Handbook of

Surface Metrology

David J Whitehouse University of Warwick

Institute of Physics Publishing Bristol and Philadelphia

Contents

Dedication v

Foreword by Professor D Dowson vii

Preface x x i i i

Acknowledgments x x v

1. General Philosophy of Measurement 1

1.1 Where does surface metrology ßt in engineering metrology? 1

1.2 Importance of surface metrology -2

2. Surface Characterization The Nature of Surfaces and the Signals obtained from them 5

2.1 Surface roughness characterization 7

2.1.1 Profile parameters 10 2.1.1.1 Amplitude Parameters 12 2.1.1.2 Spating parameters 16 2.1.1.3 Hybrid parameters 18

2.1.2 Reference lines 20 2.1.2.1 Straight lines 21 2.1.2.2 Polynomial fitting 24 2.1.2.3 Spline fundions 27 2.1.2.4 Filtering methods 27 2.1.2.5 Envelope methods 40 2.1.2.6 Summary 45

2.1.3 Statistical parameters of surface roughness 45 2.1.3.1 Amplitude probability density fundion (APDF) or p(z) 45 2.1.3.2 Material ratio 46 2.1.3.3 Autocorrelation fundion (ACF) and power spedral density (PSD) 49 2.1.3.4 Power spectrum 58 2.1.3.5 Hybrid Statistical parameters—peak and Valley charaderistics 60

2.1.4 Areal texture parameters, isotropy and lay (continuous Signal) 63 2.1.4.1 Dired methods of Statistical assessment over an area 64

X Contents

-the characterization of spatial

2.1.5 Discrete characterization 2.1.5.1 General 2.1.5.2 Alternative discrete methods

2.1.6 Assessment of isotropy and lay 2.1.7 Potential methods of characterization

2.1.7.1 Amplitude and hybrid parameters 2.1.7.2 Skew and kurtosis 2.1.7.3 Beta function 2.1.7.4 Chebyshev function and log normal function 2.1.7.5 Variations on material ratio curve 2.1.7.6 Time series analysis methods of characterization-

information 2.1.7.7 Possible methods of Classification based on a Fourier approach 2.1.7.8 Space—frequency functions

2.1.8 Fractals 2.1.9 Surface texture and non-linear dynamics in machines

2.2 Waviness 2.3 Errors of form

2.3.1 Introduction 2.3.2 Straightness and related topics 2.3.3 Generalized probe configurations for variable errors 2.3.4 Assessments and Classification 2.3.5 Flatness 2.3.6 Roundness

2.3.6.1 Nature of departures from roundness 2.3.6.2 Chordal methods 2.3.6.3 Radial methods 2.3.6.4 Nature of the signal produced by a radial departure instrument 2.3.6.5 Relation between the centred workpiece profile and the radius-suppressed polar

plot 2.3.6.6 Effect of imperfect centring 2.3.6.7 Assessment of radial, diametral and angular variations 2.3.6.8 Roundness assessment 2.3.6.9 Effect of imperfect centring on the minimum zone method 2.3.6.10 Effect of angular distortion 2.3.6.11 Equation of a reference line io fit a partial circular arc as seen by a roundness

instrument 2.3.6.12 Lobing coefficients 2.3.6.13 Roundness assessment without a formal datum 2.3.6.14 Eccentricity, concentricity 2.3.6.15 Squareness 2.3.6.16 Curvature measurement from roundness data 2.3.6.17 Estimation of curvature in the presence of noise 2.3.6.18 Estimation of radial slope 2.3.6.19 Assessment of ovality and other shapes 2.3.6.20 Two-dimensional measurement—sphericity 2.3.6.21 Interpretation of results of equations (2.354)—(2.362)

2.3.7 Cylindricity 2.3.7.1 Methods of specifying cylindricity 2.3.7.2 Assessment of cylindrical form

72 72 75 77 80 80 80 81 84 85

88 91 93 96

101 102 114 114 115 117 118 120 126 127 129 }31 132

134 135 137 139 143 143

146 150 152 156 159 159 162 172 173 175 179 181 183 184

Contents xi

2.3.7.3 Reference figures for cylinder measurement 190 2.3.7.4 Practical considerations of cylindroid references 193 2.3.7.5 Limacon cylindrical references 193

