Computational Surface and Roundness Metrology

By: Balasubramanian Muralikrishnan, Jayaraman Raja

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Hardcover | 1 October 2008

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Hardcover
284 Pages

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23.39 x 15.6 x 1.75

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"Computational Surface and Roundness Metrology" provides an extraordinarily practical and hands-on approach towards understanding the diverse array of mathematical methods used in surface texture and roundness analysis. The book, in combination with a mathematical package or programming language interface, provides an invaluable tool for experimenting, learning, and discovering the many flavors of mathematics that are so routinely taken for granted in metrology. Whether the objective is to understand the origin of that ubiquitous transmission characteristics curve of a filter we see so often yet do not quite comprehend, or to delve into the intricate depths of a deceptively simple problem of fitting a line or a plane to a set of points, this book describes it all (in exhaustive detail). From the graduate student of metrology to the practicing engineer on the shop floor, this book is a must-have reference for all involved in metrology, instrumentation/optics, manufacturing, and electronics.

Industry Reviews

Computational Surface and Roundness Metrology can be used for final-year undergraduate engineering courses (for example, manufacturing, mechanical, etc.) or as a subject on manufacturing at postgraduate level. Also, this book can serve as a useful reference for academics, manufacturing researchers, mechanical and manufacturing engineers, and professionals in related industries with manufacturing, quality, and surface and roundness metrology.

