Rough Surfaces

Rough Surfaces Second Edition

Rough Surfaces Second Edition

Tom R.Thomas Production Engineering Department, Chalmers University of Technology, Sweden

Imperial College Press

Published by

Imperial College Press 203 Electrical Engineering Building Imperial College London SW7 2BT Distributed by

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British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library

First edition published in 1982 by Longman Group UK Limited

ROUGH SURFACES, Second Edition Copyright 0 1999 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN 1-86094-100-1

Printed in Singapore by Eurasia Press Pte Ltd

For Ann

CONTENTS

xi

PREFACE

...

Xlll

ACKNOWLEDGEMENTS

1. INTRODUCTION 1.1. Surface Roughness 1.1.1. What Causes Roughness? 1.1.2. Why Is Roughness Important? 1.2. Principles of Roughness Measurement 1.2.1. Range and Resolution 1.3. References

2. STYLUS INSTRUMENTS 2.1. Mechanical Instruments 2.2. Electrical Instruments 2.2.1. Stylus and Skid 2.2.2. Transducers 2.2.3. Pickup 2.2.4. Output Recording 2.3. Sources of Error 2.3. I . Effect of Stylus Size 2.3.2. Effect of Stylus Load 2.3.3. Other Sources of Error 2.4. Calibration and Standards 2.5. References

11 11 13 15 16 18 19 20 20 23 25 28 29

3.

35 36 36 37 44 46 47 49

OPTICAL INSTRUMENTS 3.1. Profiling Techniques 3.1.1. Optical Sections 3.1.2. Optical Probes 3.1.3. Interferometers 3.2. Parametric Techniques 3.2.1. Specular Reflectance 3.2.2. Total Integrated Scatter vii

Rough Surfaces

viii

3.3.

3.2.3. Angular Distributions 3.2.4. Direct Fourier Transformation 3.2.5. Ellipsorvietry 3.2.6. Speckle References

50

52 52 54 56

4. OTHER MEASUREMENT TECHNIQUES 4.1. Profiling Methods 4.1.1. Taper Sectioning 4.1.2. Electron Microscopy 4.1.3. Capacitance 4.1.4. Scanning Microscopies 4.2. Parametric Methods 4.2.1. Mechanical Methods 4.2.2. Electrical Methods 4.2.3. Fluid Methods 4.2.4. Acoustic Methods 4.3. References

63 63 63 64 66 68 71 71 77 80 83 84

5.

91 91 95 97 100 102 106

OTHER MEASUREMENT TOPICS 5.1. 3D Measurement 5.2. Relocation 5.3. Replication 5.4. In-Process Measurement 5.4.1. Optical Techniques 5.5. References

6. DATA ACQUISITION AND FILTERING 6.1. Data Acquisition 6.2. Filtering 6.2.1. Envelope Filters 6.3. References

113 113 115 125 130

7. AMPLITUDE PARAMETERS 7.1. Extreme-Value Parameters 7.2. Average Parameters 7.3. The Height Distribution

133 134 138 139

Contents

7.4, 7.5,

Bearing Area References

8. TEXTURE PARAMETERS 8.1, Random Processes 8.2, The Profile as a Random Process 8.3, Practical Computation 8.4. Fractal Roughness 8.5. References 9.

SURFACES IN THREE DIMENSIONS 9.1, Filtering 9.2, Parameters 9.3, Random Processes in Three Dimensions 9.4, The Surface as a Random Process 9.5, Practical Computation 9.6. Anisotropy 9.7. References

ix

144 147 151 152 157 159 162 168 171 172 173 177 180 185 188 195

10. APPLICATIONS: CONTACT MECHANICS 10.1. The Contact of Rough Surfaces 10.2. Rough Contact Mechanics 10.2.1. Contact of Curved Sulfaces 10.2.2. Joint Stiffness 10.3. The Plasticity Index 10.4. References

199 201 205 212 214 2 15 220

11. TRIBOLOGY 11.1. Friction 11.2. Lubrication 11.3. Wear 11.4. Seals 11.5. References

225 225 227 229 235 238

12. SOME OTHER APPLICATIONS 12.1. Contact Resistance 12.2. Noise and Vibration

247 247 250

Rough Su$aces

X

12.3. 12.4. 12.5. 12.6. 12.7. 12.8.

INDEX

Fluid Flow Dimension and Tolerance Abrasive Machining Bioengineering Geomorphometry References

25 1 255 257 259 26 1 263

269

PREFACE

This book is intended for graduate scientists and engineers who need to know somethmg more about roughness, how to measure and describe it and what practical problems it might cause them. It assumes a general familiarity with scientific and engineering terms and concepts and a mathematical level nowhere above that of a final-year engineering course. For a non-mathematical introduction to the subject at an undergraduate level, the reader is commended to the book by Mummery cited extensively in the text. A more comprehensive and rigorously mathematical account, to which the reader will also often be referred in these pages, is that of Professor Whitehouse. The first edition of Rough Surfaces, the first comprehensive monograph on the subject in English, was published in 1982 as a multi-author work. Several of the original authors have since enjoyed professional careers of some distinction, reflecting the increased importance of the subject since that time. Advances in the intervening period have required the addition of much new material and the updating of most of the original work, so that the present book is almost entirely a new production. Some of the new material is based on lectures which I have given at Chalmers University over the last few years. The book treats roughness primarily as an engineering phenomenon, reflecting its author’s interests and background in tribology and production engineering. I am very conscious, however, of the scientific and technical communities, of hydrodynamicists, geographers, optical engineers and many others, for whom roughness is equally important, and I have tried to keep the discussion as general as possible to reflect their needs and preoccupations. This is considerably helped by the conceptual unity of the subject; techniques of characterisation used successfully by the atomic-force microscopist can often be applied virtually without change to the problems of the geomorphologist, and vice versa. For those with more specialist interests, there are monographs (on scattering, for instance, by Ogilvy, and Bennett and Mattsson) which will be referred to where appropriate in the text. The subject naturally divides into three parts: measurement, characterisation and applications, and this division will be followed in the structure of the book. A large number of people have contributed to this book in various ways and I thank them all for their help and for their encouragement over what must have Xi

xii

Rough Surfaces

seemed a very long period. I am grateful to my colleagues at Chalmers University for many valuable discussions and other lundnesses, and particularly to BengtGoran Rosen and Robert Ohlsson for their fruitful collaboration, and to Professor Ralph Crafoord for extending to me the hospitality and facilities of the Production Engineering Department. I am also grateful to the University itself for the award of a Jubilee Professorship during 1997/98 which considerably aided the writing of this book.

ACKNOWLEDGEMENTS

I am grateful for permission to use copyright material from the following copyright holders: American Institute of Aeronautics and Astronautics for my Figs. 8.8 and 12.2 from Thomas & Sayles 1975, Prog. Astronaut. Aeronaut. 29, 3-20 Figs. 5 & 8; American Physical Society for my Fig. 4.5 from Hansma & Tersoff 1987, J. Appl. Phys. 61, Rl-R23 Fig. 1, my Fig. 4.6 from Alexander et al. 1989, J. Appl. Phys. 65, 164 Fig. 1, my Fig. 10.6 from Archard 1961, J. Appl. Phys., 32, 1420-1425 Fig. 2; American Society of Mechanical Engineers for my Fig. 6.14 from Olsen 1963, Proc. Int. Prod. Eng. Res .Con$, Pittsburgh, 8, 655-658 Fig. 3, my Figs. 7.11, 9.10 and 9.11 from Sayles & Thomas 1979, J Lubr Techno1 101, 409-417 Figs. 2, 11, 12, my Fig. 7.16 from Williamson et al. 1969 in: Surface mechanics. Ling, F.F. (ed.), 24-35 Fig. 2, my Figs. 9.8 and 9.9 from Nayak 1971, J. Lubr. Tech., 93, 398-407 Figs. 4-6, 10, my Fig. 10.3 from Majumdar & Bhushan 1990, Journal of Tribology 112, 205-216 Fig. 11, my Fig. 10.10 from Greenwood & Tripp 1967, J. Appl. Mech. 34, 153-159 Fig. 5, my Fig. 12.9 from Thomas et al. 1980, J. Biomech. Eng., 102, 50-57 Fig. 3; American Society for Testing Materials for my Fig. 4.10 from Doty 1975, 42-61 Fig. 1, and my Fig. 4.13 from Henry & Hegmon 1975, 3-17 Fig. 1, both in Surface Texture versus Skidding: Measurements, Frictional Aspects and Safety Features of Tire-pavement Interactions, STP 583; ARRB Transport Research Ltd. for my Fig. 12.10 from Potter et al. 1992, Road & Transport Research 1, 6-27 Fig. 2; British Hydromechanic Research Association for my Fig. 11.9 from Thomas et al. 1975, Proc. 7th. Int. Con$ on Fluid Sealing, Paper J32, my Fig. 12.3 from Thomas & Olszowski 1974, Proc. 6th. Int Gas Bearing Symp. D6, 73-92 Fig. 5; British Standards Institution for my Fig. 6.6 from BS1134 Part 1 1988 Fig. 20, my Fig. 6.9 from BS1134 Part 2 1972 Fig. 4; Cassell plc, London, for my Fig. 2.1 from Galyer & Shotbolt 1990, Metrologyfor engineers 5e Fig. 9.3; Chalmers University, Goteborg, for my Figs. 2.6 and 5.2 from Desages & Michel 1993 Figs. 2.9, 3.5, 3.6, 3.8; Elsevier Science, Oxford, for my Fig. 1.5 from Stedman 1987, Prec. Engng., 9, 149-152 Fig. 2, my Fig. 3.16 from Vorburger & Teague 1981, Precis. Eng. 3,61-83 Fig. 19, my Fig. 7.1 from Thomas & Charlton 1981, Precis. Eng. 3, 91-96 Fig. 3, my Fig. 10.2 from Sayles & Thomas 1976, Appl. Energy, 2 , 249-267 Fig. 1, my Figs. 2.7 and 2.8 from Radhakrishnan 1970, Wear, 16, 325-335 Figs. 1 & 9, my Figs. 5.4 & xiii

xiv

Rough Surfaces

11.6 from Thomas 1972, Wear, 22, 83-90 Figs. 2 & 4, my Fig. 5.6 from George 1979, Wear, 57, 51-61 Fig. 4, my Figs. 5.8 & 5.9 from Clarke & Thomas 1979, Wear, 57, 107-116 Figs. 2, 4, 5, my Fig. 6.4(b) from Thomas 1975, Wear, 3 3 , 205-233 Fig. 1, my Fig. 6.16 from Fahl 1982, Wear 83, 165-179 Fig. 3, my Fig. 6.17 from Shunmugam 1987, Wear 117, 335-345 Fig. 3c, my Fig. 8.6b from Thomas & Sayles 1978, Tribology International, 11, 163-168 Fig. 2, my Fig. 8.7 from Thwaite 1978, Wear, 51, 253-267 Fig. 3, my Fig. 10.8 from So & Liu 1991, Wear 146, 201-218 Fig. 8, my Fig. 10.9 from Woo & Thomas 1979, Wear, 5 8 , 331-340 Figs. 1 & 2, my Fig. 10.11 from Wu & Zheng 1988, Wear, 121, 161-172 Fig.1, my Fig. 11.1 from Koura & Omar 1981, Wear, 73, 235-246 Fig. 11, my Fig. 11.2 from Ogilvy 1993, Wear 160, 171-180 Fig. 6, my Fig. 11.8 from Golden 1976, Wear, 42, 157-162 Fig. 3, my Fig. 3.6 from Brown 1995, Int. J. Mach, Tool Manufact. 35, 135-139 Fig. 1, my Fig. 4.15 from Wager 1967, Int. J. Mach. Tool Des. Res., 7, 1-14 Fig. 5, my Fig. 12.7 from Sayles & Thomas 1976, Int. J. Prod. Res 14, 641-655 Figs. 3 & 6, my Figs. 1.3 & 1.6 from Thomas 1998, Int. J. Mach. Tool Manufact. 38, 405-41 1 Figs. 1 & 2, my Fig. 9.16 from Zahouani 1998, Int. J. Mach. Tool Manufact. 38, Fig. 11, my Figs. 8.13 & 10.13 from Rostn et al. 1998, Int. J. Mach. Tool Manufact. 38, Figs. 2 & 3, reprinted with permission; the European Commission for my Table 9.1 from Stout et al. 1993, The development of methods f o r the characterisation of roughness in 3 dimensions, EUR 15178 EN Fig. 12.22; Feinpriif Perthen GmbH, Gottingen, for my Figs. 7.2, 7.3 and 8.2 from Sander 1991, A practical guide to the assessment of surfice texture Figs. 12a, 13, 27; Hallwag Verlags GmbH, Ostfildern, for my Fig. 3.15 from Lonardo 1978, Ann. CIRP27, 531-533 Fig. 5, my Fig. 4.7 from Goch & Volk 1994, CIRP Ann. 43, 487-490 Fig. 6; Hommelwerke GmbH, Schwenningen, for my Figs. 6.11, 6.12, 6.15, 7.4, 7.7, 7.8, 7.12-7.15 from Mummery 1990, Sugace texture analysis: the handbook, Figs. 2.10, 2.1 1, 3.2, 3.3, 3.4, 3.6, 3.13, 3.17, 3.18, 3.19, 3.25, 3.26, 3.29, 3.30; I. F. S. (Publications) Ltd., Bedford, for my Fig. 5.7 from Dutschke & Eissler 1978, Proc. 3rd. Con$ on Automated Inspection & Product Control 19-30 Fig. 1; Indian Institute of Technology, Madras, for my Fig. 4.14(b) from Radhakrishnan & Sagar 1970, Proc. 4th. All-India Machine Tool Design & Research Con$ Fig. 1; Industrial Press Inc., New York, for my Figs. 2.4, 3.2 and 4.14 from Farago 1982, Handbook of dimensional measurement 2e, Fig. 6.1, Tables 15.2 & 15.4, used with permission; IOP Publishing Ltd., Bristol and the authors for my Figs. 3.3, 3.8 and 3.9 from Whitehouse 1994, Handbook of surfme metrology, Figs. 4.112 & 4.1 17, my Fig. 4.3 from Bugg & King 1988, J. Phys. E: Sci. Instrum., 21, 147-151 Fig. 2, my Fig. 4.9 from Powell 1957, J . S c i . Instrum., 34, 485-492 Fig. 1; Institution of

Acknowledgements

xv

Electrical Engineers for my Figs. 2.9 and 2.10 from Reason 1944, J. Inst. P r d . Engrs., 23, 347-372 Figs. 4 & 16; Institution of Mechanical Engineers for my Fig. 2.2 from Lackenby 1962, Proc. I. Mech. E., 176, 981-1014 Fig. 1, my Fig. 3.1 from Keller 1967/8, Proc. I. Mech. E., 182, Part 3K, 360-367 Fig. 3.5, my Fig. 3.1 1 from Westberg 1967/68, Proc .I .Mech .E., 182, Part 3K, 260-273 Fig. 25.1, my Fig. 7.5 from Hydell 1967/8, Proc. I. Mech. E., 182, Part 3K, 127-134 Fig. 15.7, my Fig. 8.4 from Peklenik 1967/68, Proc. I. Mech. E., 182, Part 3K, 108126 Fig. 24.18, my Fig. 11.5 from Leaver et al. 1974, Proc. 1. Mech. E., 1 8 8 , 461-469 Fig. 1, my Fig. 11.7 from Thomas 1978, Proc. 4th Leeds-Lyon S y m p . , 99-108 Fig. 5, by permission of the Council of the Institution; International Business Machines for my Fig. 4.4 from Binnig & Rohrer 1986, ZBM Journal of Research and Development 30; 355-369 Fig.1; Japanese Society of Precision Engineers for my Fig. 2.12 from Nara 1966, Bull. Jap. SOC. Precision Engng., 1, 263-273 Figs. 5 & 8; Kluwer Academic Publishers, Dordrecht, with kind permission for my Fig. 2.14 from Song 1988, Sulface Topography, 1, 29-40 Fig. 2, my Fig. 3.4 from Bristow 1988, Sulface Topography, 1, 281-285 Fig. 1, my Fig. 3.5 from Sayles et al. 1988, Sulface Topography, 1, 219-227 Fig. 1, my Figs. 4.1 and 4.2 from Garbini et al. 1988, Surface Topography, 1, 131-142 Figs. 1 & 6, my Figs. 4.1 1 and 4.12 from Lieberman et al. 1988, Sulface Topography, 1, 115-130 Figs. 3 & 6 , my Fig. 11.4 from Chandrasekaran 1993, J. Mat. Sci. Lett. 12, 952-954 Fig. 5; Lasertec Corporation for my Fig. 3.7; Macmillan Magazines Ltd., Basingstoke, and the authors, for my Fig. 8.9 from Sayles & Thomas 1978, Nature 271, 431-434 Fig. 2, reprinted with permission; Macmillan Press, Basingstoke, and the authors, for my Fig. 2.11 from Agullo & Pages-Fita 1974, Proc. 15th. Int. Machine Tool Des. & Res. Conf., 349-362 Fig. 9, my Fig. 12.6 from Thomas 1973, Proc. 13th Int. Machine Tool Des. & Res. Conf., 303308 Fig. 3b, reprinted with permission; the McGraw-Hill Companies, New York, for my Fig. 5.1 from Terman 1937, Radio Engineering 2e, Fig. 430, my Fig. 12.4 from Hunsaker & Rightmire 1947, Engineering applications offluid mechanics Fig. 43; McGraw-Hill Publishing Co., Maidenhead, for my Fig. 6.5 from Golten 1997, Understanding signals and systems Fig. 7.8; Optical Society of America for my Fig. 3.10 from Creath 1987, Applied Optics 26, 2810-2815 Fig. 6, my Fig. 3.12 from Birkebak 1971, Appl. Opt. 10, 1970-1979 Fig. 1, my Fig. 3.17 from Fujii & Lit 1978, Appl. Opt. 17, 2690-2705 Fig. 1, my Fig. 3.13 from Bennett & Mattsson 1989, Introduction to sulface roughness and scattering Fig. 17; Plenum Publishing Corporation, New York, and the authors, for my Fig. 10.4 from Russ 1994, Fractal surfaces, p. 67 Fig. 9, my Fig. 12.8 from Longfield et al. 1969, Biomed. Engng. 4, 517-522 Fig. 1; Random House (UK) Ltd. for my Figs. 1.2 and 6.4a from Brooker

XVi

Rough &$aces

1984 ed., Manual of British standari in engineering metrology (Hutchinson), pp. 184 Fig. 1 and 191 Fig. 10.10; the Royal Society and the authors for my Fig. 9.12 from Greenwood 1984, Proc. Roy. SOC. Lond. A393, 133-157 Fig. 7, my Fig. 10.5 from Pullen & Williamson 1972, Proc. R. SOC.Lond. A327, 159-173 Fig. 3; Science History Publications Ltd. for my Fig. 1.1 from Thom & Thom 1972, J. Hist. Astron. 3, 11-26 Fig. 5; SociCtC Belge des Mecaniciens for my Fig. 3.3 from Whitehouse 1975, Rev. M. Mec. 21, 19-28 Fig. 11; Society of Manufacturing Engineers for my Fig. 2.13 and Table 11.1 from Thomas et al. 1975, S.M.E. Paper IQ75-128 Fig. 2; Society of Photo-optical Instrumentation Engineers and the authors for my Fig. 3.14 from Church et al. 1977, Opt. Eng. 16, 360-374 Fig. 11, my Fig. 9.15 from Thomas 1991, Proc. SPZE 1573, 188-200 Figs. 5 & 6 ; Society of Tribologists and Lubrication Engineers for my Fig. 10.7 from Lee & Ren 1996 Trib. Trans. 39, 67-74 Fig. 13, my Fig. 11.3 from Akamatsu et al. 1992, Trib. Trans. 35, 745-750 Fig. 8; Taylor Hobson Pneumo, Leicester, for my Fig. 6.7 from Whitehouse & Reason 1965, The equation of the mean line of surface texture found by an electric wavefilter, Figs. 11-14, my Figs. 7.6 and 9.14 from Dagnall 1980, Exploring surjiie texture, Figs. 17 & 46; VCH Verlagsgesellschaft mbH, Weinheim, and the author for my Table 4.1 from DiNardo 1994, Narwscale characterisation of surfaces and inte$aces, p. 145 Table 2. I have attempted to trace the copyright holder of all the material reproduced in this book and apologize to copyright holders if permission to publish in this form has not been obtained.

CHAPTER 1

INTRODUCTION

1.1. Surface Roughness

We are used to the idea that materials have intrinsic properties such as density, conductivity and elastic modulus. Surfaces, representing material boundaries, have perhaps rather more insubstantial properties, but we still think of some of these properties as intrinsic, like colour. There are other properties, however, which are easy to define but whose value seems to depend on the technique or scale of measurement: hardness, for instance. Roughness seems to be such a property, with the added difficulty that it is not always so easy to define as a concept. "I can't define roughness, but I know it when I see it". When we speak of "rough country", "a rough road", "a rough fabric", we imply very different scales of feature in each case, but we understand well enough what sort of surface is meant. The Concise OED has more than a column of meanings, starting with "of uneven or irregular surface, not smooth or level or polished, diversified or broken by prominences.. . .. . .. .coarse in texture.. . To develop this idea a little, it seems to have something to do with our scale of view. If the countryside, or the stretch of road, or the patch of fabric which we observed, simply rose steadily in our field of view, or contained a single prominence, we would not refer to it as "rough"; if it contained, say, ten prominences, we probably would so categorise it; if it contained a hundred such, we certainly would. So already, it seems, the ideas of sampling interval and sample size which we will introduce later are emerging and are bound up with the very concept of roughness at quite a fundamental level. .'I.

I . 1.1. What Causes Roughness? A geographer might find this a strange question. To him or her, accustomed to the scale of features of the natural world where roughness is the norm, a better question would be, "What causes flatness (or straightness)?". Generations of students have been accustomed by their education to the normality of ideal straight lines and flat surfaces. This has been exacerbated by the wide use of computer1

2

Rough Surfaces

aided drafting software, where straightness and flatness are the default assumptions. This is a conceptual problem not only for scientists and engineers, but for everyone with a Eurocentric education. The idea of straightness is built in to all Indo-European languages as a concept linked with good, power and approval, where "right", "rule", "regal" all have the same root. This is so deeply embedded in our mental software that we are disturbed by the alignements of Brittany, whose megalithic architects spent thousands of person-years constructing adjoining lines of huge boulders, kdometres long, equidistant but nowhere straight (Fig. 1.1). Clearly they understood the concept of straightness (otherwise how could they have made the lines equidistant?), but culturally it held no importance for them.

-.,.. ...... .................... ... .. ... .... ............... ......... .... .. ......... .- ._. ..... . ..._ * . ............ *.*. .... -.----....-. . . ....... ." .......... , .... . ..... ........ .... ... --. . . ..... .... .... ...........----........ .. .*.. . . .. ,...............-L.(..* . . . ........... * ' ....-.* ........ ...- . ...... . _.,.--- ....... ... .. *....... -. ., .,.. -.. .............. , . .*-........ ................ . ...... ........ -.. . ...... ..... 0

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1

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. . . . . . . . . U . " . *

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-

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50

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Figure 1 . 1 . Part of the Camac alignments, adapted tiom Thom & Thorn (1 972). Each mark represents a menhir; a typical menhir is 2m high and lm in diameter.

The fact is that roughness is the natural state of surfaces, and left to its own devices Nature will make sure they are rough. The roughness of a surface is a measure of its lack of order. Disorder is entropy under another name, and if we consider a solid surface as a closed system then the Second Law of Thermodynamics predicts that its entropy will tend to a maximum. To reduce its roughness we must reduce its entropy, and the Second Law tells us that we can only do this by doing work. Thus if we transpose the axes of the well-known figure which relates machining time to roughness, we see that it is nothing but an entropy diagram (Fig. 1.2). Many, perhaps most, natural surfaces are fractal (see Chapter 9), and it is characteristic of fractal surfaces that their roughness increases without limit. So it is that in a universe of fractal surfaces man's attempts to reduce entropy by imposing straightness and smoothness extend over only a very small range of dimensions (Russ 1994).

Introduction

3

work Figure 1.2. (a) Relationship of surface texture to production time (Brooker 1984); (b) The same figure replotted as work reducing entropy

1.1.2. Why is Roughness Important?

When I was starting research in the field of surface roughness years ago I was advised against it by a distinguished academic engineer on the grounds that roughness is essentially a second-order effect in physical systems, and would therefore never assume an important place in engineering science. Time has, I think, vindicated my judgement rather than hs, for two rather interesting reasons (Thomas 1988). The first is that while it is certainly true that roughness is a second-order effect, it is a second-order effect across a very wide spectrum of technical activity; not just tribologists and production engineers, but cartographers, radar engineers, highway and aircraft engineers, hydrodynamicists and even bioengineers find increasingly that from time to time it obtrudes into their particular specialty (Fig. 1.3). The second is that all the easy first-order problems have been solved: whatever happened, for instance, to heavy electrical engineering as an academic discipline? We live increasingly in a world where second order effects present the major remaining challenge; any fool can make an internal

Rough &$aces

4

combustion engine that works, the trick is to make one that will run for a million miles at 100 miles to the gallon.

'

100 1970

1975

1980

1985

1990

1995

Figure 1.3. Cumulative number ofpublications on surface roughness (Thomas 1997)

1.2. Principles of Roughness Measurement

By "measurement" we mean something more than mere inspxtion. We will define measurement in the present context as a process which gives, or is capable of giving, quantitative information about individual or average surface heights. Thus we exclude many forms of optical examination. These may give information about the existence and direction of the lay on machined surfaces, or about the presence and spacing of feed and chatter marks or other individual defects, but this does not fall within our definition. There are some general considerations in choosing any measuring instrument: cost, ease of operation, size and robustness. There is also the issue of whether a measurement is comparative or absolute. In addition, for roughness measuring instruments, it is necessary to decide whether or not the instrument should make physical contact with the surface, and whethei it needs to be able to measure an area of a surface or only a section or profile through it. Most important of all are the horizontal and vertical range and resolution. Some of these criteria are self-explanatory, but the issue of comparative versus absolute measurement is worth a few moments' digression. Many roughness measuring instruments, for instance stylus instruments, give absolute measurements of local heights. Thus they can be calibrated against secondary length standards such as slip gauges and so in principle at least are traceable to primary standards. Other instruments, for instance glossmeters, give average values of some surface parameter, which may depend on material properties and may vary from one finishing process to the next. Such instruments must be

Introduction

5

calibrated against an absolute instrument used under the same conditions. Under these conditions they may still be traceable, but in a much more tightly restricted way. This is likely to be of some practical importance in a manufacturing environment where the roughness instrument is part of a quality system under I S 0 9000. Vorburger and Teague (1981) classify these two kinds of instruments as "profiling" and "parametric" techtuques. Sectional measurement is usually quicker, simpler and easier to interpret than areal measurement, and all current roughness standards, as we shall see later, are written in terms of sectional measurements. For many practical purposes sectional measurements are adequate, and sectional techruques should be preferred unless there is some good reason to the contrary. However, most engineering interactions of surfaces, including all contact phenomena, are areal in nature, and the information necessary to describe their function must similarly be areal. Often this information can be inferred mathematically from sectional information, as discussed in later chapters. The problem arises when the events about which information is sought are comparatively rare. For instance, under most engineering loads the area of real contact between two surfaces is likely to be less than 1% of their nominal area. Thus a sectional measurement may underestimate or miss altogether the features of practical interest (Fig. 1.4). The special problems of areal, or three-dimensional (3D), measurement will be discussed separately below.

Figure 1.4. A sectional measurement may underestimate the number and size them altogether

.If

important features or miss

Rough Sur$aces

6

I.2.1. Range and Resolution We can say crudely (Thomas 1978) that roughness exists in two principal planes: at right angles to the surface, when it may be characterised by some kind of height, and in the plane of the surface, identified as "texture" by Reason (195 1). There are thus two sets of limitations which we need to discuss with reference to each roughness measuring instrument or technique: the largest and smallest differences of height which it will resolve, and the longest and shortest surface wavelengths with which it can cope. It is important to remember that every instrument or technique is subject to these limitations of resolution, and that the actual figures involved will vary from instrument to instrument. A very useful way of defining and comparing instrument performance at a glance is due to Stedman (1987), who suggested plotting the horizontal range and resolution of an instrument as an envelope in two-dimensional space (Fig. 1.5). If z,, and z,,, are the maximum and minimum heights that can be measured by the instrument, and similarly A,, and are the longest and shortest wavelengths, these will define a rectangle in z-/2 space outside which the instrument will not measure. But the practical operating envelope is subject to further restrictions, for instance the steepest slope em, which the instrument will measure, and the sharpest curvature C,, which it will follow. These may also be displayed in z-/2 space if some assumption is made about the form of the surface. For mathematical convenience Stedman assumes a sinusoidal surface

z

=

Rpsin(2xx//2)

where Rp is the amplitude. Slopes and curvatures are then the first and second differentials respectively: B

C

=

=

( 2 xRp/A) cos (2 n x / R )

- (4 ?Rp/A2) sin ( 2 x x / A )

The maxima of these functions occur when the trig functions are unity, so taking logs, logRp logRp

=

=

10g(8,,/2x)

+ log1

log(Cm,/4?)

+ 210gA

Introduction

7

On a logarithmic plot these are lines of slope 1 and 2 respectively which further restrict the operating envelope (Fig. 1S ) .

Figure 1.5. Envelope of instrument pe.rfomance in amplitude-wavelengthspace (after Stedman 1987)

Other restrictions on the operating envelope could be devised; Stedman includes, for instance, the effect of angular uncertainties in the instrument reference plane. The assumption of sinusoidal surfaces is also somewhat of a simplification. Nevertheless, Stedman diagrams are such a straightforward and convenient way of defining and comparing instrument performance that they will be used throughout to illustrate our discussion of measurement techmques, omitting for the sake of simplicity the restrictions due to slopes and curvatures. Readers should be aware, however, that these Stedman diagrams represent a maximum working envelope, not all of which may be available to the same instrument at the same time. Also, the examples given will usually refer to a particular instrument, that is to an exemplification of the technique rather than as a general statement about the technique. For instance, it is possible to build stylus instruments on quite different scales of size, and it would be misleading to try to present a generic Stedman diagram which would cover all possible realisations of the stylus principle. It is interesting to construct a Stedman dagram to examine summarily the global coverage of topographical measurement techniques (Fig. 1.6). A single envelope covers the current range of roughness measuring instruments, stylus, optical and AFM. Electron microscopy extends this coverage to shorter

Rough Surfaces

8

wavelengths and larger amplitudes, though it is difficult (though not impossible; for a discussion see Whitehouse 1994) to extract quantitative height information. At the upper end of the roughness range, coordinate measuring machines take over. A final envelope of surveying techniques covers everything from autocollimators at the low-range end to satellite ranging techniques at the upper end.

I

Inm

1w

1mm

lm

Figure 1.6. Global Stedman diagram (Thomas 1997).

Fig. 1.6 is not intended to be comprehensive or definitive, and for the sake of simplicity many useful measurement techniques have been omitted. It does make the point, however, that there are large areas in range-resolution space which are not accessible to any current technique. Does this matter? The lower right area of Fig. 1.6 represents small amplitudes at long wavelengths. At the moment there does not seem to be any technological requirement in this area, but it is worth noting that the error in the Hubble telescope mirror (Parks 1991) would only just come withm a shaded area; a future generation of Hubbles might well fall outside. The upper left area perhaps represents a more pressing practical problem, that of the unavailability of techruques for measuring large amplitudes at short wavelengths. It is certainly possible to think of existing artefacts whose topography falls in this area, for instance a hairbrush! More importantly, there are very many biological structures with large vertical but small horizontal dimensions, starting on a cellular scale

Introduction

9

(Boyan et a1 1996), continuing up through growing crops (Gilley & Kottwitz 1994) and ending with forest canopies (Gallagher et al. 1992). Many such structures are of great economic importance, and at the moment we have no way of describing their topography comprehensively. This task would demand a much greater ratio of vertical range to resolution than is available from current instruments. But when we reflect on the improvement in this ratio in recent years, the implications for the future are promising (Thomas 1997). At the start of the 1980s few roughness instruments offered a ratio of better than 103:1 (Farago 1982). The current state of the art provides examples both of stylus instruments (Garratt 1982) and optical instruments (Caber et al. 1993) with ratios of better than 105:1. There does not seem to be any fundamental law of instrument design preventing further improvements, if not in these techniques then perhaps in newer ones; chemical balances, for instance, have for many years been constructed with a range 108 times their resolution (Cook & Rabinowicz 1963). Bearing the above principles in mind, we will begin in the next chapter by discussing the stylus instrument, still the most popular and widely used method of measuring surface roughness. We will go on to consider the increasing use of optical instruments, both profiling and parametric. Many other techniques of measuring roughness have been developed, and some of the more popular of these are highlighted and their use in scanning mode for 3D measurement in various microscopy systems is discussed. Finally in this part of the book we examine some associated measurement questions, such as replication and in-process measurement.

1.3. References

Boyan, B. D., Hummert, T. W., Dean, D. D., Schwarz, Z., "Role of material surfaces in regulating bone and cartilage cell response", Biomaterials 17, 137-146 (1996) Brooker, K. ed., Manual of British standards in engineering metrology (Hutchmson, London, 1984) Caber, P. J., Martinek, S. J., Niemann, R. J., "A new interferometric profiler for smooth and rough surfaces", Proc. SPIE 2088 (1993) Cook, N. H., and Rabinowicz, E., Physical measurement & analysis (Addson-Wesley, Palo Alto, 1963)

10

Rough Surfaces

Farago, F. T., Handbook of dimensional measurement 2e (Industrial Press, New York, 1982) Gallagher, M. W.; Beswick, K. M.; Choularton, T. W., "Measurement and modelling of cloudwater deposition to a snow-covered forest canopy", Atmospheric Environment 26A, 2893-2903 (1992) Garratt, J.D., "Applications for a wide range stylus instrument in surface metrology", Wear 83, 13-23 (1982). Gilley, J.E.; Kottwitz, E.R., "Darcy-Weisbach roughness coefficients for selected crops", Trans. ASAE 37, 467-471 (1994) Parks, R. E., "The Hubble space telescope investigation", Optics & Photonic News 2,28 (1991) Reason, R. E., "Surface finish", Australasian Engr., 44, 48-64 (1951). Russ, J. C., Fractal surfaces (Plenum Press, New York, 1994). Stedman, M., "Basis for comparing the performance of surface-measuring machines", Prec. Engng., 9, 149-152 (1987) Thom, A,, and Thom, A. S., "The Carnac alignments", J. Hist. Astron. 3, 1126 (1972) Thomas, T. R., "Surface roughness: the next ten years", Surface Topography 1, 3-9 (1988) Thomas, T. R., "Trends in surface roughness", Trans. 7th. Int. Con$ on Metrology & Properties of Engng. Surfaces (Goteborg, 1997) Thomas, T.R., "Surface roughness measurement: alternatives to the stylus", Proc. 19th. Machine Tool Design & Research ConJ, 383-390 (UMIST, Manchester, 1978) Vorburger, T.V., Teague, E.C., "Optical techniques for on-line measurement of surface topography", Precis .Engng. 3, 61-83 (1981). Whitehouse, D. J., Handbook of surface metrology (Institute of Physics, Bristol, 1994)

CHAPTER 2 STYLUS INSTRUMENTS

We shall commence in this chapter by dealing with the techniques most commonly used for roughness measurement: those based on the use of the stylus instrument. The two most natural ways to establish the roughness of a surface are to look at it and to run a finger over it. Whitehouse (1994) has pointed out that all roughness measurement techniques can be classified as analogues of one or the other of these elementary methods. The stylus instrument is the embodiment of this second way; there were estimated to be 25,000 stylus roughness measuring instruments in the U.S.A.alone (Young & Bryan 1974).

2.1. Mechanical Instruments

The principle of the phonograph or gramophone, where a sharp probe traverses a surface and transforms its minute irregularities into another form of energy, seems ideally suited in retrospect to apply to the measurement of surfaces. Strangely enough it was a generation after the invention of the phonograph before surfaces were first measured with a stylus instrument. One early instrument used an optical lever to magnify the stylus movement (Schmaltz 1936). Another amplified the vertical movement of the stylus mechanically by a system of levers until it sufficed to cause visible fluctuations in a continuous scratch on a smokedglass plate (Reason 1944) (Fig. 2.1). This had the advantage that the stylus need not move at constant speed. In another version (Abbott et al. 1938) the vertical movements of the probe were transmitted to a mirror forming part of an optical lever, and the deflections of a light beam thus amplified were recorded on a moving photographic film. An interesting variant of the mechanical stylus instrument is the Flemming integrator (Way 1969). As the stylus moves over the rough surface an ingenious mechanical arrangement sums its displacements in a downward direction only. If this sum is divided by the length of traverse it is easy to show that the result is half the mean absolute slope. The actual figure measured will depend on the stylus 11

12

Rough Surfaces

dimensions; F l e m i n g proposed the use of two styli of Merent radii to distinguish between the slopes associated with roughness and those associated with waviness, probably the first recorded recognition that mean slope is not an intrinsic property of a surface.

FI RO

HORIZONTAL MOTION O F INSTRUMENT BODY 6

L

E

A

F SPRING SMOKED GLASS

Figure 2.1. Tomlinson roughness meter (Galyer & Shotbolt 1990)

Before we leave mechanical stylus instruments mention must be made of the wall gauge (Lackenby 1962). This instrument was developed by the British Ship Research Association (BSRA) to measure the roughness of :hips' hulls. These are very much rougher than most machined surfaces and a larger instrument is consequently appropriate. The BSRA wall gauge consists of a railway about 76 cm long carrying a trolley on which the stylus and recording gear is mounted (Fig. 2.2). The stylus is a steel ball, and through an arrangement of levers its vertical motion is amplified and recorded on a moving smoked-glass microscope slide. T h s arrangement does not require the trolley to be moved at constant speed, which is just as well because it is advanced along the track manually by the operator. The slide is subsequently mounted in a projector with a cylindncal lens to increase its

13

Stylus Instruments

relative vertical magnification and measurements are made of the projected image by hand. As gauge moves 16 cm holder moves 7.6 cm

Holder carrying standard 7 . 6 m x 2 . S m

giving horizontal reduction of 10 :I

glass slide coated with colloidal

- -

\

Pair of feet

Probe with 1.5 mm dia. ball point constrained 10move

normal to track

10 cm

Direction of travel of gauge

Figure 2.2. BSRA wall gauge (Lackenby 1962)

The device is thus an ingenious compromise. The measurement and analysis are split into two separate tasks. The former can be carried out by relatively unskilled personnel and the instrument is robust enough to survive the rigorous environmental conditions of a dry dock. The latter needs skilled technical assistance but can be performed entirely in the laboratory at leisure. These are important considerations when it is borne in mind that up to 80 measurements may be needed on a single hull. An electrically recording version of this instrument has since been developed (Chuah et al. 1990).

