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 |  موضوع: كتاب Computational Surface and Roundness Metrology الإثنين 05 سبتمبر 2016, 9:27 pm | |
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Computational Surface and Roundness Metrology
Bala Muralikrishnan, Jay Raja
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Contents
Notation xix
1 Introduction 1
1.1 Surface and Roundness Metrology 1
1.2 Scope and Objectives 1
1.3 Organization 3
References 4
Part I Filtering
2 A Brief History of Filtering 7
2.1 Introduction 7
2.2 Electrical Filters 7
2.3 Digital Filters 8
2.4 The Envelope Method 8
2.5 The Gaussian Filter 8
2.6 Overlap of Measurement Techniques 9
2.7 Recent Advances in Filtering 9
2.8 Summary 10
References 10
3 Filtering in the Frequency Domain 13
3.1 Surface Wavelengths 13
3.2 Fourier Transform, Discrete Fourier Transform,
and Fast Fourier Transform 14
3.3 Filtering in the Frequency Domain 16
3.4 Wrap-Around Effect 19
3.5 Amplitude Transmission and Phase Characteristics 19
3.6 Summary 20
Exercises 20
References 21
xixii Contents
4 Filtering in the Time Domain 23
4.1 Filtering as an Averaging Process 23
4.2 Relationship Between Frequency-Domain
and Time-Domain Filtering 26
4.3 Filtering Profiles: Putting It All Together 27
4.4 Summary 29
Exercises 30
References 31
5 Gaussian Filter 33
5.1 Introduction 33
5.2 High-Pass and Low-Pass Filters 35
5.3 Roughness, Waviness, and Form Using the Gaussian Filter 35
5.4 Effect of Cutoff 36
5.5 Phase Characteristics 36
5.6 Summary 37
Exercises 37
References 38
6 The 2RC Filter 39
6.1 Introduction 39
6.2 The 2RC High-Pass Filter 39
6.3 More on the 2RC Filter 42
6.4 Comparison of the 2RC and Gaussian Filters 44
6.5 Summary 44
Exercises 45
References 46
7 Filtering Roundness Profiles 47
7.1 Introduction 47
7.2 Gaussian Filter for Roundness 47
7.3 Amplitude Transmission Characteristics 49
7.4 Filtering Roundness Profiles in the Time Domain 50
7.5 Circular Convolution in the Frequency Domain 50
7.6 Summary 52
Exercises 52
References 53
8 Filtering 3D Surfaces 55
8.1 Areal Surface Texture Analysis 55
8.2 2D Convolution 55
8.3 Gaussian Filter in 3D 56
8.4 A Note on Indices 56
8.5 Frequency-Domain Filtering in 3D 59
8.6 Summary 62
Exercises 62
References 63Contents xiii
Part II Advanced Filtering
9 Gaussian Regression Filters 67
9.1 Introduction 67
9.2 Zero-Order Gaussian Regression Filter 68
9.3 Second-Order Gaussian Regression Filter 71
9.4 3D Zero-Order Gaussian Regression Filter 73
9.5 3D Second-Order Gaussian Regression Filter 74
9.6 Summary 75
Exercises 75
References 76
10 Spline Filter 77
10.1 Introduction 77
10.2 Amplitude Transmission Characteristics 78
10.3 Implementation of the Non-periodic Spline Filter 79
10.4 Implementation of the Periodic Spline Filter 82
10.5 Summary 86
Exercises 86
References 86
11 Robust Filters 87
11.1 Rk Filter 87
11.2 Robust Gaussian Regression Filter 90
11.3 Summary 91
Exercises 92
References 92
12 Envelope and Morphological Filters 93
12.1 Envelope Filters 93
12.2 Stylus Tip Convolution 94
12.3 Morphological Filters 96
12.4 A Word on the Fundamentals 98
12.5 3D Morphological Filtering 98
12.6 Summary 100
Exercises 100
References 101
13 Multi-scale Filtering 103
13.1 Introduction 103
13.2 Alternate Sequence Filters or Scale Space Analysis 103
13.3 Wavelet-Based Filters 107
13.4 Summary 109
Exercises 110
References 111xiv Contents
Part III Fitting
14 Introduction to Fitting Substitute Geometry 115
14.1 Introduction 115
14.2 Fitting Criteria 116
14.3 Solution Methodologies 117
References 118
15 Least-Squares Best-Fit Line and Plane 121
15.1 Introduction 121
15.2 Closed-Form Solution for LS Best-Fit Line 121
15.3 Matrix Formulation 122
15.4 Centroid as a Point on the LS Line 123