2.3.7.6 Conicity I 9 6

2.4 Comparison of deßnitions for surface metrology and coordinate-measuring machines 196 2.4.1 Other differences 198

2.5 Characterization of defect shapes on the surface 200 2.5.1 General 200 2.5.2 Dimensional characteristics of defects 200 2.5.3 Types of defect 200

2.6 Summary 202

References 202

3. Processing 2 0 9

3.1 Digital methods 21° 3.1.1 Sampling 210 3.1.2 Quantization 213 3.1.3 Numerical analysis—the digital model 214

3.1.3.1 Differentiation 214 3.1.3.2 Integration 215 3.1.3.3 Interpolation, extrapolation 217

3.2 Digital properties of random surfaces 218 3.2.1 Some numerical problems encountered in surface metrology 218

3.2.2 Definitions of a peak and density of peaks 218 3.2.3 Effect of quantization 219 3.2.4 Effect of numerical model 221 3.2.5 Effect of distance between samples on peak density value 222 3.2.6 Digital evaluation of other important peak parameters 226

3.2.6.1 Peak heighl measurement 226 3.2.6.2 Peak curvature 227 3.2.6.3 Profile slopes 229 3.2.6.4 Summary 232

3.2.7 Areal (two-dimensional) digital measurement of surface roughness parameters 233 3.2.7.1 General 233

3.2.7.2 The expected summit density and the distributions of summit height and

curvature 3.2.7.3 The effeci of the sampling interval and limiting results for the discrete surface 236

3.2.8 Patterns of sampling and their effects on discrete properties 240 3.2.8.1 Comparison of three-, four-, five- and seven-point analysis of surfaces 240 3.2.8.2 Four-point sampling scheme in a plane 240 3.2.8.3 The effect of sampling interval and limiting results on sample patterns 245 3.2.8.4 Discussion 248

3.3 Fourier transform and the fast Fourier transform 251 3.3.1 General properties of the Fourier transform 251 3.3.2 Fast Fourier transform routine 252

3.3.2.1 Fast Fourier transform analytic form 253 3.3.3 A practical realization of the fast Fourier transform 256 3.3.4 General considerations 258

3.3.4.1 The Fourier series of real data 259

234

X l l Contents

3.3.5 Applications of Fourier transforms with particular reference to the FFT 259 3.3.5.1 Use of Fourier transform for non-recursive filtering 259 3.3.5.2 Power spectral analysis 260 3.3.5.3 Correlation 260 3.3.5.4 Other convolutions 260 3.3.5.5 Interpolation 261 3.3.5.6 Other analysis 261 3.3.5.7 Roundness analysis 261

3.4 Statistical parameters in digital form 262 3.4.1 Amplitude probdbility density function 262 3.4.2 Statistical momenis of the APDF 263 3.4.3 Autocorrelaiion function (ACT) 263 3.4.4 Autocorrelation measurement using FFT 264 3.4.5 Measurement of power spectral density (PSD) 264

3.5 Properties and implementation of the ambiguity function and Wigner distribution function 267

3.5.1 General 267 3.5.2 Ambiguity function 267

3.5.2.1 Spatial shift 268 3.5.2.2 Frequency shift 268

Spatial-limiled Signals 268 Frequency-limited Signals 268 Concentration of energy 268 Total energy 268 Convolution 268 Modulation 268 Discrete ambiguity function 268

3.5.2.10 Computation of DAF 269 3.5.3 The Wigner distribution function 270

3.5.3.1 Properties 270 Symmetry 270 Realness 270 Spatial shifting 270 Frequency shifting 270 Spatial-limited Signal 270 Frequency limiting 270 Spatial energy 270 Frequency energy 270

3.5.3.10 Total energy 270 3.5.3.11 Convolution 270 3.5.3.12 Modulation 271 3.5.3.13 Analytic Signals 271 3.5.3.14 Momenis 271

3.5.4. Some examples of Wigner distribution: application to Signals—waviness 273 3.5.5 Comparison of the Fourier transform, the ambiguity function and the Wigner

distribution function 274 3.6 Digital estimation of reference lines for surface metrology 275