2.2. Electrical Instruments Finally, however, the obvious step was taken and the stylus was given a transducer to convert its vertical movement into electrical oscillations. The Abbott profilometer (Abbott & Firestone 1933) ushered in a new era in surface measurement. (We shall refrain from using the word 'profilometer' hereafter, firstly because it is apparently a regstered trade-mark in the United States and thus

Rough Surfaces

14

may not be used in a generic sense, and secondly because it is bad practice to mix two classical languages.) In its original form it had all the important components which stylus instruments have embodied ever since: a pickup, driven by a gearbox, which draws the stylus over the surface at a constant speed; an electronic amplifier to boost the signal from the stylus transducer to a useful level; and a device, also driven at constant speed, for recording the amplified signal (Fig. 2.3). Pickup

Gear-box

Datum Stylus

Transducer

Amplifier

11111

1nm

1Iy”

1mm l r n

Data logger

Chart recorder

Figure 2.3. Schematic stylus instrument

The vertical range of a stylus instrument depends on the dynamic range of the transducer and can be as much as 1 mm or more. The vertical resolution is ultimately limited by background mechanical vibrations and thermal noise in the electronics; a commercial instrument is available with a claimed resolution of 2 nm (Moody 1968). At this level of sensitivity the instrument is quite an efficient seismograph and the most stringent precautions must be taken to ensure a stable thermal and mechanical environment. The story is told that during its development a mysterious transient, thought at first to be an electronic malfunction, was finally traced, after the entire electronics had been unsuccessfully rebuilt, by observing that its appearance coincided with the departure of the milk train for London from a station several miles away! The horizontal range of stylus instruments is set by the length of pickup traverse; horizontal resolution depends on stylus dimensions. The disadvantages of the stylus instrument are manifest: its bulk, its complexity, its relative fragility, its

Stylus Instruments

15

high initial cost, its limitation to a section of a surface, the necessity of a skilled operator for any measurement out of the ordinary. The single advantage which outweighs all these is the availability of an electrical signal, which can be subjected to all the conditioning processes of modem electronics to yield any desired roughness parameter, or can be recorded for display or subsequent analysis. The stylus instrument is thus by far the most popular method of surface measurement and outnumbers all other instruments combined. It is also the instrument in terms of which all national roughness standards are defined. It is therefore appropriate to discuss its component parts in more detail.

2.2.1. Stylus and Skid

In early instruments the stylus was often a phonograph needle (Abbott & Goldschmidt 1937; Barash 1963) and more recently a sewinq needle has been used as a stylus (Gray & Johnson 1972). However, phonograph needles were found to be too large and too heavily loaded, and caused unacceptable surface damage. Diamond styli are now universally employed. In many instruments they are cones of 90" included angle and tip radius 4-12 pm (Williamson 1947). However, in one of the most popular stylus instruments the stylus is a truncated pyramid. The angle between the faces is 90" and the dimensions of the rectangular flat at the tip vary; a small flat is classed as a high-resolution stylus, while an average one is about 3 pm x 8 pm (Jungles & Whitehouse 1970). The short edge is parallel to the direction of motion. Thus the stylus cannot resolve a wavelength shorter than 6 pm (see later chapters), and integrates over a narrow strip of surface 8 pm wide. The slopes of most real surfaces are so gentle that penetration of valleys is not usually a problem. However, this is not always the case. It is sometimes necessary to measure surfaces which consist effectively of more or less smooth planes containing relatively steep-sided and deep craters, such as those of wood (Elmendorf & Vaughan 1958) or machining tools (Tsao et al. 1968). More common still is the requirement to measure surfaces of abrasive composites, either coated abrasives or grinding wheels P a u l et al. 1972; Deutsch et al. 1973; Friedman et al. 1974, Fugelso & Wu 1977), where no ordinary stylus will penetrate the gaps between the individual grits. All the above authors have described instruments designed to overcome this problem by the employment of a stylus vibrated by an electrical transducer in a vertical plane with an amplitude much greater than the anticipated variation of height on the surface. It is clearly necessary that the frequency of vibration should be different from the expected

16

Rough Su$aces

frequencies of variation of height so that it can be removed from the signal by electronic filtering. The quantity actually measured by the stylus transducer is the change in the vertical separation of the stylus and the transducer. If the pickup is constrained to move in a horizontal plane or in a curve of fixed radius then the transducer will give the instantaneous height difference between the stylus and this independent datum. Such a system involves a tedious levelling procedure, particularly so at high vertical magnifications, and for many purposes it is more convenient to use a skid. The transducer senses the difference in level between the stylus and the skid and no skilled setting up is required. The skid is attached to the pickup and rests on the surface either beside or in line with the stylus (Figure 2.4). In-line skids, either in front of or behind the stylus, are the usual arrangement, and are preferred for tracing inside small bores. Straddling skids, either as buttons or as a V-shaped support member, provide guidance parallel to the axial plane of parts with curved surfaces.. Farago (1982) describes a number of detailed skid designs for various specialised inspection applications.

Figure 2.4. (a) Aligned and (b) straddling skids (Farago 1982)

2.2.2. Transducers As with the cartridge of a high-fidelity phonograph, the performance of a stylus instrument is only as good as its transducer. Some of the less expensive stylus instruments used a piezoelectric crystal as the transducer element. Changes in pressure due to stylus movement cause a small change in charge, which can then be amplified. In practice the charge leaks steadily away from the crystal at such a rate that the transducer will not correctly transmit low frequencies, resulting in a loss of accuracy at long surface wavelengths (Reason 1956).

Stylus Instruments

17

In another system, the stylus moves the anode of a triode through a flexible diaphragm, thus causing a large change in the effective electrical resistance for a comparatively small stylus displacement (Underwood & Bidwell 1953; Chinick 1968). Because of the fragility of the vacuum tube it is essential that excessive anode movement be avoided. This is achieved by coupling the stylus to the anode extension through a viscous liquid. For high-frequency small-amplitude displacements the coupling behaves as if it were rigid, but permits increasing shear as the frequency decreases, thus acting as a high-pass filter; unfortunately its transmission characteristic, being viscosity-dependent, is a function of temperature. Moving-coil transducers are sometimes used, but their output depends on the velocity of the stylus rather than its position and must be integrated to give an amplitude. As the integrating circuits are inefficient at low frequencies this also has a built-in high-pass filter (Reason 1956; Chinick 1968). A capacitance transducer has also been described (Miyazaki 1965) where the stylus vertically displaces, through a lever arm, one plate of a capacitor whose other plate is a conducting liquid. Difficulties are reported, not surprisingly, in levelling the system.

\ & Knife edge

Figure 2 . 5 . Schematic LVDT transducer

Many modern stylus instruments use a linear variable differential transformer (LVDT). In a typical modified LVDT two coils are wound on opposite arms of an E-shaped core (Fig. 2.5). An armature attached to the stylus and pivoted about the centre arm increases the air gap of one coil as it decreases that of the other, causing a differential change in inductance. This alters the output of a bridge circuit excited by an oscillator at a frequency much higher than the maximum anticipated frequency of stylus displacement. Thls camer frequency must subsequently be removed from the signal by demodulation. The advantage of this system is that it

18

Rough Surfaces

will measure low frequencies right down to a static stylus displacement (Reason 1956; Chinick 1968). Garratt (1982) describes an interferometric transducer. The stylus arm is a pivoted lever, at one end of whtch is the stylus and at the other end of which is a reflector which acts as the measurement arm of a Michelson laser interferometer. The vertical resolution is 5 nm and the range is 2 mm, giving a ratio of range to resolution of 5 x lo5.

2.2.3. Pickup

One instrument manufacturer has used an endless rubber belt driving a trolley carrying the stylus and transducer along an optically flat guideway. Another has used a linkage which in fact drives the pickup in a pair of arcs forming a very shallow letter W. This is adequate when the stylus is used with a skid, but causes some difficulty if a smooth surface is measured relative to an absolute datum. It is sometimes inconvenient to move the pickup over the surface and instead the pickup is held motionless and the test piece is moved below the stylus. Stages are commercially available for this purpose (see the discussion of 3D measurement.

Figure 2.6. Pickup speed measured as a hnction oftime for a commercial stylus instrument (Desages & Michel 1993). AC: Traverse length; AB:run-up length; BC: evaluation length

It is essential that the pickup be driven at constant horizontal speed while measuring, as the overall design of many instruments assumes that equal intervals of time correspond to equal intervals of horizontal distance. The actual length over which measurements are made, the evaluation length (BS1134, 1981), is shorter

Stylus Instruments

19

than the total length of pickup travel, the traverse length, to allow an initial run-up for pickup acceleration and a final run-out for the pickup to slow down and stop (Fig. 2.6). The commercial instrument tested in Fig. 2.6 in fact consistently slowed down by about 3% after the first quarter of the evaluation length. Very often it is necessary to measure workpieces whose surfaces are not flat. If they have a section of constant curvature this can be achieved by constraining the stylus to move in an arc of the same curvature, and a number of ingenious mechanical devices are available commercially for this purpose. If the test piece is circular or cylindrical, matters are much easier. Instruments are commercially available which will either rotate the component by rollers against a fixed stylus or will move the stylus in an arc of variable radius around the workpiece. The slower the stylus moves, the finer the detail that can be resolved (subject to the limitations of stylus size) and accessories for commercial instruments have been available which will reduce the speed to less than 5 p d s . At the lowest speeds it is apparently difficult to guarantee constant speed because of stick-slip in the translation mechanism. At the other end of the scale, the stylus cannot be traversed too fast or it will lose contact where the surface falls away steeply. The effect of this will be to skew the slope distribution, that is to record negative slopes as being more gentle than they really are. The exact proportion of slopes misrecorded depends on the interaction of the pickup dynamics and stylus load with the geometry of the particular surface being measured (discussed in detail by Whitehouse 1994). It is dlficult to avoid thls effect completely if measurements are to be made in a reasonable time, and the design of most commercial instruments is therefore a compromise. The fastest speed of traverse normally employed is about 1 mm/s; a stylus instrument which has been reported to traverse at 5 mm/s will not follow slopes steeper than about 6 degrees (Morrison 1995).

2.2.4. Output Recording

After removal of the carrier, if any, and amplification, it is necessary to transform the signal again into some form which the operator can understand. In some early instruments the amplified signal drove a loudspeaker (Harrison 1931) or an oscilloscope (Abbott & Firestone 1933). Neither of these could provide a permanent record, and it quickly became and has remained the practice to use a chart recorder. Clearly it is essential that the recorder should run at constant speed to avoid distortion of the signal, but this constant speed may be increased to increase the horizontal magnification of the recorded signal. (The same effect may

Rough Sudaces

20

of course be achieved by slowing the pickup traverse speed relative to that of the recorder.) Chart recordings of surface profiles are clear, unambiguous and selfexplanatory; the only difficulty in interpretation arises from the distorted ratio of vertical to horizontal magnification, a problem which we discuss below. Surface parameters of various kinds can be measured from the chart recordings, but this is rather slow, and would be unsuitable for a quality-control application where a large number of workpieces must be measured in a short time. Most stylus instruments, therefore, either have additional averaging circuitry of some kind which displays a selected parameter directly on a meter, or are connected to a microcomputer which performs the same function. The definitions of these parameters and the details of the procedures for calculating them are discussed in a later chapter.

2.3. Sources of Error

2.3.1. Effect of Stylus Size The stylus is not a mathematical point but an artefact of finite dimensions. This implies that the stylus must fail to follow peaks and valleys faithfully and hence must produce a distorted record of the surface. How serious is this distortion?

/--\

/

Figure 2.7. Distortion of measured profile due to f ~ t dimensions e of stylus tip (exaggerated) (Radhakrishnan 1970)

The so-called "traced profile" (IS0 3274, 1996) recorded by the stylus instrument is the locus of the centre of the stylus. If the contacting portion of the

21

Stylus Instruments

stylus is assumed to be spherical in section the effective profile will correspond to the contacting envelope (Hullproflo of the E or envelope system (von Weingraber 1957) where the radius of the rolling circle is that of the spherical portion of the stylus tip. The radius of curvature of a peak may be exaggerated, while a valley may be represented as a cusp (Fig. 2.7). To appreciate the likely magnitude of this effect it is necessary to consider more closely the geometry of the stylus. According to I S 0 3274 a stylus may have an included angle of 60' or 90' and a tip radius of curvature of 2, 5 or 10 pm. The measurement of the actual tip dimensions is extremely difficult as they approach the limit of resolution of optical techniques (Williamson 1947; Jungles & Whltehouse 1970); Williamson succeeded in measuring the tips of four conical styli and reported average radii of curvature of from 2.5 pm to 53 pm. It would seem, therefore, that a profile containing many peaks and valleys of ra&us of curvature 10 pm or less, or many slopes steeper than 45O, would be likely to be more or less badly misrepresented by a stylus instrument. Much play has been made with the problem of measuring the Caliblock and similar specimens, roughness standards on which a very nearly rectangular one-dimensional profile is etched (Reason 1951; Peres 1953), and clearly indeed such a profile can never be followed very closely by a standard stylus.

1

0.5 2.5

I

5

1

10

1

20

1

50

I

I

la, 200 Tracing stylus radius &m

Figure 2.8. Effect of stylus tip radius on measured roughness for various machined surfaces (Radhakrishnan 1970): (1) planed (2) electro-eroded (3) milled (4) ground; (5) electrochemically sunk, ( 6 )honed

22

Rough Surfaces

In measurements of real surfaces, however, this difficulty is largely illusory, as their slopes are for the most part very gentle at the scale on which the stylus measures them. This is confirmed by the experimental findings of a number of workers (Williamson 1947; Radhakrishnan 1970) that styli of standard dimensions do not significantly misrepresent the average roughness of the surface (Fig. 2.8). Whitehouse (1974) has reached the same conclusion by a different stochastic argument. Arguments which rely on a representation of the surface as a single pure sinusoid (Nakamura 1966), though they may reach similar conclusions, are to be avoided. The misconception has arisen from the way in which profiles are commonly presented. A slope of 1" is almost imperceptible to the human eye, and the instrument manufacturers have therefore found it convenient to exaggerate the vertical magnification over the horizontal on their chart recorders. This has given generations of metrologists a totally false impression of surface microgeometry. The contact of two rough surfaces, far from resembling Bowden's famous analogy of "Austria turned upside down on top of Switzerland" (Bowden & Tabor 1950) more closely resembles Iowa on top of the Netherlands (Thomas 1973). To emphasize this point Reason (1944) showed a conventional chart recording of a ground surface with the vertical scale exaggerated 35:l over the horizontal; the stylus, distorted correspondingly (Fig. 2.9) appears now as a mere sliver. On the same figure he drew the same recording at a 1: 1 ratio. As he himself remarks, it is difficult to reconcile the two representations even with the aid of fiducial marks. There is no room here to reproduce the whole of Reasonk figure, which unfolded from the original paper to a length of a metre or so!

Y

25:1

3 -

X Y

Figure 2.9. Effect of horizontal compression of chart recording on profile presentation (adapted from Reason 1944):(a) true appearance of section XY'; (b) representation on chart recording

Stylus Instruments

23

2.3.2. Effect of Stylus Load As the dimensions of the stylus are finite, so also is the load on it. Although the load is small, 0.75 mN according to I S 0 3274, the area of contact is also so small

that the local pressure may be sufficiently high to cause significant local elastic downward deformation of the surface being measured. In some cases the local pressure may exceed the flow pressure of the material and plastic deformation, i.e. irreversible damage, of the surface may result. It is fairly easy to calculate the elastic behaviour of a surface under a chiselshaped stylus. The average vertical deflection 6 of a homogeneous isotropic elastic half-space of Hertzian modulus E' and Poisson's ratio v by a rigid indenter of rectangular cross-section ab under load W is (Timoshenko & Goodier 1951): S

=

mW(l-9)/Erd(ab)

where m is a dimensionless constant whose numerical value is a function of ah. Taking m = 0.9, W = 1 mN, v = 0.33, E' = 2 x lo5 N/mm2 for steel gives 6 = 0.83 nm. Clearly there is no danger here of appreciable error in measurements on any metal. A calculation for the spherical stylus tip specified in I S 0 3274 (1996) would gwe a similar result. The problem with metals at least, then, if any, is not elastic but plastic deformation. This has been investigated by Quiney et al. (1967), Tucker and Meyerhoff (1969) and Guerrero and Black (1972). Quiney et al. were able to make a scratch about 1.7 pm deep on an aluminium surface by using a stylus force about 10 times higher than the recommended standard. Tucker and Meyerhoff presented scanning electron micrographs of a lead surface damaged by a stylus, but admitted that no scratches could be found on harder materials. Guerrero and Black presented a number of scanning electron micrographs of so-called stylus damage, and calculated that stylus scratches on a steel surface were as much as 50 nm deep; however, their assumptions concerning stylus tip geometry are rather questionable. The trouble seems to be that the stylus generally does make a visible scratch, and the existence of this scratch is held to be prima facie evidence of unacceptable damage. Here the key word is "unacceptable". If we can show, for instance, that the surface is everywhere deformed by the same amount, the output of the instrument will then be a true profile displaced downward by a constant distance. Reason et al. (1944) traversed a profile with a stylus load of 0.06 mN, repeated the measurement with an increased load of 0.8 mN and then returned to 0.06 mN for a third traverse; the profiles were nearly identical (Fig. 2.10). Schwartz and Brown

24

Rough Surfaces

(1966) found that the stylus measurements of a step in a silver film on a glass substrate agreed with interferometric measurements to within 24 nm, while Estill and Moody (1966) found no more than 43 nm deformation even on a soft gold film. Williamson (1968), in a series of careful experiments, could find no evidence of the information from stylus measurements being affected by plastic deformation. As he remarked elsewhere, a bulldozer traversing a range of hills would leave a scar visible from many miles up, but a recording barometer carried on the vehicle would return a profile of the topography accurate enough for most practical purposes.

Figure 2.10. Effect of stylus load (Reason 1944): (a) profile measured at 6 rng load; (b) relocated profile at 80 mg load (c) relocated profile at 6 mg load again

2.3.3. Other Sources of Error

A question was raised above concerning the dynamic response of the stylus: whether there is any possibility of it losing contact with steep reverse slopes of the surface as a consequence of the speed of traverse. Again this is to overestimate the average steepness of real surfaces. Nakamura (1966) and Damir (1973) have considered the effect of stylus geometry on its dynamic response, but the input surface models in both cases are somewhat unrealistic. Nakamura's results, however, indicate that with typical surface conditions, and with styli dimensions as quoted in the international standards, the errors incurred are negligible. Funck et al. (1992) found that speed of traverse significantly affected stylus measurements of roughness on wood surfaces, but it is not clear whether these effects were due to the timedependent mechanical properties of wood. Another possibility of error lies in the lateral deflection of the stylus by asperities. Verkerk et al. (1978) recommend that the ratio of axial to lateral stiffness should be less than 0.00 I . AguIIo and Pages-Fita (I 974) have shown (Fig. 2.11) that lateral deflection can amount to as much as 1 pm between extremes

Stylus Instruments

25

when traversing a rough surface. However, the RMS excursion is more like 0.3 pm, and in any case, as we have already seen, a typical stylus is in effect integrating over a strip 8 pm wide.

Figure 2.1 1. Effect of lateral deflection of stylus (Agullo & Pages-Fita 1974): (a) artificial two-dimensional square-wave surface traversed at an angle to the lay; (bJ and (c) typical manufactured surfaces of different roughness

Rough Su$aces

26

It has been claimed that the skid itself can cause damage to the surface. Tucker and Meyerhoff (1969) observed deformation of soft surfaces such as lead and niobium by a skid. Here the same argument applies as was used in the case of stylus deformation: will it actually affect the measurements? According to Reason et al. (1944), the difference in the deformation of a peak on a steel surface relative to that of a hollow amounts to about 40 nm. It seems unlikely that this will be an important source of error on hard surfaces.

“1. b

a a

Reciprocalwavelength

Figure 2.12. Effect of skid (Nara 1966):(a) profile as seen by (top to bottom) stylus with absolute datum; stylus with skid; skid with absolute datum: (b) power spectra of (a): solid line. stylus with absolute datum; broken line: stylus with skid

Stylus Instruments

27

More importantly, the skid acts as a mechanical high-pass filter. This has two consequences. Firstly, information about longer wavelengths is lost; this is irremediable and if these wavelengths are deemed to be relevant to the problem under investigation then a skid must not be used. Secondly, the filter introduces a phase lag meason et al. 1944) which might be supposed to distort the appearance of the surface. Experiment suggests, however, that this distortion is not obtrusive (Nara 1966) (Fig. 2.12a). It appears also that the mechanical filter embodied by the skid has quite a sharp cut-off (Fig. 2.12b) and that the power spectrum, which of course contains no phase information, is relatively unaffected at shorter wavelengths. Ishigaki & Kawaguchi (198 1) conclude that varying the separation &stance of skid and stylus has little effect. The question of damage to soft surfaces has been discussed above, but what of measurements on surfaces whch easily yield elastically? Elastomers are widely used in engineering, particularly as elements in static or dynamic seals. The surface finish of the metal elements is known to have an important effect on sealing properties, and it seems reasonable to assume that the finish of the elastomer will also play a part. To assume that all the asperities on the elastomer are somehow squashed flat is to beg the question; no matter how compliant the elastomer or heavy the load, a surface wavelength will exist below which the elastomer will not conform. Calculations such as those described above suggest that a stylus under its standard load will deform the surface of an elastomer by more than 100 pm. Of course it does not follow that measurements are therefore impossible; if every element of the surface is displaced vertically by exactly the same amount then we will still record a true profile. However, as most commercial elastomers are composite materials this may be rather a severe requirement.

I mm

Figure 2.13. Stylus measurement of a compliant surface (Thomas et al. 1975): (a) profile of elastomer cooled below its glass transitiontemperature; (b) a subsequent relocated measurement at room temperature

28

Rough &$aces

To investigate compliant yielding under the stylus, measurements were made on an elastomer at two different temperatures using a relocation table (Thomas et al. 1975). The elastomer was first frozen below its glass transition temperature by a stream of evaporating liquid nitrogen. In t h s condition it is no more compliant than steel. When it had warmed up to room temperature it was measured again (Fig. 2.13), and no significant differences in the two profiles were apparent. The explanation of this remarkable and useful result is not clear, but there is some evidence that a thin surface layer of the elastomer may be much less compliant than the bulk material.

2.4. Calibration and Standards

Because the stylus instrument was the earliest roughness mzasuring instrument to achieve general acceptance, and because it is still so widely used, roughness standards are still written largely with stylus instruments in mind. Production instruments are usually calibrated from secondary calibration specimens, of which IS0 5436 (1985) distinguishes four main types. Type A, used for checking vertical magnification, has wide grooves of a known depth. Type B, for checking the condition of the stylus tip, has a series of narrow grooves of various depths and widths. Type C, for checking parameter meters, has repetitive grooves of sinusoidal or triangular section. Type D has a pseudo-random profile which extends the whole width of the standard to provide a more realistic, but less accurate, overall system check. Type C specimens of triangular section were prodused in the U.S.A. by General Motors under the trade name Cali-Block (Young & Scire 1972) with an included angle of 150 degrees. The production of sinusoidal Type C specimens has been described by Sharman (1967/8) and by Teague et al. (1982), who found that the rigorous NIST specification could best be satisfied by diamond turning. Square-wave sections have been proposed for Type C specimens (Berger 1988) but interaction with stylus geometry makes these prone to error (Peres 1953). The best-known Type D specimens are those produced at the PhysikalischeTechnische Bundesanstalt by Hasing (1965). These have a measuring area of random profiles, obtained by grinding, in the direction of traverse, which repeat every 4 mm, and cover a range of roughnesses from 1.5 pm down to 0.15 pm.. Song (1988) has improved on the PTB design by adding a smooth reference surface at each end of the traverse to provide a datum for the skid, and has extended the range of roughness down to 12 nm (Fig. 2.14).

Stylus Instruments

29

Figure 2.14. Type D modified PTB roughness calibration specimen with 8 consecutive identical profiles (Song1988)

But how are these secondaq calibration specimens to be calibrated themselves? Small height increments can be measured directly by interferometry (Spragg 1967/8, IS0 5436). In most instances, however, the most suitable instrument for the purpose is another stylus instrument, which itself must be traceably calibrated, that is there must be an unbroken and documented chain of calibration from a primary standard of length, as required by IS0 9000 (1987). For the static deflection of the stylus and transducer, traceability may be provided by a series of gauge blocks arranged in steps ( I S 0 5436), which serves to check the linearity of the transducer as well as its sensitivity. If the steps are too coarse, they can be scaled down by a reducing lever (Spragg 1967/8). Dynamic calibration of the stylus instrument is often effected by a vibrator which can be driven at variable frequency (Van Hasselt & de Bruin 1962/3, Parkes 1969, Bendeli et al. 1974); the traceability of such vibrators is discussed by Barash & Reznikov (1983).

2.5. References

Abbott, E. J. and Firestone, F. A,, "Specifying surface quality", Mech. Engng., 55, 569-572 ( 1 933).

30

Rough Sudaces

Abbott, E. J., Bousky, S. and Williamson, D. E., "The profilometer", Mech. Engng. 60, 205-216 (1938). Abbott, E. J. and Goldschmidt, E.," Surface quality", Mech. Engng., 59, pp. 8 13-25. ( 1937). Agullo, J. B. and Pages-Fita, J., "Performance analysis of the stylus technique of surface roughness assessment: a random field approach", Proc. 15th Int. Machine Tool Des. & Res. Con$, 349-362 (Birmingham University, 1974). Barash, M. M., "Measuring the finish of rough surfaces", Int. J. Mach. Tool Des. Res., 3,97-I00 (1963). Barash, V. Y. and A. L. Reznikov, "Standard vibrator in metrological certification of contact methods of roughness measurement", Measurement Technology, 26, 658-661 (1983) Baul, R. M., Graham, D. and Scott, W., "Characterization of the working surface of abrasive wheels", Tribology, 2, 169-176 (1972). Bendeli, A,, Duruz, J. and Thwaite, E.G., "A surface simulator for the precise calibration of surface roughness measuring equipment", Metrologia, 10, 137-143 (1974). Berger, J., "A new surface roughness standard fabricated using silicon technology", Surface Topography, 1, 4 1-47 (1988) Bowden, F. P. and Tabor, D., The friction and lubrication of solids Part 1, (Oxford University Press, 1950). BS 1134, "Assessment of surface texture Part 1. Methods and instrumentation" (British Standards Institution, London, 1988) Chinick H. P., "LVDT puts precision in surface texture measurement", Cutting Tool Engng., 20, 13 (1968). Chuah, K. B., Dey, S. K., Thomas, T. R., Townsin, R. L., "A digital hull roughness analyser", Int. Workshop on Marine Roughness & Drag (RINA, London, 1990) Damir, M. N. H., "Error in measurement due to stylus kinematics", Wear, 26, 219-227 (1973). Desages, F. and Michel, O., "Calibration of a 3-D surface roughness measuring device", Production Engng. Dept Report (Chalmers University, Goteborg, 1993) Deutsch, S. J., Wu, S. M. and Straklowski, C. M., "A new irregular surface measuring system", Int. .J. Mach. Tool Des. & Res., 13,29-42 (1973). Elmendorf, A. and Vaughan, T. W., "A survey of methods of measuring smoothness of wood", Forest Products J., 8, 275-82 (1958).

Stylus Instruments

31

Estill, W. B. and Moody, J. C . , "Deformation caused by stylus tracking on thin gold film", Z.S.A. Trans., 5, 373-378 (1966). Farago, F. T., Handbook of dimensional measurement 2e, (Industrial Press, New York, 1982) Friedman, M. Y., Wu, S. M., and Suratkar, P. T., "Determination of geometric properties of coated abrasive cutting edges", Trans. A.S.hLE.: J .Engng .Ind., 96B, 1239-1244 (1974). Fugelso, M., Wu, S. M., "Digital oscillating stylus profile measuring device", Irzt. J. Mach. Tool Des Res 17,191-195 (1977) Funck, J. W.; Forrer, J. B.; Butler, D. A,; Brunner, C. C.; Maristany, A. G., "Measuring surface roughness on wood: a comparison of laser-scatter and stylustracing approaches", Proc. SPIE 1821, 173-184 (1993) Galyer, J. F. W., and Shotbolt, C . R., Metrologyfor engineers 5e (Cassell, London, 1990) Garratt, J. D., "A new stylus instruent with a wide dynamic range for use in surface metrology", Prec. Engng. 4, 145-151 (1982) Gray, G. G. and Johnson, K. L., "The dynamic response of elastic bodies in rolling contact to random roughness of their surfaces", J. Sound & Vibration, 22, 323-342 (1972). Guerrero, J. L. and Black, J. T., "Stylus tracer resolution and surface damage as determined by scanning electron microscopy", Trans. A.S.M.E. J . Eng. Ind., 94B, 1087-1093 (1972). Hamson, R. E. W., "A survey of surface quality standards and tolerance costs based on 1929-1930 Precision-Grinding practice", Trans. ASME 53, 11-25 (193 1). Hasing, J., "Herstellung und Eigenschaften von Referenznormalen fur das Einstellen von Oberflachenmefigeraten",Werkstattstechnik 55, 380-382 (1965) Ishigaki, H. and I. Kawaguchi, "Effect of a skid on the accuracy of measuring surface roughness", Wear, 68, 203-21 1 (1981). I S 0 3274, "Geometric product specifications - surface texture: profile method nominal characteristics of contact (stylus) instruments" (International Organisation for Standardization, Geneva, 1996) I S 0 5436, "Calibration of stylus instruments" (International Organisation for Standardization, Geneva, 1985) IS0 9000, "Quality management and quality assurance standards" (International Organisation for Standardization, Geneva, 1987) Jungles, J. and Whitehouse, D. J., "An investigation of the shape and dimensions of some diamond styli", J. Phys: Sci. Instrum., 3E,437-440 (1970).

32

Rough Suvfaces

Lackenby, H., "The resistance of ships, with special reference to skin friction and surface condition", Proc. I. Mech. E., 176, 981-1014 (1962). Miyazaki, K., "Electronic method, based on the surface of a liquid, for measuring flatness", Microtechnic, 19,74-76 (1965). Moody, J. C., "Measurement of ultrafine surface finishes", I.S.A. Trans. 7, 67-7 1 (1968). Morrison, E., "A prototype scanning stylus profilometer for rapid measurement of small surface areas", Int. J. Mach. Tools Manufact. 35, 325-331 (1995) Nakamura, T., "On deformation of surface roughness curves caused by finite radius of stylus and tilting of stylus holder arm", Bull. Jap. Soc. Precision Engng., 1, 240-248 (1966). Nara, J., "On CLA value obtained with direct reading surface roughness testers - effects of skid and high pass filter", Bull. Jap. Soc. Precision Engng., 1, 263-273 (1966). Parkes, D. H., "Calibration, certification and traceability of surface roughness measuring equipment", A.S. T.M.E. Tech. Paper IQ69-505 (1969). Peres, N. J. C., "Geometrical considerations arising from the use of square wave calibration standards of surface finish", Aust. J. Appl. Phys., 4, 380-388 (1953). Quiney, R. G., Austin, F. R. and Sargent, L. B., "The neasurement of surface rougbness and profiles on metals", A.S.L.E. Trans. 10, 193-202 (1967). Radhakrishnan, V., "Effect of stylus radius on the roughness values measured with tracing stylus instruments", Wear, 16, 325-335 (1970). Reason, R. E., "Surface finish and its measurement", J. Inst. Prod. Engrs ., 23, 347-372 (1944). Reason, R. E., "Surface finish", Australasian Engr., 44, 48-64 (195 1). Reason, R. E., Hopkins, M. R. and Garrod, R. I., Report on the measurement of surface finish by stylus methods", (Taylor Hobson, Leicester, 1944) Reason, R. E., "Significance and measurement of surface finish part 2: how transducers affect instrument performance; how to select proper cutoff values", Grinding &Finishing, 2, 32-36 and 41 (1956). Sayles, R. S., Thomas, T. R., Anderson, J., Haslock, I. and Unsworth, A,, "Measurement of the surface microgeometry of articular cartilage", J. Biomechanics, 12, 257-267 (1979) Schmaltz, G., Technische Oberfliichenkunde (Springer-Verlag, Berlin, 1936)

Stylus Instruments

33

Schwartz, N. and Brown, R., "A stylus method for evaluating the thickness of thin films and substrate surface roughness", Trans. of the 8th National Vacuum Symp., 836-845 (1966). Sharman, H. B., "Calibration of surface texture measuring instruments", Proc. I. Mech. E., 182, Part 3K, 319-326 (1967/68). Song, J. F., "Random profile precision roughness calibration specimens", Surface Topography, 1, 29-40 (1988) Spragg, R. C., "Accurate calibration of surface texture and roundness measuring instruments", Proc. I. Mech. E., 182, Part 3K, 397-405 (1967/68). Teague, E. C., Scire, F. E., Vorburger, T. V., "Sinusoidal profile precision roughness specimens", Wear 83, 61-73 (1982) Thomas, T. R., "Influence of roughness on the deformation of metal surfaces in static contact", Proc. 6th. Int .Conf on Fluid Sealing, B3, 33-48 (BHRA Fluid Engineering, Cranfield, 1973). Thomas, T. R., Holmes, C. F., McAdams, H. T. and Bernard, J. C., "Surface features influencing the effectiveness of lip seals: a pattern - recognition approach", S.M.E. Paper IQ75-128, (1975). Timoshenko, S., and Goodier, J. N., Theory of elasticity (McGraw-Hill, New York, 1951) Tsao, K. C., Husein, A. B. and Wu, S. M., "Cutting tool crater wear measurement by the lapping-comparator technique", Znt .J. Mach. Tool Des .Res., 8, 15-26 (1968). Tucker, R. C. and Meyerhoff, R. W., "An SEM study of surface roughness measurement", Proc. 2nd Annual Scanning Electron Microscopy Symp., 389-396 (Illinois Inst. of Technol., Chicago, 1969). Underwood, A. F. and Bidwell, J.B., "New instrument for roughness measurement", Mach. & Tool Blue Book, 49, 202-215 (1953). Van Hasselt, R., and de Bruin, W., "Comparative investigation of industrial surface-roughness measuring instruments", Ann. CIRP 11, 193 (1962/3) Verkerk, J.; Orelio, J. M. B.; Willemse, H. R., "Ratio of axial to lateral stiffness, a quality parameter for stylus surface profile traciqg instruments", Int J Mach Tool DesRes 18, 107-116 (1978) Von Weingraber, H., "Suitability of the envelope line as a reference standard for measuring roughness", Microtecnic, 11,6-17 (1957) . Way, S., "Description and observation of metal surfaces", Proc. Con$ on Friction & Surface Finish, 2e, 44-75 (MIT, Cambridge, 1969). Whitehouse, D. J., Handbook of surface metrology (Institute of Physics, Bristol, 1994)

34

Rough Surfaces

Whitehouse, D. J., "Theoretical analysis of stylus integration", Ann. C.I.R.P. 23, 81-82 (1974). Williamson, D. E., "Tracer-point sharpness as affecting roughness measurements", Trans. A.S.M.E., 69, 3 19-323 (1947). Williamson, J. B. P., "Topography of solid surfaces", in Ku P. M. ed., Interdisciplinary approach to friction and wear, SP-181, 85-142 (NASA, Washington, 1968). Young, R. D. and Bryan, J. B., "The role of NE3P in the US National Measurement System for surface finish", Ann. C.I.R.P., 23, 183-184, (1974) Young, R. D. and Scire, F. E., "Precision reference specimens of surface roughness: Some characteristics of the Cali-Block", J .Res .Nut .Bur .Stand., C76C, 2 1-23 (1 972).

CHAPTER 3

OPTICAL INSTRUMENTS

When electromagnetic radiation is incident on a rough sudace a proportion of its energy, depending on the local physical properties of the surface, will be reflected. The reflected beam will carry information about the roughness on which the design of an instrument may be based. This information may appear in several different ways. The radiation may be reflected either specularly or diffusely or both (Fig. 3.1). Reflection is totally specular when the whole energy in the incident beam obeys Snell's law, that is, the angle of reflection is equal to the angle of incidence, and a surface which reflects radiation in this manner is said to be smooth. Reflection is totally hffuse when the energy in the incident beam is distributed as the cosine of the angle of reflection (Lambert's law). In practice, matters are not as simple as this. Reflections from most real surfaces are neither completely specular nor completely diffuse. Clearly the relationship between the wavelength of radiation and the texture of the surface will affect the physics of reflection; thus a surface which is smooth to radiation of one wavelength may behave as if it were rough to radiation of a different wavelength (Ogilvy 1991).

Figure 3.1. Modes of reflection of electromagnetic radiation from a solid surface (Keller 1967/8). (a) Combined specular and diffuse; @) specular only; (c) diffuse only.

35

36

Rough Surfaces

The angular arc through which reflected energy is scattered, and the proportion of specular to diffuse reflection, both depend on the surface roughness. Instruments which measure these angles and ratios directly are glossmeters or scatterometers. Other instruments may extract more detailed roughness information by further optical processing. A general account of optical roughness measuring techniques is given by Bennett & Mattsson (1989). Reviews and comparisons of optical roughness measurement techniques have been made by Vorburger and his co-workers at NIST (Young et al. 1980, Teague et al. 1981, Vorburger 1992). Vorburger & Teague (1981) give more than 200 references to optical work. There is also a lengthy discussion of optical techniques in Whitehouse (1994). The following summary relies heavily on the above accounts. We will follow Vorburger & Teague (1981) in dividing optical techniques into profiling and parametric. Profiling techniques are associated with specular reflection, parametric techniques mainly with diffuse reflection.

3.1. Profiling Techniques

3.1.1. Optical Sections

In the light-section microscope the image of a slit is thrown on to the surface at an incident angle of 45" and viewed by a microscope objective at a reflected angle of 45" (Fig. 3.2). The reflected image will appear as a straight line if the surface is smooth, and as an undulating line if the surface is rough. The relative vertical magnification of the profile is the cosecant of the angle of incidence, in this case 1.4. Resolution is about 0.5 pm and it is quite easy to measure peak-to-valley roughness. Light-section microscopes have been commercially available. The image need not be of a slit; a straight-edge, such as a razor blade, will suffice as object (Kayser 1943; Way 1969). Shaw and Peklenik (1963) used a variation of this technique to measure the roughness of a razor-blade edge by projecting its image on to an inclined screen. They reported discrepancies in the apparent magnification which they attributed to the finite thickness of the razor blades; this agrees with the suggestions made above concerning the integrating effect of profile width. In a later development, Howes (1974) modified the lightsection technique to observe the virtual image of the slit, from which local slopes

37

Optical Instruments

‘f. I

lnm

lprn

Imm l m

Figure 3.2. Principle of light-section microscope (Farago 1982).

and curvatures can be measured. The technique can be applied to surfaces too rough for the standard light-section microscope. Johnson et al. (1993) measured terrain roughness by projecting a bar of light from a flash gun onto a rough surface and photographing its image at an oblique angle. The photographic negative was digitized back in the laboratory. Horizontal and vertical resolutions were said to be 1 mm and 2 mm respectively; horizontal and vertical ranges were 0.5 m and 1 m respectively. A similar system, but using a video camera for data acquisition, has been described by Davies et al. (1994).

3.1.2. Optical Probes

One possible method of optical measurement is simply to use the light beam as a non-contacting stylus for profile measurement. The most straightforward method is to detect the change in the angle of specular reflection as the surface is translated under an incident beam (Ramgulam et al. 1993). While adequate for its intended purpose, the measurement of textile roughness, the lateral and vertical resolutions of 25 pm and 10 pm respectively make such a system unsuitable for finer surfaces. A number of more sophisticated variations exist. In constructing their Stedman dagrams below, it will be assumed unless otherwise stated that the range in the plane of the surface is 100 mm for a generic translation stage. Whitehouse (1994) summarises the designs of several other optical profilers in addition to the ones described below. The first method employs the so-called Foucault knife-edge test (Dupuy 1967/68). An image of a spot is formed on the surface (Fig. 3.3). By using a halfsilvered mirror the image of the spot can be imaged itself to the knife-edge. A field lens is placed here to image the objective lens on to a screen, I. If the conjugates of the lens, 0, are at the knife-edge and surface respectively, a uniform disc appears

Rough Sur&aces

38

on the screen. If the surface is moved away the knife-edge intercepts the rays of light in a different way resulting in a non-uniformity of light on the screen. This non-uniformity is a measure of the distance moved by the surface. Electrically maintaining the focus by means of cells A and B (which produce signals to move the objective or knife-edge) and monitoring the movement gives the required transducer effect. Vertical and horizontal resolutions of 0.01 pm and 0.5 pm respectively, and a vertical range of 60 pm, are claimed for this instrument, a specification which compares favourably with that of many stylus instruments. Whitehouse (1975) has pointed out, however, that the system has a poor frequency response and is unduly sensitive to tilt. A development of this system described by Thwaite (1977) is claimed to have vertical and horizontal resolutions of 1 nm and 1 pm respectively

1-1

mechanism

paition I

Polirioa 2

P d o n3

Figure 3.3. Dupuy optical probe (Whitehouse 1975): (a)Schematic layout; (b, simplified view; (c) view of objective.

