ROUGH SURFACES T.R Thomas M.I.Prod.E M.Sc., Ph.D., C.Eng., F.Inst.P., M.I.Mech.E., BRITISH LIBRARY LENE: e ˆ no a sợ 029 g2/3008 ©) — a — ——— ——— ——— N Longman Group Limited, Longman House, Burnt Mill, Harlow, Essex, U.K Published in the United States of America by Longman Inc., New York © Longman Group Limited 1982 “All rights reserved No part of this publication may be tted reproduced, stored in a retrieval system, Or transmi cal, mechani nic, electro means, any by or form any in photocopying, recording, or otherwise, without the prior permission of the Copyright owner First published 1982 Data British Library Cataloguing in Publication Rough surfaces Surface roughness I Thomas, TR TA418.7 620.1712 ISBN 0-582-46816-7 80-41304 Printed by Singapore National Printers (Pte) Ltd CONTENTS ix xi xiii XVi xix List of contributors Preface Acknowledgements Nomenclature Suffixes Creation of surfaces Analysis of surfaces Homogeneous and stratified textures Summary MEASUREMENT CHAPTER STYLUS INSTRUMENTS 11 T R Thomas ent General considerations of roughness measurem Design of stylus instruments The stylus Transducers Pickup and gearbox Output recording Sources of error Effect of stylus size 2.3.2 Effect of stylus load Other sources of error 2.3.3 Measurement of compliant surfaces 2.4 Relocation 2.5 Replication 2.6 a" Surface mapping Gà tè Height distribution of surfaces PART ONE 2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.3 2.3.1 J B P Williamson + ‘11 1.2 1.3 1.4 1.5 THE SHAPE OF SOLID SURFACES tư ` CHAPTER 12 12 13 16 17 18 19 21 21 24 26 28 29 32 35 Contents OTHER MEASUREMENT TECHNIQUES _ CHAPTER 3.1 3.1.1 Optical methods Geometrical optics 3.1.2 Physical optics Contact methods Tactile tests 53 Friction dynamometer 55 i x is Thetameter 55 Thermal comparator 56 Rolling ball 55 Electrical methods 3.3 Capacitance 58 Induction 59 Skin resistance 59 Fluid methods Scraping 59 Sand patch 60 Outflow meter 60 Pneumatic 64 gauging 62 Oil droplet 63 Stagnant layer 64 Flowing drop 3.4 In-process measurement 3.5 3.6 Comparison of measurement techniques PART TWO CHARACTERIZATION CHAPTER PROFILE H C Ward DESCRIPTION 4.1 4.2 4.2.1 Profile geometry Bandwidth selection Mean line fitting 4.2.2 4.3 4.3.1 Filtering Numerical assessment Vertical descriptors The E-system 76 4.3.2 4.4 4.4.1 CHAPTER Optical probes 45 Direct Fourier transformation 53 Gloss measurement 52 3.2 5.1 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 Average parameters 81 Horizontal descriptors Roughness standards Glossary of some characterization Bearing area curves 83 terms and definitions THE PROFILE AS A RANDOM used PROCESS Average roughness parameters Centre-line average R, 92 Root mean square o 92 in roughness R S Sayles | Relative merits of R, and a 92 Statistical methods Probability or distribution function Probability density function Height distribution Bearing area Random-process methods Autocovariance and autocorrelation functions Structure function Peak Vi Optical sections 45 Taper sectioning 43 T R Thomas and valley structure functions 108 | Contents 42 5.3.3 5.4 42 5.4.1 43 5.4.2 47 5.4.3 53 CHAPTER 58 59 6.1 6.2 6.3 6.3.1 59 6.3.2 6.4 © CHAPTER : 0 So 1 7.1 7.2 5} 5 Long-wavelength limit: non-stationarity THE SURFACE AS A RANDOM R D Gibson 8.1.1 8.2 8.2.1 8.2.2 8.2.3 8.2.4 8.2.5 8.3 8.4 PROCESS , 114 119 119 119 126 126 Anisotropic surfaces 131 Discussion 131 Discussion 136 Measurement of spectral moments (R S Sayles) 136 DIGITAL TECHNIQUES 144 D J Whitehouse Introduction Digital assessment Moments of the height distribution 8.1 114 109 110 111 112 Introduction Statistics of a surface profile Surface statistics Isotropic surfaces 7.2.2 7.3 7.3.1 7.3.2 7.4 7.5 4 Defining correlation parameters from profile measurements Pre-processing of data CHAPTER | Short-wavelength limit 7.2.1 PART THREE O Power spectral density function Practical considerations in parameter definition Functional filtering Polynomials 147 Centre lines 148 Filter methods 149 144 147 147 Sampling Quantization Variability Methods of assessing random-process functions 152 153 153 154 158 163 APPLICATIONS 167 Sources of