r i a l o f b o t h (1) and ( 2 ) through t h e e f f e c t s o f s u r f a c e f a t i g u e and abrasion. The changes o f t h e m a t e r i a l components o f a t r i b o - m e c h a n i c a l system due t o t h e combined a c t i o n o f t h e wear mechanisms have been s t u d i e d s y s t e m a t i c a l l y by Mdlgaard (Ref. 4.122) and a r e shown s c h e m a t i c a l l y i n F i g u r e 4.39. The p o s s i b l e m a t e r i a l components of a wearing system, c o n s i s t i n g i n i t i a l l y o f the three partners ( l ) , (2), ( 3 ) , are: the given materials

M1

t h e gaseous atmosphere

M2 G

deformed m a t e r i a l p a r t s

D2

t r a n s f e r r e d deformed m a t e r i a l back-transferred material reaction products

R1

t r a n s f e r r e d reaction products debris o f given material

ZM

debris o f reaction products

ZR

adsorbed gas

129

I

I n i t i a l state

I

1-

1ope

abrasion, surface f a t i g u e

I

Final state

I

G

F i g u r e 4.39

-I

debris

Superposition o f wear mechanisms i n a tribo-mechanical system and the changes o f t h e system's elements due t o wear processes.

I

130 I n summary, we see f r o m F i g u r e 4.39 t h a t t h e s t u d y o f wear i n a t r i b o mechanical system i s one i n v o l v i n g a complex interdependence o f many p r o cesses and p h y s i c a l parameters. I t i s most d i f f i c u l t t o i s o l a t e any one p r o cess o r parameter f o r i n v e s t i g a t i o n , and hence we a r e f o r c e d i n t o an e m p i r i c a l approach t o t h e s u b j e c t . I n o r d e r t o g i v e t h i s e m p i r i c a l approach a def i n i t e d i r e c t i o n l i k e l y t o prove s u c c e s s f u l , one must c o n s i d e r , s y s t e m a t i c a l l y , a l l t h e processes and parameters r e l e v a n t t o a g i v e n wear s i t u a t i o n . F o r t h e p r a c t i c a l a p p l i c a t i o n o f t h e systems approach t o t h i s s u b j e c t t h e data-sheet d e s c r i b e d i n Chapter 8 may be used.

4,5

LUBRICATION MODES

4 , 5 , 1 STRIBECK

CURVE AND LUBRICATION

The t r i b o l o g i c a l processes, i . e . ,

MODES

t h e c o n t a c t , f r i c t i o n and wear processes

discussed h i t h e r t o are, i n general , r e l a t e d t o d i r e c t physical i n t e r a c t i o n s between r e l a t i v e l y moving surfaces. A l l these processes can be i n f l u e n c e d o r m o d i f i e d by t h e process o f l u b r i c a t i o n . The purpose o f l u b r i c a t i o n i s t o s e p a r a t e t h e s u r f a c e s moving r e l a t i v e t o each o t h e r w i t h a f i l m o f a m a t e r i a l which can be sheared w i t h low r e s i s t a n c e w i t h o u t causing any damage t o t h e s u r f a c e s . Depending on t h e t h i c k n e s s o f t h e l u b r i c a n t f i l m (which may range from some t e n t h o f a m i l l i m e t e r down t o t h e nm range), t h e i n t e r f a c i a l h e i g h t d i s t r i b u t i o n o f t h e l u b r i c a n t f i l m and t h e degree o f geometric c o n f o r m i t y , d i f f e r e n t l u b r i c a t i o n modes can be d i s t i n g u i s h e d . The l u b r i c a t i o n modes can be c o n v e n i e n t l y d i s c u s s e d i n c o n s i d e r i n g t h e S t r i b e c k curve. S t r i b e c k i n 1900 t o 1902 performed comprehensive experiments on t h e f r i c t i o n o f s l i d i n g and r o l l i n g b e a r i n g s , measuring t h e 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 o f t h e o p e r a t i n g v a r i a b l e s l o a d T (Ref. 4.123).

FN, v e l o c i t y v and temperature

I n o r d e r t o e l i m i n a t e t h e i n f l u e n c e o f t h e temperature depen-

dence o f v i s c o s i t y on h i s r e s u l t s , S t r i b e c k r e c a l c u l a t e d t h e measured 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 o f l o a d and v e l o c i t y f o r a c o n s t a n t b u l k - o i l temperature o f 25OC. The a c c u r a t e e x p e r i m e n t a l measurements o f S t r i b e c k s e r v e d as a b a s i s f o r t h e t h e o r e t i c a l work o f Sommerfeld, Giimbel and successors i n e s t a b l i s h i n g t h e t h e o r y o f hydrodynamic l u b r i c a t e d b e a r i n g s , see S e c t i o n 1.2.3. I t i s now g e n e r a l l y accepted t h a t t h e S t r i b e c k c u r v e r e p r e s e n t s t h e

general c h a r a c t e r i s t i c o f l u b r i c a t e d moving s u r f a c e s as a f u n c t i o n o f t h e

131

l u b r i c a n t v i s c o s i t y -q , t h e v e l o c i t y v and t h e normal l o a d FN ( o r p r e s s u r e p ) . I n F i g u r e 4.40 t h e shape o f t h e S t r i b e c k c u r v e i s p l o t t e d i n a s i m p l i f i e d manner as a f u n c t i o n o f t h e parameter

1.v .

F N - l . ( T h i s parameter i s

r e l a t e d t o t h e r e c i p r o c a l o f t h e Sommerfeld number So, see S e c t i o n 4.5.2.)

t

i

I

1

B

111: h-0 11: h - R

FN

solid 1 lubricant solid 2

I I

s u r f a c e roughness R

I

I: h s R

v i s c o s i t- y n, x v e l o c i t y v l o a d FN

F i g u r e 4.40

S t r i b e c k c u r v e and l u b r i c a t i o n regimes ( s c h e m a t i c ) .

As i l l u s t r a t e d i n F i g u r e 4.40,

depending on t h e geometry, t h e m a t e r i a l s ,

t h e o p e r a t i n g c o n d i t i o n s and t h e s e p a r a t i o n h o f t h e s u r f a c e s , t h r e e main l u b r i c a t i o n regimes may be d i s t i n g u i s h e d :

I

:

Hydrodynamic l u b r i c a t i o n (and Elastohydrodynamic, EHO, l u b r i c a t i o n ) ,

I1

:

P a r t i a l EHD l u b r i c a t i o n o r Mixed l u b r i c a t i o n ,

111 : Boundary l u b r i c a t i o n .

I n regime I , t h e r i g i d s u r f a c e s a r e s e p a r a t e d by a c o n t i n u o u s l u b r i c a n t f i l m , whose t h i c k n e s s i s much l a r g e r t h a n t h e combined s u r f a c e roughness

measure R o f t h e s u r f a c e s . The f r i c t i o n r e s i s t a n c e i s due t o t h e i n t e r n a l f r i c t i o n o f t h e l u b r i c a n t . I n t h i s regime, t h e t r i b o l o g i c a l b e h a v i o u r o f t h e system i s determined by t h e r h e o l o g y o f t h e l u b r i c a n t and can be c a l -

132 c u l a t e d o r e s t i m a t e d by t h e methods o f f l u i d mechanics. I f t h e l u b r i c a t e d system under c o n s i d e r a t i o n c o n s i s t s o f nonconformal c o n c e n t r a t e d c o n t a c t s , t h e e l a s t i c ( H e r t z i a n ) d e f o r m a t i o n o f t h e s u r f a c e s and t h e p r e s s u r e dependence o f t h e l u b r i c a n t s v i s c o s i t y must a l s o t a k e n i n t o account. T h i s l e a d s t o t h e regime o f elastohydrodynamic l u b r i c a t i o n . Since i n regime I no d i r e c t p h y s i c a l c o n t a c t i n t e r a c t i o n s between t h e s u r f a c e s qccur, wear processes cannot t a k e p l a c e ( e x c e p t s u r f a c e f a t i g u e wear, c a v i t L t i o n wear o r f l u i d erosion). I f under c o n d i t i o n s o f hydrodynamic o r EHD l u b r i c a t i o t i , t h e l u b r i c a n t v i s c o s i t y o r t h e v e l o c i t y decreases o r t h e l o a d i n c r e a s e s , t h e l u b r i c a n t

f i l m g e t s " t h i n n e r " and 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 decreases. I f t h e n t h e f i r s t a s p e r i t y c o n t a c t i n t e r a c t i o n s occur, r e g i o n I 1 o f p a r t i a l EHD l u b r i c a t i o n o r mixed l u b r i c a t i o n i s reached. I n t h i s regime t h e l o a d i s c a r r i e d p a r t l y by t h e f l u i d f i l m and p a r t l y b y t h e c o n t a c t i n g s u r f a c e asp e r i t i e s . Consequently, i n t h i s regime t h e f r i c t i o n r e s i s t a n c e i s due p a r t l y t o t h e s h e a r i n g o f t h e l u b r i c a n t f i l m and p a r t l y t o t h e a s p e r i t y i n t e r a c t i o n s . I n regime 11, i n p r i n c i p l e , a l l wear mechanisms may t a k e p l a c e as discussed i n S e c t i o n 4.4.

The processes e x p l a i n e d above a r e , o f course,

i n f l u e n c e d and m o d i f i e d by t h e a c t i o n o f t h e l u b r i c a t i n g f i l m . I f i n a l u b r i c a t e d system which r u n s i n regime I 1 o f F i g u r e 4.40 t h e o p e r a t i n g c o n d i t i o n s change f u r t h e r t o t h e l e f t o f t h e S t r i b e c k curve, t h e amount o f a s p e r i t y i n t e r a c t i o n s w i t h i n t h e c o n t a c t area i n c r e a s e s , and t h e

f i l m t h i c k n e s s decreases down t o some monolayers o r below. I n regime I 1 1 o f boundary l u b r i c a t i o n , b u l k r h e o l o g i c a l p r o p e r t i e s o f t h e l u b r i c a n t a r e o f l e s s importance and t h e l o a d i s c a r r i e d a l m o s t e n t i r e l y t h r o u g h t h e d e f o r m a t i o n of t h e a s p e r i t i e s . C l e a r l y , i n regime I11 t h e physico-chemical i n t e r a c t i o n s a t t h e s o l i d / l u b r i c a n t / s o l i d i n t e r f a c e determine t h e f r i c t i o n and wear b e h a v i o u r o f t h e system. A f t e r t h i s s i m p l i f i e d s u r v e y o f t h e d i f f e r e n t l u b r i c a t i o n modes w i t h t h e use of t h e g e n e r a l i z e d S t r i b e c k diagram, t h e d i f f e r e n t l u b r i c a t i o n modes w i l l be discussed i n some d e t a i l i n t h e f o l l o w i n g .

4,5,2

HYDRODYNAMIC LUBRICATION

I n t h e process o f hydrodynamic l u b r i c a t i o n o f a t r i b o l o g i c a l system, a continuous f l u i d f i l m i s b r o u g h t between t h e s u r f a c e s i n r e l a t i v e m o t i o n i n o r d e r t o m i n i m i z e f r i c t i o n and t o e l i m i n a t e wear. The t r i b o l o g i c a l b e h a v i o u r of a h y d r o d y n a m i c a l l y l u b r i c a t e d system i s t h e n m a i n l y determined by t h e two following features:

133 (i)

The r e s i s t a n c e t o m o t i o n i s g i v e n by t h e " i n t e r n a l f r i c t i o n " o f t h e

(ii)

The e f f e c t s of wear a r e e l i m i n a t e d i f t h e geometry o f t h e s u r f a c e s i s

fluid, i.e.,

t h e shear r e s i s t a n c e o r " v i s c o s i t y " o f t h e f l u i d f i l m .

such t h a t a l o a d - c a r r y i n g p r e s s u r e i s s e t up i n t h e l u b r i c a n t f i l m d u r i n g ,the m o t i o n o f t h e surfaces l e a d i n g t o a complete s e p a r a t i o n o f the surfaces. I n ( i ) , t h e r e s i s t a n c e t o m o t i o n o f a h y d r o d y n a m i c a l l y l u b r i c a t e d system i s determined b y t h e shear f o r c e s which e x i s t i n a moving f l u i d . To g e t a meas u r e o f t h e shear r e s i s t a n c e o r v i s c o s i t y o f t h e f l u i d , c o n s i d e r a system

o f two s o l i d p l a n e s u r f a c e s , as sketched i n F i g u r e 4.41.

" ' area

A

v = o

Figure 4.41

Viscous d r a g between two p a r a l l e l p l a t e s

I n F i g u r e 4.41 t h e l o w e r s u r f a c e i s k e p t s t a t i o n a r y w h i l e t h e upper moves p a r a l l e l t o i t a t a v e l o c i t y vo. S i n c e t h e molecules o f t h e f l u i d adhere t o t h e s u r f a c e s , a t v e l o c i t i e s which a r e n o t t o o h i g h , a l a m i n a r f l o w p r o f i l e r e s u l t s w i t h i n t h e f l u i d w i t h v = vo a t t h e upper s u r f a c e and v = o a t t h e l o w e r s u r f a c e . The f o r c e , F, r e q u i r e d t o keep t h e upper s u r f a c e moving i s t h e n p r o p o r t i o n a l t o t h e area o f t h e surfaces, A, and t o vo/z, where z i s t h e d i s t a n c e between t h e p l a t e s . Thus t h e shear s t r e s s F/A i s p r o p o r t i o n a l t o t h e change o f shear s t r a i n vo/z:

o r more g e n e r a l l y :

154 The constant o f p r o p o r t i o n a l i t y 7 i s c a l l e d c o e f f i c i e n t o f v i s c o s i t y , and f l u i d s which obey p r o p o r t i o n a l i t y between the viscous shear s t r e s s and the r a t e o f change o f the shear s t r a i n %are

termed Newtonian f l u i d s . As regards p o i n t ( i i ) , f o r the generation o f a load-carrying pressure the formation o f a converging, wedge-shaped f i l m i s necessary, as shown by Reynolds i n 1886 (Ref. 4.124). A physical p i c t u r e o f the processes leading t o a generation o f a pressure i n a converging o i l f i l m can be gained by considering a simple t i l t i n g pad bearing, shown schematically i n Figure 4.42.

distribution t i l t i n g pad

Figure 4.42

A t i l t i n g pad bearing.

The t i l t i n g pad i s s t a t i o n a r y w i t h an i n l e t gap z1 l a r g e r than the o u t l e t gap z2, The whole gap i s flooded w i t h a viscous incompressible l u b r i c a n t . Assume t h a t i n i t i a l l y the i n l e t v e l o c i t y d i s t r i b u t i o n may be l i n e a r (as i n Figure 4.41). Since z l > z2 there would be an excess o f i n l e t flow over the o u t l e t f l o w i n c o n t r a s t t o the c o n d i t i o n o f c o n t i n u i t y o f flow. This automat i c a l l y leads t o the generation o f a pressure d i s t r i b u t i o n against which the i n l e t f l o w has t o work. This i n t u r n modifies the v e l o c i t y p r o f i l e s : a t t h e i n l e t the v e l o c i t y p r o f i l e i s concave and a t the o u t l e t i t i s convex as i n The area under each v e l o c i t y - p r o f i l e

d i c a t e d schematically i n Figure 4.42.

curve along the pad i s the same, thus the c o n d i t i o n o f c o n t i n u i t y o f f l o w i s f u l f i l l e d . I f t h e surfaces are f u l l y separated, r e l a t i v e motion occurs e n t i r e l y w i t h i n the 1u b r i cant f i I m .

135 F o r t h e t r i b o l o g i c a l b e h a v i o u r o f a h y d r o d y n a m i c a l l y l u b r i c a t e d mec h a n i c a l system, i . e . ,

t h e t r a n s m i s s i o n and d i s s i p a t i o n o f mechanical energy,

t h e f o l l o w i n g aspects a r e i m p o r t a n t : t h e i n f l u e n c e s o f t h e o p e r a t i n g v a r i a b l e s l i k e l o a d , v e l o c i t y , temperat u r e on t h e p r e s s u r e and f i l m t h i c k n e s s generated i n t h e l u b r i c a n t f i l m , t h e r e l a t i o n s between ( a ) and t h e system geometry and t h e m a t e r i a l s and l u b r i c a n t parameters, t h e amount o f mechanical energy d i s s i p a t e d and t h e v a l u e o f f r i c t i o n c o e f f i c i e n t , depending on ( a ) and ( b ) , t h e l i m i t s o f hydrodynamic l u b r i c a t i o n i n r e l a t i o n t o ( a ) , ( b ) and ( c ) . The main f e a t u r e s o f t h e s e p o i n t s w i l l be d i s c u s s e d i n t h e f o l l o w i n g , s t a r t i n g f r o m a c o n s i d e r a t i o n o f t h e general

equation o f motion f o r a viscous

f l u i d , t h e Navier-Stokes e q u a t i o n . The main p h y s i c a l i d e a s i n v o l v e d i n t h e d e r i v a t i o n o f t h i s e q u a t i o n a r e t h e f o l l o w i n g (Ref. 4 . 1 2 5 ) : Consider an element o f volume A V w i t h i n a f l u i d o f v i s c o s i t y 7 and d e n s i t y p which moves under t h e a c t i o n o f a s p e c i f i c p r e s s u r e p and an ext e r n a l c o n s e r v a t i v e f o r c e f i e l d o f t h e p o t e n t i a l 0 w i t h a mean v e l o c i t y v, as i n F i g u r e 4.43.

-

y 1 * c

fluid of viscosity1

-

--c

and density p

__

t

F i g u r e 4.43

A volume element w i t h i n a v i s c o u s f l u i d .

A c c o r d i n g t o Newton's law o f m o t i o n , t h e t o t a l f o r c e p e r u n i t volume i s equal t o t h e t i m e r a t e o f change o f l i n e a r momentum

force

=

-

(mass x v e l o c i t y )

F

=

p x

(acceleration)

dt

138 The f o r c e per u n i t volume F i s given as sum o f three terms:

(i)

F1:

the pressure force per u n i t volume

The pressure on the face a t x gives the f o r c e p b y b z , and the pressure on the face a t x t A x gives the f o r c e

so t h a t the r e s u l t a n t f o r c e i s

- (#)

- [p

t

(#A

x]A y A z,

A x A y A z. I f we take the

remaining p a i r s of the faces o f the cubes we see t h a t the pressure f o r c e per u n i t volume i s

or w i t h the use o f the Nabla operator

v

a

(ii)

=

a

(-a x

s

a a TIT*X I

F2: the g r a v i t y forces per u n i t volume I t i s w e l l known t h a t forces due t o g r a v i t y are conservative forces.

With a p o t e n t i a l per u n i t mass, (0

the f o r c e density r e s u l t s as

( i i i ) F3: the viscous forces per u n i t volume A t the bottom face o f the volume element, the stress

7%

acts ac-

cording t o t h e d e f i n i t i o n o f the v i s c o s i t y given above. A t y t A y the stress i s

so t h a t the r e s u l t a n t s t r e s s i s

137 Summing, i t f o l l o w s t h a t

v 2= -a'

with

ax2

2

+ a (Lap1 ace

a2

'3

operator)

az2

This expression i s v a l i d f o r incompressible f l u i d s . I n t h e general case o f c o m p r e s s i b l e f l u i d s t h e r e i s a n o t h e r t e r m i n s t r e s s which depends on o t h e r d e r i v a t i v e s o f t h e v e l o c i t y . The g e n e r a l e x p r e s s i o n f o r t h e v i s c o u s f o r c e s i s g i v e n by

where 4' i s t h e s o - c a l l e d second c o e f f i c i e n t o f v i s c o s i t y ( R e f . 1.7). T h i s q u a n t i t y i s u s u a l l y s a i d t o be r e l a t e d t o t h e normal o r shear coefficient o f viscosity

1

by t h e e x p r e s s i o n

A f t e r t h e d e t e r m i n a t i o n o f t h e f o r c e s a c t i n g on a volume element o f a v i s cous f l u i d , we need an e x p r e s s i o n f o r t h e a c c e l e r a t i o n o f a f l u i d p a r t i c l e . I n t r y i n g t o g e t an e x p r e s s i o n f o r t h e a c c e l e r a t i o n o f a f l u i d p a r t i c l e , i t must be t a k e n i n t o account t h a t i f v ( x , y, z, t ) i s t h e v e l o c i t y o f a f l u i d p a r t i c l e which i s a t t h e l o c a t i o n ( x , y, z ) a t t i m e t, then t h e v e l o c i t y o f t h e same p a r t i c l e a t t i m e t

v (x

The a c c e l e r a t i o n

At

t

t

A t i s g i v e n by

vxAt, y

t

v At, z Y

t

av v y a y

av v z T

vzAt, t +At).

i s then a v

vx

ax

(v

v

o r symbolically

) v

t -a

v

a t

av

t73T

138 Now, i n s e r t i n g i n Newton's e q u a t i o n = p x (acceleration)

F

t h e expressions o b t a i n e d f o r t h e f o r c e F = F1 t

F2

t

F3 and t h e a c c e l e r a -

t i o n A v/A t and combining e v e r y t h i n g , t h e g e n e r a l Navier-Stokes e q u a t i o n f o r t h e m o t i o n o f a viscous f l u i d i s av

P{m+ ( v

7

) v}

=

-

a p -pfj@t?lV2v

(7t 7')

t

a ( av )

T h i s e q u a t i o n i s t h e b a s i s f o r a l l o f hydrodynamics ( s i m i l a r t o t h e Maxwell e q u a t i o n s which a r e t h e b a s i s f o r a l l o f e l e c t r o d y n a m i c s ) . The e q u a t i o n and i t s d i v e r s e a p p l i c a t i o n i n t r i b o l o g y have been s t u d i e d a t l e n g t h by d i f f e r e n t a u t h o r s . F o r a d i s c u s s i o n o f t h i s aspect, see (Ref. 4.126). S t a r t i n g f r o m t h e Navier-Stokes e q u a t i o n o f f l u i d mechanics, Reynolds i n h i s fundamental paper o f 1886 l a i d t h e b a s i s o f hydrodynamic l u b r i c a t i o n t h e o r y and p r a c t i c e . The d e r i v a t i o n o f t h e Reynolds e q u a t i o n o b t a i n e d e i t h e r f r o m t h e Navier-Stokes e q u a t i o n o r o t h e r w i s e , can be found i n any s t a n d a r d t e x t b o o k o f hydrodynamics, see f o r i n s t a n c e t h e books by Cameron (Ref. 1.7) o r Hersey (Ref. 4.126). The Reynolds e q u a t i o n i s a d i f f e r e n t i a l e q u a t i o n f o r t h e p r e s s u r e d i s t r i b u t i o n , t a k i n g i n t o account t h e v e l o c i t i e s o f t h e s o l i d surfaces and t h e p r o f i l e o r c o n t o u r o f t h e l u b r i c a n t f i l m . Since, f r o m a c o n s i d e r a t i o n o f Reynolds e q u a t i o n , a p h y s i c a l p i c t u r e o f t h e hydrodynamic l u b r i c a t i o n process as w e l l as b a s i c t r i b o l o g i c a l r e l a t i o n s f o r t h e l o a d c a r r y i n g c a p a c i t y and f r i c t i o n r e s i s t a n c e can be o b t a i n e d , a b r i e f d i s c u s s i o n o f Reynolds e q u a t i o n and i t s consequences i s g i v e n i n t h e f o l l o w i n g .

f gene r a t e d pressure d i s t r i b u t ion

F i g u r e 4-44

Two-dimensional flu i d - f i1m geometry

I

139 Consider a g a i n a s i m p l e t i l t i n g pad b e a r i n g , shown s c h e m a t i c a l l y i n F i g u r e 4.44, w i t h t h e f o l l o w i n g assumptions: (a)

The f l u i d i s Newtonian

(b)

The f l u i d f l o w i s l a m i n a r

(c)

The f l u i d adheres t o t h e b e a r i n g s u r f a c e s

(d)

The f l u i d i n e r t i a can be n e g l e c t e d

(e)

The f l u i d w e i g h t can be n e g l e c t e d

(f) (9)

The f l u i d p r e s s u r e i s c o n s t a n t across t h e t h i c k n e s s o f t h e f l u i d f i l m The f l u i d i s i n c o m p r e s s i b l e .

F o r t h i s case, t h e Reynolds d i f f e r e n i a l e q u a t i o n can be w r i t t e n as:

-

-

a h

23T

"wedge" t e r m

" s t r e t c h " term

"squeeze" t e r m

The r i g h t - h a n d s i d e o f t h i s e q u a t i o n c o n t a i n s t h r e e terms o f d i f f e r e n t physical significance. (i)

"Wedge" t e r m

T h i s c o n t r i b u t i o n i s caused by t h e shape o f t h e f l u i d f i l m , - , r e l a t i v e v e l o c i t y (vo ( i i)

-

vl)

ah

and t h e

o f t h e surfaces.

"Stretch" term

T h i s t e r m r e q u i r e s t h a t t h e sum o f t h e v e l o c i t i e s i n t h e x - d i r e c t i o n change as a f u n c t i o n o f x - l o c a t i o n . T h i s t e r m n e v e r e x i s t s i n r i g i d p l a n e - s l i d e r b e a r i n g s b u t i s a p p l i c a b l e t o s p e c i a l cases o f d y n a m i c a l l y l o a d e d j o u r n a l bearings

.

( iii) "Squeeze" t e r m T h i s c o n t r i b u t i o n i s caused by r e l a t i v e m o t i o n normal t o t h e b e a r i n g f l u i d . S o l u t i o n o f t h e Reynolds e q u a t i o n s l e a d s t o t h e p r e s s u r e d i s t r i b u t i o n which, when i n t e g r a t e d i n t h e x- and z - d i r e c t i o n s , y i e l d s t h e l o a d - c a r r y i n g c a pa c ity :

140

FN

=

7 y 1 p ( x , Z) dxdz 0 0

The f l o w o f f l u i d p e r u n i t w i d t h i n t h e d i r e c t i o n o f v e l o c i t y v = ( v o

- vl)

is vh qx

h3 127

=---'2

ap

ax

and t h e z - d i r e c t i o n i s

The f r i c t i o n f o r c e t o be overcome i n a f l u i d - f i l m - l u b r i c a t e d system i s t h a t caused by v e l o c i t y - i n d u c e d and pressure-induced f l u i d shear s t r e s s e s , namely 21

FF

=

x1

5 / 1 3 dxdz

-

0 0

*1

// *1

h

g dxdz

0 0

where t h e p l u s s i g n i s used f o r t h e f o r c e a c t i n g on t h e s l o w e r moving s u r face. C l e a r l y , i n i n t e g r a t i o n s o f t h e Reynolds e q u a t i o n t h e f i l m t h i c k n e s s h = h ( x ) must be known. A f u r t h e r c o m p l i c a t i o n i s t h e v a r i a t i o n o f t h e v i s c o s i t y as a f u n c t i o n o f b o t h temperature and p r e s s u r e . I n g e n e r a l , t h e v i s c o s i t y o f l u b r i c a n t f l u i d s decreases w i t h i n c r e a s i n g temperature and i n c r e a s e s w i t h i n c r e a s i n g p r e s s u r e . The i n f l u e n c e o f t h e s e e f f e c t s on t h e b e h a v i o u r o f l u b r i c a t e d systems w i l l be d i s c u s s e d i n S e c t i o n 4.5.3

and 4.5.6. S o l u t i o n s o f Reynolds e q u a t i o n , as o u t l i n e d above, have been performed

f o r v a r i o u s types o f b e a r i n g s , such as t h r u s t b e a r i n g s and j o u r n a l b e a r i n g s , and t h e t h e o r e t i c a l s u p p o s i t i o n s and p r a c t i c a l consequences o f t h e s e s o l u t i o n s have been d i s c u s s e d i n d e t a i l (see f o r i n s t a n c e

Ref. 4.127).

These

r e s u l t s w i l l n o t b e reproduced h e r e . I n t h e f o l l o w i n g , t h e s o l u t i o n o f t h e Reynolds e q u a t i o n f o r t h e s i m p l e case o f l u b r i c a t i o n o f a c y l i n d e r n e a r a p l a n e w i l l be c o n s i d e r e d i n b r i e f , i n o r d e r t o g e t an i m p r e s s i o n o f t h e i m p l i c a t i o n s o f t h e Reynolds e q u a t i o n and t o o b t a i n a s t a r t i n g p o i n t f o r t h e d i s c u s s i o n o f t h e elastohydrodynamic l u b r i c a t i o n mode. Consider t h e geometry

o f a r i g i d c y l i n d e r n e a r a plane, as i n F i g u r e 4.45.

141

F i g u r e 4.45

A l u b r i c a t e d c y l i n d e r - p l a n e system.

Reynolds e q u a t i o n i n one dimension f o r a s t e a d i l y r u n n i n g b e a r i n g i s

v

:

surface v e l o c i t y

-q

:

viscosity

h h

:

f i l m thickness

:

f i l m t h i c k n e s s when dp/dx = 0

I n t h e s u r r o u n d i n g o f t h e minimum o f t h e gap t h e c i r c l e o f r a d i u s r can be approximated by t h e p a r a b o l i c e q u a t i o n

Using t h i s f i l m - t h i c k n e s s e q u a t i o n and a boundary c o n d i t i o n f o r p ( x ) , t h e Reynolds e q u a t i o n s can be i n t e g r a t e d . I n t h e l i t e r a t u r e , d i f f e r e n t boundary c o n d i t i o n s f o r p ( x ) a r e known: (a)

Sommerfeld c o n d i t i o n , p = 0 a t x =

(b)

H a l f Sommerfeld c o n d i t i o n , p = 0 a t x 2 0

(c)

Reynolds c o n d i t i o n , p = 0 when dp/dx = 0 a t x

+ w

=- 0

The i n t e g r a t i o n o f t h e Reynolds e q u a t i o n i n u s i n g t h e Sommerfeld c o n d i t i o n leads t o t h e pressure d i s t r i b u t i o n p

=

-2-qv-

X

h2

142 Now u s i n g t h e H a l f Sommerfeld c o n d i t i o n , i t i s p o s s i b l e t o c a l c u l a t e e a s i l y t h e t o t a l l o a d c a r r i e d p e r u n i t l e n g t h o f t h e c y l i n d e r FN/L: 0

FN/L

=

Zy 0

Use o f t h e Reynolds c o n d i t i o n l e a d s t o

FN/L

=

2 . 4 5 y 0

I n r e w r i t i n g these equations f o r t h e minimum f i l m t h i c k n e s s as a f u n c t i o n o f t h e o p e r a t i n g parameters l o a d FN and v e l o c i t y v, and t h e v i s c o s i t y 7 and t h e c y l i n d e r r a d i u s r and l e n g t h L, i t f o l l o w s t h a t

( H a l f Sommerfeld)

(Reynolds)

These r e s u l t s show t h a t f o r t h e c y l i n d e r / p l a n e system t h e s e p a r a t i n g t h i c k ness o f t h e l u b r i c a n t f i l m decreases w i t h d e c r e a s i n g v i s c o s i t y 7 , d e c r e a s i n g v e l o c i t y v, o r i n c r e a s i n g normal l o a d Fp,. A f t e r t h e s t u d y o f t h e r e l a t i o n between t h e l u b r i c a n t f i l m t h i c k n e s s and t h e r e l e v a n t system parameters, t h e q u e s t i o n o f f r i c t i o n must be cons i d e r e d . As d e s c r i b e d above, t h e f r i c t i o n f o r c e can be found by i n t e g r a t i n g t h e v i s c o u s shear f o r c e s on t h e c y l i n d e r s u r f a c e and adding t o them any hydrodynamic f o r c e a c t i n g i n t h e d i r e c t i o n of movement. The r e s u l t s o f t h i s c a l c u l a t i o n , a p p l y i n g t h e Reynolds c o n d i t i o n l e a d s t o t h e f r i c t i o n c o e f f i c i e n t (Ref. 1 . 7 ) :

143

I t i s interesting t o compare the results f o r the cylinderlplane system with t h a t f o r a journal bearing - practically, the most important hydrodynamically lubricated mechanical system (Ref. 4.128). I n Figure 4.46 the geometry of an operating journal bearing i s shown schematically, the clearance being grossly exaggerated. I

FN : load

v e rl r2 cr = I*2 - rl

Figure 4.46

:

velocity

: eccentricity : shaft

radius bearing radius : radial clearance :

Schematic representation of the geometry of a journal beari ng

.

Since i n any journal bearing a natural lubricant wedge e x i s t s as a consequence o f the clearance, a t sufficiently high velocities the pressure generated in the wedge o f lubricant supports the shaft and separates i t completely from the bearing bushing. The f r i c t i o n a l behaviour can be described conveniently as a function of operating variables and the journal bearing data in terms o f the "Sommerfeld number" (sometimes also called "GUmbel number"). The Sommerfeld number is defined as

where

p

9,

= -

=

rl

:

load/bearing projected area

:

radial clearance/shaft radius

:

viscosity

:

angular velocity

2rL

'r

7

144

According t o Vogelpohl (Ref. 4.129), the f r i c t i o n coefficient can be expressed approximately as f

=-

J1r so

for

so

1

i t follows t h a t for

so c 1

for

so > 1

In this connection i t should be remembered t h a t the parameter-qv FN-’ was used as abscissa o f the Stribeck curve Figure 4.40, the general characteri s t i c of a lubricated system.

I-EZ-l

transmission

of wn*k

-

In t h i s connection i t should be remembered that the parameter-qv FN-’ was used as abscissa of the Stribeck curve Figure 4.40, the general characteri s t i c of a lubricated system.

145 Supplementing t h e s t u d y o f t h e f r i c t i o n r e s i s t a n c e i n hydrodynamic l u b r i c a t i o n , t h e a s p e c t o f energy d i s s i p a t i o n s h o u l d be s t u d i e d . As exp l a i n e d e a r l i e r , i n a j o u r n a l b e a r i n g t h e t r a n s m i s s i o n of t h e mechanical i n p u t work i n t o t h e t e c h n i c a l l y used o u t p u t work i s performed v i a t h e t o r s i o n a l e l a s t i c d e f o r m a t i o n o f t h e b e a r i n g s h a f t . The f r i c t i o n a l energy losses a r e due t o " p a r a s i t i c " guidance l o s s e s o f t h e s h a f t . I n a f u l l - f l u i d j o u r n a l b e a r i n g t h e f r i c t i o n r e s i s t a n c e a g a i n s t m o t i o n i s g i v e n by t h e v i s cous shear r e s i s t a n c e l e a d i n g t o t h e g e n e r a t i o n o f h e a t w i t h i n t h e l u b r i c a n t which i s e i t h e r removed by t h e c i r c u l a t i n g l u b r i c a n t o r t r a n s f e r r e d t o t h e elements o f t h e b e a r i n g . R e f e r r i n g t o t h e conceptual F i g u r e s 3.6 and

3.7,

i n a s i m p l i f i e d manner, t h e processes o f mechanical energy t r a n s m i s s i o n

and d i s s i p a t i o n a r e d e p i c t e d s c h e m a t i c a l l y i n F i g u r e 4.47. I f t h e whole f r i c t i o n a l power can be expressed as f FN v , t h e n i n s t e a d y - s t a t e t h e d i s s i p a t i o n process i s d e s c r i b e d by f FN v

where

p c1 q A T ,

=

t Ch

A A T2

f

:

f r ic t i o n c o e f f i c i e n t

FN

:

normal l o a d

v

:

velocity

P

:

density o f lubricant

c1

: s p e c i f i c h e a t o f 1u b r i c a n t

9 AT,

:

volume f l o w r a t e o f l u b r i c a n t

:

mean temperature r i s e o f t h e l u b r i c a n t i n

Ch

:

convective heat-transfer c o e f f i c i e n t a t the o i l

passing through t h e bearing bearing interface

A

= 2nrL

A T2

: area o f t h e o i l b e a r i n g i n t e r f a c e :

mean temperature d i f f e r e n c e between t h e o i l i n t h e b e a r i n g and t h e b e a r i n g s u r f a c e

If

AT,

=

AT2

=

A T

i t follows t h a t f FN v

=

A T ( p c1 q + 2 ~ ChrL) c

AT

=

p c1 q + 2nChrL

f FN v

146

where, as shown above, the f r i c t i o n c o e f f i c i e n t can be w r i t t e n as f = -

JIr so

f

=-

+r so I/ 2

for

so -z 1

for

so > I

From these equations i t f o l l o w s t h a t the d e t e r m i n a t i o n o f t h e f r i c t i o n a l temperature r i s e i n a f u l l - f l u i d j o u r n a l b e a r i n g i s extremely complicated. I t f o l l o w s f u r t h e r t h a t i n a p r a c t i c a l j o u r n a l b e a r i n g design problem an

i t e r a t i v e procedure must be adopted (Ref. 4.130). This i s due t o t h e i n t e r dependence o f t h e o p e r a t i n g parameter, load, v e l o c i t y , t h e Sommerfeld number which includes the v i s c o s i t y and t h e temperature

A T w i t h i n t h e bearing. The

consequences o f these e f f e c t s on the p r a c t i c a l design o f bearings are desc r i b e d i n books on p r a c t i c a l l u b r i c a t i o n (see f o r i n s t a n c e t h e Standard Handbook o f L u b r i c a t i o n Engineering, Ref. 4.131).

4 , 5 , 3 ELASTOHYDRODYNAMICLUBRICATION The d i s c u s s i o n o f t h e hydrodynamic l u b r i c a t i o n mode has been performed mainly f o r systems o f h i g h "geometrical conformity", l i k e t i l t e d pad bearings. I n these cases the surfaces are assumed t o remain completely r i g i d under the operation. I n t h e cases o f poor geometrical conformity, as i n t h e cases o f H e r t z i a n concentrated c o n t a c t s i t u a t i o n s , t h e e f f e c t o f t h e e l a s t i c deformation o f t h e surfaces must be taken i n t o account. Owing t o t h e h i g h pressures t o be found i n l u b r i c a t e d H e r t z i a n contacts, t h e e f f e c t o f pressure on t h e l u b r i c a n t ' s v i s c o s i t y must a l s o be considered. A l l these leads t o t h e concept o f elastohydrodynamic (EHD) l u b r i c a t i o n (Ref. 4.132). I n t h e f o l l o w i n g , t h e main f e a t u r e s o f t h e elastohydrodynamic (EHD) l u b r i c a t i o n mode a r e t o be discussed i n two steps: F i r s t l y , t h e isothermal smooth surface EHD theory i s s t u d i e d and secondly, the e f f e c t s o f temperat u r e and surface roughness a r e included. Also i n t h i s s e c t i o n t h e emphasis i s on t h e t r i b o l o g i c a l fundamentals and on t h e systems aspects o f t h e sub-

j e c t matter. As a s t a r t i n g p o i n t , consider a l u b r i c a t e d c y l i n d e r / p l a n e system deformed e l a s t i c a l l y under t h e a c t i o n o f t h e load, as i l l u s t r a t e d i n F i g u r e 4.48.

147

F i g u r e 4.48

An EHD c o n t a c t o f a c y l i n d e r n e a r a p l a n e .

The s i t u a t i o n i s d e t e r m i n e d b y t h e f o l l o w i n g e q u a t i o n s : (i)

Hydrodynamic e q u a t i o n As shown above, t h e one-dimensional Reynolds e q u a t i o n i n i t s i n t e g r a t e d form i s

The s o l u t i o n o f t h i s e q u a t i o n f o r t h e hydrodynamic case has been g i v e n above. T h i s s o l u t i o n i s n o t a p p l i c a b l e , however, t o EHD s i t u a t i o n s owing t o t h e dependence o f t h e f i l m p r o f i l e h and t h e v i s c o s i t y 7 on t h e p r e s s u r e p, i . e . , (ii)

h = h ( p ) and q = y ( p ) .

E l a s t i c i t y equation The f i l m p r o f i l e h ( x ) i s g i v e n by

h

=

h

2 X +-+h o 2.,

elast

I n applying Boussinesq's equation o f e l a s t o s t a t i c s (see Section 4.2.1)

f o r helast

i t follows t h a t

148

( i i i ) Viscosity-pressure r e l a t i o n Assuming t h a t t h e f l u i d i s i n c o m p r e s s i b l e and t h a t an i s o t h e r m a l s i t u a t i o n i s given, t h e v i s c o s i t y - p r e s s u r e r e l a t i o n i s u s u a l l y expressed b y an e x p o n e n t i a l e q u a t i o n

l o: v i s c o s i t y a t atmospheric p r e s s u r e and To

a : pressure-viscosity coefficient The v a l i d i t y o f an e x p o n e n t i a l law i n d i c a t e s an enormous i n c r e a s e o f v i s c o s i t y w i t h pressure. F o r i n s t a n c e , a t a H e r t z i a n p r e s s u r e o f about 2 1 GN/m t h e v i s c o s i t y o f a m i n e r a l o i l may i n c r e a s e b y a f a c t o r o f 106 compared w i t h i t s v a l u e under atmospheric pressure. The s o l u t i o n o f t h e EHD problem i n v o l v e s an i t e r a t i v e procedure t o e s t a b l i s h a c o m p a t i b i l i t y between e q u a t i o n s ( i ) , ( i i ) and ( i i i ) . I n a s i m p l i f i e d desc r i p t i o n t h e i t e r a t i v e procedure r u n s as f o l l o w s . Assuming an i n i t i a l f i l m t h i c k n e s s d i s t r i b u t i o n which i s i n s e r t e d i n t h e Reynolds e q u a t i o n , a p r e s s u r e d i s t r i b u t i o n i s o b t a i n e d . T h i s i n t u r n i s i n s e r t e d i n t h e e l a s t i c equat i o n g i v i n g an e s t i m a t i o n o f t h e e l a s t i c displacements which i s compared w i t h t h e i n i t i a l f i l m - t h i c k n e s s d i s t r i b u t i o n . The i t e r a t i o n c o n t i n u e s u n t i l a s u f f i c i e n t degree o f c o n f o r m i t y i s o b t a i n e d . B e f o r e c o n s i d e r i n g t h e main s o l u t i o n s o f t h e EHD problem, a p h y s i c a l p i c t u r e o f t h e EHD p r e s s u r e and f i l m p r o f i l e w i l l be g a i n e d i n c o n s i d e r i n g t h e drawings shown s c h e m a t i c a l l y i n F i g u r e 4.49 f o r t h e c o n t a c t o f two cyl i n d e r s (Ref. 4.133). F i g u r e 4.49 ( a ) shows t h e w e l l known Hertzian-contact-pressure b u t i o n o f d r y s u r f a c e s s t u d i e d i n S e c t i o n 4.2.1.

distri-

Various s t u d i e s have a l s o

i n d i c a t e d t h a t under l u b r i c a t e d c o n d i t i o n s t h e c e n t r a l p a r t o f t h e gap i s a p p r o x i m a t e l y p a r a l l e l . T h i s r e q u i r e s t h a t a t t h e i n l e t r e g i o n t h e hydrodynamic p r e s s u r e i s l o w e r t h a n t h e H e r t z i a n p r e s s u r e d i s t r i b u t i o n as sketched i n F i g u r e 4.49 ( b ) . I n t h e p a r a l l e l r e g i o n o f t h e gap, t h e f l o w volume p e r u n i t gap w i d t h i s a p p r o x i m a t e l y c o n s t a n t . Now, a t t h e o u t l e t t h e H e r t z i a n p r e s s u r e r a p i d l y decreases and t h e v i s c o s i t y f a l l s s e v e r a l o r d e r s o f magni-

149

( a ) dry Hertzian contact

( b ) pressure p r o f i l e a t the i n l e t

( c ) f i l m p r o f i l e belonging t o t h e pressure p r o f i l e

( d ) pressure p r o f i l e and f i l m p r o f i l e o f

isothermal smooth-surface EHD contact

Figure 4.49

Schematic representation of an EHD contact.

160 tude t o i t s v alue under atmospheric pressure. Under these c o n d i t i o n s , t h e requirement o f t h e c o n t i n u i t y o f f l o w l e a d s t o a c o n s t r i c t i o n i n t h e f i l m p r o f i l e as i n d i c a t e d i n F i g u r e 4.49 ( c ) . T h i s i s connected, i n accordance w i t h t h e e l a s t i c i t y equation, w i t h a p r e s s u r e s p i k e a t t h e o u t l e t . A l l these c o n s i d e r a t i o n s l e a d t o a f i l m p r o f i l e and a p r e s s u r e - d i s t r i b u t i o n shape as sketched i n F i g u r e 4.49 ( d ) . R e c e n t l y , t h e s e d i s t r i b u t i o n s have been d e t e r mined e x p e r i m e n t a l l y u s i n g s p e c i a l p r e s s u r e t r a nsducers (Ref. 4.134). A typ i c a l r e s u l t i s shown i n F i g u r e 4.50 (Ref. 4.94).

The f e a t u r e s o f EHD l u b r i -

c a t i o n as des c rib ed i n Fi g u r e s 4.49 and 4.50 a r e now g e n e r a l l y accepted.

F i g u r e 4.50

Measured p r e s s u r e d i s t r i b u t i o n i n an EHD c y l i n d e r / c y l i n d e r c o n t a c t (Ref. 4.94) 4 -1 ( d H z = 10 bar, n = 20s , rl = r2 = 5cm).

Now, t u r n i n g o u r a t t e n t i o n f r o m t h e p h y s i c a l p i c t u r e o f EHD t o t h e i n f l u e n ces o f t h e v a r i o u s o p e r a t i n g v a r i a b l e s and systems parameters, a r e l a t i o n d e s c r i b i n g t h e f i l m t h i c k n e s s was f i r s t o b t a i n e d by Grubin (Ref. 4.135) i n t h e f o l l o w i n g f o rm

Late r, Dowson and H i g g i n s o n (Ref. 4.136) were a b l e t o show t h a t t h e v a r i o u s s o l u t i o n s o f t h e EHD problem c o u l d be summarized t o t he f ormula:

161

hmin r

where

hmi n

: minimum f i l m thickness

r

:

radius o f r e l a t i v e curvature

‘lo

:

v i s c o s i t y a t atmospheric pressure and a t t h e temperature o f t h e surfaces as they e n t e r the conjunction

E


a

: pressure v i s c o s i t y c o e f f i c i e n t , d e f i n e d by

T =Toexpap 1 v =2 (vl

t v*)

FN/ L

: velocity :

load per u n i t width o f contact

The r e s u l t s were d e r i v e d f o r pure r o l l i n g b u t they are a l s o a p p l i c a b l e t o moderate degrees o f s l i d i n g . The Dowson-Higginson formula has been extended i n various d i r e c t i o n s (Ref. 4.137,

4.138).

Further, refinements o f t h i s f o r -

mula have been obtained by t h e experimental methods o f o p t i c a l elastohydrodynamic f l u i d t e s t i n g (Ref. 4.139,

4.140).

I n a d d i t i o n , a h y p o t h e t i c a l con-

s t i t u t i v e r e l a t i o n f o r EHD o i l f i l m s has been proposed which combines a l i n e a r e l a s t i c response w i t h a n o n - l i n e a r shear t h i n n i n g viscous response (Ref. 4.141). The analyses o f e l astohydrodynamic l u b r i c a t i o n show t h a t t h e major v a r i a b l e s encountered i n isothermal smooth-surface EHD problems can be r e presented by t h e f o l l o w i n g dimensionless groups: h

Film-thickness parameter

:

H

Load parameter

:

w = -

V e l o c i t y parameter

:

u = - TOV

M a t e r i a l s parameter

:

G = a E

= r

FN/L Er

Er

The s e t o f t h e f o u r dimensionless groups can be reduced t o t h r e e w i t h o u t any l o s s o f g e n e r a l i t y (Ref. 4.133, f o r instance are:

4.142,

4.143).

Two o f t h e p o s s i b l e sets,

152

HG2, WG2, UG4 The r e s u l t s o f i s o t h e r m a l , smooth-surface EHD t h e o r y have been c o n f i r m e d e x p e r i m e n t a l l y and a r e now g e n e r a l l y accepted as an i d e a l i z e d b a s i s of t h i s f i e l d . I n more r e a l i s t i c s i t u a t i o n s , however, two f u r t h e r aspects must be considered (Ref. 4.144): (i)

t h e d i s s i p a t i o n o f energy w i t h i n t h e l u b r i c a n t f i l m , i . e . ,

the viscous

h e a t i n g and t h e g e n e r a t i o n o f i n t e r f a c i a l temperatures and i t s i n f l u ence on t h e l u b r i c a n t v i s c o s i t y and t h e f i l m t h i c k n e s s , ( i i ) t h e s u r f a c e roughness. and i t s i n f l u e n c e on t h e f i l m shape and t h e effect o f asperity interactions. Another o p e r a t i n g c o n d i t i o n which may f r e q u e n t l y be i m p o r t a n t b u t r a r e l y c o n s i d e r e d i s t h e s u p p l y and d i s t r i b u t i o n o f l u b r i c a n t i n t h e neighbourhood o f t h e c o n j u n c t i o n r e g i o n . I t has been shown t h a t l u b r i c a n t " s t a r v a t i o n " a l t e r s t h e EHD b e h a v i o u r o f t h e system i n s e v e r a l i m p o r t a n t ways (Ref. 4.145). Moreover, t h e i n f l u e n c e o f s t a r v a t i o n can be an o v e r r i d i n g f a c t o r on t h e performance o f machine elements (Ref. 4.146).

T ( O C ) l160 8

exit

' 1 &

h(W) 1u b r i c a n t temperature b a l l surface temperature

0.2

0.1

0

0.1

0.2

D i s t a n c e f r o m c e n t e r (mm) F i g u r e 4.51

Temperatures i n s l i d i n g EHD c o n t a c t a l o n g c o n t a c t c e n t e r l i n e (Ref. 4.147) ( b a l l - p l a n e c o n t a c t , r = 15.9mm, CiHz = 1GN/m2,

Ty

= 4OoC),

-1 v = 1.4111s ,

153

In applying the I R temperature-detecting technique, Winer and coworkers were able t o measure b o t h lubricant temperatures and surface temperatures in sliding EHD point-contact situations (Ref. 4.147). Some representative results are reproduced in Figure 4.51. The friction-induced temperature d a t a measured under various operating conditions clearly indicate the importance of the e f f e c t of the operating variables sliding velocity and contact pressure, on b o t h ball-surface and fluid temperatures. They also show significant i n l e t zone heating which in turn will reduce the lubricant viscosity and pressure viscosity coefficient, the dominant mechanical properties affecting the EHD film thickness. The influence of friction-induced temperatures on lubricant viscosity lowers the film thickness. Therefore the e f f e c t o f surface roughness and the possibility of asperity contacts cannot be neglected in EHD lubrication. The inclusion o f these effects has led t o the concept of partial EHD lubrication. A characteristic factor of partial EHD i s the r a t i o , h , of the theoret i c a l (isothermal) smooth-surface EHD film thickness ho to the combined roughness, R , o f the surfaces:

ho IT'

where

k

=

[R a i

t

RaE]

112

The value of i s calculated e i t h e r on the basis of readily measured r.m.s. or c.1.a. (R,) values, o r in more sophisticated way, by using the standard deviation of the peak-height distribution of the surface a s p e r i t i e s as described in Section 4.2.1. The h - r a t i o n o t only i s important i n the limits of lubrication and film f a i l u r e i n rolling and sliding situations (see Section 4.5.61, b u t i t can a l s o be used in describing the change-over from f u l l EHD t o partial EHD lubrication or "mixed" lubrication and to boundary lubrication. I f h > 3 t o 5 we expect a f u l l - f l u i d EHD film t o separate the surfaces. A t h = 3 the f i r s t asperity "contacts" occur. A t t h i s point, the f u l l EHD regime of the Stribeck's curve i s l e f t and the region of partial EHD ( a t the minimum o f Stribeck's curve) i s reached.

164

4,5,4

MIXED

LUBRICATION

A s i m p l e and e l e g a n t e x p l a n a t i o n o f t h e regime o f mixed l u b r i c a t i o n i s t o assume t h a t t h e t o t a l a p p l i e d l o a d i s c a r r i e d p a r t l y by t h e hydrodynamic a c t i o n o f t h e l u b r i c a n t f i l m and p a r t l y by a s p e r i t y c o n t a c t s . Consequently, t h e t o t a l f r i c t i o n f o r c e i s supposed t o be due p a r t l y t o v i s c o u s f r i c t i o n and p a r t l y t o t h e a s p e r i t y c o n t a c t . Based on t h i s assumption a c o u p l e o f models o f mixed l u b r i c a t i o n have been proposed which can b e b r o a d l y c l a s s i f i e d i n two groups: Models o f mixed l u b r i c a t i o n , i n which t h e ( c l a s s i c a l ) hydrodynamic l u b r i c a t i o n t h e o r y i s used as a s t a r t i n g p o i n t . T h e o r i e s on t h i s b a s i s a r e due t o Gumbel (Ref. 4.148), Vogelpohl (Ref. 4.149), C h r i s t e n s e n (Ref. 4.150) .and B e r t h e and Godet ( R e f . 4.151). Models o f mixed l u b r i c a t i o n , which s t a r t f r o m t h e EHD l u b r i c a t i o n t h e o r y t a k i n g i n t o account t h e a s p e r i t y c o n t a c t component, suggested by Johnson

, Greenwood

and Poon (Ref. 4.152) and by T a l l i a n (Ref.

4.153). Vogelpohl i n 1954 (Ref. 4.149) extended t h e e x p r e s s i o n f o r t h e f r i c t i o n c o e f f i c i e n t o f a hydrodynamically l u b r i c a t e d j o u r n a l bearing, described i n s e c t i o n 4.5.2 (So > 1)

t o t h e f o l l o w i n g f o r m u l a o f mixed l u b r i c a t i o n

where fo i s 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 and cr and hmin a r e t h e r a d i a l c l e a r a n c e and t h e f i l m t h i c k n e s s a t t h e minimum o f t h e S t r i b e c k curve, respectively. C h r i s t e n s e n i n h i s t h e o r y o f mixed l u b r i c a t i o n (Ref. 4.150) used a m o d i f i c a t i o n o f Reynold’s e q u a t i o n f o r s u r f a c e s w i t h roughnesses i n t h e f o r m o f continuous l o n g i t u d i n a l r i d g e s and w i t h no l a r g e - s c a l e s i d e leakage. I n i t s i n t e g r a t e d form, t h i s e q u a t i o n becomes

155

-dP_

-

E" ( h ' ) 6 W l

+

dx

where

E* ( h ' ) 3

p

i s t h e hydrodynamic pressure,

x

i s a Cartesian co-ordinate i n the d i r e c t i o n o f motion,

1 v1 and v2 and

- E* (boo)

v2)

i s t h e l o c a l dynamic v i s c o s i t y o f t h e l u b r i c a n t , are the v e l o c i t i e s o f the surfaces r e l a t i v e t o t h e i r conjunction,

h'

i s t h e l o c a l f i l m thickness,

E*

i s t h e e x p e c t a t i o n o p e r a t o r , d e f i n e d by

1 00

E*(xn)

=

xn f ( x ) dx

0

A m o d i f i c a t i o n o f t h e c l a s s i c a l Reynolds e q u a t i o n f o r a p p l i c a t i o n t o t h e c o n t a c t o f rough s u r f a c e s has a l s o been proposed by B e r t h e and Godet ( R e f . 4.151).

T h e i r approach a l s o emphasized t h e pronounced i n f l u e n c e o f s l i d i n g

v e l o c i t i e s i n t h e regime o f mixed l u b r i c a t i o n . Johnson, Greenwood and Poon ( R e f . 4.152) combined t h e smooth-surface

EHD t h e o r y o f Dowson and H i g g i n s o n w i t h t h e t h e o r y o f t h e c o n t a c t o f d r y rough s u r f a c e s developed by Greenwood and W i 11 iamson (see S e c t i o n 4.2.1) i n o r d e r t o a p p l y t o c o n d i t i o n s o f mixed o r p a r t i a l c o n t a c t .

F i g u r e 4.52

An EHD c o n t a c t w i t h rough s u r f a c e s : ( a ) p r e s s u r e d i s t r i b u t i o n s , ( b ) diagrammatic r e p r e s e n t a t i o n o f t h e f l e x i b l e elements i n an EHD c o n t a c t .

The s i t u a t i o n i s i l l u s t r a t e d i n F i g u r e 4.52 ( a ) which r e p r e s e n t e i t h e r a l i n e o r a p o i n t c o n t a c t . The t o t a l p r e s s u r e p i s made up o f t h e f l u i d p r e s s u r e pf and t h e a s p e r i t y c o n t a c t p r e s s u r e pa. As shown d i a g r a m m a t i c a l l y i n

156 F i g u r e 4.52 ( b ) , t h e b u l k ( H e r t z an) d e f o r m a t i o n o f t h e two s o l i d s under the applied loatl

FN, which g i v e s r i s e t o t h e nominal c o n t a c t area A,

is

m o d e l l e d by t h e s p r i n g Sh. The o 1 f i l m and t h e a s p e r i t i e s a r e r e p r e s e n t e d by t h e p a r a l l e l s p r i n g s S f and Sa, r e s p e c t i v e l y . A l l s p r i n g s a r e n o n - l i n e a r ; t h e s t i f f n e s s of each i n c r e a s e s w i t h compression. From t h i s model i t f o l l o w s t h a t t h e a s p e r i t y p r e s s u r e i s determined p r i m a r i l y by t h e f i l m - t h i c k n e s s - t o roughness r a t i o h , d e f i n e d above. Likewise, i n T a l l i a n ' s t h e o r y o f p a r t i a l elastohydrodynamic c o n t a c t s (Ref. 4.153),

t h e 1 - r a t i o i s c o n s i d e r e d as an i m p o r t a n t parameter. From t h e

t h e o r i e s o f p a r t i a l EHD, as o u t l i n e d by T a l l i a n and b y Johnson, Greenwood and Poon, i t may be concluded t h a t i f h i s l o w e r than a c e r t a i n l i m i t , l e s s than

h = 0.4 say, t h e l u b r i c a t i o n mode changes t o boundary l u b r i c a t i o n .

4 5 , 5 BOUNDARYL U B R I C A T I O N The l u b r i c a t i o n regime o f t h e u t m o s t l e f t p a r t o f t h e S t r i b e c k c u r v e i s termed boundary l u b r i c a t i o n . T h i s l u b r i c a t i o n mode i s c h a r a c t e r i z e d by t h e f o l l o w i n g features: (a) (b)

t h e s o l i d s u r f a c e s a r e so c l o s e t o g e t h e r t h a t a p p r e c i a b l e c o n t a c t takes p l a c e between t h e a s p e r i t i e s , hydrodynamic e f f e c t s and i n f l u e n c e s o f t h e b u l k r h e o l o g i c a l p r o p e r t i e s o f t h e l u b r i c a n t s a r e o f l i t t l e o r no importance,

(c)

t h e t r i b o l o g i c a l b e h a v i o u r i s determined by s u r f a c e i n t e r a c t i o n s between t h i n l a y e r s o f boundary l u b r i c a n t s and t h e s o l i d s u r f a c e s .

Due t o these f e a t u r e s , t h e processes which determine t h e t r i b o l o g i c a l beh a v i o u r o f s o l i d s u r f a c e s (see S e c t i o n s 4.2,

4.3,

4.4) a r e v a l i d l i k e w i s e

under boundary l u b r i c a t i o n c o n d i t i o n s , namely: (i)

t h e c o n t a c t mechanics and t h e e l a s t i c and p l a s t i c a s p e r i t y deformat i o n processes,

( i i ) t h e c o n t a c t p h y s i c s and c h e m i s t r y and t h e a c t i o n o f s u r f a c e f o r c e s , ( i i i ) t h e f r i c t i o n processes, e s p e c i a l l y t h e s h e a r i n g o f adhesive j u n c t i o n s and t h e d e f o r m a t i o n o f a s p e r i t i e s , (iv)

t h e wear processes which a r e g i v e n i n t h e g e n e r a l case by t h e superp o s i t i o n o f e f f e c t s o f s u r f a c e f a t i g u e , abrasion, adhesion and t r i b o chemical r e a c t i o n s .

