Advanced Techniques for
Surface Topography
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Advanced Techniques for
Assessment Surface Topography Development of a Basis for 3D Surface Texture Standards "SURFSTAND"
edited by
Liam Blunt & Xiangqian Jiang
First published in Great Britain and the United States in 2003 by Kogan Page Science, an imprint of Kogan Page Limited Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licences issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned addresses: 120 Pentonville Road London N1 9JTM UK www.koganpagescience.com
22883 Quicksilver Drive Sterl ing VA 20166-2012 USA
© Kogan Page Limited and contributors, 2003 The right of Liam Blunt and Xiangqian Jiang to be identified as the editors of this work has been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. ISBN 1 90399611 2
British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library.
Library of Congress Cataloging-in-Publication Data Advanced techniques for assessment surface topography : development of a basis for 3D surface texture standards "surfstand" / edited by Liam Blunt and Xiangqian Jiang. p. cm. Includes bibliographical references and index. ISBN 1-903996-11-2 1. Surfaces (Technology)—Measurement. 2. Three-dimensional display systems. I. Blunt, L. (Liam) II. Jiang, Xiangqian. TA418.7.A4542003 620'.44--dc21
2003009012 Typeset by Kogan Page Printed and bound in Great Britain by Selwood Printing, West Sussex
Contents
1. Introduction: The History and Current State of 3D Surface Characterisation Liam Blunt
1
Part 1: Characterisation
15
2. Numerical Parameters for Characterisation of Topography Liam Blunt andXiangqian Jiang
17
3. Novel Areal Characterisation Techniques Paul J. Scott
43
4. Advanced Gaussian Filters Stefan Brinkman and Horst Bodschwinna
63
5. Multi-scalar Filtration Methodologies Xiangqian Jiang
91
Part 2: Instrumentation
117
6. Calibration Procedures for Stylus and Optical Instrumentation Jean Franqois Ville
119
7. Calibration Procedures for Atomic Force Microscopes Anders Ktihle
175
Part 3: Case Studies
195
8. The Interrelationship of 3D Surface Characterisation Techniques with Standardised 2D Techniques Robert Ohlsson, Bengt Goran Rosen and John Westberg
197
9. Applications of Numerical Parameters and Filtration Liam Blunt andXiangqian Jiang
221
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Advanced Techniques for Assessment Surface Topography
10. Functionality and Characterisation of Textured Sheet Steel Products Micheal Vermeulen and Henrik Hobleke
249
11. Characterisation of Automotive Engine Bore Performance using 3D Surface Metrology Stefan Brinkman and Horst Bodsckwinna
307
Part 4: Future Developments
323
12. Surface Texture Knowledge Support - ISM Robert Ohlsson and Bengt Goran Rosen
325
13. Future Developments in Surface Metrology Liam Blunt, Xiangqian Jiang and Paul J. Scott
339
Index
349
Acknowledgements
The editors would like to thank the following list of people: Peter Breger for keeping us on the straight and narrow, Professor Tom Thomas for his constant encouragement and friendship, Professor David Whitehouse's encouragement and friendship, Evaristus Mainsah and Weiping Dong for the groundwork, Professor Harry Trumphold's encouragement and friendly criticism, Dr Brian Griffiths for his encouragement and honest friendship, and a special mention to our colleagues at DFM for pulling out for us when we needed it most. The mysterious Mr Strobel "you know who you are", the directors and colleagues at Taylor Hobson for their support over recent years. The University of Huddersfield for provision of our wonderful facilities, a special mention must be made to our wonderful group: Dr Shaoujun Xiao, Dr Feng Xie, Miss Leigh Brown, and Miss Adelle Waterworth. Last and by no means least, a special mention to Professor Ken Stout who made all of our research possible, and in particular for his initiation, organisation strategic view and constant friendship over the years. Liam and Jane
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1 Introduction: The History and Current State of 3D Surface Characterisation Liam Blunt Taylor Hobson Professor of Surface Metrology, School of Engineering, University of Huddersfield, UK
1.1 Defining the nature of a surface An appropriate question at the beginning of a text like this might be "what is a surface? ". The answer to this question is not simple, though considering a surface as a boundary is a good start. Bearing this in mind, the surface of an engineering component can therefore be thought of as the physical boundary between the work piece and the surrounding environment. The real surface of a workpiece has been defined in international standards (ISO) as: A set of features which physically exist and separate the entire workpiece from the surrounding medium (ISO 14460-1) [1], It would be false to assume that the surface of a workpiece is invariably mechanical in nature. In fact the electromagnetic surface of a workpiece is an equally valid concept. The definitions ISO 16610-1, of both are rather cumbersome but are given below. Real surface of a workpiece (mechanical) Boundary of the erosion, by a spherical ball of radius r, of the locus of the centre of an ideal tactile sphere, also with radius r, rolled over the real surface of a workpiece. Real surface of a workpiece (electro-magnetic) Locus of the effective ideal reflection point of the real surface of a workpiece, by electromagnetic radiation with a specified wavelength. For most purposes, however, especially where the workpiece interacts with its working environment through some form of mechanical contact it is the mechanical surface that is of interest. This is the surface that is measured using standard surface metrology
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Advanced Techniques for Assessment Surface Topography
techniques and it is this surface that is referred to on engineering drawings of components to be manufactured. A further rhetorical question might be, why are we interested in surfaces? The clear reason is that it has been shown that 90% of all engineering component failures in practice are surface initiated, through mechanisms such as fatigue cracking, stress corrosion cracking, fretting wear, excessive abrasive or adhesive wear, corrosion, erosion etc. Clearly then, it is important to understand the properties of the surface and near surface zones of a component. These properties can be grouped together under the term surface integrity [2]. A glance at the nominal technical drawing of an engineering component clearly shows that the drawing assumes that each surface of the component is perfectly smooth, straight, clean and free from defects. There is an assumption that the manufacturing engineer can achieve this using the techniques at his disposal. This surface, the one assumed by the drawing is called the nominal surface. The manufacturing engineer now studies the drawing and attempts to manufacture the component to the specified dimensions within the tolerance limits. When manufacturing the component the engineer knows that it is impossible to manufacture a perfectly smooth surface, as the particular manufacturing method chosen will leave a micro-scale "fingerprint" on the surface which is unique to that manufacturing process. The nature of that "fingerprint" is referred to as the surface texture or surface topography of the component. Normally, this consists of a series of peaks and valleys that have characteristic shape size and spacing. As well as affecting the shape of the surface texture the manufacturing method chosen also affects the layers directly below the surface of the component. For example, if we take the machined surface of a metal such as steel and take a cross section through the surface we can see the surface is made up of a number of layers (Figure 1.1).
Figure 1.1 Schematic cross sectional view of a surface showing the surface and sub surface layers
Introduction
3
These layers consist of: • •
• • •
An oxide layer, which all metals possess, this layer being several nanometers thick. The topographic layer, the hills and valleys that make up the shape of the surface. These result from the material removal (or addition) process and are produced by the unit manufacturing process (tool passage, electrical discharge, plating process etc.). A plastically deformed layer produced by the machining operation. A metallurgically deformed layer resulting primarily from heating during machining. The bulk material.
Figure 1.2 Ground surface cross section a) abusively ground b) gently ground Figure 1.2 shows an example of a cross section through (a) an abusively ground steel surface, and (b) a gently ground steel surface. What is clear from the image is the distinct layering of the surface zone and also how the severity of the grinding operation has affected the surface layers and the surface roughness. Whilst the sub surface layers are critically important, they are very difficult to measure without destroying the component. Therefore engineers have concentrated on measuring the surface roughness as both a means of quality assurance and as a means of inferring functional performance. The geometrical form of any surface is usually referred to as the surface texture. Conventionally the texture is made up of features defined as roughness, waviness and form (Figure 1.3). Traditionally, when the surface texture is quantitatively measured it is only the roughness that is analysed and the waviness and form elements are mechanically, electrically or digitally filtered out from the recorded data.
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Figure 1.3 Roughness, waviness and form of an engineering surface [3]
The difference between the roughness, waviness and form characteristics of the surface texture is based on the surface wavelength or peak to peak spacing. The great problem with these conventional definitions is that the point at which roughness becomes waviness (cut off) is arbitrary and is usually related to the manufacturing process from which the surface derived or from the intended function of the workpiece. For example, what would be considered as roughness on an automobile axle would be considered waviness of form error on a watch spindle [3]. As a rule roughness can be considered as being produced by the method of manufacture rather than the machine, and constitutes tool or grit marks and is usually of a periodic nature. On a finer scale there is tearing of material, as a result of built up edge formation and tool tip irregularities. Waviness is usually attributed to an individual machine, for example an unbalanced grinding wheel, tool feed irregularities and general chatter vibrations. Form errors are usually caused by a lack of rigidity of the workpiece during the machining operation allowing it to flex or bend. Slide way undulation can also cause form error. Strains in the material, surface induced trough heating or excessive surface residual stress can cause flexure and form error. Usually, form errors produce only one or two undulations over the dimensions of the assessed surface.
1.2 Surface creation Surfaces are created by a large variety of manufacturing processes and each manufacturing technique leaves its own fingerprint on the surface produced. Sometimes, the fingerprint from a surface can produce a beneficial effect on the character of the surface but on other occasions the resulting surface can deleteriously affect the ability of the surface to perform its intended function. It is therefore important that the "fingerprint" which is produced as a result of any surface manufacturing method be understood in terms of its effect on the function for which the surface is intended. If the general nature of the surface is deemed unacceptable then a surface modification technique should be
Introduction
5
undertaken to modify its suitability for the intended function. In many cases it is not the inherent nature of the machining process that is at fault but the machining conditions under which the surface has been finished. As a consequence, modifying the parameters of the final process may yield a satisfactory result. This implies that the engineer must improve his understanding of surface production methods and the effects that these production methods may have on the functional properties of the surface. Many surfaces are designed to interact with other solids and as a consequence are sometimes subjected to surface treatments that alter the properties of the surface layers. The processes most often used are plating, blasting, peening, carburising, nitriding, ion implantation etc. these treatments produce the so-called "functional surfaces". The relationship between surface topography and the functional surface has only been partially investigated and the most work that has been conducted in this area was undertaken using 2D surface analysis, using profile analysis or through the application and interpretation of auto-correlation functions.
1.3 Evolution of assessment The earliest assessments of surface finish were made simply by running a fingernail across the surface. This technique survives to this day as tactile comparison, where the finish of the workpiece is compared manually with a set of calibrated surfaces of different known roughnesses produced by the same finishing process [4]. The first quantitative measuring instrument was the light-section microscope, developed by Gustav Schmaltz in Germany early in the 20th Century [5]. An image of an illuminated slit was projected on the workpiece at an angle to the vertical, and the distortions in its reflection magnified the surface irregularities. Peak and valley heights could then be read off the calibrated eyepiece. The subject of surface finish assessment began properly when Professor Schmaltz developed a simple profilometer to enable the deviations on a selected line of a surface to be measured and recorded. This process was simply achieved by drawing a stylus across a surface and recording the vertical deviations of the surface that had been suitably differentially magnified by an optical lever (the vertical magnification being greater than the horizon). The magnified image was recorded on photosensitive paper and was presented in a partial circular arc since the screen was rotated as the stylus progressed across the surface. This simple mechanical process enabled the roughness to be measured in terms of peak to valley deviation of the surface profile and the less extreme average of the five highest peaks to the average of the five lowest valleys on the profile to be determined. It was not long before a British company, Taylor & Hobson (now known as Taylor Hobson) produced a simple instrument that enabled an electrical signal that represented the deviation of a surface to be simply processed to produce a small range of surface parameters. The first electronic surface profile employed analogue electronics to capture data from the surface, and as well as peak to valley deviation, an extreme surface amplitude parameter, and averaging of the surface roughness became possible. As a
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Advanced Techniques for Assessment Surface Topography
consequence a more useful parameter, the centre line average roughness (CLA) was calculated using an analogue computer. It was this instrument, and its German counterpart, that became an important measurement tool in metrology laboratories throughout the industrialised world. In principle, the instrument did not change except that the analogue electronics improved as the subject developed. As a result of its use and the growing need to communicate surface finish values between manufacturing organisations and within manufacturing organisations, it became necessary to develop standards that were acceptable in industries in many countries. These standards all contained the definition of average surface roughness, CLA, now termed average roughness Ra. It is because of the early analogue instrumental convenience of computing the average roughness parameter (Ra) that it became the most widely used and accepted descriptor of a surface, and as a consequence it was widely used in many industries; and to some extent although Ra is extremely limited in value, it is still widely used today even though it is determined in a different way (through digital processing) by modern instruments. By the late 1960s surface characterisation was gaining interest in the academic community and the limitations of the simple parameters described above were becoming obvious, and researchers were devising a wide range of descriptors for a surface, few of which really overcame the limitations imposed by the original descriptors. So a plethora of parameters were developed, many of which were just variants on each other but gave the researcher the opportunity to investigate whether they would improve the understanding of the character of the surface under assessment. At this time some researchers were involved with digitising the data from the electrical output of the stylus and convert this data into a form that could be processed on the mainframe computers that were available at this time. Different countries developed different routes to the establishment of the surface parameters that they preferred. In the United Kingdom the height parameters which gained most favour was the average roughness of the surface Ra and root mean square of surface roughness Rq whilst in Germany and Russia peak height and valley depth parameters were preferred (Rt, later Rtm and Rz). The original major industrial nation in Asia, Japan, chose a variation of the extreme peak height parameter, R3z which closely approximated Rz. The significance of these developments was that the UK and USA concentrated on statistically reliable and measurable parameters whilst in Germany and Russia parameters which were related to the functional significance of surfaces, but were more difficult to measure. All of the parameters were limited in their potential application and on their own did little to describe the real parameter relationship to function. Nevertheless, workers in each country felt that the parameters which were selected offered the best early compromise and offered some information which could be used in a process monitoring sense. Since the late 1970s analogue instruments have been replaced by mechanical devices supported by digital electronic computers digital computers having become available. The subject thus had the scope to develop dramatically, and much of the early development took place in academia and research establishments mostly on the continent
Introduction
7
of Europe. Digitisation of data directly from the stylus enabled data files to be established and manipulated directly on a computer dedicated to the stylus instrument. Instruments such as the Taylor Hobson Form series Talysurf and the Somicronic Surfascan 3D have led the way. The introduction and continual improvement of computers allowed engineers to develop in an unstructured way numerous numerical parameters until eventually; by the 1980s, over one hundred primary descriptors had been developed and were described in numerous national standards. Many of these parameters were poorly defined and have very limited use. This explosion in parameters was aptly defined as "parameter rash" by Whitehouse [6].
1.4 Development of the 3D approach In the early 1980s many researchers in the academic community were experimenting with the characterisation of surfaces in 3 dimensions. Work at Teesside under Dr. Thomas and at Coventry Polytechnic under Dr. Stout, was early pioneering work on the subject, though probably the first true 3D system was developed by Williamson [7], Other groups in both industry and academia, mainly in Europe, were developing their own approaches to the subject. Although there was considerable academic interest, three dimensional topography had a difficult start in terms of acceptance, since the leading manufacturers of stylus instruments at that period shunned the development, insisting at the time that three dimensional topography was an academic curiosity and did not have a place in the industrial scene. The group at Coventry developed a system of hardware with supporting software which eventually became the first prototype for the first commercial software package and provided the first comprehensive range of surface visualisation techniques. In the early 1990s Rank Taylor Hobson brought out a 3D stylus instrument using the software OEM package developed by the group originally at Coventry. There is some debate over which company was the first to launch a 3D stylus-based surface profiler, and as a consequence the answer is somewhat complicated. Somicronic, a small company near Lyon in France, delivered a prototype 3D system to the Ecole Centrale de Lyon on 1990. The system that they delivered was a pre-production prototype of their final production system. In 1991 Rank Taylor Hobson produced and marketed the first commercial "add on" system to their 2D Form Talysurf measuring system. This system had OEM software that had been specifically tailored to the RTH requirements. This early pioneering commercial system allowed only surface visualisation techniques The first stylus system manufacturer to introduce a comprehensive range of parameters to their software was Somicronic who had a range of parameters available on their system in 1994. The next major step forward in the development of characterisation of engineering surfaces came in 1990 with the European Community supported BCR research contract [1] awarded to the University of Birmingham which was coordinated by Professor Stout, formerly of Coventry Polytechnic. The research group had transferred from Coventry and
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Advanced Techniques for Assessment Surface Topography
became involved in a major European initiative which was to develop a document which could be used as a temporary standard which was available in advance of there being an international standard prepared for the subject. This document was subjected to an overview by 38 industrialists representing the major interested groups in the subject in Europe and thus this ensured a wide acceptance of the technology [8]. The outcome from this research was a report some three hundred pages long which proposed 14 3D surface parameters that described amplitude properties, spatial properties, hybrid properties and functional properties of a surface. In addition to the parameters the work investigated communication protocols which included data file formats as well as providing useful information on the way surfaces should be measured and filtered. In 1996 the "Birmingham 14" parameters were implemented on the Somicronic 3D surface profiler as well as the standard data file format which enables the data produced on their system to be transferred to other computer systems for extensive analysis. Whilst the original BCR project was deemed a success it was regarded as a rather theoretical exercise. It was considered that before a draft standard could be proposed more practical application of the work was needed as well as formalising the numerical approaches the characterisation [8]. As a result of this opinion the SURFSTAND project was born. Certainly the subject is rapidly gaining greater industrial recognition and the relevant ISO committee has commissioned John Westburg from Volvo to specify the basis of an International Standard on the subject, and we confidently expect that the "Birmingham 14" parameters will be included in the standard as well as protocols for, filtering, data file format and data communication. A number of manufacturers have now entered the market in all the fields of instrumentation. To our knowledge Taylor Hobson, Somicronic and Hommelwerke and TSK (Japan) offer 3D stylus systems. During the period of development of the more traditional stylus type instrumentation huge progress was made in the USA with regard to the development of optical interferomeric systems. These systems were capable at a very early stage (in advance of commercial 3D stylus systems) of rapid 3D surface measurement on a range of relatively smooth surfaces and the manufacturers aimed their instrumentation at the burgeoning silicon wafer market and to a lesser extent the optics industries. These instruments were the first group of real stand-alone 3D surface measurement instruments and have made a great impact in the field of surface characterisation. The main instrument manufacturers WYKO and ZYGO have made great improvements in their instrumentation, utilising techniques such as vertical scanning interferometery, extended range interferometery and now have instruments capable of measurement from sub nanometer resolution to millimetre range. Latterly, other companies have offered optical instruments such as Phase Shift Technology and Micromap. Optical focus detection systems, offered by UBM and Rodenstock, are no longer marketed. But a further group of instruments using triangulation and confocal techniques, such as those offered by the Scantron company, are now becoming available and increasingly used in applications where mechanical contact during measurement is undesirable.
Introduction
9
Last and by no means least, at the present time by far and away the greatest numbers of 3D surface measurement systems currently being sold are atomic force microscopes (AFM's) from companies such as Digital Instruments, DME, Nanoscope and others. These instruments have exploded on the scene of ultra high scale 3D surface characterisation and now represent the largest number of users. However, the users are not usually metrologists in the traditional sense and the concept of full traceable measurement is not foremost in the minds of the common user. A few metrological AFM's do exist but mostly in national laboratories. It is clear however that eventually the instruments will become a production process control tool and it is absolutely essential that standards drafted with more traditional metrology tools in mind are widely applicable to this new generation of instruments.
1.5 "SURFSTAND" The results from the SURFSTAND project form the basis of this book. The project was a multinational and multi-partner project. The primary aims of the project were firstly to evaluate the functional usefulness of the "Birmingham 14" parameters through a series of practical case studies. Secondly, the 3D surface parameter definitions were revisited in order to "tighten up" the parameter definitions, suggesting appropriate changes and even new parameters. Thirdly, a significant portion of the project dealt with the development of new surface data filtering techniques based around robust Gaussian methodologies and the use of wavelet technology as a filtering tool. Finally, issues dealing with 3D instrument calibration were investigated. The project partners and their industrial/research backgrounds are shown in Figure 1.4a and the workpackages within the project are outlined in Figure 1.4b. a)
Bioengineering
Academic University of Huddersfield (UK) Chalmers University (Swe) University of Hannover (D)
Somicronic(Fr)| Taylor Hobson (UK) DFM (DK)
Volvo (Swe)
OCAS (Bel)
DePuy J &J (UK)
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Advanced Techniques for Assessment Surface Topography
b)
Figure 1.4 a) Partner profile of SURFTAND project b) Schematic program of work packages in SURFSTAND project The following chapters bring together leading research in the field of 3D surface characterisation and are the theoretical backbone of the proposed new ISO standard in 3D surface texture. The vast majority of the reported work is novel and will provide the basis for real ground breaking progress in the field. In more detail, Chapter 2 deals with the improved definitions of the parameters which will form the basis of the new ISO standard proposal. Chapter 3 concerns the new field of areal characterisation introducing the concept of feature parameters within the context of pattern recognition methodologies. Chapter 4 introduces multi-scalar wavelet filters as a tool for surface characterisation. In particular, both first and second generation wavelet techniques are introduced. Chapter 5 is concerned with the development of robust regression Gaussian filters initially starting with 2D techniques before moving to 3D equivalents. Chapter 6 presents a practical methodology for the calibration of 3D scanning contact stylus instruments. Chapter 7 continues the instrumentation theme and discusses the issues associated with calibration and traceable measurement using scanning probe microscopes. Chapter 8 presents a study concerning the relationship between the use of traditional 2D surface parameters and 3D surface parameters in describing the functionality of automotive cylinder bores and steel sheet. Chapters 9, 10 and 11 outline a series of case studies on a range of functional surfaces which seek to provide information on the usefulness of the 3D parameter set and the surface data filtering techniques developed within the project. The specific functional surfaces studied include automotive cylinder liners, steel sheet, bearing surfaces and medical implant surfaces. Chapter 12 discusses the issues surrounding the development of expert systems and advanced databases for hosting surface measurement, function and manufacturing information. Finally, the book is concluded with Chapter 13 which deals
Introduction
11
with the perceived future development of 3D surface metrology and the forthcoming issues of standardisation of the results of the SURFSTAND and other projects. Particular attention is given to the future of characterisation in terms of feature characterisation and its implication for the characterisation of structured micro and nano-scale structured surfaces. At this point it should be made clear that the SURFSTAND project was not the only surface metrology based project sponsored by the EC in the recent period. A further three projects have been undertaken and completed CALISURF [9], AUTOSURF [10] and a project dealing with calibration of scanning probe microscopes [11]. During the lifetime of the SURFSTAND project much liaison and cross fertilisation of ideas occurred between the projects and this proved extremely useful for all concerned providing a critical mass for real progress in the whole broad spectrum of the subject.
1.6 Potential applications of project results The project promises great potential benefit in industry through improved surface characterisation that should lead to improved manufacturing surface quality and vastly improved understanding of surface functionality. Specific perceived industrial benefits are discussed below. 1.6.1 Automotive industry The automotive industry has traditionally been most receptive to the type of research carried out in the SURFSTAND project and it is anticipated that they will lead the way in the application of the research results. Fundamental to recent developments in engine technology has been the driving force of emissions regulation and the most critical part of the engine in terms of emissions is the cylinder bore/piston ring pack interaction. The research involved in the project has given rise to a greater understanding of this system and better modeling of the functional surfaces has resulted. Clearly, the potential of better understanding is the ability to further reduce system wear and in turn emissions. Reduced emission engine technology has a definite commercial advantage for automotive manufacturers. One of the biggest users of textured steel sheet is the automotive industry with around 55% utilised in automotive applications (cars and trucks), all demanding high quality steel with appropriate surface roughness. Other important steel sheet customers where surface roughness is important are: domestic appliances and building industries. By way of example the total EU production in cold rolled steel is about 34 Mtons per annum. A conservative estimate of the amount rejected on the basis of surface roughness is 30% and assuming an average cost of 400ECU/ton the roughness related problems in sheet steel production represents an annual budget of 4 billion euro. The results of the present project have significantly increased the knowledge of sheet formability as a function of surface topography. This increased knowledge will benefit end users in terms of savings on scarp and increased market share. The automotive industry is by far and away the biggest user of bearings and again service life and wear limitation are critical to market share. The 3D surface parameters and the
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Advanced Techniques for Assessment Surface Topography
knowledge-based expert system will allow much better modelling of bearing performance and specification. 1.6.2 Biomedical industry This industry has long-standing expertise in the development and manufacture of artificial human joint implant systems. With these products, predictable and long service life are fundamental their function. The metrology techniques for specifying and characterising these systems has lagged behind for some time; however, the present project has utilised 3D surface characterisation to significantly improve the specification of the bearing surfaces in such products. The understanding of the surface interaction has greatly increased and with this it will be possible to make better quality products in the future. The project partner in this industry have now invested heavily in 3D surface metrology and have seen clear benefits from its use in terms of product quality and new product development. 1.6.3 Metrology instrumentation industry The developments in the surface roughness parameters, data filtering techniques calibration procedures and artefacts will directly benefit surface metrology instrument manufacturers. The companies will be able to quickly implement the results of the project into their proprietary equipment. These manufacturers will then be the first to implement the new standard and will lead the world in the levels of sophistication and power of their instrumentation and software thus giving them a clear advantage to service the increasing demand for surface measurement in 3 dimensions. 1.6.4 Electronics and MEMS industry Advanced economies such as those in Europe are increasingly reliant of high added value manufacturing industries and manufacture such as electronics, wafer production and MEMS. The developments in technologies such as MEMS require sophisticated high precision traceable metrology and data analysis techniques to be carried out in three dimensions and this will become increasingly important as industry approaches engineering on a nanotechnology scale. The ideas set out in this project in terms of surface characterisation and, importantly, the generic aspects of instrument calibration when applied to atomic force microscopes will give a sound basis for the development of traceable measurement which the developing electronics MEMS and wafer industry require. 1.6.5 Structured surfaces Increasingly, surfaces are engineered to give very specific functions such as reflectance properties or geometrically fixed abrasives or surface geometries ideal for bone ingrowth. These surface are highly structured in their geometry and it is doubtful if traditional statistical approaches to characterisation will suffice. However, the approach given in this text concerning feature characterisation should provide a basis for developing the extraction and characterisation of the functionally important geometrical features of the surface.
Introduction
13
1.7 References 1. ISO 14460-1, "Geometrical Product Specification (GPS) - Geometric Features Part 1: General terms and definitions". 2. B Griffiths, "Manufacturing Surface Technology", Penton Press, 2001. 3. H.. Dagnall, "Exploring Surface Texture", Rank Taylor Hobson, Leicester, 1980. 4. J. Haesing, "Determining Surface Finish of Workpieces by means of Surface Standards", Microtechnic, VI5,1961, pp 24-28. 5. G. Schmaltz, "Technische Oberflachenkunde", Springer-Verlag, Berlin, 1936. 6. D.J. Whitehouse, "The Parameter Rash", Proceedings of the 2nd International Conference on the Metrology and Properties of Engineering Surface, Leicester, April 1981. 7. J. P. B. Williamson, "Microtopography of Surfaces", Proc, Inst. Mech. Eng., Vol. 182, Pt.3K, 1967-68, pp 21-30. 8. E. Mainsah and K. J. Stout, "Second International Workshop on the Development of Methods for the Characterisation of Roughness in Three-dimensions", Brussels, April 1993, Precision Engineering, Vol. 15, No. 4,1993, pp 287-288. 9. Final Report "Calisurf Project (SMT4-CT97-2176), European Commission, 2000. 10. Final Report AUTOSURF Project (BE-97-4140), European Commission, 2000. 11. Final Report "Transfer Standards for Calibration of Scanning Probe Microscopes", Project (SMT4 CT98-2209), European Commission, 2000. 12. C.J. Evans and J.B. Bryan, "Structured, Textured or Engineered Surfaces", Keynote Paper, Ann. CIRP 48 (2), 1999.
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Parti Characterisation
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Numerical Parameters for Characterisation of Topography Liam Blunt and Xiangqian Jiang School of Engineering, University of Huddersfield, UK
2.1 Introduction Numerical parameters for surface texture as used in engineering drawings are the means of communication between design, manufacture and functional performance, and the means of communication between a supplier and a customer. These parameters are not only used as a benchmark for manufacture and surface tolerance specification, but also especially in the case of 3D parameters to predict functional properties. The initial numerical parameter set for areal surface texture was developed in the early 1990s; the so-called Birmingham 14 parameters as shown in Figure 2.1 [1]. The amplitude parameters S , Sz, Sxk, and Sku as well as the spatial parameter S^ are extensions of those previously employed in the 2D characterisation methods. The other spatial parameters Str, Sal, are extracted from the areal autocorrelation function, and Std is determined through the areal power spectral density. The functional parameters are associated with the bearing area ratio curve, normalised by S^. The parameter set, though widely accepted as a success, was considered to be of somewhat theoretical nature and lacked sufficient practical evidence of applicability [2, 3].
Figure 2.1 The Birmingham 14 parameters
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There are, however, still some problems with the definitions of these parameters, the mathematical descriptions in certain instances being ambiguous. Firstly, for example, when the connectedness of summits or valleys/pits on a random surface are considered, how does one calculate the number of summits or valleys and their mean size as a function of height from the mean/reference surface? How do summits join together to form ridges, or how do valleys link up? Secondly, does one improve the accuracy of the definitions and define more useful algorithms for hybrid parameters? Furthermore, suitable parameters relevant to the material ratio curve need to be more indicative, in order to characterise common functional properties, for instance, area and volume geometrical properties, or to describe wear and tribological properties. Under the SURFSTAND project, the improvement and verification work was carried out with the emphasis on much stronger practical evidence and more feasible applications. As a result, an improved and updated set of numerical parameters was built up during the project. This was reported to CEN/TC 290 on June 2001 and forwarded to ISO/TC 213 on February 2002 [4, 5]. The work has now been taken up by both the European and International Standard Organisations and forms a core part of the new basis for 3D surface texture standards [6-9]. The new numerical parameter set for 3D surface texture is intended to address geometrical properties, namely field and feature characteristics. The field parameter set, as outlined in this chapter, is used to classify indications of averages, deviations, extremes, spacing information and generic functional properties. The feature extraction methodologies will be introduced in the next chapter and allow dominant topographical features to be identified and catalogued. The feature extraction techniques are also a strong base defining summit/valley parameters and their mean size. One thing to note is that it is not always necessary to characterise surfaces using all the parameters. Statistical techniques such as significance testing and correlation analysis are useful in defining subsets of applicable parameters. Examples of this approach are given in later chapters dealing with specific case studies; in addition, a comparison study for 2D and 3D roughness parameters discussed in Chapter 8.
2.2 General terms Big fleas have little fleas which sit on 'em and bite 'em but little fleas have smaller fleas and so on, ad infinitum The useful value of the information conveyed by surface parameters is contained in the appropriate surface components according to the functional requirements, such as rough, wavy and primary surfaces. This mainly depends on the bandwidth for the surface analysis (obtained by using digital filtration techniques [10-13]) and the associated sampling conditions. 2.2.1 Bandwidth of surface wavelength Real surfaces contain surface features of many scales and sizes. Not all of these surface features will contain useful information for monitoring the surface creation process or contribute significantly to the function of the surface. The range of the
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sizes of the surface features with useful information needs to be identified before the surface is analysed. For example, in unpainted car body panels surface wavelengths of 1mm to 8mm are of interest since it is these surface wavelengths that correlate with the paint appearance and especially the "orange peel effect" in the final car body panel. Suitable surface analysis over these surface wavelengths will help control the manufacturing process and help eliminate the "orange peel effect". One way to specify a range of sizes of feature surface is via the bandwidth of the surface wavelengths. That is, to specify the range of wavelengths on the surface in two directions that are of interest. Once this range has been specified the filter can be tuned to accept only this range of wavelengths on the surface via its cut-off wavelengths (nesting index). 2.2.2 Sampling conditions Digital computers can only handle digital data with a finite number of points whereas real surfaces are a continuum. This means that before surface data can be used by a digital computer, the surface must be sampled. To make sure that the sampled surface is representative of the real surface and to avoid problems such as ailasing, the real surface must be smoothed to remove all small-scale features. Once the real surface has been smoothed it can be sampled. Sampling conditions give the conditions for acceptable sampling, against an agreed loss in surface information, for a particular level and type of smoothing. For example, the Nyquist sampling condition states that if there is a high frequency limit to a set of infinitely long profile data (defines level and type of smoothing} then there is no loss in information (agreed loss of information) if one samples at a higher rate than twice the high frequency limit (conditions for acceptable sampling}.
2.3 Field parameters The field parameters consist of the S-parameter set and the V-parameter set. The Sparameters depend on the height amplitude and spacing frequency, for description of both amplitude and spatial information. The V-parameters give fundamental information based on a material ratio curve (or so-called Abbott-Firestone curve or bearing ratio curve).
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Figure 2.2 The S-parameter set
2.4 S-parameter set The S-parameter set contains 15 parameters and has been classified into five types, amplitude, spacing, hybrid, fractal dimension and other parameters, as shown in Figure 2.2. 2.4.1 Amplitude parameters The amplitude parameters depend on the height deviation, for description of amplitude-related properties of a surface. Six parameters are designed to characterise the amplitude property of surfaces. They are classified into two categories, average of ordinates and extreme peak and valley parameters. 2.4.1.1 Average of ordinates These parameters [1, 14] are used to describe (i) dispersion; (ii) asymmetry of the height distribution; (iii) sharpness of the height distribution as shown in Figure 2.3, the set includes: Root-mean-square deviation of the surface, Sq, is a dispersion parameter defined as the root mean square value of the surface departures within the sampling area.
where M is the number of points of per profile, and N is the number of profiles. rj(x,y) is the data set of the rough surface or the wavy surface or the primary surface texture, depending on a requirement of the surface analysis. In general, ;/(*,)>) is obtained by using filtration techniques [10-13]. Sq is a very general and widely used parameter. In statistics, it is the sample standard deviation (Figure 2.3a). Skewness of topography height distribution, Ssk, is the measurement of asymmetry of surface deviations about the mean /reference plane.
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This parameter can effectively be used to describe the shape of the topography height distribution (Figure 2.36). For a Gaussian surface, which has a symmetrical shape for the surface height distribution, the skewness is zero. For an asymmetric distribution of surface heights, the skewness may be negative if the distribution has a longer tail at the lower side of the mean/reference plane (e.g. a honed surface) or positive if the distribution has a longer tail at the upper side of the mean/reference plane (a shaped surface). In a physical sense this parameter can give some indication of the existence of "spiky" features. Kurtosis of topography height distribution, Sku, is a measure of the peakedness or sharpness of the surface height distribution.
This parameter characterises the spread of the height distribution (Figure 2.3c). A Gaussian surface has a kurtosis value of 3. A centrally distributed surface has a kurtosis value larger than 3 whereas the kurtosis of a well spread distribution is smaller than 3. By a combination of the skewness and the kurtosis, it may be possible to identify surfaces that have a relatively flat top and deep valleys such as honing. In a physical sense the kurtosis indicates the peakedness of a surface.
Figure 2.3 Height distribution
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2.4.1.2 Peak and valley These parameters are used to describe extremes of the height distribution as shown in Figure 2.4. The maximum surface peak height, Sp, defined as the largest peak height value from the mean/reference surface within the sampling area.
where 77 is the highest surface summit on the surface. The lowest valley of the surface, SV, defined as the largest valley depth value from the mean/reference surface within the sampling area. S
(2-5)
where rjv is the lowest surface valley on the surface. Maximum height of the topographic surface, Sz, defines the sum of the largest peak height value and largest valley depth value within the sampling area.
Figure 2.4 The extremes of height distribution
Typical values of amplitude parameters of a honed rough surface and a ground surface illustrated in Figure 2.5.
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Figure 2.5 The amplitude parameters from different rough surfaces
2.4.2 Spacing parameters The spacing parameters refer to the spatial properties of surfaces and are primarily dependent on the information in the scanning and tracing directions. These parameters are designed to assess the peak density, and texture strength. These parameters are particularly useful in distinguishing between highly textured and random surface structures. Three parameters are used to characterise spatial properties, density of summits, fastest decay autocorrelation length and texture aspect ratio [1, 15]. Density of summits of the surface, Sds, is the number of summits of a unit sampling area. Sds should be assessed after Wolf pruning at 5% of Sz (default) [16, 17].
The density of summits of a grinding wheel surface before and after Wolf pruning at 5% of Sz is shown in Figure 2.6, after Wolf pruning Sds = 60 (I/mm2).
Figure 2.6 Density summits on a grinding wheel surfaces
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The fastest decay auto-correlation length, Sal, is a parameter with the dimension of length and is used to describe the autocorrelation character of surface AACF's. It is defined as the horizontal distance of the AACF that has the fastest decay to 0.2. In other words the Sal is the shortest autocorrelation length that the AACF decays to 0.2 in any possible direction.
where
ACF(i:x,iv) is the areal auto-correlation function (ACF) of a surface as shown in Figure 2.6. For an anisotropic surface Sal is in a direction perpendicular to the surface lay. A large value of Sal denotes that the surface is dominated by low frequency (or long wavelength) components, while a small value of the Sal denotes the opposite case. Texture aspect ratio of the surface, Str, is a parameter used to identify texture strength i.e. uniformity of the texture aspect. Str can be defined as the ratio of the fastest to slowest decay to correlation length, 0.2, of the surface areal ACF function.
In principle, the texture aspect ratio has a value between 0 and 1. Larger values, say Str>0.5, of the ratio indicates uniform texture in all directions i.e. for no defined lay, for example, the EDM surface is as shown in Figure 2.7. Smaller values, say Str<0.3, indicates an increasingly strong directional structure or lay. Since the size of the sampling area is finite, it is possible that the slowest decay of areal ACF's for some anisotropic surfaces never reaches 0.2 within the sampling area. In this case, Str is invalid, for example, as in the honed surface shown in Figure 2.7.
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Figure 2.7 The areal ACFs of the bearing surface 2.4.3 Hybrid parameters Hybrid parameters are parameters based upon both amplitude and spatial information [1, 15]. They define numerically hybrid topography properties such as the slope of the surface, the curvature of high spots, and the interfacial area. Any changes that occur in either amplitude or spacing may have an effect on the hybrid property. The parameters have particular relevance to the electrical, thermal, sealing, wear and optical reflectance properties of a surface. Arithmetic mean summit curvature of the surface, Ssc, is defined as the arithmetic mean of the principal curvatures of the summits within the sampling area. In this case, curvature at a summit point is obtained by a least squares polynomial surface formed by surrounding points along each quadtratic direction as shown in Figure 2.8.
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Advanced Techniques for Assessment Surface Topography
Figure 2.8 The least squares polynomial surface
f(x,y)
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This parameter can only be calculated after Wolf pruning at 5% of Sz (default) [16, 17]. Root-mean-square slope of the assessed topographic surface, Sdq, is the rootmean-square value of the surface slope within the sampling area. Sdq is calculated using the Lagrangian polynomial with seven points at orthogonal directions [15, 18].
Developed interfacial area ratio, 5rfr, is the ratio of the increment of the interfacial area of a surface over the sampling area.
Where the interfacial area of the quadrilateral is as shown in Figure 2.9.
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The developed interfacial area ratio reflects the hybrid property of surfaces. A large value of the parameter indicates the significance of either the amplitude or the spacing or both.
Figure 2.9 The developed area in the bearing surface Figure 2.10 shows both the initial blasted surface and the resulting high wear surface of a femoral stem following micro abrasive wear in vivo. It is clear that after wear the interfacial area of the worn surface decreases significantly, and Sdr gives clear evidence to demonstrate this situation.
Figure 2.10 The developed area on a -worn femoral stem surface
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2.4.4 Fractal parameter The fractal dimension, Sfd, is designed to correlate with human visual perception of roughness. The rougher the perceived surface, the higher the value of the fractal dimensional parameter.
Note: The variation method has been used to define 5/a, which is equivalent to the Minkowski Bouligand dimension Dmb [19, 20]. The volume-scale plot is the log of the volume between a morphological closing and opening of the topographic surface using a square horizontal flat as a structuring element against log-size of the structuring element, see Figure 2.11.
Figure 2.11 The volume-scale plot
2.4.5 Other parameters Ten point height of the surface, S5z, is an extreme parameter defined as the average value of the absolute heights of the five highest peaks and the depths of the five deepest pits or valleys within the sampling area (Figure 2.12).
where rjpi and rjvi are the five highest surface summits and lowest surface valleys respectively, which relies on the Wolf pruning at 5% [16, 17].
Figure 2.12 Ten point height of the surface S5z
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Texture direction of the surface Std is the parameter used to determine the most pronounced direction of the surface texture with respect to the y-axis within the frequency domain, i.e. it gives the lay direction of the surface. The texture direction of a surface is given by an angle. By this definition, when the measurement trace direction is perpendicular to the lay (this is a very common case) the texture direction is 0° [1, 15].
where, ft is the position of the maximum value of the angular spectrum.
2.5 V-parameter set The V-parameter (see Figure 2.13) curves and related parameters are designed to assess the functional topographical features of the surface through analysing the material volume and void volume. The rational behind these parameters is to split the surface into three height zones, the peak zone, the core zone and the valley zones and then make volume calculations based on these three zones.
Figure 2.13 The V-parameter set 2.5.1. Linear areal material ratio curve parameters Linear areal material ratio curve parameters, the so-called Sk family parameters, are an extension (from 2D to 3D according to ISO 13565-2: 1996 [21], these parameters are specially designed for highly stressed surface textures e.g. honed cylinder bores.
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These parameters are a simple approach where the knee-shaped areal material ratio curve is approximated by a set of straight lines. The construction of the Sk family is derived from three sections of the areal material ratio curve: the peaks above the main plateaus, the plateaus themselves, and the deep valleys between plateaus. In this case, the areal material ratio curve is obtained by using a robust Gaussian regression filter [10,11].
Figure 2.14 The material ratio curve and Sk family parameters
As shown as Figure 2.14
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Sk family parameters can be calculated from the intercept of this slowest decay line and the coordination of an areal material ratio curve, see Figure 2.14c. Core roughness depth, Sk, is the vertical height between the left and right intercepts of the line through the ends of the minimum Htp 40% window. 5* correlates with the depth of the working part of the surface, the flat part of the bearing area curve. After the initial running in period (i.e. after the peaks represented by Spk are worn down), this part of the surface carries the load and most closely contacts the mating surface. Sometimes this part of the surface is called the "core roughness" or the "kernel" (hence the k subscript). Reduced peak height, Spk, is an estimate of the small peaks above the main plateau of the surface. These peaks will typically be worn off (or down) during the running-in period for a part. Generally, it would be desirable to have a fairly small Spk to reduce entrained debris. Reduced valley height, Svk, is an estimate of the depth of valleys that will retain lubricated in a functioning part. Peak material component, Smrl, is the fraction of the surface which consists of small peaks above the main plateau. Peak material component, Smr2, is the fraction of the surface which will carry the load during the practical lifetime of the part. Alternatively, 100%- Smr2 is the fraction of the surface that consists of deeper valleys that will retain lubricant. 2.5.2 Material/void volume parameters of the topographic surface The material/void parameter sets are derived from the volume information of areal material ratio curves of the topographic surface. The default assumptions for this set of parameters are that the peak material embraces 0~10% of the material ratio whilst the core material/void ranges cover 10-80% and void valley ranges 80~100% of the material ratio (as shown in Figures 2.12 and 2.13) [22]. These functional parameters can characterise not only the common functional properties of surfaces, for instance, area and volume geometrical properties, but also interpret wear and tribological properties in a running-in procedure. The volume family has enormous practical significance, and can be used to numerically evaluate the material ratio of surfaces and has absolute unit values of volume per unit area. Peak material volume of the topographic surface, Vmp, is defined as the material volume enclosed in the 10% material ratio and normalised to unity (Figure 2.12).
where
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Core material volume of the topographic surface, Vmc, is the material volume enclosed from 10% to 80% of surface material ratio and normalised to the unit sampling area (in Figure 2.15).
The material volume is not only a geometrical descriptor of the surface, but can also have significant functional implications. The material volume may reflect wear and the running-in properties. A plateaued surface, such as an automotive bearing surface which needs a good load bearing capability and good lubrication retention, will have a relatively small core material volume.
Figure 2.15 The material ratio curve and material volume parameters
Core void volume of the surface, Kvc, is the void volume enclosed from 10% to 80% of surface material ratio and normalised to the unit sampling area (Figure 2.16).
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Valley void volume of the surface, Fvv, of the unit sampling area is defined as a void volume in the valley zone from 80% to 100% surface material ratio (Figure 2.16).
The void volumes are proposed here to provide a direct inspection of lubrication and fluid retention of surfaces. It represents the fluid retention ability of a contacting surface. For the same reason a plateaued surface will give a relatively high valley volume whereas a spiked surface will give a relatively large core volume.
Figure 2.16 The material ratio curve and void volume parameters Values of material/void volume parameters of the ground and honed surface illustrated in Figure 2.17.
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Figure 2.17 The material/void volume parameters of the ground and honed surface 2.5.3 Comparison study for different curve related parameters 2.5.3.1 The original functional parameter set - index family
In the Birmingham 14 parameters, the functional parameters are also based on the material area ratio as shown in Figure 2.18 [1, 14]. It includes the bearing index, SM, core fluid retention index, Sci and valley fluid retention index, Svi. The bearing area ratio curve is divided into three parts. The peak roughness was defined as a range of heights embracing 5% of the bearing area, whilst the core and valley roughness were defined to cover 75% and 20% of the bearing area respectively. The index family is designed for a twofold purpose. One of the purposes is to identify the shape features of different types of surface waveforms by observing the location of three functional indexes in two pattern planes, SV{ vs SM and 5V, vs Sci. The other purpose is to deal with the topographical features of the surfaces, for instance, bearing, running in and fluid retention properties.
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Figure 2.18 Indications of the parameters of the index and the material area ratio A series of tests on engineering surfaces, such as ground, honed, lapped, and EDM surfaces have been carried out in order to verify the ability of the index family to characterise functional properties of the 3D surfaces. Examining Figures 2.19-2la, obtained from these experiments of engineering surfaces, the results seem ambiguous. The values of index parameters are similar to each other whether different types of surfaces or different roughness levels are considered. This makes it difficult to interpret the load bearing capability and lubrication retention properties of these engineering surfaces as no scalar information is given by the parameter. Practical work indicates that by using the index parameters it is impossible to clearly understand the nature of the development of surface topography.
Figure 2.19 Functional parameter sets for the ground surface The relationships between shape features for different surface topographies and their index family are shown in Figures 2.22-2.23a. The positions of functional parameters for different types of surfaces located in the pattern can be used to identify the shape features of these surfaces. Both pattern planes are constructed using S/>« versus SVi and Sci versus SV{. Observing Figures 2.22-2.230, it is clear that the index parameters can be used to qualitatively identify the shape features and discriminate different types of 3D surface topography. This is potentially very useful for the development of a knowledge-based expert system for the qualitative identification of 3D surface waveforms.
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2.5.3.2 Comparison study It is important that the improved functional parameter set should not only keep the benefits of the index family (identification of the shape features of surface waveforms), but also address the changes in the material and void volume for different scales of roughness, as well as analyse the running-in processes (similar to the Rk family). The bearing area ratio function contains a great deal of information about the material and void volume of a surface topography as well as this; area and volume are fundamental geometrical descriptors. Therefore, more natural functional properties can be directly derived from the volume information of a bearing ratio curve.
Figure 2.20 Functional parameter sets for the honed surface
',
Figure 2.21 Functional parameter sets for the EDM surface
A comparative study has been executed. In order to fully verify the properties of the improved functional parameters, the volume family is compared with both index family, and S* family. Figures 2.\9b-2.2\b show the sets of results. So far as the engineering surfaces are concerned, it is easy to see from the diagrams that the outcome of the three groups of engineering surfaces show that the values of the volume family vary for the different roughness levels. The results can be used to interpret surface material and void volume properties of different kinds of surface
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Advanced Techniques for Assessment Surface Topography
with different roughness levels, and the value variation is similar to the shown in Figures 2.19c-2.21c.
family as
Additionally, if values of the volume family are scaled by the root-mean-square deviation, the results obtained when plotting the two pattern planes, as shown in Figures 2.226 and 2.236, have the same relationship as the index parameters. The pattern structures are similar in Figures 2.220 and 2.23a except for a little scalar change due to the Vmp having a truncation level of 10% from the bearing area. Consequently, as well as the tribological advantages in terms of volume analysis, the volume family retains the ability to describe typical shapes of manufactured surfaces.
Figure 2.22 Svi vs. Sbi and Vw/Sq vs. Vmp/Sq for pattern recognition of engineering surfaces
Figure 2.23 5v/ vs. Sci and Vw/Sq vs. Vvc/Sq for pattern recognition of engineering surfaces
2.5.3.3 Discussion As shown by the above experiments and reference papers, the values of the index parameters are similar to each other when different types of surfaces or different roughness levels are considered. This makes it difficult to interpret the load bearing capability and lubrication retention properties of these engineering surfaces, particularly when the difference in the surfaces is only in scale. The volume family addresses the disadvantages of the index family. The practical work has shown that the values of the volume family: (1) clearly vary with the different roughness levels; (2) interpret surface material and void volume properties of different kinds of surfaces
Numerical Parameters for Characterisation of Topography
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with different roughness levels; (3) have the same relationship, when scaled by the root-mean-square deviation, as those of the index parameters (Figures 2.21 and 2.22). The results demonstrate that the volume parameters have enormous practical significance, and can be used to better evaluate the bearing area ratio numerically and functionally.
2.6 Conclusions In this chapter the field parameter set used to classify indication of averages, deviations, extremes and specific features, has been introduced. The field parameter set consists of the S-parameters and the V-parameters. The S-parameters depend on the height amplitude and spacing frequency, for description of both amplitude and spatial information. The V-parameters give fundamental information based on the Abbott-Firestone or the material ratio curve. The S-parameter set contains 15 parameters and has been divided into four basic types, amplitude, spacing, hybrid and fractal dimension and other parameters. 1. The amplitude parameters depend on the height deviation, for description of amplitude-related properties of a surface. 2. The spacing parameters refer to the spatial properties of surfaces, primarily dependent on the information in the scanning and tracing directions. These parameters are designed to assess 3D aspects of the surface texture and lay. They assess the peak density, texture strength and dominant texture direction. These parameters are particularly useful in distinguishing between highly textured and random surface structures. 3. The hybrid parameters are parameters based upon both amplitude and spatial information. They define numerically hybrid topography properties such as the slope of the surface, the curvature of high spots, and the interfacial area. The parameters have particular relevance to the contact properties, both electrical and thermal, sealing properties, wear and optical reflectance properties of a surface. 4. The fractal dimension parameter is designed to correlate with human visual perception of roughness. The rougher the perceived surface, the higher the value of the fractal dimension parameter. 5. The "other" parameters seek to maintain continuity between traditional 2D surface specification and 3D techniques by allowing common 2D parameters to be "upgraded to their 3D equivalents". It is essential at this stage to point out that the performance of some S-parameters is dependent on the correct extraction of critical points on a surface. These parameters include the density of summits of the surface (spacing), arithmetic mean summit curvature of the surface (hybrid) the ten-point height of the surface (other). They are all highly sensitive to artificial small insignificant peaks and pits due to noise. Before these particular S-parameters become meaningful, these small insignificant peaks and pits need to be eliminated. This is achieved using a feature extraction technique called Wolf pruning\ this is addressed in the next chapter. The V-parameter set is designed to assess the functional topographical features of the surface through analysing material volume and void volume. The rational behind the parameters is to split the surface into three height zones, the peak zone, the core zone and the valley zones and then to make volume calculations based on the three zones.
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1. The linear areal material ratio curve parameters are specially designed for highly stressed surface texture e.g. honed cylinder bores. 2. The volume parameter sets can characterise the common functional properties of surfaces; for instance, area and volume geometrical properties may interpret wear and tribological properties. They have enormous practical significance, and can be used to numerically evaluate the material ratio of surfaces. In this chapter, improvements upon the Birmingham 14 parameters have been highlighted. The definitions of all peaks and pits relevant parameters are now unambiguous, the hybrid parameters have been modified, and curve relevant parameters are updated.
2.7 References 1. Stout, K.J., Sullivan, P.J., Dong, W.P., Mainsah, E., Luo, N., Mathia, T. and Zahyouani, H. 1993 The Development of methods for the characterisation of roughness in three dimensions, Commission of the European Communities (ISBN 0704413132) 2. Lonardo, P. M., Trumpold, H. and Chiffre, L. D. 1996 Progress in 3D surface microtopography Characterization, Annals of the CIRP, 45, pp.589-598 3. Peters, J., Bryan, J. B., Estler W.T., Evans, C., Kunzmann, H., Lucca, D. A., Sartori, S., Sato, H., Thwaite, E.G. and Vanherck, P. 2001 Contribution of CIRP to the development of metrology and surface quality evaluation during the last fifty years, Annals of the CIRP, 50, pp.471-488 4. Report for Surfstand, at the 12th meeting of ISO/TC 213 2002-02-15, Madrid, Spain 5. ISO/TC 213 N477, Resolution adopted at the 12th meeting of ISO/TC 213 200202-12, Madrid, Spain 6. ISO/TC 213 N008, Resolution of Task Force 3D Surface Texture, 2002-06-22, ST. Petersburg, Florida, USA 7. ISO/TC 213 N487, Result of voting on surface texture - Aearl, 2002-06-14 8. ISO/TC 213 N499, Resolution adopted at the 13th meeting of ISO/TC 213 200206-25, ST. Petersburg, Florida, USA 9. ISO/TC 213 N 481 2002 New work item proposal: Geometrical Product Specification (GPS) - Surface texture: Areal - Part 1: Terms, definitions and surface texture parameters (International Standard Organization) 10. S. Birkmann, H. Bodschwinna, Chapter 4: Advanced Gaussian Filters U.S. Birkmann, H. Bodschwinna, H.W. Lemke, Accessing roughness in threedimensions using Gaussian regression filtering, Int. J. Mach. Tools and Manufact. 41(2001)2153-2162 12. X.Q. Jiang, L. Blunt and K.J. Stout, 2000, Development of a lifting wavelet representation for surface characterisation, Proc. R. Sco. Lond. A. 456 pp. 1-31 13. X.Q, Jiang, Chapter 5: Multi Scalar Filtration Methodologies
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H.Dong, W.P., Sullivan, P.J. and Stout, K.J., 1994 Comprehensive study of parameters for characterising three-dimensional surface topography III: Parameters for characterising amplitude and some functional properties, Wear, 178,pp.29-43 15. Dong, W.P., Sullivan, PJ. and Stout, K.J., 1994 Comprehensive study of parameters for characterising three-dimensional surface topography IV: Parameters for characterising special and hybrid properties, Wear, 178, pp.45-60 16. P.J. Scott, Chapter 3: Development of feature extraction for surface texture 17. P.J. Scott, An algorithm to extract critical points from lattice height data, Int. J. Mach. Tools and Manufact. 41(2001) 1889-1898 18. Chetwynd, D.G., Slope measurement in surface texture analysis, Journal Mechanical engineering Science, 20 (1978) 115-119 19. Fractal B. Dubuc, S. W. Zucker, C. Tricot, J. F. Quiniou, and D. Wehbi, "Evaluating the Fractal Dimension of Surfaces," Proceedings of the Royal Society of London Series A- Mathematical Physical and Engineering Sciences, 425 (1989) 113-127 20. B. Dubuc, J. F. Quiniou, C. Roquescarmes, C. Tricot, and S. W. Zucker, "Evaluating the Fractal Dimension of Profiles," Physical Review A, 39 (1989) 1500-1512 21. ISO 13565-2, 1996 Geometrical Product Specification (GPS) - Surface texture: profile method - surfaces having stratified functional properties Part 2: Height characterization using linear material ration curve (International Standard Organization) 22. X.Q. Jiang, L. Blunt and KJ. Stout, Functional parameters for three-dimensional surface characterisation, accepted by ASPE 15 Annual Meeting, 22nd-27th October 2000, Arizona, USA
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Novel Areal Characterisation Techniques Paul J. Scott Taylor Hobson Ltd, Leicester, UK
3.1 Introduction There are two main uses for surface texture analysis: •
•
Control of the manufacturing process - Process monitoring: This is the traditional role of profile texture parameters to monitor a manufacturing process to ensure that it is within acceptable limits. - Process diagnostics: This is used when setting up a manufacturing process or when things go wrong; when one is trying to diagnose the problems. Control of the functional performance of the component - Functional prediction: This is where one is trying to simulate the functional performance of a component. This may require experiments to be performed in order to establish the correlation between the measured texture values and the functional performance. - Functional diagnostics: This is mainly used when the component fails to perform its desired function; again one is trying to diagnose the problem.
Traditional texture parameters, such as Sk, Sq, Ra, Rz etc. use a statistical basis to characterise the cloud of measured points. These texture parameters are termed "field parameters". Field parameters and in particular 2D parameters were developed for monitoring the production process.
Figure 3.1 Grit on a worn grinding wheel I mm x I mm
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How does a human assess a surface (see Figure 3.1)? We do not usually see parameter values such as Sk, Sq, Ra, Rz etc. but patterns of features, such as hills and pits and the relationships between them. Pattern analysis assesses a surface in the same way. By detecting features and the relationships between them it can characterise the patterns in surface texture. Parameters that characterise surface features and their relationships are here termed feature parameters. When process or functional diagnostics are required, field parameters are very blunt instruments. A medical analogy is useful to illustrate this point. Many field parameters such a Ra are analogous to taking a patient's temperature; a high temperature indicates that something is wrong but it could be anything from a cold to cancer. In contrast characterising features from the patient (sore throat, running nose, chest pains, shadow on a chest X-ray etc.) are diagnostic. That is to say field parameters (statistical characterisation of a cloud of points) are very good for process monitoring but they are not as diagnostic as feature parameters (characterisation of surface features and their relationships). An early attempt to identify and characterise features on profiles was R&W analysis [1] which was developed by the French automobile industry. It is a pragmatic approach to solving many functional problems involving surface texture. As a result, the industry has built up a "surface texture data bank" based on 27000 profiles from a range of work pieces. There are however many problems with R&W analysis, the most serious being that very small changes in the profile can cause significant changes in the analysis results with "relevant" features appearing or disappearing, almost randomly. In the present chapter it is convenient to begin by discussing a framework for pattern analysis and is based on the work of Schalkoff [2].
3.2 Pattern analysis 3.2.1 Pattern generation An abstract model of pattern generation, classification and measurement is shown in Figure 3.2 and consists of three sets: The first set (class space) consists of collection of classes of objects that generate patterns. For example, it could consist of different manufacturing process so class Ci is grinding, class Cj is turning and class Ck polishing or alternatively class Ci could be a good component functionally, class Cj a borderline component functionally and class Ck a bad component functionally. The second set (pattern space) consists of a space of patterns. Each class in the class space generates patterns and thus maps onto a subspace of the pattern space. These sub-spaces from different classes may overlap to allow patterns from different classes to share attributes. The third set (observable measurements) consists of a space of observable measurements. Patterns from pattern space will map onto a subspace of the observable measurements.
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Pattern analysis obtains when given an observable measurements one desires to identify the patterns which map onto the observable measurement which are in turn used to identify the classes of objects that generated those patterns.
Figure 3.2 Abstract model of pattern generation, classification and measurement
3.2.2 Pattern recognition approaches To extract patterns from the observable measurement one needs to be able to define and identify "primitives" in these measurements, where a "primitive" is defined as an extractable characteristic of the observable measurements. The three main approaches to pattern analysis, which practical approaches may be a combination of, are identified in ref 2 as: Statistical pattern analysis assumes a statistical basis for classification. The "extracted primitives" from the observable data are statistical parameters. Statistical PA is the approach of traditional surface texture with statistical field parameters such as Ra, Sq, Rz etc. being used as the "extracted primitives". Syntactic pattern analysis uses calculable features in the observable data and their relationships as the "extracted primitives". This is the approach adopted in this chapter. Neural pattern analysis attempts to emulate how biological neural systems, such as a human brain, store and manipulate information. Whichever approach is adopted, in practice small artificial features due to noise, measurement errors etc, can distort the observable measurements. It is vital that these artificial features are managed to reduce their influence on the final pattern analysis.