Optical Instruments

39

Another optical probe utilizing a somewhat similar principle was described by Keller (1967/68). A spot object is imaged on to the surface and the diffuse reflection at some arbitrary angle, which can be varied to increase sensitivity, impinges on a pair of photoresistors differentially connected to give a null signal when the spot is in focus. The out-of-balance signal drives a servo system which alters the height of the probe until focus is again achieved. The vertical sensitivity and range are respectively 2.5 pm and several millimemes. The horizontal resolution, however, is only about 5 mm, as the probe is designed primarily for the measurement of errors of form. Also intended for form measurement is the system described by Ennos & Virdee (1986). Autocollimation of a reflected laser beam measures the local slopes, which must then be integrated to obtain a height profile. The lateral range is 15 mm but the lateral resolution is only 0.1 mm, and a single slope measurement takes 3 s. The vertical range is 0.8 pm and the vertical resolution is 0.1 nm. A system based on Nomarski microscopy is described by Bristow (1988). A laser beam passes to a translation stage which holds two mirrors (Fig.3.4). The mirrors are in a pentaprism arrangement so that small mechanical motions of the stage will not affect the 90' turning angle of the beam. The beam then passes

I

Figure 3.4. Long-pathlength optical profiler (Bristow 1988)

through a Nomarski (modified Wollaston) prism which shears it into two orthogonally polarized components. The objective focusses both beams onto the

40

Rough Surfaces

surface, the two beams separated by about a quarter of the focal spot diameter. After reflection at the surface the beams spatially recombine at the Nomarski prism retaining their polarization identities as they pass to the turning mirrors and the non-polarizing beamsplitter. The beams are finally split info their respective components by the polarizing beamsplitter and directed to either of two detectors. The surface height difference is related to the phase difference between the two beams focussed on the surface and is proportional to the voltage difference between the two detectors. The spot diameter on the surface ranges between 1 and 1.8 pm in diameter depending on the choice of the objective. Translation of the turning mirrors causes the focal spots to scan across the surface, with a maximum scan length of 100 mm. The surface slope is calculated at each point, sampled 1 pm apart, and the profile is calculated by integrating the slope data. A vertical resolution of 0.025 nm and range of 2 pm is claimed. W t R DIODE

lrn,

, ,

,

,

, ,

,

,

T L C O U l MATOR

FOCUS1NC ENS CLASS C U T E

SRCIMEN

Figure 3.5. CD player as an optical profiler (Sayles et al. 1988).

The sensor of a compact disc player is a kind of optical stylus whose operating envelope overlaps with the characteristics of machined surfaces, and it is not surprising that a number of systems have been based on its focus-detection principle. Wehbi & Roques-Carmes (1986) reported a system using both white light and laser sources which split the reflected beam so that it fell on two detectors, the ratio of their outputs being proportional to the vertical distance by

41

Optical Instruments

which the local surface was out of focus. The principle of operation was demonstrated successfully but the performance of the actual system was too poor for a practical instrument. All focus-detection systems seem to suffer from a problem in coping with sudden sharp surface discontinuities. Sayles et al. (1988) adapted an actual CD reader, in which the out-of-balance signal from the two detectors servos the moveable objective back into focus (Fig. 3.5). They extended the vertical range to 30 mm by axially displacing the light source with a stepping motor. Vertical and horizontal resolutions of 0.1 pm and 1 pm were reported. The system worked well enough at long surface wavelengths, but spurious short wavelengths were generated by inappropriate damping of the servo. In a commercial realisation of the focus-detection principle (Brown 1995), the vertical displacement of the objective is measured independently (Fig. 3.6). The light source is an infrared laser diode, and a separate optical system permits simultaneous viewing of the workpiece for setting-up purposes. Vertical range and resolution are said to be 0.1 mm and 6 nm respectively.

1 analogue output

7,

UBC14 Controller

1

(1

F------

-'

2 ! ! 3

1: Laser diode 2: Prismwithbeam splitter 3: IRmirror 4: Window 5: Photodiodes 6: Leafspring 7: Coil 8: Magnet 9: Collimator lens 10: Objective 11: Tube 12: Light barrier measurement system 13: Test surface 14: PC control card 15: Microscopewith illumination 16: CCD camera

'4 -I 1nm

13

Figure 3.6. UBM optical profiler (Brown 1995).

u inm Im lpm

Imm

42

Rough S u ~ a c e s

The confocal microscope (Hamilton & Wilson 1982) is a focus detector of sorts. A pinhole is interposed in the detector path so that the axial position of sharpest focus is also the position of maximum intensity (Fig. 3.7). The distance between the workpiece and objective is varied incrementally and the workpiece is scanned at each axial position. By recordmg the axial position of greatest intensity for each pixel, a composite picture of great depth of field can be built up. In one realisation, the vertical range and resolution are 600 pm and 10 nm respectively, and the horizontal range and resolution are 0.4 mm and 0.25 pm respectively. Confocal microscopy was not developed primarily for roughness measurement but has been adapted for this purpose (Lange et al. 1993, Sandoz et al. 1996). REAL TIME IMAGE

FOCUS PLANE SAMPLE

[b)

\ PIN HOLE DETECTOR

Figure 3.7. Confocal microscope: (a) schematic @) construction of image by stacking sections

In the polarizing interferometer of Downs et a1 (1985, 1989), which needs no independent reference, a birefringent lens preceding the microscope objective splits the light into two polarisation components (Fig. 3.8). One component, the probe beam, is focussed on the surface, and the other polarisation component, the reference beam, is unfocussed. The phase difference between these two components, the probe beam and the area-averaging reference beam, yields the surface profile. The bandwidth is limited between the focussed spot size of 1 pm

Optical Instruments

43

Beam exoonder

Polorizer

L-c

Non-polar~zmg

beam solltter

Objective I m c I.zl.1

1 ,.

'\

/ I

2

Error

:eh:s,ve

slgna'

detector

Lens vibrator

Figure 3.8. Downs polarizing interferometer (Whitehouse 1994)

and the reference spot size of 10 pm, but the vertical resolution is an impressive 0.05 nm. Another polarising instrument has been described by Sommargren (198 la, b). A heterodyne laser beam is divided by a Wollaston prism into its two polarisation components which are focussed at different places on the workpiece. (Fig. 3.9). The reflected beams are then recombined at the prism. The reference beam is coincident with the axis of rotation of the workpiece, and the measuring beam traces a circular path on the surface as the workpiece is rotated. The resulting surface profiles of about 1 mm circumference are defined by the phase difference between the probe beam at the traversing point and the stationary reference beam. Vertical range and resolution are 0.5 pm and 0.1 nm respectively. Olsen and Adams (1970) described an instrument based on a rather different principle for measuring the profiles of ocean waves from a low-flying aircraft. An amplitude-modulated laser beam is reflected from the surface at normal incidence. Changes in height will produce a path difference causing a phase shift between the transmitted and reflected signals. The vertical resolution and range are 15 mm and 3 m respectively, and the horizontal resolution is 18 mm, but the effective signal-

44

Rough Surfaces

i -

Ywoble

-

- 7

:..-.-J

neutral fblter

+ .c-

I

I

.

_]

/9

//

Rotoiable A 1 2 Dlate Fmed M i plote

Reterenre poth

-

Laser

to-noise ratio is only about 20: 1. The reference datum is the time-averaged height of the aircraft, in effect a high-pass filter. An elegant application of the phase-measuring principle has been reported by Pettigrew and Hancock (1978). A laser resonating simultaneously in several different modes is employed as the light source for a Michelson interferometer. A phase detector is used which is sensitive to the beat frequency between any two of these modes. The effective wavelength is then very much longer than either of the two beating wavelengths, giving a vertical range of up to 24 +m for a phase change of 2n. The spot dameter is only 2.5 pm. The vertical resolution is not quoted but appears to be of the order of 10 nm.

3.1.3. Interferometers

The distinction between profilers and interferometers is to some extent arbitrary. A number of the instruments in the preceding section are based on an interference

45

Optical Instruments

principle, while several of the interferometer systems described below are referred to by their designers as profilers. Many beautiful interferograms of rough surfaces were produced by Tolansky (1960, 1970a, b), but the usefulness of interferometry for roughness measurement was originally limited by several factors. In the absence of coherent light sources it was difficult to obtain fringes of sufficient sharpness and contrast. If the amplitudes of surface roughness were greater than the wavelength of the incident light, there was no easy way of distinguishing between fringes of different order. Finally, there was no convenient way of converting the surface map of the interferogram into spot heights suitable for quantitative analysis. These difficulties are confronted in a phase-shifting interferometer originally conceived by Wyant and his co-workers (1986). Fringes from a Michelson, Linnik or Mireau interferometer, depending on the required magnification, are imaged onto a charge-coupled diode and the resulting intensity variations are stored in a computer (Fig. 3.10). A slightly different design (Biegen & Smythe 1988) uses a Fizeau interferometer. The entire interferometer optics are shifted axially relative to the workpiece by a piezoelectric transducer to change the optical path, giving a different set of fringes. Three such sets of measurements give enough recorded information to solve the intensity equations point by point for local heights.

Q Reid

+piece

SbD

PZT transducer (microprocessorcontrolled

Mhu mi

chrance wrtace Minu hterfemmete amspliier plate

...._...:.

::

.'..I

;

fbrtsurtsce

Figure 3.10. Phase-shft interferometer (Creath 1987).

46

Rough SurJaces

The vertical resolution is about 0.1 nm, but early realisations of this principle were limited in vertical range to half the wavelength of the illuminating light, say about 0.3 pm (Bennett & Mattsson 1989). Combining measurements made at different wavelengths extended the vertical range to 15 pm (Creath 1987). In a more recent development, the vertical range is extended still further by combining phase-shift interferometry with what is described iis vertical scanning interferometry (Caber et al. 1993). The visibility of fringes from a white-light source drops off rapidly from its maximum value at minimum optical path difference. If the interferometer is translated axially, these maxima, and hence the local height, can be extracted on a point-by-point basis by signal processing. A typical commercial realisation of this technique claims horizontal range and resolution of 0.2 mm and 0.4 pm respectively, vertical range and resolution of 150 pm and 1 nm. The maximum measurable slope at this magnification is stated to be 14". A somewhat similar system, rather misleadingly described as "coherence radar", has been described by Hausler & Neumann (1992).

3.2. Parametric Techniques Scattering is a subject of interest to optical engineers, radar engineers and many others, and has an extensive literature of its own. The present account will only attempt to cover it in sufficient depth to treat its application to roughness measurement. The mathematical foundations of scattering theory are set out in Beckmann & Spizzichino (1963) and more recently by Ogilvy (1991). Experimental techniques are discussed at length by Bennett & Mattsson (1989). The following account follows very closely the review of Vorburger & Teague (1981). When a beam of light is reflected by a rough surface, the intensity and pattern of the scattered radiation depend on the roughness heights, the spatial wavelengths and the wavelength of the light. In general, short and long surface wavelengths diffract the light into large and small angles respectively relative to the specular direction. For most surfaces, there is a broad spectrum of surface wavelengths, and the light is therefore diffracted into a range of angles. Five main mechanisms of interaction may be distinguished between rough surfaces and electromagnetic radiation (Vorburger & Teague 1981). For surfaces whose roughness is much less than the wavelength of the incident radiation, most of the reflected light propagates in the specular direction. As the roughness increases, the intensity of the specular beam decreases while the diffracted

Optical Instruments

47

radiation increases in intensity and becomes more diffuse. I a addition, the angular distribution of diffuse radiation consists of a fine grainy structure called speckle, whxh shows up as intensity contrast between neighbouring points in the scattered field. Finally, the light wave may undergo a change in its polarization state upon reflection from the surface. All of these phenomena, the relative intensity or reflectance in the specular direction, the total intensity of the scattered light, the diffuseness of the angular scattering pattern, the speckle contrast, and the polarization, depend on the surface roughness, and all five have served as the bases for potential surface measuring instruments.

3.2.1. Specular Reflectance

One way of assessing specular reflectance is to measure what is called image clarity: the ability of the surface to reflect a clear image of a row of posts (Elmendorf & Vaughan 1958) or of a grid (Westberg 1967168). To quantify this, Halling (1954) designed an instrument in which the reflection of a series of vertical bars in the surface is observed at the specular angle. This angle is gradually decreased until the bars can no longer be distinguished. He found that the roughness was inversely proportional to the cosine of the angle of extinction.

Figure 3.11. Dflerent designs of glossmeter and definitions of their associated measurements (Westberg 1967168).

48

Rough Sufaces

A simpler approach is to measure the intensity of the specular beam. Commercial instruments following this general approach are sometimes called glossmeters, though gloss is a tenn not easily defined; Westberg (1967/68) quotes a review of 44 different definitions of gloss. He himself has reviewed the design, construction and operation of a number of designs of glossmeter at some length, and distinguishes six basic combinations of specular and diffuse measurement (Fig. 3.11). The measurement of roughness relies on the inverse correlation which exists between the specular reflectance p and the roughness Rq. For rougher surfaces (Rq > ;iy / 10 ) the true specular beam effectively disappears so p is no longer measurable. However, even in these circumstances there are a number of empirical studies that show an inverse correlation between the light intensity scattered in the specular direction and the surface roughness (Tanner & Fahoum 1976, Murray 1973, Spurgeon & Slater 1974). The main advantage of this method is speed. If the instrument is properly calibrated, a single measurement immediately yields a value for Rq. Therefore, the specular reflectance method is ideal for routine comparisons of similar surfaces. The technique is capable of studying isotropic or anisotropic surfaces and the ultimate vertical resolution is about 1 nm (Cunningham et al. 1976).

0

Figure 3.12. Roughness measured by specular reflectance and stylus methoas by six different groups of workers (adapted kom Birkebak 1971).

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There are a number of disadvantages to techniques based on specular reflection. Agreement with stylus measurements is not very good (Fig. 3.12). The measured intensities must be normalized for each material under inspection. Measurements are affected by the direction of the lay (Vashisht & Radhakrishnan 1974), though this dependence dlsappears at normal incidence (Ollard 1949). Also, even for fairly small apertures the diffuse component will be significant unless p/pois fairly close to unity. This implies that Rq must be much less than the optical wavelength 4, which means that visible light is suitable only for measuring the smoothest surfaces; for most engineering surfaces infrared radiation must be used. A final drawback of this technique is that it is primarily a function of surface amplitude and is not suitable for measuring surface wavelengths.

3.2.2. Total integrated scatter

The total integrated scatter (TIS) method is complementary to specular reflectance. Instead of measuring the intensity of the specularly reflected light, one measures the total intensity of the diffusely scattered light (Bennett & Mattsson 1989). TIS has much the same strengths and weaknesses as specular reflectance, i. e. the technique is fast, is based on an approximate theory, is practical only for surfaces smoother than the wavelength of the incident radiation, and has similar bandwidth limitations. The fundamental difference between the two is that the TIS is more dlrectly related to Rq. TIS is a fundamental quantity for the functioning and testing of optical components (Bennett et al. 1979). In many optical applications, if the TIS can be measured accurately and routinely, the roughness need not be. Using the technique for practical roughness measurements presents several problems, however. To begin with, the experimental set-up is more elaborate than that required for specular reflectance. Moreover, the bandwidth limitation arises from the fact that the collecting optics normally contain some sort of aperture or stop to prevent the specular beam from being detected along with the scattered radiation. Such an aperture or stop inevitably also blocks a portion of the scattered light and hence limits the surface wavelengths that can be detected (Bennett et al. 1979). The net result is that the technique does not seem to have been successfully applied to surfaces with Rq greater than about 10 nm. Even in the regime of very smooth surfaces, the roughness results obtained from TIS, although self-consistent, do not seem to agree well with measurements made by non-scattering techniques (Fig. 3.13). It appears then that TIS is an important technique for rapid

Rough SurJaces

50

measurements of the optical scattering characteristics of very smooth surfaces with short wavelengths. Like specular reflectance, TIS is not suitable for measuring surface wavelength parameters.

=m 200

0

8

2t

0 NWC TIS 0 BALZERS TIS A LIVERMORE OHP

0 N W C WYKO TOPO-20 0 NWC TALYSTEP

A I

20

I

I

I

I

I

I

I

I

50 100 AVERAGE IVIS ROUGHNESS. TIS d l

200

Figure 3.13. Summary of measurements on five roughness standards made by: 0 0 , TIS instruments; AO, optical profilers; 0,stylus instrument (Bennett & Mattsson 1989).

3.2.3. Angular Distributions

In principle, the entire angular distribution of the scattered radiation contains a great deal of information about the surface topography. In addition to rms roughness, measurements of the angular distributions (Tanner & Fahoum 1976, Stover 1976, Thwaite 1979) can yield other surface parameters such as the average wavelength or the average slope. The angle of incidence is normally held constant and the angular distribution is measured by an array of detectors or by a movable detector and is stored as a function I(@ where is the angle of scattering. A good example of the resulting angular distributions for a diamond-turned specimen illuminated by coherent light is shown in Fig. 3.14 (Church et al. 1977). The upper curve shows the angular distribution in the plzne of incidence and perpendicular to the predominant lay of the surface. It contains an intense specular beam at 8, =0, a broad scattering distribution due to the random component of the roughness, and a series of dwrete lines due to a periodic component of the roughness caused by the feed rate of the diamond tool. The lower curve is an

51

Optical Instruments

angular distribution measured parallel to the lay direction and it shows another broad distribution characteristic of the random roughness pattern in this direction. In principle then, one can distinguish between effects due to periodic and random roughness components and can detect the directional properties of surfaces.

6'

.-

lo-'

e lo-'

sB ,o-Q lo-'

lo-* lo-' 10.6

- 4 o ~ w - z I p o0

w

Scattering angle

200

30"

SOD

Figure 3.14. Angular distribution of light scattered &om a diamond-turnedsurface (adapted from Church et al. 1977). Upper curve, across lay; lower curve, along lay.

The kind of surface information that may be obtained from angular Qstributions depends on the roughness regime. For Rq >>% and surface spatial wavelengths il >> A,. one is working in the geometrical optics regime where the scattering may be described as purely specular scattering from a series of facets (Church 1979). The angular distribution is therefore related to the surface slope distribution, and its width is a measure of the characteristic slope of the surface. As Rq and il decrease, the distribution becomes a much more complicated function of both surface slopes and heights and is difficult to interpret. Some work has been done by Leader (1979), Smith & Hering (1970) and Chandley (1976) for Leader's comparisons between calculated and measured surfaces with Rq A., angular distributions yield interesting, qualitative idormation about the topography of painted and dielectric surfaces. The most interesting regime is where Rq 271 ) to give

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complete destructive interference at some points in the pattern and the illumination has a h g h degree of spatial and temporal coherence. Spatial coherence means that the phases of the electromagnetic field at two points spaced across the propagating wavefront are highly correlated, and temporal coherence means that the phases of the field at two points spaced along the direction of light propagation are highly correlated. Speckle contrast is unity for fully coherent monochromatic light illuminating a surface whose roughness is much larger than 4 so that the wavelet phases are uniformly distributed over the interval from 0 to 27c. Correspondingly, for coherent monochromatic illumination, as the reflecting surface becomes smoother and less complete destructive interference occurs, the contrast V decreases toward zero. Experiments to relate surface roughness to the contrast of speckle patterns produced by coherent monochromatic illumination (Fig 3.16) showed that a strong linear correlation exists between V and Ra determined by stylus profilometry for Ra values up to 0.13 pm.

0

m o D a J 3 a a Q D Q y I

2Ra (microns) Figure 3.16. Maximum average contrast of speckle intensity variations as a hnction of roughness for surfaces of various metals and finishes (Vorburger & Teague 1981).

The second broad class of techniques for relating surface roughness and speckle is speckle pattern decorrelation measurement. Here two speckle patterns are obtained from the test surface by illuminating it with different angles of incidence or different wavelengths of light. Correlation properties of the speckle patterns are then studied by recordmg the patterns on the same photographic plate by double exposure or by photoelectric detection of the two patterns. The primary attribute of this type of speckle measurement is that Rq values as large as 30 to 50 pm can be measured. Fujii & Lit( 1978) applied a speckle decorrelation technique

56

Rough Sur$aces

to the measurement of a range of ground glass and ground metal surfaces. They found good correlation between roughness deduced from correlation measurements and roughness measured by stylus instruments over a range of roughness from 0.13 pm to 6 pm (Fig. 3.17).

Figure 3.17. Roughness deduced &om speckle decorrelation measurementscompared with stylus roughness measurements for glass (circles) and metal (triangles) surfaces (Fujii & Lit 1978).

As the examples of this subsection have demonstrated, speckle patterns are rich in information about the microtopography of a test surface, though the field has not yet yielded techniques for obtaining characterizations of roughness other than the Rq value. The range of Rq values measurable with speckle techniques and their apparent insensitivity to the type of material and type of surface forming process indicate that these techniques have a high potential for roughness measurements. However, Briers (1993) has noted that speckle techniques have not in general been converted into practical instruments; he describes them as a "solution in search of a problem".

3.3. References

Anderson, W. L., "Surface roughness studies by optical processing methods", Proc. I.E.E.E., (Letters), 57, 95 (1969).

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Azzam, R. M. A,, and Bashara, N. M., Ellipsometry and polarised light (North Holland, Amsterdam, 1977) Bailey, W., "Optical inspection of cylinder bores", Trib. Int. 10, 319-322 ( 1977) Beckmann, P. and Spizzichino, A,, The scattering of dectromagnetic waves porn rough surfaces (Pergamon Press, Oxford, 1963). Bennett, J. M., Burge, D. K., Rahn, J. P., Bennett, H. E., "Standards for optical surface quality using total integrated scattering", Proc. SPIE 181, 124-128 (1979) Bennett, J. M., and Mattsson, L., Introduction to surface roughness and scattering (Opt. SOC.Am., Washington, 1989) Biegen, J. F. and Smythe, R. A,, "High-resolution phase-measuring laser interferometric microscope for engineering surface metrology", Surface Topography, 1, 287-299 (1988) Birkebak, R. C., "Optical and mechanical RMS surface roughness comparison", Appl. Opt. 10, 1970-1979 (1971) Briers, J. D., "Surface roughness evaluation", in Speckle metrology, R. J. Sirohi ed., (Marcel Dekker, New York, 1993). Bristow, T. C., "Surface roughness measurements over long scan lengths", Surface Topography, 1, 281-285 (1988) Brown, A. J. C., "Rapid optical measurement of surfaces", Int. J. Mach. Tool Munufact. 35, 135-139 (1995) Caber, P. J., Martinek, S. J., Niemann, R. J., "A new interferometric profiler for smooth and rough surfaces", Proc. SPIE 2088 (1993) Chandley, P. J., "Determination of the autocorrelation function of height on a rough surface from coherent light scattering", Opt. Quantum Electron. 8, 329-333 (1976). Church, E. L., "The measurement of surface texture and topography by differential light scattering", Wear, 57, 93-105 (1979). Church, E. L.; Jenkinson, H. A.; Zavada, J. M., "Measurement of the finish of diamond-turned metal surfaces by differential light scattering", Opt. Eng. 16, 360-374 (1977). Church, E. L.; Jenkinson, H. A.; Zavada, J. M., "Relationship between surface scattering and micro-topographic features", Opt. Eng. 18, 125-131(1979). Creath, K., "Step height measurement using two-wavelength phase-shifting interferometry", Applied Optics 26, 2810-2815 (1987)

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Cunningham, L. J., and Braundmeier, A. J., "Measurement of the correlation between the specular reflectance and surface roughness of Ag films", Phys. Rev. 14B, 479-488 (1976) Dainty, J. C . , "The statistics of speckle patterns", in E. Wolfed., Progress in Optics 14 (North Holland, Amsterdam, 1976) Davies, T.; Kun, X; Luxmoore, A. R., "Digital measurement of surface profiles by automated optical sectioning", Measurement Science & Technology 5, 710-715 (1994) Downs, M. J., Mason, N. M., Nelson, J. C. C., "Measurement of the profiles of super smooth surfaces using optical interferometry", Proc. SPIE 1009, 14-17 (1989) Downs, M. J., McGivern, W. H., Ferguson, H. J., "Optical system for measuring the profiles of super-smooth surfaces", Prec. Engng. 7, 2 11-2 15 (1985) Dupuy, O., "High-precision optical profilometer for the study of microgeometrical surface defects",. Proc .I .Mech .E., 182, Part 3K, 255-259 (1967/68). Edwin, R. P., "Light scattering as a technique for measuring the roughness of optical surfaces", J. Phys. E6, 55-59 (1973) Elmendorf, A. and Vaughan, T. W., "A survey of methods of measuring smoothness of wood", Forest Products J.,8, 275-282 (1958). Elson, J. M., and Bennett, J. M., "Relation between the angular dependence of scattering and the statistical properties of optical surfaces", J. Opt. SOC.Am. 69, 31-39 (1979) Elson, J. M., Rahn, J. P., Bennett, J. M., "Light scattering from multilayer optics: comparison of theory and experiment",Appl. Opt. 19, 669-675 (1980) Ennos, A. E. and M. S. Virdee, "High accuracy profile measurement of quasiconical mirror surfaces by laser autocollimation",Precis. Engng. 1, 5-8 ( I 982) Farago, F. T., Handbook of dimensional measurement 2e (Industrial Press, New York, 1982) Fujii, H., and Lit, J. W. Y., "Surface roughness measurement using dichromatic speckle pattern: an experimental study", Appl. Opt. 17, 2690-2705 (1978) Halling, J., "A reflectometer for the assessment of surface texture", J. Sci. Instrum., 31, 3 18-320 (1954). Hamilton, D. K.; Wilson, T., "Three-dimensional surface measurement using the confocal scanning microscope", Appl Phys 27,2 1 1-2 13 (1982). Hard, S., and Nilsson, O., "Laser heterodyne apparatus for roughness measurements of polished surfaces", Appl. Opt. 17, 3827-383 1 (1978)

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Hausler, G., and Neumann, J., "Coherence radar - an accurate 3D sensor for rough surfaces", Proc. SPIE 1822, 200-205 (1992) Howes, V. R., "An angle profile technique for surface studies", Metallography 7, 43 1-440 (1974). Johnson, F.; Brisco, B.; Brown, R. J., "Evaluation of limits to the performance of the surface roughness meter", Canadian Journal of Remote Sensing 19,140-145 (1993) Kayser, J. F., "Optical cut method for the determination of surface roughness", Foundv Trade J., 70, 137-138 (1943) Keller, B. E., "Non-contact surface contour analyser", Proc. 1. Mech. E., 182, Part 3K, 360-367 (1967/68). Lange, D. A.; Jennings, H. M.; Shah, S. P., "Analysis of surface roughness using confocal microscopy", Journal of Materials Science 28,3879-3884 (1993) Leader, J. C., "Analysis and prediction of laser scattering from rough-surface materials", J. Opt. SOC.Am. 69, 610-619 (1979) Lonardo, P. M., "Testing a new optical sensor for in-process detection of surface roughness", Ann. CZRP 27, 53 1-533 (1978) Murray, H., "Exploratoly investigation of laser methods for grinding research", Ann. CIRP 22, 137-139 (1973) Nagata, K., Umehara, T. and Nishiwaki, J., "The determination of RMS roughness and correlation length of rough surface by measuring spatial coherence function", Japan. J. Appl. Phys., 12, 1693-1698 (1973). Ogilvy, J. A,, Theory of wave scatteringfrom random rough surfaces (Adam Hilger, Bristol, 1991) Ollard, E. A., "Surface reflectometer for evaluating polished surfaces", J. Electrodepos. Tech. SOC.,24, 1-8 (1949) Olsen, W. S. and Adams, R. M., "A laser profilometer", J. Geophysical Res., 75,2185-2187 (1970). Parry, G., "Some effects of surface roughness on the appearance of speckle in polychromatic light", Opt. Comm. 12, 75-81 (1974) Pettigrew, R. M., and Hancock, F. J., "An optical profilometer", Proc. NELEX Conf: (Nat. Engng. Lab., Glasgow, 1978) Ramgulam, R. B.; Amirbayat, J.; Porat, I., "Measurement of fabric roughness by a noncontact method", Journal of the Textile Institute 84,99-106 (1993) Ribbens, W. B. and Lazik, G. L., "Use of optical data processing techniques for surface roughness stuhes", Proc. I.E.E.E. ('Letters) .56, 1637-1638 (1968).

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Sandoz, P., Tribillon, G., Gharbi, T., Devillers, R., "Ruughness measurement by confocal microscopy for brightness characterisation and surface waviness visibility evaluation", Wear 201, 186-192 (1996) Sayles, R. S., Wayte, R. C., Tweedale, P. J. and Briscoe, B. J., "The design, construction and commissioning of an inexpensive prototype laser optical profilometer", Surface Topography, 1 , 219-227 (1988) Shaw, M. C. and Peklenik, J., "A light projection technique for studying surface topology", Ann. C.Z.R.P.,12, 93-7 (1963). Smith, T., "Effect of surface roughness on ellipsometry of aluminium", Surf: Sci. 56, 252-259 (1976) Smith, T. F. and Hering, R. G., Tomparison of bidirectional reflectance measurements and model for rough metallic surfaces", Proc. 5th Symp. Thermophys. Properties, 429-435 (ASME, New York, 1970). Sommargren, G . E., "Optical measurement of surface profile", Precis. Eng. 3, 131-136 (1981a) Sommargren, G . E., "Optical heterodyne profilometry", Appl. Opt. 20, 610618 (1981b) Spurgeon, D. and Slater, R. A. C., "In-process indication of surface roughness using a fibre-optics transducer", Proc. of the 15th Int. Machine Tool Des. & Res. Conf.',Birmingham, 339-347 (1974). Stover, J. C . , "Spectral-density function gives surface roughness", Laser FOCUS12,83-85 (1976). Tanner, L. H. and Fahoum, M., "A study of the surfacc parameters of ground and lapped metal surfaces, using specular and diffuse reflection of laser light", Wear, 36,299-3 16 (1976) Teague, E. C., Vorburger, T. V., Maystre, D., Young, R. D., "Light scattering from manufactured surfaces", Ann. C I W 30,563-569 (1981). Thwaite, E. G., "The direct measurement of the power spectrum of rough surfaces by optical Fourier transformation", Wear, 57, 71-80 (1979). Thwaite, E. G., "The roughness of surfaces",Australian Physicist (November 1977) Tolansky, S . , Multiple-beam interference microscopy of metals (Academic Press, London, 1970a). Tolansky, S . , Multiple-beam interferometry of surfazes and films (Dover Publications, Inc., New York, 1970b). Tolansky, S., Surface microtopography (Longmans, London, 1960). Vashisht, S. K. and Radhaknshnan, V., "Surface studies with a gloss meter", Tribology Znt., 7, 70-76 (1974).

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Vorburger, T. V., and Ludema, K. C., "Ellipsometry of rough surfaces", Appl. Opt. 19, 561-569 (1980) Vorburger, T. V., "Methods for characterising surface topography", in Tutorials in Optics, 137-151 (Opt. Soc. Am., Washington, 1992) Vorburger, T. V.; Teague, E. C., "Optical techniques for on-line measurement of surface topography", Precis. Eng. 3,61-83 (1981). Way, S., "Description and observation of metal surfaces", Proc. Con$ on Friction & Surface Finish, 2e, 44-75 (MIT, Cambridge, 1969). Wehbi, D. and C. Roques-Carmes, "Physical limitations of optical defocussing technique," Wear 109, 287-295 (1986) West, R. N., and Stocker, W. J., "Automatic inspection of cylinder bores", Metrology &Inspection 9, 9-10 (1977) Westberg, J., "Development of objective methods for judging the quality of ground and polished surfaces in production", Proc .I .Mech .E., 182, Part 3K, 260273. (1967/68). Whitehouse, D. J., "Modern trends in the measurement of surfaces", Rev. M. Mec., 21, 19-28 (1975). Whitehouse, D. J., Handbook of surface metrology (Institute of Physics, Bristol, 1994) Williams, M. W., Ludema, K. C. and Hildreth, D. M., "Mueller matrix ellipsometry of practical surfaces", Surface Topography, 1, 357-372 (1988) Wyant, J. C., Koliopoulos, C. L., Bhushan, B., Basila, D., "Development of a three-dimensional noncontact dlgital optical profiler", Trans. ASME: J. Trib. 108, 1-8 (1986) Young, R. D.; Vorburger, T. V.; Teague, E. C., "In-process and on-line measurement of surface finish", Ann. CIRP 29,435-440 (1980).

CHAPTER 4

OTHER MEASUREMENT TECHNIQUES

We have considered stylus and optical methods in some detail because equipment using these methods comprises the major part of the installed base of roughness measuring instruments. However, a large number of other techniques have been used for the measurement of surface roughness. Some are mainly of historic interest, but may still be worth studying because the principles involved might suggest an application to some measurement problem insoluble by other means. Others are novel and still under development, and cover ranges or offer other special features which complement stylus and optical methods. We will continue to make the convenient distinction between profiling techniques, which can yield point-by-point information about the surface topography, and parametric techniques, which give directly some average measure of the surface roughness.

4.1. Profiling Methods

4.1.1. Taper Sectioning

In taper sectioning, as its name implies, a section is cut through the surface to be examined at a shallow angle, thus effectively magnifying height variations by the cotangent of the angle, and subsequently examined by optical microscopy. The technique was first described by Nelson (1969) and has since been employed by a number of other workers (Broadston 1944; Tarasov 1945; Darmody 1946; Shaw and Peklenik 1963; Dorinson 1965). Practical details are dlscussed at length by Nelson and by Rabinowicz (1950). It is necessaly to support the surface to be sectioned with an adherent coating which will prevent smearing of the contour during the sectioning operation. This coating must adhere firmly to the surface; must have a similar hardness; should not dlfise into the surface; and should not be affected by any subsequent etching. For steel these requirements are met by electroplating with nickel to a thickness of 0.5 mm. The specimen is then ground on a surface grinder at an angle of between 1 63

64

Rough Surfaces

and 6 degrees, depending on the required magnification, till the interface between coating and substrate has advanced halfway along the specimen. The taper section so produced is lapped, polished and possibly finally lightly etched or heat tinted to provide good contrast for the optical examination. The main advantage claimed for taper sectioning is its accuracy; indeed Shaw and Peklenik (1963) have gone so far as to describe it as 'probably the most accurate method that has ever been devised for studying the profile of a surface'. This seems rather an excessive claim for a technique whose vertical resolution is admitted by the Same authors to be only 0.25 pm. Great play is made, however, by Tarasov (1945) among others, of the ability of the method to show deep scratches which a stylus will not penetrate. The only measurement which can conveniently be made from a micrograph of a taper section is the peak-to-valley height, and Tarasov compares this measurement with the RMS roughness found by a stylus instrument for a number of surfaces. According to other results quoted by Shaw and Peklenik, a comparison of taper-section profiles with those of a stylus instrument revealed larger peak-to-valley roughness in every case, up to a maximum of 100 per cent discrepancy. This is not surprising when the integrating effect of taper sectioning is taken into account. Tarasov quotes peak-to-valley roughness of between 1 pm and 5 pm at a relative vertical magnification of 25. His sections must therefore have represented profiles of effective width from 25 pm to 125 pm. This compares with 8 pm for the width of a typical stylus (Jungles and Whitehouse 1970), which according to Guerrero and Black (1972) normally 'sees' an even narrower strip as it tends to ride on one edge only. Taper sectioning is thus equivalent, at a conservative estimate, to measuring 3-5 profile lengths from a stylus instrument. As the greater the profile length the higher the probability of encountering a high peak or deep valley, it is small wonder that the taper section gives a larger measurement. The other disadvantages of the technique are too obvious to need comment; we have discussed it at this length mainly because of the inflated claims made for its accuracy.

4.1.2. Electron Microscopy

Electron microscopy is thought of as primarily a technique for visualisation, but the very short wavelengths of electron beams offer the possibility of very high resolutions for quantitative work. Transmission electron microscopy (TEM), dealing as it does with specimens thin enough to pass an electron beam, is of little

Other Measurement Techniques

65

interest from the point of view of roughness measurement. Scanning electron microscopy (SEM) is at first sight more promising. An electron beam incident on the surface excites the emission of secondary electrons which are then detected. As with the STM, specimens must be electrically conducting and measured under vacuum. However, SEM has some vely attractive potential advantages. The depth offield is unusually large: features a few Angstroms high stand out plainly, and the vertical range is of the order of mm. The horizontal resolution is limited only by the beam diameter to a few nm. The beam is deflected virtually instantaneously by field coils, obviating the need for mechanical translation. The steepest slope which can be measured is about 15 degrees (Whitehouse 1994). For a general review of electron microscopy see Grundy & Jones (1976). The resulting intensity signal bears a striking resemblance to a profile measured by a stylus instrument. Unfortunately this resemblance is more apparent than real. Secondary electrons originate from regions 100 nm or so below the specimen surface, and local convexities increase the local electron flux, exaggerating topographic features. Point-by point comparisons of secondary electron images with stylus measurements (Samuels et al. 1974) show rather poor agreement. It is possible to extract true height information by analysing stereo pairs (Howell & Bayda 1972, Lee & Russ 1989), but this is laborious and may lose much of the potential high resolution. A number of workers have tried to get around this difficulty in other ways. One technique of SEM analysis employed a modified detector which followed the line-of-sight properties of back-scattered electrons (McAdams 1974). These electrons, which travel in straight-line trajectories, are thresholded according to direction and produce an electron optical sectioning of the surface along the critical trajectory direction. Surface elevation is therefore recorded as variations in detector position, as opposed to signal intensity in the standard SEM. A multipledetector technique (Lebiedzik & White 1975) produced reasonable agreement between measurements of average roughness. Holburn & Smith (1982) employed an autofocussing technique with a claimed vertical resolution of 1 pm. Myshkin and his co-workers (Kholodilov et al. 1985, Grigor'ev et al. 1988) have obtained roughness parameters from SEM measurements of secondary electron emission, but it is not clear whether they were able to reconstruct a true profile. Rasigni et al. (1981) have studied transmission electron micrographs of carbon replicas of calcium fluoride films and other surfaces, using a microdensitometer. They show that the micrograph transmittance is approximately proportional to the slope of the surface elements, which enables determination of the surface profile by integration of the microdensitometer data. This technique is

Rough Sugaces

66

able to measure roughnesses of 2 nm with a lateral resolution of better than 1 nm over an area of about 1 pm x 1 pm.

4. I.3. Capacitance

Capacitance techniques are discussed in more detail in the section on parametric techniques, but there are two designs of capacitance-based profilers which will be discussed here. Garbini et al. (1988) use a so-called fringe-field technique. A thin electrode held normal to the specimen is translated in a direction parallel to the plane of the electrode (Fig. 4.1). Lateral range is 6 mm; vertical range is not stated but appears to be about 10 pm.

Figure 4.1. Fringe-field capacitance probe (Garbini et al. 1988)

Although the electrode is only 0.3 pm wide, the capacitance between it and the specimen is influenced by regions of the specimen adjacent to the electrode in a manner analogous to the weighting function of a low-pass filter, so it is rather difficult to determine the lateral resolution. The equivalent stylus width is the length w of the electrode (about a millimetre in the practical realisation), so "profile" measurements are only meaningful on a surface produced by a process such as shaping or turning which is basically two-dimensional. In spite of these limitations, the instrument agrees with stylus measurements over a restricted range of roughness (Fig. 4.2) and appears to work well at relatively high (25 m d s )

67

Other Measurement Techniques

translation speeds. The fringe-field capacitance technique has also been used for parametric measurement (Nowicki & Jarkiewicz 1997). 4

-

3

3

'I 0

I

2

3

Surface roughness. RB

4

5

Cm)

Figure 4.2. Maximum, average and minimum roughnesses for various test samples (Garbini et al. 1988). (0)Stylus instrument; (x) fringe-field profilometer.

