Sandy Suet To · Hao Wang
`Wing Bun Lee
`Materials
`Characterisation and
`Mechanism of Micro-
`Cutting in Ultra-Precision
`Diamond Turning
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`Materials Characterisation and Mechanism
`of Micro-Cutting in Ultra-Precision
`Diamond Turning
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`Sandy Suet To (cid:129) Hao Wang
`Wing Bun Lee
`
`Materials Characterisation
`and Mechanism
`of Micro-Cutting
`in Ultra-Precision
`Diamond Turning
`
`123
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`Sandy Suet To
`The Hong Kong Polytechnic University
`Hong Kong
`China
`
`Wing Bun Lee
`The Hong Kong Polytechnic University
`Hong Kong
`China
`
`Hao Wang
`National University of Singapore
`Singapore
`Singapore
`
`ISBN 978-3-662-54821-9
`DOI 10.1007/978-3-662-54823-3
`
`ISBN 978-3-662-54823-3
`
`(eBook)
`
`Library of Congress Control Number: 2017939305
`
`© Springer-Verlag GmbH Germany 2018
`This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
`of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
`recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
`or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
`methodology now known or hereafter developed.
`in this
`trademarks, service marks, etc.
`The use of general descriptive names, registered names,
`publication does not imply, even in the absence of a specific statement, that such names are exempt from
`the relevant protective laws and regulations and therefore free for general use.
`The publisher, the authors and the editors are safe to assume that the advice and information in this
`book are believed to be true and accurate at the date of publication. Neither the publisher nor the
`authors or the editors give a warranty, express or implied, with respect to the material contained herein or
`for any errors or omissions that may have been made. The publisher remains neutral with regard to
`jurisdictional claims in published maps and institutional affiliations.
`
`Printed on acid-free paper
`
`This Springer imprint is published by Springer Nature
`The registered company is Springer-Verlag GmbH Germany
`The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
`
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`Preface
`
`Ultra-precision single point diamond turning is a key technology in the manufacture
`of mechanical, optical and optoelectronics components with a surface roughness of
`a few nanometres and form accuracy in the sub-micrometric range. As a type of
`subtractive manufacturing, ultra-precision diamond turning technology was estab-
`lished on the pillars of materials science, machine tools, modelling and simulation
`technologies, etc., bestowing the intrinsic inter-disciplinary characteristics upon the
`study of such machining process. However, in contrast to the substantial advances
`that have been achieved in machine design, laser metrology and control systems,
`relatively little research has been conducted on material behaviour and its effect on
`surface finish, such as the material anisotropy of crystalline materials. The feature
`of the significantly reduced depth of cut of the order of a few micrometres or less,
`which is much smaller than the average grain size of work-piece materials,
`unavoidably renders the existing metal cutting theories to have only partial success
`in the investigation of the mechanism of the micro-cutting process in ultra-precision
`diamond turning. With such a background, this book is dedicated to an in-depth
`study and elucidation on the mechanism of the micro-cutting process, with a par-
`ticular emphasis and a novel viewpoint on materials characterisation and its
`influences in ultraprecision machining.
`This book probes into the two critical problems in ultra-precision diamond
`turning, i.e. materials characterisation and the mechanism of micro-cutting, and
`contributes to the development of metal cutting theory for ultraprecision diamond
`turning. As for the organisation of the book: In Chap. 1, an overview of
`ultra-precision machining technology and ultraprecision diamond turning is elab-
`orated with the existing metal cutting theory tailor-made for conventional and
`precision machining and its unsolved problems. A detailed literature review on a
`variety of hot research topics in ultraprecision machining is presented in Chap. 2,
`which takes account of material characteristics and machinability, the mechanism of
`metal cutting, the dynamics of machine tools, surface generation and characteri-
`sation, modelling techniques, etc. This book began to unfold from the investigation
`on the machinability of single crystals in diamond turning in Chap. 3. The effect of
`crystallography on surface roughness and the variation in cutting force is studied by
`
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`vi
`
`Preface
`
`the degree of roughness anisotropy (DRA) factor. The study of machined surface
`integrity and the deformation behaviour of diamond-turned surface layer is pre-
`sented in Chap. 4, followed by the orientation changes of substrate materials that
`are characterised by X-ray texture study in Chap. 5. A novel technology involving
`electropulsing treatment (EPT) is explored to enhance the machinability of work
`materials in Chap. 6. A microplasticity analysis of shear angle and micro-cutting
`force variation is provided in Chap. 7. In Chap. 8, the mechanism of elastic strain
`induced shear bands and regularly space shear bands are presented and a gener-
`alised model for shear angle prediction is developed. In the final part of this book
`(Chap. 9), the high frequency tool-tip vibration and its effect on surface generation
`as well as the representative surface measurement method are presented. The
`integrated dynamic modelling of shear band formation and tool-tip vibration is
`elaborated in Chap. 10.