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3.3 Syntactical relational description of surface texture In order to use the syntactical approach of pattern recognition in surface texture we need to define the texture primitives, segmentation, and structural relationships. The approach adopted here is based on using critical points and lines as the texture primitives [3]. 3.3.1 Texture primitives and segmentation More than a hundred years ago Maxwell [3] proposed dividing a landscape into regions consisting of hills and regions consisting of dales. A Maxwellian hill is an area from which maximum uphill paths lead to one particular peak, and a Maxwellian dale is an area from which maximum downhill paths lead to one particular pit. By definition, the boundaries between hills are course lines (watercourses), and the boundaries between dales are ridge lines (watershed lines). Maxwell was able to demonstrate that ridge and course lines are maximum uphill and downhill paths emanating from saddle points and terminating at peaks and pits. Recently, the Maxwellian dale (watershed lines) has emerged as the primary tool of mathematical morphology of image segmentation, as preparation for pattern recognition. It can easily be seen that the segments are the hills and dales; Figure 3.3 gives a schematic diagram of critical points and lines defining hills and dales on artificial data.
Figure 3.3 Primitives - critical points, lines and areas
Unfortunately, segmenting a surface or image into Maxwellian dales/hills is often disappointing, as the surface/image is over-segmented into a large number of insignificant, tiny, shallow dales/hills rather than a few significant large dales/hills. What is required is to merge the insignificant dales/hills into larger significant dales/hills. It is proposed here to extend Maxwell's definitions and to define a dale as consisting of a single dominant pit surrounded by a ring of ridge lines connecting peaks and
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saddle points, and to define a hill as consisting of a single dominant peak surrounded by a ring of course lines connecting pits and saddle points. Within a dale or hill there may be other pits/peaks but they will all be insignificant compared to the dominant pit/peak. It is also important to consider edge effects. Ockham's Razor ( non sunt multiplicanda entia praeter necessitatem - entities are not to be multiplied beyond necessity) is used to extend contour lines outside the area of interest in such a way that a minimum number of new critical points are created. Ockham 's Razor leads to two possible solutions called "the virtual pit" and "the virtual peaK\ each being the dual of the other. In this chapter the concept of the virtual pit is adopted [4]. A virtual pit is assumed to be a point of infinite depth to which all the boundary points are connected. (A virtual peak is assumed to be a point of infinite height to which all the boundary points are connected.) The adoption of the virtual pit greatly simplifies the resulting discussion. 3.3.2 Structural relationships A useful way to organise the relationships between critical points in hills and dales and still retain relevant information, is that of a change tree. Kweon and Kanade [6] introduced the concept of a topographic change tree to describe the connectability of a surface. The change tree represents the relationships between contour lines from a surface and is one example of a more general topological object called a Reeb Graph [4]. The vertical direction on the change tree represents height. Hence at a given height all individual contour lines are represented by a point that is part of a line representing that contour line continuously varying with height. Saddle points are represented by the merging of two or more of these lines into one; peaks and pits are represented by the termination of a line.
Figure 3.4 Types of change trees using example from Figure 3.3
Consider filling a dale gradually with water. The point where the water first flows out of the dale is a saddle point. The pit in the dale is connected to this saddle point in the change tree. Continuing to fill the new lake, the next point where the water flows out of the lake is also a saddle point. Again, the line on the change tree, representing the
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contour of the lake shoreline, will be connected to this saddle point in the change tree. This process can be continued and establishes the connection between the pits, saddle points and the change tree. By inverting the landscape so that peaks become pits etc., a similar process will establish the connection between peaks, saddle points and the change tree. There are at least three types of change tree as shown in Figure 3.4. • • •
The Full Change Tree which represents the relationships between critical points in hills and dales The Dale Change Tree which represents the relationships between pits and saddle points The Hill Change Tree which represents the relationships between peaks and saddle points.
It should be noted that the dale and hill change trees can be calculated from the full change tree. For the rest of the change, "change tree" will imply the full change tree. 3.3.3 Areal combination In practice change trees can be dominated by very short contour lines, due to noise etc., which hinders interpretation (over-segmentation of the surface/image by Maxwellian hills and dales). A mechanism is required to prune the change tree, which reduces the noise, but retains relevant information. Areal segment combination is such a mechanism, leaving the change tree simplified but still containing relevant information. 3.3.4 Rules for areal segment combination The following is an outline of the areal segment combination algorithm for the full change tree. This algorithm can easily be modified for dale or hill combination and so these cases will not be discussed here. The simplified algorithm presented here assumes that the virtual pit condition has been applied. An algorithm without the virtual pit condition was presented in [5]. Step 1
Assuming the virtual pit condition finds all Maxwellian hills and dales and generates the full change tree.
Step 2
Classify all peaks, pits, edge peaks and edge pits significant or nonsignificant according to the function of the surface.
Step 3
Combine non-significant peaks and pits with the adjacent saddle point they is connected to in the change tree.
The resulting change tree will indicate the significant peaks, pits, edge peaks and pits and the relationships between them. Hence the change tree has been pruned, reducing the noise, but retaining relevant information.
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3.4 Which segments/motifs to combine A motif function consists of splitting a set of "events" into two distinct sets called the significant events and the insignificant events. For the motif function to give unique and stable results the motif function must satisfy the following three properties [7]: PI
Each event is allocated to one and only one of these two sets (i.e. the set of significant events and the set of insignificant events).
P2
If a significant event is removed from the set of events then the remaining significant events are contained in the new set of significant events.
P3
If an insignificant event is removed from the set of events then the same set of significant events is obtained.
It can be shown [8] that all motif functions that satisfy these three properties can be mapped one-to-one onto a certain subset of morphological closing filters. Morphological closing filters are widely used in image analysis. They are set functions with the following three defining properties [9]: 1. 2. 3.
all sets are subsets of their own closings. a closing of a closing of a set is the closing of the original set. a closing of a subset is a subset of the closing of the original set.
Note: closing filters correspond to envelope filters when the material part of a profile/surface is considered as a set. The particular subset of the closing filters that the motif functions map onto are the closings with the following properties [8]: If two sets of events give the same closing then their intersection also gives the same closing. For any closing that satisfies this property we can map it one-to-one onto a particular motif function as follows: For any set of events, consider the smallest subset of this set that gives the same closing as the original set of events. It can be shown that this particular subset is unique and well defined and corresponds to the set of significant events. The complement, with respect to the set of events, corresponds to the set of insignificant events. The inverse mapping is also well defined. Proofs of these results can be found in reference [8]. This is a powerful result since it allows one to construct all possible motif combination functions from the morphological closing filters whose properties are very well known, including how to generate all possible finite closing filters [9].
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3.5. Critical point definitions The data measured on areal surface texture instruments take the form of height values on a discrete rectangular lattice. The definitions of critical points and lines for this type of data are a very important issue for stable algorithms. Many of the published definitions fail to meet some very simple properties that are always true for continuous data 3.5.1 Continuous data: critical points There are essentially two types of definitions for critical points on a continuous surface: those based on a local slope at the critical point and those based on examination of the local neighbourhood of the critical point. 3.5.2 Slope-based definitions Essentially, the definition of a critical point is that the local slope at the critical point is horizontal in all directions [13]. This definition includes peaks, pits and saddle points. One way to distinguish between different types of critical points is to look at local paths through the critical point in different directions [14]. All slope-based definitions assume that the slope of the surface exists at the critical point. This assumption is not always valid and so slope-based definitions are less generic than those definitions based on the local neighbourhood of the critical point. 3.5.3 Local closed path based definitions The local neighbourhood definitions adopted here are based on examination of all closed paths that contain the critical point within the neighbourhood of the critical point. The definitions are as follows: Peak There exists a neighbourhood that contains the critical point such that all closed paths within the neighbourhood that contains the critical point are lower in height than the critical point.
Pit There exists a neighbourhood that contains the critical point such that all closed paths within the neighbourhood that contains the critical point are higher in height than the critical point. Saddle Point There exists a neighbourhood that contains the critical point such that all closed paths within the neighbourhood that contains the critical point have at least two portions of the closed path that are lower in height and two portions higher in height than the critical point. These definitions are generic. For the rest of the chapter these definitions, based on local closed paths, are used.
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3.5.4 Topological properties One topological property of critical points which is always true for continuous surfaces is the Euler criterion [15, 16] that is: Euler criterion Number of peaks + Number of Valleys - Number of saddles = Euler number of the surface The Euler number for a plane is 2. This version of the Euler criterion assumes that all saddle points are standard saddle points. That is to say, two higher regions and two lower regions surround the saddle point. If a monkey saddle, which is a saddle point surrounded by three higher regions and three lower regions, or an even higher order saddle is encountered then this formula has to be modified accordingly. Two other topological properties [11] that are important for the above definitions of critical points are the following: Closed path separation All closed paths separate the surface into two unconnected regions. Remove point connected If we remove any point from a closed path then the two unconnected regions become connected. Although these two properties seem "obvious" for continuous surfaces they become important when considering critical point definitions on lattice data. 3.5.5 Lattice data: critical points In practice, measured data does not consist of continuous surfaces but often of height values taken on a discrete rectangular lattice extracted from a continuous surface. This type of data is called lattice height data or lattice data. The extraction operation consists of some form of smoothing of the surface followed by sampling. If the type of smoothing is known then it is often possible to reconstruct the smoothed surface from the sampled data. When this is possible the continuous definitions given above can be used to locate the critical points on the reconstructed smoothed surface. It will be assumed that throughout the rest of the chapter that knowledge of the method of reconstruction of the smoothed surface from the lattice data is not known and all that is known is the lattice height data. 3.5.6 Early algorithms The early debate with critical point definitions on lattice data centred on how many points to include in the definition. Sayles and Thomas [17] gave two definitions of a peak one using four nearest-neighbour ordinates, and the other eight. Whitehouse and Phillips [7] used the four nearest-neighbour ordinates to define peaks. Douglas and Pucker [ 10] give a more comprehensive definition for all types of critical points based on eight nearest-neighbour ordinates.
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All these early definitions have topological difficulties. For example Takahashi [4] showed that the Douglas-Pucker definition of peaks, valleys and saddle points fails to meet the Euler criteria. Definitions based on the four and eight nearest-neighbour ordinates also fail to meet the Euler criteria. Thus the collection of critical points produced from these early algorithms could not have come from a genuine continuous surface giving difficulties with interpretation of the results.
Figure 3.5 8-neighbour connections fail the closed path separation property and the 4-neighbour connection fails the remove point connected property All of these early definitions can be recast as local closed path based definitions. Unfortunately, the 4-neighbourhood and the 8-neighbourhood fail to satisfy the other topological properties stated in section 3.5.4. The 8-neighbourhood violates the closed path separation property and the 4-neighbourhood violates the remove point connected property (see Figure 3.5). The 6-neighbourhood is the only neighbourhood scheme consistent in the plane that satisfies all the topological properties, see Takahashi [4] for detail. The 6neighbourhood is equivalent to triangulation of the rectangular lattice. In fact any arbitrary triangulation of the lattice is also consistent topologically (see Figure 3.6).
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Figure 3.6 Triangulation is consistent topologically
3.5.7 Triangulation Triangulation of the lattice is equivalent to reconstructing a continuous surface from the lattice points as follows: for each rectangle on the lattice joining one of the rectangle's diagonals creates two triangular planar facets. It is that interpolation method which introduces the least number of new critical points (invoking Ockham's razor) on the reconstructed continuous surface. The fact that triangulation is equivalent to a particular reconstructed continuous surface is the reason that any arbitrary triangulation of the lattice is consistent topologically. The question now becomes for each rectangle which diagonal should be joined? Takahashi [4] suggested for each rectangle uses that diagonal which produces the "flattest" pair of facets. Label the points clockwise around the rectangle A, B, C & D and denote Z(A), Z(B), Z(C) & Z(D) the heights at the receptive points then a good approximation to the "flattest" criterion is: [Z(D) - Z(B)]2 > [Z(A) - Z(C)]2 use diagonal A-C [Z(D) - Z(B)]2 < [Z(A) - Z(C)]2 use diagonal D-B If they are equal then it is suggested that one diagonal should be chosen arbitrarily i.e. A-C. Kovalevsky [5] suggested using the same diagonal throughout i.e. either A-C or D-B. Alternatively one could determine the envelope of the four points. That is to say, rest a plane on top of the four points and ascertain the facets by rocking the plane to determine which sets of three points the plane can touch at any one time. This is equivalent to: Z(D) + Z(B) > Z(A) + Z(C) use diagonal D-B Z(D) + Z(B) < Z(A) + Z(C) use diagonal A-C
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Equality means the rectangle is perfectly flat and one diagonal should be chosen arbitrarily i.e. A-C. Unfortunately, there is no philosophical meta-criteria (such as Ockham's razor) to appeal to, to determine which is the "best" triangulation method - they are all as good as each other. The approach adopted here is to consider only those topological properties that are true for all possible triangulations. Applying this criterion to peaks and valleys, only the "eight point" peaks and valleys remain peaks and valleys throughout all possible triangulations. It is a little more difficult to apply this criterion to saddle points. (The "eight point" saddle point definition is not the correct definition since the Douglas-Pucker definitions of critical points are all "eight point" definitions and that has been shown not to satisfy the Euler criteria.) We can use the Euler criteria to justify an approach to determine the appropriate saddle points. Given that on all possible triangulations the number of "eight point" peaks and valleys is always the same, the Euler criteria then tell us that the number of saddle points should also be the same on all possible triangulations. The following procedure makes use of this fact: Take an arbitrary triangulation (in this case the envelope triangulation) and calculate the Reeb graph (change tree) [4, 5, 6J. Prune out of the Reeb graph [5] all peaks and valleys that are not "eightpoint". This will leave all "eightpoint"peaks and valleys and a stable number of saddle points in the pruned Reeb graph. The question then is how will these saddle points that remain in the Reeb graph vary over different triangulations? 3.5.8 Contour lines Kovalevsky [11] provides a partial answer; in this paper he is addressing the definition of contour lines on a lattice of height data. To overcome topological difficulties all contour lines have to have a non-zero thickness (one pixel wide). A contour of a narrow region may touch itself, Figure 3.7, and thus at the contact point the contour becomes ambiguous because of the non-zero thickness of the contour line.
Figure 3.7 Contour having self contact
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However, the contact point of a self-touching contour line is none other than a saddle point. Hence for lattice height data all saddle points are inherently ambiguous with the position of the saddle point moving up to a pixel with a corresponding change in height. This is exactly what is seen when all triangulations are considered - the "eight point" peaks and valleys are stable but the saddle points move around up to a pixel in distance with the corresponding height change.
3.6 Change tree pruning In the literature there are now several publicised references to methods that are analogous to pruning a change tree [12,19, 20]. Wolf [12] presents a method to prune a Pfaltz graph. A Pfaltz graph is another topological object that can be used in the efficient calculation of a change tree [4]. Hence pruning a Pfalz graph is equivalent to pruning a change tree. Very recently methods to merge watersheds (Maxwellian dales) have appeared in the literature [19, 20]. Watershed merging is equivalent to change tree pruning only if the triangulation of the lattice is assumed to be a continuous surface (i.e. triangular facets). 3.6.1 Wolf pruning The methodology for Wolf pruning involves calculating for each peak and pit the height difference between the peak or pit and the adjacent saddle point they are connected to on the change tree. Wolfs pruning method consists of finding the peak or pit with smallest height difference and combining with the adjacent saddle point on the change tree. The other peak or pit also connected to this saddle point is now connected to another saddle and so its height difference is adjusted to reflect this. The process is then repeated with that peak or pit with the smallest height difference to its adjacent saddle point on the change tree being eliminated until some threshold is reached. This threshold could be when all remaining height differences are above a fixed value or alternative when a fixed number of peaks or pits are left. It is easily proved that both criteria lead to a motif function that satisfies the three required properties given in section 3.4. Using the change tree given in Figure 3.3, P6 to S7, P2 to S2 & VI to S3 all take the value the smallest height difference of 0.5, Pruning these leads to the change tree given in Figure 3.8. Using Wolf pruning until five peaks and five pits are left on a surface gives a stable definition of the ten point height parameter. These peaks/pits may not be the highest/lowest but they will be the tallest. Note Mount Everest may be the highest mountain on earth but it is not the tallest (base to peak) - that belongs to Mauna Kea on Hawaii. This example illustrates that attributes of a hill or dale can be used to create a functional motif function that can be used for pruning the change tree as long as they satisfy the three properties given in section 3.4.
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Figure 3.8 Wolf pruning on a change tree 3.6.2 Watershed merging (merging Maxwellian dales) Automatic watershed merging has recently been investigated in response to oversegmentation of the Maxwellian dales in images, as preparation for pattern recognition. The basic idea is to replicate the process of watershed merging that takes place when rain falls over a real landscape: smaller watersheds progressively fill until an overflow occurs. The water then flows to a nearby larger or deeper watershed, in which the overflown watersheds are merged. Algorithmically, the Maxwellian dales are found using an algorithm based on immersion simulations [21]. The insignificant dales are detected and filled in up to their lowest overflow height and the Maxwellian dales are again found from the filledin surface. This procedure is repeated until no insignificant dales are left. In practice, the pixels belonging to a filled-in insignificant dale are often distributed between two or more significant dales and so the process is not equivalent to a change tree pruning operation. The distribution of pixels from insignificant dales is entirely due to the discrete nature of the data and the current way the insignificant dales are filled. At non-filled-in pixels that neighbour the filled-in region, the local slope alters. This can lead to the merging of insignificant dales with two or more significant dales. On continuous data filled-in insignificant dales are always merged with one and only one other dale (assuming all saddle points have unique heights) and so are equivalent to a change tree pruning operation. A modification of the current filling in algorithm that does not lead to local slope changes at non-filled-in pixels is required to simulate continuous data.
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3.7 Examples 3.7.1 Example 1 - grinding wheel (identifying active grains) The cutting edges on a grinding wheel are geometrically undefined in location and shape. In order to ascertain the qualitative measurement of cutting edges it is necessary to develop techniques to identify the individual cutting edges from topographic data (Figure 3.9).
Figure 3.9 Grit from a grinding wheel 0.5 x 0.5mm (a) initial critical points (b) hill segmentation after 5% Wolf pruning
Blunt and Ebdon [22] describe an approach based on using local peaks to count the number of cutting edges. Unfortunately, using the number of local peaks produces an overestimate (409 peaks in Figure 3.9a). Blunt and Ebdon [22] recognised this counting problem and suggested sub-sampling the measured data to achieve the "correct count". The optimal sub-sampling corresponds to approximately one peak on each grinding wheel grain. Hence, changing the grain size changes the distance of the optimal sub-sampling. Owing to the non-uniform packing and grain shapes this may vary considerably within a given grinding wheel. Wolf pruning at different thresholds, Figure 3.10 produces different counts of the number of significant hills. By comparing these counts to counting by eye it was determined that Wolf pruning at 5% (i.e. 5% of the peak-to-valley of the data) produces the correct count for all grain sizes. For Figure 3.9b this produces 60 peaks. Wolf pruning has the added advantage that the significant peak in each segment is given allowing further analysis. For example, a height analysis can distinguish which of these peak could be active i.e. come into contact with the workpiece. Thus Wolf pruning can help in the characterisation of grinding wheels.
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Figure 3.10 Grit from grinding wheel showing hills at different Wolf pruning levels
3.7.2 Example 2 - anodised extruded aluminium Figure 3.11 shows a 0.5 x 0.5mm portion of the surface of anodised extruded aluminium. The texture consists of three types of features: extrusion marks, grain boundaries of the anodised oxide coating and isolated deep pits. The extrusion marks are easily seen running across the surface, as are the connected grain boundaries of the anodising. The anodising is porous and results in deep isolated pits within each grain. The manufacturers of this surface require a separate characterisation of these three types of features in order to control the manufacturing process, especially between the deep isolated pores and the connected valleys at the crystal boundary. In order to control the production process a sample of the anodised extruded aluminium is measured and inspected. Currently, this inspection is carried out by eye. Wolf pruning at 15% (Figure 3.lib) discriminates between the connected crystal boundaries and the deep isolated pits. Thus Wolf pruning allows the inspection process to be automated.
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Figure 3.11 Anodised Extruded Aluminium 0.5 x 0.5mm (a) initial critical points (b) hill segmentation after Wolf pruning
3.8 Conclusions The two main uses of surface texture have been discussed. Field parameters, such as the traditional surface texture parameters, use a statistical basis to characterise a cloud of points. Field parameters are excellent for process monitoring. Feature parameters characterise surface features and their structural relationships. Feature parameters are more functionally diagnostic than field parameters. Pattern analysis concepts are introduced to surface texture as a framework for feature parameters. The definition of critical points for continuous and lattice data is also discussed in detail. Surface segmentation and the rules for segment combination are discussed as a process to determine significant features in a surface. Specifically the concept of a change tree and methods to prune a change tree to determine significant features is introduced. Finally two examples are given to illustrate the techniques developed in this chapter.
3.9 References [1]
[2]
[3]
[4]
ISO 12 085 Geometrical Product Specifications (GPS) - Surface texture - Profile method - Motif method for measurement of surface roughness and waviness. Schalkoff, Robert (1992) Pattern recognition - Statistical, Structural and Neural Approaches, John Wiley & sons Inc., ISBN 0-471-52974-5 (cloth). Maxwell, J.C. (1870) On hills and dales, The London, Edinburgh, and Dublin Phil. Mag. and J. Sci., Series 4,40, pp 421-425. Takahashi, S. et. al. (1995) Algorithms for extracting correct critical points and constructing topological graphs from discrete geographical elevation data, Computer Graphics Forum,
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[5]
[6]
[7]
[8] [9]
[10]
[11] [12]
[13]
[14] [15] [16] [17]
[18]
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voll4,No.3,ppC181-C192. Scott, P.J. (1997) Foundations of topological characterization of surface texture, 7th International Conference on Metrology and Properties of Engineering Surfaces, Gothenburg. Kweon, I.S. and Kanade, T. (1994) Extracting topographic terrain features from elevation maps, CVGIP: image understanding, 59, no 2, pp 171-182. Scott, P.J. (1992) The Mathematics of motif combination and their use for functional simulation, Int J. Mech. Tools Manufact., vol 32, No 1-2 pp 69-73. Scott, P.J. (to be published) Pattern Analysis and Metrology: The extraction of stable features from observable measurements, submitted to Proc. R. Soc. Lond. A (Sept 2002). Serra, J. and Vincent, L. (1992) An Overview of Morphological Filtering, Circuits Systems Signal Process, Vol 11, No.l,pp 47-108. Peucker, T. K. and Douglas, D. H. (1975) Detection of Surface-Specific Points by Local Parallel processing of Discrete Terrain Evaluation Data, Computer Graphics and Image Processing, No.4 pp 375-385. Kovalevsky, V.A. (1984) Discrete topology and contour definition, Pattern Recognition Letters, No.2, pp 281-288. Wolf, G.W. (1991) A Fortran subroutine for cartographic generalization, Computers and Geoscience, Vol 17, No. 10, pp 1359-1381. Morse, M. (1925) Relations between the critical points of a real function of n independent variables, Transactions of the American Mathematical Society, 27 (July 1925), pp 345-396. Morse, S.P. (1968) A Mathematical Model for the Analysis of Contour-Line Data, Journal of the Association for computing machinery, vol 15, No 2, pp 205-220. Henle,M.(1979) A Combinatorial Introduction to Topology, W.H. Freeman and Company, San Francisco. (Dover edition, first published in 1994, ISBN 0-486-67966-7). Stewart,!. (1991) A Swift Trip over Rugged Terrain - Mathematical Recreations, Scientific American, (June 1991), pp 89-91. Sayles, R.S. and Thomas, T.R. (1977) Measurement of the statistical microgeometry of engineering surfaces, Proc. 1st Joint Polytechnic Symposium on Manufacturing Engineering, Leicester, Leicester Polytechnic. Whitehouse, D.J. and Phillips, M.J. (1982) Two-dimensional discrete properties of random surfaces, Phil. Trans. R. Soc. Lond. A 305, pp 441-^68.
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[19]
[20]
[21]
[22]
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Bleau, A. and Leon, L.J. (2000) Watershed-based segmentation and region merging, Computer Vision and Image understanding, 77, pp 317-370. Barre, F. and Lopez, J. (2000) Watershed lines and catchment basins: a new 3D-motif method, Int J. Mech. Tools Manufact., vol 40, pp 1171-1184. Vincent, L. and Soille, P. (1991) Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Trans, Pattern Anal. Machine intell. 13, pp 583-598. Blunt, L. and Ebdon, S. 1996 The application of three-dimensional surface measurement techniques to characterizing grinding wheel topography. Int. J. Mach. Tools Manufact. 36, pp 1207-1226.
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Advanced Gaussian Filters Stefan Brinkman and Horst Bodschwinna Volkswagen AG, Salzgitter, Germany; and Institute for Measurement and Control, University of Hannover, Germany
4.0 Introduction When surfaces of cylinder liners are measured in three dimensions, not only is the roughness structure of the surface acquired, the measurements are also sensitive to the form as well as to waviness. An assessment of micro topography by surface parameters is useful only when long wavelength components are removed from the measured surface data using mathematics. In this chapter, robust Gaussian regression filtering techniques are developed. These include routines and algorithms, which allow the 3D topographical nature of a surface to be better described. Firstly, a robust 2D regression filter that works without running-in and running-out lengths was developed and this algorithm is based on the internationally standardised Gaussian filter (ISO 112562) which is globally established. Subsequently, the results of this research proved to be transferable to 3D filtering of surfaces. With these robust algorithms even highly strained surfaces can be filtered without distortion of functionally relevant surface details such as laser spots and honing marks in engine bore surfaces or EDM-craters in steel sheet.
4.1 The ISO 11562 Gaussian filter The transmission properties of a filter are determined by its so called weighting function. The weighting function, standardised in ISO 11562 [1] for the filtering of 2D surface profiles in the form of the Gaussian probability function is mathematically described by
The filter effect of the weighting function s(x) is exclusively determined by the constant a. A filter mean line w(x), which emerges from the convolution of the measured profile z(x) with the weighting function s(x) is the result of the filtering. The convolution integral is given by:
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and is equivalent to a weighted averaging. Mathematically, the filtering effect of the Gaussian filter is described in ISO 11562 by its attenuation on harmonic functions. After execution of the convolution operation demonstrated in equation (4-2), the filtering mean line can be expressed: (4-3)
if the surface profile z(x) is given in a complex harmonic function with real amplitude AQ . The function S(aA) is called the transfer function of the filter and is positive and real. It is clear that the amplitude of the harmonic front-end function which depends on the relation a A of the transfer function S(a A) is being attenuated. The phase between the input and output signal stays the same. As a result of this property the Gaussian filter is called a phase correct filter. The yet to be fixed constantCTof the Gaussian bell curve is, according to ISO 11562, set in a way that guarantees a 50% damping of the harmonic front-end function z(x) with its typical cut-off wavelength X=X . This definition produces the following result for the constant: (4-4)
The form of the Gaussian weighting function and its attenuation on harmonic frontend functions is described by the constant a derived from equation (4-4) and is illustrated in Figure 4.1. The transfer function, S(X CO A), elucidates the correspondence between the filter mean line (gained from the weighting function) and the low-pass filtered surface profile. Profile components with wavelength greater than the cut-off wavelength (X CO A <1) emerge with nearly no damping from the filtering whereas components with smaller wavelength than the cut-off wavelength are attenuated heavily. On account of this property the Gaussian filter is in principle suitable for approximation of form components of longer wavelength.
Figure 4.1 Weighting and transfer function of the Gaussian filter
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It has been assumed up to now that the profile z(:c) is a continuous function. In reality the profile z(x) is given by i = 0,1 • •-,« -1 only at n discrete measuring points xt = i • Ax, so that the discrete convolution: k=-m
applies instead of equation (4-2). In surface metrology the distances between measuring points Ax are usually that small, that through discrete convolution the convolution integral (4-2) is still approximated adequately and the filtering properties derived for the continuous case have validity for the discrete case too. Strictly speaking, the summation in equation (4-5) must be made for an infinite number of ordinates, it can be restricted to a finite interval because for summation outside of this interval it is close to zero and its bearing upon the averaging is insignificant. This latitude width, 2 • m • Ax, of the weighting function has a decisive influence on the calculation of the filter mean line. According to equation (4-5) the first point of the filter line w(x) cannot be determined until jc = m-Ax since the weighting function at this precise point fully enters into the averaging for the first time. Accordingly, the last valid point of the filter line lies at x = (n -1 - m) • Ax. Thus the output signal w(x) will be 2 - m - A x shorter than the input signal z(x), that is, exactly the width of the weighting function. The marginal areas in which w(x) is not defined are called the running-in and running-out lengths of the filter. In practice, the latitude width of the weighting function is selected to be the same as the cut-off wavelength Xco of the filter. That is why the filter mean line H-(JC) is exactly Xco shorter than the profile z(#). In 3D filtering, which means filtering of captured surface data, the described running-in and running-out lengths of the filter have even graver consequences. If the (standard size) measuring surface of 2 x 2mm for instance is taken as a basis the filtering with cut-off wavelength of X co = 0.8mm would result in reduction of the data by 64 %.
4.2 Novel 2D profile filtering 4.2.1 2D regression filter Calculation of the filter mean line w(x) with assistance of the convolution integral (4-2) is but one way to execute a profile filtering. Another way is to take the filter mean line as a function of regression, that is, best fitted to the surface profile in the sense of smallest error squares. The advantage of this method is that for every point of the measured section, a function value of the filter mean line is defined. The regression arrangement can mathematically be described by the following minimisation problem [2]:
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The filter mean line function value vv(jc) of the filtered profile minimises the squared deviations to the measured profile z(x-£) weighted by function s(%) and integrated over the interval 0 < ( x - £ ) < / (/ is the measured length). The integration limits are selected in a way that guarantees the inclusion of the overall measured length. By zeroing of the partial derivation in the direction of the filter mean line
the minimising problem is solved. Resolving for the desired function value leads to the following formula for calculation for the filter mean line:
x
l
Additionally, the regression filter carries out a weighted averaging (demonstrated in equation 4-8). In contrast to the Gaussian filter the averaging takes place over a finite interval. The weighting function s0 (x) is scaled so that its area always takes on a value of 1. The regression filter is equal to the phase correct filtering according to ISO 11562 with transfer function according to equation (4-3) if s(jt) is replaced again by the Gaussian probability function and the integration limits are expanded up to -00 < X - <J < CO .
Finally, a real surface profile shall serve as an example for both of the filter methods. For s(x) of the regression filter the Gaussian density function is selected and the parameterCT,according to (4-4), fixed at a cut-off wavelength X co = 0.8mm. In Figure 4.2 the weighting functions s(x) and s0 (x) are described for selected positions of x.
Figure 4.2 Comparison of two low-pass filters: Gaussian filter and regression filter
A turned profile with shortened measured length of 2.4mm serves as the input signal. The latitude of the weighting function for the Gaussian filter amounts to X co = 0.8mm, so that the left part of the figure shows the running-in and running-out lengths of 0.4mm (accentuated in this figure). By comparison a look at the right part of the figure shows that the regression filter approximates the components of longer wavelength over the complete measured length. Besides this, the weighting function
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50 (*) is asymmetrically cut off in the marked range and its surface is corrected according to equation (4-8). The filter mean line is identical outside the range accentuated in Figure 4.2, since there are practically no differences between the weighting functions of both of the filtering techniques. Using a complementary description in ISO 11562 the regression filter could in future regulate the calculation of filter mean lines in the marginal areas of the profile in order to make use of the whole measured length, that is without running-in and running-out lengths of the filter. 4.2.2 2D regression filter with form approximating properties In this section the behaviour of the regression filter during filtering of surface profiles with proportionally large form components will be analysed. To this end a profile for which the long wave form components are to be approximated by the regression filter as shown in Figure 4.3.
Figure 4.3 Application of the regression filter to a profile with large form components
The measured length of the unfiltered profile is 5.6mm. For the filter mean line shown in the figure a cut-off wavelength of Xco = 2.5mm was selected. Looking at the figure it is clear that the filter mean line cannot approximate the form components in the marginal areas at all. It can follow in the central area but trickles away underneath the unfiltered real profile. In order to analyse this behaviour it is assumed that the form component /(#) in the neighbourhood of a random point XQ can be approximated within the measured length by a Taylor's series. Such a series expansion up to second degree can usually produce a sufficient result [2].
If the filter mean line is evaluated in compliance with equation (4-8) at w(x0) for surface profile z(x) - f ( x } according to equation (4-9) the following function value is obtained:
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With an ideally working form approximating filter, it is to be expected that the function value of the filter mean line at XQ is equivalent to the form components and H>(JCO) = /(*0). In equation (4-10) the filter mean line is being influenced either by the first or by the second derivation of the form component, as the case may be, because the integrals appearing as factors are usually non-zero. In Figure 4.3 shows this effect, especially in the marginal areas of the profile, since here on the one hand the gradient of the form component reaches its peak and on the other hand the product appearing in the integral has a maximum value. Here the objective is to modify the regression filter in a way, that makes the integrals appearing in equation (4-10) disappear for every JCQ. This demand leads, compared with equation (4-6), to the slightly altered minimisation problem [2]. (4-11) Pursuing the object of minimisation the partial differentials in direction (3,, (32 and w(jt) are zeroed. The emerging linear equation system delivers the form approximating regression filter, which is mathematically described by the following weighted averaging.
The formula of the calculation for the new scaling functions from k0(x) to k2(x) is given in appendix A. In order to ensure a similar dynamic systems behaviour to the earlier described filters again the Gaussian density function is selected for its capacity as a weighting function. The integration interval -QO<JC:-£
ao (
In equation (4-13) s2;00 (x) still contains the Gaussian probability density function, but it is modified by a correcting function k(x). The corresponding transfer function s 2 o o (aA) of the form approximating regression filter can be determined in the usual way according to the equation through calculating the filter mean line for the complex input signal z(x) = AQ - exp(j2;r#/A) described previously.
The definition of the cut-off wavelength is made as before according to ISO 11562. A constant is the result.
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(4-15)
The weighting function s2oo(x) and the transfer function 5 2 o o (X c o A) are shown in Figure 4.4. The left part of the figure shows that the Gaussian density function obviously dominates the appearance of the weighting function s2t00 (x) and is altered only negligibly by correcting instruction £(jc)in the marginal areas. It is typical though that the function s2tao (x) takes on negative ordinate values in order to attain the required approximation qualities.
Figure 4.4 Weighting function ^ooC-^/^co) and transfer function S2oo(^co/k^ of the form approximating regression filter The transfer function of the form approximating regression filter in the right part of the figure is always positive and real. Therefore, just as the Gaussian filter, it is a phase correct filter. Contrary to the Gaussian filter the form approximating regression filter shows the properties of a rapidly dropping branch in the area of wavelength Xco whereas the transfer properties of both of the filters are almost identical with one another in the remaining wavelengths. In Figure 4.5 the surface profile with large form components serves as an example to illustrate the efficiency of the form approximating regression filter. The measured length stays the same (5.6mm). Again, a cut-off wavelength of X co = 2.5mm was set for the filter mean line. Its progression march within the unfiltered profile has no running-in and running-out filter characteristic. Additionally, the associated weighting function s2(jc) for some selected positions of x is drawn into the design in Figure 4.5 above the surface profile. While the appearance of s2(x) in the central area of the measured length is nearly identical with 5 2oo (jc), it takes on a clearly different mode near the margin of the measured section.
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Figure 4.5 Application of the form approximating filter to a profile with large share of form
4.2.3 Robust profile filtering A profile filter is referred to as "robust" if the so called 'freak values' do not lead to distortion of the filter mean line. Deep pits or profile peaks on a surface for example are called freak values. It is important that the robust filter behaves neutrally for instance with ground or turned surfaces, meaning that the filter mean lines of both the robust filter and the not robust filter are well nigh identical. This is necessary since otherwise the roughness parameters would change and completely new drawing inscriptions would be indicated. From the field of statistics an algorithm can be taken that develops the already described filter methods further to a robust filter [3]. The basis for the process is extension of the regression procedures (4-6) and (4-11) by application of an additional weighting function 8(x) that results in a vertical weighting of the profile ordinates and extracts freak values by a proportionately lower weighting. Hence this mathematical minimising problem follows:
The function ®(£) takes the different regression arrangements into account. The resulting index / indicates an iterative process. The weights 8(x) are assigned after every iteration step as follows: First step: i-th iteration: with
8, (x) = \
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In a first step the filter mean line w, (x) is calculated in the previously discussed way, since initially the weighting 8, (x) = 1 applies. Subsequently, the median is determined from the absolute value of the difference profile z(x) - w{(x). It now girdles the first filter mean line with a weighting band 82 (£) for the profile ordinates. According to equation (4-17) and (4-18) all profile ordinates further away from the mean line than four times the median now get a weight of 82 (£) = 0. The closer the profile ordinate lies to the first filter mean line the higher its weight becomes. Profile ordinates lying directly on the mean line itself are given the maximum weight. Under consideration of the weights assigned by function S 2 (£) a second mean line w2(x) is calculated which serves as line of reference for the next reference band to be calculated. The iteration is carried out until the change of the median of the absolute values z(x) - w, (x) between two iteration steps lies within a tolerance limit. Finally, the capacity of the combined robust algorithm and form approximating regression filter is shown for three surface profiles. In Figure 4.6 the measured length for all three surface profiles is 5.6mm. For the calculation of the mean lines of the filter a cut-off wavelength of X co =0.8m/nwas used. The left side of the figure shows the surface profiles filtered by the standardised Gaussian filter. On the right side, with the same surface profiles, the effect of the robust form approximating regression filter is demonstrated making the analysis of the entire measured length possible because the superfluous running-in and running-out lengths of the filter are removed. A comparison of the upper both profiles does not suggest any differences in the function course of the mean lines. In the lower portion of Figure 4.6 a plateau-honed surface is displayed. Since the contact behaviour of this surface is determined mainly by the plateaux, its character should not be influenced by the profile filtering. The filtering of a surface with a standardised Gaussian filter shows though that the filter mean line in the area with distinct scoring is being distorted. This makes it practically useless when it comes to further analysis, whereas the mean line determined by the robust form approximating regression filter follows the plateau as shown in the partial view on the right. Even in the area of the actual running-in and running-out lengths the filter works impeccably.
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Figure 4.6 Examples of robust profile filtering of various surface topologies
4.3 3D surface filtering The 3D filter is now discussed in more detail in the following paragraphs. It has been developed to have the following features: 1. There is a continuous filter concept for 2D and 3D surface analysis. 2. The filter works without any running-in and -out sections, there are no transient effects. The full measured area can be analysed. 3. Robustifying allows the distortionless filtering of plateaulike surfaces with deep scores, such as plateau honed cylinder liners. 4. Additionally, the filter will work impeccably with distinctive forms. 5. It is defined in the spatial as well as in the frequency domain. 6. Transmission characteristics are comparable to that of the Gaussian filter (ISO 11562). 4.3.1 3D regression filter In section 4.2.1 filter techniques for the exclusive evaluation of 2D surface profiles have been dealt with. By means of the regular regression filter according to previous sections it will now be demonstrated how regression filters including the robust algorithms are suitable to 3D surface filtering on principle. For a 3D regression filter to carry out surface filtering, the weighting function determining the transfer behaviour of the filter has to be extended by one dimension. The 3D-regression arrangement equivalent to the minimising problem (4-6) can be formulated:
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(4-19) A two-dimensional Gaussian probability density function is used as weighting function:
One can see in equation (4-20) that the 2D Gaussian density function can be attributed to the multiplication of two one-dimensional weighting functions. Due to the fact that the further course of calculation becomes far easier, first the minimising problem (419) is solved by a partial derivation in the direction of the required surface w(x,y), just as in the case of a 2D profile filtering. Considering the property $(*, y) = s(x) - s(y) surface w(x, y) is now:
with
A function value of the surface w(x,y) is consequently calculated by first executing a weighted averaging with sx0 (x) along the x-axis followed by a weighted averaging with sy 0 (x) along the y-axis. This leads to the conclusion that the 3D regression filter can be put down to the 2D regression filter as described earlier. The result of this is that the transfer behaviour of the 2D filter must be applicable to the 3D filter too. The constants ax and
The 3D regression filter therefore offers the chance to set two different cut-off wavelengths Xco towards x-axis and y-axis. In Figure 4.7 the appearance of the 2D weighting function of the 3D regression filter is demonstrated for three different positions within the measured surface. In this case the cut-off wavelengths are the same Xcox =Xco y . The weighting function drawn in to the figure at position 3 lies exactly in the middle of the measured surface and takes on a rotationally asymmetrical form because of the identical cut-off wavelengths. In the marginal areas at position 1 and 2 however the weighting functions are asymmetrically cut off and their volume is corrected according to equation (4-22). Within a measured surface the volume of a weighting function sx0 (x) and s y0 (x) of a 3D regression filter always takes on the value 1 for any random position. A plateau-honed surface demonstrates well the function of the 3D regression filter. The rough data surveyed by the measuring device is displayed on the left of Figure 4.8. The measuring surface amounts to 4x 4mm. The high-frequency component is to be eliminated from the surface by applying the 3D regression filter as they superpose
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on the structure of the hone marks. For this purpose the cut-off wavelengths of the filter are set to Xcox =Xcoy = 0.3mm. On the right the result of the surface measuring is displayed in conformity with equation (4-21). The long wavelength structures superposed on the left have been removed by the regression 3D filtering as expected. The surface susceptible to analysis still amounts to 4x4m/H. That means the filtering took place with no loss of data.
Figure 4.7 2D weighting function for three different positions within the measured surface plateau honed surface
Figure 4.8 3D regression filtering of a plateau honed surface. On the left the unfiltered surface, on the right the low-pass filtered surface with Acox = faoy 4.3.2 Mathematical definition of a 3D regression filter of n-th order The filter is described by the following implicit definition [4-6] of the filter plane.
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Because of the minimising (regression) approach the filter is named a regression filter. This double integral over the measured surface is the compound of two terms. The first term contains the error square between the measured surface ordinate z(x,y) and the ordinate of the reference plane w(x,y). The second term represents the local variant weighting function of the low-pass filter 5 which results from a local invariant Gaussian weighting function s and the local variant correction function c [4]
In this formula the known (Gaussian) weighting function s characterises the system behaviour of the filter in the spatial or time domain. The correction function c allows filtering in the marginal sections and leads to a better approximation of large form components with the filter of second order, for example. The derivation of the unknown correction function c is described in the following. The filter plane is determined by differentiating equation (4-24) with respect to H>(JC,>>) and by equating to zero. We then obtain the local variant convolution integral: (4-26) 0 0
For the implementation of the convolution in computer software fast FFT algorithms can be applied. Tracing the mathematical way from equating (4-24) to equation (4-26) the local variant weighting function has to conform to the following volume condition for every position (x,y) (4-27) In order to take the approximation of form by the filter into consideration it is supposed, that the form /(£,/;) at a point (jc,jy)in the measuring plane can be indicated by a Taylor's eries of n-th order
If /(£, 77) is inserted into the minimising problem from equation (4-26) we obtain the following statement:
The filter plane w(x9y) shall now approximate to the form /(£,//) with no deviations. That means f(x,y) = w(x,y) should be result of the filtering process. If
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this demand for the modified weighting function is to be met a multidimensional moment condition arises additionally beside the volume condition [4]
(4-30)
Therefore, a correction function c for the regression filter is required, so that the modified weighting function s conforms to both, the volume and the moment condition. Due to the order, n, of the Taylor's Series the filter in the following is called a regression filter ofn-th order. The statistical uncertainty of the calculated filter plane is influenced by the roughness of the surface. With a smaller uncertainty of the filter plane a minor influence arises from the roughness. In that case the cut-off wavelengths tend towards infinity (Xcc^ —> oo, \coy -> oo) and a lower bound of the minimal achievable uncertainty is given. To reduce the influence of the correction function c c on the variance of the filter plane it is consequently necessary to look only at such functions that result in a minimal rest uncertainty. These are determined by the following function [4]:
For the solution of the unknown correction function c a variational problem with secondary conditions results from equation (4-28) and (4-30). The correction function is calculated to:
The Lagrangian Multipliers PhJ-h(x,y) are calculated by inserting of the correction function into the equations (4-28) and (4-30). In the local discrete area the calculation is developed in the same way by replacing the double integrals by double sums. In the following sections the Gaussian probability function will now be utilised as a weighting function of the low pass regression filter. This will result in the formulation of a Gaussian regression filter of zero and second order. 4.33 Gaussian regression filter of zero order The local invariant weighting function of the 3D Gaussian filter results from multiplication of two one-dimensional Gaussian probability functions. According to [4,6,7]
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The filter is described by the cut-off wavelengths Xccx, and Xco^, in x- and y-direction and the filter parameter o according to the damping of the filter. Since only the volume condition has to be met, the modified weighting function 5 results in [4, 7]
The transmission characteristic of the filter for 0.5-Xco^ < x>- 77) = 1 applies. Accordingly from the Fourier transformation of equation (4-34) the transfer function results in [4, 7]:
The damping of the filter for a wave front with the wavelength Ar = Ax • cos(^>) = Ay • sin(
The choice of the two cut-off wavelengths is of great importance for sensible adjustment of the filter. If the direction of the waviness on the measured surface can be assessed by previous knowledge the cut-off wavelength Acor should be set according to the direction to achieve an optimal filter plane. Having surfaces with unknown waviness both cut-off wavelengths Xco^, Xco^ should be set equal to get the first information on the surface waviness. Using this information a better approximation may be calculated by adjusting Xco^, Xcoy to the determined direction of the waviness. In practice the direction of the waviness is most times equivalent to the machining lay, such as the chatter marks of a grinding process for example. 4.3.4 3D Gaussian regression form filter of 2nd order The 3D form filter can approximate distinct form components since it fits a polynomial surface of second order locally around a point (x,y) [4, 6]. In order to determine the filter surface though, six secondary conditions have to be met according to equation (4-27) and (4-30). Since mixed terms (x-^)-(y- 77) occur in equation (432), the solution is a complex equation system. Orthogonalisation as with the filter of zero order can not be executed here (see [4, 6, 8]).
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For the determination of the weighting function and the transmission characteristic of the 3D form filter an infinite measuring surface is simplistically looked at to avoid any edge effects at this time. This means that both integrals in equations (4-27) and (4-30) span from -<x> to +00. This leads to the following result for the Lagrangian multipliers of correction function c:
Therefore the weighting function of the 3D form filter can be indicated by:
The index oo identifies in this case the operational mode of an infinitely extended measured area. The weighting function of the form filter consists of the Gaussian bell curve 5 and the given correction function c. For the transfer function S
out of equation (4-38). The damping of the filter depends here on the direction of a wave front too, so far as different values for the cut-off wavelengths are given. If Ar = A, • cos(p) = A,, -sin(^) and Acox = Acoy - faor apply, the transfer function is given by
For dampening of the amplitude by 50% at a wave front with a wavelength Ar = Acor the filter parameter cr is to be fixed at cr = 0.2916. Figure 4.9 shows a comparison of the weighting function for the filter of zero and second order. The volume condition causes a scaling of the weighting function at the margins of the limited measured surface. The moment condition has influence only on the filter of second order. That can be seen at the negative weights [6] and the greater sphere of influence.
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Figure 4.9 Comparison of the weighting function of the 0-order and 2nd order filter for three different positions
4.3.5 Robust surface filtering The regression filter described above allows the calculation of good reference planes for many surfaces. It is still necessary however to execute the filter robustly and in this case the influence of distinct peaks and deep scores and pores is dampened. Plateau honed engine bores or sintered bearings are examples of such surfaces. At present, the special filter according to ISO 13565 or DIN 4776 [9], which dampens scores within profiles is being used world wide for the filtering of these so called "functionally stratified" surfaces. The disadvantages of this method are problems with peaks. The robust method comes from the field of statistics and can be utilised universally for all types of surfaces. For that the approach of the regression filter (equation (4-24)) is now generalised by a so called Q -function. (4-41) 0 0 fa
In this formula Az is the difference of the surface ordinates z(x,y) and the filter plane w(x, y). /0(Az) = Az2 will result in the non robust Gaussian regression filter, as already discussed. Using the Beaton-Function as p -function though, a so-called "hard redescendent" robust filter can be derived. Figure 4.10 shows the different courses of the least-square and the Beaton-function. In reviewing the least square function, the growing influence of Az attracts attention. That means that great deviations, Az as for example distinct scores, enter the minimising problem with great impact. This is the reason for the misbehaviour of the filter with most surfaces having plateau like structures with deep scores for example. Opposed to that with the Beaton-function ordinates Az greater than a threshold value CB enter the minimising problem only with a constant value. Profile ordinates closed to the reference line are processed nearly identically by both types of filter.
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Figure 4.10 Comparison of the two p -functions: Least-square-function and Beaton function Utilisation of the Beaton-function leads to a modification of equation (4-24) with an additional vertical weighting d,(x,y) for each profile ordinate: 'v/<
Since the unknown threshold value CB has to be estimated by statistics, the filter surface must be calculated iteratively. CB converges with engineered surfaces after 25 iterations. The estimated value for CB is C This relation is proved by statistics in [4]. The vertical weighting £f(x,y) iteration loop is calculated by [4-6]
for one
otherwise The iterative algorithm (indexed i) is shown in Figure 4.11 as a flowchart. Usually, the filter mean plane of a non robust filtering can be taken for a first raw estimation of CB. Then the vertical weights ^s(x,y) are determined using CB. The next iteration loop starts again with the calculation of a new filter plane. These iterations are repeated until the change of CB between two iteration loops is smaller than the given tolerance value t.
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Figure 4.11 Flow chart showing the iterative improvement of the filter plane
4.4 Development and application of robust filtering techniques for the description of engineering surfaces 4.4.1 General formula for Gaussian regression filter The 3D Gaussian regression filter in its general form can be formulated by the following minimising problem:
This applies for the surface z(x, y) e /., for the Gaussian weighting function s(x,y) e .*. and for the polynomial coefficients flhj-h(x,y) e \ . The equation shows that the filter surface at the position (x,y) is being approximated by fitting a polynomial of n-th order and using the Gaussian bell curve as a weighting function s. Solving this minimising problem leads to the known factors fihj-h(x,y) of the polynomial surface. The filter surface derives w(x,y) - J300(x,y). For a mathematically reduced description the form approximation given by the polynomial can be forced by varying the shape of the weighting function. This will then lead to the minimising problem, which is equivalent to a convolution integral
having two secondary conditions for the modified weighting function s(x, y)
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and
The degree of form approximation of the filter depends on the applied polynomial degree n. Polynomial degrees higher than two are not very useful since the data processing involved increases with them. With filters of zero and first order great multitudes of data can be filtered in seconds by orthogonalisation and application of fast FFT routines. With the filter of second order a useful form filter is given but an orthogonal decomposition is no longer possible and longer calculations times are to be expected. The Gaussian regression filter is ideal especially for the calculation of the reference surface with turned, milled or ground surfaces in mechanical engineering [4-6]. However, exceptionally high demands are made on the filter when it comes to the evaluation of plateaulike surfaces which are used for highly stressed functional applications. 4.4.2 General formula for robust Gaussian regression filter Due to the strong asymmetrical amplitude distribution filtering of these surfaces with standard mean value filters mostly leads to a distortion of the roughness near deep scores or jutting out peaks. Therefore it is necessary to use robust methods for the calculation of the filter plane. From the field of robust regression and robust statistics methods for the robustification of equation (4-46) can be found by changing the leastsquare-norm to a more robust norm. Inserting a symmetrical p -function into equation (4-46) leads to [4-6] (4-49) By differentiating this equation the solution is given by
with
Figure 4.12 shows the function course of different Q -functions and the resulting \yfunctions. For the least-square—function /?(Az) = Az2 arises from the non robust Gaussian filter as described in the previous chapters. Here greater |Az| results in greater quadratic dominance. The resulting y -function is linear with a slope of one. More robust functions are given by the L^ -norm and the M-estimators of Huber and Beaton-Tukey. For these Q -functions greater spaces |Az| come into play linearly or with a constant value. This behaviour is reflected by the y -function too. For small
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deviations Az the M-estimator by Beaton-Tukey or Huber are approximations of the least-square function which leads to an equivalent transmission characteristic for those values [10, 11]. Table 4.1 gives an overview of the mathematical definition of these functions. The numerical solution of equation (4-50) leads, when using the robust estimator, usually to an iterative procedure for the filter surface because of a non-linear ^ function [4, 12]. For the iterative algorithm the non-linear equation system can be solved by linearisation with the differential coefficient under the assumption:
Consequently, an iterative step m is calculated according to the equation:
However, this happens to be the solution the of the minimising problem /10/:
The problem goes back to a regression filtering as discussed above but with an additional vertical weighting function 8(m) (£, 77). Robust statistics delivers two types of weighting functions £(Az) for these robust estimators: The group of the soft redescenders, approximating zero weighting asymptotically (Huber) and hard redescenders, allowing zero weighting (Beaton-Tukey).
Figure 4.12 Function courses of different
p -function
Still open is how to choose w^°' at the beginning of the iteration and the threshold values CH,CB. Experience has proved that it is best to start with a non robust regression filtering setting £(Az) = l. With technical surfaces, the position of the filter surface is stable after a 3-5 iterations using the Beaton-Tukey-function [4-6].
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For the Huber and Beaton-Tukey functions the threshold values CH and CB have to be defined automatically. Determination of these threshold values shall be defined by the statistics of the calculated roughness. If the underlying surface has a Gaussian roughness distribution pGaiasian(r)its' standard deviation cr0 can be used in the estimation of the threshold values. Again, a robust procedure is necessary for the estimation since the roughness r = z - w may contains outliers. A suitable method is given by the median of the absolute values zkj -wkj [11]. For a roughness r(x,y) with the distribution function pGa,asian (r) and /JGa,asian = 0 one calculates. Table 4.1 Robust estimators Least-SquareNorm
p-Function
p
V-Function
V
8-weighting (not robust) p-Function -Norm
vj/-Function 8- weighting (robust) p-Function
Hubert-Estimator
\l/-Function
8- weighting (robust)
p-Function
Beaton-Tukey(M)-Estimator
y-Function
8- weighting (robust)
S
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median(\r\)
In practice, for characterising technical functional surfaces the following definitions have been used: CH
=<j 0 =1,4826 -medianfM)
(4-56)
CB
= 3 - cr0 = 4,4478 • median (\r\)
(4-57)
Since the Beaton-Tukey-function is very suitable for the characterisation of plateaulike functional surfaces because of its capability of zeroing outliers, it has been used within the scope of the SURFSTAND-project for the robustiflcation of the Gaussian regression function. 4.4.3 Application of 3D Gaussian regression filter and parameter study The application of this filter to different surfaces in mechanical engineering will now be shown. The following figures each show a 3D surface plot, a profile segment with a robust and a non-robust filter line, the Abbott-curves after the filtering and some selected parameters for a turned surface in Figure 4.13, for a milled surface in Figure 4.14, for a ground surface in Figure 4.15 and for a plateau honed surface in Figure 4.16. When robust filtering the turned or milled surface a shift in the z-height of the filter plane is visible, though the filter planes are almost parallel. Hence there is almost no distinction between the functional parameters from the Abbott-curve. A negligible influence can be noted on the calculation of the amplitude parameters as the robust filter does not work free of the offset. No differences between robust and non-robust filter occur when the zero offset is corrected for at the mean plane value. Application of this robust filter is therefore suitable for surfaces with no need for robust filtering and robust or non-robust filtering of the ground surface showed no differences in the results. With nearly Gaussian surfaces, such as ground surfaces, the robust algorithm has no influence.
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Figure 4.13 Evaluation of a turned surface
Figure 4.14 Evaluation of a milled surface
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Figure 4.15 Evaluation of a ground surface
Figure 4.16 Evaluation of a plateau honed surface distorted due to the deep valleys in the surface
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A distinct influence however appears with the filtering of the plateau honed surface. The robust filtered surface is affected by the plateau of the surface, which is after all the functionally important criterion. Compared with this, the filtered surface of the non-robust filter is clearly affected by the filtering process itself in terms of false peaks adjacent to the deep valleys. The parameters of the Abbott-curve reflect this too, especially in the small values for the core Rk, Sc und Scj parameters. The robust filtering supplies a flatter datum closer to the functional "reality".
4.5 Conclusion In this chapter, robust filtering techniques for 3D surfaces were described. The main achievement is the development of the robust Gaussian regression filter, which has proved to be a powerful tool for the evaluation of 3D surface topography. By changing the order of the filter it can approximate to any form. Its robust algorithm reduces the effect of outliers and gives very good results with functional stratified surfaces, i.e. bearing faces, engine bore surfaces or rolling faces. A draft document for the implementation of the 3D surface filter into the GPS standard chain format has been provided besides this report. The 2D version of this filter is to be implemented in the German automotive industry in the very near future. Additionally, the 2D version of the filter has already been delivered as Technical Report to ISO.
4.6 References 1. ISO 11562 (1996): Geometrical Product Specification (GPS) - Surface texture: Profile method - Metrological characterisation of phase correct filters 2. Bodschwinna, H., Seewig, J.: Verbesserung des phasenkorrekten Filters nach E DIN ISO 11562 zur Trennung von Rauheit, Welligkeit und langwelligen Formabweichungen. DIN-Tagung GPS - Geometrische Produktspezifikation und priifung, 14. und 15. Oktober 1997, Erlangen 3. Hampel, F.: Robust Statistics, John Wiley & Sons, New York, 1995 4. Seewig, J.: Praxisgerechte Signalverarbeitung zur Trennung der Gestaltabweichungen technischer Oberflachen, Thesis, University of Hanover, 2000 5. Brinkmann, S., Bodschwinna, H., Lemke, H.-W.: Development of a robust Gaussian regressions filter for three-dimensional surface analysis, 10. International Colloquium on Surfaces 31.1./1.2.2000, Chemnitz, Germany, ISBN 3-8265-6999-7 6. Brinkmann, S., Bodschwinna, H., Lemke, H.-W.: Accessing Roughness in threedimensions using Gaussian regression filtering , 8. International Conference "Metrology and Properties of Engineering surfaces", 26.-28.4.2000, Huddersfield, UK 7. Stout, K.J., et.al: The Development of Methods for the Characterisation of Roughness in three Dimensions, ISBN 0-7044-1313-2
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8. Institute for Measurement and Control, University of Hanover: 3D Filtering Techniques for functional Surfaces, First Year Report of the European Project "Surfstand", The Development of a Basis for 3D Roughness Standards, 1999 9. DIN 4776,1990: Kenngrofien Rk,Rpk,Rvk,Mrl ,Mr2 zur Bestimmung des Materialanteil im Rauheitsprofil 10. Hampel, F. R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics, John Wiley & Sons, New York, 1985 11. Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection, John Wiley & Sons, New York, 1987 12. Seber, G.A.F.: Linear regression analysis, John Wiley & Sons, New York, 1977
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Appendix A Regression Filter Constants By zeroing the partial derivation in direction to j3,, |32 and w(x) in equation (4-11) the following linear system of equations in matrix notation is achieved:
Inversion of 3x3 matrix and following coefficient comparison leads according to [6, 12] for the unknown functions from £0(x) to k2(x) to:
5
Multi-scalar Filtration Methodologies Xiangqian Jiang School of Engineering, University of Huddersfield, UK
5.1 Introduction Under "normal" circumstances surface analysis only considers the extraction of roughness and waviness components of a surface. This is normally accomplished by using filtering techniques, especially Gaussian filtering, ISO 11562 [1-3]. These techniques are employed to isolate the roughness/waviness frequency bands relevant to the surface, by breaking down a surface signal. These techniques take the waveform created in the surface data and decompose it. In fact, Gaussian filtering, used to extract the roughness and waviness components, is based on a presupposition: a surface signal is a combination of a series of harmonic components. If surface waveforms conform to this assumption, the roughness and waviness can be well identified and extracted from the original surfaces though with a modified amplitude resulting from the transmission characteristics of a Gaussian function. In order to monitor manufacturing processes and identify surface texture, random process techniques have been applied to surface analysis in which the surface topography is assumed to be a stationary random system. The spectral and correlation techniques based on Fourier transforms are used to study time-averaging frequency information of surfaces [4]. Wallach, Weszka et al., Sato and Ohori, and Sherrington and Smith [5-8] applied the areal spectra to diagnoses and analyses of the processes of manufacturing and the machine tool marks of surfaces. Stout et al. [1] demonstrated that the areal spectra provide distinctive spectral patterns to represent the directionality of the surface texture. However, the disadvantage of random analysis is that significant differences involved in a surface, such as large peaks/pits or ridges/valleys, will be smoothed over the space of a signal, without indicating the location of the frequency events. Identification of topographic features of engineering surfaces have been made by Whitehouse and Zhang [9, 10]. The two possible functions that linked the spatial and spectral domains, the ambiguity function (in radar application) and Wigner distribution (in quantum mechanics), were introduced. The frequency shift can be preserved in the Wigner distribution and Wigner function has a real-valued capability whereas the ambiguity function is complex and has a complicated phase property, Whitehouse and Zhang selected the Wigner transform as a tool to investigate the decomposition of the surface signal into a space-frequency plane. The energy distribution in the space-frequency plane, offered by Wigner transform, can be used to
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identify the variation of a surface topography. The result of this is that the information concerning the surface frequencies and their locations within a surface signal has been used to monitor and adjust the manufacturing process. However, it is also well known that although the Wigner transform can offer an analysis of the energy distribution of a signal, it only yields an imperfect descriptor concerning the energy distribution, due to its substantial interference terms. Even now, a reasonable algorithm does not exist that allows reconstruction of atomic decomposition of a signal by using the Wigner transform [11]. Analysis of multi-scalar properties of a surface topography needs not only to provide both the frequencies of the signal and their location, but also is expected to accurately recover and perfectly reconstruct these topographic features. Considering the needs of surface assessment, wavelet analysis has been applied to surface characterisation. In this chapter, the major wavelet models used in surface metrology are considered. The basic theory, algorithms and the properties of these models are introduced and discussed.
