Verfügbarkeit: Computational surface and roundness metrology

Computational surface and roundness metrology:

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Bibliographische Detailangaben
Hauptverfasser:	Muralikrishnan, Bala (VerfasserIn), Raja, Jay (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	London Springer 2009
Schlagworte:	Mesure de la rondeur Surfaces (Technologie) - Mesure Roundness measurement Surfaces (Technology) > Measurement Oberflächenmessung Betriebsmesstechnik Unrundheit
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XX, 263 S. Ill., graph. Darst.
ISBN:	9781848002968

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adam_text	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 Parti 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 Contents 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 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 Effector Cutoff ........................................... 36 5.5 Phase Characteristics ...................................... 36 5.6 Summary ................................................ 37 Exercises ...................................................... 37 References ..................................................... 38 The 2RC Füter................................................. 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 Filtering Roundness Profiles ..................................... 47 7.1 Introduction .............................................. 47 7.2 Gaussian Filter ίοτ 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 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 ..................................................... 63 Contents 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 Ä/fc 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 ...................................................... HO References ..................................................... HI xjv Contents Partin Fitting 14 Introduction to Fitting Substitute Geometry .......................115 14.1 Introduction ..............................................115 14.2 Fitting Criteria ............................................116 14.3 Solution Methodologies ....................................117 References ..................................................... П8 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 П: 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 ........................149 Contents 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 .....................................................199 xvi Contents 23 3D Surface Texture Parameters ..................................201 23.1 Introduction ..............................................201 23.2 Amplitude and Shape Parameters ............................201 23.3 AACV,APSD, and ВАС for 3D Surfaces ......................202 23.4 Spacing and Hybrid Parameters ..............................205 23.5 Summary ................................................206 Exercises ......................................................206 References .....................................................206 PartV 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 .....................................................237 Contents 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 .............................................................261
adam_txt	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 Parti 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 Contents 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 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 Effector Cutoff . 36 5.5 Phase Characteristics . 36 5.6 Summary . 37 Exercises . 37 References . 38 The 2RC Füter. 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 Filtering Roundness Profiles . 47 7.1 Introduction . 47 7.2 Gaussian Filter ίοτ 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 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 . 63 Contents 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 Ä/fc 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 . HO References . HI xjv Contents Partin Fitting 14 Introduction to Fitting Substitute Geometry .115 14.1 Introduction .115 14.2 Fitting Criteria .116 14.3 Solution Methodologies .117 References . П8 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 П: 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 .149 Contents 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 .199 xvi Contents 23 3D Surface Texture Parameters .201 23.1 Introduction .201 23.2 Amplitude and Shape Parameters .201 23.3 AACV,APSD, and ВАС for 3D Surfaces .202 23.4 Spacing and Hybrid Parameters .205 23.5 Summary .206 Exercises .206 References .206 PartV 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 .237 Contents 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 .261
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id	DE-604.BV035084482
illustrated	Illustrated
index_date	2024-07-02T22:08:23Z
indexdate	2024-07-09T21:21:50Z
institution	BVB
isbn	9781848002968
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016752679
oclc_num	227916837
open_access_boolean
owner	DE-703 DE-Aug4 DE-83
owner_facet	DE-703 DE-Aug4 DE-83
physical	XX, 263 S. Ill., graph. Darst.
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	Springer
record_format	marc
spelling	Muralikrishnan, Bala Verfasser aut Computational surface and roundness metrology Bala Muralikrishnan ; Jay Raja London Springer 2009 XX, 263 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mesure de la rondeur Surfaces (Technologie) - Mesure Roundness measurement Surfaces (Technology) Measurement Oberflächenmessung (DE-588)4172249-8 gnd rswk-swf Betriebsmesstechnik (DE-588)4145052-8 gnd rswk-swf Unrundheit (DE-588)4352876-4 gnd rswk-swf Betriebsmesstechnik (DE-588)4145052-8 s Oberflächenmessung (DE-588)4172249-8 s Unrundheit (DE-588)4352876-4 s DE-604 Raja, Jay Verfasser aut Erscheint auch als Online-Ausgabe 978-1-84800-297-5 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016752679&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Muralikrishnan, Bala Raja, Jay Computational surface and roundness metrology Mesure de la rondeur Surfaces (Technologie) - Mesure Roundness measurement Surfaces (Technology) Measurement Oberflächenmessung (DE-588)4172249-8 gnd Betriebsmesstechnik (DE-588)4145052-8 gnd Unrundheit (DE-588)4352876-4 gnd
subject_GND	(DE-588)4172249-8 (DE-588)4145052-8 (DE-588)4352876-4
title	Computational surface and roundness metrology
title_auth	Computational surface and roundness metrology
title_exact_search	Computational surface and roundness metrology
title_exact_search_txtP	Computational surface and roundness metrology
title_full	Computational surface and roundness metrology Bala Muralikrishnan ; Jay Raja
title_fullStr	Computational surface and roundness metrology Bala Muralikrishnan ; Jay Raja
title_full_unstemmed	Computational surface and roundness metrology Bala Muralikrishnan ; Jay Raja
title_short	Computational surface and roundness metrology
title_sort	computational surface and roundness metrology
topic	Mesure de la rondeur Surfaces (Technologie) - Mesure Roundness measurement Surfaces (Technology) Measurement Oberflächenmessung (DE-588)4172249-8 gnd Betriebsmesstechnik (DE-588)4145052-8 gnd Unrundheit (DE-588)4352876-4 gnd
topic_facet	Mesure de la rondeur Surfaces (Technologie) - Mesure Roundness measurement Surfaces (Technology) Measurement Oberflächenmessung Betriebsmesstechnik Unrundheit
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016752679&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT muralikrishnanbala computationalsurfaceandroundnessmetrology AT rajajay computationalsurfaceandroundnessmetrology

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