`This book serves as a practical tool for investigating materials characterisation in
`ultra-precision machining with carefully documented experimental techniques and
`analytical methodology accumulated over the years through the authors’ research
`endeavours. This book contributes to enhancing the understanding of the metal
`cutting theory of ultraprecision diamond turning from the perspective of materials
`science and machining dynamics. The multidisciplinary work in this book also
`covers the modelling approaches based on the theory of microplasticity.
`The authors would like to thank the Research Committee and the Department of
`Industrial and Systems Engineering of The Hong Kong Polytechnic University and
`the Department of Mechanical Engineering, Faculty of Engineering, National
`University of Singapore for providing the financial support for this book. Many
`thanks are extended to the Guangdong Innovative Research Team Program and the
`National Natural Science Foundation of China for providing the partial financial
`support under the Project Nos. 201001G0104781202 and 51275434 respectively.
`
`Hong Kong, China
`Singapore
`
`Sandy Suet To
`Hao Wang
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`Contents
`
`Part I Fundamentals
`
`1
`
`2
`
`Single Point Diamond Turning Technology. . . . . . . . . . . . . . . . . . . .
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`Factors Influencing Machined Surface Quality . . . . . . . . . . . . . . . . .
`2.1 Machine Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.2 Vibration in Machining. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.3 Cutting Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.4 Single Point Diamond Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.5 Environmental Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.6 Workpiece Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2.7 Deformation Behaviour of Materials in Machining. . . . . . . . . . . .
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`3 Modelling and Simulation for Ultra-Precision Machining . . . . . . . .
`3.1 Analytical and Numerical Methods for Machining Process
`Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.1.1 Slip-Line Field Modelling of Machining . . . . . . . . . . . . . .
`3.1.2 Molecular Dynamics Simulation of Machining . . . . . . . . .
`3.1.3 Quasicontinuum (QC) Method . . . . . . . . . . . . . . . . . . . . .
`3.1.4 Meshfree Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.1.5 Discrete Element Method . . . . . . . . . . . . . . . . . . . . . . . . .
`3.1.6 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2 Models of Chip Formation and Shear Bands Theory . . . . . . . . . .
`3.2.1 The Chip Formation Process and Models
`in Metal Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2.2 Shear Band Formation and Chip Morphology. . . . . . . . . .
`3.2.3 The Shear Angle Relationship. . . . . . . . . . . . . . . . . . . . . .
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`3
`6
`
`7
`7
`8
`9
`11
`12
`13
`15
`17
`
`21
`
`21
`21
`22
`23
`24
`26
`27
`29
`
`29
`32
`34
`35
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`viii
`
`Contents
`
`Part II Materials Characterisation in Ultra-Precision
`DiamondTurning
`
`4 Machinability of Single Crystals in Diamond Turning . . . . . . . . . . .
`4.1 Key Aspects in Diamond Turning of Single Crystals . . . . . . . . . .
`4.1.1 The Ultra-Precision Machine. . . . . . . . . . . . . . . . . . . . . . .
`4.1.2 Diamond Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.1.3 Measurement of Surface Roughness . . . . . . . . . . . . . . . . .
`4.1.4 Measurement of Cutting Force . . . . . . . . . . . . . . . . . . . . .
`4.1.5 Work Materials and Cutting Conditions . . . . . . . . . . . . . .
`4.2 Effect of Crystallography on Surface Roughness . . . . . . . . . . . . .
`4.2.1 Surface Features with Crystallographic Orientation . . . . . .