5.2 Brief wavelet theory A basic idea behind wavelet analysis is the transfer a complex frequency analysis into a simple scalar analysis. Wavelet analysis employs time-frequency windows and offers the relevant time-frequency analysis, which uses long windows at low frequencies and short windows at high frequencies (shown in Figure 5.la). Wavelet mathematics provides a mathematical microscope that "can divide functions into different frequency components, and then study each component with a resolution which is matched to its scale" [12, 13]. The wavelet transform is an update of the classical short-time Fourier transform (STFT) or Gabor transform [14, 15] as well as the Wigner distribution. In contrast, STFT uses a single analysis window (shown in Figure S.lb), and offers the same accurate analysis in the whole time-frequency plane. The wavelet transform is related to space-frequency analysis and is similar to the Wigner-Ville distribution [16], and it is better able than the STFT to "zoom in" on very short-lived high frequency phenomena, such as transients in signals or singularities in functions. A point to be noted is that wavelet analysis takes the signal decomposition to a space-scalar (time-frequency) plane, and separates then reconstructs these components in the space domain. In contrast, Wigner analysis also decomposes a signal into the space-frequency plane, then studies the energy
Figure 5.1 The different windows of the wavelet and the STFT
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distribution of these components but they can not be recovered and reconstructed perfectly.
5.3 Prototype wavelet A wavelet is a waveform that has compact support in both the space and frequency domains and whose integral is zero. In wavelet analysis the signal is broken down into rescaled and shifted versions of the original waveform. This then transfers spacebased information into scale-based information, which represents the frequency and location properties of the original signal. In one-dimension, the wavelets, y fl ^(0» (basis functions) can be obtained by dilation and translation of the prototype wavelet y / ( t ) . a is the scalar parameter that can be used to illustrate dynamic transmission bandwidths or cover different frequency ranges, and b is the translation parameter. Typical one-dimensional continuous wavelets are expressed by:
In the real world, most signals are in discrete data sets. In the discrete case, the dilation and translation parameters both take only discrete values. The rescaled wavelets, i//jQ(t) = i//(a~Jt)arQ dilated by the factor a~J, when a = 2as shown in Figure 5.2.y is the scalar parameter that can be used to illustrate dynamic transmission bandwidths or cover different frequency ranges. The shifted wavelets Vo,*W = V(t-k) are translated by k (translation parameter) as shown in Figure 5.26. By changing £, the time location centre has will be moved. Typical one-dimensional wavelets ^Jtk(x) are dilated j times and shifted k times. The discrete wavelets are expressed by: Y Thus a signal can be divided into different scales, with the signal data now being represented on a 'time-scalar plane'. Multi-resolution divides the frequencies into octave bands, from CD to2o). Frequencies shift upward by an octave when time is rescaled by two. Figure 5.la shows how the time-frequency plane is partitioned naturally into rectangles of constant area.
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Figure 5.2 Discrete wavelets For a discrete signal y(x) e L 2 (Z), its discrete wavelet transform can be expressed by:
It was shown by Daubechies and Chui [12, 13] that the discrete wavelet transform is reversible. So the signal y(x) can be recovered with the following equation. For a discrete signal y(x) e L2 (Z) ,the discrete wavelet transform can be expressed by:
where the *¥Jtk =(F*F)~]y/jk. The main approach to wavelets uses a two-channel filter bank as shown in Figure 5.3, and the dilation equation of the basis wavelets and corresponding scaling functions develop lowpass HQ and highpass //, filter coefficients. A popular wavelet is the Daubechies or so-called orthogonal wavelet. It was first used for surface analysis by Chen and Raja et al and Jiang and Li from 1994 [17, 18]. The orthogonal wavelet has a finite impulse, compact support and can be reconstructed perfectly.
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The main problem with the orthogonal wavelet is that the approach itself generates wavelets. In the orthogonal case, the dilation equations of the basis wavelets and corresponding scaling functions develop lowpass H0 and highpass //, filter coefficients. However, due to the fact that the frequency responses of the two-channel filters, so-called analysing filters, are not ideal brick wall filters, this normally leads to aliasing, amplitude modification and phase distortion. Therefore, a normally orthogonal wavelet with a high order was used to improve the phenomenon resulting from phase distortion. This technique led to a large measurement area, a great deal of computation and a huge memory requirement for areal analysis of surfaces.
Figure 53 Decomposition of the original signal z(x,y)
5.4 First bi-orthogonal wavelet The requirement for filtering in surface analysis includes: linear phase shift, finite pulse response and perfect reconstruction. Only bi-orthogonal wavelets satisfy these conditions. In order to overcome these defects, the bi-orthogonal wavelet for surface analysis was proposed by Jiang and Blunt et al in 1997 [19-21]. The bi-orthogonal wavelet allows the construction of symmetric wavelets and thus a linear phase filter. In the bi-orthogonal case, the other two-channel filters: G0 and G, (so-called synthesis filters), have been specially designed to compensate for these errors of the analysing filters HQ and //,. When the frequency responses of the synthesis filters, G 0 (z), G t (z), are the inverses of the analysis filters, // 0 (z), //,(z) and they satisfy [22]
the errors in this analysis bank are cancelled. Where / is time delay, the distortion term must be z~l, and aliasing term must be zero. This means that the two-channel filter banks should be bi-orthogonal. In the bi-orthogonal case, the impulse responses, /*,)(&), /Zj(A:), of analysis filters would not be double-shift orthogonal to themselves, they would be double-shift bi-orthogonal to gQ(k), g, (k), of the synthesis filters.
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According to wavelet theory [12, 13], the dilation equations of the analysis wavelet equation, y/(x), and synthesis wavelet function, y(jc) can be performed in the light of the impulse responses of the analysis and synthesis highpass filters respectively,
(5-6)
the scale equation can be given by:
(5-7)
The (x,y) can be expressed by:
(5-8) Using the scale function pair, the analysis wavelets and synthesis wavelets are built by:
where, ij/h(x,y), fiv(x,y) and ysd(x,y) give the analysis wavelets in the horizontal, vertical and diagonal directions, respectively. i//h(x,y), yv(x,y) and yd(x,y) give the synthesis wavelets of the three directions. By employing a 2D bi-orthogonal wavelet pair, a 3D discrete signal z(jt,)>)eL 2 (Z) can be transformed to a wavelet series by decomposing the signal data z(x,y) on the 2D bi-orthogonal wavelets basis
ajk's are approximation coefficients of the signal z(x,y)at the scale 2~ y , and diw-djjjj—djji are a group of detail coefficients of z(x,y)at the scalar range of 2~J(j = 1 ~ j) as shown in Figure 5.4. ajk is generated by the set of inner products:
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Figure 5.4 Decomposition in the frequency domain Aj_}(x,y) is called a discrete scalar approximation of z(x,y) at the scale 2~ (jH) , and it represents the low frequency components of z(x,y) at the scale 2~ (jH) . When scale j = 0, the scalar approximation Ag(x,y) equals z(x,y). A}(x,y) at the scale 2~'can be reconstructed by ajk, using the inverse wavelet transform:
The detail coefficient, d, *j,kk,» is a combination of three directional detail parts:
Similarly, the inverse wavelet transform of the detail coefficient djk gives the high frequency components of z(x,y) at the scale 2~J and it is called a discrete detail Dj(x*y) °f z(*>y) at the scale 2~J
The equations show that in the two-dimensional case, the approximation and detail coefficients are computed by separate filtering of the signal z(x,y) along the abscissa and ordinate. The wavelet decomposition can thus be interpreted as a signal decomposition in a set of independent, spatially oriented frequency channels. Figure
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5.4 shows, in the frequency domain, how the approximation coefficient Oj_lk is decomposed into ajk, d h j k , dvjk and d d j k . Oj k corresponds to the lower frequencies, djk
gives vertical high frequencies (horizontal edges), dvjk the horizontal high
frequencies (vertical edges) and ddjk high frequencies in both directions (the corners). Consequently, the 3D signal z(x,y) can be reconstructed by:
An interesting example is shown in Figure 5.5. Figure 5.5a presents the 3D concave bearing surfaces of the equatorial region of a precision polished alumina acetabular cup. It was obtained by scanning the surface topography using a 3D Form Talysurf stylus instrument which employs an *-gearbox and a ^-translation table with a precision lead screw for translation of the specimen, with a sample matrix of 164x164 and a sample interval of Ax = Ay = 6 jam. The figure clearly shows that the surface topographies of the measured acetabular cup include a very considerable amounts of table error derived from the y-axis of the measurement instrument.
Figure 5.5 Bearing surface of a precision acetabular cup before and after wavelet filtering
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In order to observe the table error generated by the y-axis directional measurement, the surface of the precision acetabular cup (shown in Figure 5.5a) is firstly fitted by a quadratic polynomial to remove its approximate spherical form before applying the wavelet transform. The surface is then decomposed with a 2D bi-orthogonal wavelet at the order of 6.8 (to preserve the signal reconstruction accuracy under sampling conditions limited by the Form Talysurf) and the scales of 2~J (j = 1 ~ 3). The figure shows that the third scalar approximation, A3, gives the reference datum of the fitted cup surface. As shown in Figure 5.6, the y-axis table error, which influences the horizontal high frequencies of roughness, has also been separated from the roughness and included in the reference surface. The roughness of the cup can then be extracted and analysed. Furthermore, in comparison with Figure 5.50, the multi-scalar features have been reconstructed accurately and the localised positions of the peaks or pits/scratches have been retained precisely in Figure 5.56. The table error caused by the 3D stylus measurement is also clearly been "filtered out".
Figure 5.6 Multiscalar decomposition using first generation bi-orthogonal wavelet
The significant point of the bi-orthogonal wavelet is that it has a brick wall, linear phase (leading to real output without aliasing and phase distortion) and a traceably located property so that the different component surfaces obtained can more naturally record the real surface. However, wavelets, y,,*(0, (basic functions) are built by dilation and translation of the prototype wavelet ^(/) which relied on the Fourier transform. The wavelet transform needs to be applied along three directions,
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horizontal, vertical, and diagonal [12, 23]. The theory and corresponding algorithm [12, 13, 22-25] are very complex, and a great deal of computer memory and computation time is needed. Furthermore, there is still the boundary destruction inherent when using the Fourier transform.
5.5 Second generation biorthogonal wavelet For industrial application purposes the methods used for surface functional characterisation should have considerable merits. They need to be simple and natural. In other words, the method of separation and reconstruction of different components of the surface should have both the 'simplicity' of a Gaussian filter and 'naturalness* of a biorthognal wavelet filter. From a point of view of the above requirement, a lifting wavelet model (based on the algorithm of a second generation wavelet [2628]) has been developed by Jiang and Blunt and Scott [29-31]. The second generation algorithm, uses the lifting scheme to replace the Fourier transform as its construction tool and gives up the dilation and translation, but it still preserves all properties of the first generation algorithm. In this implementation, the analysis highpass filter, //,, and synthesis lowpass filter, G0, of the initial finite biorthogonal wavelet filter set, {// 0 ,//,,G 0 , G, } within the first generation, are transferred to H , G which can be found by the lifting scheme as
where the S(z) is a Laurent polynomial. Substituting this new set into the equation (5-5), the perfect reconstructed condition for the second generation bi-orthogonal wavelet is:
and
In order to reconstruct perfectly, the filter frequency responses should also be satisfied:
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Except for the equation (5-5) where, in this case, S(z2) = S(z 2 ). After lifting has been performed, the new bi-orthogonal wavelet pair can be found by:
Where the coefficients s( • ), are from the Laurent polynomial S(z). The power behind the lifting scheme is that s( • ) can be used to fully control all wavelets and synthesis scaling functions. A simple example is that the linear subdivision (N = N = 2) can be obtained by lifting from the "lazy wavelet*', which only subsamples the original signal, Ag(x,y), in even A$2k and odd 4u*+i samples. The "lazy wavelet" is the simplest biorthogonal wavelet with N - N - 0. If a linear subdivision occurs; N = 2 after lifting, the coefficients, s(/)= —,— , the wavelet coefficient dlk encodes the difference between the exact sample 4>,2*+i
an(
^ *ts linear prediction of two even neighbours
4),2* > 4),2*+2 • 1*can be written:
(\ \\ Employing the dual lifting scheme, N = 2, that is, the coefficient s\k) = —,— , the V4 4; scalar coefficients a}k of A^^k would be updated by wavelet coefficients dlk and d} k+l. This can be expressed as
Following the above idea, the algorithm of the forward lifting wavelet transform can be described by:
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Figure 5.7 The lifting scheme
This illustrates significant built-in features that predict p and update // and can be flexibly designed by the coefficient s( - ) and the Laurent polynomial 5(z) according to the intending requirement of surface analysis. The block diagram of the two lifting steps is shown in Figure 5.7. Using an inverse wavelet transform, high and low frequencies can be recovered flexibly and immediately in the different transmission bands in terms of the functional analysis requirements. The inverse wavelet transform is simply performed by reversing the operation and toggling negative to positive for all operations. In order to obtain high frequencies, the scalar coefficients, a k , are set to zero and then backed out, and vice versa for low frequency as shown in Figure 5.8.
Figure 5.8 Inverse lifting wavelet transform
5.6 Cubic-spline wavelet A cubic polynomial spline has been selected to build thes( • )by Jiang et al [30, 32]. The filtering and lifting coefficients of the filters are calculated according to Neville's algorithm [33] and the lifting scheme. For cubic polynomial interpolation, four neighbouring points are used; therefore, there are N - 4 coefficients for each case. Figure 5.9 shows the cubic spline scaling and wavelet functions, as well as the lifting scheme of the cubic spline wavelet for the case of centre points. The filter coefficients of the bi-orthogonal cubic spline are: 1/16 {-1,0,9,1,9,0,-!}. For cases near the boundary, the procedure is the same, the only difference being the choice of the relative filter coefficients. Table 5.1 lists all of the filter coefficients for the cubic
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spline. One property of these filter coefficients is that every set of TV coefficients for every case adds up to 1. To preserve properties of the original data such as the average, first or second moment, the coefficients need to be updated with the help of the wavelet coefficients. The update can be calculated by using four neighbouring wavelet coefficients. In this
case, the lifting5 factors are / = (
,—,—,
), and the scalar coefficients can be
updated to
Figure 5.9 Lifting scheme of the bi-orthogonal Cubic-spline wavelet
Table 5.1 Filtering coefficients for cubic spline interpolation obtained by Neville's spline interpolating Cubic spline interpolation
Filtering coefficients
neighbour number on the left
neighbour number on the right
k-7
0 1 2 3 4
4 3 2 1 0
-0.3125
k-5
0.0625 1.3125
k-3
-0.0625 -0.3125 -2.185
k-1 0.3125 0.5625 0.9375 2.1875
k+1 2.1875 0.9375 0.5625 0.3125
k+3 -2.1875 -0.3125 -0.0625
k+5 1.3125 0.0625
k+7 -0.3125
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ju(di+lj)is a weighting update which is based on the wavelet coefficients and It's are referred to as named lifting factors. The lifting factors can be calculated in the following manner. Firstly, an initial moment matrix for all coefficients at the first level is defined. The matrix aims to preserve the value of the integral of lifting wavelet along the real line as zero. The moment matrix is only relative to the sampling matrix size of z(x,y) and wavelet coefficient points attending a weighting update.
where, s is a sampling number in the processing direction, x or y of z(x,y). Updating the moment matrix requires an indication of how many filtering factors of corresponding wavelet coefficients will be contributed to this update. When neighbouring point numbers on each side are the same, the moments can be expressed by:
where
Therefore, lifting factors are solved using this linear system.
In this wavelet algorithm, assuming a raw data signal derived from an arbitrarily curved surface in a given space interval, a cubic spline interpolation is employed. Four neighboring sampled data will attend the weighting prediction. Three cases should take into account: (1) two neighbouring points on either side in an interval, (2) one sample point on the left and three on the right at the left boundary of an interval, and (3) vice versa at the right boundary. These cases are considered in order to guarantee boundary 'naturalness' without including any artifacts. The result of this is that running-in and running-out lengths are not needed. With the implementation of the wavelet transform, the 3D raw signal z(x,y) has been driven to wavelet subsets, di+]j and aMJ which record high and low frequency events at the scale 2~('+1) of z(x,y). The whole decomposition of z(x,y) is a simple
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repetitive scheme through rows and columns and all computations are done in-place. After i steps of decomposition in scalar domain, an original z(x,y) is replaced with the wavelet series, a J t dljt • • • , d j , it can be expressed by:
Figure 5.10 shows this schedule where i illustrates a decomposed level of Wavelet transform in scalar domain. Simultaneously, a 2D discrete Wavelet transform W(z(x,y)) has transformed z(x,y)into a Wavelet series. In terms of surface metrology, a 3D surface, z(x,y), is superimposed by a series of frequency components:
where, TJ(X, y) stands for roughness with high frequency, 1 / ^ ~ 1 / Ac, 1 / A, indicates high frequency limit by sample interval, and l//l c is roughness frequency limit. 77'(x.y) and rj"(x.y) are waviness and form error with low frequencies (waviness 1 / Ac ~ 1 / &„, 1 / Aw is waviness frequency limit and form < 1 / A w ) respectively. In that case, all multi-scale events, ), hide in the bands of roughness and waviness, whose wavelength would cover a wide frequency range (I/A, ~1/A W ) as shown in Figure 5.10. Comparing equations (5-28) and (5-29), it can be seen that if a wavelet transmission bank in the scalar domain is designed as a combination of a series of lowpass, sublowpass and highpass bands, the wavelet series, ai •/ , d, *J,, •••, d i ___/.._. , actually V1 V represents the distribution of all frequency components in scalar space, a , 's '•pr
represent the output of the lowpass filter band, ( 1 / A W ~ 1 / / ) , wavelet coefficients, dlfj, • • • , d j indicate output of the high frequency band, l / ^ ~ l / / l c , and ''2*
d
. - , . . . , d . represent the output (waviness) of the sub-lowpass filter band, '+1.4 2'
'.r^r
Figure 5.10 Relationship between surface -wavelengths and wavelet components
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5.7 Reconstruction of 3D relevant surfaces Based on the above and using an inverse wavelet transform, a variety of surfaces can be recovered flexibly and immediately in the different transmission bands in terms of different functional requirements. The inverse wavelet transform is simply performed by reversing the operation and toggling negative to positive for all coefficients. 5.7.1 Separation of rough, wavy and form surfaces If the general replacement for all surface filters is needed, using a wavelet implementation, all components, from roughness to dimensional deviation measurement, can be easily obtained by:
(5-31) A point to note is that A j (x,y) 's here is assumed as zero.
Figure 5.11 Bearing surface in the polar region Typical examples of bioengineering surfaces (Figures 5.11 and 5.12) and engineering surfaces (Figures 5.13 and 5.14) have been selected to show the behaviour of wavelet
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filtering. The illustrations in Figures 5.1 la and 5.\2a show different topographies in polar and equatorial regions of the worn metallic femoral heads produced using a phase-shifting interferometer with a sampling area of 228 x 203jum . The surfaces have two different kinds of scratches: regular and shallow scratches, possibly produced by manufacturing processing; and random deeper scratches resulting from functional performance in service. The latter scratches have a wider frequency band and higher amplitude, some with arc structures. In order to indicate this transmission flexibility, the cut-off wavelengths of roughness may be selected as Ac = 0.05mm. The cut-off length of waviness is limited by practical applications, in the above examples, A, = 0.10mm is for the worn head.
Figure 5.12 The bearing surface in the equatorial region The following examples shown in Figures 5.\3a and 5.140 are derived from the normal manufacturing processes of grinding and facing milling. The cut-off wavelengths of roughness for both of examples are selected as Ac = 0.8mm. The cutoff length of waviness is A, = 2.5mm .
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Using only one operation of wavelet filtering, surface contents, roughness, waviness and form error, can be detected and recognised. The outcomes (from Figure 5.116, c, d to Figure 5.146, c, d) are that rough, wavy and corresponding form error surfaces can be immediately separated and perfectly reconstructed within a requirement transmission bank.
Figure 5.13 Decomposed components of a ground surface
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Figure 5.14 Decomposed components of a facing milled surface
From Figures 5.11 to 5.14, it can be seen that the accuracy of the surfaces of these components covers the levels from micrometers to nanometers. There are no distortions caused by peaks/pits and scratches and boundaries, which can be often found in normal surface filtering [34]. More verification work has been carried out covering a range of typical engineering and bioengineering surfaces, which can be found in the literature [30, 35, 36]. 5.7.2 Extraction of 3D functional surfaces If a functional evaluation of 3D surfaces of orthopaedic joint prostheses is needed to cover the topographical information from roughness, through multi-scalar events, to waviness, a functional surface can be built by:
Figure 5.150 shows lapped topography in the polar region of a new ceramic femoral head with sampling area 300x240//w. Figure 5.156 shows how the wavelet model has removed form deviation revealing high quality functional surface. As illustrated, the multi-scalar topographic features are the dominant factors of the functional surface of this new head, and roughness and waviness may not influence the functional performance of the head in service due to their relatively low levels.
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Figure 5.\6a shows a slope intensity image of the measured data of a worn metallic head surface. The functional surface, derived from the wavelet filtering method, is shown in the Figure 5.166. It can be seen that the two images are similar each other without any relative phase shift in sampling area. The deeper scratch information on the bearing surfaces conveyed is recorded completely.
Figure 5.15 Rearing surface of a worn metallic femoral head
Figure 5.16 Bearing surface of a worn metallie femoral head
5.7.3 Capture of 3D morphological feature surfaces The identification of multi-scalar events in the bands of roughness and waviness is important in order to study the functional performance of the 3D surface topography of an orthopaedic joint system. In fact, wavelet coefficient sets over the transmission bands have "naturally" recorded the information concerning amplitude and location of these events. An amplitude threshold d . (xk,yt) is selected to pick out the '•£ roughness and waviness. This process is based on an assessment that the amplitude distribution of each wavelet coefficient set, d (*,.y), belonging to roughness and ^ waviness components, would obey the normal distribution. If the absolute value of the amplitude is equal to or larger than d }, (xk ,>>,), a thresholding estimator is applied.
Multi-scalar Filtration Methodologies
111
Where the absolute value of the peak amplitude is smaller than d . (xk,yt), the
V
coefficient should be replaced by a zero. In the case of a detail coefficient being larger than or equal to d . (xk^yl) the coefficient should be retained. As a consequence, ''IF detail coefficients that represent only the information of the peaks, pits and scratches are obtained. The amplitude threshold d , (xktyl)is the value of an intersection of '•F the probability curve of the cumulative amplitude distribution of each wavelet coefficient set. From the experiments carried out, the threshold approaches a standard deviation of each wavelet coefficient set.
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Advanced Techniques for Assessment Surface Topography
The multi-scalar topographic features can then be built by using the 2D inverse discrete wavelet transform equation (5-29)
The following examples are used to capture the functionally relevant morphological features derived from a worn head. The left-hand illustrations in Figures 5.17'a and 5.18a show lapped topographies in both the polar and equatorial regions of a new alumina ceramic polished replacement femoral head with a sampling area 300x240//m. The surfaces have isolated large pits and small peaks, and one-off scratches in the polar area. The right-hand images in Figures 5.176 and 5.186 show that the significant features of functionally relevant topography can be naturally recorded and perfectly reconstructed by using wavelet models. More examples for the morphological feature extraction are shown in Chapter 8 and in the literature [37].
Figure 5.17 Bearing surface in the equatorial region of a new metallic femoral head
Figure 5.18 Bearing surface in the equatorial region of a new metallic femoral head
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5.8 Conclusion In this chapter, the full potential nature of the wavelet analysis has been exploited through developing appropriate algorithms. Application to multi-scalar surfaces has been investigated. It has been shown that: 1. The theory of the lifting wavelet model is relatively new, simple and natural. The wavelet filtering process comprises three steps. The first is to decompose a surface original signal z(x,y) to a sequence of subsets that transfers space based information into scale based information which represents both the frequencies of z(x,y)and their location in scalar space. Following this, the next step is to separate and capture the different frequency components involved in z(x,y) within selected transmission bands, and finally the different frequency surfaces can be reconstructed in the spatial domain. 2. The wavelet transform algorithm is much easier and faster than conventional filtering methods, and the transform procedure only embraces three stages: "plus", "minus", and application of the weighting algorithm. All computations are carried out in-place through rows and columns, no extended memory is needed and the algorithm procedure is much faster than normal filtration methods. 3. The behaviour of the wavelet technique for surface analysis has initially been tested by experimental work. The practical evidence given shows that the filtered outcomes resemble the original waveforms very closely with no relative shift in the defined transmission band, as a result the components have similar positions upon emerging from filtering and the peaks and valleys can be preserved unambiguously. 4. Using the segment property in scalar domain, various surfaces can be flexibly, perfectly and immediately reconstructed according the intended requirements of functional analysis. The surface textures can be highlighted and multi-scalar topographical events can be identified and clearly recovered. The information obtained could be fed back to monitor a manufacturing processes for example, or to study actual contact stress, loaded area, asperity volume and lubrication regimes occurring during the initial stages of wear of surfaces in service. The wavelet methods and the corresponding algorithms allow a better understanding of the 3d surface. The different frequency components of surfaces can be considered and retrieved with the excellent refinement accuracy in the light of these algorithms. For industrial application purposes, the method has considerable merits.
5.9 References 1.
ISO 11562 1996 Geometrical Product Specification (GPS) - Surface texture: Profile method - Metrological characterisation of phase correct filters
2.
Stout K.J., Sullivan P.J., Dong, W.P., Mainsah, E., Luo, N., Mathia, T. and Zahyouani, H. 1993 The Development of methods for the characterisation of roughness in three dimensions, Commission of the European Communities, (ISBN 070441 313 2)
3.
Whitehouse, D.J. 1994 Surface Metrology, 1st edn, Bristol and Philadephia, Institute of physics publishing
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Advanced Techniques for Assessment Surface Topography
4.
Nayak, P.R. 1971 Random process model of rough surface, Tran. ASME, J. Lubric. Technol, 39, pp.398-407
5.
Wallach, J. 1969 Surface topography description and measurement. Proc. of ASME Symposium on Surface mechanics, New York
6.
Weszka, J. S., Dyer, C. R. and Rosenfeld, A. 1976 A comparative study of texture measures for terrain classification. IEEE Trans. Systems, Man, and Cybernetics, 6, pp.269-285
7.
Sato, H. and O-hori, M. 1981 Characteristics of two dimensional surface roughness taking self-excited chatter marks as objective. Ann. CIRP, 30, pp.481 486
8.
Sherrington, I. and Smith, E. H. 1988 Fourier models of the surface topography of engineering components. Surf Topography, 1, pp.11-25
9.
Whitehouse, D.J. and Zhang, K.G. 1992 The use of dual space-frequency functions in machine tool monitoring, Meas. Sci. Techno!., 3, pp.796-808
10. Zhang, K. and Whitehouse, D.J. 1992 The application of the Wigner distribution function to machine tool monitoring,. Proc., Inst. Mech. Eng, 206, pp. 249-264 11. Meyer, Y. 1993 Wavelets: algorithms and applications, 1st edn, Philadelphia, SIAM 12. Daubechies, I. 1992 Ten lectures on Wavelets, 1st edn, Philadelphia, SIAM 13. Chui, C.K. 1992 An Introduction on Wavelets, Philadelphia, SIAM 14. Gabor, D. 1946 Theory of communication, J. of the IEE, 93, pp.429-457 15. Allen, J. B. and Rabiner, L. R. 1977 Aunified approach Short-Time Fourier analysis and synthesis, Proc. IEEE, 65, pp. 1558-1564. 16. Wigner, E. 1932 On the quantum correction for thermo dynamic equilibrium, Phys. Rev., 40, pp.749-759 17. Chen, X., Raja, J. and Simanapalli, S. 1995 Multi-scale analysis of engineering surfaces. Int. J. Mach. Tools Manufact., 35, pp.231-238. 18. Jiang, X.Q. and Li Z., 1994 The development Wavelet spectral analysis system for surface characterisation, NNSF No: 59375255, China 19. Jiang, X.Q., Blunt, L. and Stout, K.J. 1997 Recent development in the characterisation technique for bioengineering surfaces. Transactions, of the 7th Metrology and Properties of Engineering Surface, 2nd-4th, April, Sweden 20. Jiang, X.Q., Blunt, L. and Stout, K.J. 1997 Evaluation of functional features of the orthopaedic joint prostheses surfaces using Wavelet analysis. Proc. ofASPE 1997 Spring Topical Meeting, Advances in Surface Metrology, Annapolis, Maryland 21. Jiang, X.Q., Blunt L. and Stout, K.J., 1999 Three-dimenssional surface characterization for orthopaedic joint prostheses, Journal oflnstn. Mech. Engrs, Part H 213 pp.49-68 22. Strang, G. and Nguyen, T. 1996 Wavelets and filter banks, 1st edn, WellesleyCambridge Press
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23. Mallat, S.Q. 1989 A theory for multiresolution signal decomposition: The Wavelet representation, IEEE transaction on pattern analysis and machine intelligence, 11, pp. 674-693 24. Daubechies, I. 1990 The Wavelet transform time-frequency localisation and signal analysis. IEEE Trans, on Info. Theory, 36, pp.961-1005 25. Stollntz, E.J., Derose, T.D. and Salesin, D.H. 1996 Wavelets for computer Graphics, Morgan Kaufhiann Publishers, San Francisco 26. Swelden, W. 1996 The lifting scheme: a custom-design construction of biorthogonal Wavelets, Appl Comput Harmon A 3 (2) pp. 186-200 27. Swelden, W. 1998 The lifting scheme: a construction of second generation Wavelets, Bell Laboratories Siam JMath Anal 29 (2) pp.511-546 28. Swelden, W. 1996 The lifting scheme: A new philosophy in Biorthogonal wavelet constructions, Bell Laboratories 29. Jiang, X.Q., Blunt, L. and Stout, K.J., Wavelet framework for surface analysis, Proceedings of The Fourth International Symposium of Measurement technology and intelligent instruments 2nd-4th Sept. 1998, University of Miskolc, H-3515, Miskolc, ISBN 963 8455 578 pp. 165-172 30. X.Q. Jiang, L. Blunt and K.J. Stout, 2000, Development of a lifting wavelet representation for surface characterisation, Proc. R. Sco. Lond. A. 456 pp. 1-31 31. ISO/DTS 16610-29,2002 Geometrical Product Specification (GPS) - Filtration Part 29: Linear profile filters: Spline Wavelets 32. SJ. Xiao, X.Q. Jiang, L. Blunt and P.J. Scott, 2001 Comparison study of biorthogonal spline wavelet filtering for areal rough surfaces, Int. J. Mach. Tools Manufact. 41, pp.2103-2112 33. Stoer, J. and Bulirsch, R. 1980 Introduction to Numerical Analysis, 1st edn, New York Springer Verlag 34. Trumpold, H., 1998 Why Filtering surface profiles, Int. J. Mach. Tools Manufact. 38,pp.263-271 35. X.Q. Jiang, L. Blunt and K.J. Stout, 2001 Application of the Lifting to rough surface, J. of the International Society for Precision Engineering and Nanotechnology, 25 pp. 83-89 36. X.Q. Jiang and L. Blunt, Report 4 for 3D Surface Metrology for the Machine Tool Diagnostics and Control, EPSRC Project GR/R13401/01 37. X.Q. Jiang and L. Blunt, 2001 Morphological assessment of in Vivo wear of orthopedic implants using Multiscale wavelets, Wear, 250 pp.217-221
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Parti Instrumentation
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6
Calibration Procedures for Stylus and Optical Instrumentation Jean Francois Ville Hommel Somicronic, Saint Andre De Corey, France
6.1 Introduction The primary purpose of chapter is to outline the development of procedures for the calibration of 3D surface metrology instruments; namely contacting stylus type and scanning optical probe types. In terms of a definition calibration of a 3D surface texture measuring instrument is carried out for the purpose of verifying that a measurement instrument produces results that are in accordance and traceable to the appropriate national and or international standards. Throughout the chapter the actions of calibration and verification have been intentionally separated. •
Calibration consists of measuring an element whose dimensions are known and checking whether the instrument performs the measurement correctly. The calibration process therefore comprises the modification of internal parameters, which characterise the relation between the variations given by the probe and its real displacement.
•
Instrument verification consists of measuring a certain number of artefacts (calibration specimens or software) and verifying whether the measurement results correspond to the results expected. Importantly, no modifications of internal parameters of the instrument are subsequently implemented.
Additionally for the sake of clarity various families of instrument were defined during the development of the procedures. •
Type 1: tactile instruments; composed of two mechanical drives translationing along horizontal X and Y axes, with a tactile probe measuring the altitudes of the sampled points (Z axis). A further sub division of this family can be made as follows: • Type 1.1: Tactile three-dimensional instruments of the first type with a low vertical measuring range, specifically designed for the measurement of surfaces whose main generatrix is plane.
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Advanced Techniques for Assessment Surface Topography •
•
Type 1.2: Tactile three-dimensional instruments of the first type with a high vertical measuring range, designed for the measurement of skewed or formed surfaces.
Type 2: optical instruments driven by translation mechanisms; composed of two mechanical drives operating in translation along horizontal X and Y axes, with an optical probe measuring remotely the altitudes of the sampled points (Z axis). A further sub division of this family can be made as follows: • Type 2.1: Optical three-dimensional instruments of the second type with a low vertical measuring range, specifically designed for the measurement of surfaces whose main generatrix is plane. • Type 2.2: Optical three-dimensional instruments of the second type with a high vertical measuring range, designed for the measurement of skewed or formed surfaces.
•
Type 3: optical instruments; composed of one high magnification microscope, e.g. an interferometric system measuring the altitudes of the sampled points (Z axis) where the measurement area is defined by the optics of the microscope, usually a CCD camera.
Further information regarding the types of standards artifacts defined in the chapter and instrument acceptance and periodical verification tests are given in Appendix A.
6.2 Definition of measurement errors 6.2.1 Working hypothesis • It was assumed that the instruments are used in their field of application (local slopes compatible with diamond tip and/or light reflection). •
Temperature conditions (the temperature variations observed in the measurement rooms are small enough to be considered negligible).
•
Only the systematic errors linked with the instruments are taken into account. No account is taken of the random errors (errors linked with measurement method or due to the operator) that are not directly linked with instrument characteristics; therefore, they are not taken in account during the calibration process.
•
The instruments discussed in this survey use an indirect measurement method of characterizing the 3 dimensions X, Y and Z of the surface.
Calibration Procedures for Stylus and Optical Instrumentation
121
Figure 6.1 Classification of 3D surface measurement instruments
6.2.2 Working method • Determination of the origins of the systematic errors by decomposing the sources of errors. •
Expressing the features measured by the instrument as functions of the different parameters linked with these sources of errors.
•
Determination of the systematic errors on each of the identified components by measuring basic measurement standards (master or calibration specimens) presenting a very simple geometry and featuring the smallest possible uncertainty on their main dimension (examples: optical flat, sphere).
The measurement error is then: I
=
I Result of measurement of one feature Systematic errors
(one) true value of this feature | Random errors
The systematic errors comprise: • Residual errors obtained after corrections. • Errors due to the quality of components. • Errors linked with the measurement uncertainty of calibration specimens.
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Advanced Techniques for Assessment Surface Topography
The random errors are due to: • Errors due to the operator. • Errors due to the measurement method. • Errors due to the variations of environmental conditions.
Figure 6.2 Error correction chain and sources of error for a scanning stylus tip
Calibration Procedures for Stylus and Optical Instrumentation
123
Table 6.1 Parameters influencing the measurement of instrument quantities Items
Components
Parameters
Quantities involved
H = Vertical height from the tip to the probe spindle
X
Arc distortion
L = Horizontal length from the tip to the probe spindle
X
Stylus tip
rtip = Radius of the tip
Transducer
Cz = Calibration coefficient
Stylus
Hyz = Vertical hysteresis Probe
Transducer and pivot Fz = Response curve Analog-to-digital converter
Horizontal positioning control
Dz = Vertical acquisition step
XandZ
Z Z Z
Fx, Fy = Response curves Linear encoder, lead screw, ...
Cx, Cy = Calibration coefficients
XandY
Dx, Dy = Acquisition steps (sampling) ORT = orthogonality between the X and Y displacements
Z
FLATZ (X,Y) = Z component of the flatness of the reference guide with respect to the XY plane. It could be expressed in terms of: STRZ (X) = Z component of the straightness along the X axis STRZ (Y) = Z component of the straightness along the Y axis
XandY
Areal reference guide, horizontal component (twisting)
STRy (X) = Y component of the straightness along the X axis STRX (Y) = X component of the straightness along the Y axis
Z
3D measurement process
Bdf = Dynamic background noise
Areal reference guide, vertical component Drive units
Hyx, Hyy = Repositioning hystereses
XandY
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Advanced Techniques for Assessment Surface Topography
6.2.3 Definition of the transfer characteristic Transfer characteristics, linearity deviation and amplification coefficient graph is shown below.
Figure 6.3 Schematic response curve for and 3D scanning instrument Table 6.2 Classification of error origins for each instrument family
\
y
3D measurement process Drive unit Stylus / beam y twisting Drive unit Stylus \ twisting Drive unit Probe
\,y&z
Stylus / beam Measurement loop and surrounding conditions Measured sample
Family 1 H, L Hyx & Hyy Fx, Dx & Cx H,L,&r t i D STRx(y) Fy, Dy & Cy
Parameters Family 2 Hyx & Hyy Fx, Dx & Cx r
beam
STRx(y) Fy, Dy & Cy
Ttin
Rbeam
STRV (x) STR2 (x) + STRz(y) Fz, Cz, Hyv & Dz
STRV (x) STRZ (x) + STRI(y) Fz, Cz, Dz, Hyv, CLv & RSv
rtio Bdf Tribological features
Family 3 For white light interferometers: • The achromatic characteristic of the lens • The knowledge of the wavelength Wavelength stability Shifting error Datum mirror flatness CCD resolution
BDF
Rbeam
Bdf Optical features
Optical features
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125
Table 6.3 Assessment of errors and evaluation of correction methods Parameter
Origin of the error
H&L
AH, AL = Arc error due to a bad knowledge of the stylus geometry Artip = Bad knowledge of the radius value
r«ip
r
beam
Fz
Cz
Dz
CLv RSv
Hyv
Residual error
Correction method Calibration on a sphere and assessment of these parameters
•
Assessment of the radius value using a microscope.
•
•
?
•
•
Measurement of the • response curve using a laser interferometer and • compensation
ACz = Bad knowledge of the calibration coefficient ACz = f (measurement length) ADz = ± 1 digit of the A to D converter
•
Calibration of the vertical amplitudes Tool: a sphere or a calibrated groove.
• •
None. High resolution ADC
Phase shifting due the response delay of the close loop Bad sensitivity to low reflected light rays
•
None except the improvement of the close loop None Reducing of the measurement speed can improve results
Arbean, = Bad knowledge of the radius value AFz = Linearity deviation of the probe AFv = f (measured amplitude)
AHyv = Different reactions linked with the type of variations of the measured amplitudes
•
• •
•
•
•
•
Residual error check Uncertainty on the • Measurement sphere radius of a sphere Form deviation of the sphere Form deviation of • Measurement the radius of a sphere Uncertainty of the • Measurement radius of a stylus measurement check sample ? • Measurement of a stylus check sample Measurement • Measurement uncertainty on the of calibrated interferometer spheres Linearity • Measurement deviation of step gages repeatability Uncertainty on the • Measurement characteristics of of calibrated the calibration spheres sample • Measurement of step gages
Not applicable •
Measurement of step gages
•
Measurement of roughness gages with different reflectivity Measurement of a calibrated sphere Measurement of roughness specimens
Not applicable
Not applicable
None
• Not applicable
•
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Advanced Techniques for Assessment Surface Topography
Parameter Fx,Fy
Origin of the error AFx & AFhy = Linearity deviation of the positioning, function of the measured stroke
Correction method • Measurement of the response curve using a laser interferometer
•
Dx,Dy
Cx, Cy
STR (\)/ o i i^-j V STRz(y)
STRy (X)
STRx(y)
Hyx,Hyy
Bdf
Bad definition • of the horizontal • position of the measured points
ACx = (Cy) Bad knowledge of the horizontal calibration coefficient. ACx(Cy) = f[X(Y) measurement lengths] ASTRZ = vertical component of the straightness deviation of the drive units ASTRz = f[X(Y) length] ASTRy (x) =Twisting of the x axis with respect to the y axis ASTRX (y) =Twisting of they axis with respect to the x axis AHyx,Hyy = Repositioning error to the starting point of each profile AHyx, Hyy creates a connection error between the measured profiles ABdf = Measurement noise
•
•
•
compensation None Increasing the sampling improves the accuracy Calibration of the horizontal amplitudes. Using a double sphere or a double scratch Software compensation if repeatable
•
the •
and •
Residual error Measurement uncertainty on interferometer Linearity deviation repeatability
Residual error check Measurement in both directions of step calibrated specimens
Not applicable
•
•
Uncertainty of the calibration sample characteristics
Straightness deviation of the drive units due tonon repeatability of the straightness deviation
•
None
Not applicable
•
None
Not applicable
•
None
Not applicable
•
Measurement of horizontal gages
•
Measurement of a horizontal optical flat
•
Measurement of a vertical optical flat
•
3 dimensional measurement on a sphere
•
Measurement of an optical flat
In order to realise the aims of this chapter a number of general calibration specimens used to calibrate the measured dimensions X, Y and Z were proposed, as well as methods for controlling the metrological characteristics available for all kinds of 3D surface texture measuring instruments. Instrument checking is realised in two stages: 1. By exclusive usage of the specimen supplied with the instrument for its usual calibration, to determine the essential parameters which are liable to vary along with environmental factors. The following parameters are concerned: Cz= amplification coefficient of the probe for the dimension Z Cx= amplification coefficient for the horizontal dimension X Cy= amplification coefficient for the horizontal dimension Y H & L = parameters of the stylus geometry, which are essential in the case of probes with high vertical measurement range. ORT = Orthogonality between X and Y axes.
Calibration Procedures for Stylus and Optical Instrumentation
127
2. By verification, checking of all the parameters having influence on the measurement characteristics. The operation (requiring complex means and high accuracy specimens) could be carried out by the instrument users for some parameters or would need to be reported to the instrument manufacturer or to accredited laboratories. Operations requiring a link to the national organisations implies the use of certified specimens as a means of control. Note: the choice of a time interval between two verifications is left to the user; however, a one year interval is recommended. The following parameters are concerned: rtip or rbeam = tip radius Fv = response curve in Z Hyz = hysteresis according to Z Fx, Fy = response curve in X or Y Hyx, Hyy = hysteresis according to X or Y Bdf = measurement background noise FLAT2(X,Y) = Z component of the flatness of the reference guide with respect to the XY 'plane. It could be expressed in terms of: STRZ (X) STRZ (Y) STRy(X) STRX(Y)
= = = =
Z component of the straightness along the X axis Z component of the straightness along the Y axis Y component of the straightness along the X axis X component of the straightness along the Y axis
The goal of the above is the assessment of the calibration coefficients Cx, Cx and Cz with the best possible accuracy and as a result, the calibration specimens may be chosen as follows: Table 6.4 Suggested calibration specimens Instrument type Calibration mode for the dimension Z Calibrated groove 1.1 Specimen sphere 1.2 2.1 Calibrated groove 2.2 Specimen sphere 3 Calibrated groove
ISO 5436-1 designation AlorA2 El AlorA2 El AlorA2
6.3 Calibration of type 1 and type 2 instruments 6.3.1 Calibration of vertical amplitudes: dimension Z The goal of this section of work was the assessment of the calibration coefficient Cz with the best possible precision. Several possibilities were considered: A first option was to use the same specimens as those used for traditional twodimensional surface texture measuring instruments, such as specimens characterised by averaged parameters (Ra or Rz for instance).
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Advanced Techniques for Assessment Surface Topography
A detailed description of these parameters is not given, since their description may be found in the draft of the ISO 5436-1 [1] standard, under the denomination "D type specimens". However, these specimens were not considered desirable for the calibration of instruments, as they appear to be better suited to the verification of instruments for the following reasons: •
•
•
The procedure involved usually consists of measuring these specimens, then applying computation algorithms and finally determining the averaged surface texture parameters, which presents the interesting feature in that it checks the global line of acquisition, which in return considerably raises the calibration uncertainty. The construction of these specimens is generally delicate and their characteristic dimension (Ra for instance) is known with a rather significant uncertainty, which directly affects the precision of the calibration. The characteristic dimension of these specimens originates from a mean computed over n local values, this mean is thus a function of the measurement length, and of the area and starting point of the measurement.
According to ISO 5436-1 a number of specimens are available that are useful for the calibration of amplitudes: these are the "specimens type Al or A2" (depth measurement standards), which may be used with no difficulty by type 1 tactile systems as well as type 2 optical systems. However, the A2 type is strongly recommend in order to obtain a better compatibility of the measured slopes with the measurement ability of surface finish instruments combined with easy and inexpensive manufacture. These specimens offer a number of advantages: •
Ease of construction.
• •
Their characteristic dimension (depth) may be known with a high precision. They are easy to operate and to measure.
Drawbacks: •
To a certain extent, the accuracy of the knowledge of their characteristic height (approximately one percent) may not be considered sufficient for top of the range instruments.
•
They only calibrate one point within the vertical measuring range of the probe, the one that corresponds to the depth of the groove. Consequently, the linearity deviation is not taken into consideration.
•
They do not allow the assessment of the stylus geometry (parameters H & L), which is fundamental whenever measurements of contours are performed.
An alternative is given by the spherical specimens type El (precision sphere) cited in the standard [1]. This kind of specimen offers numerous advantages over type A specimens, among which are the following: • •
A high precision sphere can be obtained very easily. The characteristic dimension (the radius) is known very accurately.
Calibration Procedures for Stylus and Optical Instrumentation • • •
129
Knowledge of the radius allows calibration of the dimension Z (used for determining Cz). Knowledge of the form allows assessment of the stylus geometry (parameters H & L) which then makes it possible to correct the arc distortion. The measurement of a sphere with a wide vertical range of measurement allows control of the linearity deviation of the probe.
Drawbacks: • •
The calibration procedure necessitates a measurement process (positioning on the top of the sphere) and a relatively complex algorithm. This kind of calibration applies to instruments of the first type essentially, since optical probes do not present arc distortions due to their geometry (which corresponds to L=0).
In fact, calibration on a sphere is especially advantageous when applied to threedimensional surface texture measurements of workpieces with form, or twodimensional measurement of workpieces with form. This is because the arc distortion may be corrected thanks to the knowledge of the H and L parameters for the instruments of the first type. Although the arc distortion does not affect the roughness components of a two-dimensional profile, it causes the profiles that comprise a threedimensional measurement to shift (in the direction perpendicular to the profiles' measurement axis) if the measured piece contains a form component. However, the influence of the arc distortion is considered to be negligible for the measurement of levelled plane pieces. As a consequence, it seems appropriate to divide the first type of instruments into a two new categories: •
Type 1.1: Tactile three-dimensional instruments of the first type with a low vertical measuring range, specifically designed for the measurement of surfaces whose main generatrix is plane.
•
Type 1.2: Tactile three-dimensional instruments of the first type with a high vertical measuring range, designed for the measurement of skew surfaces.
As a result, the calibration mode may chosen as follows: Table 6.5 Calibration technique for different types of instruments Type 1.1 1.2 2 3
Calibration mode for the dimension Z calibrated groove specimen sphere calibrated groove calibrated groove
ISO 5436-1 designation AlorA2 El
AlorA2 AlorA2
6.3.2 Calibration of the horizontal drives: X and Y dimensions In the same way as for vertical amplitudes, the aim here is to assess the calibration coefficients Cx and Cy with the best possible precision.
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Advanced Techniques for Assessment Surface Topography
As with the previous calibration, a first option would be to use the same specimens as those used for two-dimensional surface texture measuring instruments, such as specimens characterised by averaged parameters (for instance Sm or Ra), where these specimens are defined in accordance with the ISO 5436-1 [1] as "D type specimens". Nevertheless, these specimens are not really suitable for the purpose of a calibration procedure. The specimens are much better adapted to the verification of an instrument for the same reasons as those given in the previous section, in addition to the fact that the calibration of the X and Y axes would have to be carried out twice, given that one measurement is required for each axis. Additionally, the specimen would have to be positioned very accurately (levelling of the specimen relative to X and Y displacements) in order to minimise the calibration uncertainty. Therefore, it seems useful to define a specimen for which the essential feature can be assessed with a high accuracy and which would allow a global calibration of both X and Y axes with an easy set-up. It would therefore seem relevant to define a specimen whose essential characteristic could be determined with a high precision and which would allow a global calibration of the X and Y dimensions, while offering as simple a procedure as possible. Several possibilities are conceivable, depending on the type of instruments considered: 6.3.3 Spaced twin groove spaced specimen (ER1)
Figure 6.4 Twin grooved calibration specimen (ER1)
Calibration Procedures for Stylus and Optical Instrumentation
131
Advantages of this kind of specimen: •
Easy manufacturing, two ground groves may be machined on a gage block.
•
The distance between the two grooves can be assessed with a high accuracy.
•
Applicable to all kinds of instruments.
Disadvantages: •
As mentioned above, this kind of specimen requires two measurements (one for each axis) and a fine levelling.
6.3.4 Specimen with a twin net of two perpendicular grooves (ER2)
Figure 6.5 Specimen with a twin net of two perpendicular grooves (ER2) Advantages of this kind of specimen: •
Allows a global calibration of both the X and Y axes through a single 3D measurement.
•
The levelling with respect to the horizontal drive is not required (however a vertical levelling is still advisable), as it may be performed mathematically. Indeed, it would even be preferable to tilt the specimen (rotation around the vertical axis) in order to ensure the correct measurement of the groove bottom.
•
Applicable to all kinds of instruments.
•
The distance between the two grooves can be assessed with a high accuracy.
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Advanced Techniques for Assessment Surface Topography
Disadvantages: •
The perpendicularity requirements between both nets of groves may be difficult to manufacture.
•
A groove presenting a constant depth is probably also difficult to obtain.
6.3.5 Specimen with circular groove (ER3)
Figure 6.6 Calibration specimen with a circular groove (ER3) Advantages of this kind of specimen: • • • • • •
Allows a global calibration of both the X and Y axes through a single 3D measurement. The levelling with respect to the horizontal drive is not required (however a vertical levelling is still advisable). A mathematical algorithm may calibrate both axes thanks to the known diameter of the groove. The small circularity defects of the carved groove may be compensated for analytically by determining the least squares circle. Applicable to all kinds of instruments. Relatively easy manufacturing by carving (with a laser for instance) on a precision spindle.
Calibration Procedures for Stylus and Optical Instrumentation
133
Drawbacks: •
Difficulty in realising a groove with a consequent and constant depth.
•
Uncertainty in the knowledge of the carved diameter.
6.3.6 Specimen intersection plane/sphere (ESI)
Figure 6.7 Calibration specimen having an intersection plane/sphere (ESI) Advantages of this kind of specimen: •
Allows a global calibration of both the X and Y axes through a single 3D measurement.
•
The levelling with respect to the horizontal drive is not required (however a vertical levelling is still advisable). A mathematical algorithm may calibrate both axes thanks to the diameter resulting from the intersection between the plane and the sphere.
• •
There is a high precision on the knowledge of the circle diameter since it is obtained analytically using the known sphere radius and the measured remaining height.
•
Easy manufacturing, sufficient to only machine a precision plane, whilst high precision spheres can be easily found.
Drawback: • Only applicable to type 1.2 instruments due to the required wide vertical range of measurement.
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6.3.7 Specimen intersection plane/sphere (ES2)
Figure 6.8 Calibration specimen comprising an intersection plane/sphere (ES2) Advantages of this kind of specimen: • •
Allows a global calibration of both the X and Y axes through a single 3D measurement. The levelling with respect to the horizontal drive is not required (however, a vertical levelling is still advisable).
•
A mathematical algorithm may calibrate both axes thanks to the diameter resulting from the intersection between the plane and the sphere.
•
High precision on the knowledge of the circle diameter since it is obtained analytically using the known sphere radius and the measured portion of the sphere.
•
Applicable to all kinds of instruments, since only a small vertical measuring range is required.
Drawback: •
More complex manufacturing than the previous specimen, as a very high quality flat needs to be machined on a ball.
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6.4 Synthesis of the calibration of the three dimensions X, Y & Z An examination of the specimens described in the previous sections shows that a number of specimens used for the calibration of the horizontal dimensions could also be employed for the calibration of the dimension Z. In general, it should be possible to use these specimens for the calibration of the dimension Z, provided that an additional dimension, such as the depth, be characterised. However, it would probably be preferable to carry out two measurements in order to achieve this calibration. In fact, the calibration of the Z dimension necessitates a much higher precision than that required by the horizontal dimensions, given their respective magnitudes (um vertically and mm horizontally). Furthermore, the calibration process usually imposes an associated mode of measurement such as the positioning on the top of a sphere, which may vary according to the dimension considered. •
•
An initial two-dimensional measurement for the calibration of vertical amplitudes (dimension Z) based on a given characteristic of the specimen (groove depth or sphere radius) A three-dimensional measurement for the calibration of the horizontal drives (dimensions X and Y) based on the additional characteristics of these samples.
Note: an entirely automatic measurement process which would perform two and three-dimensional acquisitions with no need for any user intervention could easily be developed. The following specimens could be appropriate for this purpose: •
ER1: Spaced twin groove specimen: The inter-groove distance characteristic would apply to the calibration of the dimensions X and Y via two two-dimensional measurements. The depth characteristic of one or two grooves would apply to the calibration of the dimension Z via a two-dimensional measurement.
•
ER3: Specimen with a circular groove: The radius characteristics (K) of the circular groove is appropriate to the calibration of the quantities X and Y and the depth characteristics (//) applies to the calibration of the quantity Z via a single three-dimensional measurement. Additionally, this allows the assessment of the perpendicularity between the two X and Y drive units.
•
ES1: Specimen intersection plane/sphere: The diameter of the circle resulting from the intersection between the plane and the sphere would apply to the calibration of the dimensions X and Y via a single three-dimensional measurement. The sphere radius and possibly the height of the portion of the sphere would apply to the calibration of the dimension Z via a two-dimensional measurement.
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6A.I Summary Given the observations made in the previous sections, a summary table of the calibration modes as a function of the types of instruments may be established: Table 6.6 Calibration artefact designation Calibration modes of the dimensions X, Y and Z Type of specimen
Double calibrated groove
Double net of perpendicular grooves
Intersection sphere/plane
Designation of the specimen
ER1
ER3
ESI
ISO 5436-1 designation close or applicable to the form of the groove
recommended A2 (possible Al)
recommended A2 (possible Al)
El
Type of instrument
1.1, 2 and 3
1.1, 2 and 3
1.2
Further information concerning the standard artefact types in given in Appendix A. 6.5 ESI calibration specimen tests 6.5.1 Characteristics of the master
Figure 6.9 Schematic representation of ESI calibration sample
The essential characteristics of the master, that are used during the calibration of the instrument, are the following: •
the height of the segment of the sphere: H
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the diameter of the circle defined as the intersection between the sphere (S) and the plane (P): Di
The height may be determined through a straightforward measurement. For the determination of the intersection diameter Di however, it is necessary to perform the measurement of other characteristics, which will be referred to as secondary characteristics. In any case, the essential characteristics of the master are irremediably dependent on its secondary characteristics. •
Sphere radius: R The sphere radius has to be known with precision for an accurate determination of the Di characteristics:
The uncertainty on Di, denoted ADi, is therefore directly linked to the uncertainty on R and H. It may be determined as follows:
The flatness deviation of the plane P: AP This deviation also plays an important role in the uncertainty of the essential characteristics of the master, indeed the determination of H is directly dependent onAP:
Figure 6.10 Schematic representation of flatness deviation on the reference plane surface Nevertheless, it is possible to integrate AP when determining H: the measurement area should be close enough to the sphere and the flatness should be taken into account in the instrument calibration process. The sphericity deviation of the sphere: AR This deviation has a similar degree of influence as that of the flatness, but it is more directed at the Di characteristics. Unfortunately, it cannot really be compensated through tricks in the measurement or in the process. On the other hand, it may be considered negligible given the quality of reference spheres (please refer to the table in the following paragraph). It should be noted that sphericity is difficult to measure with the instruments available on the market today. Hence, in the present project, circularity measurements along multiple meridians were carried out.
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Values obtained on the masters # ES1-001 and n° ESI-002: The essential and the secondary characteristics of the manufactured master were determined in the following way: •
Determination of the sphere radius R: The sphere radii were given by the supplier; this company was accredited by the Bureau des Poids et Mesures of Berne. In this development phase it did not seem necessary to control these values. However, in order to respect the calibration chain, the intention is to obtain the certification of these spheres from a suitable national standards organisation. The radii obtained were the following: ESI-001: R001 = 15 010.1 fim± 0.3 pm ESI-002: R002 - 14 994.2 urn ± 0.3 pm
•
Determination of the circularity deviation AR: As for the previous case, values given by the supplier were used, as before, however, the intention is to obtain the certification of these spheres from a suitable national standards organisation. The circularity deviations were as follows: ES1-001: AR001 = 0,040 fim ± 0.001 fim ESI-002: AR002 = 0.030 fim ± 0.001 um
•
Determination of the flatness deviation of the plane AP: A three-dimensional measurement of the whole surface of the plane P was realised using a Surfascan 3D instrument. The measurement resulted in a planar surface on which the form deviation could be obtained after applying a small low-pass filter (cut-off 0.25 mm) to remove the undesirable roughness components. The form deviation was then assessed using an St type parameter. In order to determine the measurement uncertainty, an optical flat was measured on the same zone and the same filtering process was applied. The results were the following: ES1-001: AP001 = 1.6 pm ± 0.3 pm ES1-002: AP001 = 2.2 >im ± 0.3 jim
•
Determining the height H: The height of the segment of the sphere above the plane was determined using a Surfascan 2D instrument that was previously calibrated on a certified sphere with radius close to that of the ESI master. Some profiles were measured every 10
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degrees (36 measurements) along the meridians of the master, in order to gain an idea of the dispersion with respect to the flatness deviation of the plane P. The values obtained were: Table 6.7 Height values for ESI masters Master n° ESI -001 ES1-002
Min H (nm) 5114.7 2092.4
Max H (jim) 5116.3 2094.9
Std dev. (urn) 0.4 0.35
Mean H (nm) 5115.5 2093.1
To consolidate these results, other means of measurements were employed: - a measurement column relative to a master step; - a numeric gauge applied with respect to a master step. In both cases, there was a need to cope with uncertainty problems on these control devices: - for the measurement column: uncertainty of repeatability = ± 1 um; - for the numeric gauge: uncertainty of repeatability = ± 2 um due to a backlash on the summit of the sphere. Once averaged of the results obtained confirm those obtained above. As a result, the averaged value of H obtained through the measurements will be used throughout as: ES1-001: H001 = 5115.5 jim ± 0.8 pm, ES1-001: H002 = 2093.1 fun ± 0.7 >im, The uncertainty is determined over a basis of two standard deviations. As for the other uncertainties these shall be certified by a suitable organisation. •
Determination of the intersection diameter Di: As has been shown previously, the diameter Di, defined as the intersection of the sphere and of the plane, is a function of the characteristics R and H. After applying the formula, the following was obtained: ES1-001: DiOOl = 22 570.8 jim ± 3.1 jun ES1-002: Di002 = 15 287.8 jirn ± 3.3
Table 6.8 Nominal characteristics of the ESI masters ES1-001 Parameter Sphere radius, R Height, H Intersection diameter, Di Flatness deviation, AP Circularity deviation, AR
Nominal value 15010.1 urn 5115.5^ra 22 574 um 2.2 urn 0.040 urn
Uncertainty ± 0.3 um ± 0.8 um ± 3 . 1 um ± 0.3 urn ± 0.001 ^im
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Nominal value 14 994.2 um 2093.1 um 15288 urn 2.2 jim 0.030 um
Uncertainty ± 0.3 urn
± 0.7 um ± 3.3 um ± 0.3 urn ± 0.001 urn
After improvement of the ESI-001 especially in terms of flatness, better results were obtained.