3.6.1 Numerical filtering meihods for establishing mean lines for roughness and waviness profiles 275

3.6.2 Convolution filtering 275

3.5.2.3 3.5.2.4 3.5.2.5 3.5.2.6 3.5.2.7 3.5.2.8 3.5.2.9

3.5.3.2 3.5.3.3 3.5.3.4 3.5.3.5 3.5.3.6 3.5.3.7 3.5.3.8 3.5.3.9

Contents

3.6.3 Standard filier 3.6.4 Phase-correded (linear phase) filters, other filters and filiering issues 3.6.5 Gaussian filier 3.6.6 Box fundions 3.6.7 Truncation 3.6.8 Alternative methods of computation 3.6.9 Equal-weight lechniques 3.6.10 Recursive filters 3.6.11 The discrete iransfer fundion

3.6.12 The ICK filier 3.6.13 Use of the FFT in surface meirology filiering—areal case 3.6.14 Examples of numerical problems in straightness and flatness 3.6.15 Effect of Computer ward format

3.7 Algorithms 3.7.1 Differences between surface and dimensional meirology algorilhms: leasl-squares

evaluation of geometric elements 3.7.1.1 Oplimimlion 3.7.1.2 Linear leasl Squares 3.7.1.3 Eigenvectors and Singular value decomposition

3.7.2 Best-fit shapes 3.7.2.1 Best-fit plane 3.7.2.2 Circles, spheres, etc 3.7.2.3 Cylinders and cones

3.7.3 Other methods 3.7.3.1 Minimum zone method

3.7.4 Minimax methods—constrained optimization 3.7.5 Simplex methods 3.7.6 Basic concepts in linear programming

3.7.6.1 General 3.7.6.2 Dual linear programmes in surface meirology 3.7.6.3 Minimum radius circumscribing limacon 3.7.6.4 Minimum zone, straighl lines and planes 3.7.6.5 Minimax problems

3.8 Transformations in surface metrology 3.8.1 General 3.8.2 Hartley Iransform 3.8.3 Square wave fundions—Walsh fundions 3.8.4 Space—frequency fundions 3.8.5 Gabor transforms

3.9 Graphical methods 3.9.1 The planimeter and its uses in surface metrology 3.9.2 Graphical ways of estimating random process parameters

3.9.2.1 Autocorrelation fundion 3.9.2.2 Harmonie analysis

3.10 Other methods of processing 3.10.1 Correlation

3.10.1.1 Real-time magnetic tape correlator 3.10.1.2 Optical analogue method (simultaneous method) 3.10.1.3 Optical analogue method (sequential method) 3.10.1.4 Stylus method—sequential Operation

275 280 282 283 284 286 287 289 289 293 294 295 297

299

299 300 300 301 301 301 301 304 310 310 311 311 314 314 314 315 317 319

321 321 322 323 325 327

328 328 331 331 332

337 337 338 338 339 339

xiv Contents

3.10.2 Quantization correlators 340 3.10.2.1 Sampled and clipped Signals involuing digital Urne compression 341 3.10.2.2 Power spectra 341

3.11 Surface gener Man 343 3.11.1 Profile generation 343 3.11.2 Two-dimensional surface generation 347

3.12 Summary 351 References 351

4. Instrumentation 355

4.1 Introduction and historical 355 4.1.1 Historical details 355 4.1.2 Some early dates of importance in the metrology and produdion of surfaces 356 4.1.3 Specification 358 4.1.4 Design criteria for instrumentation 359 4.1.5 Kinematics 359 4.1.6 Pseudo-kinematic design 362 4.1.7 Mobility 362 4.1.8 Linear hinge mechanisms 364 4.1.9 Angular motion flexures 367 4.1.10 Measurement and force loops 368 4.1.11 Alignment errors 369

4.1.11.1 Abbe offset 369 4.1.12 Other mechanical considerations—balance of forces 370 4.1.13 Systematic errors and non-lineariiies 371 4.1.14 Material selection 372 4.1.15 Drive Systems 3 73