157 A l l these s o l i d / s o l i d i n t e r a c t i o n s are modified through the a c t i o n o f t h e boundary l u b r i c a n t , so t h a t t h e t r i b o l o g i c a l b e h a v i o u r o f a boundary l u b r i c a t e d system i s determined by t h e processes a t t h e s o l i d / l u b r i c a n t / s o l i d i n t e r f a c e i n f l u e n c e d by t h e e n v i r o n m e n t a l atmosphere. Compared w i t h t h e o t h e r l u b r i c a t i o n regimes o f t h e S t r i b e c k c u r v e and t h e d r y s t a t e , t h e t r i b o l o g y o f a boundary l u b r i c a t e d system i s most complex due t o t h e v a r i e t y o f i n t e r a c t i o n s and parameters i n v o l v e d . Concerning t h e l u b r i c a t i n g a c t i o n o f a boundary l u b r i c a n t , i t s main purpose i s t o i n t e r p o s e between t h e moving s u r f a c e s a f i l m t h a t i s a b l e t o reduce t h e amount o f d i r e c t s o l i d / s o l i d i n t e r a c t i o n and t h a t i s i t s e l f e a s i l y sheared. T h i s i s p r o v i d e d b e s t by an i n t e r f a c i a l f i l m c o n s i s t i n g o f l o n g c h a i n molecules possessing t h e f o l l o w i n g p r o p e r t i e s : (a)

s t r o n g a t t r a c t i o n between t h e c h a i n s t o r e s i s t p e n e t r a t i o n by s u r f a c e a s p e r i t i e s ( t h u s m i t i g a t i n g wear processes),

(b) (c)

low shear s t r e n g t h t o g i v e a low f r i c t i o n , h i g h m e l t i n g p o i n t so t h a t i t p r o v i d e s s o l i d - f i l m p r o t e c t i o n up t o a h i g h temperature.

Since t h e mechanisms o f boundary l u b r i c a t i o n a r e determined m a i n l y by t h e p h y s i c s and c h e m i s t r y o f t h e s o l i d / l u b r i c a n t / s o l i d

interface, a b r i e f re-

view o f t h e chemical c o m p o s i t i o n o f l u b r i c a n t s i s f i r s t g i v e n f o l l o w e d by a d i s c u s s i o n o f t h e processes o f boundary f i l m f o r m a t i o n and i t s t r i b o l o g i cal behaviour. The v a r i o u s k i n d s o f l u b r i c a n t s may be c l a s s i f i e d i n t o t h r e e g e n e r a l groups:

( I ) "Nonreactive" o r

"

i n d i f f e r e n t " 1u b r i c a n t s

Hydrocarbons and most o t h e r base o i l s f a l l i n t h i s c l a s s . U s u a l l y t h e most i m p o r t a n t p r o p e r t y o f these m a t e r i a l s i s v i s c o s i t y , which depends on chem i c a l s t r u c t u r e i n a f a i r l y r e g u l a r f a s h i o n . The hydrocarbons o r base o i l s f r o m p e t r o l e u m may be c l a s s i f i e d a c c o r d i n g t o t h e i r s t r u c t u r e i n t o s a t u r a t e d ( p a r a f f i n s and naphthenes) and u n s a t u r a t e d ones ( o l e f i n s and aromat i c s ) . The f o u r c l a s s e s can be t y p i f i e d by t h e f o l l o w i n g s t r u c t u r e s : (a)

Paraffin

CH3

-

CH2

-

CH

I CH3

-

CH2

-

CH3

168

(b)

Naphthene

'CH2 7H2

\ CH CH2

I

I

CH

(c)

Olefin

CH2

=

CH

- CH - CH3

I

CH 3

(d)

Aromatic

CH

I

CH\

CH

I1

A l l m i n e r a l o i l s c o n s i s t o f molecules which g e n e r a l l y c o n t a i n more t han one type o f hydrocarbon m o i e t y . C l a s s i f i c a t i o n o f o i l s as p a r a f f i n i c , naphthen i c (i.e., c y c l o p a r a f f i n ) o r aromatic i n d i c a t e s the r e l a t i v e concentrations o f t h e moieties.

( II )

" O i 1 i n e s s " agents

L u b r i c a n t a d d i t i v e s c o n t a i n i n g a p o l a r group a t t a c h e d t o l o n g chains o f methylene groups ( i .e., (-CH2-)n where n > 10) a r e o f t e n r e f e r r e d t o as " o i l i n e s s " o r " l u b r i c i t y " a d d i t i v e s ; oxygen i s t h e most usual hetero-atom i n t h e commonly used m a t e r i a l . T y p i c a l examples are:

159

S t e a r i c acid: CH3 (-CH2-)15

0 // C-OH

Oleic acid:

0 // CH3 (-CH2-)7 CH

=

CH (-CH2-)7 C-OH

Each of these a d d i t i v e s possesses an unbranched hydrocarbon chain with a polar group a t i t s extremity. Besides the long-chain f a t t y acids c e r t a i n alcohols and e s t e r s of s i m i l a r s t r u c t u r e a r e a l s o used. These materials can be dissolved in small q u a n t i t i e s (about 1 per c e n t ) in a base o i l a n d will then a t t a c h themselves t o the metal surfaces. (111)

"

Extreme pressure" ( E P ) and "anti-wear'' (AW) additives

These 1 ubri cant a d d i t i v e s usually contain t h e heteroatoms phosphorus, sulf u r o r chlorine and may a d d i t i o n a l l y o r even p r i n c i p a l l y contain oxygen, lead, zinc, boron, selenium, e t c . Examples are: Dibenzyldisulfide:

0CH2

Zinc d i o c t y l - d i t h i o - p h o s p h a t e :

Zn

ij L

These a d d i t i v e s function under boundary l u b r i c a t i o n conditions by reacting with the contacting metal a s p e r i t i e s t o form films which a i d in the reduction of i n t e r m e t a l l i c contact and wear and t o prevent c a t a s t r o p h i c surface f a i l u r e s (Ref. 4.154, 4 . 1 5 5 ) .

The major determined operating f a c t o r f o r

these actions i s the operating temperature i n the i n t e r f a c e . In order t o understand the mechanisms o f boundary l u b r i c a t i o n , the physico-chemical processes of i n t e r f a c i a l film formation must be considered.

160 The l u b r i c a n t / s o l i d i n t e r a c t i o n s which l e a d t o t h e g e n e r a t i o n o f a p r o t e c t i v e boundary f i l m can be c l a s s i f i e d i n t o t h r e e mechanisms (Ref. 4.156,

4.157) : (a)

PHYSICAL ADSORPTION (PHY SISORPTION)

I n a b o u n d a r y - l u b r i c a t i o n system, p h y s i c a l a d s o r p t i o n occurs when t h e molec u l e s o f t h e l u b r i c a n t a r e h e l d t o t h e s u r f a c e by van d e r Waals s u r f a c e forces (i.e.,

d i p o l e - d i p o l e i n t e r a c t i o n s , see S e c t i o n 4.2.2).

The molecules

a r e weakly bonded, and t h e f i l m f o r m a t i o n i s c h a r a c t e r i z e d by r e v e r s i b i l i t y and monomolecular o r mu1 t i m o l e c u l a r l a y e r s . P o l a r molecules, p a r t i c u l a r l y l o n g c h a i n hydrocarbons, adsorb w i t h p r e f e r r e d v e r t i c a l o r i e n t a t i o n , see F i g u r e 4.53.

( F o r i n s t a n c e : adsorbed s t e a r i c a c i d molecules a r e 19

R

high,

Ref. 4.158.)

unreactive metal

F i g u r e 4.53

Schematic r e p r e s e n t a t i o n o f p h y s i s o r p t i o n .

The p o l a r a d d i t i v e s condense on t h e s u r f a c e t o f o r m a s o l i d f i l m . Many molec u l e s pack i n as c l o s e l y as p o s s i b l e and s t r e n g t h e n t h e f i l m w i t h l a t e r a l cohesive f o r c e s . T h i s s o l i d f i l m , a d h e r i n g t o t h e s u r f a c e and w i t h t h e molec u l e s c o h e r i n g t o each o t h e r , t h e n has t h e a b i l i t y t o r e s i s t p e n e t r a t i o n o f a s p e r i t i e s and t h u s i n h i b i t m e t a l - t o - m e t a l c o n t a c t . I n a d d i t i o n , a zone o f low shear s t r e n g t h i s formed between t h e outermost s u r f a c e s o f two monolayers adsorbed on opposing metal s u r f a c e s . A boundary l u b r i c a t e d system w i t h phys i c a l a d s o r p t i o n o f t h e f i l m i s temperature s e n s i t i v e because h e a t causes

161 d e s o r p t i o n , d i s o r i e n t a t i o n , o r m e l t i n g o f t h e f i l m . Thus, boundary l u b r i c a t i o n dependent upon p h y s i c a l a d s o r p t i o n i s l i m i t e d t o l o w b u l k temperatures and c o n d i t i o n s o f low f r i c t i o n a l h e a t g e n e r a t i o n , i . e . ,

l o w l o a d s and l o w

sliding velocities. (b)

CHEMICAL ADSORPTION (CHEMISORPTION)

I n a b o u n d a r y - l u b r i c a t i o n system, c h e m i s o r p t i o n occurs when t h e molecules o f t h e l u b r i c a n t a r e h e l d t o t h e s u r f a c e by chemical bonds, i . e . ,

short-

range s u r f a c e f o r c e s . Compared w i t h p h y s i s o r p t i o n , i t i s g e n e r a l l y n o t comp l e t e l y r e v e r s i b l e and shows h i g h e r heats o f a d s o r p t i o n ( P h y s i s o r p t i o n :

2,000 t o 10,000 cal/mole; Chemisorption: 10,000 t o 100,000 c a l / m o l e ) . A w e l l known example o f c h e m i s o r p t i o n i n boundary l u b r i c a t i o n i s t h e r e a c t i o n o f s t e a r i c a c i d w i t h i r o n o x i d e i n t h e presence o f w a t e r t o f o r m a "metal soap" f i l m o f i r o n s t e a r a t e on t h e s u r f a c e , as i n F i g u r e 4.54.

/

\

H-C-H /

H-C-H \

H-C-H /

H-C-H

/

\

H-C-H /

H-C-H \

H-C-H /

H-C-H

i

i

\

\

H-C-H /

H-C-H

H-C-H /

H-C-H \

\

H-C-H

H-C-H /

H-C-H

/

H-C-H

adhesion

F i g u r e 4.54

Schematic r e p r e s e n t a t i o n o f c h e m i s o r p t i o n .

These metal soaps n o t o n l y have d e s i r a b l e shear p r o p e r t i e s , t h e y a l s o have m e l t i n g p o i n t s c o n s i d e r a b l y h i g h e r than t h o s e o f t h e o r i g i n a l f a t t y a c i d . F o r example, t h e m e l t i n g p o i n t o f s t e a r i c a c i d i s 69OC; o f i t s metal soaps, i t i s about 120°C. Chemisorbed f i l m s l u b r i c a t e e f f e c t i v e l y up t o t h e i r

m e l t i n g p o i n t , whether t h e f i l m i s formed " i n s i t u " on a r e a c t i v e s u r f a c e o r spread on an u n r e a c t i v e s u r f a c e . Boundary chemisorbed f i l m s p r o v i d e l u b r i c a t i o n a t moderate loads, temperatures and s l i d i n g v e l o c i t i e s and f a i l

162 under severe o p e r a t i n g c o n d i t i o n s . The f a i l u r e t o l u b r i c a t e i s a r e s u l t o f t h e d i s o r i e n t a t i o n , s o f t e n i n g o r m e l t i n g o f t h e f i l m under t h e combined act i o n o f t h e o p e r a t i n g v a r i a b l e s and t h e energy t r a n s a c t i o n s . (c)

CHEMICAL REACTION

I n a b o u n d a r y - l u b r i c a t i o n system, chemical r e a c t i o n between t h e s o l i d s u r faces and t h e l u b r i c a n t molecules occurs when t h e r e i s an exchange of val e n c e e l e c t r o n s and a new chemical compound i s formed as i l l u s t r a t e d i n F i g u r e 4.55.

S

S

S S

F i g u r e 4.55

S S

S

S

S

Schematic r e p r e s e n t a t i o n o f a boundary f i l m formed by chemical r e a c t i o n .

The boundary f i l m s a r e u n l i m i t e d i n t h i c k n e s s (governed by d i f f u s i o n p r o cesses through t h e c r y s t a l l i n e l a t t i c e s ) and c h a r a c t e r i z e d by h i g h a c t i v a t i o n and bonding en e r g i e s and i r r e v e r s i b i l i t y . Most o f t h e c h e m i c a l l y react i v e boundary l u b r i c a n t s c o n t a i n s u l p h u r , c h l o r i n e and phosphorus atoms i n t h e molecule. They a r e b e l i e v e d t o f u n c t i o n b y f o r m i n g m e t a l - s a l t f i l m s o f low shear s t r e n g t h b u t o f h i g h m e l t i n g p o i n t , such as s u l f i d e , c h l o r i d e o r phosphide, a t t h e i n t e r f a c e . These f i l m s a r e more s t a b l e t h a n any p h y s i c a l l y o r c h e m i c a l l y adsorbed f i l m . Boundary l u b r i c a n t s dependent upon chemical r e a c t i o n a r e s u i t a b l e f o r h i g h load, h i g h temperatures, and h i g h s M d i n g speeds and l i m i t e d t o r e a c t i v e m e t a l s . These c o n d i t i o n s a r e commonly r e f e r r e d t o as "extreme-pressure" c o n d i t i o n s , a1 though t h e g r e a t e s t s e v e r i t y a r i s e s f ro m h i g h temperatures. A1 though "EP" a d d i t i v e s f u n c t i o n by r e a c t i n g w i t h t h e s urf ac es t h e y must n o t be t o o r e a c t i v e , o t h e r w i s e t r i b o - c h e m i c a l wear may reach v ery h i g h r a t e s .

163

Concerning the t r i b o l o g i c a l behaviour of a boundary-lubrication system, since the boundary films may be considered t o be s o l i d and t o behave “ a s a r i g i d continuation of the s o l i d body” (Ref. 4.159), the contact, f r i c t i o n and wear processes a s discussed in Sections 4.2, 4.3 and 4.4 a r e v a l i d i n p r i n c i p l e . I n order t o describe the f r i c t i o n a l behaviour of the various boundary f i l m s , s t y l i z e d diagrams have been used (Ref. 4.160, 4.161) as in Figure 4.56.

Figure 4.56

F r i c t i o n behaviour o f boundary-lubrication systems (schema t i c ) .

I n t h i s diagram, the c o e f f i c i e n t o f f r i c t i o n f i s plotted a g a i n s t the temperature T. Curve I i s f o r a system l u b r i c a t e d w i t h a non-polar base o i l . I t shows t h a t the f r i c t i o n is i n i t i a l l y r e l a t i v e l y high and increases with increasing temperature as the weak physical adsorption bonds are loosened. Curve I1 i s f o r a f a t t y acid dissolved i n the base o i l . This l u b r i c a n t rea c t s w i t h the metal s u r f a c e forming a m e t a l l i c soap which i s e a s i l y sheared a t t h e area of real contact. Up t o Tm, the melting point of the metal soap, the f r i c t i o n i s low and constant b u t above t h i s point r i s e s steeply. Curve 111 is representative of an EP a d d i t i v e dissolved in the base o i l . The add i t i v e r e a c t s very slowly below a c e r t a i n reaction temperature Tr. When Tr i s reached, the chemical reaction s t a r t s and the f r i c t i o n c o e f f i c i e n t decreases as the r a t e of f i l m formation permits a s o l i d f i l m t o carry the load. In t h i s case e f f e c t i v e l u b r i c a t i o n i s provided up t o high temperature. Curve IV i s a hypothetical curve f o r an e f f e c t i v e combination of I1 and 111.

Good l u b r i c a t i o n i s p r o v i d e d by t h e f a t t y a c i d below Tr, w h i l e above t h i s temperature t h e g r e a t e r p a r t o f t h e l u b r i c a t i o n i s due t o t h e EP a d d i t i v e . I f t h e wear behaviour o f t h e d i f f e r e n t b o u n d a r y - l u b r i c a t i o n systems i s t o be described i n t h e form o f s t y l i z e d diagrams, t h e c h a r a c t e r i s t i c s shown i n F i g u r e 4.57 r e s u l t .

Wear rate K'

F O c r it F i g u r e 4.57

Load FN

Wear behaviour o f b o u n d a r y - l u b r i c a t i o n systems (schematic).

I n t h i s diagram, t h e wear c o e f f i c i e n t K' (wear volume x load-' distance-')

x sliding

on a l o g s c a l e i s p l o t t e d versus t h e l o a d FN.

Curve ( a ) represents t h e wear behaviour o f a d r y metal/metal s l i d i n g system. As a r e s u l t o f t h e wear processes d e s c r i b e d i n S e c t i o n 4.4 occurr i n g i n i t i a l l y a t t h e " o u t e r " s u r f a c e l a y e r s (see F i g u r e 4.5) a c e r t a i n wear r a t e K',

r e s u l t s . I f t h e l o a d i s r e l a t i v e l y low, t h e s u r f a c e l a y e r s

worn o f f may be r e p l a c e d under t h e a c t i o n o f t h e gaseous environment ( " m i l d wear" regime). I f however, t h e l o a d reaches a c e r t a i n l i m i t , FOcrit, t h e wear process may p e n e t r a t e t o t h e " i n n e r " surface l a y e r s l e a d i n g t o "severe wear" and t o an i n c r e a s e o f t h e wear r a t e over several o r d e r s o f magnitude. Curve ( b ) i s f o r a system l u b r i c a t e d w i t h a base o i l . The i n f l u e n c e o f chemical a d d i t i v e s i n a base o i l may l e a d t o two d i f f e r e n t e f f e c t s :

166

K' by a c e r t a i n amount A KO,

(i)

a r e d u c t i o n o f t h e wear r a t e

(ii)

an i n c r e a s e o f t h e l o a d - c a r r y i n g c a p a c i t y Fcrit

by a c e r t a i n

amount A F. I f t h e a c t i o n of an a d d i t i v e l e a d s p r i m a r i l y t o t h e e f f e c t ( i ) , as shown i n curve (c), i t i s c a l l e d "anti-wear"

(AW) a d d i t i v e . The most common t y p e s

o f AW a d d i t i v e s a r e those c o n t a i n i n g phosphorus, l i k e m e t a l - d i a l k y l d i t h i o phosphate, t r i c r e s y l phosphate o r d i a l k y l p h o s p h i t e . Organic c a r b o x y l i c a c i d s , l i k e s t e a r i c a c i d s and o l e i c a c i d s and t h e i r e s t e r s have a l s o good

AW

p r o p e r t i e s . I f t h e a c t i o n o f an a d d i t i v e l e a d s p r i m a r i l y t o t h e e f f e c t

( i i ) , as shown i n c u r v e ( d ) o f F i g u r e 4.57,

i t i s termed "extreme p r e s s u r e

( E P ) " a d d i t i v e . As mentioned above, t h e most common t y p e o f EP a d d i t i v e s

a r e those c o n t a i n i n g s u l f u r and/or c h l o r i n e . T y p i c a l s u l f u r - c o n t a i n i n g add i t i v e s a r e s u l f u r i z e d f a t t y e s t e r s , terpenes and o l e f i n s o r d i b e n z y l d i s u l f i d e . The most common c h l o r i n e - c o n t a i n i n g EP a d d i t i v e s a r e c h l o r i n a t e d p a r a f f i n s , c o n t a i n i n g up t o 70% C 1 . A l t h o u g h i t i s c l e a r t h a t t h e a d d i t i v e s under boundary c o n d i t i o n s f o r m p r o t e c t i v e s u r f a c e l a y e r s by t h e physico-chemical processes e x p l a i n e d above, t h e chemical d e t a i l s and t h e k i n e t i c s o f t h e f i l m f o r m a t i o n and i t s d i s p e r s a l a r e s t i l l under d i s c u s s i o n . C l e a r l y , i n t h e d i s c u s s i o n o f a d d i t i v e p e r formance b e s i d e s t h e p r o p e r t i e s o f t h e l u b r i c a n t a l s o t h e p r o p e r t i e s of t h e metal s u b s t r a t e must be c o n s i d e r e d (Ref. 4.162).

The l i t e r a t u r e on boundary

l u b r i c a t i o n p r o p e r t i e s o f a d d i t i v e s and t h e i r v a r i o u s combinations i s enormous and cannot be d i s c u s s e d i n d e t a i l i n t h e scope o f t h i s volume.

For

r e c e n t r e v i e w s , see t h e a r t i c l e s by Godfrey ( R e f . 4.156, 4.157), Campbell (Ref. 4.161), F e i n ( R e f . 4.163). The t r e a t i s e on t h e b o u n d a r y - l u b r i c a t i o n mode o f a t r i b o l o g i c a l system s h o u l d n o t be c l o s e d w i t h o u t a c o m p i l a t i o n o f t h e main i n f l u e n c i n g paramet e r s o f t h i s most complex f i e l d . Some o f these parameters a r e c o n t a i n e d i n a f o r m u l a proposed by C.N. Rowe (Ref. 4.164,

4.165) f o r t h e r a t e o f adhesive

wear o f a boundary l u b r i c a t e d system. The f o r m u l a c o n t a i n s two d i m e n s i o n l e s s groups, one o f which i s d e s c r i p t i v e o f t h e s l i d i n g m e t a l c o u p l e and t h e o t h e r i s o f the effectiveness o f the l u b r i c a n t f i l m a t the surface, conside r i n g t h a t t h e h e a t o f a d s o r p t i o n may be t h e c o n t r o l l i n g f a c t o r i n t h e e f f e c t i v e n e s s o f t h e boundary l u b r i c a n t . The model l e a d s t o t h e e x p r e s s i o n :

166 The parameters i n v o l v e d i n t h i s r e l a t i o n may be c l a s s i f i e d under t h e f o l l o w i n g headings: Operating variables:

FN

: load

v

: velocity : s l i d i n g distance : a b s o l u t e temperature o f t h e s l i d i n g s u r f a c e

1

TS

M a t e r i a l s parameters: p, Q Rc

: f l o w p r e s s u r e o f t h e s o f t e r metal : heat o f adsorption m o l a r gas c o n s t a n t :

Interaction characteristics: da to

: d i a m e t e r o f t h e area a s s o c i a t e d w i t h an adsorbed m o l e c u l e : fundamental o s c i l l a t i o n t i m e o f an adsorbed m o l e c u l e

f

: friction coefficient

K,

: wear c o e f f i c i e n t o f t h e s l i d i n g metal s u r f a c e s

V

: wear volume o f t h e boundary l u b r i c a t i o n system

The g r e a t number o f i n f l u e n c i n g f a c t o r s o f a b o u n d a r y - l u b r i c a t i o n system urges t h e need f o r a s y s t e m a t i c parameter c o m p i l a t i o n o f t r i b o l o g i c a l systems as attempted i n Chapter 8.

4,5,6

THE L I M I T S OF

LUBRICATION

The surveys p r e s e n t e d i n t h e f o r e g o i n g s e c t i o n s show t h a t l u b r i c a t i o n i s t h e most i m p o r t a n t means o f i n f l u e n c i n g t h e t r a n s a c t i o n s o f energy and m a t e r i a l s i n t r i b o l o g i c a l systems and r e d u c i n g f r i c t i o n and m i t i g a t i n g wear. Conseq u e n t l y , any d i s t u r b a n c e o r f a i l u r e o f l u b r i c a t i o n has d e t r i m e n t a l consequences f o r t h e t r i b o l o g i c a l b e h a v i o u r o f t h e system. Besides an understandi n g o f t h e mechanisms o f p r o p e r l u b r i c a t i o n , i t i s t h e r e f o r e necessary t o g a i n some i n s i g h t i n t o t h e processes and f a c t o r s which d e t e r m i n e a f a i l u r e o f l u b r i c a t i o n , i.e.,

the possible " l i m i t s " o f lubrication.

S t a r t i n g f r o m c o n d i t i o n s o f f u l l - f l u i d - f i l m l u b r i c a t i o n and f o l l o w i n g t h e course o f t h e S t r i b e c k c u r v e e i t h e r t o t h e r i g h t o r t o t h e l e f t , two d i f f e r e n t types o f t h e l i m i t s o f l u b r i c a t i o n a r e met:

167 (a)

To t h e r i g h t , as f o r i n s t a n c e w i t h i n c r e a s i n g v e l o c i t y , t h e c o n d i t i o n s

o f l a m i n a r f l u i d f l o w may change t o t u r b u l e n t f l o w . (b)

To t h e l e f t , f o r i n s t a n c e w i t h d e c r e a s i n g v e l o c i t y , r u n n i n g t h r o u g h t h e v a r i o u s non-hydrodynamic l u b r i c a t i o n regimes, t h e l u b r i c a n t f i l m may e v e n t u a l l y break down l e a d i n g t o c a t a s t r o p h i c f a i l u r e i n t h e f o r m o f " s c u f f i n g " o r " s e i z u r e " (Ref. 4.166).

I n f l u i d mechanics, c o n s i d e r i n g a f l u i d o f v i s c o s i t y T and d e n s i t y p f l o w i n g w i t h a v e l o c i t y v p a s t a l o n g c y l i n d e r o f d i a m e t e r d, t h e change f r o m l a m i n a r t o t u r b u l e n t f l o w i s d i s c u s s e d i n terms o f t h e Reynolds number

Re

= - vP d

rl

F o r Re < 1 a l a m i n a r f l u i d f l o w mode i s found. F o r Re > 1 v a r i o u s e f f e c t s o f d i s t u r b a n c e s and t u r b u l e n c e s o c c u r , l i k e t h e "KBrmln v o r t e x s t r e e t " app e a r i n g f o r Re > 40 ( R e f . 4.167). I n j o u r n a l b e a r i n g s o f t h e t y p i c a l c l e a r a n c e r a t i o s 0.001 < c r / r

1, permanent s u r f a c e topography changes due t o p l a s t i c

a s p e r i t y f l o w must be expected. The p l a s t i c c o n t a c t d e f o r m a t i o n changes t h e s u r f a c e roughness data, such as Ra o r RZ ( s e e S e c t i o n 4.2.1)

and m o d i f i e s

t h e shape and t h e c h a r a c t e r i s t i c s o f t h e a s p e r i t y h e i g h t d i s t r i b u t i o n c u r v e and t h e a u t o - c o r r e l a t i o n f u n c t i o n o f t h e s u r f a c e p r o f i l e .

180 I t i s w e l l e s t a b l i s h e d t h a t many e n g i n e e r i n g s u r f a c e s have a Gaussian

h e i g h t d i s t r i b u t i o n . I f the i n i t i a l surface preparation technique involves a l a r g e number o f r e p e a t e d events which o c c u r randomly o v e r t h e s u r f a c e , i t f o l l o w s immediately from t h e C e n t r a l L i m i t Theorem o f s t a t i s t i c s (Ref. 5.1) t h a t t h e topography o f t h e s u r f a c e w i l l t e n d towards a Gaussian h e i g h t d i s t r i b u t i o n . Consequently, any p l a s t i c c o n t a c t d e f o r m a t i o n changes t h e i n i t i a l h e i g h t d i s t r i b u t i o n curve. The e f f e c t o f p l a s t i c c o n t a c t deformat i o n on t h e changes o f t h e s u r f a c e c o n t a c t topography i s i l l u s t r a t e d i n Figure 5.2.

40

-

-5 30 -+ 25 r .," 20 35

a

I

15

-

10

-

500 pn O-O-O-

5 -

L

I

I

I

I

I

I

I

1

5

20

50

80

95

99

I

99.9

Cumulative h e i g h t d i s t r i b u t i o n F i g u r e 5.2

(W)

Cumulative h e i g h t d i s t r i b u t i o n s showing e f f e c t o f p r e s s i n g an i n i t i a l l y rough s u r f a c e (Ref. 5.1).

I n t h i s diagram, t h e c u m u l a t i v e h e i g h t d i s t r i b u t i o n curves o f t h e i n i t i a l and t h e p l a s t i c a l l y deformed s u r f a c e s a r e p l o t t e d on p r o b a b i l i t y paper (Ref. 5.1).

( I n t h i s diagram paper, a Gaussian d i s t r i b u t i o n i s r e p r e s e n t e d

as a s t r a i g h t l i n e . ) I t can be seen t h a t t h e i n i t i a l Gaussian h e i g h t d i s t r i b u t i o n ( A ) i s increasingly disturbed w i t h increasing s e v e r i t y o f the c o n t a c t d e f o r m a t i o n process (B),

(C).

Since most e n g i n e e r i n g s u r f a c e s i n i -

t i a l l y possess a Gaussian s u r f a c e h e i g h t d i s t r i b u t i o n , t h e curves shown i n F i g u r e 5.2 appear t o r e p r e s e n t b a s i c f e a t u r e s o f t h e s u r f a c e topography changes due t o p l a s t i c d e f o r m a t i o n . The o t h e r group o f t r i b o - i n d u c e d s u r f a c e changes a r e t h e changes due t o wear processes. The appearance o f worn s u r f a c e s has been d e s c r i b e d i n

181 S e c t i o n 4.4 (see Table 4.3).

F o r t h e changes o f t h e s u r f a c e topography due

t o wear, depending on t h e i n i t i a l s u r f a c e f i n i s h t h e r e a r e two p o s s i b i l i t i e s : ( i ) t h e wear processes may roughen smooth s u r f a c e s , ( i i ) t h e wear processes may smooth o u t rough s u r f a c e s . There i s a general consensus t h a t t h e s u r f a c e s o f moving machine p a r t s s h o u l d n o t be t o o "smooth". F o r example, f o r t h e d e s i g n o f p i s t o n s , a s u i t a b l e s u r f a c e f i n i s h f o r t h e c y l i n d e r bores o f Ra = 0.4 t o 0.6 pm has been suggested (Ref. 5 . 2 ) .

(These f i g u r e s s h o u l d n o t be g e n e r a l i z e d because t h e y

depend on t h e system under c o n s i d e r a t i o n ) .

As i n t h e case o f p l a s t i c c o n t a c t d e f o r m a t i o n , t h e wear-induced changes o f s u r f a c e topography can be c o n v e n i e n t l y i l l u s t r a t e d by c o n s i d e r i n g t h e c u m u l a t i v e h e i g h t d i s t r i b u t i o n o f s u r f a c e a s p e r i t i e s (Ref. 5 . 3 ) .

I n Figure

5 . 3 t h e e f f e c t o f wear on t h e i n i t i a l l y Gaussian h e i g h t d i s t r i b u t i o n i s shown ( R e f . 5 . 1 ) .

1

5

20

50

80

95

99

99.9

Cumulative h e i g h t d i s t r i b u t i o n ( % ) F i g u r e 5.3

Cumulative h e i g h t d i s t r i b u t i o n s showing t h e e f f e c t o f wear on t h e i n i t i a l l y Gaussian h e i g h t d i s t r i b u t i o n o f a beadb l a s t e d s u r f a c e (Ref. 5.1).

The s i x non-Gaussian d i s t r i b u t i o n s r e p r e s e n t , f r o m

(A) t o (C), p r o g r e s s i v e

stages i n t h e w e a r i n g process. I t can be seen t h a t a l m o s t i m m e d i a t e l y t h e t o p 20% o f t h e s u r f a c e was a l t e r e d , t h e r e s t remained c o m p l e t e l y u n a f f e c t e d . T h i s b e n t d i s t r i b u t i o n , and t h e c o r r e s p o n d i n g changes i n b e a r i n g c u r v e a r e t y p i c a l l y a s s o c i a t e d w i t h l i g h t l y worn s u r f a c e s . As wearing progressed, t h e

182 t r a n s i t i o n p e r c e n t i l e between t h e new topography c r e a t e d b y t h e wear p r o cess and t h e i n i t i a l s u r f a c e topography moved s t e a d i l y l o w e r u n t i l t h e o r i g i n a l t e x t u r e had been almost t o t a l l y r e p l a c e d . I n mechanical e n g i n e e r i n g , t h e s u r f a c e f i n i s h and t h e wear-induced changes o f s u r f a c e topography a r e c o n s i d e r e d t o be o f g r e a t importance f o r t h e f u n c t i o n a l performance o f moving mechanical components (Ref. 5.4,

5.5,

5.6). G e n e r a l l y speaking, t h e wear-induced changes o f s u r f a c e topography may have an i n d i f f e r e n t , b e n e f i c i a l , d e t r i m e n t a l o r c a t a s t r o p h i c i n f l u e n c e on t h e f u n c t i o n a l b e h a v i o u r o f t h e whole t r i b o - m e c h a n i c a l system. Some asp e c t s o f t h e d e t r i m e n t a l i n f l u e n c e o f s u r f a c e topography changes have been discussed i n c o n n e c t i o n w i t h t h e l i m i t s o f l u b r i c a t i o n ( S e c t i o n 4.5.6).

The

b e n e f i c i a l aspects o f s u r f a c e topography changes l e a d t o t h e w e l l known r u n n i n g - i n e f f e c t o f b e a r i n g s u r f a c e s (Ref. 5.7,

5 .9 ). Consider, as an example o f t h e r u n n i n g - i n e f f e c t , a s i m p l e t r i b o mechanical disc-on-plane s l i d i n g system. The i n f l u e n c e o f a r u n n i n g - i n 5.8,

process on t h e t r i b o l o g i c a l b e h a v i o u r has been s t u d i e d i n two steps. F i r s t l y , t h e S t r i b e c k c u r v e o f t h e s l i d i n g system l u b r i c a t e d w i t h a p u r e p a r a f f i n i c m i n e r a l o i l has been measured t o g e t h e r w i t h t h e n o - c o n t a c t t i m e f r a c t i o n determined by e l e c t r i c a l c o n t a c t - r e s i stance measurement t e c h n i q u e s . These curves, v a l i d f o r t h e i n i t i a l s u r f a c e roughness, were determined f o r cons t a n t values o f l o a d and temperature by v a r y i n g t h e s l i d i n g v e l o c i t y f r o m h i g h t o l o w values w i t h i n a few seconds. ( W i t h t h i s procedure, S t r i b e c k l s c u r v e i s r u n t h r o u g h f r o m r i g h t t o l e f t w i t h n e g l i b l e surface-roughness changes. ) Secondly, a f t e r a " r u n n i n g - i n " process has been performed under c o n d i t i o n s o f boundary l u b r i c a t i o n , t h e S t r i b e c k curve and t h e n o - c o n t a c t t i m e f r a c t i o n have been determined again. The r e s u l t s o f t h e s e measurements a r e shown i n F i g u r e 5.4.

I n a d d i t i o n , t h e surface-roughness c h a r a c t e r i s t i c s

b e f o r e and a f t e r t h e r u n - i n procedure a r e c o m p i l e d i n F i g u r e 5.5. I n comparing t h e curves f o r t h e system w i t h t h e i n i t i a l s u r f a c e roughness d a t a ( a ) , w i t h those o f t h e r u n - i n system ( b ) , t h e f o l l o w i n g main consequences o f t h e r u n n i n g - i n process can be n o t e d : (i)

A r e d u c t i o n o f t h e h e i g h t o f t h e h i g h e s t a s p e r i t y peaks i n d i c a t i n g

a g r e a t e r c o n f o r m i t y o f t h e s l i d i n g s u r f a c e s and consequently, an i n c r e a s e o f t h e l u b r i c a n t gap between t h e s l i d i n g s u r f a c e s . (ii)

A s h i f t o f t h e minimum o f t h e S t r i b e c k c u r v e t o t h e l e f t , i . e . , e x t e n s i o n o f t h e regime o f hydrodynapic l u b r i c a t i o n .

( i i i ) A l o w e r i n g o f t h e f r i c t i o n v a l u e a t t h e minimum o f t h e S t r i b e c k curve.

an

183

-0.14

Y-

-0.12

c

0 .r

C I -

V

.r

L lt

-0.10

YO

c , -

c

.-VW

-0.08

Y-

01 0

v

-

-0.06

Sliding velocity v F i g u r e 5.4

(cm/s)

S t r i b e c k c u r v e and n o - c o n t a c t t i m e f r a c t i o n b e f o r e ( a ) and a f t e r ( b ) r u n n i n g - i n .

184

Rt = 3.00 pm Ra = 0.49 pm

Peak d i s t r i bu ti on

Bearing-area curve

nr

-c,

20 40 60 80 100 Bearing percentage

0

0

50 100 150 Peak number

( a ) : Before r u n n i n g - i n

-

100 pm

Rt = 2.20 pin Ra = 0.34 pm

I

Bearina-area curve

Peak d i s t r i b u t i o n

Bearing percentage

Peak number

(b) A f t e r running-in F i g u r e 5.5

Surface roughness data b e f o r e ( a ) and a f t e r ( b ) r u n n i n g - i n.

186 C l e a r l y , t h e e x t e n s i o n o f t h e hydrodynamic regime as a consequence o f t h e r u n n i n g - i n process enhances t h e " o p e r a t i n g s e c u r i t y " o f t h e system.

I n mechanical e n g i n e e r i n g , owing t o t h e g r e a t importance o f r u n n i n g - i n procedures f o r t h e f u n c t i o n a l b e h a v i o u r o f moving machine elements, i t i s a t t e m p t e d t o o p t i m i z e t h e r u n n i n g - i n procedure i n o r d e r t o o b t a i n p r o p e r l y r u n - i n s u r f a c e s w i t h i n a minimum o f r u n n i n g - i n d u r a t i o n . F o r example, i n t h e d e t e r m i n a t i o n o f r u n n i n g - i n schedules f o r D i e s e l engines, t h e schedules have been o p t i m i z e d w i t h r e s p e c t t o b o t h r e l i a b i l i t y and economy t h r o u g h measuring t h e amount o f wear d u r i n g t h e r u n n i n g - i n procedure by means o f s e n s i t i v e r a d i o n u c l i d e measuring methods ( R e f . 5.10).

D e t a i l e d s t u d i e s were made on t h e

i n f l u e n c e s o f o p e r a t i n g c o n d i t i o n s , l i k e l o a d and speed, on c r i t e r i a l i k e engine power, s p e c i f i c f u e l and o i l consumption and s u r f a c e s t a t e o f p i s t o n r i n g and l i n e r . As a t y p i c a l 'example, i n F i g u r e 5.6 t h e b e a r i n g a r e a curves o f t h e c y l i n d e r l i n e r o f a D i e s e l engine a t d i f f e r e n t stages o f r u n n i n g - i n a r e shown.

l a-• t = 30 h

+0-

x-xt= W

m

2

100

-

80

-

20

-

S

W

2

W

t = 90 min t = 15 min

0

.r

W

m

0

1

I

I

I

I

I

I

I

I

2

3

4

5

6

7

8

9

S u r f a c e p r o f i l e d e p t h (pm) F i g u r e 5.6

B e a r i n g area curves o f t h e c y l i n d e r l i n e r o f a D i e s e l e n g i n e a t d i f f e r e n t stages o f r u n n i n g - i n (Ref. 5.10).

The s u r f a c e s a r e p r o p e r l y r u n - i n i f a c e r t a i n b e a r i n g - a r e a p e r c e n t a g e a t a c e r t a i n p r o f i l e depth i s o b t a i n e d and a s t a b i l i z e d (minimum) wear r a t e i s reached. The marked i n f l u e n c e o f t h e o p e r a t i n g c o n d i t i o n s on r u n n i n g - i n a r e i l l u s t r a t e d i n F i g u r e 5.7.

186 -

t = 2 h (optimized) Mt =16 h

0 -

- t = O

$ 100 + l

5 V

8060

-

40

-

L

m

:.L m

20-

0

1

2

3

4

5

6

7

8

Surface p r o f i l e depth ( p n ) F i g u r e 5.7

B e a r i n g a r e a curves o f t h e c y l i n d e r l i n e r o f a D i e s e l e n g i n e a f t e r d i f f e r e n t r u n n i n g - i n procedures (Ref. 5.10).

I t can be seen t h a t w i t h an o p t i m i z e d r u n n i n g - i n schedule t h e r e q u i r e d s u r -

face q u a l i t y was reached a f t e r a r u n n i n g - i n d u r a t i o n o f 2 hours, whereas i n a c o n v e n t i o n a l non-optimized r u n n i n g - i n procedure f o r a comparable s u r f a c e q u a l i t y a r u n n i n g - i n d u r a t i o n o f more t h a n 16 hours was needed.

5 , 2 , 2 SURFACE COMPOSITION

CHANGES

T h i s aspect o f t h e t r i b o - i n d u c e d changes o f t h e s t r u c t u r e o f a mechanical system i s e x t r e m e l y c o m p l i c a t e d b o t h f r o m t h e t h e o r e t i c a l and e x p e r i m e n t a l p o i n t o f view. T h e o r e t i c a l l y , owing t o t h e n a t u r e o f s u r f a c e s (see F i g u r e 4.5) and t h e c o m p l e x i t y o f t h e t r i b o l o g i c a l m a t e r i a l s - l u b r i c a n t - a t m o s p h e r e i n t e r a c t i o n s as discussed i n Chapter 4, i t appears e x t r e m e l y d i f f i c u l t t o develop models f o r t h e a c t u a l dynamic c o m p o s i t i o n o f t r i b o l o g i c a l l y s t r e s s e d s u r f a c e s . E x p e r i m e n t a l l y , owing t o t h e i n a c c e s s i b l e c o n t a c t i n t e r f a c e , i t i s n o t generally possible t o study " i n s i t u " the actual composition o f surfaces

ir: c o n t a c t . Nevertheless, some p r o g r e s s has been made i n r e c e n t y e a r s i n a p p l y i n g t h e new p h y s i c a l s u r f a c e - a n a l y t i c a l t o o l s , 1 ike Auger e l e c t r o n spectroscopy o r ESCA (see S e c t i o n 7.6),

i n connection w i t h sophisticated

s u r f a c e - p r e p a r a t i o n techniques. I n t h e f o l l o w i n g , some o f t h e b a s i c aspects o f t r i b o - i n d u c e d changes o f s u r f a c e c o m p o s i t i o n a r e d i s c u s s e d f o r systems of increasing complexity.

187

( a ) Before contact

(C)

( d ) After 20 passes

After 5 passes

severe

,h 2 . 4 .r

v1

2.0

4J

r:

'-

L

1.6

a

2m

1.2

0

o

c,

0.8

1045 steel

mild

transfer

Figure 5.8

I

1

4

8

T=23 OC; I

I

I

, 24

v=O.2 m/min Torr (13 n P a )

12 16 20 Number of rider passes

Aluminium adhesive transfer t o steel surface during sliding (Ref. 5.11).

iaa (a)

SURFACE-COMPOSITION CHANGES OF A SLIDING SYSTEM UNDER ULTRA-HIGH-VACUUM CONDITIONS.

I n t h i s case, the t r i b o l o g i c a l system consists o f only two partners and t h e tribo-induced surface composition changes are mainly the m a t e r i a l t r a n s f e r from one partner t o the other and vice versa. The physical causes f o r t h i s material t r a n s f e r , i. e . , the adhesion mechanisms, have been explained i n Sections 4.2.2 and 4.4.4. As mentioned there, i n adhesion experiments of metal-metal pairs, i t has been observed t h a t under the a c t i o n o f pure normal contact and separation forces the cohesively weaker material t r a n s f e r s t o the cohesively stronger. With r e l a t i v e tangential motion between the surfaces, as i n s l i d i n g , r o l l i n g , o r o s c i l l a t i n g , i n t e r f a c i a l m a t e r i a l s t r a n s p o r t becomes more complex. Under such conditions, p l a s t i c deformation, shear and high surface temperatures due t o f r i c t i o n a l heating are some f a c t o r s which must be given a t t e n t i o n . I n the l a s t few years i t has become possible t o study the tribo-induced changes i n the composition o f the uppermost l a y e r s o f surfaces by means o f Auger e l e c t r o n Spectroscopy (AES). As an example, the changes o f the compos i t i o n o f a s t e e l surface s l i d i n g against an aluminium counterface w i l l be discussed (Ref. 5.11). Before s l i d i n g contact, i r o n and carbon peaks were detected from the steel surface by means o f AES. I n s l i d i n g , i t was found t h a t the aluminium t r a n s f e r s t o the steel surfaces. The degree o f the "contamination" o f the steel surface w i t h A1 was detected by measuring the r a t i o o f t h e aluminium t o carbon AES peak i n t e n s i t i e s . This r a t i o , as a f u n c t i o n o f the number o f passes o f the A 1 r i d e r over t h e s t e e l surface, i s shown i n Figure 5.8.

I t can be seen t h a t a m i l d t r a n s f e r regime i s followed by a

severe t r a n s f e r regime. This example shows the importance o f surface-compos i t i o n changes on the behaviour o f tribo-mechanical systems: i t i s the severe adhesive wear, i n d i c a t e d i n the right-hand s i d e o f the graph o f Figure 5.8, which o f t e n causes the catastrophic f a i l u r e o f components o f mechanical sys terns. (b)

SURFACE COMPOSITION CHANGES OF A SLIDING SYSTEM UNDER ATMOSPHERIC CONDITIONS.

I n these cases, surface composition changes due n o t o n l y t o materials transf e r b u t also t o the i n t e r a c t i o n o f the atmospheric environment w i t h the s l i d i n g surfaces a c t i v a t e d by the f r i c t i o n a l energy, take place. Important examples are the tribochemical o x i d a t i o n processes i n dry s l i d i n g o f s t e e l surfaces. The corresponding changes i n surface composition have o f t e n been i n v e s t i g a t e d i n studying the chemical composition o f the surface debris.

189 F i n k and Hoffmann observed i n 1932 i n a c l a s s i c paper t h a t under c o n d i t i o n s o f r o l l i n g w i t h s l i p , t h e s u r f a c e d e b r i s c o n s i s t e d o f Fe, Fe203 and Fe304; FeO was n o t d e t e c t a b l e (Ref. 5.12).

I n a n o t h e r fundamental

paper, Dies i n 1939 s t u d i e d t h e connections between t h e c o m p o s i t i o n o f t h e d e b r i s and t h e wear o f a s t e e l specimen (0.04% C ) s l i d i n g under atmospheric c o n d i t i o n s a t v = lm/s a g a i n s t a hardened s t e e l (0.86% C, 1.64% C r ) d i s c (Ref. 5.13).

I n F i g u r e 5.9, t h e r e s u l t s o b t a i n e d by Dies as a f u n c t i o n o f

t h e c o n t a c t p r e s s u r e a r e shown

70 60 50 40

30 20 10 50

100

150

200

C o n t a c t p r e s s u r e ( N/cmL)

F i g u r e 5.9

Composition o f wear d e b r i s as f u n c t i o n o f c o n t a c t p r e s s u r e ( R e f . 5.13).

The broken curves r e p r e s e n t t h e measured wear r a t e i n r e l a t i v e u n i t s . (The c h a r a c t e r i s t i c shape o f t h e wear c u r v e i s d i s c u s s e d i n t h e n e x t s e c t i o n , i n c o n n e c t i o n w i t h t h e t r i b o - i n d u c e d changes o f s u r f a c e s t r e n g t h p r o p e r t i e s . ) The f u l l curves o f F i g u r e 5.9 show t h e v a r i a t i o n o f t h e c o m p o s i t i o n o f t h e d e b r i s w i t h i n c r e a s i n g c o n t a c t pressure. I t can be seen t h a t a t t h e minimum o f t h e wear r a t e , d e b r i s c o n t a i n e d m a i n l y

a - Fe203 whereas

a t the

maximum o f wear, t h e d e b r i s c o n s i s t e d m a i n l y o f m e t a l l i c i r o n . S i m i l a r changes have been r e p o r t e d t o o c c u r a l s o as a f u n c t i o n o f t h e s l i d i n g v e l o c i t y ( R e f . 5.14,

5.15). From t h i s work i t may be concluded t h a t

a t r i b o - c h e m i c a l wear mechanism o p e r a t e s a t l o w c o n t a c t p r e s s u r e s and l o w

190

s l i d i n g v e l o c i t i e s whereas a t h i g h e r values o f t h i s o p e r a t i n g v a r i a b l e s metal -metal adhesion becomes t h e dominant Near process. Q u i n n and Wooley (Ref. 5.16) were a b l e t o show t h a t under m i l d c o n d i t i o n s , t h e o x i d e Fe203 was generated b u t t h a t a t r a n s i t i o n t o Fe304 o c c u r r e d as t h e l o a d o r vel o c i t y was i n c r e a s e d above c e r t a i n l e v e l s . (c)

SURFACE COMPOSITION CHANGES OF A SLIDING SYSTEM UNDER LUBRICATED CONDITIONS.

I n t h e s e s i t u a t i o n s , t h e whole complex o f s o l i d - s o l i d - l u b r i c a n t - a t m o s p h e r e i n t e r a c t i o n s must be taken i n t o c o n s i d e r a t i o n . Some o f t h e main p h y s i c o chemical aspects o f t h e s e processes have a l r e a d y been d i s c u s s e d i n connect i o n w i t h t h e boundary l u b r i c a t i o n mode (see S e c t i o n 4.5.5).

One o f t h e

advantages o f t h e presence o f a l u b r i c a n t i n a t r i b o - m e c h a n i c a l system i s the p o s s i b i l i t y o f i n f l u e n c i n g t h e actual composition o f t h e s l i d i n g surf a c e by l u b r i c a n t a d d i t i v e s . Through t h e i n t e r f a c i a l t r i b o - c h e m i c a l react i o n s , b e n e f i c i a l s u r f a c e l a y e r s may be b u i l d up. Obviously, as i n d r y s l i d i n g , oxygen and w a t e r p l a y e x t r e m e l y import a n t r o l e s f o r the " i n s i t u " composition o f t r i b o l o g i c a l l y stressed surfaces and, consequently, f o r t h e i r f u n c t i o n a l behaviour. I n c r e a s i n g oxygen c o n c e n t r a t i o n s seem t o have a f a v o r a b l e e f f e c t on t h e amount o f wear, as w e l l as on 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 s l i d i n g s u r f a c e s . F o r systems l u b r i c a t e d w i t h p l a i n hydrocarbon l u b r i c a n t s , as t h e oxygen a v a i l a b i l i t y i n creases, t h e i n o r g a n i c wear p r o d u c t s f r o m t h e s l i d i n g s u r f a c e s change f r o m i r o n and i r o n c a r b i d e FeC t o t h e i r o n o x i d e s Fe304 and a

-

Fe203. I f t h e

l u b r i c a n t c o n t a i n s " l u b r i c i t y " agents, l i k e f a t t y a c i d s , c a r b o x y l a t e "soaps" a r e formed when oxygen o r w a t e r i s p r e s e n t . The i n o r g a n i c f i l m s formed " i n s i t u " f r o m extreme p r e s s u r e agents on metal s u r f a c e s , such as s u l f i d e s , c h l o r i d e s , and phosphides, p r o v i d e l u b r i c a t i o n a t v e r y h i g h temperatures (see also S e c t i o n 4.5.5).

These t r i b o - c h e m i c a l l y formed s u r f a c e f i l m s a r e

more s t a b l e than any p h y s i c a l l y o r c h e m i c a l l y adsorbed f i l m . Reacted f i l m s need n o t t o be t r i b o - c h e m i c a l , b u t t h e r a t e o f r e a c t i o n can be enhanced b y t h e exposure o f s u r f a c e and t h e r u b b i n g temperature. The a c t u a l s u r f a c e c o m p o s i t i o n i s n o t w e l l known, and a s t u d y o f t h e l i t e r a t u r e shows t h a t o n l y i n a few cases have t h e a c t u a l compounds been i d e n t i f i e d on worn s u r f a c e s . T h i s i n a b i l i t y t o d e f i n e t h e chemical n a t u r e o f t h e s u r f a c e s p e c i e s has been due m a i n l y t o t h e f a c t s t h a t t h e l a y e r s a r e e x t r e m e l y t h i n ( a b o u t 10-3pm) and a r e f r e q u e n t l y amorphous. Recently, i n a p p l y i n g t h e newly developed s e n s i t i v e X-ray p h o t o e l e c t r o n spectroscopy t e c h n i q u e (ESCA o r XPS, see S e c t i o n 7 . 6 ) examinations o f s t e e l s u r f a c e s

191 before and a f t e r wear t e s t i n g have been p e r f o r m e d (Ref. 5.17, 5.18). I n these s t u d i e s , t h e s u r f a c e c o m p o s i t i o n a f t e r t h e a c t i o n o f t y p i c a l a n t i wear (AW) a d d i t i v e s , l i k e z i n c d i a l k y l d i t h i o p h o s p h a t e (ZDDP) and t y p i c a l extreme p r e s s u r e (EP) a d d i t i v e s , l i k e d i b e n z y l d i s u l p h i d e (060s) have been s t u d i e d . The r e s u l t s o f t h e s e s t u d i e s i n d i c a t e t h a t o f t h e elements z i n c , s u l f u r , phosphorus, carbon and oxygen i n t h e AW a d d i t i v e , o n l y s u l f u r underwent a d e t e c t a b l e change i n chemical n a t u r e d u r i n g wear t e s t i n g of t h e s t e e l s u r f a c e (Ref. 5.17).

The s u l f u r s u r f a c e s p e c i e s produced was i d e n t i f i e d as

a metal s u l p h i d e . The r e s u l t s suggest t h a t t h i s s u r f a c e s u l p h i d e i s a s s o c i a t e d w i t h boundary l u b r i c a t i o n (see S e c t i o n 4.5.5).

L i k e w i s e , i n t h e case o f

t h e EP a d d i t i v e DBDS, t h e rubbed s u r f a c e s had t h i c k d i s c o n t i n u o u s l a y e r s o f s u l p h i d e ( R e f . 5.18). These f i n d i n g s a r e c o m p a t i b l e w i t h those o f Coy and Q u i n n (Ref. 5.19) who a l s o observed t h i c k s u l p h i d e l a y e r s f o r t h e h i g h EP region.

5,2,3

SURFACE STRENGTH

PROPERTIES

CHANGES

There a r e two p o s s i b i l i t i e s o f t r i b o - i n d u c e d changes o f t h e s t r e n g t h p r o p e r t i e s o f i n t e r a c t i n g moving s u r f a c e s : (i)

an i n c r e a s e i n s t r e n g t h as a consequence o f e f f e c t s l i k e " s t r a i n hardening" due t o c o n t a c t s t r e s s e s and t h e g e n e r a t i o n o f i n t e r n a l stress fields,

( i i ) a decrease i n s t r e n g t h due t o t h e " s o f t e n i n g " e f f e c t o f f r i c t i o n induced h e a t i n t h e c o n t a c t i n t e r f a c e . I n t h i s connection t h e question o f the t r i b o l o g i c a l l y r e l e v a n t strength p r o p e r t i e s a r i s e s . From a d i s c u s s i o n o f t h e v a r i o u s a t t e m p t s t o e s t a b l i s h c o r r e l a t i o n s between wear b e h a v i o u r and mechanical p r o p e r t i e s

-

neglecting

t h e " i n t e r a c t i o n e f f e c t s " o f adhesion and t r i b o - c h e m i c a l r e a c t i o n s

-

i t has

been concluded t h a t many o f t h e r e l e v a n t parameters can be expressed i n terms o f t h e r a t i o o f t h e e l a s t i c modulus E t o t h e hardness H ( R e f . 5.20). I t has a l r e a d y been e x p l a i n e d above t h a t t h e r a t i o E/H i s p a r t o f t h e

p l a s t i c i t y i n d e x J, which i s a s a t i s f a c t o r y c r i t e r i o n b y which t o d e t e r m i n e

i n which regime a g i v e n c o n t a c t d e f o r m a t i o n process l i e s . I t may t h e r e f o r e be s u f f i c i e n t h e r e t o r e s t r i c t t h e d i s c u s s i o n t o t h e t r i b o - i n d u c e d changes o f E and H. The e l a s t i c modulus, E, o f a p o l y c r y s t a l l i n e metal i s p h y s i c a l l y speaking a " s t r u c t u r e - i n s e n s i t i v e p r o p e r t y " , and i s o n l y l i t t l e a f f e c t e d b y b o t h d e f e c t s and i m p u r i t i e s and temperature and s t r a i n r a t e ( R e f . 5 . 2 1 ) .

192

On t h e c o n t r a r y , t h e i n d e n t a t i o n hardness, H, o f m a t e r i a l s i s a markedly " s t r u c t u r e - d e p e n d e n t p r o p e r t y " . I t f o l l o w s t h a t t h e i n d e n t a t i o n hardness may b e t h e most r e l e v a n t s t r e n g t h p r o p e r t y c h a r a c t e r i z i n g t h e t r i b o - i n d u c e d changes o f s u r f a c e s t r e n g t h p r o p e r t i e s . B u r w e l l and S t r a n g (Ref. 5.22) have shown t h a t s t e e l - s t e e l s l i d i n g couples e x h i b i t a t r a n s i t i o n f r o m m i l d t o severe wear when t h e apparent c o n t a c t p r e s s u r e reaches a v a l u e o f about o n e - t h i r d o f t h e hardness o f t h e s o f t e r m a t e r i a l . As t h i s p r e s s u r e corresponds q u i t e c l o s e l y t o t h e u n i a x i a l b u l k f l o w s t r e s s o f t h e metal, i t was suggested t h a t t h e wear t r a n s i t i o n was due t o t h e i n t e r a c t i o n o f p l a s t i c zones beneath c o n t a c t i n g a s p e r i t i e s and t h e onset o f b u l k p l a s t i c d e f o r m a t i o n . I n s t u d y i n g t h e t r i b o - i n d u c e d changes o f t h e hardness o f s l i d i n g surfaces, however, t h e whole s t r e s s f i e l d o f normal and t a n g e n t i a l s t r e s s e s must be t a k e n i n t o c o n s i d e r a t i o n (Ref. 5.23). Since t h e t a n g e n t i a l s t r e s s e s depend on t h e f r i c t i o n a l b e h a v i o u r o f t h e system, those p r o p e r t i e s which determine t h e f r i c t i o n ( l i k e s u r f a c e contamination, atmospheric environment, e t c ) must a l s o be i n c l u d e d . A char a c t e r i s t i c example o f t h e changes o f t h e hardness o f s l i d i n g s u r f a c e s w i t h r e l a t i o n t o t h e v a r i o u s i n f l u e n c i n g f a c t o r s i s g i v e n i n F i g u r e 5.10. The f i g u r e s shows c r o s s - s e c t i o n s o f p i n s of p u r e i r o n , which have been s l i d a g a i n s t a d i s c i n d r y s y n t h e t i c a i r o f d i f f e r e n t pressure, t o g e t h e r w i t h micro-hardness d a t a (Ref. 5.24,

5.25). Under c o n d i t i o n s o f normal atmospheric

p r e s s u r e through t r i b o - c h e m i c a l r e a c t i o n o f t h e i r o n w i t h t h e oxygen an o x i d e l a y e r i s formed as can be seen i n t h e upper p a r t o f t h e micrograph o f F i g u r e 5.10. The f r i c t i o n a l shear s t r e s s e s a c t m a i n l y i n t h e o x i d e l a y e r s w i t h t h e r e s u l t t h a t t h e sub-surface l a y e r s a r e s t r a i n - h a r d e n e d o n l y t o s m a l l degree 2 ( H = 2000-3000 N/mm ) . I f , however, under t h e same o p e r a t i n g c o n d i t i o n s o f c o n t a c t p r e s s u r e , s l i d i n g v e l o c i t y , ambient temperature and s l i d i n g d i s tance, t h e t e s t s a r e performed i n a vacuum o f

T o r r a d i f f e r e n t behaviour

i s found. Here, a l e s s e r amount o f oxygen f o r o x i d e l a y e r f o r m a t i o n i s a v a i l a b l e and h i g h e r f r i c t i o n c o e f f i c i e n t v a l u e s a r e measured. The combined a c t i o n of t h e normal f o r c e s and t h e i n c r e a s e d t a n g e n t i a l f r i c t i o n f o r c e s a c t m a i n l y i n t h e m e t a l l i c p a r t s and l e a d t o a c o n s i d e r a b l e i n c r e a s e i n t h e subs u r f a c e hardness (H = 2000-6000 N/mm 2 ). The importance o f t h e changes o f s u r f a c e hardness and s u r f a c e composit i o n on t h e wear b e h a v i o u r o f a t r i b o - m e c h a n i c a l system i n d r y s l i d i n g i s i l l u s t r a t e d i n F i g u r e 5.11. I n t h i s graph, t h e wear c o e f f i c i e n t K ' o f 0.52 p e r c e n t carbon s t e e l as a f u n c t i o n o f t h e l o a d FN i s p l o t t e d (Ref. 5.26, 5.27).