Figure 6.11 3D map and 2D profiles of ESI master
6.5.2 Three-dimensional measurement tests Once the essential characteristics of the ESI masters were determined, interest was focused on the functional aspects of this type of master, such as the calibration or the verification of the X, Y and Z dimensions of a three-dimensional instrument. The following analysis is focused on the ESI master because this master allows the calibration of most dimensions, whilst remaining easy enough to manufacture. It may prove less convenient to use with optical systems than the ES2 master, but this latter is far more difficult to manufacture.
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The analysis was realised through numerous three-dimensional measurements using a Surfascan 3D. Figure 6.11 is a 2D representation of such a measurement seen from above. To take advantage of these measurements, profiles were extracted along the X and Y axes and then batch processed using 2D procedures. The aim is the following: To determine the X, Y and Z dimensions of a three-dimensional instrument through the measurement of the master. Of initial interest are the X and Y dimensions, which in fact come from determining the values of the diameter Di along these two axes. Indeed, if one axis yields an error with respect to the other one, the intersection circle presents a deformation in the considered direction, as shown below in Figure 6.12:
Figure 6.12 Schematic representation of XY axis error It is necessary to compare the diameters Di(X) and Di(Y) obtained along the two axes with the nominal diameter Di to determine the associated positioning errors. A simple method would involve extracting a profile going through the summit of the sphere along the X axis (or Y axis), to determine the points of intersections between the circle and the line obtained and then to measure the distance between those two points in order to get Di(X) (respectively Di(Y)) measured by the instrument. Unfortunately, this method has a number of drawbacks: • •
It is difficult to ensure that the extracted profile is on the summit of the sphere, because of the acquisition step. Even if this could be ensured, the slightest defect or measurement anomaly would considerably increase the uncertainty.
Hence a method is used that would minimise this source of error thanks to a higher number of extracted profiles and the filtering of these profiles using the least squares method.
6.6 Improving the ESI master The essential characteristics of this master, that are critical for the calibration of an instrument are: The height of the sphere (S) summit with respect to the plane (P): H
142 •
Advanced Techniques for Assessment Surface Topography The diameter of the circle resulting from the intersection between the sphere and the plane: Di
The height H may be determined through a direct measurement, whereas the diameter Di is determined through an indirect process: other "secondary" characteristics need to be measured for determination of Di. These dimensions are all a function of the following parameters: • • •
The sphere radius: R The flatness deviation of the plane P: AP The sphericity deviation of the sphere: AR
On the first prototypes of ESI masters, it was observed that the sphericity deviation was small enough to be neglected (< 0.1 um). The uncertainty over the sphere radius is also negligible (± 0.3 um). On the other hand, the flatness default of the plane P had a significant effect on the final uncertainty of the dimensions R and Di. Improving the flatness: In order to obtain the initial prototypes with a good flatness, a preliminary finish was achieved through plane rectification followed by plane grinding. This method remains best suited for this kind of realisation and the task was to improve it, whilst keeping in mind that if grinding usually yields excellent results, it is sensitive to certain factors such as edges. The geometry of the specimen is shown below:
Figure 6.13 Schematic geometry of improved ESI specimen In order to obtain an intersection between the plane P and the sphere S, it is necessary that the edge A be as fine as possible and that it correspond to the sphere tangent. This condition is fundamental for the correct three-dimensional measurement of the master.
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Indeed, if the edge A is not sharp enough, the stylus may well get caught in it, in particular if it uses a fine tip with a 2 um radius. Although the sharp edge is easy to obtain during machining, it becomes a problem during the grinding process: As a rule, the conditions that are required to obtain an excellent flatness through grinding are the following: • • •
The material should be homogeneous, sufficiently hard, stabilised and free from residual external constraints. The surface to ground should be of appropriate size. The material thickness should be constant.
In the case of the master ESI, the first condition is met. On the other hand, the surface available is not very large and more importantly still, the material thickness is not constant because of the bevelled edge. Such a configuration results in the unfortunate situation in which undesirable variations are created near the edges. These variations are always found near the edges of ground pieces because of the slight "rocking" that occurs when switching grinding direction. In this case, this phenomenon is amplified because of the decreasing thickness of the material near the edge, which considerably reduces the rigidity of the piece in this area. As a result, the material tends to deflect, thereby diminishing the cutting action of the abrasive. Clearly, these edge variations impede a sufficiently precise definition of the plane P and are mainly responsible for the consequent flatness deviation AP. An attempt was therefore undertaken to reduce these variations. Given that it is physically impossible to eliminate the bevel, an attempt was made optimise the grinding process by "tweaking" the following parameters: •
•
•
Material chosen: Different varieties of highly alloyed steel were tested and a good compromise between stainless quality, ease of manufacture, dimensional stability and behaviour during thermal processes was found. Improvement of the thermal process: In order to prevent a premature wear of the calibration artefact because of the tactile probing, the required hardness should be at least 55 HRc. Various possibilities may be employed to reach this target. For instance, brittle materials such as ceramics or carbides could have been used; however, these were ignored due to prohibitive manufacturing cost of the prototypes. However, these solutions could still be adopted should larger quantities be manufactured. It was therefore decided to focus upon more traditional, cost-effective and straightforward methods initially. A heat treatment process that would ensure a long-lasting dimensional stability was also investigated. Finally, the grinding process itself was optimised so far as the abrasive (its nature and size and hardness) was concerned, together with an increased duration of the operation.
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As a result of these investigations, it was decided that better prototypes be manufactured, and as a result much better results were obtained. Table 6.9 Improved specification of the new ESI-002 specimen Parameter Sphere radius, R Height, H Intersection diameter, Di Flatness deviation, AP Circularity deviation, AR
Nominal value 14 994.2 Mm 2 092.65 Mm 15280,84 urn 0.5 Mm 0.030 Mm
Uncertainty ± 0.3 nm ± 0.25 Mm ± 1.3 Mm ±0.15 Mm ± 0.001 Mm
6.7 Master certification It is essential that the master be certified by an official organisation. In order to ensure a minimal uncertainty on the determination of the masters' characteristic dimensions the primary French calibration laboratory, the ETCA, was utilised. The spheres were previously assessed and the radius and sphericity deviation measured. Regarding the measurements, the uncertainties were: • •
Radius: +/- 0.3 um. The sphericity could not be wholly assessed; as a result, only a circularity measurements were carried out. However, this should sufficiently meaningful, since the spheres are manufactured in such a way that, in principle, all circular sections are nearly equivalent. Furthermore, the spheres that were used were supplied by a company that has been chosen by many measurement instrument manufacturers. The circularity measurement uncertainty was: +/- 0.08
At this stage the other characteristic dimensions of the master were not been assessed, however the ETCA were contacted regarding the measurement uncertainties that would be expected: •
Regarding the flatness deviation of the plane P, an interferometric measurement should be feasible, which would yield a measurement uncertainty of: +/- 0.02 urn.
•
Regarding the determination of the sphere summit, the appropriate way to assess this may be by using laser interferometry. The measurement uncertainty is not clearly defined yet.
6.8 Study of the calibration principle The calibration principle is composed of four successive stages that will be described hereafter. The various parameters to be computed by the calibration (X, Y, Z, H [stylus height], Lfstylus length], Rp[tip radius]...) are processed simultaneously so as to save time and to minimise the uncertainty that would arise from the realisation of several distinct measurements.
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6.8.1 Initial calibration It is assumed, during the whole of the study, that the instrument will have been calibrated through a standard two-dimensional calibration procedure, prior to the actual three-dimensional procedure. This initial calibration will adjust the approximate dimensions of the probe and stylus system: length, height and radius tip, that are originally given to the software. At first, the master will be used as a reference tool in order to confirm the validity of the calibration. 6.8.2 Measurement of the master The master is probed through a sequence of parallel measurements, with an interval step that will have to be optimised with respect to the accuracy obtained and the overall measurement time. In fact, this time may range from a few minutes to several hours, depending on the number of effective profile measurements to be performed. The measurement yields a spatial representation of the sphere/plane ensemble that is then interpreted, Figure 6.14.
Figure 6.14 Probing of ESI master The form obtained is directly linked to the defaults on the different measurement axes, be they displacement defects or perpendicularity; as a consequence each profile is processes separately. 6.8.3 Processing of the three-dimensional measurement In order to interpret the mesh obtained during the 3D measurement, a least squares plane(LSP) upon which all the following calculations and interpretations will be based was calculated. Before creating this LSP, the sphere needs to excluded from the calculations. To determine the exclusion zone, the following procedure is used: •
• •
Firstly, the middle profile of the surface along the X axis is used and a least squares line fitted to the extremities of this profile, in order to exclude the sphere. The least squares circle that corresponds to the vertical section of the sphere is assessed and the two points of intersection between the least squares line and the least squares circle are computed. The same process is then applied to the middle profile of the surface along the Y axis and another two points are obtained. An estimation is then made of the least squares circle over these four points, and the radius is increased by 5%, in order to ensure that the resulting circle encompasses all of the intersection sphere/plane when using it as the exclusion zone (Figure 6.15).
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The LSP, termed P', is then computed, over the surface excluding the previously assessed zone.
Figure 6.15 Exclusion zone for least squares calculations 6.8.4 Individual processing of profiles The three-dimensional measurement is interpreted as a set of profiles spaced out by a given step, which obviously determines the number of profiles. These profiles are all interpolated using an identical step to the one separating each profile, so that profiles may be extracted from the surface along the perpendicular direction as well. Only profiles that have an amplitude greater than 20% of the overall surface amplitude are processed since they contain enough points of the sphere to produce significant results. Besides, this selection automatically discards profiles near the edges of the sphere, which are undesirable anyway given the imperfections of the surface between the plane and the sphere. For the sphere to be completely described, profiles are therefore extracted along both the X and the Y directions, which also yields a more dense and significant amount of data. Thus the sphere is assessed over a grid of profiles as in Figure 6.16:
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Figure 6.16 Grid of profiles used for sphere assessment An extracted profile with the general shape is processed as follows: Firstly, the profile should be levelled through a rotation in order to be studied with respect to the reference plane, while preserving the distances. The rotation is carried out with respect to the generating line associated with P' corresponding to the extracted profile.
Figure 6.17 Levelling the extracted general profile with respect to P'
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Secondly, a four-segment 3rd order B-Spline is computed over the portion of the profile that corresponds to the sphere and the points of intersection with the generating line PI and P2 are determined, Figure 6.18. The sphere section could have been approximated with a least squares circle, since the measurement included a compensation for the arc error induced by the stylus rotation, given the precise knowledge of its dimensions H and L obtained through the two-dimensional calibration. However the B-spline fitting was retained in order to work with measurement instruments that do not posses such features.
Figure 6.18 B-spline fitting to the profile to find intersection points Thirdly, from the two points of intersections PI and P2 between the B-Spline and the generating line P', the mid point P3, which will be used to determine the sphere/plane intersection centre, can easily be determined.
Figure 6.19 Intersection points PI & P2 and sphere midpoint P3 6.8.5 Determination of sphere/plane intersection centre Once the intersection points PI and P2, and the middle points P3 have been found on all the profiles along the X and Y axes, two least squares lines are computed. One with all the points P3 found on profiles along X, and the other with the points P3 found on profiles along Y. The sphere/plane intersection centre is then determined as the intersection between these two lines. This centre will then be used to operate a translation of the referential, which will simplify the computations on the "ellipse". 6.8.6 Calibration of dimension Z The dimension Z is calibrated by comparing the certified height H of the hemisphere above the plane to the measured height Hm. The process is as follows: •
Firstly, the surface is leveled by rotating it according to the plane P' determined earlier.
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Secondly, a portion of the surface that includes the highest point of the surface is selected as well as a couple of points before and after in both the X and Y directions, Figure 6.20.
Figure 6.20 Points selected at highest surface point • •
Thirdly, three-dimensional interpolation is then carried out using a 4 by 4 segment, 3rd order B-Spline in order to obtain a resolution that is 100 times better. The highest point of the B-Spline then corresponds to Hm since the surface was previously levelled with respect to P'. It is worth noting that although the resolution is only multiplied by 100, this is sufficient to ensure a precise determination of the height since the top of the sphere is nearly flat.
Thus dimension Z may be calibrated, which will now be considered to be accurate for the rest of the study.
6.9 Calibration of Y axis with respect to X axis Form this point forward the area of interest is the set of points of intersections PI and P2, which define the boundary of the sphere/plane intersection. This data set needs to be interpreted in order to characterise the measurement and to allow the calibration. Since there is no need to assess the already calibrated Z dimension, the intersection points are represented by a (X,Y) reference system. Assuming that this reference system is orthonormal, then, depending on the displacement error of one axis with respect to the other, two different kinds of curves, both of them ellipses may be obtained: • •
Smaller displacement in Y: Longer displacement in X:
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Figure 6.21 Schematic representation of error in the XY reference system However, the hypothesis according to which the original reference system is orthogonal supposes that the X and Y axes are perfectly orthogonal, which clearly is not the case. The aim of this study is therefore to characterise this defect, along with the displacement differences, in order to allow a calibration of the instrument. 6.9.1 Theoretical study of calibration procedure In theory, if both axes were perpendicular, XY calibration should result in an ellipse oriented along the axis and with a difference between the two radii that is representative of the displacement difference between the two axes. Now consider the Y' axis, which represents the actual measurement axis, presenting an angle with respect to the Y axis of the orthogonal reference system, Figure 6.22:
Figure 6.22 Schematic representation of angular error in the Y axis Each point of the original ellipse is translated according to its ordinate and to the distance between axes Y and Y'. The following matrix performs this transformation:
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1 0 0
tan( 0 ) 1 0
0 0 1
This can be illustrated as follows by a transformed ellipse, Figures 6.23 and 6.24:
Figure 6.23 Schematic representation of translated Y axis error
Figure 6.24 Schematic representation of actual Y axis angular error
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Interpretation of the results and calibration process As shown above, the figure obtained (Figures 6.23 and 6.24) is an ellipse (please refer to the mathematical demonstration above). Using the method developed by David Manthey, "General Least-Squares: Direct Solutions and Bundle Adjustments", the data set can be fitted to an ellipse and its equation obtained. From this equation, the following parameters may be obtained: • •
The perpendicularity defect 0 between the axes X and Y'. As the ellipse has already been characterised in the orthogonal reference system, and since the equation of the least-squares ellipse using the parameters of this "orthogonal" ellipse has been also obtained, then it follows that the values a and b are determined.
The next section deals with the quality of the study. The computed least squares ellipse may be influenced by some erratic data points and thus be less precise than needed. A possible remedy to this problem involves the computation of a robust LSE, the principle of which is given in the mathematical demonstration section. Hence this robust LSE shall be used to obtain the desired parameters. • • •
•
• •
0, a and b will again be computed using the new equation. The perpendicularity defect between the two axes may then be corrected. Given that if the displacements along the X and Y axes were identical, a circle would have been obtained; it is sufficient to correct the defects relative to the Y axes so as to equate the ellipse parameters a and b. It is then possible to compare a ( = b) to half the diameter Di determined previously, hence the X and Y axes may be corrected and the real displacements obtained. At this stage the instrument calibration is now complete, this being suitable for form as well as for roughness measurements. However, it is possible to compute a quality coefficient, which gives an idea of the general mechanical quality of the instrument. A null coefficient would then imply a perfectly linear displacement of the concerned axis. The calculation method for the coefficient is developed in the mathematical study section.
6.10 Mathematical study of calibration mode The transformed ellipse As shown previously, the following transformation matrix P was used to obtain the observed matrix from the orthogonal matrix: 1 0 0
tan( 0 ) 1 0
0 0 1
Now consider the equation of an ellipse centred on O(0 ; 0) in an othonormal reference system: IT := X* + Y2 = 1 Eq *
a2
b2
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The ellipse has the following figure:
Figure 6.25 Mathematically defined ellipse Four points can easily be determined on this ellipse: those found on the vertical and horizontal tangents, which have the following coordinates:
Their transformation through P can easily be determined. However, another point is needed in order to determine the equation of the ellipse. In fact, this point will give the orientation of the ellipse. This point, nominally defined here as point M, has the following coordinates, expressed according to the ellipse characteristic parameters a and b:
Figure 6.26 Definitions of a and b and 0
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The coordinates of the transformed points can now be computed:
If an ellipse is found that passes through these five points, then this shows that the ellipse transformed through the matrix P is indeed an ellipse. Hence an attempt is made to compute the parameters of such an ellipse (Figure 6.26). The following equation is the reduced form of the general equation of an ellipse:
6.10.1 Determination of least-squares ellipse Given the data set M, composed of n points with coordinates x and y in a plane: Mi(xi; yi)
with ie[l ; n]
and given that the equation of an ellipse is:
There is a need to minimise the following sum of squared values:
with D the distance from the origin to the ellipse, calculated for the corresponding point to Mi. To accomplish this, a method based on a linear equation that comes from the general equation of an ellipse is used. This linear equation is called the " reduced general equation" and it is given below:
This linear method consists of an adjustment using zero as the initial estimate of all parameters. The following equation is then established:
The Jacobian matrix associated with Fi(A,B,C) is then determined:
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Assuming null initial conditions, the vector K is determined, which is the vector of the residuals. A residual is the difference between the observation (ki) and the equation calculated using the initial values. As a linear method is being used here, initial estimates are supposed to be null. The equation calculated from these estimates is null and the sum is minimised to 1. As a consequence, the following matrix is obtained:
The eigen value matrix W of the system is needed, this being associated with the identity matrix:
The equation may then be solved in order to determine the unknown A, B, C:
where J T is the transpose of J. The resolution of this final equation may be summarised as follows:
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Topography
Once this system is solved, numerical values for the coefficients A, B, C may be obtained, which in turn are used to determine the values of the coefficients that determine the orthogonal ellipse: a, 6, tan(0). Thus, the following equations are obtained:
6.10.2 Determination of quality coefficient This coefficient is simple in its definition, although rather difficult to evaluate. In effect, it involves assessing the mean deviation of the sampled points with respect to the least squares ellipse calculated above. These deviations are expressed along both measurement axes X and Y. The distances of the points with respect to the ellipse are also computed, which we shall use to compute the robust least-squares ellipse. Consider the equation of the ellipse:
By choosing a point that does not belong to the ellipse, it is possible to define a line that passes through this point and through the origin (Figure 6.27).
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Figure 6.27 Ellipse and line used for determining the quality coefficient
The distance between point A and the ellipse is calculated over the line, using equation y = c x x. To obtain this distance, the coordinates of the point of intersection between the least squares ellipse with line D are needed. To accomplish this, two cases need to be considered •
ifXa>0
Then the following second order, two unknown system of two equations is used:
X can then be obtained using:
Using the same system with the other condition applied to X, then:
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In either case, the Y coordinate of the point is simply Yl = c XI. It is now possible to compute the deviations found according to the X and Y axes:
With n the number of points Xai the abscissa of the experimental point Ai Yai the ordinate of the experimental point Ai Xi the absissa of the point on the least squares ellipse Yi the ordinate of the point on the least squares ellipse The average distance of the measured points with respect to the least squares ellipse is now obtained:
6.10.3 Determination of robust least squares ellipse Given the distribution of the distances between the sampled points and the least squares ellipse, all the points that present a distance greater than twice the standard deviation are moved in such a way that their distance to the ellipse is reduced to twice the standard deviation. The standard deviation is expressed as:
where d is the average distance and di is the distance of a single point with respect to the least squares ellipse. The reason for choosing to keep ± 2a of the data unchanged is because, according to the normal law, this represents 95% of the whole data, whereas a deviation of ± a would only represent 68% of data.
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6.11 Study of optimal measurement step Two parameters have to be taken into account for the choice of the optimal measurement step: the accuracy, which should be good enough to allow a correct assessment of the instrument quality, and the measurement time, which may range from a few minutes to several hours. To assess the quality obtained with respect to the calibration duration, one measurement with a 20 um step was used, from which every second, third, etc profile was extracted in both directions in order to obtain surfaces with effective measurement steps of 40, 60, 80, 100, 200, 300,400, SOOum. As a result it was then possible to observe the influence of the step over the different parameters computed: the ellipse centre O(xO ;yO), its radii, the perpendicularity deviation angle between X and Y and finally the height of the sphere summit Hm. The actual results applied to an actual instrument are presented in Table 6.10. Note: These values have been determined through the robust least squares ellipse computation, which was only run once. Table 6.10 Calibration data collected for an actual instrument yO(nm)
a(jtm)
b(Mm)
ex(nm)
ey(nm)
0
H(i^m)
9520,223 9500,297 9480,26 9460,413 9440,203
7640,668 7640,617 7645,615 7645,042 7640,623
7644,765 7644,749 7650,013 7649316 7644,738
6,74722 6,749785 6,789224 6,902748 6,766569
6,741838 6,731778 6,785578 7,00269 6,73055 1
0,037526 0,044692 0,066737 0,017756 0,067961
2097,659 2094,711 2094,607 2094,489 2094,48
fpflpPIMfe^^^ 8439,868 9240,237 7655,469 8433,999 9143,746 7653,759 8444,619 9075,477 7655,217
7643,957 7653,65 7681,243
8,769767 11,29798 17,975
8,128401 1130398 19,57793
-0,761 0,746221 6,997688
3»M» 2094,191 2093,541 2091,579
meas, xO(|im) n° 1 8660356 2 8640,486 3 8621,595 4 8600,045 5 6 7
8 9
8580,854
step time (Mm) (min) 20 1275 40 681 60 454 80 342 100 230 200 130 300 87 400 67 500 54
Following are the various curves showing the evolution of each parameter with respect to the step size.
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Figure 6.28 Graph of influence of step on axes
Figure 6.29 GropA of influence of step on XO
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Figure 6.30 Graph of influence of step on YO
Figure 631 Graph of influence of step on summit
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Figure 6.32 Grap/i of influence of step on errors
Figure 6 33 Graph of influence of step on measurement time From these curves, the best compromise between precision and measurement time would seem to be measurement n° 6 with a 200nm measurement step.
6.12 Acceptance and verification tests Further information concerning acceptance and periodical verification tests are given in Appendix A.
6.13 Conclusion This chapter has outlined a number of practical approaches to the calibration of 3D scanning instruments. The instruments have been "broken down*' into their sub-
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elements and their implications on the calibration process have been discussed. The essential elements of a suitable artefact have been elucidated and the ball intersecting a sphere has been suggested as the best practical solution. The chapter forms a best practice guide for calibration rather than a theoretical approach and would provide the basis for relatively easy implementation.
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Figure A6.1 Twin groove standard
Figure A6.2 Intersecting parallel groove standard
Figure A6.3 Circular groove standard
Assessment of the characteristics The characteristics of the standards should be in accordance with required measurement uncertainty. The following features have to be taken into consideration: • • • •
The form deviation of the groove(s), The parallelism between two grooves (ER1 & ER2), The perpendicularity between the net of grooves and the flatness of the top surface of the standard (ER2), The flatness of the top surface of the standard.
The depth d of the grooves should be assessed in accordance with the ISO 5436-1 standard. ER1: "Two parallel groove standard" The assessment of the inter-groove distance / is accomplished using the following method: •
Assessment of the least square circle (LSCI) of the groove bottom radii,
166 • •
Advanced Techniques for Assessment Surface Topography Assessment of the centre of the LSCI, Assessment of projected distance / on the upper plane P between the centres of the previously computed LSCI.
ER2: "Double net of parallel groove standard" The assessment of the inter-groove distance l\ and manner.
is accomplished in a similar
ER3: "Circular groove" The assessment of the diameter Df is carried out similarly to the above standards with respect to the X and Y axes.
A6.3 ES standards These standards comprise a sphere S and a plane P. ESI: "Sphere/plane standard" These standards are characterised by the radii R of the sphere, by the height hc of the raised portion of the sphere and by the diameter Di of the circle prescribed by the intersection between the sphere S and the plane P (see Figure A6.4). The local slope at the sphere/plane intersection should not exceed 30°. ES2: "Plane/sphere standard" These standards are characterised by the radius R of the sphere, by the height ht from the plane P to the opposite pole of the sphere S and by the diameter Di of the circle issued of the intersection between the sphere S and the plane P (see Figure A6.5).
Figure A6.4 Intersecting sphere and plane standard ESI
Figure A6.5 Intersecting sphere and plane standard ES2
A6.4 Assessment of standards characteristics ESI: "Sphere/plane standard" The value of the diameter is a function of the height hc and the radius R of the sphere. Its assessment is obtained as follows:
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ES2: "Plane/sphere standard" The value of the diameter is a function of the height ht and the radius R of the sphere. Its assessment is obtained as follows:
A6.5 Acceptance and periodical verification tests A6.5.1 Conditions and preliminary adjustments Like most other instruments, those dedicated to the measurement of the areal surface texture are used in a measurement room or directly in the workshop. In the second case, some metrological characteristics may not be taken into account. This section describes the tests for the metrological characteristics defined earlier. The user has the possibility to apply a part or the totality of the proposed tests regarding the perceived needs. For the acceptance procedures, the tests defined hereafter should be carried out with all the available styli of the instrument. The exchange of a stylus should only occur when all the tests are complete. For the periodical verification, the tests should only be carried out with the default stylus. Nevertheless, it is necessary to check the geometry of the tips of the other styli. The uncertainty of the standards used during the tests should be taken into account in accordance with ISO 12179. A6.5.2 Measurement conditions The measurement conditions of the profiles are in accordance with the ISO 4288 or the ISO 12085. The measurement conditions of the surfaces are in accordance with the one given in the parts 1 to 8 of the ISO 4287 standard, with the following additional specifications: • •
Unless specified, the measurement speed should be 0.5 mm/s; For the assessment of the surface texture parameters linked with the mean line and for the form parameters, the areal default filter should be used .
Note: This filter shall be defined in the appropriate standard at a later date. At this time, the use of an areal filter based on that defined in the ISO 11562 is allowed. •
•
For the computation of the parameters linked with the method of the "Motifs", the following nesting index are to be used: A = 0,5 mm and B = 2,5 mm (in accordance with ISO 12085). For the assessment of the measurement noise of the instruments computing "Motifs" parameters, it is allowed not to respect the minimum of 150 increments of the vertical digitisation as defined in the ISO 12085 standard.
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Additionally, it is recommended that the instrument under test is isolated as well as possible from the surrounding vibrations. Finally, in accordance with the ISO 12179 standard, the measurement conditions for the periodical verification should be as close as possible to those of the expected use of the instrument. A6.5.3 Preliminary adjustment of the instrument If possible, proceed to the user adjustment of the instrument using the delivered standards. A6.5.4 Number of measurements A minimum of three measurements profiles and one measurement for the surfaces need to be performed. If several measurements are performed for the same characteristic, the average and the span (or the standard deviation for more than five measurements) are taken into consideration for the conformity of that characteristic.
A6.6 Test processing A6.6.1 Measurement of static noise The aim here is to assess the electronic noise of the instrument and especially the surrounding conditions (vibrations transmitted through the floor and phonic vibrations).The measurement is carried out without movement, the stylus is in contact with the standard (see Table A6.1). A6.6.2 Validation of vertical user adjustment Validation using a groove standard (see Table A6.1). Validation using a sphere (or a crown of a sphere) This verification applies to the measuring instruments having a large vertical range of measurement and more specifically having an arc error correction (See Table A6.1). A6.6.3 Validation of horizontal user adjustment Validation using a groove standard This verification applies to the measuring instruments having a limited vertical range of measurement and more specifically not having an arc error correction (See Table A6.1). Validation using a sphere/plane standard This verification applies to the measuring instruments having a large vertical range of measurement and more specifically having an arc error correction (See Table A6.1). A6.6.4 Estimation of perpendicularity deviation (see Table A6.1).
Calibration Procedures for Stylus and Optical Instrumentation
A6.7 Verification of characteristics A6.7.1 Estimation of flatness deviation (see Table A6.2). A6.7.2 Measurement of dynamic noise (see Table A6.2). A6.7.3 Estimation repositioning hysteresis along X axis (resp. Y) (see Table A6.3). A6.7.4 Verification with a roughness standard (see Table A6.3).
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Table A6.1 Validation of the vertical user adjustment
Measurement of the static noise Profile Type of measurement Used standard
Optical flat (levelled in accordance with ISO 12179)
Measurement Equivalent measurement length (In order to apply the computation algorithms): 16 mm parameters
Validation on a standard with grooves
Validation on a sphere or crow of a sphere
Profile
Profile
Standard with grooves: Al or A2 (Following ISO 5436-1) or ER
Type El in accordance with ISO 5436-1 or ESI
Measurement length: 4 mm
Z Vertical range: minimum 50% of the total probe vertical range (if the height of the stylus is big enough)
Depth d of the groove The method for the assessment of d is similar to the one described in the ISO 5436-1
Radius of the least square circle: Rd
Sampling length: 0,8 mm (in accordance with ISO 4288) Motifs nesting index: A = 0,5 mm, B = 2,5 mm, (in accordance with ISO 12085) Assessed parameters
A minimum of 3 measurements has to be done, with Measurement A minimum of 3 measurements has to be done, with each stylus type each stylus type. method The measurement is performed without movement, the stylus is in contact with the standard. Results
The average values of the obtained parameters R and Rq should be added to the tolerances (maximum values of the parameters) of the equivalent parameters defined in Section 6.6.
The relative deviation between the average of the parameter d and the conventional true value should not exceed ± 2,5%
Roundness deviation: Assessment of RONt3 (in accordance with NF EN ISO 12181-1 using LSCI b and Xc = 0,8 mm) A minimum of 3 measurements has to be done
The relative deviation between the averaged parameters Rd and RONta and the conventional true value should not exceed: - For Rd:± 0,03% - For the form deviation: RONt < 1 urn
a
If the considered instrument does not allow the computation of the parameter RONt, it is possible to assess the parameter Wt computed a low pass filtering of the profile (Xc = 0,8 mm) or the parameter Wte in accordance with the ISO 1 2085, after applying a form removal using a least square circle. b
LSCI: Least square circle
Note The uncertainty of the measure and of the used standards for the acceptances and verifications should be taken into account in accordance with the ISO 12179
Table A6.1 (continued) Validation of the horizontal user adjustments
Estimation of the perpendicularity deviation
Validation with the sphere/plane standard
Validation with a standard with grooves Type of measurement
Areal
Areal
Areal
Used standard
Standard with grooves: ER 2 or ER3
Sphere/plane standard: ES 1
ER2, ER3, ESI orES2
Measurement parameters
Measurement area: In function of the standards characteristics
Measurement area: In function of the standards characteristics
Measurement area, filtering, horizontal sampling interval: In function of the standards characteristics
Assessed parameters
For ER2: Inter-groove distance along X and along Y Components of the diameter Di along X and Y axes
Primary surface: ORT
For ER3: Components of the diameter Df along X and Y axes
Measurement method
A minimum of 3 profiles measurements with the standard stylus in several areas of the measurement range.
At least 3 profile measurements with each stylus
Areal measurement of the standard in the central zone of the measuring range
Results
The relative deviation between the average of the parameter d and the conventional true value should not exceed ± 0,2%
The relative deviation between the average of the parameter d and the conventional true value should not exceed ±0.1%
Maximum deviation: ORT ^ 1 um / 1 mm
Table A6.2 Measurement of the dynamic noise
Estimation of the flatness deviation Type of measurement
Areal
Areal
Used standard
Optical flat (Levelled in both X and Y axes in accordance with ISO 12179)
Optical flat (Levelled in both X and Y axes in accordance with ISO 12179)
Measurement parameters
Measurement area: All the available measurement range of the instrument avoiding the end switches
Measurement area: 5 mm x 5 mm Profile filter: Xs along the X axis, in accordance with ISO 3274 standard C filter: 0,8 mm x 0.8 mm
Horizontal sampling interval: Dx in accordance with the ISO 3274 and Dy = 50 jim Assessed parameters
Assessment of FLTtb in accordance with ISO 1 278 1 with LSPL - Xc = 0,8 mm a
Assessment of STRt in accordance with ISO 12780 with LSLI - Xc = 0,8 mm
Primary Surface: St Filtered Surface: Sq
Table A6.2 (continued) Measurement One measurement with the standard stylus method
Results
One measurement at one corner of the measurement range One measurement in the middle of the measurement range One measurement at the opposite corner of the measurement range The 3 measurements are aligned on a diagonal in the (X,Y) plane
MAX [FLTt ] <, 0,4 urn over the whole area of 20 mm2 1 um over the whole area of 50 mm2 2 um over the whole area of 100 mm2 along the X and Y axes
Parameter St < (0,2 um + 2 times the Rq value of the static noise)
MAX [STRt ] £
Parameter Sq < ( 0,03 um + Rq value of the static noise)
0,2 um over the whole area of 20 mm 0.5 um over the whole area of 50 mm 1 um over the whole area of 100 mm along the X and Y axes a
If the instrument does not allow the computation of the FLATt parameter, it is possible to assess the parameter St computed on the low-pass filtered surface (S Cut off = 0,8 mm) after applying an F filter (Levelling of the surface using a least square plane). b
In order to reduce the measurement time and taking into consideration the fact that the micro-geometry is not taken in account for the flatness deviation, a large sampling interval can be used along both X and Y axes. We do advise to follow the recommendations given in the ISO TS 16611 standard.
Table A6.3 Estimation repositioning hysteresis Areal Type of measurement Used standard
A, E in accordance with the ISO 5436-1 or ER2, ER3.
Measurement Measurement area: 5 mm x 5 mm parameters Profile filter A,s along the X axis, in accordance with ISO 3274 standard
Assessed parameters
Verification of the roughness standard Profile Roughness standard Certified parameters of the standard Measurement length - 16 mm for the parameters in accordance with the ISO 12085 standard - Following criteria (NF EN ISO 4288) for the others
Horizontal sampling interval: Dx in accordance with the ISO 3274 and Dy = 50 um
Sampling length: Following criteria (NF EN ISO 4288)
Primary surface: Max straightness deviation along the X (resp. Y) axes of the position of the bottom of the groove over die whole surface: STRt (HYSx) and STRt (HYSy)
Following roughness criteria. Depends on the standard
Table A6.3 Estimation repositioning hysteresis
Verification of the roughness standard
Measurement method
Even if the obtained measurement in a surface, it is in fact a measurement of several profiles without any movement along the Y axis in such a way that all profiles measurements are done at the same location of the groove. The repositioning hysteresis is characterised by a straightness deviation of the bottom of the groove with respect to the X axis (Respectively Y).
A minimum of 5 measurements for each stylus with a lateral gap of 0.1 mm between each measurement
Results
Parameter STRt < 1 \im If the instrument is not able to assess the parameter STRt along the X axis, (Respectively Y), it is then possible to assess graphically the straightness deviation on a isometric top view.
The relative deviation between the average of the parameter d and the conventional true value should not exceed: ± 2%
8
If the instrument does not allow the computation of the FLAT parameter, it is possible to assess the parameter St computed on the low-pass filtered surface (S Cut off= 0,8 mm) after applying an F filter (Levelling of the surface using a least square plane).
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7
Calibration Procedures for Atomic Force Microscopes Anders Kuhle Danish Institute of Fundamental Metrology, Lyngby, Denmark
7.0 Introduction The main aim of this chapter is to discuss a range of calibration procedures for atomic force scanning units optimised for 3D measurement and characterisation of surface roughness, as, at present, no official standard exists which can be used for calibration of AFM instruments in the sub-micron range. The use of AFM's for practical traceable characterisation of functional surfaces is a new area but is preconditional on calibration of the instrument's movement (scanning translation in xyz) as well as practical consideration of the tip's interaction with the representative surfaces. By measuring test samples and comparing these with corresponding measurements performed using other techniques it should be possible to bring AFM technology into its place in the spectrum of surface characterisation methods available today.
7.1 Pilot measurements and appraisal of error sources measured using AFM equipment The work described in this chapter was carried out has via a combination of measurements, analysis of measurements, discussions and reviewing available literature [1]. Errors in AFM equipment can be related to the individual components of the unit: the xyz positioning system, the force detection system, and the probe. In addition, errors also result from the operator - not necessarily because of poor operating skills in using the instrument, but due to lack of awareness of the physics of the instrument. A great number of these errors can be minimised by using a set of detailed procedures for the measurements and for calibrating the instrument. In the following sections a brief overview of error sources in AFM equipment is given.
7.2 XYZ positioning system In general, AFMs can be divided into two classes: open loop systems and closed loop systems, both with scan volumes in the range of 100 um x 100 um x 10 um. More than 90% of existing AFMs are of the open loop type. A closed loop system is a microscope where the three assumed orthogonal axes are equipped with position
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sensors of high accuracy. An open loop system is a microscope with no feedback on the three axes; in this case the user has to rely on knowledge of the characteristics of the (usually piezo-electric) actuators. Few papers in international scientific journals state the estimated uncertainty of AFM measurements. Inter comparisons between users of open loop instruments have only been reported a few times to the international societies, and it is therefore difficult to assess exactly the uncertainty. However, deviations in the range of 2% to 10% in the lateral plane and 5% to 20% vertically are expected. For closed loop systems, a much better accuracy can be achieved: 0.1% to 1% in the lateral plane using etched grid patterns and vertically on step heights around 1% according to specifications. At some national metrological institutes, microscopes which realise the metre by interferometers have been developed but at a high cost [2]. 7.2.1 Scaling of xyz axes One fundamental error source comes from the finite accuracy of the calibration of the microscope. The calibration of both open and closed loop systems is based on the use of transfer standards. Transfer standards are commercially available, most without any certificate, some with a self-declared traceability, and a few with certificates from national metrology institutes [3]. For the horizontal calibration one or twodimensional grids are used, with uncertainties ranging from about 0.1% for micron sized periods to about 1% for periods in the order of 100 nm. For the vertical axis transfer standards with steps are used for calibration. The error in the calibration of the step heights themselves is a few percent for step heights below 30 nm and less than 1% for step heights in the order of one micron. 7.2.2 Linearity of xyz axes A large error source is the non-linearity of the positioning system (open loop microscopes) or the non-linearity of the sensor system (closed loop microscopes). For open loop systems, the non-linear error is mainly caused by hysteresis and creep in the piezo-electric actuator (see below). In closed loop systems the non-linear error is mainly caused by the non linearity in the position sensors. For open loop systems the relative error in the xy-plane is of the order of 5-10 percent, but up to 20% along the z-axis (measured on step heights). For a state of the art closed loop system the relative error from the non-linearity of the sensors is one percent or less. 7.2.3 Hysteresis, non-linearity, and creep of the piezo actuator Open loop systems, and only these systems, suffer from creep, non-linearity and hysteresis in the piezo actuator. These effects give rise to the main source for the nonlinear error in the x, y, and z positioning system (see earlier). Hysteresis is the name of the difference in expansion or contraction of the piezo-electric actuator at a particular voltage when this voltage is approached from lower voltage and from higher voltage, Figure 7.1. The hysteresis, i.e. the positioning error, is typically in the range of 2% for hard piezo materials and 15% for soft piezo materials. The hysteresis error is typically reduced significantly in the lateral plane by an online correction of the applied voltage [4], but is not corrected for in the vertical direction. Creep is a characteristic of all piezo materials and is a short term dimensional stabilisation following a change in applied voltage. It cannot be corrected for in the vertical direction. Piezo actuators
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also give rise to errors because the sensitivity changes as function of temperature and time of use (ageing).
Figure 7.1 Hysteresis in the piezo actuator 7.2.4 Coupling between the xyz axes Orthogonality. The positioning system will never move along exactly orthogonal axes; in open loop systems because of inaccuracy in the mechanical construction of the positioning device; in closed loop systems because of inaccuracy in the placement of the position sensors So far, there has been almost no investigations of these error sources in the literature. The author's investigations suggest that for open loop systems the error is typically less than one degree and for state of the art close loop system it is typically less than 0.1°. Image Bow. Coupling between the xy-axes and the z-axis gives rise to a vertical bow in the image, that is, an ideally flat plane will be imaged as, e.g., the cap of a sphere or a saddle. For the largest scan areas in an open loop system the saddle form typically gives rise to a maximal vertical error of 100 run. For a state-of-the-art closed loop system an error in the range of 10 nm is achieved. This image bow can give a significant contribution to the calculated roughness; if appropriate from removal and levelling is not carried out (see later sections). 7.2.5 Thermal drift For mechanical systems an error due to thermal drift is always present. For open loop systems the error is caused by the fact that the tip is moving relative to the sample due to the thermal expansion/contraction of the mechanical connection between tip and sample caused by small temperature fluctuations. For closed loop systems the error is caused by the fact that the gap between the position sensors is changing relative to the tip and sample because the temperature in the mechanical connection is fluctuating and because the material used does not compensate for temperature changes. Immediately after a sample change the rate of drift is often as high as 6 urn/hour - for some systems even higher. After about an hour it is typically down to 0.05-0.2 urn/hour.
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Figure 7.2 Drift along the z axis is seen as a variation in the mean height along the slow scanning y axis. The pointer in the image shows where an abrupt height jump is observed, more easily seen in the profile to the right
7.3 Force detection system 7.3.1 Sudden jumps Sometimes during image acquisition a sudden jump in the height level occurs (Figure 7.2). It is not possible to give a general explanation for the observed jumps. Some jumps are definitely correlated to visible contamination on the surface. When the tip hits a particle it will drag the particle over the surface for some time giving rise to an apparent height change. The particle which interacts with the tip can be at the edge of the scanning area and therefore not visible in the image. Other causes can be instability in the force detection system. Laser diodes, which are used in many force detection system, are known to jump between different modes as the cavity changes length caused by temperature changes. Such jumps are followed by small changes in the intensity of the laser beam and hence in the detected force. More speculatively, the friction between tip and sample could electrically charge the tip and sample. Jumps can occasionally give rise to error heights up to several tens of nanometers. Other sources of jumps than those mentioned here must be expected to exist. 7.3.2 Optical interference In most AFMs the force between the tip and the surface is sensed by the angular deflection of a cantilever spring at the end of which the tip is situated. The cantilever bending is measured by detecting the deflection of a laser beam reflected on the reverse side of the cantilever (Figure 7.3). In most AFMs optical interference is present. Interference can be caused by the superposition of the beam reflected from the cantilever and laser light reflected from the sample but also by multiple reflections in the optics of the instrument itself. The result is that the detected signal depends on the position of the cantilever as well as the deflection which causes interference fringes on e.g. a flat surface (Figure 7.4).
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Figure 7.3 Force detection principle in the AFM
Figure 7.4 (a) This image of a height calibration standard shows the effect of interference in the optical force detector of the AFM as a waviness with a spacing of about L 7um on the flat silicon bearing plane. In the left part of the image ringing can vaguely be seen as a closely spaced vertical modulation, (b) Interference is easily revealed by recording the sensor signal as a function of the separation between tip and sample as shown above. To the right the tip and sample are separated, to the very left contact is established resulting in a steep rise. The waviness of the "flat" part of the curve is easily observed
7.4 Scan speed 7.4.1 Feedback loop A feedback loop which essentially is an integrating regulator keeps the force between tip and sample constant by adjusting the z position of either the probe or the sample while scanning according to the local topography. The response time of the feedback loop is limited by the point in amplification level where the loop starts oscillating (inherent to regulators due to the physical delays in the signal path). This limits how the tip can track steep slopes without a significant change in the applied force. As the topographic signal, recorded, is the output of the feedback loop this implies loss of information. Hence, the error depends on scan-speed and the feedback loop amplification factor. So parameters must be chosen so that the error is acceptable, e.g., small compared with the desired resolution. On low aspect ratio surfaces the scanning speeds in contact mode can be as high as 200 um/s. However, as the aspect ratio becomes high the scan speed has to be reduced.
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7.4.2 Cantilever relaxation time In the resonant vibrating cantilever modes (tapping mode, non-contact etc) it is the amplitude of vibration which is kept constant by the regulating circuit. However, in this case the limiting time constant in the system is often the relaxation time of the resonant vibrating cantilever. For typical cantilevers with resonance frequencies in the range of 150-350 kHz and quality factors in the range 100-500 this time constant is of the order of a few milliseconds. This often becomes the limiting factor, in particular when the tip has to track a steep downward slope (or a step down). Typical maximum scanning speeds are in the range 10-50 um/sec. In contact mode the response time of the cantilever itself is seldom a problem since the resonance frequencies are almost always higher than 10-20 kHz, whereas typical surface topography frequencies are lower than 1 kHz. 7.4.3 Ringing Another limit to the scan speed in many AFMs is set by the magnitude of the acceleration/deceleration at the end of each scan-line where the scan direction changes. If the velocity change is too high the moving mechanical parts can be kicked into damped oscillation - ringing. This effect poses the largest problem when nanometer sensitivity is needed and at small scan ranges, where the ringing might not die out until far into each scan line. A scan speed of 20 um/s might work well on a 20 um scan range (1 line/sec.) but might cause problematic ringing on the 1 (im scan range (20 lines/sec.).
7.5 Probe and sample 7.5.1 Tip shape The shape of the tip will affect all the surface features. The tip apex radius of curvature and the opening angle sets a limit to the smallest wavelengths that can be measured (Figure 7.5). Typical apex radii of curvature are nowadays in the range of 10-30 nm and opening angles in the range of 20-70°.
Figure 7.5 Tip/surface interaction
An asymmetric tip will give characteristic shapes to the imaged features, e.g. a double tip will tend to make doublets of all features in the corresponding size range. The error can be estimated from knowledge of the tip shape, e.g., from the manufacturer or from scanning electron micrographs. Tip test samples consisting of arrays of inverted tips or very sharp edges are commercially available. With these the tip can be characterised in the AFM itself; however this is limited by the quality of the tip tester. 7.5.2 Tip/sample compression Under certain conditions the force between the tip and the surface induces local indentation of the sample or compression of the tip. If the force is too high the result is poor resolution - or even false results - and either a quickly worn tip or a damaged surface. Typical forces are in the range of 0.1 to 10 nN. The magnitude of the error is very difficult to assess in general as it depends critically on the sample and
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experimental condition, i.e. the contact area and hence the actual pressure exerted on the surface by the tip is usually not known. For hard materials and calibration standards the error it is often negligible. For soft materials such as polymers the error is significant - up to tens of nanometres. 7.5.3 Mode switching Tapping mode, dynamic mode or non-contact mode is when the cantilever of the probe is vibrated in a resonant mode such that the tip and sample are in intermittent contact only. However, it is possible for the vibrating probe to operate in one of at least two dynamic states according to the dominating tip-surface interaction. The typical error visible in an image is switching between two states which shows up as abrupt height jumps of 1-5 run - in particular at the edge of high-aspect ratio features, see Figure 7.6 [5].
Figure 7.6 (a) More dynamic vibrational states exist for a resonant vibrating cantilever. (b) Structures of protein aggregates on an atomicallyflat surface. The height scale is 4 nm. (c) Switching between two dynamic modes of the vibrating cantilever in the AFM causes the structures to appear as "buried" in the surface. The mode is "attractive" between the structures and "repulsive " on top of the structures
7.6 Comparative measurements In surface metrology the AFM systems are often in "competition" with optical interferometric devices. Both instruments operate using different principles. However, it is useful to compare the results of each instrument when similar surfaces are measured. The aim with this section is to compare AFM measurements with measurements performed using optical interferometric techniques. Two samples were chosen for this task. Both samples were polar regions of prosthetic femoral heads (hip joints). These components are usually manufactured via polishing to possess surface roughnesses in the region of 1-1 Onm Sq. One head was manufactured from a metal CoCr alloy, and from an alumina, A^Oa ceramic. First the samples were measured using interference microscopy (Wyko NT 2000 instrument). Subsequently the samples were cleaned in acetone/propanol in an ultrasonic bath removing any loose contamination, making the samples straight forward to scan. For all images form removal has been carried out by fitting a sphere to the images after which they were filtered using a Gaussian filter (ISO 11562) with a cut-off wavelength of 1/5 of the longest image side length (e.g. 12 um for the 60 |im x [60 or 46 um] images. For the AFM images 1. order line wise levelling has been performed - after the spherical form removal. After this procedure the rms. roughness, Sq, was calculated.
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Figure 7.7 (a) 60 jum x 60 jjm AFM image of the A12O3 ceramic head The inset shows a 10 fjm x 10 fjm scan, (b) Interference microscopy image 60 /jm x 46 //m of the same surface -but not at the same location. The roughness parameter, S^, is given on both images
Representative images from the ceramic head are shown in Figure 7.7. In the left part of the figure (a) is shown an AFM image, and in (b) is shown an interference microscope image. There is a striking difference in the qualitative look of the surface. The calculated rms roughness is about twice as high for the AFM image as for the optical image, but both of the order of 1-2 nm. Figure 7.8 shows a set of images acquired on the metal sample [6]. The qualitative difference between AFM image (a) and interference microscope image (b) is not as big as for the ceramic head, but it is there. Again, the level of detail is remarkably higher in the AFM image which can be seen in the profiles (c) and (d). The roughness calculated from the AFM image is also in this case higher (about x2) higher than for the interference microscope image. Big (contamination) particles are dominating the optical image. If Gaussian filtering is omitted and instead additional 3. order plane filtering is applied to the data, the particles' influence on Sq is reduced: Sq increases to 3.9 nm - closer to the value for the AFM image. In order to test the effect of probe size a low pass filter was been applied to the AFM data in Figure 7.8 (a), before carrying out the usual high pass filtering with a Gaussian filter with cut-off wave length of lOOOnm. The result was a reduction of Sq to 2.55 nm. There are possible explanations for the observed differences: •
The two images have not been recorded at exactly the same spot on the samples.
•
The difference in resolution of the two instruments, i.e. the AFM tip's ability to track into narrow grooves and pits.
•
Both instruments used are well calibrated, so the observed difference is most unlikely a calibration issue.
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Figure 7.8 (a) AFM image of the metal head. The scan area is 60 jam x 60 fjan. The inset shows a 3 jum x 3 fjm magnification at the place indicated, (b) Interference microscope image 60 fjm x 46 fjm of the same surface - however not at the same location. The roughness parameter Sq is given on the images. The influence on Sq of the big particles in (b) is reduced by the Gaussian filtering. In (c) and (d) are shown profiles along the dashed lines in (a) and (b), respectively
Figure 7.9 Top part of the AFM image in Figure 7.8(a) cut to the same size as the interference microscope image in Figure 7.8 (b) and low pass filtered with a Gaussian filter with a cut-off wave length of 1000 nm
7.6.1 Conclusions In order to compare AFM measurements with other 3D surface tools such as interference microscopy, it is first of all necessary to compare clean surfaces as contamination often disturbs AFM measurements or in the worst case is measured as a
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part of the surface. Our investigations demonstrate the high resolution of the AFM compared to e.g. interference microscopes. This is probably the reason for the higher roughness observed from AFM images compared to interference microscope images. In order to compare measurements directly it is therefore required to low pass filter AFM images such as to match the effective probe size of the other instrument. The type of filter required depends on the type of instrument but a rolling ball filter might for example be suitable for comparing with stylus instruments. The difference in measured roughness in the ceramic image can be explained by the fact that the interference microscope relies on a "clean" reflection from the surface of the specimen. In contrast with the metallic sample the ceramic surface is somewhat transparent at the measurement scale and hence reflection is obtained from subsurface layers thus distorting the measured image when compared to the AFM imaging of the ceramic surface.
7.7 Procedure for lateral calibration of an atomic force microscope The objective of this calibration procedure is to calibrate the (fast scanning) x-scale Sx and the (slow scanning) y-scale Sy of an AFM image. The procedure has been developed to be used with an AFM of the closed loop type which has a remaining non-linearity of less than 0.1% [7]. However, the procedure can be used for other AFMs including those of the open loop type, given that they have been satisfactory linearised. The recorded images are therefore treated as linear and the remaining nonlinearity is included as an uncertainty. 7.7.1 The standard The standard used in this procedure consists of a two dimensional lattice of features (bumps or pits) on a silicon wafer. The lattice is made by pattering a mask-layer by holography, in other words using the beam coherence of a laser to form an interference pattern on the photo resist. The exposed (or non exposed) part of the resist is then removed and the pattern is subsequently etched into the wafer surface. The lattice is defined by the average length between closest features, La and Lb, and the angle y between the corresponding rows of features, see Figure 7.10. These three quantities have been measured traceable to the definition of the metre [8]. The expanded uncertainties of the three quantities are given in the calibration certificate. Temporal drift of silicon is of the order of 10"8 per year and is insignificant. In general the two-dimensional lattice is not perfectly quadratic but rather a little bit oblique, that is IL I * |Lj and y * 90 .
Figure 7.10 Schematic illustration of the reference standard. The lengths La and Lf, are the lengths between closest neighbours of the characteristic features forming the lattice. The angle between the rows is denoted y
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7.7.2 Theory of calibration The following section gives the theoretical principle for estimating the linear correction parameters and the algorithms for the associated software used. Let the uncorrected image of the standard described above recorded by the microscope be denoted "the scanned image" z(x\ y'). The linear transformation C of the distorted plane into a corrected plane, (x', y ^-K*, y) is required, so that the measured distances in the corrected co-ordinate system with co-ordinates (x, y) are correct. The corrected co-ordinate system can be chosen so that the *-axis is parallel to the x 'axis of the scanned co-ordinate system (x', y *) and the linear transformation can then be written as [9, 10].
where Cx,, Cy, and Cxy are the unknown correction parameters to be estimated by the calibration. If the scanned x- and >>-axis are perpendicular, then Qy - 0, and Cx and Cy are simply the scale factors for the x- and the ^-direction respectively, that isx = Cxx' and y = Cyy'. The physical angle between the fast scanning direction (the x-axis) and the slow scanning direction (the >>-axis) is equal to cot'^C^/ Cy). The unit cell of the lattice on the standard as observed by the microscope, is defined by the two vectors a' = (a[,a'v) and 6' = ( b [ , b ' y ) . The observed average nearest neighbour distances are thus ia' = |oi and Lb' = |£j. y' is the angle between the observed unit cell vectors. The lattice is in the corrected image defined by the two vectors a = ( a x , a > ) a n d b _ = ( b x , b y ) . Again, their lengths and the angle between them are La, L\» and y, respectively. A sketch of the two lattices and their relation is shown in Figure 7.11. The relationship between these quantities are:
Figure 7.11 To the left is the observed and uncorrected image were the vectors a' and b' define the unit cell. The angle is a corrected image where \q\, \b\ and y and Y
The linear transformation of the observed unit cell vector a' = (a'x,a'y) and b' = (b'x,b^) can be written as
where Cx, Cy and C^ are the unknown parameters to be estimated and dx and dy are associated with the limited stability of the instrument due to drift (see section 7.7.7).
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7.7.3 Calculation of correction parameters By inserting (7-2) into (7-3) into (7-4), a restraint between the unknown matrix elements Cx, Cy and Qy, and the certified dimensions La, Lb and y is obtained resulting in three equations with three unknowns [9,10]:
where A = 7.7.4 Measurement procedure The AFM is calibrated by acquiring images of the standard oriented in different ways and with different tips according to Table 7.1. The average temperature and humidity under the calibration is recorded. Between the measurements Cl, C2 and C3, the following experimental conditions are changed: the tip, tip-sample interaction (force), feedback gain, orientation of the sample and location of sample in the microscope and the investigated region on the standard. The temperature and humidity are inevitably changing within the permitted range for calibration made at different times. By changing the tip a different Abbe offset is achieved. The environmental condition, temperature and humidity are influence parameters that change the permeability of the air which affects the capacity of the position sensors in the AFM. It is along the fast scanning x direction that the best calibration of the AFM is obtained. An example of an image is shown in Figure 7.12. Table 7.1 Calibration parameters ID#
Standard
La,Lh wlOOOnm
Scan size
Orientatio Scan -rate n of (a) standard
Mode
Scan direction
Tip
lOum x 10 urn
0°
lOHz
Contact
Trace, up
Tl
C2
20um x 20 urn
45°
2Hz
Tapping
Retrace, up
T2
C3
60um x 60 urn
90°
IHz
Contact
Trace, down
T3
Cl
(a)
Always 512x512 pixels. (b) The approximate orientation of one particular row of pitch on the sample.
7.7.5 Determination of observed unit cell parameters The determination of the vectors a', b' from the recorded images of the standard is carried out using a software algorithm implemented in the image processing tool SPIP [11]. The algorithm (called "Fine Linearity Correction") is engaged within the program and works as follows:
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• First an estimate of the unit cell is found by calculating the Fourier transform of the image, and a template (an image) unit cell is generated, See Figure 7.12. • Next, the cross-correlation image between the template and the original image is calculated. The peaks in the cross correlation image represent positions of the unit cell template in the recorded image. These positions are identified at sub-pixel level and compared with those predicted from the unit cell template. The differences ex and ey are named the position errors are further minimised by tuning the unit cell template. • The co-ordinates of the vectors a', b' are calculated by averaging the nearest neighbour vectors between peaks in the cross-correlation image, see Figure 7.12. It is verified from a graph (not shown) that the standard deviation for the position errors ex and ey that represent the remaining non-linearity in the microscope are less than 0.1%. The software used (Scanning Probe Image Processor, SPIP [11]) is an image processing program with special tools for accurate characterisation of image structures and calibration of, in particular, scanning probe microscopes. The calculation of correction parameters in the version used is tested by artificially generated images with known lattice distances. It is verified and logged that the programme gives correct results for these images. Each version of the software is identified by a number which is stored in each data file generated.
Figure 7.12 Example of an image recorded of a standard, the identified unit cell template, and the cross-correlation image
bv, and b, 7.7.6 Variation of determined unit cell co-ordinates a, If no drift was present the variation in observed unit cell co-ordinates a \, a 'y, b 'x, and b 'y would be limited by the remaining non-linearity in the instrument, tilt of the sample relative to the scanning plane, and by the statistics within images i.e. number of observed unit cells and (finite) number of pixels. As a result, there is a standard uncertainty representing the repeatability of the method for the determination of each co-ordinate. The estimates in Table 7.2 are based on the calibration history for the correction parameter Cx and by the investigations of computer generated (artificial) images.
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7.7.7 The temporal drift of the microscope dx and dy The drift speed vd is the speed with which the tip is observed to move over the surface when it is supposed to stand still. For the instrument used in the present work the drift is the sum of the thermal drift in the mechanics plus the change in the indication of the capacitive distance sensors due to e.g. temperature and humidity variations. The average drift speed is estimated to be 0 nm/s with a finite standard uncertainty, w(v
7.7.9 Evaluation of results In principle, the estimated correction parameters could be used to correct for the nonorthogonal scanning, when Cxy differs from zero, and to determine possible significant corrections as a function of scan range and scan speed. In practice, however, only the average values of the correction parameters Cx and Cy are implemented. This is done in order to simplify the measurement procedure on unknown samples. For the instrument used in the present study this is justifiable, as the capacitive distance sensors were very linear, even for the largest scan area. The influence of remaining non-linearity as function of scan speed and scan area were be taken into account as a contribution to the uncertainty.
