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| | كتاب Dimensioning and Tolerancing Handbook |  |
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عدد المساهمات : 18996
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تاريخ التسجيل : 01/07/2009
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العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
 | | موضوع: كتاب Dimensioning and Tolerancing Handbook الثلاثاء 03 أبريل 2012, 12:13 am | |
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تذكير بمساهمة فاتح الموضوع : أخوانى فى الله
أحضرت لكم كتاب
Dimensioning and Tolerancing Handbook
Paul J. Drake, Jr.
و المحتوى كما يلي :
Foreword . xxi
About the Editor . xxii
Contributors xxiii
Preface xxv
Acknowledgments xxix
Part 1 History/Lessons Learned
Chapter 1: Quality Thrust . Ron Randall
1.1 Meaning of Quality 1-1
1.2 The Evolution of Quality . 1-2
1.3 Some Quality Gurus and their Contributions 1-2
1.3.1 W. Edwards Deming 1-2
1.3.2 Joseph Juran . 1-3
1.3.3 Philip B. Crosby . 1-4
1.3.4 Genichi Taguchi . 1-5
1.4 The Six Sigma Approach to Quality 1-6
1.4.1 The History of Six Sigma 1-6
1.4.2 Six Sigma Success Stories . 1-7
1.4.3 Six Sigma Basics . 1-7
1.5 The Malcolm Baldrige National Quality Award (MBNQA) 1-9
1.6 References . 1-10
Chapter 2: Dimensional Management Robert H. Nickolaisen, P.E.
2.1 Traditional Approaches to Dimensioning and Tolerancing . 2-1
2.1.1 Engineering Driven Design 2-2
2.1.2 Process Driven Design 2-2
2.1.3 Inspection Driven Design 2-2
2.2 A Need for Change 2-3
2.2.1 Dimensional Management 2-3
2.2.2 Dimensional Management Systems . 2-3
2.2.2.1 Simultaneous Engineering Teams 2-4
2.2.2.2 Written Goals and Objectives . 2-4
2.2.2.3 Design for Manufacturability (DFM) and Design for Assembly (DFA) 2-5
2.2.2.4 Geometric Dimensioning and Tolerancing (GD&T) . 2-6
2.2.2.5 Key Characteristics 2-6
2.2.2.6 Statistical Process Control (SPC) 2-6
2.2.2.7 Variation Measurement and Reduction 2-7
2.2.2.8 Variation Simulation Tolerance Analysis 2-7
2.3 The Dimensional Management Process 2-8
2.4 References . 2-10
2.5 Glossary 2-10
Contentsvi Contents
Chapter 3:Tolerancing Optimization Strategies Gregory A. Hetland, Ph.D.
3.1 Tolerancing Methodologies 3-1
3.2 Tolerancing Progression (Example # 1) 3-1
3.2.1 Strategy # 1 (Linear) . 3-2
3.2.2 Strategy # 2 (Combination of Linear and Geometric) 3-5
3.2.3 Strategy # 3 (Fully Geometric) 3-6
3.3 Tolerancing Progression (Example # 2) 3-6
3.3.1 Strategy # 1 (Linear) . 3-8
3.3.2 Strategy # 2 Geometric Tolerancing ( ) Regardless of Feature Size 3-11
3.3.3 Strategy # 3 (Geometric Tolerancing Progression At Maximum
Material Condition) . 3-12
3.3.4 Strategy # 4 (Tolerancing Progression “Optimized”) 3-13
3.4 Summary 3-15
3.5 References . 3-15
Part 2 Standards
Chapter 4: Drawing Interpretation Patrick J. McCuistion, Ph.D
4.1 Introduction 4-1
4.2 Drawing History . 4-2
4.3 Standards . 4-2
4.3.1 ANSI 4-2
4.3.2 ISO 4-3
4.4 Drawing Types . 4-3
4.4.1 Note 4-3
4.4.2 Detail 4-3
4.4.2.1 Cast or Forged Part 4-4
4.4.2.2 Machined Part 4-4
4.4.2.3 Sheet Stock Part 4-4
4.4.3 Assembly . 4-4
4.5 Border . 4-4
4.5.1 Zones and Center Marks 4-4
4.5.2 Size Conventions 4-13
4.6 Title Blocks . 4-13
4.6.1 Company Name and Address . 4-13
4.6.2 Drawing Title 4-13
4.6.3 Size 4-13
4.6.4 FSCM/CAGE . 4-13
4.6.5 Drawing Number . 4-14
4.6.6 Scale 4-14
4.6.7 Release Date 4-14
4.6.8 Sheet Number 4-14
4.6.9 Contract Number . 4-14
4.6.10 Drawn and Date 4-14
4.6.11 Check, Design, and Dates 4-14
4.6.12 Design Activity and Date 4-15
4.6.13 Customer and Date . 4-15
4.6.14 Tolerances 4-15
4.6.15 Treatment . 4-15
4.6.16 Finish . 4-15
4.6.17 Similar To 4-15
4.6.18 Act Wt and Calc Wt 4-15
4.6.19 Other Title Block Items 4-15
4.7 Revision Blocks . 4-16
4.8 Parts Lists 4-16
4.9 View Projection . 4-16Contents vii
4.9.1 First-Angle Projection 4-16
4.9.2 Third-Angle Projection . 4-16
4.9.3 Auxiliary Views 4-16
4.10 Section Views 4-16
4.10.1 Full Sections . 4-19
4.10.2 Half Sections 4-19
4.10.3 Offset Sections 4-19
4.10.4 Broken-Out Section 4-19
4.10.5 Revolved and Removed Sections 4-22
4.10.6 Conventional Breaks 4-22
4.11 Partial Views 4-23
4.12 Conventional Practices 4-23
4.12.1 Feature Rotation 4-23
4.12.2 Line Precedence . 4-23
4.13 Isometric Views 4-24
4.14 Dimensions 4-25
4.14.1 Feature Types 4-25
4.14.2 Taylor Principle / Envelope Principle . 4-25
4.14.3 General Dimensions . 4-26
4.14.4 Technique . 4-27
4.14.5 Placement . 4-27
4.14.6 Choice . 4-28
4.14.7 Tolerance Representation . 4-28
4.15 Surface Texture . 4-28
4.15.1 Roughness . 4-29
4.15.2 Waviness 4-29
4.15.3 Lay 4-29
4.15.4 Flaws . 4-29
4.16 Notes . 4-29
4.17 Drawing Status 4-30
4.17.1 Sketch . 4-30
4.17.2 Configuration Layout 4-30
4.17.3 Experimental 4-30
4.17.4 Active . 4-30
4.17.5 Obsolete . 4-30
4.18 Conclusion . 4-30
4.19 References . 4-31
Chapter 5: Geometric Dimensioning and Tolerancing . Walter M. Stites
.Paul Drake, P.E.