4.2 Measurement Systems 376 4.2.1 General Stylus Systems 376 4.2.2 Stylus characteristics 378

4.1.2.1 Tactile considerations 378 4.2.2.2 Pick-up dynamics 383 4.2.2.3 Conclusions about mechanical pick-ups of instruments using the

conventional approach 389 4.2.2.4 Relationship between static and dynamic forces 391 4.2.2.5 Alternative Stylus Systems and effect on reaction/random surface 396 4.2.2.6 Criteria for scanning surface instruments 397 4.2.2.7 Forms of the pick-up eaualion 398 4.2.2.8 Measurement Systems 402 4.2.2.9 Spatial domain instruments 406 4.2.2.10 Open- and closed-loop considerations 408

4.2.3 Scanning microscopes 409 4.2.3.1 Scanning tunnelling microscope (STM) 409 4.2.3.2 Other scanning microscopes 410 4.2.3.3 Operation and theory of the STM 412 4.2.3.4 Spedroscopy 414 4.2.3.5 Some simple scanning Systems 415 4.2.3.6 The atomic force microscope 418

4.2.4 Aspects of Stylus instruments 421

Contents

4.2.4.1 Pick-up configuration 421 4.2.4.2 Generation of the skid datum 423 4.2.4.3 Stylus instruments where the Stylus integrates 432 4.2.4.4 Alignment of the Stylus System 433 4.2.4.5 Limitations of 'references' used in roundness measurement 434 4.2.4.6 Other Stylus methods 436 4.2.4.7 Replication 440

4.2.5 Areal (3D) mapping of surfaas using Stylus methods 441 4.2.5.1 General problem 441 4.2.5.2 Mapping 442 4.2.5.3 Criteria for areal mapping 443 4.2.5.4 Movement positions on surface and sampling patterns 446 4.2:5.5 Contour and other maps of surfaces 452

4.3 Optical techniques for the measurement of surfaces 453 4.3.1 General 453 4.3.2 Properties of the focused spot 455 4.3.3 Optical followers 457 4.3.4 Hybrid microscopes 463 4.3.5 Oblique angle methods 466 4.3.6 Phase detection Systems 468

4.3.6.1 Spatial and temporal coherence 468 4.3.6.2 Interferometry and surface metrology 469

4.3.7 Heterodyne methods 471 4.3.7.1 Frequency-splitting method 471 4.3.7.2 Other methods in interferometry comparable with heterodyne methods 475 4.3.7.3 Relative merits of different nanometre instruments 476 4.3.7.4 High-precision non-contacting metrology using short coherence interferometry 479

4.3.8 Moire methods 481 4.3.8.1 General 481 4.3.8.2 Strain measurement 483 4.3.8.3 Moire contouring 483 4.3.8.4 Shadow moire 484 4.3.8.5 Projection moire 484 4.3.8.6 Summary 486

4.3.9 Holographie techniques 486 5.3.9.1 Introduction 486

4.3.10 Speckle methods 491 4.3.11 Diffraction methods 501 4.3.12 Scatterometers (glossmeters) 512 4.3.13 Flaw detection 517

4.3.13.1 General 517 4.3.13.2 Transform plane methods 518 4.3.13.3 Image plane detection 522 4.3.13.4 'Whole-field' measurement—plane detection 525 4.3.13.5 Comment 526

4.3.14 Comparison of optical techniques 527 4.3.14.1 General optical comparison 528

4.4 Capacitance techniques for measuring surfaces 532 4.4.1 General 532 4.4.2 Scanning capacilative microscopes 534

xvi Contents

4,4.3 Capacitance as a proximity gauge 535 4.5 Inductance technique for measuring surfaces 535 4.6 Impedance technique—skin effect 535 4.7 Other non-standard techniques 536

4.7.1 General 536 4.7.2 Fridion deuices 536

4.7.2.1 The fridion dynamometer 536 4.7.3 Rolling-ball device 536 4.7.4 Liquid methods—water 536 4.7.5 Liquid methods—oik 537 4.7.6 Pneumatic methods 537 4.7.7 Thermal method 538 4.7.8 Ultrasonics 538 4.7.9 Summary 540

4.8 Electron microscopy 540 4.8.1 General 540 4.8.2 Readion of eledrons voith solids 543 4.8.3 Scanning electron microscope 544 4.8.4 Transmission eledron microscope 546