The i n i t i a l hardness o f t h e specimen was 268 DPN. A t low l o a d s m i l d

Hardness (GN/m 2 )

(a)

atmospheric p r e s s u r e : p = 760 T o r r ( 0 . 1 MPa) f r i c t i o n c o e f f i c i e n t : f = 0.55 - 0.64 wear c o e f f i c i e n t : K = 0.00002

2 Hardness (GN/m ) (b)

atmospheric p r e s s u r e : p = T o r r (130 mPa) f r i c t i o n c o e f f i c i e n t : f = 0.81 - 0.97 wear c o e f f i c i e n t : K = 0.00058

F i g u r e 5.10

T r i b o - i n d u c e d hardness changes.

194 wear occurs u n t i l a t FN = 1N t h e t r a n s i t i o n T r 1 t o severe wear occurs. The severe wear mode p e r s i s t s up t o a l o a d o f a b o u t FN = 25 N. A t t h i s p o i n t , a second t r a n s i t i o n T r 2 occurs when t h e wear mode r e v e r t s . I t was found, f r o m m e t a l l o g r a p h y and micro-hardness t e s t s , t h a t above t h e T r 2 t r a n s i t i o n t h e s u r f a c e l a y e r s o f t h e specimens were hardened by a phase change. The v a l u e o f t h e T r 2 t r a n s i t i o n l o a d was determined f o r a number o f s l i d i n g v e l o c i t i e s and f o r s t e e l s o f v a r i o u s carbon c o n t e n t s , and i n each case t h e v a l u e o f t h e f l a s h temperature was c a l c u l a t e d . B e a r i n g i n mind a number o f u n c e r t a i n t i e s i n t h e s e c a l c u l a t i o n s , t h e o v e r a l l p a t t e r n o f r e s u l t s suggests t h a t t h e s u r f a c e h a r d e n i n g i s caused by a m a r t e n s i c t r a n s f o r m a t i o n , and t h a t i t i s caused by t h e f l a s h temperatures and t h e i r d u r a t i o n a t t h e t r u e a r e a

o f c o n t a c t . The o v e r a l l e f f e c t s i l l u s t r a t e d i n F i g u r e 5.11 have been conf i r m e d by Uetz and co-workers ( R e f . 5.28). The r e s u l t s c l e a r l y i n d i c a t e t h e importance o f t h e combined e f f e c t s o f s u r f a c e c o m p o s i t i o n changes and s u r face s t r e n g t h changes on t h e t r i b o l o g i c a l b e h a v i o u r o f s l i d i n g systems.

LTr

10-6

-8

T r 1-

\

m

5

v

a, CI 4

L

L

s

4

d=25.. mm 10-10

/

&.% v = l m/s m

10-11

1

F i g u r e 5.11

10 Load FN ( N )

100

Wear modes as f u n c t i o n o f l o a d (Ref. 5.26).

195

5,3 MATERIAL LOSSES I f , i n a t r i b o - m e c h a n i c a l system i t i s n o t p o s s i b l e t o e l i m i n a t e wear processes ( s e e S e c t i o n 5.4) o r t o m i t i g a t e these processes t o a " z e r o l e v e l " ( s e e S e c t i o n 6 . 6 ) t h e t r i b o l o g i c a l processes between two moving s u r f a c e s g e n e r a l l y l e a d t o l o s s e s o f m a t e r i a l f r o m t h e system. Phenomenologically, d i f f e r e n t regimes o f m a t e r i a l l o s s e s may be d i s t i n g u i s h e d . D e n o t i n g t h e amount o f t h e m a t e r i a l l o s s by t h e o u t p u t symbol ZM, t h r e e s i m p l e t i m e r e l a M t i o n s f o r Z may be expected which a r e i n d e e d observed e x p e r i m e n t a l l y . F i r s t l y , t h e p r o b a b i l i t y o f t h e o c c u r r e n c e o f elementary wear e v e n t s may decrease w i t h t i m e . T h i s case i s g i v e n , f o r i n s t a n c e , i f t h r o u g h changes o f s u r f a c e topography t h e i n t e r a c t i o n r a t e o f s u r f a c e a s p e r i t y c o l l i s i o n s decreases. I n t h i s " r u n n i n g - i n "

p e r i o d t h e system self-accommodates. I n t h e s i m p l e s t case, t h e amount o f l o s s - o u t p u t s w i l l be g i v e n as a s q u a r e - r o o t f u n c t i o n o f time

dZM dt

-

c1 _ 3 Z M ZM

(t)

=

pp]

Secondly,the

s t r u c t u r e o f t h e system may a c q u i r e a r e l a t i v e l y s t a b l e behavi o u r under t h e a c t i o n o f t h e t r i b o l o g i c a l processes. I n t h i s case t h e proba-

b i l i t y o f wear e v e n t s remains c o n s t a n t . T h i s " s t e a d y - s t a t e " s i t u a t i o n i s c h a r a c t e r i z e d by a constancy o f t h e m a t e r i a l - l o s s o u t p u t p e r u n i t o f t i m e w i t h o u t change i n t h e t r i b o l o g i c a l processes. I t f o l l o w s t h a t

dt

=

c2

+ ZM ( t )

=

C2t

T h i r d l y , when t h e amount o f m a t e r i a l - l o s s o u t p u t reaches a c e r t a i n value, a q u a l i t a t i v e t r a n s i t i o n i n t h e s t a t e o f t h e system may o c c u r c o n s i s t i n g o f a s i g n i f i c a n t change i n t h e t r i b o l o g i c a l p i c t u r e o f t h e phenomena. The changes i n t h e s t a t e o f t h e system a r e o f a d i r e c t e d n a t u r e and t h e i n c r e ments i n t h e wear processes i n t h i s regime a r e m u t u a l l y dependent. Here l a r g e increments i n one i n t e r v a l o f t i m e cause even l a r g e r increments i n the next time i n t e r v a l . I t follows t h a t

196 I n t h i s case t h e worn m a t e r i a l - l o s s o u t p u t i n c r e ases r a p i d l y w i t h time. Depending on t h e v a l u e s o f Co and Cj s e l f - a c c e l e r a t i o n o f t h e process occur which may l e a d t o c a t a s t r o p h i c damage o f t h e s t r u c t u r e o f t h e system and, acco rd ingly , t o " f a i l u r e " o f t h e whole system (see a l s o S e c t i o n 6.4). The t h r e e modes o f m a t e r i a l - l o s s o u t p u t s diqcussed may f o l l o w each o t h e r i n t i m e as shown i n F i g u r e 5.12.

I n F i g u r e 5 . 1 2 ZMlim

denotes a maxi-

mum l e v e l o f a dmiss i b l e m a t e r i a l l o s s - o u t p u t s . A t t h i . l e v e l , t h e s t r u c t u r e o f t h e system has changed as a consequence o f t h e materl.1 l o s s - o u t p u t s , i n such a way t h a t t h e f u n c t i o n a l i n p u t - o u t p u t - r e l a t i o n s v i a t h e s t r u c t u r e o f t h e system

L

-

-

which a r e performed

a r e s e v e r e l y d i s t u r b e d (see S e c t i o n 6.4).

I

I

Time

F i g u r e 5.12

Schematic r e p r e s e n t a t i o n o f t h e m a t e r i a l l o s s - o u t p u t curves o f a t r i b o - m e c h a n i c a l system.

R e l a t i v e l y few workers i n t h e f i e l d o f t r i b o l o g y have attempted t o d e r i v e c o r r e l a t i o n s f o r w e a r - p a r t i c l e dimensions generated by t h e wear process. Rabinowicz proposed a c o r r e l a t i o n between mean adhesive wear, p a r t i c l e d i a meter and t h e "surface-energy c r i t e r i o n " which i s t h e r a t i o o f t h e work o f adhesion between two m e t a l s t o t h e hardness o f t h e weaker m a t e r i a l (Ref. 5.29). T h i s t h e o r e t i c a l approach has r e c e n t l y been m o d i f i e d (Ref. 5.20) and t h e f o l l o w i n g i n e q u a l i t y has been suggested t o d e s c r i b e t h e mean wearp a r t i c l e diame t e r d

d

6

15 (E/H)'

E

: e l a s t i c modulus

H

: p e n e t r a t i o n hardness

(nm)

197 C h a r a c t e r i s t i c s o f wear regimes s t u d i e d ( s c h e m a t i c ) : Lubricated state

Dry s t a t e

( S t r i beck c u r v e )

( T r a n s i t i o n s diagram)

(c) lubricant f i l m breakdown

( f ) severe adhesive

wear

( a ) quasi-

t

1 , (severe) o x i d a t ive wear

c, W

m L

-

( b ) boundary

Load

Regime

Load

-

P a r t i c l e d e s c r i p t i o n and m a j o r dimension, d

Surface d e s c r i p t i o n

Wear rate

F r e e metal p a r t i c l e s ; d c 5pm

V a r i e s between p o l i s h e d and v e r y rough

+Zero

F r e e metal p a r t i c l e s ; d < 15 pn

S t a b l e , smooth l a y e r w i t h a few grooves

F r e e metal p a r t i c l e s ; d c 150 pm

Ploughed w i t h e v i dence o f p l a s t i c f l o w and s u r f a c e cracking

Low High

--Red o x i d e p a r t i c l e s , a - Fe203, d UP t o 150 pm

Ploughed w i t h areas of o x i d e s on t h e surface

High

Black oxide p a r t i c l e s y Fe20g, Fe304, FeO,

Ploughed w i t h areas o f o x i d e s on t h e surface

High

-

d up t o 150 pm F r e e metal p a r t i c l e s , d up t o 1 mn

F i g u r e 5.13

S e v e r e l y ploughed, gross p l a s t i c f l o w and smearing

C h a r a c t e r i s t i c s o f wear p a r t i c l e s and t r i b o - i n d u c e d s u r f a c e f e a t u r e s (Ref. 5.30).

Catastrophic

198

The dependence on (E/H)

2

i s assumed t o be an upper bound, obeyed under

c o n d i t i o n s o f c l e a n s u r f a c e s . When normal l a b o r a t o r y c o n d i t i o n s o r more contaminated environments p e r t a i n , t h e dependence f o r p a r t i c l e s i z e reduces e m p i r i c a l l y t o (E/H)

.

E x p e r i m e n t a l l y , t h e f o l l o w i n g f i n d i n g s on t h e chemical c o m p o s i t i o n and t h e s i z e o f t h e m a t e r i a l l o s s d e b r i s appear t o have been observed q u i t e g e n e r a l l y f o r s l i d i n g systems o p e r a t i n g under normal atmospheric c o n d i t i o n s : (i)

I n t h e s o - c a l l e d m i l d wear regime, t h e worn d e b r i s c o n s i s t s o f s m a l l p a r t i c l e s w i t h a d i a m e t e r o f l e s s t h a n a b o u t 5 pm. These p a r t i c l e s a r e formed m a i n l y i n t r i b o - o x i d a t i v e wear processes and f o r s l i d i n g m e t a l couples o f t e n c o n s i s t o f o x i d e s . F o r example, t h e wear d e b r i s o f i r o n , c o b a l t , magnesium s l i d i n g a g a i n s t themselves under d r y c o n d i t i o n s consists of

. I

-

Fe203, COO and MgO. The f o r m a t i o n o f t h e s e o x i d e s can be

e x p l a i n e d i n accordance w i t h t h e thermodynamics o f t h e o x i d a t i o n p r o cesses i f t h e f r i c t i o n induced temperatures and t h e c o r r e s p o n d i n g d a t a o f f r e e energy o f t h e m a t e r i a l s a r e used. ( i i ) I n t h e s o - c a l l e d severe wear regime m e t a l l i c p a r t i c l e s r a n g i n g i n s i z e up t o a p p r o x i m a t e l y 1 mm a r e found. These p a r t i c l e s a r e m a i n l y observed under severe m e t a l 1 i c adhesion processes. There i s some e x p e r i m e n t a l evidence t h a t f o r l i k e m e t a l l i c s l i d i n g couples t h e s i z e o f l o o s e wear p a r t i c l e s i s l a r g e r than f o r u n l i k e metal-metal p a i r s . The d e t a i l s o f t h e c h a r a c t e r i s t i c s o f t h e wear p a r t i c l e s generated a t t h e i n t e r f a c e o f l u b r i c a t e d and d r y s l i d i n g c o n c e n t r a t e d A I S I 52100 s t e e l cont a c t s have been s t u d i e d (Ref. 5.30) i n l a b o r a t o r y t e s t s u s i n g t h e F e r r o g r a p h t e c h n i q u e d e s c r i b e d i n S e c t i o n 7.5.

I n F i g u r e 5.13 t h e c h a r a c t e r i s t i c s o f

t h e worn m a t e r i a l loss o u t p u t and t h e wear-induced s u r f a c e changes a r e comp i l e d . As can be seen, each regime produced wear p a r t i c l e s o f c h a r a c t e r i s t i c morphology and c o m p o s i t i o n . S i n c e a l l t h e t y p e s o f p a r t i c l e s have been found l i k e w i s e i n t h e l u b r i c a t i n g o i l o f f i e l d o p e r a t i n g machines, t h e c o m p i l a t i o n o f F i g u r e 5.13 appears t o r e p r e s e n t a good s u r v e y o f t h e n a t u r e o f t h e wearinduced m a t e r i a l s l o s s e s and t h e c o r r e s p o n d i n g changes o f t h e o p e r a t i n g s u r f a c e s o f mechanical systems. The d a t a o f F i g u r e 5.13, which a r e v a l i d f o r c o n d i t i o n of p u r e s l i d i n g , show t h a t f r o m t h e s t u d y o f t h e s i z e d i s t r i b u t i o n and t h e shape and c o m p o s i t i o n o f wear p a r t i c l e s i m p o r t a n t i n f o r m a t i o n on t h e o p e r a t i n g wear modes and t h e a c t u a l c o n d i t i o n o f t h e s t r u c t u r e o f a t r i b o mechanical system can be o b t a i n e d (Ref. 5.31). Based on t h i s i n f o r m a t i o n , a p r o g n o s i s o f t h e imminent b e h a v i o u r o f machinery can t h e n be undertaken.

199

5 , 4 SOLUTIONSFOR NO-WEAR CONDITIONS I n t h e p r e v i o u s s e c t i o n s , we s t u d i e d some o f t h e b a s i c aspects o f t h e changes o f t h e s t r u c t u r e o f mechanical systems o c c u r r i n g as a consequence o f t h e t r i b o l o g i c a l processes between t h e moving components o f t h e system.

Now, t u r n i n g f r o m d i a g n o s i s t o t h e r a p y , t h e q u e s t i o n a r i s e s how t o a v o i d d e t r i m e n t a l e f f e c t s and how t o r e a l i z e t r i b o - m e c h a n i c a l systems w i t h unchanging s t r u c t u r e s t h u s p r o v i d i n g t h e p r e r e q u i s i t e f o r a p r o p e r f u n c t i o n a l b e h a v i o u r o f t h e whole system. The r e s u l t s o f t h e p r e v i o u s s e c t i o n s have shown t h a t i n almost e v e r y case t h e d e t r i m e n t a l changes o f t h e system's s t r u c t u r e a r e due t o t h e i n t e r f a c i a l wear processes. I t f o l l o w s t h a t t h e wear-induced changes o f t h e s y s t e m ' s s t r u c t u r e a r e e l i m i n a t e d i f a s u i t a b l e i n t e r f a c i a l element e n t i r e l y p r e v e n t s t h e s o l i d - s o l i d c o n t a c t between t h e moving components o f a mechanical system. There a r e f o u r b a s i c e n g i n e e r i n g s o l u t i o n s t o t h i s problem, as i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 5.14.

,,I

(a) F l u i d f i l m

1 - 1

( c ) Elastomers

F i g u r e 5.14

( b ) Magnetic f i e l d

c ( d ) F l e x u r a l means

Schematic r e p r e s e n t a t i o n o f s o l u t i o n s f o r no-wear c o n d i t i o n s .

The most common method f o r t h e e l i m i n a t i o n o f wear processes f r o m a t r i b o mechanical system ( w i t h t h e e x c e p t i o n o f s u r f a c e - f a t i g u e wear o r , perhaps, f l u i d e r o s i o n o r c a v i t a t i o n ) i s by t h e use o f l i q u i d o r f l u i d l u b r i c a n t s , F i g u r e 5.14 ( a ) . I n t h e cases where a c o n v e r g i n g gap e x i s t s , t h e r e l a t i v e

200

m o t i o n o f t h e elements (1) and ( 2 ) drags t h e f l u i d i n t o t h i s gap t h u s genera t i n g a load-carrying pressure w i t h i n t h e f l u i d f i l m . A l t e r n a t i v e l y , the p r e s s u r e may be p r o v i d e d by an e x t e r n a l pumping system as i n a h y d r o s t a t i c o r a e r o s t a t i c b e a r i n g . Another p o s s i b i l i t y , i n d i c a t e d i n F i g u r e 5.14 ( b ) , i s t h e use o f magnetic o r o t h e r r e p u l s i v e f o r c e f i e l d s c a r r y i n g t h e normal l o a d and s e p a r a t i n g t h k moving s u r f a c e s ( 1 ) and ( 2 ) . I f t h e r e l a t i v e m o t i o n between t h e elements ( 1 ) and ( 2 ) i s o f f a i r l y small a m p l i t u d e , t h e s o l u t i o n s shown s c h e m a t i c a l l y i n F i g u r e s 5.14 ( c ) and ( d ) may be a p p l i c a b l e . Here, t h e moving s u r f a c e s a r e separated by an e l a s t i c a l l y deforming i n t e r f a c i a l e l e ment (3), and t h e r e s i s t a n c e t o a r e l a t i v e m o t i o n between ( 1 ) and ( 2 ) i s g i v e n by t h e i n t e r n a l d e f o r m a t i o n ( i n t e r n a l f r i c t i o n ) o f element ( 3 ) . The p r i n c i p l e s shown i n F i g u r e 5.14 have t h e advantage t h a t t h e y e l i m i n a t e wear processes a1 t o g e t h e r f r o m a t r i b o - m e c h a n i c a l system t h u s p r o v i d i n g an " i n v a r i a n t s t r u c t u r e " o f t h e system, Due t o t h e i r g r e a t importance, t h e main f e a t u r e s o f t h e p r i n c i p l e s i l l u s t r a t e d i n F i g u r e 5.14 w i l l be d i s cussed b r i e f l y .

5 , 4 , 1 FLUID F I L M S The advantages o f hydrodynamic l u b r i c a t i o n as d e s c r i b e d i n S e c t i o n 4.5.2 are u t i l i z e d n o t o n l y i n bearing applicatiqns b u t also i n o t h e r t r i b o mechanical systems l i k e hydrodynamic s e a l s o r i n m a n u f a c t u r i n g processes l i k e hydrodynamic l u b r i c a t e d w i r e d r a w i n g systems. Besides t h e s e l f - a c t i n g hydrodynamic l u b r i c a t i o n mode, h y d r o s t a t i c o r a e r o s t a t i c l u b r i c a t i o n i s app l i e d i n e x t e r n a l l y p r e s s u r i z e d b e a r i n g s . A l t h o u g h these h y d r o s t a t i c b e a r i n g s may r e q u i r e r e l a t i v e l y expensive and complex f l u i d s u p p l y equipment, t h e y o f f e r t h e f o l l o w i n g advantages: (i)

No s o l i d - s o l i d c o n t a c t , i . e . no wear a t any o p e r a t i n g v e l o c i t y ( i n c l u d i n g v = 0 ) o r l o a d f o r a l l types o f r e l a t i v e motion. Low f r i c t i o n (determined b y t h e i n t e r n a l f r i c t i o n o f t h e f l u i d ) .

(ii) ( i i i ) P r e d i c t a b l e f u n c t i o n a l performance (see S e c t i o n 6.1).

I n F i g u r e 5.15 a t y p i c a l h y d r o s t a t i c t h r u s t b e a r i n g i s shown s c h e m a t i c a l l y . The b e a r i n g pad, i n t h i s i n s t a n c e t h e l o w e r member, c o n t a i n s a recess o r pocket w i t h a depth considerably greater than the lands o r s i l l s . (Sometimes t h e pad i s above, e.g.,

on s k i d s f o r moving heavy machines on

p l a t e s l e t i n t o t h e f l o o r . ) As f l u i d i s s u n p l i e d t o t h e recess a t a h i g h p r e s s u r e a p r e s s u r e d i s t r i b u t i o n b u i l d s up, whose i n t e g r a l must equal t h e

201 load which i s applied t o the bearing. Figure 5.15 i n d i c a t e s t h a t h y d r o s t a t i c bearings can operate w i t h a uniform f i l m thickness h = const ( i n c o n t r a s t t o hydrodynamic bearings) and a l s o w i t h no r e l a t i v e tangential motion. Thus, i n the Reynolds equation, t r e a t e d i n Section 4.5.2, the right-hand s i d e equals zero (since vo, vl, Oh may be p u t equal t o zero). The Reynolds equation then reduces t o

This i s Laplace's equation i n two dimensions which must be solved f o r t h e p a r t i c u l a r geometry o f the bearing under consideration. pressure distribution

1and recess

Figure 5.15

'

A h y d r o s t a t i c t h r u s t bearing.

For t h e c o n f i g u r a t i o n o f Figure 5.15 t h e f o l l o w i n g r e l a t i o n s govern the behaviour o f the system (Ref. 5.32).

The pump pressure p

needed f o r the support o f t h e load FN i s given by

Pp

=

2FN

-In

d2 -

dml

dl

TC

P

i n the recess

202

Flow r a t e q1 and f i l m thickness are r e l a t e d v i a the equation

7 : lubricant viscosity

determines the necessary power o f the pump. I f the upper p a r t P o f t h e h y d r o s t a t i c bearing r o t a t e s w i t h an angular v e l o c i t y w, a f r i c t i o n a l The term qlp torque,

MF, has t o be overcome which i s given by the i n t e r n a l f r i c t i o n o f

the l u b r i c a n t f i l m o f equal thickness h t o be calculated from the shear stress. I t follows t h a t icTwd,l MF

=

(d2,,, t 12)

4h

This corresponds t o a f r i c t i o n a l power MFw and a f r i c t i o n c o e f f i c i e n t

Since wear processes are eliminated from h y d r o s t a t i c bearings the t r i b o l o g i c a l behaviour can be described e n t i r e l y i n terms o f t h i s data and equations. For other bearing geometries the r e l e v a n t equations may be o f more o r l e s s d i f f e r e n t form (Ref. 5.33,

5,4.2

MAGNETIC

5.34).

FIELDS

T r i b o l o g i c a l systems employing the p r i n c i p l e s o f magnetism f o r the separat i o n o f t h e surfaces i n r e l a t i v e motion can be d i v i d e d broadly i n t o two classes (Ref. 5.35): (i)

Systems which u t i l i z e the e f f e c t o f a load-carrying f o r c e generated by the flow o f conducting f l u i d s w i t h i n a magnetic f i e l d (Magnetohydrodynamic, MHD, bearings).

( i i ) Systems w i t h no l u b r i c a n t , d e r i v i n g t h e i r load-carrying a b i l i t y from the a t t r a c t i o n and repulsion associated w i t h magnetic f i e l d s (Magnetic supens i o n bearings )

.

203 Magnetohydrodynamic b e a r i n g s ( i ) o p e r a t e t h r o u g h mechanical f o r c e s produced by magnetic f i e l d s on a c o n d u c t i n g f l u i d . From t h e laws o f e l e c t r o m a g n e t i c s , i t i s w e l l known t h a t an e l e c t r i c charge q moving w i t h a v e l o c i t y v w i t h i n a magnetic f i e l d B e x p e r i e n c e s a f o r c e F, t h e L o r e n t z f o r c e , a c t i n g perpend i c u l a r t o t h e d i r e c t i o n o f m o t i o n and t h e d i r e c t i o n o f t h e magnetic f i e l d : A

F

A

=

-

q e ( v x B )

F o r MHD l u b r i c a t i o n , i t f o l l o w s t h a t when an e l e c t r i c a l l y c o n d u c t i n g f l u i d f l o w s across a magnetic f i e l d t h e p r e s s u r e developed i n t h e f l u i d can exceed t h e o r d i n a r y h y d r o d y n a m i c a l l y generated p r e s s u r e . The t h e o r e t i c a l t r e a t m e n t o f MHD b e a r i n g s s t a r t s f r o m a c o m b i n a t i o n o f t h e f l u i d - m e c h a n i c s e q u a t i o n s and t h e e l e c t r o m a g n e t i c e q u a t i o n s l e a d i n g t o a magnetohydrodynamic f o r m o f Reynolds e q u a t i o n (Ref. 5.36).

A c o n s i d e r a b l e amount o f t h e o r e t i c a l work has

been undertaken i n d i c a t i n g t h e p o s s i b i l i t i e s o f MHD b e a r i n g s . However, t h e i m p r a c t i c a b i l i t i e s o f t h e magnet and a s s o c i a t e d equipment s i z e have as y e t r e s t r i c t e d applications. The o t h e r c l a s s ( i i ) o f magnetic b e a r i n g s needs no l u b r i c a n t a t a l l and d e r i v e s i t s l o a d - c a r r y i n g a b i l i t y f r o m t h e a t t r a c t i o n and r e p u l s i o n ass o c i a t e d w i t h magnetic f i e l d s . The mechanical f o r c e s produced by e i t h e r p e r manent magnets o r by e l e c t r o m a g n e t s can be used t o f r e e l y s u p p o r t one p a r t n e r o f a b e a r i n g . The p r i n c i p l e i s i l l u s t r a t e d i n F i g u r e 5.16.

F i g u r e 5.16

P r i n c i p l e of t h e s u p p o r t o f a b e a r i n g s h a f t by f o u r electromagnets.

204

One problem with bearings having a member freely supported i n a magnetic f i e l d i s s t a b i l i t y . This problem can be solved with a servo-control system. If an external disturbing force acts on the "free" body, the corresponding displacement of the body detected by non-contacting sensors thus producing an electrical current which in turn i s fed to the electromagnets generating an additional force compensating the disturbing displacement. Owing t o the advantageous tribological structure, (no solid-solid cont a c t , no lubricant, low f r i c t i o n ) , magnetic bearings are able t o operate under a broad spectrum of operating conditions. Charateristic data of commercially available bearings are (Ref. 5.37): l o a d capacity velocity temperature

: 0.2 N

-

15 kN

: up t o 800,000 r.p.m. :

u p t o 800 K

The lifetime of the bearing depends on the bulk materials properties; operating lifetimes up t o 105h have been obtained independently o f rotation velocity. The advantages of the tribological structure of these bearings are utilized in technical applications like the transmission of motion into closed chambers ( f o r instance, vacuum chambers) or high-speed trackedvehicle support.

5 , 4 , 3 INTERFACIAL ELASTOMERS In t h i s solution, wear processes in a tribo-mechanical system are eliminated by replacing sliding surfaces with the internal mobility o f elastomers (Ref. 5.38). The elastomer a c t as a k i n d of lubricant and the resistance to motion i s due t o the internal f r i c t i o n of the elastomer. The most common elastomeric "lubricant" i s natural rubber, because of i t s excellent strength and fatigue properties, b u t many synthetic elastomers can be used as well. The principle of a typical elastomeric bearing i s i l l u s t r a t e d i n Figure 5.17. Basically, the elastomeric bearing i s comprised of alternating layers of rubber and metal laminates. The elastomer i s vulcanized and bonded t o the metal laminates as well as to the attachment metal components - inner and outer "races". The design of an elastomers bearing depend on types of load and motion ( r a d i a l , axial, spherical, etc.). For instance, the "sandwich-type" bearing shown in Figure 5.17 i s designed t o support high axial loads FN while accornodating torsional ( A q ) or lateral motions ( A s ) through the compression and shear characteristics of the elastomer, respectively.

205

As

laminates

races

F i g u r e 5.17

Typical elastomeric a x i a l bearing.

T h i s t y p e o f b e a r i n g i s v e r y s t i f f i n t h e a x i a l modes and s o f t i n shear. I n g e n e r a l , t h e d e s i g n o f e l a s t o m e r i c b e a r i n g s must Zake i n t o c o n s i d e r a t i o n f a c t o r s such as t h e t y p e and frequency o f l o a d s and motions as w e l l as space-envelope l i m i t a t i o n s and l i f e r e q u i r e m e n t s . The advantage o f t h e e l a s t o m e r i c b e a r i n g i s t h a t t h e v a r i o u s c h a r a c t e r i s t i c s o f t h e guidance o f m o t i o n and t h e t r a n s m i s s i o n and d i s s i p a t i o n o f mechanical work can be d e t e r mined, a t l e a s t i n p r i n c i p l e , f r o m t h e b u l k m a t e r i a l p r o p e r t i e s o f t h e i n t e r facial material.

5,4,4

FLEXURALMEANS

F o r t r i b o - m e c h a n i c a l a p p l i c a t i o n s i n which o n l y l i m i t e d t r a n s l a t o r y o r angular motions are required, f l e x u r a l bearings, i.e.,

b e a r i n g s wh ch f l e x

o r t w i s t i n an e l a s t i c member t o s u p p o r t t h e l o a d , possess a wear- r e e i n v a r i a b l e t r i b o l o g i c a l s t r u c t u r e . These b e a r i n g s do n o t r e q u i r e a l u b r i c a n t and t h e f r i c t i o n a l r e s i s t a n c e t o m o t i o n i s s i m p l y t h e e l a s t i c s t r e s s

i n bending o r t o r s i o n i n t e g r a t e d t o g i v e t h e f o r c e . Depending on t h e modes o f l o a d and motion, d i f f e r e n t t y p e s o f f l e x u r a l b e a r i n g s have been designed (Ref. 5.39).

As an example, a p a r a l l e l s p r i n g s u p p o r t f o r t r a n s l a t o r y mo-

t i o n i s shown i n F i g u r e 5.18 (Ref. 5.40).

206

F

S

--c

7 1

F i g u r e 5.18

A f l e x u r a l bearing.

The moving p a r t s o f t h e b e a r i n g , (1) and

( Z ) , a r e separated

by two p a r a l l e l

f l e x u r e s t r i p s ( 3 ) which a r e made o f h e a t - t r e a t e d s t e e l o r phosphor bronze. For a t r a n s l a t o r y motion, s, o f t h e upper p a r t (1) o f t h e b e a r i n g , a f o r c e , FF, i s necessary which i s determined by t h e i n t e r n a l f r i c t i o n o f t h e f l e x ure s t r i p s :

FF =

2 E b h 3 s

E

: e l a s t i c moduls

b , h, 1

: dimensions o f

S

:

the s t r i p s

l3

displacement

The c o n t r a c t i o n p e r p e n d i c u l a r t o t h e m o t i o n i s g i v e n by

Summing up, t h e above examples show t h a t t h e r e a r e d i f f e r e n t ways o f e l i m i n a t i n g s o l i d - s o l i d wear processes from mechanical systems under c e r t a i n circumstances, thus p r o v i d i n g t h e p r e r e q u i s i t e f o r a c o n s t a n t , i n v a r i a n t s t r u c t u r e o f t h e t r i b o - m e c h a n i c a l system. The advantages o f t h e s e s o l u t i o n s are: (i)

The t r i b o l o g i c a l processes i n such systems a r e due t o i n t e r n a l p r o cesses ( i n t e r n a l f r i c t i o n and f a t i g u e ) o f t h e i n t e r f a c i a l components (fluids

,

1 i q u i ds , e l a s t i c m a t e r i a l s ) ,

207 (ii)

The f r i c t i o n a l l o s s e s and t h e l i f e t i m e p r o p e r t i e s can be e s t i m a t e d f r o m t h e b u l k p r o p e r t i e s o f t h e i n t e r f a c i a l components.

( i i i ) The f u n c t i o n a l b e h a v i o u r of these systems can be d e s c r i b e d by a p p l y i n g analogue models of t h e w e l l e s t a b l i s h e d t h e o r i e s o f e n g i n e e r i n g systems a n a l y s i s ( s e e S e c t i o n 6.1).

5 , 4 , 5 WEAR

RESISTANT COATINGS

With the s o l u t i o n s described i n the foregoing sections, i t i s possible t o s e p a r a t e c o m p l e t e l y t h e moving s u r f a c e s o f a t r i b o - e n g i n e e r i n g system e l i m i n a t i n g any wear process f r o m t h e system.

I f t h e s o l u t i o n s d e s c r i b e d above a r e n o t a p p l i c a b l e , an advantageous s t r u c t u r e o f a t r i b o - m e c h a n i c a l system may be e s t a b l i s h e d by a p p l y i n g a s u i t a b l e surface treatment o f the surfaces i n order t o m i t i g a t e t r i b o induced changes o f s u r f a c e p r o p e r t i e s . There a r e s e v e r a l d i f f e r e n t s u r f a c e t r e a t m e n t s a v a i l a b l e which a r e s u i t e d f o r t r i b o - e n g i n e e r i n g a p p l i c a t i o n s (Ref. 5.41,

5.42). A c o m p i l a t i o n o f these methods i s g i v e n i n Table 5.1.

I n t h e c h o i c e o f a s u i t a b l e c o a t i n g f o r a g i v e n problem two b a s i c aspects s h o u l d be considered, i n a d d i t i o n t o a c o s t - b e n e f i t a n a l y s i s : (a)

The t e c h n i c a l f u n c t i o n o f t h e system under c o n s i d e r a t i o n and t h e values o f t h e o p e r a t i n g c o n d i t i o n s o f l o a d , v e l o c i t y and t e m p e r a t u r e .

(b)

The t y p e o f wear mechanism o r mechanisms expected t o a c t i n t h e i n t e r f a c e o f t h e moving components.

Depending on t h e t y p e o f t h e dominant i n t e r f a c i a l wear mechanisms, d i f f e r e n t s u i t a b l e s u r f a c e c o m p o s i t i o n s have been suggested. I n c o n s i d e r i n g t h i s asp e c t from t h e view o f t h e " d e 1 a m i n a t i o n t h e o r y o f wear" f o r low-speed d r y s l i d i n g wear c o n d i t i o n s , Suh and co-workers (Ref. 5.43) suggested t h a t a s o f t metal s u r f a c e l a y e r s h o u l d be t h i n n e r t h a n a c r i t i c a l t h i c k n e s s t o p r e v e n t t h e a c c u m u l a t i o n o f d i s l o c a t i o n s i n t h e p l a t e d l a y e r and t h e format i o n o f t h e d e l a m i n a t e d l a y e r . T h i s s u g g e s t i o n was i n v e s t i g a t e d by p l a t i n g annealed A I S I 1018 s t e e l w i t h 0.1 pm cadmium l a y e r s on b o t h o f t h e contact i n g s u r f a c e s . I n a s p e c i a l case t h i s has l e d t o a r e d u c t i o n o f t h e wear r a t e o f about t h r e e o r d e r s o f magnitude. Some general a d v i c e f o r t h e d e s i g n o f s u r f a c e c o a t i n g s i n r e l a t i o n t o t h e i n t e r f a c i a l wear mechanisms i s compiled i n F i g u r e 5.19 ( R e f . 5 . 4 4 ) : I f i n a s l i d i n g system t h e adhesive wear mechanism i s expected t o dominate,

s u r f a c e l a y e r s o f l o w tendency f o r " c o l d w e l d i n g " and w i t h l o w shear s t r e n g t h

208

TREATMENT

CONSTITUENTS

DEPOSITED COATIgGS Electroplating Electrochemical Co-depos iti on Chemical Vapour Deposition (CVD) Arc Deposition Powder/Wi r e Spraying P1asma Spraying Detonation Gun

1 I

Cr, Rh, N i , Sn-Ni, Ag Co/CrpC3, Pb/PTFE

T i c , TiN, WC Co-Cr-Ni A1 l o y s

Ceramics, Cermets

-

Spraying/Brushi ng

MoSZ

Sputtering

MoS2 Films

Porous Sintered Layers Porous Anodic Films

Bronze/PTFE, CO/PTFE Ti/PTFE, Al/PTFE

Resin Bonded

CHEMICAL CONVERSION COATINGS

Anodize

Phosphate

Ferrous A1 1oys T i t a n i um & A1 -A1 1oys

Oxal ate D i chromate

Magnesium A l l o y s

Copper A1 1oys

DIFFUSION COATINGS Carburi z i ng

C

N it r i d i n g

N,C

Sulfoni t r i d i n g Siliconizing

NsS

B o r i d i ng

8, FeeB

Chromizing Beryl 1id i ng

Be i n Titanium

Si

i n Ferrous A1 loys

Cr

~~

Table 5 . 1

Surface treatments f o r tribo-engineering a p p l i c a t i o n s

may be applied. Depending on t h e material o f the counterpartner, t h i n surface layers o f s o f t m a t e r i a l s w i t h a hexagonal c r y s t a l l o g r a p h i c s t r u c t u r e may f o r example be s u i t a b l e . (Thin s o f t coatings are a l s o useful from the p o i n t of the delamination theory; they may a l s o

-

i n a broader sense

-

p o s i t i v e l y i n f l u e n c e surface f a t i g u e wear processes.) I f the abrasive wear component dominates, very hard surface coatings, l i k e t i t a n i u m carbides, may lead t o low wear r a t e s . Hard coatings, e.g., TiN, w i l l also reduce adhesion of s t e e l as w e l l as t h e wear r a t e . I f superposition o f various wear processes i s t o be expected, m u l t i - l a y e r e d surface coatings may be b e n e f i c i a l (Ref. 5.45,

5.46).

For c e r t a i n cases o f a p p l i c a t i o n , t h e f o l l o w -

i n g r u l e s f o r the design of a t r i b o l o g i c a l l y stressed surface as i l l u s t r a t e d i n the lower p a r t o f Figure 5.19, may be favourable:

A t h i n outmost surface l a y e r should prevent adhesional c o l d welding

(i)

effects w i t h the counterpartner. (ii)

Below the t h i n l a y e r a hard l a y e r o f s u f f i c i e n t d u c t i l i t y should bear the maximum o f Hertzian contact stresses. This l a y e r should e x h i b i t a gradient o f mechanical strength p r o p e r t i e s increasing from the outside t o the i n s i d e o f the specimen.

( i i i ) Below the hard intermediate l a y e r the strength decreases progressively u n t i l t h e lower values o f the base material are reached.

pizZzG-1

Design of component shear strength coatin material

coatin material

surface f a t i g u e material Figure 5.19

S u i t a b l e composition o f surface coatings.

1

210 These r a t h e r q u a l i t a t i v e p o i n t s s h o u l d be supplemented by an example o f t h e d e s i g n o f an a c t u a l t r i b o - e n g i n e e r i n g component. Consider as a c h a r a c t e r i s t i c example t h e design o f a b e a r i n g bushing (Ref. 5.47),

as

shown s c h e m a t i c a l l y i n F i g u r e 5.20.

0.3-1.5

mm

flash overlay diffusion barrier bearing l a y e r

Pb o r Sn Pb-Sn-Cu Ni bronze

s t e e l back

steel

Design o f a b e a r i n g bushing.

F i g u r e 5.20

I t can be seen t h a t a contemporary b e a r i n g may c o n s i s t o f f i v e l a y e r s t o

f u l f i l l i t s t e c h n i c a l purpose. The p r o t e c t i o n a g a i n s t ( c o r r o s i v e ) e n v i r o n mental a t t a c k i s p r o v i d e d by t h e outermost l a y e r , t h e f l a s h . The t r i b o l o g i c a l b e h a v i o u r i s determined m a i n l y by t h e o v e r l a y and t h e b e a r i n g l a y e r . ( B o t h l a y e r s a r e separated by a t h i n n i c k e l l a y e r which p r e v e n t s t h e d i f f u s i o n o f t i n from t h e o v e r l a y t o t h e copper o f t h e b e a r i n g l a y e r which may o c c u r a t e l e v a t e d temperatures. ) Whereas t h e o v e r l a y forms t h e s l i d i n g s u r f a c e , t h e purpose o f t h e b e a r i n g l a y e r i s t o embed h a r d p a r t i c l e s and t o r e p l a c e t h e s l i d i n g s u r f a c e i f t h e o v e r l a y i s worn away. The purpose o f t h e s t e e l back i s t o c a r r y t h e normal l o a d and t o connect t h e bushing w i t h

**

'

i t s housing. T h i s example again i l l u s t r a t e s t h e importance o f a s u i t a b l e s t r u c t u r a l design o f t h e components o f t r i b o - m e c h a n i c a l systems.

211

6 Influence of tribological processes on the function of mechanical systems 6 , 1 GENERAL CONSIDERATIONS Whereas i n t h e p r e c e d i n g c h a p t e r t h e i n f l u e n c e o f t r i b o l o g i c a l processes on t h e i n t e r n a l s t r u c t u r e o f mechanical systems has been discussed, i n t h i s c h a p t e r t h e i n f l u e n c e o f t r i b o l o g i c a l processes on t h e e x t e r n a l f u n c t i o n o f mechanical systems w i l l be s t u d i e d . I t has been shown i n Chapter 3 t h a t t h e t e c h n i c a l f u n c t i o n o f t h e v a r i o u s t r i b o - m e c h a n i c a l systems can be des c r i b e d f o r m a l l y by t r a n s f o r m a t i o n s o f c e r t a i n system i n p u t s , such as m o t i o n and work, i n t o t h e o u t p u t s which a r e used t e c h n i c a l l y . D e t r i m e n t a l i n f l u ences o f t h e f r i c t i o n and wear processes d e s c r i b e d i n Chapter 4 may t h e n l e a d t o d i s t u r b a n c e s o f t h e f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s , f o r example f r i c t i o n - i n d u c e d s t i c k - s l i p e f f e c t s , u n f a v o u r a b l e mechanical e f f i c i e n c i e s o r even gross f u n c t i o n a l f a i l u r e s . Although t h e d e t r i m e n t a l i n f l u e n c e s o f t h e v a r i o u s t r i b o l o g i c a l processes on t h e m a n i f o l d mechanical systems ( a s comp i l e d i n t h e Appendix A) may be a p p a r e n t l y r a t h e r d i f f e r e n t , f r o m a systems p o i n t o f view t h e r e a r e some f e a t u r e s which appear t o be o f g e n e r a l importance. These b a s i c aspects w i l l be s t u d i e d i n t h i s c h a p t e r and c o n c l u s i o n s f o r a p r o p e r f u n c t i o n a l b e h a v i o u r o f t r i b o - m e c h a n i c a l systems w i l l be drawn. To o b t a i n a s t a r t i n g p o i n t f o r a systems approach t o t h e s t u d y o f t h e

main i n f l u e n c e s o f t r i b o l o g i c a l processes on t h e f u n c t i o n o f mechanical systems, f i r s t t h e f u n c t i o n a l b e h a v i o u r o f mechanical systems w i t h n e g l i g i b l e d e t r i m e n t a l t r i b o l o g i c a l i n f l u e n c e s w i l l be d i s c u s s e d i n t h i s s e c t i o n . I f d e t r i m e n t a l i n f l u e n c e s o f t r i b o l o g i c a l processes a r e n e g l i g i b l e and

i f a mechanical system possesses a c o n s t a n t , i n v a r i a n t s t r u c t u r e (see Sect i o n 5.4),

i t i s p o s s i b l e t o a p p l y t h e network approach o f e n g i n e e r i n g

212

systems a n a l y s i s t o t h e d e s c r i p t i o n o f t h e f u n c t i o n a l b e h a v i o u r o f t h e system. As o u t l i n e d i n S e c t i o n 2.3, t h e c h a r a c t e r i z a t i o n o f t h e f u n c t i o n a l b e h a v i o u r o f a mechanical system by means o f t h e network approach o f e n g i n e e r i n g systems a n a l y s i s s t a r t s w i t h t h e i d e n t i f i c a t i o n and m o d e l l i n g o f t h e elements o f t h e system. Next, t h e i n p u t and o u t p u t v a r i a b l e s o f t h e system a r e i d e n t i f i e d and c l a s s i f i e d i n t o " a c r o s s " and " t h r o u g h " v a r i a b l e s o r " e f f o r t " and " f l o w " v a r i a b l e s . Then network graphs and s i g n a l f l o w graphs a r e drawn and t h e s t a t e e q u a t i o n s a r e f o r m u l a t e d . F o r t h i s purpose, t h e K i r c h h o f f ' s mesh and node laws a r e o f t e n u t i l i z e d . The r e s u l t i n g e q u a t i o n s a r e t h e n s o l v e d a p p l y i n g s u i t a b l e methods, l i k e t h e Laplace t r a n s f o r m , o r by u t i l i z i n g d i g i t a l o r analogue computers i n o r d e r t o c h a r a c t e r i z e t h e f u n c t i o n a l b e h a v i o u r o f t h e system.

M1

Figure 6.1

Simple gear t r a i n and i t s schematic r e p r e s e n t a t i o n .

A mechanical system which i s f r e q u e n t l y used t o i l l u s t r a t e t h e a p p l i c a t i o n o f t h e network t e c h n i q u e i s t h e " i d e a l " gear t r a i n (no f r i c t i o n l o s s e s , no wear e f f e c t s ) . A s i m p l e gear t r a i n i s shown i n F i g u r e 6.1. The gear t r a i n c o n s i s t s o f two gears w i t h r a d i i rl and r2, and t h e r a t i o o f i t s r a d i i i s c a l l e d t h e gear r a t i o N = r2/r1. The gear t r a i n i s t r a n s m i t t i n g b o t h t o r q u e

M1-M2

and a n g u l a r v e l o c i t y u1-u2

and i t i s sometimes c a l l e d a

mechanical-mechani c a l energy c o n v e r t e r . The f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s o f t h e g e a r - t r a i n system can be found by an e l e c t r i c a l analogue f r o m t h e g e n e r a l i z e d K i r c h h o f f ' s laws (see S e c t i o n 2.3): (i)

From f o r c e e q u i l i b r i u m , t h e f o r c e e x e r t e d m u t u a l l y by t h e i n t e r a c t i n g gear t e e t h must be equal, i . e .

F2 =

F1. I n t r o d u c i n g t h e gear r a t i o , N,

i t f o l l o w s t h a t t h e o u t p u t t o r q u e M2 i s equal t o t h e i n p u t t o r q u e M1

213

times t h e gear r a t i o N : M2

=

N M1

( i i ) From q e o n i e t r i c a l c o m p a t i b i l i t y , t h e s u r f a c e v e l o c i t i e s must be t h e same, i . e . v2 = vl.

T h i s l e a d s t o a r e l a t i o n between t h e i n p u t and o u t p u t

a n g u l a r v e l o c i t i e s wl,

and w 2 :

W2

=

1

W1

The r e l a t i o n s between i n p u t and o u t p u t t o r q u e and a n g u l a r v e l o c i t y can be combined u s i n g a m a t r i x r e p r e s e n t a t i o n . velocity

I n p u t t o r q u e M1 and i n p u t a n g u l a r

u 1 a r e d e s c r i b e d t o g e t h e r as an i n p u t v e c t o r

x =

r "1

This i n p u t vector i s transformed i n t o the output vector

by t h e t r a n s f o r m a t i o n m a t r i x

The f u n c t i o n a l b e h a v i o u r o f an i d e a l gear t r a i n can be t h e n symbolized by t h e r e p r e s e n t a t i o n shown i n F i g u r e 6.2.

Figure 6.2

Network r e p r e s e n t a t i o n o f gear t r a i n system.

214 T h i s i s t h e t y p i c a l network r e p r e s e n t a t i o n o f a ( l i n e a r ) " t w o - p o r t ' ' system. I f more t h a n two i n p u t and o u t p u t v a r i a b l e s a r e connected w i t h t h e system, t h e g e n e r a l i z a t i o n o f t h e m o d e l l i n g t e c h n i q u e l e a d s t o t h e g e n e r a l c h a r a c t e r i z a t i o n o f a n - p o r t system as shown i n F i g u r e 6.3.

Input 1

0

0

0

U

. Input n

output 1

System structure

0

0

---

o

output

Output m

Input System

variables

1,.

F i g u r e 6.3

. . ,m

description

1, ...,n

Network r e p r e s e n t a t i o n o f n - p o r t system.

The t e c h n i q u e i l l u s t r a t e d i n F i g u r e s 6.2 and 6 . 3 o n l y works i f t h e elements o f t h e a c t u a l system can be m o d e l l e d by s i m p l e p h y s i c a l elements w i t h l i n e a r c a u s e - e f f e c t i n t e r r e l a t i o n s h i p s between t h e i n p u t and o u t p u t v a r i a b l e s . Moreover, t h e network t e c h n i q u e assumes a l o s s - f r e e s t e a d y - s t a t e f u n c t i o n o f t h e system and a c o n s t a n t system s t r u c t u r e . Due t o these r e s t r i c t i o n s t h e c o n v e n t i o n a l network technique, as i l l u s t r a t e d by t h e s i m p l e gear t r a i n example, has t o be m o d i f i e d f o r t h e f u n c t i o n a l d e s c r i p t i o n o f t r i b o - m e c h a n i c a l systems. An e x t e n s i o n o f t h e network method f o r t h e s t e a d y - s t a t e case o f power t r a n s m i s s i o n systems which takes i n t o account f r i c t i o n a l energy l o s s e s has been proposed b y S c h l o s s e r (Ref. 6.1).

I n t h i s model a Coulomb-type o f

f r i c t i o n i s assumed, i n t r o d u c i n g a c o n s t a n t c o e f f i c i e n t o f f r i c t i o n f o r a g i v e n s e t o f c o n d i t i o n s . W i t h t h i s model t h e t r a n s f e r and l o s s - c h a r a c t e r i s t i c s o f t h e v a r i o u s mechanical p o w e r - t r a n s m i s s i o n systems can be d e s c r i b e d . I n o r d e r t o s t u d y t h e dynamics o f t r i b o - m e c h a n i c a l systems, v a r i a b l e f r i c t i o n c o n d i t i o n s a r e t o be taken i n t o c o n s i d e r a t i o n as d i s c u s s e d i n t h e n e x t section.

215

6,2

TRANSMISSION OF MOTION

AND

STICK-SLIPEFFECTS

6,2,1 DYNAMICSOF T R I B O - M E C H A N I C A L SYSTEMS The f u n c t i o n a l b e h a v i o u r o f any t r i b o - m e c h a n i c a l system i s connected, by d e f i n i t i o n , w i t h r e l a t i v e m o t i o n o f one o r more o f t h e components o f t h e system. As d e s c r i b e d i n Chapter 3, t h i s m o t i o n may c o n s t i t u t e a t r a n s f e r o f work, i n f o r m a t i o n o r m a t e r i a l t h r o u g h t h e t r i b o - m e c h a n i c a l system. I n any case, t h e m o t i o n and t h e dynamics o f t h e whole system a r e i n f l u e n c e d by t h e i n t e r f a c i a l f r i c t i o n processes between t h e moving components. Clearly,

t h e d e t a i l s o f t h e i n f l u e n c e s o f t r i b o l o g i c a l processes on t h e

dynamics o f m o t i o n may be q u i t e d i f f e r e n t f o r t h e v a r i o u s t r i b o - m e c h a n i c a l systems, f o r example, b a l l b e a r i n g s ( R e f . 6 . 2 ) ,

s l i d e w a y s (Ref. 6 . 3 ) o r

metal machining systems (Ref. 6 . 4 ) . C o n s i d e r i n g t h e f u n c t i o n a l t r a n s m i s s i o n o f m o t i o n t h r o u g h t h e v a r i o u s t y p e s o f t r i b o - m e c h a n i c a l systems, t h e i n f l u e n c e s o f t h e t r i b o l o g i c a l processes d e s c r i b e d i n S e c t i o n 4 . 3 may l e a d t o unwanted v i b r a t i o n s o f t h e moving p a r t s , and t o " s t i c k - s l i p " motion. These d i s t u r b i n g i n f l u e n c e s on t h e f u n c t i o n a l b e h a v i o u r can be observed i n v a r i o u s t r i b o - m e c h a n i c a l systems: f r o m t h e s q u e a l i n g o f brakes t o t h e c h a t t e r i n g o f machine t o o l s d u r i n g c u t t i n g processes. Since t h e o c c u r r e n c e o f s t i c k - s l i p e f f e c t s may i n f l u e n c e t h e f u n c t i o n a l b e h a v i o u r o f any t r i b o mechanical system, t h i s e f f e c t w i l l be s t u d i e d i n some d e t a i l . Many t r i bo-mechani c a l systems whose f u n c t i o n a l purpose i s connected w i t h t h e t r a n s m i s s i o n o f m o t i o n can be m o d e l l e d i n a s i m p l i f i e d manner by t h e c o n f i g u r a t i o n shown i n F i g u r e 6.4. The model system c o n s i s t s o f a body ( 1 ) o f mass ml,

moving r e l a t i v e l y t o i t s c o u n t e r p a r t ( 2 ) o f mass m2 f i x e d

t o t h e ground v i a a s p r i n g w i t h a s p r i n g c o n s t a n t C s 2 and a damper w i t h a damper c o n s t a n t Cd. The body ( 1 ) i s d r i v e n v i a t h e s p r i n g Csl

a t constant

v e l o c i t y vo = s / t . The m o t i o n o f body ( 1 ) o f v e l o c i t y v1 and d i s t a n c e x r e l a t i v e l y t o body ( 2 ) o f v e l o c i t y v2 and d i s t a n c e z i s i n f l u e n c e d by t h e f r i c t i o n f o r c e FF a c t i n g i n t h e i n t e r f a c e ( 3 ) between body ( 1 ) and body ( 2 ) . From t h e f o l l o w i n g simple q u a l i t a t i v e consideration (Ref. 6.5),

i t follows t h a t the

t y p e o f m o t i o n i s determined by t h e v a l u e o f t h e f r i c t i o n f o r c e a t vrel

= 0

and t h e dependence o f t h e f r i c t i o n f o r c e on t h e v e l o c i t y FF = f ( v ) . L e t t h e i n i t i a l s t a t e o f t h e system shown i n F i g u r e 6.4 be such t h a t t h e s p r i n g s Csl

and C s 2 a r e uncompressed and ml

and m2 a r e a t r e s t . When t h e

m o t i o n o f v e l o c i t y vo i s i n t r o d u c e d t h e r e w i l l be no movement o f ml

relative

216

Friction f o r c e , FF

F i g u r e 6.4

Model o f a t r i b o - m e c h a n i c a l system.

F i g u r e 6.5

Network r e p r e s e n t a t i o n .

F i g u r e 6.6

S i g n a l f l o w graph.

217 t o m2 ( " s t i c k " phase) u n t i l t h e d r i v i n g f o r c e on ml i s h i g h enough t o o v e r come t h e ( s t a t i c ) f r i c t i o n f o r c e between ml and m2. I f t h e n t h e m o t i o n o f

m l r e l a t i v e t o m2 s t a r t s ( " s l i p " phase) t h e s p r i n g s decompress. Thus t h e d r i v i n g f o r c e i s lowered b y a c e r t a i n amount. I f now t h e d r i v i n g f o r c e on

ml f a l l s below t h e ( k i n e t i c ) f r i c t i o n f o r c e , a second " s t i c k " phase may e v o l v e . T h i s i n t u r n l e a d s t o an i n c r e a s e o f t h e d r i v i n g f o r c e u n t i l t h e m o t i o n o f t h e second s l i p phase s t a r t s , and so on. The b a s i c e q u a t i o n s which govern t h e f u n c t i o n a l b e h a v i o u r o f t h e mec h a n i c a l t r a n s m i s s i o n system shown i n F i g u r e 6.4 can b e f o r m u l a t e d by u t i l i z i n g t h e network approach o f systems a n a l y s i s ( s e e S e c t i o n 2.3).

Table 6.1

Mechanical

Electrical

mass

capacitor

spring

inductor

damper

resistor

---+'r

-+=-

Analogue mechanical and e l e c t r i c a l system elements.

I n F i g u r e 6.5,

t h e netMork graph o f t h e system o f F i g u r e 6.4 i s drawn. The

network graph i s based on t h e e l e c t r o - m e c h a n i c a l analogue c o m p i l e d i n T a b l e

I n a p p l y i n g t h e v e l o c i t y - e f f o r t , f o r c e - f l o w analogy d e s c r i b e d i n Sect i o n 2.3, f r o m a l o o p p o i n t o f view t h e v e l o c i t y can be seen i n analogy t o

6.1.

a " v o l t a g e d r i v e r " o f t h e c i r c u i t . The f o r c e s F a r e t h e n t h e " f l o w " v a r i a b l e s t h r o u g h t h e elements o f t h e c i r c u i t , i . e . t h e masses ml, m2, t h e s p r i n g s sl,

s2 and t h e damper d. The c o r r e s p o n d i n g s i g n a l f l o w graph o f t h e

network graph o f F i g u r e 6.5 i s shown i n F i g u r e 6.6. From t h e network and s i g n a l - f l o w graphs, t h e e q u a t i o n s d e s c r i b i n g t h e f u n c t i o n a l b e h a v i o u r of t h e t r i b o - m e c h a n i c a l system can be e a s i l y d e r i v e d . U t i l i z i n g K i r c h h o f f ' s node l a w t h e f o l l o w i n g e q u a t i o n s r e s u l t : node 1)

node 2 )

218

(I)

Csl

(11)

-FF

(vot =

-

x)

=

Cs2z t m?

FF t

m,ii

t Cdl

or

F o r t h e s o l u t i o n o f these d i f f e r e n t i a l e q u a t i o n s , d i f f e r e n t methods can be used. ( F o r a r e v i e w o f a n a l y t i c a l methods see Ref. 6.5.)

I n the following,

these e q u a t i o n s and t h e s t i c k - s l i p b e h a v i o u r o f t h e t r i b o - m e c h a n i c a l system shown i n F i g u r e 6.4 w i l l be s t u d i e d b y means o f an analogue computer.

6,2,2

SIMULATION

OF STICK-SLIP

BEHAVIOUR

I f a system can be r e p r e s e n t e d b y d i f f e r e n t i a l e q u a t i o n s , t h e b e h a v i o u r o f t h e system can be s t u d i e d w i t h an analogue computer. The systems elements can be r e p r e s e n t e d w i t h reasonable accuracy by s t a n d a r d computer elements. Whereas f o r t h e t r i b o - m e c h a n i c a l system m o d e l l e d i n F i g u r e 6.4 t h e values o f t h e s p r i n g s and t h e damper Csl,

Cs2 and Cd, r e s p e c t i v e l y , can be e a s i l y

a d j u s t e d by p o t e n t i o m e t e r s e t t i n g s , t h e model1 i n g o f t h e f r i c t i o n charact e r i s t i c s r e q u i r e s an a p p r o p r i a t e f u n c t i o n g e n e r a t o r . The above q u a l i t a t i v e d i s c u s s i o n o f t h e s t i c k - s l i p e f f e c t has i n d i c a t e d t h a t t h e s t i c k - s l i p m o t i o n may be determined by t h e t y p e o f t h e dependence o f t h e f r i c t i o n f o r c e FF ( o r t h e f r i c t i o n c o e f f i c i e n t f ) on t h e v e l o c i t y . I n o r d e r t o s t u d y t h e s t i c k - s l i p m o t i o n w i t h s u f f i c i e n t g e n e r a l i t y , i n t h i s study, f o r t h e f r i c t i o n - v e l o c i t y c h a r a c t e r i s t i c t h e shape o f t h e S t r i b e c k c u r v e has been chosen and t h e b e h a v i o u r o f t h e t r i b o - m e c h a n i c a l system a t t h e d i f f e r e n t p a r t s o f t h e S t r i b e c k c u r v e has been s t u d i e d (Ref. 6.6). The analogue computer f l o w diagram f o r t h e system i s shown s c h e m a t i c a l l y i n F i g u r e 6.7. I t can be seen t h a t t h e upper and t h e l o w e r p a r t s o f t h e computer f l o w

diagram correspond t o t h e above d i f f e r e n t i a l e q u a t i o n s ( I ) and (11) and t h a t the coupling o f these d i f f e r e n t i a l equations v i a the f r i c t i o n force ( o r t h e f r i c t i o n c o e f f i c i e n t ) i s s i m u l a t e d by t h e f u n c t i o n g e n e r a t o r i n t h e m i d d l e

219 o f F i g u r e 6 . 7 . The a p p r o p r i a t e s c a l i n g f a c t o r s a r e determined f r o m t h e d e s i g n parameters o f a p i n - o n - d i s c t r i b o m e t e r m o d e l l e d b y F i g u r e 6.4.

csl ml X

1

-

Function

\

generator FFb)

Z ~

'd -

cs2 m2

8

Figure 6 . 7

Analogue computer f l o w diagram.