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The criteria for acceptance of the microscope (that is the performed calibration) were: • the maximal difference between any of the three estimated correction parameters Cj must not exceed 0.01 and for Cy it must not exceed 0.05; • the matrix element C^ must be smaller than 0.01; • the mean position error and standard deviation for the remaining non-linearity exy must not exceed 0.5 pixel for any of the scan areas. If the average value of Cx differs by more than 0.5% from the last calibration or the average value of Cy differs by more than 2.5% the internal correction parameters of the microscope should be adjusted. 7.7.10 Stated uncertainty for the calibration Based on the above acceptance criteria and procedure, the measurement uncertainty of the microscope was evaluated. An expanded uncertainty u v of the x-scale Sx and an expanded uncertainty u s for the y-scale Sy as summarised in Table 7.3 was obtained. The stated uncertainty corresponds to the combined standard uncertainty multiplied by the coverage factor k = 2, in accordance with EAL-R2 [12]. Table 7.3 Measurement uncertainty Scan direction
Scale, S
Uncertainty U
X
1 000 nm < Sx < 70 000 nm
U s < =lnm + 0.01xS x
Y
1 000 nm < Sy < 70 000 nm
U sy =5nm + 0.05xS vy
7.8 Vertical calibration: line-wise levelling Due to z-axis drift and jump effects (see sections 7.2 and 7.3) it is necessary to perform line-wise levelling of AFM images when measuring flat structures such as polished or self-assembled surfaces in the low and sub-nanometre range. Experience from AFM measurements shows that the drift velocity varies with time - often within the time it takes to acquire a single image. The result is that the recorded images are not only tilted mostly along the slow scanning direction but have a varying height level along this axis. In order to avoid the influence of hysteresis phenomena the fast scan lines in the AFM images are always recorded in the same direction, e.g. from left to right. This means that in fact only every second scan line is recorded, since the return scan is not used. Therefore there is a time gap between the recording of adjacent lines causing them to be offset in height and slope due to the drift. Offset between scan lines can also be caused by creep in the z-axis piezo electric actuator of the AFM when the particular AFM is not of the linearised type. Hence a simple tilt correction will not remove this artifact. The described artefact can be compensated for by applying a line-wise levelling procedure. The procedure is based on fitting n 'th order polynomials to each scan-line and then subtracting the resulting reference plane from the image (line wise). In case of zero order fitting (n = 0) the mean height of all scan lines is equalised. For n = 1 additionally the average slope of each line is subtracted so all lines have zero mean slope and so forth across the image. After a line-wise levelling procedure, form
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removal and filtering can be carried out following the general guidelines for the calculation of roughness of surfaces. Figure 7.13 shows the image from Figure 7.8 in 3D perspective before and after 1st order line wise levelling. In order to use line-wise levelling care has to be taken since only truly random surfaces are well suited for this. Particles, if few, may disturb the procedure resulting in the off-setting of those scan-lines containing the particle. Also, if systematic topographical variations like waviness are present it will be removed if the wave vector is parallel to the y axis. Therefore, samples with structures which have a preferred directionality should always be placed so that the preferred direction is along the y axis, and certainly not along the fast scanning x axis. For roughness measurements one should therefore in general take one image where the fast scanning direction is along the x axis (usual configuration) and one image where the fast scanning axis is the y axis (most instruments can do this). Line-wise levelling of these two images and subsequent roughness analysis should give the same result. If this is not the case, re-adjustment of the sample is necessary. If this does not help, line wise levelling should be avoided.
Figure 7.13 10 um x 10 um AFM image before (left) and after (right) 1st order line wise levelling 7.8.1 Principles for vertical calibration of an atomic force microscope This section describes a principle for vertical calibration of atomic force microscopes based on the use of transfer standards. The procedure has been developed to be used with an AFM of the closed loop type for which it can be assumed that no z-axis hysteresis is present. Despite the vertical calibration on step heights, three dimensional calibrated roughness measurement is not straight-forward due to image bow, drift, tip convolution etc. as described in section 7.2. Additionally, there is a remaining nonlinear error for height measurements with different offset [«2%], i.e. the sensitivity is offset dependent. A methodology for calibration of the z axis is now suggested. The method is based on the use of transfer standards calibrated by well accepted classical techniques followed by a subdivision of the z-scale.
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The discussion of calibration and height measurements here is only valid for profiles due to the above mentioned drift in the z-direction (section 7.2). 7.8.2 The standards To calibrate and subdivide the z-scale reference step heights flat surfaces are used. The standards consist of silicon/silicon-oxide covered by a metallic film (Ptlr-Cr) of « 70 nm thickness. Line patterns (of different width) and a waffle pattern have been etched into the substrate by the use of standard photo-lithography and semiconductor etching techniques. The standards are certified by interference microscopy by PTB, Germany. In the present case we the line patterns are used for calibration. The interpretation of the measured step height is shown in Figure 7.14, which essentially shows a cross-section of a line pattern on the standard.
Figure 7.14 Principle of specification and interpretation of height measurements. The bold line is the observed average profile of a line with a small height. Due to non-linearity of the instrument, the profile has a superimposed bow (marked by the dashed line). The vertical distance between the solid broad lines is the certified reference height estimated by interferometry. The line marked His interpreted as the equivalent height of an AFM measurement
7.8.3 Measurement procedure, data analysis For each measurement a rectangular area consisting of 64 scan lines each 512 pixels wide is scanned. The standard is placed so that the long axis of the step height is aligned along the slow scanning >>-axis and carefully centred on the x-axis of the image. A series of measurements are performed at different positions on the standard. Other operating parameters should also be changed between measurements (see section 7.7.4). Each image is line-wise levelled to order 1 and the average profile is calculated. The image bow (see Figure 7.14) is quantified as the second order term CX2 of a polynomial least mean square fit to the average profile of an observed image of a flat surface or the equivalent peak to peak height Azflt of the second order term within the image area. In fact,, two fits to the measurement are made, one which follows the surface of the step and one which follows the surface on both sides of the step (see Figure 7.14). The vertical distance between the two best fits gives the observed step height, H. The average and the standard deviation is calculated for the measurements. The variation in sensitivity as a function of z offset is determined by measuring a step height for different average z-positions. An uncertainty budget is calculated on the basis of the standard deviation of the measurements, the measured variation in sensitivity (as function of offset) and the uncertainty stated on the calibration certificate of the standards.
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7.8.4 Example of calibration Table 7.4 shows [6] the measured step height as function of the reference step for three standards: 13 nm, 80 nm and 800 nm (nominally). It can be seen that the uncertainties of the reference heights of 13 nm and 80 nm are much larger than the experimental standard deviation for the AFM measurements. Subdivision of the zscale thus requires further justification. Figure 7.14 shows the measured step height as function of the average z-position during recording for a 180 nm step height standard. For an average offset within ± Ij^m the correction factor is within ± 0.8%. From images of a flat surface (not shown) it was found that image bow in the x-direction of the tested microscope were 5±1 nm for offset within ± 1 um. After subtraction of the fitted plane, the roughness, Sq , for the remaining surface was approximately 1 nm. Table 7.4 The observed step height and the certified reference step height Standard deviation. For> 10 measurements
Relative stand, dev.
s(Azo) [nm]
s(Az0)/Az0 [%]
759.7
1.1
0.14
759.7
4.1
81.66
0.35
0.44
81.4
2.3
12.8
0.14
1.2
13.2
1.6
Observed step height Azo [nm]
Certified value A^nm]
Uncertainty on certified value u(Azref) [nm]
Figure 7.15 The measured correction factor C2for a 180 nm step as function of the average z position Za during recording of the image
7.8.5 Stated uncertainty for calibration In the present study the z-axis (height) of a metrological AFM equipped with distance sensors was successfully calibrated by the use of certified reference standards. Based on the investigation of flat surfaces and tilted step heights the non-linearity and measurement uncertainty of the system was assessed. If z is the observed height and Azmax is the maximal height in the image an expanded uncertainty of Uz = 2 nm + Q.02-Azmax (confidence of 95%) can be achieved with the calibrated microscope.
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7.9 References [1] J. E. Griffith, D. A. Grigg, J. Dimensional metrology with scanning probe microscopes, Appl. Phys. 74, R83-R109 (1993). [2] R. leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield and A. Yacoot Advances in traceable nanometrology at the National Physical Laboratory, Nanotechnology 12, Rl (2001). [3] J. Garnaes, N. Kofod, J. F. J0rgensen, A. Kiihle, P. Besmens, O. Ohlsson, J. B. Rasmussen, P. E. Lindelof, G. Wilkening, L. Koenders, W. Mirande, K. Hasche, J. Haycocks, J. Nunn, M. Stedman, Nanometre scale transfer standards, Proceedings for euspen 1 st international conference and general meeting of the european society for precision engineering and nanotechnology, Edited by: P. McKeown, J. Corbett et al., on May31st-June 4th 1999, Congress Centre Bremen, Germany, Vol 2, 134-137 (1999). [4] K. Dirscherl, J. Garnaes, L. Nielsen, J. F. J0rgensen, M. P. S0rensen, J, Modelling the hysteresis of a scanning probe microscope, Vac. Sci. Technol. B 18(2), 621625 (2000). [5] A. Kiihle, A. H. S0rensen, J. B. Zandbergen, and Jakob Bohr, Contrast artifacts in tapping tip atomic force microscopy, Appl. Phys. A 66, S329-S332 (1998). [6] J. Garnaes, N. Kofod, A. Kiihle, C. Nielsen, K. Dirscherl, L. Blunt Treaceable step height and roughness measurements with atomic force microscopes, extended abstract for the 2nd International Conference of the european society for precision engineering and nanotechnology, Turin May 29th-31st 2001. A paper will be submitted to the proceedings of the above conference. The proceedings will appear in the international scientific journal of Precision Engineering. [7] Dimension 3100 with metrology head from Digital Instruments (now Veeco), Santa Barbara, CA, USA, www.di.com. [8] National Physical Laboratory (NPL), United Kingdom by the use of Littrow diffraction (green He-Ne laser) using a manual angle table with two readings on an optical screen. [9] N. Kofod, J. Garnaes, J. F. J0rgensen Methods for lateral calibration of Scanning Probe Microscopes based on two dimensional transfer standards, Proceedings of the 4th seminar on Quantitative Microscopy QM 2000 Dimensional measurements in the micro- and nanometre range, Edited by Klaus Hasche, Werner Mirande, Giinter Wilkening, Semmering, Austria, January 12-14 2000, PTB-Bericht, page 36-43 (2000). [10]N. Kofod, J. Garnaes, J. F. J0rgensen Calibrated line measurements with an atomic force microscope, European society for precision engineering and nanotechnology: Proceedings for the 1st Topical Conference on Fabrication and Metrology in Nanotechnology, Edited by L. De Chiffre, K. Carneiro, Copenhagen May 28-30, Vol. 2, page 373-381 (2000). [ll]Nils Koppels Alle Scanning Probe Image Processor, Image Metrology Aps., 402, DK-2800 Lyngby, Denmark, www.imagemet.com.
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[12JISO/BIPM, "ISO Guide to Expression of Uncertainty in Measurement", Corrected and reprinted, 1995, 1993(E).
Part 3 Case Studies
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8
The Interrelationship of 3D Surface Characterisation Techniques with Standardised 2D Techniques Robert Ohlsson, Bengt Goran Rosen and John Westberg Volvo Truck Corporation, Goteborg, Sweden; and School of Business and Engineering, Halmstad University, Sweden; and Volvo Car Corporation, Goteborg, Sweden
8.1 Introduction The objectives and main aim of the work discussed in this chapter is to compare 2D with 3D surface roughness parameters measured on functional surfaces. The functional surfaces provided were automotive cylinder liners, steel sheet product and ball bearings. Tests designed to throw light on the dispersion and variability, when measuring and calculating 2D and 3D parameters, were also carried out. These results indicated the number of measurement needed for a surface to receive a stable mean value for the topography. Additionally, work is discussed which shows the functional relationship between traditional 2D surface parameters and a range of the newly developed 3D parameters. This study allowed a deeper understanding of the functionality of automotive cylinder bores, and empirical wear relationships are proposed. Finally, studies were carried out on sheet steel for the purpose of comparing optical and tactile measurement techniques
8.2 Surface roughness parameters in relation to functional demands It is important to find relationships between functional performances for different surfaces and specific surface roughness parameters. By accomplishing this goal it should be easier to control the optimal manufacturing of these surfaces and it will also help to justify specification of functionally critical surface roughness parameters. This is especially important for the development of 3D parameters since one goal is to keep their number to a minimum. Three different types of surfaces have been evaluated: cylinder liners, ball bearings and a set of steel sheets with different textures. For the cylinder liner and its counterpart, the piston ring, the most important functional demands are oil consumption, blow-by, and wear specially at the TDC (top-dead centre). One important performance characteristic
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for the steel sheets is lubricated friction and this has been investigated through a set of BUT (bending-under-tension) tests.
8.3 Cylinder liner topography and functionality For this work a factorial designed experiment (FDE) was performed where surface roughness was correlated to functional performance indicators such as oil consumption, wear, and blow-by in a 10 litre truck engine. The choice was to vary the roughness of the piston ring over three levels (Ra) and the cylinder liners with two variables both varied over three levels. For the liners the variables were the so-called "plateaux ness" (Rvk/Rk), which described the surface structure and an amplitude parameter (Rz), described the size of the topography. The values can be seen in Table 8.1. Table 8.1 The test plan used in the FDE Piston Ring
Test no
Rz
Ra 1
a
3 4 5 6 7
Cylinder Liner -v?%:j,i •-.,» • .; RvW^fcXE 3 3
16
0,5-0,6 <0,2
4 0,3-0,4
10
0,3-0,4
1,5
1
0,5-0,6 4
10
1,5
16 1
<0,2
0,3-0,4
10
1,5
The measured responses in these experiments were the functional performance indicators: A: B: C:
Oil consumption Blow-by Wear
Oil consumption was measured as the mean consumption for different loads and revolutions (g/kWh). Blow-by was measured as the gas flow that passes the ring pack (1/s). The wear was measured after the test at TDC (top dead centre) of the cylinders. The wear was characterised by the maximum wear depth in micrometers. Values for the correlation factors between the surface roughness parameters and the functional performance (the response) are shown in Table 8.2. Values between 0,3 and 0,3 are considered as not significant. The sign is important and must be taken into account. When the sign is positive, the parameter and the response have the same variation. When the sign is negative, their variation is contrary. For instance, when Rar (Ra on the ring) increased, blow-by decreased since Rar has a negative response. Figure 8.1 shows a graphic representation of this matrix for the correlation between the engine
3D Surface Characterisation Techniques with Standardised 2D Techniques
199
performance factors and the responses. Only the ten largest correlations are shown in this graphical view. Table 8.2 The correlation factor between the surface roughness parameter value used and the functional performance (the response), where A=oil consumption, B=blow-by, and C=wear. Rar is the Ra value for the rings
Rar Rar Rz Rvk/Rk A B C
Rz
Rvk/Rk
A
B
C
1 -0,1337 0,174711 -0,240277 -0,838345 0,625148 1 -0,209439 0,965298 0,244934 0,583006 -0,1337 1 -0,355595 -0,244315 -0,308528 0,174711 -0,209439 -0,240277 -0,838345 0,625148
0,965298 0,244934 0,583006
-0,355595 -0,244315 -0,308528
1
0,321418
0,321418 0,481782
1
0,481782 -0,397573
-0,397573
1
Figure 8.1 Graphical representation of the correlation factor matrix for the ten largest correlations Figure 8.1 shows the correlation for the chosen parameters in the FDE. It can be seen that the biggest influence on oil consumption (A) is Rz measured on the liner followed by Rvk/Rk. Blow-by (B) is most strongly correlated to the Ra measured on the rings (Rar) and has a negative correlation. The strongest correlation to wear (C) has Rar followed by Rz. A further interesting result is the correlation A/C which implies that an increasing wear will have an increasing oil consumption. Less logical and harder to explain is the negative correlation B/C that implies that increasing wear is followed by decreasing blow-by (bearing in mind that TDC wear is considered); this may be due to a build up of carbon deposits at TDC.
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By using this correlation approach and by analysing the correlation coefficient from the results it was possible to determine relationships between two properties i.e. information about the correlation of each surface roughness parameter and a response. These results are displayed in the following tables. The first table, Table 8.3, contains the results for the 2-D parameters. The second, Table 8.4, contains the values for the 3-D parameters. The bold-type parameters had similar correlation values for both 2-D and 3-D parameters. Table 83 The correlation coefficients for the FDE and 2D parameters Correlation between
1 ; 0,9 0,9 ; 0,7 0,7 ; 0,5 0,5 ; 0.3 0,3 ; -0,3 -0,3 ; -0.5 -0,5 ; -0,7 -0,7 ; -0,9 -0.9 ; -1
Ra, R. R/AR, W, W/AW. Rsrn Oil CR, CF, Rsk, VQ consumption Rq, Rp, AW, CL Rv, Rpk, Rvk, Rk, Rz
AR
Blow-by
Wear
AR
Rsk
Ran no Mr1, ' Rvk/Rk
Mr2
Rz, Ra, Rq, Rp, Rpk, Rv, Rku, Rk.W, Rsm, Mr1, R/AR, Mr2,Rvk, RvWRk, W/AW, CR, CF VO.RAW, Rsk,CL
Ra ring, Rz, Ra, Rp, Rpk, Rq, Rv. Rk, CR, Mr1, Mr2, Rsm, CF.W, AR Rvk, Vo, W/AW R, R/AR, AW.CL
Rku
Raring
Rvk/Rk
Rku
A large number parameters were correlated with the oil consumption.. The roughness of the rings was most important for blow-by whilst Rku and Rsk were most important for the wear. The negative correlation between Ra ring and blow-by means would seem to suggest that, when the roughness of the ring increases, blow-by decreases. For the blowby, there are other factors that play a part, so it is logical that a strong correlation between the roughness of the cylinder liner and blow-by is not found. In addition the ring gap and the clearance between the piston rings and the piston can also determine blow. Form errors in the cylinder liner are important too and it was surprising that a good correlation between the ratio Rvk/Rk and wear was not found. This can however have its origin in how the wear is defined and therefore a new wear "model" will now be discussed. A new alternative wear model has been suggested and applied in Table 8.4. The model is based on the material ratio curve and calculated from: Wear = (Sk + Spk) before test - (Sk + Spk) after test
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These values are derived from relocated 3D measurements, performed before and after the engine tests. This relocation technique and the material ratios' strong correlation to the important part of the topography for describing wear, explains the large increase in parameters that are correlated to this new wear "model". The parameters that are illustrated by bold text are placed in corresponding boxes for both 2-D and 3-D parameters. 8.3.1 Oil consumption For oil consumption, most parameters had a strong correlation and are important. This indicates that the surface of the cylinder liner was strongly correlated with this functional demand. From the tables it was found that a large number of parameters had an important role for oil consumption. The valleys in the surface are of course important for oil consumption and parameters that are influenced by valley depth have a strong correlation. Rq, Rk and Rvk increase with oil consumption, have a strong correlation and have very similar correlations for 2D and 3D. This is logical for Rvk since it is directly related to the oil retaining volume, Vo: Vo = Rvk (100-MR2)/200 Rk defines the smoothness of the plateau zone of the surface which also contains small oil reservoirs which will be burned, therefore Rk influences the oil consumption. The French parameters based on the Motif technique dissociate the roughness and the waviness. R/AR and W/AW showed that roughness is as important as the waviness for oil consumption. For the 3D parameters, the hybrid parameters are well correlated with oil consumption. These parameters make it possible to characterise the slope of the surface and the curvature of the summits. 8.3.2 Blow-by According to this study, the parameters that seem to have a relatively important role for blow-by are Ra ring, Svi and Sv.
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Table 8.4 Correlation coefficients for the FDE and 3D parameters. The "new -wear model" is related to the decrease in material ratio which occurs due to wear and shows better correlation than standard wear measurements
Correlation between
1 ; 0.9
0,9 ; 0,7
0,7 ; 0,5
0,5 ; 0.3
0,3 ; -0,3
Oil consumption
Sq, Sdq. Ssc, Sdr. Sci, Sk, Svk
Ssk, Sal. Sc, Spk
Sz
Sr2
Sm
Sal, Sc, Sk, Sr2
Blow-by
Wear
Ssk
New wear model MID
Sq, Sal, Sdq, Ssc, Sdr, Sc, Sk, Spk,
Sci, Svk
Sz, Sr2
New wear model TDC
Sq, Sal, Sdq, Ssc, Sdr, Sci. Sc. Sk, Spk, Svk
Sz,
S$k, Sr2
Sz, Ssk, Sq, Sdq, Ssc, Sdr, Skn.Str, Spk, Svk, SfttSH Sci, Sri, Svk/Sk Sz
-0,3 ; -0,5
-0,5 ; -0,7
Std, Svi, Sv,
Sri
Sku, Str, Svk/Sk
Sds
Sm
Svi, Sv
-OJ ; -0,9
-0.9 ; -1
Sds.Sbi
Sq, Sz, Sdq. Ssc.Sdr. Sci, Sk. Spk, Svk
Sal, Svi, Sm, Sc,Sv, Sz
Sir. Sr2
Sds, Std, Sbi, Svk/Sk
Sku
Ssk
Sri
Sku. Str, Std, Sm
Svi, Sv, Svk/Sk
Sds, Sbi
Sm.SrI
Sku, Str, Std,
Svi, Sv, Svk/Sk
Sds, Sbi
Sri
The contact between the ring and the cylinder liner clearly influences the blow-by. But blow-by is also due to many other factors such as compression factors, roundness of the cylinder liner and of the piston rings which can explain the rather weak correlation to other topography parameters. 8.3.3 Wear In terms of wear the parameters that seem to have played an important role for TDC-wear were: Rku, Rsk, Svk/Sk, Ssk, and Sku Rku is sensitive to atypical peaks or valleys. As peaks, especially atypical peaks are in particular concerned with initial wear, Rku and Sku were consequently correlated with wear and not only at the TDC of the cylinder liner. The values of Rsk and Ssk were
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negative, because there are more valleys than peaks. The new wear model: (Sk + Spk) before test - (Sk + Spk) after test is better describes the wear in the cylinder liner especially as it is possible in an easy way to describe the wear in other areas of the cylinder liner and not just in the TDC. Using this simplified approach a strong correlation was found with Spk, Sk, Svk, Sc and Sci. Overall from the correlation study (Tables 8.3 and 8.4) it is clear that from the spread of the correlation values the 3D parameters give a better functional correlation than the 2D parameters.
8.4 Steel sheet topography measurement and functionality For the sheet steel study measurements were performed on steel sheets textured by cold rolling with six different textures on the rolls: SBM and SBR (shot blasted), EBT, FFCR and FPCR (electron beam texturing), and BCD (electro-chromium deposition) with each surface having a differing topography, see Figure 8.2. The lubricated friction coefficient was measured using a BUT-test (bending-under-tension).
Figure 8.2 The different tested steel sheets textures 8.4.1 Comparison of optical and contact measurement techniques To be able to compare parameters values obtained using differing measurement techniques, it is essential that the measurement conditions should be as close as possible. They should describe the same size of area, the filtering applied must be same, as should the parameter calculation scheme.
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Advanced Techniques for Assessment Surface Topography Table 8.5 Stylus and interference measurements for each of the six steel sheets 2D measurements Number of measure Measurement step Filtering Cut off length
3D measurements: Number of measure Measuring area Sampling distance Filtrering
Somicronic
- ;..:..
25 • •
4 Mm ISO / Roughness GAUSS (Ra, Rz) DIN / Double GAUSS (Rk, Rpk. Rvk) 0.8mm
Somicronic
Wyko
3
25
2*2 mm 8*8 urn Form removal 1 * 1 mm
2,6* 1,9 mm 4*4 urn Form removal 1,23*0,92 mm
To evaluate the sensitivity of a parameter to the measurement technique, the difference between the stylus measurements (Somicronic) and the optical measurements (Wyko) were calculated. The study includes a stylus instrument as a benchmark, due to their wide use in industry and the fact that current standards assume the use of a contacting stylus instrument. The optical system utilised was an interferometric system used because of the measurement rapidity and a supposed good correlation with stylus measurements. Early investigations on uncoated steel sheets, with relocated measurement areas showed that the resulting Sa-values show very small deviations (often <10%), see Figure 8.3.
Figure 8.3 Measure relocated area 1x1 mm2, sampling distance 4 /jm in both x-and y-direction
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Carrying out 6x25 3D measures on the Somicronic would have taken an excessive amount of time. Consequently, only 3 3D stylus measurements on each steel sheet were carried out; hence no dispersion bars were calculated for the measurements. The parameter values were obtained with similar filtering (using the same software) (Surfascan), in order to really highlight the influence of the measuring technique on the parameters values. Comparisons between the Wyko and the Somicronic results, for selected parameters, are shown in Figures 8.4 and 8.5, for the both techniques, plotted on the same scale.
Figure 8.4 Comparison of the Sa value measured by the Wyko and the Somicronic instruments
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Figure 8.5 Comparison of the Sa value measured by the Wyko and the Somicronic instruments
The above graphs are examples of comparisons between Wyko and Somicronic 3D measurements. The error bars for the Wyko measurements represent the dispersion obtained with the T-distribution for 25 measurements. The conclusion from the 3D measurements with Wyko and Somicronic were that the parameter values were rather well correlated. This is the reason why it was possible to compare 3D Wyko measurements with 3D Somicronic measurements, when measuring these uncoated steel sheets. 8.4.2 Comparison between 2D and 3D parameters The parameter values obtained by the 2D measurements are generally slightly lower than corresponding parameters from the 3D measurements, Figure 8.6. One reason is that, when measuring 3 dimensionally with more than one hundred times as many data points collected, the chances of measuring extreme asperities increases and therefore the measured parameter values increase. This is especially the case where extreme point parameters are considered such as Rz/Sz.
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Figure 8.6 Comparison between Sa and Ra. The bars are the mean value of 25 measurements for each steel sheet both in 2D and 3D and the error bars are calculated according to the 95% confidence level 8.4.3 Correlation between surface roughness parameters and friction The primary objective for this work was to evaluate how the surface topography influenced the frictional behaviour of the steel sheets. In this study, the first step was to identify and rank the 3D parameter affecting the friction. The secondary goal was to establish what relationship, if any, exists between the surface topography and friction. In this work, parameter values were obtained as described earlier in this chapter and a mean value of 25 measurements was used. Simulation of the forming process using the bending-under-tension, (BUT) test Friction tests can either be carried out in tools in a press or by simulation of a critical part in a tool. In the work presented in this study, the conditions at the die radius have been simulated. The test used for this purpose is called the bending-under-tension test. The test equipment consists of a cylindrical tool bar, two hydraulic cylinders, clamps for fastening the strips, and a control system. One cylinder is for the drawing; the other will hold the strip back so that the tension is achieved in the material. The parameters, which can be varied in the BUT test, are sliding speed, contact pressure, lubricant, amount of lubricant and the surface texture of the steel sheet material. Frictional study of uncoated steel sheets The tests where performed with the 6 different textures, 3 EBT(electron beam textured), 2 SB (shot blasted), and one ECD (electro-chromic deposition).
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For evaluation of the influence the surface topography on frictional behaviour, 2D and 3D measurements where performed on the steel sheets' texture (before the BUT test). 25 measurements were made for each texture, and thus for 2D and 3D measurements. The filtering used in the 2D measurements was Gaussian and double Gaussian filters with a cut-off 0.8mm. The filtering used for 3D measurements was a spline form removal with a filter length of approx. 1mm. For each parameter (2D and 3D), a graph was plotted where the measured friction coefficient was plotted against the parameter value, for each steel-sheet. A trend was calculated for each scatter graph, among those 6 points and the R-squared value was calculated. The R-squared value, also known as the coefficient of determination, is an indicator that ranges in value from 0 to 1 and reveals how closely the estimated values from the trend line corresponds to the reality. A trend-line is more reliable when the R-squared value is close tol and should preferably exceed 0.9 in order to assume good correlation. Correlation to the BUT-friction test The best correlation obtained for all 3D parameters was for Sk and this is shown in Figure 8.7. The 95% confidence interval for the parameter is also plotted for each steel sheet.
Figure 8.7 Correlation: friction Sk The correlation obtained for each of the 3D parameters is shown in Figure 8.8.
3D Surface Characterisation Techniques with Standardised 2D Techniques
Figure 8.8 The correlation for each 3D parameter and the friction
209
coefficient
The best correlations are realised with the parameters Sk and SCF, both are derived from the material ratio curve and both describe the core roughness depth in the surface. The coefficient of determination is only 0,64, which is far from 1 and the result and no strong correlation can be assumed. The existing 3D parameters applied to virgin surfaces are therefore less suitable for predicting the lubricated friction level on these kinds of steel sheets. Tests have shown that new parameters such as the number of isolated oil pockets (the so called WC parameter) have a better correlation for this typical functional demand i.e. the lubricated friction coefficient. The following parameters and their correlation to friction was tested: NIOP: number of isolated oil pockets AIOP: area (total) of isolated oil pockets MBL@Ra: mean border length of closed oil pockets at level Ra below the mean plane The following correlation was received: NIOP - friction => AIOP - friction => NIOP*MBL@Ra - friction =>
R2=0.42 R2=0.20 R2=0.71
To sum up, the proposed 3D parameters in this instance were found to be relatively poor at predicting the lubricated frictional behaviour of uncoated steel sheets. The results above showed that the more advanced use of pocket calculations are needed to obtain a
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correlation above 0.7. There are other indexes such as the WC-index that gives even better correlation, R2>0.9, which are more suitable for this kind of friction prediction. There is obviously a need for 3D parameters that describe texture properties such as isolated oil pockets etc. when friction on lubricated steel sheet is to be evaluated.
8.5 Repeatability and variability study of 2D and 3D surface roughness measurements Accurate surface finish measurements require care and a stable environment. If these conditions are not met, the chances of large errors in the measuring results are greatly increased. A single roughness measurement analyses only a fraction of the work-piece surface. Taking multiple measurements in different areas on the work-piece can produce measurement results with a large range. The range of the measured results is due to variations of the surface texture across the surface of the sample. Consequently, the results of any single measurement may not be representative of the overall surface quality. One solution to the problem of variation in the measured values is to take multiple measurements in different areas of the surface. The average surface texture is the arithmetic average, or mean of the results. The number of measurements that are taken on a part is determined by the measured results and the part tolerance. But how many measurements does one have to perform to be inside this tolerance? Further, how big a tolerance can one accept?
8.6 Statistical approach A statistical method can be used. Such a method is able to analyse process variation with the aim of anticipating an out-of-tolerance result. A work-piece is taken and the desired characteristic is measured. After each new measure, the mean and the standard deviation are calculated for each of the subgroups. This information is displayed on a graph, an example of which is shown in Figure 8.9.
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Figure 8.9 Chart of confidence interval for EBT texture, parameter Sz (using T-distribution)
The X-axis represents the number of measurements performed and the Y-axis represents the confidence interval as a percentage for each case. In this example, for an EBT surface and parameter Sz, the mean of 12 measures had to be within ±10% for the part to be consider within tolerance. This tolerance is used, when possible, since it is a practical rule-of-thumb that ±10% is an acceptably low value for dispersion of topography.
8.7 Steel sheet topography Results of an attempt to assess "how many measurements" need to carried out in order to obtain parameter values within a certain limit when measuring uncoated steel sheets (described earlier) are shown in Figures 8.10 and 8.11.
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Figure 8.10 The numbers of measurements needed to keep the ID-parameter value within ±10% using the T-distribution with 95% confidence level
Figure 8.11 The number of measurements needed to keep the SD-parameter value within ±10% using the T-distribution with 95% confidence level The measurement conditions regarding the steel sheets are the same as described in Table 8.4. The main conclusion when measuring these uncoated steel sheets, at the given sample spacing and measurement area size, is that it is sufficient to take a mean value of 5 measurements to obtain 3D parameter values within ±10% at 95% confidence level; this is compared to 10-20 2D-measurments to get parameter values within ±10% at the same confidence level.
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8.8 Cylinder liner topography A typical plateau-honed cylinder liner from an automotive petrol engine car was measured using a stylus instrument (Surfascan 3D) according to following measurement conditions: Table 8.6 Measurement conditions for cylinder bores 2D measurements Number of measure Measurement step Filtering Cut off length
SotttiefQiBC ^ 25 • •
4 jim ISO / Roughness GAUSS (Ra, Rz) DIN / Double GAUSS (Rk, Rpk, Rvk) 0,8 mm2
3D measurements:
Somicronic
Number of measure Measuring area Measurement step Filtering 1 Filtering 2 Filtering 3 Filtering 4
2*2 mm2 8*8 urn Level + polynomial form removal Level + surfstand gauss, cut-off 0.8 mm Level + surfstand robust, cut-off 0.8 mm Level + somicronic gauss, cut-off 0.8 mm
25
Following filtering, the 3D measurements were evaluated and the parameters were calculated suing the SURFSTAND software. Similar dispersion graphs to those shown in Figures 8.10 and 8.11 were produced and a summary of the results are shown in Figures 8.12 and 8.13.
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Figure 8.12 77ze number of measurements needed to keep the parameter value within ±20% at the 95% confidence level
Figure 8.13 The number of measurements needed to keep the parameter value within ±20% at the 95% confidence level. 4 different filters are compared The main conclusion when measuring cylinder liners in terms of dispersion is that the same number of measurements are needed, using 3D or 2D measurements This is
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probably due to the more difficult form removal problems, when evaluating the measured area. The Gaussian filters shows slightly better results than the polynomial form removal indicating that waviness is persistent within the filtered data and needs better filtering in order to be successfully removed.
8.9 Ball bearing topography The topography of ground and polished balls from a ball bearing were additionally studied due to its extremely smooth roughness (Sq=0.007). 25 measurements were performed on a typical ball before and after a lubricated sphere-on-disk wear testing . The dispersion of these measurements is shown in Figure 8.14.
Figure 8.14 The number of measurements needed on a ball bearing ball to keep the parameter value within ±20 and ± 10 percentage at the 95% confidence level. The graphs show measurements from an unused ball and from the same ball after the sphere-on-disk test
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As can be seen in Figure 8.14, the dispersion was too large for the ± 10% to be of use. In this case, when using a ±20% limit, the number of measurements needed to create a stable mean value was 5-10 for most parameters. Some parameters, however particularly those significantly affected by extreme data points, needed more than 25 measurements in order to create a stable mean value which is alarming in terms of their application. The effect of running-in results in a decrease in number of needed measurements for a sphere-on-disk tested ball. This is probably due to the fact that the running-in process removed the small number of extreme peaks that occur within the data.
8.10 Comments on dispersion in 2D and 3D The dispersions in 2D profile measurements on a single surface are well known and reluctantly accepted. The common practice is therefore to measure a number of profiles and to use the mean value when grading the quality of the surface. There are also standards that deal with these matters such as the 16% rule described in ISO 4288. This standard states that it is acceptable for 16% of the measurements to be outside a written tolerance and still approve a part. The expectation of 3D measurement is that only one measurement (or at least a small number) should be sufficient for the analysis of a part, mainly due to the time needed per measurement. The large number of data points in one 3D measurement was hoped to give a statistically stable basis for the analysis of a surface. The results shown in this chapter however, point out that a single 3D measurement is usually insufficient for the grading of a surface if a specific parameter value is desired. The number of measurements needed for the calculation of a stable mean value depends to a large extent on which parameter is needed. It was found that it is often necessary to perform at least 5 measurements to obtain a stable mean value for many roughness parameters while others needed a larger number. The reason for this is that there is often one or a few measurements that diverge from the expected normally distributed result. It can always be argued that this dispersion depends on the manufacturing process being unstable, resulting in a surface that is not equal at different places on a part. The point made here is that the investigated surfaces are typical engineering surfaces and the dispersions presented here will be the reality when measuring 3D surface roughness. Therefore, it is most likely that some kind of rule (similar to the 16%) is needed to take account of the natural deviations that occur within a standard engineering surface.
8.11 Uncertainties in 3D characterisation due to measuring strategy An important but also difficult issue regarding 3D surface roughness measurements is the choice of measuring strategy. The choice of area size is important since the chosen area should be large enough to characterise a representative part of the surface or at least generate stable parameter values. The choice of sampling interval is also important and should be chosen according to the surface wavelength of interest. Both sampling interval
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217
and measuring area have a strong influence on the measuring time and must therefore be optimised. The results presented in the following section are from measurements performed on two different plateau-honed cylinder liner surfaces from truck engines. One smooth (Sa=0.4) and one rough (Sa=1.7), this example has been evaluated in order to cover the full range of roughness levels used for these types of surface. 5 large measurements (4*4mm) were performed on each type of liner with the smallest possible sampling distance (4um). From these data files smaller areas were isolated, 3*3, 2*2 and l*lmm. For each area size, different sampling spaces were then used (4, 8, 12, 16 jam). Form removal was initially carried out and then a Gaussian robust filter was applied using the SURFSTAND software and parameters were calculated. The results are shown in Table 8.6 of the mean value and standard deviation of 5 measurements, for each combination of area and sampling. One quite stable amplitude parameter was chosen (Sq) in combination with one less stable parameter (Sdr) to show the extreme cases obtained, and these are presented in Figure 8.15.
Figure 8.15 Results from the "smooth " cylinder liner where area size and sampling space have been changed A typically robust parameter Sq is stable down to l*lmm and 16 jam sampling. A less robust parameter such as Sdr shows rather large dispersions for any changes. Values are normalised to 4*4mm and 4|im sampling, Figure 8.15.
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Similar results was found for both types of cylinder liners both rough and smooth. A typical robust parameter such as the amplitude parameter Sq is a good example of a parameter with small dispersions and it is relatively insensitive to sampling and area size. A more sensitive parameter such as the developed surface area ratio, Sdr, was also evaluated. It is clear from Figure 8.15 that Sdr is very sensitive to area size and a big dispersion is obtained immediately, even for 3*3mm. Concerning sampling space, it was seen that 8 um sampling will give a rather large deviation from the original measured 4um. The large dispersion in the Sdr parameter is not unexpected as the algorithm for calculation of the parameter value is based on the sample spacing. It is used here to demonstrate the critical nature of the choice of sample spacing and to illustrate the need to standardise measurement conditions when comparative measurements or measurements against standard tolerances are carried out.
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Table 8.7 Smooth cylinder Liner (Sa=0.4) - mean and standard deviation of 5 measurements normalised to area=4*4 mm and sampling=4 fjm Mean
sampling14 4x4 3x3 2x2
Amplitude St Sa Sq Sz Ssk Sku Spatial Sds Str Sal Std Hybrid Sdq Ssc Sdr Functional Sk Spk Svk Sr1 Sr2 Sbi Sci Svi Sm Sc Sv
1,000
1,238
0,970
0,756
1,115
1,000
0,923 0,914
1,001
0,930
0,585 0,884
1,000
0,970 0,984
0,956
0,879
1,000
1,075
0,811
1,003 0,837
0,859
1,000
0,323 1,490
0,450 2,013
0,935 0,689
0,163 2,258
0,373 1,512
1,000
sampling18 4x4 3x3 2x2
sampling 12 4x4 3x3 2x2
sampling 16 4x4 3x3 2x2
0,592
0,341
0,326
0,572
0,480
0,186
0,955
0,901
0,911
1,008
0,850
0,825
0,907
0,930
0,326
0,889 0,327
1,013
0,559
0,969 0,714
0,690
0,530
0,851 0,195
0,754 0,466
0,868 0,538
0,766 0,346
0,556 0,432
0,809 0,482
0,262 0,940
0,852 0,339
0,354
0,360
0,184
0,011
0,043
0,121
0.031
0,006
1,168 0.934
0,990
7,525
9,276
3,061
7,525
2,418 1,787
1,189 2.228
1,270 1,614
1,393 0,579
8,401 3,156
1,000
1,017
1,044
1,000
0,785
0,862
1,000
0,852 0,698
0,779 0,698
1,025 1,307
0,698
0,698
1,731 1,172 1,307
1,075 1,007 1,034
1,027
0,770
0,745
0,681
0,561
0,149
0.306
0,515
0,268
0,108
1,007 0,959
0,448 0,604
0,403 0,528
0,381 0,467
0,213 0,327
0,012 0,025
0.051 0,099
0,150 0,273
0,033 0,077
0,006 0,013
1,000
0,968
0.919
0,998
0,928
0,870
0,921
1,006
0,835
0,751
0,868 0,934
0,775 0.793
1,098 0,991
1,012
1,161 0,857
0,846 0,801
1,325 0,983
1,543
0.922
0,672 0,771
0,939 1,271
0,948
1,000 1.000
0,885 0,706
1,000
1,015
0,954
1,013
0,981
1,025
1,001
1,004
1,040 1,014
0,995
1,005
1.021 1,017
1,021
1,000
1,005
0,984
0,979
1,000 1,000 1,000 1,000
1,000
1,055
1,000
0,959
1,024 0.984
1.000 1,000
0.995 0,977
1.000 0.861
1,000 1,000
0.971 0,969
0.920 0.914
1,008 0,980
1,190 0,997
Standard deviation Amplitude St 1,000 Sa 1,000 Sq 1,000 1,000 Sz 1,000 Ssk Sku 1,000 Spatial Sds 1.000 Str 1.000 1.000 Sal Std 1,000 Hybrid Sdq 1,000 1,000 Ssc Sdr 1,000 Functional Sk 1,000 Spk 1,000 Svk 1,000 Sr1 1,000 Sr2 1,000 Sbi 1,000 Sci 1,000 Svi 1,000 Sm 1,000 Sc 1,000 Sv 1,000
0,852
0,996 1,015
0.955 1,007 0,998
1,003
0,863
1,863
1,477
1,769 0,620
1,045
0,728 1,071
1,409
1,530
1,380
0,825 1,055
0,626 0,774
0,531 0,867
1,082
1,142
1,107
1,137
1,375
1,377
0,918 1,024
0,889
0,915
0,883
0,720
0,746
1.168 0,849
1,019
1,026
1,033
1,091
1.153
1,228 0,904
10,10 0,793 0,906
1,264
1,023
1,190 0,841 0,958
0,826 0,999
1,523 0,624 0,953
1,710 0,656 1,011
1,103
0,501
0,831
0.382
0,326
0,297
0,279
0,338
0.543
0,112
1.025
1,027
1,020
2,131
1,575
0,972
2,117
1.038
1,099
1.031
0,938
0,975 1,021
0,910
0,544
0,661
0.450
1,995 0,307
1,209 0,264
1,083
0,716
0,956 0,349
1,562 2.347
0,465
0,867
1,800 0,157
1,557 1,724
1,900 3,529
0,875 0.535
2,219 3,228
0,405 0,205
0.830 0.481
0,341 0,150
0,887 0,503
0,691 0,423
3.234 1,291
1,192 0,322
1,050 0.874 0,571
1,107 0,792
0,305 1,701 0,912
0,261 1,467
0,443 0.757
0,006 0,000
0,042
0,101
4,186
0.758 0.016
1,225
0,000 1,007
0,000 0,000
3.438 0,819 1,225
0,039 0.000
0,458 0,016
0,160 1,959 0,924
0,009 3,418 0,000 1,064
1,385 0,689 0,706
1,601 0,198 0,766
1,450 0.038 0,232
1,601 0,069 0,432
0,138 0,672
0,719 0,933
0,844
4.875 0.227
3,313
0,016
0,512 0,016
1,225
3,990 0.913 1,587
4.183
1,326 0,645 0,927
2,663
1,708 1,242
0,750
0.844
1,125
0,563
0,815 0,168
1,185
2,050
0,700
3,115 1,261
3,260 1,114
1,185 0,961 1,754 1,196
1,371 1,386
1,048 0,982
1,395
1.124
1,217
1,165
0,408 1,264
0,087
0,658 2,691 1,190
2,168 0,994
0,723
2,106 1,223
3,039 2,199 1,739
2,123 3,732 1,826
1,353
2,150
0,986 1,160
1,566 1.062 1,087
1,059 1,071
0,901 0,611
1,803 1,012 1,414
1,430
1,406 2,202 0,948
0.000 2.009 2,903 0,082 0,727
0,968 0,013
1,780
3,188 0,034
2,111 1,385
0,090
1,316 3,284 3,674
1,466 1,484
1,773
1,294
3,251
2,773
0,954
0,953 1,002
1,686
1,142
1.099
0.950 1,069
1,106
1,531 2,265
3,306
3,078
0,508
2,615
1,749
1,231
2,915
3,945
0,582
3.984
1,226
3,306 0,987
3,078 1,139
0,508 0,958
2,615 0,996
1,749
1,231 0,922
2,915 1,313
3,945 1,419
0,582 0,926
3.984 2,465
1,226 1,202
1,129
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8.12 Conclusions This chapter has concentrated on a comparison between traditional 2D surface measurement techniques and 3D techniques. Three functional surfaces have been measured in order to illustrate the comparison. The overall results showed that it was clear that single 3D surface measurements are not normally sufficient to statistically quantify a surface, the number of measurements required is usually below that required by 2D techniques. The required number is small but never the less this may be still too time consuming in a production situation where contact measurement is the only option. Optical systems however due to their speed can overcome this problem and normally give comparable results to contact instruments. The claims that 3D surface metrology gives a better functional correlation is somewhat borne out by the study of wear of cylinder liners. The correlation factors indicate that the 3D technique more closely follows the functions of oil consumption blow by and wear. The work on analysing the variation of 3D parameter value with the sampling interval showed the expected results, in that amplitude based parameters are relatively stable whereas hybrid and spatial information based parameters are highly influenced by the sampling interval and to a lesser extent the area size. The results show that the choice of interval is critical and should at least reflect the surface unit event size as well as being held constant for all comparative measurements.
9
Applications of Numerical Parameters and Filtration Liam Blunt and Xiangqian Jiang School of Engineering, University of Huddersfield, UK
9.0 Introduction In order to give strength to the concepts and procedures developed as part of the SURFSTAND project a number of case studies were undertaken. The primary goal of the case studies was to demonstrate the use of 3D surface parameters and filtration techniques in real engineering applications. Other chapters of this book deal with specific applications of the work undertaken in the SURFSTAND project such as automotive cylinder bore functionality and sheet metal functionality. However other illustrative case studies were undertaken as part of the project, these case studies covering the area of biotechnical surfaces, sheet product and automotive applications.
9.1 Case study: the development of surface topography during wear of matt finish femoral stems 9.1.1 Introduction Total hip replacement is a procedure carried out to improve the quality of life for patients with debilitating disorders such as rheumatoid arthritis, chronic osteoarthritis, and severe fractures of the femur. During total hip replacement the head of the femur is removed and replaced with a prosthetic head, which is secured by inserting a metallic stem into the medullary canal of the femur. This prosthetic head articulates with a replacement cup usually manufactured from UHMWPE to provide a good bearing surface. A successful implant can be expected to perform well for in excess of 10 years; however of the large number of operations performed each year, up to 10% can be to revise prematurely failed prostheses [1]. These revision operations are more complex, have a lower rate of success and are more costly. Premature failure of the prostheses is often attributed to aseptic loosening of the stem, the main cause of this being metallic debris, generated by wear of the components, causing bone resorption of the areas surrounding the prostheses and causing loosening of one or more of the components [2, 3].
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There are several designs of prostheses, one of the large differences being that of surface finish. Traditionally, the surface finish of the stem was that of a highly polished nature. In the 1970's a move was made towards a "matt" bead blasted stem, the rationale behind this being greater stability of the stem through "mechanical locking" with the bone cement used for fixation. Over time it was noted that there was in fact a greater incidence of aseptic loosening with certain designs of stem with the bead blasted finish [4]. This study concentrates on this "matt" design of stem. The wear and subsequent loosening of stems in-vivo is generally attributed to the mechanism of fretting. Studies on explanted stems have shown evidence of characteristic fretting damage on both polished and matt stems, of varying material and geometric designs [5, 6]. In the case of matt stems, though, there appears to be an additional wear mechanism involved which precedes the incidence of fretting damage. It is suggested that before fretting occurs there is a polishing of the matt surface where the rough "asperities" are removed [7]. 9.1.2 The study A series of 25 explanted matt finish femoral stems were examined. The degree of wear varied on each, however the position of wear on explanted femoral stems does appear to follow a pattern due to the loading regime in vivo [5]. The surface topography of the stems was classified using a visual grading system (Table 9.1). Table 9.1 The number of stems displaying each wear grade
Classification polO poll po!2 po!3 po!4
Degree of wear No wear
Severe wear
N° stems
25 18 18 9 5
Note: measurements of pol 0 were taken outside the area, which was in contact with bone cement and therefore deemed to have undergone no wear. Table 9.1 also shows the distribution of wear grades throughout the series of 25 stems examined. Classified areas on the specimen surfaces were then measured using a Wyko NT 2000 optical interferometer operating in the vertical scanning mode. From the axonometric plots in Figure 9.1, it can be seen that the rough asperities caused by the bead blasting process are progressively worn away and the surface becomes smooth. Debris is generated, through a form of contact wear between the stem and the bone cement, and is a large factor contributing to aseptic loosening of the stem which then contributes to failure of the prostheses.
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Figure 9.1 Axonometric projections showing the change in surface texture with increasing -wear In the present study, each of the 3D surface characterisation parameters were calculated for each data set taken from the explanted stems. To gain an overall picture of the suitability of the parameters for characterisation of the development of surface topography during the wear of femoral stems an average and standard deviation was taken for each parameter for each grade of wear. The average and standard deviation parameter values were plotted against visual grade of wear. From these results it was possible to determine which parameters were suitable for characterisation of the development of topography during wear of matt finish femoral stems. 9.1.3 Results From the results, the most useful parameters for showing wear of explanted replacement hip femoral stems were determined; a summary of the strong relationship between increase in grade of wear and 3D surface parameter can be seen in Figure 9.2 a, b and Table 9.2.
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Figure 9.2a Wear grade as a function ofSAq - Root mean square slope of the surface
Figure 9.2b Average functional volume group, showing: Vmp Material volume of the surface Vvc Core void volume of the surface Vw Valley void volume of the surface
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Table 9.2 Useful parameters for describing wear of femoral stems
Amplitude Parameters Sq
•
Sz •
Ssk •
Hybrid Parameters
Spatial Parameters Sku
Sds
Str
Sal
Std
A
A
0
A
0
SAq
Ssc
S
•
A
•
Functional Parameters Sbi •
Sci
Svi
Vmp
Vvc
Fw
A
A
•
•
•
• significant discrimination, A some discrimination, o little or no discrimination
As the mechanism behind the wear of matt finish femoral stems is not fully understood, a move towards quantifying the amount of wear of stems in vivo is crucial to determining the wear mechanism. A semi quantitative methodology for determining volume loss due to wear was developed. Following characterisation of the visually graded stems with the 3D surface parameter set, Table 9.2, the 3D bearing area curve was generated for the most worn area of the stem (pol 4). The plateau shown in Figure 9.3 indicates the mean height of the worn surface/plane. This is used as a baseline to determine the volume of material left above this level at the other stages of wear (pol 0-pol 3).
Figure 9.3 Bearing ratio curve of worn stem (pol 4)
In addition to this, an unworn area of stem was subjected to a digital truncation model simulating pure abrasive wear truncation. The material was removed digitally at intervals of 0.5 um, the volume loss at each truncation level was calculated.
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Figure 9.4 Truncation analysis of real and simulated stem surfaces Both the actual measured volume loss and the data from the truncation model were plotted against Sq, Figure 9.4. The curves showed good correlation between the actual volume loss and the purely abrasive truncation model. 9.1.4 Discussion Fretting wear is the mechanism presently attributed to the wear of femoral stems in vivo. The term fretting denotes a small oscillatory movement between two solid contacting surfaces [8]. The factors that differentiate fretting from other forms of sliding wear are the magnitude of movement and the nature of the damage caused. Fretting is concerned with amplitudes of less than 25um and certainly not greater than 130um [9]. From this study of matt finish femoral stems it is apparent that the wear could be classified as fretting in terms of the magnitude of micro-movements between the stem and the bone cement, due to the stress reversals of the limbs. The damage observed on the stem does not exactly replicate that which would be expected of fretting. According to Waterhouse R B [9] "It is a general observation that the higher the degree of surface finish the more serious is the fretting damage" [9]. When analysing the semi-quantitative results obtained in this study it is apparent that the matt stems undergo considerable material loss although the surface finish is of a rough nature. The semi-quantitative volume loss results indicate that this could be due to ideal abrasive and sliding mechanisms, referring to ideal abrasive wear as Rabinowicz [11] illustrates, "blunting of the abrasive surface after wear" [10]. It is considered that matt finish stems have a high failure rate due to initial relatively severe
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abrasive wear. Overall wear of matt and polished stems is due to two different wear mechanisms. The authors consider that the initial wear of matt stems is of an abrasive form, which when the matt stems become more polished then changes to a more classical fretting nature.
9.2 Case Study: Wear of UHMWPE pins on TIN coated plates for use in total knee implants 9.2.1 Introduction To enhance the wear properties of the metallic articulating surfaces of total knee implants femoral components have been coated with a layer of TIN. In the present case two coatings were considered and the levels of wear on the UHMWPE counterface analysed. The results showed very significant differences in the levels of wear between the two surfaces. The plate specimens for pin on plate wear tests were supplied by two manufacturers, Ml and M2. Initial standard 2D surface metrology of the two types of plate surfaces showed that both were within surface roughness specification. Ra = 3050nm and no differences were obvious. These initial roughness measurements however only utilised a limited number of roughness parameters based upon amplitude information of the topography and therefore taking no account of spatial properties of the topography. 9.2.2 The study Multi-directional pin on plate wear tests were then carried out and the accumulated wear of UHMWPE pins articulating against the plates was measured by weight. The total stroke length was 10mm with a vertical load of 180N; the contact area for the pin was based on a 20mm diameter. The wear test values after week 1 are shown in Figure 9.5. Figure 9.5 clearly shows significant differences between the wear values obtained from the two manufacturers. It was known that the base materials were identical and the coating thickness levels were within specification. The task of the study was firstly to analyse the reasons behind the differences in wear and secondly to outline which 3D surface parameters showed differences between the two types of surface and could therefore be used as parameters indicative of wear performance. Visual interpretation of 3D measurements of the two types of surface showed clear differences, Figure 9.6. Ml surface appeared to be a classic example of a precision polished/lapped surface possessing randomly orientated polishing scratches. Occasionally, some of the scratches appeared deeper than the surrounding features. The TiN Coating process appears to have coated evenly and produced a coated surface reproducing the original underlying topography. The M2 surfaces appeared very different, having a topography that consisted of shallow pits interspersed with a relatively few large peaks of material This surface is unusual in appearance and clearly bears little resemblance to the underlying polished topography. Further measurements showed little difference in the pre-test and post roughness of the plates. The initial task of the study
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was to define which parameters showed clear ability to discriminate between the two types of surface.
Figure 9.5 Wear test results for week J
Figure 9.6 Axonometric plots of plate surfaces, Ml top M2 below
Figure 9.7 Graphs showing results for representative 3D parameters from the four parameter groups. Note pins 1-3 refer to Ml plates, pins 4-6 refer to M2 plates
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Figure 9.7 (cont'd) Graphs showing results for representative 3D parameters from the four parameter groups. Note pins 1-3 refer to Ml plates, pins 4-6 refer to M2 plates
Analysis of the 3D surface roughness parameters of the two plate surfaces showed that the hybrid parameters (which use both spacing and amplitude information) along with the amplitude distribution parameter Sku, and the peak volume gave the best discrimination between the two surface types. The results are outlined in the figures and Table 9.3. Table 9.3 Showing the ability of the 3D parameters to distinguish between the two surface types
Amplitude Parameters Sq
A
Sz
o
55*
A
Sku •
Sds •
Str
Sal
O
O
Functional Parameters
Hybrid Parameters
Spatial Parameters Std o
SAq
•
Ssc
Sdr
•
•
Sbi o
Sci o
Svi
Vmp
Vvc
Vw
A
•
A
•
• significant discrimination, A some discrimination, o little or no discrimination
9.2.3 Discussion Overall, it is considered that the two surfaces can be identified through the use of a select number of 3D parameters. Visually, the identification is obvious in that one surface has a polished like topography whilst the other is dominated by relatively isolated large peaks. The obvious set of parameters for use in this identification are: • • • • •
Sq for scalar appreciation; Sds for summit density (given suitable filtering this parameter would be even better); Sdq, Ssc for peak form assessment; Sdr gives and appreciation of real surface areas; Sm, Sc and Sv are useful to distinguish between the functional zones of the two types surfaces.
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Overall it seems clear that the origin of the high wear of the M2 surface is due to the presence of the large peaks in the surface topography. It is these peaks that act as load bearing asperities during function. For a given load the load bearing asperities will be of the order of tens per mm2 rather than tens of thousands as is the case for the low wear Ml surface. It is therefore considered that at these contacting asperities the contact stress will be very high and will consequently induce wear in the form of a cutting action in the UHMWPE pins, thus increasing the wear significantly.
9.3 Case study: wear ranking of hard on hard bearings for prosthetic hip joints 9.3.1 Introduction The pursuit of minimal wear in the function of prosthetic hip implants has led manufacturers to re-investigate the possibility of using hard on hard bearing combinations as the femoral head and acetabular cup surfaces in replacement hip joints. Currently, common joint systems use a hard femoral head component running on an ultra high molecular weight polyethylene (UHMWPE) acetabular cup. The clinical problem is that wear in the bearing system and the associated debris cause macrophage activity, granulomatous tissue and necrosis of the bone surrounding the prosthesis. Attempts to reduce the amount of wear debris generated by lowering the frictional forces in the joint system have been made by using hard on hard bearing surfaces. These have included alumina A^Os on alumina, cobalt chrome alloy on cobalt chrome alloy and alumina on CoCr. An example of the overall penetration or wear rates for the three basic material combinations of total hip replacement noted by Semlitsch and Willert [11] are shown in Table 9.4. Table 9.4 Overall clinical penetration rates in total hip replacements [11]
Material pairings on total hip replacements Acetabular cup Femoral Head Metal Ceramic Metal Ceramic
UHMWPE UHMWPE Metal Ceramic
Overall clinical wear rate (urn/year) 100-300 50-150 2-20 2-20
9.3.2 The study The present study has compared the relative wear resistance rankings of a combination of hard on hard hip replacements and ranked the material pairings. Secondly, the case study has attempted to relate this wear performance to the topographical and material properties of the materials. It seems likely that wear is influenced by some combination of material and topographic properties. Wear mechanisms are so complex, particularly in a biological environment, that it may be unrealistic to look for an explicit and comprehensive wear model. A more
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profitable approach might be to select some dimensionless parameters whose correlation with wear might prove to be of more general applicability. One well-established dimensionless parameter is the material property ratio £"///, where His the hardness of the softer of the contacting materials and the Hertzian elastic modulus £' is given by
where vis Poisson's ratio. This was incorporated by Greenwood & Williamson [12] into the plasticity index, also dimensionless:
where ft is the mean summit radius of curvature of peaks in the surface topography. They were able to show that for surfaces with high plasticity indices the highest percentiles of summits on the surface would deform plastically under even the lightest loads, while conversely for surfaces with low plasticity indices, the highest summits would deform elastically under even the heaviest loads. There are some difficulties with measuring these roughness parameters, as discussed below, and an alternative formulation originally due to Mikic [13] is preferred by some workers:
where 0is the mean absolute profile slope of the surface. It seems a priori likely that the plasticity index should be a predictor of wear, and correlations have been found between wear measurements and plasticity index e.g. Rosen et al. [14]. A rather different combination of roughness parameters was first suggested by Greenwood & Tripp [15].This is the dimensionless product SqflSds, which according to Whitehouse [16] is a constant for a random Gaussian surface. It is physically plausible that this combination of parameters should correlate with wear performance; increasing the roughness, and increasing the summit density and hence the number of potential wear sites are both likely to have an influence in the direction of increasing wear. 9.3.3 Wear testing and results Combinations of metal and ceramic components of various sizes were subjected to standard wear tests which ranked them in order of increasing wear as indicated in Tables 9.5 and 9.6. Table 9.5 Measurement interval for wear tests
No Cycles
Interval 1
Interval 1
Interval 1
Interval 1
Interval 1
0
500,000
1,000,000
2,000,000
3,000,000
5,000,000
The wear level was assessed by dimensional assessment of the cups in accordance with a CMM/Unigraphic procedure. Gravimetric assessment of the wear rates was also completed simultaneously.
