ASME B46.1 2019

$75.42

ASME B46.1-2019: Surface Texture (Surface Roughness, Waviness, and Lay)

Published By	Publication Date	Number of Pages
ASME	2019	145

Guaranteed Safe Checkout

Category: ASME

Description

This Standard is concerned with the geometric irregularities of surfaces. It defines surface texture and its constituents: roughness, waviness, and lay. It also defines parameters for specifying surface texture. The terms and ratings in this Standard relate to surfaces produced by such means as abrading, casting, coating, cutting, etching, plastic deformation, sintering, wear, erosion, etc. Intended for design, drafting, mechanical, manufacturing, production, tool/gage, quality, process and project engineers, CAD/CAM/CAE specialists, inspectors and educators across a broad range of global manufacturing. Special emphasis on aerospace, automotive, medical device, precision instrumentation and related industries.

PDF Catalog

PDF Pages	PDF Title
4	CONTENTS
10	FOREWORD
12	ASME B46 COMMITTEE ROSTER
13	CORRESPONDENCE WITH THE B46 COMMITTEE
15	EXECUTIVE SUMMARY
16	ASME B46.1-2019 SUMMARY OF CHANGES
18	Section 1 Terms Related to Surface Texture 1-1 GENERAL 1-1.1 Scope 1-1.2 Limitations 1-1.3 SI Values 1-1.4 References 1-1.5 Cleanliness 1-2 DEFINITIONS RELATED TO SURFACES 1-2.1 Surfaces
19	1-2.2 Components of the Real Surface Figures Figure 1-2.1-1 Schematic Diagram of Surface Characteristics
20	1-3 DEFINITIONS RELATED TO THE MEASUREMENT OF SURFACE TEXTURE BY PROFILING METHODS 1-3.1 Profiles 1-3.2 Reference Lines 1-3.3 Peaks and Valleys, Height Resolution, and Height Range Figure 1-3.1-1 Measured Versus Nominal Profile
21	1-3.4 Spacings Figure 1-3.1.1-1 Stylus Profile Displayed With Two Different Aspect Ratios
22	1-3.5 Measurement and Analysis Lengths Figure 1-3.2-1 Filtering a Surface Profile
23	1-4 DEFINITIONS OF SURFACE PARAMETERS FOR PROFILING METHODS 1-4.1 Height (z) Parameters Figure 1-3.2-2 Examples of Nominal Profiles
24	Figure 1-3.3-1 Profile Peak, Valley, and Element Figure 1-3.5-1 Surface Profile Measurement Lengths Figure 1-4.1.1-1 Rt, Rp, and Rv Parameters
25	Figure 1-4.1.1-2 The Rt and Rmax Parameters Figure 1-4.1.1-3 Illustration for the Calculation of Roughness Average Ra
26	1-4.2 Spacing Parameters 1-4.3 Shape Parameters and Functions Figure 1-4.1.1-4 Surface Profile Containing Two Sampling Lengths, l1 and l2, Also Showing the Rpi and Rti Parameters Figure 1-4.1.2-1 The Waviness Height, Wt
27	Figure 1-4.2-1 The Mean Spacing of Profile Elements, RSm
29	Figure 1-4.2-2 The Peak Count Level, Used for Calculating Peak Density Figure 1-4.3-1 Amplitude Density Function — ADF(z) or p(z)
30	1-4.4 Hybrid Parameters Figure 1-4.3-2 The Bearing Area Curve and Related Parameters
31	Figure 1-4.3-3 Three Surface Profiles With Different Kurtosis Figure 1-4.3-4 The Profile Bearing Length
32	1-4.5 Linear Material Ratio Curve Height Parameters 1-4.6 Material Probability Curve Height Parameters 1-5 DEFINITIONS RELATED TO THE MEASUREMENT OF SURFACE TEXTURE BY AREA PROFILING AND AREA AVERAGING METHODS 1-5.1 General 1-5.2 Reference Mean Surfaces 1-5.3 Area Peaks and Valleys Figure 1-4.3-5 Three Surface Profiles With Different Skewness