`4.2.2 Surface Roughness Profiles Along Radial Sections . . . . . .
`4.2.3 Degree of Roughness Anisotropy (DRA) . . . . . . . . . . . . .
`4.3 Variation of Cutting Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`4.3.1 Effect of Feed Rate on the Cutting Force . . . . . . . . . . . . .
`4.3.2 Effect of Depth of Cut on the Cutting Force . . . . . . . . . . .
`4.4 Observation on Chip Formation . . . . . . . . . . . . . . . . . . . . . . . . . .
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`43
`43
`43
`43
`46
`50
`50
`52
`52
`56
`57
`59
`59
`60
`61
`68
`
`71
`71
`71
`73
`76
`77
`79
`79
`
`5 Materials Deformation Behaviour and Characterisation . . . . . . . . .
`5.1 Techniques for Materials Characterisation . . . . . . . . . . . . . . . . . .
`5.1.1 X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.1.2 Nano-indentation Measurements . . . . . . . . . . . . . . . . . . . .
`5.1.3 Nanoscratch Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.1.4 Transmission Electron Microscopy (TEM) . . . . . . . . . . . .
`5.2 Characterisation of the Diamond-Turned Surface Layer . . . . . . . .
`5.2.1 X-ray Diffraction Line Profile Analysis . . . . . . . . . . . . . . .
`5.2.2 Microhardness and Elastic Modulus
`of Machined Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2.3 Friction Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2.4 Dislocation Density and Structure of Diamond-Turned
`82
`Surface Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`89
`5.3 Influences of Material Swelling upon Surface Roughness. . . . . . .
`89
`5.3.1 Materials Swelling Effect . . . . . . . . . . . . . . . . . . . . . . . . .
`5.3.2 Characterisation Techniques . . . . . . . . . . . . . . . . . . . . . . .
`95
`5.3.3 Formation of Surface Roughness in Machining. . . . . . . . . 101
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
`
`79
`81
`
`6 Material Electropulsing Treatment and Characterisation
`of Machinability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
`6.1 Basics of Electropulsing Treatment. . . . . . . . . . . . . . . . . . . . . . . . 106
`6.1.1 Development of Electropulsing Treatment. . . . . . . . . . . . . 106
`6.1.2 Theory of Electropulsing Treatment . . . . . . . . . . . . . . . . . 106
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`
`6.2 Effect of Electropulsing Treatment
`on Microstructural Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
`6.2.1 Technical Aspects of Electropulsing Treatment . . . . . . . . . 112
`6.2.2 Phase Transformation and Microstructural Changes . . . . . 116
`6.2.3 Dislocation Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
`6.2.4 Driving Forces for Phase Transformations . . . . . . . . . . . . 129
`6.2.5 Electropulsing Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
`6.3 Machinability Enhancement by Electropulsing Treatment. . . . . . . 131
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
`
`7 Microplasticity Analysis for Materials Characterisation. . . . . . . . . . 147
`7.1 Shear Angle and Micro-Cutting Force Prediction . . . . . . . . . . . . . 147
`7.1.1 Microplasticity Model for Shear Angle Prediction . . . . . . 147
`7.1.2 Texture Softening Factor. . . . . . . . . . . . . . . . . . . . . . . . . . 151
`7.1.3 Criterion for Shear Angle Prediction . . . . . . . . . . . . . . . . . 154
`7.1.4 Prediction of Micro-Cutting Forces Variation . . . . . . . . . . 156
`7.2 Variation in Shear Angle and Cutting Force. . . . . . . . . . . . . . . . . 159
`7.2.1 Shear Angle Predictions and Experimental Methods . . . . . 160
`7.2.2 Power Spectrum Analysis of Cutting Force. . . . . . . . . . . . 168
`7.3 Microstructual Characterisation of Deformation Banding . . . . . . . 175
`7.3.1 Typical Cutting-Induced Shear Band. . . . . . . . . . . . . . . . . 175
`7.3.2 Orthogonal Cutting-Induced Kink Band . . . . . . . . . . . . . . 177
`7.3.3 Cutting Induced Kinking Within the Sliding Region. . . . . 179
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
`
`Part III Theory and Mechanism of Ultra-Precision Diamond Turning
`
`8
`
`Shear Bands in Ultra-Precision Diamond Turning . . . . . . . . . . . . . . 189
`8.1 Shear Band Theory for Deformation Processes in Machining. . . . 189
`8.2 Regularly Spaced Shear Bands and Morphology