5.1 Introducing Geometric Dimensioning and Tolerancing (GD&T) . 5-1
5.1.1 What is GD&T? . 5-2
5.1.2 Where Does GD&T Come From?—References . 5-2
5.1.3 Why Do We Use GD&T? . 5-4
5.1.4 When Do We Use GD&T? 5-8
5.1.5 How Does GD&T Work?—Overview . 5-9
5.2 Part Features . 5-9
5.2.1 Nonsize Features 5-10
5.2.2 Features of Size 5-10
5.2.2.1 Screw Threads .5-11
5.2.2.2 Gears and Splines 5-11
5.2.3 Bounded Features .5-11
5.3 Symbols .5-11
5.3.1 Form and Proportions of Symbols 5-12
5.3.2 Feature Control Frame . 5-14
5.3.2.1 Feature Control Frame Placement 5-14
5.3.2.2 Reading a Feature Control Frame 5-16
5.3.3 Basic Dimensions . 5-17viii Contents
5.3.4 Reference Dimensions and Data 5-18
5.3.5 “Square” Symbol 5-18
5.3.6 Tabulated Tolerances . 5-18
5.3.7 “Statistical Tolerance” Symbol . 5-18
5.4 Fundamental Rules . 5-18
5.5 Nonrigid Parts 5-19
5.5.1 Specifying Restraint . 5-20
5.5.2 Singling Out a Free State Tolerance 5-20
5.6 Features of Size—The Four Fundamental Levels of Control . 5-20
5.6.1 Level 1—Size Limit Boundaries . 5-20
5.6.2 Material Condition . 5-23
5.6.2.1 Modifier Symbols 5-24
5.6.3 Method for MMC or LMC . 5-25
5.6.3.1 Level 2—Overall Feature Form . 5-26
5.6.3.2 Level 3—Virtual Condition Boundary for Orientation . 5-33
5.6.3.3 Level 4—Virtual Condition Boundary for Location . 5-34
5.6.3.4 Level 3 or 4 Virtual Condition Equal to Size Limit (Zero Tolerance) 5-35
5.6.3.5 Resultant Condition Boundary 5-37
5.6.4 Method for RFS 5-38
5.6.4.1 Tolerance Zone Shape . 5-38
5.6.4.2 Derived Elements 5-38
5.6.5 Alternative “Center Method” for MMC or LMC 5-43
5.6.5.1 Level 3 and 4 Adjustment—Actual Mating/Minimum Material Sizes 5-43
5.6.5.2 Level 2 Adjustment—Actual Local Sizes 5-45
5.6.5.3 Disadvantages of Alternative “Center Method” . 5-46
5.6.6 Inner and Outer Boundaries . 5-46
5.6.7 When do we use a Material Condition Modifier? . 5-47
5.7 Size Limits (Level 1 Control) 5-48
5.7.1 Symbols for Limits and Fits 5-48
5.7.2 Limit Dimensioning 5-49
5.7.3 Plus and Minus Tolerancing 5-49
5.7.4 Inch Values . 5-49
5.7.5 Millimeter Values 5-49
5.8 Form (Only) Tolerances (Level 2 Control) 5-50
5.8.1 Straightness Tolerance for Line Elements 5-51
5.8.2 Straightness Tolerance for a Cylindrical Feature . 5-52
5.8.3 Flatness Tolerance for a Single Planar Feature 5-52
5.8.4 Flatness Tolerance for a Width-Type Feature 5-52
5.8.5 Circularity Tolerance 5-53
5.8.5.1 Circularity Tolerance Applied to a Spherical Feature . 5-55
5.8.6 Cylindricity Tolerance . 5-55
5.8.7 Circularity or Cylindricity Tolerance with Average Diameter . 5-56
5.8.8 Application Over a Limited Length or Area . 5-57
5.8.9 Application on a Unit Basis 5-57
5.8.10 Radius Tolerance . 5-58
5.8.10.1 Controlled Radius Tolerance 5-59
5.8.11 Spherical Radius Tolerance . 5-59
5.8.12 When Do We Use a Form Tolerance? 5-60
5.9 Datuming . 5-61
5.9.1 What is a Datum? . 5-61
5.9.2 Datum Feature . 5-61
5.9.2.1 Datum Feature Selection . 5-61
5.9.2.2 Functional Hierarchy . 5-63
5.9.2.3 Surrogate and Temporary Datum Features . 5-64
5.9.2.4 Identifying Datum Features . 5-65
5.9.3 True Geometric Counterpart (TGC)—Introduction . 5-67
5.9.4 Datum 5-69
5.9.5 Datum Reference Frame (DRF) and Three Mutually Perpendicular
Planes 5-69Contents ix
5.9.6 Datum Precedence . 5-69
5.9.7 Degrees of Freedom 5-72
5.9.8 TGC Types 5-74
5.9.8.1 Restrained versus Unrestrained TGC 5-75
5.9.8.2 Nonsize TGC . 5-75
5.9.8.3 Adjustable-size TGC . 5-75
5.9.8.4 Fixed-size TGC . 5-77
5.9.9 Datum Reference Frame (DRF) Displacement . 5-80
5.9.9.1 Relative to a Boundary of Perfect Form TGC . 5-81
5.9.9.2 Relative to a Virtual Condition Boundary TGC . 5-83
5.9.9.3 Benefits of DRF Displacement 5-83
5.9.9.4 Effects of All Datums of the DRF . 5-83
5.9.9.5 Effects of Form, Location, and Orientation 5-83
5.9.9.6 Accommodating DRF Displacement 5-83
5.9.10 Simultaneous Requirements . 5-86
5.9.11 Datum Simulation 5-89
5.9.12 Unstable Datums, Rocking Datums, Candidate Datums 5-89
5.9.13 Datum Targets . 5-91
5.9.13.1 Datum Target Selection 5-91
5.9.13.2 Identifying Datum Targets . 5-92
5.9.13.3 Datum Target Dimensions . 5-94
5.9.13.4 Interdependency of Datum Target Locations 5-95
5.9.13.5 Applied to Features of Size . 5-95
5.9.13.6 Applied to Any Type of Feature 5-97
5.9.13.7 Target Set with Switchable Precedence 5-99
5.9.14 Multiple Features Referenced as a Single Datum Feature . 5-100
5.9.14.1 Feature Patterns . 5-100
5.9.14.2 Coaxial and Coplanar Features . 5-103
5.9.15 Multiple DRFs . 5-103
5.10 Orientation Tolerance (Level 3 Control) . 5-103
5.10.1 How to Apply It . 5-103
5.10.2 Datums for Orientation Control 5-104
5.10.3 Applied to a Planar Feature (Including Tangent Plane Application) . 5-104
5.10.4 Applied to a Cylindrical or Width-Type Feature . 5-106
5.10.4.1 Zero Orientation Tolerance at MMC or LMC 5-107
5.10.5 Applied to Line Elements 5-107
5.10.6 The 24 Cases . 5-109
5.10.7 Profile Tolerance for Orientation . 5-109
5.10.8 When Do We Use an Orientation Tolerance? . 5-109
5.11 Positional Tolerance (Level 4 Control) .5-113
5.11.1 How Does It Work? 5-113
5.11.2 How to Apply It 5-114
5.11.3 Datums for Positional Control .5-116
5.11.4 Angled Features .5-117
5.11.5 Projected Tolerance Zone 5-117
5.11.6 Special-Shaped Zones/Boundaries . 5-121
5.11.6.1 Tapered Zone/Boundary 5-121
5.11.6.2 Bidirectional Tolerancing . 5-122
5.11.6.3 Bounded Features 5-126
5.11.7 Patterns of Features 5-127
5.11.7.1 Single-Segment Feature Control Frame 5-127
5.11.7.2 Composite Feature Control Frame . 5-129
5.11.7.3 Rules for Composite Control . 5-131
5.11.7.4 Stacked Single-Segment Feature Control Frames 5-134
5.11.7.5 Rules for Stacked Single-Segment Feature Control Frames . 5-136
5.11.7.6 Coaxial and Coplanar Features . 5-136
5.11.8 Coaxiality and Coplanarity Control . 5-137x Contents
5.12 Runout Tolerance 5-138
5.12.1 Why Do We Use It? 5-138
5.12.2 How Does It Work? . 5-138
5.12.3 How to Apply It . 5-139
5.12.4 Datums for Runout Control . 5-140
5.12.5 Circular Runout Tolerance . 5-141
5.12.6 Total Runout Tolerance 5-143
5.12.7 Application Over a Limited Length 5-143
5.12.8 When Do We Use a Runout Tolerance? . 5-144
5.12.9 Worst Case Boundaries . 5-145
5.13 Profile Tolerance . 5-145
5.13.1 How Does It Work? . 5-145
5.13.2 How to Apply It . 5-145
5.13.3 The Basic Profile . 5-147
5.13.4 The Profile Tolerance Zone . 5-147
5.13.5 The Profile Feature Control Frame 5-149
5.13.6 Datums for Profile Control 5-149
5.13.7 Profile of a Surface Tolerance 5-149
5.13.8 Profile of a Line Tolerance 5-149
5.13.9 Controlling the Extent of a Profile Tolerance . 5-150
5.13.10 Abutting Zones 5-153
5.13.11 Profile Tolerance for Combinations of Characteristics 5-153
5.13.11.1 With Positional Tolerancing for Bounded Features 5-153
5.13.12 Patterns of Profiled Features . 5-154
5.13.12.1 Single-Segment Feature Control Frame 5-154
5.13.12.2 Composite Feature Control Frame . 5-154
5.13.12.3 Stacked Single-Segment Feature Control Frames 5-155
5.13.12.4 Optional Level 2 Control 5-155
5.13.13 Composite Profile Tolerance for a Single Feature . 5-156
5.14 Symmetry Tolerance 5-156
5.14.1 How Does It Work? . 5-157
5.14.2 How to Apply It . 5-159
5.14.3 Datums for Symmetry Control . 5-159
5.14.4 Concentricity Tolerance . 5-160
5.14.4.1 Concentricity Tolerance for Multifold Symmetry about a Datum Axis . 5-160
5.14.4.2 Concentricity Tolerance about a Datum Point . 5-161
5.14.5 Symmetry Tolerance about a Datum Plane 5-161
5.14.6 Symmetry Tolerancing of Yore (Past Practice) . 5-161
5.14.7 When Do We Use a Symmetry Tolerance? . 5-162
5.15 Combining Feature Control Frames . 5-162
5.16 “Instant” GD&T 5-163
5.16.1 The “Dimension Origin” Symbol 5-163
5.16.2 General Note to Establish Basic Dimensions 5-163
5.16.3 General Note in Lieu of Feature Control Frames 5-164
5.17 The Future of GD&T 5-164
5.18 References . 5-166
Chapter 6: Differences Between US Standards and Other Standards .