F o r g i v e n c o n s t a n t d a t a of m l ,

m2, Csl,

Cd,

depending on t h e l o c a t i o n o f

t h e f r i c t i o n c o e f f i c i e n t w i t h i n t h e S t r i b e c k curve, a d i f f e r e n t dynamic b e h a v i o u r o f t h e t r i b o - m e c h a n i c a l system can be observed. W i t h o u t g o i n g i n t o numerical d e t a i l s , t h e t h r e e f o l l o w i n g d i f f e r e n t g e n e r a l p a t t e r n s o f t h e m o t i o n b e h a v i o u r o f t h e m o d e l l e d t r i b o - m e c h a n i c a l system o f F i g u r e 6 . 4 can be d i s t i n g u i s h e d : (i)

F o r t h e c o n d i t i o n o f f r i c t i o n around t h e minimum o f t h e S t r i b e c k curve, t h e system i s u n s t a b l e and t h e m o t i o n f o l l o w i n g a d i s t u r b a n c e i s divergent, i . e . ,

t h e system e x c i t e s i t s e l f t o v i b r a t i o n s , as shown

i n F i g u r e 6.8. (ii)

F o r t h e c o n d i t i o n s o f f r i c t i o n on t h e l e f t p a r t o f t h e S t r i b e c k c u r v e t h e t y p i c a l s t i c k - s l i p m o t i o n diagram r e s u l t s as i n F i g u r e 6.9.

( i i i ) F o r t h e c o n d i t i o n s o f f r i c t i o n on t h e r i g h t p a r t o f S t r i b e c k ' s c u r v e t h e system i s s t a b l e , i . e .

v i b r a t i o n s i n t r o d u c e d t o t h e system a r e

damped a u t o m a t i c a l l y . T h i s b e h a v i o u r can be seen i n F i g u r e 6.10 f o r f i v e d i f f e r e n t s l o p e s of t h e r i g h t p a r t o f t h e S t r i b e c k c u r v e and f i v e o p e r a t i n g v a l u e s o f t h e f r i c t i o n c o e f f i c i e n t f. The r e s u l t s c o n f i r m t h e e x p e r i m e n t a l o b s e r v a t i o n t h a t s t i c k - s l i p e f f e c t s a r e l i k e l y t o o c c u r if t h e s l o p e of t h e f r i c t i o n - v e l o c i t y c u r v e i s n e g a t i v e

220

Friction characteristic

Motion behaviour

Y

Sliding velocity-

Time

-

F i a u r e 6.8

I n s t a b l e m o t i o n behaviour f o r c o n d i t i o n s a t t h e minimum o f t h e S t r i b e c k c u r v e ( A : range o f v a r i a t i o n o f f, v ) .

F i g u r e 6.9

S t i c k - s l i p o s c i l l a t i o n s f o r c o n d i t i o n s on t h e l e f t p a r t o f t h e S t r i b e c k c u r v e (f0=0.6).

F i g u r e 6.10

S t a b l e m o t i o n b e h a v i o u r f o r c o n d i t i o n s on t h e r i g h t p a r t o f t h e S t r i b e c k c u r v e (f=1.0; 0.7; 0.5; 0.3; 0.02).

221

o r equal t o zero,

df < dv

0, as i n t h e l e f t p a r t o f t h e S t r i b e c k curve. Thus,

s t i c k - s l i p e f f e c t s may o c c u r o n l y under c o n d i t i o n s o f s o l i d f r i c t i o n o r boundary o r mixed l u b r i c a t i o n b u t a r e u n l i k e l y t o o c c u r under c o n d i t i o n s o f hydrodynamic 1u b r i c a t i o n . These r e s u l t s show t h a t t h e s t i c k - s l i p b e h a v i o u r o f t r i b o - m e c h a n i c a l systems can be c o n v e n i e n t l y s t u d i e d by analogue computer s i m u l a t i o n . I f an a c t u a l t r i b o - m e c h a n i c a l system i s m o d e l l e d i n t h i s way, i t i s a l s o p o s s i b l e t o use t h i s model as a b a s i s f o r a t t e m p t s t o e l i m i n a t e s t i c k - s l i p e f f e c t s and t o o p t i m i z e t h e dynamic b e h a v i o u r o f t h e system. The o p t i m i z a t i o n d a t a can be o b t a i n e d by v a r y i n g t h e values o f t h e analogue computer s e t t i n g s , t h u s s i m u l a t i n g a change i n t h e d e s i g n of t h e elements o f t h e system (masses, s p r i n g s , dampers) o r a change o f t h e f r i c t i o n c o n d i t i o n s . F u r t h e r , c r i t i c a l o p e r a t i n g c o n d i t i o n s o f t h e m o d e l l e d system may be s t u d i e d . I t f o l l o w s t h a t t h e a p p l i c a t i o n o f a c o m b i n a t i o n o f system m o d e l l i n g t e c h niques and analogue computer s t u d i e s may be o f g r e a t h e l p f o r o b t a i n i n g a p r o p e r f u n c t i o n a l b e h a v i o u r o f a g i v e n t r i b o - m e c h a n i c a l system.

6,3 MECHANICAL EFFICIENCY I n Chapter 3 t h e f u n c t i o n a l t r a n s f e r o f mechanical work t h r o u g h a t r i b o mechanical system has been d e s c r i b e d as a process o f t r a n s l a t i o n and t r a n s f o r m a t i o n o f mechanical energy. T h i s can be c h a r a c t e r i z e d i n a s i m p l i f i e d manner by t h e diagram shown i n F i g u r e 6.11.

I n p u t work 'in

-

System structure

"

F i g u r e 6.11

Output work

Losses "

Work t r a n s a c t i o n s o f a t r i b o - m e c h a n i c a l system.

Wout

-

222

The a b i l i t y o f a mechanical system t o t r a n s f e r work, mechanical energy o r power i n t o a t e c h n i c a l l y u s e f u l o u t p u t i s u s u a l l y expressed by t h e e f f i c i e n c y -q o f t h e system d e f i n e d as

efficiency

=

T '

u s e f u l o u t p u t work i n p u t work

W,,t 'in

Because o f i t s economic importance, t h e e f f i c i e n c y o f a mechanical system i s one o f i t s b a s i c e n g i n e e r i n g c h a r a c t e r i s t i c s and most s t a n d a r d books o f mechanical e n g i n e e r i n g c o n t a i n some d a t a on t h e e f f i c i e n c y o f machine e l e ments. (See f o r i n s t a n c e Ref. 6 . 7 . ) However, due t o t h e g r e a t v a r i e t y o f t r i b o - m e c h a n i c a l systems and t h e c o m p l e x i t y o f t r i b o l o g i c a l processes, t h e r e e x i s t s no g e n e r a l t h e o r y c o r r e l a t i n g t h e e f f i c i e n c y o f mechanical systems w i t h t h e t r i b o l o g i c a l processes o c c u r r i n g w i t h i n t h e system as d i s cussed i n S e c t i o n 4.3.4.

I n t h e f o l l o w i n g , t h e i n f l u e n c e o f f r i c t i o n on t h e

e f f i c i e n c y o f a t r i b o - m e c h a n i c a l system w i l l b e s t u d i e d phenomenologically i n d i s c u s s i n g a s i m p l e t e c h n i c a l example. From t h e r e s u l t s o f t h i s example some g e n e r a l c o n c l u s i o n s w i l l be drawn. Consider a s i m p l e "wedge d r i v e " as i l l u s t r a t e d i n t h e upper p a r t o f F i g u r e 6.12.

The system c o n s i s t s o f a h o r i z o n t a l l y moving wedge (1) and a

v e r t i c a l l y moving wedge ( 2 ) . The t e c h n i c a l purpose o f t h e system i s t o t r a n s f o r m t h e i n p u t motion, i . e . t h e i n p u t t r a n s l a t i o n x i n t o an o u t p u t m o t i o n y a t a r i g h t a n g l e t o i t , and t o l i f t a l o a d F a t t h e o u t p u t by Y i n t r o d u c i n g an i n p u t f o r c e Fx. The b a s i c p r i n c i p l e o f t h e t r a n s f o r m a t i o n

o f i n p u t s o f f o r c e and m o t i o n (Fx, x ) i n t o t e c h n i c a l l y u s e f u l o u t p u t s o f f o r c e and m o t i o n ( F y ) by means o f a "wedge e f f e c t " i s u t i l i z e d i n v a r i o u s Y' t r i b o - m e c h a n i c a l machine elements, i n c l u d i n g t r a n s l a t i o n screws, worm-wheel d r i v e s , cam-and-follower s e t s , e t c . The e f f i c i e n c y o f t h e wedge d r i v e system shown i n F i g u r e 6.12 can b e c a l c u l a t e d w i t h t h e f o l l o w i n g s t e p s (Ref. 6 . 8 ) : (a)

draw free-body diagrams o f t h e elements o f t h e system,

(b)

draw v e c t o r diagrams o f t h e f o r c e s a c t i n g on t h e system's elements,

(c)

determine t h e c o n d i t i o n s o f f o r c e e q u i l i b r i u m ,

(d)

c a l c u l a t e t h e e f f i c i e n c y T d e f i n e d as 7 = Fy. y/F;

x.

223

tY

I iFY+ F3

FN2 Fx

FY

F i g u r e 6.12

C h a r a c t e r i s t i c o f "wedge d r i v e " system.

224

As i n d i c a t e d i n F i g u r e 6.12,

t h e t r a n s m i s s i o n o f t h e i n p u t f o r c e Fx

i n t o t h e o u t p u t f o r c e F i s i n f l u e n c e d by t h r e e sources o f f r i c t i o n : Y FF1 i s t h e f r i c t i o n f o r c e a c t i n g a t t h e s u p p o r t o f wedge ( l ) , (i) (ii)

FF2 i s t h e f r i c t i o n f o r c e a c t i n g a t t h e i n t e r f a c e between wedge ( 1 ) and wedge ( 2 ) ,

( i i i ) FF3 i s t h e f r i c t i o n f o r c e a c t i n g i n t h e guides o f wedge ( 2 ) . S p l i t t i n g up these f o r c e s i n t o components normal and t a n g e n t i a l t o t h e surfaces, t h e f o r c e v e c t o r diagrams shown i n t h e r i g h t - h a n d p a r t o f F i g u r e 6.12 can be drawn. I n these diagrams, 6 denotes t h e a n g l e between t h e t a n g e n t i a l ( f r i c t i o n ) f o r c e component FT and t h e normal f o r c e component FN, t h e t a n g e n t o f which i s e q u i v a l e n t t o t h e c o e f f i c i e n t o f f r i c t i o n , i . e . , t a n 5 = FT/FN = f. From t h e p a r t i a l f o r c e v e c t o r diagrams t h e r e s u l t i n g f o r c e v e c t o r diagram, d e s c r i b i n g t h e e q u i l i b r i u m c o n d i t i o n between t h e f o r c e s Fx, F1,

F3, Fy can be determined, see F i g u r e 6.12 below. From t h e

t r i g o n o m e t r i c r e l a t i o n s f o r t h e two t r i a n g l e s w i t h i n t h i s diagram, i t f o l 1ows t h a t

sin

p1

sin

p2

and

-FXsin

Thus

p3

- - F2 sin

p4

225

I f i t i s assumed t h a t t h e c o n d i t i o n s o f f r i c t i o n ( i ) , ( i i ) , ( i i i ) a r e equal, i .e. t h a t

fl

=

f*

f3 =

=

f,

i t follows t h a t

1

F

Y=

t a n (cp t 26)

FX

Since t h e r e l a t i o n between t h e d i s t a n c e s x and y i s g i v e n by y

=

11

=-

x tancp,

then f o r the e f f i c i e n c y Fy

'

Y

Fx

*

x

i t follows t h a t

tang

11'

t a n ( c p t 26)

T h i s r e l a t i o n i n d i c a t e s t h a t f o r a g i v e n v a l u e o f t h e wedge anglecp, t h e e f f i c i e n c y i s determined b y t h e f r i c t i o n c o e f f i c i e n t f = t a n 6 a t t h e t h r e e f r i c t i o n a l i n t e r f a c e s shown i n F i g u r e 6.12. S i m i l a r e x p r e s s i o n s a r e a l s o o b t a i n e d f o r o t h e r t r i b o - m e c h a n i c a l systems. F o r i n s t a n c e , t h e e f f i c i e n c y o f a t r a n s l a t i o n screw (Ref. 6.9) i s g i v e n by t h e r e l a t i o n t a n cp

T '

tan ( g t 6 )

which i s q u i t e s i m i l a r t o t h a t o f t h e wedge-drive system. A graph o f t h e e f f i c i e n c y o f t h e wedge-drive system f o r a wedge a n g l e c p = 30' t i o n o f t h e c o e f f i c i e n t o f f r i c t i o n i s p l o t t e d i n F i g u r e 6.13.

as a func-

226

I

90

80 70

h

z F

6o

F i g u r e 6.13

E f f i c i e n c y o f a wedge d r i v e system as f u n c t i o n o f f r i c t i o n .

I t can be seen t h a t t h e e f f i c i e n c y v a r i e s o v e r a broad range as a f u n c t i o n

of t h e c o e f f i c i e n t of f r i c t i o n , F o r t y p i c a l f r i c t i o n and l u b r i c a t i o n regimes t h e f o l l o w i n g ranges a r e found: (I)

dry s l i d i n g f r i c t i o n

:

(11)

boundary l u b r i c a t i o n

:

(111) (IV)

hydrodynamic l u b r i c a t i o n

: :

rolling friction

1 z 5 t o 40% x 60 t o 70%

1

= 90

t o 98%

-q

= 97

t o 99%

These d a t a i n d i c a t e t h a t f o r s l i d i n g s i t u a t i o n s , e f f i c i e n c i e s g r e a t e r t h a n

90 p e r c e n t can o n l y be o b t a i n e d w i t h f u l l f l u i d l u b r i c a t i o n , and t h a t h i g h e s t e f f i c i e n c i e s can be r e a l i z e d by s u b s t i t u t i n g s l i d i n g f r i c t i o n by r o l l i n g elements. Although these f i g u r e s a r e d e r i v e d f o r t h e s p e c i f i c wedged r i v e system, they c h a r a c t e r i z e b r o a d l y t h e t y p i c a l e f f i c i e n c y ranges o f t r i b o - m e c h a n i c a l systems o p e r a t i n g under d i f f e r e n t t r i b o l o g i c a l c o n d i t i o n s .

227

I f e x a c t e f f i c i e n c y d a t a of a g i v e n t r i b o - m e c h a n i c a l system a r e needed, e x p e r i m e n t a l measurements s h o u l d be used i n a d d i t i o n t o an a n a l y t i c a l e s t i m a t i o n . F o r example, f o r t h e a c c u r a t e d e t e r m i n a t i o n o f t h e e f f i c i e n c y o f gear systems, b o t h e x p e r i m e n t a l measurements and mathematical model s i m u l a t i o n s were performed i n o r d e r t o d e t e r m i n e t h e i n f l u e n c e o f such f a c t o r s as d i a m e t r a l p i t c h , c o n t a c t r a t i o , magnitude o f t r a n s m i t t e d l o a d , and speed upon t h e e f f i c i e n c y (Ref. 6 . 1 0 ) .

I f d i f f e r e n t tribo-mechanical

systems a c t t o g e t h e r , t h e e f f i c i e n c i e s must be m u l t i p l i e d . F o r i n s t a n c e , f o r a s p u r gear system o f e f f i c i e n c y

11 , which 9

i s s u p p o r t e d by two b e a r i n g s

o f e f f i c i e n c y q b t h e t o t a l e f f i c i e n c y i s g i v e n by

I n g e n e r a l i z i n g t h e s e r e s u l t s , i t f o l l o w s t h a t a multi-component mechanical system o f h i g h t o t a l e f f i c i e n c y can o n l y be r e a l i z e d i f a l l i n d i v i d u a l subsystems a r e designed w i t h e f f i c i e n c i e s as h i g h as p o s s i b l e . F o r t h e d e t e r m i n a t i o n o f t h e t o t a l e f f i c i e n c y o f a multi-component system t h e procedure o f "systems t e a r i n g " as e x p l a i n e d i n Chapter 2 may be used.

6 4 FUNCTIONAL FAI LURES I

6,4,1 CAUSES

OF FAILURE

The d i s c u s s i o n s i n t h e p r e c e d i n g s e c t i o n s have shown t h a t t r i b o l o g i c a l p r o cesses determine t h e e f f i c i e n c y o f mechanical systems and may a l s o d i s t u r b t h e f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s . If i n t h e performance o f a g i v e n system, t h e f u n c t i o n a l t r a n s f o r m a t i o n o f t h e s y s t e m ' s i n p u t s i n t o t h e t e c h n i c a l l y used o u t p u t s i s d i s t u r b e d i n such a way t h a t t h e o p e r a t i n g c o n d i t i o n s exceed c e r t a i n t o l e r a n c e l i m i t s i t i s s a i d t h a t a " f u n c t i o n a l f a i l u r e " o f t h e system has o c c u r r e d . Since i n any system, t h e i n p u t s a r e t r a n s f o r m e d i n t o t h e o u t p u t s v i a t h e s t r u c t u r e o f t h e system, i n g e n e r a l t h e e f f e c t o f a f u n c t i o n a l f a i l u r e i s a s s o c i a t e d w i t h , o r caused by, s i g n i f i c a n t changes o f t h e s t r u c t u r e o f t h e system (see Chapter 5 ) . These s t r u c t u r a l changes i n t u r n a r e i n f l u e n c e d o r caused by t h e t r i b o l o g i c a l processes o c c u r r i n g w i t h i n t h e system d u r i n g t h e f u n c t i o n a l t r a n s f o r m a t i o n o f t h e i n p u t s i n t o t h e o u t p u t s . B e f o r e s t u d y i n g t h e r o l e o f t r i b o l o g i c a l processes i n t h e f a i l u r e o f

228

mechanical systems, some general t h e o r e t i c a l c o n s i d e r a t i o n s o f t h e aspects o f s a f e t y and f a i l u r e o f e n g i n e e r i n g systems w i l l f i r s t be made. Why do f a i l u r e s and a c c i d e n t s happen and what should be done t o p r e v e n t them? According t o S t a n t o n (Ref. 6.11) t h e r e a r e t h r e e i m p o r t a n t t h e ories i n this field. The f i r s t i s H e i n r i c h ' s domino sequence t h e o r y which p o s t u l a t e s t h a t f i v e f a c t o r s , o c c u r r i n g i n sequence, l e a d t o an a c c i d t i t ( R e f . 6 . 1 2 ) . These f i v e f a c t o r s a r e : ( a ) p e r s o n a l t r a i t s , e i t h e r i n h e . i t e d o r a c q u i r e d f r o m t h e environment;

( b ) a p e r s o n a l d e f i c i e n c y , i.e.,

t h e s e t r a i t s pre-

dispose a person t o commit an u n s a f e a c t ( o r o m i s s i o n ) o r t o a l l o w a p h y s i c a l o r mechanical hazard t o e x i s t ; ( c ) an u n s a f e a c t ( o r o m i s s i o n ) o r a p h y s i c a l o r mechanical hazard; i d ) t h e a c c i d e n t ; and a t t h e end o f t h e sequence, ( e ) t h e i n j u r y . Each f a c t o r i s l i k e a domino s t a n d i n g on end. As one f a l l s , i t knocks t h e o t h e r s down. To p r e v e n t a c c i d e n t s , H e i n r i c h sugg e s t s removal o f one o f t h e dominoes, p r e f e r a b l y t h e domino l a b e l l e d "unsafe a c t o r mechanical o r p h y s i c a l hazard". The second i m p o r t a n t t h e o r y i s Haddon's abnormal energy exchange t h e o r y (Ref. 6.13). A c c o r d i n g t o t h i s t h e o r y , damage occurs when a system exchanges energy w i t h i t s environment beyond some a c c e p t a b l e o r normal l e v e l . " L e v e l " can mean q u a n t i t y , q u a l i t y , o r r a t e o f t r a n s f e r . "Energy" can be o f i t s d i f f e r e n t forms, e.g.

e l e c t r i c a l , mechanical, a c o u s t i c a l , r a d i a t i o n , t h e r -

mal, e t c . A p p l y i n g Haddon's t h e o r y t o t h e p r e v e n t i o n o f f a i l u r e r e q u i r e s t h a t we know t h e l e v e l s o f energy i n p u t f r o m o r t h e o u t p u t t o i t s e n v i r o n ment which w i l l i n i t i a t e damage t o t h e o b j e c t under study. The t h i r d i m p o r t a n t t h e o r y i n t h e f i e l d o f s a f e t y i s G r i m a l d i ' s r i s k a c c e p t a b i l i t y t h e o r y (Ref. 6 . 1 4 ) . He r e c o g n i z e s t h a t t h e i d e a l o f e l i m i n a t i n g o r n e u t r a l i z i n g a l l hazards can n e v e r be achieved i n r e a l l i f e . The " a c c e p t a b i l i t y " o f a hazard i s determined by t h e t o l e r a b i l i t y o f t h e r i s k a s s o c i a t e d w i t h t h a t hazard. The magnitude o f t h e r i s k ' s t o l e r a b i l i t y i s conceived as a t h r e e - d i m e n s i o n a l space. The dimensions o f t h i s space a r e ( i ) s e n s i t i v i t y t o exposure, ( i i ) p r o b a b i l i t y o f occurrence, and, ( i i i ) seriousness o f t h e e f f e c t s . S e n s i t i v i t y o f exposure i n v o l v e s such m a t t e r s as l e g a l i t y , confidence, and e t h i c a l r e s p o n s i b i l i t y , o r values. To c o n t r o l a c c i d e n t s by a p p l y i n g G r i n i a l d i I s t h e o r y , we reduce t h e p r o b a b i l i t y o f occ u r r e n c e by u s i n g f a i l - s a f e devices, reduce t h e seriousness by exposing fewer people f o r s h o r t e r p e r i o d s o f time, and reduce t h e s e n s i t i v i t y by making o u r designs more a c c e p t a b l e t o t h e changing values o f o u r s o c i e t y (Ref. 6.11).

229

Causes o f f a i l u r e

I

Occurrence sliding bearings

bearings

manufacturing f a u l t s

14.4

10.7

d e s i g n and c a l c u l a t i o n f a u l t s

13.8

9.1

m a t e r i a l s f a u l t s o f components

1.9

3.6

s e r v i c e f a u l t s , maintenance faults, f a i l u r e o f monitoring equi pment

37.4

39.1

wear

28.5

30.5

4.0

7.0

f a i l u r e t h r o u g h e x t e r n a l causes Table 6.2

Causes o f f a i l u r e o f r o l l i n g and s l i d i n g b e a r i n g s ( R e f . 6.16).

Damage types

Table 6.3

Occurrence ( % )

breakages due t o o v e r s t r e s s i n g

60

scuffing, seizure

18

mechanical and c o r r o s i v e s u r f a c e damage

15

cracks

5

d e f l e c t i o n s , deformations

2

Types o f damage o f mechanical c l u t c h e s (Ref. 6.16).

T u r n i n g o u r a t t e n t i o n now t o t h e f i e l d o f mechanical f a u l t s , i n a d d i t i o n t o t h e general t h e o r i e s o f s a f e t y and f a i l u r e , i t i s necessary t o c o n s i d e r t h e causes o f f a i l u r e observed e x p e r i m e n t a l l y . I n r e v i e w i n g t h e causes o f mechanical f a i l u r e , C o l l a c o t t i n h i s r e c e n t book on "Mechanical f a u l t d i a g n o s i s and c o n d i t i o n m o n i t o r i n g " (Ref. 6.15) d i s t i n g u i s h e s between t h e f o l l o w i n g main a s p e c t s : (a)

Service f a i l u r e s

(b)

Fatigue

(c)

Excessive d e f o r m a t i o n

230 (d)

Wear

(e)

Corrosion

(f)

Blockages

(9)

Design, m a n u f a c t u r i n g and assembly causes o f f a i l u r e

T h i s c o m p i l a t i o n o f t h e main c l a s s e s o f f a i l u r e a l r e a d y i n d i c a t e s t h a t t h e r e a r e s e v e r a l n o n - t r i b o l o g i c a l causes which may l e a d t o f a i l u r e o f mechanical equipment. T h i s can a l s o be seen f r o m t h e d a t a o f Tables 6.2 and 6.3 i n which f a i l u r e c h a r a c t e r i s t i c s o f t y p i c a l t r i b o - m e c h a n i c a l systems, namely r o l l i n g and s l i d i n g b e a r i n g s and mechanical c l u t c h e s , a r e l i s t e d . The d a t a have been c o m p i l e d by t h e i n s u r a n c e company ALLIANZ (Ref. 6.16).

Table 6 . 2 c o n t a i n s t h e r e s u l t s o f i n v e s t i g a t i o n s o f t h e causes

o f 1400 r o l l i n g - b e a r i n g f a i l u r e s and 530 s l i d i n g - b e a r i n g f a i l u r e s . I t can be seen t h a t f o r these t r i b o - m e c h a n i c a l systems, about 30 p e r c e n t o f t h e f u n c t i o n a l f a i l u r e s a r e due t o wear processes. Table 6.3 c o n t a i n s t h e p e r centage o f t h e main t y p e s o f damage o f mechanical c l u t c h e s . Also i n t h i s case t h e damage o c c u r r i n g a t t h e l o a d - t r a n s m i t t i n g s u r f a c e s has been f o u n d t o c o n s t i t u t e about 30 p e r c e n t o f t h e t o t a l f a i l u r e causes. These examples show t h a t b e s i d e s t h e t r i b o - i n d u c e d causes o f f a i l u r e , v a r i o u s non- tri b o l o g i c a l causes may 1ead t o f a i 1u r e o f mechanical equi pment. T u r n i n g now t o t r i b o l o g i c a l causes o f f a i l u r e , i n t h e n e x t s e c t i o n t h e systems approach t o t h e s t u d y o f t h e f a i l u r e o f mechanical systems w i l l be o u t l i n e d by d i s c u s s i n g an example.

6,4,2 A

CASE STUDY:

I n S e c t i o n 6.1,

FAILURE

MODES OF GEARS

an i d e a l g e a r t r a i n was s t u d i e d b y t h e systems a n a l y s i s

network method t o i l l u s t r a t e " i d e a l " f u n c t i o n a l behaviour. I n t h i s s e c t i o n t h e main aspects o f t h e f a i l u r e modes o f gears w i l l be considered, as an example o f a s y s t e m a t i c s t u d y o f t h e f a i l u r e o f a t r i b o - m e c h a n i c a l system. I n a r e c e n t r e v i e w , P.M.

Ku o u t l i n e d t h e many f a c t o r s i n f l u e n c i n g g e a r

f a i l u r e , emphasizing t h e importance o f b o t h gear mechanics and gear l u b r i c a t i o n on gear f a i l u r e modes ( R e f . 6.17).

He p o i n t e d o u t t h a t any r a t i o n a l

approach t o gear d e s i g n must c o n s i d e r , as a minimum, t h e impact o f t h e v a r i o u s modes o f g e a r - t o o t h f a i l u r e on gear performance, o p e r a t i n g l i f e , r e l i a b i l i t y , s i z e , w e i g h t , and c o s t . I t has been emphasized above t h a t f a i l u r e o f a t r i b o - m e c h a n i c a l system occurs t h r o u g h t h e a c t i o n o f t h e o p e r a t i n g v a r i a b l e s on t h e s t r u c t u r e o f

231 the system c h a r a c t e r i z e d by a severe d i s t u r b a n c e o f t h e f u n c t i o n a l i n p u t o u t p u t r e l a t i o n s . Accordingly, a study of t h e f a i l u r e o f a gear system must, by necessity, i n c l u d e a c o n s i d e r a t i o n o f t h e t o t a l e f f e c t o f t h e f o l l o w i n g participating factors :

I

OPERATING VARIABLES ( a ) type o f motion, i . e . t h e kinematics, ( b ) f o r c e s which may be s t u d i e d under steady-state c o n d i t i o n s ("pseudos t a t i c s " ) and under dynamic c o n d i t i o n s , (c) velocities, ( d ) ambient temperature, (e) operating duration.

I 1 STRUCTURE OF THE SYSTEM R e s t r i c t i n g t h e discussion t o the case o f a simple two-gears system, t h e f o l l o w i n g aspects o f the system s t r u c t u r e must be taken i n t o consideration: ( a ) System components

(1) the f i r s t gear ( 2 ) the second gear ( 3 ) the l u b r i c a n t

( 4 ) the atmospheric environment ( b ) P r o p e r t i e s o f the system elements (i) (ii)

m a t e r i a l and surface c h a r a c t e r i s t i c s o f gear (1) and gear ( Z ) , l u b r i c a n t ( 3 ) c h a r a c t e r i s t i c s , b o t h p h y s i c a l and chemical ,

( i i i ) c h a r a c t e r i s t i c s o f the surrounding atmosphere (4), b o t h phys i c a l and chemical. ( c ) I n t e r a c t i o n s o f t h e system elements The t r i b o l o g i c a l i n t e r a c t i o n s embrace the various processes d i s cussed i n d e t a i l i n Chapter 4, namely:

(i )

Contact processes c o n t a c t mechanics ( c o n t a c t deformation, t o o t h d e f l e c t i o n s , t o o t h misalignment),

(ii)

L u b r i c a t i o n modes elastohydrodynamic l u b r i c a t i o n w i t h some s p e c i a l c o n d i t i o n s , l i k e unsteady EHD c o n d i t i o n s (dynamic t o o t h l o a d and squeezef i l m e f f e c t s ) , l u b r i c a n t s t a r v a t i o n , non-isothermal f l o w c o n d i t i o n s , e l l i p t i c gear-mesh conjunctions, surface-roughness and s u r f a c e - t e x t u r e e f f e c t s , non-Newtonian f l o w behaviour,

232

boundary l u b r i c a t i o n i n c l u d i n g t h e v a r i o u s p h y s i c a l and chemical aspects o f t h e m a t e r i a l - l u b r i c a n t - a t m o s p h e r e interactions. (iii)

F r i c t i o n processes s l i d i n g / r o l l i n g f r i c t i o n o f the counterformal gear-tooth c o n t a c t under dynamic l o a d s and v e l o c i t i e s .

(iv)

Wear processes g e a r - t o o t h wear o c c u r r i n g t h r o u g h t h e a c t i o n o f one o r more o f t h e b a s i c wear mechanisms, namely s u r f a c e f a t i g u e , a b r a s i o n , adhesion, t r i b o - c h e m i c a l r e a c t i o n s .

The nomenclature o f t h e American S o c i e t y o f Gear Manufacturers (AGMA) c i t e s

2 1 modes o f g e a r - t o o t h f a i l u r e . According t o Ku (Ref. 6.17), i t i s t h o u g h t t o be more l o g i c a l t o c l a s s i f y t h e g e a r - t o o t h f a i l u r e modes i n two b a s i c c a t e g o r i e s , namely, s t r e n g t h - r e l a t e d modes and l u b r i c a n t - r e l a t e d ( o r more g e n e r a l l y t r i b o - r e l a t e d ) modes. M a j o r modes o f s t r e n g t h - r e l a t e d f a i l u r e a r e p l a s t i c f l o w and breakage. M a j o r modes o f t r i b o - r e l a t e d f a i l u r e a r e r u b b i n g wear, s c u f f i n g ( o r s c o r i n g ) , and p i t t i n g . From a systems p o i n t o f view t h e s e processes a r e p r i m a r i l y connected w i t h changes i n t h e s t r u c t u r e o f t h e system under c o n s i d e r a t i o n (see S e c t i o n 5.2).

These t r i b o - i n d u c e d changes o f

t h e system s t r u c t u r e t h e n determine t h e f u n c t i o n a l t r a n s m i s s i o n o f power through t h e system: i n t h e absence o f s t r e n g t h - r e l a t e d f a i l u r e s , t h e maximum power t h a t can be t r a n s m i t t e d t h r o u g h a s e t o f homologous gears i s p r i m a r i l y l i m i t e d a t low v e l o c i t i e s by r u b b i n g wear, a t i n t e r m e d i a t e v e l o c i t i e s by p i t t i n g o r s c u f f i n g and a t h i g h v e l o c i t i e s by s c u f f i n g . Some o f t h e b a s i c aspects o f these f a i l u r e - i n d u c i n g t r i b o l o g i c a l processes have a l r e a d y been s t u d i e d i n Chapter 4. I n t h e f o l l o w i n g , some aspects o f t h e most pronounced g e a r - f a i l u r e mechanisms, namely p i t t i n g and s c u f f i n g w i l l be discussed. Being a s u r f a c e f a t i g u e phenomenon, p i t t i n g i s t h e consequence o f r e p e a t e d s t r e s s c y c l i n g o f t h e s u r f a c e s beyond t h e m a t e r i a l ' s endurance l i m i t . I t takes some t i m e t o develop and l e a d s t o s u r f a c e o r subsurface cracks and e v e n t u a l l y t o t h e detachment o f fragments f r o m and t h e f o r m a t i o n o f p i t s on one o r b o t h s u r f a c e s . L i k e a l l s u r f a c e f a t i g u e e f f e c t s p i t t i n g occurs even i f t h e s u r f a c e s a r e c o m p l e t e l y s e p a r a t e d by an i n t a c t o i l f i l m . T h i s i s because t h e presence o f an o i l f i l m m e r e l y modulates t h e i n t e n s i t y o f t h e repeated s u r f a c e s t r e s s i n g , b u t does n o t e l i m i n a t e i t a l t o g e t h e r . The l u b r i c a n t s does however have two s p e c i f i c i n f l u e n c e s : (i)

i t has been observed t h a t t h e p i t t i n g l i f e i s l a r g e l y a f u n c t i o n o f

t h e r a t i o o f t h e o i l f i l m t h i c k n e s s t o t h e composite s u r f a c e roughness

233

( i i ) t h e r e i s some evidence t h a t w i t h o i l s o f d i f f e r e n t chemical composit i o n s , t h e chemical e f f e c t on p i t t i n g l i f e cannot be i g n o r e d . From t h e m a t e r i a l p o i n t o f view, t h e s t e e l c o m p o s i t i o n and t h e m e t a l l u r g i c a l s t r u c t u r e e x e r t an i n f l u e n c e on p i t t i n g l i f e . T h i s i s i n f l u e n c e d a l s o by l o a d - s h a r i n g and t o o t h - p r o f i l e m o d i f i c a t i o n . The e f f e c t o f p i t t i n g o c c u r s w i t h gears o f l o w c o n t a c t r a t i o s u s u a l l y n e a r t h e p i t c h l i n e where t h e m o t i o n i s n e a r l y p u r e r o l l i n g b u t t h e H e r t z i a n s t r e s s i s a maximum. F o r gears w i t h h i g h e r c o n t a c t r a t i o s , t h e l o a d s h a r i n g p a t t e r n i s q u i t e d i f f e r e n t and t h e maximum H e r t z i a n s t r e s s may v e r y w e l l o c c u r i n t h e mesh c y c l e where t h e s l i d i n g v e l o c i t y may be h i g h . S c u f f i n g i s t h e o t h e r m a j o r f a i l u r e mode o f gears, and i s a severe f o r m o f adhesive wear which cannot o c c u r i f an o i l f i l m o f s u f f i c i e n t t h i c k n e s s separates t h e s u r f a c e s . I n c o n t r a s t t o t h e time-dependent f a i l u r e mode o f p i t t i n g , s c u f f i n g f a i l u r e s may o c c u r q u i t e p r e c i p i t o u s l y . I t i s b e l i e v e d t h a t , i n o r d e r t o ensure f u l l EHD l u b r i c a t i o n t h e o p e r a t i n g c o n d i t i o n s must be such t h a t f o r a g i v e n system t h e r a t i o o f o i l f i l m t h i c k n e s s t o composite surface roughness,h, S e c t i o n 4.5.6,

i s i n t h e o r d e r o f t h r e e . As has been e x p l a i n e d i n

f a i l u r e o f a f u l l EHD l u b r i c a t e d systems occurs o n l y i f two

c o n d i t i o n s a r e met: ( i ) t h e necessary c o n d i t i o n f o r t h e breakdown o f t h e EHD f i l m , ( i i ) an a d d i t i o n a l c o n d i t i o n f o r t h e breakdown o f t h e s u r f a c e f i l m s . Whereas i t appears p o s s i b l e t o t a c k l e c o n d i t i o n ( i ) f r o m b a s i c EHD p r i n c i p l e s t a k i n g i n t o account t h e dynamic i n f l u e n c e s o f temperate and p r e s s u r e induced v i s c o s i t y changes and s u r f a c e roughness e f f e c t s , t h e r e i s s t i l l some d i s c u s s i o n on t h e p h y s i c a l mechanism o f t h e c o n d i t i o n ( i i ) . I t appears t h a t t h e r e m i g h t be a c r i t i c a l i n t e r f a c i a l " s u r f a c e temperature" o r a c r i t i c a l "power i n p u t " o r a c r i t i c a l "power i n t e n s i t y i n p u t " t h a t a g i v e n boundary l u b r i c a t i o n f i l m may w i t h s t a n d . C l e a r l y , t h e c r i t i c a l f a i l u r e c o n d i t i o n depends on t h e m a t e r i a l s - l u b r i c a n t - a t m o s p h e r e

i n t e r a c t i o n under t h e a c t i o n

o f the s e t o f the operating load-velocity-temperature-time

variables.

T h i s survey on gear f a i l u r e i s based on t h e r e v i e w a r t i c l e by (Ref. 6.17),

Ku

and i s p r e s e n t e d h e r e as an example o f t h e f a i l u r e modes o f a

t r i b o - m e c h a n i c a l system because i t c l e a r l y demonstrates t h e m u l t i p l i c i t y o f f a i l u r e - i n d u c i n g parameters and f a i l u r e - i n d u c i n g e f f e c t s . I t a l s o i n d i c a t e s t h e c l o s e i n t e r r e l a t i o n s between t r i b o - i n d u c e d changes o f t h e system's s t r u c t u r e and t h e f u n c t i o n a l b e h a v i o u r o f t h e system. A l t h o u g h t h e v a r i o u s aspects o f f a i l u r e have been d i s c u s s e d elsewhere f o r o t h e r t r i b o - m e c h a n i c a l

234 systems, f o r example p l a i n b e a r i n g s (Ref. 6.18), r o l l i n g c o n t a c t b e a r i n g s (Ref. 6.19) o r p i s t o n r i n g s (Ref. 6.20), i t i s somewhat d i f f i c u l t t o genera l i z e these f i n d i n g s . An approach t o d e a l i n g w i t h t h e v a r i o u s aspects o f f a i l u r e i n a g e n e r a l i z e d way i s p r o v i d e d by t h e p r o b a b i l i s t i c r e l i a b i l i t y e s t i m a t i o n f o r components and systems as d i s c u s s e d in t h e n e x t s e c t i o n .

6,5

MECHANICAL EQUIPMENTRELIABILITY

R e l i a b i l i t y i s d e f i n e d as " t h e p r o b a b i l i t y o f a d e v i c e p e r f o r m i n g i t s p u r pose adequately f o r t h e p e r i o d o f t i m e i n t e n d e d under t h e o p e r a t i n g cond i t i o n s encountered". T h i s i s t h e c l a s s i c d e f i n i t i o n o f r e l i a b i l i t y g i v e n by t h e Radio E l e c t r o n i c s and T e l e v i s i o n Manufacturers A s s o c i a t i o n i n 1955. Since t h a t time, t h e r e l i a b i l i t y o f e l e c t r o n i c equipment has r e c e i v e d i n c r e a s i n g a t t e n t i o n , as apparatus has grown more c o m p l i c a t e d and has been a p p l i e d t o a g r e a t v a r i e t y o f i m p o r t a n t t a s k s . Now, t h e t h e o r y and p r a c t i c e o f e l e c t r o n i c equipment r e l i a b i l i t y i s o f a f a i r l y h i g h s t a n d a r d and methods f o r r e l i a b i l i t y p r e d i c t i o n and d e s i g n i n g f o r r e l i a b i l i t y have been developed i n c l u d i n g t h e aspects o f redundancy (Ref. 6.21, 6.22, 6.23). Attempts of w e l l - f o u n d e d c o n s i d e r a t i o n s o f mechanical equipment r e l i a b i l i t y a r e o f o n l y r e c e n t o r i g i n (Ref. 6.24, 6.25). The d i f f e r e n c e s i n t h e s t a t e o f t h e a r t o f r e l i a b i l i t y c o n s i d e r a t i o n s o f e l e c t r i c a l and mechanical systems may be due t o t h e d i f f e r e n c e s i n t h e i r " i n t e r n a l s t r u c t u r e s " as d i s c u s s e d i n S e c t i o n 3 . 1 (see F i g u r e 3 . 1 ) . Consider, as a s t a r t i n g p o i n t f o r t h e r e l i a b i l i t y c o n s i d e r a t i o n s o f t r i b o - m e c h a n i c a l systems, t h e wear b e h a v i o u r as a f u n c t i o n o f time. I n S e c t i o n 5.3 i t was e x p l a i n e d t h a t f o r t h e l o s s - o u t p u t wear r a t e s o f a t r i b o - m e c h a n i c a l system t h r e e main d i f f e r e n t c h a r a c t e r i s t i c s may be d i s t i n g u i s h e d (Ref. 6.26, 6.27):

(I)

s e l f accommodation

(11)

steady s t a t e

(111) s e l f a c c e l e r a t i o n

("running in'') ( " c a t a s t r o p h i c damage")

These t h r e e modes o f change i n t h e system b e h a v i o u r may f o l l o w each o t h e r i n time, as i n d i c a t e d i n F i g u r e ' 6 . 1 4 .

I n F i g u r e 6.14, ZMlim

denotes a

maximum a d m i s s i b l e l e v e l o f t h e wear losses. A t t h i s l e v e l t h e system s t r u c t u r e has changed i n such a way t h a t t h e f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s o f t h e system a r e d i s t u r b e d s e v e r e l y . Repeated measurements show random v a r i a t i o n s i n t h e data, as i n d i c a t e d b y t h e dashed l i n e s i n F i g u r e

235

6.14. From sample functions of the wear process a distribution of the "lifetime" of the system, i.e., a failure distribution can be derived.

failure distribution

Tine t Figure 6.14

Wear curves and failure distribution,

In a quantitative way the reliability of a mechanical system may be characterized mathematically as follows: Generally, the reliability of a mechanical system is expressed by a probabilistic function R(t) based on the following definitions: F(t)

: probability distribution function of

the time to fai 1 ure f(t)

=

dF0 dt

:

A(t)

=

f o 1-F( t)

: failure rate

1-F(t)

: reliability function

R(t) MTBF

=

density function

(h(t)dt is a conditional probability that the system will fail during the time t + dt under the condition that the system i s safe until the time t)

: mean time to failure

(measure of reliability for repairable equipment)

236

I n some cases, the f a i l u r e r a t e h ( t ) o f a component i n a system can be estimated from the p o i n t o f view o f the physical behaviour o f the mater i a l used. Empirically, and sometimes t h e o r e t i c a l l y , the f o l l o w i n g proba-

b i l i t i e s are proposed (Ref. 6.28): (a)

EXPONENTIAL DISTRIBUTION h(t)

=

constant

f(t)

=

C . exp (-Ct)

R(t)

=

C

exp (-Ct)

I n t h i s case the f a i l u r e r a t e i s constant. I t means p h y s i c a l l y t h a t any f a i l u r e occurs a c c i d e n t a l l y without any accumulation o f f a t i g u e - l i k e e f f e c t s during i t s service time under c e r t a i n stresses. Many kinds o f e l e c t r o n i c components f o l l o w t h i s type o f f a i l u r e . Components i n a machine break down i n t h i s mode when the f a i l u r e i s b r i t t l e f r a c t u r e . As an example, i n Figure 6.15 the density f u n c t i o n o f the f a i l u r e of a Diesel engine c o n t r o l u n i t i s

p l o t t e d showing an exponential d i s t r i b u t i o n (Ref. 6.29). (b)

RAYLEIGH DISTRIBUTION h(t)

=

Ct

f(t)

=

-Ct C t . exp (-)

2

2

I n t h i s case the f a i l u r e r a t e increases w i t h time. The constant, C , i n d i cates the r a t e o f d e t e r i o r a t i o n o f the component which depends upon the stress l e v e l applied t o it. (c)

NORMAL DISTRIBUTION (TRUNCATED)

Many components of machines obey t h i s d i s t r i b u t i o n , e s p e c i a l l y i f the f a i l u r e occurs due t o wear processes. The f a i l u r e r a t e o f t h i s d i s t r i b u t i o n cannot be expressed i n a simple form.

237

lo0l 150

1

50

5

10

15

20

25

Time (103h) F i g u r e 6.15

Density f u n c t i o n f ( t ) o f t h e f a i l u r e o f Diesel engine c o n t r o l u n i t s (Exp. d i s t r i b u t i o n ) ( R e f . 6 . 2 9 ) . 0.95 0.90 0.80 0.50

0.20 0.10 0.05

F i g u r e 6.16

F a i l u r e d i s t r i b u t i o n f u n c t i o n F ( t ) o f b a l l bearings (Wei b u l l d i s t r i b u t i o n ) ( R e f . 6 . 3 0 ) .

150 f ( t)x10-6 100

50

5

10

15

20

Time (103h) F i g u r e 6.17

Density f u n c t i o n f ( t ) o f the f a i l u r e o f Diesel engine p i s t o n s (Gamna d i s t r i b u t i o n ) ( R e f . 6 . 2 9 ) .

238 (d)

WEIBULL DISTRIBUTION h(t)

c

= - t to

c-1

T h i s i s a d i s t r i b u t i o n w i t h two parameters, to, t h e nominal l i f e and t h e c o n s t a n t C. The d i s t r i b u t i o n i s found t o r e p r e s e n t f a i l u r e o f many k i n d s o f mechanical systems, such as f a t i g u e i n b a l l b e a r i n g s . As an example, i n F i g u r e 6.16 t h e p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n o f t h e t i m e t o f a i l u r e , F ( t ) , as determined by t e s t i n g 500 grease l u b r i c a t e d b a l l b e a r i n g s a t 1000 r.p.m., (e)

where

i s shown (Ref. 6.30).

GAMMA DISTRIBUTION

r(x) i s

a Gamma f u n c t i o n . T h i s i s a l s o a d i s t r i b u t i o n w i t h two para-

meters. T h e o r e t i c a l l y , t h e importance o f t h i s d i s t r i b u t i o n i s a t t r i b u t e d t o t h e f a c t t h a t t h e e q u a t i o n i s an x - f o l d c o n v o l u t i o n o f t h e e x p o n e n t i a l funct i o n . I t means p h y s i c a l l y t h a t a component f a i l s a t x - t h shock which occurs as a Poisson s t a t i s t i c a l process. As an example, i n F i g u r e 6.17 t h e d e n s i t y f u n c t i o n o f t h e f a i l u r e o f t h e p i s t o n s o f D i e s e l engines i s p l o t t e d showing a Gamma d i s t r i b u t i o n w i t h x = 2 (Ref. 6.29). These d i s t r i b u t i o n s a r e r e p r e s e n t a t i v e ones which appear i n t h e f a i l u r e process o f v a r i o u s components and systems. As a general overview, i n Table 6.4 a c o m p i l a t i o n o f t h e phenomena o f d e t e r i o r a t i o n and t h e mode o f f a i l u r e i n c o n n e c t i o n w i t h t h e u n d e r l y i n g p h y s i c a l processes i s g i v e n . The t a b l e i s due t o Yoshikawa (Ref. 6.28). I t can be seen t h a t d i f f e r e n t f a i 1u r e modes and d i f f e r e n t e l ementary

f a i l u r e processes a r e a s s o c i a t e d w i t h d i f f e r e n t t y p e s o f f a i l u r e d i s t r i b u t i o n f u n c t i o n s . I t f o l l o w s , t h a t i n t u r n from t h e e x p e r i m e n t a l d e t e r m i n a t i o n o f f a i l u r e d i s t r i b u t i o n curves c o n c l u s i o n s on t h e t y p e o f f a i l u r e mechanism may be drawn. F o r most t r i b o - m e c h a n i c a l systems f a i l i n g as a consequence o f wear processes, t h e f a i l u r e b e h a v i o u r i s c h a r a c t e r i z e d by t h e normal d i s t r i b u t i o n o r the Weibull d i s t r i b u t i o n . I f f o r a given type o f tribo-mechanical system t h e f a i l u r e mode and t h e t y p e o f f a i l u r e d i s t r i b u t i o n a r e known, t h i s knowledge can be used t o improve t h e r e l i a b i l i t y o f t h e system.

239

I

D e t e r i o r a t i o n (Mode o f f a i l u r e ) Phys ic a l

I

Physical process I

I

Fracture

I

I

I

I

I

0

Yielding

Rusting

Ray1 e igh

~-

Wear

Normal Gamma

Staining Table 6.4

0

0

Exponential

Phenomena o f d e t e r i o r a t i o n and mode o f f a i l u r e ( R e f . 6.28).

F o r i n s t a n c e , t h i s approach can be used t o s e l e c t t h e t y p e o f a b a l l o r r o l l e r b e a r i n g system t o o p e r a t e under a g i v e n s e t o f o p e r a t i n g c o n d i t i o n s w i t h h i g h o p e r a t i o n a l s a f e t y ( R e f . 6.31,

6.32). I n t h i s connection, the

importance o f 1u b r i ca t i on techno1 ogy on t h e r e 1 ia b i 1 it y o f tri bo-mechani c a l system;

has been emphasized (Ref. 6.33, 6 . 3 4 ) .

To conclude t h e d i s c u s s i o n on t h e f a i l u r e and r e l i a b i l i t y o f t r i b o mechanical systems, t h e dependence o f t h e f a i l u r e r a t e on t h e o p e r a t i n g d u r a t i o n o f a system s h o u l d be considered. I f t h e f a i l u r e r a t e i s p l o t t e d as f u n c t i o n o f time, a curve, known as t h e " b a t h - t u b - c u r v e " ,

i s found, as

shown i n F i g u r e 6.18. I n t h i s c u r v e t h r e e regimes can be d i s t i n g u i s h e d : ( a ) e a r l y f a i l u r e s , ( b ) random f a i l u r e s ,

( c ) wear-out f a i l u r e s . None o f t h e d i s t r i b u t i o n curves

d i s c u s s e d above have t h i s bath-tub-shaped f a i l u r e c u r v e b u t an a p p r o x i m a t i o n may be o b t a i n e d by s e l e c t i n g an a p p r o p r i a t e p r o b a b i l i t y d e n s i t y f u n c t i o n f o r each o f t h e t h r e e regimes (Ref. 6.35).

Regime ( a ) d e s c r i b e s t h e r e g i o n o f

t h e " i n f a n t death" o f t h e system. T h i s regime i s c h a r a c t e r i z e d by a decrease o f t h e f a i l u r e r a t e w i t h t i m e f o r example i n e f f e c t i v e r u n n i n g - i n . The r e gime ( b ) o f c o n s t a n t f a i l u r e r a t e i s t h e r e g i o n o f normal r u n n i n g . Here,

240

f a i l u r e occurs as a consequence o f s t a t i s t i c a l l y independent f a c t o r s . Regime ( c ) i s c h a r a c t e r i z e d by an i n c r e a s e o f t h e f a i l u r e r a t e w i t h t i m e . Here f a i l u r e may be due t o ageing e f f e c t s . As d e s c r i b e d above, f o r a g r e a t deal o f t r i b o - i n d u c e d f a i l u r e s t h e f a i l u r e r a t e i n c r e a s e s w i t h t i m e . Thus r e g i o n ( c ) o f t h e " b a t h - t u b curve" of F i g u r e 6.18 appears t o be r e l e v a n t f o r t h e normal mode o f wear induced f a i l u r e o f mechanical systems.

(b) Fai 1ure rate

I

' I

I

Time

F i g u r e 6.18

6,6

"Bath-tub'' f a i l u r e r a t e curve.

REQUIREMENTS

FOR

PROPER FUNCTIONAL BEHAVIOUR

Having s t u d i e d i n some d e t a i 1 t h e i n f l u e n c e s o f tri b o l o g i c a l processes on t h e f u n c t i o n o f mechanical systems, f i n a l l y t h e requirements f o r a p r o p e r f u n c t i o n a l behaviour o f t r i b o - m e c h a n i c a l systems should be considered. The f o u r main aspects t h a t may be i m p o r t a n t i n t h i s c o n n e c t i o n w i l l be discussed i n t h e f o l l o w i n g s e c t i o n s (see a l s o Chapter 8 ) .

6,6,1 STUDY

OF ALTERNATIVE

SOLUTIONS

B e f o r e d e s i g n i n g a mechanical system, t h e p o s s i b i l i t y o f e l i m i n a t i n g t r i b o induced d i f f i c u l t i e s by u s i n g an a l t e r n a t i v e t e c h n i c a l s o l u t i o n s h o u l d f i r s t be considered. T h i s r e q u i r e s c a r e f u l c o n s i d e r a t i o n o f t h e t e c h n i c a l purpose o f t h e system under q u e s t i o n and t h e c o m p i l a t i o n o f t h e t e c h n i c a l l y r e q u i r e d i n p u t s and use-outputs (see T a b l e 3 . 1 and 3 . 2 ) .

I f t h i s a n a l y s i s shows t h a t

241

the system's inputs and o u t p u t s needed t o f u l f i l the required technical purpose a r e e s s e n t i a l l y mechanical in nature, i . e . comprise the transmission of motion, mechanical work and/or m a t e r i a l s , the technical purpose can, of course, be f u l f i l l e d only by a mechanical system. There a r e , howe v e r , some technical systems t h a t a r e not i n t r i n s i c a l l y mechanical in nature b u t a r e realized by mechanical means only f o r h i s t o r i c a l reasons, since mechanical methods have o f t e n , in the p a s t , been the f i r s t means a v a i l a b l e f o r the solution of technical problems. The function of such systems i s connected mainly with the generation, transmission o r reproduction of "information". Examples of t h i s c l a s s of (pseudo-mechanical) systems a r e the portable mechanical clock ( t h e prototype was invented and b u i l t by P. Henlein around 1510), the mechanical c a l c u l a t i n g machine ( t h e prototype was invented by B. Pascal a n d G.W. Leibniz between 1640 and 1670), or mechanical devices f o r the control of machinery or production processes. The technical function of these engineering systems i s essent i a l l y the generation or reproduction of information. Whereas the t r a d i tional mechanical r e a l i z a t i o n s of these technical systems, l i k e the clock, a r e based on the motion o f macroscopic bodies. such as gears o r l e v e r s , the contemporary e l e c t r o n i c r e a l i z a t i o n s of these systems a r e based on the motion o r impulses of sub-microscopic p a r t i c l e s , namely e l e c t r o n s . Although in b o t h types of clock the external technical function i s i d e n t i c a l , the internal system s t r u c t u r e s a r e e n t i r e l y d i f f e r e n t . Clearly, the replacement of the motion o f macroscopic bodies by the motion of sub-microscopic part i c l e s not only eliminates t r i b o l o g i c a l processes b u t a l s o leads t o a microdimensional design and t o a f a s t and r e l i a b l e function of the system. In the f u t u r e some other tribo-mechanical systems t r a d i t i o n a l l y used f o r the generation, transmission or reproduction of information may be replaced by technically more s u i t a b l e e l e c t r o n i c s o l u t i o n s . The replacement of conventional mechanical systems by e l e c t r o n i c systems, consisting of mini-chips, large s c a l e integrated c i r c u i t s , microprocessors, e t c . , and the corresponding i n d u s t r i a l changes have some f a r reaching s c i e n t i f i c , technical, economical and sociological consequences. ( I n the j o u r n a l i s t i c language t h i s has been already termed the " t h i r d i n d u s t r i a l revolution", Ref. 6.36.) Cramer has recently pointed t o some of these consequences in discussing the e l e c t r o n i c t e l e t y p e as an example f o r the " s t r u c t u r a l changes" in precision engineering (Ref. 6.37). I n the study of a l t e r n a t i v e engineering s o l u t i o n s f o r tribo-mechanical systems, however, in addition t o the functional input-output r e l a t i o n s the

242

i n f l u e n c e s o f d i s t u r b i n g i n p u t s f r o m t h e environment s h o u l d be t a k e n i n t o account. S p e c i a l c a r e i s then r e q u i r e d f o r example, i n t h e d e s i g n o f e l e c t r o n i c components s u i t e d f o r a p p l i c a t i o n s i n a v i b r a t i n g environment, as i n a m o t o r - c a r o r an a i r c r a f t . From t h i s p o i n t o f view, a r o b u s t mechanical s o l u t i o n may be more a p p r o p r i a t e t h a n a f r a g i l e e l e c t r o n i c s o l u t i o n .

6,6,2

PROPER D E S I G N OF

SYSTEM STRUCTURE

The main aspects o f t h e a p p r o p r i a t e design o f t h e s t r u c t u r e o f t r i b o mechanical systems have a l r e a d y been d i s c u s s e d i n S e c t i o n 5.4. Some f u r t h e r suggestions f o r t h e design o f b e a r i n g systems can be found i n Ref. 6.38, 6.39,

6.40. D i s c u s s i n g t h e requirements o f a c o r r e c t design o f t r i b o - m e c h a n i c a l

systems, Peeken p o i n t e d o u t t h a t t h e c o n v e n t i o n a l p r o d u c t i o n - o r i e n t e d and k i n e m a t i c s - o r i e n t e d design o f mechanical systems i s o f t e n n o t i n accordance w i t h t r i b o l o g i c a l requirements (Ref. 6.41).

A d e s i g n e r who t r i e s t o d e s i g n

a mechanical system i n a t r i b o l o g i c a l l y c o r r e c t manner s h o u l d a t t e m p t t o solve the basic engineering task o f t r i b o l o g y : t o design i n t e r a c t i n g surfaces i n r e l a t i v e m o t i o n i n such a way t h a t f o r c e s can be t r a n s m i t t e d through t h e i n t e r f a c e w i t h a minimum o f wear. Peeken mentioned t h r e e p o i n t s which may be t a k e n i n t o c o n s i d e r a t i o n i n o r d e r t o improve t h e d e s i g n o f tri bo-mechani c a l systems : (i)

I n f l u e n c e i n t e r f a c i a l b e a r i n g geometry t h r o u g h e l a s t i c and thermoe l a s t i c processes by changing t h e shape o f t h e moving s u r f a c e s .

(ii)

Lower t h e f o r c e s t o be t r a n s m i t t e d . E q u a l i z e t h e f o r c e and p r e s s u r e d i s t r i b u t i o n s and i n f l u e n c e t h e v e l o c i t i e s by changing t h e g e o m e t r i c a l design.

( i i i ) Change t h e k i n e m a t i c s , f o r example by changing t h e t y p e o f i n t e r f a c i a l f r i c t i o n (e.g.,

sliding friction or rolling friction)

t a k i n g i n t o c o n s i d e r a t i o n t h e consequences on p r o d u c t i o n . I n d e s i g n i n g t r i b o - m e c h a n i c a l systems where r e l i a b i l i t y i s a t a premium, c e r t a i n b a s i c p r i n c i p l e s o f d e s i g n s h o u l d be c a r e f u l l y t a k e n i n t o cons i d e r a t i o n . These a r e t h e use o f d i v e r s i t y , redundancy and d e s i g n i n g w i t h a p r e f e r r e d mode o f f a i l u r e i n mind such as always endeavouring t o produce a " f a i l - s a f e " c o n d i t i o n . The p r i n c i p l e o f equipment redundancy i m p l i e s t h a t t h e system w i l l g e n e r a l l y s u r v i v e a s i n g l e equipment f a u l t and c o n t i n u e w i t h i t s i n t e n d e d o p e r a t i o n a l f u n c t i o n . One method o f redundancy i s t o have

243 one system i n o p e r a t i o n and t h e o t h e r on standby. I f f a i l u r e o f t h e o p e r a t i n g system t a k e s p l a c e t h e n a u t o m a t i c change-over t o t h e standby system s h o u l d i m m e d i a t e l y t a k e p l a c e . Another method o f redundancy i s t o have two systems o p e r a t i n g " p a r a l l e l " . These p r i n c i p l e s o f redundancy which can be e a s i l y r e a l i z e d i n e l e c t r o n i c systems a r e , however, n o t so e a s i l y r e a l i z e d i n t r i b o - m e c h a n i c a l systems. An i n s t r u c t i v e example c o n c e r n i n g t h e redundant d e s i g n o f b e a r i n g assemblies i s shown i n F i g u r e 6.19 ( R e f . 6 . 4 2 ) .

Centre race

( a ) Standby redundancy F i g u r e 6.19

( b ) Para1 1e l redundancy

Redundant d e s i g n o f a b e a r i n g assembly.