`of Serrated Chips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
`8.3 Finite Element Method Modelling for Elastic Strain-Induced
`Shear Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
`8.3.1 Characterisation of Elastic Strain-Induced Shear Bands . . . 197
`8.3.2 Finite Element Method Modelling. . . . . . . . . . . . . . . . . . . 198
`8.4 Analytical Model of Shear Band Formation and Influences . . . . . 207
`8.4.1 Onset of the Formation of Shear Bands . . . . . . . . . . . . . . 208
`8.4.2 Formation of Shear Bands. . . . . . . . . . . . . . . . . . . . . . . . . 210
`8.4.3 An Analytical Model of Cyclic Fluctuation
`of Cutting Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
`8.4.4 The Cyclic Fluctuation of the Displacement
`of the Tool Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
`8.5 Generalised Shear Angle Model . . . . . . . . . . . . . . . . . . . . . . . . . . 215
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
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`9
`
`Contents
`
`Tool-Tip Vibration at High Frequencies . . . . . . . . . . . . . . . . . . . . . . 219
`9.1 Identification of Tool-Tip Vibration
`by Power Spectrum Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
`9.2 Characteristic Twin Peaks and Material Properties . . . . . . . . . . . . 221
`9.3 Modelling of Tool-Tip Vibration . . . . . . . . . . . . . . . . . . . . . . . . . 226
`9.3.1 An Impact Model Without Damping. . . . . . . . . . . . . . . . . 226
`9.3.2 Non-harmonic Periodic Excitation with Process
`Damping Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
`9.4 Representative Measurement Method . . . . . . . . . . . . . . . . . . . . . . 234
`9.4.1 Influence of Tool-Tip Vibration
`on the Machined Surface. . . . . . . . . . . . . . . . . . . . . . . . . . 234
`9.4.2 Effect of Sample Locations on Surface Roughness . . . . . . 240
`9.4.3 Effect of Sample Area Ratios and Representative
`Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
`9.5 Modelling and Characterisation of Surface Roughness
`Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
`9.5.1 Surface Generation Model with Tool-Tip Vibration . . . . . 246
`9.5.2 Formation of Spiral Marks on the Machined Surface . . . . 248
`9.5.3 Spatial Error on the Profile in the Feed Direction . . . . . . . 250
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
`
`10 Dynamic Modelling of Shear Band Formation and Tool-Tip
`Vibration in Ultra-Precision Diamond Turning . . . . . . . . . . . . . . . . 253
`10.1 A Transient Analysis for Shear Band Formation . . . . . . . . . . . . . 256
`10.2 Dynamic Model for Shear Band Formation . . . . . . . . . . . . . . . . . 257
`10.2.1 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
`10.2.2 The Effect of Equivalent Cutting Velocity . . . . . . . . . . . . 259
`10.2.3 Validation and Application . . . . . . . . . . . . . . . . . . . . . . . . 260
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
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`Part I
`Fundamentals
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`Chapter 1
`Single Point Diamond Turning Technology
`
`Abstract Manufacturing with high precision is a development which has been
`gathering momentum over the last 200 years and accelerating over the last 30 years
`in terms of research, development and applications in product innovation. It has
`been driven by demands for much higher performance of products, higher relia-
`bility, longer life and miniaturisation. This development is widely known as pre-
`cision engineering and today is generally understood as manufacturing to tolerances
`smaller than one part in 104 or perhaps one part in 105. This chapter profiles the
`categorisation of machining processes with a highlight on the ultra-precision single
`point diamond turning technology.
`
`Trent and Wright (2000) definition defines the term machining as chip-forming
`operations in the engineering industry, ranging from large-scale production to
`extremely delicate components (Fig. 1.1). In terms of achievable tolerance and part
`dimensions, machining processes can be categorised into normal machining, pre-
`cision machining and ultra-precision machining, corresponding to specific indus-
`trial and/or scientific applications.