. Alex Krulikowski
Scott DeRaad
6.1 Dimensioning Standards . 6-1
6.1.1 US Standards 6-2
6.1.2 International Standards . 6-2
6.1.2.1 ISO Geometrical Product Specification Masterplan . 6-4
6.2 Comparison of ASME and ISO Standards . 6-5
6.2.1 Organization and Logistics . 6-5
6.2.2 Number of Standards . 6-5
6.2.3 Interpretation and Application 6-5Contents xi
6.2.3.1 ASME 6-6
6.2.3.2 ISO 6-6
6.3 Other Standards 6-27
6.3.1 National Standards Based on ISO or ASME Standards . 6-27
6.3.2 US Government Standards 6-28
6.3.3 Corporate Standards 6-28
6.3.4 Multiple Dimensioning Standards . 6-29
6.4 Future of Dimensioning Standards . 6-30
6.5 Effects of Technology . 6-30
6.6 New Dimensioning Standards 6-30
6.7 References . 6-30
Chapter 7: Mathematical Definition of Dimensioning and Tolerancing Principles
Mark A. Nasson
7.1 Introduction 7-1
7.2 Why Mathematical Tolerance Definitions? . 7-1
7.2.1 Metrology Crisis (The GIDEP Alert) . 7-2
7.2.2 Specification Crisis . 7-3
7.2.3 National Science Foundation Tolerancing Workshop . 7-3
7.2.4 A New National Standard 7-4
7.3 What are Mathematical Tolerance Definitions? . 7-4
7.3.1 Parallel, Equivalent, Unambiguous Expression . 7-4
7.3.2 Metrology Independent . 7-4
7.4 Detailed Descriptions of Mathematical Tolerance Definitions . 7-4
7.4.1 Introduction 7-4
7.4.2 Vectors 7-5
7.4.2.1 Vector Addition and Subtraction 7-5
7.4.2.2 Vector Dot Products . 7-6
7.4.2.3 Vector Cross Products 7-6
7.4.3 Actual Value / Measured Value . 7-7
7.4.4 Datums 7-8
7.4.4.1 Candidate Datums / Datum Reference Frames . 7-8
7.4.4.2 Degrees of Freedom 7-8
7.4.5 Form tolerances 7-9
7.4.5.1 Circularity . 7-9
7.4.5.2 Cylindricity 7-12
7.4.5.3 Flatness 7-13
7.5 Where Do We Go from Here? 7-14
7.5.1 ASME Standards Committees 7-14
7.5.2 International Standards Efforts 7-14
7.5.3 CAE Software Developers . 7-14
7.6 Acknowledgments . 7-15
7.7 References . 7-15
Chapter 8: Statistical Tolerancing Vijay Srinivasan, Ph.D
8.1 Introduction 8-1
8.2 Specification of Statistical Tolerancing . 8-2
8.2.1 Using Process Capability Indices 8-2
8.2.2 Using RMS Deviation Index 8-4
8.2.3 Using Percent Containment 8-5
8.3 Statistical Tolerance Zones . 8-5
8.3.1 Population Parameter Zones 8-6
8.3.2 Distribution Function Zones . 8-7
8.4 Additional Illustrations . 8-7
8.5 Summary and Concluding Remarks . 8-9
8.6 References . 8-10xii Contents
Part 3 Design
Chapter 9: Traditional Approaches to Analyzing Mechanical Tolerance Stacks .
Paul Drake
9.1 Introduction 9-1
9.2 Analyzing Tolerance Stacks 9-1
9.2.1 Establishing Performance/Assembly Requirements 9-1
9.2.2 Loop Diagram . 9-3
9.2.3 Converting Dimensions to Equal Bilateral Tolerances 9-5
9.2.4 Calculating the Mean Value (Gap) for the Requirement 9-7
9.2.5 Determine the Method of Analysis . 9-8
9.2.6 Calculating the Variation for the Requirement 9-9
9.2.6.1 Worst Case Tolerancing Model 9-9
9.2.6.2 RSS Model . 9-12
9.2.6.3 Modified Root Sum of the Squares Tolerancing Model . 9-18
9.2.6.4 Comparison of Variation Models . 9-22
9.2.6.5 Estimated Mean Shift Model . 9-23
9.3 Analyzing Geometric Tolerances . 9-24
9.3.1 Form Controls . 9-25
9.3.2 Orientation Controls . 9-26
9.3.3 Position . 9-27
9.3.3.1 Position at RFS . 9-27
9.3.3.2 Position at MMC or LMC 9-27
9.3.3.3 Virtual and Resultant Conditions . 9-28
9.3.3.4 Equations 9-28
9.3.3.5 Composite Position 9-32
9.3.4 Runout . 9-33
9.3.5 Concentricity/Symmetry 9-33
9.3.6 Profile 9-34
9.3.6.1 Profile Tolerancing with an Equal Bilateral Tolerance Zone 9-34
9.3.6.2 Profile Tolerancing with a Unilateral Tolerance Zone 9-35
9.3.6.3 Profile Tolerancing with an Unequal Bilateral Tolerance Zone . 9-35
9.3.6.4 Composite Profile . 9-36
9.3.7 Size Datums . 9-36
9.4 Abbreviations 9-37
9.5 Terminology . 9-39
9.6 References . 9-39
Chapter 10: Statistical Background and Concepts Ron Randall
10.1 Introduction 10-1
10.2 Shape, Locations, and Spread 10-2
10.3 Some Important Distributions 10-2
10.3.1 The Normal Distribution . 10-2
10.3.2 Lognormal Distribution . 10-6
10.3.3 Poisson Distribution . 10-8
10.4 Measures of Quality and Capability . 10-10
10.4.1 Process Capability Index . 10-10
10.4.2 Process Capability Index Relative to Process Centering (Cpk) 10-12
10.5 Summary 10-14
10.6 References . 10-14
10.7 Appendix . 10-15Contents xiii
Chapter 11: Predicting Assembly Quality (Six Sigma Methodologies to Optimize
Tolerances) Dale Van Wyk
11.1 Introduction .11-1
11.2 What is Tolerance Allocation? .11-1
11.3 Process Standard Deviations 11-2
11.4 Worst Case Allocation .11-5
11.4.1 Assign Component Dimensions 11-6
11.4.2 Determine Assembly Performance, P .11-7
11.4.3 Assign the process with the largest si to each component 11-8
11.4.4 Calculate the Worst Case Assembly, twc6 11-8
11.4.5 Is P³t
wc6? .11-9
11.4.6 Estimating Defect Rates 11-10
11.4.7 Verification 11-12
11.4.8 Adjustments to Meet Quality Goals 11-13
11.4.9 Worst Case Allocation Summary 11-13
11.5 Statistical Allocation 11-13
11.5.1 Calculating Assembly Variation and Defect Rate .11-15
11.5.2 First Steps in Statistical Allocation .11-15
11.5.3 Calculate Expected Assembly Performance, P6 .11-15
11.5.4 Is P³P
6? 11-16
11.5.5 Allocating Tolerances 11-17
11.5.6 Statistical Allocation Summary 11-20
11.6 Dynamic RSS Allocation .11-20
11.7 Static RSS analysis .11-23
11.8 Comparison of the Techniques 11-24
11.9 Communication of Requirements 11-25
11.10 Summary .11-26
11.11 Abbreviations .11-26
11.12 References 11-27
Chapter 12: Multi-Dimensional Tolerance Analysis (Manual Method) Dale Van Wyk
12.1 Introduction 12-1
12.2 Determining Sensitivity . 12-2
12.3 A Technique for Developing Gap Equations . 12-4
12.4 Utilizing Sensitivity Information to Optimize Tolerances 12-12
12.5 Summary 12-13
Chapter 13: Multi-Dimensional Tolerance Analysis (Automated Method)
Kenneth W. Chase, Ph.D.
13.1 Introduction 13-1
13.2 Three Sources of Variation in Assemblies . 13-2
13.3 Example 2D Assembly – Stacked Blocks 13-3
13.4 Steps in Creating an Assembly Tolerance Model 13-4
13.5 Steps in Analyzing an Assembly Tolerance Model 13-12
13.5.5.1 Percent rejects 13-21
13.5.5.2 Percent Contribution Charts 13-22
13.5.5.3 Sensitivity Analysis 13-24
13.5.5.4 Modifying Geometry . 13-24
13.6 Summary 13-26
13.7 References . 13-27xiv Contents
Chapter 14: Minimum-Cost Tolerance Allocation Kenneth W. Chase, Ph.D.