error CONTACT MECHANICS A W Bush Introduction Elastic contact equations Contact of a parabola and a plane 169 paraboloid and a plane 170 Contact of an elliptic Elastic contact of a rough and a smooth surface The Greenwood and Williamson model The Whitehouse and Archard model The Nayak model Bearing area The elliptic model Plastic contact Anisotropic surfaces 168 168 168 170 171 173 176 178 180 181 184 vũ Contents CHAPTER TRIBOLOGY 9.1 9.1.1 Introduction Number and spacing of micro-contacts 189 190 9.2 9.2.1 Lubrication Reynolds’ equation for rough surfaces 194 194 9.2.2 9.2.3 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.4 CHAPTER 10 10.1 10.2 10.2.1 10.2.2 10.3 10.4 10.5 10.6 10.7 Average ‘width’ of a micro-contact 191 micro-contact 192 Two-dimensional Contact through lubricant film Pitting 200 Asperity models Criteria for plastic contact Transitional surface topographies Boundary lubrication Practical difficulties The adhesion index Mechanisms of scuffing OTHER APPLICATIONS Introduction Functional filtering Choosing the cut-offs Examples T R Thomas and R S Sayles of curved Roller-bearings 214 Machine-tool stiffness 215 Contact 220 resistance surfaces 216 Mechanics of human joints 217 Contact Bearing vibration 223 Running-in Lip seals Fluid flow Dimension and tolerance Grinding Index of Principal Authors Subject Index C Average area of a Transverse ridges 195 Longitudinal ridges 196 roughness 197 Stokes’ terms 197 References vill 189 J A Greenwood 198 201 202 203 205 205 207 208 211 211 212 212 214 226 231 233 236 238 241 253 257 LIST OF CONTRIBUTORS T R Thomas M.Sc., Ph.D., C.Eng., F.InstP., M.I.Mech.E., M.1.Prod.E Head, Department of Mechanical Engineering, Teesside Polytechnic, Middlesbrough A W Bush ematics and R D Gibson B.Sc., Ph.D Senior Statistics, Teesside Lecturer, Polytechnic B.Sc., M.Sc., Ph.D., F.ILM.A School of Mathematics, Tyne Polytechnic Department Professor and Head Statistics and Computing, J A Greenwood B.A., Ph.D of Math- Fellow of Peterhouse, Cambridge, University Lecturer in Engineering R S Sayles Engineering, B.Sc., Ph.D Lecturer, Imperial College H C Ward M.Sc., C.Eng., F.1.Prod.E of Mechanical Engineering, Teesside Department of Engineering, and Mechanical Senior Lecturer, Department Polytechnic, Middlesbrough D J Whitehouse B.Sc., Ph.D., C.Eng., M.Inst.P., M.I.E.E of Mechanical University of Newcastle upon Department of Engineering, J B P Williamson Ph.D., C.Eng., F.Inst.P., Consultant, Williamson Interface Ltd F.I.E.E., Professor Warwick F.I.Mech.E ix } ad wee ¬— PREFACE The roughness of solid surfaces is an effect of second order only in physical terms, but one which has profound practical consequences in many fields of engineering and pure science where the challenge of first-order effects has now been largely overcome A glance at the ị bibliography will show that these fields may range from quality assur- C) tribology, biomechanics and hydrodynamics, to oceanography and selenology at the other The present work attempts to bring together for the first time within two covers the threads of this vast and growing | | | ! ©) ance and control in production engineering at one extreme, through subject It is intended for engineers, physicists and others whose work involves them in problems of measuring or describing the topography of solid surfaces or of applying these measurements and descriptions in practical or scientific contexts The subject material falls naturally into three sections: measurement, characterisation and applications In the first part the general problems of roughness measurement are reviewed and the many existing and proposed techniques are described and compared In the second part the problems of describing and quantifying these measurements are discussed and mathematical and computational methods are presented at length In the final part the application of these experimental and analytical tools to scientific and engineering problems in contact mechanics, tribology and many other areas are discussed and illustrated with a number of practical examples from the recent literature The level of exposition