4.9 Merit of transducers 547 4.9.1 Comparison of transducer Systems 547 4.9.2 Types of conversion and transducer noise 553

4.9.2.1 Limitation 553 4.9.2.2 Random noise limitation 554

4.9.3 Types of conversion and types of transducer 555 4.9.3.1 General 555 4.9.3.2 Variable resistance 55$ 4.9.3.3 Variable inductance 555 4.9.3.4 Variable reludance 557 4.9.3.5 Voltage or current generators 558 4.9.3.6 Variable capacitance 558 4.9.3.7 Self-generation voltage or circuii 558 4.9.3.8 Photodetectors 558

4.9.4 Merit and cosl 559 4.9.5 Examples of transducer properties 561

4.9.5.1 Induciive 561 4.9.5.2 Capacitative transducer 563 4.9.5.3 Optical lateral positional sensor 564 4.9.5.4 Optical area pattern phoiodiodes, transducer for lateral displacement 565

4.9.6 Talystep 565

4.9.7 Comparison of techniques—general summary 570

References 572

5. Traceability—Standardization—Variability 579

5.1 Introduction 579 5.2 Nature of errors 580

5.2.1 Systematic errors 580 5.2.2 Random errors 580

5.3 Deterministic or systematic error model 580

Contents xvii

5.4 Basic components of accuracy evaluation 5S1

5.5 Basic error theory for a System 582

5.6 Propagation of errors 5S3

5.6.1 Deterministic errors 583

5.6.2 Random errors 584

5.7 Some useful Statistical tests for surface metrology 585 5.7.1 Confidence intervals for any parameter 585 5.7.2 Tests for the mean value of a surface—the student t test 585 5.7.3 Tests for the Standard deviation—the J 2 test 587 5.7.4 Goodness offit 588 5.7.5 Tests for variance—the F test 588 5.7.6 Measurement of relevance—factorial design 588

5.7.6.1 The interactions 590 5.7.7 Lines of regression 592 5.7.8 Methods of discrimination 593

5.8 Uncertainty in instruments—calibration in general 593

5.9 The calibration of Stylus instruments 595

5.9.1 Stylus calibration 596 5.9.2 Calibration of amplification 599 5.9.3 X-ray methods 603 5.9.4 Practical Standards 605 5.9.5 Calibration of transmission characteristics 607 5.9.6 Filter calibration Standards 610

5.10 Calibration of form instruments 612 5.10.1 Magnitude 612

5.10.1.1 Magnitude of diametral change 613 5.10.2 Separation of errors—calibration of roundness and form 613 5.10.3 General errors due to motion 620

5.10.3.1 Radial motion 621 5.10.3.2 Face motion 622 5.10.3.3 Error motion—general case 622 5.10.3.4 Fundamental and residual error motion 623 5.10.3.5 Error motion versus run-out (or TIR) 624 5.10.3.6 Fixed sensitive direction measurements 625 5.10.3.7 Considerations on the use of the two-gaugehead system for a fixed sensitive

direction 626 5.10.3.8 Other radial error methods 627

5.11 Variability of surface parameters 628

5.12 National and international Standards 632 5.12.1 Selected list of Standards applicable to surface roughness measurement 632

5.13 Specißcation on drawings 636

5.13.1 Surface roughness 636 5.13.1.1 Indications generally—multiple Symbols 640 5.13.1.2 Reading the Symbols 640 5.13.1.3 General points 641 5.13.1.4 Other points 644

5.14 Summary $44 References &45

xviii Contents

6. Surface Metrology in Manufactwe 647

6.1 Introduction 647 6.2 Manufacturing processes 648

6.2.1 General 648 6.3 Cutting 649

6.3.1 Turning 649 6.3.1.1 General 649 6.3.1.2 Finish machining 650 6.3.1.3 Effect of iool geometry—theoretical surface finish—secondary cutting edge 650 6.3.1.4 Primary cutting edge finish 654 6.3.1.5 Fracture roughness 655 6.3.1.6 Built-up edge 655 6.3.1.7 Other surface roughness effects in finish machining 657 6.3.1.8 Tool wear 659