I n t h e standby case, a c o m b i n a t i o n of a p l a i n b e a r i n g and a b a l l b e a r i n g a l l o w s one t o f a i l b u t for o p e r a t i o n t o c o n t i n u e on t h e o t h e r t y p e o f b e a r i n g . T h i s i s an i n t e r e s t i n g example because i t a l s o b r i n g s i n t h e i d e a o f d i v e r s i t y which i s o f t e n used t o overcome a common f a u l t c o n d i t i o n . I n t h e case o f t h e p a r a l l e l redundant b e a r i n g assembly, t h e l o a d can be c a r r i e d by a s i n g l e r a c e hence s u r v i v i n g under c e r t a i n c o n d i t i o n s a f a i l u r e on t h e o t h e r r a c e . I n t h i s case, checks s h o u l d be made a t maintenance, whereas i n t h e standby arrangement i t would be u s e f u l t o have a m o n i t o r i n g system t o sense when t h e p l a i n b e a r i n g i s working.

244

6,6,3 PROPER C H O I C E

OF

OPERATING VARIABLES

I n order t o o b t a i n a proper functional behaviour o f a tribo-mechanical system o f a g i v e n design, t h e o p e r a t i n g c o n d i t i o n s ( l o a d FN o r p r e s s u r e p, v e l o c i t y v, o p e r a t i n g temperature T, o p e r a t i n g d u r a t i o n t ) s h o u l d n o t exceed c e r t a i n 1 i m i t s . See a l s o Haddon's abnormal energy exchange t h e o r y (Ref. 6 - 1 3 ) , discussed i n S e c t i o n 6.4.1.

These l i m i t s o f o p e r a t i n g v a r i a b l e s

may be found from t h e c o n d i t i o n t h a t t h e a c t i o n o f t h e o p e r a t i n g v a r i a b l e s may n o t l e a d t o i n t o l e r a b l e changes o f t h e s t r u c t u r e o f t h e system. Although t h e r e i s no g e n e r a l t h e o r y o f t h e l i m i t s o f o p e r a t i n g c o n d i t i o n s , f o r mec h a n i c a l systems o f s i m p l e geometry, t h e procedure o f t h e s o - c a l l e d " z e r o wear model" (Ref. 6.43) may be a c o n v e n i e n t s t a r t i n g p o i n t f o r e s t i m a t i n g the l i m i t s o f operational 'conditions f o r a quasi-constant s t r u c t u r e o f a t r i b o - m e c h a n i c a l system. "Zero wear" i s taken t o be wear o f such a magnitude t h a t t h e s u r f a c e roughness i n t h e wear t r a c k i s n o t s i g n i f i c a n t l y d i f f e r e n t from t h e i n i t i a l s u r f a c e f i n i s h i n t h e unworn p a r t o f t h e s u r f a c e . To q u a n t i f y t h i s s t a t e ment, t h e z e r o wear l i m i t i s assumed when t h e depth o f t h e wear t r a c k equals o n e - h a l f o f t h e p e a k - t o - v a l l e y s u r f a c e roughness. The model s t a t e s t h a t wear can be c o n t r o l l e d by l i m i t i n g t h e maximum ( H e r t z i a n ) shear s t r e s s

T,,,~~

a c t i n g i n t h e c o n t a c t r e g i o n . D e f i n i n g one "pass" as a d i s t a n c e 1 o f s l i d i n g equal t o t h e l e n g t h o f t h e g e o m e t r i c c o n t a c t a r e a i n t h e d i r e c t i o n o f s l i d i n g , t h e n as an example, f o r 2000 passes s u r f a c e topography changes s h o u l d be o f a " z e r o l e v e l " i f t h e o p e r a t i n g c o n d i t i o n s l e a d t o ty : y i e l d s t r e s s i n shear

The v a l u e o f

y R depends on t h e m a t e r i a l s i n c o n t a c t and t h e degree o f

1u b r i c a t i o n . For quasi-hydrodynamic l u b r i c a t i o n i t i s p o s t u l a t e d t h a t

< yRQ

0.54

1

For boundary l u b r i c a t i o n o r d r y s l i d i n g t h e f o l l o w i n g values a r e s e l e c t e d :

or

y R = 0.54

i f t h e system has a l o w s u s c e p t i b i l t y f o r t r a n s f e r

yR

i f t h e system has a h i g h s u s c e p t i b i i t y f o r t r a n s f e r

=

0.20

245 F o r i z= 2000 passes t h e " z e r o wear c o n d i t i o n " i s g i v e n by

From t h i s r e l a t i o n , f o r a g i v e n t r i b o - m e c h a n i c a l system o f known values o f y R and t t h e a l l o w a b l e number o f s l i d i n g passes ( f o r g i v e n o p e r a t i n g Y' shear s t r e s s e s t m a x ) o r t h e a l l o w a b l e o p e r a t i n g shear s t r e s s e s ( f o r a g i v e n number o f passes i ) may be e s t i m a t e d . Since t h i s model i s based almost e n t i r e l y on s t r e s s c o n s i d e r a t i o n s i t may be n o t a p p l i c a b l e f o r wear process i n c l u d i n g a c o n s i d e r a b l e adhesive wear component ( R e f . 6 . 4 4 ) . Indeed, t h e f o r m o f t h e above e q u a t i o n , i . e . ,

t h e one-ninth-power depen-

dence, i m p l i e s t h a t t h e model may be a p p l i c a b l e o n l y f o r f a t i g u e wear s i t u a t i o n s (see S e c t i o n 4.4.2). F o r h y d r o d y n a m i c a l l y l u b r i c a t e d j o u r n a l b e a r i n g s , V o g e l p o h l ' s method may be a p p l i e d i n c h a r a c t e r i z i n g t h e a l l o w a b l e l i m i t s o f o p e r a t i n g v a r i a b l e s (Ref. 6.45).

Vogelpohl found t h a t t o a r e a s o n a b l e degree o f accuracy t h e f o l -

lowing r e l a t i o n characterize t h e conditions a t t h e t r a n s i t i o n from f u l l f l u i d f i l m l u b r i c a t i o n t o mixed l u b r i c a t i o n a t t h e minimum o f t h e S t r i b e c k c u r v e :

where

v

:

5 2 mean b e a r i n g p r e s s u r e (10 N/m )

:

v i s c o s i t y ( 1 0 - ~ ~ a=s CP)

:

s u r f a c e v e l o c i t y (m/s)

From t h i s c o n d i t i o n , f o r two g i v e n values o f t h e s e t

( p , ~ ,v )

the c r i t i c a l

t r a n s i t i o n v a l u e o f t h e t h i r d one may be e s t i m a t e d . F i n a l l y , f o r a l u b r i c a t e d system o p e r a t i n g i n t h e low speed, h i g h l o a d p a r t o f t h e S t r i b e c k c u r v e , under c o n d i t i o n s o f mixed o r boundary l u b r i c a t i o n , t h e o p e r a t i o n a l l i m i t s o f t h e system may be c h a r a c t e r i z e d by d e t e r m i n i n g e x p e r i m e n t a l l y t h e " f a i l u r e s u r f a c e " f o r t h e g i v e n system (see S e c t i o n 4.5.6,

Figure 4.62).

246

6,6,4 MONITORING

THE FUNCTION

OF THE SYSTEM

The p r i m a r y method o f r e l a t i n g d e t e r i o r a t i o n o f a system t o consequence i s t h e m o n i t o r i n g o f t h e performance o f t h e system. The s i m p l e s t f o r m o f such m o n i t o r i n g i s t h e r e g u l a r r e c o r d i n g o f r e l e v a n t parameters i n a l o g book. Regular l o g g i n g o r a u t o m a t i c r e g i s t e r i n g o f i m p o r t a n t parameters and t h e i r d e r i v a t i v e s , i n comparison w i t h r e f e r e n c e i n f o r m a t i o n , p r o v i d e s t h e b a s i s f o r performance-trend m o n i t o r i n g .

In t r y i n g t o m o n i t o r t h e p e r f o r -

mance o f a system, i t i s necessary t o decide w h i c h r e l e v a n t parameters t o m o n i t o r . From a systems p o i n t o f view two c l a s s e s o f parameters may be distinguished:

(I)

I n p u t and o u t p u t v a r i a b l e s o f t h e system.

( 1 1 ) Relevant parameters o f t h e system s t r u c t u r e . I n r e c e n t years, s e v e r a l t e c h n i q u e s have been developed which can be used f o r t h e o n - l i n e m o n i t o r i n g o f o p e r a t i n g t r i b o - m e c h a n i c a l systems. I n a feed-back loop, t h e s i g n a l s f r o m t h e m o n i t o r i n g d e v i c e may t h e n be used t o influence o r c o n t r o l the system's i n p u t operating variables i n order t o o b t a i n a p r o p e r f u n c t i o n a l b e h a v i o u r o f t h e system. The main techniques a p p l i c a b l e t o t h e m o n i t o r i n g o f t r i b o - m e c h a n i c a l system a r e t o be d i s c u s s e d i n d e t a i l i n S e c t i o n 7.5. T h i s c h a p t e r on t h e f u n c t i o n a l behaviour o f t r i bo-mechanical systems may be b e s t concluded by c i t i n g some i n t e r e s t i n g remarks o f t h e g r e a t mathematician John von Neumann c o n c e r n i n g t h e f u n c t i o n and m a l f u n c t i o n o f e n g i n e e r i n g and l i v i n g systems. I n a l e c t u r e a t t h e Hixon Symposium, September, 1948, i n Pasadena, C a l i f o r n i a , e n t i t l e d "The g e n e r a l and l o g i c a l t h e o r y o f automata'' von Neumann made t h e f o l l o w i n g remarks (Ref. 6.46): " I n l i v i n g organisms m a l f u n c t i o n s o f components occur. The organism o b v i o u s l y has a way t o d e t e c t them and r e n d e r them harmless. The system must, t h e r e f o r e , c o n t a i n t h e necessary arrangements t o diagnose e r r o r s as they occur, t o r e a d j u s t t h e organisms so as t o m i n i m i z e t h e e f f e c t s o f t h e e r r o r s , and f i n a l l y t o c o r r e c t o r t o b l o c k permanently t h e f a u l t y components. Our modus procedendi with r e s p e c t t o m a l f u n c t i o n s i n o u r a r t i f i c a l automata i s e n t i r e l y d i f f e r e n t . Every e f f o r t i s made t o d e t e c t e v e r y e r r o r as soon as i t occurs. Then an a t t e m p t i s made t o i s o l a t e t h e component t h a t caused t h e e r r o r as r a p i d l y as f e a s i b l e . T h i s may be done p a r t l y a u t o m a t i c a l l y , b u t i n any case a s i g n i f i c a n t p a r t o f t h i s d i a g n o s i s must be e f f e c t e d by i n t e r v e n t i o n f r o m t h e o u t s i d e . Once t h e f a u l t y component has

241

been i d e n t i f i e d , i t i s i m m e d i a t e l y c o r r e c t e d o r r e p l a c e d . Note t h e d i f ferences i n these two a t t i t u d e s . The b a s i c p r i n c i p l e o f d e a l i n g w i t h malf u n c t i o n s i n n a t u r e i s t o make t h e i r e f f e c t as u n i m p o r t a n t as p o s s i b l e and t o a p p l y c o r r e c t i v e s , i f t h e y a r e necessary a t a l l , a t l e i s u r e . I n o u r d e a l i n g s w i t h a r t i f i c i a l automata, on t h e o t h e r hand, we r e q u i r e an immed i a t e d i a g n o s i s . T h e r e f o r e , we a r e t r y i n g t o arrange t h e automata i n such a manner t h a t e r r o r s w i l l become as c o n s p i c i o u s as p o s s i b l e , and i n t e r v e n t i o n and c o r r e c t i o n f o l l o w i m m e d i a t e l y . The r a t i o n a l e o f t h i s d i f f e r e n c e i s n o t f a r t o seek. N a t u r a l organisms a r e s u f f i c i e n t l y w e l l conceived t o be a b l e t o o p e r a t e even when m a l f u n c t i o n s have s e t i n . They can o p e r a t e i n s p i t e o f m a l f u n c t i o n s , and t h e i r subsequent tendency i s t o remove these m a l f u n c t i o n s . An a r t i f i c i a l automaton c o u l d c e r t a i n l y be designed so as t o be a b l e t o o p e r a t e n o r m a l l y i n s p i t e o f a l i m i t e d number o f m a l f u n c t i o n s i n c e r t a i n l i m i t e d areas. Any m a l f u n c t i o n , however, r e p r e s e n t s a c o n s i d e r a b l e r i s k t h a t some g e n e r a l l y d e g e n e r a t i n g process has a l r e a d y s e t i n w i t h i n t h e machine. I t i s , t h e r e f o r e , necessary t o i n t e r v e n e i m m e d i a t e l y , because a machine which has begun t o m a l f u n c t i o n has o n l y r a r e l y a t e n dency t o r e s t o r e i t s e l f , and w i l l more p r o b a b l y go f r o m bad t o worse."

248

7 Tribometry: test, simulation, and control methods 7 , 1 I NTRODUCTIO N I t i s obvious t h a t i n a m u l t i d i s c i p l i n a r y s u b j e c t l i k e t r i b o l o g y , t h e e x p e r i m e n t a l t e c h n i q u e s o f i n v e s t i g a t i n g and t e s t i n g p l a y an i m p o r t a n t r o l e . I n f o l l o w i n g t h e t e r m i n o l o g y o f Coulomb, who d e s c r i b e d h i s f r i c t i o n measuring d e v i c e as a " t r i b o m e t e r " ,

t h e whole f i e l d o f e x p e r i m e n t a l s t u d y

i n t r i b o l o g y i s c a l l e d " t r i b o m e t r y " . T h i s t o p i c i s v e r y broad, r a n g i n g f r o m f r i c t i o n and wear measurements, t h e t e s t i n g o f l u b r i c a n t s and evaluat i o n o f t r i b o - t e c h n i c a l components t o machinery c o n d i t i o n m o n i t o r i n g and r e 1 i a b i l i t y t e s t i n g . A1 though a t f i r s t glance t h e e x p e r i m e n t a l determinat i o n o f t h e t r i b o l o g i c a l b e h a v i o u r of m a t e r i a l s o r l u b r i c a n t s seems easy, inasmuch as f r i c t i o n and wear a r e a p p a r e n t l y n o t d i f f i c u l t t o measure, t h e d i f f i c u l t i e s l i e i n the i n t e r p r e t a t i o n o f t h e t e s t r e s u l t s i n connection w i t h t h e v a r i o u s t r i b o - t e c h n i c a l a p p l i c a t i o n s o f m a t e r i a l s and l u b r i c a n t s (Ref. 7.1). D u r i n g t h e f i r s t h a l f o f t h i s c e n t u r y a number o f t r i b o m e t e r s came i n t o e x i s t e n c e w i t h some f e a t u r e s i n common: (i)

s i m p l e geometry,

(ii) cheap t e s t p i e c e s , ( i i i ) used f o r " a c c e l e r a t e d " t e s t i n g , (iv)

a t b e s t o f moderate accuracy,

(v)

y i e l d i n g r e s u l t s t h a t can n o t be i n t e r p r e t e d i n a s i m p l e way.

The t e r m " h y b r i d t e s t e r s " was proposed, s i n c e s e r v i c e c o n d i t i o n s were n o t a c c u r a t e l y reproduced n o r were p h y s i c a l parameters w e l l d e f i n e d (Ref. 7 . 2 ) .

249

Today t h e same equipment i s s t i l l p o p u l a r i n I n d u s t r i a l L a b o r a t o r i e s , because i t i s c o n v e n i e n t f o r acceptance t e s t i n g and p r o d u c t i o n c o n t r o l . However, i f t h e r e s u l t s a r e i n t e r p r e t e d as models o f r e a l tri b o - e n g i n e e r i n g events, grave. q u a n t i t a t i v e e r r o r s may be made ( R e f . 7 . 2 ) .

Recently research

l a b o r a t o r i e s , t a k i n g advantage o f modern i n s t r u m e n t a t i o n , have developed v a r i o u s general-purpose t r i b o m e t e r s . Equipped w i t h s e n s i t i v e r e c o r d e r s and a n a l y z e r s , such s o p h i s t i c a t e d i n s t r u m e n t s p e r m i t t h e s t u d y o f a g r e a t many v a r i a b l e s (Ref. 7 . 3 ) . These few p o i n t s i n d i c a t e t h e g r e a t v a r i e t y o f t r i b o m e t r i c t e c h n i q u e s and i m p l y t h a t t h e i r a p p l i c a t i o n and t h e i n t e r p r e t a t i o n o f r e s u l t s r e q u i r e s g r e a t c a r e . I n t h e f i e l d of t r i b o m e t r y i t i s a g a i n found t h a t t h e systems approach can be used as a c o n v e n i e n t g u i d e - l i n e f o r t h e d e s c r i p t i o n o f t h e v a r i o u s t r i b o m e t r i c methods and t h e i r p o s s i b i l i t i e s . I t has been emphasized i n t h e f o r g o i n g c h a p t e r s t h a t b o t h s t r u c t u r a l and f u n c t i o n a l aspects o f a t r i b o l o g i c a l system must be s t u d i e d , and t h i s l e a d s t o t h e f o l l o w i n g c l a s s i f i c a t i o n o f tri b o m e t r i c techniques :

(I)

S t r u c t u r a l aspects

\

( a ) elements

t e s t i n g o f system component properties

( b ) p r o p e r t i e s o f elements ( c ) interaction

o f elements

,investigation processes

o f tribological

(11) F u n c t i o n a l aspects F u n c t i o n a l b e h a v i o u r o f t h e system -simul

a t i ve t r i bo- t e s t i n g

-machinery

condition monitoring

C o n s i d e r a t i o n o f t h e v a r i o u s aspects o f t r i b o m e t r y f r o m a systems p o i n t

o f view shows t h a t t h e t r i b o m e t r i c t e c h n i q u e s can be c l a s s i f i e d i n t o f o u r b a s i c a l l y d i f f e r e n t groups. I t s h o u l d be n o t e d a g a i n t h a t each group has i t s own (and l i m i t e d ) t e c h n i c a l purpose and p r e d i c t i v e value. G r e a t c a r e i s needed f o r a mutual comparison o f t h e r e s u l t s o b t a i n e d by methods bel o n g i n g t o d i f f e r e n t groups. I n t h e f o l l o w i n g , t h e f o u r main groups o f t r i b o m e t r y w i l l be s t u d i e d by d i s c u s s i n g t h e main f e a t u r e s o f t h e s e t e c h niques and r e v i e w i n g t h e i r r e q u i r e m e n t s and p o s s i b i l i t i e s . The t r e a t m e n t s t a r t s w i t h l a b o r a t o r y methods, i . e . ,

the t r i b o m e t r i c techniques f o r t h e

i n v e s t i g a t i o n o f f r i c t i o n and wear processes and s i m u l a t i v e t r i b o - t e s t i n g , and t h e n t u r n s t o t h e more i n d u s t r i a l aspects o f t r i b o - t e s t i n g ,

namely

t r i b o - t e c h n i c a l component t e s t i n g and m a c h i n e r y - c o n d i t i o n m o n i t o r i n g .

260

7,2 FRICTION AND WEAR TEST METHODS One o f t h e main aspects o f t r i b o m e t r y i s t h e i n v e s t i g a t i o n o f f r i c t i o n and wear processes by means o f l a b o r a t o r y t r i b o - t e s t i n g d e v i c e s . Reviewing t h e r e s u l t s o f wear t e s t s p u b l i s h e d i n t h e i n t e r n a t i o n a l p e r i o d i c a l WEAR o v e r a p e r i o d o f 13 years, i t has been found t h a t a p p r o x i m a t e l y 50% o f t h e r e p o r t e d wear t e s t s were o b t a i n e d w i t h l a b o r a t o r y t e s t r i g s and t h a t o n l y

17% o f t h e wear t e s t s were performed w i t h a c t u a l machine elements (Ref. 7.4) These d a t a c l e a r l y i l l u s t r a t e t h e g r e a t importance o f l a b o r a t o r y t r i b o t e s t i n g devices. I t was i n d i c a t e d p r e v i o u s l y t h a t i n r e c e n t y e a r s a c c u r a t e general-purpose t r i b o m e t e r s equipped w i t h s e n s i t i v e r e c o r d e r s and a n a l y z e r s have been developed i n r e s e a r c h l a b o r a t o r i e s . I n combining such t r i b o m e t e r s

w i t h t h e new p o w e r f u l s u r f a c e a n a l y t i c a l t o o l s , i t i s p o s s i b l e t o s t u d y t h e elementary f r i c t i o n and wear processes i n d e t a i l . I t s h o u l d be emphasized, however, t h a t t h e a p p l i c a t i o n o f these t r i b o m e t e r s i s u s e f u l m a i n l y f o r i n v e s t i g a t i o n s o f t h e system s t r u c t u r e

-

as f o r i n s t a n c e t h e changes i n t h e

p r o p e r t i e s o f t h e system components due t o wear processes. As a consequence o f t h e c o n c e n t r a t i o n on t h e s t r u c t u r a l aspects, from a systems p o i n t o f view t h e e n g i n e e r i n g " u s e - f u n c t i o n " i s f r e q u e n t l y degenerate i n t r i b o m e t r i c models

.

I n F i g u r e 7 . 1 t h e main parameters r e l e v a n t t o t r i b o - t e s t i n g a r e comp i l e d (Ref. 7 . 5 ) .

I n t h e c e n t r a l p a r t o f t h e f i g u r e t h e elements, i . e . ,

t h e m a t e r i a l components o f t h e t e s t system a r e sketched. I n most cases t h e test

system c o n s i s t s o f two s o l i d specimens ( l ) , ( 2 ) t o g e t h e r w i t h t h e

l u b r i c a n t ( 3 ) and t h e atmosphere ( 4 ) . The i n p u t s o f t h e t e s t - s y s t e m a r e g i v e n by t h e o p e r a t i n g v a r i a b l e s compiled on t h e l e f t - h a n d s i d e o f F i g u r e

7.1. Through t h e a c t i o n o f t h e o p e r a t i n g v a r i a b l e s on t h e t e s t - s y s t e m elements, f r i c t i o n and wear processes o c c u r . F o r t h e d e s c r i p t i o n o f these t r i b o l o g i c a l processes t h e t r i b o m e t r i c c h a r a c t e r i s t i c s compiled on t h e r i g h t o f F i g u r e 7.1 have t o be measured. Supplementing t h e s e t r i b o m e t r i c c h a r a c t e r i s t i c s , s u r f a c e c h a r a c t e r i s t i c s o f t h e specimens (1) and ( 2 ) have t o be determined. I n t h e f o l l o w i n g s e c t i o n s t h e main f e a t u r e s o f t h e parameters and c h a r a c t e r i s t i c s shown i n F i g u r e 7 . 1 w i l l be d i s c u s s e d b r i e f l y . (The measuring techniques d i s c u s s e d i n t h i s s e c t i o n i n c o n n e c t i o n w i t h l a b o r a t o r y t e s t r i g s may be a d e q u a t e l y used a l s o i n t h e t e s t i n g o f t r i b o - t e c h n i c a l components, see S e c t i o n 7.4, see S e c t i o n 7 . 5 . )

and i n machinery c o n d i t i o n m o n i t o r i n g ,

251

Tri bometric characteristics

Tri bometer t e s t system

Operating variables

I

u

-

Type of motion

c-

( 2 ) Tribo-element ( 3 ) Lubricant

I

F r i c t i o n force

FF

F r i c t i o n coeff.

f

1

I

Temperature

Duration

TtA;

Wear r a t e

-\

Contact conditions

t Surface c h a r a c t e r i s t i c s

Figure 7 . 1

C h a r a c t e r i s t i c s and parameters relevant t o t r i b o - t e s t i n g .

252

7 , 2 , 1 TRIBOMETERTEST SYSTEM TYPES As e x p l a i n e d above, i n most t r i b o m e t e r s used i n t h e l a b o r a t o r y , t e s t specimens o f s i m p l e geometry a r e u t i l i z e d i n o r d e r t o s t a r t t h e t e s t s w i t h t e s t c o n d i t i o n s as w e l l d e f i n e d as p o s s i b l e . U s u a l l y one o f t h e moving specimens c o n s i s t s o f a r o t a t i n g c y l i n d e r o r d i s c a g a i n s t which another s o l i d specimen o f d i f f e r e n t c u r v a t u r e i s pressed t h u s l e a d i n g t o nominal p o i n t , l i n e o r f l a t c o n t a c t . I n a c o m p i l a t i o n o f f r i c t i o n and wear d e v i c e s e d i t e d by t h e American S o c i e t y o f L u b r i c a t i o n Engineers (ASLE) which i n cludes 234 t e s t r i g s (Ref. 7 . 6 ) ,

t h e v a r i o u s t e s t devices a r e c l a s s i f i e d

a c c o r d i n g t o t h e i r geometry i n t o t h e f o l l o w i n g groups:

1.

M u l t i p l e sphere

2.

Crossed c y l i n d e r s

3.

P i n on f l a t ( r e c i p r o c a t i n g o r 1 i n e a r m o t i o n )

4.

(a)

Moving p i n

(b)

Moving f l a t

(c)

M u l t i p l e contact

F l a t on f l a t ( r e c i p r o c a t i n g o r l i n e a r m o t i o n )

5.

R o t a t i n g p i n s on d i s c ( f a c e loaded)

6.

P i n on r o t a t i n g d i s c ( f a c e loaded)

7.

C y l i n d e r on c y l i n d e r ( f a c e loaded)

8.

C y l i n d e r o r p i n on r o t a t i n g c y l i n d e r (edge loaded)

9.

Rectangular f l a t on r o t a t i n g c y l i n d e r (edge loaded)

10. D i s c on d i s c (edge loaded) 11. Mu1t i p l e specimens 12.

M i s c e l 1aneous

Besides t h e c h a r a c t e r i z a t i o n o f t h e t e s t systems geometry, t h e o t h e r r e l e v a n t p r o p e r t i e s o f t h e elements o f t h e t e s t system must be s p e c i f i e d as c l o s e l y as p o s s i b l e . F o r t h i s purpose, P a r t I 1 1 o f t h e " T r i b o l o g i c a l Systems Data Sheet" developed i n S e c t i o n 8.2 can be c o n v e n i e n t l y used ( s e e F i g u r e 8.5). Table 7 . 1 c o n t a i n s t h e r e l e v a n t parameters t o be s p e c i f i e d i n o r d e r t o c h a r a c t e r i z e t h e s t r u c t u r e o f t h e t e s t system. I n a d d i t i o n , t h e c l e a n i n g and s u r f a c e p r e p a r a t i o n t e c h n i q u e a p p l i e d t o t h e t e s t specimens

(1) and ( 2 ) s h o u l d be s p e c i f i e d .

253

-

T r i b o element

11

Tribo - elemen t 12)

Lubricant

131

Atmosphere I4 )

Geametry/Oimensi ons/ Volume Chemical composition

8 8

Hardness vlscscosity qlbpl other Other d a t a

c 121

Table 7.1

Tribologicol i n t e r a c t i o n s 111

-

Parameters t o be s p e c i f i e d t o c h a r a c t e r i z e t h e s t r u c t u r e o f a t r i b o - t e s t i n g system.

A very important aspect o f the d e s c r i p t i o n o f t h e s t r u c t u r e o f t h e t e s t system concerns t h e " i n t e r a c t i o n c h a r a c t e r i s t i c s " , i n c l u d i n g f o r i n s t a n c e (i)

t h e i n i t i a l c o n t a c t area and i t s changes d u r i n g t h e t e s t (Ref. 7 . 7 ) ,

(ii)

t h e i n i t i a l c o n t a c t p r e s s u r e and i t s changes d u r i n g t h e t e s t (Ref. 7 . 7 ) ,

( i i i ) t h e r a t i o o f t h e area o f c o n t a c t t o t h e whole wear t r a c k ( R e f . 7.8), (iv)

t h e r e l a t i v e volumes and s u r f a c e areas o f t h e t e s t specimens (Ref. 7 . 9 ) .

These p o i n t s a r e i m p o r t a n t f o r t h e t r a n s m i s s i o n , t r a n s l a t i o n and d i s s i p a t i o n o f mechanical work i n t r o d u c e d t o t h e t e s t system. For example, as e x p l a i n e d i n Chapter 3 and 4 t h e t r a n s m i s s i o n o f mechanical work occurs v i a t h e c o n t a c t a r e a whereas f o r t h e e m i s s i o n o f f r i c t i o n - i n d u c e d a c o u s t i c o r thermal energy i n t o t h e environment, t h e s u r f a c e s n o t a c t u a l l y i n cont a c t p l a y an i m p o r t a n t r o l e . These p o i n t s a r e d i s c u s s e d i n S e c t i o n 7.3 i n c o n n e c t i o n w i t h s i m u l a t i ve t r i bo- t e s t i ng .

254

7,2,2

CONTROL OF

OPERATING VARIABLES

The o p e r a t i n g v a r i a b l e s o f a f r i c t i o n and wear t e s t s h o u l d be s e l e c t e d t o be c o n s i s t e n t w i t h t h e n a t u r e o f t h e i n v e s t i g a t i o n . As shown on t h e l e f t of F i g u r e 7.1,

t h e o p e r a t i n g v a r i a b l e s o f a t r i b o m e t e r a r e g i v e n by t h e

f o l lowing q u a n t i t i e s :

-

velocity v

-

( a m b i e n t ) temperature T

-

t e s t duration t

type o f motion l o a d FN

The t y p e of m o t i o n i s connected w i t h t h e geometry o f t h e t e s t system and

i s g i v e n by one o f t h e f o u r b a s i c m o t i o n t y p e s , namely:

-

sliding

-

rolling spin impact

o r by a s u p e r p o s i t i o n o f these b a s i c t y p e s ( s e e S e c t i o n 8.2.2). (a)

LOAD

The l o a d can be a p p l i e d by v a r i o u s means t o t h e t e s t system, e.g.

as a

mass (dead l o a d ) , by a s p r i n g , b y h y d r a u l i c means o r by e l e c t r o m a g n e t i c means.

256

I n F i g u r e 7.2 t h e d i f f e r e n t p o s s i b i l i t i e s f o r t h e a p p l i c a t i o n o f t h e l o a d a r e shown s c h e m a t i c a l l y f o r t h e example o f a p i n - o n - c y l i n d e r t e s t sy s tern.

I n s t a t i c loading the d i f f e r e n t principles o f load application lead t o t h e same v a l u e o f t h e l o a d f o r c e FN. I n dynamic l o a d i n g , however, owing t o t h e d i f f e r e n t mass-spring-damper combinations i n e v i t a b l y i n v o l v e d i n t h e d i f f e r e n t l o a d i n g p r i n c i p l e s , d i f f e r e n t l o a d - t i m e b e h a v i o u r may r e s u l t . T h e r e f o r e t h e dynamic F N ( t ) b e h a v i o u r may be d i f f e r e n t f r o m t h e i n i t i a l s t a t i c l o a d FN, (Ref. 7.10). F o r t h e measurement o f t h e l o a d , f o r c e t r a n s d u c e r s based on s t r a i n gauges, i n d u c t i v e elements or p r e s s u r e - s e n s i t i v e d e t e c t o r s e v a p o r a t e d on t h e s u r f a c e o f t h e specimen i n t h e c o n t a c t zone a r e a v a i l a b l e . The measurement o f t h e l o a d b y means o f an e l e c t r o - m e c h a n i c a l f o r c e t r a n s d u c e r has t h e g r e a t advantage t h a t t h e F N - s i g n a l t o g e t h e r w i t h t h e s i g n a l o f t h e f r i c t i o n f o r c e FF can be f e d t o an e l e c t r o n i c d i v i d e r which c a l c u l a t e s d i r e c t l y t h e a c t u a l v a l u e o f t h e f r i c t i o n c o e f f i c i e n t f = FF/FN d u r i n g t h e t e s t , T h i s a s p e c t i s d i s c u s s e d i n more d e t a i l i n t h e n e x t s e c t i o n . The l o a d FN a p p l i e d t o t h e t e s t system determines, i n c o n n e c t i o n w i t h t h e area o f c o n t a c t A , t h e c o n t a c t p r e s s u r e p = FN/A. S i n c e t h e v a l u e o f A may change duc-ts wear during--the t e s t t h e v a l u e - o f p may a l s o undergo some changes as f u n c t i o n o f t i m e , as i n d i c a t e d i n t h e f o r e g o i n g s e c t i o n (Ref.

7.7). (b)

VELOCITY

F o r t h e c h a r a c t e r i z a t i o n and c o n t r o l o f t h e v e l o c i t y between t h e t e s t specimens o f a t r i b o t e s t i n g system, t h e same c o n s i d e r a t i o n s as i n t h e case o f t h e l o a d r e l a t e t o t h e dynamic b e h a v i o u r . F o r t h e c o n t r o l o f t h e v e l o c i t y , e l e c t r o n i c o r opto-electronic transducers are commercially available. The v e l o c i t y i s an i m p o r t a n t parameter i n t r i b o t e s t i n g i n as much as i t determines t h e l u b r i c a t i o n regime w i t h i n t h e S t r i b e c k c u r v e (see S e c t i o n

4.5.1).

I t i s a l s o t h e independent v a r i a b l e i n t h e p r o d u c t FFv w h i c h g i v e s

t h e f r i c t i o n - i n d u c e d power l o s s o f a t r i b o - t e s t i n g system. (c)

TEMPERATURE

The (ambient) t e m p e r a t u r e o f t h e t e s t system i s a n o t h e r i m p o r t a n t o p e r a t i n g v a r i a b l e s i n c e i t determines t h e thermal s t a t e o f t h e system

-

a t least a t

t h e i n i t i a l s t a g e o f t h e t e s t . (The problem o f t h e f r i c t i o n - i n d u c e d tempera t u r e i s discussed i n t h e n e x t s e c t i o n . ) For t h e c o n t r o l o f t h e temperature, t h e f o l l o w i n g two t e c h n i q u e s a r e u t i l i z e d most o.ften:

256

(i)

thermocouple techniques

(ii)

i n f r a r e d - p y r o m e t e r techniques

The c h a r a c t e r i s t i c s o f these techniques a r e discussed i n t h e n e x t s e c t i o n , (d)

TEST DURATION

The s e t o f t h e o p e r a t i n g v a r i a b l e s ( l o a d FN, v e l o c i t y v , temperature T ) a c t s on t h e t r i b o t e s t i n g system as f u n c t i o n o f t i m e o r d u r a t i o n t. As f o r t h e s e t (FN, v, t ) t h e t e s t d u r a t i o n t a l s o s h o u l d be s e l e c t e d t o be cons i s t e n t w i t h t h e n a t u r e o f t h e i n v e s t i g a t i o n . Attempts a r e f r e q u e n t l y made t o s h o r t e n t h e t e s t d u r a t i o n i n s o - c a l l e d " a c c e l e r a t e d t e s t s " by i n c r e a s i n g t h e s e v e r i t y o f t h e o p e r a t i n g c o n d i t i o n s o f FN, v, T. T h i s procedure, however, i s o n l y p e r m i s s i b l e i f t h e n a t u r e o f t h e t r i b o l o g i c a l processes i s n o t changed. Consider, f o r example, a c e r t a i n t e s t system r u n n i n g under g i v e n o p e r a t i n g v a r i a b l e s (FN, v, T) w i t h t r i b o l o g i c a l processes o c c u r r i n g w i t h i n t h e " o u t e r " s u r f a c e l a y e r s ( s e e F i g u r e 4.5) o f t h e t e s t specimens, thus g i v i n g a v e r y l o w wear r a t e . Consequently, i n o r d e r t o c b t a i n s u f f i c i e n t removal o f m a t e r i a l f o r an a c c u r a t e wear measurement, a l o n g t e s t d u r a t i o n i s needed. If, i n o r d e r t o s h o r t e n t h e t e s t d u r a t i o n , t h e s e v e r i t y o f t h e t e s t i s now increased, e.g.,

by i n c r e a s i n g t h e l o a d FN, a h i g h e r

wear r a t e may i n d e e d r e s u l t . However, t h e t r i b o l o g i c a l processes may now a c t w i t h i n t h e " i n n e r " s u r f a c e l a y e r s thus changing e n t i r e l y t h e f r i c t i o n and wear mechanisms and i n c r e a s i n g t h e p o s s i b i l i t y o f c a t a s t r o p h i c f a i l u r e due t o s c u f f i n g or s e i z u r e . T h i s s i m p l e example i n d i c a t e s t h e importance o f t h e p r o p e r c h o i c e o f o p e r a t i n g c o n d i t i o n s o f FN, v, T i n c o n n e c t i o n w i t h the t e s t duration t f o r a given t e s t s i t u a t i o n . Instead o f increasing t h e s e v e r i t y o f t h e o p e r a t i n g c o n d i t i o n s i t m a y be more a p p r o p r i a t e t o i n crease, where p o s s i b l e , t h e s e n s i t i v i t y o f t h e d e t e c t o r s and a n a l y z e r s i n o r d e r t o o b t a i n t h e necessary q u a n t i t i e s w i t h i n a c e r t a i n t e s t d u r a t i o n . The t r i b o - t e s t i n g o p e r a t i n g v a r i a b l e s d i s c u s s e d h i t h e r t o r e f e r t o t e s t systems o f a " c l o s e d s t r u c t u r e " , g i v e n f o r example by t e s t systems i n which t h e elements ( l ) , ( 2 ) , (3), ( 4 ) o f t h e t r i b o - t e s t i n g system a r e e n t i r e l y w i t h i n a c l o s e d s p e c i i e n chamber as i n d i c a t e d i n F i g u r e 7.1.

I f , on t h e

o t h e r hand, t h e t e s t system s t r u c t u r e i s "open" w i t h r e s p e c t t o l u b r i c a n t ( 3 ) and environmental atmosphere ( 4 ) , t h e f l o w r a t e s o f ( 3 ) and ( 4 ) a r e a l s o i m p o r t a n t o p e r a t i n g v a r i a b l e s . Where, f o r i n s t a n c e , a 1i q u i d l u b r i c a n t c i r c u l a t i n g system i s used, t h e l u b r i c a n t f l o w r a t e and t h e r e s i d e n c e t i m e o f t h e l u b r i c a n t f i l m on t h e t e s t specimens s h o u l d be c o n t r o l l e d , i n a d d i t i o n t o t h e o p e r a t i n g v a r i a b l e s discussed above. Another group o f systems

257

w i t h an open system's s t r u c t u r e concerns t e s t systems r e l a t e d t o i n d u s t r i a l processes as i n a g r i c u l t u r e , mining, e a r t h moving, d r i l l i n g , d r e d g i n g , e t c . The o p e r a t i n g " i n p u t " o f these systems i s v a r i a b l e due t o t h e n a t u r e o f s o i l s , r o c k s , sledges, e t c . S p e c i a l c a r e i s needed i n t h e t e s t i n g o f such systems w i t h an " i n t r i n s i c a l l y open system s t r u c t u r e " (Ref. 7.11).

7 2 , 3 TRI BOMETRI c I

CHARACTERISTICS

The t r i b o m e t r i c c h a r a c t e r i s t i c s t o be measured i n t r i b o - t e s t i n g s h o u l d a l l o w p r o p e r c h a r a c t e r i z a t i o n o f t h e f r i c t i o n and wear processes. A c c o r d i n g t o t h e g e n e r a l scheme developed i n Chapter 3 t h e s e c h a r a c t e r i s t i c s can be c l a s s i f i e d i n t o t h r e e groups: (i)

Mechanical q u a n t i t i e s

:

F r i c t i o n force, friction coefficient, n o i s e and v i b r a t i o n .

(ii)

Thermal q u a n t i t i e s

( i i i ) Material quantities

:

F r i c t i o n - induced temperatures

:

Wear r a t e s .

Besides t h e s e t r i b o m e t r i c c h a r a c t e r i s t i c s , i n f o r m a t i o n on t h e c o n t a c t c o n d i t i o n s , such as t h e l u b r i c a n t f i l m t h i c k n e s s o r t h e amount o f m e t a l l i c c o n t a c t , s h o u l d be o b t a i n e d . (a)

FRICTION FORCE AND FRICTION COEFFICIENT

F i g u r e 7.3

Schematic diagram o f a two-component f o r c e t r a n s d u c e r , t o t h e r i g h t d e t a i l s o f t h e d e s i g n o f t h e f o u r r o d s a r e shown.

258 For t h e measurement o f t h e f r i c t i o n f o r c e , e l e c t r o - m e c h a n i c a l f o r c e t r a n s d u c e r s based m a i n l y on s t r a i n - g a u g e t e c h n i q u e s o r i n d u c t i v e e f f e c t s a r e a v a i l a b l e commercially. As i n d i c a t e d i n t h e f o r e g o i n g s e c t i o n , i t i s advantageous t o measure b o t h f r i c t i o n f o r c e FF and l o a d FN and t o c a l c u l a t e the f r i c t i o n c o e f f i c i e n t d i r e c t l y during the t e s t . A force transducer f o r t h e simultaneous measurement o f FN and FF i n d e p e n d e n t l y f r o m each o t h e r i s shown i n F i g u r e 7.3. The f o r c e t r a n s d u c e r i s a d e v i c e c o n t a i n i n g f o u r b a r s w i t h notches

I n t h e c e n t r e o f symmetry o f t h e

p e r p e n d i c u l a r t o each o t h e r (Ref. 7.12).

f o u r b a r s one o f t h e specimens o f a t r i b o m e t e r pin-on-disc tribometer

-

-

f o r instance the p i n o f a

i s i n s e r t e d . I n each n o t c h a s t r a i n gauge i s

f i x e d , d e t e c t i n g t h e s t r a i n s as f u n c t i o n s o f FN and FF. The s e n s i t i v i t y and t h e eigenfrequency o f t h e f o r c e t r a n s d u c e r can be v a r i e d t h r o u g h t h e dimens i o n s o f t h e b a r s and t h e l o c a t i o n s and dimensions o f t h e notches. The b l o c k diagram o f t h e d e t e r m i n a t i o n o f t h e f r i c t i o n c o e f f i c i e n t f r o m t h e s i g n a l s o f FF and FN by means o f an e l e c t r o n i c d i v i d e r i s shown i n F i g u r e 7.4. With t h e h e l p o f t h i s measuring d e v i c e i t i s p o s s i b l e t o o b t a i n a l l necessary i n f o r m a t i o n on t h e mechanics o f a t r i b o - t e s t i n g system a s a f u n c t i o n o f t i m e . Moreover, w i t h t h e use o f a d i s c r i m i n a t o r i t i s p o s s i b l e t o stop the t e s t i f c e r t a i n (adjustable) l e v e l s o f the f r i c t i o n c o e f f i c i e n t a r e passed.

r - - - - - - - - - - - -1 I

F i g u r e 7.4 (b)

Tribome ter

I

B l o c k diagram o f s i g n a l f l o w .

N O I S E AND VIBRATION

As o t h e r "mechanical" c a p a b i l i t i e s o f a t r i b o - t e s t i n g device, measurements o f n o i s e and v i b r a t i o n s s h o u l d be mentioned (Ref. 7.13). A l t h o u g h i m p o r t a n t i n f o r m a t i o n on t h e c o n t a c t s i t u a t i o n o f t h e t e s t system may be deduced f r o m

259

such measurements, they have n o t u s u a l l y been r e p o r t e d i n connection w i t h l a b o r a t o r y f r i c t i o n and wear t e s t r i g s . These techniques are, however, o f t e n used i n m o n i t o r i n g t h e f u n c t i o n a l behaviour o f complete t r i b o - e n g i n e e r i n g systems, such as b a l l bearings o r gear t r a i n s (see Section 7.5). (c)

TEMPERATURE

I metal 1 p 1FN ~

4 " ' s

yUt\,

To

metal 2

t ,

V C J

dynamic thermocouple

thermoel ement

P

i n f r a r e d pyrometer

F i g u r e 7.5

t

Temperature measuring methods.

The main techniques f o r t h e measurement o f f r i c t i o n - i n d u c e d temperatures are i l l u s t r a t e d i n F i g u r e 7.5.

As can be seen, i n most cases thermocouples

o f d i f f e r e n t types o r o p t i c a l i n f r a r e d pyrometer techniques are u t i l i z e d . The techniques may be d i f f i c u l t t o handle o r t h e r e s u l t s d i f f i c u l t t o i n t e r p r e t , so t h a t i t i s s t i l l n o t easy t o perform accurate and meaningful measurements o f f r i c t i o n - i n d u c e d temperatures. The thermoelements commercially a v a i l a b l e have time reponses from 10 sec t o 10 msec, depending on t h e s i z e and t h e thermocouple m a t e r i a l s . I n using thermocouples two methods may be applied: (i)

one ( o r b o t h ) o f t h e a c t u a l t e s t specimens forms p a r t o f t h e thermocouple ( " n a t u r a l thermocouple"),

( i i ) one o r more complete thermocouples are i n s e r t e d i n one o r b o t h o f t h e t e s t specimens.

260

force transducer

i n f r a r e d camera

Representation o f isotherms

Location F i g u r e 7.6

Measurement o f f r i c t i o n - i n d u c e d temperature w i t h i n f r a r e d camera.

26 1

I n case ( i ) i t i s possible, i n p r i n c i p l e , t o o b t a i n i n f o r m a t i o n d i r e c t l y from the f r i c t i o n a l i n t e r f a c e . This i n f o r m a t i o n , however, may be i n f l u e n c e d by i n t e r f a c i a l e l e c t r o m o t i v e f o r c e s r e s u l t i n g , f o r example, from t h e a c t i o n

of l u b r i c a n t a d d i t i v e s . Also c i r c u l a t i n g c u r r e n t s i n m u l t i p l e contacts may be of i n f l u e n c e . I n case ( i i ) i t i s n o t p o s s i b l e t o o b t a i n t h e temperature information d i r e c t l y from t h e f r i c t i o n a l i n t e r f a c e . Therefore, attempts have sometimes been made t o determine temperature g r a d i e n t s by i n s e r t i n g several thermocouples a t d i f f e r e n t distances from t h e i n t e r f a c e and e x t r a p o l a t i n g from these measurements t o an estimated value a t the f r i c t i o n a l i n t e r f a c e . ( F o r a discussion o f t h e t h e o r i e s o f f r i c t i o n - i n d u c e d temperatures see Sect i o n 4.3.4). With pyrometric techniques, e i t h e r t h e temperature r a d i a t i o n e m i t t e d from t h e surrounding o f the f r i c t i o n a l i n t e r f a c e o f o p t i c a l l y non-transpare n t specimen i s detected o r one p a r t n e r has t o be made o p t i c a l l y t r a n s p a r e n t i n the i n f r a r e d region. I n b o t h instances t h e o p t i c a l e m i s s i v i t y as a funct i o n o f temperature and wavelength o f the r a d i a t i o n i s the c r u c i a l p o i n t . An experimental example o f t h e a p p l i c a t i o n o f t h e IR-technique t o t h e d e t e r mination o f f r i c t i o n - i n d u c e d temperatures by measuring t h e r a d i a t i o n from the back o f a t h i n f o i l ( d - 7 0 pm) s l i d i n g a g a i n s t a r o t a t i n g s h a f t i s ill u s t r a t e d i n F i g u r e 7.6 (Ref. 7.14). I n a s i m i l a r way, by u s i n g an o p t i c a l l y transparent p a r t n e r Winer and co-workers determined t h e a c t u a l temperatures w i t h i n a s l i d i n g EHD c o n t a c t (see F i g u r e 4.51).

I n comparing these e x p e r i -

m e n t a l l y determined data w i t h temperature c a l c u l a t i o n s from the B l o k - t h e o r y a good c o r r e l a t i o n between t h e experimental and t h e t h e o r e t i c a l values has been found (Ref. 7.15).

(d)

WEAR

Also f o r t h e determination o f wear, d i f f e r e n t measuring techniques may be u t i l i z e d (Ref. 7.16, 7.17). According t o t h e German standard

DIN 50321,

"Wear-quanti t i e s " , wear may be detected by measuring " d i r e c t " wear-quantit i e s , such as (a)

changes o f geometry o f t h e specimens:

(i) changes i n l i n e a r dimensions ( i i) changes i n cross-sections ( i i i ) changes i n volume

(b)

changes o f the mass o f the specimens

(c)

the amount o f worn m a t e r i a l - l o s s

o r " r e l a t i v e " wear-quantities,

i.e.,

wear r a t e s such as

262

(d)

t h e w e a r - t i m e - r a t i o (wear v e l o c i t y )

(e)

t h e wear-di s t a n c e - r a t i o

o r t h e wear c o e f f i c i e n t , d e f i n e d as (f)

K'

=

wear volume 1o a d - d i stance

mm

(-1Nm

o r t h e dimensionless A r c h a r d ' s wear c o e f f i c i e n t (9)

K

=

wear vo1ume.hardnes.s loadedistance

For each t y p e o f wear measurement ( a ) , ( b ) , ( c ) , a p p r o p r i a t e d e t e c t o r s a r e commercially a v a i l a b l e . Some o f t h e b a s i c wear-measuring t e c h n i q u e s a r e d i s c u s s e d i n r e l a t i o n t o t h e c o n d i t i o n - m o n i t o r i n g o f machines, see S e c t i o n

7.5.

The t y p e o f t h e measuring t e c h n i q u e s h o u l d be chosen t o be c o n s i s t e n t

w i t h t h e n a t u r e o f t h e i n v e s t i g a t i o n , and t h e wear d a t a o b t a i n e d s h o u l d be r e p o r t e d i n terms t h a t a r e u s e f u l f o r e n g i n e e r i n g a p p l i c a t i o n s ( R e f . 7.18). I n t h i s c o n n e c t i o n i t s h o u l d a g a i n be emphasized t h a t t h e wear-quantit i e s must n o t be m i s i n t e r p r e t e d as i n t r i n s i c m a t e r i a l c o n s t a n t s b u t must be t r e a t e d as system-dependent q u a n t i t i e s which depend on b o t h t h e o p e r a t i n g v a r i a b l e s and t h e s t r u c t u r e o f t h e wearing system under c o n s i d e r a t i o n . A c h e c k - l i s t t o a s s i s t i n the compilation o f r e l e v a n t data i n connection w i t h wear measurements i s developed i n Chapter 8. Supplementing t h e measurement o f t h e mechanical, thermal and m a t e r i a l s c h a r a c t e r i s t i c s , i n f o r m a t i o n on t h e c o n t a c t c o n d i t i o n w i t h i n a t r i b o m e t e r may be u s e f u l . Here two groups o f c h a r a c t e r i s t i c s a r e o f i n t e r e s t : (i)

t h e e x t e n t o f r e a l s o l i d - s o l i d c o n t a c t ( i n c l u d i n g t h e r e a l area o f contact)

( i i ) the l u b r i c a n t f i l m thickness F o r t h e measurements ( i ) , t h e techniques o f o p t i c a l microscopy, d e s c r i b e d i n S e c t i o n 7.6, and t h e e l e c t r i c a l c o n t a c t r e s i s t a n c e (ECR) measuring t e c h n i q u e s have been a p p l i e d (Ref. 7.19). The p r i n c i p l e o f t h e ECR t e c h n i q u e i s i l l u s t r a t e d i n t h e b l o c k diagram i n F i g u r e 7.7 (Ref. 7.20). A small e l e c t r i c a l v o l t a g e (10-100 mV)' i s a p p l i e d t o t h e specimens and t h e t i m e dependence o f t h e v o l t a g e drop on a s e r i e s r e s i s t a n c e i s d e t e c t e d . U s u a l l y t h e v o l t a g e drop f l u c t u a t e s o v e r s e v e r a l o r d e r s o f magnitude ( < 0.1R up t o > 100 k R ) w i t h impulse d u r a t i o n s down t o t h e psec range as i l l u s t r a t e d i n

F i g u r e 7.8. By r a p i d e l e c t r o n i c means ( d i s c r i m i n a t o r s , a m p l i f i e r s , c o u n t e r s )

263

Figure 7 . 7

Block diagram o f ECR signal processing.

Figure 7.8

Typical ECR oscillogram o f system ( a ) , Figure 7.9.

(a) (b) (c) (d)

hexadecane hexadecane + o l e i c acid hexadecane + ZDDP hexadecane + DBDS

(additive concentrations: 0.03 mole/l) I

I

I

8

102 103 lo4 lo5 Contact resistance Rc ( Q )

100

Figure 7.9

101

ECR fluctuation rates (lubricate sliding AISI 52180 steel cylinders, r=2.5mn, poH=0.67GN/me, v=1.5cm/s, T=25 C ) .

264

i t i s p o s s i b l e t o c a l c u l a t e c h a r a c t e r i s t i c s such as t h e " n o - c o n t a c t - t i m e

f r a c t i o n " (see F i g u r e 4.58) o r i m p u l s i v e f l u c t u a t i o n r a t e s as shown i n F i g u r e 7.9. Although these r e s u l t s p e r m i t c o n c l u s i o n s on t h e e x t e n t o f m e t a l l i c c o n t a c t o r on t h e a c t i o n o f l u b r i c a n t a d d i t i v e s t o be drawn, g r e a t c a r e i s needed i n t h e i r i n t e r p r e t a t i o n because o f t h e e f f e c t s o f m u l t i p l e contact o r i n t e r f a c i a l electromotive forces. L u b r i c a n t f i l m t h i c k n e s s ( i i ) may a l s o be s t u d i e d by means o f o p t i c a l microscopy (see S e c t i o n 7 . 6 ) , by t h e c a p a c i t a n c e method, o r by an X-ray technique. A d e t a i l e d d i s c u s s i o n o f t h e v a r i o u s methods f o r measuring l u b r i c a n t f i l m t h i c k n e s s i s p r o v i d e d i n Ref. 7.21. Having d i s c u s s e d t h e v a r i o u s measuring t e c h n i q u e s r e l e v a n t t o f r i c t i o n and wear t e s t i n g i t i s now p o s s i b l e t o supplement t h e c o m p i l a t i o n o f t h e r e l e v a n t t e s t parameters l i s t e d i n F i g u r e 7.1 by t h e c o r r e s p o n d i n g measuring techniques. Although i n t r i b o t e s t i n g a p p l i c a t i o n s i t may n o t be p o s s i b l e t o measure a l l o f t h e parameters l i s t e d i n F i g u r e 7.1 i t s h o u l d be emphasized once more t h a t e v e r y parameter can i n f l u e n l c e markedly t h e r e s u l t s o f a f r i c t i o n and wear t e s t .

7 3 SIMULATIVETRIBO-TESTI N G I

I n s i m u l a t i v e t r i b o - t e s t i n g an a t t e m p t i s made t o s i m u l a t e t h e t r i b o l o g i c a l b e h a v i o u r o f a p r a c t i c a l t r i b o - e n g i n e e r i n g system, or t h e b e h a v i o u r o f some p a r t o f i t , by means o f a l a b o r a t o r y t e s t system. Obviously, t h i s f i e l d o f t r i b o m e t r y i s e x t r e m e l y d i f f i c u l t due t o t h e c o m p l e x i t y o f t r i b o l o g i c a l p r o cesses, i t s numerous i n f l u e n c i n g f a c t o r s and t h e a d d i t i o n a l requirement o f an a p p r o p r i a t e " s i m u l a t i o n c r i t e r i o n " (Ref. 7.22,

7.23).

The s t a r t i n g p o i n t i n s i m u l a t i v e t r i b o - t e s t i n g s h o u l d be t h e c o l l e c t i o n o f a v a i l a b l e d a t a on t h e p r a c t i c a l system (PS) and t h e t e s t system (TS).

t h e c o l l e c t i o n o f these d a t a and " c a s e h i s t o r i e s " ,

For

t h e d a t a s h e e t developed

i n S e c t i o n 8.2 can be c o n v e n i e n t l y used. Based on these d a t a , t h e c o n d i t i o n s f o r s i m u l a t i v e t e s t i n g may t h e n be s p e c i f i e d . From a f o r m a l systems p o i n t o f view, t h e procedure o f s i m u l a t i v e t r i b o - t e s t i n g r e q u i r e s : (a)

A s i m i l a r i t y o f t h e f u n c t i o n s o f PS and TS, i . e . :

(i) (ii) (b)

s i m i l a r i t y o f t h e i n p u t s and t h e o u t p u t s s i m i l a r i t y o f the f u n c t i o n a l input-output r e l a t i o n s

A s i m i l a r i t y o f t h e s t r u c t u r e s o f PS and TS, i . e . : (i)

s i m i l a r i t y o f system elements

265

(ii)

s i m i l a r i t y o f system element p r o p e r t i e s

( i i i ) similarity o f tribological interactions

I n t r y i n g t o f u l f i l these conditions, f i r s t the materials, the l u b r i c a n t s and t h e atmospheric environment s h o u l d be chosen t o be i d e n t i c a l i n b o t h

PS and TS. Then t h e g e o m e t r i c a l and c o n t a c t c o n d i t i o n s o f t h e t e s t system s h o u l d be a d j u s t e d t o t h o s e o f t h e p r a c t i c a l system, t a k i n g i n t o account t h e problem o f a p p r o p r i a t e s c a l e f a c t o r s . F i n a l l y , t h e o p e r a t i n g v a r i a b l e s s h o u l d be a d j u s t e d i n o r d e r t o o b t a i n t h e same t r i b o l o g i c a l i n t e r a c t i o n s i n t h e t e s t system as i n t h e p r a c t i c a l system. C l e a r l y , s i m u l a t i v e t r i b o t e s t i n g as o u t l i n e d i n t h e s e few sentences i s an e x t r e m e l y d i f f i c u l t t a s k and a g e n e r a l l y accepted procedure i s n o t y e t a v a i l a b l e . I n o r d e r t o obt a i n a t l e a s t a k i n d o f g u i d e l i n e , some o f t h e main aspects o f s i m u l a t i v e t r i b o t e s t i n g , w i l l be d i s c u s s e d b r i e f l y here, c o n s i d e r i n g as a s t a r t i n g p o i n t a p i n - o n - d i s c t r i b o m e t e r t e s t system, shown i n F i g u r e 7.10.

A.

AW2

F i g u r e 7.10

/--

Geometrical c h a r a c t e r i s t i c s o f a t r i b o t e s t i n g model system.

For the task o f simulative t r i b o - t e s t i n g ,

t h e t e s t system shown may be

applicabl'e f o r pure continuous s l i d i n g w i t h the m a t e r i a l s ( l ) , ( 2 ) ident i c a l w i t h t h o s e o f t h e p r a c t i c a l system. The c o n d i t i o n s o f d r y o r l u b r i c a t e d s l i d i n g s h o u l d be r e a l i z e d w i t h t h e atmosphere and l u b r i c a n t i d e n t i c a l t o those i n t h e p r a c t i c a l system. Then t h e i m p o r t a n t "system-independent'' p r o p e r t i e s o f t h e elements, i n c l u d i n g chemical c o m p o s i t i o n , e l a s t i c modulus, hardness, v i s c o s i t y , e t c . w i l l i n h e r e n t l y be i d e n t i c a l i n PS and TS. A f t e r

266

t h e c h o i c e o f t h e elements o f t h e system and t h e i r sys,tem-independent p r o p e r t i e s , t h e g e o m e t r i c a l and c o n t a c t c o n d i t i o n s o f t h e t e s t system s h o u l d be compared w i t h t h o s e o f t h e p r a c t i c a l system. I n t h i s c o n n e c t i o n t h e q u a n t i t i e s l i s t e d i n Table 7.2 a r e i m p o r t a n t .

Geometric o r c o n t a c t p rope r ties

I

I

Volume Mantle surface

I

Am1

C o n t a c t area (geom. )

1 C o n t a c t area

I

v1

I

Am2

-

An

I

(real)

No-contact area

I Aml-Ao Am2-A0

Wear t r a c k area

Table 7.2

v2

AW2

Geometric c h a r a c t e r i s t i c s o f t e s t specimens.

The c h a r a c t e r i s t i c s compiled i n T a b l e 7.2 a r e n o t o n l y i m p o r t a n t f o r t h e c o n t a c t pressures po = FN/Ao and pr = FN/Ar t h e y a r e a l s o r e l e v a n t t o t h e processes o f t h e t r a n s m i s s i o n and d i s s i p a t i o n o f mechanical work i n t h e system, as e x p l a i n e d i n Table 7.3.