14.1 Tolerance Allocation Using Least Cost Optimization . 14-1
14.2 1-D Tolerance Allocation 14-1
14.3 1-D Example: Shaft and Housing Assembly . 14-3
14.4 Advantages / Disadvantages of the Lagrange Multiplier Method . 14-7
14.6 2-D and 3-D Tolerance Allocation 14-8
14.5 True Cost and Optimum Acceptance Fraction 14-8
14.7 2-D Example: One-way Clutch Assembly . 14-9
14.7.1 Vector Loop Model and Assembly Function for the Clutch . 14-10
14.8 Allocation by Scaling, Weight Factors . 14-10
14.8.1 Proportional Scaling by Worst Case .14-11
14.8.2 Proportional Scaling by Root-Sum-Squares .14-11
14.8.3 Allocation by Weight Factors .14-11
14.9 Allocation by Cost Minimization . 14-12
14.9.1 Minimum Cost Tolerances by Worst Case 14-13
14.9.2 Minimum Cost Tolerances by RSS 14-14
14.10 Tolerance Allocation with Process Selection 14-15
14.11 Summary 14-16
14.12 References . 14-17
14.13 Appendix: Cost-Tolerance Functions for Metal Removal Processes . 14-18
Chapter 15: Automating the Tolerancing Process . Charles Glancy
James Stoddard
. Marvin Law
15.1 Background Information 15-2
15.1.1 Benefits of Automation 15-2
15.1.2 Overview of the Tolerancing Process 15-2
15.2 Automating the Creation of the Tolerance Model 15-3
15.2.1 Characterizing Critical Design Measurements . 15-3
15.2.2 Characterizing the Model Function . 15-4
15.2.2.1 Model Definition 15-4
15.2.2.2 Model Form 15-5
15.2.2.3 Model Scope 15-5
15.2.3 Characterizing Input Variables . 15-6
15.3 Automating Tolerance Analysis . 15-6
15.3.1 Method of System Moments 15-6
15.3.3 Distribution Fitting 15-8
15.3.2 Monte Carlo Simulation . 15-8
15.4 Automating Tolerance Optimization 15-9
15.5 Automating Communication Between Design and Manufacturing . 15-9
15.5.1 Manufacturing Process Capabilities . 15-10
15.5.1.1 Manufacturing Process Capability Database . 15-10
15.5.1.2 Database Administration 15-11
15.5.2 Design Requirements and Assumptions .15-11
15.6 CAT Automation Tools . 15-12
15.6.1 Tool Capability 15-12
15.6.2 Ease of Use . 15-12
15.6.3 Training . 15-13
15.6.4 Technical Support . 15-13
15.6.5 Data Management and CAD Integration 15-13
15.6.6 Reports and Records . 15-13
15.6.7 Tool Enhancement and Development . 15-14
15.6.8 Deployment 15-14
15.7 Summary 15-14
15.8 References . 15-14Contents xv
Chapter 16: Working in an Electronic Environment .Paul Matthews
16.1 Introduction 16-1
16.2 Paperless/Electronic Environment 16-2
16.2.1 Definition . 16-2
16.3 Development Information Tools 16-3
16.3.1 Product Development Automation Strategy 16-3
16.3.2 Master Model Theory . 16-4
16.3.3 Template Design . 16-7
16.3.3.1 Template Part and Assembly Databases . 16-7
16.3.3.2 Template Features 16-8
16.3.3.3 Templates for Analyses 16-9
16.3.3.4 Templates for Documentation 16-9
16.3.4 Component Libraries . 16-9
16.3.5 Information Verification . 16-10
16.4 Product Information Management .16-11
16.4.1 Configuration Management Techniques .16-11
16.4.2 Data Management Components 16-12
16.4.2.1 Workspace . 16-12
16.4.2.2 Product Vault 16-12
16.4.2.3 Company Vault . 16-12
16.4.3 Document Administrator . 16-13
16.4.4 File Cabinet Control 16-13
16.4.5 Software Automation . 16-13
16.5 Information Storage and Transfer . 16-13
16.5.1 Internet . 16-13
16.5.2 Electronic Mail 16-14
16.5.3 File Transfer Protocol . 16-14
16.5.4 Media Transfer 16-15
16.6 Manufacturing Guidelines . 16-15
16.6.1 Manufacturing Trust . 16-15
16.6.2 Dimensionless Prints 16-15
16.6.2.1 Sheetmetal . 16-16
16.6.2.2 Injection Molded Plastic . 16-17
16.6.2.3 Hog Out Parts . 16-17
16.6.2.4 Castings 16-18
16.6.2.5 Rapid Prototypes . 16-18
16.7 Database Format Standards 16-19
16.7.1 Native Database . 16-19
16.7.2 2-D Formats 16-19
16.7.2.1 Data eXchange Format (DXF) . 16-19
16.7.2.2 Hewlett-Packard Graphics Language (HPGL) 16-20
16.8 3-D Formats 16-20
16.8.1 Initial Graphics Exchange Specification (IGES) . 16-20
16.8.2 STandard for the Exchange of Product (STEP) 16-20
16.8.3 Virtual Reality Modeling Language (VRML) 16-20
16.8.4 STereoLithography (STL) 16-21
16.9 General Information Formats . 16-21
16.9.1 Hypertext Markup Language (HTML) 16-21
16.9.2 Portable Document Format (PDF) . 16-22
16.10 Graphics Formats . 16-22
16.10.1 Encapsulated PostScript (EPS) . 16-22
16.10.2 Joint Photographic Experts Group (JPEG) 16-22
16.10.3 Tagged Image File Format (TIFF) 16-22
16.11 Conclusion . 16-23
16.12 Appendix A IGES Entities 16-23xvi Contents
Part 4 Manufacturing
Chapter 17: Collecting and Developing Manufacturing Process Capability Models
. Michael D. King
17.1 Why Collect and Develop Process Capability Models? . 17-1
17.2 Developing Process Capability Models 17-2
17.3 Quality Prediction Models - Variable versus Attribute Information 17-3
17.3.1 Collecting and Modeling Variable Process Capability Models . 17-3
17.3.2 Collecting and Modeling Attribute Process Capability Models . 17-7
17.3.3 Feature Factoring Method . 17-7
17.3.4 Defect Weighting Methodology 17-7
17.4 Cost and Cycle Time Prediction Modeling Variations . 17-8
17.5 Validating and Checking the Results of Your Predictive Models 17-9
17.6 Summary .17-11
17.7 References 17-11
Part 5 Gaging
Chapter 18: Paper Gage Techniques .Martin P. Wright
18.1 What is Paper Gaging? . 18-1
18.2 Advantages and Disadvantages to Paper Gaging . 18-2
18.3 Discrimination Provided By a Paper Gage 18-3
18.4 Paper Gage Accuracy . 18-3
18.5 Plotting Paper Gage Data Points . 18-4
18.6 Paper Gage Applications . 18-4
18.6.1 Locational Verification 18-5
18.6.1.1 Simple Hole Pattern Verification 18-5
18.6.1.2 Three-Dimensional Hole Pattern Verification 18-8
18.6.1.3 Composite Positional Tolerance Verification 18-10
18.6.2 Capturing Tolerance From Datum Features Subject to Size Variation . 18-12
18.6.2.1 Datum Feature Applied on an RFS Basis . 18-12
18.6.2.2 Datum Feature Applied on an MMC Basis 18-12
18.6.2.3 Capturing Rotational Shift Tolerance from a Datum Feature
Applied on an MMC Basis 18-16
18.6.2.4 Determining the Datum from a Pattern of Features 18-19
18.6.3 Paper Gage Used as a Process Analysis Tool . 18-21
18.7 Summary 18-23
18.8 References . 18-23
Chapter 19: Receiver Gages — Go Gages and Functional Gages James D. Meadows
19.1 Introduction 19-1
19.2 Gaging Fundamentals 19-2
19.3 Gage Tolerancing Policies . 19-3
19.4 Examples of Gages . 19-4
19.4.1 Position Using Partial and Planar Datum Features . 19-4
19.4.2 Position Using Datum Features of Size at MMC 19-6
19.4.3 Position and Profile Using a Simultaneous Gaging Requirement . 19-9
19.4.4 Position Using Centerplane Datums . 19-12
19.4.5 Multiple Datum Structures 19-14
19.4.6 Secondary and Tertiary Datum Features of Size . 19-17Contents xvii
19.5 Push Pin vs. Fixed Pin Gaging . 19-20
19.6 Conclusion . 19-20
19.7 References . 19-20
Part 6 Precision Metrology
Chapter 20: Measurement Systems Analysis Gregory A. Hetland, Ph.D.