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The surface roughness of the heads and cups were measured prior to starting the test and at the completion of the test. The measurement positions were pole (1 position), 30 degrees (4) and equatorially (4) on the heads. At the end of the test the heads were also be assessed for sphericity and diametrical clearance. All the test stations were wear stations and were tested in line with a proposed ISO draft standard as shown in Figure 9.8. The lubricant used in the test was a 25% bovine calf serum with sodium azide.
Figure 9.8 Load cycle regime for wear testing using hip simulators
On each component 3D surface measurements were made at 9 sites using an optical phase shifting interferometric technique, and the mean values and uncertainties of the above roughness parameters were established. In accordance with the conditions of Greenwood & Williamson [12], only summits more than 2Sq above the mean plane were counted. To avoid the difficulty of trying to average very large radii of curvature, summit curvatures were averaged and the mean summit radius of curvature was taken as the reciprocal of the mean curvature ie. Mean summit radii = 1/Ssc. For each combination of surfaces, the roughness parameters for the rougher surface were used. In Figures 9.9a-d, results and their derived uncertainties are ranked in the order of increasing wear for the two different formulations of the plasticity index, then for the SqpSds parameter, and finally for the product of this parameter with the material property ratio.
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Table 9.6 Wear test pairs and material properties, ranked in order of increasing wear Description Large dia Alumina/Alumina Large dia Alumina/CoCr cup Large dia CoCr/CoCr (Ultima) Small dia CoCr/CoCr Medium dia CoCr/CoCr
Overall
Wear rate (cu. mm/million cycles) Bedding period Steady State 0.076 0.145 1.264 0.062 0.829 0.602 0.975 6.300 4.850
Table 9.7 Wear ranking of material and size combinations Wear ranking 1
2 3 4 5
Femoral head
Acetabular cup
#(GPa)
E> (GPa)
Large dia ceramic Large dia metal
Large dia ceramic Large dia ceramic Large dia metal Small dia metal Medium dia metal
22.0
378
4.2
370
4.2 4.2 4.2
363 363 363
Large dia metal Small dia metal Medium dia metal
Figure 9.9 Comparison of wear rankings with: (a) Mikic [13]; (b) Greenwood & Williamson plasticity indices [12]; (c) SqftSds parameter; (d) product of Sq/3Sds parameter with material property ratio. Error bars are standard errors of the mean
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9.3.4 Discussion Both formulations of the plasticity index in Figure 9.9a and b give the same rankings, neither of which is in accordance with the results of the wear tests (Tables 9.6 and 9.7). A possible explanation may be that the conditions for the plasticity index to apply require that one of the contacting surfaces be significantly softer than the other, which is not the case for most of the present contact systems. The SqflSds parameter gives rather better agreement (Figure 9.9c), but with larger uncertainties, and fails to discriminate adequately between the first three ranked contacts. The best discrimination (Figure 9.9d) is achieved when the SqfiSds parameter is combined with the material property ratio, £"'///. It is considered that this combination contains the pertinent topography as well as the material characteristics of both materials. Surface finish at the levels currently encountered on femoral components (Sq of the order of 3-10nm) lend themselves perfectly to measurement by interferometery and characterisation through 3D surface analysis. For the above analysis where summit curvature, surface slope and summit density are required the 3D primary set are well suited to this type of analysis. Table 9.8 3D parameters useful for analysis of plasticity indexes
Amplitude Parameters Sq
•
Sz
o
Hybrid Parameters
Spatial Parameters
Ssk
Sku
o
0
Sds •
Str o
Sal
Std
0
o
SAq •
Ssc •
Functional Parameters
Sdr
Sbi
Sci
Svi
Vmp
Vvc
Vw
O
0
o
0
o
o
o
• significant discrimination, A some discrimination, o little or no discrimination
9.4 Case study: machining assessment of journal bearings on transmission pumps using wavelet analysis 9.4.1 Introduction A series of transmission oil pumps were manufactured by a company for use in heavy earth moving vehicles. The journal bearings in the pumps were finished using a grinding process. Unfortunately, increasing performance demands on the pumps had led to a number of early service failures. The problem of the surfaces of the journal bearing was highlighted as the only possible reason for failure. The journal bearings on the transmission pumps were manufactured and finished on a production grinder to a company specification of Ra = 1.6pm, the usual roughness achieved from the shop floor being Ra =0.8//m. The initial failures of journal bearings appeared on the pump drive shafts and the pumps failed due to total wear out of the bronze bush counter faces. The manufacturers reduced the surface roughness of the bearings by machining their pump journals on a tool room grinder. This led to improved service performance and no further failures were reported. The tool room grinder, however, is not well suited for mass manufacture and so the production grinder was operated in such a way as to achieve the
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same or similar levels of roughness as the tool room grinder and roughness levels of Ra = 0.6//w were achieved. Machining at this level of roughness appeared to be initially successful until further pump failures were again reported. Alarmed by this situation, the manufacturers went on to produce pumps having targeted roughness levels of Ra = 0.3//m on the tool room grinder. Recently, a new computer numerical control (CNC) grinding machine has been introduced into the production line and an improvement in service life has been reported. The following case study seeks to examine the differences between the ground surfaces and make some assumptions regarding the service performance. 9.4.2 The study The 3D surface measurement and characterisation was employed to analyse the manufacturing processes. Four sets of journals were measured. Each journal was measured three times at 120 degree steps around the circumference using a WYKO NT2000 interferometer in vertical scanning mode. All of the specimens provided in the four groups were measured over an area of 0.9x1.2mm2. The set of measured journals are outlined below: • • • •
Production from 1999 shafts. Failed 1999 shafts. Tool room production shafts. CNC production from 2000 shafts.
After initial form removal, the axonometric projections of the measured surfaces of journal pumps are as shown in Figure 9.10. It can be seen that there is evidence of waviness in the surface texture of the components ground on the production grinder and also on failed specimens (in Figure 9.10a-6). The waviness is significant across the lay of the surfaces. When considering the bearing area ratio curve, it is clear that the tool room and CNC surface have flatter bearing ratio curves, at roughness levels of 0.2um height below the mean plane (company specification of the manufacturer); the bearing ratios are 78% ~ 85.5% as shown in Figure 9.11.
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Figure 9.10 Surface textures of the four groups of journal bearings
Figure 9.11 Bearing ratio curves for the four groups of journal bearings
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Figure 9.12 Profiles derived from decomposed rough and wavy surfaces of the four groups of journal bearings
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9.4.3 Wavelet analysis In this study, a wavelet filter based on the second generation bi-orthogonal lifting scheme [17] is employed to separate and extract the roughness and waviness elements of journal surface of the pumps. Using wavelet filtering, the benefit is that filtered surfaces will record the nature of real waveform, shape and amplitude within a permitted cut-off wavelength, and there will be no distortion of the filtered surface within this cut-off wavelength. Consequently, the real waveforms have not suffered any attenuation for wavelengths up to the cut-off wavelength as would be the case using conventional filter cut-off techniques. Identification of roughness and waviness in above surface textures can be accomplished by suitable choice of cut-off wavelengths. Figure 9.12 shows low frequency and high frequency profiles derived from the decomposed roughness and wavy surfaces that have been filtered using Ac= 0.08mm for the roughness and A, =1.2mro for waviness. It is considered that roughness levels are below Ra = 0.3//m and waviness below Wa = 0.2//m. All ground surfaces have a similar roughness structure with only slight differences in amplitude. Significantly there are different levels of waviness among the four groups. The axonometric projections of the wavy surfaces are shown in Figure 9.13. The production surface does appear to contain more waviness components. The CNC surface has a similar wavy structure to the tool room ground surface with the amplitude of the waviness greatly reduced when compared to the production ground surfaces.
Figure 9.13 The wavy surface of the four group journal bearings
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9.4.4 Discussion Overall, the study showed significant differences between the tool room ground surfaces and the production ground surfaces. These were centred around the presence of waviness within the surface texture of the production ground surfaces. The CNC ground surface shows a significant improvement compared with production ground surfaces. By using wavelet analysis, it is clear that the particular grinding practices produced considerable waviness in the surface texture. The waviness was a result of grinding chatter, which adversely affect the workpiece surface finish and performance. Chatter was associated with vibrations in the grinding process. Vibrations during grinding were probably caused by bearings, spindles and the unbalance of grinding wheels as well as external sources. Such waviness is thought to be evident on the surfaces measured in the present study and particularly evident on the workpieces machined on the production grinder. After analysis of the production grinder the waviness was attributed to grinding wheel unbalance. The waviness on the journal surfaces led to high spot contact during service causing local high contact stress zones above failure limits at the more stringent service conditions. Elimination of the waviness has led to no more reported pump failures.
9.5. Case study: characterisation of the 2B finish on stainless steel flat products 9.5.1 Introduction As the usage of stainless steel increases there is a demand for better and improved variations, including different surface finishes which are not only aesthetically pleasing but also whose reactions to forming processes can be predicted and controlled. It is to be expected that variations in the processing history will influence both the appearance and the properties of the established finishes, see Table 9.9. These finishes are not normally subject to any quantitative specification, except possibly comments on relative 'dullness'. However, it is now accepted that the nature of the topography of a surface can have a significant influence on the efficiency and functional performance of the surface [18]. An example chosen to demonstrate the use of the primary parameter set is the 2B finish, a surface produced by cold rolling, annealing, pickling and skin passing (a light, high-speed pass used as final geometric control rather than gauge reduction). Of the 400 million tons of steel produced annually, about 2% is stainless and approximately 60% is produced as cold rolled sheet with the bulk of production being the 2B surface finish. The surface of a 2B sheet does not have macro-roughness; it appears smooth but not as shiny or reflective as the bright annealed 2R finish. The 2B surface is usually described as being 'pearly grey' in appearance and is the finish that is used for products such as building cladding, industrial containment vessels and other general engineering duties. The sheet is usually formed into products using drawing and/or bending techniques. The 2B finish is also employed as the most frequent starting point for a range of other surfaces, either developed within the process route (roll patterning or coil polishing) or during and after
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fabrication (shot or bead blasting, directional or non-directional mechanical or electrochemical polishing). For many applications it is important that the surface finish is produced consistently and it would be advantageous to have a means of specifying and checking the surface properties by selecting parameters that are relevant to the end functions. Table 9.9 Definitions of designated finishes (Adapted from BSEN 10088-2:1995) Surface Name
Process route
Finish
2D
Cold rolled, annealed and pickled
Matt, low reflectivity
2B
Cold rolled, annealed, pickled, skin passed
Smooth, pearly grey
2R (BA)
Cold rolled, bright annealed
Smooth and shiny
9.5.2 The study Firstly, features of the original hot band surface and those imprinted during its descaling that have endured the rolling operations may be retained. These can be in the form of defects in the sheet, like deep pits or heavy shot blast marks (used to clean the sheet); other shallower troughs may also be present. At the white-hot band stage the surface is very rough and irregular. The cold rolling process is not only used to reduce the gauge of the sheet but also to improve and consolidate the surface. The differences in methods and tribological conditions of cold rolling generate various surface characteristics, often the shallower pits present on the hot band surface are eliminated and the intermediate descaling (pickling) effects are minimised. After being rolled to the intended final gauge the material for 2D and 2B finishes is annealed again and must be descaled in an agitated acid bath. This descaling method is highly influential to the surface and chemical attack on the metal substrate can be preferential, for example at grain boundaries in the recrystallised, annealed structures, giving rise to etching effects on the surface. It creates a 'matrix* of interconnected grain boundary valleys, Figure 9.14, where the metal surface has been depleted in chromium during the oxidising process. Some of the grain boundaries are left intact so the remaining grain 'plateau' regions vary in size. This is the cold rolled, annealed and descaled surface that has a matt finish with low reflectivity, known as 2D (see Table 9.9). The plateau regions are relatively untouched at this stage, since they are the 'new* grains, so most have not been rolled. 'Skin passing', in a light but high-speed mill can enhance strip geometry and surface brightness. The skin pass does not alter the mechanical properties materially but it serves to improve gauge and 'shape' tolerances and gives a final finish to the plateau regions. Being a light pass it does not totally smooth out the plateau regions but merely removes or flattens the higher asperities making the surface
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brighter. The skin pass also acts as a tensioning device, which helps to alleviate the effect of form and waviness created in the rolling process. The surface is now designated as the 2b finish that has a pearly grey appearance. So there are two main features to be examined on the 2d and 2b surfaces, plateau regions and a pattern of valleys and to fully quantitatively characterise the surface every detail of these features must be measurable.
Figure 9.14 Interferometer images showing grain boundaries in 2B stainless steel 9.5.3 Results and discussion Numerous samples of the 2B finish on stainless steel were analysed and a test protocol devised to ensure that the data acquisition method was correctly selected. A Wyko NT2000 optical interferometer in vertical scanning mode was employed to measure the surfaces at 100 times magnification, yielding an area of approximately 45 by 60 um for each measurement. The primary set parameters were calculated and graphs of parameter values for each sample were examined to determine which parameters characterise the features of the 2B finish. Certain parameters from the set were deemed to be of greater interest due to their specificity for the important functional features of the sheet, i.e. analysing the plateaus and valleys. Of the 17 parameters, the amplitude family should have consistent values for repeated measurements of 2B given that the sampling interval and area sizes are the same. Graphs of the Sq and Sz values collected are shown below (Figure 9.15) with the red lines indicating the mean values of the sets and the blue lines at two standard deviations. Most of the data points are within two standard deviations of the means indicating stable values of Sq and Sz across the sample set. Sz is an extreme parameter, the average height of the five highest peaks and five deepest valleys or pits. Since the surface topography contains few large peaks it is the depth of the valleys that will have a major influence on variations in this parameter. The other two parameters in the amplitude group are Ssk and Sku, the skewness and kurtosis of the surface respectively (not shown graphically). The skewness is a measure of the symmetry of surface deviations about the mean plane. The value of Ssk for the 2B
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Advanced Techniques for Assessment Surface Topography
surface is negative, indicating a skewed surface dominated by the valleys interspersed with relatively flat plateau regions. The kurtosis is a measure of the sharpness of the amplitude distribution curve. For a Gaussian surface the Sku value is 3. For the 2B surface the value was between 11 and 14 showing a relatively sharp amplitude distribution. The spatial and hybrid families are not particularly useful for functionally characterising the 2B surface, as it has no particular texture or lay. However, the value of Sal is very small, approximately 0.002mm, indicating that the surface is dominated by high frequency (or short wavelength) components, probably the grain size. This parameter would be more significant if the size of the plateaus was consistent. Sdr, the developed interfacial area ratio, is an important indicator of skin-pass efficiency. The parameter is influenced by variations in the skin pass, since the process decreases the actual interfacial area.
Figure 9.15 Graphs ofSq and Sz showing little variation across range of samples The functional indexes are also good for the comparison of similar surfaces i.e. to compare a good 2B finish with a bad one. However, they are not as useful in a practical sense when only one surface is under examination, as it is here.
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Absolute values for volumes are calculated using the functional volume family of parameters. They were deemed useful to distinguish between the functional zones of two bearing surfaces. These parameters are highly relevant to the 2B surface, both for investigating the manufacturing process and to predict the quality of its response to further processing such as forming. The material volume ratio is relatively high for the 2B finish; it is an indication of the load bearing properties of a surface. The same is true for other so called flat-topped surfaces, such as a honed surface and in this case reflects the relative flatness of the plateaus. Sv gives a direct indication of the lubrication and fluid retention properties of the surface. The volume of fluid that can be retained by a standard 2B surface is approximately 45000 jim /mm . •5
f\
The usefulness of the primary set parameters for characterising the 2B surface finish on stainless steel is summarised below, in Table 9.10. Table 9.10 The use of the 3D parameters for characterising the 2B surface finish Amplitude Parameters Sq
•
Sz •
Hybrid Parameters
Spatial Parameters
55*
Sku
•
A
Sds o
Str o
Sal
A
Std o
SAq
A
Ssc o
Sdr •
Functional Parameters Sbi
Sci
Svi
A
A
A
Vmp •
Vvc •
Vw •
• significant discrimination, A some discrimination, o little or no discrimination
9.6 Case study: morphological assessment of in vivo wear of orthopaedic implants using multi-scalar wavelets 9.6.1 Introduction The femoral counterface of the hip joint system is actually one of the most important variables in the tribological design of artificial joints. The multi-scalar features of the surfaces such as pits/peaks or scratches superimposed on the base ultra fine roughness and their wear properties are quite different from normal engineering finish surfaces in which the roughness of the surface will dominate its wear function. It has been reported that if 1-2 um defects or deep scratches are present on a diamond like carbon (DLC) coated head, the third-body damage can cause a 7 ~ 15 fold increase in a UHMWPE counterface wear rate. Typical third-body damage that can result can give up to a 30 ~ 70 fold increase when compared with smooth surfaces [19-21]. Traditional surface texture characterisation is based on statistical parameters calculated from the measured surface, which average out surface features. As a result, traditional surface texture parameters are not very diagnostic when individual surface features contribute heavily to the functional properties of the surface. This has led to new analysis tools based on wavelet theory being developed to identify and characterise individual surface features. The following example illustrates a methodology for extracting the morphological features of femoral bearing surfaces of orthopaedic implants on the basis of utilising multi-scalar wavelet analysis.
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Advanced Techniques for Assessment Surface Topography
9.6.2 The study A set of specimens of worn ceramic and unworn (diamond like coating) DLC coated metallic femoral heads were supplied and measured. Two particular surfaces, a worn ceramic prosthetic femoral head and an unworn DLC coated femoral head, were then chosen to illustrate the extraction capability of the wavelet filters. The worn ceramic head was measured using an interferometer in phase shifting mode employing a 20x lens. The DLC specimen was measured using an interferometer in vertical-scanning mode using a 1 Ox lens. Figures 9.160 shows the lapped topographies in the worn ceramic femoral heads obtained by using a phase-shifting interferometer, and sampling an area of 300 x 240^m. The worn ceramic surfaces is essentially smooth and having some short and deep scratches. These random deep scratches are a result of wear during functional performance. Also evident are elongated pits again resulting from the wear process. The DLC surface shown in Figure 9.\7a was obtained by employing a vertical-scanning interferometer using a lOx lens over a sampling area of 460 x 600^im, and has a morphological structure consisting of relatively large pits.
Figure 9.16 Measured and morphological surfaces of a worn ceramic head
Figure 9.17 Measured and morphological surfaces of an unworn DLC head
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9.6.3 Morphological assessment using multi-scalar wavelets On the basis of the multi-resolution analysis of the wavelet methods, a signal can be separated into a series of wavelet coefficients. By applying the thresholding estimator to the finest levels of the wavelet coefficients, the coefficients, which only represent the features, have been separated and then the morphological features of surface topography of orthopaedic joint prostheses was obtained by the inverse wavelet transform. Figures 9.16 and 9.176 show how the wavelet model (2nd generation lifting scheme) [17] has removed roughness, waviness and form deviation, revealing morphological surfaces. As illustrated, the morphological features are the dominant factors of the bearing surface structure of the heads, and roughness and waviness do not seem to heavily influence the functional performance of the head in service due to their relatively low levels.
Figure 9.18 The Y and Xprofiles of a worn ceramic head surfaces
Figure 9.19 The Y and Xprofiles of an unworn DLC head surfaces (Lower profiles are from the morphological feature surface while the upper profiles are from the original measured surfaces) Figure 9.18 and 9.19 show those Y and X profiles of the prosthetic surfaces. It is clear that the morphological features have been fully reserved on the morphological surfaces with no distortion and phase shift. Examining these different surfaces and profiles (Figures 9.18 and 9.19), it can be seen that: (1) the components of waveforms of traces resemble each other with no relative phase shift in the sampling area; (2) the morphological information on the 3D bearing surfaces, conveyed by the wavelet model, is recorded completely and (3) there are no running-in and running-out lengths. These morphological surfaces therefore have excellent refinement accuracy, which is suited to the need for assessment of a range of functional properties of the components and study of their functional performance as
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Advanced Techniques for Assessment Surface Topography
bearing surfaces. The information revealed by such wavelet analysis can then be fed back to monitor manufacturing processes or study tribology and wear; or to study actual contact stress, loaded area, asperity volume, and additionally lubrication regimes occurring during the initial stages of wear. 9.6.4 Discussion The main conclusions from the point of view of application are as follows: (1) The practical evidence given shows that the outcomes of the filtering resemble the original waveforms very closely with no relative shift in the defined transmission band As a result the components have similar positions upon emerging from multi-scalar analysis and the peaks and valleys can be preserved unambiguously. (2) Using the segment property in the scalar domain, morphological surfaces can be flexibly and immediately reconstructed according the intended requirements of functional analysis. Overall, the wavelet model has allowed a better understanding and characterisation of the morphological surface of the hip joint system to be gained. The singularities on surfaces can be considered and retrieved with excellent refinement accuracy in the light of the multi-scalar wavelet. For industrial application purposes, the method has considerable merits. Practical examples have demonstrated the feasibility and applicability of the wavelet model.
9.7 Overall conclusions The range of case studies described in the present chapter has shown the usefulness of using 3D characterisation techniques for describing surface function and how the topography plays a significant that function. It is clear that 3D surface metrology has given a significant advantage to engineers and tribologists in gaining a deeper understanding of surface functionality. Whilst it is recognised that the case studies shown here are somewhat brief in description and analysis, it was considered more useful to give a broad ranges of case studies rather than making a deeper analysis, which is given in Chapters 8 and 11.
9.8 References 1. Murray DW, Carr AJ, Bulstrode CJ "Which Primary Total Hip Replacement?" Journal of Bone and Joint Surgery 77-B No.4 1995 pp 520-526. 2. Fowler JL, Gie GA, Lee AJC, Ling RMS "Experience with the Exeter Total Hip Replacement Since 1970" Orthopaedic Clinics of North America Vol 19 No 1988 pp 477-489. 3. Cook SD, Barrack RL, Clemlow AJT "Corrosion and wear at the Modular Interface of Uncemented Femoral Stem" Journal of Bone and Joint Surgery 76-B No. 11994 pp 68-72. 4. Howie DW, Middleton RG, Costi K "Loosening of Matt and Polished Cemented Femoral Stems" Journal of Bone and Joint Surgery 80-B No. 4 1998 pp 573-576. 5. Cook JE "Fretting Wear of Total Hip Replacement" The University of Exeter Exeter, UK 1998.
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6. Mohler CG, Callaghan JJ, Collis DK, Johnstone RC "Early Loosening of the Femoral Component at the Cement-Prosthesis Interface after Total Hip Replacement" Journal of Bone and Joint Surgery 77-A No. 9 1995. 7. Brown L., Howell, J Blunt L., "The Development of Surface Topography during Wear of Matt Finish Femoral Stems" Tribology in Environmental Design 2000 Bournemouth, UK September 2000. 8. Hutchings IM "Tribology Friction and Wear of Engineering Materials" Edward Arnold Publishers London UK 1992. 9. Waterhouse, RB "Fretting Corrosion " Pergamon Press Hungary 1972. 10. Rabinowicz E "The Friction and Wear of Materials" 2nd Ed. Wiley and Sons USA 1995. 11. Semlitsch M. and Willert H.G. "Clinical Wear Behaviour of Ultra-high Molecular Weight Polyethylene Cups Paired with Metal and Ceramic Ball Heads in Comparison to Metal on Metal" Proc. Inst. Mech. Eng 1997 Vol.211 No HI, 73-88. 12. Greenwood J.A. and Williamson J.B.P "Contact of Nominally Flat Rough Surfaces" Proc. Royal Soc. Lond A295 pp 300-319 1966. 13. Mikic, B. B., "Thermal Contact Conductance: Theoretical Considerations", Int. J. Heat Mass Transfer, Vol 17, 205-224 (1974). 14. Rosen, B.-G., Ohlsson, R., Thomas, T. R., "Nano Metrology of Cylinder Bore Wear", Int. J. Mach. Tools Manufact. Vol 38, 519-527 (1998). 15. Greenwood, J. A. and Tripp, J. H., "The Contact of Two Nominally Flat Rough Surfaces", Proc. /. Mech. E., 186, 625-633 (1970/71). 16. Whitehouse, D. J., "Handbook of Surface Metrology'\ Institute of Physics, Bristol, 1994 17. X.Q. Jiang, L. Blunt and K.J. Stout "Application of the Lifting Wavelet to Rough Surfaces" Precision Engineering 25(2001) 83-89. 18. D.J. Whitehouse, D.K. Bowen, V.C. Venkatesh, P. Leonardo and C.A. Brown, "Gloss and Surface Topography", Annals of the CIRP (1994) 2, 1-9. 19. J Fisher, P Firkins, E.A. Evans, J.L. Hailey, G.H. Isaac, "The Influence of Scratches to Metallic Counterfaces on the Wear of Ultra High Molecular Weight Polyethylene", Proc, Inst Mech. Eng. 209 (1995) 263. 20. P Firkins, J.L. Hailey, J. Fisher "Wear of Ultra High Molecular Weight Polyethylene Against Damaged and Undamaged Stainless Steel and DLC Coated Counterfaces", J. Mater Sci. Mater. Med. 6(1998) 597-601. 21. P.S.M. Barbour, D.C. Barton, J. Fisher "The Influence of Contact Stress on Wear Of UHMWPE for Total Hip Prostheses", Wear 181-183 (1995) 250-257.
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10
Functionality and Characterisation of Textured Sheet Steel Products Micheal Vermeulen and Henrik Hobleke OCAS, Zelzate, Belgium
10.0 Introduction During deep drawing operations steel sheet is forced to slide against the surfaces of the tools. During these tribological contacts complex phenomena are taking place and many parameters are interacting, one of which is surface topography. Therefore, steel sheet manufacturers want to optimise the surface topography of the steel sheet in order to enhance the forming process during deep drawing operations. In order to be able to optimise the surface topography of steel sheet, roughness parameters need to be established correlating with formability behaviour in sheet steel operations. Until recently, however, the vast majority of research, industrial applications and national and international standards were based on 2D measurement techniques. The assumption was that 2D profiles were a sufficiently valid representation of 3D surfaces. However, it is now clear that the characteristics of surfaces cannot be completely interpreted without 3D information: in order to fully study and control surface manufacture, studies needed to be carried out from a 3D perspective. This chapter deals with the correlations of the tribological behaviour of sheet steel during deep drawing, in particular galling, with surface topography from a 3D point of view. A coherent set of experiments was designed in order to test different steel sheet structures in relation to forming, more specifically galling. In designing the experiments special attention was paid to provide statistically well-proven results from a sufficient number of tests. This experimental study yields the use of a new test procedure referred to as the DBS multi-strip approach in order to increase the severity of the galling tendency occurring on the draw beads of the test device. Based on the results for three uncoated Sibetex materials a full set of sheet steel materials, covering a wide variety of surface topographies, was chosen for the galling experiments according to the DBS multi-strip approach. Before the start of the functional testing a full 2D and 3D roughness characterisation was performed on all materials: existing parameters having been derived from these roughness measurements. In order to find an objective quantification of the galling severity for all materials and an unambiguous ranking, a new approach was elaborated based on 2D profile
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measurements leading to the definition of a new index, which proved to be a good measure for the galling severity. 2D profiling is still used here, as the galling phenomena on sheet is essentially a clearly structured pattern of parallel scratches, which can be assessed by perpendicular 2D profiling. In order to correlate the tribo-behaviour of steel sheet with surface topography the concept of dominant summits was elaborated aimed at discriminating between fine asperities and rounded "hills". This new concept was applied to three uncoated Sibetex materials generating some important characteristics of the dominant bumps on the surface. The surface topography parameters resulting from the dominant summit approach have been used for the definition of a 3D plasticity index calculated for the dominant summits of the steel sheet surface and giving an indication of the tendency to plastic deformation. In order to study the underlying physical phenomena during sheet-die contact in more detail and to really quantify the load capacity of a surface, a mixed lubricated - plastic contact model was developed. The relative importance of the EHL load versus the plastic load is a potential measure to assess the tribological behaviour of the sheet-die contact. Finally, the outcomes of the experimental approach, the 3D plasticity index and the mixed lubricated-plastic contact model have been compared to each other in the case of uncoated Sibetex materials.
10.1 Design of experiments: choice of test device and procedure for investigation of galling An extensive set of experiments was performed in order to study the effect of different test systems and test conditions on the capability of galling testing and to find the test conditions to promote the galling effect. The aim of these studies was to determine a final choice of the galling device for a full series oftribo-tests. Therefore two preliminary studies have been performed comparing different tribological test rigs for coated and uncoated materials. A first DOE study focused on the effect of the tool geometry and sliding velocity in the multifrottement test for an electrogalvanised (ELO) and a prephosphated electrogalvanised coating (ELO-PH). A second DOE study dealt with the comparison of the modified flat die inland set-up with two other tribological test rigs, Optimol SRV and draw bead simulator, in order to investigate galling phenomena. Cold rolled steel sheets (uncoated) having three different roughness textures were used to study the capability of the three different galling tests to accelerate the occurrence of galling. Experimental set-up and friction results of these two studies are discussed in the following sections. All galling test procedures of the aforementioned two studies performed failed in generating galling on uncoated Sibetex materials. However the multifrottement principle, using the single-strip/multi-pass approach, does seem to discriminate materials such as electrogalvanised materials (ELO) that are sensitive to galling. In order to increase the severity of the galling tendency occurring on draw beads, a variant of the multifrottement test was utilised. The principle of this test was
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previously used to study the galling tendency of pre-welded blanks [1]. This procedure is referred to as the multi-strip approach (in contrast with the multi-pass approach). First, the three uncoated Sibetex materials were tested using this alternative DBS galling test. Based on these test results a final test procedure was chosen to study the galling tendency of a full set of materials, such as EBT (coated and uncoated), EOT and ECD (Pretex).
10.2 First design of experiment study: influence of tool geometry and sliding velocity in 'multifrottement' test 10.2.1 Test description and conditions In this design of experiments study, the influence of tool geometry and sliding velocity in the so-called 'multifrottement' test was investigated. The multifrottement test is usually seen as an accelerated galling test. In such a multifrottement test (or "multipassage"), a sheet strip is oiled only once and then successively pulled through a pair of tools until cold welding and/or galling occurs. Normally, a maximum of 10 strokes (passes) is proposed. If no galling appears after 10 strokes, one can conclude that the tested tribo-system is not prone to galling. Two different tool set-ups were proposed in this study: aflat-flat tool set-up (i.e. flat die test) resulting in a flat contact on both sides of the strip and aflat-cylindrical tool set-up (i. e. inland test or modified flat die test) resulting in a line contact at one side of the strip. Figure 10.1 shows both tool geometries.
Figure 10.1 Flat die geometry (left) and inland geometry (right) Table 10.1 summarises both the Renault and OCAS test conditions.
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Advanced Techniques for Assessment Surface Topography Table 10.1 Multifrottement test conditions Test sample size Die set-up Die size Die radius Die material Die hardness Die roughness (A,c = 0.8mm): Ra Load Sliding velocity Stroke Lubricant Number of passes (max.)
RN D31 1738/B 350 mm * 50 mm inland 20 mm * 50 mm 10mm Z80WD06T6
OCAS 350 mm * 50 mm flat die 20 mm * 50 mm
—
60 to 65 HRC 0.8-1.3 jim
DIN 1. 3207 ('geant 100') 60 to 65 HRC 0.05 jim
5000 N 20 mm/min 55 mm Quaker N6 130
5000 N 500 or 1500 mm/min 150mm Quaker N6130
10
10
According to procedure RN D31 1738/B [2] a sliding velocity of 20mm/min should be used. Use of this extreme low velocity found its origin in the early eighties: it was the maximum velocity that Renault could reach with their multifrottement set-up (incorporated in a press). This low velocity is criticised nowadays. The only requirement for a multifrottement galling test is to realise boundary regime conditions during the 10 passes. This means that the velocity must be low enough (probably v < 2000mm/min) to avoid mixed lubrication. The Renault test can be seen as more severe and prone to galling than the OCAS test due to the line contact (inland) which imposes significantly higher pressures and wipes the oil film in the successive passes (the oil amount reduces with successive passes). The effect of a lower velocity to produce galling is doubted, but stick-slip is easily induced with 20 mm/min, as it is difficult to control a constant movement at such a low speed. On the other hand, the extreme high die roughness in the Renault test will initiate galling easier. Other studies ([3], [4]) concluded that tool roughness is the main factor influencing the tribo-behaviour in a flat die test. In the case of a too high a die roughness, this die roughness will mask the tribo-effect of the sheet! One last difference is the applied pulling length: 150mm in the 'OCAS test* and 55mm in the 'Renault test', which makes the OCAS test more severe in this aspect. One has also to bear in mind that the degreasing and oiling procedures are extremely important for a galling test. To understand the effect of tool geometry and sliding velocity, more research was required. The next DOE-design focused on the effect of the tool geometry and sliding velocity in the multifrottement test for an electrogalvanised coating (ELO) and a prephosphated electrogalvanised coating (ELO-PH). Degreasing and oiling
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procedure, tool roughness and sheet roughness were not investigated. Table 10.2 summarises the Renault and OCAS multifrottement conditions. Table 10.2 Summary of Renault and current OCAS multifrottement test
Simulation
Renault Die radii areas
Tool Roughness
Ra> Masks tribo-effect sheet
Sliding Velocity
v = 20 mm/min Introduces easily stick-slip
Contact
Line contact Wiping off oil: severe lub. conditions. High contact pressures: severe 55 mm
Stroke
OCAS Area between die and blankholder Ra< Tribo-effect sheet becomes dominant v = 500 or 1500 mm/min v » can cause mixed lubrication Flat contact Longer contact area tool-sheet Smaller contact pressures: less severe 150mm Longer stroke makes test more severe
10.2.2 Conditions: L12-design A mixed 2 & 3 level design (LI 2) was used to make a detailed study of the effect of tool geometry and sliding velocity for two different coatings (ELO; ELO-PH) in a multifrottement test. Following factors were taken into account: • Factor 1 -» tool geometry: flat-flat (flat die) and flat-cylinder (inland set-up). • Factor 2 -» sheet coating: electrogalvanised (ELO) and prephosphated electrogalvanised (ELO-PH). • Factor 3 -> sliding velocity: <100 mm/min, 500 mm/min and 1500 mm/min. Remarks: • The target value of the low velocity was 20 mm/min, although it was almost impossible to guarantee a reproducible, constant velocity for such a low speed on the OCAS test rig (same problem for the current CRM / Renault test rig). Therefore a sliding velocity v < 100 mm/min was assumed. • Care was taken regarding drawing conclusions from the effects generated by factor 2 (coating), as both coatings have differing sheet roughness. • Sheet steel characteristics: • ELO: ELC ZE 75/75 - EBT C (deterministic texture) - sheet thickness = 0.98mm. • ELO-PH: Stl5 ZE75/75 & prephosphate layer (1.3g/m2) - shot blast (= stochastic texture) - sheet thickness = 0.72mm. Table 10.3 summarises the test conditions of the LI2 'multifrottement' design of experiments:
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Advanced Techniques for Assessment Surface Topography Table 103 Conditions L12-design
2 2-level factors, 1 3-leveI factors, 12 * 2 runs, full fraction Coating Test Tool Geometry Sliding Velocity [mm/min] 1 Flat - Flat ELO <100 2 Flat - Flat ELO 500 3 Flat - Flat ELO 1500 4 Flat - Flat ELO-PH <100 5 Flat - Flat ELO-PH 500 6 ELO-PH 1500 Flat - Flat 7 ELO <100 Flat - Cyl. 8 ELO 500 Flat - Cyl. 1500 9 Flat - Cyl. ELO <100 10 Flat - Cyl. ELO-PH 11 ELO-PH 500 Flat - Cyl. 1500 12 ELO-PH Flat - Cyl. The following parameters were kept constant: • Tools: DIN 1.3207 (Ra = 0.05 urn at Kc = 0.8 mm). • Degreasing in US-bath with Sonochlor during 1 minute. • Lubricant: Prelube oil Quaker Ferrocoat N6130 (3 drops / side). • Load:5kN. • Sliding length: 150mm. • 10 passages of same strip without extra oiling (= 'multifrottement'). • All tests were done twice. These test conditions differed from the Renault procedure. In the case of the line contact using the inland set-up (flat/ cylinder), a DIN 1.3207 with Ra = 0.05um was used as tool material combined with a sliding stroke of 150mm. The purpose of this DOE was only to study the effect of the tool geometry and the sliding velocity, but not the tool material, nor tool roughness. The mean friction coefficient over the full stroke (= 150mm) was calculated for each pass (maximum 10) of the tested combination. 10.2.3 Results This section deals with the main results of the L12-design. The mean friction coefficient over a sliding distance from 20 to 150 mm was calculated for each pass. In the first section, the evolution of the friction coefficient with the number of passes is observed. In the following section, the tribological behaviour is intensively studied for each pass separately. The significant effects have been summarised in a Pareto diagram (95% C.L.). The effect of tool geometry and sliding velocity for ELO and ELO-PH are illustrated in a diagram (Figure 10.2). Friction behaviour Figure 10.2 shows the evolution of the mean friction coefficient f of the ELO-material during the 10 passes in the multifrottement test for 3 different sliding velocities. Scatter (= mean value ± stdev.) and the mean friction coefficient is shown. The closed symbols represent tests performed with the flat-flat geometry, while the open symbols represent tests carried out with the inland configuration (flat-cylinder).
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Figure 10.2 Evolution of friction coefficient ffor ELO and 3 different velocities Due to severe galling, the multifrottement test had to be stopped in the case of the extreme low sliding velocity (v < 100 mm/min). For this low velocity a strong increase of the friction coefficient with each pass was found, especially for the line contact (inland test). Galling initiation already occurred after 4 strokes with the line contact and 7 strokes with the flat contact. For a sliding velocity of 500 mm/min a regular increase of friction f was found from the 4th pass in the case of the inland test (flat-cylinder), although galling initiation was not observed. With the flat die test, the friction coefficient remained stable for sliding velocities of 500mm/min and 1500 mm/min without initiation of galling. The inland test applied at 1500 mm/min also resulted in stable friction behaviour without galling. From these results one could already conclude that the sliding velocity is influencing galling initiation. With this ELO-material galling only occurred in the case of the lowest speed < 100 mm/min. Furthermore, as expected, the galling effect was most pronounced in the case of the inland test set-up resulting in a line contact. Figure 10.3 shows the evolution of the mean friction coefficient f of the ELO-PHmaterial during the 10 passes in the multifrottement test for 3 different sliding velocities.
Figure 10.3 Evolution of friction coefficient f for ELO-PH and 3 different velocities
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Advanced Techniques for Assessment Surface
Topography
Here, the scatter on the mean friction coefficients is not presented, as it was always very small. Again, the closed symbols represent tests performed with the flat die, the open symbols tests with the inland set-up. With the prephosphated ELO-PH material, galling did not occur in both multifrottement tests performed. The sliding velocity seems to have no effect on the friction coefficient. With the flat-flat contact (flat die) the friction coefficient remained stable during all 10 passes. With the line contact (inland) one could observe a small decrease of f with the number of passes. One can conclude that the tribo-behaviour of the ELO-PH material is governed by the prephosphate layer (no effect of speed, stable friction behaviour). Frictional behaviour in each pass Pass 1 Figure 10.4 summarises the main results of the mean friction coefficient f during the first pass.
Figure 10.4 Pareto-diagram (left) and friction behaviour (right) during the first pass Both tool geometry and sheet coating significantly affect the friction behaviour during the first pass. Tool geometry is the dominating factor and this most pronounced for ELO-coatings. All tests performed with a flat-cylinder contact (inland) show the lowest friction coefficients. However, in the case of ELO-PH, the difference between the friction behaviour in both tool set-ups is minimal. The sliding velocity seems to influence the friction coefficient f only significantly in the case of ELO, and more specifically with a flat-flat contact. Pass 2 Figure 10.5 summarises the main results of the mean friction coefficient f during the second pass.
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Figure 10.5 Pareto-diagram (left) and friction behaviour (right) during the second pass
No significant factors were found during the second stroke. The most important factor seems to be the Zn-coating. One can observe that the prephosphated ELO-PH sheet shows generally lower friction values than ELO coated sheet steel. The influence of the sliding velocity is not significant and not consistent: for ELO the friction coefficient f seems to decrease with increasing speed and for ELO-PH the opposite is found. Pass 3 Figure 10.6 summarises the main results of the mean friction coefficient f during the third pass.
Figure 10.6 Pareto-diagram (left) and friction behaviour (right) during the third pass
Both coating type and sliding velocity seem to show a significant effect on f in the third pass. From the right hand figure it becomes clear that this is only the case for ELO. For ELO-PH no effect of tool geometry and sliding velocity is found. In the case of ELO, friction decreases with increasing speed for both tool geometries. For the lowest speed, one finds now the highest friction coefficient with the flat-cylinder geometry. Pass 4 Figure 10.7 summarises the main results of the mean friction coefficient f during the fourth pass.
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Figure 10.7 Pareto-diagram (left) and friction behaviour (right) during the fourth pass Sliding velocity now becomes the most significant factor. The effects already explained in pass 3 for the ELO-coating are now even more pronounced: the friction coefficient f strongly increases for low velocities. For ELO-PH no significant effect of tool geometry and sliding velocity was found. Pass 5-Pass 7 Figure 10.8 summarises the main results of the mean friction coefficient f during the 6th pass of the multifrottement test.
Figure 10.8 Pareto-diagram (left) and friction behaviour (right) during the sixth pass During passes 5 to 7 the friction coefficient is significantly influenced by the sliding velocity and type of coating. In the case of ELO, elevated friction coefficients were found for low speed. The situation is worst for ELO tested in the flat-cylinder tool. For ELO-PH, again no influence of speed was found. The flat-flat contact resulted in a somewhat higher f than the flat-cylinder contact. Pass 8-Pass 10 Figure 10.9 summarises the main results of the mean friction coefficient f during the 10th pass of the multifrottement test. In the case of ELO and low velocity (< 100 mm/min) the friction coefficients were not always measured: due to severe galling, under these conditions the tests were stopped.
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Figure 10.9 Pareto-diagram (left) and friction behaviour (right) during the tenth pass The same tendencies were found as in the previous passes. Cold welding and galling behaviour
Figure 10.10 Pareto-diagram (left) and galling behaviour (right)
Cold welding behaviour is here indicated by the pass number where galling or cold welding occurs. Galling is defined as a visual appearance of (galling) grooves on the sheet strip. In the case of no galling 10 is used (= maximum number of passes in the performed multifrottement tests). Figure 10.10 summarises the galling tendency results. From Figure 10.10 sliding velocity and type of coating appear to be significant factors for galling and cold welding behaviour of steel sheet. Tool geometry is not a significant factor. Only for ELO coated material applied at very low speed (< 100 mm/min) galling could be observed. In that case galling is initiated sooner within the flat-cylinder tool geometry. The studied ELO-PH material is not prone to galling at all. 10.2.4 Discussion Figure 10.11 summarises the tribo-results found in the L12-design.
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Advanced Techniques for Assessment Surface Topography
Figure 10.11 Summary oftribo trends found for ELO and ELO-PH
Galling is only initiated on the ELO-sheet in the case of a very low sliding velocity. Friction increase and galling is most pronounced when applying the inland test (flatcylinder set-up) with line contact. For the higher velocities tested (500 and 1500 mm/min), friction remained stable (or increased slightly) and no galling was found after 10 strokes. In the case of prephosphated material (ELO-PH) no galling occurred and very low friction coefficients were found during the 10 passes. In the following, possible explanations for the results are proposed. The friction coefficientfcan
be written as:
with: F = friction force N = normal force Ta = apparent shear stress pa = apparent pressure The friction force itself is equal to: with: Ar = real contact area ir = real shear stress The apparent pressure pa can be divided in a contact pressure at the contact spots (pr) and a pressure generated by the lubricant pressure (pi): with: a = contact area fraction (= Ar / Aa with Aa apparent contact area) pr = real contact pressure pi = lubricant pressure The apparent shear stress can also be split into a contact and lubricant part:
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It is often assumed that the lubricant pressure is negligible (pi « 0), which means that there are no hydrostatic and micro-hydrodynamic effects. Furthermore, it is known that the shear stress of the lubricant is much smaller than the shear stress acting on the contact spots (TI <« tr). Therefore, it can be assumed that TI = 0. Equations (10-1), (10-3), (10-4) can then be simplified to (10-5) and finally (10-6).
During the multifrottement test (or a standard friction test) the apparent contact pressure is kept constant (pa = constant; N = 5kN). The real pressure pr is related to the real contact area and to the mechanical properties of the material. During the multifrottement test one can assume that pi decreases (if at all) with the number of passes, as the lubricant is continuously wiped off, while the real contact pressure pr remains about the same. Following (10-3) one can conclude that in such a case the contact area fraction a also has to increase with the number of passes. This can be easily understood: in previous studies ([2], [3]) it was already shown that the real contact area Ar (and also a) increases in a flat die and/or draw bead simulator test due to the flattening of the top summits. The increase of a will be most pronounced in the case of the inland test (line contact) with the highest contact pressure (Ar - 1 / pa and pajiat die = 5MPa; pa inland * 580MPa: see Appendix). This increase of a will also cause an increase of the apparent shear stress Ta (10-4) - if Tr remains equal - and following (10-1), also an increased friction coefficient f. The decrease in oil amount with successive passes in the multifrottement test will also cause the friction to increase. The real shear stress of the interface xr can be split into: with: Tad = shear stress governed by surface chemistry, lubricant, additives Tpi = shear stress due to ploughing, cutting, plastic wave. TPI depends on work hardening of sheet, tool roughness, real contact area A r ,... Within the multifrottement test, the oil amount decreases with every pass. In the case of a lack of oil, there will be insufficient oil to lubricate the tribo contact spots. Due to the breakdown of the lubricant interface, the relative 'weight' of Tad will decrease while Tpi will increase strongly (TPI » Tad). This finally results in a larger Tr and again a larger friction coefficient. For the prephosphated material (ELO-PH) the prephosphate interface will govern the tribe-behaviour. A breakdown of this interface is avoided and friction will remain about the same. The real shear stress Tr is only function of Tad with Tad = Tprephosphate layerThe experimental results for ELO-PH show a slight decrease in f with the line contact: the flat die results show a somewhat higher f than the inland ones. A possible explanation can be that Tad in the flat die multifrottement test is still influenced by the
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Advanced Techniques for Assessment Surface Topography
oil, while in the case of the inland test (with higher contact pressure) it is rather governed by the prephosphate layer itself (and Tad_0ii < tad_prephosphate). Another reason why only galling was observed with v < 100 mm/min can be explained by stick-slip. Stick-slip behaviour was always observed with the sliding velocity lower than 100 mm/min. In general, stick-slip is strongly influenced by the stiffness of the tool set-up, oiling conditions and small variations in speed and other parameters. Because of the sensitivity of stick-slip to all these parameters it is hardly reproducible and difficult to interpret. Within the performed multifrottement tests, it can be assumed that stiffness remains the same for all tests. Oiling conditions differ with each passage. With v < 100 mm/min, stick slip is probably caused by speed variations (and enlarged by a lack of oil). Such a very low speed can hardly be controlled: no constant, stable movement is guaranteed and the sheet material 'sticks' within the tools, resulting in a sudden increase of f, followed by a decrease when the 'movement' starts again. In such a case, friction can be assumed as successive 'static* friction coefficients. Generally, this static friction coefficient is larger than the mean friction coefficient. Strong stick-slip often ends in elevated friction coefficients and finally severe galling. No tests performed with at 500 mm/min and 1500 mm/min show any stick-slip behaviour, nor galling. 10.2.5 Conclusions An L12-design was used to study the effect of tool geometry (line or flat contact) and sliding velocity (< 100, 500 and 1500 mm/min) for an ELO and ELO-PH material within the multifrottement test. Such a multifrottement test aims to characterise the galling behaviour of a sheet-oil-die tribo-system. Galling was only observed on the ELO-material at very low speed (v < 100 mm/min) and most pronounced with the line contact. At very low speed, lubricant breakdown cannot be avoided giving rise to larger friction coefficients and finally galling. The prephosphated ELO-PH material showed a stable friction behaviour within the multifrottement test and no initiation of galling was observed. From these test results it can be concluded that the multifrottement test can only be used as an accelerated 'galling' test for very low velocities. Both a line contact (inland test and Renault procedure) as a flat contact (flat die) can be used in such a case (but galling is most pronounced with the inland test!). The only problem lies in the fact that such a low speed is difficult to control. Stickslip cannot be avoided in such a case and as a consequence the tribo-behaviour will not be reproducible. Further research was required and therefore a second study has been carried out, see section 10.3. 10.2.6 Appendix Summary of Hertz elastic contact stress formulae for a line contact [4]. E* = combined E-modulus
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unit length For the line contact in the OCAS inland test one finds: with P = 5kN, R = 10mm, length = 50mm and E* * E / 2 (= lOSOOOMPa): • semi-contact width a = 11 Oum • maximum contact pressure po = 578MPa.
10.3 Second design of experiments: comparison of tribological test rigs and final choice of galling test device
different
10.3.1 Introduction A preliminary set of experiments has been performed in order to study the effect of tool geometry on the capability of galling testing and to find the test conditions to promote the galling effect, as discussed in section 10.1. Electrogalvanised sheet steel, prone to galling, was used for these galling experiments. The main results of that part of the DOE study were: • •
The modified flat die geometry (inland set-up with line contact) is suitable and preferable to the ordinary flat die test (flat-flat tool set-up), as this test is faster in generating galling. A combination of high load and very low speeds is necessary. On the actual test rig, the low speed condition can lead to stick slip phenomena, resulting in large scatter in results on friction coefficients. This again might influence the tribobehaviour itself.
In this study two other tribological test rigs (Optimol SRV and draw bead simulator (DBS) were compared with the modified flat die inland set-up to investigate galling phenomena. The aim of the study is to determine a final choice of the friction and galling device for a full series of tribo-testing. Cold rolled steel sheet (uncoated) with the same mechanical properties and 3 different roughness textures (Sibetex C, Sibetex B and Sibetex A) was used to study the capability of these three different galling tests to accelerate galling and/or cold welding. 10.3.2 Experimental set-up Materials Cold rolled steel sheet (i.e. uncoated) with virtually the same mechanical properties and 3 different roughness textures (Sibetex C, Sibetex B and Sibetex A) is used for
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Advanced Techniques for Assessment Surface Topography
the second design of experiments study. Table 10.4 summarises the main characteristics (sPa measured with Wyko RST+). Table 10.4 Sheet steel characteristics
Material
Texture
YS (MPa)
g4-A s7-B s5-C
Sibetex A Sibetex B Sibetex C
166 167 170
TS (MPa) 307 306 304
sPa (urn)
1.52 2.29 2.52
Following pictures (Figure 10.12) show a top view of the 3 tested materials measured with a Wyko RST+ (measurement area = 2.5mm * 1.8mm).
Figure 10.12 3D roughness measurements on Sibetex A, B and C: top view
A tool steel DIN 1.3207 was used as a standard tool material. The tool materials have been ground to a roughness Ra of about 0.05um (kc = 0.8mm). Prelube oil Quaker Ferrocoat N6130 was used as lubricant. Galling test procedures In this paragraph, the performed friction and galling test procedures for the modified flat die (FD inland multifrottement), draw bead simulator (DBS multifrottement) and Optimal SR V test are described. More details on these test rigs can be found in [5]. Multifrottement test The multi-pass or multi-stroke principle (multifrottement) is used as an accelerated galling test. In such a multifrottement test, a sheet strip is oiled only once and then successively pulled through a pair of tools until cold welding and/or galling occurs. Normally, a maximum of 10 strokes (passes) is proposed. If no galling appears after 10 strokes, one can conclude that the tested sheet-oil-die tribo-combination is not prone to galling.
Figure 10.13 Flat-cylinder inland (left), DBS (right)
Two different tool set-ups are proposed in this study: a flat-cylindrical tool set-up (flat die inland) resulting in a line contact at one side of the strip and a draw bead simulator set-up simulating the situation at a draw bead in a die. The effect of flat die geometry (flat versus line contact) and sliding velocity has already been investigated in the first
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design of experiments (see section 10.2). Figure 10.13 shows the FD inland and DBS multifrottement test. The DBS multifrottement test is applied at full penetration (with largest draw bead height of 10.6 mm) with fixed beads. For a galling test, there is no need to determine the friction coefficient within the DBS, which means that no tests with rolling beads are needed. Table 10.5 summarises both the FD inland and DBS multifrottement test conditions. Table 10.5 Multifrottement test conditions Test sample size Die set-up Die size Die radius Die material Die hardness Die roughness (A,c = 0.8mm): Ra Load Sliding velocity Stroke Lubricant Number of passes (max.) # tests / tribo-combination Galling procedure
Flat die inland 350 mm * 50 mm inland 20 mm * 50 mm 10mm DIN 1. 3207 Ogeant 100') 60 to 65 HRC 0.05 urn
Draw bead simulator 350 mm * 50 mm DBS 20 mm * 50 mm 6mm (radius beads) DIN 1.3207 ('geant 100') 60 to 65 HRC 0.05 urn
5000 N 200 mm/min 150mm Quaker N6 130
Max. for full penetration 1 500 mm/min 150mm Quaker N6130
10 3
10 3
1 oiled strip, 10 passes
1 oiled strip, 10 passes
The degreasing and oiling procedure was always kept constant in the multifrottement tests: • Sheet strip is first degreased in US-bath with Sonochlor® (1 min) • Prelube oil Quaker Ferrocoat N6130 is applied with 3 drops/side. All tests are performed in a boundary lubrication regime to avoid microhydrodynamic wedge effects on the top summits of the sheet steel roughness, as micro-hydrodynamics decrease the tendency to galling. For the flat die inland multifrottement test a sliding velocity of 200 mm/min is used, as a result of the DOE study described in section 10.2. Draw bead simulator (DBS) tests can be performed at higher sliding velocities (1500 mm/min) without changing the lubrication regime (still boundary lubrication).
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Advanced Techniques for Assessment Surface Topography
Optimol SRV
Figure 10.14 Optimol SRV- sample arrangement The OCAS Optimol testing method is based on a modified set-up on the SRVtribometer, designed for test sheet samples of small dimensions. In the Optimol SRV test, a tool sample is imposed with a horizontal reciprocating movement and a vertical load. For the tribological research on sheet steel, a special sample arrangement was developed (Figure 10.14) in order to reduce the contact pressure between sheet and tool material to levels encountered in the deep drawing process. Before testing, all samples are cleaned for one minute in an ultrasonic bath with Sonochlor®. Most of the experiments were performed with an excess of oil achieved by applying one single droplet on the steel disc. A tool steel DIN 1.3207 is used as standard material. These tools were ground to a predefined roughness with Ra < O.OSum (Xc = 0.8mm). Table 10.6 and Figure 10.15 show the measurement conditions and the imposed load function. Table 10.6 Optimol SRV- measurement conditions Procedure Stroke Frequency Sliding distance Mean velocity Temperature Tool Oil # tests
280 003 1.5 mm 17 Hz 46m 50mm/s 40 °C DIN 1.3207 QN6130 6
During the test the tool performs a reciprocating movement with a stroke of 1.5mm and a frequency of 17Hz, equivalent to a mean velocity of 50mm/s. The load increases linearly from 0.5 to 2 MPa over a 15 minute period corresponding to a sliding distance of 46m. The temperature is kept constant at 40°C.
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Figure 10.15 Optimal SRV- loading conditions The friction coefficient f is derived from the friction force and load curve. The reported value of f is the mean value over the total sliding distance. Statistical analysis showed that a minimum of 6 tests is necessary in order to obtain a significant difference in (mean) friction coefficient of 0.02. 10.3.3 Results Flat die multifrottement (inland) Table lOJsummarises the flat die inland multifrottement test results. The friction coefficient f is given for each pass (maximum 10 strokes). Table 10.7 Flat die (inland) multifrottement test results: friction coefficient f A_l 0.152
A_2
A_3
A_AVG
0.149
0.149
0.141
B_3 0.144
0.143
CJ 0.154
C_2 0.150
C_3 0.150
C_AVG
0.146
B_l 0.145
B_AVG
1 2
0.154
0.148
0.153
0.152
0.146
0.144
0.143
0.144
0.151
0.152
0.156
0.153
3
0.157
0.155
0.156
0.156
0.155
0.154
0.153
0.154
0.157
0.158
0.160
0.158
4
0.156
0.153
0.153
0.154
0.161
0.162
0.160
0.161
0.161
0.162
0.162
0.162
5
0.148
0.146
0.144
0.146
0.164
0.162
0.164
0.163
0.163
0.162
0.162
0.162
6
0.142
0.142
0.144
0.143
0.160
0.162
0.160
0.161
0.158
0.160
0.160
0.159
7
0.138
0.140
0.144
0.141
0.156
0.160
0.158
0.158
0.154
0.156
0.156
0.155
8
0.138
0.140
0.143
0.140
0.150
0.156
0.156
0.154
0.151
0.154
0.152
0.152
9
0.142
0.143
0.147
0.144
0.150
0.156
0.152
0.153
0.151
0.150
0.150
0.150
10
0.144
0.143
0.145
0.144
0.149
0.152
0.150
0.150
0.149
0.150
0.148
0.149
Passage
B_2
0.151
The following figures show the evolution of the friction coefficient in the performed FD (inland) multifrottement tests on Sibetex A, B and C. For each material, the friction coefficient f of each test (total: 3) and the average friction coefficient f are shown.
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Advanced Techniques for Assessment Surface Topography
Figure 10.16 Friction coefficient fvs number of strokes in the flat die inland multifrottement test for Sibetex A (top left), B (top right) and C (bottom) The tribological behaviour of the 3 uncoated materials (A, B and C) over the ten strokes seems to be very reproducible in the flat die inland multifrottement test procedure performed. Figure 10.17 shows the evolution of the mean friction coefficient f (average value of 3 repetitions each material) in the FD inland multifrottement test.
Figure 10.17 Evolution of friction coefficient f for Sibetex A, B and C (FD inland multifrottement)
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The frictional behaviour of Sibetex A improves with the number of passes compared to Sibetex B and C. After four passes lower friction values are found with A. Initially, Sibetex B shows the lowest friction coefficient f. After 4 passes, the frictional behaviour of Sibetex B en C is about comparable. The three tested materials (A, B and C) did not show galling, nor stick slip during the 10 passes of the FD inland multifrottement test. If galling occurs, one generally finds a strong increase of the friction coefficient with the number of passes (e.g. in the case of electrogalvanised materials). From the flat die inland multifrottement results one can conclude that the test can only discriminate the galling behaviour of materials which are prone to galling. The 3 tested (uncoated) materials are not prone to galling and one can only find a relatively small difference in frictional behaviour (friction coefficient). DBS multifrottement Table 10.8 summarises the DBS multifrottement test results. The mean traction force Ft to pull the strip through the draw bead simulator DBS (fixed beads) is given for each pass (maximum 10 passes). Table 10.8 DBS multifrottement results (mean traction force Ft) Passage 1 2 3 4 5 6 7 8 9 10
A_l 4545 4405 3948 3566 3186 3032 2850 2707 2566 2476
A_2 4517 4296 3831 3496 3247 3022 2851 2706 2583 24%
A_3 4573 4398 3881 3525 3211 3041 2834 2695 2567 2458
A_AVG 4545 4366 3887 3529 3215 3032 2845 2703 2572 2477
B_l 4656 4522 4043 3603 3327 3062 2857 2665 2596 2499
B_2 4603 4591 4027 3636 3560 3052 2924 2468 2566 2546
B_3 -
B_AVG 4630 4557 4035 3620 3444 3057 2891 2567 2581 2523
C_l 4855 4634 4065 3651 3403 3066 2933 2786 2656 2579
C_2 4944 4641 4115 3700 3402 3115 3002 2748 2644 2534
C_3 C_AVG 4814 4871 4670 4648 4128 4103 3759 3703 3354 3386 3129 3103 2959 2943 2772 2769 2650 2649 2512 2542
Figure 10.18 shows the evolution of the traction force Ft in the DBS multifrottement test for the 3 uncoated materials Sibetex A, B and C.
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Advanced Techniques for Assessment Surface Topography
Figure 10.18 Traction force vs. number of strokes in the DBS multifrottement test for Sibetex HC (top left), FF (top right) and FP (bottom) One can observe a very reproducible tribological behaviour in the DBS multifrottement test. Figure 10.19 summarises the evolution of the average traction force in the DBS multifrottement test.