33	1-5.4 Sampling Areas 1-6 DEFINITIONS OF SURFACE PARAMETERS FOR AREA PROFILING AND AREA AVERAGING METHODS 1-6.1 Height Parameters Figure 1-5.1-1 Topographic Map Obtained by an Area Profiling Method Figure 1-5.3-1 Area Peaks (Left) and Area Valleys (Right)
34	1-6.2 Waviness Parameter 1-6.3 Area Spacing Parameters 1-6.4 Shape Parameters 1-6.5 Other Parameters
35	Figure 1-6.3-1 Comparison of Profiles Measured in Two Directions on a Uniaxial Periodic Surface Showing the Difference in Peak Spacing as a Function of Direction
37	Figure 1-6.5-1 Indication of Surface Lay
38	Section 2 Classification of Instruments for Surface Texture Measurement 2-1 SCOPE 2-2 RECOMMENDATION Figure 2-1-1 Classification of Common Instruments for Measurement of Surface Texture
39	2-3 CLASSIFICATION SCHEME 2-3.1 Type I: Profiling, Contact, Skidless Instruments 2-3.2 Type II: Profiling, Noncontact Instruments 2-3.3 Type III: Scanned Probe Microscopes
40	2-3.4 Type IV: Profiling, Contact, Skidded Instruments 2-3.5 Type V: Skidded Instruments With Parameters Only 2-3.6 Type VI: Area Averaging Methods
41	Section 3 Terminology and Measurement Procedures for Profiling, Contact, Skidless Instruments 3-1 SCOPE 3-2 REFERENCES 3-3 TERMINOLOGY 3-3.1 Profiling, Contact, Skidless Instruments 3-3.2 Measuring Loop 3-3.3 Profile Coordinate System 3-3.4 Stylus
42	Figure 3-3.3-1 Profile Coordinate System Figure 3-3.4.2-1 Conical Stylus Tip
43	3-3.5 Pickup Figure 3-3.4.3-1 Other Stylus Tip Geometries
44	3-3.6 Drive Unit 3-3.7 Amplifier 3-3.8 Analog-to-Digital Conversion 3-3.9 Primary Measured Profile 3-3.10 Instrument Sinusoidal Transmission Function 3-3.11 Instrument Nonlinearity
45	3-3.12 Instrument Measuring Range 3-3.13 Instrument Measuring z Resolution 3-3.14 Instrument z Range-to-Resolution Ratio 3-3.15 Zero Point Drift 3-3.16 Residual Profile 3-3.17 x-Axis Profile Component Deviations 3-3.18 Short-Wave Transmission Limit 3-3.19 Profile Filter 3-3.20 Profile Filter Cutoff Selection Figure 3-3.8.3-1 Aliasing
46	3-3.21 Profile Recording and Display 3-3.22 Profile Evaluation 3-4 MEASUREMENT PROCEDURE 3-4.1 Stylus Inspection Tables Table 3-3.20.1-1 Cutoff Values for Periodic Profiles Using RSm Table 3-3.20.2-1 Cutoff Values for Nonperiodic Profiles Using Ra
47	3-4.2 Instrument Calibration 3-4.3 Workpiece Cleanliness 3-4.4 Workpiece Fixturing 3-4.5 Instrument/Workpiece Leveling and Alignment 3-4.6 Assessment of the Workpiece Surface
48	Section 4 Measurement Procedures for Contact, Skidded Instruments 4-1 SCOPE 4-1.1 General 4-1.2 Type IV and Type V Instruments 4-2 REFERENCES 4-3 PURPOSE 4-4 INSTRUMENTATION 4-4.1 Roughness Average Value Ra From Averaging and Digital Readout Instruments
49	4-4.2 Cutoff Selection Figure 4-1.2-1 Schematic Diagrams of a Typical Stylus Probe and Fringe-Field Capacitance Probe Table 4-4.2-1 Measurement Cutoffs and Traversing Lengths for Continuously Averaging Instruments Using Analog Meter Readouts
50	4-4.3 Response Time for Analog Averaging Instruments 4-4.4 Traversing Length for Analog Averaging Instruments 4-4.5 Stylus Probe 4-4.6 Fringe-Field Capacitance (FFC) Probe Table 4-4.2-2 Measurement Cutoffs and Minimum Evaluation Lengths for Instruments Measuring Integrated Roughness Values Over a Fixed Evaluation Length