An instrument of much higher resolution is described by Bugg & King (1988). In the scanning capacitance microscope the electrode is a fine vertical wire. Most of the capacitance between the electrode and the specimen is due, as in the fringe-field device, to the surrounding field, but the effect of this field is ingeniously removed by vibrating the wire in a vertical plme and measuring the differential capacitance. In practice a servo arrangement is used to keep the separation of transducer and specimen constant during translation. The height variation is given by the servo signal, thus obviating the inherent non-linearity of the transducer (Fig. 4.3). In a commercial realisation of this instrument (Bugg 1991), lateral range and resolution are given as 26 mm and 10 pm respectively. The vertical resolution is O.lpm, and the vertical range is said to be 5 mm, presumably with the aid of some vertical translation device.

Rough Surfaces

68

Figure 4.3. Scanning capacitance microscope ( B u g & King 1988)

4.1.4. Scanning Microscopies

Although the techniques described below are all basically profiling techniques, they are generally used in a raster scan mode to make area measurements. The lateral displacements required are too small for conventional mechanisms requiring relative motion between their components, so piezo drives are used for translations in all three axes. Piezo drives are well suited for this, but are limited in lateral range to some fraction of a millimetre. They are also susceptible to hysteresis, which can then appear as an apparent form error. T h s wide variety of techniques shares many common elements (Teague 1988): servo control of tip-specimen spacing to maintain constant reaction; precise mechanical scanning of the tip with respect to the specimen; high sensitivity of the output to tip-specimen spacing, requiring stiff microscope structures and isolation from mechanical noise; lateral resolution determined by tip dimensions, with a resultant emphasis on the problem of probe formation. If a conducting probe is placed very close to a conducting surface a small potential difference across the gap will encourage electrons to cross the gap by quantum tunnelling. The resulting current is highly sensitive to the width of the gap. As the probe is translated across the rough surface the width of the gap, and thus the tunnelling current, changes. This is the principal of the scanning tunnelling microscope (STM) (Binnig & Rohrer 1986) (Fig. 4.4).

Other Measurement Techniques

69

Figure 4.4. Principle of STM (Binnig & Rohrer 1986)

There are two possible modes of operation (Fig. 4.5). The probe can be servoed to maintain a constant gap as it is translated, in which case the restoring servo voltage is a measure of the local height. This is relatively slow but can more easily follow the rougher surfaces. Alternatively, the probe can be maintained at a constant height and the change in tunnelling current can be measured. This is quicker but works best on smooth surfaces. CONSTANT CURRENT Y M E

I

CONSTANT NIGHT YXIE

Figure 4.5. Alternative modes of operation of STM (adapted from Hansma & Tersoff 1987)

The vertical resolution is a few Angstroms, and if a sufficiently fine probe is used the horizontal resolution is in principle atomic. The vertical range is limited in practice by the exponential fall-off in the tunnelling current as the gap increases. Also, the specimen must be in a vacuum chamber and must be of a conducting material. Within these limitations the S T M is a very powerful and flexible

70

Rough Surfaces

instrument and many commercial versions are available. Fu et al. (1992) have described an STM with a lateral range of 0.5 mm and lateral resolution of 1 nm. A recent review (DiNardo 1994) lists 400 or so references to STM and related techniques. In the atomic force microscope (AFM) (Binnig & @ate 1986), a probe mounted on a cantilever is repelled by the van der Waal's forces as it travels over the rough surface. The force deflects the cantilever and the deflection is sensed, either by an STM (Binnig & Quate 1986) or by the angular displacement of a reflected laser beam (Fig. 4.6), giving the added amplification of an optical lever (Alexander et al. 1989). Either repulsive forces or attractive electrostatic forces can be used, sometimes in the same instrument. Again the measured force may either be recorded directly or used as the control parameter for a feedback circuit which maintains the force at a constant value (McClelland et al. 1987).

Figure 4.6. AFM with optical lever mounted on the cantilever (Alexander et al. 1989)

The AFM avoids two disadvantages of the STM, its restriction to conducting specimens and the requirement for a hard vacuum. Note that although the AFM appears at first sight to be a kind of small-scale stylus instrument, the probe does not actually make contact with the surface. Translation arrangements, ranges and resolutions are similar to those of the STM, and the AFM is also commercially available in a number of models. In the scanning near-field acoustic microscope (SNAM), the friction of the air and other damping effects in the small gap between a vibrating tip and the measured surface change the frequency of vibration (Goch & Volk 1994). A standard diamond tip fixed to the constantly excited tuning fork from a wristwatch

Other Measurement Techniques

71

is guided along the surface at a separation of about 100 nm. A servo moves the fork up and down to maintain constant frequency, hence constant separation (Fig. 4.7), so the servo signal gives the varying surface height. Vertical resolution is about 1 nm, but lateral resolution is limited to about 0.5 l m by the radius of curvature of the diamond tip.

,nm

I F

4-

tm

inspected surface

Figure 4.7. Schematic of an acoustic microscope (Goch & \ olk 1994)

DiNardo (1994) describes a number of other techniques operating on a similar scale to STM and AFM and using similar translation systems (Table 4.1). These all yield topographic information of some kind so could in principle be used to measure roughness.

4.2. Parametric Methods

4.2.1. Mechanical Methods

The basic idea of a tactile test is that a probe of some kind is run across the surface to be measured and the friction between the surface and the probe is compared with that from a similarly machined surface of known roughness. The simplest and cheapest probe is the human fingernail, and it is surprisingly effective. Indeed one American engineer (Broadston 1947) waxed lyrical at the thought that every machinist carried $100,000 worth of surface-measuring equipment about his person, i.e. 10 fingers at $10,000, the cost of a good stylus instrument, each. The human fingernail is more sensitive to some frequencies than to others (Abbott & Goldschmidt 1937), so there is presumably an optimum speed with which it should be drawn along the surface. Schlesinger (19 12) performed some

Rough Surfaces

72

Table 4.1. Near-field surface characterisationprobes (adapted from DiNardo 1994).

Measurement principle

Lateral resolution

Reference

Scanning thermal profiler (STP)

surface temperature

< 30 nm

Williams & Wickramasinghe (1986)

Scanning chemical potential microscope (SCPM)

thermoelectric voltage

< 1 nm

Williams & Wickramasinghe (1991)

Optical absorption microscope (OAM)

effects of light absorption

< 1 nm

Weaver et al. (1989)

Scanning ion conductance microscope (SICM)

ion current

< 0.1 nm

Hansma et al. (1989)

Laser force microscope (LFM) Attractive force microscope

probe vibration amplitude van der Waals force

N.A.

Whitehouse (1994)

< 100 nm

DiNardo (1994)

Charge force microscope ( C M , EFM)

electrostatic force

< 200 nm

Whitehouse (1994)

Magnetic force microscope @EM)

magnetic force

< 100 nm

Whitehouse (1994)

Scanning near-field optical microscope (SNOM or NSOM)

near-field optical reflection

< 25 nm

Pohl et al. (1984)

Photon scanning tunnelling microscope

near-field optical transmission

50 nm

Reddick et al. (1990)

Instrument ......

73

Other Measurement Techniques

careful tests in which subjects were asked to differentiate between pairs of test pieces of increasingly different roughness. He found that for some finishes differences in roughness of as little as 20 per cent could be detected by the majority of his test panel (Fig. 4.8). A similar experiment by Haesing (1961) found a correlation between the subjects' assessments and stylus readings which, not unexpectedly, was stronger for peak height than for average roughness.

30 20

0-025 0.05

0.1

0.2

0.4

0.8

1.6

3.2

6.4

I3

25

Ra (microns) Figure 4.8. Tactile comparison (Schlesinger 1942). Percentage difference in roughness which could be assessed by 9 out of 10 testers: A, lapped, honed and ground B, milled C, turned and shaped.

This technique is of some scientific interest as it appem to be sensitive only to a narrow band of wavelengths, namely to those corresponding to the thickness of the probe. The maximum height difference detectable is presumably set by the protrusion of the nail beyond the fingertips while the minimum is set by the sensitivity of the human nervous system. It is quicker, cheaper and simpler than any other method providing a suitable range of reference specimens is available, but to give reliable results a fair amount of experience is probably necessary on the part of the tester. Watanabe & Fukui (1995, 1996) have shown that the subjective sensation of roughness is affected by vibrating the measured surface at ultrasonic frequencies. A development is the Mecrin tester, where a thin flexible steel blade is pushed along the surface at a gradually increasing angle till it buckles (Rubert 1967/68). As the device presumably relies on just failing to overcome static friction it must be sensitive to the mean slope. It is not clear what is gained in performance over the fingernail for the extra complexity.

74

Rough Su8aces

Another friction method is based on the retardaticn of the swing of a pendulum due to friction between the tested surface and a smooth shoe attached to the pendulum. The pendulum is released from a position 30 degrees from the vertical and the apparatus simultaneously begins to eject a paper tape at constant speed. The length of tape ejected before the pendulum comes to rest is taken as a measure of the finish of the test piece (Jost 1944). Dynamic friction is influenced by at least two surface parameters, RMS roughness and mean slope (Hirst & Hollander 1974), so the instrument must be used with reservations even as a comparator. The long-wavelength cut-off will depend on the nominal contact area, which in turn will depend on the load and the geometry of the contacting surfaces. The vertical resolution will depend ultimately on the finish of the shoe. The apparatus is easy and quick to operate but rather expensive to build; its measurements will also be affected by the cleanliness of the test surface. In a method employing spherical contact a ball of radius r rolls down an inclined plane as soon as the angle a of tilt exceeds a value which increases with the roughness of the planes (Bikerman 1970). If Rp is the peak-to-valley roughness, Rp

=

r(1 - cos a)

This relation is stated to hold approximately for surfaces rougher than 1 pm. Although this method makes use of the phenomenon of static friction the equation shows that it is independent of material parameters. Assuming contact is elastic, the area measured is probably not larger than 10 pm in diameter. The method gives an absolute measurement. It is very cheap, robust and simple to use, and might be suitable for production-line gauging, though it might be easier to set up in the form of a rolling cylinder. The thetameter is a device which presses a smooth steel sphere into the test surface under a known load. The increase in load required to increase its penetration by a fixed amount is measured (Tornebohm 1936). The 'theta' of its title is the effective change in the Hertzian elastic modulus of the test piece due to its roughness. A rigorous theory of the elastic contact of a sphere with a rough plane was not developed until many years later by Greenwood and Tripp (1 967), apparently in ignorance of the existence of an instrument bssed on this principle. The effect of roughness prevails only at light loads, and then not in a simple relationship with load. Asperity density and curvature are also involved. As the instrument reading is the result of a combination of at least two surface parameters

Other Measurement Techniques

75

it is probably not suitable even for a comparison without exhaustive calibration against a less ambiguous instrument using the range of surfaces to be tested. On the other hand the thetameter is reasonably cheap, robust, quick and easy to use and reproducible. Its sensitivity will decrease with decreasing roughness and the limit of vertical resolution will be set by the load-measuring device. The long-wavelength cutoff will depend on the Hertzian contact area. No dimensions are given in the reference, but an estimate of 10 pm diameter for the contact area seems plausible. In another technique involving contact with a sphere, two 16 mm diameter metal balls are mounted in a block of thermally insulating material (Fig. 4.9) (Powell 1957). One is completely recessed while the other protrudes slightly. They are connected by a differential thermocouple. The apparatus is placed in an oven till it attains constant temperature and then removed and placed, under a load of about 1 N, on the surface whose roughness is to be measured. The protruding ball will cool faster because it is in contact with the test surface, and this is quantified as a voltage reading from the differential thermocouple after a certain time has elapsed from contact.

Phosphor-bronze balls Balsa wood

m' I

I

,--

Figure 4.9. Thermal comparator (Powell 1957).

Clearly, this technique relies on far too many parameters, most of them difficult to quantifj, to be suitable for an absolute determination of roughness. The rate of cooling of the ball not in contact will depend on its initial temperature and on various material and atmospheric properties. The increased rate of cooling of the ball in contact will depend on the thermal conductance of the contact, which in turn will depend on the thermal conductivities of the contacting materials and their elastic moduli or relative hardness, depending on whether the contact is elastic or

Rough Surfaces

76

plastic, in addition to the surface properties and the load (Thomas & Probert 1972). The relevant surface properties are probably the RMS roughness and the mean slope (Thomas & Probert 1970). The sensitivity increases as the test surfaces become smoother. The useful upper roughness limit is probably about 4 pm RMS. The lower limit would probably be set by the roughness of the balls themselves. The range of wavelengths measured depends on whether contact is elastic or plastic, but the long-wavelength cut-off for this particular instrument is probably about 10 pm. An instrument based on this principle might be useful on a production line as a golno-go gauge, possibly with a built-in heater; it would be relatively cheap and robust and very simple to operate. Thermal comparators for general-purpose use have been commercially available. A scraping technique uses molten asphalt poured on to the surface whose roughness is to be measured (Blkerman 1970). After cooling and solidlfication, the excess is scraped off with a razor blade, leaving only the asphalt below the highest peaks over the area A measured. Its volume V is determined and the ratio v/! taken as RpI2. The ratio of VIA to the RMS roughness measured with a stylus instrument was reported as between 2.4 and 1.9. The height resolution is presumably set by the straightness of the edge of the razor blade. The method is simple and cheap but rather tedious.

I 1

g

1.15

0.10

I

II

-

I

I I

I

10

I 20

I

30

I

40

Test number r Figure 4.10. Scatter in sand-patch measurements of roughness (Doty 1975)

On somewhat similar lines, an open-bottomed vessel is placed on the surface to be measured and filled with fine sand to a predetermined level. The volume of sand required to fill the interstices of the surface is deduced by comparing the amount of sand needed with that needed on a perfectly flat smooth surface, and

Other Measurement Techniques

77

hence the average depth of the surface roughness is calculated @oty 1975). This test is intended for road surfaces, but could be used for finer surfaces if a finer particle size were employed. The longest and shortest wavelengths are clearly set by the diameter of the vessel and the diameter of a sand grain respectively. The latter dimension also limits the height resolution in theory, though in practice the mass or volume measurement of the differential quantity of sand would probably be the limiting factor. The upper height limit is set only by the height of the vessel. The method is simple, cheap and fairly quick, but is unduly sensitive to long wavelengths, as confirmed by the very large scatter in reported results (Fig. 4.10).

4.2.2. Electrical Methods

Capacitance profilers have been dealt with above, but the capacitance principle, being an areal rather than a sectional phenomenon, is better suited to parametric applications. The capacitance between two conducting elements is directly proportional to their area and the dielectric constant of the medium between them and inversely proportional to their separation. If a rough surface is regarded as the sum of a number of small elemental areas at different heights it is fairly easy to work out the effective capacitance between it and a smooth plate for various deterministic surface models (Sherwood & Crookall 1967/68; Ten Nape1 & Bosma 1970/71). Unfortunately, real surfaces are rarely deterministic. The capacitance of a condenser, one of whose plates is rough with a probability distribution of surface heights p(z), is proportional to

-m

where h is the separation of the mean planes. The difficulty is at once apparent: unless we have some grounds to truncate the height distribution at a height less than the mean plane separation we will always end up with infinite capacitance. Some numerical solutions for a Gaussian height distribution truncated at various arbitrary heights indicate that the capacitance is very sensitive to the mean plane separation and to the height of the highest point on the surface (Thomas 1978). Instruments for measuring surface

78

Rough Su$aces

roughness based on a capacitance principle have been commercially available (Fromson et al. 1976, Brecker et al. 1977, Risko 1981). The readings of Fromson's instrument correlated well with stylus measurements over a rather restricted range of roughness, but as the roughness increased the relationship became non-linear. A more versatile capacitance-based instrument was described by Lieberman et al. (1988). The electrode is a flexible diaphragm which when pressed against the rough surface conforms to more and more peaks as the load P increases (Fig. 4.11). Modelling the diaphragm as a two-dimensional elastic beam, the degree of conformity is calculated iteratively from stylus profile traces by assuming the maximum load is that which gives stable capacitance for an electrode in contact with a sinusoidal surface of wavelength 0.8 mm. The effective plate separation can then be calculated and agrees reasonably well with measured values. Vertical resolution is stated to be 25 nm. P =0 (Rigid Beam)

Figure 4.1 1. Progressive stages of the sagging-beam calculation for modelling the compliance of the capacitance probe (Liebeman et al. 1988).

When these values are compared with stylus measurements of a wide range of roughnesses and finishing processes (Fig. 4.12), although the surface model is twodimensional, it seems to work just as well for finishes without a lay. However, while the overall trend is clear, the scatter is such that many individual measurements disagree with stylus values by 50% or more. This is a pity, as the method, being fast and non-destructive, is potentially well-suited to production applications. The inductance between two magnetic surfaces will also be a hnction of their roughness, again because inductance falls off with increasing separation. Radhakrishnan ( 1977a) has measured the inductance between a magnetic recording head and a number of rough surfaces, and compared his results with

Other Measurement Techniques

79

../ '

Figure 4.12. Capacitance versus stylus roughness far 41 surfaces, with best fit straight line (Lieberman et al. 1988)

stylus measurements. Useful correlation with average roughness was obtained only when the comparison was restricted to a particular machining process. A stronger correlation was reported with peak density, again indicating a sensitivity to local maxima. As the measurement is quick and cheap this technique also has possibilities for quality control, though of course it is restricted to magnetic materials. Skin resistance is a also a phenomenon affected by roughness. Alternating electric currents of high frequencies are shifted from the central to the peripheral annuli of a wire; thus, the major part of the current flows in a surface layer, which, for copper, would be about 0.4 pm thick at 25 GHz (Bikerman 1970). Thus, at high frequencies, the thickness of the actively conducting region is of the order of magnitude of the height of surface hills. Consequently, the experimental resistivity of a wire deviates from that calculated under the assumption of no rugosity, and the degree of roughness can be deduced from this deviation. The largest height difference which can be detected decreases as the fiequency increases. The smallest detectable height difference will depend on the resolution of the resistance change. The long-wavelength cut-of€ will be set by the wavelength of the a.c. current and the velocity of its propagation in the metal; for the above frequency it would be about 5 mm for a steel wire. The method is suitable only for measurement of wire specimens, but for these it might well be the only practicable technique.

Rough Su#aces

80 4.2.3. Fluid Methods

In the outflow meter, an open-bottomed vessel with a compliant annulus at its lower end is placed in contact with the surface to be measured and filled with water to a predetermined level. The time taken for a given volume of water to escape through the gap between the compliant seal and the rough surface is measured. Moore (1965) has defined the ratio of the total effective cross-sectional area of the gap to the perimeter as the mean hydraulic radius (MHR). According to his analysis, which assumes laminar flow, the time of escape is inversely proportional to the fourth power of the MHR and should therefore be very sensitive to changes in surface texture. This device was intended to measure road surfaces, though there seems no reason why the principle should not be applied to much smoother surfaces. To work out the vertical and horizontal ranges is rather difficult, as the roughness measured is actually that of an annular section. The compliant seal acts as a highpass filter whose cut-off depends in a complicated way on its elastic properties and on the roughness itself. A low-pass cut-off of sorts is set by the width of the annulus. The maximum height range is governed only by the rate of discharge of water through an open pipe, and the minimum height resolution by the operator's patience!

Timer contacts Ground contact

Figure 4.13. Sectional view of an outflow meter (Henry & Hegmon 1975).

Other Measurement Techniques

81

A more sophisticated version has been described (Henry & Hegmon 1975) (Fig. 4.13) in which a marked temperature dependence has been found for smooth but not for coarse surfaces. This leads the authors to suggest that flow is turbulent for coarse surfaces and that Moore's analysis is therefore invalid. The device is fairly simple and fairly cheap and should give reproducible results, though no one seems to have compared its measurements with those of more orthodox equipment on the same surfaces. If the outflow meter employs a compressible rather than an incompressible fluid its theory becomes a little more complicated, but the basic strategy remains the same: to measure the effective cross-sectional area of outflow. However, as the viscosity of compressible fluids is so much lower an instrument employing one is more suited to engineering surfaces. Pneumatic gauges are used extensively in manufacturing industry; the general principles of their design, and various practical realisations, are discussed at length by Farago (1982). They were first employed to measured surface roughness by Nicolau (1937), but the theory was not worked out till rather later (Graneek & Wunsch 1952).

Figure 4.14. (a) Principal elements of a pneumatic gauging system (Farago 1982): (1) continuous supply of pressurised air; (2) pressure reducing valve; (3) metering device; (4)pressure indicator; (5) gauge head (6) specimen surface: (b) various nozzle cross-sectionsused for roughness measurement, outer diameter 25-30 mm (Radhakrishnan & Saga 1970)

The essential elements are a gauging nozzle in proximity to the test surface connected through a metering device to a source of air at constant pressure (Fig.

82

Rough Su$aces

4.14a). Air escapes between the gauging nozzle and the rough surface, thus lowering the pressure downstream of the metering device. A circular nozzle was orignally used, but various other shapes have been tried including slits and cruciform sections (Fig. 4.14b). A sufficiently fine slit should provide something nearly like a profile measurement, with the high-pass cutoff set by its length. The horizontal and vertical resolutions presumably depend in principle on the gas laws, but in practice the useful horizontal range of measurement is set by the range of linearity of the relationship between pressure and roughness. Measurements have been reported (Graneek & Wunsch 1952; Wager 1967) which correlate very well with roughness readings from a stylus instrument over a range from 0.1 pm to 5 pm (Fig. 4.15). Tanner (1979, 1980, 1981, 1982) has described a pneumatic Wheatstone bridge for roughness measurement.

Figure 4.15. Variation ofpneumatic gauge reading with roughness (Wager 1967)

This pneumatic technique seems to have possibilities which would repay development. With a circular nozzle it is unduly sensitive to long wavelengths, but offers the compensating advantage of giving a reading independent of orientation of a surface with a lay. Its reading depends on height parameters only. Up till now it has only been used as a comparator, but a more rigorous theory could probably be devised to give an absolute interpretation. It is cheap, robust, simple, quick and non-contacting, in fact well suited to a production line. When the sensitivity is improved by electrical pressure sensing and the nozzle is miniaturised, it can even be used as a profiler, as described in the section on in-process measurement.

Other Measurement Techniques

83

In the oil-droplet method, a droplet of oil of volume V is placed on to a rough solid and squeezed with an optical flat (Bikerman 1970). If the greatest area of the oil patch which can be achieved is A , then V/A is the average thickness of the patch. This is claimed to be approximately equal to half Rp, though this relationship almost certainly depends both on the finish of the surface and on the size of the oil droplet. The vertical resolution will depend on the waviness of the optical flat. The method is simple and cheap, but slow and not very reliable. In the stagnant-layer method, a plate is covered with a non-volatile liquid and suspended vertically (Bikerman 1970). The mass and thus also the volume Vof the liquid remaining on the plate after time t is determined from time to time. The experimental function V = f (t) deviates from that predicted by hydrodynamics in such a manner as if a stagnant layer were present. The deduced thickness of the layer is from one to two times the RMS roughness. The height resolution will depend on the resolution of the weighing arrangements; a difference in roughness of 0.1 pm on an area of 100 cm2 would cause a change of mass of only about 1 mg in a total mass of perhaps 100 g. The method is not very simple and requires quite expensive equipment; it is slow and not very reliable; and it is only suitable for workpieces of the appropriate geometry. Using a somewhat similar principle, an oil drop is timed as it flows down a fixed length of an inclined test piece (Kamnev 1966). The theory is not discussed, but one might expect both the mean slope and the RMS roughness to affect the performance. This is confirmed by a difference in behaviour between surfaces finished in various ways. Roughness was found to be proportional to the 3.7 power of the time for filed and milled surfaces but the 1.74 power for etched surfaces. Sensitivity falls off rapidly as the surface gets rougher. The long-wavelength cutoff must be set by the diameter of the drop. The method is simple, cheap and surprisingly reproducible, but rather slow.

4.2.4.Acoustic Methods

Acoustic radiation interacts with rough surfaces in ways analogous to the various interactions of electromagnetic rahation, for instance by backscattering (Ogilvy 1988, Blakemore 1993). In addition acoustic waves can be transmitted through a rough interface, and the transmission may yield information about the roughness itself (Nagy & Adler 1987, Pecorari et al. 1992, 1995b) and the real area of contact (Krolikowski & Szczepek 1992, Polijaniuk & Kaczmarek 1993, Pecorari et al. 1995a).

84

Rough Su$aces

If the acoustic wavelengths are short compared to the surface wavelengths then specular reflection may occur, and the topography of underwater surfaces is investigated in this way by sonar, giving vertical resolutions of better than a meter and lateral resolutions of a few meters (Russ 1994). On a smaller scale, Blessing & Eitzen (1988) have obtained profiles of machined surfaces acoustically, but with rather poor resolution. Acoustics show more promise for parametric measurement of roughness. De Billy et al. (1976), using backscattering techniques, have measured roughnesses in the range from 3 pm to 100 pm, and Stor-Pellinen & Luukkala (1995) have investigated the possibility of measuring the roughness of paper using ultrasound. Chiang et al. (1994) have suggested that ultrasound could measure the roughness of articular cartilage in vivo. Gezanhes et al. (1982) measured the roughness of cmcrete surfaces using acoustical speckle correlation. The surface to be measured was illuminated by two coherent ultrasonic waves at different angles of incidence. The correlation between the two scattered waves depends on the roughness, the angles of incidence and the acoustic wavelength. With a so-called "acoustic interferometer" constructed on this principle they were able to measure roughnesses of between 25 pm and 2.4 mm.

4.3. References

Abbott, E. J. and Goldschmidt, E., "Surface quality", Afech. Engng., 59, 813825 (1937). Alexander, S., Hellemans, L., Marti, O., Schneir, J., Elings, V., Hansma, P. K., "An atomic-resolution atomic-force microscope implemented using an optical lever", J. Appl. Phys. 65, 164 (1989). Bikerman, J.J., Physical surfaces, (Academic Press, New York, 1970). Binnig, G., and Quate, C. F., "Atomic force microscope", Phys. Rev. Lett. 56, 930-933 (1986). Binnig, G.; Rohrer, H., "Scanning tunnel microscopy", IBM Journal of Research and Development 30, 355-369 (1986) Blakemore, M., "Scattering of acoustic waves by the rough surface of an elastic solid", Ultrasonics 31, 161-174 (1993) Blessing, G. V. and Eitzen, D. G., "Surface roughness sensed by ultrasound", Surface Topography, 1, 143-158 (1988) Brecker, J. N., Fromson, R. E.; Shum, L. Y., "Capacitance-based surface texture measuring system", Ann. C I W 26,375-377 (1977).

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85

Broadston, J. A., "Control and measurement of surface finishes"' Steel, 120, No. 2, pp.82-3, 116, 118 and 121 (1947). Broadston, J. A., "Measuring methods described for surface roughness specification", Prod. Engng. 15, 806-810 (1944). Bugg, C. D., "Noncontact surface profiling using a novel capacitive technique: scanning capacitance microscopy", Proc. SPIE 1573, 2 16-224 (1 99 1) Bugg, C.D. and King, P.J., "Scanning capacitance microscopy", J. Phys. E: Sci. Instrum., 21, 147-151 (1988) Chiang, E. H.; Adler, R. S.; Meyer, C. R.; Rubin, J. M.; Debrick, D. K.; Laing, T. J., "Quantitative assessment of surface roughness using backscattered ultrasound: the effects of finite surface curvature", Ultrasound in Medicine and Biology 20, 123-135 (1994) Darmody, W, J., "Tapering for surface inspection", Am. Mach., 90, 134-135 (1946). de Billy, M., Cohen-Tenoudji, F., Jungman, A,, Quentin, G. J., "Possibility of assigning a signature to rough surfaces using ultrasonic backscattering diagrams", IEEE Trans Sonics Ultrason SU-23,356-363 (1976). DiNardo, N. J., Nanoscale characterisation of surfaces and interfaces, (VCH, Weinheim, 1994) Dorinson, A., "Microtopography of finely ground steel surfaces in relation to contact and wear", A.S.L.E. Trans., 8, 100-108 (1965). Doty, R. N., "Study of the sand patch and outflow meter methods of pavement surface texture measurement", in Rose, J. G. ed., Surface Texture versus Skidding: Measurements, Frictional Aspects and Safety Features of Tire-pavement Interactzons, STP 583, 42-61 (ASTM, 1975) Farago, F. T., Handbook of dimensional measurement 2e (Industrial Press, New York, 1982) Fromson, R. E.; Shum, L. Y.; Brecker, J. N., "Universal surface texture measuring system", SME IQ76-597, (1976) Fu, J., Young, R. D., Vorburger, T. V., "Long-range scanning for scanning tunnelling microscopy", Rev. Sci. Instrum. 63, 2200-2205 (1992) Garbini, J. L., Jorgensen, J. E., Downs, R. A. and Kow, S. P., "Fringe-field capacitive profilometry", Surface Topography, 1, 13 1-142 ( 1 388) Gezanhes, C ; Calaora, A.; Condat, R., "Acoustical measurement of surface roughness by speckle correlation", Signal Process n 2-3 (Apr 1982) Goch, G., Volk, R., Tontactless surface measurement with a new acoustic sensor", CIRP Ann. 43,487-490 (1994)

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Graneek, M. and Wunsch, H. L., "Application of pneumatic gauging to the measurement of surface finish", Machinery, 81, (1952). Greenwood, J. A. and Tripp, J. H., "The elastic contact of rough spheres", Trans. A.S.M.E: J.Appl. Mech., 34E, 153-159 (1967). Grigor'ev, A. Ya., Myshkin, N. K., Semenyuk, N. F. and Kholodilov, O.V., "Evaluating specific surface area by the secondary electron emission method", Trenie i Iznos, 9, 793-798 (1988) Grundy, P. J., and Jones, G. A,, Electron microscopy in the study of materials, (Edward Arnold, London, 1976) Guerrero, J. L. and Black, J. T., "Stylus tracer resolution and surface damage as determined by scanning electron microscopy", Trans. A.S.M.E: J. Eng. Ind., 94B, 1087-1093 (1972). Haesing, J., "Determining surface finish of workpieces by means of surface standards", Microtecnic, 15, 24-28 (1961). Hansma, P. K., and Tershoff, J., 5canning tunnelling microscopy", J. Appl. Phys. 61, Rl-R23 (1987). Hansma, P. K., Drake, B., Marti, O., Goud, S. A. C., Prater, C. B., Science 243, 641-643 (1989) Henry, J. J. and Hegmon, R. R., "Pavement texture measurement and evaluation", in Rose, J. G. ed., Surface Texture versus Skidding: Measurements, Frictional Aspects and Safety Features of Tire-pavement Interactions, STP 583, 317 (ASTM, 1975) Hirst, W. and Hollander, A. E., '*Surfacefinish and damage in sliding", Proc. R. SOC.Lond. A337,379-394 (1974). Holburn, D. M. and Smith, K. C. A., "Topographical analysis in the SEM using an automatic focusing technique", J. Microscopy, 127, 93-103 (1982) Howell, P. G. T. and Bayda, A., Proc. 5th. SEMSymp., Chicago, 1972 Jost, H . P., "A case for the qualitative inspection of surface finish", Machy. 65,483-486 (1944) Jungles, J. and Whitehouse, D. J., "An investigation of the shape and dimensions of some diamond styli", J. Phys. E: Sci. Instrum., 3,437-440 (1970). Kamnev, V. V., "Integral evaluation of surface roughness", Meas. Tech., 2, 261-263 (1966). Kholodilov, 0. V., N. K. Myshkin and A. Y. Grigor'ev, "Microtopography evaluation with scanning electron microscope", Soviet Journal of Friction Wear, 6, 133-136, (1985) Krolikowski, J.; Szczepek, J., "Phase shift of the reflection coefficient of ultrasonic waves in the study of the contact interface", Wear 157, 51-64 (1992)

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Lebiedzik, J. and White, E. W., "Multiple detector method for quantitative determination of microtopography in the SEM", Proc. 8th Annual Symp. Scanning Electron Microscopy, 101-188 (Illinois Inst. of Technol., Chicago, 1975). Lee, J. H., and Russ, J. C., "Metrology of microelectronic devices by stereo SEM", J. Computer-assisted Microscopy 1,79-90 (1989) Lieberman, A. G., Vorburger, T. V., Giaque, C. H. W., Risko, D. G. and Rathbun, K. R., "Comparison of capacitance and stylus measurements of surface roughness", Surface Topography, 1,115-130 ( 1988) McAdams, H. T., "Scanning electron microscope and the computer: new tools for surface metrology", Modem Machine Shop, 82-9 1 (1974). McClelland, G. M., Erlandsson, R., Chiang, S., "Atomic force microscopy: general principles and a new implementation" in Review of progress in quantitative nondestructive evaluation, 6B, D. 0. Thompson and D. E. Chimenti eds., 1307-1314, (Plenum, New York, 1987). Moore, D. F., "Drainage criteria for runway surface roughness", J. Roy. Aeronaut. SOC.,69, 337-342 (1965). Nagy, P. B. and L. Adler, "Surface roughness induced attenuation of reflected and transmitted ultrasonic waves", Journal of the Acoustical Society of America, 82, 193-197 (1987) Nelson, H. R.,"Taper sectioning as a means of describing the surface contour of metals", Proc. ConJ on Friction & Surface Finish, 2e, 217-237 (MIT, Cambridge, 1969). Nicolau, M. P., "Application du micrometre solex a la mesure de l'etat des surfaces", Mecanique, 80-83 (Mar-Apr 1937) Nowicki, B., and Jarkiewicz, A,, "The in-process surface roughness measurement using fringe field capacitive method", Trans. 7th Int. Con$ on Metrology & Properties of Engng Surfaces, 325-332 (Gothenburg, 1997) Ogilvy, J. A., "Computer simulation of acoustic wave scattering from rough surfaces", J. Phys. D: Appl. Phys., 21,260-277 (1988) Pecorari, C., Mendelsohn, D. A,; Adler, L., "Ultrasonis wave scattering from rough, imperfect interfaces. Part I. Stochastic interface models", Journal of Nondestructive Evaluation 14, 109-116 (1995a) Pecorari, C., Mendelsohn, D. A,; Adler, L., "Ultrasonic wave scattering from rough, imperfect interfaces. Part 11. Incoherent and coherent scattered fields", Journal of Nondestructive Evaluation 14, 117-126 (1995b) Pecorari, C.; Mendelsohn, D. A.; Blaho, G.; Adler, L., "Investigation of ultrasonic wave scattering by a randomly rough solid-solid interface", Journal of Nondestructive Evaluation 11,211-220 (1992)

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Pohl, D. W., Denk, W., Lam, M., Appl. Phys. Lett. 44,651-653 (1984) Polijaniuk, A,, Kaczmarek, J., "Novel stage for ultrasonic measurement of real contact area between rough and flat parts under quasi-static load", Journal of Testing &Evaluation 21, 174-177 (1993) Powell, R. W., "Experiments using simple thermal comparator for measurement of thermal conductivity, surface roughness and thickness of foils or of surface deposits", J.Sci. Instrum., 34, 485-492 (1957). Rabinowicz, E., "Taper sectioning, A method for the examination of metal surfaces",Metal Industry, 76, 83-86 (1950). Radhakrishnan, V. and Sagar, V., "Surface roughness assessment by means of pneumatic measurement", Proc. 4th. All-India Machine Tool Design & Research Con$, (Indian Inst. Tech., Madras, 1970) Radhakrishnan, V., "Application of inductive heads for non-contact measurement of surface finish", Proc. Int. ConJ Prod. Eng. 2 (Inst. of Eng., Calcutta, 1977). Rasigni, M., Rasigni, G . , Palmari, J.-P., Llebaria, A,, "Study of surface roughness using a microdensitometer analysis of electron micrographs of surface replicas:- 1. surface profiles", J. Opt. SOC.Am. 71, 1124-1133 (1981). Reddick, R. C. R., Warmack, R. J., Chilcott, D. W., Sharp, S. L., Ferrell, T. L., Rev. Sci. Instrum. 61, 3669-3677 (1990) Risko, D. G., "Quick, non-destructive method for measuring surface finish using capacitance", Carbide Tool J 13,26-29 (1981) Rubert, M. P., "Functional assessment of surface roughness", Proc. I. Mech. E., 182, Part 3K, 350-359 (1 967/68). Russ, J. C., Fractal surfaces, (Plenum Press, New York, 1994). Samuels, J. M., Hoover, M. R., Tarhay, L., Johnson, G . C . , White, E. W., "Quantitative SEM and raster profilometer analysis of fracture surfaces", in Bradt R. C. et al. Eds., Fracture mechanics of ceramics, (Plenum Press, New York, 1974) Schlesinger, G., Surface finish, (Inst. of Prod. Engrs., London, 1942). Shaw, M. C. and Pekleruk, J., "A light projection technique for studying surface topology", Ann. C.I.R.P., 12, 93-97 (1963). Shenvood, K. F. and Crookall, J. R., "Surface finish assessment by an electrical capacitance technique", Proc. I. Mech. E., 182, Part 3K, 344-349 (1967/68). Stor-Pellinen, J., Luukkala, M., "Paper roughness measurement using airborne ultrasound", Sensors and Actuators, A: Physical 49, 37-40 (1995)

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89

Tanner, L. H., "A self-balancing pneumatic Wheatstone bridge for surface roughness measurement", Wear 83, 37-47 (1982) Tanner, L. H., "An improved pneumatic Wheatstone bridge for roughness measurement", J. Phys: Sci. Instrum. 13E., 593-594 (1980) Tanner, L. H., "Pneumatic Wheatstone bridge for surface roughness measurement", J. Phys: Sci. Instrum. 12E, 957-960 (1979) Tanner, L. H.,"A self-balancing pneumatic potentiometer and Wheatstone bridge with electrical readout. Applications to surface roughness measurement, pneumatic gauging and to measurement of pressure difference ratios", Precis. Eng. 3,201-207 (1981). Tarasov, L. P., "Relation of surface roughness readings to actual surface profile", Trans. A.S.M.E, 67, 189-194, (1945). Teague, E. C . , "Scanning tip microscopies: an overview and some history", in G. W. Bailey ed., Proc. 46th. Annual Meeting of the Electron Microscopy Society ofAmerica, 1004-1005 (San Francisco Press, San Francisco, 1988) Ten Napel, W. E. and Bosma, R., "The influence of surface roughness on the capacitive measurement of film thickness in elastohydrodynamic contacts", Proc. I. Mech. E., 185,635-639 (1970/71). Thomas, T. R. and Probert, S. D., "Correlations for thermal contact conductance in vacuo", Trans. Am. SOC.Mech. Engrs., 94C, 176-180 (1972) Thomas, T. R. and Probert, S. D., "Thermal contact resistance: The directional effect and other problems", Int. J. Heat Mass Transfer, 13, 789-807 (1970). Thomas, T. R., "Surface roughness measurement: alternatives to the stylus", Proc. 19th. MTDR ConJ, 383-390 (UMIST, Manchester, 1978) Tornebohm, H., "Modern tolerance requirements and their scientific determination", Mech. Engng., 58, 41 1-417 (1936). Wager, J. G., "Surface effects in pneumatic gauging", Int. J. Mach. Tool Des. Res., 7, 1-14 (1967). Watanabe, T.; and Fukui, S., "Control of tactile surface-roughness sensation using ultrasonic vibration", Trans. JSME C62, 1329-1334 (1996) Watanabe, T.; and Fukui, S., "Method for controlling tactile sensation of surface roughness using ultrasonic vibration", Proc. IEEE Int. Con$ on Robotics andAutomation 1, 1134-1139 (IEEE, Piscataway, NJ, 1995) Weaver, J. M. R., Walpita, L. M., Wickramasinghe, H. K., Nature 342, 783785 (1989) mt e house , D. J., Handbook of surface metrology, (Institute of Physics, Bristol, 1994)

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Williams, C. C. and Wickramasinghe, H. J., J. Vac. Sci. Technol. B9, 537540 (1991) Williams, C. C. and Wickramasinghe, H. J., Proc. Ultrasonics Symp. 393397 (IEEE, Piscatawy, NJ, 1986)

CHAPTER 5

OTHER MEASUREMENT TOPICS

There are a number of important topics connected with the measurement of roughness which cannot readily be considered under the various headings of instrument design. Before we leave the subject of measurement and move on to characterisation, it is convenient to collect these topics here for discussion. We begin with the special problems of 3D measurement (3D characterisation will be discussd at length later). We go on to consider the Miculties of repeatedly finding a small area on a surface in a sequence of measurements, and the techniques necessarily employed if for some reason it is not possible or convenient to bring the instrument to the surface under investigation. Finally we discuss the measurement or inspection of roughness during manufacture.