Figure 10.19 Evolution of traction force in the DBS multifrottement test for Sibetex HC.FFandFP
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No significantly different tribo-behaviour was found for the 3 materials (A, B and C) in the DBS multifrottement test. The traction force always decreases with the number of passes in the DBS multifrottement tests performed. No galling or stick slip was observed during the performed test procedure. Severe galling would increase the traction force in the DBS multifrottement test. One can conclude from these results on uncoated Sibetex materials that the DBS multifrottement test (in its original form as single-strip/multi-pass) does not discriminate between the tribological behaviour of the 3 uncoated Sibetex materials (A, B and C). Neither galling nor stick slip was generated during the 10 passes of the DBS multifrottement test. It should be mentioned that all 3 textures are the result of earlier development and optimisation in OCAS based on frictional behaviour. Optimol SRV Table 10.9 summarises the mean friction coefficient f for contact pressures between 0.5 and 2MPa (15 minutes) measured in the Optimol SRV. Table 10.9 Optimol SRV results Material Sibetex A Sibetex B Sibetex C
Friction coefficient f (avg ± stdev) 0.160 ±0.019 0.172 ±0.019 0.171 ±0.026
Figure 10.20 shows the evolution of the friction behaviour (as a function of time) in the Optimol SRV test.
Figure 10.20 Friction coefficient fas a function of time in the Optimol SRV test for Sibetex A, BandC Sibetex A shows a lower friction coefficient than Sibetex C and B. The friction evolution in the Optimol SRV seems to be comparable with that in the FD inland multifrottement test.
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Advanced Techniques for Assessment Surface Topography
Again, the 3 materials did not show galling or stick slip. The uncoated Sibetex materials are not prone to galling. 10.3.4 Conclusions Up to now, none of the galling test procedures discussed in this paragraph, using the single-strip/multi-pass (multifrottement) principle, could promote galling and/or cold welding on uncoated Sibetex materials. The multifrottement principle however does seem to discriminate between materials which are sensitive to galling (e.g. electrogalvanised materials, materials without 'dedicated' anti-galling roughness). Therefore, one can conclude that the proposed multifrottement procedures can only rank the galling tendency of materials with sufficiently different tribo-characteristics. Uncoated materials with closely related roughness grades (e.g. the tested Sibetex samples which are known as anti-galling textures) could not be discriminated. In order to increase the severity of the galling tendency occurring on draw beads, a variant of the multifrottement test is investigated hereafter. This alternative galling test consists of applying first one oiled strip and consecutively non-oiled fresh strips through the fixed beads until galling or cold welding occurs. This procedure will be referred to as the multi-strip approach and is discussed in section 10.4.
10.4 Most suitable set-up for testing materials on galling tendency: DBS multi-strip test procedure 10.4.1 Introduction All the galling test procedures of the aforementioned two studies performed failed in generating galling on uncoated Sibetex materials. The multifrottement principle using the single-strip/multi-pass approach only seems to discriminate between materials that are sensitive to galling, such as electrogalvanised materials (ELO). Therefore, a variant of the multifrottement test has been used in order to increase the severity of the galling tendency occurring on draw beads. This alternative galling test consists in applying first one oiled strip and consecutively non-oiled fresh strips through the fixed beads until galling or cold welding occurs. This principle has already been used to study the galling tendency of pre-welded blanks [1]. This procedure is referred to as the multi-strip approach (in contrast with the multi-pass approach). First, the 3 uncoated Sibetex materials (A, B and C) have been tested with this alternative DBS galling test. Based on these test results a final test procedure has been chosen to study the galling tendency of a full set of 16 different materials including EBT, EDT and ECD (Pretex). 10.4.2 Draw bead simulator (DBS): multi-strip test procedure The configuration of the DBS is schematically represented in Figure 10.21. Steel strips are pulled between the three fixed beads as indicated in this figure.
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Figure 10.21 DBS multi-strip principle
The DBS multi-strip test is applied at full penetration (with largest draw bead height of 10.6 mm) with fixed beads. For a galling test there is no need to determine the friction coefficient within the DBS, which means that no tests with rolling beads are needed. Tool material and roughness are kept constant during the DBS test. Before performing the DBS multi-strip test all samples are degreased in a US-bath with Sonochlor for 1 minute and dried with air. As already mentioned above, the first strip is supplied with a prelube oil (Quaker Ferrocoat N6130, 3 drops/side) and then pulled through the beads. The subsequent strips are kept free from oil and are pulled through the beads until galling or cold welding occurs. Normally, a maximum of 20 strokes (passes) is proposed. The failing criterion can then be defined as: subsequent non-oiled strips will be applied until the appearance of visual scratches on both sides of the strip. The number of strips applied is a measure for the galling tendency. If no galling occurs after 20 strokes, one can conclude that the tested sheet-oil-die tribo-combination is not prone to galling. Each test is repeated 3 times in order to assure statistical reliability. The traction force is measured by means of a load cell with strain gauges. All tests are performed in a general boundary lubrication regime. However, microhydrodynamic wedge effects on the top summits of the steel sheet roughness decrease the tendency to galling. Table 10.10 gives a survey of the DBS multi-strip measurement conditions. Table 10.10 DBS multi-strip measurement conditions Die material Die radius Die set-up Die size Die hardness Load Lubricant Multi-strip procedure Number of strips (max.) Die roughness (Xc = 0.8mm): Ra Sliding velocity Stroke Test sample size # Tests / tribo-combination
DIN 1. 3207 ('geant 100') 6mm (radius beads) DBS 20 mm * 50 mm 60 to 65 HRC Maximum for full penetration (10.6 mm) Quaker Ferrocoat N6130 1 oiled strip, consecutive non-oiled strips 20 0.05 urn 1500mm/min 150mm 350 mm * 50 mm 3
10.4.3 DBS multi-strip test: results for uncoated Sibetex materials Table 10.11 summarises the traction force (N) in the DBS multi-strip galling test. Initiations of galling and/or severe galling are indicated.
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Advanced Techniques for Assessment Surface Topography Table 10.11 DBS multi-strip results (traction force) AJ
A_2
A_3
A_»vg
CJ
4561.2
4473,0
4434.8
4489.6
4530.9
4665.4
4350.8
4441.4
4485.8
4593.9
4685. 1
4383.6
4589.9
4552.9
4884.8
4607.2
$214,2
4971.5
5092.8
5092.8
5005.0
=F
4927,1
4616. 1
4985.7
4988,1
5024.4
4713.9
5063.7
4971.2
4m#
"
S2W.7
Sirip 1 2 3 4
C_2
CJ*
C_avg
4701.1
4789.9
4414.9
4650,8
B_3
Bj«vg
»J
B_2
4674,0
4840.4
4618.8
4709.9
4723.0
4553.2
4676.0
4609.8
4629.6
4638.4
4555.1
4682.4
4662.5
4569.4
4691.5
4641.2
4762,5
4787.8
4851.7
4889.0
4560.2
4717.7
4722.3
4759.7
4760.1
4836.0
4839.8
4591.1
4715.5
4715.5
50233
4894.6
4844.8
4920.9
4501.0
4688.5
4706.4
4632.0
5059.7
5118,1
4902.6
4449.2
4823.3
4907.2
4699.5
4707.3
4771.3 4760.3
4761.4
5134.7
5112,1
4828,7
4780,6
4907.1
4897.4
4787.9
4595.6
4m$
4963.9
5344.9
4902.3
4889.5
5045.6
4979,5
4755.3
4686.4
4807.0
4417.1
4988.7
5320.6
49843
4940.9
5081.9
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It was found that the galling behaviour of each material showed some scatter. However, the tendency to galling of these 3 textures in the multi-strip galling test is clearly different. Figure 10.22 shows the traction force (N) as a function of the number of strips in the DBS multi-strip test.
Figure 10.22 Traction force ft vs. number of strips within the DBS multi-strip test
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One can observe that in the case of Sibetex A, a sudden increase of the traction force corresponds with initiation to galling. For Sibetex C a slight increase of the traction force with the number of strips is found. For Sibetex B, where galling is less pronounced, no increase of Ft is observed. 10.4.4 Galling conclusions for uncoated Sibetex materials The Draw bead simulator multi-strip galling test succeeds in ranking the severity of the galling tendency occurring on draw beads of the 3 tested Sibetex materials. This alternative galling test consists in applying first one oiled strip and consecutively nonoiled fresh strips through the fixed beads until galling or cold welding occurs. Pseudostochastic Sibetex A is by far the most prone to galling (despite the tendency to lower friction coefficients in the multifrottement test). Sibetex B remains the best antigalling texture: Sibetex B > Sibetex C > Sibetex A
10.5 Galling experiments according to DBS multi-strip approach Before starting the actual galling experiments, a full characterisation of the surface topography of all materials that were be used in the galling experiment was carried out. A full description of the roughness instruments and the measuring methods is given in section 10.5.1, as well as a survey of the measurement results for the full set of materials. The galling tendency of the set of materials has been assessed by application of the DBS multi-strip test. Results of the galling experiments have been analysed and discussed. After testing, samples were analysed and evaluated by visual inspection of the surface within the zone touched by the tools. In order to quantify the galling severity for all materials and to rank them unambiguously, a new approach has been elaborated based on 2D profile measurements and leading to the definition of a new index, which proved to be a good measure for the galling severity. The correlation between galling behaviour and surface topography of the steel sheet has been addressed based on the outcome of this galling experiment. 10.5.1 Roughness measurements Roughness instruments Introduction Two roughness instruments have been used for the roughness characterisation of the full set of materials used for the galling experiments according to the DBS multi-strip test: • Rank Taylor Hobson (Form Talysurf Series S6 PGI) based on the mechanical stylus measuring principle allowing both 2D and 3D surface characterisation. • WYKO RST+ based on vertical scanning interferometry (VSI) principle only allowing 3D-characterisation of the surface.
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Topography
3D-characterisation Table 10.12 3D roughness characterisation Characteristics Manufacturer Type Measuring Principle Vertical Range Vertical Resolution # Data Points (X/Y) X / Y resolution
Stylus Taylor Hobson FormTalysurfS6PGI Mech. Stylus (radius 2um) 10mm 13nm 4096 / 256 0.25um/ lum
Optical Wyko RST+ VSI and PS1 SOOum(VSI), 160nm(PSI) 50nm (VSI), [3 nm (VSI), 3 A (PSI) ] 736 / 471 or 368 / 236 or 256 / 256 3.38 / 3.80um, 0.9 / 1 ,lum,...= f (objectives)
Software Data format Inputs Data Format Outputs Conversion to ASCII?
Mountains 1.0 MAP, SUR SUR SDF Technician, high level
Vision 1.8 OPD OPD, SDF, TIFF SDF (only for < 368/236) Technician, high level
Operator Skill ID-characterisation
Table 10.13 2D roughness characterisation Stylus Characteristics Taylor Hobson Manufacturer FormTalysurfS6PGI Type Traverse Unit (+ max. travel) 120mm Phase Grating Interferometry Pick Up 2^m, 1.5mm Stylus (tip) radius No skid Skid lOrnm Vertical Range 13nm Vertical Resolution 0.25nmor lym Horizontal Resolution 0.5jim over 1 20mm, 0. 1 jim over 20mm Straightness Software Data Format Inputs Data Format Outputs Conversion to ASCII Operator Skill
FTS V6. 1 3, Talyprofile V 1 .3 PRF, PRO, PRA PRF, PRA PRA (ASCII, <8192 points!) Technician, mean level
Measuring methods Standard SD-measurement method Table 10.14 Standard 3D-measurement method Characteristics Manufacturer Type # Data Points X / Y resolution Surface Area Measuring Time
Stylus Taylor Hobson FormTalysurfS6PGI 256 / 256 10/10um 2.56 * 2.56mm ±75 minutes
Optical Wyko RST+ 736/468 3.38 / 3.80um 2.5* 1.8mm ± 2 minutes
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Standard 2D-measurement method Table 10.15 Standard ID-measurement method :
: f*inf*u*jf*m »>imitj»m • ' ' : - : ' ' - • ::- •• v twfcWWCSSppisp^.^^/^'^^:^,/^^^-
. -, -• :•.
Manufacturer Type Lt (travel length) Lo (assessment length) # data points Skid Travel speed Filter DIN filter Cut-off Xc X*/Xs = 300 Measuring direction Parameters (only those mostly used!)
Sg&f
;.:.,,-
Taylor Hobson FormTalysurfS6PGI 15mm 12.5mm 60000
No
lmm/s Gauss M1/DIN4777 2.5mm
yes 45° Ra, Rz, Sm, PC and Abbott
10.5.2 Surface topography characterisation of EBT, EDT and ECD materials As already stated a full 2D (RTH, stylus) and 3D (WYKO) roughness characterisation was carried out on all materials (EBT, EDT, ECD) before starting the galling experiment. Materials with EBT texture were delivered by the Sidmar plant and other materials were collected from competitors. Table 10.16 shows the main mechanical properties of these materials. Note the similarity in material thickness.
SI S3 S5 S6 S9 S10 g4CRS sSCRS s7CRS
Bl B3 B6 B8 H2 Hll P2
EBT EBT EBT EBT EBT EBT EBT EBT EBT EDT EOT EDT EDT EDT EDT ECD
D B C C C A A C B
w> a
ie U
ELO ELO
GI GI GA ELO CRS CRS CRS ELO ELO
GI GA GI GA GI
1? a, "5
*e 128 163 157 165 171 159 161 161 161 129 135 153 132 162 150 156
OH 9^ 8^ "^ tf d < b 275 45.0 299 43.3 292 44.8 290 44.9 296 40.5 294 42.0 40.0 301 301 40.0 301 40.0 294 32.0 307 43.0 313 41.9 301 45.0 285 48.8 283 43.1 40.2 306
2.87 2.32 2.52 2.23 1.88 2.44 2.29 2.29 2.29 1.71 1.79 2.15 2.45 2.47 2.11 1.88
0)
13 a 0.249 0.210 0.235 0.228 0.202 0.210 0.211 0.211 0.211 0.233 0.230 0.238 0.230 0.228 0.209 0.228
Thickness (mm)
Texture
Material Code
Table 10.16 Characteristics of materials measured
0.81 0.80 0.78 0.79 0.75 0.61 0.76 0.76 0.76 0.80 0.81 0.81 0.81 0.80 0.70 0.78
278 Advanced Techniques for Assessment Surface Topography The WYKO measured pictures are depicted in the tables below. Table 10.17 EBT materials & BCD material
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Table 10.18 EDT materials
Table 10.19 summarises the commonly used 2D and 3D surface roughness parameters obtained by means of 2D Stylus and 3D Wyko measurements. Table 10.19 2D and 3D roughness parameters
Material iiiSn i »^ "•
*
SI S3 S5 S6 S9 S10 g4CRS sSCRS s?CRS Bl B3 B6 B8 H2 Hll P2
Ra Oim) 0.85 1.85 1.01 1,80 1.83 1.02 1.35 2.14 2.07 1.25 1.47 1.58 1.02 1.03 1.46 1.12
Fc w HSC (pks/cm) (pks/cm) (pun)
(pirn)
sPa (jtm)
1.40 3.33 1.43 2.03 3.22 1.17 2.67 4.14 3.70
0.1955 0.2722 0.2282 0.2630 0.2652 0.1825 0.1862 0.2469 0.2914
1.03 1.95 1.26 2.19 2.08 1.22 1.52 2.52 2.29
32.6 40.0 52.0 75.0 61.0 155.7
2.57 2,75 2.68 1.34 1.25 2.41
59.1
1.22
0.3521 0.3560 0.3329 0.2369 0.2378 0.2575 0.2459
1.47 1.67 1.91 1.25 1.21 1.70 1.35
Rt RzDIN dim) Own)
Sm (jim)
6.39 12.00 9.06 12.59 12.83 5.85 8.46 13.86 14,43
5.65 10.17 7.01 10.65 11.33 5,19 7.62 12.19 12.10
125.8 160.1 122.9 153.8 124.5 122,1 121.5 158.8 166.7
81.6 63.0 83.4 67.0 82.2 82.4 83.0 63.8 62.0
48.5 53.5 52.6 53.1 63.9 61,7 66.6 53.2 52.6
9.27 10,45 10.84 6.73 6.41 13.09 8.15
7.46 7.95 8.26 5.87 5.18 11.01 6.83
153.2 166.7 150.6 65.9 106.5 46.7 105.7
68.4 62.8 69.2 158.8 95.8 221.6 97.8
FFT
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10.6 Functional testing: DBS multi-strip galling test 10.6.1 Galling test device The test device used for studying the galling behaviour of different steel sheet materials is the draw bead simulator (DBS). The test will be applied according to the DBS multi-strip procedure. Test device and description of the multi-strip procedure have already been discussed in section 10.4. 10.6.2 Material selection Based on the results of the three uncoated Sibetex materials with different textures A, B and C a full set of EBT and EOT materials were chosen and subjected to the same DBS galling test in order to study the galling tendency. The selected materials with their characteristics are enumerated in Table 10.16. 10.6.3 DBS multi-strip galling experiments: results When pulling a strip through the fixed beads of the draw bead simulator, the traction force measured is recorded. In the DBS galling test the traction force is averaged over the sliding length for each strip, which enables the change in traction force in relation to the number of passes performed to be studied. For example, Table 10.22 summarises the average traction force (N) in the DBS multi-strip galling test for the three series of three materials having different textures, but the same coating (GI): • P2: ECD(Pretex) • S5: EBTC • B6: EDT Significant galling at one side of the strip (yellow) and galling at both sides of the strip (purple) are indicated in the table. As already mentioned in the design of experiments, the maximum number of passes is 20. The traction force and the number of passes of all other materials have been collected in the same way. Table 10.20 DBS multi-strip results of (Gl-coated) P2, S5 andB6 (traction force, number of passes)
; J No galling observed Significant galling at one side of the strip Galling at both sides of the strip (severe galling)
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The information covered in Table 10.20 can graphically be summarised by plotting the traction force as a function of the number of passes, averaged over the 3 series, as shown in Figure 10.23 for all Gl-coated materials.
Figure 10.23 Average traction force vs. number of passes (Gl-coated materials), visual quantification of galling Studying these graphs one can see that a sudden increase of the traction force corresponds with the initiation of galling. Based on that assumption, one would conclude from Figure 10.23 that material B6 will show the best behaviour with regard to the occurrence of galling as the increase of traction force is much bigger for P2 (and H2) than for B6. Applying the same reasoning, one should expect that the galling behaviour of material S5 (and S6) would be situated in between P2 and B6. Analogous graphs can be made for all other materials too. To illustrate this, Figure 10.24 represents graphically the average traction force (Ft average) as a function of the number of passes for all galvannealed materials used in this galling experiment. One can clearly observe that the traction force remains almost constant over the whole number of strips (passes) applied. Comparing the materials individually there seems to be only a (small) difference in the average level of the traction force. This is probably due to the mechanical properties, which are not exactly the same for these materials.
Figure 10.24 Average traction force vs. number of passes (GA-coated materials), visual quantification of galling
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The results for the ELO-coated materials are represented in Figure 10.25. As these curves are close to each other, it is very hard to rely on the visual inspection for a reliable ranking of the different materials. This fact stresses again the need for a better ranking method as discussed in section 10.6.7.
Figure 10.25 Average traction force vs. number of passes (ELO-coated materials), visual quantification of galling As mentioned earlier (section 10.4), each test was repeated 3 times in order to assure statistical reliability. For each material the number of passes till (severe) the occurrence of galling on both sides has been averaged over these 3 repetitions resulting in the general ranking of Figure 10.26.
Figure 10.26 DBS multi-strip test average number of passes till occurrence of galling on both sides, based on visual inspection and refined by GSI method From Figure 10.26 one can clearly observe that the coating type seems to strongly affect the galling behaviour of the steel sheet. This conclusion was confirmed by visual inspection of the steel strips after the galling experiments (see section 10.6.5).
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10.6.4 Galling results: discussion The coating very much dominates the effect of texture on galling tendency. Based on the DBS multi-strip results one can rank the different coatings as follows: From Figure 10.26, one can clearly observe that GA shows the best anti-galling coating independent of the texture type: all galvannealed materials reached 20 passes without galling appearance. ELO seems to be the coating that is most sensitive to galling. After a few passes through the DBS severe cold welding of the coating occurs on the draw bead tools. The difference in galling appearance is too small to rank the different galvanised materials individually, i.e. the very soft ELO coating masks the influence of surface texture. The galling behaviour of GI coated materials can be situated in between GA and ELOy but it is still very hard to rank the GI materials mutually by texture type based on the ranking achieved in Figure 10.26. Although the difference in number of passes seems to be more pronounced than in the case of ELO materials and therefore allows a certain ranking, there is still a need for a better ranking method, see section 10.6.7. Concerning the uncoated materials, referred to as CRS or cold rolled steel, the draw bead simulator multi-strip galling test succeeds in ranking the severity of the galling tendency occurring on draw beads of these 3 Sibetex materials (A, B, C). The tendency to galling of these 3 textures in the multi-strip galling test is clearly different. Based on the traction force and the number of passes it can be concluded that pseudo-stochastic Sibetex A is by far most prone to galling, while Sibetex B remains the best anti-galling texture, somewhat better than Sibetex C. This results in the following ranking from best to worst:
In summary one can conclude that the DBS multi-strip test succeeds in ranking different coatings. Applying the current procedure and failing criterion it was not possible to rank the materials by texture type within each coating group (ELO, GI, GA) due to other interacting factors: • •
The galling behaviour of each material shows some scatter. Not only the average number of passes, but also the (increase in) traction force must be taken into account. • Texture effect is mostly masked by coating type. • The failing criterion is not fully objective, but is dependant on the operator's decision to terminate a series of strokes (visual inspection). Therefore it would be better to have a ranking method that is able to rank all materials mutually and is independent of the operator. A new concept complying with those conditions was developed and will be introduced in section 10.6.7.
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10.6.5 Analysis of the sheet steel samples after DBS multi-strip test After the galling experiments, it was decided to perform a 'visual' analysis on the samples in order to achieve a better understanding of the galling phenomenon and its relation to coating type and texture. Two different approaches were adopted: firstly some pictures have been taken from the samples with a digital camera; secondly a micro-analysis (SEM) has been carried out on the surface together with a study of the cross-section of some samples having a different coating. Visual analysis of galling After the galling experiments a picture has been taken in the zone where contact with the beads took place for the last strip of one series of each material. The difference in galling severity for the different coatings is illustrated in Figure 10.27: these pictures confirm the findings and ranking by coating type discussed in section 10.6.4.
Figure 10.27 Illustration of galling severity for uncoated and the different coated materials Figure 10.28 gives a survey of the galling pictures for all other materials subjected to the BS multi-strip test.
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Figure 10.28 Galling pictures for all other materials Micro-analysis of the coatings after DBS multi-strip test In order to get a better understanding of the influence of galling on different types of coating (ELO, GI, GA), a micro-analysis (SEM) of the surface was performed after the DBS multi-strip test. Both sides of the samples have been studied in the area touched by the tools as well as in a 'fresh' part of the strip. Additionally, some crosssections of the samples were made in order to study the difference in coating thickness before and after the galling test. For the three materials having different coatings, the first and the fifth strip of a particular series were selected for SEM-analysis, in order to ensure that samples with the same test conditions should be analysed. The selected strips are listed in Table 10.21. Table 10.21 DBS samples used for micro-analysis Material Texture SI EBT,D S6 EBT,C S9 EBT,C
Coating ELO
GI GA
Selected Strips 1&5 1&5 1&5
Figure 10.29 gives a typical example of the outcome of the SEM surface analysis for each of the investigated materials. Results for the top of the first strip within the 'touched* area are depicted for each of them in order to enable comparison. Two different magnifications were used for the SEM analysis: 50 and 250.
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Advanced Techniques for Assessment Surface Topography
Figure 10.29 SEM pictures at the top of the first strip within the 'touched' zone Additionally, 3D surface measurements have been performed within the area touched by the draw bead tools for the first strip of all materials subjected to the DBS multistrip galling test. In order to study the effect of the sliding of the surface against the tools, 3D surface measurements were carried out on the corresponding virgin surfaces too, which have been used as reference surfaces. For these roughness measurements, the WYKO instrument was used. Details of the characteristics of this measuring device and the applied measurement method have been described in section 10.5.1. Figure 10.30 shows the results for the materials in Table 10.21, on which a microanalysis was performed.
Figure 10.30 WYKO measurements of the first strip within the 'touched' zone From the SEM pictures as well as the WYKO pictures, it should be noticed that in these galling experiments the EBT patterns remain clearly visible after sliding. This fact basically supports the concept of the micro-hydrodynamic wedge effect that will be discussed in section 10.7. Furthermore, the surface study revealed that there was no touching of the substrate for any of the samples examined. In other words, no spots of substrate appeared on the
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surface after the DBS multi-strip test. Despite this conclusion, an obvious difference in the decrease of thickness of the coating layer could be observed: the GA coated material showed no decrease in the original coating thickness, while a relatively large decrease was found for the ELO coated material. The GI coating showed only a small decrease in thickness. The decrease of the thickness was most pronounced at that side of the strip that was sliding against two of the three beads. This could be expected, as this side is most critical with respect to galling. Figure 10.31 illustrates the difference in decrease of coating thickness by means of cross-sections resulting from the metallographic study.
Figure 10.31 Cross-sections of 5th strip by metallography A last conclusion that could be drawn from this study was that all GA coated strips showed a lot of cracks in the coating layer perpendicular to the pulling direction after the galling experiments. This is caused by the bending occurring in the draw beads and the brittle character of the very hard GA coating. 10.6.6 Galling conclusions The draw bead simulator multi-strip galling test succeeds in ranking the galling tendency on draw beads of 4 groups of materials having a different coating (or no coating). This alternative galling test consists in first applying one oiled strip and consecutively non-oiled fresh strips through the fixed beads until galling or cold welding occurs. Galvannealed (GA) materials seem to have the best behaviour with regard to the occurrence of galling independent of the surface texture. However, they might suffer from flaking and powdering, not investigated in this analysis. In the case of uncoated Sibetex materials the galling behaviour is dependent on the type of surface texture: Sibetex B performs very well and somewhat better than Sibetex C, while Sibetex A is most prone to galling. The galling behaviour of GI coated materials can be is situated in between GA and ELO, but it is not possible to rank the GI materials mutually by texture type in a statistically reliable manner based on the results achieved in Figure 10.26.
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Advanced Techniques for Assessment Surface Topography
ELO coated materials are by far most prone to galling. The type of coating here is obviously dominant over the influence of texture with respect to galling. A better ranking method is required in order to be able to rank all materials mutually in an objective manner (i.e. independent of the operator). In the following section a new method will be discussed for the quantification of galling severity based on 2D profile measurements in the touched area of the strips. 10.6.7 Galling quantification by means of profile measurements As mentioned above, the DBS multi-strip test clearly succeeds in ranking materials having a different type of coating. But ranking materials having the same coating but different texture, is hardly possible when applying the failing criterion described in section 10.4 (visual inspection), as the coating appears to be dominant over the effect of texture with regard to galling. Only the uncoated Sibetex materials could be ranked reliably this way. Therefore a new approach was developed. In order to find an objective quantification of the galling severity for all materials and moreover an unambiguous ranking, it is suggested that 2D roughness measurements after functional testing are performed. These profile measurements were carried out across the width of each strip, within the zone touched by the DBS tools, and compared to a reference profile taken in the fresh area of the strip in order to study the increase in galling severity. Profile measurement procedure After the DBS multi-strip galling experiments, all strips were subjected to profile measurements across the pulling direction both in the 'touched' and 'untouched' zone. This is illustrated in Figure 10.32. Furthermore the start and the end of the sliding stroke are indicated and the sliding stroke itself has been hatched.
Figure 10.32 Profile measurements after galling test
The profiles in the 'untouched' zones will be used as reference profiles for the corresponding profiles in the 'touched' zones (= galling profiles). It is important to notice that all roughness measurements are performed on the bottom of the strip, being the side where galling will be most pronounced. This is illustrated in Figure 10.33.
Figure 10.33 Strip after galling test
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The conditions for the profile measurements are summarised in Table 10.22. Table 10.22 Profile measurement conditions 45 mm, centered Length of the measured profile Spacing (resolution) 1 um Position of reference profiles at 40 mm from the start of the sliding stroke, in the ''untouched' area (see Figure 10.32) Position of galling profiles at 100 mm from the start of the sliding stroke, in the ''touched' area (see Figure 10.32) Calculation and definition of the galling severity index (GSI) After collection of the roughness data, the roughness profiles of each strip were subjected to several operations resulting in a new parameter, called galling severity index (GSI), which seems to be a good measure for the galling severity. The different processing steps generating the galling severity index, can be summarised as follows: • Reduction of the length of the profiles: all roughness profiles (original length = 45 mm) are reduced to 40 mm by cutting 2.5 mm on both ends. • Robust filtering: in order to eliminate the very long wavelengths related to form errors, a robust filtering using a cut-off of 8 mm is applied on the reduced profiles resulting in filtered roughness profiles of 40 mm. The program used for the filtering is the 2D robust gaussian filtering implemented by Hannover University [7]. Although the first order filter will be standardised, a second order filter (quadratic approximation) was required in order to avoid unwanted end effects due to the remarkable form error occurring on the galling profiles. This is illustrated in Figure 10.34 for an arbitrary 'galling profile'.
Figure 10.34 Robust filtering: first versus second order Fast Fourier Transform (FFT): the spectra of the filtered profiles are calculated by means of FFT. Based on the spectra obtained, for each series of strips the mean amplitude between 0.8 and 8 mm is computed for the galling (GAX) and corresponding reference (GAref) profiles of every strip. The galling severity index (GSI), giving the relative mean increase of amplitude within the bandwidth 0.8-8 mm, is then defined by:
GSI
GA.
GA ref
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Advanced Techniques for Assessment Surface Topography
•
GSI versus strip number (pass): The galling severity index is calculated for each strip of a series and plotted as a function of the number of the strips (pass) in the galling experiment.
•
As each experiment was repeated 3 times for each material, the plot "GSI versus strip number" is averaged over these 3 series.
A galling quantification program was developed in Matlab in order to execute all the processing steps described above for a batch of materials. The output of the program consists of several graphs and a data file containing the GSI's of each series of strips. Galling quantification: examples The quantification of galling based upon profile measurements can be illustrated by showing the results of this new approach for Pretex (ECD) material, having a GI coating. The GSI versus strip number is drawn for each of the three repetitions in Figure 10.35.
Figure 10.35 GSI vs. strip numberfor Pretex (P2) One can clearly observe the increase of GSI corresponding to the increase of the galling severity as more strips had been pulled through the draw beads during the galling experiment. As can be seen in Figure 10.35, there is some scatter between the three repetitions and within each series the curve is not increasing continuously, but is sometimes nonmonotonous. This could be expected, as for each strip only one profile was measured within the touched zone and one on the virgin surface. In order to enhance the statistical reliability it is better to take the average of those three series for each pass (= strip number). When doing so, a trendline can be drawn through the averaged data set by using regression analysis. In this case a polynomial fit of second order (parabolic) was performed resulting in an R-squared value of 0.9773 and therefore a very reliable trendline. Both averaged data set and corresponding trendline are shown in Figure 10.35 as well.
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The increase in galling severity is obviously visible too when looking at the roughness profiles measured within the zone touched by the draw beads: see Figure 10.36. In Figure 10.36 all profiles of one series of strips have been cut to 40 mm and subjected to a robust filtering (second order, cut-off = 8 mm) in order to remove the form error caused by the bending of the strip in the draw beads. In order to allow linking the increase of galling severity to the increase of amplitude for some wavelengths, the spectra of all profiles have been included in Figure 10.36 (on the right hand side) for a wider bandwidth (0.1 to 20 mm).
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Advanced Techniques for Assessment Surface Topography
Figure 10.36 Pretex (P2) - Roughness profiles within the touched area and corresponding spectra The same approach was applied for all other materials too. Figures 10.37 and 10.38 summarise the results for material S5 having a Gl coating as well.
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Figure 10.37 GSI vs. strip number for material S5 (EBT, GI)
Figure 10.38 EBTS5 - Roughness profiles within the touched area and corresponding spectra It should be noted that the profiles and spectra of strips 3 till 7 were dropped from Figure 10.38 focusing on the most important parts. When comparing Figure 10.35 with Figure 10.37 as well as Figure 10.36 and Figure 10.38, it should be very clear that material EBT S5 shows a better behaviour with regard to galling than material P2
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Advanced Techniques for Assessment Surface Topography
(Pretex): in the case of material P2 the occurrence of (deep) scratches starts much sooner during the DBS multi-strip test. It might be interesting to compare the roughness profiles of some materials having different types of coating. This is shown in Figure 10.39: only the roughness profiles for GA and ELO material are represented here, as two GI materials have already been discussed above.
Figure 10.39 Roughness profiles within touched area - comparison ofGA and ELO This figure and Figure 10.36 (or Figure 10.38) confirm the previously achieved conclusion that the coating type strongly affects the galling behaviour of steel sheet. Galvannealed materials (GA) seem to have the best behaviour with regard to the occurrence of galling, while ELO coated materials are by far most prone to galling. The galling behaviour of GI coated materials is situated in between GA and ELO. Galling quantification: results and ranking The quantification method for galling severity explained above was applied to all materials used in the DBS multi-strip test. As the coating type is strongly affecting the galling behaviour of steel sheet, the results of the galling quantification by means of profile measurements have been split up by coating type: see Figure 10.40. This allows the influence of surface topography (texture) on galling tendency within each group of materials having the same coating to be studied.
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Figure 10.40 Galling quantification: results by coating type (average of 3 series)
Based on the results represented in Figure 10.40, it is possible to rank the materials within the following groups of coatings, from best to worst: • • •
CRS (uncoated): GI: ELO:
Sibetex B > Sibetex C > Sibetex A B6 s S6 > S5 > P2 > H2 B1>B3>S3>S10>S1
It should be noticed that Figure 10.26 includes this internal ranking "retro-actively". For the galvannealed materials (GA) it is not possible to rank them individually due to the very good galling behaviour of this type of coating: no galling could be observed after 20 passes for none of the GA materials used in the DBS multi-strip test. Although the 'mean' GSI value of B8 is obviously somewhat higher than S9 and HI 1, no galling could be observed after 20 strips for material B8 either. The difference is probably due to differences in mechanical properties between B8 and S9/ HI 1. 10.6.8 Conclusions and discussion The new approach for quantifying the galling severity based upon profile measurements succeeds in ranking materials having the same coating, but different texture. This conclusion applies for uncoated materials (CRS) and materials with a soft coating (ELO, GI). For galvannealed materials having a hard coating it is not possible to rank the materials individually: they all show an excellent behaviour with regard to the occurrence of galling, independent of surface texture. From this analysis it can be concluded that the coating type strongly affects the galling behaviour of steel sheet: this confirms the findings of section 10.6.
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Furthermore, it is clearly demonstrated that, in the case of the uncoated Sibetex materials, the approach by means of the galling severity index correlates well with the experimental galling behaviour achieved during the DBS multi-strip test: they both lead to the same ranking. As the behaviour of different coatings is clearly different with respect to galling, it is recommended to split the materials by coating type in order to study the effect of surface texture on galling behaviour. Within the coating groups one could define a fixed threshold for the strip number in order to rank the materials by the GSI value at this threshold, on condition that enough strips are pulled through the draw beads for all materials and subsequently severe cold welding (galling) occurs. This can be illustrated for the GI materials: looking at Figure 10.40 and taking as threshold value '8 strips', this results in the ranking achieved in section 10.6.4. An alternative approach could be to determine a threshold value for GSI and rank the materials by the corresponding strip number. This approach could not be applied yet, as for some materials there will be no point intersection between the GSI curve and the threshold value. For instance, if one sets the GSI threshold value at 3 for the GI materials, there will be no point of intersection for materials B6 and S6, as not enough strips were pulled through the draw beads to reach a GSI level of 3. This approach is recommended and more strips have to be used in the DBS multi-strip test in order to obtain a higher GSI level and therefore a more severe galling. The most important achievement from this study is that one now is able to set up a reliable, repeatable and operator-independent procedure for quantifying galling.
10.7 Development of new parameters 10.7.1 Concept of dominant summits The definition of a "summit" seems to be ambiguous. Currently available software packages for evaluation of 3D surface measurements include the calculation of summit density and radius, but they are all based on the rather naive concept of defining a summit by comparing the z-value of a particular point with its immediate neighbours, see e.g. [8]. Based on this concept, one obtains extremely high numbers for summit density (ranging from 5000 to 10000 per mm2) and very small curvature radii (ranging from 2.5 to 20 um). Moreover, these numbers are very much dependent on the measurement resolution, making them nearly inappropriate for theoretical modelling or practical use.
Figure 10.41 Concept of dominant summits for EBT surfaces
From a surface measurement point of view there is clearly a problem of scale. A new concept for surface characterisation is developed here. In order to discriminate between fine asperities and rounded "hills" the idea of dominant summits versus micro-summits has been introduced. The surface topography is split into different scale features:
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dominant summits (EBT features) with mean curvature and height distribution, showing a low density (10 to 100 / mm2). During deep drawing operations microhydrodynamic wedge (or EHL) effects are taking place on these roughness summits contributing to the total load capacity of the surface, needed to sustain the applied (apparent) pressure between sheet and tool. micro-summits (high frequency roughness), having a high density (1000 to 10000 / mm2). These very tiny, high frequency asperities will deform plastically immediately during the normal approach between sheet and tool. They might also be able to generate micro-pools according to the MPHL (micro-plastic hydrodynamic lubrication) concept described in [9].
However, no technique is readily available yet for quantifying these values. The recently developed theory of the change tree system by P. Scott [10], enabling the splitting between "important" and "subordinate" features such as summits and valleys, could be a very promising technique for the characterisation of these dominant summits, on condition that adequate pruning could be applied (e.g. based on curvature and areal extension). 10.7.2 Fitting of dominant summits (EBT bumps) In order to correlate the galling behaviour of steel sheet with surface topography, the concept of dominant summits described above has been elaborated for the three uncoated Sibetex materials (g4-A, s5-C and s7-B). For EBT surfaces one can easily compute the density of EBT bumps (being dominant summits) from the top view of a 3D surface measurement due to the deterministic pattern of EBT surfaces. Radius of curvature and summit height of the bumps are more difficult to quantify. Because of the lack of appropriate software, a semi-manual procedure based on the dominant summits concept, has been applied on the 3 uncoated Sibetex materials (A, B and C) in order to characterise the dominant summits by means of their radius of curvature and height. After location of an approximate lateral position of the summits, a paraboloid surface is fitted through each of them, using the least square technique. Subsequently, for each paraboloid the height of the top and its principal curvature radii are calculated. One has to emphasise that the z-position of the summit is important here. Therefore one has to transfer the classical height distribution curve, which includes all measured points, into a distribution curve related to the heights of the dominant summits. The applied procedure for the characterisation of the dominant summits is explained in Figure 10.42 by means of the uncoated Sibetex material B.
Figure 10.42 Determination of dominant summits (example: surface EBT CRS, B)
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Figure 10.43 Determination of dominant summits: EBT CRSA (left), EBT CRS C (right) Applying the same procedure for the other Sibetex materials (A and C) results in Figure 10.43. While the EBT process guarantees a repeatable form of the EBT-bumps, the curvature radius is averaged over all individual bumps to give a mean value: RDS- In fact, RDS is calculated form the curvatures in x and y directions. 10.7.3 Development of a new parameter: 3D plasticity index OF3DS) of dominant summits In classical contact theory, one often uses the plasticity index to judge the tendency" of a surface to deform in an elastic or plastic mode against a smooth counter body. Up to now, this index has been most frequently determined from a 2D profile plot. It is obvious that the very tiny, high frequency asperities will deform plastically immediately during the normal approach. A dominant bump however will be much "stronger". During sheet-tool contact every dominant bump of the steel sheet will deform either in an elastic or plastic mode, depending on its radius of curvature and its height position. It is therefore suggested that a plasticity index calculated for the dominant summits is defined as a 3D-parameter, giving an indication of the tendency to plastic deformation:
In this equation, E* is the equivalent Young modulus and H the hardness of the sheet material. It is assumed that the steel sheet hardness is always less then the tool hardness, even for modern HSS grades. RDS is the mean radius of curvature averaged over all individual bumps, while a is the standard deviation of the dominant summit height distribution. Both parameters result from applying the dominant summit approach to the Sibetex surfaces by means of the fit procedure explained in section 10.7.5. Classical contact theory indicates that a high plasticity index will lead to a high tendency for plastic deformation of the peaks. Low values are usually preferred for avoiding adhesive cold welding and thus galling. The dominant summit approach was applied to the 3 uncoated Sibetex materials: fitting the EBT bumps of these surfaces leads to the mean dominant summit radius RDS and the summit height distribution a. Subsequently, the 3D plasticity index was calculated for each of them. These 3 uncoated EBT materials are originating from the
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same mother coil and therefore have the same mechanical properties, ¥305 will only depend on the surface topography parameters a and RDS- Results of this analysis are summarised in Table 10.23 together with some other conventional surface characteristics. Table 10.23 Characteristics of the different uncoated EBT surfaces Surface type Sa [urn] Dominant summit density [# / mm2] Fitted dominant summit radius, RDS [um] Standard deviation of summit's top position, a [um] Conventional density Sds [# / mm2] Conventional summit radius =l/Ssc [um] 3D Dominant Summit Plasticity index
G4-A 1.52
S7-B 2.29
S5-C 2.52
58 630
15
11
0.20
2930 0.27
1060 0.16
5000 13.5 4.26
5000 16.0 2.29
5000 16.7 2.94
V3DS H
The values listed in Table 10.23 suggest that surface s7-B should perform best in galling experiments, as it shows the lowest value for the 3D plasticity index. The correlation between the theoretical concept of the plasticity index and the performed galling experiments will be discussed in section 10.7.5. 10.7.4 Mixed EHL-plastic contact model for describing the load conditions of the dominant summits In order to study the physical phenomena during sheet-die contact in more detail and to really quantify the load capacity of a surface, a mixed lubricated - plastic contact model was developed. The load capacity is calculated for a set of spheres with a constant radius but with a normal distribution of their heights. Therefore, an EHL approach is used, modelling the micro-hydrodynamic wedge effects on the roughness summits. However, as the higher summits will be in contact much earlier than the lower ones, it is necessary to include a model for plastically deformed peaks as well. The relative importance of the EHL load versus the plastic load is a potential measure for assessing the tribological behaviour of the sheet-die contact. The more summits can generate an EHL load, the less the peaks will deform plastically and the better the surface will be in preventing galling. The EHL load capacity of an individual bump is derived from the EHL formula presented by Hamrock and Dowson [11]:
In this expression H, U, G and W are non-dimensional parameters for film thickness, speed, material and load respectively. The full description can be found in the original work [11]. In our model the tool is a perfect plane and the EBT bump is modelled as a part of a sphere, so Rx = RDS and the ellipticity parameter k = 1. The material parameter G is a
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combination of the pressure-viscosity coefficient (being
Figure 10.44 Definition of tool position versus an individual sphere (left), plastic loading of a bump (right)
From this observation, it is also assumed that a good approximation for the transition of the EHL to the plastic regime would be by assuring the continuity of load. It means that if the tool is sliding over the bump more closely to the sheet, the EHL load will increase up to a limit value at which the bumps start to flow plastically, supporting a "plastic" load FP|. As a first approximation, it is calculated by using the contact area defined by its half contact radius a and its hardness H. This means that for a given position of the tool a single plastically deformed bump supports a load Fpi, given by:
Figure 10.45 Generalised load capacity of a single sphere (EHL and plastic) for radii
different
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The position of the tool ho is defined as zero when it is tangent to the undeformed single bump and positive when the tool moves towards the sheet surface that contains that bump, see Figure 10.44. For the stated speed, viscosity and steel material, the single bump load is then only depending on its curvature radius R, leading to Figure 10.45. One can now take into account the height distribution of the individual summits, as calculated from the measured surfaces by applying the dominant summit approach. However, as the manual method used for finding the lateral position of the summits is not appropriate, a new simulated surface was generated with 250 summits having the same height distribution a curvature radius RDS and lateral density, but with randomised lateral positins. The geometric tool position now is defined to be zero, when it is tangential to the summit top, which is at the mean height u of the Gaussian distribution of the summits. For a given tool position, the total load for the full set of 250 bumps can now be determined as the sum of the individual bump loads (either EHL or plastic). For surfaces g4-A and s7-B, and assuming a hardness H = 750 MPa, this leads to the plots indicated in Figure 10.46.
Figure 10.46 Load capacity of a set of bumps for surfaces g4-A (left) and s7-B (right): total, EHL and plastic load
One clearly observes that for surface g4-A, having much sharper summits (RDs = 630 urn) than surface s7-B (Ros = 2930 um), the EHL contribution to the total load capacity is very small compared to surface s7-B.
Figure 10.47 Ratio of plastic to total load versus apparent pressure between surface and tool
Taking into account the summit density of each surface, one can easily convert the load over a given number of bumps into an apparent pressure p. This is the total load spread over the area occupied by the chosen set of 250 bumps. The higher the EHL contribution, the better the surface will behave (less plastically deformed spots),
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thus the better galling can be avoided. In order to judge the surfaces, the ratio plastic load to total load is represented in Figure 10.47 for all 3 surfaces. From this figure, it is clearly observed that surfaces g4-A and s5-C are rapidly going into the plastic "regime", while surface s7-B remains mainly in the EHL regime for quite a wide range of sheet-tool pressures. This analysis of the tendency to plastic deformation (and galling) agrees with the results of the galling experiments on those uncoated EBT surfaces described in section 10.6 and confirms the ranking obtained by this functional testing. 10.7.5 3D Plasticity index ^DS versus experimental galling behaviour: discussion Galling experiments have been performed on the 3 uncoated Sibetex surfaces mentioned above by using the draw bead simulator. In order to increase the severity of the galling tendency occurring on draw beads, a multi-strip procedure was used. This consists of pulling first one oiled strip and consecutively non-oiled fresh strips through the fixed beads until galling or cold welding occurs. Figure 10.48 (left) shows the traction force as a function of the number of strips in the DBS multi-strip test until galling occurs, averaged over 3 tests. The tendency to galling of these 3 textures is clearly different. The ranking is A, C, B from worse to best.
Figure 10.48 Results of galling tests and relation with 3D plasticity index calculated for the dominant summits When comparing the experimental behaviour with the 3D plasticity index (Figure 10.48, right), a good correlation was found: lower values of the plasticity index correspond to a better galling behaviour. It is clearly demonstrated that both the experimental approach and the theoretical plasticity index lead to the same ranking. Moreover, the theoretical analysis of the EHL and plastic loading of a set of bumps also clearly proved that the "dominant summits" approach is a valid base for studying the contact between a rough sheet and a tool. As the method implicitly includes the presence of sufficient lubricant being available for "wetting" the surface, it is obvious that a sufficient number of voids should be present in the surface.
10.8 Overall conclusions - suggestions for further research 10.8.1 Overall conclusions As none of the classic test set-ups was able to generate galling on uncoated Sibetex materials, a variant of the multifrottement test was developed in order to increase severity of galling tendency occurring on draw beads. This procedure is referred to as the DBS multi-strip approach and was applied to an extended set of materials in
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order to correlate galling behaviour with surface topography. Full roughness characterisation was performed on all tested materials. In this way a good correlation was obtained between the tribological behaviour during deep drawing, in particular galling, with surface topography. Some new theories have been developed and appear to be very promising, but further research based on these theories and experiments is still required. The DBS multi-strip galling test revealed that the type of coating strongly affects the galling behaviour of steel sheet and dominates over the effect of texture on galling tendency. Materials having different coatings could be easily discriminated by the DBS multi-strip test. But ranking materials having the same coating but different texture is hardly possible based on the number of strips pulled through the draw beads and evaluated by visual inspection. Therefore a new approach was elaborated. In order to find an objective quantification of the galling severity for all materials and an unambiguous ranking, a new evaluation system was developed, by performing 2D roughness measurements on all strips after functional testing. Based on these profile measurements a new index was defined, called galling severity index (GSI), which proved to be a good measure for the galling severity. This new approach for quantifying the galling severity succeeds quite well in ranking materials having the same coating, but different texture. This conclusion applies for uncoated materials (CRS) and materials with a rather soft coating (ELO, GI). For galvannealed materials having a hard coating it is not possible to rank the materials individually: they all show an excellent behaviour with regard to the occurrence of galling, independent of surface texture up to 20 strips. If (unrealistically) more strips are tested, the same method could be used. In order to correlate the tribo-behaviour of steel sheet with surface topography the concept of dominant summits was elaborated aiming for the discrimination between fine asperities and rounded "hills". Because of a lack of appropriate software enabling the splitting between "important" and "subordinate" features, a semi-manual procedure based on the dominant summits concept was applied on three uncoated Sibetex materials, in order to characterise the dominant bumps by means of their radius of curvature and height. After location of an approximate lateral position of the bumps, a paraboloid surface was fitted through each bump by means of the least squares technique resulting in the summit height and the radii of curvature. During sheet-tool contact every dominant bump of the steel sheet will deform either in an elastic or plastic mode, depending on its radius of curvature and its height position. Therefore it was suggested that a plasticity index calculated for the dominant summits be defined as a 3D-parameter VI/SDS, thus giving an indication of the tendency to plastic deformation. The surface topography parameters enclosed in the plasticity index will be derived from the dominant summit approach. The plasticity index has been determined for the 3 uncoated Sibetex materials after fitting of the dominant summits. In order to study the physical phenomena during sheet-die contact in more detail and to really quantify the load capacity of a surface, a mixed lubricated - plastic contact model was developed. Consequently, an EHL approach is used, modelling the microhydrodynamic wedge effects on the roughness summits. However, as the higher
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summits will be in contact much earlier than the lower ones, it is necessary to include a model for plastically deformed peaks as well. The relative importance of the EHL load versus the plastic load is a potential measure for assessing the tribological behaviour of the sheet-die contact. The more summits can generate an EHL load, the less the peaks mil deform plastically and the better the surface mil be in preventing galling. For the galling experiments carried out for 3 uncoated Sibetex surfaces, the comparison with the 3D plasticity index yields a good correlation: lower values of the plasticity index correspond to a better galling behaviour. It has been clearly demonstrated that the experimental approach, the 3D plasticity index and the mixed lubricated - plastic contact model lead to the same ranking. 10.8.2 Possible further research • The galling quantification method based upon 2D profile measurements could by extended by 3D analysis of the "touched" area. The "beamlet concept" (a variant of wavelet analysis) might be an appropriate tool for a fundamental study of the early incipience of galling by 3D analysis on the "galled" strips. •
A semi-manual procedure was used for the characterisation of the dominant summits of three uncoated Sibetex surfaces. The recently developed theory of the change tree system, enabling the splitting between "important" and "subordinate" features such as summits and valleys, could be a very promising technique for an automated characterisation of these dominant summits, on condition that adequate pruning can be applied (e.g. based on curvature and areal extension).
•
The concept of dominant summits might be extended to non-deterministic surfaces (like EDT and ECD) as well.
•
The definition of the 3D plasticity index might be improved by inclusion of a dominant summit density correction. The relation between the summit density and the plasticity index is probably non-linear and should be based on a sound theoretical analysis.
•
The definition of the 3D plasticity index might be extended to coated materials taking into account the mechanical properties of the coating layer as well. The equivalent Young modulus E* will then be depending on both substrate and coating layer.
•
Additionally more experiments, including a wider variety of textures, need to be performed to validate the hypothesis describing the correlation between galling behaviour and plasticity index.
10.9 References [1]
M. Vermeulen, J. Scheers, Effect of Pre-Welded Blanks on the Wear of Deep Drawing Tools, Proceedings World Tribology Congress, London, (8-12/09/97).
[2]
Renault, Test method D31 1738, Sheet metals - ability to sliding.
[3]
Jan Scheers, Carl De Mare; Study of the Frictional Behaviour of Steel Sheet Surfaces during Deep Drawing by use of Design of Experiments, Final Report PO950211, No. JaS9815, (August, 1998).
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[4]
Jan Scheers, Carl De Mare; Study of the Frictional Behaviour of Steel Sheet Surfaces during Deep Drawing by use of Design of Experiments, Proceedings IDDRG 1998, (June 1998).
[5]
K.L. Johnson, Contact Mechanics, Cambridge University Press, 1985.
[6]
M. Vermeulen, J. Scheers, OCAS Friction devices, miv.doc, (Surfstand report, 20 Nov. 1998).
[7]
First Year Progress Report of the European Project "Surfstand" (1998-2001), The Development of a Basis for 3D Surface Roughness Standards, Workpackage 6: Filtering techniques for Functional Surfaces, 1999.
[8]
K.J. Stout, T. Matthia, P.J. Sullivan, W.P. Dong, E. Mainsah, N. Lou, H. Zahouani, The development of Methods for the Characterisation of Roughness in three dimensions, EC Brussels, DGXII, BCR programme, Report EUR 15178 EN, ISBN 0 7044 1313 2, 1993.
[9]
S. W. Lo, W. Wilson, A theoretical model of Micro-pool Lubrication in Metal Forming, Proceedings of 1st Int. Conf. on Tribology in Manufacturing Processes 1997, Gifu, Japan.
WP3.3_DlJricdevice_
[10] Final Report of the European Project "Surfstand" (1998-2001), The Development of a Basis for 3D Surface Roughness Standards, Workpackage 7: Novel Areal Characterisation techniques Surfaces, 2001. [11] B. Hamrock, Fundamentals of fluid film lubrication, ISBN 0-07-113356-9, McGraw-Hill, 1994.
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11 Characterisation of Automotive Engine Bore Performance using 3D Surface Metrology Stefan Brinkman and Horst Bodschwinna Volkswagen AG, Salzgitter, Germany; and Institute for Measurement and Control, University of Hannover, Germany
11.0 Introduction The study of the functionality of automotive engine cylinder bores using 2D and 3Dsurface metrology has probably been the most analysed tribo-system, with numerous published papers in many journals [1, 2, 3, 4, 5, 6, 7]. Whole standards have been derived around specifying measurement and analysis procedures [8, 9, 10]. What is clear from the previous work (almost solely carried out using 2D techniques) is that no single set surface of parameters or characterisation methodologies has yet gained universal approval and acceptance. In terms of 2D surface analysis three basic systems prevail; firstly, the system based on the Rk family of parameters [8] which uses the bearing area curve to define peak core and valley zones which are then subsequently parameterised; secondly, there is the system based upon using probability curves to define functional bands of the surface (ISO 13565-pt3)[**], finally there is the French R and W system based upon the Motif Combination methodology[**]. The present chapter seeks to investigate engine performance as a function of 3D surface topography. Central to the investigation were a series of engine bench tests undertaken by Volkswagen as part of the overall SURFSTAND project. During these bench tests the functional performance and the wear of the cylinder bores of engines with different surface finishes were examined. For monitoring the functional performance, power, torque and oil consumption were recorded. Additionally, geometrical changes such as the cylindricity of the bore and the geometrical change of the counterparts, piston and piston ring were measured. The change of surface topography throughout the engine life was examined using 3D surface metrology.
11.1 Engine tests on dynamometers The test engine used throughout the study was the Volkswagen Golf 2.3-ltr 5 cyl. VR engine, Figure 11.1.
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Figure 11.1 Volkswagen Golf2.3-ltr 5 cyl. VR engine
Figure 11.2 Full load curve for the VR engine Table 11.1 Engine ratings and component description
Power rating: Torque rating: Maximum combustion pressure: Bore: 1.3.2 Stroke: Piston:
110kWat6000rpm 205 Nm at 3200 rpm 80 bar 81.0mm 90.2mm Mahle Autothermatic
Figure 11.3 Piston manufactured by Mahle, nominal diameter: 81 mm
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Piston rings Table 11.2 Piston ring specification Piston ring 1st groove Goetze KV1, plasma coated, rectangular section ring
Piston ring 2 groove Goetze STD, tapered compression ring 30'
Rectangular section ring domed Plasma coated
Grooved tapered compression Double bevelled ventilated oil control ring with spiral type ring expander Height 1.75 mm Height 3 mm Tangential force 7.5 N to 11.3 N
Height 1.5 mm
Oil scraper ring Goetze double bevelled ventilated oil control ring with spiral type expander, chrome
Crankcase materials Series: Grey cast iron GG 25 2-stage honing Laser processed :Grey cast iron GG 25 with reduced titanium content (0.013 %) 3-stage honing and fluid blasted with Laser texture in the area 5 to 135 mm from the top Bore diameter 175 um Distance 1.8 mm, slight displacement to next row
Figure 11.4 VR series crankcase
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Figure 11.5 SEMpictures: a) 2-stage honed surface b) laser textured surface Cylinder head Aluminium with 2 valves per cylinder
Figure 11.6 Longitudinal and cross-section of the engine Engine management Bosch Motronic, sequential injection
11.2 Engine tests 11.2.1 Test preparation The components were measured in the as-new condition before the tests. The diameter of the cylinder, the diameter of the piston, the width of the first and second piston rings and the tangential force of the third ring were all recorded. The roughness of the cylinder was measured in comparison to a new cylinder surfaces using 2 D and 3D techniques.
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11.2.2 Engine tests Extended tests were carried out to assess the wear on pistons, piston rings and cylinder liners. A varying load program with a large variation in revolutions and with a high full load percentage was selected for testing purposes.
Figure 11.7 Load and revolutions in extended test The test engines were operated over varying periods in this program. The following tests were carried out: 2 tests with 0.5 hr running time 2 tests with 2 hr running time 2 tests with 25 hr running time 2 tests with 100 hr running time 6 tests with 250 hr running time Total of 1755 hr test running time. New pistons, piston rings and crankcases were used for each test. All relevant measurements such as output, blow-by quantities, water temperatures, oil temperature and fuel consumption were recorded during the tests. 11.2.3 Test results Function results Power output The output during the tests was between 108 kW and 119 kW at the rated output point, Figure 11.8. Major differences were not recorded. A comparison of the performance between the individual tests shows a tendency towards higher output from engines with laser-processed cylinders. The difference in performance between shorter and longer test running times is somewhat less. The frictional power with test honing in the new condition without run-in time is clearly slightly less than series production honing.
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Figure 11.8 Comparison of output
Oil consumption Oil consumption in the first hours of operation is considerably lower with 3-stage honing with laser texturing than with the standard series production honing, Figure 11.9.
Figure 11.9 Comparison of oil consumption (running time 25 hr)
The level of oil consumption with the 3-stage honing with laser texture is 10 g/hr to 20 g/hr lower than series the production honing in the 250 hr Test. The levels become less distinct with longer running periods, Figure 11.10.
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Laser Honing
Series Honing
Laser Honing
Series Honing
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o
Figure 11.10 Comparison of oil consumption levels (running time 250 hr)
11.2.4 Wear results The components were measured again after the extended tests in order to determine to the extent of the wear. Pistons The extent of wear on pistons tends to be lower in cylinders with the laser matrix than in series production cylinders. However, cylinder 3 shows levels of wear which are in contradiction to this statement. The extent of piston wear in cylinder 4 is the same in both versions.
Figure 11.11 Piston wear
Piston rings The piston ring wall thickness was used to determine the level of wear after the extended tests. The difference in wall thickness is taken as a measure of the wear. The differences in wear between series production honing and honing with laser texture is not the same in all cases. The wear measurements for cylinders 2,3 and 5 are shown here as examples, Figure 11.12.
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Whilst the piston ring wear on cylinder 1 with laser texture is greater than with series production honing, the tendency is opposite for cylinder 5. Cylinders 1, 3 and 4 show a balanced wear response.
Figure 11.12 Piston ring wear Cylinders The level of wear on the cylinders is low. A maximum change in diameter of up to 6 was recorded for the series production cylinders. The cylinders with laser texture showed no measurable changes in diameter. 11.2.5 Summary of results from engine tests In comparison with series production honing, honing with the laser matrix demonstrates a number of advantages for running in and for levels of oil consumption. The run-in time of the cylinder is reduced considerably by the third stage of honing. The wear on the pistons and piston rings cannot be definitively assessed. The measurable differences are too small to be able us to make a clear statement for this small number of tests. Influence on the levels of fuel consumption and emissions were not taken into consideration for this series of tests as the primary objective was to assess levels of wear. Further tests are necessary to gain more detailed information on levels of wear, fuel consumption and emissions.