6.3.2 Diamond tuming 660 6.3.3 Milling and broaching 661

6.3.3.1 General 661 6.3.3.2 Roughness on the surface 664 6.3.3.3 Theoretical milling finish 665

6.4 Abrasive processes 666 6.4.1 General 666 6.4.2 Types of grinding 671 6.4.3 Comments on grinding 671 6.4.4 Nature of the guiding process 672

6.4.4.1 General 672 6.4.4.2 Factorial experiment 613

6.4.5 Centreless grinding 674 6.4.5.1 General 674 6.4.5.2 Importani parameters for roughness and roundness 675 6.4.5.3 Roundness considerations 677

6.4.6 Cylindrical grinding 678 6.4.6.1 Spark-out 678

6.4.6.2 Elastic effects 679 6.4.6.3 Texture generated in grinding 681 6.4.6.4 Chatter 682 6.4.6.5 Other types of grinding 683

6.4.7 General comments on grinding 684 6.4.8 Nanogrinding 686 6.4.9 General comments on roughness 690 6.4.10 Honing 694 6.4.11 Polishing (lapping) 696

6.5 Unconventional machining 699 6.5.1 Ultrasonic machining 699 6.5.2 Magnelic float polishing 699 6.5.3 Physical and chemical machining 700

6.5.3.1 Electrochemical machining (ECM) 700 6.5.3.2 Electrolytic grinding 701 6.5.3.3 Electrodischarge machining (EDM) 702

Contents

6.5.4 Forming processes 703 6.5.4.1 General 703 6.5.4.2 Ballizing 703

6.5.5 Micro- and nanomachining 703 6.5.5.1 General 703 6.5.5.2 Micropolishing 704

6.5.6 Atomic-scale machining 708 6.5.6.1 General 708 6.5.6.2 Electron beam machining 708 6.5.6.3 Ion beam machining 711 6.5.6.4 General comment on atomic-type processes 714

6.6 Surface roughness produced by machining difßcult materials 716 6.7 Surface effects other than geometry 716

6.7.1 Surface effects resulting from the machining process 716 6.7.2 Surface alterations 717 6.7.3 Residual stress 717

6.7.3.1 General 717 6.7.3.2 Grinding 723 6.7.3.3 Turning 725 6.7.3.4 Milling 725 6.7.3.5 Shaping 725

I 6.7.3.6 General comment 725 6.7.4 Measurement of stresses 726

6.7.4.1 General 726 6.7.4.2 Indirect methods 726 6.7.4.3 Direct methods 727

6.7.5 Subsurface properiies influencing function 729 6.7.5.1 General 729 6.7.5.2 Influences of residual stress 729

6.8 Surface geometry—a ßngerprint of manufacture 732 6.8.1 General 732 6.8.2 Use of random process analysis 733

6.8.2.1 On turned parts—single-point machining 733 6.8.2.2 Abrasive machining 735

6.8.3 Space-freauency functions (the Wigner function) 737 6.8.4 Non-linear dynamics 738

6.9 Summary 742 References 743

7. Surface Geometry and its Importance in Function 749

7.1 Introduction 749 7.2 Two-body interaction—the static Situation 751

7.2.1 Contact 751 7.2.1.1 Point contact 753

7.2.2 Macroscopic behaviour 754 7.2.2.1 Two spheres in contact 756 7.2.2.2 Two cylinders in contact 757 7.2.2.3 Crossed cylinders at any angle 758

Contents

7.2.2.4 Sphere on a cylinder 758 7.2.2.4 Sphere inside a cylinder 759

7.2.3 Microscopic behaviour—number of asperity contads and behaviour under load 759 7.2.3.1 General 759 7.2.3.2 Microcontad under load 760 7.2.3.3 Elastic/plastk balance—plasticüy index 762 7.2.3.4 Contads and areas, profiles and maps 775

7.2.4 Effect of waviness on contact 778

7.3 Functional properties of contact 77S> 7.3.1 General 779 7.3.2 Sliffness 781 7.3.3 Mechanical seals 787 7.3.4 Adhesion 787 7.3.5 Thermal condudivity 792 7.3.6 Relationship between eledrical and thermal condudivity 796 7.3.7 Summary 800