5.1. 3D Measurement

By 3D measurement we mean more than a measurement of average area properties such as that given by glossmeters. We mean an actual determination of surface relief over an area, so that at least in principle a topographic map can be constructed. On a surveying scale this was traditionally done by triangulation; that is, starting from an original baseline, the position of individual points on a landscape was determined by measuring their angular displacement from two fixed points and solving the resulting triangle. Interestingly, this is basically a digital method, though not of course based on a rectangular grid. More recently, height information has been extracted from pairs of stereo photographs of the same area taken at slightly different angles by stereophotogrammetry, a technique which has been applied to surface roughness (Unsworth & Hepworth 1971). Contour maps on a smaller scale may be obtained directly by interferometry (Tolansky 1960, 1970a,b) but do not by themselves give quantitative height information. The volume of data from 3D measurements is so large and its processing so tedious that in practice, whatever the original measuring technique, relief information is at some stage extracted in the form of individual heights scanned on a rectangular grid. 91

92

Rough Sudaces

There is a paradox inherent in 3D measurement in the sense in which we have defined it above. To approximate as closely as possible to spot height measurement the footprint of the probe or sensor on the surface must be as small as possible. How can this small window on the surface map an area? The traditional answer is a raster scan, used for many years by television engineers to build up pictures on cathode ray tubes. The raster moves the transducer over the surface in a number of closely spaced parallel lines (Fig. 5.1). If the output of the transducer is processed and displayed according to an appropriate protocol, a picture of the surface being scanned will be built up line by line. 1Aperture

%nes indicafing path and direction foJlowedby aperiwe

Figure 5.1. Raster scanning of an area (Terman 1937). The "aperture"correspondsto the footprint of a roughness measuring probe.

In a television the scanning device is an electron beam, easy to move, and the display is analogue. For roughness measurement, movement is not usually so easy and acquisition and processing of data are digital. The aim of the measurement procedure is to build up a matrix of individual height readings in the computer whch can then be processed numerically, either to create graphical representations of the surface or to extract quantitative information about the relief. In principle such a scan need not be Cartesian; polar scans (Edmonds et al. 1977, Newman et al. 1989) and even spiral scans (Mollenhauer 1973) have been employed, but the non-Cartesian spacing is inconvenient for subsequent analysis. Thus there are no 3D measuring instruments as such: all so-called 3D instruments are basically profilers, and any of the profiling instruments described in previous chapters can in principle be used for 3D measurement using raster

Other Measurement Topics

93

scanning. Individual scanning devices have individual strengths and weaknesses which have already been discussed. But there are some general problems, of which the first is translation in the plane of the measured surface. In electron microscopy this is achieved by deflecting the electron beam. In scanning interferometers the fringes from an area are imaged onto an array of detectors which is simply read out sequentially by the computer. In STM's and similar instruments a deflecting voltage is applied to a piezo element. In general, however, it is more convenient to keep the measuring probe stationary and move the workpiece. This is partly due to the ready availability of precision x-y translation tables already developed for optical engineering. The requirements for such tables are formidable, as they must not only offer precisely controlled movement in very small increments but also give accurate positional information and provide an absolute reference datum of height. Desages & Michel (1993) measured two kinds of error on a proprietary translation table used for roughness measurements. A laser interferometer measured the errors in x and y separately at various table positions (Fig. 5.2a, b). Positional errors of more than 60 pm were detected in a 280 x 280 mm area.

Figure 5.2. Positional errors (a) in x, (b) standard deviation of (a), (c) in z,of a translation table (Desages & Michel 1993).

94

Rough Surfaces

They went on to measure the error in z by mounting an optical flat on the table and translating it in the x-direction (Fig. 5 . 2 ~ ) .Height errors of more than a micron were detected, with a marked periodicity. Both positional and height errors occur at wavelengths of the order of millimetres, and their effect would probably be filtered out in many roughness calculations. Note also that there are considerable differences in the time taken by different instruments to map the same area; while data acquisition by a scanning interferometer is virtually instantaneous, a scanning stylus profiler may take several hours. This is a period of time long enough for changes in the environment, for instance temperature changes, to affect the measuring system. Such changes usually appear as spurious errors of form and again will probably be filtered out in roughness calculations. In Fig. 5.1 the probe is moved in a true raster, that is with each measuring scan always in the same direction and followed by a return passage when no measurements are taken. This presents no difficulties when the probe is an electron beam whose movement is effectively instantaneous, but with a mechanically translated probe the return passage may represent a significant time overhead. Instrument designers often attempt to reduce this overhead by employing boustrophedon scanning (pouozpocpqFov = "as the ox turns", i.e. in ploughing a field), where measurements are taken on the return stroke also (Teague 1988). With many probes this causes no particular problem, but users should be aware that styli are usually designed to be dragged, and the dynamic effects of pushing them instead can introduce serious measuring errors (Sayles & Thomas 1976). Analysis of 3D data will be dealt with in a later chapter. Before analysis can begin, however, there is a problem of visualising the data. The amount of data collected in a single area measurement is so large that it is difficult to make a preliminary appreciation unless the data is processed by software to appear in some visual form. 3D visualisation software is now widely available in mathematical packages such as MathematicaTMand MatlabTMand even in general-purpose spreadsheets like ExcelTM,and most 3D roughness measuring systems are bundled with their own proprietary software. At the very least a customer should expect to be able to see his data as a contour map or as an isometric wire-frame view, often with perspective and rendering available as well (Fig. 5.3). There should be facilities to zoom in on areas of arbitrary size, to change the number and heights of contours, to reject obviously defective data points, and to export the data in a portable format. The facility to reject data points, though desirable to clean up measurements which may be impossible to repeat, should be treated with care. Problem data

95

Other Measurement Topics

points usually represent regions where the local surface is too high, or too low, or too steep, for the sensor to follow. If the user is only interested in average or typical features, this may not matter, but extreme-value roughness parameters may be sigrufcantly affected by missing data. Any area measurement which contains more than say 10% of rejected heights should be discarded unless there are pressing reasons to the contrary. If changing the instrument settings does not improve the rejection rate, the wrong instrument is being used. Particular care should be taken to read the small print of the program manual; the default settings of some software packages simply interpolate over the top of bad data without flagging it, a recipe for drawing wrong conclusions.

a

b

r

I

Y

d Figure 5.3. (a) 0.12 mm x 0.12 mm of a plateau-honed surface mapped with an AFM, height contours at 1 p intervals; @) isometric view of (a); (c) 40 pn x 20 p &om (a), contours at 0.2 pn intervals; (d) isometric view of @)

5.2. Relocation

There are many situations, particularly in research, where it would be very useful to look at a single profile through a surface before and after some experiment such

96

Rough Sui$aces

as running-in to see what changes have occurred to the surface geometry. It is clearly essential that exactly the same section is traversed each time, otherwise the changes observed could be attributed to the displacement of the profile and small but significant changes might not be observed at all. This requirement is very difficult to achieve in practice; the action of returning the profiling transducer to the start of its traverse is often enough to displace it laterally by a few microns, and as a typical stylus is only 8 pm wide, and other sensors may well be smaller, this is sufficient to invalidate the result. The problem was overcome by Williamson and Hunt (1968) who designed what they called a relocation table. The table is bolted to the bed of the stylus instrument, and the specimen stage is kinematically located against it at three points and held in position pneumatically. The stage can be lowered and removed, an experiment of some kind performed on the specimen, and the stage replaced on the table. Relocation of the stylus then occurs to within the width of the original profile. It is necessary to raise the stylus during the return stroke of the pickup, and of course the specimen may not be removed from the stage during the course of the experiment.. Fig. 5.4 shows a succession of relocated profiles of a surface which was initially rough turned (Thomas 1972). After each measurement the stage was transferred to the table of a surface grinder and a slightly deeper cut taken. The progressive dtsappearance of the peaks and the persistence of the valleys can be followed in great detail.

Figure 5.4. Relocated profiles of an initially turned surface at progressive stages of grinding (Thomas 1972)

Other Measurement Topics

97

The original device has been widely copied and used to study wear in rolling and sliding contact (Grieve et al. 1970; Efeoglu et al. 1993a, b), contact mechanics (OCallaghan & Probert 1973), rolling of sheet metal (Atala & Rowe 1975), running-in (Stout et al. 1977), effect of successive coats of paint (King & Thomas 1978), and impact wear (Engel & Millis 1982). Detailed designs of relocation table have been described by Edmonds et al. (1977) and Sherrington & Smith (1993). When we move on from profile measurement to area measurement there is a tendency to assume that relocation is no longer so important because of the increased statistical reliability of the much larger data set. For measurement of average roughness parameters this is probably true in many cases, but there are other situations where a more detailed examination of the relocated surface is necessary. Several workers have found it necessary to use relocation for 3D work (Bengtsson & Ronnberg 1984, 1986, Jeng & Lalonde 1992) The very homogeneity of a well-machined surface can make it difficult to return to exactly the same area on an apparently featureless plain. A 99% match in x and y implies a mismatch of 2% in area, quite enough to interfere with extreme-value calculations; in fact Newman et al. (1989), scanning wear scars with a stylus instrument, found linear relocation within 0.1% necessary to avoid sigdicant error in scar volumes. Rather than rely on mechanical relocation, Newman et al. marked the workpiece with a pattern of indentations which could be realigned visually, a practice also followed by Blunt et al.( 1994).

5.3. Replication

Replication of the original surface to be measured is needed with some optical methods to provide a transparent specimen (Anderson 1969, Dyson 1955, Herschman 1945, Lech et al. 1984). It is also needed in electron microscopy (Andersson 1974, Butler 1973, Chan et al. 1976) to provide a conducting specimen from a non-conducting workpiece. Its use with stylus instruments is generally to obtain measurements on parts which are not easily accessible, such as internal surfaces (Timms & Scoles 1948) or underwater surfaces (Sawyer 1953), or which cannot conveniently be brought to the instrument, such as gear teeth (Timms & Scoles 1948, Young & Clegg 1959), crankshafts (Davis 1979), the rollers from steel mills (Pearson & Hopkins 1948), ships' hulls (Karlsson 1978, King et al. 1981, King 1982), large optical components (Gourley et al. 1985) and human teeth

98

Rough Sudaces

(Mathia et al. 1989a,b). It has also been used with compliant surfaces in the belief that direct measurement would damage or misrepresent the surface (Dawson et al. 1967/68). The principle is usually to place the surface to be measured in contact with a liquid which will subsequently set to a solid, hopefully faithfully reproducing the detail of the original as a mirror image, what might be termed a negative. Materials such as plaster of Paris and dental cement have been employed, but it is now customary to use a polymerizing liquid. The vital question is how closely the replica reproduces the features of the original. Lack of fidelity may arise from various causes. The liquid may not wet the surface completely; usually it will first be necessary to degrease the surface carefully. If the surface is itself already wet, as may be the case for biological specimens, there may be problems of diffusion or even of chemical reaction during setting. Portions of the replica may adhere to the surface as they are parted unless a release agent is used. In any case the replica is a negative and a stylus instrument does not respond to a valley bottom in the same way as to a peak, so a further positive replica may need to be made (Fig. 5.5). In the case of transparent replicas, optical techniques often rely on detecting an optical path difference which is a function of refractive index. Misinterpretation can occur here due to inhomogeneity of the replica or to changes in refractive index due to temperature. A rigid replica may not reproduce short wavelengths faithfully, while a flexible replica may not be faithful to long wavelengths.

Figure 5 . 5 . Plateau-honed cylinder liner and positive replica (Ohlsson & Rosen 1993)

One series of careful comparisons made (Sayles et al. 1979) has found replicas of an optical flat of negligible measured roughness to show roughnesses of between 0.03 pm and 0.13 pm, and replicas of machined surfaces to disagree in

Other Measurement Topics

99

roughness with the originals by up to 17 per cent. Shunmugam & Fbdhakrishnan (1976), Narayanaswamy et al. (1979) and George (1979) have attempted to compare the power spectra of replica and original. This approach can show dramatically the range of wavelengths over which the replication material is effective (Fig. 5.6). Wavelength in p m

Wavelength in p m

Strand

dais

Warwick chemicals plymaster

resin B

-I 10

in I00 Spatial frequency in cycled mm-'

I@l

Spatid frequency in cycledmm

-1

Wavcleneth in am

Wavelength In p m

I

I

-I I

Parent wrface hefore and after acrulile replica

Strand glass rcsin C

in

I

In1 Spatial frequency in cycler/mm-'

,

-

I

-

IIY)

Spatial frcqucncy in cyclcrimm-1

Figure 5.6. Comparison of power spectra of original and replica for three diEerent replicating materials (George 1979). Effect of the act of replication on the original surface is also shown. Bands are 50% confidence limits

Replicas of calibration specimens have been made by electroforming (Song et al. 1988). Again this is a two-stage process ending up with a positive replica. The originals were essentially two-dimensional, that is to say the same "random" profile was reproduced across the whole width of the specimen, so the issue of relocation

100

Rough Su$aces

did not arise in comparing replica with original. Flatness did not reproduce well, and the nickel replicas were not as hard as the originals, but comparison of a number of different roughness parameters showed agreement usually within 2%, which is of the order of the traceable uncertainty of roughness measurements. This technique is probably too specialized and laborious for routine use in quality control.

5.4. In-process Measurement

A method of measuring the surface roughness of a component during its machining would clearly be valuable, either to terminate the machining process as soon as the required finish was obtained and thus increase throughput per machine, or to take part in some adaptive-control loop. Slow attainment of the required finish, for instance, might signal the need for tool replacement. The requirements for in-process measurement are fairly stringent. Measurement must be continuous and rapid and should preferably provide an electrical signal of some kind. The sensor must be robust and relatively insensitive to environmental changes such as temperature and the intermittent presence of films or sprays of lubricating or cutting fluids. It should be small and adaptable to as wide a range as possible of workpiece shapes and sizes. For obvious reasons the sensor should preferably not contact the workpiece. Young et al. (1980) conclude that only area (i.e. parametric) measurements made by optical instruments will satisfy a similar list of requirements, but in fact, as we will see below, a variety of methods have been used with varying degrees of success. A similar problem applies to inspection (Thomas 1997). Of course the majority of roughness instruments sold are used for inspection purposes, usually off-line and on a statistical sampling basis. But modem trends of quality control increasingly require 100% inspection (Kennedy et al. 1987), and this is now the norm for many other product parameters. Most existing roughness instruments are too slow for 100% inspection of mass-produced components. For a component produced at a rate of 3000 an hour, not excessive for many production lines, the total time available for setting up, data acquisition and processing is not much more than a second. Although stylus instruments have made impressive advances in speed (Morrison 1995), the only current techniques which can approach the speeds required for inspection are capacitance (Garbini et al. 1988, Table 5.1) or optical. For many comparative purposes these work well enough; difficulties arise when it is necessary to validate their performance in terms of legal standards,

Other Measurement Topics

101

which are still exclusively written in terms of stylus instruments and their limitations. Pneumatic gauging looks promising for in-process work, and it has been established (Wager 1967) that the dynamic effects of the moving workpiece are not serious. This is rather surprising, as the theory of the pneumatic gauge (Graneek & Wunsch 1952) assumes isothermal conditions whereas fluctuations at, say, turning speeds are more likely to be adiabatic. The pneumatic gauge is robust and the air jet will help to clear unwanted surface fluid. It also measures a parametric roughness integrated over the entire path of movement of the surface. Its dlsadvantages are that a nozzle fixed relative to the workpiece will be unduly affected by waviness, and that it is too insensitive to measure fine finishes. By miniaturising the nozzle and pressure transducers, Woolley (199 1) has succeeded in making a pneumatic profiler whch will resolve height differences of 12 nm at very high rates of translation (Table 5 . l), though the lateral resolution is no better than 75 pm.

I.Casing

2. Wheel flanges 3. Workpiccc 4. Bearing 5. Leaf-springjoint 6 . Leaf springs 7. Guide

8. Tracer pin

13

4

14

9. Leaf springs 10. Ferrite I I . Coil

12. Shock absorber 13. Inductive signal 14. Mount

Figure 5.7. Sectional schematic ofrotating stylus device for in-process roughness measurement (Dutschke & Eissler 1978).

The stylus instrument, which might be thought a priori unsuitable, has proved itself a serious contender in the measurement of turned surfaces (Dutschke & Eissler 1978). The measuring device is a steel cylinder which rotates in contact with the workpiece being machined. At every revolution of the cylinder a stylus, piercing a hole in its circumference, is deflected, producing an electrical signal

Rough Su$aces

102

which is read out through telemetry (Fig. 5.7). Surprisingly good correlations with orthodox roughness measurements were reported. A development of this design by Zhao & Webster ( 1 989) achieved translation speeds of 1 . 1 m/s (Table 5.1). Acoustic techniques have also been applied to in-process measurement of roughness. Blessing & Eitzen (1988) measured the amplitude of ultrasonic backscattering from stationary and moving surfaces. Roughnesses of between 1 pm and 40 pm were successfully determined at speeds of up to 5 m/s (Table 5.1). This work has since been extended by Coker and Shin (Shin et al. 1995, Coker & Shin 1996). The issue of speed would certainly seem to favour parametric methods, most of which are effectively instantaneous by comparison with machining speeds. However, for in-process measurement the critical speed is not the cutting speed but the speed of translation of the workpiece, which is generally much lower. Profiling techniques are steadily increasing in speed (Table 5.1) and are now well within the range of translation speeds for many machining techniques. Table 5.1. Profilers for in-process measuremenf in order oftranslation speed (adapted &om Thomas 1997).

Technique

Speed ( d s >

Reference

Capacitance

0.025

Garbini et al. 1988

Stylus

1.1

Zhao & Webster 1989

Optical

1.7

Mitsui 1986

Ultrasound

5

Blessing & Eitzen 1988

Pneumatic

52

Woolley 199 1

5.4.I . Optical Techniques

Optical techmques for in-process measurement have been reviewed extensively by workers at NIST (Young et al. 1980, Vorburger & Teague 1981). More recently, Mitsui (1986) has described a number of optical instruments designed for in-

Other Measurement Topics

103

process use. Instrumentation can be removed to a safe and convenient place by using fibre-optic techniques to interpose a flexible conduit (Adkins 1969; Spurgeon & Slater 1974, Takeyama et al. 1976, Mitsui 1986). Then there are the problems of variation in reflectivity and optical path length due to the intervention of fluid spray or films or particles of swarf, or an actual alteration in colour due to thermal changes during machining. Some of these variations might be removed by signal processing, for instance by taking the first or second differential of the reflected intensity of a continuously chopped signal (Tipton & Roberts 1967/68). A more promising technique might be polarization of coherent light; here the only measured quantity is the ratio of polarization of incident and reflected light, which is insensitive to any amplitude changes in the signal (Gee et al. 1975). The advent of coherent light sources has led to their application to in-process measurement of roughness (Fad1 & Parsons 1978; West & West 1978, Shiraishi 1980, Yanagi et al. 1986, Persson 1992). Takaya and Miyoshi (Takaya et al. 1995, Miyoshi et al. 1995) have used Fraunhofer diffraction to measure the roughness of polished silicon wafers in-process to better than 1 nm, calibrating their optical system against a stylus instrument. Optical stylus methods have also been used. Mitsui et al. (1985) built a focus-detection system based on astigmatic focussing with a vertical range and resolution of 1 pm and 1 nm respectively. Bodschwinna & Bohlmann (1991) measured the finish of milled crankshaft housings with a proprietary optical stylus; although this system was part of the production line it does not actually seem to have been used in-process. Kiyono et al. (1994) describe a system using two optical styli simultaneously, one of which has a greater vertical range but poorer lateral resolution. The coarse stylus thus acts as an optical skid for the fine stylus, filtering out waviness and also cancelling out extraneous sources of noise. In the laser scanning analyser (Clarke & Thomas 1979) a laser beam is reflected from a polygonal mirror rotating at high speed, down on the workpiece surface, where it is reflected into a fixed photodetector receiver with wide aperture (Fig. 5.8). The detector output is amplified and applied to the vertical deflection coils of an oscilloscope whose time base is provided by the rotation of the mirror. Localized variations in the reflectance of the surface thus appear as changes in signal strength whose position on the workpiece can be established from the time elapsed since start of the current scan. The spot diameter can be set from 200 prn upwards. When used to measure roughness the receiver aperture is masked to a narrow slit and the angular reflectance function is produced as the spot scans a strip whose width is dependent on the range from the surface and the angular width required.

104

Rough Sur$aces

At a given moment in any scan the fixed detector is receiving light scattered from the single point on the strip which happens at that instant to be illuminated by the deflected beam. The picture &splayed on the oscilloscope screen is therefore a symmetrical curve whose height at any point is proportional to the intensity of light scattered into the corresponding angle, and whose maximum corresponds to the reflection received at the specular angle. If the curve is characterized by its width at half the maximum amplitude the reflectance is effectively normalized. When this half-width is plotted against measurements by a stylus instrument for a range of surfaces correlation is better with slope than with roughness (Fig. 5.9).

Figure 5.8. Schematic of a laser scanning analyser (Clarke & Thomas 1979).

Another optical technique intended for in-process roughness measurement, this time by ellipsometry, has been described by Lonardo (1978). The quantity used to characterize the roughness is the deviation between the value of one of the ellipsometric angles for a smooth reference surface and its value for the rough surface measured. He found good agreement, approximately linear in some cases, between this deviation and the average roughness as measured by stylus. He also investigated the effect of contaminants on in-process ellipsometric measurements

Other Measurement Topics

105

of roughness during grinding, and found the error to be generally less than 10 per cent.

Figure 5.9. Variation of half-width with (a) roughness (b) mean absolute slope (Clarke & Thomas 1979). A: milled B: turned; C: spark eroded; D: shaped E: ground;; F: criss-cross lapped G: parallel lapped.

Several instruments measure the ratio of the specular intensity to the intensity at an off-specular angle. Since this ratio generally dec:eases with increasing surface roughness, it could provide a measure of the roughness itself. Peters ( 1 965) used this technique with the detector held 40 degrees off specular to determine the roughness of cylindrical parts while they were being ground. His results show good correlation between the diffuseness and roughness over a range of roughness up to 0.3 pm. Even under different lubrication conditions (oil, water, dry) the results are well fitted bv a single curve. A similar instrument was developed by Corey (1978) to measure roughness in the range 0.2 pm to 2 pm for high-speed quality control of the surface finish of machined hemispherical parts. Essential features of the instrument are its nondestructive capability and its ability to scan the entire surface of the part. The instrument uses the ratio of the intensity measured 15 degr2es off-specular to the specular intensity to yield a value for roughness. In order to make meaningful roughness measurements for a particular type of surface, a set of roughness specimens that have been manufactured in a way similar to the test specimens with known roughness values are required. Another system, developed by Takeyama et al. (1976), measures the ratio of the specular intensity at the surface-normal to the back-scattered intensity 30 degrees off-normal. This system is designed to be quite insensitive to surface vibration with its use of fibre optics bundles to transmit the incident and reflected

106

Rough Surfaces

light. Indeed, the measured signals from spinning parts are fairly stable with time. Takeyama et al's ratio measurements were performed on machined surfaces with high peak-to-valley roughness ranging from 5 to 80 pm. They found that the experimental curves of intensity ratio against roughness were a function of the tool radius used to machine the surfaces. This dependence on the manufacturing process again implies a need for a set of calibration specimens. Takeyama et a1 claimed that the curves of intensity ratio versus roughness were independent of the surface material, but this claim does not seem to be supported by all of their data.

5.5. References

Adkins, H., "A look at surface finish", Am. Mach., 113, 111-116 (1969). Anderson, W. L., "Surface roughness studies by optical processing methods", Proc. I.E.E.E., (Letters), 57, 95 (1969). Anderson, S., "Plastic replicas for optical and scanning electron microscopy", Wear, 29, 271-274 (1974) Atala, H. F. and Rowe, G. W., "Surface roughness changes during rolling", Wear, 32, 249-268 (1975). Bengtsson, A. and A. Ronnberg, "Absolute measurement of running-in.", Wear, 109, 329-342, (1986) Bengtsson, A. and A. Ronnberg, "Wide range three-dimensional roughness measuring system", Precision Engineering, 6 , 141-147, (1984) Blessing, G. V. and Eitzen, D. G., "Surface roughness sensed by ultrasound", Surface Topography, 1, 143-158 (1988) Blunt, L., Ohlsson, R., Rosen, B.-G., "A comprehensive comparative study of 3D surface topography measuring instruments", in P. Hedenqvist, S. Hogmark and S. Jacobson eds., Proc. 6th. Nordic Symp. On Tribology, Uppsala (1994). Bodschwinna, H., and Bohlmann, H., "Online surface roughness measurement in production lines for process control", 12th. IMEKO World Congress (Beijing, 1991) Butler, D. W., "A stereo electron microscope technique for microtopographic measurements", Micron, 4, 410-424 (1973) Chan, E. C.; Marton, J. P.; Brown, J. D., "Evaluation of surface roughness of metal films by transmission electron microscopy and ellipsometry", J. Vac. Sci. Technol. 13,981-984 (1976). Clarke, G. M., T. R. Thomas, "Roughness measurement with a laser scanning analyser", Wear, 57, 107-116 (1979).

Other Measurement Topics

107

Coker, S. A., and Shin, Y. C., "In-process control of surface roughness due to tool wear using a new ultrasonic system", Int. J. Machine Tools & Manufacture 36, 411-422 (1996) Corey, H. S., "Surface finish from reflected laser light", Proc. SPIE 153, 27 (1978) Davis, F. A,, "Replica techniques in the study of crankshaft journal topography", Automotive Engr. 46-47 (ApriWMay 1979) Desages, F. and Michel, O., Calibration of a 3 - 0 surface roughness measuring device, (Prodn. Engng. Dept., Chalmers University, Gothenburg, 1993) Dutschke, W. and Eissler, W., "A new sensor for measuring the surface roughness in-process on a grinding machine", Proc. 3rd. Con. on Automated Inspection & Product Control, 19-30 (Nottingham University, 1978) Dyson, J., "Examining machined surfaces by interferometry", Engineering, 179, 274-276 (1955). Edmonds, M. J., A. M. Jones, P. W. O'Callaghan and S. D. Probert, "A threedimensional relocation profilometer stage", Wear, 43, 329-340 (1977) Efeoglu, I.; Amell, R.D.; Tinston, S.F.; Teer, D.G., "Mechanical and tribological properties of titanium nitride coatings formed in a four magnetron closed-field sputtering system", Surface & Coatings Technology 57, 61-69 (1993a) Efeoglu, I.; Arnell, R. D.; Tinston, S. F.; Teer, D. G., "Mechanical and tribological properties of titanium aluminum nitride coatings formed in a four magnetron closed-field sputtering system", Surface & Coatings Technology 57, 117-121 (1993b) Engel, P.A. and H. B. Millis, "Study of surface topography in impact wear", Wear, 75,423-442 (1982). Fadl, M. F. A,, and Parsons, F. G., "Electro-optical flaw detection", Proc. 3rd. C o n . on Automated Inspection & Product Control, 111- 118 (Nottingham University, 1978) Garbini, J. L., Jorgensen, J. E., Downs, R. A. and Kow, S. P., "Fringe-field capacitive profilometry", Surface Topography, 1, 131-142 (1988) Gee, S., King, W. L., and Hegmon, R. R., "Pavement texture measurement by laser: a feasible study", in Surface texture versus skidding: measurements, frictional aspects and safety features of tire-pavement interactions, STP 583, 2941 (ASTM, 1975). George, A. F., "A comparative study of surface replicas", Wear, 57, 51-61 (1 979).

108

Rough Su6ace.s

Gourley; D., H. E. Gourley and J. M. Bennett, "Evaluation of the microroughness of large flat or curved optics by replication." Thin Solids Films, 124, 277-282, (1985) Graneek, M. and Wunsch, H. L., "Application of pneumatic gauging to the measurement of surface finish", Machinery, 81, 701-707 (1952). Grieve, D. J., Kaliszer, H., and Rowe, G. W., "A normal wear process examined by measurements of surface topography", Ann. C.I.R.P., 18, 585-592 (1970). Herschman, H. K., "Replica method for evaluating finish of a metal surface", Mech. Eng. 67, 119-122 (1945). Jeng, Y.-R., Lalonde, G. A., "3-D surface topography measurement system and its applications", in Special Publications 936, 175-182 (SAE,Warrendale, PA, 1992) Karlsson, R.I., "Effect of irregular surface roughness on the frictional resistance of ships", Proc. Int. Symp. on Ship Viscous Resist. 9, 1-20 (Gothenburg, 1978) Kennedy, C. W., Hoffman, E. G., Bond, S. D., Inspection and gaging 6e (Industrial Press, New York, 1987). King, M. J. and Thomas, T. R., "Stylus measurement of the microgeometry of a coated surface", J. Coatings Tech., 50, 56-61 (1978) King, M. J., "The measurement of ship hull roughness", Wear 83, 385-397 (1982). King, M. J., Chuah, K. B., Olszowski, S. T. and Thomas, T. R., "Roughness characteristics of plane surfaces based on velocity similarity laws", ASME Paper 81-FE-34 (1981) Kiyono, S., Yamatani, M., Ohe, A., Huang, P., Suzuki, H., "Critical angle type optical stylus with optical skid (2nd report) - construction by two optical sources and one receiving optical system", Seimitsu Kogaku Kaishi/Journal of the Japan Society for Precision Engineering 60, 114-118 (1994) Lech, M., I. Mruk and J. Stupnicki, "Comparison of tribological parameters of surfaces determined by the stylus method and by the immersion method of holographic interferometry." Wear, 93, 167-179 (1984) Lonardo, P. M., "Testing a new optical sensor for in-process detection of surface roughness", Ann CIRP 27, 531-534 (1978) Mathia, T. G., Brugirard, J. L., Duarte, J. and Maurin-Perrier, B., "Enamel and hydrocolloide dental replica surfaces: Part 1. Statistical characterisation of enamel topography" Surface Topography, 2, 157-172 (1989a)

Other Measurement Topics

109

Mathia, T. G., Brugirard, J. L., Balleydier, M., Duarte, J. and MaurinPerrier, B., "Enamel and hydrocolloide dental replica surfaces: Part 2. New statistical criteria for evaluation of replica fidelity", Surface Topography, 2, 173191 (1989b) Mitsui, K., "In-process sensors for surface roughness and their applications.", Precision Engineering, 8, 212-220, (1986) Mitsui; K., N. Ozawa and T. Kohno, "Development of a high resolution inprocess sensor for surface roughness by laser beam.", Bulletin of the Japan Society of Precision Engineering, 19, 142-143, (1985) Miyoshi, T., Takaya, Y., Saito, K., "Nanometer measurement of silicon wafer surface texture based on Fraunhofer diffraction pattern", CIRP Ann. 44, 489-492 (1995) Mollenhauer, C., "Surface topography measurement techniques", Proc. Int. Con$ on Surface Technol., Pittsburgh, 173-186 (SME, 1973). Morrison, E., "A prototype scanning stylus profilometer for rapid measurement of small surface area", Int. J. Mach. Tools Manufact. 35, 325-33 1 (1995) Narayanasamy, K., V. Radhakrishnan and R. G. Narayanamurthi, "Analysis of surface reproduction characteristics of different replica materials", Wear, 57, 6369 (1979) Newman, P. T., Radcliffe, S . J. and Skinner, J., "The accuracy of profilometric wear volume measurement on the rough LClB coated surfaces of an articulating joint", Surface Topography, 2, 59-77 (1989) O'Callaghan, P. W. and Probert, S. D., "Effects of static loading on surface parameters", Wear, 24, 133-145 (1973). Ohlsson, R., and Rosen, B.-G., "On replication and 3D stylus profilometry techniques for measurement of plateau-honed cylinder liner surfaces", in R. J. Hocken ed., Proc. ASPEAnnual Meeting, Seattle, 146-149 (1993) Pearson, J. and Hopkins, M. R., "Plastic replicas for surface-finish measurement",J. Iron & Steel Inst. 67-70 (May, 1948). Person, U., "Real time measurement of surface roughness on ground surfaces using speckle-contrast technique", Optics and Lasers in Engineering 17, 6 1-67 ( 1992) Peters, J., "Messung des Mitterauswertes Zylindrischer Teile Wahrend des Schleifens", VDI-Berichte 90, 27 (1965) Sawyer, J. W.,"Method for recording roughness of submerged surfaces", Am. SOC.Nav. Eng. J., 65, 816-821 (1953).

110

Rough &$aces

Sayles, R. S., Thomas, T. R., "Mapping a small area of a surface", J. Phys. E: Sci. Instrum. 9,855-861 (1976). Sherrington, I.; Smith, E. H., "Design and performance assessment of a Kelvin clamp for use in relocation analysis of surface topography", Precision Engineering 15, 77-85 (1993) Shin, Y. C.; Oh, S. J.; Coker, S. A., "Surface roughness measurement by ultrasonic sensing for in-process monitoring", Trans. ASME: J. Eng. Ind. 117, 439-447 (1995) Shiraishi, M., "In-process measurement of surface roughness in turning by laser beams", ASME Paper 80-WAPROD- 17 (1980) Shunmugam, M. S. and Radhaknshnan, V., "An analysis of the reference lines of the surface profile and its true replica", Wear, 40, 155-163 (1976) Spurgeon, D. and Slater, R. A. C., "In-process indication of surface roughness using a fibre-optics transducer", Proc. 15th Int. Machine Tool Des. & Rex Con$, Birmingham, 339-347 (1974). Song, J. F., Vorburger, T. V. and Rubert, P., "Comparison between precision roughness master specimens and their electroformed replicas. ", Precision Engineering 14, 84-90 (1992) Stout, K. J., King, T. G. and Whitehouse, D. J., "Analytical techniques in surface topography and their application to a running-in experiment", Wear, 13, 99-1 15 (1977) Takaya, Y., Miyoshi, T., Arai, M., Hayashi, K., Setaka, M., "Development of random micro-roughness measuring apparatus based on Fraunhofer diffraction subnanometer measurements by the new error calibration method", Seimifsu Kogaku Kaishi/Journal of the Japan Society for Precision Engineering 61, 377381 (1995) Takeyama, H., Sekiguchi, H., Murata, R., Matsuzaki, H., "In-process detection of surface roughness in machining", Ann CIRP 25,467-471 (1976) Teague, E. C., "Scanning tip microscopies: an overview and some history", in G. W. Bailey ed., Proc. 46th. Annual Meeting of the Electron Microscopy Society ofAmerica, 1004-1005 (San Francisco Press, San Francisco, 1988) Terman, F. E., Radio Engineering 2e (McGraw-Hill, New York, 1937) Thomas, T. R., "Trends in surface roughness", Trans. 7th Int. Con$ on Metrology & Properties of Engineering Surfaces (Chalmers University, Gothenburg, 1997) Thomas, T. R., "Computer simulation of wear", Wear, 22, 83-90 (1972). Timms, C. and Scoles, C. A., "Some applications of the plastic replica process to surface finish measurement", Machinery, 73, 871-875 (1948)

Other Measurement Topics

111

Tipton, H. and Roberts, J. I., "New optical method of assessing surface quality", Proc. I. Mech. E., 182, Part 3K, 274-278 (1967/68). Tolansky, S., Multiple-beam interferometry of surfaces and f h s , (Dover Publications, Inc., New York, 1970a). Tolansky, S., Multiple-beam interference microscopy of metals, (Academic Press, London, 1970b). Tolansky, S., Surface microtopography, (Longmans, London, 1960). Unsworth, A., and Hepworth, A,, "A new stereo-adapter for use with the scanning electron microscope", J. Microscopy 94, 252 (1971) Vorburger, T. V.; Teague, E. C., "Optical techniques for on-line measurement of surface topography", Precis. Eng. 3,61-83 (1981). Wager, J.G., "Surface effects in pneumatic gauging", Znt. J. Mach. Tool Des. Rex, 7, 1-14 (1967). West, R. N., and West, P., "New applications of laser scanners for on-line product inspection", Proc. 3rd. Conf on Automated Inspection & Product Control, 133-138 (Nottingham University, 1978) Williamson, J. B. P. and Hunt, R. T., "Relocation profilometry", J. Phys .E: Sci .Instrum., 1, 749-752 (1968). Woolley, R. W., "Pneumatic method for making fast, high-resolution. noncontacting measurement of surface topography", Proc. SPIE 1573, 205-2 15 (1991) Yanagi; K., T. Maeda and T. Tsukada, "Practical method of optical measurement for the minute surface roughness of cylindrical machined parts.", Wear, 109, 57-67, (1986) Young, A. P. and Clegg, B. H., "Replica method for examining surface profiles" Rev. Sci. Instrum., 30, 444-446 (1959). Young, R. D.; Vorburger, T. V.; Teague, E. C., "In-process and on-line measurement of surface finish", Ann. CIRP 29,435-440 (1980). Zhao, Y. W. and Webster, J., "An in-process roughness measuring system for adaptive control of plunge grinding", Surface Topography, 2, 247-26 1 ( 1989)

CHAPTER 6

DATA ACQUISITION AND FILTERING

6.1. Data Acquisition

The use of digital techniques is now so widespread that one is unlikely to find any new roughness measurement instrument which relies solely on analogue methods. Even if the transducer itself is non-electrical, processing and presentation are likely to involve digital electronics. The process of analogue-to-digital conversion (ADC) amounts to the representation of the continuous analogue signal by a series of discrete numbers. This discretisation occurs in two ways (Fig. 6.1). In the amplitude domain, the signal is split into a number of levels parallel to the plane of the surface. This process is called quantisation. In the frequency or wavelength domain, the instantaneous value of the signal is recorded at equal intervals in the plane of the surface. This process is called sampling. Amplitude domain: quantisation

V

Frequency domain: sampling

Figure 6.1. Analogue-to-digital conversion: quantisation and sampling

113

114

Rough Suflaces

The number of quantisation levels is determined by the resolution of the ADC hardware, usually expressed as a number of bits (powers of 2). Thus an 8-bit converter will quantize to 256 levels and so on, that is it will resolve amplitude variations to 1 part in 256. There are several points to watch here. One is that quantisation is likely to represent the limiting resolution of the overall measurement system; there is no point spending money on a transducer capable of resolving to one part in a thousand if its output is to be processed by an 8-bit ADC. The second is that the computing arrangements may themselves embody several components, and the limiting quantisation of the system will be the lowest of any of the components. A 16-bit ADC followed by an 8-bit processor, or a processor running software which will only represent numbers to 8 bits, is still an 8-bit system.

u ”

ul

L

Figure 6.2. Too few quantisation levels cause loss of detail

In deciding on an appropriate quantisation level it must be remembered that the quoted figure represents the entire range of the transducer, what for analogue instruments would be called the full-scale deflection (FSD). In practice, an instrument is usually set up so that the hghest peak in the entire signal is safely below FSD and the lowest valley is similarly above zero. Thus it can easily happen that for a nominal quantisation of 8 bits, for two-thirds of the length of a signal with a Gaussian amplitude distribution the variation in height is actually represented by only about 50 levels. This can lead to a sih:ation (Fig. 6.2) where small peaks which may be functionally significant are missed altogether. The remedy is obviously to increase the quantisation, but remembering that there will be a corresponding price to pay in longer conversion times and larger data storage requirements. Most commercial systems use at least 16 bits, and quantisation of less than 10 or 12 bits is not recommended. Similarly if the signal is sampled too often it will lead to data storage and processing difficulties. But if it is sampled too seldom, then any wavelengths

Data Acquisition & Filtering

115

present in the signal which are shorter than the sampling interval may be misinterpreted as longer wavelengths of the same amplitude (Fig. 6.3a). This effect is known as aliasing. According to the Nyquist sampling theorem (Wade 1994), the shortest measurable wavelength AN is twice the sampling interval. The effect of aliasing is to mirror the power spectrum of the aliased frequencies about (Fig. 6.3b), so that a real frequency oN + o appears as the Nyquist frequency oN, an aliased frequency of wN - w.