J. Paul Davim (from the International Journal of Mechatronics and Manufacturing Systems)

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Notation	p. xix
Introduction	p. 1
Surface and Roundness Metrology	p. 1
Scope and Objectives	p. 1
Organization	p. 3
References	p. 4
Filtering
A Brief History of Filtering	p. 7
Introduction	p. 7
Electrical Filters	p. 7
Digital Filters	p. 8
The Envelope Method	p. 8
The Gaussian Filter	p. 8
Overlap of Measurement Techniques	p. 9
Recent Advances in Filtering	p. 9
Summary	p. 10
References	p. 10
Filtering in the Frequency Domain	p. 13
Surface Wavelengths	p. 13
Fourier Transform, Discrete Fourier Transform, and Fast Fourier Transform	p. 14
Filtering in the Frequency Domain	p. 16
Wrap-Around Effect	p. 19
Amplitude Transmission and Phase Characteristics	p. 19
Summary	p. 20
Exercises	p. 20
References	p. 21
Filtering in the Time Domain	p. 23
Filtering as an Averaging Process	p. 23
Relationship Between Frequency-Domain and Time-Domain Filtering	p. 26
Filtering Profiles: Putting It All Together	p. 27
Summary	p. 29
Exercises	p. 30
References	p. 31
Gaussian Filter	p. 33
Introduction	p. 33
High-Pass and Low-Pass Filters	p. 35
Roughness, Waviness, and Form Using the Gaussian Filter	p. 35
Effect of Cutoff	p. 36
Phase Characteristics	p. 36
Summary	p. 37
Exercises	p. 37
References	p. 38
The 2RC Filter	p. 39
Introduction	p. 39
The 2RC High-Pass Filter	p. 39
More on the 2RC Filter	p. 42
Comparison of the 2RC and Gaussian Filters	p. 44
Summary	p. 44
Exercises	p. 45
References	p. 46
Filtering Roundness Profiles	p. 47
Introduction	p. 47
Gaussian Filter for Roundness	p. 47
Amplitude Transmission Characteristics	p. 49
Filtering Roundness Profiles in the Time Domain	p. 50
Circular Convolution in the Frequency Domain	p. 50
Summary	p. 52
Exercises	p. 52
References	p. 53
Filtering 3D Surfaces	p. 55
Areal Surface Texture Analysis	p. 55
2D Convolution	p. 55
Gaussian Filter in 3D	p. 56
A Note on Indices	p. 56
Frequency-Domain Filtering in 3D	p. 59
Summary	p. 62
Exercises	p. 62
References	p. 63
Advanced Filtering	p. 67
Gaussian Regression Filters	p. 67
Introduction	p. 67
Zero-Order Gaussian Regression Filter	p. 68
Second-Order Gaussian Regression Filter	p. 71
3D Zero-Order Gaussian Regression Filter	p. 73
3D Second-Order Gaussian Regression Filter	p. 74
Summary	p. 75
Exercises	p. 75
References	p. 76
Spline Filter	p. 77
Introduction	p. 77
Amplitude Transmission Characteristics	p. 78
Implementation of the Non-periodic Spline Filter	p. 79
Implementation of the Periodic Spline Filter	p. 82
Summary	p. 86
Exercises	p. 86
References	p. 86
Robust Filters	p. 87
Rk Filter	p. 87
Robust Gaussian Regression Filter	p. 90
Summary	p. 91
Exercises	p. 92
References	p. 92
Envelope and Morphological Filters	p. 93
Envelope Filters	p. 93
Stylus Tip Convolution	p. 94
Morphological Filters	p. 96
A Word on the Fundamentals	p. 98
3D Morphological Filtering	p. 98
Summary	p. 100
Exercises	p. 100
References	p. 101
Multi-scale Filtering	p. 103
Introduction	p. 103
Alternate Sequence Filters or Scale Space Analysis	p. 103
Wavelet-Based Filters	p. 107
Summary	p. 109
Exercises	p. 110
References	p. 111
Fitting
Introduction to Fitting Substitute Geometry	p. 115
Introduction	p. 115
Fitting Criteria	p. 116
Solution Methodologies	p. 117
References	p. 118
Least-Squares Best-Fit Line and Plane	p. 121
Introduction	p. 121
Closed-Form Solution for LS Best-Fit Line	p. 121
Matrix Formulation	p. 122
Centroid as a Point on the LS Line	p. 123
Normal LS in Parametric Form	p. 124
Lagrange Multiplier Method	p. 126
Back to the LS Line	p. 127
LS Best-Fit Plane	p. 128
Summary	p. 129
Exercises	p. 129
References	p. 130
Non-linear Least-Squares I: Introduction	p. 131
Introduction	p. 131
Formulating the Circle in a Plane Problem	p. 131
The Steepest Descent Algorithm	p. 132
The Gauss-Newton Algorithm	p. 134
The Levenberg-Marquardt Algorithm	p. 136
Summary	p. 137
Exercises	p. 138
References	p. 138
Non-linear Least-Squares II: Circle, Sphere, and Cylinder	p. 139
Introduction	p. 139
Initial Estimates for Center and Radius of Circle	p. 139
Best-Fit Sphere	p. 142
Best-Fit Cylinder	p. 143
Summary	p. 144
Exercises	p. 144
References	p. 144
Fitting Radius-Suppressed Circle Data	p. 145
Introduction	p. 145
The Limacon Approximation	p. 145
LS Best-Fit Circle	p. 146
LS Best-Fit Cylinder	p. 148
Errors in the Limacon Approximation	p. 149
Summary	p. 150
Exercises	p. 151
References	p. 151
Exchange Algorithms for Minimum Zone	p. 153
Introduction	p. 153
Exchange Algorithms	p. 153
Exchange Algorithm for Line	p. 154
Exchange Algorithm for Plane	p. 157
Exchange Algorithm for Circle	p. 159
Summary	p. 162
Exercises	p. 163
References	p. 163
Reference Circle-Fitting Using Linear Programming Simplex	p. 165
Introduction	p. 165
LP Simplex	p. 165
Formulating the MI Problem	p. 167
Formulating the MC Problem	p. 171
Duality	p. 172
LP and Exchange Algorithms	p. 174
Exchange Algorithms for MI and MC Circles	p. 176
Summary	p. 176
Exercises	p. 176
References	p. 177
Parameterization
Surface Finish Parameters I: Amplitude, Spacing, Hybrid, and Shape	p. 181
Introduction	p. 181
Amplitude Parameters	p. 181
Spacing Parameters	p. 183
Hybrid and Shape Parameters	p. 186
Summary	p. 188
Exercises	p. 189
References	p. 190
Surface Finish Parameters II: Autocorrelation, Power Spectral Density, Bearing Area	p. 191
Autocovariance and Autocorrelation Function	p. 191
Power Spectral Density	p. 193
Amplitude Density Function and Bearing Area Curve	p. 195
Summary	p. 198
Exercises	p. 199
References	p. 199
3D Surface Texture Parameters	p. 201
Introduction	p. 201
Amplitude and Shape Parameters	p. 201
AACV, APSD, and BAC for 3D Surfaces	p. 202
Spacing and Hybrid Parameters	p. 205
Summary	p. 206
Exercises	p. 206
References	p. 206
Errors and Uncertainty
Uncertainty Considerations	p. 209
Introduction	p. 209
Random and Systematic Components	p. 209
Uncertainty Modeling	p. 210
Uncertainty Propagation	p. 210
Systematic Errors: an Example	p. 210
References	p. 211
Uncertainty Propagation in Computations	p. 213
Introduction	p. 213
Intervals at Some Level of Confidence	p. 214
The Central Limit Theorem	p. 215
Limitations of GUM	p. 217
The Monte Carlo Method	p. 217
Filtering Surface Profiles	p. 218
Fitting Substitute Geometry	p. 221
Summary	p. 223
Exercises	p. 224
References	p. 224
Error Separation Techniques in Roundness Metrology	p. 225
Introduction	p. 225
Full Reversal	p. 225
Two-Position Method	p. 226
Two-Probe Method	p. 229
Three-Probe FFT Method	p. 229
Three-Probe Sequential Method	p. 231
Three-Position FFT Method	p. 233
Error Separation by Solving Linear Equations	p. 234
Uncertainty Propagation	p. 236
Summary	p. 236
Exercises	p. 236
References	p. 237
Other Relevant Topics	p. 239
Introduction	p. 239
Parameter Extraction	p. 239
Tools for Correlation and Diagnostics	p. 240
Challenges	p. 241
References	p. 241
Answers to Selected Exercises	p. 243
Index	p. 261
Table of Contents provided by Ingram. All Rights Reserved.

Computational Surface and Roundness Metrology

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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