51	4-4.7 Possible Sources of Skid Errors 4-4.8 Instrument Accuracy 4-4.9 Operational Accuracy Figure 4-4.2-1 Effects of Various Cutoff Values
52	Figure 4-4.7-1 Examples of Profile Distortion Due to Skid Motion Figure 4-4.7-2 Examples of Profile Distortion
53	Section 5 Measurement Techniques for Area Profiling 5-1 SCOPE 5-2 REFERENCES 5-3 RECOMMENDATIONS 5-4 IMAGING METHODS 5-5 SCANNING METHODS
54	Section 6 Measurement Techniques for Area Averaging 6-1 SCOPE 6-2 EXAMPLES OF AREA AVERAGING METHODS
55	Section 7 Nanometer Surface Texture and Step Height Measurements by Stylus Profiling Instruments 7-1 SCOPE 7-2 APPLICABLE DOCUMENTS 7-3 DEFINITIONS 7-3.1 Step Height, Zs 7-3.2 Noise 7-3.3 Type A Evaluation (of Uncertainty) 7-3.4 Type B Evaluation (of Uncertainty) 7-3.5 Standard Uncertainty 7-3.6 Combined Standard Uncertainty 7-3.7 Expanded Uncertainty 7-3.8 Coverage Factor, k
56	7-4 RECOMMENDATIONS 7-4.1 Instruments 7-4.2 Methodology
57	7-4.3 Environment 7-5 PREPARATION FOR MEASUREMENT 7-5.1 Instruments Figure 7-4.2.4-1 The Radius of Curvature for a Surface Sine Wave Figure 7-4.2.5-1 Stylus Tip Touching Bottom and Shoulders of Groove
58	7-5.2 Environment 7-6 CALIBRATION ARTIFACTS 7-6.1 Calibration Specimens 7-6.2 Calibrated Displacement Actuators 7-6.3 Ultrasmooth Surface Artifacts 7-6.4 Artifact Calibration Requirements Figure 7-4.2.5-2 The Stylus Tip Contact Distance, x
59	7-7 REPORTS 7-7.1 Data 7-7.2 Annotations to the Data 7-7.3 Reporting Example
60	Section 8 Nanometer Surface Roughness as Measured With Phase Measuring Interferometric Microscopy 8-1 SCOPE 8-2 DESCRIPTION AND DEFINITIONS: NONCONTACT PHASE MEASURING INTERFEROMETER 8-3 KEY SOURCES OF UNCERTAINTY
61	Figure 8-2-1 A Typical Phase Measuring Interferometer System Figure 8-2-2 Demonstration of the Detector Array With Element Spacing, Δ, and the Measurement of the Longest Spatial Wavelength, λL, Covering the Total Number of Pixels, N
62	8-4 NONCONTACT PHASE MEASURING INTERFEROMETER INSTRUMENT REQUIREMENTS 8-4.1 Tilt Adjustment 8-4.2 Sample Stage 8-4.3 Focusing Means 8-4.5 Reference Path rms Variation 8-5 TEST METHODS 8-5.1 Instrument Preparations and Environmental Stability 8-5.2 Instrument Accuracy 8-6 MEASUREMENT PROCEDURES 8-6.1 Direct Profile Method Figure 8-2-3 Demonstration of the Detector Array With Element Spacing, Δ, and the Measurement of the Smallest Spatial Wavelength, λR, Covering Five Pixels
63	8-6.2 Subtract Reference Method 8-6.3 Absolute Rq Method 8-7 DATA ANALYSIS AND REPORTING 8-8 REFERENCES
64	Section 9 Filtering of Surface Profiles 9-1 SCOPE 9-2 REFERENCES 9-3 DEFINITIONS AND GENERAL SPECIFICATIONS 9-3.1 Notes on Terms Defined Previously
65	9-3.2 Definitions of Terms Associated With Filtering 9-4 2RC FILTER SPECIFICATION FOR ROUGHNESS 9-4.1 The 2RC Transmission Band 9-4.2 Long-Wavelength Cutoff 9-4.3 Transmission Characteristics
66	Figure 9-3.2-1 Wavelength Transmission Characteristics for the 2RC Filter System Figure 9-3.2-2 Gaussian Transmission Characteristics Together With the Uncertain Nominal Transmission Characteristic of a 2 μm Stylus Radius
67	9-4.4 2RC Filter Long-Wavelength Roughness Weighting Function 9-5 PHASE CORRECT GAUSSIAN FILTER FOR ROUGHNESS 9-5.1 Phase Correct Gaussian Filter Mean Line 9-5.2 Gaussian Filter Roughness Profile 9-5.3 Long-Wavelength Cutoff of the Gaussian Phase Correct Filter 9-5.4 Short-Wavelength Cutoff of the Gaussian Roughness Profile Figure 9-3.2-3 Weighting Function of the Gaussian Profile Filter