20.1 Introduction 20-1
20.2 Measurement Methods Analysis 20-2
20.2.1 Measurement System Definition (Phase 1) . 20-2
20.2.1.1 Identification of Variables 20-2
20.2.1.2 Specifications of Conformance 20-3
20.2.1.3 Measurement System Capability Requirements . 20-3
20.2.2 Identification of Sources of Uncertainty (Phase 2) . 20-3
20.2.2.1 Machine Sources of Uncertainty 20-4
20.2.2.2 Software Sources of Uncertainty . 20-4
20.2.2.3 Environmental Sources of Uncertainty . 20-5
20.2.2.4 Part Sources of Uncertainty 20-5
20.2.2.5 Fixturing Sources of Uncertainty . 20-5
20.2.2.6 Operator Sources of Uncertainty . 20-6
20.2.3 Measurement System Qualification (Phase 3) 20-6
20.2.3.1 Plan the Capabilities Studies 20-6
20.2.3.2 Production Systems . 20-7
20.2.3.3 Calibrate the System 20-7
20.2.3.4 Conduct Studies and Define Capabilities . 20-8
20.2.4 Quantify the Error Budget (Phase 4) 20-8
20.2.4.1 Plan Testing (Isolate Error Sources) . 20-8
20.2.4.2 Analyze Uncertainty 20-9
20.2.5 Optimize Measurement System (Phase 5) 20-9
20.2.5.1 Identify Opportunities 20-9
20.2.5.2 Attempt Improvements and Revisit Testing . 20-9
20.2.5.3 Revisit Qualification 20-10
20.2.6 Implement and Control Measurement System (Phase 6) 20-10
20.2.6.1 Plan Performance Criteria . 20-10
20.2.6.2 Plan Calibration and Maintenance Requirements .20-11
20.2.6.3 Implement System and Initiate Control 20-11
20.2.6.4 CMM Operator Competencies 20-11
20.2.6.5 Business Issue . 20-12
20.3 CMM Performance Test Overview 20-17
20.3.1 Environmental Tests (Section 1) 20-17
20.3.1.1 Temperature Parameters . 20-17
20.3.1.2 Other Environmental Parameters 20-20
20.3.2 Machine Tests (Section 2) . 20-21
20.3.2.1 Probe Settling Time 20-21
20.3.2.2 Probe Deflection 20-24
20.3.2.3 Other Machine Parameters . 20-27
20.3.2.4 Multiple Probes . 20-27
20.3.3 Feature Based Measurement Tests (Section 3) . 20-28
20.3.3.1 Number of Points Per Feature 20-30
20.3.3.2 Other Geometric Features 20-34
20.3.3.3 Contact Scanning 20-34
20.3.3.4 Surface Roughness 20-35
20.4 CMM Capability Matrix 20-35
20.5 References . 20-38xviii Contents
Part 7 Applications
Chapter 21: Predicting Piecepart Quality . Dan A. Watson, Ph.D.
21.1 Introduction 21-1
21.2 The Problem 21-2
21.3 Statistical Framework 21-3
21.3.1 Assumptions . 21-3
21.3.2 Internal Feature at MMC 21-5
21.3.3 Internal Feature at LMC . 21-7
21.3.4 External Features 21-8
21.3.5 Alternate Distribution Assumptions . 21-8
21.4 Non-Size Feature Applications . 21-9
21.5 Example . 21-9
21.6 Summary 21-10
21.7 References 21-11
Chapter 22: Floating and Fixed Fasteners .Paul Zimmermann
22.1 Introduction 22-1
22.2 Floating and Fixed Fasteners 22-1
22.2.1 What is a Floating Fastener? . 22-4
22.2.2 What is a Fixed Fastener? . 22-4
22.2.3 What is a Double-Fixed Fastener? . 22-4
22.3 Geometric Dimensioning and Tolerancing (Cylindrical Tolerance Zone
Versus +/- Tolerancing) 22-5
22.4 Calculations for Fixed, Floating and Double-fixed Fasteners . 22-8
22.5 Geometric Dimensioning and Tolerancing Rules/Formulas for Floating Fastener 22-8
22.5.1 How to Calculate Clearance Hole Diameter for a Floating Fastener Application 22-8
22.5.2 How to Calculate Counterbore Diameter for a Floating Fastener Application 22-9
22.5.3 Why Floating Fasteners are Not Recommended 22-10
22.6 Geometric Dimensioning and Tolerancing Rules/Formulas for Fixed Fasteners 22-10
22.6.1 How to Calculate Fixed Fastener Applications 22-10
22.6.2 How to Calculate Counterbore Diameter for a Fixed Fastener Application . 22-10
22.6.3 Why Fixed Fasteners are Recommended .22-11
22.7 Geometric Dimensioning and Tolerancing Rules/Formulas for Double-fixed
Fastener .22-11
22.7.1 How to Calculate a Clearance Hole .22-11
22.7.2 How to Calculate the Countersink Diameter, Head Height Above and Head
Height Below the Surface .22-11
22.7.3 What Are the Problems Associated with Double-fixed Fasteners? . 22-13
22.8 Nut Plates: Floating and Nonfloating (see Fig. 22-14) 22-14
22.9 Projected Tolerance Zone . 22-15
22.9.1 Comparison of Positional Tolerancing With and Without a Projected Tolerance
Zone . 22-16
22.9.2 Percent of Actual Orientation Versus Lost Functional Tolerance . 22-18
22.10 Hardware Pages 22-18
22.10.1 Floating Fastener Hardware Pages . 22-20
22.10.2 Fixed Fastener Hardware Pages 22-21
22.10.3 Double-fixed Fastener Hardware Pages . 22-23
22.10.4 Counterbore Depths - Pan Head and Socket Head Cap Screws 22-25
22.10.5 Flat Head Screw Head Height - Above and Below the Surface . 22-26
22.11 References . 22-26Contents xix
Chapter 23: Fixed and Floating Fastener Variation .Chris Cuba
23.1 Introduction 23-1
23.2 Hole Variation . 23-2
23.3 Assembly Variation 23-4
23.4 Fixed and Floating Fasteners 23-4
23.4.1 Fixed Fastener Assembly Shift 23-5
23.4.2 Fixed Fastener Assembly Shift Using One Equation and Dimension Loop . 23-6
23.4.3 Fixed Fastener Equation 23-7
23.4.4 Fixed Fastener Gap Analysis Steps . 23-7
23.4.5 Floating Fastener Gap Analysis Steps 23-8
23.5 Summary 23-9
23.6 References . 23-10
Chapter 24: Pinned Interfaces . Stephen Harry Werst
24.1 List of Symbols (Definitions and Terminology) 24-1
24.2 Introduction 24-2
24.3 Performance Considerations . 24-2
24.4 Variation Components of Pinned Interfaces . 24-3
24.4.1 Type I Error . 24-3
24.4.2 Type II Error 24-3
24.5 Types of Alignment Pins . 24-4
24.6 Tolerance Allocation Methods - Worst Case vs. Statistical 24-6
24.7 Processes and Capabilities 24-6
24.8 Design Methodology 24-7
24.9 Proper Use of Material Modifiers 24-10
24.10 Temperature Considerations 24-11
24.11 Two Round Pins with Two Holes .24-11
24.11.1 Fit 24-12
24.11.2 Rotation Errors 24-12
24.11.3 Translation Errors . 24-13
24.11.4 Performance Constants 24-13
24.11.5 Dimensioning Methodology 24-14
24.12 Round Pins with a Hole and a Slot 24-14
24.12.1 Fit 24-14
24.12.2 Rotation Errors 24-16
24.12.3 Translation Errors . 24-17
24.12.4 Performance Constants 24-17
24.12.5 Dimensioning Methodology 24-17
24.13 Round Pins with One Hole and Edge Contact 24-18
24.13.1 Fit 24-19
24.13.2 Rotation Errors 24-20
24.13.3 Translation errors . 24-20
24.13.4 Performance Constants 24-20
24.13.5 Dimensioning Methodology 24-20
24.14 One Diamond Pin and One Round Pin with Two Holes . 24-23
24.14.1 Fit 24-23
24.14.2 Rotation and Translation Errors . 24-24
24.14.3 Performance Constants 24-24
24.14.4 Dimensioning Methodology 24-24
24.15 One Parallel-Flats Pin and One Round Pin with Two Holes . 24-26
24.15.1 Fit 24-26
24.15.2 Rotation and Translation Errors . 24-27
24.15.3 Performance Constants 24-27
24.15.4 Dimensioning Methodology 24-28
24.16 References . 24-29xx Contents
Chapter 25: Gage Repeatability and Reproducibility (GR&R) Calculations .