7.4 Two-body interactions—dynamic effect 800 7.4.1 General 800 7.4.2 Fridion 800

7.4.2.1 Mechanisms—general 800 7.4.2.2 Fridion—wear, dry conditions „ 805

7.4.3 Wear Classification 805 7.4.4 Lubrication 809

7.4.4.1 General 809 7.4.4.2 Hydrodynamic lubrication and surface geomeiry 811

7.4.5 Contact between two surfaces via a third body 824

7.4.5.1 General 824 7.4.5.2 EHD lubrication and the influence of roughness 824

7.4.6 Boundary lubrication 831 7.4.6.1 General 831 7.4.6.2 Mechanical properties of thin boundary layer films 834 7.6.4.3 Breakdoion of boundary lubrication 834

7.5 Surface roughness and mechanical System life 835 7.5.1 Weibull and dual-frequency—space functions 835 7.5.2 Running-in process 836 7.5.3 Surface roughness 'one-number' spedfication and running-in 837 7.5.4 Influence of roughness on scuffing failure 838 7.5.5 Rolling fatigue failure (pitting, spalling) 844

7.5.5.1 Rolling failure 845 7.5.5.2 Roughness effects on 3D body motion 847 7.5.5.3 Rough surfaces and rolling 853 7.5.5.4 Pitting due to debris and subsequent surface effects 856

7.5.6 Vibrating effects 856 7.5.6.1 Dynamic effects 856 7.5.6.2 Squeeze films and roughness 857 7.5.6.3 Fretting and fretting fatigue 859

7.6 One-body interactions 861 7.6.1 General 861 7.6.2 Fatigue 861

•

Contents

7.6.3 Corrosion and corrosion fatigue on the effect of roughness 867

7.6.3.1 Corrosion fatigue—general 86s

7.6.4 Corrosion 810

7.6.4.1 General 870

7.6.4.2 Localized attack—electromechanical 871

7.6.4.3 Heterogeneities 87* 7.6.4.4 Localized attack—electrochemical 872

7.7 One body with radiation (optical). The effect of roughness on the scattering of electromagnetic and other radiation S73

7.7.1 Optical scatier—general 873

7.7.1.1 Models 873

7.7.2 General optical 874

7.7.3 Smooth random surface 879

7.7.4 Geometrie ray-tracing criterion—rough random surfaces 879

7.7.4.1 Effect of surface curvature 881

7.7.4.2 Estimation of l, the facet length 882

7.7.5 Scatter from deterministic surf aces 883

7.7.6 Smooth deterministic signal 883

7.7.7 Geometrie ray condition, rough deterministic surf aces 884

7.7.8 Summary of results, scalar and geometrical 884

7.7.9 Mixture of two random components 885

7.7.10 Other considerations on light scatter 886

7.7.10.1 Angle effects 887

7.7.10.2 Multiple reflections 888

7.7.10.3 Shadowing 89Z

7.7.11 Scattering from non-Gaussian surf aces 897

7.7.11.1 Fresnel scattering 898

7.7.11.2 Caustics 898

7.7.11.3 Fractal surf aces 8"

7.7.11.4 Fractal slopes: subfractal model 902

7.8 Scattering by different worts of waves 904

7.8.1 General 904

7.8.1.1 EM waves 904

7.8.1.2 Elastic, ultrasonic and acoustic scattering 905

7.8.2 Scattering from particks and influence of surface roughness 905 7.8.2.1 Rayleigh scattering 905

7.8.3 Bragg scattering 905

7.8.3.1 Non-elastic scattering 906

. 7.8.3.2 Influence of roughness—thin-film measurement 907

7.9 System funetion 910

7.9.1 Surface geometry and tolerances and fits 91°

7.9.2 Tolerances 91° 7.10 Summary and conclusions 914

917

References

8. Summary and Conclusions 9 2 9

8.1 General 929

8.2 Characterization and nature of Signals 930

8.3 Data processmg

xxii Preface

8.4 Measurement trends 937 8.5 Calibration 940 8.6 Manufactwe 941 8.7 Function 942 8.8 Overview 944

Index