68	9-5.5 Short-Wavelength Transmission Characteristic 9-5.6 Weighting Function for the Roughness Short-Wavelength Cutoff 9-5.7 Weighting Function for the Roughness Long-Wavelength Cutoff 9-5.8 Transmission Characteristic of the Gaussian-Filtered Waviness Profile (Roughness Mean Line) Table 9-4.3.2-1 Limits for the Transmission Characteristics for 2RC Long-Wavelength Cutoff Filters
69	9-5.9 Transmission Characteristic of the Gaussian Filtered Roughness Profile 9-5.10 Errors of Approximations to the Gaussian Filter 9-5.11 Transmission Band Figure 9-5.8-1 Gaussian Transmission Characteristic for the Waviness Short-Wavelength Cutoff, λsw, or for Deriving the Roughness Mean Line Having Cutoff Wavelengths, λc
70	9-5.12 Cutoff Ratio 9-6 FILTERING FOR WAVINESS 9-6.1 Gaussian Filter Waviness Profile 9-6.2 Waviness Long-Wavelength Cutoff and Evaluation Length Figure 9-5.9-1 Gaussian Transmission Characteristic for the Roughness Long-Wavelength Cutoff Having Cutoff Wavelengths, λc
71	Figure 9-5.10-1 Example of a Deviation Curve of an Implemented Filter From the Ideal Gaussian Filter as a Function of Spatial Wavelength Table 9-5.11-1 Typical Cutoffs for Gaussian Filters and Associated Cutoff Ratios
72	9-6.3 Waviness Traversing Length 9-6.4 Methods for Determining the Waviness Mean Line 9-6.5 Waviness Transmission Band 9-7 FILTERING OF SURFACES WITH STRATIFIED FUNCTIONAL PROPERTIES Table 9-6.3-1 Typical Values for the Waviness Long-Wavelength Cutoff, λcw, and Recommended Minimum Values for the Waviness Traversing Length
73	Section 10 Terminology and Procedures for Evaluation of Surface Textures Using Fractal Geometry 10-1 GENERAL 10-1.1 Scope 10-1.2 Limitations 10-2 DEFINITIONS RELATIVE TO FRACTAL-BASED ANALYSIS OF SURFACES 10-2.1 Basic Terms Relating to Fractal Geometry of Engineering Surfaces
74	Figure 10-2.1.3-1 Self-Similarity Illustrated on a Simulated Profile Figure 10-2.1.4-1 An Idealized Log-Log Plot of Relative Length (of a Profile) or Relative Area (of a Surface) Versus the Scale of Observation Figure 10-2.1.9-1 An Idealized Log-Log Plot of Relative Length or Relative Area Versus the Scale of Observation (Length-Scale or Area-Scale Plot), Showing Multifractal Characteristics and Crossover Scales
75	10-2.2 Analysis Methods and Associated Terms Figure 10-2.2.1-1 Three Stepping Exercises From a Length-Scale Analysis on a Simulated Profile
76	10-3 REPORTING THE RESULTS OF FRACTAL ANALYSES Figure 10-2.2.2-1 Four Tiling Exercises From an Area-Scale Analysis
77	10-3.1 Limits on the Scales of Observation Figure 10-2.2.2.4-1 An Area-Scale Plot Including the Results of the Tiling Series in Figure 10-2.2.2-1 Table 10-3-1 Example of a Report on Fractal Analysis
78	10-3.2 Plot of a Geometric Property Versus Scale 10-3.3 Complexity Parameter 10-3.4 Fractal Dimension 10-3.5 Slope of Plots of Geometric Property Versus Scale 10-3.6 Smooth-Rough Crossovers (SRC) 10-4 REFERENCES
80	Section 11 Specifications and Procedures for Precision Reference Specimens 11-1 SCOPE 11-2 REFERENCES 11-3 DEFINITIONS 11-4 REFERENCE SPECIMENS: PROFILE SHAPE AND APPLICATION 11-4.1 Amplification (Step Height): Type A Figure 11-4.1-1 Type A1 Groove