. Gregory A. Hetland, Ph.D.
25.1 Introduction 25-1
25.2 Standard GR&R Procedure 25-1
25.3 Summary 25-7
25.4 References . 25-7
Part 8 The Future
Chapter 26: The Future . Several contributors
Figures . F-1
Tables . T-1
Index I-1
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أخوانى فى الله
أحضرت لكم كتاب
Dimensioning and Tolerancing Handbook
Paul J. Drake, Jr.
و المحتوى كما يلي :
Foreword . xxi
About the Editor . xxii
Contributors xxiii
Preface xxv
Acknowledgments xxix
Part 1 History/Lessons Learned
Chapter 1: Quality Thrust . Ron Randall
1.1 Meaning of Quality 1-1
1.2 The Evolution of Quality . 1-2
1.3 Some Quality Gurus and their Contributions 1-2
1.3.1 W. Edwards Deming 1-2
1.3.2 Joseph Juran . 1-3
1.3.3 Philip B. Crosby . 1-4
1.3.4 Genichi Taguchi . 1-5
1.4 The Six Sigma Approach to Quality 1-6
1.4.1 The History of Six Sigma 1-6
1.4.2 Six Sigma Success Stories . 1-7
1.4.3 Six Sigma Basics . 1-7
1.5 The Malcolm Baldrige National Quality Award (MBNQA) 1-9
1.6 References . 1-10
Chapter 2: Dimensional Management Robert H. Nickolaisen, P.E.
2.1 Traditional Approaches to Dimensioning and Tolerancing . 2-1
2.1.1 Engineering Driven Design 2-2
2.1.2 Process Driven Design 2-2
2.1.3 Inspection Driven Design 2-2
2.2 A Need for Change 2-3
2.2.1 Dimensional Management 2-3
2.2.2 Dimensional Management Systems . 2-3
2.2.2.1 Simultaneous Engineering Teams 2-4
2.2.2.2 Written Goals and Objectives . 2-4
2.2.2.3 Design for Manufacturability (DFM) and Design for Assembly (DFA) 2-5
2.2.2.4 Geometric Dimensioning and Tolerancing (GD&T) . 2-6
2.2.2.5 Key Characteristics 2-6
2.2.2.6 Statistical Process Control (SPC) 2-6
2.2.2.7 Variation Measurement and Reduction 2-7
2.2.2.8 Variation Simulation Tolerance Analysis 2-7
2.3 The Dimensional Management Process 2-8
2.4 References . 2-10
2.5 Glossary 2-10
Contentsvi Contents
Chapter 3:Tolerancing Optimization Strategies Gregory A. Hetland, Ph.D.
3.1 Tolerancing Methodologies 3-1
3.2 Tolerancing Progression (Example # 1) 3-1
3.2.1 Strategy # 1 (Linear) . 3-2
3.2.2 Strategy # 2 (Combination of Linear and Geometric) 3-5
3.2.3 Strategy # 3 (Fully Geometric) 3-6
3.3 Tolerancing Progression (Example # 2) 3-6
3.3.1 Strategy # 1 (Linear) . 3-8
3.3.2 Strategy # 2 Geometric Tolerancing ( ) Regardless of Feature Size 3-11
3.3.3 Strategy # 3 (Geometric Tolerancing Progression At Maximum
Material Condition) . 3-12
3.3.4 Strategy # 4 (Tolerancing Progression “Optimized”) 3-13
3.4 Summary 3-15
3.5 References . 3-15
Part 2 Standards
Chapter 4: Drawing Interpretation Patrick J. McCuistion, Ph.D
4.1 Introduction 4-1
4.2 Drawing History . 4-2
4.3 Standards . 4-2
4.3.1 ANSI 4-2
4.3.2 ISO 4-3
4.4 Drawing Types . 4-3
4.4.1 Note 4-3
4.4.2 Detail 4-3
4.4.2.1 Cast or Forged Part 4-4
4.4.2.2 Machined Part 4-4
4.4.2.3 Sheet Stock Part 4-4
4.4.3 Assembly . 4-4
4.5 Border . 4-4
4.5.1 Zones and Center Marks 4-4
4.5.2 Size Conventions 4-13
4.6 Title Blocks . 4-13
4.6.1 Company Name and Address . 4-13
4.6.2 Drawing Title 4-13
4.6.3 Size 4-13
4.6.4 FSCM/CAGE . 4-13
4.6.5 Drawing Number . 4-14
4.6.6 Scale 4-14
4.6.7 Release Date 4-14
4.6.8 Sheet Number 4-14
4.6.9 Contract Number . 4-14
4.6.10 Drawn and Date 4-14
4.6.11 Check, Design, and Dates 4-14
4.6.12 Design Activity and Date 4-15
4.6.13 Customer and Date . 4-15
4.6.14 Tolerances 4-15
4.6.15 Treatment . 4-15
4.6.16 Finish . 4-15
4.6.17 Similar To 4-15
4.6.18 Act Wt and Calc Wt 4-15
4.6.19 Other Title Block Items 4-15
4.7 Revision Blocks . 4-16
4.8 Parts Lists 4-16
4.9 View Projection . 4-16Contents vii
4.9.1 First-Angle Projection 4-16
4.9.2 Third-Angle Projection . 4-16
4.9.3 Auxiliary Views 4-16
4.10 Section Views 4-16
4.10.1 Full Sections . 4-19
4.10.2 Half Sections 4-19
4.10.3 Offset Sections 4-19
4.10.4 Broken-Out Section 4-19
4.10.5 Revolved and Removed Sections 4-22
4.10.6 Conventional Breaks 4-22
4.11 Partial Views 4-23
4.12 Conventional Practices 4-23
4.12.1 Feature Rotation 4-23
4.12.2 Line Precedence . 4-23
4.13 Isometric Views 4-24
4.14 Dimensions 4-25
4.14.1 Feature Types 4-25
4.14.2 Taylor Principle / Envelope Principle . 4-25
4.14.3 General Dimensions . 4-26
4.14.4 Technique . 4-27
4.14.5 Placement . 4-27
4.14.6 Choice . 4-28
4.14.7 Tolerance Representation . 4-28
4.15 Surface Texture . 4-28
4.15.1 Roughness . 4-29
4.15.2 Waviness 4-29
4.15.3 Lay 4-29
4.15.4 Flaws . 4-29
4.16 Notes . 4-29
4.17 Drawing Status 4-30
4.17.1 Sketch . 4-30
4.17.2 Configuration Layout 4-30
4.17.3 Experimental 4-30
4.17.4 Active . 4-30
4.17.5 Obsolete . 4-30
4.18 Conclusion . 4-30
4.19 References . 4-31
Chapter 5: Geometric Dimensioning and Tolerancing . Walter M. Stites
.Paul Drake, P.E.