11.3 3D Measurements during functional testing on the engine bores In section 1 1 .2 the bench tests of the Volkswagen VR engines were described and the results discussed. Also investigated was the application of 3-D surface metrology to these engines in order to describe the running in wear of cylinder liners. The measurements were carried out using a tactile 3-D profilometer "Surfascan 3S" by Somicronic. In order to position the engines on the test table, the engine blocks were sectioned. Both the thrust and anti-thrust side of the cylinder bore were kept intact. Usually, the wear of a cylinder liner is greatest at the top dead centre position (TDC) and in the centre of the cylinder liner. The strain on the surface at TDC is very high because of the high gas pressure in the ignition cycle and the temperature of combustion. Moreover, the relative velocity between piston ring and cylinder wall is nearly zero, which often results in mixed friction instead of pure viscous friction. The reason for the increased wear in the centre of the cylinder liner is maximum piston
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speed and the maximum radial force at the thrust side leading into the piston over the con-rod [11, 12, 13, 14]. Due to the expected wear, surface measurements were taken at TDC and in the middle of the cylinder liner and the thrust and anti-thrust side were distinguished. For each measurement point two to three measurements were carried out in order to obtain representative results. In total over 140 tactile 3D measurements were undertaken. This is equivalent to approximately 900h measuring hours. For an easier, automated evaluation of the measurements and simplified data organisation it was necessary to collect the measurement results into a database. For this database a structure was developed under the mathematical programming environment MATLAB comprising all the calculation algorithms required, allowing administration of the measuring records and parameter evaluation concerning the running period. In order to guarantee exact calculation of the parameters within the scope of the SURFSTAND project, access to the parameters of the Surfstand-Software was needed. Therefore, an interface connecting the MATLAB-Database to the calculation routines was created. Figure 11.13 shows the surface topography of the cylinder liner of the serial engine at TDC after differing running times. Clearly visible is the smoothing of the surface within the first hours. The study in hand utilises the parameters as defined in this research project. The definitions of the single parameters can be found in preceding chapters. Another set of parameters recently discussed within the German motorcar industry were also considered. These are based on the evaluation of the Abbott-Curve and are comparable to DIN 4776. Just as with the functional parameters suggested by Stout et. al, fixed borders are given for Mrl and Mr2. Following this, the parameters SR, Spk, SVk, Spkx, Svkx are calculated. The parameters Vmk, Vmp, Vmpx result from the material volume curve and the parameters VVk, Vvv, Vvvx from the void volume curve. Fixed values Mr} = 10% and Mr2 = 80% delineate the peak, core and valley zones. Figure 11.14 shows the change of the parameters during the engine running time.
Figure 11.13 Change of engine bore surface during functional bench tests (top dead centre)
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Figure 11.14 Change in the 3D surface parameters with engine running time
It is clear that for the first operation hours of the engine a noticeable change of the 3D surface parameters occurs. The amplitude parameters show the flattening of the surface and the shaping of the plateaus. Over all the range of the surface amplitudes levels are decreasing. In particular, the peaks (Spk) and the core (Sfr) are reduced. However, the valleys (Svk) stay nearly constant. The development of the plateau is also clearly marked by the parameters Ssk and Sku. The parameter sets for the description of functional surface confirm this change of the topography. The peak volume and the core volume are clearly decreasing whilst the free volume of the valleys hardly changes with the running time.
11.4 Relationship between functional performance and 3D surface topography From this study the relationship between the functional performance of the cylinder engine bore and its 3D surface topography has been shown. In particular the laser
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textured and 3-stage honed engine shows significantly lower oil consumption during the running-in period than the conventionally honed series engine. Additionally, less cylinder wear (diameter) was recorded for the optimised surface topography. On the other hand, for both engine power and piston ring wear no significant differences were evident.
11.5 Running-in wear of engine cylinder bores The study as described in section 11.2-11.4 has shown that 3-D surface metrology is able to detect and describe surface wear. Now, the running-in behaviour of cylinder liners will be analysed in detail, utilising 3-D roughness metrology. 11.5.1 Wear mechanism DIN 50320 defines the term wear [16]: "Wear is the progressive loss of material from the surface of a solid body (basic body), caused mechanically, that is by contact- and relative motion of a solid, a liquid or a gaseous opposed body". Different surface wear mechanisms within a tribological system can be distinguished [14, 16, 17, 25]: 1. 2. 3. 4.
surface fatigue; abrasion; adhesion; tribochemical reactions.
The contacting surface regions must absorb the normal and tangential forces, which cause, together with the relative motion of the contact partner, the material strain within every tribological system. Surface cracks resulting from surface fatigue, and similarities can be drawn with the fatigue of "massive" materials loaded with alternating forces. The description of this process is based on material science models of dislocation theory and fracture mechanics [18,19,20]. Surface abrasion is the effect of normal and radial forces in tribological contacts. Material abrasion takes place by micro cutting, ploughing or breaking. During the relative motion, material is removed from the softer body (cylinder liner) by the harder contact partner (piston ring) [17]. This is the main wear process in the tribological system piston-piston ring-cylinder, especially during "the running-in period. The wear mechanism termed adhesion is a cold welding process resulting from local welding at a defined surface roughness elevations/position. The natural oxide and lubrication coating is broken down and local interfacial adhesion emerges. During the relative motion of both bodies local fretting may occur. Adhesion may occur due to a lack of lubrication in the TDC region of the engine system. Tribochemical reactions are chemical reactions of basic and opposed bodies with components of the precursor or the ambient medium caused by the tribological strain. Certain surface zones may be activated thermally or mechanically so that the micro contact spots have greater chemical reactivity. When such phenomena occur, the behaviour of the outer boundary layer of the contact partners changes, leading to
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higher or in some cases to reduced wear (oxide film for reduction of the adhesion propensity). All of these wear processes have been observed in numerous studies on the wear process of cylinder bores of internal combustion engines. For a comprehensive classification of the wear processes occurring during the tests, the metallurgical and chemical changes in the outer surface layers have to be examined in conjunction with the surface geometrical properties. However, because of the complexity of the system analysed, in this research only the change of surface geometry has been studied. 11.5.2 Wear-time-diagram With sliding wear which is observed in the tribological piston ring-cylinder liner system time lapses can be observed. A typical wear-time-plot is shown in Figure 11.15.
Figure 11.15 Schematic wear time diagram [14] Phase I represents the so-called running in wear. A "flattening" of the contacting roughness asperities takes place in this region. The change to the micro-geometry of the liner surface results in a steady state wear process. In this case the literature provides the assumption that the wear volume wv(t) can be described by [14].
Phase II is typical of almost constant load conditions and the wear rate is constant. In this case there is a linear interrelationship between wear volume Wv and duration of load / :
In Range III acceleration of the wear may occur. This can be described by a linear increase of wear rate and therefore an exponential increase of the overall wear (11-3)
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For phases I and II the equation for the sliding abrasion can be found in Bayer [21 ]:
Here Fn is the normal force. The exponents m and n depend on the contact geometry and have to be determined by experiment. A disadvantage of the two formulations as described above is that at t = 0 a wear speed of dWv/dt -> <x> is given. Following equation (6-3) the authors prefer a degressive exponential formulation for this phase. This degressive approach can be described with the linear decrease of wear rate and therefore exponential decrease of the over all wear volume W
The time constant TE characterises the running-in duration. The wear speed is at its maximum and almost constant in the range / -» 0. A similar procedure for the ranges I and II can be found in [21]. Additionally, it can be assumed for the bench test within this research that range III will not be reached within the duration of the maximum of 250 working hours and in this case does not have to be taken into consideration. 11.5.3 Wear volume Geometrically, the wear of a surface can be described by changes in the material volume. Figure 11.16 shows the change of the Abbott-curve during the functional tests. The curves are fitted by the least-square-method in a way that gives an overlapping region between 75% to 95% bearing area. The form of the Abbott-curve of the worn surfaces is flatter in the core region. Almost no peaks are left and the valleys stay almost the same. From the definition of the functional parameters the transition point from the core to the valleys was set to 80% by experience. For the following considerations it is assumed that this point does not change significantly during running in. This means that the valleys are hardly affected while the peaks and the core of the surface are worn. The reliability of this assumption is illustrated by the parameter study in section 11.3.
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Figure 11.16 Change of the Abbott-curve through wear Based on this the wear volume Wv(t) can be calculated
(11-6)
Wv(t) = Vmw/0(t = Oh) - Vmm%(t)
The volume Vm%Q0/0(t) is the material volume found above the 80% surface material point. The volume values can easily be determined from the calculated parameters. For the serial engine the results are given in the first 2 columns of Table 11.3. For the laser textured engine the first results are given in the two last columns. The star (*) marks engines whose surfaces were not measured. Table 11.3 Material volume and wear volume for both test engines Load duration t [h] 0 0.5 2 5 25 100 250
Series Engine Wv(t) vm,w%(t) [nmVmm2] [unrVmm2] 0.84 0 0.65 * 0.47 0.44 * 0.20
0.19 * 0.37 0.40 * 0.64
Lasertextured Engine Wv(t) Vm,W%(t) 2 [\im3/mm2] [unrVmrn ] 0 0,67 * * 0.07 0.60 — 0.21 0.46 * * 0.42 0.25
The data taken from Table 11.3 is plotted in Figure 11.17. Applying equations (6-2) and (6-5) the running-in time, the wear rate at the beginning and the constant wear rate in phase II can be determined. The results calculated from these equations are given in Table 11.4. For the calculation of the unknown parameters very high reliabilities for the series engine are found (R 2 z 93%). For the series engine the running-in period is approximately 2.5h. In this time the wear rate Wv0 is significantly higher than the wear rate after the running in period wvc. For the laser textured engine in Figure 11.17 the calculated data is plotted too. It is clear that the wear is much less than with the series engine. As the test conditions for both engines are equal this improvement is mainly related to the surface topography.
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Figure 11.17 Wear volume: measured data and mathematical approximation Table 11.4 Parameters calculated for the wear model for the series engine Series engine
Vvfl
TE
0.395 nmVmm2
2.56 h
Wv,c 0.001 ^irnVmrn2
R2 0,93
Overall, it can be stated that surface metrology is able to detect and describe surface wear of cylinder engine bores by analysing the 3D-Abbott curve and the associated volume curves. The experimental date provided by the full engine bench tests show a running-in period with a high wear rate. After this running-in time a period having a significantly smaller but constant wear rate was found.
11.6 Conclusions Engine bench tests have proved a relationship of functional performance of engine cylinder bores and 3D surface topography exists. The flatter laser textured engine surface, with pockets retaining lubricant, shows less wear then the surface manufactured by conventional honing. For a description of the wear, the material volume change in the surface was measured using 3D surface metrology. It was shown that a significant change to the surface occurs during the first hours of running of the engine. A mathematical model describing the wear-time-relationship was developed for the test engines. It was possible to determine the running-in time and the wear rates for the running-in period and the period of linear wear.
11.7 References 1. J Nadel, T Eyre "Cylinder liner wear in low speed diesel engines" Tribology Int'lpp 267-271 Oct 1978. 2. K.J. Stout, E.J. Davis "Surface topography of cylinder bores - the relation between characterisation manufacture and function." Wear 95 pp 111-125 1984. 3. P Pawlus "A study of functional properties of honed cylinder liners during running in wear" Wear 176 pp 247-254 1994.
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4. K.J. Stout T.A. Spedding "Characterisation of I.C. engines" Wear 83 pp 311326 1982. 5. EJ. Abbott, F.A. Firestone, "Specifying Surface Quality" Mechanical Engineering 55, pp 569-572 1933. 6. D.J. Whitehouse "Some theoretical aspects of practical problems of practical measurement problems in plateau honing" J Int Prod Res, vol 21 No2, pp 215221, 1983. 7. T.S. Eyre, K.K. Dutta, F.A. Davis, "Characterisation and simulation of wear occurring in the cylinder bore of the internal combustion engine" Tribology Int'l, Vol 23 Nol, pp 11-16 1990. 8. M.C. Malburg, J Raja, "Characterisation of surface texture generated the by plateau honing process", Annals of CIRP Vol 42/1, pp 637-639 1993. 9. B.G. Rosen, R Ohlsson, T.RR. Thomas "Nano metrology of cylinder bore wear" Int J Mach Tools and Manuf. Vol 5-6 pp 519-527 1998. 10. DIN 4776 "Measurement of surface roughness: parameters Rk, Rpk, Rvk, Mrl, Mr2 for describing the material portion (profile bearing length ratio) in the roughness profile:measuring conditions and evaluation procedures, Deutsches Institut fur Normung Berlin 1997. 11. ISO 12085 Geometrical Product Specifications (GPS) - Surface texture: Profile method Motif parameters. 12. Ishizuki, Y., Sato, F., Takase, K.: Effect of cylinder liner wear on oil consumption in heavy duty diesel engines, S AE paper no 810931, 1981. 13. Strobel, J.: Beitrag zur Beurteilung verschleiBmindernder MaBnahmen im System Kolbenring-Zylinder, Disserattion Universitat Hannover, 1992. 14. Miiller, H.K. Abdichtung bewegter Maschinenteile, Medienverlag, Waiblingen, 1990. 15. Czichos, H., Habig, K.H. Tribologie-Handbuch - Reibung und VerschleiB, Vieweg & Sohn Verlagsgesellschaft, Braunschweig Wiesbaden, 1992, ISBN 3-528-06354-8. 16. Butler, D.L., Blunt, L.A., O'Connor, R.F., Stout, K.J.: The Characterisation of Cylinder Liner Bore Polishing with 3-Dimensional Functional Indices. 17. DIN 50320 VerschleiB; Begriff, Systgemanalyse von VerschleiBvorgangen, Gliederung des VerschleiBgebietes 1979. 18. Zum Gahr, K.-H. Abrasiver VerschleiB metallischer Werkstoffe, VDI Forschrittsbericht, Reihe 5, Nr, 57, 1981, ISBN 0341-1664. 19. Hailing, J. A contribution of the theory of mechanical wear, Wear 34, 239, 1975. 20. Suh, N.P. The delamination theory of wear, Wear 25,111, 1973. 21. Hirth, J.P., Rigney, D.A. Crystal plasticity and delamination theory of wear, Wear 39, 133, 1976. 22. Bayer, R.G. Mechanical Wear Prediction and Prevention, Marcel Dekker, Inc., New York, Basel, Hong Kong, 1994.
Part 4 Future Developments
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Surface Texture Knowledge Support - ISM Robert Ohlsson and Bengt Goran Rosen Volvo Truck Corporation, Goteborg, Sweden; and School of Business and Engineering, Halmstad University, Sweden
12.0 Introduction In the recent past there has been a step change in manufacturing strategies and technologies primarily as a result of globalisation and extreme pressure on increasing competitiveness. To be competitive and maintain profit in such a dynamic environment, a manufacturing enterprise must be capable of adjusting quickly to the market. This has lead to the emergence of a new manufacturing strategies such as agile manufacturing, where multiple companies co-operate under flexible virtual enterprise structures. The main purpose of AM is to obtain high quality, shortest leadtime, good service at the lowest cost to satisfy customers' requirements. To respond to the market rapidly, companies have to work closely with their suppliers, customers, and partners to shorten the product development lifecycle and to highlight potential problems. Simultaneous requirements of high quality and rapid co-operative business demands effective information and data handling systems. Specifying surface texture for products will have a heavy impact on the cost and function of the final product and consequently becomes a critical factor in AM based product specification. Various studies have shown the need and use for computer aided tools in order to realise the functional demands on the surface of a product [1, 3, 5]. Rosen [5] has presented the outlines for a decision support system called ISM (interactive surface modelling). Here, the methodology of specifying a surface based on consideration of the functional requirement of the surface via translations into design, manufacturing and quality control specifications were outlined. The system proposed was based on a CAD system (autoCAD) with access to a surface texture knowledge database. This approach enabled the designer to have access to knowledge e.g. company standards in the CAD integrated environment. This work was followed-up by Rosen, Ohlsson and Westberg 1994 [4] where a PC-Windows based version of ISM was discussed. The need for a systematic structuring of the surface information was emphasised. The structuring being not only to make information retrievable from the database, but more to enable the construction of a generic knowledge database not only able to host data but also to generate design-rules developed from structured data. Different stored products with similar functional requirements can'be combined to generate general statements concerning, for example, surface texture parameter selection to use when specifying a particular function for general use. The evident lack of strong rules
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connecting surface textures to functions was said to call for databases with a generic capability to improve the design rules used to increase product quality. If combinations of CAD systems, computers and databases will theoretically support the quality and the speed of the product development cycle regarding the surface texture, the requirement of agile productions in terms of co-operation with partners and suppliers will have to be dealt with separately. In the paper "Inspection Information Modelling based on STEP in Agile Manufacturing " by Hongjun, Rosen [2], the possibilities of the use of an ISO standardised data and information format (standard for the exchange of the product model data, STEP) for tolerancing data i.e. surface texture was introduced. A use of a standardised format not only promotes the portability of the data between different users, but also ensures the longevity of the data to secure the lifetime of the data independently of the soft and hardware solutions used. Today, the usage of STEP is growing rapidly and many commercial software e.g. CAD/CAM systems like AutoCAD, CATIA and ProEngineer all support STEP. To support the co-operation between companies, the systems used for product specification benefit from being accessible in a distributed network environment. In the following paragraphs a research database has been implemented to test the possibilities of a distributed solution. The internet based solution is based on a client server strategy, using platform independent Java-applets and html-forms for information transfer. The solution displays some of the possibilities for future systems. Here, surface texture data can be archived, combined and interrogated for the generation of new knowledge. Today, archiving and managing of general product data (geometry, analyses, assembly instructions, handbooks, manufacturing data etc.) is carried out by so-called product data management (PDM) or business systems. Many of the current PDM systems are highly capable of archiving and management of documentation in the product life cycle from idea to scrap, but the lack of knowledge support for the actual product SDecification is evident. While current and old designs are retrievable through the PDM systems, detailed information needed to support creation of new specifications and modification of old specifications to meet changing functional demands from the market are missing, hence creating a niche for knowledge support systems like ISM.
12.1 The current situation Today, the persons involved in the process of making design/manufacturing and quality-specifications work mostly from scratch. A common situation when designing surfaces is "has it been done before", meaning that their knowledge about surfaces with similar functional demands is stored somewhere? The problem is that this "somewhere" can be in the mind of a skilled operator, in books and standards, or published "somewhere".
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Figure 12.1 Current information flow. Information is found in different parts within the company e.g. as documents stored away somewhere, or know-how from colleagues This procedure generates knowledge that is meant only for the current product. The result is that the knowledge generated during the design procedure will not be persistent or easy to find for future use.
12.2 The future with the ISM system Instead of repeating work and spending much effort to find information not quality checked the designer should use one channel (designer => database). Here, experts using the system have verified the data stored in the database.
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Figure 12.2 Information flow when all information is structured and stored in a central database available for all users within the company
123 What is a knowledge based expert system? The definition of a "knowledge based expert system", in this context is founded on the idea of several users working in different networks, spread globally, sharing the same data and generating new data for the shared database. The new data is generated with help from different support-applications that are available in the system.
Figure 12.3 Information is retrieved from the database and used to generate new data The users of the system act in different roles depending on the purpose of their transactions with the database. The users belong to one or both of the following main categories: 1. Product developers. 2. Measuring engineers, test engineers.
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The product developers use the database to extract information from the data that is produced by the tests that the measuring/test engineers carry out. The extracted information is used as a decision support tool for the design parameter determination. The measuring/test engineers use raw data from the measuring machines to produce representative data for the tests, e.g. different surface parameters, Sa, Ssc etc, or different functionality parameters e.g. skew, lift off, speed.
12.4 Knowledge database The "database" will consist of different "islands" of information. Each "island" is built by relationships between object-classes' and modelled according to a classic relational database model. The different "islands " are: • • • • •
test database (raw test data); expert knowledge (rules); specifications; standards (ISO, company, etc.); external (other published material).
12.5 The (expert) knowledge structure The "expert knowledge" subject for storage is categorised in three main competence categories each described as a set of rules. The set of rules are design rules, manufacturing rules and measuring/quality rules. Each set of rules can be accessed at different levels (see Figure 12.4) for different purposes of use.
Figure 12.4 The structure of the "expert-knowledge " area in the database. Design rules are decomposed in three different levels. Here, from pure test data to an abstract level of theoretical formulas
Object class: database term that roughly means a clearly distinct subject that contains concrete data, such as parameters, administrative data. Relational classes connect object classes.
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12.6 Test data database
Figure 12.5 The relational database model for the test-data. The model illustrates the functional relationship between different sets of data
Figure 12.5 above shows a general model that can be used for most kinds of products and different kinds of tests, e.g. heat tests, surface roughness tests etc. The difficulties arise in the representative data entry. To extract data and to compare two different measurements, there must be some kind of standard format for the representative data entry. However, this model takes care of different standards by splitting the contents of the representative data into a number of value pairs, there is then the possibility of dynamically defining which parameters are to be included in the representative data entry. The cost of the dynamic structure is paid for in the implementation model. In this case it will be harder to develop templates for the representation of the data; instead, there must be an interface that can adjust to any number of parameters and their corresponding values.
12.7 The distribution of database information in a network This section deals with some alternatives, regarding network topology and software, for distributing data between users located in the same, or a different local networks.
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12.7.1 Internet/World Wide Web The internet is a global network where companies, universities, individual users etc are connected via modems or leased lines. The internet has been fully operational for the last twelve years and it is not "owned" by any specific organisation However the World Wide Web is a recent phenomenon that started seeing widespread use from the mid 1990s. Soon after the invention of advanced graphical web browsers like Mosaic and Netscape, companies and their customers gave the web their attention. The new tools made it easy to graphically transfer rich information with just a click with the mouse, instead of having to know a numerous cryptic commands that have to be typed in by hand. 12.7.2 The intranet Instead of using the classical client-server model, there is an option to use internet techniques for sharing and distributing data among users in a local intranet, and external users via the internet. This model makes the system transparent, with respect to the OS. The idea is to have web-servers that contain both the databases and the applications. The client application interfaces are available via html-files that are downloaded via the http-protocol. When it comes to the execution of programs, which are started by the users through the html-interfaces in a web-browser, there are three options: 1. Program processing is executed on the server. Eventual confirmation is sent to the user in html-form (see Figure 12.6). 2. Program processing is executed on the client side. When the user downloads the html-application-interface, the user also downloads the application Java. The application, however, connects to the server to perform eventual database transactions (see Figure 12.7). 3. Program processing is executed on the user side. When the user downloads the html-application-interface the user also downloads the application (ActiveX). The application opens a connection to a server-database on the same local net. The first alternative makes use of CGI techniques (common gateway interface.) to connect to the server. It provides the server with the actions taken by the user on the html-page (e.g. values entered by the user in the html-form). When the server receives the request to process a program-execution the program reads the parameters entered by the users. The program is then executed. During the program-execution the program stores information in an html-file that is returned to the user (see Figure 12.6).
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Figure 12.6 Persistent data and information-flow, process initiation from the server, on request from the client The second alternative uses Java to execute the application on the client computer, after downloading both an html-file and a Java-applet from the web-server. The client computer then compiles the downloaded Java-applet. The application executes at the client computer and connects to the remote database via JDBC, which is an interface between the application and the database, Figure 12.7.
Figure 12.7 Persistent-data/ information flow and process execution/compilation, the client requests a html-page via a web browser and receives the html-page and the Java-code, which is compiled at the client by the clients' web browser. The Java-application is then executed at the client. The Java application finally connects to a database server and commits transactions via TCP/IP The distribution of Java-applets through html-pages makes the system platform independent. This is because the received Java-applet is a 6yte2-code that has been 2
The byte-compiled code is evaluated by the byte-code interpreter, instead of being executed directly by the machine's hardware (which true compiled code is), byte-code is completely transportable from machine to machine without recompilation.
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virtually compiled (see glossary, under Java) by the provider. The client has to compile the code for the client hardware, using a compiler that is provided by the web-browser program.
12.8 Java-JDBC The system consists of the following components: • • • •
Database. JDBC, or ODBC-JDBC bridge. Java applet, or Java-application. Html-page embedding the Java-applet.
Compared to the CGI-ODBC connection, the Java-JDBC connection performs the database transfers and communication on the client machine. Because of this, there might be problems connecting to the database if there is a firewall between the client network and the server network. The client must also be able to authenticate the right to connect to the database. Currently, there is much development going on with the JDBC and all major database and software vendors join and support the JDBC. There also exists a bridge for databases that does not support the JDBC: the ODBC-JDBC bridge. This bridge allows a connection with the help of ODBC. The strongest argument for using Java is platform independence. Theoretically, all clients who can access the web-server containing an html-page are able to download the Java applet/application. One advantage is that the security in Java protects the client machine and "put sticks in the wheel" because the applet is not allowed to do file operations such as make files, delete files and read files. The Java applets and Java applications were developed with Microsoft Visual J++ 1.01. There were no testing of JDBC, but Microsoft provides a special database interface (limited functionality) object in Visual J++ that was used to connect to local desktop databases. The development environment is very sophisticated (the standard Microsoft developer studio environment that are used for most Microsoft software products e.g. C++), but the features in Visual J++ for visual programming is yet not that good. The functionality to develop good user interfaces exists in a very limited way, however Java is in an early development phase.
12.9 Bearing surface application In order to test the feasibility of the test database discussed above, a prototype system based on the Oracle relational database, Java application, Java applet, JDBC and html was implemented. The specifications applied to the system were to enable central archiving of measured surfaces and functional tests. The system should also permit different clients to browse the database, extend the database with new tests and finally to generate answers on user queries combining the stored functional and surface data into new knowledge, hence utilising a demonstrator of an interactive decision support for surface texture specification.
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The application consists of two parts. Part one is an administrative application with a users interface to store new or modify old test data in the central database. Here, tests consist of measured functional and surface data, as well as representative data compiled by domain experts to support user queries. The second part is an application permitting browsing through the test database and queries to extract information. The browsing part is accessible for the clients via the Internet on an html page has been queried for surfaces being subjected to input parameter Velocity less than SOrpm and output data from the test Traction (friction) between 0.05 and 0.1. The search resulted in a surface WB0983b with the surface parameters and visual appearance as shown below. In this way, all tests in the database can be combined to extract surfaces fitting users' specific requirements thus generating new knowledge combining surface texture and functional behaviour. All queries are based on the data stored as the representative data in the database.
Figure 12.8 A query to the database regarding velocity and traction (friction) resulted here in a link to a surface in a specific named test. Here, both the 3D texture parameters and one of the surfaces' images is visible Part one, the administrative application, is via a separate Java based applications file accessible for the administrative user via a batch file starting the Java applet shown. Here, the administrator can store tests along with data and descriptions according to the structure given in Figure 12.18 above. Representative data, descriptive documents and source data can here be added or modified to new or existing tests in the database.
12.10 Conclusion Agile manufacturing concepts stress the need for computer aided tools to increase lead times and promote co-operation within and between organisations. Within distributed organisations, the need for fast access to data and the broad variation of information types, (documents, pictures, tables, raw test data, extracted
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high level knowledge etc calls for distributed web-base solutions and standardised information formats. To improve the usability of computer-based decision support, the use of the concept of user views to the knowledge database system, e.g. designer, manufacturing and quality control views is beneficial. The user views are pre-defined sets of data suitable for the individual users needs. Representative data extracted from tests enable the comparison of different tests and the possibility to continuously add new data to a database. This is a key feature of a successful knowledge database. The distribution of knowledge support will be eased by the use of platformindependent solutions e.g. based on Java applets and applications. A pilot system has been developed to illustrate the usage of knowledge support in surface texture applications - the bearing surface application. Here, an initial workbench to further investigate the possibilities with distributed knowledge support was created and showed good promise. In the future, use of computer aided knowledge support will be forced upon organisations by the agile production and systems based upon those described in this section will be necessary tools to ensure competitive business.
12.11 Glossary ActiveX: Components developed in PC-operative-system programming languages e.g. Visual Basic, C++ or Delphi. The components are compiled by the host programming language as ActiveX-components, which means that dll-files are created (with an .ocx extension instead of.dll). The components could be embedded in an html.page an downloaded to users via Internet. The technique is platform dependent (Windows 95, 98, NT, 2000). The component is permitted to use the clients operative-system e.g. to make file-manipulation etc (compared to Java which is not allowed to use file-handling functions). Microsoft developed the ActiveX-technology to compete with Java. CGI: (Common Gateway Interface}. A standard communications interface that allows web servers to communicate with back-end processes e.g. database applications, or other server based applications. Client-server: Distributed data processing between a client and a server connected via a network. The server is a computer (or many) that owns programs or data that it can provide to clients asking for it. The client is the computer (or process) that requests a service from the server computer (or process). The client handles the user interface and sends input data to the server, which processes the input-data and responds to the client. Extranet: For corporate businesses who want to co-operate on certain projects. Useful to join parts of their intranets with each other over the Internet. The connection must be transparent so that the users on each intranet could co-operate as if they were
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on the same intranet. The technique to go through firewalls via Internet is called tunnelling (see glossary: tunnelling). For example: imaging Microsoft and IBM in a project, they would like to reveal some parts of their intranets to each other (the concerned departments), but they would not like to have their merged intranets exposed on the Internet. Not only intranet users, but also standalone users sometimes wish to set up this kind of communication to other stand-alone users/intranets. Groupware: Software that allows multiple users to work as a group on the same set of data or documents. Groupware often consists of several types of office-software e.g. e-mail and other group-oriented communication features. Lotus Notes is an example of a groupware. Most groupware use client-server architecture. Intranet: A network that uses http and other internet-techniques to view and deploy information, within the network only, not to the public. A TCP/IP protocol is necessary to set the communication up. The network does not have to be connected to internet. Java: A programming language created specifically for the web environment. In contrast to traditional programming languages like C/C++, which must be compiled into versions that only run on specific platforms, Java is delivered in an uncompiled form and is interpreted at the web client end. Javascript: An interpreting language that is used to enhance html pages. The language differs quite a lot from Java, it is written in the html page that should use it and the language is not truly object oriented. Javascript is a tool for non-programmers and provides a fast way to enhance html pages (e.g. add functions that can be invoked by pressing input buttons on the html page). JDBC: Java Database Connectivity Standard is part of the Java Enterprise API3. JDBC is an SQL based database access interface. It provides Java programmers with a uniform interface to a wide range of relational databases, and also provides a common base on which higher-level tools and interfaces can be built (similar to ODBC, but platform independent). ODBC: Open Database Connectivity. A methodology for communication with databases through a driver interface that works on the same principle as a printer driver. In this way an application can control a certain database by choosing the ODBC for that database, (see JDBC for a similar approach for a platform independent method.) TCP/IP: Transport Control Protocol / Internet Protocol includes standards for how computers communicate and conventions for connecting networks and routing traffic.
3
API: Application Programming Interface, A set of routines or function calls that allow an application to control, or be controlled by, other applications.
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Tunnelling: Relative to the Internet, tunnelling is using the Internet as part of a private secure network. The "tunnel" is the particular path that a given company message or file might travel through the Internet. A protocol or set of communication rules called Point-to-Point Tunnelling Protocol (PPTP) has been proposed that would make it possible to create a private network through "tunnels" over the Internet. Effectively, a corporation would use a WAN as a single large local area network. This would mean that companies would no longer need their own leased lines for widearea communication, hence securely using the public networks. VBscript: An interpreting script language that Microsoft invented together with the ActiveX technology. VBscript is similar to Javascript. The intention of VBscript is to make html pages use ActiveX components and provide non-programmers with some functionality to enhance their html pages.
12.12 References 1. K.J. Stout, P.H. Osanna, B.-G. Rosen, The Structure for functional control of manufacturing processes, submitted end of December to IQMM'2001 International NAISO Symposium on Information Science Innovations in Intelligent Quality Management and Metrology, Dubai, February 2001. 2. Hongjun Wang, B.G. Rosen, J. Rosen, Inspection Information Modelling based on STEP in Agile manufacturing, abstract submitted to the CIRP conference in Design in the New Economy, Stockholm, in the summer 2001. 3. Rosen B-G., Mathematical Machining, a way to control the surface engineering cycle, presented at the Workshop on Engineered Surfaces, June 3-4, Hotel de la Poste Corps la Salette, Grenoble, France, (1998). 4. Rosen B.-G., Ohlsson R., Westberg J., Interactive surface modelling, an implementation of an expert system for specification of surface roughness and topography, In; K.J. Stout (ed.) Proceedings of the 6th Int. Conf.: Metrology and Properties of Engineering Surfaces, Birmingham, UK, April 6-8, (1994). & Int. J. of Machine Tools & Manufacture, Vol.35, No.2, pp. 317-324, (1995). 5. Rosen B.-G., Crafoord R., Interactive surface modelling: model of a functionoriented expert system for specification of surface properties, Industrial metrology, Vol.2, Nr.2, pp. 107-119, (1992).
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13
Future Developments in Surface Metrology Liam Blunt, Xiangqian Jiang and Paul J. Scott School of Engineering, University of Rudders field, UK; and Taylor Hobson Ltd, Leicester, UK
13.0 Introduction Although the SURFSTAND project laid the foundations for areal surface texture standardisation, there is still a lot of work to be carried out before international standardisation is finalised with full integration into the Geometrical Product Specifications and Verification (GPS) system. GPS defines, in technical documentation such as engineering drawings, the geometry, dimensions and surface characteristics of a workpiece which ensure optimum functioning of the workpiece, together with the dispersion around the optimum where the function is still satisfactory. Further, the system specifies how these workpieces will be measured in order to compare them with the specification. The GPS system includes: size, location, orientation, form, surface texture etc. and is the common language between designers, production engineers and metrologists to control the geometrical requirements of engineered components. Figure 13.1 shows the relationship between designer, production engineer and metrologist in the GPS system.
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Figure 13.1 Relationship between designer, production engineer and metrologist in the GPS system Standards in the field of GPS are being prepared within the International Organisation for Standardisation (ISO) by Technical Committee 213 "Dimensional and geometrical product specifications and verification'' (ISO TC213). ISO TC213 was formed in June 1996 and has a remit that deals with basic definitions, symbolic representation, specification and verification principles, measuring equipment and calibration requirements including the uncertainty etc. in the GPS system [1]. Since surface metrology is part of the GPS system, as the GPS system develops so may surface metrology and visa versa.
13.1 The next generation GPS system The current GPS system developed from three distinct sources: 1. Geometrical tolerancing. 2. Co-ordinate metrology. 3. Surface texture and form measurement. Initially, experts from ISO TC213 developed a masterplan [2] to bring the three areas together, to systematically identify the contradictions and gaps in the standards that cover GPS. As experience was gained and general GPS principles developed, experts in ISO TC213 soon recognised that a truly integrated GPS system was possible, based on fundamental GPS principles rather than sticky plastering the three GPS sources together. The new integrated GPS system was termed 'the next generation GPS" [3]. Most of the current workload of ISO TC 213 is aimed at developing the fundamental GPS principles for the next generation GPS using well-founded mathematics. One particular challenge with the current GPS system that affects surface texture is the fact that there are two workpiece co-ordinate systems. The workpiece co-ordinate
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system for surface texture is based on the direction of the surface lay. A surface texture profile is measured perpendicular to the surface lay. The rest of the current GPS system uses a workpiece co-ordinate system that is based on the geometry of the workpiece. For example, a straightness profile is measured parallel to an edge of a face or parallel to an axis. The fundamental GPS principle, which can address this particular challenge, is the recognition that it is surfaces that interact with each other functionally, not profiles. Hence, the principal GPS definitions should be based on surfaces, with profile definitions as secondary simplified operators. Thus, the next generation GPS will be one system based on surfaces. Currently, the principal surface texture definitions are based on profiles [4-6]. Adoption of the next generation GPS will mean a paradigm shift for surface texture with areal surface metrology becoming the principal definition and profile surface texture a secondary simplified operator. It is envisioned that areal surface texture will be mainly used for research, diagnostics and function and that profile surface texture will still be the dominant approach for control of the production process.
13.2 The surface texture toolbox The full specification of surface texture has many stages: from the size, shape and location of the measuring window (partition), the sampling procedure (extraction), the scale of the features of interest (filtration) to the definition of the surface texture characteristic (measurand), see Figure 13.2. At each stage there are many choices to be made, depending on the design requirements of the surface to be specified. The challenge for the future is to standardise a set of tools for each stage that will enable optimisation of the design requirements and especially the functional requirements of a surface. The increasing demand for the manufacture of more precise parts at less cost and the improvement in technology has required more flexibility in surface texture standards. The toolbox approach to specifying surface texture provides this flexibility and will include already established tools as well as the development of new tools. For example, consider the filtration stage. Currently (2002), only the Gaussian filter is standardised in the GPS system [7]. ISO TC 213 set up Advisory Group Nine (AG9) to include investigation into possible filtration techniques that could be used as new filter tools for GPS. AG9 have recommended a toolbox of new and novel filter tools that include mean line filters, envelope filters, robust filters and techniques that decompose surface texture into different scale components. The recommended toolbox was developed to meet current and future GPS requirements in filtration. Further, all of the recommended filter tools in the filtration toolbox are applicable to surface texture. It is intended to publish the filtration toolbox as an ISO technical specification so GPS users can assess their utility first, before publication as a full standard.
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Figure 13.2 The duality principle which defines the relationship between specification and verification
133 Default rules In the past designers have not adequately specified their surface texture requirements but left many of the specification stages for others to specify. Ambiguities in specification, if left unresolved, can lead to very real economic problems. This is especially true in today's global economy where outsourcing of manufacturing can mean that the designers, production engineers and metrologists are not necessarily on the same site to clarify the ambiguities. Further one fundamental GPS principal, the duality principle, states that specification determines the verification (Figure 13.2). In other words, the tools and their values chosen in the specification should determine the tools and their values in the verification. This puts greater emphasis on the designers to adequately specify their design requirements and not to let the metrologists surmise which tools and values to use during verification. Thus each callout on technical documentation shall include all the relevant information for an unambiguous specification. To stop technical documentation becoming cluttered with long callouts, with all the relevant information for an unambiguous specification, the GPS system provides a mechanism to simplify callouts through default rules. A default rule is a standardised way to predetermine a specification tool with fixed values if not otherwise indicated in a callout. For example if only Rz=0.2^m was indicated in a surface texture callout then the default rules predetermined in ISO 4288 [5] would be used. Here there is a table and an iterative algorithm to determine the default filter cut-off values and evaluation length to use, dependent on the measured value of Rz.
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For surface texture, only default rules for surface roughness profile parameters currently exist [5]. The default rules for areal surface texture are still being debated and are part of a general discussion within ISO TC 213 on a generic approach to default rules. The default rules for surface texture (areal and profile) shall have to be consistent with the agreed generic default rules for the GPS system, though it is envisioned that any changes to the profile default rules will be minor, consisting of tightening up the mathematical definitions.
13.4 Comparison rules Comparison rules are used to compare a measured parameter value(s) with the specified value to check if it is within tolerance. The uncertainty of the measurement procedure is an important element of comparison rules. The tolerance zone, in which the measured value(s) must lie, may have to be modified to take into account the uncertainty. For profile surface texture parameters there are two standardised comparison rules [5]. The default comparison rule is called the 16% rule. Here 16% of the measured values taken in an (unspecified) neighbourhood around the place of "maximum roughness" on the surface are allowed to be larger than the specified tolerance value. The 16% rule modifies the tolerance zone to take into account the fact that for surface texture the largest uncertainty contributor for a measured parameter value is usually the variation of the parameter's value over the surface. The other comparison rule is called the max rule. Here all measured values taken on the surface under inspection shall be smaller than the specified tolerance value. The comparison rules for areal surface texture are still being debated, though it is envisioned that they will be the same, or very similar to, the profile comparison rules with any changes being very minor and consisting of tightening up the mathematical definitions.
13.5 Pattern analysis and structured surfaces The surface creation process (such as grinding, milling, turning, etching, rolling etc.) all leave their unique signatures in the surface texture of the surface. These signatures consist of various types of patterns on the surface with different creation processes forming different patterns. For surface texture the analysis and characterisation of these patterns can help with diagnostics of the surface creation process as well as with functional prediction and diagnostics. Many of the traditional surface creation processes (such as grinding, milling, turning etc.) leave stochastic patterns on the surface. Surface texture parameters that characterise the cloud of surface points, using statistical techniques, are called field parameters. Field parameters are quite good at characterising stochastic patterns. This is one reason why traditional profile parameters have been so successful in process monitoring traditional surface creation processes.
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Topography
Figure 13.3 A typical structured surface 1 x 1mm Improvement in technology, however, has resulted in optimised-engineered surfaces being increasingly used by industry to both increase functional performance and to lower costs. Many of these optimised-engineered surfaces leave highly distinctive structured patterns on the surface such as for example nominal square based abrasive pyramids (Trizact™) [8], see Figure 13.3. The definition of the structured surfaces was given by Evans and Bryan[8] as structured surfaces are those where the surface structure is a design feature intended to give a specific functional performance(e.g. retro-reflective pyramids in a road sign) These so-called structured textured patterns are becoming economically more and more important. For example 3M reported that in 2000 its microreplication process, used to produce structured surfaces, had grown into a $1 billion business [9]. Unfortunately, field parameters are not very good for characterising structured surfaces. Rather than characterising the required differences between features, characterisation using field parameter is dominated by the regular structure of the features. Its is becoming increasing clear that much development in the field of structured surfaces at both the micro and nano-scale will result in high aspect ratio, highly structured surfaces. Micro replication surfaces such as the 3M surfaces and very high aspect ratio surface features resulting from etching of silicon will represent a new challenge to surface metrologists. What is likely to result are hybrid techniques utilising feature extraction technology as well as techniques borrowed from the coordinate measuring machine world. It is envisaged that the analytical approach will be initially used to isolated the dominant features, recognise their standard geometry, and then finally perform a statistical analysis on the deviation from the idealised form of the structural elements within the surface. The information in all surface geometrical patterns is contained in the attributes of the individual pattern features and the structural relationships between these features.
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Thus, to extract this information the individual pattern features need first to be identified before characterisation. Care is need in extracting these features since the measurement process can produce many insignificant artificial features that swamp the subsequent pattern analysis. The stable extraction of significant surface features is discussed in detail in Chapter 3. Surface texture parameters that characterise feature attributes or the structural relationships between these features are called feature parameters. Feature parameters are much more diagnostic than field parameters. A medical analogy is useful to illustrate this point. Many field parameters such as Sq are analogous to taking a patient's temperature - a high temperature indicates that something is wrong but it could be anything from a cold to cancer. In contrast, characterising symptoms from the patient (sore throat, running nose, chest pains, shadow on a chest X-ray etc.) are diagnostic. Techniques to characterise structured surfaces are still being researched with some very promising novel ideas being developed [10]. It is envisioned that pattern analysis, through feature parameters, will become a very important tool for the future in the surface texture toolbox and this will be an essential requirement of precision and nanoscale metrology of high aspect ratio features such as those resulting from MEMs processes
13.6 Instrumentation There are many different types of instrumentation that measure surface texture, each using a different physical principle to interact with the "surface" (e.g. mechanical stylus, white light interferometry, scanning probe, capacitative, pneumatic etc.). The type of surface that results from a measurement depends on the nature of the species of the object that interacts with the "surface". Currently, the two most common are based on a mechanical stylus and light photons resulting in the "mechanical surface" and an "optical surface" respectively. By convention, in the next generation GPS system the default surface is the mechanical surface based on a rolling sphere [11], and hence mechanical stylus instrumentation (CMMs, contact stylus texture instruments, AFMs etc.) will remain the reference surface measurement method. This does not preclude other approaches from being used in practice. In fact, it is envisaged that though contact stylus instrumentation will remain the principal method for surface texture profile measurement, other true areal measuring systems, such as white light interferometry, will prevail in practice for areal surface texture measurement due to their speed of measurement, amongst other factors. Whichever exotic approach is used to measure a surface there is an important requirement to make that measurement traceable to international standards. Further, since the mechanical surface is the default surface if no other surface is specified there will be a need to relate the actual measurement surface back to the mechanical surface. Tracability of both hardware and software is very important, especially for outsourcing in a global economy. For only through tracability and the associated uncertainty calculations can different surface texture measurement instruments throughout the world hope to achieve compatible results. Traceability of hardware is
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currently achieved via certified calibration standards [12]. Calibration standards will need to be evolved to include areal calibration of surface texture instrumentation (see Chapter 6. Traceability of software will be achieved via certified softgauges and reference software [13], though here there is still much work to be done. A lot of future work, especially at national laboratories, will go into achieving global traceability. It is envisioned that there will be many international collaborative projects developing standardised procedures for traceability, especially for certified softgauges and reference software for areal surface texture.
13.7 Timetable of events As mentioned in the introduction, although the foundations for areal surface texture standardisation have been laid, there is still a lot of work to be carried out before international standardisation is finalised. The following presents a timetable of events leading to international standardisation of areal surface texture. Some events are historical, others are in the future: April 1990
Start of project " Development of Methods for the Characterisation of Roughness in Three Dimensions" under the leadership of Birmingham University.
April 1993
End of project "Development of Methods for the Characterisation of Roughness in Three Dimensions" under the leadership of Birmingham University.
Sept 1993
"Blue book" published [14] containing the Birmingham 14 Parameters.
May 1998
Start of SURFSTAND project under the leadership of Huddersfield University.
May 2001
End of SURFSTAND project under the leadership of Huddersfield University.
Jan 2002
SURFSTAND & AUTOSURF projects presentations to ISO/TC213 in Madrid, Spain.
June 2002
Surface texture taskforce set up by ISO/TC213 to determine requirements for standardisation of areal surface texture.
Jan 2003
ISO TC213 set up new Working Group WG16 to develop new surface texture system as part of GPS 2002.
2006
Publication of areal surface texture technical specification documents by ISO.
2007
Publication of areal surface texture standards documents by ISO.
2400
Dr Spock uses Taly-triquarter 2400 on the Enterprise to measure surface geometry characteristics of dilithium crystals.
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13.8 References [I] [2] [3] [4] [5] [6] [7] [8] [9]
[II] [12] 13] [14]
GPS Business plan http://l 29.142.8.149/isotc213/213business%20plan.pdf. ISO/TR 1463 8 Geometrical product specification - Masterplan (1995). ISO/TC 213 N 355 Annex 1 Next generation of the Geometrical Product Specifications (GPS) language, the vision for an improved engineering tool (2001). ISO 4287 Geometrical Product Specifications (GPS) - Surface texture: Profile method- Terms, definitions and surface texture parameters (1997). ISO 4288 Geometrical Product Specifications (GPS) - Surface texture: Profile method-Rules and procedures for the assessment of surface texture (1996). ISO 3274 Geometrical Product Specifications (GPS) - Surface texture: Profile method - Nominal characteristics of contact (stylus) instruments (1996). ISO 11562 Geometrical Product Specifications (GPS) - Surface texture: Profile method - Metrological characteristics of phase correct filters (1996). Evans, C.J. & Bryan, J.B. Structured, textured or engineered surfaces, Keynote Paper, Ann. CIRP 48 (2) (1999). 3M The one-billion-dollar lens, [10] Porrino A, Sacerdotti F, Visintin M, Benati F, "Applications of Gram-Schmidt Filtering technique to ElectronBeam-Textured Surfaces", Proceedings of the 17 Instrumentation and Measurement technology Conference, Baltimore (USA), May 2000, p 442446. ISO 14 406 (to appear) Geometrical Product Specifications (GPS) Extraction. ISO 5436-1 Geometrical Product Specifications (GPS) - Surface texture: Profile method; Measurement standards - Part 1: Material measures (2001). ISO 5436-2 Geometrical Product Specifications (GPS) - Surface texture: Profile method; Measurement standards - Part 2: Software measurement standards (2001). Stout, K.J. et. al. "The development of methods for the characterisation of roughness in three dimensions", Report EUR 15178 EN, EC Brussels, ISBN 0 704413132(1993).
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Index
16% rule 343 2B finish, stainless steel flat products on 239 characterisation of 239 2D profile filtering 65 regression filter 65, 67 2D and 3D dispersion in 216 parameters, comparison 206 roughness characterisation, full 249 surface roughness measurements 210 3D approach 7 characterisation, uncertainties in 216 functional surfaces, extraction 109 Gaussian regression form filter >nd order of 77 parameter study and, application of 85 morphological feature surfaces 110 parameters, 2D and comparison 206 plasticity index 250 dominant summits of 298 regression filter 72 n-th order 74 relevant surfaces 106 roughness characterisation, full 2D and 249 surface characterisation 1 et seq techniques, standardised 2D technique 197etseq filtering 72 metrology
automotive engine bore performance using 307 et seq topography, functional performance and 316 3D Gaussian regression form filter, 2nd order 77 3D techniques, standardised relationship with 2D surface characterisation techniques 197 et seq Abbott-Firestone curve 19 amplitude parameters 20 analysing filters 95 anodised extruded aluminium 58 areal characterisation technique, novel 43 et seq combination 48 material ratio curve parameters, linear 30 segment combination 48 arithmetic mean summit curvature 25 atomic force microscopes (AFM's) calibration lateral 184 procedures 175 et seq vertical 190 equipment, error sources measured using 175 auto-correlation length, fastest decay 24 automotive engine bore performance 3D surface metrology using 307 et seq industry 11 AUTOSURF 11 average roughness center line 6 surface 6
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Advanced Techniques for Assessment Surface Topography
ball bearing topography 215 beamlet concept 304 bearing ratio curve 19 surface application 333 bending-under-tension (BUT) test forming process 207 friction, correlation to 208 biomedical industry 12 bi-orthogonal wavelet 95, 100 first 95 second generation 100 Birmingham 14 parameters 17 blow-by 201 brick wall, linear phase 99 calibration horizontal drives 129 lateral, atomic force microscope 184 mode, mathematical study of 152 principle 144 procedures atomic force microscopes 175 et seq stylus, optical instrumentation and 119etseq specimen, ES1 tests of 136 three dimensions of the, synthesis of 135 type 2 instruments, type 1 and 127 vertical amplitudes 127 atomic force microscope of 190 CALISURF 11 cantilever relaxation time 180 centre line average roughness 6 change tree 48, 55, 304 pruning 55 system 304 circular groove 132,164,166 specimen with (ER3) 132 class space 44 closed path based definitions, local 50 separation 51 cold welding, galling behaviour and 259
component, functional performance, control of 43 contact measurement techniques, optical and 203 continuous data, critical points 50 contour lines 54 core material volume 33 roughness depth 32 void volume 33 cubic-spline wavelet 102 curve 19,30,35 Abbott-Firestone 19 bearing ratio 19 parameters, linear areal material ratio 30 related parameters 35 cylinder liner topography 198, 213 functionality and 198 database information, distribution of in network 330 DBS (draw bead simulator) multifrottement 269 test 265 multi-strip approach 249, 302 test 272, 273, 280 galling 280 procedure 272 default rules 342 developed interfacial area ratio 27 dominant summits 250 duality principle 342 dynamometers, engine tests 307 electronic surface profile 5 electronics, MEMS industry and 12 engine bore performance, automotive 3D surface metrology 307 et seq bores, functional testing 314 tests, dynamometers 307 engineering surfaces, description of 81 ER type standards 164 (ER3), specimen with circular groove 132 error sources, measured using AFM equipment 175 ES standards 166 ESI calibration specimen, tests of 136
Index
master 141 estimators, robust 84 Euler criterion 51 extraction sampling procedure 341 fastest decay auto-correlation length 24 feedback loop scan speed 179 field parameters 19,43 filter Gaussian advanced 63 et seq ISO 11562 63 regression form of 2nd order, 3D 77 parameter study, application of 85 zero order of 76 regression, 2D and 3D 65, 67, 72 filtering 3D regression 72 profile 2D 65 robust 70 techniques, robust 81 filters 63 et seq, 95 analysing 95 Gaussian, advanced 63 et seq filtration 221,341 numerical parameters and 221 flat-cylindrical tool set-up 251 die multifrottement 267 -flat tool 251 force detection system 178 form roughness, waviness and 3 surfaces, rough, wavy and 106 Fourier transform 92 fractal 29 dimension 29 parameter 29 fretting 226 friction, surface roughness parameters and 207 functional diagnostics 43 performance 3D surface topography and 316 component, of the 43 prediction 43 surfaces, extraction of 3D 109
351
testing, engine bores 314 Gabor transform 92 galling behaviour, cold welding and 259 severity 249 index (GSI) 289, 303 test DBS multi-strip 280 device 263 Gaussian filter filters, advanced 63 et seq ISO 11562 63 regression 81 3D, parameter study and application of 85 form, 2nd order of, 3D 77 zero order of 76 robust 82 geometrical product specifications and verification (GPS) system 339, 340 next generation 340 grinding wheel 57 ground surface, evaluation of 87 hard on hard bearings, wear ranking of 230 prosthetic hip joints 230 height maximum, topographic surface of the 22 reduced peak 32 valley 32 ten point, surface of the 29 horizontal drives, calibration of 129 hybrid parameters 25 image bow 177 insignificant events 49 instrument verification 119 Internet/World Wide Web 331 intersection plane/sphere, specimen 133,134 intranet 331 ISM surface texture knowledge support 325 et seq system 327 ISO 11562 Gaussian filter 63
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Advanced Techniques for Assessment Surface Topography
ISO 14460-1 1 Java-JDBC 333 journal bearings, machining assessment of 234 wavelet analysis 234 knowledge-based expert system 328 database 329 structure (expert) 329 kurtosis of topography height distribution 21 L12-design 253 lateral calibration, atomic force microscope 184 lattice data, critical points 51 least-squares ellipse 154,158 robust 158 light-section microscope 5 linear areal material ratio curve parameters 30 phase, brick wall 99 line-wise levelling 189 local closed path based definitions 50 located property 99 lowest valley of the surface 22 machining assessment, journal bearings of 234 wavelet analysis 234 manufacturing process, control of 43 et seq master certification 144 ESI 141 material/void volume parameters 32 matt finish femoral stems 221 max rule 343 measurand 341 measurement errors 120 techniques optical, contact and 203 MEMS industry, electronics and 12 metrology instrumentation industry 12 milled surface, evaluation of 86 mode switching 181 morphological
assessment, multi-scalar wavelets using 245 feature surfaces, 3D 110 multifrottement flat die 267 test 251,264 DBS 265 multi-scalar filtration methodologies 91 et seq wavelets morphological assessment using 245 orthopaedic implants using in vivo wear 243 named lifting factors 104 nominal surface 2 novel areal characterisation techniques 43 et seq n-th order, 3D regression filter 74 numerical parameters characterisation of topography 17 filtration and 221 etseq observable measurements 44 Ockham's Razor 47 oil consumption 201 optical instrumentation, stylus and calibration procedures 119 et seq instruments translation mechanisms driven by 120 interference 178 measurement techniques, contact and 203 optimol SRV 266, 271 orthogonality 177 orthopaedic implants, multi-scalar wavelets using 243 in vivo wear 243 parallel groove standard double net of 164, 166 two 164, 165 parameter fractal 29 S-, set 19,20 study, 3D Gaussian regression filter
Index
application of 85 V-, set 19,30 parameters 2D, 3D and comparison 206 amplitude 20 Birmingham 14, 17 curve related 35 field 19,43 hybrid 25 linear areal material ratio curve 30 material/void volume 32 numerical characterisation of topography 17 filtration and 221 et seq spacing 23 surface roughness friction and 207 relation to functional demands 197 valley depth 6 pattern analysis 44 neural 45 statistical 45 structured surfaces and 343 syntactic 45 generation 44 recognition 45 space 44 peak height 6 reduced 32 material component 32 volume 32 phase correct filter 64 pit 50 plane/sphere standard 166,167 plateau honed surface, evaluation of 87 profile filtering 70 2D 65 robust 70 profiles, individual processing of 146 profilometer 5 prosthetic hip joints 230 hard on hard bearings, wear ranking of 230
353
quality coefficient 156 real surface, workpiece of a 1 regression filter 3D 72 nth order 74 constants 90 form of 2nd order, 3D Gaussian 77 Gaussian 81 3D parameter study and, application of 85 robust 82 zero order of 76 remove point connected 51 ringing 180 root-mean-square deviation of the surface 20 slope, assessed topographic surface ofthe 27 surface roughness 6 rough, wavy, form surfaces and 106 roughness average centre line 6 surface 6 characterisation full 2D, 3D and 249 depth, core 32 measurements, 2D and 3D surface 210 parameters, surface friction and 207 relation to functional demands 197 surface, root-mean-square of 6 waviness, form and 3 running-in lengths 65 running-out lengths 65 saddle point 47, 50 scan speed 179 significant events 49 skewness of topography height distribution, Ssk 20 sliding velocity 258 slope-based definitions 50 spaced twin groove spaced specimen (ER1) 130 spacing parameters 23 S-parameter 19,20
354
Advanced Techniques for Assessment Surface Topography set 20
sphere/plane 148,166 intersection centre 148 standard 166 Sq, root-mean-square deviation of the surface 20 Ssk, skewness of topography height distribution 20 static noise 168 steel products, textured sheet functionality, characterisation of 249 et seq sheets, uncoated frictional study 207 sheet topography 211 measurement, functionality and 203 stainless, flat products 2B finish on, characterisation of 239 structured surfaces 12, 343 pattern analysis 343 stylus, optical instrumentation and 119 et seq calibration procedures 119 et seq sudden jumps 178 summits of the surface, density of 23 3D, characterisation 1 et seq techniques, standardised 2D techniques with 197 et seq application, bearing 333 creation 4 density of summits 23 filtering 3D 72 robust 79 ground, evaluation of 87 integrity 2 lowest valley of the 22 maximum height of the topographic 22 metrology 3D, automotive engine bore performance using 307 et seq future developments in 339 et seq milled, evaluation of 86 nature of 1
nominal 2 peak height, maximum 22 plateau honed, evaluation of 87 profile, electronic 5 real, workpiece of 1 root-mean-square deviation 20 slope of topographic 27 roughness average 6 measurements 2D,3Dand 210 parameters friction and 207 relation to functional demands 197 root-mean-square of 6 ten point height of the 29 texture 2 aspect ratio, surface of 24 knowledge support - ISM 325 et seq syntactical relational description 46 toolbox 341 topography 2, 221 3D, functional performance and 316 turned, evaluation of 86 wavelength, bandwidth of 18 SURFSTAND project 9 tactile instruments 119 test processing 168 texture aspect ratio, surface of the 24 direction 30 primitives, segmentation and 46 textured sheet steel products 249 et seq functionality, characterisation and 250 et seq thermal drift 177 three dimensional measurement processing of 145 test 140 three dimensions, calibration of synthesis of 135 TiN coated plates, wear of UHMWPE 227 tip 180
Index
/sample compression 180 shape 180 topographic surface assessed, root-mean-square slope 27 maximum height 22 topography ball bearing 215 characterisation of, numerical parameters 17 cylinder liner 213 functionality and 198 height distribution kurtosis of 21 skewness of 20 steel sheet 211 measurement, functionality and 203 surface 221 3D, functional performance and 316 translation mechanisms, optical instruments driven by 120 triangulation 53 tribological test rigs 263 turned surface, evaluation of 86 twin net, specimen with 131 type 2 instruments, type 1 and 127 calibration 127 UHMWPE, wear of 227 TiN coated plates 227
valley depth parameters 6 height, reduced 32 lowest, surface of the 22 void volume 34 verification tests 167 acceptance, periodical and 167 vertical amplitudes calibration of 127 calibration, atomic force microscope of 190 virtual 47 peak 47 pit 47
355
vivo wear, orthopaedic inplants, multiscalar wavelets using 243 void volume parameters, material 32 valley 34 volume core material 33 void 33 parameters, material/void 32 peak material 32 valley void 34 V-parameter set 19, 30 watershed merging 56 wavelet analysis 238 machining assessment, journal bearings of 234 bi-orthogonal first 95 second generation 100 cubic-spline 102 prototype 93 theory 92 wavelets, multi-scalar 243, 245 morphological assessment using 245 orthopaedic implants using in vivo wear 243 waviness, roughness, form and 3 wavy, rough, form surfaces and 106 wear 202, 227, 230, 243 in vivo orthopaedic implants, multi-scalar wavelets using 243 ranking, hard on hard bearings of prosthetic hip joints 230 UHMWPE, of TiN coated plates 227 Wigner distribution 92 Wigner-Ville distribution 92 Wolf pruning 55 workpiece, real surface of 1 World Wide Web/Internet 331