81	11-4.2 Stylus Condition: Type B 11-4.3 Parameter Measurements: Type C 11-4.4 Overall Instrument Performance: Type D 11-5 PHYSICAL REQUIREMENTS 11-5.1 Materials 11-5.2 Size of the Specimen 11-5.3 Waviness and Flatness Limits 11-6 ASSIGNED VALUE CALCULATION Figure 11-4.1-2 Type A2 Groove Figure 11-5.3-1 Allowable Waviness Height, Wt, for Roughness Calibration Specimens
82	11-7 MECHANICAL REQUIREMENTS 11-7.1 Types A1 and A2 11-7.2 Types B1, B2, and B3 11-7.3 Types C1, C2, C3, and C4 11-7.4 Types D1 and D2
83	11-8 MARKING 11-9 CALIBRATION INTERVAL
84	Figure 11-7.1-1 Assessment of Calibrated Values for Type A1 Table 11-7.1-1 Nominal Values of Depth or Height and Examples of Width for Type A1
85	Table 11-7.1-2 Nominal Values of Depth and Radius for Type A2 Table 11-7.1-3 Tolerances and Uncertainties for Types A1 and A2
86	Figure 11-7.2-1 Type B1 Grooves: Set of Four Grooves Table 11-7.2-1 Tip Size Estimation From the Profile Graph for Type B1
87	Figure 11-7.2-2 Type B2 or Type C2 Specimens With Multiple Grooves Figure 11-7.2-3 Use of Type B3 Specimen
88	Figure 11-7.3-1 Type C1 Grooves Table 11-7.3-1 Typical Ra and RSm Values for Type C1
89	Figure 11-7.3-2 Type C3 Grooves Table 11-7.3-2 Tolerances and Uncertainties for Types C1 Through C4 Table 11-7.3-3 Typical Values of Ra and RSm for Type C2
90	Figure 11-7.3-3 Type C4 Grooves Table 11-7.3-4 Typical Values of Ra for Type C4
91	Figure 11-7.4-1 Unidirectional Irregular Groove Specimen Having Profile Repetition at 5λc Intervals (Type D1 With λc = 0.8 mm) Table 11-7.4-1 Tolerances and Uncertainties for Types D1 and D2
92	Section 12 Specifications and Procedures for Roughness Comparison Specimens 12-1 SCOPE 12-2 REFERENCES 12-3 DEFINITIONS 12-4 ROUGHNESS COMPARISON SPECIMENS 12-4.1 Individually Manufactured (Pilot) Specimens 12-4.2 Replica Specimens 12-5 SURFACE CHARACTERISTICS 12-6 NOMINAL ROUGHNESS GRADES 12-7 SPECIMEN SIZE, FORM, AND LAY
93	12-8 CALIBRATION OF COMPARISON SPECIMENS 12-9 MARKING Table 12-6-1 Nominal Roughness Grades, Ra, for Roughness Comparison Specimens Table 12-7-1 Form and Lay of Roughness Comparison Specimens Representing Various Types of Machined Surfaces
94	Table 12-8-1 Examples of Sampling Lengths for Calibration of Comparison Specimens, mm
95	NONMANDATORY APPENDICES NONMANDATORY APPENDIX A GENERAL NOTES ON USE AND INTERPRETATION OF DATA PRODUCED BY STYLUS INSTRUMENTS A-1 INTRODUCTION A-2 ROUGHNESS AVERAGE A-3 STYLUS TIP RADIUS A-4 SKIDDED MEASUREMENTS A-5 TRAVERSING LENGTH AND MEASUREMENT STATISTICS A-6 FILTER CUTOFF SELECTION
96	A-7 METHODS FOR ROUGHNESS AND WAVINESS SEPARATION
97	NONMANDATORY APPENDIX B CONTROL AND PRODUCTION OF SURFACE TEXTURE B-1 SPECIFICATION B-2 PRODUCTION B-3 INSPECTION
98	Figure B-2-1 Surface Roughness Produced by Common Production Methods
99	B-4 SURFACE TEXTURE OF CASTINGS B-5 SURFACE TEXTURE OF PARTS FABRICATED BY ADDITIVE MANUFACTURING
101	NONMANDATORY APPENDIX C A REVIEW OF ADDITIONAL SURFACE MEASUREMENT METHODS C-1 INTRODUCTION C-2 OPTICAL METHODS
102	Figure C-2.2-1 Schmaltz Profile Microscope Figure C-2.3-1 Reflectance Measurement
103	Figure C-2.4-1 Schematic Diagram of Circular Path Profiler Figure C-2.5-1 Multiple-Beam Interferometer