5.1 Introducing Geometric Dimensioning and Tolerancing (GD&T) . 5-1
5.1.1 What is GD&T? . 5-2
5.1.2 Where Does GD&T Come From?—References . 5-2
5.1.3 Why Do We Use GD&T? . 5-4
5.1.4 When Do We Use GD&T? 5-8
5.1.5 How Does GD&T Work?—Overview . 5-9
5.2 Part Features . 5-9
5.2.1 Nonsize Features 5-10
5.2.2 Features of Size 5-10
5.2.2.1 Screw Threads .5-11
5.2.2.2 Gears and Splines 5-11
5.2.3 Bounded Features .5-11
5.3 Symbols .5-11
5.3.1 Form and Proportions of Symbols 5-12
5.3.2 Feature Control Frame . 5-14
5.3.2.1 Feature Control Frame Placement 5-14
5.3.2.2 Reading a Feature Control Frame 5-16
5.3.3 Basic Dimensions . 5-17viii Contents
5.3.4 Reference Dimensions and Data 5-18
5.3.5 “Square” Symbol 5-18
5.3.6 Tabulated Tolerances . 5-18
5.3.7 “Statistical Tolerance” Symbol . 5-18
5.4 Fundamental Rules . 5-18
5.5 Nonrigid Parts 5-19
5.5.1 Specifying Restraint . 5-20
5.5.2 Singling Out a Free State Tolerance 5-20
5.6 Features of Size—The Four Fundamental Levels of Control . 5-20
5.6.1 Level 1—Size Limit Boundaries . 5-20
5.6.2 Material Condition . 5-23
5.6.2.1 Modifier Symbols 5-24
5.6.3 Method for MMC or LMC . 5-25
5.6.3.1 Level 2—Overall Feature Form . 5-26
5.6.3.2 Level 3—Virtual Condition Boundary for Orientation . 5-33
5.6.3.3 Level 4—Virtual Condition Boundary for Location . 5-34
5.6.3.4 Level 3 or 4 Virtual Condition Equal to Size Limit (Zero Tolerance) 5-35
5.6.3.5 Resultant Condition Boundary 5-37
5.6.4 Method for RFS 5-38
5.6.4.1 Tolerance Zone Shape . 5-38
5.6.4.2 Derived Elements 5-38
5.6.5 Alternative “Center Method” for MMC or LMC 5-43
5.6.5.1 Level 3 and 4 Adjustment—Actual Mating/Minimum Material Sizes 5-43
5.6.5.2 Level 2 Adjustment—Actual Local Sizes 5-45
5.6.5.3 Disadvantages of Alternative “Center Method” . 5-46
5.6.6 Inner and Outer Boundaries . 5-46
5.6.7 When do we use a Material Condition Modifier? . 5-47
5.7 Size Limits (Level 1 Control) 5-48
5.7.1 Symbols for Limits and Fits 5-48
5.7.2 Limit Dimensioning 5-49
5.7.3 Plus and Minus Tolerancing 5-49
5.7.4 Inch Values . 5-49
5.7.5 Millimeter Values 5-49
5.8 Form (Only) Tolerances (Level 2 Control) 5-50
5.8.1 Straightness Tolerance for Line Elements 5-51
5.8.2 Straightness Tolerance for a Cylindrical Feature . 5-52
5.8.3 Flatness Tolerance for a Single Planar Feature 5-52
5.8.4 Flatness Tolerance for a Width-Type Feature 5-52
5.8.5 Circularity Tolerance 5-53
5.8.5.1 Circularity Tolerance Applied to a Spherical Feature . 5-55
5.8.6 Cylindricity Tolerance . 5-55
5.8.7 Circularity or Cylindricity Tolerance with Average Diameter . 5-56
5.8.8 Application Over a Limited Length or Area . 5-57
5.8.9 Application on a Unit Basis 5-57
5.8.10 Radius Tolerance . 5-58
5.8.10.1 Controlled Radius Tolerance 5-59
5.8.11 Spherical Radius Tolerance . 5-59
5.8.12 When Do We Use a Form Tolerance? 5-60
5.9 Datuming . 5-61
5.9.1 What is a Datum? . 5-61
5.9.2 Datum Feature . 5-61
5.9.2.1 Datum Feature Selection . 5-61
5.9.2.2 Functional Hierarchy . 5-63
5.9.2.3 Surrogate and Temporary Datum Features . 5-64
5.9.2.4 Identifying Datum Features . 5-65
5.9.3 True Geometric Counterpart (TGC)—Introduction . 5-67
5.9.4 Datum 5-69
5.9.5 Datum Reference Frame (DRF) and Three Mutually Perpendicular
Planes 5-69Contents ix
5.9.6 Datum Precedence . 5-69
5.9.7 Degrees of Freedom 5-72
5.9.8 TGC Types 5-74
5.9.8.1 Restrained versus Unrestrained TGC 5-75
5.9.8.2 Nonsize TGC . 5-75
5.9.8.3 Adjustable-size TGC . 5-75
5.9.8.4 Fixed-size TGC . 5-77
5.9.9 Datum Reference Frame (DRF) Displacement . 5-80
5.9.9.1 Relative to a Boundary of Perfect Form TGC . 5-81
5.9.9.2 Relative to a Virtual Condition Boundary TGC . 5-83
5.9.9.3 Benefits of DRF Displacement 5-83
5.9.9.4 Effects of All Datums of the DRF . 5-83
5.9.9.5 Effects of Form, Location, and Orientation 5-83
5.9.9.6 Accommodating DRF Displacement 5-83
5.9.10 Simultaneous Requirements . 5-86
5.9.11 Datum Simulation 5-89
5.9.12 Unstable Datums, Rocking Datums, Candidate Datums 5-89
5.9.13 Datum Targets . 5-91
5.9.13.1 Datum Target Selection 5-91
5.9.13.2 Identifying Datum Targets . 5-92
5.9.13.3 Datum Target Dimensions . 5-94
5.9.13.4 Interdependency of Datum Target Locations 5-95
5.9.13.5 Applied to Features of Size . 5-95
5.9.13.6 Applied to Any Type of Feature 5-97
5.9.13.7 Target Set with Switchable Precedence 5-99
5.9.14 Multiple Features Referenced as a Single Datum Feature . 5-100
5.9.14.1 Feature Patterns . 5-100
5.9.14.2 Coaxial and Coplanar Features . 5-103
5.9.15 Multiple DRFs . 5-103
5.10 Orientation Tolerance (Level 3 Control) . 5-103
5.10.1 How to Apply It . 5-103
5.10.2 Datums for Orientation Control 5-104
5.10.3 Applied to a Planar Feature (Including Tangent Plane Application) . 5-104
5.10.4 Applied to a Cylindrical or Width-Type Feature . 5-106
5.10.4.1 Zero Orientation Tolerance at MMC or LMC 5-107
5.10.5 Applied to Line Elements 5-107
5.10.6 The 24 Cases . 5-109
5.10.7 Profile Tolerance for Orientation . 5-109
5.10.8 When Do We Use an Orientation Tolerance? . 5-109
5.11 Positional Tolerance (Level 4 Control) .5-113
5.11.1 How Does It Work? 5-113
5.11.2 How to Apply It 5-114
5.11.3 Datums for Positional Control .5-116
5.11.4 Angled Features .5-117
5.11.5 Projected Tolerance Zone 5-117
5.11.6 Special-Shaped Zones/Boundaries . 5-121
5.11.6.1 Tapered Zone/Boundary 5-121
5.11.6.2 Bidirectional Tolerancing . 5-122
5.11.6.3 Bounded Features 5-126
5.11.7 Patterns of Features 5-127
5.11.7.1 Single-Segment Feature Control Frame 5-127
5.11.7.2 Composite Feature Control Frame . 5-129
5.11.7.3 Rules for Composite Control . 5-131
5.11.7.4 Stacked Single-Segment Feature Control Frames 5-134
5.11.7.5 Rules for Stacked Single-Segment Feature Control Frames . 5-136
5.11.7.6 Coaxial and Coplanar Features . 5-136
5.11.8 Coaxiality and Coplanarity Control . 5-137x Contents
5.12 Runout Tolerance 5-138
5.12.1 Why Do We Use It? 5-138
5.12.2 How Does It Work? . 5-138
5.12.3 How to Apply It . 5-139
5.12.4 Datums for Runout Control . 5-140
5.12.5 Circular Runout Tolerance . 5-141
5.12.6 Total Runout Tolerance 5-143
5.12.7 Application Over a Limited Length 5-143
5.12.8 When Do We Use a Runout Tolerance? . 5-144
5.12.9 Worst Case Boundaries . 5-145
5.13 Profile Tolerance . 5-145
5.13.1 How Does It Work? . 5-145
5.13.2 How to Apply It . 5-145
5.13.3 The Basic Profile . 5-147
5.13.4 The Profile Tolerance Zone . 5-147
5.13.5 The Profile Feature Control Frame 5-149
5.13.6 Datums for Profile Control 5-149
5.13.7 Profile of a Surface Tolerance 5-149
5.13.8 Profile of a Line Tolerance 5-149
5.13.9 Controlling the Extent of a Profile Tolerance . 5-150
5.13.10 Abutting Zones 5-153
5.13.11 Profile Tolerance for Combinations of Characteristics 5-153
5.13.11.1 With Positional Tolerancing for Bounded Features 5-153
5.13.12 Patterns of Profiled Features . 5-154
5.13.12.1 Single-Segment Feature Control Frame 5-154
5.13.12.2 Composite Feature Control Frame . 5-154
5.13.12.3 Stacked Single-Segment Feature Control Frames 5-155
5.13.12.4 Optional Level 2 Control 5-155
5.13.13 Composite Profile Tolerance for a Single Feature . 5-156
5.14 Symmetry Tolerance 5-156
5.14.1 How Does It Work? . 5-157
5.14.2 How to Apply It . 5-159
5.14.3 Datums for Symmetry Control . 5-159
5.14.4 Concentricity Tolerance . 5-160
5.14.4.1 Concentricity Tolerance for Multifold Symmetry about a Datum Axis . 5-160
5.14.4.2 Concentricity Tolerance about a Datum Point . 5-161
5.14.5 Symmetry Tolerance about a Datum Plane 5-161
5.14.6 Symmetry Tolerancing of Yore (Past Practice) . 5-161
5.14.7 When Do We Use a Symmetry Tolerance? . 5-162
5.15 Combining Feature Control Frames . 5-162
5.16 “Instant” GD&T 5-163
5.16.1 The “Dimension Origin” Symbol 5-163
5.16.2 General Note to Establish Basic Dimensions 5-163
5.16.3 General Note in Lieu of Feature Control Frames 5-164
5.17 The Future of GD&T 5-164
5.18 References . 5-166
Chapter 6: Differences Between US Standards and Other Standards .