'Apparent waveform Sample points

Figure 6 .3 . Aliasing: (a) short wavelengths misinterpreted as longer wavelengths by sampling too seldom; (b) aliased frequencies reflected about Nyquist frequency falsify power spectrum.

The sampling interval is usually matched to the dimensions of the probe. The simplest way to sample is "on-the-fly", that is to keep the translation mechanism in constant motion and sample the resultant signal at equal intervals of time, assuming that these represent equal intervals of horizontal distance. This will only be true if the translation is at constant speed, which is not always safe to assume (see Section 2.2.3). It must also be remembered that the actual ADC process takes a finite time, and that this time represents an integration of fine surface detail over a finite length of the signal, though this length is usually small compared with the sampling interval. The alternative to on-the-fly sampling is the added complication of an independent measurement of horizontal displacement.

6.2. Filtering

It very rarely happens that the output of any instrument is perfectly matched to the application for whch it is intended. Sometimes the instrument produces too little

116

Rough Surfaces

information for the intended purpose. More often it produces too much information, and the useful information has to be extracted or the extraneous information suppressed. In electrical engineering terms, theuseful information is the signal and the extraneous information is noise, and separating the noise from the signal is an essential preliminary to characterisation. This process of separation is calledjltering. The concept of filtering is borrowed from electronic engineeering, where the signal and the noise are both treated as essentially sinusoidal, continuous (i.e. indefinitely long signals are available for measurement and analysis) and stationary (i.e. increasing the length of the signal does not change the information present in it), and the problem therefore resolves into one of sorting groups of sinusoids. This approach is ill-suited to describing surfaces for several reasons: common experience tells us that surfaces are not sinusoids; the instruments which measure them do not produce continuous signals; and many real surfaces are not stationary. Nevertheless, because the properties of signals have been widely worked out in sinusoidal terms, it will be convenient for the time being to use this terminology. Restricting ourselves to two dimensions for the time being, we may think of a generalised measured profile consisting of a continuous spectrum of surface wavelengths. The width of the spectrum, i.e. the range of wavelengths, is fixed by the measuring instrument itself. The instrument will be unable to ”see” any wavelengths longer than its traverse length, and in fact the longest wavelength reliably represented in the spectrum will be only a fraction of the traverse length (see the later discussion on measurement of power spectra). At the other end of the spectrum, the instrument will be unable to see any profile wavelengths smaller than the dimensions of its own sensor. But there is no a priori reason why the spectrum of wavelengths produced by the instrument, designed as a general purpose device to suit a range of applications, should coincide with the spectrum of wavelengths associated with any particular application. In engineering metrology, for instance, the spectrum was once divided into six (DIN 4760, 1982), of which only the first three classifications need detain us here. The longest wavelengths are associated with errors of form; shorter wavelengths constitute waviness; and the shortest wavelengths are called roughness (Fig. 6.4a). DIN 4760 prescribes that the length of an error of form should be at least 1000 times its amplitude, and the ratio of wavelength to amplitude of the waviness should be between 1OO:l and 1OOO:l. This division is quite arbitrary; wavelengths associated with errors of form on a machined surface would be described as roughness on a ship’s hull, for instance. In manufacturing engineering, the problem is usually to remove the waviness and errors of form from

Data Acquisition & Filtering

117

the signal so that the remaining property of the surface wtiich is assessed is the roughness. Note again that there is no generally agreed wavelength which divides roughness from waviness, it is a matter for subjective assessment.

of danimni

Catternl Error of

1 I Wavelength

Figure 6.4. (a) Surface characteristics(Brooker 1984) and (b) their associated power spectrum (Thomas 1975)

One important reason for this removal is that for almost all real surfaces, the longer the wavelength, the larger the amplitude (Fig. 6.4b). This is a typical property of self-af€ine fractals, as we shall see in a later chapter, and it has the consequence that the numerical value of any parameter which depends on the amplitude properties of a profile will be dominated by the longest wavelengths present. For many practical purposes, then, filtering means hzgh-puss filtering. In the language of communication engineering, a high-pass filter stops long wavelengths (low frequencies) but passes short wavelengths (high frequencies). Using this terminology permits us access to the large body of existing work on digital filter design (see for example Wade 1994, Rorebaugh 1997, Golten 1997). Although this body of work is mainly concerned with low-pass filters, which stop short wavelengths but pass long wavelengths, the conceptual arguments are similar, as a high-pass filter is equivalent to subtracting the output of a lowpass filter from the original signal. Consider the internal computer representation of a profile, after analogue-todigital conversion, as a series of discrete heights. Conceptually a filter may be thought of as a sequence of weighting terms (the

Rough Sur$aces

118

impulse response) which is moved along the profile z(i), multiplying it term by term and thus smoothing it as it goes (Fig. 6.5).

WelgM1ng function

m

Figure 6.5. Convolution as a low-pass filter (Golten 1997)

The sequence itself may be chosen arbitrarily, say of length 2m + 1 terms, and the output of the filter z’(i) is the convolution of the impulse response with the original signal :

The transmission coeflcient at a given wavelength is the ratio of the amplitude of the filtered signal at that wavelength to that of the unfiltered signal. The cutoffof the filter is the wavelength at which the transmission coefficient is some specified fraction of the input amplitude (Fig. 6 . 6 ) . The roll-off characteristic of the filter describes how sharply the transmission coefficient varies on either side of the cutoff. Clearly for roughness work as sharp a roll-off as possible is desirable. Eqn. 6.1 implies that an infinitely sharp cutoff, where transmission is 100% right up to the cutoff and zero immediately after it, is not realisable. Thus all real high-pass filters let some long-wmelength power bleed through and simultaneously stop some short-wavelength power which should have been admitted. All filter design is therefore a compromise. The large number of hfferent designs of filter which have been proposed all have particular advantages and disadvantages.

119

Data Acquisition & Filtering

025

06

25

80

Wnvelerqth in mm

Figure 6 .6 . Transmission curves showing roll-off charactenstics at four standard cutoff lengths for a 2CR high-pass analogue filter (BS 1134, 1988)

Causal filters can only operate with historic data, that is for values of z (x + i) for which i < 0. All physically realisable filters are causal, because a filter operating in real time cannot "see" future data. But this is not a limitation for many roughness measurements, where pre-recorded data are being filtered, and non-causal filters may operate on values of z(x + i) wit]? positive values of i . Recursive filters are modified by a feedback from the output. Recursive filters are also called inJnite impulse response (IIR) filters because their weighting sequence cannot be represented by a fixed number of terms, whereas the weighting sequence of non-recursive filters is finite (FIR). IIR filters may potentially be unstable, whereas FIR filters are always stable. Because of the feedback mechanism implicit in IIR filters, fewer terms are needed to achieve a similar roll-off performance and so IIR filters are more efficient. On the other hand, linear phase response characteristics are impossible to achieve with IIR filters, whereas non-causal FIR filters do not introduce any phase distortion. The relative advantages of IIR and FIR filters for roughness assessment are discussed at length by Medhurst (1989). To determine the frequency response of the filtx, that is how the transmission coefficient varies with wavelength, it is necessary to take the Fourier transforms of the weighting sequence and the input signal and multiply them together. Their product is the Fourier transform of the frequency response, which may be recovered by inversion. This multiplication in the frequency domain is formally equivalent to convolution in the distance domain. So it is possible to proceed in the reverse direction, to decide on a required frequency response and hence to deduce the appropriate weighting sequence.

120

Rough Su$aces

To begin with filters were analogue, operating on the actual instrument output in real time with physical components. The first internationally agreed filter (IS0 3274, 1975) was a cascade of two resistor-capacitor circuits, the socalled 2CR filter (Fig. 6.6), with a cutoff of 75%. The mean line with respect to which roughness parameters were calculated was taken as the zero voltage level of the output (the so-called M-system). This filter had an asymmetrical weighting function, the practical effect of which was to cause phase distortion of the output signal (Fig. 6.7).

Figure 6.7. Phase distortion caused by 2CR filter (Whitehouse & Reason 1965)

To avoid this distortion, Whitehouse (1967/68) proposed the use of a phasecorrected (PC) filter. He noted that a suitable weighting function would need to be concentrated in a central lobe and die away quickly on either side, though not so quickly as to produce undesirable harmonics. The effects on various machined surfaces of phase-corrected filters were computed by Shunmugam & Radhakrishnan (1976a). Whitehouse considered various weighting functions, including a Gaussian weighting function which satisfied the above criteria, but practical realisation was limited by the existing state of technology. With the advent of fast cheap digital processing, Gaussian PC filters are now practicable and have become the standard (DIN 4777, 1990). I S 0 11562 (1996) prescribes the weighting function as

where a = 0.4697 is a numerical constant. The cutoff is now defined as 50% transmission so that the mean line of the profile may be extracted by subtracting

Data Acquisition & Filtering

121

the high-pass filtered profile from the original, and the transmission coefficient at wavelength A, that is the ratio of the unfiltered amplitude a. to the filtered amplitude, is an/ao= 1

- exp f

-71

(&/A)

}

As well as desirable phase characteristics, the PC filter also has a sharper roll-off than the 2CR filter (Fig. 6.8).

Figure 6.8. Frequency responses of 2CR and PC filters compared for a cutoff of 0.8 mm

There are many other possible filtering techniques, some of which are in common use. Most are not capable of representation in terms of Eqn. 6.1, so although it is usually possible to define their cutoff, it is rarely possible to specie their frequency response. Earlier standards described the decomposition of the profile into a number of consecutive equal sample lengths (BS1134, 1972). To each sample length a separate straight mean line is fitted, by least squares or an equivalent method, then all the mean lines are joined in a single straight line (Fig. 6.9). This is an effective high-pass filter, but its operation cannot be specified in terms of Fourier transforms. Also, unless a separate algorithm is used to match the ends of the profile segments, the resulting discontinuities will give rise to spurious short wavelengths in the output spectrum.

122

Rough Su$aces

Figure 6.9. High-pass filtering by fitting straight lines to consecutive sample lengths (BSll34, 1972)

A polynomial filter (Fig. 6.10) can use any one of a number of well-known numerical techniques to fit a least-squares polynomial to the input profile. This and the previous filter are interesting as examples of techniques which will work adequately for roughness measurements with their short signal lengths, but would be unsuitable for the continuous signals of communications engineering.

Figure 6.10. Profile (a) fitted with a 12" order polynomial (b) after subtractingthe polynomial

Another filtering technique whose behaviour is difficult to quantify is the valley suppression filter (Schneider et al. 1988), prescribed by DIN 4776 (1990) and I S 0 13565 (1996) for use with surfaces containing deep valleys. Filtering takes place in three stages (Fig. 6.11). First, a high-pass PC filter is applied to determine the mean line. Next, all valleys below the mean line are removed and the profile is filtered again. Finally, the original profile is referred to the mean line from the second filter. The practical implementation of a filter algorithm is fraught with problems. How wide should the impulse response be? If it is too narrow, it will be fast but the filter will ring. If it is too wide, it will be slow, it may not have enough profile to process in order to give a stable result, or alternatively if it overlaps the ends of the profile it may create end effects. Unfortunately the width of the weighting function

Data Acquisition & Filtering

123

Step 1

step 3

Figure 6.1 1 . The three stages of the valley suppression filter (Mummery 1990)

is not specified in the standards, and manufacturers tend to make their own decisions on commercial grounds, decisions whch they are not likely to share with their customers. This is called "method divergence" and is just one reason why software from two suppliers, both conforming to the letter of the standards, may give quite different roughness values for the same profile (Fig. 6.12). However, from Eqn. 6.2, the standard deviation of a Gaussian filter 0Y 0.19Ac. If the width is taken as ?C 3 s equivalent to 99.5% of the possible area of the weighting function, then 6 0 = 1.I&; that is, conveniently, the width of the window is about the length of the cutoff. Low-pass filters, which let through long wavelengths and stop short wavelengths, are not so much used in roughness work &cause the instrument sensor, as already pointed out, is its own low-pass filter, and because in any case short wavelengths, with their small amplitudes, have little effect on amplitudebased parameters. If for whatever reason a low-pass filter is required, a simple running average is often enough. If something more elaborate is required, many mathematical software packages offer spline filters. There is a good deal to be said for a first difference check on new profile data in any case. If this throws up occasional slopes of say 30 degrees or greater, when the steepest slope which the sensor will measure is 10 degrees, then there is a problem which needs dealing with before any further processing. International standards prescribe a range of preferred cutoff wavelengths, roughly in the ratio of 3 : l . The cutoffs most used on measuring instruments for

124

Rough Sur$aces

Unfiltered profile

2 Rc fitter

Phase Corrected filter (DIN 4777)

ValleySup ression

mer (DIN8776)

Figure 6.12. The effect of three different standard filters on the same profile (Mummery 1990)

. .:

. . . . .

. a

. .. . ...

.

.

- ...

..

..

.. .. .

. _.

. *

.I

1.

2

4

6

U

10

12

14

16

18

28

Rq (microns) at 2.5 mm cutoff

Figure 6.13. Roughness of 200 profiles measured on the same surface at high-pass cutoffs of 2.5 mm and 50 mm (Medhurst 1989)

Data Acquisition & Filtering

125

production engineering are 2.5 mm, 0.8 mm, and 0.25 mm. As has already been mentioned, amplitude-dependent roughness parameters increase with high-pass cutoff wavelength (often approximately as its square root, see later), so when a roughness parameter is quoted, on a drawing or elsewhere, it is necessary also to spec@ the cutoff. If no cutoff is specified, a default value of 0.8 mm is assumed. This curious distance apparently arises because it was the width of the field of view in the earliest light-section microscopes, though I cannot trace a reliable source for this story. It is sometimes suggested that choice of cutoff is not particularly important if measurements are being used for comparative purposes only. It is argued that if roughness values are ranked in a particular order when measured at one cutoff, then they will probably be ranked in the same order when measured at any other cutoff. This amounts to claiming that there is a strong correlation between measurements made at different cutoffs. Fig. 6.13 should be enough to disabuse most readers of this misapprehension.

6.2.1. Envelope Filters

The M- or mean-line system, now undisputed, was once in contention with the socalled E- or envelope system. In the E-system (von Weingraber 1957), the reference lines are defined by the loci of centres of circles of different radii rolled along the profile. The locus of the centre of the larger circle gives the curve of form (Formprojl) while that of the smaller circle gives the contacting profile (Hullprojil) (Fig. 6.14). The geometrical projle is now drawn; this is defined as a profile of the surface determined by the design, neglecting errors of form and surface roughness. The area between the geometrical profile and the curve of form represents the errors of form; the area between the curve of form and the contacting profile represents the secondary texture or waviness; and the area between the contacting envelope and the effective profile (defined as the nearest instrumental approximation to the true profile) represents the primary texture or roughness. The E-system mean line is defined as the contacting envelope displaced downwards by a distance such that the areas enclosed by the effective profile above and below it are equal. The advantages of the E-system over the M-system are claimed to be that the E-system is physically more significant in that many engineering properties of a surface are determined by its peaks, and that the mean line is easier and quicker to construct graphically. The contacting profile and curve of form can be obtained

Rough Sur$aces

126

Geometrical profile I

Locus of centre for rolling circle

w w -

-

Curve of form (Formprofil)

Errors of form

Contacting envelope (Hiillprofil)

Waves

Effective profile

Peak to valley

Figure 6.14. Terminology ofthe E- (envelope) system of reference lines in which the filters are two circles of radius r and R rolling along the profile (Olsen 1963)

mechanically by using skids of appropriate shape, and instruments so designed were apparently commercially available at one time. Algorithms for computing the various reference lines have also been published (Shunmugam & Radhakrishnan 1976b). The skids were in fact spheres rather than circles, causing an integrating effect which can alter the form of the various reference lines (Shunmugam & Radhakrishnan 1974). Standard radii were 25 mm for roughness and 250 mm for waviness, though other radii have been proposed (Radhakrishnan 1972). The system does, however, exhibit certain disadvantages. On a visual display, where the vertical magnification is exaggerated, the rolling circle becomes a "rolling ellipse". The mean line, composed as it is of a succession of intersecting arcs, is mathematically discontinuous. Attempts to reconcile the two systems (Ishlgaki & Kawaguchi 1981) have not been successful as it is difficult to represent the envelope action as a weighting function. A successor to the E-system has gained wider acceptance. This is the French system of so-called motif analysis, which is now the subject of an international standard (IS012085, 1996). Motif analysis is more than just a filtering technique, it is a whole new method for classifying surfaces, but it will be convenient to deal with it here. It is basically a set of algorithms which purports to embody the collective expertise, based on subjective visual judgement of profiles, of inspectors

Data Acquisition & Filtering

Figure 6.15. Motifanalysis (Mummery 1990). For explanation see text.

127

128

Rough Surfaces

in the French automobile industry. The conceptual foundation of the method is described by Fahl (1982). An experienced inspector, scanning a profile chart recording by eye, picks out a number of characteristic featuies or motifs which he knows are typical of the surface and on which the fitness of the surface for its purpose may be assessed. This is essentially a pattern-recognition process at which the human brain is known to excel. Motif analysis is an attempt to reduce this complex and almost instinctive process to a list of instructions.

T? 1, and elastically under any load for ly < 0.6, where y~

=

(E'/H)t/(o,/R)

(10.17)

In the region 0.6 < ly < 1 the mode of deformation is dependent on the load. The plasticity index ry is thus a dimensionless figure of merit which can predict the dominant mode of deformation. Many workers have used the plasticity index, with some success, as a qualitative index of comparison witlun a series of tests, i.e. the higher the plasticity index, the more likely a surface is to suffer wear or similar problems. There are difficulties in comparing results between laboratories or in using it as an absolute index, however, because of the difficulties in quantifying the surface parameters R and o,. Because these are both properties of the peak distribution they depend on the definition of a peak, and raise the problems which we have encountered previously. For this reason various other formulations of the plasticity index have been proposed, for instance one due to Mikic (1974) which replaces peak parameters by the mean slope. Bush et al. (1978) developed an expression for the plasticity index of a strongly anisotropic surface in terms of Nayak's moments: (10.18)

216

Rough Sudaces

where moo is the variance of surface heights, moa m2a mO4and m40 are the secondand fourth moments of the power spectra of profiles parallel to and across the lay, respectively, and (10.19)

moo 'mqo .

where

a,=

- moo

2 , a 2 17220

Om04 2 m02

(10.20)

According to Bush et al., deformation will be plastic for y > 0.7, elastic for ty < 0.5, and load-dependent in the intermedate region. How anisotropic must a surface be to require the rather laborious anisotropic treatment? According to Wu & Zheng (1988) the correction for anisotropy increases very slowly with the degree of anisotropy y (Fig. 10.11). Their paper does not appear to distinguish between strong and weak anisotropy, but this does not affect the present argument. The degree of anisotropy is the ratio of the major and the minor asperity radii of curvature, which is approximately the square of the ratio of the major and minor axes of the ellipse projected when the asperity intersects a plane parallel to the surface mean plane (Bush et al. 1978).

2.0

1.8 1.6

1.4

1.2 1 .o 0.8

1

1 . 5 2

3

4

5

Figure 10.11. Anisotropy correction factor for plasticity index as a function of degree of anisotropy y(Wu & Zheng 1988)

Contact Mechanics

217

Remembering that the plasticity index only deals with the highest regions of the surface, one may observe that the higher one looks on any surface, however anisotropic, the less elliptical the tips of asperities appear (Fig. 10.12). If one attempts to fit a best ellipse to some of these irregular shapes, the ratio of major to minor axes is not more than about 3, corresponding to y = 0.1, in which case, from Fig. 10.11, the anisotropy correction would be only about 10%. Bearing in mind the large statistical uncertainties in measurement of somc of the other surface parameters, it seems likely for many surfaces that isotropic calculations will suffice, in which case Eqn. 10.18 simplifies to

(10.21)

Figure 10.12. "And we in dreams behold the Hebrides": contours more than 1 prn above the mean plane on a plateau-honed surface do not look very elliptical

218

Rough Surfaces

Recalling that the second moment of the profile power spectrum is related to the mean slope Bby Eqn. 9.15:

so (10.21)

or (10.22)

This formulation of the plasticity index simplifies the measurement problem considerably. Instead of measuring asperity radii of curvature or power spectra directly, we can replace these by the much easier measurement of the profile slope, which merely requires computation of the standard deviation of the first differential of the profile. But there are still some remaining practical obstacles. The slope is a function of the sampling interval and increases as the sampling interval decreases. This simply indicates that as asperities get smaller they also get sharper. It follows that, by varying the sampling interval, we can obtain any desired value of the slope, and hence of the plasticity index. To put this another way, there always will be features on the surface so small and sharp that they will deform plastically on contact. In obtaining numerical solutions in all the above cases the basic problem is the same: the choice of the low-pass cutoff. This amounts to asking the question: What is the smallest surface feature which will affect contact? There does not seem to be any general answer to this question. Many workers have implicitly, and Ganti & Bhushan (1995) have explicitly, assumed that no features smaller than the resolution of the particular instrument are important, but it is difficult to find physical grounds to justify this. One possible approach is to work back from the plasticity index itself (Thomas & Sayles 1977). As asperities get smaller and sharper, a size will be reached below which they will deform plastically during the very first cycle of contact and so dlsappear (Archard 1961). During the subsequent lifetime of the component, it will behave elastically as if the corresponding range of surface wavelengths did not exist; in other words, the initial encounter of the surface will act as a natural low-pass filter. The critical wavelength at which this filtering

219

Contact Mechanics

occurs may be found from the relationship between the second moment and the plasticity index. If vCis the critical value of the plasticity index above which deformation will be plastic at any load, then the critical second moment r n Z c = (71( 2

- nJ2 )I-”

wc2 ( H I E ’ )

(10.23)

The exact form of Eqn. 9.22 is m2 = B (3

+ p).’ ( 271)-p

(

e3+p - m3+p)

(10.24)

If p> 1 and the bandwidth of surface wavelengths is reasonably wide, i.e. oL)) oH, then Eqn. 10.24 reduces to

m2 E B The critical wavelength dc= 271/

Q , ~ +1~( 3

+ p ) ( 271)p

CL)LC, so combining Eqns.

(10.25) 10.23 and 10.25,

(10.26)

From Bush et a1 1978, IY, , = 0.7. Combining this with the numerical constant, replacing B and p by the corresponding fractal parameters from Eqns. 8.10 and 8.11 and rearranging, we have finally 20-1

(10.27)

where f ( D ) = (-)@z)iO-LT(I1175 1-20

2D)cos- 2 - 0

(10.28)

2

This is a relationship between three dimensionless numbers: the critical wavelength normalized by the topothesy, the fractal dimension and the material property ratio. The dimensionless wavelength is highly sensitive to the other parameters (Fig. 10.13), and for a given fractal dimension and material property

220

Rough Su?$aces

ratio the critical wavelength increases as the topothesy. Thus we can in principle now find a unique short-wavelength cutoff, depending only on material properties and intrinsic topography parameters, which we can use to determine the elastic behaviour of the contact.

90 0

E-IH

Figure 10.13.

Dimensionless critical wavelength as a function of material ratio and fiactal dimension ( R o s h et al. 1997)

10.4. References Archard, J. F., "Elastic deformation and the laws of friction", Proc. Royal SOC.,A243, 190-205 (1957). Archard, J. F., "Single contacts and multiple encounters", J. Appl. Phys., 32, 1420-1425 (1961). Back, N., Burdekin, M, and Cowley, A., "Review of the research on fixed and sliding joints", Proc. 13th Int. Machine Tool Des. & Rex Con$, 87-97 (1973). Bhushan, B.; Majumdar, A., "Elastic-plastic contact model for bifractal surfaces", Wear 153, 53-64 (1992) Bush, A. W., Gibson, R. D., Keogh, G. P., "Strongly anisotropic rough surfaces", Trans. ASME: J. Lub. Tech. 101, 15-20 (1979)

Contact Mechanics

22 1

Bush, A. W., Gibson, R. D. and Thomas, T. R., "The elastic contact of a rough surface", Wear, 35, 87-111 (1975). Dobychin, M. N., "Elastic contact of rough cylindrical bodies", Soviet Journal ofFriction and Wear 9, 1-5 (1988) Ganti, S., Bhushan, B., "Generalized fractal analysis and its applications to engineering surfaces", Wear 180, 17-34 (1995) Greenwood, J. A., "Contact of rough surfaces", 37-56 in I. L. Singer & H. M. Pollock eds., Fundamentals of piction: macroscopic & microscopic processes, (Kluwer, Dordrecht, 1992). Greenwood, J. A. and Tripp, J. H., "The contact of two nominally flat rough surfaces", Proc. 1. Mech. E., 186,625-633 (1970/71). Greenwood, J. A. and Williamson, J. B. P., "Contact of nominally flat surfaces", Proc. Royal SOC.A295, 300-319 (1966). Handzel-Powiem, Z., Klimczak, T. and Polijaniuk, A., "On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces", Wear, 154, 115-124 (1992) Hills, D. A., D. Nowell and A. Sacwield, Mechanics of elastic contacts (Butterworth-Heineman, Oxford, 1993). Johnson, K. L., Contact mechanics (Cambridge University Press, London, 1985). Klimczak, T., "Predicting microcontact spots size distribution in contact problems", Ann. CIRP 41,609-612 (1992) Lee, S. C., and Ren, N., "Behavior of elastic-plastic rough surface contacts as affected by surface topography, load, and material hardness", Trib. Trans. 39, 6774 (1996) Lo, C. C., "Elastic contact of rough cylinders", Int. J. Mech. Sci., 11, 105-115 (1969). Majumdar, A.; Bhushan, B., "Role of fractal geometry in roughness characterization and contact mechanics of surfaces", Trans. ASME. Journal of Tribology 112,205-216 (1990) Majumdar, A.; Bhushan, B., "Fractal model of elastic-plastic contact between rough surfaces", Trans. ASME. Journal ofTribology 113, 1-11 (1991) Majumdar, A.; Tien, C. L., "Fractal characterization and simulation of rough surfaces", Wear 136, 313-327 (1990) McCool, J. J., "Comparison of models for the contact of rough surfaces", Wear 107,3760 (1986)

222

Rough Surfaces

Merriman, T. and J. Kannel, "Analysis of the role of surface roughness on contact stresses between elastic cylinders with and without soft surface coating." Journal of Tribology, 111,87-94, (1989) Mikic, B. B., "Thermal contact conductance: theoretical considerations", Int. J. Heat Mass Transfer, 17,205-224 (1974). Moalic; H., J. A. Fitzpatrick and A. A. Torrance, "A spectral approach to the analysis of rough surfaces", Journal of Tribology, 111, 359-363, (1989) Nayak, P. R., "Random process model of rough surfaces", Trans. A.S.M.E. Ser. F. J. Lubr. Tech., 93, 398-407 (1971). Newland, D. E., "The effect of a footprint on perceived surface roughness", Proc. Roy. SOC.Lond. A405,303-327 (1986) Men, P. I.; Majumdar, A.; Bhushan, B.; Padmanabhan, A,; Graham, J. J., "AFh4 imaging, roughness analysis and contact mechanics of magnetic tape and head surfaces", Journal of Tribology, Transactions of the ASME 114, 666-674 (1992) Poon, C. Y., and Bhushan, B., "Nano-asperity contact analysis and surface optimisation for magnetic head slider/disk contact", Wear 202,83-98 (1996) Poon, C. Y., and Bhushan, B., "Numerical contact and stiction analyses of Gaussian isotropic surfaces for magnetic head slideddisk contact", Wear 202, 6882 (1996) Poon, C. Y.; Sayles, R. S., "Numerical contact model of a smooth ball on an anisotropic rough surface", Journal of Tribology, Transactions of the ASME 116, 194-200 (1994) Pullen, J . and Williamson, J. B. P., "On the plastic contact of rough surfaces", Proc. R. SOC.Lond. A327, 159-173 (1972). Ro&, B.-G., R. Ohlsson and T. R. Thomas, "Nano metrology of cylinder bore wear", Trans. 7th. Int. Con$ On Metrology h Properties of Engng Surfaces, pp. 102-110 (Giiteborg, 1997) Russ, J. C., Fractal surfaces (Plenum Press, New York, 1994). Sayles, R. S. and T. R. Thomas, "Computer simulation of the contact of rough surfaces", Wear, 49, 273-296 (1978). Sayles, R. S. and Thomas, T. R, "Thermal conductance of a rough elastic contact", Appl. Energy, 2, 249-267 (1976) So, H.; Liu, D. C., "An elastic-plastic model for the contact of anisotropic rough surfaces", Wear 146,201-218 (1991) Thomas, T. R., "Calculation of elastic contact stresses for rough-curved surfaces", ASLE Trans., 22, 184-189 (1979)

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223

Thomas, T. R., and King, M. J., Surface topography in engineering: a state of the art review and bibliography (BHRA, Cranfeld, 1977) Thomas, T. R. and Probert, S. D., "Establishment of contact parameters from surface profiles", J. Phys. D: Appl. Phys., 3,277-289 (1970). Thomas, T. R. and Sayles, R. S., discussion to Radhakrishnan, V., "Analysis of some of the reference lines used for measuring surface roughness", Proc. 1. Mech. E., 187, 575-582 (1973). Thomas, T. R. and Sayles, R. S., "Random-process approach to the prediction of joint stiffness", Trans. ASME: J. Eng. Znd. 99B, 250-256 (1977) Thomas, T. R., Uppal, A. H. and Probert, S. D., "Hardness of rough surfaces", Nature Physical Sci., 229, 86-87 (1971). Thornley, R. H. and Lees, K., "The effect of planforni shape on the normal dynamic characteristics of metal to metal joints", I. Mech. E., Paper C62/71, (1972). Tian, X., and Bhushan, B., "A numerical three-dimensional model for the contact of rough surfaces by variational principle", Trans. ASME: J. Trib. 118, 3342 (1996) Timoshenko, S., and Goodier, J. N., Theory of elasticity (McGraw-Hill, New York, 1951) Uppal, A. H., Probert, S. D. and Thomas, T. R., "The real area of contact between a rough and a flat surface", Wear, 22, 163-183 (1972). Warren, T. L.; Krajcinovic, D., "Fractal models of elastic-perfectly plastic contact of rough surfaces based on the Cantor set", Internatanal Journal ofSolids and Structures 32,2907- 2922 (1995) Whitehouse, D. J. and Archard, J. F., "The properties of random surfaces in contact", In: Surface Mechanics. Ling, F.F. (Ed.) 36-57 (A.S.M.E., New York, 1969). Williamson, J. B. P., Pullen, J. and Hunt, R. T., "The shape of solid surfaces", In: Surface Mechanics. Ling, F.F. (Ed.). 24-35 (A.S.M.E., New York. 1969). Woo, K. L. and T. R. Thomas, "Contact of rough surfaces: A review of experimental work", Wear, 58, 33 1-340 (1980). Wu, C. and Zheng Linqing, "General expression for plasticity index." JVear, 121, 161-172, (1988) Yu, M. M., and Bhushan, B., "Contact analysis of three-dimensional rough surfaces under frictionless and frictional contact", Wear 200, 265-280 (1996)

CHAPTER 11

TRIBOLOGY

Discussion of the effect of roughness on contact mechanics leads naturally to a discussion of the effect of roughness on friction, lubrication and wear. As we would argue that all real contact is rough contact, it follows that roughness is a complication in all tribological situations. There is no space here to do justice to the full scale of the tribological implications of roughness, and we will confine ourselves to discussing a few of the more interesting examples which illustrate some of the previous topics. No comprehensive account of rough surface tribology appears to exist, though Bhushan (1990) has a useful review.

11.1. Friction

It was recognised very early that friction was associated with surface roughness, to the point where Coulomb suggested that friction was due to the effort required for one surface to climb up the asperities of the other during translation (Bikerman 1944, Bowden & Tabor 1950). When it was pointed out that the energy thus dissipated would be largely recovered when the surface slid down the reverse slopes of the asperities, the Coulombic theory lost some of its popularity, but microgeometry remains a important factor in friction. Manj workers have found a correlation between roughness parameters and friction; friction increases with average roughness (Furey 1963, Koura 1980) and also with mean profile slope (Myers 1962, Ghabrial & Zaghlool 1974, Eiss & Warren 1975, Koura & Omar 1981, Moalic et al. 1987) (Fig. 11.1). Road roughness is llkely to influence friction between a wet road and a tyre as asperities pierce the intervening film of water (Taneerananon & Yandell 1981). An opposite effect of roughness on friction has also been reported. Ogilvy (1991, 1993) developed a statistical roughness model for adhesive friction which predicted that friction would decrease with increasing roughness, tending to a constant value independent of roughness. A wholly elastic and a mixed elasticplastic versionof the model were developed, dependin3 on two roughness parameters, the RMS roughness height and the correlation length. In tests with a 225

Rough Surfaces

226

thin molybdenum disulphide film on a rough steel subtrate, the theory gave good qualitative agreement, and reasonable quantitative agreement, with experiment (Fig. 11.2).

Figure 11.1. Variation of dynamic friction coefficient with mean profile slope (Koura & Omar 198 1)

-

dosli-plastic model w b l l y elastic model

I ’ 0.00

0-10

cipwimenlol volucs

0.20 0-30 0.40 rms heipht (microns)

0 50

Figure 11.2. Variation of fiction coefficient with roughness for steel coated with MoSz (Ogilvy 1993)

Chapman & Rizkallah-Ellis (1979) provide an interesting example of the effect of scale of roughness on tribological interactions. They found a pronounced directional effect in the coeficient of friction of automobile brake linings which, after eliminating other possible causes, they concluded was due to the surface topography. Reflectance measurements showed directional differences which could

Tribology

227

not always be detected by a stylus instrument. The implication is that at least some of the surface features responsible for friction in this casc were smaller than a stylus can resolve. Proctor & Coleman (1988) and Harris and Shaw (1988) showed that the roughness of floor surfaces was an important parameter in determining pedestrian slip-resistance, at levels of floor roughness much lower than had been reported by other researchers. It was well known that values of peak-to-trough surface roughnesses (Rtm) of 15-600 pm had an effect (Jung and Riediger, 1982). However, this level of roughness is many times higher than the Rtm values found by Harris and Shaw to have an important influence on the safety of water wetted floors. The significance of this finding was that it opened up new possibilities for ensuring the safety of floors exposed to contamination by water. In essence, all that is required is to incorporate a degree of roughness into the floor surface, that is small enough not to detract from the aesthetic appearance or create problems for cleaning. Since water is the most common floor contaminant, especially in public areas exposed to wet footwear, this is a significant development. Other researchers have confirmed the importance of surface roughness for assessing both floor surfaces and footwear (Manning et al., 1991, Stevenson, 1989. Gronqvist et al., 1990). Manning found that footwear soles of a granular construction that maintain surface roughness during wear, retain their slip resistant properties, whereas footwear soles that wear smooth, do not. He found a correlation between sole roughness Rtm and coefficients of friction measured during walking. He also found that the footwear ranked in approximately the same order on seven floor/contaminant combinations; this suggest; that surface structure determines the footwear ranking (Proctor 1993). Lloyd & Stevenson (1992) obtained a correlation between slip resistance and a combination of Rq, skewness and average wavelength.

11.2. Lubrication A large number of papers have appeared describing or modelling the effect of roughness on various lubrication regimes. Rough boundary lubrication has been investigated by Hisakado (1978), Nivatvongs et al. (1991) and Denape et al. (1992, 1995). Christensen (1965/6, 1971, 1972), Rao & Mohanran: (1993), Wakuri et al. (1995) and Liu et al. (1996) have reported work on rough mixed lubrication. Rough hydrodynamic lubrication has been treated by Bush & Gibson (1980), Kumar (1980), Nakahara et a1.(1984), Bayada & Chambat (1988), Cheng & Xie

228

Rough Sufaces

(1992), Sugimara & Yamamoto (1995) and Tonder and his co-workers (Christensen & Tonder 1971, Tonder & Christensen 1972, Prakash et al. 1979, Tonder 1980, 1987). Rough elastohydrodynamic lubrication (EHL) has been investigated by Tallian et al. (1965/6),Coy & Sidik (1979), Johnson et al. (1972), Kaneta & Cameron (1980), Karami et al. ( 1987), Lubrecht et al. (1988), Sadeghi & Sui (1989), Sinha et al. (1987), Fan & Zheng (1991), Kaneta (1992), Chang et al. (1993, 1994) and Ishibashi & Sonoda (1994). Chang (1995) has also reported on rough partial EHL. Micro-EHL, which by definition deals with rough surfaces, has been investigated by Baglin (1986), Kweh et al. (1989, 1992), Huang & Wen (1993), and Chang & Zhao (1995); the topic has been reviewed by Chang (1995). The specific application of lubrication in rough sliding has been dealt with by Tzeng & Saibel (1967), Patir & Cheng (1979), Shukla & Kumar (1979), Hughes (1981) and Anderson & Salas-Russo 1994. Other practical applications of rough lubrication include compliant surfaces (Darbey et al. 1979), improvement of roller bearing fatigue life (Akamatsu et al. 1991. 1992) (Fig. 11.3) and gear contacts (Peeken et al. 1990). Unfortunately some of these researches have confined themselves to simple deterministic roughness models and are thus of limited applicability.

Skewness Figure 11.3. Influence of skewness on relative fatigue life of rolling bearings (Akamatsu et al. 1991)

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An early application of functional filtering was to the case of a roller-bearing operating in a regime of mixed lubrication (Leaver et a1 1974). The surface finish of the bearings and races was measured before and after running-in, and a pronounced difference was noted, though no scuffing or other damage was apparent on the run-in surfaces. Measurements of the film thickness, however, showed it to be much smaller than the combined roughnesses of the contacting surfaces, and it was difficult to reconcile this with the absence of damage. Application of the principle of functional filtering suggested that all wavelengths longer than the Hertzian contact width should be ignored, as they took no part in the interaction with the lubricant film. The effect of this was to reduce the effective roughnesses to about a tenth of their measured valces, thus obtaining at a stroke a far more plausible set of film-thickness ratios and allowing the no-contact times to be predicted in fair agreement with experiment. One suspects that if this principle were more generally employed it would result in a substantial increase in the numerical values quoted in the literature for the so-called lambda ratio, the ratio of oil film thickness to roughness. Cann et al. (1994), in a review of the literature on lambda ratios, conclude that the behaviour inside the Hertzian contact zone depends on the mean slope and the asperity density as well as the roughness. They admit that many systems are known to run successfully at low lambda ratios. They point out that as soon as the lubricated surfaces are rough and the roughness heights are not negligible compared with the mean oil film thickness, the local pressure fluctuations cause3 by the asperities will have an influence on the elastic deformations of the surfaces.