1

I

T r i b o l o g i c a l process

Relevant g e o m e t r i c a l q u a n t i t y

Generation o f f r i c t i o n a l heat

Contact a r e a (Ao, Ar)

Absorption o f f r i c t i o n a l heat

Volume (Vl,

LEG o f f r i c t i o n a l

Table 7.3

I

V2)

No-contact a r e a

Relevance o f g e o m e t r i c a l q u a n t i t i e s f o r t r i b o l o g i c a l processes

Besides these g e o m e t r i c c h a r a c t e r i s t i c s , r e l a t i v e q u a n t i t i e s may a l s o be i m p o r t a n t , f o r example t h e r a t i o o f t h e h e a t - e m i t t i n g a r e a t o t h e h e a t a b s o r b i n g volume o f each o f t h e elements ( 1 ) and ( 2 ) :

26 I

=

0

0

ratio

heat e m i t t i n g area h e a t a b s o r b i n g volume

:

Am1,2 1,2

-

"1,2

Another i m p o r t a n t r e l a t i v e q u a n t i t y i s g i v e n by:

=

E

ratio

c o n t a c t area wear t r a c k area

:

F o r t h e example o f t h e p i n - o n - d i s c t r i b o m e t e r , i t f o l l o w s t h a t f o r the p i n

:

E~

=

1

f o r the d i s c

:

E~

.c

.tJ

a

1

7

W (Y

10-1

(A)

(6) (C) ( i ) a d h e s i v e wear b e h a v i o u r

abrasive-paper-on-disc;

lo2

T = 23 0C ; t = 6 rnin

W

U

c

*

corundum paper grade 220

p = 1.9 N/cm2; n = 125 rpm

4

.,"

lo1

ul

L W

L

3 1

3 W

>

.r-

2

7

W

CT

10-1

EO c

m w

bul d

v u

(A)

F i g u r e 8.11

N

O

(5) (C) ( i i ) a b r a s i v e wear b e h a v i o u r

(D)

Wear r e s i s t a n c e o f s u r f a c e c o a t i n g s t e s t e d under (i)adhesive and ( i i ) a b r a s i v e wear c o n d i t i o n s .

324

-

vacuum: lo-’

FN

=

10

bar

N; v = 0.1 m/s; T = 23 0C; s

= 1 km

10 pm

Figure 8.12

Appearance o f wear surfaces o f pins a f t e r t e s t i n g i n vacuum.

325 (d)

RESULTS

I n F i g u r e 8.11 t h e r e l a t i v e wear r e s i s t a n c e o f t h e s u r f a c e c o a t i n g s under c o n d i t i o n s o f adhesive wear and a b r a s i v e wear t o g e t h e r w i t h t h e a p p l i e d t e s t c o n d i t i o n s i s shown w i t h t y p i c a l r e s u l t s . I n t h e adhesive-wear s i t u a t i o n , t h e measured wear r e s i s t a n c e and t h e c o r r e s p o n d i n g appearance o f worn s u r f a c e s , shown i n F i g u r e 8.12 i n d i c a t e t h a t t h e n i t r i d e d s u r f a c e c o a t i n g s e x h i b i t t h e b e s t w e a r - r e s i s t a n c e behavi o u r . The p o o r e s t wear r e s i s t a n c e has been found f o r t h e ( v e r y h a r d ) vanad i z e d s t e e l . I n t h i s case, t h e s u r f a c e - c o a t i n g l a y e r was p e n e t r a t e d so t h a t t h e adhesive wear a c t i o n extended t o t h e ( s o f t ) base m a t e r i a l . I t s h o u l d be mentioned t h a t t h e adhesive wear r e s i s t a n c e o f t h e b o r i d e d c o a t i n g , which a l s o shows a r e l a t i v e l y p o o r b e h a v i o u r a c c o r d i n g t o F i g u r e 8.11,

i s markedly

improved i f oxygen i s a v a i l a b l e . I n t h i s case, t h e adhesive wear r e s i s t a n c e of b o r i d e d s t e e l i s c l e a r l y b e t t e r t h a n t h a t o f case-hardened s t e e l . I n c o n t r a s t , i n t h e abrasive-wear s i t u a t i o n , t h e b e s t w e a r - r e s i s t a n t b e h a v i o u r i s f o u n d f o r t h e vanadized s u r f a c e c o a t i n g . As d e s c r i b e d i n S e c t i o n

4.4.3,

t h i s b e h a v i o u r can be e x p l a i n e d i n terms o f t h e hardness o f t h e t e s t e d

m a t e r i a l s and t h e a b r a s i v e . Since corundum, which was used as an a b r a s i v e 2 (hardness HV = 17000 N/mm ), i s c o n s i d e r a b l e h a r d e r than b o t h t h e case-hardened s t e e l ( A ) and t h e n i t r i d e d s t e e l ( B ) , b o t h m a t e r i a l s ( A ) ,

(B) are i n the

"severe wear" regime, whereas t h e b o r i d e d s t e e l ( C ) and t h e vanadized s t e e l

( 0 ) a r e s t i l l i n t h e " m i l d wear" regime due t o t h e i r h i g h hardness. I f t h e

2 t e s t s were performed w i t h a s i l i c o n c a r b i d e a b r a s i v e paper (HV = 27000 N/mm ) , t h e b o r i d e d s t e e l a l s o changes t o t h e severe wear regime, whereas t h e vanad i z e d s t e e l remains i n t h e m i l d wear regime. I n summary, t h e s t u d i e s on t h e adhesive and t h e a b r a s i v e wear r e s i s t a n c e of some d i f f u s i o n s u r f a c e c o a t i n g s show t h a t under t h e choosen t e s t c o n d i t i o n s a q u i t e d i f f e r e n t ( i n f a c t , a reverse) ranking o f t h e surface coatings i n o r d e r o f m e r i t i s found i n t h e two cases: (i)

adhesive wear r e s i s t a n c e

:

1. n i t r i d i n g 2. case h a r d e n i n g 3. b o r i d i ng

4. v a n a d i z i n g ( i i ) a b r a s i v e wear r e s i s t a n c e

:

1. v a n a d i z i n g 2. b o r i d i n g

3. case h a r d e n i n g 4. n i t r i d i n g

326 (d)

FOLLOW-UP

The r e s u l t s o f t h i s s t u d y c o n f i r m t h a t f o r a p r e - c h a r a c t e r i z a t i o n o f t h e wear b e h a v i o u r o f s u r f a c e c o a t i n g s besides t h e o p e r a t i n g c o n d i t i o n s t h e dominating wear mechanism must be known. I t f o l l o w s t h a t d i f f e r e n t s u r f a c e t r e a t m e n t s may be suggested t o be used i n d i f f e r e n t t r i b o - e n g i n e e r i n g appl ic a t i o n s . F o r example, f o r t h e p r e v e n t i o n o f severe adhesive wear ( o r s c u f f i n g ) o f gears, n i t r i d i n g may be s u i t a b l e whereas f o r t h e m i t i g a t i o n o f a b r a s i v e wear a t t a c k , as i n dredge pumps, v a n a d i z i n g may be b e s t .

8 , 5 , 3 MATERIAL (a)

S E L E C T I O N F O R OFF-SHORE B E A R I N G A P P L I C A T I O N

PROBLEM

A m a t e r i a l s e l e c t i o n f o r a j o u r n a l b e a r i n g o p e r a t i n g a t 30 m below sea l e v e l (component o f anchor-buoy) has t o be made. A c c o r d i n g t o t h e dimensions o f t h e j o u r n a l b e a r i n g , a l i n e a r wear r a t e o f 0.6 pm/h o f t h e b e a r i n g b u s h i n g corresponds t o a s p e c i f i c wear r a t e o f a p p r o x i m a t e l y 4

3

mm /Nm. Because

o f s t r e n g t h c o n s i d e r a t i o n s , t h e wear r a t e o f t h e j o u r n a l i s t o be s m a l l e r than 0.1

*

3 loe6 mm /Nm. The o b j e c t i v e was t o f i n d a m a t e r i a l c o m b i n a t i o n t h a t

meets these requirements. Moreover, a t t a c k ( s c r a t c h i n g ) o f t h e j o u r n a l s u r f a c e s h o u l d be as m i l d as p o s s i b l e i n o r d e r t o m i n i m i z e t h e chance o f s c r a t c h induced f a t i g u e e f f e c t s o c c u r r i n g . (b)

APPROACH

The t r i b o l o g i c a l systems parameters which have t o be taken i n t o c o n s i d e r a t i o n i n t h e m a t e r i a l - s e l e c t i o n process can be seen from t h e t r i b o l o g i c a l d a t a sheet o f a j o u r n a l b e a r i n g , F i g u r e 8.6. F o r m a t e r i a l s e l e c t i o n a simul a t i v e t r i b o - t e s t i n g procedure w i t h a p i n - a n d - r i n g t e s t r i g was a p p l i e d . A diagrammatic p r e s e n t a t i o n o f t h i s r i g i s shown i n F i g u r e 8.13. The specimen assembly c o n s i s t s o f a p i n (1) and a r i n g ( 2 ) . The p i n , made f r o m t h e beari n g m a t e r i a l t o be t e s t e d , i s pressed under a known normal f o r c e a g a i n s t t h e curved s u r f a c e o f t h e r o t a t i n g r i n g , made f r o m t h e j o u r n a l m a t e r i a l t o be t e s t e d . The c o n t a c t s u r f a c e o f t h e p i n i s preshaped t o f i t t h e r a d i u s o f c u r v a t u r e o f t h e r i n g . Diameter r i n g : 50 mm; dimensions p i n ( r e c t a n g u l a r cross s e c t i o n ) :

12.0 x 8.0 mm; o v e r l a p percentage E = 7.6%. The specimens

were surrounded by a box, f i l l e d w i t h a r t i f i c i a l sea water o f 2loC. The specimens were c o m p l e t e l y submerged.

327

I I I

1.

I ,'

I

lever

-

-L pressurized air

r

Diagrammatic p r e s e n t a t i o n o f p i n - a n d - r i n g t e s t r i g .

F i g u r e 8.13

Pin-and-ring t e s t r i g Type o f m o t i o n Load F,

sliding (reciprocating)

(N)

sliding (continuous)

3.85 4.0

*

10'

.

lo7

v = 0.05 Total s l i d i n g

18 __-__

Geometry and d imen s ion s

Journal diameter 0.42 m

Ring d i a m e t e r 50 mm P i n cross section 12 x 8 mm

Environment

Seawater ( 5 - 3 5 ' ~ )

A r t i f i c i a l seawater (21OC)

Table 8.4

C o n d i t i o n s i n p r a c t i c e and i n s i m u l a t i v e t r i b o - t e s t i n g .

I I

328 ( i ) O pera t in g v a r i a b l e s :

A l l experiments were performed under a normal f o r c e FN = 3850 N and a t a s l i d i n g speed o f v = 0.05 m/s ( c o n t i n u o u s r o t a t i o n ) . A t FN = 3850 N , t h e p r o j e c t e d pre s s ure p = 4.0 107 N/m, i . e . equal t o p i n p r a c t i c e . The s l i d i n g speed v was s e t a t 0.05 m/s ( i . e . 5 t i m e s vmax i n p r a c t i c e ) . For an ex-

-

peri ment d u r a t i o n t = 100 h r s , t h e t o t a l s l i d i n g d i s t a n c e s i n one e x p e r i ment was 100 x 3600 x 0.05 x 0.001 = 18 km. Table 8.4 compares t h e c o n d i t i o n s i n p r a c t i c e w i t h those i n s i m u l a t i v e t e s t i n g . I t can be seen t h a t t h e r e a r e some d i f f e r e n c e s between t h e pract i c a l s i t u a t i o n and t h e t e s t s i t u a t i o n , a s s o c i a t ed w i t h FN, v and s . As t o FN, t h e c h oic e o f a much l o w e r v a l u e i n l a b o r a t o r y t e s t i n g was j u s t i f i e d p r i m a r i l y by c o n s i d e r i n g t h a t by e q u a l i z i n g t h e pressure p, t h e amount o f deformation i n v o l v e d i n t h e l a b o r a t o r y t e s t w i l l be equal t o t h a t i n pract i c e . As t o v, t h e r e a s o n i n g was t h a t t h e main e f f e c t o f an i n c r e a s e i n v i s t o i n c r e a s e t h e temperature i n t h e c o n j u n c t i o n area due t o f r i c t i o n a l hea t in g. Although t h i s w i l l c e r t a i n l y be t h e case i n t h e p r e s e n t s i t u a t i o n , even a t v = 0.05 m/s t h e above temperature r i s e was so l o w ( o r d e r o f magn i t u d e : a few degrees K) t h a t i t c o u l d p r o b a b l y be n e g l e c t e d ( n o t e t h a t t h e sea-water p r e s e n t i n p r a c t i c e as w e l l as i n t h e l a b o r a t o r y t e s t c o o l s t h e r u b b i n g s urf ac es q u i t e e f f e c t i v e l y ) . As r e g a r d s s , t h e acceptance o f 18 km i n s t e a d o f 1000 km was based on t h e assumption t h a t t h e wear process would r a p i d l y re ac h a s t e a d y - s t a t e c o n d i t i o n . Again, by v i r t u e o f t h e f a c t t h a t thermal e f f e c t s a r e v i r t u a l l y n e g l i g i b l e , t h i s assumption seemed r e a l i s t i c . (ii) Materials M a t e r i a l s f o r p i n and r i n g were p r e s e l e c t e d on t h e b a s i s o f a number o f n o n - t r i b o l o g i c a l c r i t e r i a , f o r i n s t a n c e , r e s i s t a n c e t o sea-water c o r r o s i o n and p r i c e , as w e l l as t r i b o - t e c h n i c a l e x p e r i e n ce and handbook data. Event u a l l y i t was decided t o make t h e t e s t specimens f rom t h e m a t e r i a l s desc r i b e d i n Table 8.5. Because o f r e s t r i c t e d time, o n l y a l i m i t e d number o f combinations o f p i n and r i n g m a t e r i a l s was t e s ted. (c)

RESULTS

A summary o f r e s u l t s i s g i v e n i n Table 8.6. T h i s shows t h a t , f rom t h e two bronzes w i t h MoS2, t y p e ( a ) d i d n o t come up t o e x p e c t a t i o n s . However t y p e (b), combined w i t h r i n g m a t e r i a l s ( C ) and (E), met t h e requirements as r e gards wear r a t e . However, even w i t h m a t e r i a l ( b ) t h e r i n g s were s l i g h t l y damaged, see F i g u r e 8.14. Combinations o f d i f f e r e n t c o b a l t - t y p e a l l o y s ,

329 i.e.,

m a t e r i a l combinations (cD), (cE), ( c F ) and (dF), were s u c c e s s f u l as

f a r as t h e wear r a t e o f t h e p i n ( b u s h i n g ) m a t e r i a l was concerned. However, i n a l l cases an u n a c c e p t a b l y h i g h wear r a t e o f t h e r i n g s was observed, r a n g i n g from 0.5 u n i t s f o r c o m b i n a t i o n ( c F ) t o 1.5 u n i t s f o r c o m b i n a t i o n ( d F ) .

M a t e r i a1

Code

Type

Hardness 1eve1

(lo7 N I ~ ) Pin

c a s t bronze w i t h MoS2

(bushing) C

(1)

e f 9 h

Ring

A

(journal)

B C

(2)

150-250

.------cobal t-chromium a l l o y s

__--__-_

I -

phenolic r e s i n s

+

500 - 600

----

fillers

30-40

t solid lubricant

Cr-Ni a l l o y

-----

Cu-Ni a l l o y

_--

----_

Fe-Ni a l l o y

-

-

- 200 -200

--250 ~ -5 00 -600

Table 8.5

Types o f p r e s e l e c t e d m a t e r i a l s .

F i n a l l y , a l l combinations i n v o l v i n g r e s i n - b a s e d p i n s were s u c c e s s f u l i n t h a t wear r a t e o f t h e p i n s never exceeded 4 u n i t s . M i n o r damage o f t h e r i n g s

o f t h e t y p e shown i n F i g u r e 8.14 o c c u r r e d w i t h m a t e r i a l combinations (eA), ( f E ) and (hB). However, i f used i n c o m b i n a t i o n w i t h p i n m a t e r i a l s ( e ) and

( g ) , r i n g s o f m a t e r i a l ( B ) remained c o m p l e t e l y undamaged, see example i n

F i g u r e .8.15. (d)

FOLLOW-UP

On t h e b a s i s o f t h e above r e s u l t s , a p p l i c a t i o n o f m a t e r i a l s ( e ) , ( 9 ) and (B) seemed w e l l j u s t i f i e d . F u r t h e r , i t l o o k e d as i f c o m b i n a t i o n (bC) o r (bE) m i g h t w e l l be chosen as a p o s s i b l e back-up s o l u t i o n . Since p e r f o r m i n g t h e l a b o r a t o r y t e s t s , p r o t o t y p e t e s t i n g has been p e r formed w i t h combinations (gB) and (bC) t e s t d u r a t i o n : 0.5 y e a r ; t o t a l s l i d -

330

F i g u r e 8.14

F i g u r e 8.15

P r o f i l e diagram and photomicrograph o f p i n s u r f a c e a f t e r t e s t . M a t e r i a1 c o m b i n a t i o n : bC. Damage c l a s s i f i c a t i o n : 51 ig h t l y damaged.

P r o f i l e diagram and photomicrograph o f p i n s u r f a c e a f t e r t e s t . M a t e r i a l combination: gB. Damage c l a s s i f i c a t i o n : undamaged.

331

ing distance: 25 km). The r e s u l t s f u l l y corroborate the pin and r i n g res u l t s and thus j u s t i f y in r e t r o s p e c t the choice of t h e t e s t conditions i n the laboratory tests.

Wear r a t e Materi a1

KI ( ~ o - ~ ~ ~ / N ~ )

pin

ring

pin

ring

10

72 72

e 0.01

60

Table 8.13

’

< 0.01 0.7

10 15 40 60

> 72 > 72 > 72 9 0.5 0.5

c: 0.01 *:

3

1 < 0.02 0.02

1.8 2.4 4.1

20 30 40 50 60 70

coefficient of friction f

0.01

< 0.01 42 50 62

0.8 -0.6 0.8-0.6 0.6 0.6

0.6 0.6 0.6

0.6-0.5 0.5 0.5

Results obtained w i t h Ag-Au-Cu s l i d i n g against Cu-Ni-Zn.

R.H.

(%I

C r i t i c 1 load

(lo-? N)

0

8

20 40 50 60

8 8 8 40 40

80

-

-

10 10 10

10 50 50

Table 8.14

T r a n s i t i o n load as a function o f r e l a t i v e humidity f o r Ag-Au-Cu s l i d i n g against Cu-Ni-Zn.

Table 8.15

C r i t i c a l r e l a t i v e humidity f o r various m a t e r i a l combinations (FN = 0.4 N, p i n material Ag-Au-Cu).

345

o f t h e surrounding atmosphere, i.e.,

by a p r o p e r t y o f the element ( 3 ) o f

t h e t r i b o - e n g i n e e r i n g system under study. (d)

FOLLOW-UP

Some telephone exchange u n i t s , o p e r a t i n g i n extremely d r y environments, were provided w i t h a i r c o n d i t i o n i n g . This ( r a t h e r expensive) s o l u t i o n proved t o be e n t i r e l y s a t i s f a c t o r i l y . I n o t h e r cases, g o l d p l a t i n g o f t h e e l e c t r i c a l contacts ( a l s o expensive) e f f e c t i v e l y e l i m i n a t e d t h e problem. (With g o l d p l a t e d contacts, adhesive m a t e r i a l t r a n s f e r always occurs; however formation o f loose wear p a r t i c l e s i s a r e l a t i v e l y r a r e e v e n t . ) F i n a l l y , i n r e p l a c i n g exchange u n i t s w i t h mechanical contacts by f u l l y e l e c t r o n i c u n i t s , precedence was given t o r e p l a c e u n i t s , o p e r a t i n g i n extremely d r y environments.

8,5,8 COMPILATIONOF

CHARACTERISTICSOF METAL-WORKING

PROCESSES (a)

PROBLEM

An important area o f t r i b o l o g y which has n o t been t r e a t e d e x p l i c i t l y i n t h i s volume so f a r concerns t h e t r i b o l o g y o f manufacturing processes. Also i n t h i s f i e l d , progress i s p o s s i b l e o n l y through a b e t t e r understanding o f the g r e a t number o f c o n t r o l l i n g v a r i a b l e s . While i t i s n o t p o s s i b l e t o ent e r i n t o d e t a i l s o f t h i s f i e l d w i t h i n the scope o f t h i s volume, a t l e a s t a b r i e f o v e r a l l view o f i t s main "systems parameters" should be attempted here. (b)

APPROACH

I n the Appendix ( A ) , a c o m p i l a t i o n o f t h e various manufacturing processes i s given. C l e a r l y , i n a l l these processes the t r i b o l o g i c a l mechanisms, des-

c r i b e d i n Chapter 4, i.e.,

t h e contact, f r i c t i o n , wear and l u b r i c a t i o n pro-

cesses, a c t a l l a t t h e workpiece-tool i n t e r f a c e . I n manufacturing, t h e trib o l o g i c a l processes p l a y a "dual" r o l e : (i)

On one hand, t r i b o l o g i c a l processes i n f l u e n c e d i r e c t l y the surface p r o p e r t i e s o f the manufactured workpiece. Thus, t r i b o l o g i c a l processes determine t o a g r e a t e x t e n t t h e q u a l i t y o f t h e manufactured workpiece, i.e.,

t h e q u a l i t y o f t h e "use-output" o f t h e manufacturing system.

346 ( i i ) On t h e o t h e r hand, t r i b o l o g i c a l processes a t t h e w o r k p i e c e - t o o l i n t e r f a c e a r e r e s p o n s i b l e f o r t o o l - w e a r and t o o l - w o r k p i e c e f r i c t i o n . Thus, as i n any t r i b o - e n g i n e e r i n g system, t r i b o l o g i c a l processes a r e a l s o r e s p o n s i b l e , o f course, f o r t h e energy and m a t e r i a l " l o s s - o u t p u t s " o f t h e m a n u f a c t u r i n g system. M a n u f a c t u r i n g processes can be c l a s s i f i e d b r o a d l y i n two groups: " c u t t i n g " o r "machining" processes, and " f o r m i n g " processes. I n machining, m a t e r i a l i s removed f r o m a c r u d e p i e c e o f s t o c k t o l e a v e b e h i n d a p r e c i s i o n - s h a p e d u s e f u l p a r t . M a n u f a c t u r i n g by t h i s method i s , however, w a s t e f u l o f m a t e r i a l ; sometimes as much as 90 p e r c e n t o f t h e o r i g i n a l m a t e r i a l i s removed and d i s c a r d e d i n t h e process. I n f u t u r e , such waste may become i n t o l e r a b l e as a consequence o f t h e i n c r e a s i n g e f f o r t s o f c o n s e r v a t i o n o f m a t e r i a l s . Thus, t h e u l t i m a t e method o f manufacture i n t h e f u t u r e w i l l be " c o n s o l i d a t i v e processing"

-

t h e manufacture o f goods by f o r m i n g o r assembling m a t e r i a l i n

a c o n t r o l l e d p r e c i s e manner (Ref. 8.16). One o f t h e m a j o r areas o f c o n s o l i d a t i v e m a n u f a c t u r i n g processes i s t h e f i e l d o f m e t a l - w o r k i n g processes. I n t h e f o l l o w i n g , t h e main systems parameters r e l e v a n t t o t h e t r i b o l o g y o f met a l - w o r k i n g processes w i l l be s t u d i e d i n b r i e f . (c)

A

RESULTS

comprehensive r e v i e w o f t h e t r i b o l o g y o f m e t a l - w o r k i n g processes was pub-

l i s h e d by Schey i n 1970 (Ref. 8 . 1 7 ) . F u r t h e r r e v i e w s o f t h e o v e r a l l f i e l d o r s p e c i a l i m p o r t a n t aspects can be found i n Refs 8.18 t o 8.22.

I f on t h e

b a s i s o f t h i s work t h e main systems parameters o f t h e t r i b o l o g y o f m e t a l w o r k i n g processes a r e compiled w i t h t h e h e l p o f t h e t r i b o l o g i c a l systems d a t a sheet (see F i g u r e 8.5),

1.

the following compilation results:

T e c h n i c a l f u n c t i o n o f m e t a l - w o r k i n g systems Forming o f m a t e r i a l s t h r o u g h :

11.

-

drawing

-

pressing

-

rolling forging extrusion

O p e r a t i n g v a r i a b l e s o f m e t a l - w o r k i n g process

-

type o f motion a t the workpiece-die i n t e r f a c e

-

s u r f a c e and/or d e f o r m a t i o n v e l o c i t y , v e l o c i t y d i s t r i b u t i o n

l o a d and/or i n t e r f a c i a l pressure, s t r a i n r a t e

341

-

w o r k i n g temperature (ambient temperature and f r i c t i o n - i n d u c e d

-

operating duration

-

m a t e r i a l f l o w and/or d e f o r m a t i o n r a t e

temperature)

111.

S t r u c t u r e o f metal-work ng system (a)

Components o f meta - w o r k i n g system

(1)

(b)

Workpiece

(2)

Die

(3)

Lubricant/coolant

(4)

S u r r o u n d i n g atmosphere

P r o p e r t i e s o f m e t a l - w o r k i n g components

(1) Workpiece: m a t e r i a l , geometry and dimensions, c o m p o s i t i o n , d u c t i l i t y , hardness, s u r f a c e roughness, p r e t r e a t m e n t (2)

D i e : m a t e r i a l , geometry and dimensions, c o m p o s i t i o n , s u r f a c e c o a t i n g ( i f a n y ) , hardness, s u r f a c e roughness

(3)

L u b r i c a n t : type, chemical composition, v i s c o s i t y , T-T-

(4)

(c)

and 1 - p - b e h a v i o u r , - q - s t r a i n o r v e l o c i t y dependence

Atmosphere: c o m p o s i t i o n , h u m i d i t y

T r i b o l o g i c a l processes a t t h e w o r k p i e c e - t o o l i n t e r f a c e

-

c o n t a c t d e f o r m a t i o n processes: t y p e , s t a t e o f s t r e s s and s t r a i n , s t a t e o f deformation

-

adhesion and t r i b o c h e m i c a l processes

-

f r i c t i o n processes wear processes, w i t h r e s p e c t t o (1) workpiece and ( 2 ) d i e

IV.

l u b r i c a t i o n modes

T r i b o l o g i c a l "loss-output'' c h a r a c t e r i s t i c s

-

f r i c t i o n d a t a ( a l s o amount o f f r i c t i o n - i n d u c e d power l o s s o r heat generation)

-

wear and p i c k u p d a t a and s u r f a c e c o n d i t i o n o f d i e s u r f a c e c o n d i t i o n o f workpiece

I n a d d i t i o n t o t h i s g e n e r a l c o m p i l a t i o n o f e f f e c t s and parameters o f t h e t r i b o l o g y o f m e t a l - w o r k i n g processes, t y p i c a l ranges o f t h e b a s i c o p e r a t i n g v a r i a b l e s o f p r e s s u r e , p r o d u c t speed and temperature a r e o u t l i n e d i n T a b l e 8.16 f o r t h e main m e t a l - w o r k i n g processes.

348 Basic operating variables M e t a l w o r k i n g process

temperature

. .

(OC)

0.0005 ( b a r and t u b e )

. . .20

I

...1 ieavier wire)

.

, ,15-30 fine wire)

c o l d : room temperature t AT=200-300 warm: 400-600 h o t : 800 f o r Mo,W

i 4 \ a tmos uhere

I

Pressing

, .80

0.02-0.5

5-25 (cold rolling) 20-150 0.1-0.5 (hot r o l l ing)

+

I Forgi

0.02-0.2 30- 130

( h y d r . presse:

. . .10 (hammers)

I

Extrusion

0.05

( I' h o t s h o t I' ) 100-200 0.5-5

room or elevated temperature (e.9. 500-800 for Ti)

room temperature or elevated temperature (400-1250, h o t r o l l ing) 100-200 (cold)

500-600 (warm )

..

.1200 (hot forging)

room or elevated temperature (1000-1200 hot extrusion: 600 non-ferroL

L

Table 8.16

Some c h a r a c t e r i s t i c s o f m e t a l - w o r k i n g processes.

349

(d)

FOLLOW-UP

Clearly, t h e given compilation o f c h a r a c t e r i s t i c s o f metal -working processes m u s t be s p e c i f i e d and e x t e n d e d f o r a g i v e n a c t u a l s i t u a t i o n . However, t h e s y s t e m a t i c c o m p i l a t i o n o u t l i n e d i n b r i e f may b e u s e d f o r p u r p o s e s o f m a t e r i a l and l u b r i c a n t s e l e c t i o n as w e l l as a framework f o r r e p o r t i n g e x perimental variables o r performing simulative t r i b o - t e s t i n g o f metal-working processes.

350

Appendix A compilation of basic tribo- engineering systems The t r e a t i s e on t h e t r i b o l o g y o f mechanical systems, p r e s e n t e d i n t h i s volume i n a g e n e r a l i z e d manner, a p p l i e s t o a g r e a t v a r i e t y o f a c t u a l t r i b o e n g i n e e r i n g systems. As a supplement t o t h e g e n e r a l t r e a t i s e on t h e t r i b o l o g y o f mechanical systems, a c o m p i l a t i o n o f b a s i c e n g i n e e r i n g systems i n which t r i b o l o g i c a l processes, i .e.,

c o n t a c t , f r i c t i o n , l u b r i c a t i o n and wear

processes, occur i s g i v e n i n t h i s s e c t i o n o f t h e appendix. I n general terms, a t r i b o - e n g i n e e r i n g system i s d e f i n e d as an e n t i t y whose t e c h n i c a l f u n c t i o n i s connected w i t h " t h e i n t e r a c t i o n o f m a t e r i a l s u r f a c e s i n r e l a t i v e motion". I t was d e s c r i b e d i n Chapter 3 how t h e t e c h n i c a l f u n c t i o n s r e a l i z e d through i n t e r a c t i n g m a t e r i a l s u r f a c e s can be b r o a d l y c l a s s i f i e d i n t h e f o l l o w i n g groups: (a)

Transmission o f MOTION

(b)

Transmission o f WORK ( o r POWER)

(c) (d)

T r a n s p o r t a t i o n o f MATERIALS

(e)

Forming o f MATERIALS

Generation o r r e p r o d u c t i o n o f INFORMATION

Using t h i s c l a s s i f i c a t i o n , a c o m p i l a t i o n o f b a s i c t r i b o - m e c h a n i c a l systems o f technology and b i o l o g y i s g i v e n i n t h e f o l l o w i n g . Most o f t h e t r i b o systems named can be a d d i t i o n a l l y c l a s s i f i e d . F o r example, t h e group o f " s l i d i n g b e a r i n g s " can be c l a s s i f i e d f u r t h e r i n t o j o u r n a l b e a r i n g s , t h r u s t bearings, dry bearings, f l u i d bearings, etc.,

o r t h e group o f "human j o i n t s "

can be c l a s s i f i e d f u r t h e r i n t o h i p j o i n t s , knee j o i n t s , e t c . While n o t c l a i m i n g t o be complete, t h i s l i s t i n g shows t h e e x t r e m e l y wide r e l e v a n c e o f t h e t r i b o l o g y o f mechanical systems. I t s h o u l d be emphasized t h a t t h e sys-

361 terns l i s t e d below are the basic, i.e.,

t h e " s i m p l e s t " , tribo-mechanical

systems which may be combined t o systems o f h i g h e r r a n k i n g o r d e r

-

i.e.,

complete machines, instruments, vehicles, e t c . - as e x p l a i n e d i n Chapter 2, F i g u r e 2.1.

I

T r i bo-engineering system ( o r t r i b o - e n g i n e e r i n g processes)

Primary t e c h n i c a l f u n c t i o n

t

( a l ) Guidance o r transmission o f

I S1 i d i n g bearings B a l l and r o l l e r bearings Needle bearings P i v o t bearings Gyros cop ic bea r in gs Guides S1 ideways Ball-and-screw mechanisms Spindles Hinges Engineering j o i n t s Human and animal j o i n t s Shoe ( o r f o o t ) on ground

MOTION

4

~

(a2) Coupling o f MOTION

F1anges Gear couplings Splines Cone clutches Disc clutches Band clutches

(a3) A n n i h i l a t i o n o f MOTION

Block brakes Band brakes Disc brakes Fastener sets Bol t sets F r i c t i o n dampers

I ~

(b)

Transmission o f WORK o r POWER

Rack-and-pinions Spur gears Bevel gears Hypoid gears P l a n e t a r y gears Worm gears Power screws Chain d r i v e s Be1t d r i v e s Rope d r i v e s Crank d r i v e s Cam d r i v e s Actuators F r i c t i o n drives Hydraulic drives

352

T r i bo-engineering system ( o r t r i bo-engineering processes)

Primary technical f u n c t i o n

( c l ) Generation o f INFORMATION

C1ock-works Cam-and-fol lowers E l e c t r i c a l contacts Switches Re 1ays Printing units Typewriter u n i t s Writing units

(c2) Reproduction o f INFORMATION

Tape-recorder heads S1 i p - r i n g assemblies Audio pick-ups Video pick-ups

( d l ) Transportation o f MATERIALS

Wheel and r a i l Tyre and road Pipe1 ines Conveyors Earth movement u n i t s Human and animal veins

(d2) Control o f f l o w o f MATERIALS

Seals Valves Packings Washers Piston-cyl inder assemblies

( e l ) Forming o f MATERIALS

Drawing Deep drawing Pressing Extrusion Forging

Rolling Casting I n j e c t i o n moulding Spinning Weaving ~~~

(e2) Tearing o f MATERIALS

~

Mining Well d r i l l i n g Quarrying Comminution Dredging Human and animal t e e t h

363

Primary technical f u n c t i o n

(e3) Machining o f MATERIALS

Tribo-engineering system ( o r tribo-engineering processes Cutting Punching Sawing Filing Turning Shaping and Planing Boring D r i 11i n g Grinding Abrasive c u t t i n g Chipless c u t t i n g Lapping Polishing B1a s t i n g Brushing

Suppl ement ing remark: The compilation o f basic tribo-engineering systems shows t h e g r e a t v a r i e t y o f mechanical systems i n which f r i c t i o n , l u b r i c a t i o n , and wear processes occur. While i t i s n o t p o s s i b l e t o deal w i t h s p e c i f i c d e t a i l s o f the i n d i vidual tribo-engineering systems w i t h i n t h e scope o f t h i s volume, the trib o l o g i c a l fundamentals r e l e v a n t t o the various mechanical systems are presented i n t h e preceding chapters under the headings:

-

Contact processes, Section 4.2, page 47 F r i c t i o n processes, Section 4.3, page 69 --Wear processes, Section 4.4, page 97 L u b r i c a t i o n modes, Section 4.5, page 130

-

The influences o f f r i c t i o n and wear processes on mechanical engineering systems are discussed i n general t e n s under t h e headings: S t r u c t u r a l aspects : --D Surface topography changes, Section 5.2.1, page 179 Surface composition changes, Section 5.2.2, page ,186 -L Surface s t r e n g t h p r o p e r t i e s changes, Section 5.2.3, page 191 Solutions f o r no-wear conditions, Section 5.4, page 199 Functional aspects:

-

Dynamic behaviour, Section 6.2.1, page 215 S t i c k - s l i p e f f e c t s , Section 6.2.2, page 218 -- E f f i c i e n c y , Section 6.3, page 221 F a i l u r e and safety, Section 6.4, page 227 R e l i a b i l i t y , Section 6.5, page 234 Machinery c o n d i t i o n monitoring, Section 7.5, page 277 ----c Requirements f o r proper f u n c t i o n a l behaviour, Section 6.6,

page 240

354

Appendix (B) Elements of tri bo-engineering systems The t r i b o - e n g i n e e r i n g systems c o m p i l e d i n Appendix ( A ) c o n s i s t o f ( m a t e r i a l ) elements d i r e c t l y i n v o l v e d i n t h e c o n t a c t , f r i c t i o n , l u b r i c a t i o n and wear processes. The components f o r m i n g t h e " i n t e r a c t i n g s u r f a c e s i n r e l a t i v e mot i o n " o f a g i v e n t r i b o - e n g i n e e r i n g system a r e termed t r i b o - e l e m e n t (1) and t r i b o - e l e m e n t ( 2 ) . I t was emphasized i n Chapters 4 and 5 t h a t f o r an unders t a n d i n g o f f r i c t i o n , l u b r i c a t i o n and wear, t h e i n t e r a c t i o n o f a l l t h e mater i a l elements i n v o l v e d i n t h e i n t e r f a c i a l t r i b o l o g i c a l processes must be taken i n t o c o n s i d e r a t i o n . Thus, t h e i n t e r f a c i a l medium ( 3 ) ( i f any) between components (1) and ( 2 ) and t h e s u r r o u n d i n g medium ( 4 ) a r e i n t e g r a l c o n s t i t u e n t o f any t r i b o - e n g i n e e r i n g system. I n t h e f o l l o w i n g , t h e elementary e l e ments ( l ) , ( Z ) ,

(3), ( 4 ) o f t r i b o - e n g i n e e r i n g systems a r e l i s t e d as examples

from e v e r y group o f t h e b a s i c t r i b o - e n g i n e e r i n g systems c o m p i l e d i n Appendix

(A)

*

356

T r i bo-engi n e e r i ng sys tern ( o r process)

1

Elements o f the system T r i bo-element

(1) (moving o r stationary)

T r i bo-element (2) (moving o r stationary)

Interfacial medi um

Surrounding medium

(3)

(4)

(all S l i d i n g bearing Human h i p j o i n t

Shaft Femur

Bushing Acetabulum

Lubricant Synov ia

(a21 Band c l u t c h Spline

Shaft Inner s p l i n e

Band Outer s p l i n e

Grease

(a3 1 Disc brake Fastener s e t

Disc Bolt

Pad Nut

Contami n ant

Air Air

worm Shaft

Gear Be1t

Gear o i l

3el t d r i v e

Air Air

(cl) :am and f o l l o w e r Printing u n i t

Cam P r i nt-head

Fol 1ower Paper

Lubricant Dye

Air

Brush Sapphire t i p

Spray

Cover gas Air

idheel Fluid

Rai 1 Pipe

Contaminant

Air

P1ug Piston r i n g

Val ve-body Cylinder

Fluid Lubricant

Fluid Fluid

tot extrusion

dire 3 i llet

Die Die

Borax G1ass

Air Air

[e2) Jell d r i l l i n g lredgi ng

3orer kedge

Soil Earth

Jorkpiece lorkpiece

Cutting tool Grinding whee

(b)

dorm gear s e t

(c2) E l e c t r i c a l contaci Ring h d i o pick-up Record

id2) la1 ve 'iston assembly

:el) h redrawing

:a31

rurning kinding

-

-

-

-

Cutting f l u i c Cutting f l u i o

Air

-

Air Air

Air

-

Air

Air Air

356

Appendix (C) Bibliographic work: DOCUMENTATION TRIBOLOGY

The l i t e r a t u r e in the f i e l d of tribology i s extremely voluminous owing t o the vast number o f topics included. For example, as mentioned already in Section 1.3, in the period 1966 t o 1977 some 55,000 papers were published i n t h i s f i e l d . An international and comprehensive bibliography i s provided by the DOCUMENTATION TRIBOLOGY:

-

an annual systematic bibliography of t i t l e s covering the e n t i r e f i e l d of wear, f r i c t i o n and lubrication, including l i t e r a t u r e from a l l over the world (English translations of the t i t l e s are given in brackets wherever the t i t l e s are Non-English), a comprehensive source material, also referring t o parallel publications, translations and abstract material, edited and published by the Bundesanstal t f u r Materialprufung (BAM) in Berlin (West), Germany

-

-

p r o v i d i n g d i r e c t and easy access t o required re7erences from various points of i n t e r e s t by a detailed and lpgical classification of the f i e l d , consisting o f ten main sections and more than 100 subsections, relieving the individual s c i e n t i s t o r engineer of the pains of currently scanning the l i t e r a t u r e and registering the relevant t i t l e s referring t o his/her f i e l d of i n t e r e s t , total number o f references a t present 6000-8000 t i t l e s per year, among these are:

357 m a t e r i a l s and p a i r i n g s w e a r - r e s i s t a n t coatings lubricants, lubricant testing bearings transmissions manufacturing processes, t o o l s

-

650 450 600 1250 250 1200

may be ordered through a bookstore o r d i r e c t l y from t h e p u b l i s h e r : BAM, Unter den Eichen 87,

D-1000 B e r l i n 45 I n the f o l l o w i n g , a summary o f the c l a s s f i c a t i o n o f main sections and subsections of t h e

DOCUMENTATION TRIBOLOGY i s given:

1.

General, monographs, reviews

2.

Experimental methods and equipment

3.

T r i b o l o g i c a l fundamentals, f r i c t i o n and wear: laws, mechanisms, e f f e c t s

3.1

Mechanical and a c o u s t i c a l phenomena

3.2

Chemical , physi co-chemical and thermal phenomena

3.3

E l e c t r i c a l and o p t i c a l phenomena

4.

Appearance o f damage

5.

Wear and f r i c t i o n under s p e c i f i c s t r e s s i n g c o n d i t i o n s

5.0 5.1 5.2 5.3

6.

Resting and p r e l i m i n a r y displacement i n s t a t i c f r i c t i o n Sliding, including s t i c k - s l i p Rolling, r o l l i n g with s l i d i n g Spin

5.4

Impact

5.5

Grain s l i d i n g

5.6

Fretting, f r e t t i n g corrosion

5.7

Wear caused by f l o w i n g media

5.8

Thermal wear, a b l a t i o n

M a t e r i a l s and combinations o f m a t e r i a l s ( w i t h and w i t h o u t i n t e r m e d i a t e m a t e r i a l s ) 6.1

Metals

6.2

Minerals, ceramics

6.3 6.4

Composites ( g l a s s - f i b r e r e i n f o r c e d m a t e r i a l s , cermets,

Polymers ( p l a s t i c s and rubber) laminated m a t e r i a l s e t c . )

358

6.8

Textile materials, leather

6.9

Other m a t e r i a l s and combinations o f m a t e r i a l s ( i n c l u d i n g wood, paper, shoe soles, f l o o r i n g s , g r a n u l a r m a t e r i a l s , b i o l o g i c a l materials, dental m a t e r i a l s )

7.

I n f l u e n t i a l f a c t o r s and c o n t r o l parameters 7.1

7.2

7.3

M a t e r i a1 -dependent f a c t o r s 7.1.1

Strength

7.1.2

Composition, t e x t u r e , s t r u c t u r e

7.1.9

Other material c h a r a c t e r i s t i c s ( i n c l u d i n g c o m p a t i b i l i t y )

Surface-dependent f a c t o r s 7.2.1

Topography

7.2.2

S u r f a c e l a y e r s (adsorbed f i l m s , o x i d e l a y e r s )

7.2.3

S u r f a c e t r e a t m e n t (mechanical and h e a t t r e a t m e n t )

7.2.4

Surface coatings

Operating conditions 7.3.1

7.4

8.

M o t i o n and v e l o c i t y

7.3.2

Shear f o r c e , l o a d

7.3.3

Temperature

7.3.4

Environment

Other i n f l u e n t i a l f a c t o r s 7.4.1

E l e c t r i c p o t e n t i a l , c u r r e n t passage

7.4.2

S o l i d i n t e r m e d i a t e p a r t i c l e s , d u s t , contaminants

7.4.3

Irradiation

7.4.4

Geometric f a c t o r s , e f f e c t s o f d e s i g n

Lubrication 8.1

T h i c k - f i l m l u b r i c a t i o n , e s p e c i a l l y hydrodynamic 1u b r i c a t i o n

8.2

T h i n - f i l m l u b r i c a t i o n (boundary 1u b r i c a t i o n , e l a s t o hydrodynamic l u b r i c a t i o n )

8.3

L u b r i c a t i o n i n s p e c i a l environments

8.4

L u b r i c a t i o n a t extreme temperatures

8.5

L u b r i c a t i o n under r a d i a t i o n and/or i n r e a c t o r t e c h n i q u e

8.6

Extreme p r e s s u r e l u b r i c a t i o n

8.7

L u b r i c a n t s , 1u b r i c a n t t e s t i n g

8.8

L u b r i c a t i o n systems and methods

8.9

Hygiene and m i c r o b i o l o g i c a l problems

359

9.

F i e l d s o f a p p l i c a t i o n . T e c h n i c a l designs and processes 9.0

L i f e , r e l i a b i l i t y and maintenance o f t e c h n i c a l systems

9.1

Machinery and components: s e l e c t i o n and performance

9.2

9.1.1

Bearings

9.1.2

Transmissions

9.1.3

Couplings, c l u t c h e s and b r a k e s

9.1.4

Seals

9.1.5

Machines, s e t s . V e h i c l e s and v e s s e l s

9.1.6

Wheel and r a i l

9.1.7

T y r e and r o a d

9.1.8

Specific industries

9.1.9

O t h e r machine elements and p r o d u c t s

M a n u f a c t u r i n g processes. T o o l s 9.2.1

10.

Forming

9.2.2

Chipless c u t t i n g

9.2.3

Machining

9.2.4

Surface f i n i s h i n g

9.2.5

Joining

9.2.6

Coating

9.3

Materials testing

9.4

Rock mechanics, geomechanics

B a s i c i n f o r m a t i o n on s o l i d s u r f a c e s and c o n t a c t s 10.1

S o l i d surfaces 10.1.1 10.1.2

Morphology S t r e n g t h , s u r f a c e t e n s i o n and energy, chemical r e a c t i o n s , environmental e f f e c t s

10.2

Contacts 10.2.1

Area o f c o n t a c t , d e f o r m a t i o n o f c o n t a c t , h e a t t r a n s f e r

10.2.2

J o i n t c h a r a c t e r , adhesion

360

References

CHAPTER 1.1

1.2

1

R.H. Cannon, Jr., Dynamics o f Physical Systems, Mc Graw-Hill, New York, 1967. A Glossary o f Terms and D e f i n i t i o n s , Organisation f o r Tribology Economic Co-operation and Development, OECD, Paris, 1969.

-

1.3

L u b r i c a t i o n (Tribology) Education and Research - A r e p o r t on the present p o s i t i o n and i n d u s t r y ' s needs, Her Majesty's Stationery Office, London, 1966.

1.4

F.P. Bowden and D. Tabor, The F r i c t i o n and L u b r i c a t i o n o f Solids, Clarendon Press, Oxford, 1964.

1.5

E. Rabinowicz, F r i c t i o n and Wear o f Materials, Wiley, New York, 1965.

1.6

1 . V . K r a g e l s k i i , F r i c t i o n and Wear, Butterworths, London, 1965.

1.7

A. Cameron, The P r i n c i p l e s o f Lubrication, Longmans, London, 1966. J. H a l l i n g ( E d i t o r ) , P r i n c i p l e s o f Tribology, MacMillan, London, 1975. G. Amontons, De l a Resistance Caus6e dans l e s Machines, H i s t o i r e Acad. Roy. Sci., Paris, 12(1699) 206.

1.8 1.9 1.10

E. Coulomb, Th'eorie des machines simples, Mem. Math. Phys., Paris , 10( 1785) 161. 1.11 J.T. Desagulier, A Course o f Experimental Philosophy, London , 1734. 1.12 L. Reti ( E d i t o r ) , Leonardo-Kunstler, Forscher, Magier, S. Fischer Verlag, Frankfurt, 1974.

1.13

W.B. Hardy and J.K. Hardy, Note on s t a t i c f r i c t i o n and on the l u b r i c a t i n g properties o f c e r t a i n chemical substances, P h i l . Mag., 6(1919) 32.

361

1.14 G.A. Tomlinson, A molecular theory o f f r i c t i o n , P h i l . Mag., 7 (1929) 905. 1.15 R. Holm, Die Reibungskraft i n der wahren Kontaktflache, Wiss. V e r o f f . Siemens Werke, 17(1938) 38. 1.16 H. E r n s t and M.E. Merchant, Surface f r i c t i o n between metals -

A basic f a c t o r i n the metal c u t t i n g process, Proc. Special Summer Conf. F r i c t i o n and Surface F i n i s h , M I T Press, Cambridge, Mass., 1940, p. 76. 1.17 F.P. Bowden and D. Tabor, The theory o f m e t a l l i c f r i c t i o n and t h e r o l e o f shearing and ploughing, Council Sci. and Ind. Research, Comm. o f A u s t r a l i a , B u l l e t i n 145, 1942. 1.18 F.P. Bowden and 0. Tabor, The F r i c t i o n and L u b r i c a t i o n o f S o l i d s , Clarendon Press, Oxford, 1954.

1.19

M. Fuchsel, Ober V e r s c h l e i B b a r k e i t d e r Werkstoffe b e i trockener Reibung, Organ F o r t s c h r . Eisenbahnwes., 84( 1929) 413.

1.20 M. F i n k und U. Hofmann, Zur Theorie der Reiboxydation, A r c h i v Eisenhuttenwes., 6(1932) 161. 1.21 R. Mailander und K. Dies, B e i t r a g z u r Erforschung d e r Vorgange beim VerschleiR, Tech. M i t t . Krupp Forsch.-Ber., 5(1942) 209. 1.22 E. Siebel, Ober d i e p r a k t i s c h e Bewahrung der m i t VerschleiRversuchen gewonnenen Ergebnisse, Tagungsband VDI-VerschleiDtagung, S t u t t g a r t , 1938, 5.4.

1.23 I-Meng Feng, Metal t r a n s f e r and wear, J. Appl. Phys., 23( 1952) 1011. J.T. Burwell and C.D. Strang, On t h e e m p i r i c a l law o f adhesive wear, J. Appl. Phys., 23(1952) 18.

1.24 M. Kerridge, Metal t r a n s f e r and t h e wear process, Proc. Phys. SOC. B, London, 68(1956) 400. 1.25 J.F. Archard, Contact and rubbing o f f l a t surfaces, J . Appl. Phys. 24(1953) 24. J.F. Archard and W . H i r s t , The wear o f metals under u n l u b r i c a t e d c o n d i t i o n s , Proc. Roy. SOC., London, A 236(1956) 397. 1.26 J.T. Burwell, Survey o f p o s s i b l e wear mechanisms, Wear, l(1957) 119. 1.27 c i t e d i n : R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. 11, Addison-Wesley, Reading, 1964, p. 40-3.

1.28 0. Reynolds, On t h e theory o f l u b r i c a t i o n and i t s a p p l i c a t i o n t o Mr. Beauchamp Tower's experiments, i n c l u d i n g an experimental determination o f t h e v i s c o s i t y o f o l i v e o i l , P h i l . Trans.,

177( 1886) 157. 1.29

R. S t r i b e c k , Die wesentlichen Eigenschaften der G l e i t - und Rollenlager, V D I - Z e i t s c h r i f t . 46(1902) 1341, 1432, 1463.

1.30 A. Sommerfeld, Zur hydrodynamischen Theorie der Schmiermittelreibung, Z . Math. Phys., 50(1904) 97. 1.31 C. B i e l , Die Reibung i n G l e i t l a g e r n b e i Zusatz von V o l t o o l zu Mineral01 und b e i Veranderung der Umlaufzahl und der Temperatur, V D I - Z e i t s c h r i f t , 64(1920) 449, 483.

362

1.32

G. Vogelpohl , B e t r i e b s s i c h e r e G l e i t l a g e r , S p r i n g e r V e r l ag , B e r l i n , 1958.

1.33 W.B. Hardy and J. Doubleday, Boundary l u b r i c a t i o n , The p a r a f f i n s e r i e s , Proc. Roy. SOC., London, A lOO(1922) 550. 1.34 K. Kirschke, H. Czichos, K.-H. Habig, P. S t u d t , T r i b o l o g i e F o r s c h u n g s b e r i c h t zum Schwerpunktprogramm VerschleiB, Reibung, Schmierung, Franz S t e i n e r Verlag, Wiesbaden, 1971.

1.35

The i n t r o d u c t i o n o f a new technology, Report 1966-1972 o f t h e Committee on T r i b o l o g y , Her M a j e s t y ’ s S t a t i o n e r y O f f i c e , London, 1973.

1.36

G.H. G o t t n e r , T r i b o l o g i e - B e g r i f f , Wesen und Bedeutung, Schmiertechnik und T r i b o l o g i e , 17( 1970) 285.

1.37

P. J o s t , Some economic f a c t o r s o f t r i b o l o g y , Proc. JSLE-ASLE I n t e r n a t . L u b r . Conf. ( E d i t o r : T. S a k u r a i ) , E l s e v i e r , Amsterdam, 1976, p. 2 .

1 . 3 8 D. Summers-Smith, 10 y e a r s a f t e r J o s t : t h e e f f e c t on i n d u s t r y , Proc. T r i b o l o g y Convention, I n s t . Mech. Engrs, 1976, p. 21. 1.39 DOCUMENTATION TRIBOLOGY - Wear, F r i c t i o n and L u b r i c a t i o n , 11 Volumes, 1967-1974, E d i t e d by B u n d e s a n s t a l t f u r M a t e r i a l p r u f u n g (BAM), Fachgruppe Rheologie und T r i b o l o g i e , D-1 B e r l i n 45.

CHAPTER 2 2.1 2.2

L. von B e r t a l a n f f y , Genetal System Theory, Penguin, Condm, 1971. K.E. Boulding, General systems t h e o r y Management Science, 2 ( 1956) 197.

-

-

t h e s k e l e t o n o f science,

2.3

G. Ropohl, Systemtechnik Munchen, 1975.

Grundlagen und Anwendung, Hanser Verlag,

2.4

M.D. Mesarovic, Views on General Systems Theory, Wiley, New York, 1964.

2.5

G.J. K l i r , An Approach t o General Systems Theory, Van Nostrand Reinhold, New York, 1969.

2.6

J . J . van Dixhoorn and F.J. Evans, ( E d i t o r s ) , P h y s i c a l S t r u c t u r e i n Systems Theory, Academic Press, London, 1974.

2.7

P. F a u r r e and M. Depeyrot, Elements o f System Theory, N o r t h Holland, Amsterdam, 1977.

2.8

S. Seely, An I n t r o d u c t i o n t o E n g i n e e r i n g Systems, Pergamon, New York, 1972, p. 55.

2.9

J.U. Thoma, I n t r o d u c t i o n t o Bond Graphs and T h e i r A p p l i c a t i o n , Pergamon, Oxford, 1975, p. 167.

2.10

H.M. Paynter, A n a l y s i s and Design o f E n g i n e e r i n g Systems (Class notes f o r M.I.T. course 2.751), The M.I.T. Press, Cambridge, Mass., 1960.

2.11

0. Karnopp and R. Rosenberg, Systems Dynamics: A U n i f i e d Approach, W i l e y , New York, 1975.

363 2.12

N. Wiener, C y b e r n e t i c s o r C o n t r o l and Communication i n t h e Animal and t h e Machine, The M.I.T. Press, Cambridge, Mass., 1948.

2.13

A.D. H a l l , A Methodology f o r Systems E n g i n e e r i n g , Van Nostrand, New York, 1962.

CHAPTER 3 3.1

G. F l e i s c h e r , Systembetrachtungen z u r T r i b o l o g i e , Wiss. Z . TH Magdeburg, 14(1970) 415.

3.2

G. Salomon, A p p l i c a t i o n o f systems t h i n k i n g t o t r i b o l o g y , ASLE Trans, 17(1974) 295.

3.3

H. Czichos, The p r i n c i p l e s o f systems a n a l y s i s and t h e i r a p p l i c a t i o n t o t r i b o l o g y , ASLE Trans, 17(1974) 300.

3.4

H. Czichos, Systemanalyse und Physik t r i b o l o g i s c h e r Vorgange, T e i l 1: Grundlagen, T e i l 2: Anwendungen, S c h m i e r t e c h n i k und T r i b o l o g i e , 22(1975) 126 und 23(1976) 6.

3.5

H. Czichos, and J. Mdlgaard, Towards a g e n e r a l t h e o r y o f t r i b o l o g i c a l systems, Wear, 44(1977) 247.

3.6

J. Mfilgaard, The d r y wear o f m e t a l s as a process i n an open system, Wear, 32( 1975) 353.

3.7

W.M.J. Schlosser, A c o n t r i b u t i o n t o t h e s t u d y o f a n a l o g i e s o f power t r a n s m i s s i o n i n machines, Proc. J. Mech. E. London, 188(1974) 1.

3.8

J.U. Thoma, Bondgraph d e s i g n f o r h y d r o s t a t i c b e a r i n g s , T r i b o l o g y , 6(1973) 97.

3.9

J.N. Brdnsted, On t h e concept o f h e a t , Det K g l . Danske Videnskabernes Selskab, Mat.-fysk. Meddelelser, 19(1941) No. 8, 79p.

CHAPTER 4 4.1

A.D. de P a t e r and J.J. K a l k e r ( E d i t o r s ) , The Mechanics o f t h e C o n t a c t between Deformable Bodies, D e l f t U n i v e r s i t y Press, D e l f t , 1975.

4.2

F.F. L i n g , S u r f a c e Mechanics, Wiley, New York, 1973.

4.3

H. H e r t z , Ober d i e Beruhrung f e s t e r e l a s t i s c h e r Korper, J. f u r d i e r e i n e u. angew. Mathem., 92(1881) 156.

4.4

M.H. Jones, R.I.L. Howells, and S.D. P r o b e r t , S o l i d s i n s t a t i c c o n t a c t - a review, Wear, 12(1968) 225.

4.5

J.F. Archard, S u r f a c e topography and t r i b o l o g y , T r i b o l o g y , 7(1974) 213.

4.6

D.J. Whitehouse, The measurement and a n a l y s i s o f s u r f a c e s , T r i b o l o g y , 7(1974) 249.

4.7

T.R. Thomas, Recent advances i n t h e measurement and a n a l y s i s o f s u r f a c e microgeometry, Wear, 33j1975) 205.

4.8

H. v. Weingraber, M o g l i c h k e i t e n f u r e i n e s t a t i s t i s c h e Auswertung t e c h n i s c h e r Oberflachen, F e i n g e r a t e t e c h n i k , 19(1970) 416.

4.9

J. P e k l e n i k , Grundlagen z u r K o r r e l a t i o n s t h e o r i e t e c h n i s c h e r Oberflachen, I n d . Anz., 87(1965) 456.

364

4.10

A.M. Jones, P.W. O'Callaghan and S.D. P r o b e r t , P r e d i c t i o n o f c o n t a c t parameters f r o m t h e topographies o f c o n t a c t i n g surfaces, Wear, 31(1975) 89.

4.11

P.T. S u r a t k a r , S.M. P a n d i t and S.M. Wu, A s t o c h a s t i c approach t o t h e mode o f d e f o r m a t i o n and c o n t a c t between rough surfaces, Wear, 39(1976) 239.

4.12

J.F. Archard, Contact and r u b b i n g o f f l a t s u r f a c e s , J. Appl Phys., 24( 1953) 981.

4.13

J.F. Archard, E l a s t i c d e f o r m a t i o n and t h e laws of f r i c t i o n , Proc. Roy. SOC., London, A 243(1957) 190.

4.14

J.A. Greenwood and J.H. T r i p p , The e l a s t i c c o n t a c t o f rough spheres, Trans ASME: J . A p p l . Mech., 89(3967) 153.

4.15

A. S e i r e g and E.J. W e i t e r , Behaviour o f f r i c t i o n a l H e r t z i a n c o n t a c t s under i m p u l s i v e l o a d i n g , Wear, 8(1965) 208.

4.16

K.C. Ludema and D. Tabor, The f r i c t i o n and v i s c o - e l a s t i c p r o p e r t i e s o f p o l y m e r i c s o l i d s , Wear, 9(1966) 329.

4.17

R. S t r i b e c k , K u g e l l a g e r fur b e l i e b i g e Belastungen, V D I - Z e i t s c h r i f t , 45(1901) 73.

4.18

J.A. Greenwood and J.B.P. Williamson, The c o n t a c t o f n o m i n a l l y f l a t s u r f a c e s , Proc. Roy. SOC., London, A 295(1966) 300.

4.19

D.J. Whitehouse and J.F. Archard, The p r o p e r t i e s o f random s u r f a c e o f s i g n i f i c a n c e i n t h e i r c o n t a c t , Proc. Roy. SOC., London, A 316(1970) 97.

4.20

0. Tabor, A s i m p l i f i e d account o f s u r f a c e topography and t h e c o n t a c t between s o l i d s , Wear, 32(1975) 269.