15.5 Normal LS in Parametric Form 124
15.6 Lagrange Multiplier Method 126
15.7 Back to the LS Line 127
15.8 LS Best-Fit Plane 128
15.9 Summary 129
Exercises 129
References 130
16 Non-linear Least-Squares I: Introduction 131
16.1 Introduction 131
16.2 Formulating the Circle in a Plane Problem 131
16.3 The Steepest Descent Algorithm 132
16.4 The Gauss–Newton Algorithm 134
16.5 The Levenberg–Marquardt Algorithm 136
16.6 Summary 137
Exercises 138
References 138
17 Non-linear Least-Squares II: Circle, Sphere, and Cylinder 139
17.1 Introduction 139
17.2 Initial Estimates for Center and Radius of Circle 139
17.3 Best-Fit Sphere 142
17.4 Best-Fit Cylinder 143
17.5 Summary 144
Exercises 144
References 144
18 Fitting Radius-Suppressed Circle Data 145
18.1 Introduction 145
18.2 The Limaçon Approximation 145
18.3 LS Best-Fit Circle 146
18.4 LS Best-Fit Cylinder 148
18.5 Errors in the Limaçon Approximation 149Contents xv
18.6 Summary 150
Exercises 151
References 151
19 Exchange Algorithms for Minimum Zone 153
19.1 Introduction 153
19.2 Exchange Algorithms 153
19.3 Exchange Algorithm for Line 154
19.4 Exchange Algorithm for Plane 157
19.5 Exchange Algorithm for Circle 159
19.6 Summary 162
Exercises 163
References 163
20 Reference Circle-Fitting Using Linear Programming Simplex 165
20.1 Introduction 165
20.2 LP Simplex 165
20.3 Formulating the MI Problem 167
20.4 Formulating the MC Problem 171
20.5 Duality 172
20.6 LP and Exchange Algorithms 174
20.7 Exchange Algorithms for MI and MC Circles 176
20.8 Summary 176
Exercises 176
References 177
Part IV Parameterization
21 Surface Finish Parameters I:
Amplitude, Spacing, Hybrid, and Shape 181
21.1 Introduction 181
21.2 Amplitude Parameters 181
21.3 Spacing Parameters 183
21.4 Hybrid and Shape Parameters 186
21.5 Summary 188
Exercises 189
References 190
22 Surface Finish Parameters II:
Autocorrelation, Power Spectral Density, Bearing Area 191
22.1 Autocovariance and Autocorrelation Function 191
22.2 Power Spectral Density 193
22.3 Amplitude Density Function and Bearing Area Curve 195
22.4 Summary 198
Exercises 199
References 199xvi Contents
23 3D Surface Texture Parameters 201
23.1 Introduction 201
23.2 Amplitude and Shape Parameters 201
23.3 AACV, APSD, and BAC for 3D Surfaces 202
23.4 Spacing and Hybrid Parameters 205
23.5 Summary 206
Exercises 206
References 206
Part V Errors and Uncertainty
24 Uncertainty Considerations 209
24.1 Introduction 209
24.2 Random and Systematic Components 209
24.3 Uncertainty Modeling 210
24.4 Uncertainty Propagation 210
24.5 Systematic Errors: an Example 210
References 211
25 Uncertainty Propagation in Computations 213
25.1 Introduction 213
25.2 Intervals at Some Level of Confidence 214
25.3 The Central Limit Theorem 215
25.4 Limitations of GUM 217
25.5 The Monte Carlo Method 217
25.6 Filtering Surface Profiles 218
25.7 Fitting Substitute Geometry 221
25.8 Summary 223
Exercises 224
References 224
26 Error Separation Techniques in Roundness Metrology 225
26.1 Introduction 225
26.2 Full Reversal 225
26.3 Two-Position Method 226
26.4 Two-Probe Method 229
26.5 Three-Probe FFT Method 229
26.6 Three-Probe Sequential Method 231
26.7 Three-Position FFT Method 233
26.8 Error Separation by Solving Linear Equations 234
26.9 Uncertainty Propagation 236
26.10 Summary 236
Exercises 236
References 237Contents xvii
27 Other Relevant Topics 239
27.1 Introduction 239
27.2 Parameter Extraction 239
27.3 Tools for Correlation and Diagnostics 240
27.4 Challenges 241
References 241
Answers to Selected Exercises 243
Index
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رابط تنزيل كتاب Computational Surface and Roundness Metrology- Bala Muralikrishnan, Jay Raja 
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