11.3. Wear

The accommodation of two sliding surfaces over a period of time, variously known as running-in, brealung-in or shakedown, causes changes in their initial topography, and itself depends on that topography (Kapoor et al. 1994, Anderson et al. 1996). Kang & Ludema (1986) reported an optimum initial roughness of about 0.1 pm; smoother and rougher surfaces failed more quickly. Chandrasekaran (1993) found a proportionality between reniprocal wear rate and the reciprocal of initial roughness (Fig. 11.4). Summers-Smith (1969) dstinguishes two basic types of running-in mechanism. On the one hand he describes what he calls a “plastic squeezing” of the surface, that is a change in its shape by redistribution of material due to plastic flow without net loss. On the other hand there are the various wear mechanisms, adhesive or abrasive, all of

230

Rough &$aces

which do involve net material loss. These two types of running-in are associated with quite different geometrical effects.

Figure 11.4. Wear rate of steel sliding against steel as a function of initial roughness (Chandrasekaran 1993)

The plastic redistribution of material during running-in is related to the finishing process known as roller burnishing (Black & Kalen 1973). The unit event is the compression of a single asperity by the roller until the plastic limit is exceeded, when the asperity will deform plastically so as to redistribute its material into the adjoining valleys. In general it will change its shape only until the new contact area is large enough to support the stresses elastically. The zone of affected asperities will therefore approximate to the nominal area of Hertzian contact between the roller and the rough sphere. Surface features significantly larger than this zone wilt not be affected by the burnishing process. If the length of the nominal contact is small compared with that of the cut-off of the measuring filter, very little change in roughness will be apparent from this type of running-in, because the roughness measurement is weighted heavily by the greater power associated with longer wavelengths. Whitehouse and Archard (1969), for instance, found a maximum change in R a of less than 20% in these

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23 1

conditions, although the changes in the actual profile were clearly visible to the naked eye. One way of overcoming this difficulty is to compare worn and unworn values of roughness as the filter cut-off is progressively shortened (Fig. 11.5a). If burnishing has occurred then power will have been lost by some band of wavelengths and hence some cut-off will be reached where the roughnesses diverge. The power spectrum is a more rational way of presenting the same information (Fig. 11Sb). (a)

I

i

2 6.(m

Cut-off wavelength (urn)

10 -6

f

I

I

I

1

1

2

3 4

6

810

1

1

1

1

I

l

l

I

20

3040 6 0 8 0 1 0 0 200 Frequency cyclelmrn :lmm

Figure 11.5. Topography of worn (circles) and unworn (crosses) inner races of a taper roller bearing characterised as (a) roughness v. high-pass filter cutoff (b) power spectra (Laver et al. 1974)

232

Rough Surfaces

The simplest case of abrasive wear is a clean removal of the tops of the asperities without smearing or tearing. This may be performed experimentally under rather artificial conditions (Thomas 1972), but probably does not often occur in practice. However, it is convenient to investigate because it is easily simulated by computer (Thomas 1972; Willn 1972). As successive layers of the surface are abraded, parameters such as roughness, mean slope and mean peak curvature decrease in a systematic manner (Fig. 11.6).

A

I

P

I T'i

-0 ,

IS

I

I

I

10

5

0

-5

- 10

Height of worn surface above original mean line (rm) Figure 11.6. Effect of pure abrasion on (circles) RMS roughness (triangles) mean peak curvature (squares) profile curvature standard deviation (lozenges) mean absolute slope. Open symbols are simulated results, filled symbols are experimental. P = highest peak, V = lowest valley on unworn profile. Solid line is Gaussian bearing-area curve (Thomas 1972)

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These parameters are secondary rather than primary, as they can all be represented by joint probability distributions of heights. A more fundamental representation, then, is the height distribution. Hence it is important to describe correctly what happens to the distribution. Suppose we have a distribution, originally p{z), abraded until there are no heights higher than h above the mean line. This is sometimes described as being truncated at h, so that the new distribution

p{z)

p{z) for z 2 h Oforz>h

=

=

In fact the change is correctly described as being censored at h (Marcus 1967): p(z) =

= p(z) for z < h p(h)forz>h

Figure 11.7. Proposed typology of running-in (Thomas 1978). From top to bottom: unworn profile with power spectrum and height distribution; censoring without filtering; low-pass filtering without censoring; high-pass filtering without censoring; high-pass filtering with censoring

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That is, for a truncated distribution the fraction of values of z greater than h vanishes, but for a censored distribution it becomes equal to h, causing a Dirac spike at h (Fig. 11.7). The distinction makes a considerable difference to the moments of the distribution. It is more characteristic of abrasive wear in general, and also of adhesive wear, that changes in topography are due to the progressive removal of many small particles over long periods of time. Golden (1976) made a mathematical investigation of the effect on an initially Gaussian height distribution of a wear mechanism such that the rate of loss in height of an individual asperity with time is proportional to the depth to which the asperity has penetrated the opposing surface. He concluded that the resulting topography is that of the original surface up to some height representing the mean separation of the contacting surfaces. Above this height is superimposed another distribution, also Gaussian but smoother; as time progresses it will remain Gaussian but become smoother still (Fig. 11.8). Topographies of this type have been found experimentally by Ostvik and Christensen (1968/69) and also by Williamson et al. (1969) (see Section 7.4).

10-5 10-6

-

-

lo-'10-8 10-91

I

I

I

I

-10.00-R.00-6.00 -4.00 -2.00

I

I

0.00 2.00

I

I

4.00

6.00

Height, units of standard deviation Figure 11.8. Transitional double Gaussian height distribution of a surface at progressive stages of wear (Golden 1976)

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Censoring a random process reduces the amplitude of the autocovariance h c t i o n but has little effect on its form. When the autocovariance function is normalized to the autocorrelation function by the profile variance, the change due to censoring is barely perceptible even when abrasion has progressed as far as the mean line, as shown theoretically by Marcus (1967) and King et at. (1978) and confirmed by experiment (Willn 1972). Radhakrishnan (1977) divided the profile along the mean line and cross-correlated worn peaks and unworn valleys, but without any greater success. It follows that no change will be seen in the normalized power spectrum as this merely presents the same information in a m e r e n t form. A tentative classfication of run-in topographies was proposed by Thomas (1978) (Fig. 11.7). The original surface may be censored without filtering, or it may be high-pass filtered or low-pass filtered or both with or without censoring. In principle, then, it should be possible to define a run-in topography fairly closely by three or four parameters: the cut-off wavelength or wavelengths, the censoring level of the height distribution and, if a transitional topography, the roughness of the superimposed finish.

11.4. Seals

Roughness is a factor in determining the rate of leakage through seals, both static w t c h e l l & Rowe 1967/8, 1969, Wallach et al. 1968, Chivers & Hunt 1978, Hehn 1970, Kazamaki 1974, Otto 1974, Warren et al. 1988, Matsuzaki et al. 1992, 1993, Etsion & Front 1994) and dynamic (Lucas et al. 1994, 1995). Vacuum seals are a special case of static seals where the performance criterion in terms of leakage rate is particularly rigorous (Roth 1966, 1971, Yanagisawa et al. 1991). The performance of radial lip seals is known to depend on roughness, but the actual mechanism is not clear (Horve 1991, van Bavel et al. 1995). In the absence of a satisfactory physical model, a discriminant analysis approach has been applied (Thomas et al. 1975a, b) to distinguish between a set of rubber lip seals, individual members of which had either sealed or leaked. Worn and unworn profiles on the seals were measured and first 9 and then 11 parameters were computed. Two basic and relatively straightforward procedures were implemented in the analysis of the data. In the first, each of the nine features was examined individually. The procedure of evaluation was based on simple analysis of variance. The seals were first sorted into sealed or leaked categories. Then one of the surface measurements (e.g. zero-crossing density) was examined. An average value for this parameter

236

Rough Su$aces

was computed for each performance category, and the overall or grand average value for all data was calculated. Then the pooled sum of squares was computed for the difference between each individual measurement and its corresponding group mean. This quantity is called the within sum of squares. Next, a sum of squares was computed by observing the difference between each group mean and the grand mean. This sum of squares, expressed on a per-observation basis, is called the between sum of squares. The ratio of the latter to the former sum provides a measure of the discriminating information available from the measurement in question. It is reasonable to consider that the greater this ratio the better the ability to discriminate between good and bad seals on the basis of a single parameter. In particular, if the ratio is large, it connotes a wide separation between the two groups of measurements but a relatively close clustering of individual measurements within each group. Accordingly, the several measurements can be ranked according to their (individual) ability to differentiate between effective and ineffective seals. It turns out that this ranking is different for the worn and unworn cases. Table 1 1 . 1 . Discrimination between sealed and leaked in terms of 1 1 surface parameters measured from worn and unworn profiles of 15 lip seals (Thomas et al. 1975a)

Discriminants

Rq Ra

Eigenvector x 10 Unworn -6.9 7.2 0.8

WOA.n

-0.5 0.4 -0 6

DO Peak height 5.8 -2.6 Valley depth 3.4 -0 1 Peak curvature -0.8 10.0 Valley curvature 1.4 -3.0 Profile curvature 0.1 -7 1 Slope -6.4 3.9 Sk 1 .o 07 3 ........ ................. ............K .*/................. .................. 0.5 ................................_.. .-1 ...............__ Rather than attempt a classification of seals on the basis of a single 'best' parameter, one may make much more effective use of the infomation contained in

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the data by means of linear discriminant functions. In this approach, the various parameters are combined as a weighted sum and the weights are adjusted so as to maximize the ratio of between to within sum of squares. The construction of the transformations appropriate to multiple linear discriminant functions is straightfonvard and well documented. In essence, the approach defines a sum of squares ratio in terms of the coefficients of a linear expansion. The ratio is then differentiated with respect to the coefficients and solved for the values which maximize the ratio. The problem reduces to finding the eigenvectors of a nonsymmetric matrix, and can be solved in a straightforward manner by any of a number of standard eigenvectodeigenvalue routines. The eigenvector is composed of the nine coefficients in the linear expansions. The associated eigenvalue provides a measure of the amount of variance accounted for by the discriminant function. Separate analyses for worn and unworn surfaces ezch separated the two categories and showed that the order of importance in which the parameters were ranked for the worn surfaces was quite different from that of the unworn (Table 11.1). The hypothesis advanced to explain this was that the geometry of the worn surfaces directly affects the sealing process, whereas that of the unworn surfaces affects it indirectly only in so far as it influences the production of the final geometry of the worn surfaces. As a result of the analysis it is possible to reconstruct ideal models of successfully and unsuccessfully sealing surfaces (Fig. 11.9).

Figure 11.9. Reconstructions from pattem-recOgnition analysis of profiles of the contacting surfaces of (a) an ideally good @) an ideally bad lip seal (discussion to Thomas et al. 1975b)

238

Rough Surfaces

Although this form of analysis cannot replace a proper understanding of a particular problem it can aid it in several ways. By its assignation of degrees of importance to particular parameters it can offer the theoretician a useful initial guide for the formulation of ideas. In some practical cases it may be necessary to go no further, and the discriminant functions themselves may serve as part of the manufacturer's armoury of quality controls. The technique is also well suited to interactive computing work, where successive parameters can be dropped from the analysis until the engineer's subjective judgement decides that separation is no longer adequate.

11.5. References

Akamatsu, Y., Tsushima, N., Goto, T. and Hibi, K., "Influence of surface roughness skewness on rolling contact fatigue life", Trib. Trans. 35, 745-750 (1992) Akamatsu, Y., Tsushima, N., Goto, T., Hibi, K., Itoh, K., "Improvement of roller bearing fatigue life by surface roughness modification", SAE Trans. 100, 4449 (1991) Anderson, P., Juhanko, J., Nikkila, A.-P., Lintula, P., "Influence of topography on the running-in of water-lubricated silicon carbide journal bearings", Wear 201, 1-9 (1996) Anderson, S., Salas-Russo, E., "Influence of surface roughness and oil viscosity on the transition in mixed lubricated sliding stee: contacts", Wear 174, 71-79 (1994) Archard, J. F., "Elastic deformation and the laws of friction", Proc. Royal SOC.,A243, 190-205 (1957). Archard, J. F., "Single contacts and multiple encounters", J. Appl. Phys., 32, 1420-1425 (1961). Baglin, K. P., "Micro-elastohydrodynamic lubrication and its relationship with running-in", Proc. I. Mech. E, 200, 415-424 (1986) Bayada, G. and M. Chambat, "New models In the theory of the hydrodynamic lubrication of rough surfaces."Journal of Tribology, 110, 402-407, (1988) Bhushan, B., Tribology and mechanics of magnetic storage devices (Springer-Verlag, New York, 1990) Bikerman, J. J., "Surface roughness and sliding friction", Rev. Mod. Phys., 16, 53-68 (1944).

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Black, J. T. and Kalen, S. E., "The anatomy of a rolier burnished surface", Proc. Int. Conf: on Surface Technol., 507-526 (SME, Dearborn, 1973) Bowden, F. P. and Tabor, D., The friction and lubrication of solids Part 1 (Oxford University Press, 1950). Bush, A. W.; Gibson, R. D., "Effect of surface roughness and elastic deformation in hydrodynamic lubrication - A perturbation approach", in Surface roughness effects in hydrodynamic and mixed lubrication, 173-191 (ASME, New York, 1980). Cann, P.; Ioannides, E.; Jacobson, E.; Lubrecht, A. A,, "Lambda ratio - a critical re-examination", Wear 175, 177-188 (1994) Chandrasekaran, T., "On the roughness dependence of wear of steels: a new approach", J. Mat. Sci. Lett. 12,952-954 (1993) Chang, L., "Deterministic model for line-contact partial elasto-hydrodynamic lubrication", Tribology International 28,75-84 (1995) Chang, L., "Deterministic modeling and numerical simulation of lubrication between rough surfaces - a review of recent developments", Wear 184, 155-160 (1995) Chang, L.; Jackson, A,; Webster, M. N., "Effects of 3-D surface topography on the EHL film thickness and film breakdown", Tribology Transactions 37, 435444 (1994) Chang, L.; Webster, M. N.; Jackson, A,, "On the pressure rippling and roughness deformation in elastohydrodynamic lubrication of rough surfaces", Journal of Tribology, Transactions of the ASME 115,439-444 (1993) Chang, L. ; Zhao, W., "Fundamental differences between Newtonian and nonNewtonian micro-EHL results", Journal of Tribology, Transactions of the ASME 117,29-35 (1995) Chapman, R. J. and A. A. Rizkallah-Ellis, "Effect of the surface finish of brake rotors on the performance of brakes", Wear, 57, 345-356 (1979). Cheng, Y., Xie, Y., "Study of squeeze film between non-normal rough surfaces under partial hydrodynamic lubrication", Journal of Xi 'an Jiaotong University 26,59-65 (1992) Chivers, R. C. and Hunt, R. P., "The achievement of minimum leakage from elastomeric seals", 8th Znt. ConJ on Fluid Sealing, Paper 24 (BHRA, Cranfeld, 1978) Christensen, H. and Tonder, K., "The hydrodynamic lubrication of rough bearing surfaces of finite width", Trans. A.S.M.E. Ser.F. J.Lubr.Tech., 93, 324-330 (1971).

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Christensen, H., "A theory of mixed lubrication", Proc. I. Mech. E., 186, 421-430 (1972).

Christensen, H., "Nature of metallic contact in mixed lubrication", Proc. Instn.Mech. Engrs., 180, Pt.3B (1965/66) Christensen, H., Yome aspects of the functional influence of surface roughness in lubrication", Wear, 17, 149-162 (1971). Coy, J. J., S. M. Sidik, "Two-dimensional random surface model for asperity contact in elastohydrodynamic lubrication", Wear, 57, 293-3 11 (1979). Darbey, P. L.; Higginson, G. R.; Townend, D. J., "Lubrication of rough compliant solids", , Proc. 5th. Leeds-Lyon Trib. Symp. 398-403 (MEP. London, 1979) Denape, J.; Marzinotto, A,; Petit, J. A., "Roughness effect of silicon nitride slidmg on steel under boundary lubrication", Wear 159, 173-184 (1992) Denape, J.; Masri, T.; Petit, J.-A,, "Influence of surface roughness and oil ageing on various ceramic-steel contacts under boundary lubrication", Proc. I. Mech. E: J. Eng. Trib. 2095, 173-182 (1995) Eiss, N. S. and Warren, J. H., "The effect of surface finish on the friction and wear of PCTFE plastic on mild steel", S.M.E. Paper IQ75-125 (1975). Etsion, I.; Front, I., "Model for static sealing performance of end face seals", Tribology Transactions 37, 1 1 1-1 19 (1994) Fan, Y., Zheng, L., "A study on the limit criterion of full and partial lubrication", Wear 143,22 1-229 (199 1) Furey, M. J., "Surface roughness effects on metallic contact and friction", A.S.L.E.Trans., 6,49-59 (1963). Ghabrial, S. R. and Zaghlool, S. A,, "The effect of surface roughness on static friction", Int. J. Mach. Tool Des. Res., 14, 299-309 (1974). Golden, J. H., "The actual contact area of moving surfaces", Wear, 42, 157162 (1977). Gronqvist, R., Roine, J., Korhonen, E., Rahikainen, A,, "Slip resistance versus surface roughness of deck and other underfoot surfaces on ships", J. Occup. Accid. 13, 291-302 (1990) Harris, G. W. and Shaw, S. R., "Slip resistance of floors: users' opinions, Tortus instrument readings and roughness measurements", J. Occup. Accid. 9, 287-298 (1988) Hehn, A. H., "Effects of friction and wear on a sealing interface", Lubr. Engng. 26, 206-212 (1970). Hisakado, T., "Influence of surface roughness on friction and wear in boundary lubrication", J. Mech. Eng. Sci. 20,247-254 (1978).

24 1

Tribology

Home, L., "Correlation of rotary shaft radial lip seal service reliability and pumping ability to wear track roughness and microasperity formation", SAE Trans. 100,620-627 (1991) Huang, P.; Wen, S. Z., "Sectional microelastohydrodynamic lubrication", Journal ofTribology, Transactions of the ASME 115, 148-151 (1993) Hughes, W. F., "A cell theory of rough surface lubrication", Wear, 67, 31-53 (1981). Ishibashi, A., Sonoda, K., "Mirrorlike finishing of precision rollers and changes on the roller surfaces caused by loaded running", JSME International Journal, Series 3 35,286-293 (1992) Johnson, K. L., Contact mechanics (Cambridge University Press, London, 1985). Johnson, K. L., Greenwood, J. A. and Poon, S. Y., "A simple theory of asperity contact in elastohydrodynamiclubrication", Wear, 19, 91-108 (1972). Jung, K. and Riediger, G., "Recent developments regarding the inspection of non-slip floor coverings", Die Berufgenossenschaft 6,l-7 (1982) Kaneta, M.; Cameron, A., "Effects of asperities in elastohydrodynamic lubrication", ASME Papern 79-Lub-6 (1979). Kaneta, M., "Effects of surface roughness in elastohydrodynamic lubrication", JSME International Journal, Series 3: 35,535-546 (1992) Kang, S. C., and Ludema, K. C., "The breaking-in of lubricated surfaces", Wear 108,375-384 (1986) Kapoor, A.; Williams, J. A.; Johnson, K. L., Steady state sliding of rough surfaces", Wear 175,81-92 (1994) Karami; G., H. P. Evans and R. W. Snide, "Elastohydrodynamic lubrication of circumferentially finished rollers having sinusoidal roughness." Proc. I. Mech. E. Part C, Mechanical Engineering Science, 201,29-36, (1987) Kazamaki, T., "An investigation of air leakage between contact surfaces. (3rd report, in which iron and brass were used as specimen)", Bull. J.S.M.E., 17, 1321-1331 (1974). King, T. G., Watson, W., Stout, K. J., "Modelling the microgeometry of lubricated wear", Proc. 4th. Leeds-Lyon Symp., 333-343 (MEP, London, 1978) Koura, M. M., "The effect of surface texture on friction mechanisms", Wear, 63, 1-12 (1980). Koura, M. M. and M. A. Omar, "The effect of surface parameters on friction", Wear, 73, 235-246 (1981) Kumar, S., "Stochastic models with variable viscosity for hydrodynamic lubrication of rough surfaces", Wear, 62, 329-336 (1980). 'I

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Kweh; C. C., H. P. Evans and R. W. Snidle, "Micro-elastohydrodynamlc lubrication of an elliptical contact with transverse and three-dimensional sinusoidal roughness." Journal of Tribology, 111,577-584, (1989) Kweh, C. C., Patching, M. J., Evans, H. P. and Snidle, R. W., "Simulation of elastohydrodynamic contacts between rough surfaces", J. Trib., ASME, 114, 412419 (1992) Leaver, R. H., Sayles, R. S. and Thomas, T. R., "Mixed lubrication and surface topography of rolling contacts", Proc. I. Mech. E., 188,461-469 (1974). Lee, S. C., and Ren, N., "Behavior of elastic-plastic rough surface contacts as affected by surface topography, load, and material hardness", Trib. Trans. 39, 6774 (1996) Liu, K., Liu, X. J., Xie, Y. B., "Definition of the transition from fluid lubrication to mixed lubrication for rough surface", Lubrication Science 8, 287-295 (1996) Lloyd, D. G., and Stevenson, M. G., "An investigation of floor surface profile characteristics that will reduce the incidence of slips and falls", Mech. Eng. Trans: Inst. Engrs. Australia ME17, 99-105 (1992) Lubrecht; A. A., W. E. ten Nape1 and R. Bosma, "The influence of longitudinal and transverse roughness on the elastohydrodynamic lubrication of circular contacts."Journal of Tribology, 110, 421-426, (1988) Lucas, V., Bonneau, O., Frene, J., "Roughness influence on turbulent flow through annular seals including inertia effects", ASME Paper 95-TRIB-11 (1995) Lucas, V., Danaila, S., BOMeaU, O., Frene, J., "Roughness influence on turbulent flow through annular seals", Journal of Tribology, Transactions of the ASME 116,321-329 (1994) Manning, D. P., Jones, C., Bruce, M., "A method of ranking the grip of industrial footwear on water wet, oily and icy surfaces", Safety Science 14, 1-12 (1991) Marcus, A. H., "Statistical model of a flooded random surface and applications to lunar terrain", J. Geophysical Rex, 72, 1721-1726 (1967). Matsuzaki, Y., Funabashi, K., Hosokawa, K., "Effect of surface roughness on contact pressure of static seals. (Effect of tangential force on conical inside-seal surface)", JSME International Journal, Series 3: 36, 119-124 (1993) Matsuzaki, Y., Hosokawa, K., Funabashi, K., "Effect of surface roughness on contact pressure of static seals", JSME International Journal, Series 3: 35,470-476 (1992)

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Merriman, T. and J. Kannel, "Analysis of the role of surface roughness on contact stresses between elastic cylinders with and without soft surface coating. " Journal ofTribology, 111, 87-94, (1989) Mitchell, L. A. and Rowe, M. D., "An assessment of face seal performance based on the parameters of a statistical representation of surface roughness", Proc. I. Mech. E., 182, Part 3K, 101-107 (1967/68). Moalic; H., J. A. Fitzpatrick and A. A. Torrance, "A spectral approach to the analysis of rough surfaces", Journal of Tribology, 111, 359-363 (1989) Myers, N. O., "Characterization of surface roughness". W7ear, 5 , 182-189 (1962). Nakahara, T., M. Takesue and H. Aoki, "Effects of surface roughness and bearing slenderness ratio on hydrodynamic lubrication." Journal JSLE Int Ed, No.5, 65-70, (1984) Nivatvongs, K., Cheng, H. S., Ovaert, T. C. and Wilson, W. R. D., "Influence of surface topography on low-speed asperity lubrication breakdown and scuffing", Wear, 143, 137-148 (1991) Ogilvy, J. A,, "Predicting the friction and durability of MoS2 coatings using a numerical contact model", Wear 160,171-180 (1993) Ogilvy, J. A,, "Numerical simulation of friction between contacting rough surfaces", Journal of Physics D (Applied Physics) 24, 2098-2 109 (1991) Ostvik, R. and Christensen, H., "Changes in surface topography with running-in", Proc. I. Mech. E., 183, part 3P, 57-65 (1968/69). Otto, D. L., "Triangular asperities control seal leakage and lubrication", S.A.E. Paper No. 740201, (1974). Patir, M., Cheng, H. S., "Application of average flow model to lubrication between rough sliding surfaces", J. Lubr. Technol. Trans. ASUE 101, 220-230 (1979). Peeken, H.; Ayanoglu, P.; Knoll, G.; Welsch, G., "Measurement of lubricating film thickness, temperature and pressure in gear contacts with surface topography as a parameter", Lubrication Science 3, 33-42 (1990) Poon, C. Y., and Bhushan, B., "Numerical contact and stiction analyses of Gaussian isotropic surfaces for magnetic head slideddisk contact", Wear 202, 6882 (1996) Poon, C. Y., and Bhushan, B., "Nano-asperity contact analysis and surface optimisation for magnetic head slideddisk contact", Wear 202, 83-98 (1996) Prakash, J.; Tonder, K.; Christensen, H., "Micropolarity roughness interaction in hydrodynamic lubrication", ASME Paper 79-Lub-8 (1979).

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Proctor, T. D., "Slipping accidents in Great Britain - an update", Safety Science 16, 367-377 (1993) Proctor, T. D., and Coleman, V., "Slipping, tripping and falling accidents in Great Britain - present and future", J. Occup. Accid. 9, 269-285 (1988) Fbdhakrishnan, V., "The application of correlation functions in wear measurements", Wear 41, 169-177 (1977). Rao, A. Ramamohana; Mohanram, P. V., "Study of mixed lubrication parameters of journal bearings", Wear 160, 111-118 (1993) Rosen, B.-G., R. Ohlsson and T. R. Thomas, "Nano metrology of cylinder bore wear", Trans. 7th. Int. ConJ On Metrology & Properties of Engng Surfaces, 102-110 (Goteborg, 1997) Roth, A., "The interface-contact vacuum sealing processes", J. Vacuum Sci. & Technol. 9, 14-23 (1971). Roth, A,, Vacuum sealing techniques (Pergamon, Oxford, 1966) Sadeghi, F. and P. C. Sui, "Compressible elastohydrodynamlc lubrication of rough surfaces." Journal of Tribology, 111, 56-62, (1989) Shukla, J. B. and S. Kumar, "Effects of viscosity variation and surface roughness in the lubrication of a slider bearing", Wear, 52, 235-242 (1979) Sinha; P., J. S. Kennedy and C. M. Rodkiewicz, "Effects of surface roughness- and additives in lubrication: generalised Reynolds equation and its application to elastohydrodynamic film." Proc. I. Mech. E. Part C, Mech. Eng. Sci., 201, 1-9, (1987) Sugimara, J., and Yamamoto, Y., "Hydrodynamic lubrication of self-affhe fractal surfaces", Trans. JSME 61C, 475 1-4756 (1 995) Summers-Smith, D., An introduction to tribology in industry (Machinery Publishing Co., London, 1969) Tallian, T. E., McCool, J. I. and Sibley, L. B., "Partial elastohydrodynamic lubrication in rolling contact", Proc. I. Mech. E., 180, Part 3 8 , 169-84 (1965/66). Taneeranonon, P. and W. 0. Yandell, "Microtexture roughness effect on predicted road-tyre friction in wet conditions", Wear, 69, 321-337( 1981). Thomas, T. R., "Computer simulation of wear", Wear, 22, 83-90 (1972). Thomas, T. R., "The characterisation of changes in surface topography during running-in", Proc. 4th Leeds-Lyon Symp., 99-108 (MEP, London, 1978) Thomas, T. R., Holmes, C. F., McAdams, H. T. and Bernard, J. C., "Surface features influencing the effectiveness of lip seals: a pattern - recognition approach", S.M.E. Paper 1475-128 (1975a).

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Thomas, T. R., Holmes, C. F., McAdams, H. T. andBernard, J. C., "Surface microgeometry of lip seals related to their performance", Proc. 7th. Int. Con$ on Fluid Sealing, Paper J32 (BHRA,Cranfield, 1975b) Tonder, K. and Christensen, H., "Waviness and roughness in hydrodynamic lubrication", Proc. I. Mech. E., 186, 807-812 (1972). Tonder, K., "Effects of skew unidirectional striated roughness on hydrodynamic lubrication. Part 2- Moving roughness." Journal of Tribology, 109, 671-678, (1987) Tonder, K., "Numerical investigation of the lubrication of doubly periodic unit roughness", Wear, 64, 1-14 (1 980). Tzeng, S. T. and Saibel, E., "Surface roughness effect on slider bearing lubrication", A.S.L.E. Trans., 10,334-338 (1967) Van Bavel, P. G. M.; Ruijl, T. A. M.; Van Leeuwen, H. J.; Muijdennan, E. A., "Upstream pumping of radial lip seals by tangentially deforming, rough seal surfaces", ASME Paper 95-TRIB-13 (1995) Wakuri, Y., Hamatake, T., Soejima, M., Kitahara, T., "Study on the mixed lubrication of piston rings in internal combustion engine", Nippon Kikai Gakkai Ronbunshu, 61C, 1123-1128(1995) Wallach, J., Hawley, J. K., Moore, H. B., Rathben, F. V. and Gitzendanner, L. G., "Calculation of leakage between metallic sealing surfaces", A.S.M.E. Paper 68-LUB-15, (1968). Warren; W. E., J. G. Curro and D. E. Amos, "On the nature of O-rings in contact with rough surfaces. Journal ofTribology, 110,632-637, (1988) Willn, J. E., "Characterisation of cylinder bore surface finish - A review of profile analysis", Wear, 19, 143-62 (1972). Yanagisawa, T., Sanada, M., Koga, T., Hirabayashi, H., "Influence of designing factors on the sealing performance of C-seal", ME Trans. 100, 651-657 (1991) Yu, M. M., and Bhushan, B., "Contact analysis of threedmensional rough surfaces under frictionless and frictional contact", Wear 200,265-280 (1996) Is

CHAPTER 12

SOME OTHER APPLICATIONS

So far we have had the opportunity to discuss the application of surface roughness studies to contact mechanics in some detail, and we have also been able to outline briefly some of the more important areas of application in tribology. Regrettably, it is not possible within the scope of tlus book to cover the whole range of the other engineering and scientific effects of roughness. In this concluding chapter we will select a few of these applications, chosen at least partly to illustrate our earlier arguments about functional filtering. Contact resistance is interesting to electrical engineers and also important in heat transfer studies. The effect of roughness on fluid flow is appreciated in many technical fields, from aero- and hydrodynamics to chemical engineering, and also to workers in the earth sciences. Machining problems are the domain of manufacturing and production engineers, and Qmension and tolerance are also important to quality control personnel and inspectors. Finally we conclude by touching briefly on two topics of interest to their eponymous communities, bioengineering and geomorphology.

12.1. Contact Resistance

In many engineering applications involving contact it is sufTicient to know the real contact area. However, an important practical class of problems where a more detailed knowledge is necessary is that of thermal or electrical contact resistance. When two surfaces are in contact and electricity or conductive heat passes between them, it does so through the discrete areas of contact. The lines of equal potential, parallel at a distance from the interface, become increasingly distorted as the contact zone is approached, and the flow lines bunch together to pass through the individual contacts (Fig. 12.1). Holm (1958) has shown that the conductance of a single contact spot is proportional not to its area but to its radius. The conductance per unit nominal area of the interface is

c, = 2Kn t/a 247

(12.1)

248

Rough Sursaces

where a is the mean contact spot area, n is their number per unit area and K is the thermal or electrical conductivity. It is therefore necessary to determine the variation with load both of the number of contact spots and of their individual size.

Figurel2.1. Contact resistance due to constriction of flow lines

Electrical conductivity is of practical importance in the electronics and electrical power industries, and the effect of roughness has received some attention (Barkan & Tuohy 1965, Harada & Mano 1968, Hisakado 1977, Lanchon et al. 1986, Bryant 1994, Clausen & Leistiko 1995). The economic importance of thermal contact resistance is also considerable (Thomas & Probert 1972). In the form of the resistance between the fuel element and its container, it affects the economics of nuclear power (Boeschoten & van der Held 1$57, Tillack & Abelson 1995). In space technology also, the electronic equipment inside a satellite or space vehicle generates heat which can only be dissipated by solid conduction to the outside (Chung et al. 1993, Chung 1995, Chung & Shefield 1995). The property of the contiguous solids most difficult to define quantitatively is the topography of their contacting surfaces (Yip & Venart 1967/68, Cooper et al. 1969, Mikic 1974, Thomas 1982, Majumdar & Tien 1991, McWaid & Marschal 1992). Not only the surface roughness is involved but its waviness also, and a number of workers have considered the combined resistances of both (OCallaghan et al. 1989, Lambert & Fletcher 1995, Torii & Nishino 1995). It seems generally to be felt that the resistances are additive, so that the total resistance of the interface is the sum of a macroscopic resistance due to wavkiess and a microscopic resistance due to roughness. The microscopic resistance is due to the convergence of lines of flow through individual microscopic contact areas which are due to the

Other Applications

249

surface roughness. Clusters of these spots are held to be contained within larger macroscopic contour areas due to waviness. The effective of waviness on thermal contact resistance was investigated (Thomas & Sayles 1975) by considering the behaviour of the interface at very light loads W when it could be treated as a three-point Hertzian elastic contact. Here the high-pass cut-off was again a hnction of the diameter of the bar, and a low-pass cut-off was sought such that the enclosed bandwidth would contain only three asperities. This was found by substituting the appropriate asperity density into the integrated moment equation and solving the resulting transcendental equation iteratively. The strategy was as follows. One starts by assuming a form for the spectrum of wavelengths and goes on to define a pass-band representing waviness. The long-wavelength limit of this band must be set by the size A of the nominal contact area; the low-pass cut-off is found in terms of the contact size from the initial contour area density. Knowledge of the bandwidth permits calculation of the mean height and radius of curvature of the contacting asperities. The usual Hertzian formula will then give the area of real contact in terms of the nominal contact size and the total roughness at that size. This total roughness may be found from the measured roughness, leading to a figure of merit, sensitive to the effect of waviness on resistance, which is a function of readily measurable parameters.

Figure 12.2. Thermal contact resistance:experimental results of Fried (1965) replotted as a fhnction of waviness number 1. Its predictions are qualitatively reasonable; for a high load on a small smooth contact of low Hertzian modulus, jwill be large and the waviness will flatten to let the microscopic resistance predominate; for a low load on a large rough contact of high elastic modulus, cwill be small and the macroscopic resistance will predominate. One set of experimental results replotted in terms of waviness number can be seen in Fig. 12.2. The sharp dog-leg indicating a change of regime occurs near 500 m)(BS 4500: 1969); solid line: I = 0.4 + $10" x D ) (Sayles &Thomas 1978)

From a production engineering point of view the fractal relationship can be considered at two different levels. Firstly it gives us an insight into the way in which the increase in tolerance is linked to size; an empirical fact whch has long been established and taken for granted. Secondly, and on a more practical level, it can provide the production engineer with a means of monitoring the condition of a machine. We know that machines producing the same components can generate differing values of fractal parameters, a good measure of machine condition and environment. We have shown how the fractal parameters can be related to a class of tolerance; thus it seems possible to classlfy a machme quality in terms of its

257

Other Applications

ability to produce components within a given tolerance grade. Periodic checks on the fractal parameters of surfaces being produced would also act as a good indication of the potential useful life of the machine.

12.5. Abrasive Machining

Ground surfaces have a welldefined lay owing to the parallel orientation of grinding scratches, which are much longer in the direction of rotation of the grinding wheel than they are wide. It is of interest in the study of grinding processes to determine the average dimensions of a grinding scratch. Thts is not readily done by direct observation, as the scratches are superimposed on each other to a confusing degree. A possible solution is to examine profiles taken at various angles to the lay; it can plausibly be shown that the correlation length should represent the average dimension of a scratch in that direction (Fig. 12.6). There can be seen a marked peak in the direction of the lay; the average length and breadth of a grinding scratch in this case were deduced a$ 252 pm and 34 pm respectively (Thomas 1973b).

E

0

0

120 '

0

0

3 IOU

'B 000

0

I

I

80

I

I

7 0 6 0

I

1

5 0 4 0

I

M

I 20

I 10

I

I

0 - 1 0

Angle to lay (degrees) Figure 12.6.Correlation length as a function of angle of stylus traverse kom the lay of a ground surface (Thomas1973b)

The height distribution of a ground surface is often cited as Gaussian and a practical example of the central limit theorem. However, Sayles & Thomas (1979) found a highly sigruficant negative skewness in samples of several hundred thousand height readings from a number of ground surfaces (Fig. 7.11). The

258

Rough Sur$aces

distributions were truncated at their upper ends, in effect possessing fewer high peaks than a normal distribution. A study of the literature revealed that a similar skewness is in fact almost always present in height distributions from simple abrasive processes, and is often present to a lesser extent in ground surfaces. Kapteyn (as quoted in Hald 1960) developed a statistical theory of skew distributions in terms of a function which can be interpreted as the effect of the abrasion or grinding mechanism at the interface. This mechanism has been the subject of much dxussion, but it has generally been established that a combination of conventional cutting, ploughing and plastic deformation exists. Such a mechanism suggests that the geometry of the abrasive surface imposes itself on the machined surface, irrespective of the metal removal or deformation mechanism involved at each individual grain. If this is so, then where light cuts are involved and several passes are made without increasing the feed, Kapteyn's theory would predict a Gaussian height distribution; conversely, with heavy cuts and single passes a truncated distribution would result. Distributions of both types are reported in the litenture; it is suggested, however, that the strict Gaussian distribution, heretofore accepted as the norm, is an artefact of the care taken to obtain a specimen, and that on the production line, where single-pass and plunge grinding are extensively employed, the height distributions created on many engineering components are negatively skewed. If so, this may have important practical implications: for instance, the degree of truncation of the height distribution has been found to influence the running-in of cylinder bores (Campbell 1972), and it might also be supposed that in a seal with a ground surface the sealing action would be affected by the number of high peaks on the surface. A detailed theoretical consideration of the grinding process (Sayles & Thomas 1976b) enabled a prediction of an effective height distribution for a grinding wheel which showed a strong positive skewness. This will produce its mirror image, a negatively skewed height dwtribution, on the ground surface. The exact form of the distribution depends on the number of effective profiles n on the grinding wheel which intersect with the surface; for small n the distribution is closely Gaussian, but becomes increasing skewed as n increases (Fig. 12.7a). The parameter n is a function of wheel and work speed, number of passes and wheel specification; the ratio of workpiece roughness to grit size can thus be calculated explicitly (Fig. 12.7b). Roughness is approximately inversely proportional to the square of the logarithm of n, in accordance with everyday experience that changing to a finer wheel is an easier way to improve the finish than prolonged machining with a coarser wheel.

Other Applications

N

d

c,.

259

1.0 0.8

0.6 0.4

0.2 0.0

-3.0

-2.0

0.0

-1.0

1.0

2.0

3.0

0.4

5.0

z/R9

0.04

: : :

0.m 0.0010'

102

103

104

105

106

Figure 12.7.(above) Height distributionsofthe envelopes of n effective abrasive profiles, assuming a normal distribution for a single profile; (below) variation of workpiece roughness, normalised with respect to grain size r, with number of effective abrasiveprofiles: circles are experimental, solid line is theory (Sayles & Thomas 1976b)

12.6. Bioengineering

In human joints the bone ends are separated by a soft porous tissue known as articular cartilage. The entire joint is enclosed in a sealed capsule containing a lubricating medium called synovial fluid (Fig. 12.8). Considered as a bearing, then, the joint behaves as two porous compliant surfaces backed by rigid solids and separated by a fluid. Roughness of artificial hip joints is known to be associate with increased wear perbyshire et al. 1994). The mechanism of lubrication of this bearing is far from clear, but its roughness is believed to be an important factor (Tandon & Rakesh 1981).