4.21

J.F. N i c h o l a s , The d i s s i p a t i o n o f energy d u r i n g p l a s t i c d e f o r m a t i o n , Acta Met., 7(1959) 544.

4.22

H.C. Gatos, S t r u c t u r e o f s u r f a c e s and t h e i r i n t e r a c t i o n s , i n : I n t e r d i s c i p l i n a r y Approach t o F r i c t i o n and Wear, ( E d i t o r : P.M. NASA SP-181, Washington, 1968, p.7.

.

Ku),

4.23

G. Schmaltz, Technische Oberflachenkunde, S p r i n g e r , B e r l i n , 1936.

4.24

H.B.G. Casimir, Proc. K o n i n k l . Ned. Akad. Wetenshap, B 51(1948) 795.

4.25

B.J. B r i s c o e and 0. Tabor, S u r f a c e f o r c e s i n f r i c t i o n and adhesion, Faraday Spec. Disc. Chem. SOC., No. 2(1972) 7.

4.26

J.M. Ziman, E l e c t r o n s i n M e t a l s - A S h o r t Guide t o t h e Fermi Surface, T a y l o r and F r a n c i s , London, 1963.

4.27

J. F e r r a n t e and J.R. Smith, A t h e o r y o f adhesion a t a b i m e t a l l i c i n t e r f a c e : o v e r l a p e f f e c t s , Surface Science, 38(1973) 77.

4.28

J. F e r r a n t e and J.R. Smith, Metal i n t e r f a c e s : adhesive e n e r g i e s and e l e c t r o n i c b a r r i e r s , S o l i d s t a t e comm., 20(1976) 393.

4.29

H. Czichos, The mechanism o f t h e m e t a l l i c adhesion bond, J . Phys. 0: Appl. Phys., 5(1972) 1890.

4.30

D.H. Buckley, Adhesion o f v a r i o u s m e t a l s t o a c l e a n i r o n (011) s u r f a c e s t u d i e d w i t h LEED and Auger e m i s s i o n spectroscopy, NASA TN D-7018, Washington, 1971.

365

4.31

F.P. Bowden and G.W. Rowe, The adhesion o f c l e a n m e t a l s , Proc. Roy. SOC. London, A 233(1956) 429.

4.32

M.E. S i k o r s k i , C o r r e l a t i o n o f t h e c o e f f i c i e n t o f adhesion w i t h v a r i o u s p h y s i c a l and mechanical p r o p e r t i e s o f m e t a l s , Trans. ASME, D 85( 1963) 279.

4.33

D.H. Buckley, The i n f l u e n c e o f c r y s t a l s t r u c t u r e , o r i e n t a t i o n and s o l u b i l i t y on t h e adhesion and s l i d i n g o f v a r i o u s metal s i n g l e c r y s t a l s i n vacuum (10-11 T o r r ) , ASTM STP No. 431,

1967, p.248. 4.34

D.H. Buckley and R.L. Johnson, The i n f l u e n c e o f c r y s t a l s t r u c t u r e and some p r o p e r t i e s of hexagonal m e t a l s on f r i c t i o n and adhesion, Wear, l l ( 1 9 6 8 ) 405.

4.35

K.-H. Habig, Der E i n f l u B d e r g e g e n s e i t i g e n L o s l i c h k e i t von M e t a l l e n auf e i n i g e i h r e r t r i b o l o g i s c h e n Eigenschaften, M e t a l l o b e r f l a c h e , 24(1970) 375.

4.36

D.H. Buckley, F r i c t i o n , Wear and L u b r i c a t i o n i n Vacuum, NASA SP-277, Washington, 1971, p.66.

4.37

D.H. B u c k l e y , The i n f l u e n c e o f t h e atomic n a t u r e o f c r y s t a l l i n e m a t e r i a l s on f r i c t i o n , Trans. ASLE, l l ( 1 9 6 8 ) 89.

4.38

K.-H. Habig, Zur S t r u k t u r - und Orientierungsabhangigkeit d e r Adhasion und d e r trockenen G l e i t r e i b u n g von M e t a l l e n , M a t e r i a l p r u f u n g , lO(1968) 417.

4.39

D.H. Buckley, E f f e c t o f v a r i o u s m a t e r i a l p r o p e r t i e s on t h e adhesive stage o f f r e t t i n g , AGARD Conf. Proc. NO. 161, 1975, p. 13-1.

4.40

N. Gane, P.F. P f a e l z e r and D. Tabor, Adhesion between c l e a n s u r f a c e s a t l i g h t l o a d s , Proc. Roy. SOC., London, A 340(1974) 495.

4.41

K.L. Johnson, K. K e n d a l l and A.D. Roberts, S u r f a c e energy and t h e c o n t a c t o f e l a s t i c s o l i d s , Proc. Roy. SOC., London, A 324(1971) 301.

4.42

K.N.G. F u l l e r and 0. Tabor, The e f f e c t o f s u r f a c e roughness on t h e adhesion o f e l a s t i c s o l i d s , Proc. Roy. SOC., London, A 345(1975) 327.

4.43

R.D. M i n d l i n , Compliance o f e l a s t i c b o d i e s i n c o n t a c t , Trans. ASME, J . Appl. Mech., 71(1949) 259.

4.44

J . S . Mc F a r l a n e and 0. Tabor, R e l a t i o n between f r i c t i o n and adhesion, Proc. Roy. SOC., London, A 202(1950) 244.

4.45

J . S . C o u r t n e y - P r a t t and E. E i s n e r , 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 bodies, Proc. Roy. SOC., London, A 238(1957) 529.

4.46

H. Czichos, F e s t k o r p e r r e i b u n g Umschau (1971) 116.

4.47

M. Godet, S u r f a c e and shape e f f e c t s i n t h e measurement o f f r i c t i o n f o r c e s , Wear, 28(1974) 115.

4.48

R. C o u r t e l , Modes d ' i n t e r p r e t a t i o n de l a t r o i s i e m e dimensions dans l e s processus de f r o t t e m e n t i n t e r m g t a l l i q u e . Role du b o u r r e l e t f r o n t a l , B u l l . I n s t . S c i . Techn. du Centre E n e r g i e A t . , 90(1965) 3.

-

Teilgebiet der Tribologie,

366

4.49

L.A. M i t c h e l l and C . Osgood, A t h e o r y o f f r i c t i o n and wear based on a new c h a r a c t e r i z a t i o n o f a s p e r i t y i n t e r a c t i o n s , Wear, 40( 1976) 203.

4.50

D.H. B u c k l e y , The m e t a l - t o - m e t a l i n t e r f a c e and i t s e f f e c t on adhesiop and f r i c t i o n , J . C o l l . I n t e r f a c e S c i . , 58(1977) 36.

4.51

D. Tabor, I n t e r a c t i o n between Surfaces: Adhesion and F r i c t i o n , i n : S u r f a c e Physics o f M a t e r i a l s , Vol. I 1 ( E d i t o r : J.M. B l a k e l y ) Academic Press, New York, 1975, p. 475.

4.52

H. Czichos, D i e Energieverlustmechanismen d e r R o l l r e i b u n g , Schmiertechnik und T r i b o l o g i e , 16( 1969) 62.

4.53

0. Reynolds, On r o l l i n g f r i c t i o n , P h i l . Trans. Roy. SOC., London, 116( 1876) 155.

4.54

H.L. Heathcote, The b a l l b e a r i n g , Proc. I n s t n . Automotive Engrs, 15(1921) 1569.

4.55

F.W. C a r t e r , On t h e a c t i o n o f a l o c o m o t i v e d r i v i n g wheel, Proc. Roy. Soc., London, A 112(1926) 151.

4.56

H. P o r i t s k y , Stresses and d e f l e c t i o n s o f c y l i n d r i c a l bodies i n c o n t a c t w i t h a p p l i c a t i o n t o c o n t a c t o f gears and o f l o c o m o t i v e wheel, Trans. ASME, J. Appl. Mech., 72(1950) 191.

4.57

L. Foppl, D i e s t r e n g e Losung f u r d i e r o l l e n d e Reibung, Munchen, 1947.

4.58

D.

4.59

B.G. B r o t h e r s and G.R. Bremble, The e f f e c t o f g e o m e t r i c c o n f o r m i t y

Tabor, The mechanism of r o l l i n g f r i c t i o n , 11, t h e e l a s t i c range, Proc. Roy. SOC., London, A 229(1955) 198.

between a b a l l and i t s t r a c k on t h e f r e e r o l l i n g r e s i s t a n c e , Wear, 20(1972) 175.

4.60 4.61

0. Tabor, The mechanism o f r o l l i n g f r i c t i o n , P h i l . Mag., 43( 1952) 1055. D.G. Flom and A.M. Bueche, Theory o f r o l l i n g f r i c t i o n f o r spheres, J . Appl. Phys., 30(1959) 1725.

4.62

J.B. Halaunbrenner, E l a s t o - o p t i c a l i n v e s t i g a t i o n s o f r o l l i n g o f a r i g i d c y l i n d e r on a v i s c o - e l a s t i c base, Wear, 8(1965) 30.

4.63

K.R. Eldredge and 0. Tabor, The mechanism o f r o l l i n g f r i c t i o n , I, t h e p l a s t i c range, Proc. Roy. SOC.,

London, A 229(1955) 181.

4.64

L.D. Dyer, R o l l i n g f r i c t i o n on s i n g l e c r y s t a l s o f copper i n t h e p l a s t i c range, A c t a Met., 9(1961) 928.

4.65

K.L. Johnson, A r e v i e w o f t h e t h e o r y o f r o l l i n g c o n t a c t s t r e s s e s , Wear, 9(1966) 4.

4.66

A.W. Crook, Simulated g e a r - t o o t h c o n t a c t s : some experiments upon t h e i r l u b r i c a t i o n and s u b s u r f a c e deformations, Proc. Conf. Lubr. Wear, I , Mech. Eng., 1957, 701.

4.67

G. M. Hamilton, P l a s t i c f l o w i n r o l l e r s loaded above t h e y i e l d p o i n t , Proc. I n s t . Mech. Engrs, 177(1963) 667.

4.68

J.W. Merwin and K.L. Johnson, A n a l y s i s o f p l a s t i c d e f o r m a t i o n r o l l i n g c o n t a c t , Proc. I n s t . Mech. Engrs, 177(1963) 676.

4.69

H. Czichos, Ober den Zusammenhang zwischen Adhasion und E l e k t r o n e n s t r u k t u r von M e t a l l e n b e i d e r R o l l r e i b u n g i m e l a s t i s c h e n Bereich, Z. angew. Physik, 27(1969) 40.

367

4.70

K. K e n d a l l , R o l l i n g f r i c t i o n and adhesion between smooth s o l i d s , Wear, 33(1975) 351.

4.71

B.V. D e r j a g u i n and V.P. Smilga, E l e c t r o s t a t i c component o f t h e r o l l i n g f r i c t i o n f o r c e moment, Wear, 7(1964) 270.

4.72

J.H. Dismant, R e v i v i n g t h e c l a s s i c a l t h e o r y o f f r i c t i o n b y a modern d i s l o c a t i o n t h e o r y o f d e f o r m a t i o n r e v i s i o n , J. Appl. Phys., 31(1960) 221.

4.73

B.J. K o s t e t s k i i and P.V. Natarenko, I n f l u e n c e o f changes o f d i s l o c a t i o n s t r u c t u r e on t h e r e l a t i o n between f r i c t i o n and normal Doklady, p r e s s u r e (The Amontons-Coulomb l a w ) , S o v i e t P h y s i c s

-

9( 1965) 1011. 4.74

R. Feder and P. Chaudhari, Transmission e l e c t r o n microscopy of wear t r a c k s , Wear, 19(1972) 109.

4.75

G. E R. Schul t z e , Metal 1p hys ik , Akademi e - V e r l ag , Be r l in ,

.

1967, p. 217. 4.76

N. Gane and J. S k i n n e r , The g e n e r a t i o n o f d i s l o c a t i o n s i n m e t a l s under a s l i d i n g c o n t a c t and t h e d i s s i p a t i o n o f f r i c t i o n a l energy, Wear, 25(1973) 381.

4.77

G. A n d a r e l l i ,

4.78

J.G. B o l l i n g e r , Noise

4.79

D.M. T o l s t o i , S i g n i f i c a n c e o f t h e normal degree o f freedom and n a t u r a l normal 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,

4.80

Triboluminescence, d t v - L e x i k o n d e r P h y s i k , Deutscher TaschenbuchVerlag, Munchen, 1971, Bd. 9, p. 168.

4.81

J. F e r r a n t e , E x o e l e c t r o n e m i s s i o n f r o m a clean, annealed magnesium s i n g l e c r y s t a l d u r i n g oxygen a d s o r p t i o n , ASLE Trans., 20( 1977).

4.82

J . Wortmann, Z u r Exoelektronenemission (EEE), i n "Verhal t e n und

D. Maugis and R. C o u r t e l , O b s e r v a t i o n o f d i s l o c a t i o n s c r e a t e d by f r i c t i o n on aluminium t h i n f o i l s , Wear, 23(1973) 21.

-

an i n d u s t r i a l p o l l u t a n t o f i n t e r n a t i o n a l concern, C I R P Annals, 22( 1973) 197.

lO(1967) 199.

E i g e n s c h a f t e n von m e t a l l i s c h e n Oberflachen", TU B e r l i n , Fachbereich 17 (Fachseminar WS 75/76) 1976, p. 280.

4.83

H.S. Carslaw and J.C. Jaeger, Conduction o f Heat i n S o l i d s , Clarendon Press, Oxford, 1947, p. 56.

4.84

R. Holm, C a l c u l a t i o n o f t h e t e m p e r a t u r e development i n a c o n t a c t h e a t e d i n t h e c o n t a c t s u r f a c e , and a p p l i c a t i o n t o t h e problem o f t h e temperature r i s e i n a s l i d i n g c o n t a c t , J. Appl. Phys.,

4.85

19( 1948) 361. H. B l o k , T h e o r e t i c a l s t u d y o f temperature r i s e a t s u r f a c e s o f a c t u a l c o n t a c t under o i l i n e s s l u b r i c a t i n g c o n d i t i o n s , Proc. Gen. D i s c . Lubr., I n s t . Mech. Engrs, London, 1937, v o l . 2, p. 14.

4.86

J.F. Archard, The temperature o f r u b b i n g s u r f a c e s , Wear,

2( 1958/59) 438. 4.87

P.S. Kounas, A.D. Dimarogonas and G.N. Sandor, The d i s t r i b u t i o n o f f r i c t i o n h e a t between a s t a t i o n a r y p i n and a r o t a t i n g c y l i n d e r , Wear, 19(1972) 415.

4.88

F. Charron, Partage de l a c h a l e u r e n t r e deux corps f r o t t a n t s , E d i t i o n s Blonde1 l a Rougery, P a r i s , 1943.

368

4.89

J.F. Archard, Wear, i n : I n t e r d i s c i p l i n a r y Approach t o F r i c t i o n and Wear (Editor: P.M. Ku), NASA SP-181, Washington, 1968, p. 267.

4.90

H. Czichos und K.-H. Habig, Grundvorgange des Verschleisses metal l i s c h e r Werkstoffe Neuere Ergebnisse der Forschung, VDI-Ber. N r . 194, 1973, S. 23.

4.91

P.A. Engel, Impact Wear o f Materials, Elsevier, Amsterdam, 1976. O.R. Lang, Surface f a t i g u e o f p l a i n bearings, Wear,

4.92

-

43(1977) 25. 4.93

K.H. Kloos und E. Broszeit, Zur Frage der Dauerwalzfestigkeit, Z. f . Werkstofftechnik, 5(1974) 181.

4.94

M.J.W. Schouten, Der E i n f l u B elastohydrodynamischer Schmierung auf Reibung, VerschleiB und Lebensdauer von Getrieben, Schmiertechnik und Tribologie, 20( 1973) 147.

4.95

W.E. Littmann, The mechanism o f contact fatigue, i n : I n t e r d i s c i p l i n a r y approach t o the l u b r i c a t i o n o f concentrated contacts, NASA SP-237, Washington, 1970, p. 309. Y.P. Chiu, T.E. T a l l i a n and J . I . Mc Cool, An engineering model o f s p a l l i n g fatigue f a i l u r e i n r o l l i n g contact, I , The subsurface model, Wear, 17(1971) 433.

4.96

T.E. T a l l i a n and J.I. Mc Cool, 11, The surface model, Wear, 17(1971) 447.

T.E. T a l l i a n , 111, Engineering discussion and i l l u s t r a t i v e examples, Wear, 17(1971) 463.

4.97

J . C . Tyler, R.A. Burton and P.M. Ku, Contact f a t i g u e under o s c i l l a t o r y normal load, ASLE Trans., 6(1963) 255.

4.98

P. Haasen, Physi kal ische Metal 1kunde, Springer-Verlag, B e r l i n , 1974, p. 298.

4.99

D. Kuhlmann-Wilsdorf and C, Laird, D i s l o c a t i o n behaviour i n fatigue, Mat. Sci. Eng. , 27(1977) 137. E. Hornbogen, The r o l e o f f r a c t u r e toughness i n the wear o f metals, Wear, 33(1975) 251.

4.100

4.101 N.P. Suh, The delamination theory o f wear, Wear, 25( 1973) 111. 4.102 J.P. H i r t h and D.A. Rigney, Crystal p l a s t i c i t y and the delamination theory o f wear, Wear, 39(1976) 133. 4.103 T.S. Eyre, Wear c h a r a c t e r i s t i c s of metals, Tribology I n t e r n a t i o n a l , (1976) 203. 4.104 K. Wellinger und H. Uetz, GleitverschleiB. SpulverschleiD, StrahlverschleiD u n t e r Wirkung von kornigen Stoffen, VDI-Forschungsheft 449, Beilage zu Forsch. Ing. Wes. Zl(1955) 1.

4.105 K. Wellinger, H. Uetz und M. Gurleyik, GleitverschleiBuntersuchungen 4.106

an Metallen und nichtmetallischen H a r t s t o f f e n unter Wirkung korniger Stoffe, Wear, ll(1968) 173. M.M. Khrushov, Resistance o f metals t o wear by abrasion; r e l a t e d t o hardness, Proc. Conf. Lubr. and Wear, I n s t n . Mech. Engrs, London, 1957, p. 655.

369 4.107

M.M. Khrushov, P r i n c i p l e s o f a b r a s i v e wear, Wear, 28(1974) 69.

4.108

R.C.D. Richardson, The wear o f m e t a l s by r e l a t i v e l y s o f t a b r a s i v e s , Wear, 11( 1968) 245.

4.109

P.L. H u r r i c k s , Some m e t a l l u r g i c a l f a c t o r s c o n t r o l l i n g t h e a d h e s i v e and a b r a s i v e wear r e s i s t a n c e o f s t e e l , a r e v i e w , Wear, 26(1973) 285.

4.110

H. Uetz und J . F o h l , V e r s c h l e i D und Reibung a l s komplexe mechanisch-physikal isch-chemische Prozesse, E r z m e t a l l , 23( 1970) 205.

4.111

D.H. Buckley, Wear and i n t e r f a c i a l t r a n s p o r t o f m a t e r i a l , NASA TMX-71781, 1975.

4.112

M. Cocks, S h e a r i n g o f j u n c t i o n s between metal s u r f a c e s , Wear, 9(1966) 320.

4.113

M. A n t l e r , Stages o f wear o f a prow f o r m i n g m e t a l , ASLE Trans. , 13( 1970) 79.

4.114

D. Landheer and J.H. Zaat, The mechanism o f m e t a l t r a n s f e r

4.115

i n s l i d i n g f r i c t i o n , Wear, 27(1974) 129. D.H. Buckley, E f f e c t o f v a r i o u s m a t e r i a l p r o p e r t i e s on t h e adhesive s t a g e o f f r e t t i n g , NASA TMX-71582,

1974.

4.116

P.A. Thiessen, K. Meyer und G. H e i n i c k e , Grundlagen d e r Tribochemie, Akademie-Verlag, B e r l i n , 1967.

4.117

T.F.J. Quinn, The e f f e c t o f " h o t s p o t " temperatures on t h e u n l u b r i c a t e d wear o f s t e e l , ASLE Trans., lO(1967) 158.

4.118

P.L. H u r r i c k s , The mechanism o f f r e t t i n g Wear, 15(1970) 389.

4.119

R.B.

4.120

R . B . Waterhouse, P h y s i c s and m e t a l l u r g y o f f r e t t i n g , AGARD-CP-161, 1975, p. 8-1.

4.121

H.

4.122

J. Mdlgaard, D i e E n t w i c k l u n g von VerschleiBprozeBthesen, Schmi e r t e c h n i k und T r i b o l o g i e, 23( 1976) 126.

4.123

see Ref. 1.29.

4.124

see Ref. 1.28.

-

a review,

Waterhouse, F r e t t i n g C o r r o s i o n , Pergamon, Oxford, 1972

Czichos, D i s c u s s i o n on t h e adhesive s t a g e o f f r e t t i n g , AGARD-CP-161, 1975, p. 13-16.

4.125

see Ref. 1.27,

4.126

M.D. Hersey, Theory and Research i n L u b r i c a t i o n , W i l e y , New York, 1966, p. 34.

4.127

H.C. R i p p e l , 0. Decker and Z. Zudans, NASA C o n t r i b u t i o n s t o A Survey, NASA SP-5058, Fluid-Film Lubrication Washington , 1969.

4.128

J. H o l l a n d , D i e E r m i t t l u n g d e r KenngroRen f u r z y l i n d r i s c h e G l e i t l a g e r , K o n s t r u k t i o n , 13( 1961) 100.

4.129

G. Vogelpohl, B e t r i e b s s i c h e r e G l e i t l a g e r , S p r i n g e r - V e r l a g , B e r l i n , 1958, p. 73.

Chapter 40.

-

370 4.130

D.F. Moore, P r i n c i p l e s and Applications o f Tribology, Pergamon, Oxford, 1975, p. 346.

4.131

J.J. O'Connor, J. Boyd, E.A. Avallone, ( E d i t o r s ) , Standard Handbook o f L u b r i c a t i o n Engineering, McGraw-Hill , New York, 1968. L.D. Wedeven, What i s EHD?, Lubr. Engng, 31(1975) 291.

4.132 4.133

F.H. Theyse, Elastohydrodynami k, Schmiertechni k, 15(1967) 15.

4.134

4.135

J.W. Kannel, J.C. B e l l and C.M. Allen, Methods f o r determining pressure d i s t r i b u t i o n s i n l u b r i c a t e d r o l l i n g contact, ASLE Trans., 8(1965) 250. see Ref. 1.7, p. 203.

4.136

0. Dowson and G.R. Higginson, New r o l l e r - b e a r i n g l u b r i c a t i o n

4.137

H.S. Cheng and F.K. Orcutt, A c o r r e l a t i o n between the t h e o r e t i c a l and experimental r e s u l t s on the elastohydrodynamic l u b r i c a t i o n o f r o l l i n g and s l i d i n g contact, Proc. I. Mech. E., London, Vol. 180, P a r t 38, (1965/66) 158. A.J. Petrousevitch, D.S. Kodnir, R.G. Salukvadze, D.L. Bakashvili and V.Sh. Schwarzman, The i n v e s t i g a t i o n o f o i l f i l m thickness i n l u b r i c a t e d b a l l - r a c e r o l l i n g contact, Wear, 19(1972) 369. F.J. Westlake and A. Cameron, Optical elastohydrodynamic f l u i d t e s t i n g , ASLE Trans., 15(1972) 81.

formula, Engineering, London, 192( 1961) 158.

4.138

4.139 4.140

A. Jackson, F i l m thickness i n EHL p o i n t contacts: r e v i s i o n o f Westlake and Cameron's equations, ASLE Trans., 19(1976) 48.

-

4.141

J. Tevaarwerk and K.L. Johnson, A simple non-linear c o n s t i t u t i v e equation f o r elastohydrodynamic o i l f i l m s , Wear, 35( 1975) 345.

4.142

0. Dowson, T r a n s i t i o n t o boundary l u b r i c a t i o n from elastohydrodynamic l u b r i c a t i o n , i n : Boundary Lubrication, (Editors: F.F. Ling, E.E. Klaus and R.S. Fein), ASME, New York, 1969, p. 229.

4.143

A. Dyson, discussion in: I n t e r d i s c i p l i n a r y approach t o the l u b r i c a t i o n o f concentrated contacts, NASA SP-237, Washington, 1970, p. 58. J.F. Archard, Elastohydrodynamic l u b r i c a t i o n o f r e a l surfaces, Tribology, 6(1973) 8. L.D. Wedeven, Traction and f i l m thickness measurements under starved elastohydrodynamic conditions, Trans. ASME, JOLT, 97( 1975) 321.

4.144 4.145

4.146

H. Munnich, E i n f l u B der Schmierung auf Lebensdauer, Reibung und VerschleiB von Walzlagern, Schmiertechnik und Tribologie, 16( 1968) 87.

4.147

V.K. Ausherman, H.S. Nagaraj, D.M. Sanborn and W.O. Winer, I n f r a r e d temperature mapping i n elastohydrodynamic l u b r i c a t i o n , Trans. ASME, F, 98(1976) 236. L. Gumbel, Der EinfluD der Schmierung auf d i e Konstruktion, Jb. schiffbautechn. Ges., 18(1917) 299.

4.148 4.149

G. Vogelpohl , Die Stribeck-Kurve a l s Kennzeichen des allgemeinen Reibungsverhaltens geschmierter GleitflPchen, VDI-Z., 96(1954) 261.

371

4.150 H. Christensen, A theory o f mixed l u b r i c a t i o n , Proc. I n s t n . Mech. Engrs, London, 186(1972) 421. 4.151 D. Berthe and M. Godet, A more general form o f Reynolds equation - a p p l i c a t i o n t o rough surfaces, Wear, 27(1974) 345. 4.152 K.L. Johnson, J.A. Greenwood and S.Y. Poon, A simple theory o f a s p e r i t y c o n t a c t i n elastohydrodynamic l u b r i c a t i o n , Wear,

19(1972) 91. 4.153 T.E. T a l l i a n , The theory o f p a r t i a l elastohydrodynamic contacts, Wear, Zl(1972) 49. 4.154 E.S. Forbes, Antiwear and extreme pressure a d d i t i v e s f o r l u b r i c a n t s , Tribology, 3(1970) 145. 4.155 P. Studt, Schmieroladditive f u r hohe Flachenpressung und i h r e Wirkung, VDI-Berichte, 156(1970). 4..156 D. Godfrey., Boundary l u b r i c a t i o n , i n Ref. 4.131, Chapter 2. 4.157 D. Godfrey, .Boundary l u b r i c a t i o n , i n : I n t e r d i s c i p l i n a r y Approach t o F r i c t i o n and Wear, ( E d i t o r : P.M. Ku), NASA SP-181, Washington, 1968, p. 335. 4.158 J.S. Courtney-Pratt, An o p t i c a l method o f measuring the thickness o f adsorbed monolayers, Proc. Roy. SOC., London, 212(1952) 505. 4.159 R. Holm, E l e c t r i c Contacts, H. Gebers Forlag, Stockholm, 1946, p. 198. 4.160 F.P. Bowden and D. Tabor, F r i c t i o n - An I n t r o d u c t i o n t o T r i b o l o g y , Heinemann, London, 1973, p. 128. 4.161 W.E. Campbell, Boundary l u b r i c a t i o n , i n : Boundary L u b r i c a t i o n , ( E d i t o r s : F.F. Ling, E.E. 1969, p. 87.

4.162

Klaus and R.S.

Fein), ASME, New York,

F.G. Rounds, I n f l u e n c e o f s t e e l composition on a d d i t i v e performance, ASLE Trans., 15(1972) 54. Fein, Chemistry i n concentrated - c o n j u n c t i o n l u b r i c a t i o n , i n : I n t e r d i s c i p l i n a r y Approach t o t h e L u b r i c a t i o n o f Concentrated Contacts, NASA SP-237, Washington, 1970, p . 489.

4.163 R.S. 4.164 C.N.

Rowe, Some aspects o f the heat o f a d s o r p t i o n i n t h e f u n c t i o n o f a boundary l u b r i c a n t , ASLE Trans., 9(1966) 100. Rowe, A r e l a t i o n between adhesive wear and heat o f adsorption f o r the vapor l u b r i c a t i o n o f graphite, ASLE Trans., lO(1967) 10.

4.165 C.N.

4.166 A. Dyson, S c u f f i n g - a review, T r i b o l o g y , 8(1975) 77 and 117. 4.167 T.v. M r m i n , Ober den Mechanismus des Widerstandes, den e i n bewegter Korper i n e i n e r F l u s s i g k e i t e r f a h r t , Nachrichten der K. Ges. d. Wissenschaften, Math-phys. Klasse, Gottingen, 1911.

4.168 G.I. Taylor, S t a b i l i t y o f a viscous l i q u i d contained between two r o t a t i n g c y l i n d e r s , Trans. Roy. SOC., London, A 223(1923) 289. 4.169 R.C. d i Prima, A note on t h e s t a b i l i t y o f f l o w i n loaded j o u r n a l bearing, ASLE Trans., 6( 1963) 249. 4.170 V.N. Constantinescu, Analysis o f bearings o p e r a t i n g i n t u r b u l e n t regime, Trans. ASME, D, 84(1962) 139. 4.171 E. Saibel, Turbulence i n l u b r i c a t i o n , i n Ref. 1.7, p. 441.

372 4.172

4.173

4.174

T.E. T a l l i a n , Y.P. Chiu, D.F. H u t t e n l o c her, J.A. Kamenshine, L.B. S i b l e y and N.E. S i n d l i n g e r , L u b r i c a n t f i l m s i n r o l l i n g c o n t a c t o f rough s u r f a c e s , ASLE Trans., 7(1964) 109. H. Czichos, Untersuchungen uber d i e V e r t e i l u n g met al1 i s c h e r und n i c h t m e t a l l i s c h e r K o n t a k t a n t e i l e b e i Mischreibung, Wear, 17(1971) 209. H. Czichos, I n f l u e n c e o f a s p e r i t y c o n t a c t c o n d i t i o n s on t h e f a i l u r e o f s l i d i n g elastohydrodynamic c o nt act s, Wear, 41(1977) 1.

4.175

R.S. Fein, C.N. Rowe and K.L. Kreuz, T r a n s i t i o n temperatures i n s l i d i n g systems, ASLE Trans., 2(1959) 50.

4.176 4.177

R.S. Fein, O p e r a t i n g procedure e f f e c t s on c r i t i c a l temperatures, ASLE Trans., 10( 1967) 373. H. Czichos and K. Kirschke, I n v e s t i g a t i o n s i n t o f i l m f a i l u r e ( t r a n s i t i o n p o i n t ) o f l u b r i c a t e d c o n c e nt rat ed cont act s, Wear, 22( 1872) 321.

4.178

H. Czichos, F a i l u r e modes o f s l i d i n g l u b r i c a t e d concent rat ed

4.179

A. B e g e l i n g e r and A.W.J. d e Gee, T h i n f i l m l u b r i c a t i o n o f s l i d i n g p o i n t c o n t a c t s o f A I S I 52100 s t e e l , Wear, 28(1974) 103.

4.180

H. Czichos, F a i l u r e c r i t e r i a i n t h i n f i l m l u b r i c a t i o n : t h e concept o f a f a i l u r e s u r f a c e , T r i b o l o g y , 7(1974) 14.

4.181

G. Salomon, F a i l u r e c r i t e r i a i n t h i n f i l m l u b r i c a t i o n I R G program, Wear, 36(1976) 1.

4.182

H. Czichos, T r i b o m e t r i s c h e Untersuchung d e r Versagensgrenzen von G le it rei b u n g s s y s t e m e n m i t Hertzschem Kont akt i m Mischreibungsg e b i e t , M a t e r i a l p r u f u n g , 16(1974) 32.

4.183

A. Sethuramiah, H. Okabe, T. Sakurai, C r i t i c a l temperatures i n EP l u b r i c a t i o n , Wear, 26(1973) 187. M. Tomaru, S. Hironaka and T. S a k u r a i , E f f e c t s o f oxygen on t h e l o a d - c a r r y i n g a c t i o n o f some a d d i t i v e s , Wear, 41(1977) 117. M. Tomaru, S. Hironaka and T. Sakurai, E, f f ect s o f some chemical f a c t o r s on f i l m f a i l u r e under EP c o n d i t i o n s , Wear, 41(1977) 141.

c o nt a c t s , Wear, 28(1974) 95.

4.184 4.185

-

the

4.186

A. B e g e l i n g e r and A.W.J. de Gee, L u b r i c a t i o n o f s l i d i n g p o i n t the influence o f curvature, c o n t a c t s o f A I S I 52100 s t e e l Wear, 36(1976) 7.

4.187

H. Czichos, F i l m f a i l u r e o f s l i d i n g H e r t z i a n cont act s: The i n f l u e n c e o f c o n t a c t geometry, Proc. JSLE-ASLE I n t e r n a t . Lubr. Conf. Tokyo 1975, ( E d i t o r : T. S a k u r a i ) , E l s e v i e r , Amsterdam, 1976, p. 368.

-

CHAPTER 5 5.1

5.2 5.3

J.B.P. Williamson, J . P u l l e n and R.T. Hunt, The shape o f s o l i d surfaces, i n : S u r f a c e Mechanics ( E d i t o r F.F. Ling), The American SOC. o f Mech. Engrs, New York, 1969, p. 32. M.J. Neale ( E d i t o r ) , T r i b o l o g y Handbook, But t erwort hs, London, 1973, p. A31. K.J. S t o ut , T.G. K i n g and D.J. Whitehouse, A n a l y t i c a l techniques i n s u r f a c e topography and t h e i r a p p l i c a t i o n t o a r u n n i n g - i n experiment, Wear, 43(1977) 99.

373

5.4

J.E. W i l l n , C h a r a c t e r i z a t i o n o f c y l i n d e r b o r e s u r f a c e f i n i s h a r e v i e w o f p r o f i l e a n a l y s i s , Wear, 19(1972) 143.

5.5

J.C. Campbell, C y l i n d e r b o r e s u r f a c e roughness i n i n t e r n a l combustion engines: i t s a p p r e c i a t i o n and c o n t r o l , Wear, 19( 1972) 163.

5.6

J.R. Dowd and F.T. B a r w e l l , T r i b o l o g i c a l i n t e r a c t i o n between p i s t o n and c y l i n d e r o f a model h i g h p r e s s u r e h y d r a u l i c pump, ASLE Trans., 18(1975) 21.

5.7

R. g s t v i k and H. C h r i s t e n s e n , Changes i n s u r f a c e topography w i t h r u n n i n g - i n , Proc. I n s t n . Mech. Engrs, London, Vol. 183 P t 3P, (1968/69) 57.

5.8

G.W. Rowe, S u r f a c e t o p o g r a p h i c changes a t breakdown o f t h i n - f i l m investigal u b r i c a t i o n ; a s h o r t account o f a c o l l a b o r a t i v e C . I . R . P . t i o n , Wear, 28(1974) 125.

5.9

E. S a i b e l , A s t a t i s t i c a l approach t o r u n - i n and t h e dependence o f t h e c o e f f i c i e n t o f f r i c t i o n on v e l o c i t y , Wear, 35(1975) 383.

5.10

J . Volz, E r s t e l l u n g o p t i m i e r t e r Einlaufprogramme von Dieselmotoren ( E i n System u n t e r Anwendung von Radionukl i d e n ) Kernforschungszentrum K a r l s r u h e , L a b o r a t o r i u m f u r I s o t o p e n t e c h n i k , KFK 2432, Marz 1977.

5.11

D.H. Buckley, Wear and i n t e r f a c i a l t r a n s p o r t o f m a t e r i a l , J. Vac. S c i . Technol., 13( 1976) 88.

!5.12

M. F i n k and

5.13

K. Dies, D i e Vorgange beim V e r s c h l e i B b e i r e i n g l e i t e n d e r t r o c k e n e r Reibung, V D I - Z . , 83(1939) 307.

5.14

T.S. Eyre and D. Maynard, S u r f a c e aspects o f u n l u b r i c a t e d m e t a l - t o metal wear, Wear, 18(1971) 301.

5.15

S. Hogmark, 0. Vingsbo and S. F r i e d s t r o m , Mechanisms o f d r y wear o f some m a r t e n s i t i c s t e e l s , Wear, 31(1975) 39.

5.16

T.F.J. Q u i n n and J.L. Wooley, The u n l u b r i c a t e d wear o f 3% Cr-1/2% Mo s t e e l , L u b r . Eng., 26(1970) 226.

5.17

B.A. Baldwin, Chemical c h a r a c t e r i z a t i o n o f wear s u r f a c e s u s i n g X-ray p h o t o e l e c t r o n spectroscopy, L u b r . Engng, 32( 1976) 125.

5.18

R.J. B i r d and G.D. G a l v i n , The a p p l i c a t i o n o f p h o t o e l e c t r o n s p e c t r o scopy t o t h e s t u d y o f E . P . f i l m s on l u b r i c a t e d s u r f a c e s , Wear, 37( 1976) 143.

5.19

R.C. Coy and T.F.J. Quinn, The use o f p h y s i c a l methods o f a n a l y s i s t o i d e n t i f y s u r f a c e l a y e r s formed by organosulphur compounds i n wear t e s t s , ASLE Trans, 18(1975) 163.

5.20

G. Levy, R.G. L i n f o r d and L.A. M i t c h e l l , Wear b e h a v i o u r and mechanic a l p r o p e r t i e s : t h e s i m i l a r i t y o f seemingly u n r e l a t e d approaches, Wear, 21(1972) 167.

5.21

see Ref. 1.5, p. 18. J.T. B u r w e l l and C.D. Strang, On t h e e m p i r i c a l law o f adhesive wear, J. Appl. Phys., 23(1952) 18.

5.22 5.23

U. Hofmann, Zur T h e o r i e d e r Reiboxydation, A r c h i v f . d . Eisenhuttenwesen, 6(1932) 161.

R.D. A r n e l l , A.P. Herod and D.G. Teer, The e f f e c t o f combined s t r e s s e s on t h e t r a n s i t i o n f r o m m i l d t o severe wear, Wear, 31(1975) 237.

374

5.24

K.-H. Habig, K. Kirschke, W.-W. Maennig, H. T i s c h e r , F e s t k o r p e r g l e i t r e i b u n g und V e r s c h l e i B von Eisen, K o b a l t , Kupfer, S i l b e r , Magnesium und Aluminium i n einem Sauerstoff-Stickstoff-Gemisch zwischen 760 und 2 10-7 T o r r , BAM-Berichte N r . 13, B e r l i n , J u n i 1972.

5.25

K.-H. Habig, K. K i r s c h k e , W.-W. Maennig, H. T i s c h e r , F e s t k o r p e r g l e i t r e i ’ b u n g und V e r s c h l e i B von Eisen, Kobal t, Kupfer, S i l b e r , Magnesium und Aluminium i n einem Sauerstoff-Stickstoff-Gemisch zwischen 760 und 2 10-7 T o r r , Wear, 22(1972) 373.

-

5.26

N.C. Welsh, The d r y wear o f s t e e l . I, The general p a t t e r n o f behaviour; 11. I n t e r p r e t a t i o n and s p e c i a l f e a t u r e s , P h i l . Trans. Roy. SOC., London, A 257(1965) 31.

5.27

see Ref. 4.89.

5.28

H. Uetz and J. Fohl, P r u f t e c h n i k b e i einem VerschleiBsystem a u f Grund d e r VerschleiBanalyse, insbesondere d e r thermischen Analyse, VDI-Berichte, N r . 194, 1973, p. 57.

5.29

see Ref. 1.5, p. 151 ff.

5.30

A.A. Reda, R. Bowen and V . C . Westcott, C h a r a c t e r i s t i c s o f p a r t i c l e s generated a t t h e i n t e r f a c e between s l i d i n g s t e e l s u r f a c e s , Wear, 34( 1975) 261.

5.31

T.E. T a l l i a n , G.H. B a i l e , H. D a l a l , O.G. Gustafsson, R o l l i n g B e a r i n g Damage A M o r p h o l o g i c a l A t l a s , SKF I n d u s t r i e s , Technology Center, K i n g o f P r u s s i a , Pa, 1974. E.R. Bowen, V.C. Westcott, Wear P a r t i c l e A t l a s , Report No N00156-74c-1682, prepared f o r Naval A i r E n g i n e e r i n g Center, Lakehurst, N.J., J u l y 1976. see Ref. 4.129, p. 252 ff.

5.32

-

5.33

H.C. R i p p e l , D e s i g n i n g f l u i d - f i l m b e a r i n g s by computer, Mech. Engng, (1970) 30.

5.34

P.B. Davies and R.B. Howarth, H y d r o s t a t i c l u b r i c a t i o n , see Ref. 1.8, p. 308 f f .

5.35

C.M. T a y l o r , Unusual b e a r i n g s : a i r and magnetic suspension, I n d . L u b r i c a t i o n and T r i b o l o g y , 24( 1972) 234.

5.36

M . I . Anwar and C.M. Rodkiewicz, S l i d e r b e a r i n g w i t h segmented e l e c t r i c f i e l d , Wear, 29(1974) 173.

5.37

R. K a t t e r l o h e r , Magnetlager auch i m Maschinenbau: Aufbau, Eigens c h a f t e n , Anwendungen, Maschinenmarkt, 81( 1975) 315.

5.38

J.L. P o t t e r , The e l a s t o m e r i c b e a r i n g : what i t can do f o r you, Mech. Engng, (1973) Dec, 22.

5.39

see Ref. 4.131, p. 5-110.

5.40

S. Hildebrand, Feinmechanische Bauelemente, VEB V e r l a g Technik,

B e r l i n , 1967, p. 456 f. 5.41

see Ref. 5.2,

5.42

M. Donovan, J.L. Sanders, R. Hazzard, G.R. B e l l , R.E. Mansford, S u r f a c e c o a t i n g s ( P a r t I t o I V ) , T r i b o l o g y , 5(1972) 205.

5.43

S. Jahanmir, N.P. Suh and E.P. Abrahamson, 11, The d e l a m i n a t i o n t h e o r y o f wear and t h e wear o f composite surface, Wear, 32(1975) 33.

5.44

see Ref. 4.90.

s e c t i o n C2.

375

5.45

see Ref. 1.6, p. 301 f f .

5.46

G. Cros and J . - L . P o l t i , E i n i g e t h e o r e t i s c h e und p r a k t i s c h e Gesichtspunkte d e r Reibung, Schweizer A r c h i v , 36(1970) 147.

5.47

E. Roemer, W e r k s t o f f e und S c h i c h t a u f b a u b e i G l e i t l a g e r n , Z . f. W e r k s t o f f t e c h n i k, 4( 1973) 2.

CHAPTER 6 6.1

W.M.J. Schlosser, A c o n t r i b u t i o n t o t h e s t u d y o f a n a l o g i e s o f power t r a n s m i s s i o n s i n machines, Power d r i v e s , (1974) 48 and 49.

6.2

C.T. W a l t e r s , The dynamics o f b a l l b e a r i n g s , Trans ASME, JOLT, (1971) 1.

6.3

D.G. S t e w a r t , J.B. Hunt, R e l a x a t i o n o s c i l l a t i o n s on a machine t o o l s l i d e w a y , Proc. I n s t . Mech. Engrs, London, Vol. 184 P t 3L, (1969/70) 33.

6.4

J.A. B a i l e y , F r i c t i o n i n metal machining Wear, 31(1975) 243.

-

mechanical aspects,

6.5

L. Eaton, F r i c t i o n i n s t a b i l i t y , i n Ref. 1.8, p.147.

6.6

H.-U. Mittmann and H. Czichos, Analogue computer s t u d i e s o f s t i c k s l i p e f f e c t s , BAM, Berlin-Dahlem, (1976) unpublished.

6.7

G. Niemann, Maschinenelemente, Bd 1 und Bd 2, S p r i n g e r - V e r l a g , B e r l i n , 1961.

6.8

F. Sass, Ch. Bouch6, A. L e i t n e r , DUBBEL Taschenbuch f u r den Maschinenbau, Bd 1, S p r i n g e r - V e r l a g , B e r l i n , 1970, p. 232.

6.9

R.H. Creamer, Machine Design, Adison-Wesley Publ. Co. Reading, 1976, p. 281 f.

6.10

E. Radzimovsky and A. M i r a r e f i , Dynamic b e h a v i o u r o f gear systems and v a r i a t i o n o f c o e f f i c i e n t o f f r i c t i o n and e f f i c i e n c y d u r i n g t h e engagement c y c l e , Trans ASME, B, 97(1975) 1274.

6.11

G.B. Stanton, Jr., The f u t u r e o f s a f e t y and h e a l t h : a c h a l l e n g e t o e n g i n e e r i n g managers, Trans ASME, J. o f Engng f o r I n d u s t r y , (1976) 761.

6.12

H.W. H e i n r i c h , I n d u s t r i a l a c c i d e n t p r e v e n t i o n : a s c i e n t i f i c approach, Mc G r a w - H i l l , New York, 1950, p. 11 f f .

6.13

W. Haddon, J r , The p r e v e n t i o n o f a c c i d e n t s , i n P r e v e n t i v e M e d i c i n e ( E d i t o r s : D.M. C l a r k and B. Mac Mahon) L i t t l e , Brown, Boston, 1967, c h a p t e r 33.

6.14

J.V. G r i m a l d i , A p p l y i n g systems a n a l y s i s t e c h n i q u e s i n s a f e t y s i t u a t i o n s , The Center o f S a f e t y , New York U n i v e r s i t y , New York, Apr. 1968, p. 3 1 ff.

6,15

R.A. C o l l a c o t t , Mechanical f a u l t d i a g n o s i s and c o n d i t i o n m o n i t o r i n g , Chapman and H a l l , London, 1977, c h a p t e r 2.

6.16

A l l i a n z , Handbuch d e r Schadenverhutung, A l l i a n z Versicherungs AG, Munchen und B e r l i n , 1. A u f l a g e , 1972, p. 361 and p. 376; 2. e r w e i t e r t e und u b e r a r b e i t e t e A u f l a g e , 1976, p. 645 and p. 695.

6.17

P.M. Ku, Gear g a i l u r e modes - importance o f l u b r i c a t i o n and mechanics, ASLE Trans, 19(1976) 239.

376

6.18 S.O. Rafique, Failures o f p l a i n bearings and t h e i r causes, Proc. I n s t . Mech. Engrs, London, Vol. 178, P t 3N, (1963/64) 180. 6.19 F.F. Simpson, F a i l u r e of r o l l i n g contact bearings, Proc. I n s t . Mech. Engrs, London, Vol. 178, P t 3N, (1963/64) 215. 6.20 D. Scott, A. Smith, J. T a i t , G.R. Tremain, Materials and metall u r g i c a l aspects o f p i s t o n r i n g s c u f f i n g Wear, 33(1975) 293.

6.21

-

a l i t e r a t u r e survey,

E. Dombrowski , Einfuhrung i n d i e Zuverlassigkei t e l e k t r o n i s c h e r Gerate und System?, AEG-TELEFUNKEN, B e r l i n , 1970.

6.22 J.C. Cluley, E l e c t r o n i c equipment r e l i a b i l i t y , Mac M i l l a n Press, London, 1974. 6.23 R.A. Bones, Designing f o r r e l i a b i l i t y , Engineering, 216( 1976) 798. 6.24 W. Gerisch, Zuverlassigkeit aus philosophischer, mathematischer und ingenieurwissenschaftlicher S i c h t , M a t e r i a l und Technik, (1973) 51. 6.25 Messerschmi t t - B o l kow-Blohm (Herausgeber) , Technische Zuverlassigk e i t , Springer-Verlag, B e r l i n , 1971. 6.26 6. Mathhai , Ober den G l e i t v e r s c h l e i a ungeschmierter Oberflachen, Forsch. Ing. Wes., 30(1964) 1. 6.27 H. Thum, Zuverlassigkeit und VerschleiR von mechanischen Baugruppen, Schmierungstechnik, 3(1972) 139. 6.28 H. Yoshikawa, Fundamentals o f mechanical r e l i a b i l i t y and i t s a p p l i c a t i o n to'computer aided machine design, C I R P Annals,

24( 1975) 297. 6.29

G. Fleischer, P r o b l e m der Zuverlassigkeit von Maschinen, Wiss. 2 .

TH Magdeburg, 16(1972) 289. 6.30 G. Bergling, Betriebszuverlassigkeit von Walzlagern, Kugellager-Zeitschrift, 51(1976) 1. 6.31 P. Eschmann, B e t r i e b s s i c h e r h e i t und Gebrauchsdauer von Walzlagern, Walzlagertechnik, 13(1974) 3. 6.32 H. P i t t r o f f , Funktionssichere Walzlagerungen f u r Elektromaschinen, Kugel l a g e r - Z e i t s c h r i f t , 51(1977) 10. 6.33 W.J. Bartz, Tribotechnik a l s Grundlage zur Vermeidung van Schaden an Maschinenelementen, Schmiertechni k und T r i bologie,

20(1973) 50. 6.34 G. Fleischer, Der EinfluB der Schmierungstechnik auf d i e Minderung der V e r s c h l e i a i n t e n s i t a t und d i e Sicherung e i n e r hohen Zuverlassigk e i t , Standardisierung und Q u a l i t a t , 21( 1975) 83.

-

6,35 M.L. Shooman, P r o b a b i l i s t i c r e l i a b i l i t y an engineering approach, Mc Graw-Hill , New York, 1968. 6.36 N.N., "Darunter kommt a l l e s i n s Rutschen": Moderne E l e k t r o n i k

-

schafft Arbeitslosigkeit sowohl bei H e r s t e l l e r f i r m e n a l s auch bei den Abnehmern, Der Spiegel, 30(1976) Nr. 51, 87.

6.37 B. Cramer, Der elektronische Fernschreiber a l s B e i s p i e l f u r den Strukturwandel i n der Feinwerktechnik, Feinwerktechni k und MeBtechnik, 85(1977) 1.

311

6.38

D.F. Wilcock and E.R. Booser, B e a r i n g d e s i g n and a p p l i c a t i o n , Mc Graw-Hi 11, New York, 1957.

6.39

E . E . B i s s o n and W.J. Anderson, Advanced b e a r i n g t e c h n o l o g y , NASA, SP-38, Washington, 1964.

6.40

F.E. Kennedy and H.S. Cheng ( E d i t o r s ) , Computer-aided Design o f B e a r i n g s and Seals, The American SOC. o f Mech. Engrs, New York, 1976.

6.41

H. Peeken, D i e t r i b o l o g i s c h r i c h t i g e K o n s t r u k t i o n , VDI-Z., 118( 1976) 201.

6.42

A.E. Green and A.J. Bourne, R e l i a b i l i t y , Technology, W i l e y - I n t e r s c i e n c e , London, 1972, p. 19.

6.43

R.G. Bayer and T.C. Ku, Handbook o f a n a l y t i c a l d e s i g n f o r wear, Plenum Press, New York, 1964.

6.44

J.H. Dumbleton and S.R. Rhee, The a p p l i c a t i o n o f a z e r o wear model t o m e t a l l p o l y e t h y l e n e s l i d i n g p a i r s , Wear, 35( 1975) 233.

6.45

see Ref. 4.129.

6.46

J.v. Neumann, The g e n e r a l and l o g i c a l t h e o r y o f automata, i n : Modern systems r e s e a r c h f o r t h e b e h a v i o r a l s c i e n t i s t ( E d i t o r : W. B u c k l e y ) , A l d i n e Publ. Co, Chicago, 1968, p. 97.

CHAPTER 7 7.1

J . B l o u e t , T r i b o m i i t r i e , Le F r o t t e m e n t e t l ' U s u r e , Journkes d'Etude, 5/6 d6c 1966, 1.

7.2

G. Salornon, The s t r u c t u r e o f t r i b o l o g i c a l systems, Lubr. Engng, 32(1976) 458.

7.3

H. Czichos, E x p e r i m e n t e l l e Methoden z u r Untersuchung t r i b o l o g i s c h e r E f f e k t e i m M i s c h r e i b u n g s g e b i e t , V D I - B e r i c h t e , 156, 1970, 5 .

7.4

H. Wiegand u. E. B r o s z e i t , Z u r Frage d e r Beanspruchungszeit b e i Verschleinuntersuchungen u n t e r Mischreibungsbedingungen, Motortechn. Z e i t s c h r i f t , 34( 1973) 33.

7.5

H. Czichos, T r i b o l o g i s c h e M a t e r i a l p r u f u n g P h y s i k a l i s c h e Grundl a g e n und technisch-wirtschaftliche Bedeutung, Amts- u. M i t t e i l u n g s b l a t t d e r BAM 7(1977) 5.

7.6

R. Benzing, 1. G o l d b l a t t , V. Hopkins, W. Jamison, K. Mecklenburg, M. Peterson, F r i c t i o n and Wear Devices, 2nd e d i t i o n , ASLE, Park Ridge, 1976.

7.7

K.R. Mecklenburg, The e f f e c t o f wear on t h e compressive s t r e s s i n t h e sphere-on-plane c o n f i g u r a t i o n , ASLE Trans, 17( 1974) 149.

7.8

G.H. G o t t n e r , D e f i n i t i o n und E r f a s s u n g e i n i g e r B e g r i f f e z u r Beschreibung des Geschehens i n R e i b s t e l l e n b e i Mischreibung, Schmiertechni k und T r i b o l o g i e , 20( 1973) 22.

7.9

E.D. Braun, M o d e l l i e r u n g - e i n e o b j e k t i v e Methode z u r B e u r t e i l u n g d e r Reibungseigenschaften von W e r k s t o f f e n , Schmierungstechni k, Z(1971) 12.

7.10

J.A. E l d e r , J r . and N.S. E i s s , J r . , A s t u d y o f t h e e f f e c t o f normal s t i f f n e s s on k i n e t i c f r i c t i o n f o r c e s between two b o d i e s i n s l i d i n g c o n t a c t , ASLE Trans, 12(1969) 234.

-

7.11

G. Salomon, The s i m u l a t i o n o f m a r g i n a l c o n t r o l , Lubr. Engng, 32(1976) 570.

7.12

H.-U. Mittmann, N. Czaika and H. Czichos, A new d e v i c e f o r simultaneous measurement o f f r i c t i o n f o r c e , normal f o r c e and f r i c t i o n c o e f f i c i e n t , Wear, 31(1975) 179.

7.13

E. B r o s z e i t , K.H. Kloos, F.J. Hess und E. Wagner, E i n f l u B von Schwingungen a u f d i e V e r s c h l e i R e i g e n s c h a f t e n e i nes Rei bsys terns, Wear, 28( 1974) 395.

7.14

H. Czichos und K. Kaffanke, Zur Bestimmung von Grenzflachentemperaturen b e i tri b o l o g i s c h e n Vorgangen, VDI-Z. , 112( 1970) 1491 und 1643.

7.15

see Ref. 4.147.

7.16

K.-H. Habig, M o g l i c h k e i t e n d e r Modell-VerschleiBprufung, M a t e r i a l p r u f u n g , 17( 1975) 358.

7.17

R.G. Bayer ( E d i t o r ) , S e l e c t i o n and Use o f Wear Tests f o r M e t a l s , ASTM T e c h n i c a l P u b l i c a t i o n 615, P h i l a d e l p h i a , 1976.

7.18

K.-H. Habig, On t h e d e t e r m i n a t i o n o f wear r a t e s , Wear, 28(1974) 135.

7.19

R. Holm, E l e c t r i c a l c o n t a c t s , S p r i n g e r - V e r l a g , B e r l i n , 1967.

7.20

H. Czichos, W. Grimmer and H.-U. Mittmann, Rapid measuring techniques f o r e l e c t r i c a l c o n t a c t r e s i s t a n c e a p p l i e d t o l u b r i c a n t a d d i t i v e s s t u d i e s , Wear, 40(1976) 265.

7.21

B.B. Seth and T. W i l l i s , Techniques f o r f i l m t h i c k n e s s measurements i n elastohydrodynamic l u b r i c a t i o n , Trans ASME, Paper 76-Det-79.

7.22 7.23

A.K. Pogosian, F o r c e c a s t i n g t h e v i a b i l i t y o f f r i c t i o n p a i r s i n a c c e l e r a t e d t e s t s , Wear, 26(1973) 175. S.V. P i n e g i n , A.V. C i c i n a d z e und E.D. Braun, E n t w i c k l u n g s r i c h t u n g e n der M o d e l l i e r u n g z u r B e u r t e i l u n g von Reibungs- und V e r s c h l e i B v o r gangen, Schmierungstechni k, 6 ( 1975) 5.

7.24

D. P l a y and M. Godet, Design o f h i g h performance d r y b e a r i n g s , Wear, 41(1977) 25.

7.25

A.W.J. de Gee, S e l e c t i o n c r i t e r i a f o r l u b r i c a t e d j o u r n a l b e a r i n g s , Wear, 36(1976) 33.

7.26

G. Heinke, V e r s c h l e i B e i n e Systemeigenschaft; Auswirkungen a u f d i e VerschleiBprufung, Z. W e r k s t o f f t e c h n i k, 6 ( 1975) 164,

7.27

R.D. Brown, T e s t methods, i n : Boundary l u b r i c a t i o n , e d i t e d by F.F. L i n g , E.E. Klaus and R.S. Fein, ASME, New York, 1969, p. 241.

7.28

K. Kutzbach, Reibung und Abnutzung von Zahnradern, V D I - Z . , 70(1926) 999.

7.29

see Ref. 4.131, c h a p t e r 26.

7.30

R.B. Howarth, L u b r i c a n t p r o p e r t i e s and t e s t i n g , i n Ref. 1.8,

7.31

C. Zerbe, M i n e r a l o l e und verwandte Produkte, S p r i n g e r - V e r l a g , B e r l i n , 1969.

7.32

H. Junemann, Mechanische P r u f v e r f a h r e n fur S c h m i e r s t o f f e , Erdol und Kohle, 29(1976) 259.

7.33

see Ref. 4.131,

-

p. 20-17.

p. 202.

379 7.34

S.C.

7.35

see Ref. 4.131,

Dodson and L.A. Godsave, L u b r i c a t i n g o i l s , i n Ref. 1.7, p. 501.

7.36

D. S c o t t , F a i l u r e d i a g n o s i s and i n v e s t i g a t i o n , T r i b o l o g y , (1970) 22.

7.37

see Ref. 6.15.

7.38

F.K. O r c u t t , Das A u f f i n d e n von Storungen an mechanischen Komponenten, v e r u r s a c h t durch Reibung und V e r s c h l e i B , Technica, (1970) 883.

7.39

G.H. G o t t n e r , Zur Funktionsdiagnose von M a s c h i n e n b a u t e i l e n und -anlagen g e e i g n e t e MeRgroBen, Schmiertechnik und T r i b o l o g i e , 24(1977) 3.

7.40

K. Z i e g l e r , Funktionsuberwachung von Maschinen und B a u t e i l e n r n i t H i l f e d e r SchallmeBtechnik, S c h m i e r t e c h n i k und T r i b o l o g i e , 24(1977) 5.

7.41

K.A. Bowen and T.S. Graham, Noise and a n a l y s i s : a maintenance i n d i c a t o r , Mech. Engng, (Oct. 1967) 31.

7.42

ALLIANZ, Handbuch d e r Schadenverhutung, 2. erwei t e r t e und u b e r a r b e i t e t e A u f l a g e , Munchen, 1976, p. 672.

p. 27-8.

7.43

see Ref. 7.36.

7.44

A. Beerbower, Spectrometry and o t h e r a n a l y s i s t o o l s f o r f a i l u r e p r o g n o s i s , L u b r . Engng, 32(1976) 285.

7.45

see Ref. 6.15,

7.46

A. Gervb, E i n s a t z r n o g l i c h k e i t e n von R a d i o n u k l i d e n z u r Untersuchung k o n s t r u k t i v e r und s c h m i e r s t o f f a b h a n g i g e r E i n f l u s s e a u f den V e r s c h l e i R von M a s c h i n e n t e i l e n , V D I - B e r i c h t e , N r . 196(1973) 43.

7.47

W.W. S e i f e r t and V . C . Westcott, A method f o r t h e s t u d y o f wear p a r t i c l e s i n l u b r i c a t i n g o i l , Wear, 21(1972) 27. A.W. R u f f , C h a r a c t e r i z a t i o n o f d e b r i s p a r t i c l e s r e c o v e r e d f r o m w e a r i n g systems, Wear, 42( 1977) 49.