104	Figure C-2.6-1 Differential Interference Contrast Photograph of Automobile Engine Cylinder Wall Figure C-2.7-1 Differential Interferometry C-3 REPLICAS
105	Figure C-3-1 Zehender Method Figure C-4.1-1 Comparison of Optical and Transmission Electron Microscopes C-4 ELECTRON MICROSCOPE METHODS
106	Figure C-4.2-1 Diagram of Scanning Electron Microscope C-5 SURFACE EXAMINATION REFERENCES
108	Figure D-2.1-1 Average Peak-to-Valley Roughness NONMANDATORY APPENDIX D ADDITIONAL PARAMETERS FOR SURFACE CHARACTERIZATION D-1 INTRODUCTION D-2 INTERNATIONAL STANDARDS AND PARAMETERS D-3 AUTOCOVARIANCE FUNCTION (ACV) D-4 UNIFORMITY OF SURFACE
109	Figure D-2.2-1 Average Spacing of Roughness Peaks Figure D-2.3-1 Swedish Height of Irregularities D-5 GENERAL REFERENCES ON SURFACE TEXTURE MEASUREMENTS
110	Figure D-3-1 Measured Profiles and Their Autocorrelation Functions
111	NONMANDATORY APPENDIX E CHARACTERISTICS OF CERTAIN AREA PROFILING METHODS E-1 INTRODUCTION E-2 IMAGING METHODS E-3 SCANNING METHODS
112	Figure E-3.1.1-1 Schematic Diagram of an Optical Focus-Sensing Instrument
113	Figure E-3.2.1-1 Schematic Diagram of Nomarski Differential Profiler
114	Figure E-3.3.1-1 Area Scanning Stylus Profiler
115	Figure E-3.4.1-1 Basic Structure of an Early STM
116	Figure E-3.5.1-1 Schematic Diagram of an Atomic Force Microscope With an Optical Lever Sensor E-4 REFERENCES
117	Figure E-3.6-1 Schematic Diagram of a Confocal Microscope
118	NONMANDATORY APPENDIX F DESCRIPTIONS OF AREA AVERAGING METHODS F-1 PARALLEL PLATE CAPACITANCE (PPC) F-2 TOTAL INTEGRATED SCATTER (TIS)
119	Figure F-1-1 Comparison of Roughness Void Volumes Figure F-1-2 Principle of Capacitance Between Parallel Plates Figure F-2-1 Schematic Diagram of an Instrument for Measuring TIS F-3 ANGLE RESOLVED SCATTER (ARS)
120	Figure F-3-1 Schematic Diagram of an Instrument for Measuring ARS or BRDF F-4 REFERENCES
121	NONMANDATORY APPENDIX G OBSERVATIONS ON THE FILTERING OF SURFACE PROFILES G-1 INTRODUCTION G-2 DIGITAL INSTRUMENTS
123	NONMANDATORY APPENDIX H REFERENCE SUBROUTINES H-1 INTRODUCTION H-2 REFERENCE H-3 SOURCE CODE H-4 SUBROUTINES
124	Figure H-4-1 Subroutines
131	NONMANDATORY APPENDIX I A COMPARISON OF ASME AND ISO SURFACE TEXTURE PARAMETERS
132	Table I-1 ASME B46.1-2019 Parameters
134	Table J-1 Reference Standards NONMANDATORY APPENDIX J FUNCTIONAL STANDARDS
135	NONMANDATORY APPENDIX K SUGGESTED TERMINOLOGY AND PROCEDURES FOR THE EVALUATION OF FUNCTIONAL CORRELATIONS OF SURFACE TEXTURES WITH PROCESSING AND PERFORMANCE K-1 GENERAL K-2 DEFINITIONS RELATIVE TO FUNCTIONAL CORRELATIONS
136	Table K-3-1 Elements for Reporting a Functional Correlation K-3 REPORT OF FUNCTIONAL CORRELATIONS
137	K-4 EXAMPLES K-5 REFERENCES K-6 BIBLIOGRAPHY OF ARTICLES WITH FUNCTIONAL CORRELATIONS
138	Figure K-4.1-1 Roughness, Rz, Versus Feed Figure K-4.2-1 Mean Relative Areas Versus Scale, μm, From Surfaces Created With All Five Discharge Pulse Energies
139	Figure K-4.2-2 Mean Area-Scale Fractal Complexities (Asfc) Versus Scale for All Pulse Energies
140	Figure K-4.2-3 Multiscale Correlation Strengths of the First Kind
141	Figure K-4.3-1 Example of Regression Analysis and a Strong Functional Correlation
142	Figure K-4.3-2 Multiscale Correlation Strengths of the Second Kind