Rough Sur$aces

260

Hydrodynamic, elastohydrodynamic and boundary regimes have all been postulated, but there are experimental objections to all of them. One theory of "boosted lubrication" (Longfield et al. 1969) relied on the observation that articular cartilage is rough. It was suggested that lubrication under light or moderate loads is normally hydrodynamic. Under high-impact loads, as when walking or jumping, the sudden approach of the surfaces squeezes the watery components of the synovial fluid into the pores of the cartilage. The larger molecules which are left are trapped in the pools formed by the interlocking asperities and act as a boundary lubricant

Spmd membne Artmrlar cartilage

Bone

Figure 12.8. Schematic of a human joint (Longtield et al. 1969)

The problem of direct measurement of a yielding surface with a stylus instrument was discussed in Section 2.3.3. It turns out that the surface is highly irregular and that the distribution of heights is quite closely Gaussian (Fig. 12.9). A hip joint is basically a ball-and-socket joint in engineering terms, and calculations can be carried out on it in exactly the same way as for other engineering contacts (Thomas et al. 1980). Assuming a 40 mm diameter for the femoral head the high-pass cut-off becomes 20 mm and from the cartilage measurements the effective roughness was 20 pm. The plasticity approach gave a low-pass cut-off of 4.1 pm. It is of some medical interest to know the configuration of the joint under a high transient load, for instance at heel-strike in the normal walking cycle. This can be deduced in some detail from the surface measurements and material properties, using now the elastic theory of Eqns. 10.1410.16 which requires only the first two even moments of the profile power spectrum-

Other Applications

26 1

It turns out that the real area of elastic contact calculated under these conditions is 104 mm2, the mean plane separation is 58 pm, the real contact pressure is 24 N/mm2 and the stlffness is 185 kN/mm, more than two orders of magmtude less than that of the machine-tool interface quoted previously. None of these predictions is in serious conflict with existing experimental measurements. The volume enclosed between the cartilage surfaces at heel strike can be calculated to be about two-thirds of the volume when standing still, thus lending support to the theory of boosted lubrication of human joints.

lo p m

I

H I mm

Height above mean line ( g m ) Figure 12.9. (a) Profile of surface of human articularcartilage: (b) distribution of profile heights; broken line is Gaussian distribution with the same standard deviation (Thomas et al. 1980)

Roughness also affects the assimilation to the body of surgical implants and prostheses of various kinds. Where these are inserted into bone, it is essential that the bond between the implant and the living tissue should possess mechanical strength. To ensure this, individual cells must adhere to the surface of the implant itself or to its fasteners, and the local roughness is an important determinant of this adhesion. Wennerberg (1996) reviews the extensive literature on the effects of implant roughness with more than 200 references.

12.7. Geomorphometry

Geomorphometry has been defined as the science which treats of the geometry of landscape, and plays a vital role in both military and civil engineering (Bekker

262

Rough Su$aces

1969, Mitchell 1991). Geomorphometry is a recognized sub-field within geology, geography, geomorphology, hydrology and digital cartography (Thorn 1988, Richards 1990, Clarke 1990). Its specific applications range from measuring highway roughness (Hegmon 1979, Xu et al. 1992, al-Mansour et al. 1994), mapping sea-floor terrain (Hennings et al. 1994), and assessing soil erosion (Hagen & Armbrust 1992, 1994, Govindaraju & Kawas 1994) to meteorology (Wieringa 1992, Roberts et al. 1994, Hignett & Hopwood 1994), and analysing wildfire propagation (Kasischke et al. 1994). Recent technical advances have presented information on geographical relief as Cartesian data sets similar to those acquired by scanning microscopes and similar instruments, though of course on a much larger scale. Such data sets are referred to in the literature as digital elevation models OEMs). The field is reviewed by Plke (1995a), who has also published a bibliography of the geomorphometric literature (Pike 1993) which with supplements (Pike 1995b, 1996) runs to more than 3000 entries.

PUR 10 1

0

I 0

50

100 150 Roughness (dkm)

200

Figurel2.10. Ride quality (Pavement User Rating) as a function ofzero crossing density (Potter et al. 1992)

The measurement of terrain roughness is an essential preliminary to the study of vehicle dynamics (Van Deusen 1967). Levels of vibration in truck shipments (Marcondes & Singh 1992), dynamic pavement loadings (Gyenes et al. 1992, Lin et al. 1994) and bridge loadings (Hung et a1 1992) can be predicted from road roughness. Subjective perception of ride quality also appears to depend on pavement roughness (Potter et al. 1992, Gerardi & Schmerl 1995); comfort decreases as the average wavelength shortens (Fig. 12.10). Wambold & Henry (1982) review techniques for measuring road roughness with nearly 40 references.

Other Applications

263

12.8. References Ananthapadmanaban, T. and Radhakrishnan, V., "An investigation on the role of surface irregularities in the noise spectrum of rolling and sliding contacts", Wear 83, 399-409 (1982) Aziz, S. M. A,; Seireg, A,, "Parametric study of frictional noise in gears", Wear 176,2528 (1994) Barkan, P. and Tuohy, E. J., "A contact resistance theory for rough hemispherical silver contacts in air and in vacuum", Trans. I.E.E.E. PAS-84, 1132-1143 (1965). Bauer, T. W., Taylor, S. K., Jiang, M., Medendorp, S. V., "An indirect comparison of third-body wear in retrieved hydroxyapatite-coated, porous and cemented femoral components", Clinical Orthopaedics & Related Research 298, 11-18 (1994) Bekker, M. O., Introduction to Terrain-Vehicle Systems (Univ. Michigan Press, Ann Arbor. 1969) Ber, A. and Yarnitzky, Y., "Functional relationship between tolerances and surface finish", Microtecnic, 22, 449-45 1 (1968). Boeschoten, F. and Van der Held, E. F. M., "The thermal conductance of contacts between aluminium and other metals", Physica 23, 37-44 (1957) Bryan, J. and Lindberg, E., "Relationship of surface finish to dimensional tolerance", Proc. Int. Con$ on Surface Technol., Pittsburgh, 117-130, (S.M.E., 1973). Bryant, M. D., "Resistance buildup in electrical connectors due to fretting corrosion of rough surfaces", IEEE Transactions on Components, Packaging, and Manufacturing Technology 17A, 86-95 (1994) Campbell, J. C., "Cylinder bore surface roughness in internal combustion engines: its appreciation and control", Wear, 19, 163-168 (1972). Chaplin, P. D., "The analysis of hull surface roughness records", European Shipbuilding, 16, 40-47 (1967). Chung, K. C.; SheEeld, J. W.; Sauer, H. J. Jr.,; O'Keefe, T. J.; Williams, A,, "Thermal contact conductance of a phase-mixed coating layer by transitional buffering interface", Journal of Thermophysics and Hear Transfer 7, 326-333 (1993) Chung, K. -C., "Experimental study on the effect of metallic-coated junctions on thermal contact conductance", JSME International Journal, Series B: Fluids and Thermal Engineering 38, 100-107 (1995)

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Chung, K.-C., Sheffield, J. W., "Enhancement of thermal contact conductance of coated junctions", Journal of Thermophysics and Heat Transfer 9, 329-334 (1995) Clausen, T., Leistiko, O., "Surface roughness and specific contact resistance of AuGeNflnP ohmic contacts", Materials Research Society Symposium Proceedings 355,389-394 (Materials Research Society, Pittsburgh, 1995) Cooper, M. G., Mikic, B. B., and Yovanovich, M. H., "Thermal contact conductance", Int. J. Heat Mass Transfer 12, 279-300 (1969). Derbyshire, B.; Fisher, J.; Dowson, D.; Hardaker, C.; Brummitt, K., "Comparative study of the wear of UHMWPE with zirconia ceramic and stainless steel femoral heads in artificial hip joints", Medical Engineering & Physics 16, 229-236 (1994) Dowson, D., El-Hady Diab, M M., Gillis, B. J., Atkinson, J. R., %fluence of counterface topography on the wear of ultra high molecular weight polyethylene under wet or dry conditions", in Lee ed., Polymer wear and its control 171-187 (Amer. Chem. Soc.,St. Louis, 1985) Fried, E., "Study of interface thermal contact conductance", General Electric Co. Report 65SD4395 (1965) Gerardi, T., Schmerl, H., "Ride quality as a part of airport pavement management systems", Transportation Congress, Proceedings 1, 588-599 (ASCE, New York, 1995) Gray, G. G. and Johnson, K. L., "The dynamic response of elastic bodies in rolling contact to random roughness of their surfaces", J. Sound & Vibration, 22, 323-42 (1972). Gyenes, L.; Mitchell, C. G. B.; Phlipps, S. D., "Dynamic pavement loads and tests of road-friendliness for heavy vehicle suspensions", SAE Technical Paper 922464 (1992) Hald, A., Statistical theory with engineering applications (Wiley, New York, 1960) Harada, S. and Mano, K., "The effects of surface roughness on contact resistance of sphere-plane contact", Proc. 4th Int. Res. Svmp. Electric Contact Phenomena, Chicago, 25-28 (Illinois Inst. of Technol., Chicago, 1968). Hess, D. P.; Soom, A,, "Normal vibrations and friction under harmonic loads. 11. Rough planar contacts", Transactions of the ASME. Journal of Tribology 113,87-92 (1991) Hisakado, T., "Effects of surface roughness and surface films on contact resistance", Wear, 4, 345-359 (1977). Holm, R., Electric contacts handbook 3e (Springer-Verlag, Berlin, 1958)

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265

Huang, D., Wang, T.-L., Shahawy, M., "Impact analysis of continuous multigirder bridges due to moving vehicles", Journal of Structural Engineering 118,3427-3443 (1992) Hunsaker, J. C. and Rightmire, B. G., Engineering applications of fluid mechanics (McGraw-Hill, New York, 1974) Kanai; H., M. Abe and K. Kido, "Estimation of the surface roughness on the race of bails of ball bearings of vibration analysis." Journal of Vibration, Acoustics, Stress, and Reliability in Design, 109,60-68 (1987) King, M. J., Chuah, K. B., Olszowski, S. T. and Thomas, T. R., "Roughness characteristics of plane surfaces based on velocity similarity laws", ASME Paper 81-FE-34 (1981) Lackenby, H., "The resistance of ships, with special reference to skin friction and surface condition", Proc. I. Mech. E., 176, 981-1014 (1962). Lambert, M.A.; Fletcher, L.S., Thermal contact conductance of nonflat, rough metals in vacuum", ASMEIJSME Thermal Engineering Joint Conference Proceedings 1, 3 1-42 (ASME, New York, 1995) Lanchon; H., B. Makaya; J. Saint Jean Paulin; E. Kroener and A. Mirgaux, "Mathematical study to obtain qualitative effects of roughness in technical problems." Wear, 109, 99-111, (1986) Lau, H. and Harman, C.M., "Externally pressurized compliant air bearing operating on a rough moving surface", Trans. A.S.M.E.,Ser. F., J. Lubr. Tech., 97, 63-68 (1975). Lin, W.-K., Chen, Y.-C., Kulakowski, B. T.; Streit, D. A., "Dynamic wheeVpavement force sensitivity to variations in heavy vehicle parameters, speed and road roughness", Heavy Vehicle Systems 1, 139-155 (1994) Lon@ield, M. D., Dowson, D., Walker, P. S., Wright, V., "Boosted lubrication of human joints by fluid enrichment and entrapment", Biomed. Engng. 4 , 5 17-522 (1969) Majumdar, A.; Tien, C. L., "Fractal network model for contact conductance", Transactions of the ASME. Journal ofHeat Transfer 113, 516-525 (1991) Marcondes, J., Singh, S. P., "Use of road roughness to predict vertical acceleration in truck shipments", Advances in Electronic Packaging 2, 999-1004 (ASME, New York, 1992) McWaid, T. H.; Marschall, E., "Application of the modified Greenwood and Williamson contact model for the prediction of thermal contact resistance", Wear 152,263-277 (1992)

266

Rough Surfaces

Mengen, D.; Weck, M., "How to ensure precise analysis of gear surfaces and diagnosis of changes during operation", Proc 92 Int Power Transm Gearing Conf DE43,605-612( ASME, New York, 1992) Mikic, B. B., "Thermal contact conductance: theoretical considerations", Int. J. HeatMass Transfer, 17,205-214 (1974). Nayak, P. R., "Contact vibrations", J. Sound & Vibration, 22, 297-322 (1972). O'Callaghan, P., Babus'Haq, R. and Probert, S., "Predictions of contact parameters for thermally-distorted pressed joints", Am. Inst. Aeron. & Astron., 24th Thermophysics Con$, Paper AIAA-89-1659 (1989) Osanna, H. P., "Surface roughness and size tolerance", Wear, 57, 227-236 (1979). Plke, R. J., A bibliography of geomorphometry, with a topical key to the literature and an introduction to the numerical characterization of topographic form. - U.S. Geol. Survey Open-file Rept. 93-262-A (1993) Pike, R. J., "Geomorphometry - progress, practice and prospect", in Pike & Dikau eds., Advances in geomorphometry, 2. Geomorph. Supplementband 101, 221-238 (1995a) Pike, R. J., A bibliography ofgeomorphometry, Supplement 1.0. - U.S. Geol. Survey Open-file Rept. 95-046 (1995b). Pike, R. J., A bibliography ofgeomorphometry, Supplement 2.0. - U.S. Geol. Survey Open-file Rept. 96-726 (1996). Poon, S. Y. and Wardle, F. P., "Running quality of rolling bearings assessed", Chartered Mechanical Engineer (April 1978) Potter, D., Hannay, R., Cairney, P., Makarov, A,, "Investigation of car users' perceptions of the ride quality of roads", Road and Transport Research 1, 6-27 (1992) Sayles, R. S. & S. Y. Poon, "Surface topography and rolling element vibration", Precis. Eng 3, 137-144 (1981). Sayles, R. S. and Thomas, T. R., "Thermal conductance of a rough elastic contact", Appl. Energy, 2, 249-267 (1976a) Sayles, R. S., Thomas, T. R., "Stochastic explanation of some structural properties of a ground surface", Int J Prod Res 14,64 1-655 (1976b) Sayles, R. S. and Thomas, T. R., "Surface topography as a nonstationary random process", Nature, 271,43 1-434 (1978) Sayles, R. S.; Thomas, T. R., "Measurements of the statistical microgeometry of engineering surfaces", J Lubr Techno1 TransASME 101,409-417 (1979).

Other Applications

267

Schlesinger, G. "Surface finish and the function of parts", Proc. I. Mech. E., 151, 153-158 (1944) Singh, K. and Lumley, J. L., "Effect of roughness on the velocity profile of a laminar boundary layer", Appl. Sci. Res. 24, 168-186 (1971). Strahler, A. N., "Quantitative geomorphology of drainage basins and channel networks", in: Chow, V. (ed.)Handbook of applied hydrology 4, 39-76 (McGrawHill, New York, 1964). Su, Y.-T.; Lin, M.-H.; Lee, M.-S., "Effects of surface irregularities on roller bearing vibrations", Journal of Sound and Ebration 165,455-466 (1993) Tandon, P. N. and L. Rakesh, "Effects of cartilage roughness on the lubrication of human joints", Wear, 70, 29-36 (1981). Thomas, T. R., "Influence of roughness on the deformation of metal surfaces in static contact", Proc. 6th Int. ConJ on Fluid Sealing, B3, 33-48 (BHRA, Cranfeld, 1973a). Thomas, T. R., "Correlation analysis of the structure of a ground surface", Proc. 13th Int. Machine Tool Des. &Re x Con$, Manchester, 303-308 (1973b). Thomas, T. R., "Defining the microtopography of surfaces in thermal contact", Wear 79, 73-82 (1982). Thomas, T. R. and Olszowski, S. T., "Theory, design and performance of a porous-diaphragm hoverpallet", Proc. 6th. Int Gas Bearing Symp. D6, 73-92 (BHRA, Cranfeld, 1974) Thomas, T. R. and Probert, S. D., "Thermal contact resistance: The directional effect and other problems", Int. J. Heat Mass Tran.sfir, 13, 789-807 (1970). Thomas, T. R. and Probert, S. D., "Correlations for thermal contact conductance in vacuo", Trans. Am. Soc. Mech. Engrs., 94C, 176-180 (1972) Thomas, T. R. and Sayles, R. S., "Random-process analysis of the effect of waviness on thermal contact resistance", A.I.A.A. Paper No. 74-691, (1974). Thomas, T. R., Sayles, R. S. and Haslock, I., "Human joint performance and the roughness of articular cartilage", Trans. Am. SOC.Mech. Engrs: J. Biomech. Eng., 1026,50-57 (1980) Thompson, D. J., "Wheel-rail noise generation, Part I: Introduction and interaction model", Journal of Sound and Vibration 161,387-400 (1993) Thompson, D. J., "Wheel-rail noise generation, Part V: Inclusion of wheel rotation", Jourvlal of Sound and Vibration 161,467-482 (1993) Tillack, M. S.; Abelson, R. D., "Interface conductance between roughened Be and steel under thermal deformation", Fusion Engineering and Design 27,232-239 (1995)

268

Rough Surfaces

Toni, K., Nishino, K., "Thermal contact resistance of wavy surfaces", Revista Brasileira de Ciencias Mecanicas 17,56-76 (1995) Van Deusen, B. D., "A statistical technique for the dynamic analysis of vehicles traversing rough yielding and non-yielding surfaces", NASA Report CR659 (1967). Wambold, J. C., and Henry, J. J., "Evaluation of pavement surface texture significance and measurement techniques", Wear 83, 351-368 (1982) Wennerberg, A., On surface roughness and implant incorporation, PhD thesis, Goteborg University (1996) Yhland, E., "Waviness measurement - an instrument for quality control in rolling bearing industry", Proc. I. Mech. E., 182, Part 3K, 438-445 (1967/68). Yip, F. C. and Venart, 3. E. S., "Surface topography effects in the estimation of thermal and electrical contact resistance", Proc. I. Mech. E., 182, Part 3K, 81-91 (1967/68).

INDEX

Abrasive composites, 15 Abrasive machining, 156 ACF. See autocorrelation function Acoustic interferometer, 84 speckle, 84 waves, 83,84 ACVF. See autocovariance fimction ADC.See analogue-todigital conversion Adhesive Giction, 225 AFM. See atomic force microscope Air bearings, 251 gap, 17 jet, 101 Aircraft, 1,43,44 engineers, 3 Aliasing, 115 Alignements, 2 Allison system, 136, 137 Amplifier, 14 Amplitude parameters, 1 33, 151, 161, 173,186 Analogue methods, 113 Analogue-todigital conversion, 1 13, 117 Angle of extinction, 47 Angular distribution, 47, 50, 5 1, 52 reflectance function, 103 uncertainties, 7 Anisotropy,48, 133, 169, 171, 177, 190, 1 92- 1 98 correction factor, 2 16 Anode, 17 Area of contact, 23 Area of real contact, 5 ARMA. See autoregressive movingaverage Armature, 17 Articular cartilage, 84,259-261,267

Asperities, 225,229,230,232,241,243. 251,260 collisions, 25 1 density, 74,229,249 Astigmatic focussing, 103 Asymmetry, 143 Atomic force microscope, 70 Autocollimation, 8, 39 Autocorrelation, 133, 151, 153, 155, 157, 161, 176-178 Autocovariance fimction, 153,235 Autofocussing, 65 Automobile brake linings, 226 Autoregressive moving-average, 156 Average slope, 50, 162 wavelength, 152, 170,227,262 Averaging circuitry, 20

Back-scattered electrons, 65 Backscattering, 83, 84, 85 Bad data, 95 Ball filter, 173 Ball-cage interaction, 25 1 Bandwidth, 181, 184,185,249 Beamsplitter, 40 Bearing area, 144, 145, 146, 153, 167, 176 Gaction, 144, 176 ratio, 144 Beta distribution, 143 Bifractal, 167, 168 Birmingham 14, 173, 174,177, 186 Boosted lubrication, 260,261 Boundary lubrication, 227,240 Boustrophedon scanning, 94 Breaking-in, 229,241 Bridge circuit, 17

269

270

Rough Surfaces

Bridge loadings, 262 Bulldozer, 24 Burnishing, 230,23 1

Calcium fluoride films, 65 Cali-block, 2 1,28, 34 Calibration, 28,29, 30, 32, 33, 133 specimens, 28,29, 33, 99, 106 Cantilever, 70 Cantor set, 11,25 Capacitance, 17, 66-68, 77,78, 85, 87, 88,100 Carbon replicas, 65 Carnac, 2 Carrier, 17, 19 Cartographers, 3 Cartridge, 16 Casting, 16, 167 Catchment areas, 194 Cathode ray tubes, 92 Causal filters, 119 Censoring, 233-235 Central limit theorem, 141 Characteristic depth, 129 Charge force microscope, 72 Charge-coupled diode, 45 Chart recorder, 19,22 Chatter, 167 Chemical balances, 9 Chisel-shaped stylus, 23 Circular lay, 190, 192 profiler, 44 Closed contours, 4, 5,6 Clusters of contacts, 249 Coefficient of variation, 133 Coherence radar, 46 Coherent light, 45, 50, 54, 57, 103 Compact disc player, 40 Compliant seal, 80 surfaces, 27,98,228,259 Compressible fluids, 8 1 Concrete surfaces, 84

Conductance, 247,250,263-267 Conducting probe, 68 Confocal microscope, 42 Constriction of flow lines, 248 Contact spots, 248 Contacting envelope, 2 1 Convolution, 118, 119, 161 Coordinate measuring machines, 8 Core fluid retention index, 176 Comer frequency, 167 Correlation length, 11, 133, 153, 159, 161, 174,257 Correlogram, 152, 170 Coulombic theory of friction, 225 Crankshaft, 97, 103, 107 Crops, 9, 10 Cross-correlation, 180,235 Cross-covariance function, 190 Crystal faces, 53 Cutoff, 74, 76, 79, 80, 83, 118-125, 130, 138,161, 183,184,231 cutting fluids, 100 speed, 102 Cylinder bores, 258

Damping effects, 70 Data acquisition, 94, 100 Datum, 16, 18,26,28 Default settings, 95 DEM. See digital elevation models Demodulation, 17 Density of extrema, 181 Dental cement, 98 Diamond styli, 15 Diamond-turned, 50,51, 57 Dielectric surfaces, 5 1 Differential thermocouple, 75 Diffracted radiation, 47 Diffuse reflection, 36, 39, 60 Digital cartography, 262 elevation models, 262 filter, 117

Index Dimensional tolerance, 255,263 Directional properties, 5 1, 188, 190 Discretisation, 113 Discriminant analysis, 235 Dry dock, 13 Dynamic range, 14,31 response, 24,31 stiffness, 16

Effective hardness, 8 profile, 2 1 Elastic contact, 250,261 Elastohydrodynamic lubrication, 228, 238-244 Elastomers, 27 Electrical contact resistance, 1,247,268 Electroforming, 99 Electromagnetic radiation, 35,46 Electron beam, 92-94 microscopy, 7,64, 86, 93, 97, 106 Electrostatic forces, 70 Ellipsometry, 53,60,61, 104, 106 Ensemble averaging, 161, 179 Entropy, 2 , 3 Error trap, 159 Errors of form, 39,94, 116, 125 E-system, 21, 125, 126, 131 Evaluation length, 18, 135, 138 Excel, 94 Extreme-value parameters, 133, 136, 137,139

Face turning, 190 Facets, 51 Fast Fourier transform, 160 Fatigue life, 228,238 Feed rate, 50 Feedback circuit, 70 Femoral head, 260,264 Fibre optics, 103, 105

27 1 Field coils, 65 Film-thwkness ratio, 229 Filtering, 116, 117, 121, 122, 126, 134, 159, 161, 170, 172, 176, 186, 197, 198,229,233 Finger, 11 Fingemail, 71, 73 Finite impulse response, 119 FIR. See finite impulse response Flagging, 95 Flash gun, 37 Flatness, 1, 100 F l e m i n g integrator, 11 Flexible diaphragm, 78 Floor surfaces, 227 Flow pressure, 23 Fluid dynamics, 162 Fluid flow, 247,25 1 Focus-detection, 40,41, 103 Footprint, 2,24, 92 Footwear, 227,242 Forest canopies, 9 Form error, 68 Formprofil, 125 Foucault knife-edge, 37 Fouling, 254 Fourier transform, 119, 121, 154, 160, 161 Fourier transforming lens, 52 Fractal, 162, 164, 165, 166, 167, 168, 169, 170, 185, 194, 195, 196,244, 256 dimension, 165 Fracture surfaces, 162, 168, 169 Fraunhofer diffraction, 103, 109, 110 Frequency response, 119, 121 Friction, 225-22'7,238-245,253,254, 264,265 Fringe-field technique, 66 Fringes, 45,46, 93 FSD. See full-scale deflection Fuel element, 248 Full-scale deflection, 114 Functional filtering, 3, 229 parameters, 176

272

Rough Surfaces

Gamma function, 164 Gauge block, 29, 133 Gauging nozzle, 8 1 Gaussian distribution, 114, 139-147, 157, 180, 183,234,254,261, filter, 123, 173 weighting function, 120 Gear contacts, 228,243 teeth, 97 General surface texture, 136 Geography, 262 Geology, 262 Geomorphology, 194,247,262,267 Geomorphometry, 261,266 Glass transition, 27,28 Glossmeter, 36,47,48, 91 Goodness-of-fit test, 142 Gramophone, 11 Grinding, 134, 142, 149, 169, 172, 195, 257,258 scratch, 257 wheel, 257,258 Gritblasting, 185, 194, 195 Ground glass, 56, 160 GST. See general surface texture

Hairbrush, 8 Half-width, 104, 105 Heavy electrical engineering, 3 Heel-strike, 260 Height distribution, 10, 133, 140-149, 155, 176,234,235,253,254,257, 258 Hemispherical parts, 105 Hertzian elastic modulus, 74 Heterodyne laser, 43 High-fidelity, 16 High-pass filter, 117, 118, 121, 130, 155,161 High-spot count, 151 spacing, 151

Highway roughness, 262 Hip joints, 259,264 Honing scratches, 195 Horizontal compression, 22 magnification, 19 range, 6 resolution, 14,65,69 Housing aligumnt, 251 HSC. See high-spot count H-system, 136 Hubble, 8, 10 Hull fnction, 1 Hiillprofl, 2 1, 125 Human teeth, 97 Huygen’s principle, 54 Hybrid parameters, 173, 175, 176 Hydrodynamic lubrication, 227,238-245 Hydrodynamicists, 3 Hydrology, 262,267 Hyperbola, 147, 167, 168 Hysteresis, 68

W. See infinite impulse response Image clarity, 47 Impact wear, 97,107 Implant, 261,268 Impulse response, 1 18, 1 19, 122 Inclined plane, 74 Indenter, 23 Index of refraction, 53 Inductance, 17,78 Infrared laser diode, 4 1 In-process measurement, 100, 102, 103 Inspection, 16, 91, 100, 111, 172,241 Instrument performance, 6 , 7 reference plane, 7 Intensity equations, 45 signal, 65 Interferometry, 42-46, 91, 93, 94, 107, 108,111 Internal combustion engine, 4

Index

Interrupted finishes, 145 Inverse Fourier transform, 161 Isometric display, 94, 95

Kurtosis, 143, 173

Lambda ratio, 229 Lambert's law, 35 Laminar flow, 80 sublayer, 254,255 Landscape, 9 I , 166 Laser force microscope, 72 interferometer, 18 scanning analyser, 103, 104, 106 Lateral deflection, 24,25 resolution, 66,68,70,71, 84, 101 stiffness, 24, 33 Lathe, 255 bed, 16 saddle, 16 Leakage rate, 235 Length of traverse, 11 Leptokurtic, 143 Levelling, 16, 17 Light-section microscope, 36, 37, 125, 134 Linear discriminant functions, 237 Lip seals, 235,236,244,245 Log-normal distribution, 143 Long-crestedness, 192 Loudspeaker, 19 Low-pass filter, 66, 117, 118, 123, 194 LVDT. See linear variable differential transformer

Macroscopic resistance, 248,250 Magnetic force microscope, 72 Material ratio curve, 144

273 Mathernatica, 94

Matlab, 94 Mean absolute slope, 105, 158, 159 contact spot radius, 4, 5 hydraulic radius, 80 line crossing, 152 peak curvatwe, 157 peak height, 157,158,182 peak radius of curvature, 159 plane, 172, 176, 185,252,261 Mechanical noise, 68 vibrations, 14 Mecrin tester, 73 Megalithic, 2 Menhir, 2 Meteorology, 262 Method divergence, 123 MHR. See mean hydraulic radius Michelson interferometer, 44 Microdensitometer, 65, 88 Microscopic resistance, 248,250 Milling, 190, 193 Mireau interferometer, 45 Mixed lubrication, 227,229,239-245 Molten asphalt, 76 Molybdenum disulphide film, 226 Moment of distribution, 133, 140, 143, 155,162,183,249 Monochromatic illumination, 55 Motif analysis, 126, 130, 193 combination, 128, 129, 131 filter, 173 Moving-coil transducer, 17 MPRC. See mean peak radius of curvature M-system, 120, 125, 130 Multifractal, 166, 167 Multiprocess surface, 133, 145, 147

Nearest neighbows, 186, 187 Negative slopes, 19

274

Rough Surfaces

Nickel replicas, 100 Noise, 116, 156, 168,250,251,263,267 Nomarslu microscopy, 39 Nominal contact area, 74 Non-causal filters, 1 19 Non-contacting stylus, 37 Non-recursive filters, 119 Nonstationarity, 133 Nozzle cross-sections, 81 Nuclear power, 248 power stations, 1 Nyquist frequency, 1 15 sampling theorem, 1 15

Ocean surfaces, 180 waves, 43 Oil-droplet method, 83 On-the-fly sampling, 1 15 Operating envelope, 6, 7 Optical absorption microscope, 72 flat, 83, 94, 98 instruments, 9 lever, 11 path, 45,46,52,98,103 probe, 37-39 profilers, 37, 50 sections, 36 stylus, 40, 103, 108 Oscillator, 17 Oscilloscope, 19, 103, 104 Outflow meter, 80, 81, 85 Out-of-balance signal, 39,41

Paper tape, 74 Parameter rash, 133, 150 Partial EHL, 228 Pass-band, 155, 183 Pattern recognition, 128, 193 Pavement loadings, 262

roughness, 262 user rating, 262 PC. See phase-corrected filter Peak height, 73, 137,146,157,158,181 182 Peak-to-trough roughness, 227 Peak-to-valley height, 64, 74, 128, 129 Pendulum, 74 Perspective view, 94 Phase diirerence, 40,42,43, 54 distortion, 119, 120 lag, 27 shift, 43 Phase-corrected filter, 120, 130 Phonograph, 11, 15, 16 Photodetector, 103 Photographic film, 52 Photographic negative, 37 Photon scanning tunnelling microscope, 72 Photoresistors, 39 Pickup, 14, 16, 18-20 Piezo drives, 68 Piezoelectric crystal, 16 transducer, 45 Pmhole, 42 Piston term, 172 Plaster of paris, 98 Plastic deformation, 258 Plateau honed surface, 95, 177, 178 Platykurtic, 143 Pneumatic gauging, 81,86, 89, 101, 108,253 profiler, 101 Poisson’s ratio, 9 Polar scans, 92 Polarization, 40,42, 43,47, 52, 54, 103 Polarizing interferometer, 42,43 Polygonal mirror, 103 Polynomial filter, 122 fitting, 172 Portable data format, 94 Positional error?, 93

Index

Positive replica, 98, 99 Power spectra, 11, 18,20,27, 51, 52, 99, 115, 117, 129, 130, 133, 153-155, 160, 163, 173, 177, 178, 182, 192, 231,233,235,250,254,255 Pressure transducers, 101 Pnmary standards, 4 Probability density, 140, 141, 155, 181, 182, 197 Production engineers, 3 Production time, 3 Profile curvature, 157,232 length ratio, 152 Profilometer, 13, 30, 32 Projector, 12 Prostheses, 261 PSDF. See power spectrum Pt, 134, 135, 148 PTB, 28,29 Pushrod, 15 F'yramid, 15

Quality control, 20, 100, 105, 145,238, 247, 268 system, 5 Quantisation, 113, 114, 137 Quantum tunnelling, 68

R3z, 136 Ru, 133, 138, 139, 143-149,230 Rru'Rq, 139 Radar engineers, 3 Railroad operation, 250 Raster scan, 68, 92, 93 Rayleigh distnbution, 143 Razor blade, 36,76 Real contact area, 4, 10 Reciprocating contact, 3 Recording barometer, 24 Recursive filters, 119

275 Reflected beam, 35,40,43, 54 Refractive index, 52, 98 Relocation, 24,27, 28, 96, 97 Rendering of image, 94 Replica, 52,98,99, 100, 108, 109, 110, 254 Repulsive forces, 70 Resolution, 4, 6, 8, 9 Resonances, 25 1 Reverse slopes, 24 Reynolds number, 253,254 &de quality, 262,264 Rk,145,146, 148,150 RI, 152 Rm,135 Road roughness, 225,262,265 Road surfaces, 77, 80 Rocker arm, 15 Roller burnishing, 230 Rolling ball, 173 bearings, 229,250,266 circle, 2 1 contact, 250,264 ellipse, 126 Rolling of sheet metal, 97 Roll-off, 118, 119, 121, 130 Rough pipe, 253 sliding, 228, 243 Roughness of floor surfa.:es, 227 regime, 51 standards, 5, 15,21, 28 Rp, 74,76,83, 135, 145, 146, 148 Rq, 138, 139, 142, 144, 145, 147, 158, 162,167,236 Running average, 123 Running-in, 96, 97, 106, 110,229, 230, 233,238,243,244 Rm-out, 19 Rvk, 145, 146, 148 Ry, 135,136 Rz, 136

276

Rough Surfaces

SAq, 174,175

Safety of floors, 227 Sample length, 121,122,135 Sampling, 113, 115, 135, 137, 152, 158, 159, 176, 183-187 interval, 1, 137, 158, 159, 183-185 Sand grain roughness, 253 Sand-patch, 76 Satellite, 1, 248 ranging techniques, 8 Sbi, 174, 176 scanning chemical potential microscope, 72 ion conductance microscope, 72 near-field acoustic microscope, 70 near-field optical microscope, 72 thermal profiler, 72 tunnelling microscope, 68, 72 Scattering, 46,84 Scattering, 84 angle, 51 theory, 46 Scatterometers, 36 Sci, 174, 176, 198 Scraping technique, 76 Scuffing, 229,243 Sds, 174, 182 Sea-floorterrain, 262 Seals, 235-251 Second law of thermodynamics, 2 Secondary electrons, 65 length standards, 4 Second-order effect, 3 Sectional measurement, 5 Seismograph, 14 Self-afine fractals, 117, 164, 165, 170 Self-similarity, 162 SEM. See scanning electron microscopy Separable filter, 173 Servo control, 68 Sewing needle, 15 Shakedown, 229 Shaping, 66, 190 Sharpest curvature, 6 Shps' hulls, 12, 97,254

Shock noise, 251 Shortest correlation length, 174 Shot-blasting, 141 Silicon wafers, 103 Sinusoidal surface, 6 , 7 Skewness, 143, 173, 177, 186,227,228, 238,257 Skid, 126 Skid, 16, 18,26-32, 126 Skin friction, 253 resistance, 79 Sliding contact, 97 Slip gauges, 4 Slope, 6,7,20,65,73,74,76,83, 104, 105, 123, 146, 149, 152, 158, 159, 162,164,166,175, 181, 182, 188, 225,226,229,232,255 distribution, 19 measurement, 39 Sm,151,155,169,170 Smoked-glass plate, 11 Smoothing, 118, 161 SNAM. See scanning near-field acoustic microscope Snell's law, 35 Soil erosion, 262 Sonar, 84 Space vehcle, 248 Spark erosion, 166 Spatial coherence, 55 Speckle, 47,54-59, 84, 85 contrast, 47, 54, 55 pattern decorrelation, 54,55 Specular reflection, 36, 37,47-50, 58, 84, 147 Speed of traverse, 19,24 Spherical contacts, 15 Spindle runout, 167 Spiral scans, 92 Spline filters, 123 Spot diameter, 103 Sq, 173,174,176,177,188 Stagnant-layer method, 83 Static friction, 73,74

Index

seals, 235,242,251 Stationarity, 116, 155, 161, 169, 180, 255 Std, 174 Stedman diagram, 7, 8, 37 Steepest slope, 6,65, 123, 159 Stereo pairs, 65 Stereophotogrammetry, 9 1 Stick-slip, 19 Stm,68 Str, 174, 196 Straddling skids, 16 Straightness, 1,2 Strain state, 53 Stratified surface, 145, 146, 148, 190, 195 Strong anisotropy, 192, 193,194 Structure h c t i o n , 155, 156, 164-169, 177,179,180 Stylus dimensions, 12, 14 geometry, 24,28 instrument, 4, 7, 9-21,28-32, 96-104, 167,227,260 load, 19,23,24 tip, 20,21,23,28 transducer, 14, 16 width, 66 S h t , 10, 142, 171-190, 197 definition, 186 Surface bearing index, 176 damage, 15,23,3 1 discontinuities, 41 slope, 182 vibration, 54, 105 Surgical implants, 26 1 Surveying, 91 Svi, 174, 176 Swad, 103 Switchgear, 1 Synovial fluid, 259,260

Tactile test, 71

277 Taper roller bearing, 23 1 sectioning, 63,64 Telemetry, 102 Television, 92 TEM. See transmission electron microscopy Temporal coherence, 55 Ten-point height, 136, 173, 174, 186 Terrain roughness, 262 Textile roughness, 37 Texture, 1, 3,6 aspect ratio, 174, 175, 192 direction, 174, 176, 177 Thermal comparator, 75, 76 conductance, 75 expansion effects, 255 noise, 14 resistance, 1 Thermoelectric, 72 Thetameter, 74, 75 Three-dimensional filtering, 171 Time series, 153, 161 Tip radius, 15,21 TIS. See total integrated scatter Tolerance, 255,256 Tool radius, 106 replacement, 100 Topothesy, 162, 164, 185, 194, 195 Total integrated scatter, 49, 57 T,’ 139, 144, 145 Traceability, 29, 32 Traceable uncertainty, 100 Traced profile, 20 Transducer, 113, 114 Transducer, 13-18,29, 32, 113, 114 Transition region, 254 Transitional topography, 235 Translation, 115, 125 speeds, 67,102 stage, 37,39 tables, 93 Transmission characteristic, 17

278

Rough Surfaces

coefficient, 1 18, I 19, 121 design, 251 Transmittance, 52,65 Transparent replica, 52 Traverse length, 19 Trend removal, 172, 182 Tribology, 225,244 Triode, 17 Truck shipments, 262,265 Tuning fork, 70 Tunnelling current, 68,69 Turbulent flow, 253 Tyre-road interactions, 1

Ultrasonic back-scattering, 102 Ultrasound, 84, 85,88 Uncertainty, 11, 133 Underwater surfaces, 84,97

Vacuum chamber, 69 seals, 235 Valley depth, 137,145,146 fluid retention index, 176 suppression filter, 122, 123 Van der waal's forces, 70 Vehicle dynamics, 262 Vertical range, 4, 9, 14, 37-46,65-69, 103 resolution, 14, 18, 3748, 64-69,74, 75, 82-84 scanning interferometry, 46 Vibration, 250,251,262-267 Vibrator, 29, 30 Video camera, 37 Viscosity, 81,238,241,244 Visibility of fringes, 46

Wall gauge, 12 Walsh functions, 155, 169

Watersheds, 194 Waviness, 12, 83, 103, 116, 125, 126, 130, 167, 170,248-251,267 number, 250 Weak anisotropy, 192, 193 Wear, 227-244,259,263,264 scars, 97 Weighting function, 66, 120-126 sequence, 1 19 terms, 117 Wheatstone bridge, 82, 89 White light, 40 Wiener-Khinclune relation, 154 Wildfire propagation, 262 Wire-frame view, 94 Wollaston prism, 39,43 Wood, 15, 17,24, 30, 31, 33 Wristwatch. 70

Zero crossing density, 262 Zonal filter, 173 Zoom, 94