7.48

D. S c o t t , W.W. S e i f e r t and V.C. W e s t c o t t , The p a r t i c l e s o f wear, S c i e n t i f i c American, 230( 1974) 88.

7.49

H. Czichos, MeRtechnische Methoden z u r Untersuchung t r i b o l o g i s c h b e a n s p r u c h t e r W e r k s t o f f o b e r f l a c h e n , Schmiertechnik und T r i b o l o g i e , 21(1974) 25.

7.50

G. Nomarski e t A.R. W e i l l , A p p l i c a t i o n d l a m 6 t a l l o g r a p h i e des msthodes i n t e r y e r e n t i e l l e s a’ deux oudes p o l a r i s b e s , Revue de M e t a l l u r g i e , 52(1955) 121.

7.51

H.-U. Mittmann und H. Czichos, Reibungsmessungen und Oberflachenuntersuchungen an K u n s t s t o f f M e t a l l - G l e i t p a a r u n g e n . M a t e r i a l p r u f u n g , 17(1975) 366.

7.52

S. Tolansky, M u l t i p l e - b e a m I n t e r f e r o m e t r y o f Surfaces and F i l m s , C1 arendon Press, Oxford, 1948.

7.53

H. Trumpold, Die Anwendungsgrenzen d e r L i c h t i n t e r f e r e n z e n b e i Rauheitsmessungen, F e i n g e r a t e t e c h n i k , 18(1969) 247.

7.54

K.H. Habig, Der E i n s a t z des Raster-Elektronenmikroskops z u r A u f k l a r u n g von VerschleiBmechanismen, Bei tr. Elektronenmi kroskop D i r e k t a b b . O b e r f l . 3(1970) 235.

p. 258.

380

7.55

L. Reimer und G. P f e f f e r k o r n , Rasterelektronenmikroskopie, S p r i n g e r - V e r l a g , B e r l i n , 1973.

7.56

R. S t i c k l e r , C.W. Hughes, G.R. Booker, A p p l i c a t i o n o f t h e s e l e c t e d area ECP method t o d e f o r m a t i o n s t u d i e s , Proc. 4 Annual SEM Symp., JJTRJ, Chicago, A p r i l 1971, p . 473.

7.57

H.

7.58

J.B.P. Williamson, Microtopography o f s u r f a c e s , i n : P r o p e r t i e s and M e t r o l o g y o f Surfaces, Proc. I n s t . Mech. Engrs, London, Vol. 182,

Czichos und D. K l a f f k e , Deforrnationsuntersuchungen an t r i b o l o g i s c h beanspruchten M e t a l l o b e r f l a c h e n m i t d e r Methode d e r e l e c t r o n chanell i n g p a t t e r n , BAM, Berlin-Dahlem, (1977) u n v e r o f f e n t l i c h t .

3K(1968) 21. 7.59

T.F.J. Quinn, The a p p l i c a t i o n o f modern p h y s i c a l techniques t o t r i b o l o g y , Newnes B u t t e r w o r t h , London, 1971, p. 221.

7.60

A. Benninghoven, New developments i n t h e s u r f a c e a n a l y s i s o f s o l i d s , Appl. Phys. l ( 1 9 7 3 ) 3.

7.61

J. F e r r a n t e , D.H.

7.62

R. Holm und S. S t o r p , Monolagenanalyse an "schmutzigen" Oberflachen?, Phys. B l a t t e r , 32( 1976) 342.

7.63

D.H. Buckley, The use o f a n a l y t i c a l s u r f a c e t o o l s i n t h e fundamental s t u d y o f wear, Proc. I n t . Conf., Wear o f M a t e r i a l s , S t . L o u i s , Apr. 1977, ASME, New York, 1977, p. 12.

7.64

0. R. Wheeler, X-ray p h o t o e l e c t r o n s p e c t r o s c o p i c s t u d y o f s u r f a c e c h e m i s t r y o f d i b e n z y l - d i s u l p h i d e on s t e e l under m i l d and severe wear c o n d i t i o n s , s u b m i t t e d t o Wear.

7.65

A. Benninghoven und S. S t o r p , Untersuchung d e r Grenzflachen und des MassenspekVol umens dunner Schi chten m i t H i 1 f e d e r Sekundarionen t r o s k o p i e , 2 . angew. P h y s i k , 31(1971) 31.

7.66

P.L. Stohr, Nachweis und Analyse von R e a k t i o n s s c h i c h t e n b e i metall i s c h e n R e i b p a r t n e r n i m ReibverschleiB-Modellgerat und i m Verbrennungsmotor, D i s s e r t a t i o n , Eberhard-Karls-Universitat, Fachbereich Physik, Tubingen, 1976.

7.67

E.W. M u l l e r , F i e l d i o n microscopy, American E l s e v i e r , New York, 1969.

-

Buckley, S . V . Pepper, W.A. B r a i n a r d , Use o f LEED, Auger e m i s s i o n spectroscopy and f i e l d i o n microscopy i n m i c r o s t r u c t u r a l s t u d i e s , i n : M i c r o s t r u c t u r a l A n a l y s i s - T o o l s and Techniques, ( E d i t e d by J.L. Mc C a l l and W.M. M u e l l e r ) , Plenum Publ. Co, New York, 1973, 241 f f .

-

CHAPTER 8 8.1

A. Pieuchot, J . B l o u e t , R. Gras, M. A l f r e d and R. C o u r t e l , M'ethodologie e t classement des e s s a i s de f r o t t e m e n t e t de l e u r s r ' e s u l t a t s , Mbc. E l e c t r . Oct. 1969, p. 8.

8.2

H. Czichos, A systems a n a l y s i s d a t a sheet f o r f r i c t i o n and wear t e s t s and an o u t l i n e f o r s i m u l a t i v e t e s t i n g , Wear, 41(1977) 45.

8.3

M.N. Gardos, L a b y r i n t h s e a l i n g o f aerospace mechanisms and p r a c t i c e , ASLE Trans., 17(1974) 237.

-

theory

381 8.4

G. Katzenmeier, Das V e r s c h l e i B v e r h a l t e n und d i e T r a g f a h i g k e i t von G l e i t l a g e r n i m Obergangsbereich von d e r V o l l s c h m i e r u n g zu p a r t i e l l e m Tragen (Untersuchungen m i t H i 1 f e von R a d i o i s o t o p e n ) , Kernforschungszentrum K a r l s r u h e , KFK, 1569, Febr. 1972.

8.5

D.H. Buckley and R.L. Johnson, Marked i n f l u e n c e o f c r y s t a l s t r u c t u r e on t h e f r i c t i o n and wear c h a r a c t e r i s t i c s o f c o b a l t and c o b a l t - b a s e a l l o y s i n vacuum t o m i l l i m e t e r mercury, NASA TND-2523, Washington, 1964.

8.6

J.K. Appeldorn, J.B. Goldniann and F.F. Tao, C o r r o s i v e wear by a t mospheric oxygen and m o i s t u r e , ASLE Trans, 12(1969) 140.

8.7

J . Mdlgaard, A s i m u l a t i v e wear s t u d y c r i t i c a l l y reviewed, Wear, 41(1977) 57.

8.0

J.K. L a n c a s t e r , D r y b e a r i n g s : a s u r v e y o f m a t e r i a l s and f a c t o r s a f f e c t i n g t h e i r performance, T r i b o l o g y i n t e r n a t i o n a l , 6(1973) 219.

8.9

L.H. Lee ( E d i t o r ) , Advances i n Polymer F r i c t i o n and Wear, Polymer s c i e n c e and technology, Vol. 5 , P a r t s A and 6, Plenum Press, New York, 1974.

8.10

see Ref. 7.51.

8.11

B.J. B r i s c o e , C.M. Pooley and D. Tabor, F r i c t i o n and t r a n s f e r o f some polymers i n u n l u b r i c a t e d s l i d i n g , see Ref. 8.9, P a r t 5A, p . 191. K.H. Habig, R. C h a t e r j e e - F i s c h e r und F. Hoffmann, Zum t r i b o l o g i s c h e n Verhal t e n von O b e r f l a c h e n s c h i c h t e n , d i e d u r c h E i n d i f f u s i o n von S t i c k s t o f f , B o r oder Vanadin i n E i s e n w e r k s t o f f e g e b i l d e t werden, Hartereitechn. Mitteilungen, i n p r i n t . H. Hubner, Unterdruckung s t i c k - s l i p i n d u z i e r t e r Kurvengerausche b e i Eisenbahnschienen d u r c h p h y s i k a l i s c h - c h e m i s c h e Oberflachenbehandlung, D i s s e r t a t i o n , TU-Berl i n , 1973, D83. H. Czichos und H. Hubner, Modelluntersuchungen uber s t i c k - s l i p Vorgange, BAM, B e r l in-Dahlem, (1973), u n v e r o f f e n t l i c h t . G.H.G. Vaessen and A.W.J. de Gee, I n f l u e n c e o f w a t e r vapour on t h e wear of l i g h t l y l o a d e d c o n t a c t s , Wear, 18(1971) 325.

8.12

8.13

8.14

8.15 8,16

M.E. Merchant, F r i c t i o n and Adhesion, i n : I n t e r d i s c i p l i n a r y approach t o f r i c t i o n and wear ( E d i t o r : P.M. 1968, p. 198.

Ku), NASA SP-181, Washington,

8.17

J.A. Schey, M e t a l Deformation Processes. F r i c t i o n and L u b r i c a t i o n , Marcel Dekker, New York, 1970.

8.18

G.W. Rowe, P r i n c i p l e s o f I n d u s t r i a l M e t a l w o r k i n g Processes, Arnold, London, 1977.

8.19

A. G i l e j i , Bildsame Formgebung d e r M e t a l l e , Akademie-Verlag, B e r l i n , 1967. 0. Pawelski, G. Graue und D. Lohr, Reibungsbeiwert und Temperaturv e r t e i l u n g beim Warmformen von S t a h l m i t verschiedenen Schmiermi tt e l n , S c h m i e r t e c h n i k und T r i b o l o g i e , 17(1970) 120 und 170.

8.20

a. 2 1

H. Krause und A.H. D e m i r c i , F a c t o r s i n f l u e n c i n g t h e r e a l t r e n d o f t h e c o e f f i c i e n t o f f r i c t i o n o f two e l a s t i c b o d i e s r o l l i n g o v e r each o t h e r i n t h e presence o f d r y f r i c t i o n , i n Ref. 4.1.

8.22

M. Gierzynska, Problem o f f r i c t i o n i n r o l l i n g and f o r g i n g processes, i n : T r i b o l o g y i n i r o n and s t e e l works, ISI P u b l i c a t i o n , The I r o n and S t e e l I n s t i t u t e , London, 1970, p . 156.

List

I

symbols

Characteristics o f a system (Chapter 2 ) set o f the elements o f a system s e t o f element's p r o p e r t i e s s e t o f i n t e r r e l a t i o n s between elements s t r u c t u r e o f a system inputs o f a system use-outputs o f a system loss-outputs o f a system input-output r e l a t i o n ( t r a n s f e r f u n c t i o n )

I 1 General symbols a

c o e f f i c i e n t o f adhesion

a,

radius o f Hertzian contact

A

(see I )

Ac

Arrhenius constant

A,

geometric area o f contact

Am

mantle surface o f a body

383

Ar

r e a l area o f c o n t a c t

*W

w e a r - t r a c k area

b

Burgers v e c t o r

B

magnetic f i e l d s p e c i f i c heat

:1

C

0

velocity o f l i g h t

‘r

r a d i a l clearance

C

general c o n s t a n t

‘d

damper c o n s t a n t

CS

spring constant

d

diameter

E

modulus o f e l a s t i c i t y

AE

energy

A E~

mechanical energy o r work

Ee

energy o f edge d i s l o c a t i o n

A ES errergy o f screw d i s l o c a t i o n

E:

power

f:.W

mechanical power

f

coefficient o f friction

F

force

FA

f o r c e o f adhesion

FF

f r i c t i o n force

FN

normal f o r c e

FS

separation force

FT

tangential force

F(t)

failure distribution function

9

a c c e l e r a t i o n due t o g r a v i t y

G

shear modulus

h

f i l m thickness

384 TI

Planck's constant / 2 n

H

hardness

AH

enthalpy

i

electric current

i, j

counter

J

mechanical e q u i v a l e n t o f h e a t

k

thermal c o n d u c t i v i t y

5'k 2

Hamaker c o n s t a n t s

kP K, K '

parabolic o x i d a t i o n r a t e constant wear c o e f f i c i e n t s c r a c k parameter

KC

length o r distance

I

rn

mass

M

torque

MF

f r i c t i o n torque

n

a s p e r i t y d e n s i t y p e r u n i t area

"1'

n2

e l e c t r o n number d e n s i t y

N

gear r a t i o

0

ratio:

P

pressure

-

heat e m i t t i n g area e a t a b s o r b i n g volume

P

l o a d / b e a r i n g p r o j e c t e d area

pH

maximum H e r t z p r e s s u r e

-

pH pP PY P

mean H e r t z p r e s s u r e pump p r e s s u r e y i e l d pressure (see I )

qe

e l e c t r i c charge

9

flow r a t e

qm

flow r a t e o f mass

385

91

flow r a t e o f lubricant

Q

amount o f h e a t

r

radius

R

(see I )

1?

mean roughness c e n t e r - l i n e - a v e r a g e roughness peak-to-Val 1ey-hei g h t roughness gas c o n s t a n t r e l i a b i l i t y function standard d e v i a t i o n (see I )

AS

entropy

S

enthalpy f l o w generation r a t e

so

Sommerfeld number

t

time

T

(see I )

T

temperature

U

voltage

Au

p o t e n t i a l energy

V

v e l oc it y

V

v o l ume

"W

wear volume

W

wear r a t e

W

work

'i

c o o r d i n a t e s ( i = 1, 2, 3 )

X

(see I )

Y

surface p r o f i l e height

Y

(see I )

Z

d i s t a n c e o f approach o r s e p a r a t i o n

2 Z

(see I )

(A) a u t o - c o r r e l a t i o n

function of p r o f i l e

pre s s ure -vi s c o s i ty c o e f f i c i e n t radius o f a s p e r i t y curvature s u r f a c e f r e e energy c o n s t a n t (zero-wear model ) gamma f u n c t i o n f r i c t i o n angle difference o f quantities c o n t a c t area wear t r a c k area wear r e s i s t a n c e ratio:

no-c o nt a c t t i m e f r a c t i o n viscosity efficiency c o nv ec t io n h e a t - t r a n s f e r c o e f f i c i e n t adhesion parameter thermal d i f f u s i v i ty

f i l m thickmess t o roughness r a t i o failure rate mean o f normal d i s t r i b u t i o n Poisson number c r i t i c a l oxide f i l m thickness density stress o r strength (general) adhesion bond s t r e n g t h y i e l d strength mean d e v i a t i o n o f a s p e r i t y h e i g h t shear s t r e s s

387 tS

shear strength

Ip

angle (general)

@

potential

cc1

p l a s t i c i t y index ratio: radial clearance shaft radius angular velocity

Jlr

w

Nabla operator

V2= a* - + -a+2 L ax2

ay2

a22

Laplace operator

Author index

The numbers are reference numbers, composed o f the number o f the chapter i n which an author's work i s r e f e r r e d t o and the running number. The comp l e t e references are l i s t e d on pages 360 t o 381. Abrahamson, E.P. , 5.43 Alfred, M., 8.1 Allen, C.M., 4.134 ALLIANZ, 6.16 Amontons, G., 1.9 Andarel li, G., 4.77 Anderson, W. J. , 6.39 Antler, M., 4.113 Anwar, M.I., 5.36 Appeldorn, J . K . , 8.6 Archard, J . F . , 1.25, 4.5, 4.12, 4.13, 4.19, 4.86, 4.89, 4,144 Arnell, R.D., 5.23 Ausherman, V. K. , 4.147 Avallone, E.A., 4.131 B a i l e , G.H., 5.31 Bailey, J.A., 6.4 Bakashvil i, D. L. , 4.138 Baldwin, B.A., 5.17 Bartz, W.J., 6.33 Barwell, F.T., 5.6 Bayer, R.G., 6.43, 7.17 Beerbower, A., 7.44 Begelinger, A., 4.179, 4.186 B e l l , J.C., 4.134 Bell, G.R., 5.42 7.60, 7.65 Benninghoven, A., Benzing, R., 7.6 Bergling, G., 6.30 Bertalanffy, L. von, 2.1

Berthe. D. , 4.151 B i e l , C., 1.31 Bird, R.J., 5.18 Bisson, E.E., 6.39 Blok, H., 4.85 Blouet, J . , 7.1, 8.1 Bones, R.A., 6.23 Booker, G.R., 7.56 6.38 Booser, E.R., B o l l i n g e r , J.G.. 4.78 Bouchk, Ch., 6.8 Boulding, K.E., 2.2 Bourne, A.J., 6.42 Bowden, F.P., 1.4, 1.17, 1.18, 4.31, 4.160 Bowen, E.R., 5.30, 5.31 Bowen, K.A., 7.41 Boyd, J . , 4.131 Brainard, W.A., 7.61 7.9, 7.23 Braun, E.D., Bremble, G.R., 4.59 4.25, 8.11 Briscoe, B.J., Brdnsted, J.N., 3.9 Broszeit, E., 4.93, 7.4, 7.13 Brothers, B.G., 4.59 Brown, R.D., 7.27 4.30, 4.33, 4.34, Buckley, D.H., 4.36, 4.37, 4.39, 4.50, 4.111, 4.115, 5.11, 7.61, 7.63, 8.5 Bueche, A.M., 4.61 Burton, R.A., 4.97 Burwell, J.T., 1.23, 1.26, 5.22

389 Cameron, A., 1.7, 4.139 Campbell, J.C., 5.5 Campbell, W.E., 4.161 Cannon, R.H., 1.1 Carslaw, H.S., 4.83 Carter, F.W., 4.55 Casimir, H.B.G., 4.24 8.12 Chaterjee-Fischer, R., Charron, F., 4.88 Chaudhari, P., 4.74 4.137, 6.40 Cheng, H.S., Chiu, Y . P . , 4.96, 4.172 Christensen, H., 4.150, 5.7 cizinadze, A.V., 7.23 Cluley, J.C., 6.22 4.112 Cocks, M., C o l l a c o t t , R.A., 6.15 Constantinescu, V.N., 4.170 Coulomb, E., 1.10 Courtel, R., 4.48, 4.77, 8.1 Courtney-Pratt, J.S., 4.45, 4.158 5.19 Coy, R.C., Cramer, B . , 6.37 Creamer, R.H., 6.9 Crook, A.W., 4.66 5.46 Cros, G., Czaika, N., 7.12 Czichos, H., 1.34, 3.3, 3.4, 3.5, 4.29, 4.46, 4.52, 4.69, 4.90, 4.121, 4.173, 4.174, 4.180, 4.182, 4.187, 6.6, 7.3, 7.5, 7.12, 7.14, 7.20, 7.49, 7.51, 7.57, 8.2, 8.14 Dalal, H., 5.31 Davies, P.B., 5.34 de Gee, A.W.J., 4.179, 4.186, 7.25, 8.15 8.21 Demirci, A.H., de Pater, A.D., 4.1 Depeyrot, M., 2.7 Derjaguin, B.V. , 4.71 Desagulier, J.T., 1.11 Dies, K., 1.21, 5.13 Dimarogonas, A.D., 4.87 d i Prima, R.C., 4.169 Dismant, J.H., 4.72 Dombrowski, E., 6.21 7.34 Dodson, S.C., Dixhoorn, J.J. van, 2.6 5.6 Dowd, J.R., Doubleday, J., 1.33 Donovan, M., 5.42 Dowson, D., 4.136, 4.142 Dumbleton, J.H. , 6.44 D,yer, L.D., 4.64 Dyson, A., 4.143, 4.166

Eaton, L., 6.5 Eisner, E., 4.45 Eiss, N.S., Jr., 7.10 E l d e r , J.A., J r . , 7.10 4.63 Eldredge, K.R., Engel, P.A., 4.91 E r n s t , H., 1.16 6.31 Eschmann, P., Evans, F.J., 2.6 4.103, 5.14 Eyre, T.S., Faurre, P., 2.7 Feder, R., 4.74 Fein, R.S., 4.161, 4.163, 4.175, 4.176, 7.27 F e r r a n t e , J., 4.27, 4.28, 4.81, 7.61 1.27 Feynman, R . P . , Fink, M., 1.20, 5.12 F l e i s c h e r , G. , 3.1, 6.29, 6.34 Flom, D.G., 4.61 Fohl, J., 4.110, 5.28 FOppl, L., 4.57 Forbes, E . S . , 4.154 Friedstrom, S., 5.15 Fuchsel, M., 1.19 F u l l e r , K.N.G., 4.42 Galvin, G.D., 5.18 Gane, N . , 4.40, 4.76 Gardos, M.N., 8.3 4.22 Gatos, H.C., Gerisch, Id., 6.24 7.46 Gerv6, A,, Gierzynska, M. , 8.22 G i l e j i , A., 8.19 Godet, M., 4.47, 4.151, 7.24 Godfrey, D., 4.156, 4.157 Godsave, L.A., 7.34 G o l d b l a t t , I . , 7.6 Goldmann, J.B., 8.6 Gottner, G.H., 1.36, 7.8, 7.39 Graham, T.S., 7.41 Gras, R., 8.1 Graue, G . , 8.20 Green, A.E., 6.42 4.14, 4.18, 4.152 Greenwood, J.A., Grimaldi, J. V . , 6.14 7.20 Grimmer, W., Gumbel , L., 4.148 G u r l e y i k , M . , 4.105 Gustafsson, O.G., 5.31 Haasen, P., 4.98 Habig, K.-H., 1.34, 4.35, 4.38, 4.90, 5.24, 5.25, 7.16, 7.18, 7.54, 8.12

390 Haddon, W. J r . , 6.13 Halaunbrenner, 3.6. , 4.62 2.13 H a l l , A.D., H a l l i n g , J., 1.8 Hamil ton, G.M., 4.67 Hardy, J.K., 1.13 1.13 Hardy, W.B., Hazzard, R., 5.42 Heathcote, H.L. 4.54 H e i n i k e , G., 4.116 Heinke, G., 7.26 H e i n r i c h , H.W., 6.12 5.23 Herod, A.P., Hersey, M.D., 4.126 H e r t z , H., 4.3 Hess, F.J., 7.13 Higginson, G.R., 4.136 H i l d e b r a n d , S., 5.40 Hironaka,S,, 4.184, 4.185, 5.15 1.25 H i r s t , W., H i r t h , J.P., 4.102 Hofmann, U., 1.20, 5.12 5.15 Hogmark, S., Holland, J . , 4.128 Holm, Ragnar, 1.15, 4.84, 4.159, 7.19 Holm, R., 7.62 Hopkins, V . , 7.6 Hornbogen, E., 4.100 5.34, 7.30 Howarth, R.B., Howells, R.I.L., 4.4 Hubner, H., 8.13, 8.14 Hughes, C.W., 7.56 Hunt, J.B., 6.3 Hunt, R.T., 5.1 H u r r i c k s , P.L., 4.109, 4.118 H u t t e n l o c h e r , D.F., 4.172 I-Meng, Feng,

2.11 Karnopp, D., K a t t e r l o h e r , R., 5.37 Katzenmeier, G., 8.4 4.41, 4.70 Kendall, K., Kennedy, F.E., 6.40 K e r r i d g e , M., 1.24 4.106, 4.107 Khrushov, M.M., King, T.G., 5.3 Kirschke, K., 1.34, 4.177, 5.24, 5.25 K l a f f k e , D., 7.57 4.142, 7.27 Klaus, E . E . , K l i r , G.J., 2.5 Kloos, K.H., 4.93, 7.13 4.138 Kodnir, D.S., K o s t e t s k i i , B.J., 4.73 Kounas, P.S., 4.87 Kragelskii, I.V., 1.6 8.21 Krause, H., Kreuz, K.L., 4.175 4.89, 4.97, 4.157, 6.17 Ku, P.M., Ku, T.C., 6.43 Kuhlmann-Wilsdorf, D., 4.99 Kutzbach, K., 7.28 4.99 L a i r d , C., Lancaster, J.K., 8.8 Landheer, D., 4.114 Lang, O.R., 4.92 Lee, L.H., 8.9 L e i g h t o n , R.B., 1.27 L e i t n e r , A,, 6.8 5.20 Levy, G., L i n f o r d , R.G., 5.20 Ling, F.F., 4.2, 4.142, L i t t m a n n , W.E., 4.95 Lohr, D., 8.20 4.16 Ludema, K.C.,

4.161,

7.27

1.23

Jackson, A., 4.140 Jaeger, J.C., 4.83 Jahanmir, S., 5.43 7.6 Jamison, W., Johnson, K.L., 4.41, 4.65, 4.68, 4.141, 4.152 Johnson, R.L., 4.34, 8.5 Jones, A.M., 4.10 4.4 Jones, M.H., J o s t , P., 1.37 7.32 Junemann, H., Kaffanke, K., 7.14 K a l k e r , J.J., 4.1 4.172 Kamenshine, J.A., Kannel, J.W., 4.134 Kirmkn, T. von, 4.167

Maennig, W.-W., 5.24, 5.25 Mansford, R.E., 5.42 Mathhai, G., 6.26 4.77 Maugis, D., Maynard, D., 5.14 4.96 Mc Cool, J . I . , Mc F a r l a n e , J.S., 4.44 Mecklenburg, K., 7.6, 7.7 Merchant, M.E., 1.16, 8.16 Merwin, J.W., 4.68 Mesarovic, M.D., 2.4 Messerschmitt-Bo1 kow-Blohm, Meyer, K . , 4.116 M i n d l i n , R.D., 4.43 6.10 M i r a f e r i , A., M i t c h e l l , L.A., 4.49, 5.20 Mittmann, H.-U. , 6.6, 7.12, 7.51

6.25

7.20,

391 Mblgaard, J., 3.5, 3.6, 4.122, Moore, D.F., 4.130 M u l l e r , E.W., 7.67 Munnich, H., 4.146 4.147 Nagaraj, H.S., Nazarenko, P.V., 4.73 Neale, M.J., 5.2 Neumann, J. von, 6.46 Nicholas, J.F., 4.21 Niemann, G., 6.7 Nomarski, G., 7.50 O'Cal laghan, P.W., 4.10 4.131 O'Connor, J.J., O r c u t t , F.K., 4.137, 7.38 Osgood, C., 4.49 5.7 b s t v i k , R., Pandit, S.M., 4.11 Pawelski, O., 8.20 Paynter, H.M., 2.10 6.41 Peeken, H., Peklenik, J., 4.9 Pepper, S . V . , 7.61 Peterson, M.B., 7.6 4.138 Petrousevitch, A.J., P f a e l z e r , P.F., 4.40 P f e f f e r k o r n , G., 7.55 Pieuchot, A., 8.1 7.23 Pinegin, S.V., Pittroff,H., 6.32 Pogosi an, A . K. , 7.22 P o l t i , J.-L., 5.46 Pooley, C.M., 8.11 Poon, S.Y., 4.152 4.56 P o r i t s k y , H., P o t t e r , J.L., 5.38 Probert, S.D., 4.4, 4.10 Pullen, J., 5 . 1 Quinn, T.F.J.,

5.16,

5.19,

Rabinowicz, E., 1.5 Radzimovsky, E., 6.10 6.18 Rafique, S.O., Reda, A.A., 5.30 Reimer, L., 7.55 R e t i , L., 1.12 Reynolds, O., 1.28, 4.53 Rhee, S.R., 6.44 4.108 Richardson, R.C.D., Rigney, D.A., 4.102 Rippel, H.C., 4.127, 5.33 4.41 Roberts, A.D., Rodkiewicz, C.M., 5.36 5.47 Raemer, E . ,

7.59

8.7

Ropohl, G., 2.3 Rosenberg, R., 2.11 Rounds, F.G., 4.162 Rowe, C.N., 4.164, 4.165, 4.175 Rowe, G.W., 4.31, 5.8, 8.18 R u f f , A.W., 7.47 Saibel, 4.171, 5.9 Sakurai, T., 4.183, 4.184, 4.185, 4.187 Salomon, G., 3.2, 4.181, 7.2, 7.11 4.138 Salukvadze, R.G., Sanborn, D., 4.147 Sanders, J.L., 5.42 Sandor, G.N., 4.87 Sands, M., 1.27 Sass, F., 6.8 Schey, J.A., 8.17 Schlosser, W.M.J., 3.7, 6 . 1 Schmaltz, G., 4.23 4.94 Schouten, M.J.W., Schultze, G.E.R., 4.75 Schwarzman, V.Sh., 4.138 6.20, 7.36, 7.48 S c o t t , D., Seely, S . , 2.8 S e i f e r t , W.W., 7.47, 7.48 Seireg, A., 4.15 7.21 Seth, B.B., Sethuramiah, A., 4.183 Shooman, M.L., 6.35 S i b l e y , L.B., 4.172 S i e b e l , E., 1.22 S i k o r s k i , M.E., 4.32 Simpson, F.F., 6.19 S i n d l i n g e r , N.E., 4.172 Skinner, J., 4.76 Smilga, V.P., 4.71 6.20 Smith, A., Smith, J.R., 4.27, 4.28 1.30 Sommerfeld, A . , Stanton, G.B., 6.11 Stewart, D.G., 6.3 S t i c k l e r , R., 7.56 7.66 Stohr, P.L., Storp, S., 7.62, 7.65 Stout, K.J., 5.3 1.23, 5.22 Strang, C.D., S t r i b e c k , R., 1.29, 4.17 1.34, 4.155 S t u d t , P., Suh, N.P., 4.101, 5.43 Summers-Smith, D., 1.38 Suratkar, P.T., 4.11 Tabor, D., 1.4, 1.17, 1.18, 4.16, 4.20, 4.25, 4.40, 4.42, 4.44, 4.51, 4.58, 4.60, 4.63, 4.160, 8.11

392

T a i t , J., 6.20 T a l l i a n , T.E., 4.96, 4.153, 4.172, 5.31 Tao, F.F., 8.6 5.35 Taylor, C.M., Taylor, G . I . , 4.168 5.23 Teer, D.G., Tevaarwerk, J . , 4.141 Theyse, F.H., 4.133 Thiessen, P.A., 4.116 Thorna, J.U., 2.9, 3.8 Thomas, T.R., 4.7 Thum, H . , 6.27 Tischer, H., 5.24, 5.25 Tolansky, S., 7.52 T o l s t o i , D.M., 4.79 Tomlinson, G . A . , 1.14 Tremain, G.R., 6.20 Tripp, J.H., 4.14 Trumpold, H., 7.53 Tyler, J . C . , 4.97 Uetz, H., 5.28

4.104,

4.105, 4.110,

Vaessen, G.H., 8.15 Vingsbo, O., 5.15 Vogelpohl, G., 1.32, 4.129, Volz, J., 5.10

7.13 Wagner, E., Walters, C.T., 6.2 Wedeven, L.D., 4.132. 4.145 W e i l l , A.R., 7.50 Weingraber, H. von, 4.8 Weiter, E.J., 4.15 Wellinger, K., 4.104, 4.105 Welsh, N.C., 5.26 Westcott, V.C., 5.30, 5.31, 7.47, 7-48 Westlake, F.J., 4.139 Wheeler, D.R., 7.64 4.6, 4.19, 5.3 Whitehouse, D.J., Wiegand, H., 7.4 Wiener, N., 2.12 Wilcock, D.F., 6.38 Williamson, J.B.P., 4.18, 5.1, 7.58 W i l l i s , T., 7.21 W i l l n , J.E., 5.4 Winer, W.O., 4.147 Wooley, J.L., 5.16 Wortmann , J., 4.82 Wu, S.M., 4.11 Yoshikawa, H . ,

4.149

6.28

Zaat, J.H., 4.114 Zerbe, C . , 7.31 Z i e g l e r , K., 7.40 4.26 Ziman, J.M., Zudans, Z., 4.127

393

Subject index

Abrasion, .- t h r e e body, 113 - two body, 113 A b r a s i v e c u t t i n g , 353 A b r a s i v e wear mechanisms, 112 A b r a s i v e wear r e s i s t a n c e o f s u r f a c e c o a t i n g s , 323 A c o u s t i c waves, e m i s s i o n o f , 9 1 Across v a r i a b l e s , 19 A c t u a t o r s , 351 Adhesion, bonding mechanisms, 58 -. c o e f f i c i e n t , 63 - hypothesis o f f r i c t i o n , 5 - i n r o l l i n g f r i c t i o n , 86 -. i n s l i d i n g f r i c t i o n , 78 -. o f s o l i d s , 59 - parameter, 68 Adhesive wear mechanisms, 119 Adhesive wear r e s i s t a n c e o f s u r f a c e c o a t i n g s , 323 A l l o y i n g elements, i n f l u e n c e on adhesive wear, 121 Almen t e s t , 276 A l t e r n a t i v e s o l u t i o n s t o mechanical systems, 240 Amontons-Coulomb laws, 73, 79 Amsler t e s t , 276 A n a l o g i e s between systems, 19 Analogue computer, use i n s t i c k - s l i p s t u d i e s , 218 Analogue system elements, 217 Analysis o f t r i b o - t e c h n i c a l systems, 302 Anchor-buoy b e a r i n g , 326 Anti-wear (AW) a d d i t i v e s , 159, 165

-

Archard, - wear c o e f f i c i e n t , 262 - wear law, 100 Area o f c o n t a c t , 53 Aromatic hydrocarbons, 158 A t t r i t i o n , 41 Audio pick-ups, 352 Auger e l e c t r o n spectroscopy (AES), 293 - a p p l i c a t i o n example, 188 Auto-correlation function o f s u r f a c e p r o f i l e , 52 B a l l and r o l l e r b e a r i n g s , 351 B a l l -and-screw mechanisms, 351 Band brakes, 351 Band c l u t c h e s , 351 B a t h - t u b f a i l u r e r a t e curve, 240 B e a r i n g area curve, 51 B e a r i n g bushing design, 210 B e a r i n g m a t e r i a l s , s i m u l a t i ve t e s t i n g o f , 268 Bearings, c o m p i l a t i o n o f , 351 B e l t d r i v e s , 351 Bevel gears, 351 B i b l i o g r a p h i c work i n t r i b o l o g y , 356 B i n d i n g e n e r g i e s i n adhesion, 66 Black-box d e s c r i p t i o n , 25, 29 B l a s t i n g , 353 B l o c k brakes, 351 B l o k temperature t h e o r y , 94 B o l t s e t s , 351 Bond graph methods, 20 B o r i d i n g , 208, 322 B o r i n g , 353 Boundary l u b r i c a t i o n , 156

394 B o u r r e l e t f r o n t a l , 78 Boussinesq problem, 48, 147 Bowden-Tabor t h e o r y o f f r i c t i o n , 76 B r i t t l e solids, f r i c t i o n of, 81 Brushing, 353 Cam-and-fol 1owers , 352 Cam d r i v e s , 351 Cam-tappet wear r e d u c t i o n , 335 C a r b u r i z i n g , 208, 322 Carter-Poritsky-Foppl s l i p i n r o l l i n g f r i c t i o n , 83 Case s t u d i e s o f t r i b o l o g i c a l s o l u t i o n s , 315 Casting, 352 C a v i t a t i o n wear, 103 Chain d r i ves, 351 Check-list f o r tribo-mechanical systems, 303, 309 Chemical conversion c o a t i n g s , 208 Chemical r e a c t i o n s i n boundary l u b r i c a t i o n , 162 Chemical vapour d e p o s i t i o n (CVD), 206 Chemisorption, 161 C h i p l e s s c u t t i n g , 353 C1 assi f i cation, - o f mechanical systems, 35 o f systems, 2 1 o f t r i b o - e n g i n e e r i n g systems, 350 o f wear, 102 C l e a n i n g o f t e s t specimens, 252 Clock-works, 352 Coefficient , o f adhesion, 63 - o f f r i c t i o n , 4, 73, 308, 317 - o f wear, 262 Cohesion o f s o l i d s , 59 Cold-welded j u n c t i o n s , 119 Comminution, 352 Components t e s t i n g , 272 C o n d i t i o n m o n i t o r i n g techniques, 277 Cone c l u t c h e s , 351 Con t a c t , - area, 53 - area i n t r i b o - t e s t i n g , 253 - area t o w e a r - t r a c k area r a t i o , 267 f a t i g u e , 108 mechanics, 47 p h y s i c s and c h e m i s t r y , 56 - p r e s s u r e , H e r t z i a n , 49 - p r e s s u r e i n t r i b o - t e s t i n g , 253 - processes, 47 Contaminants, 57 d i s p e r s a l o f , 72 i n f l u e n c e on f r i c t i o n , 8 1

-

-

Control, - methods, 248 o f operating variables i n tribo-testing, 254 Conveyors, 352 Cou 1omb-f r ic t i o n , - laws o f , 73 - v a l i d i t y o f , 316 C o v a l e n t adhesion bonding, 58 Corrosion, f a i l u r e d i s t r i bution o f , 239 Crack i n i t i a t i o n and p r o p a g a t i o n , 109 Crank d r i v e s , 351 Creep, f a i l u r e d i s t r i b u t i o n o f , 239 Crystal structure, i n f l u e n c e on adhesion, 63 i n f l u e n c e on adhesive wear, 120 C u t t i n g , 353 C y b e r n e t i c s , 21

-

-

Data banks, 315 Data sheet f o r t r i b o l o g i c a l systems, 309 Deep drawing, 352 D e l a m i n a t i o n t h e o r y o f wear, 111 Description o f tribo-engineering systems, 310 Oesi gn, - o f t r i b o - m e c h a n i c a l systems, 242 p r i n c i p l e s o f redundancy, 243 D e t e r i o r a t i o n modes, 239 D i b e n z y l d i s u l f i d e , 159 Die, 347 Diffusion, c o a t i n g s , 208, 321 f a i l u r e d i s t r i b u t i o n o f , 239 D i s c brakes, 351 D i s c c l u t c h e s , 351 D i s l o c a t i o n processes, i n f r i c t i o n , 89 i n wear, 110 D i s s i p a t i v e systems, 16 D i s s i p a t i v e processes, i n c o n t a c t mechanics, 54 i n f r i c t i o n , 87 DOCUMENTATION TRIBOLOGY, 356 Donor-acceptor h y p o t h e s i s o f m e t a l l i c adhesion bonding, 6 1 Dowson-Higginson formula, 151 Drawing, 346, 352 Dredging, 352 D r i l l i n g , 353 D u r a t i o n o f t e s t i n g , 256 Dynamics , o f p h y s i c a l systems, 1 o f tri bo-mechanical systems , 215

-

-

-

-

-

-

396 E a r t h moving u n i t s , 352 E f f i c i e n c y , 222 - i n f l u e n c e o f f r i c t i o n and l u b r i c a t i o n , 226 - o f t r a n s l a t i o n screw, 225 - o f wedge d r i v e system, 225 E f f o r t v a r i a b l e s , 19 E l a s t i c contact, - d e f o r m a t i o n , 48 - displacement, 70 E l a s t i c h y s t e r e s i s , 55 - i n r o l l i n g f r i c t i o n , 84 E l a s t i c waves g e n e r a t i o n , 54 Elastohydrodynamic (EHD) l u b r i c a t i o n , 146 E l a s t o m e r i c b e a r i n g , 204 E l a s t o s t a t i cs, 48 E l e c t r i c a l c o n t a c t s , 352 - r e s i s t a n c e measuring t e c h n i q u e s , 262 - f a i l u r e i n v e s t i g a t i o n o f , 341 E l e c t r o n c h a n e l l i n g p a t t e r n (ECP) technique, 289 E l e c t r o n gas, 60 E l e c t r o n i c s t r u c t u r e o f m e t a l s , 61 E l e c t r o n probe m i c r o a n a l y z e r IEPMA), 291 E l ec t r o n sca t t e r i ng f o r c hemi ca 1 a n a l y s i s (ESCA), 293, 296 - a p p l i c a t i o n examples, 190 Electroplating, 208 E l e c t r o s t a t i c adhesion, 58 Elements o f t r i b o - m e c h a n i c a l systems, 305, 354 Emission o f f r i c t i o n a l energy, 9 1 Energy, - balance, 18 - d i s s i p a t i o n , 56, 87 - t r a n s a c t i o n s , 36 ENPORT computer program, 20 E n t r o p y g e n e r a t i o n due t o f r i c t i o n , 38 Equidensi t i e s o f i n t e r f e r o g r a m s , 288 E r o s i o n , 103 a b r a s i o n , 114 - f a i l u r e d i s t r i b u t i o n o f , 239 Exo-el e c t r o n e m i s s i o n (EEE) , 92 E x p o n e n t i a l d i s t r i b u t i o n , 236 E x t e r n a l l y p r e s s u r i z e d b e a r i n g s , 200 Extreme p r e s s u r e (EP) a d d i t i v e s , 159, 165

-

F a i 1u r e , causes, 229 condition i n lubrication, d i s t r i b u t i o n s , 236

-

169, 175

-

investigations o f electrical c o n t a c t s , 341 - modes, 239 modes o f gears, 230 o f b a l l b e a r i n g s , 237 o f D i e s e l engine u n i t s , 237 o f e n g i n e e r i n g systems, 228 r a t e , 235 s u r f a c e , 172 F a l e x t e s t , 276 F a s t e n e r s e t s , 351 F a t i g u e , 105 failure distribution, 239 f a i l u r e i n r o l l i n g c o n t a c t , 108 Ferrography, 284 F i e l d i o n microscopy (FIM), 293, 299 F i l i n g , 353 Film-thickness-to-roughness r a t i o , 153 Flanges, 351 F1 ash t e m p e r a t u r e , 94 F l e x u r a l b e a r i n g s , 205 Flow v a r i a b l e s , 19 F l u i d f i l m s , 200 F o r g i n g , 346, 352 Force t r a n s d u c e r , 258 Four b a l l t e s t , 276 Fracture, - failure distribution, 239 - processes i n adhesive wear, 121 - processes i n s u r f a c e f a t i g u e wear, 109 F r e t t i n g wear, 127 Friction, 1 - adhesion h y p o t h e s i s o f , 5 - c o e f f i c i e n t , 4, 73, 317 - c o e f f i c i e n t , formal representat i o n , 308 - dampers, 351 - d r i v e s , 351 - energy e m i s s i o n processes, 9 1 - i n boundary l u b r i c a t i o n , 163 - i n s t a b i l i t i e s , 215 - measuring t e c h n i q u e s , 257 - processes, 69 - r o l l i n g , 81 - roughness h y p o t h e s i s o f , 4 - s l i d i n g , 73 - studies, h i s t o r i c s o f , 3 - t e s t methods, 250 - t e s t r i g s , 252 F r i c t i o n a l h e a t , 94 F u l l - s c a l e t e s t s , 277 Function, - o f a system, 17 - o f t r i b o - m e c h a n i c a l systems, 27, 211 F u n c t i o n a l f a i l u r e s , 227

-

-

396 Gamma d i s t r i b u t i o n , 238 Gear, c o u p l i n g s , 351 f a i l u r e modes, 230 t e s t r i g s , 273 Gear t r a i n , - i d e a l f u n c t i o n a l behaviour, 212 - network r e p r e s e n t a t i o n , 213 Geometry o f t e s t systems, 252, 265 Gouging abrasion, 114 G r i f f i t h theory, 111 G r i n d i n g abrasion, 114 Guides, 351 Gyroscopic bearings, 351

-

Hamaker constants, 60 Hardness, i n f l u e n c e on wear, 115, 192 Heat g e n e r a t i o n i n f r i c t i o n , 38, 267 Heathcote-sl i p i n r o l l i n g f r i c t i o n , 83 H e r t z t h e o r y , 49 H i e r a r c h y o f systems, 15 Hinges, 351 Human, - j o i n t s , 351 t e e t h , 352 - v e i n s , 352 Hydrocarbons, 157 Hydraul ic d r i v e s , 351 Hydrodynamic 1u b r i c a t i o n , 132 H y d r o s t a t i c b e a r i n g s , 200 Hypoid gears, 351

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Impact wear, 103 I m p u l s i v e c o n t a c t , 54 Inertia, p r i n c i p l e of, 4 Information, g e n e r a t i o n systems, 350 r e p r o d u c t i o n systems, 350 t r a n s m i s s i o n o f , 27 I n f r a r e d pyrometer, 259 I n j e c t i o n moulding, 352 I n n e r s u r f a c e l a y e r s , 57 Interfacial , - bonding, 57 - s l i p , 54 I n t e r f e r e n c e microscopy, 286 I n t e r r e l a t i o n s between t h e elements o f t r i b o - t e c h n i c a l systems, 306

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J e l l i u m model o f m e t a l l i c adhesion, 60 J o s t r e p o r t , 10 Journal b e a r i n g , 143 - d a t a sheet o f , 311

Junction, growth, 71 - interfacial,

-

57

Kirm’an v o r t e x s t r e e t , 167 Khrushov diagram o f a b r a s i v e wear r e s i s t a n c e , 116 K i r c h h o f f ’ s laws, 19, 212, 217 Kramer e f f e c t o f e x o - e l e c t r o n s , 92 Lamellar solids, f r i c t i o n o f , 81 Laminar f l u i d f l o w , 167 Lap1ace e q u a t i o n , 201 Lapping, 353 L i m i t s o f l u b r i c a t i o n , 166 Load a p p l i c a t i o n methods i n t r i b o t e s t i n g , 254 L o a d - c a r r y i n g c a p a c i t y , 165, 170 Long range f o r c e s , 59 Low energy e l e c t r o n d i f f r a c t i o n (LEED), 293, 295 Lubricant, f i l m t h i c k n e s s , measuring methods, 264 - s e l e c t i o n procedure, example, 332 supply, m o n i t o r i n g o f , 281 - t e s t methods, 274 - types, 157 Lubri c a t i o n , - modes, 130 - o f mechanical systems, 33 - studies, h i s t o r i c s o f , 8

-

-

Machinery c o n d i t i o n m o n i t o r i n g , 246, 277 Magnetic, c h i p d e t e c t o r s , 283 - f i e l d s , 202 - suspension b e a r i n g s , 202 Magnetohydrodynami c (MHD) b e a r i n g s , 202 Malfunctions , - o f e n g i n e e r i n g systems, 246 - o f l i v i n g systems, 246 M a n u f a c t u r i n g processes, 345 M a r t e n s i t i c t r a n s f o r m a t i o n , 194 Mass balance, 41 Material, f o r m i n g systems, 350 l o s s e s due t o wear, 195 quantities i n tribo-testing, 257 s e l e c t i o n procedure, example, 326 - t r a n s a c t i o n s , 40 - t r a n s p o r t a t i o n systems, 350 Maxwell model o f v i s c o e l a s t i c i t y , 55 Mean t i m e t o f a i l u r e , 235

-

-

397

Mechanical, c a l c u l a t i n g machine, 241 c l o c k , 241 - e f f i c i e n c y , 221 equipment r e l i a b i l i t y , 234 .- f a u l t s , 229 - q u a n t i t i e s i n t r i b o - t e s t i n g , 257 - systems, c l a s s i f i c a t i o n o f , 35, 350 M e t a l l i c adhesion bonding, 58 Metal-working, 345, 348 Methodology f o r t h e s o l u t i o n o f f r i c t i o n and wear problems, 315 M i c r o - c o n t a c t areas, 53 M i c r o - c u t t i n g processes, 112 Microdisplacements, 73 M i c r o p r o c e s s o r s , 241, 278 Micro-slip, 54 i n r o l l i n g f r i c t i o n , 82 M i l d wear, 99 M i n i n g , 352 Mixed l u b r i c a t i o n , 154 Monolayer a n a l y s i s techniques, 293 Motion, 1, 4 - i n f l u e n c e o f f r i c t i o n on, 215 - t r a n s m i s s i o n systems, 350 - types, 304 M u l t i p o r t system, 214

-

-

-

Naphthenic hydrocarbons, 158 Navier-Stokes e q u a t i o n s , 135, 138 Needle b e a r i n g s , 351 Network, - t h e o r y , 18 - r e p r e s e n t a t i o n o f gear t r a i n system, 213 - representation o f n-port system, 214 Newtonian f l u i d s , 134 N i t r i d i n g , 208, 322 No-contact t i m e f r a c t i o n , 167 Noise, - measuring t e c h n i q u e s , 258, 279 - r e d u c t i o n , example o f , 338 - spectrum o f w h e e l - r a i l system, 338 Nomarski o p t i c a l microscopy, 286 Non r e t a r d e d van d e r Waals f o r c e s , 59 Normal d i s t r i b u t i o n , 236 No-wear c o n d i t i o n s , s o l u t i o n s f o r , 199 Off-shore bearing a p p l i c a t i o n , O i l i n e s s aqents, 158 O l e f i n i c hydrocarbons, 158 O l e i c a c i d . 159 O n - l i n e m o n i t o r i n g techniques,

326

277

O p e r a t i n g v a r i a b l e s , 30 - conditions f o r proper choice of, 244 - i n t r i b o t e s t i n g , 251 - o f t r i b o - t e c h n i c a l systems, 304 O p t i c a l microscopy, 286 O p t i m i z a t i o n o f dynamic b e h a v i o u r o f t r i b o - m e c h a n i c a l systems, 221 Outer s u r f a c e l a y e r s , 57 Oxygen, i n f l u e n c e on boundary l u b r i c a t i o n , 190, 314 Packings, 352 P a r a f f i n i c hydrocarbons, 157 P a r t i a l elastohydrodynamic (EHD) lubrication, 155 P e t r o f f ' s formula, 8 Phonons, e m i s s i o n o f , 9 1 Photons, e m i s s i o n o f , 92 P h y s i s o r p t i o n , 160 P i n - o n - d i s c t r i b o m e t e r , 265, 313 P i p e l i n e s , 352 P i s t o n - c y l i n d e r assemblies, 352 - c o n d i t i o n moni t o r i n g , 282 - f a i l u r e d i s t r i b u t i o n , 237 P i t t i n g o f gears, 232 P i v o t b e a r i n g s , 351 - l u b r i c a t i o n o f , 332 P l a n e t a r y gears, 351 P l a n i n g , 353 P l a s t i c c o n t a c t processes, 55 P l a s t i c deformation i n r o l l i n g f r i c t i o n , 85 P l a s t i c i t y i n d e x , 55, 101, 179 P l o u g h i n g component o f s l i d i n g f r i c t i o n , 77 Poisson s t a t i s t i c a l process, 238 P o l i s h i n g , 353 P o l y e t h y l e n e (HDPE), f r i c t i o n a l b e h a v i o u r o f , 317 Polymer-steel s l i d i n g p a i r s , f r i c t i o n o f , 316 P o l y t e t r a f l u o r e t h y l e n e (PTFE) , f r i c t i o n a l b e h a v i o u r o f , 317 Power, balance, 37 - c i r c u l a t i n g p r i n c i p l e , 274 - screws, 351 - t r a n s m i s s i o n systems, 350 P r e l i m i n a r y displacements, 73 P r e s e n t a t i o n o f r e s e a r c h data, 312 P r e s s i n g , 346, 352 P r i n t i n g u n i t s , 352 P r o f i 1ometer t e c h n i q u e , 289 P r o p e r t i e s o f t h e elements o f t r i b o - m e c h a n i c a l systems, 306

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398 Prow f o r m a t i o n , Punching , 353

121

Q u a r r y ing , 352 Quinn's theory o f t r i b o o x i d a t i v e wear, 124 Rack-and-pinions, 351 R a d i o a c t i v e t r a c e r methods, 283 R a y l e i g h d i s t r i b u t i o n , 236 Real a r e a o f c o n t a c t , 53 Reduction, o f f r i c t i o n - i n d u c e d noise, example, 338 o f severe wear, example, 335 Redundancy, 242 o f mechanical systems, 243 Relays, 352 Re1ia b i 1 ity, 234 - f u n c t i o n , 235 - o f mechanical equipment, 234 Rep1acement o f mechanical systems, 241 Requirements f o r p r o p e r f u n c t i o n a l behaviour, 240 Research d a t a p r e s e n t a t i o n , 312 Retarded van d e r Waals f o r c e s , 60 Reynolds, - c o n d i t i o n , 141 e q u a t i o n , 139, 147, 155 * - number, 167 - s l i p i n r o l l i n g f r i c t i o n , 82 Roll ing, c o n t a c t f a i l u r e , 108 - f r i c t i o n , 81 - i n metalworking, 346, 352 Rope d r i v e s , 351 Roughness, - hypothesis o f f r i c t i o n , 4 - o f surfaces, 51 Runni ng- in , o f b e a r i n g s u r f a c e s , 182 - schedules, 185 Rusting, f a i l u r e d i s t r i b u t i o n o f , 239

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-

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SAE t e s t , 276 S a f e t y o f e n g i n e e r i n g systems, 228 Sawing, 353 Scale f a c t o r s i n s i m u l a t i v e t r i b o t e s t i n g , 267 Scanning e l e c t r o n microscopy (SEM) , 289 S c u f f i n g , 119, 167 - i n c i p i e n t , 171 o f gears, 233 Seals, 352

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Secondary i o n mass spectroscopy ( S I M S ) , 293, 296 Seizure, 119, 167 Severe wear, 99 Shakedown l i m i t i n r o l l i n g , 85 Shaping, 353 Shoe-on-ground, 351 S h o r t range f o r c e s , 59 S i mu1 a t ion, methods, 248 o f s t i c k - s l i p behaviour, 218 S i m u l a t i v e t e s t i n g , 264 - o f b e a r i n g m a t e r i a l s , 268 schematic o u t l i n e o f , 270 S1 ideways , 351 S l i d i n g b e a r i n g s , 351 S l i d i n g f r i c t i o n , 73 S1 i p - r i ng assembl i e s , 352 S l i p systems i n c r y s t a l s , 66 S o l u b i l i t y o f m e t a l s and t r i b o l o g i c a l behaviour, 63, 120 S o l u t i o n s o f t r i b o l o g i c a l problems, 315 Sommerfel d, c o n d i t i o n , 141 number, 143 Sound, emission o f , 91, 338 Spalling fatigue failure i n r o l l ing c o n t a c t , 108 S p e c t r o g r a p h i c o i 1 a n a l y s i s procedure (SOAP), 282 S p i n d l e s , 351 Spinning, 352 S p l i n e s , 351 Spur gears, 351 Squeeze t e r m o f Reynolds e q u a t i o n , 139 Staining, f a i l u r e d i s t r i b u t i o n o f , 239 S t a r v a t i o n o f l u b r i c a n t , 152 S t e a r i c a c i d , 159 S t i c k - s l i p e f f e c t s , 215 analogue computer s i m u l a t i o n , 218 i n w h e e l - r a i l system, 338 Storage o f f r i c t i o n a l energy, 89 S t r a i n gauges, 258 S t r a i n h a r d e n i n g due t o f r i c t i o n and wear, 192 S t r e t c h t e r m o f Reynolds e q u a t i o n , 139 S t r i b e c k curve, 130, 219 Structure, o f a system, 16 o f t r i b o - m e c h a n i c a l systems, 30, 176, 305 Subsurface c o n t a c t shear s t r e s s e s , 107

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-

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399 S u p e r p o s i t i o n o f wear mechanisms, 127 Surface, c o a t i n g s , 208 c o m p o s i t i o n , 57, 186, 190 composition i n v e s t i g a t i o n techniques, 291 c o n t o u r maps, 291 energy, 67 energy c r i t e r i o n , 196 f a t i g u e wear mechanisms, 105 i n v e s t i g a t i o n t e c h n i q u e s , 286 preparation i n tribo-testing, 252 roughness, 51 roughness i n EHD l u b r i c a t i o n , 170 s t r e n g t h p r o p e r t i e s , 191 'topography, 51, 180, 181 topography measuring techniques, 286 S w i tches , 352 Sys tem, concept, 14 definition, 16 dependent c h a r a c t e r i s t i c s , 65, 265 .- f u n c t i o n , 16, 27, 211, 303 .- h i e r a r c h y , 15 independent c h a r a c t e r i s t i c s , 65, 274 methodology, 300, 315 m o d e l l i n g techniques, 18 structure, 16, 30, 176, 242, 305 t e a r i n g , 25

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~

-

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I

I

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Tangential forces i n contact processes, 69 Tape r e c o r d e r heads, 352 T a y l o r v o r t e x f l o w , 167 Technical f u n c t i o n s o f t r i b o - m e c h a n i c a l systems, 27, 211, 303, 350 Temperature, c o n t r o l l e v e l s f o r b e a r i n g s , 280 e f f e c t s i n EHD l u b r i c a t i o n , 153, 170 measuring techniques, 255, 259 .- r i s e s due t o f r i c t i o n , 94 Test, d u r a t i o n , 256 - methods, 248 T e s t i n g , 248 full-scale, 277 o f l u b r i c a n t s , 274 o f machine elements, 272 Thermal, - e f f e c t s due t o f r i c t i o n , 94 -. q u a n t i t i e s i n t r i b o - t e s t i n g , 257 -. t r a n s a c t i o n s , 38 Thermocouples , 259 Through v a r i a b l e s , 19

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-

T i l t i n g pad b e a r i n g , 134 Timken t e s t , 276 Topography o f s u r f a c e s , 5 1 Transactions o f q u a n t i t i e s i n systems, 21, 30 T r a n s i t i o n s i n l u b r i c a t i o n modes, 168, 171 Transmission o f m o t i o n , i n f l u e n c e o f f r i c t i o n , 215 T r i b o - c h e m i c a l wear mechanisms, 123 T r i bo-engi n e e r i ng systems, c o m p i l a t i o n o f , 350 Tribology, - d e f i n i t i o n , 11 - g e n e r a l t h e o r y , 24 - h i s t o r i c a l development, 3 - meaning o f , 11 T r i b o l o g i c a l processes, 33, 45 , 307 - i n f l u e n c e on t h e f u n c t i o n o f mechanical systems, 211 - i n f l u e n c e on t h e s t r u c t u r e o f mechanical systems, 176 T r i b o l o g i c a l systems d a t a sheet, 301, 309 T r i b o l umi nescence , 92 Tribo-mechanical system, d e f i n i t i o n , 27 T r i b o m e t e r , 4, 248 T r i b o m e t r i c c h a r a c t e r i s t i c s , 251 T r i bometry, 248 T r i b o - p r o c e s s diagram, 32 T r i bo- t e s t i n g , 248 Turbulences, 167 T u r n i n g , 353 Two-port system, 214 T y p e w r i t e r u n i t s , 352 T y r e and road, 352

U n i t event, - i n f r i c t i o n , 75 - i n wear, 100 Valency f o r c e s , 59 Valves, 352 Vanadi z i ng , 322 Van d e r Waals adhesion, 58 V e l o c i t y c o n t r o l methods i n t r i b o t e s t i n g , 255 V i b r a t i o n measuring t e c h n i q u e s , 258. 279 Video p i c k - u p s , 352 V i scoel a s t i c i ty, 55 V i s c o s i t y , 134 - p r e s s u r e c o e f f i c i e n t , 148 - temperature dependence, 153 Vogelpohl ' s method, 245

400

V o i g t model o f v i s c o e l a s t i c i t y , Vortex f l o w , 167

55

Washers, 352 Wear, 2 c o e f f i c i e n t , 262 - c l a s s i f i c a t i o n , 7, 102 - d e b r i s , 189 - i n boundary l u b r i c a t i o n , 164 - m o n i t o r i n g techniques, 281 - p a r t i c l e s , 122, 197, 198 processes, 97 processes, s u p e r p o s i t i o n o f , 127 q u a n t i t i e s , 261 - q u a n t i t i e s , formal representation, 308 - r e d u c t i o n , example, 335 - r e s i s t a n c e , d e f i n i t i o n , 114 - r e s i s t a n t c o a t i n g s , 207, 321 - studies, h i s t o r i c s o f , 6 t e s t methods, 250, 262, 281 - t e s t r i g s , 252 t i m e behaviour, 195, 235

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-

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Weaving, 352 Wedge d r i v e , 222 Wedge t e r m o f Reynolds equation, 139 W e i b u l l d i s t r i b u t i o n , 238 Well d r i l l i n g , 352 Wheel and r a i l , 338, 352 Workpiece d i e i n t e r f a c e , 347 Work, t r a n s a c t i o n s , 36 t r a n s m i s s i o n systems, 350 Worm gears, 351 W r i t i n g u n i t s , 352

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Yielding, f a i l u r e d i s t r i b u t i o n of, 2 39 Zinc dioctyl-dithio-phosphate, Zero-wear model, 244

159

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