`“Ultra-precision machining” means the achievement of dimensional tolerance of the
`order of 0.01 lm and surface roughness of 0.001 lm (1 nm). The dimensions of parts or
`elements of parts produced may be as small as 1 lm and the resolution and repeatability
`of the machines used must be in the order of 0.01 lm (10 nm) (Taniguchi 1983). These
`accuracy targets for today’s ultra-precision machining cannot be achieved by a simple
`extension of conventional machining process and techniques. Satisfying such high
`accuracy is one of the most important challenges facing the manufacturing engineering
`today. In fact, we have seen the development and introduction into practice of a whole
`new range of materials processing technologies for the manufacture of parts to this
`order of accuracy. A comprehensive review of the elements of machine tools, e.g.
`guideway bearings, displacement
`transducers/measuring equipment and servo-
`positioning techniques has been given by Taniguchi (1983) (Fig. 1.2).
`The history of single point diamond turning (SPDT) technology started in the
`1960s. In the early stages, SPDT was usually used to produce components with
`simple cylindrical or flat shapes to meet the demands of computers, electronics and
`
`© Springer-Verlag GmbH Germany 2018
`S.S. To et al., Materials Characterisation and Mechanism of Micro-Cutting
`in Ultra-Precision Diamond Turning, DOI 10.1007/978-3-662-54823-3_1
`
`3
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`4
`
`1 Single Point Diamond Turning Technology
`
`Fig. 1.1 Relationship between part dimension and dimensional tolerance for three groups of
`machining processes (Trent and Wright 2000)
`
`Fig. 1.2 The development of achievable accuracy (after Taniguchi 1983)
`
`defence applications. Typical products were disks for computer memory systems.
`The pioneering work led by Bryan et al. (1967) was carried out in its application to
`optical components of complex forms at
`the Lawrence Livermore National
`Laboratory USA (Taniguchi 1983; Ikawa et al. 1991). The rapid development of
`diamond turning technology emerged in the USA and the UK in the 1970s.
`A high-quality mirror with a surface roughness 0.01 lm Rmax and with a profile
`accuracy of about 0.1 lm was achieved. In the 1970s, the technique was applied to
`the production of a variety of optical components for its high precision, versatility and
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`1 Single Point Diamond Turning Technology
`
`5
`
`low overall manufacturing cost. In the 1980s, the technique was extended to indus-
`trial use for the manufacturing of aluminium scanner mirrors, aluminium substrate
`drums in photocopying machines and aluminium substrates for computer memory
`disks, all of which require very fine surface finish of a few tens of nanometres
`roughness and micrometre to submicrometre form accuracy (To and Lee 1995; To
`et al. 2006a, b, c, 2007, 2008, 2013, 2015a, 2015b; To and Wang 2011). These
`extensive efforts have resulted in the development of highly advanced machine tools
`with sophisticated metrology and the control of diamond tools of reliable quality.
`Summaries of the machine tools developed for ultra-precision metal cutting research
`and manufacturers of the early complex components, together with the builders of
`ultraprecision machine tools are given by Taniguchi (1983) and McKeown (1997).
`Ultra-precision diamond cutting critically depends on a number of highly developed
`“subsystem” techniques, e.g. the machine tool, metrology and control, cutting tool,
`environmental control and machining strategies and software. A collection of rep-
`resentative SPDT machines at different development stages is shown in Fig. 1.3. The
`critical factors associated with ultra-precision diamond turning which directly affect
`the nanosurface generation are discussed in the forthcoming chapter.
`
`Fig. 1.3 From top left anticlockwise: ca 1975 Moore M18 DTM, Cranfield LDTM (1979),
`Cranfield NION DTM (1989) and Moore 500FG (1999). Courtesy of Moore, CUPE, CPE Ltd and
`Moore Nanotechnology Systems (reprinted from the work by Shore and Morantz 2012)
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`6
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`References
`
`1 Single Point Diamond Turning Technology
`
`Bryan, J. B., Clauser, R. W., & Holland, E. (1967). Spindle accuracy. American Machinist, 4, 149.
`Ikawa, N., Donaldson, R. R., Komanduri, R., König, W., Aachen, T. H., McKeown, P. A., et al.