assumes mathematical competence appropriate to a first degree in engineering or the physical sciences The genesis of this book was a series of short courses entitled “Surface Topography in Engineering” organised by the Mechanical Engineering Department of Teesside Polytechnic and held at Teesside Polytechnic annually from 1976 The distinguished contributors to this book have all lectured on the Teesside course at one time or another and between them embody a considerable part of the world expertise on the subject Brian Williamson was one of the earliest workers to apply statistical and computer techniques to roughness measurement in his days as Research Director of the Burndy Corporation in Norwalk, Connecticut, where both Jim Greenwood and I worked for him at xi rn Preface the Metrology Laboratory at different times Harry Ward has run centre of expertise for much of Teesside Polytechnic for many years as a s was my own student and the North-East of England Richie Sayle to Imperial by way of bearing collaborator at Teesside before travelling Dennis Gibson was also at research at Ransome Hoffman Pollard the Maths Department Last Teesside as a collaborator of Alan Bush in f Research Engineer at Rank but not least, Dave Whitehouse was Chie r to the legendary R E Taylor Hobson for many years as successo Reason Xii () ee Ue r= F ACKNOWLEDGEMENTS The author is grateful to the following for permission to reproduce copyright material: American Institute of Aeronautics and Astronautics for our Figs 5.21 and 10.8 by Thomas and Sayles from Progress in Astronautics and Aeronautics, Vol 39; A.S.T.M for our Fig 3.10 by Doty, A.S.T.M STP 583 and our Figs 3.11a/b by Henry and Hegman from A.S.T.M STP 583, Copyright American Society For Testing and Materials, Philadelphia Reprinted with permission; American Society of Lubrication Engineers for our Fig 9.6 by Tallian, Chin, Huttenlocher, Kamenshine, Sibley and Sindlinger from ASLE Transactions, All rights reserved by the American Society for Lubrication Engineers; American Society of Mechanical Engineers for our Fig 10.3 by Greenwood and Tripp from Journal of Applied Mechanics, 34E, our Fig 4.6 by Olsen from Proceedings of the International Conference, Production Engineering, 8, our Figs 5.10, 6.7-6.11 by Sayles and Thomas from Journal of Lubrication Technology, 101F, our Fig 10.2 by Thomas and Sayles from Journal of Engineering for Industry, 99B and our Figs 1.31.5, 9.7 by Williamson, Pullen and Hunt from Surface Mechanics; Applied Science Publishers Ltd for our Fig 10.9 by Sayles and Thomas from Applied Energy, Vol 2; BHRA Fluid Engineering for our Figs 10.22 by Thomas and 10.18 by Thomas, Holmes et al from 6th International Conference on Fluid Sealing Proceedings, organised and published by BHRA Fluid Engineering; British Standards Institution for our Fig 4.5 from BS 1134 Part 1972 Elsevier Sequoia S A for our Figs 2.5a and 2.6 by Radhakrishnan from Wear 16 (1970) pp 325335, our Fig 2.14 by Thomas from Wear 22 (1972), our Fig 10.17 by Golden from Wear 39 pp 25-44, our Figs 2.15 by George and 10.20b by Manning from Wear 57 (1979) pp 51-62 and 365-376, and the author for our Figs 3.4, 3.5 and 10.15 by E L Church from Wear 57 (1979) pp 93-106; Groupement pour |’Avancement de la Mecanique Industrielle for our Fig 2.3 by Thomas from Mecanique-Materiaux- Electricite No 337 (1978); I.F.S (Publications) Ltd for our Figs 3.13a/b by Dutschke and Eissler and 3.15 a/b by Clarke and Bedford from Proceedings of the 3rd International Conference on xiii ... Copyright owner First published 1982 Data British Library Cataloguing in Publication Rough surfaces Surface roughness I Thomas, TR TA418.7 620.1712 ISBN 0-582-46816-7 80-41304 Printed by Singapore... Suffixes Creation of surfaces Analysis of surfaces Homogeneous and stratified textures Summary MEASUREMENT CHAPTER STYLUS INSTRUMENTS 11 T R Thomas ent General considerations of roughness measurem... not ‘What the subject from is the shape rather ‘How surfaces acquire their shape?’ 1.1 a completely of surfaces? ’ but Height distribution of surfaces The word ‘shape’ means, in this context, the