`(1991). Ultraprecision metal cutting—the past, the present and the future. Annals of the CIRP,
`40, 587–594.
`McKeown, P. A. (1997). From precision to micro and nano-technologies. Nanotechnology,
`UNIDO Emerging Technology Series (p. 1).
`Shore, P., & Morantz, P. (2012). Ultra-precision: enabling our future. Philosophical Transactions
`of the Royal Society A, 370, 3993–4014.
`Taniguchi, N. (1983). Current status in, and future trends of, ultraprecision machining and ultrafine
`materials processing. Annals of the CIRP, 32(2), 573.
`To, S., & Lee, W. B. (1995). A study of the surface microtopography of aluminium alloys in
`single point diamond turning. America Society of Precision Engineering (ASPE) (pp. 124)
`(October 15–20).
`To, S., & Wang, H. (2011). Finite element modelling of squeezing effect in ultra precision
`diamond turning. Materials Research Innovations, 15(suppl. 1), S175–S178.
`To, S., Wang, E. Q., Lee, W. B., & Cheung, C. F. (2006a). A study of a digital manufacturing
`procedure for freeform optics. Materials Science Forum, 532–533, 693–696.
`To, S., Wang, E. Q., Lee, W. B., & Cheung, C. F. (2006b). Investigation into virtual
`manufacturing procedure for freeform optics. Journal of Applied Optics, 27(6), 485–490.
`(in Chinese).
`To, S., Wang, E. Q., Lee, W. B., & Cheung, C. F. (2007). Investigation on error factor of injection
`molding plastic for freeform optics. Journal of Applied Optics, 28(6), 684–688. (in Chinese).
`To, S., Wang, H., Li, B., & Cheung, C. F. (2008). An empirical approach for identification of
`sources of machining errors in ultra-precision raster milling. Key Engineering Materials,
`364–366, 986–991.
`To, S., Wang, H., Li, B., Cheung, C. F., & Wang, S. J. (2006c). Study on the tool path generation
`of an automotive headlamp reflector in ultra-precision raster milling. Materials Science Forum,
`532–533, 673–676.
`To, S., Wang, H., & Jelenkovićz, E. V. (2013). Enhancement of the machinability of silicon by
`hydrogen ion implantation for ultra-precision micro-cutting. International Journal of Machine
`Tools and Manufacture, 74, 50–55.
`To, S., Zhu, Z. W. & Wang, P. (2015a). Evolutionary diamond turning of optics for error
`correction covering a wide spatial spectrum. Optical Engineering, 54, No. 1, paper no. 015103.
`To, S., Zhu, Z. W. & Zeng, W. H. (2015b). Novel end-fly-cutting-servo system for deterministic
`generation of hierarchical micro–nanostructures. CIRP Annals - Manufacturing Technology,
`64, Issue 1, pp. 133–136.
`Trent, E. M. & Wright, P. K. (2000). Metal cutting, 4th edn (pp. 98–102).
`
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`Chapter 2
`Factors Influencing Machined
`Surface Quality
`
`Abstract Ultra-precision diamond turning aims at producing advanced compo-
`nents with not only a high-dimensional accuracy but also a good surface roughness
`and form accuracy. Since the achievable machining accuracy is governed by the
`accuracy of the relative motion between the cutting edge and the workpiece, the
`performance of machine tools is of prime importance. Optimum conditions of
`factors such as machine tools, cutting tools, workpiece materials, cutting variables,
`cutting fluid, working environment, etc., need to be chosen to achieve a good result
`in diamond turning. This chapter elaborates all these key factors influencing the
`machined surface finish.
`
`2.1 Machine Tools
`
`In diamond turning, as in any metal cutting operation, the geometry of the cutting
`tool and the characteristics of the machine tool determine the achievable form
`accuracy and surface finish. Improvements in surface finish and form accuracy in
`diamond turning have depended mainly upon advances in the design of the machine
`tool. In the early stages of development of ultra-precision cutting, hydrostatic
`bearings (either gas or fluid) for machine tool spindles played a dominating role
`through their ability to operate at submicron rotational accuracy. The development
`of air bearing spindles in the 1960s most significantly affected progress in ultra-
`precision machining (Krauskopf 1984; Ikawa et al. 1991). The introduction of
`machine tools with high stiffness, laser position feedback, hydrostatic slideways,
`materials with high thermal stability and techniques to characterise machine tool
`errors have also improved the diamond turning process. Along with the refinement
`of conventional mechanical elements in machine tools, new designs have arisen;
`traction or friction drives for linear motion and positioning with nanometric reso-
`lution (Bryan 1979; Donaldson and Patterson 1983; Shimokohbe et al. 1989),
`piezoelectric microfeed devices for nanometric tool positioning (Patterson and
`Magrab 1985) and the error compensation of hydrostatic bearings (Kanai 1983;
`Shimokohbe et al. 1989).
`
`© Springer-Verlag GmbH Germany 2018
`S.S. To et al., Materials Characterisation and Mechanism of Micro-Cutting
`in Ultra-Precision Diamond Turning, DOI 10.1007/978-3-662-54823-3_2
`
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`2 Factors Influencing Machined Surface Quality
`
`2.2 Vibration in Machining
`
`For decades, vibration has been recognised in the force measurement of real cutting
`processes such as conventional machining, high-speed machining (HSM) and
`ultra-precision machining. Based on these vibration signals, a branch of research
`work focused on the sources of nonlinearities and chatter generation, in which the
`single-degree-of-freedom (SDOF) and the multi-degree-of-freedom (MDOF)
`dynamic models of cutting system are employed. Such models are capable of
`determining the stability of the cutting system, i.e. the transition between stable
`cutting and chatter vibration with regard to the change of cutting parameters, such
`as depth of cut and spindle speed (Wiercigroch and Budak 2001). The starting
`points of such dynamic models are the nonlinearities in metal cutting systems.
`Early work in such area was done by Wu (1986) to model the shear angle
`oscillation in dynamic orthogonal cutting based on the work-hardening slip line
`field theory. Wiercigroch and Budak (2001) proposed a closed-loop model of
`dynamic and thermodynamic interaction in the metal cutting system. They inves-
`tigated the four mechanisms of machining chatter: variable friction, regenerative
`cutting, mode coupling, and the thermomechanics of chip formation on the varia-
`tion of shear angles in the course of machining. Moon and Kalmar-Nagy (2001)
`reviewed the prediction of complex, unsteady and chaotic dynamics associated with
`the material cutting process through nonlinear dynamical models. The developed
`dynamic models of cutting systems have been widely applied in the prediction and
`monitoring of system stability (Liu et al. 2004b; Schmitz et al. 2001; Khraisheh
`et al. 1995; Chae et al. 2006; Berger et al. 1998). Complex mathematical tools have
`been employed to establish the nonlinear models, such as Receptance Coupling
`Substructure Analysis (RCSA) (Schmitz et al. 2001), and wavelet decomposition
`(Berger et al. 1998). Khraisheh et al. (1995) used wavelet transform with the
`traditional Gaussian wavelet, phase plane, power spectrum, Poincaré map and
`fractal dimensions to analyse the experimental data to ascertain system stability and
`cutting status. Vela-Martinez et al. (2008) used a multiple degree of freedom model
`for chatter prediction in turning. Abouelatta and Madl (2001) used a regression
`method to find a correlation between surface roughness and cutting vibrations in
`turning, while Baker and Rough (2002) used the finite element method (FEM) to
`include both cutting tool and workpiece flexibility in the analysis.
`The correlation between vibration and surface roughness has become another
`focus of research. Abouelatta and Madl (2001) employed a mathematical tool to
`analyse the vibration and surface roughness data obtained in a series of cutting
`experiments. The proposed correlation model did not take account of the material
`removal mechanism in metal cutting process; therefore, no physical model was
`sought to explain the vibration effect on surface roughness of the machined surface.
`Cheung and Lee (2000a, b) proposed a surface roughness simulation model which
`considered the effect of process parameters, tool geometry and relative vibration
`between the tool and the workpiece. The authors assumed that the relative vibration
`between the tool and the workpiece was a steady simple harmonic motion with
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`small amplitude and a low frequ