. Alex Krulikowski
Scott DeRaad
6.1 Dimensioning Standards . 6-1
6.1.1 US Standards 6-2
6.1.2 International Standards . 6-2
6.1.2.1 ISO Geometrical Product Specification Masterplan . 6-4
6.2 Comparison of ASME and ISO Standards . 6-5
6.2.1 Organization and Logistics . 6-5
6.2.2 Number of Standards . 6-5
6.2.3 Interpretation and Application 6-5Contents xi
6.2.3.1 ASME 6-6
6.2.3.2 ISO 6-6
6.3 Other Standards 6-27
6.3.1 National Standards Based on ISO or ASME Standards . 6-27
6.3.2 US Government Standards 6-28
6.3.3 Corporate Standards 6-28
6.3.4 Multiple Dimensioning Standards . 6-29
6.4 Future of Dimensioning Standards . 6-30
6.5 Effects of Technology . 6-30
6.6 New Dimensioning Standards 6-30
6.7 References . 6-30
Chapter 7: Mathematical Definition of Dimensioning and Tolerancing Principles
Mark A. Nasson
7.1 Introduction 7-1
7.2 Why Mathematical Tolerance Definitions? . 7-1
7.2.1 Metrology Crisis (The GIDEP Alert) . 7-2
7.2.2 Specification Crisis . 7-3
7.2.3 National Science Foundation Tolerancing Workshop . 7-3
7.2.4 A New National Standard 7-4
7.3 What are Mathematical Tolerance Definitions? . 7-4
7.3.1 Parallel, Equivalent, Unambiguous Expression . 7-4
7.3.2 Metrology Independent . 7-4
7.4 Detailed Descriptions of Mathematical Tolerance Definitions . 7-4
7.4.1 Introduction 7-4
7.4.2 Vectors 7-5
7.4.2.1 Vector Addition and Subtraction 7-5
7.4.2.2 Vector Dot Products . 7-6
7.4.2.3 Vector Cross Products 7-6
7.4.3 Actual Value / Measured Value . 7-7
7.4.4 Datums 7-8
7.4.4.1 Candidate Datums / Datum Reference Frames . 7-8
7.4.4.2 Degrees of Freedom 7-8
7.4.5 Form tolerances 7-9
7.4.5.1 Circularity . 7-9
7.4.5.2 Cylindricity 7-12
7.4.5.3 Flatness 7-13
7.5 Where Do We Go from Here? 7-14
7.5.1 ASME Standards Committees 7-14
7.5.2 International Standards Efforts 7-14
7.5.3 CAE Software Developers . 7-14
7.6 Acknowledgments . 7-15
7.7 References . 7-15
Chapter 8: Statistical Tolerancing Vijay Srinivasan, Ph.D
8.1 Introduction 8-1
8.2 Specification of Statistical Tolerancing . 8-2
8.2.1 Using Process Capability Indices 8-2
8.2.2 Using RMS Deviation Index 8-4
8.2.3 Using Percent Containment 8-5
8.3 Statistical Tolerance Zones . 8-5
8.3.1 Population Parameter Zones 8-6
8.3.2 Distribution Function Zones . 8-7
8.4 Additional Illustrations . 8-7
8.5 Summary and Concluding Remarks . 8-9
8.6 References . 8-10xii Contents
Part 3 Design
Chapter 9: Traditional Approaches to Analyzing Mechanical Tolerance Stacks .
Paul Drake
9.1 Introduction 9-1
9.2 Analyzing Tolerance Stacks 9-1
9.2.1 Establishing Performance/Assembly Requirements 9-1
9.2.2 Loop Diagram . 9-3
9.2.3 Converting Dimensions to Equal Bilateral Tolerances 9-5
9.2.4 Calculating the Mean Value (Gap) for the Requirement 9-7
9.2.5 Determine the Method of Analysis . 9-8
9.2.6 Calculating the Variation for the Requirement 9-9
9.2.6.1 Worst Case Tolerancing Model 9-9
9.2.6.2 RSS Model . 9-12
9.2.6.3 Modified Root Sum of the Squares Tolerancing Model . 9-18
9.2.6.4 Comparison of Variation Models . 9-22
9.2.6.5 Estimated Mean Shift Model . 9-23
9.3 Analyzing Geometric Tolerances . 9-24
9.3.1 Form Controls . 9-25
9.3.2 Orientation Controls . 9-26
9.3.3 Position . 9-27
9.3.3.1 Position at RFS . 9-27
9.3.3.2 Position at MMC or LMC 9-27
9.3.3.3 Virtual and Resultant Conditions . 9-28
9.3.3.4 Equations 9-28
9.3.3.5 Composite Position 9-32
9.3.4 Runout . 9-33
9.3.5 Concentricity/Symmetry 9-33
9.3.6 Profile 9-34
9.3.6.1 Profile Tolerancing with an Equal Bilateral Tolerance Zone 9-34
9.3.6.2 Profile Tolerancing with a Unilateral Tolerance Zone 9-35
9.3.6.3 Profile Tolerancing with an Unequal Bilateral Tolerance Zone . 9-35
9.3.6.4 Composite Profile . 9-36
9.3.7 Size Datums . 9-36
9.4 Abbreviations 9-37
9.5 Terminology . 9-39
9.6 References . 9-39
Chapter 10: Statistical Background and Concepts Ron Randall
10.1 Introduction 10-1
10.2 Shape, Locations, and Spread 10-2
10.3 Some Important Distributions 10-2
10.3.1 The Normal Distribution . 10-2
10.3.2 Lognormal Distribution . 10-6
10.3.3 Poisson Distribution . 10-8
10.4 Measures of Quality and Capability . 10-10
10.4.1 Process Capability Index . 10-10
10.4.2 Process Capability Index Relative to Process Centering (Cpk) 10-12
10.5 Summary 10-14
10.6 References . 10-14
10.7 Appendix . 10-15Contents xiii
Chapter 11: Predicting Assembly Quality (Six Sigma Methodologies to Optimize
Tolerances) Dale Van Wyk
11.1 Introduction .11-1
11.2 What is Tolerance Allocation? .11-1
11.3 Process Standard Deviations 11-2
11.4 Worst Case Allocation .11-5
11.4.1 Assign Component Dimensions 11-6
11.4.2 Determine Assembly Performance, P .11-7
11.4.3 Assign the process with the largest si to each component 11-8
11.4.4 Calculate the Worst Case Assembly, twc6 11-8
11.4.5 Is P³t
wc6? .11-9
11.4.6 Estimating Defect Rates 11-10
11.4.7 Verification 11-12
11.4.8 Adjustments to Meet Quality Goals 11-13
11.4.9 Worst Case Allocation Summary 11-13
11.5 Statistical Allocation 11-13
11.5.1 Calculating Assembly Variation and Defect Rate .11-15
11.5.2 First Steps in Statistical Allocation .11-15
11.5.3 Calculate Expected Assembly Performance, P6 .11-15
11.5.4 Is P³P
6? 11-16
11.5.5 Allocating Tolerances 11-17
11.5.6 Statistical Allocation Summary 11-20
11.6 Dynamic RSS Allocation .11-20
11.7 Static RSS analysis .11-23
11.8 Comparison of the Techniques 11-24
11.9 Communication of Requirements 11-25
11.10 Summary .11-26
11.11 Abbreviations .11-26
11.12 References 11-27
Chapter 12: Multi-Dimensional Tolerance Analysis (Manual Method) Dale Van Wyk
12.1 Introduction 12-1
12.2 Determining Sensitivity . 12-2
12.3 A Technique for Developing Gap Equations . 12-4
12.4 Utilizing Sensitivity Information to Optimize Tolerances 12-12
12.5 Summary 12-13
Chapter 13: Multi-Dimensional Tolerance Analysis (Automated Method)
Kenneth W. Chase, Ph.D.
13.1 Introduction 13-1
13.2 Three Sources of Variation in Assemblies . 13-2
13.3 Example 2D Assembly – Stacked Blocks 13-3
13.4 Steps in Creating an Assembly Tolerance Model 13-4
13.5 Steps in Analyzing an Assembly Tolerance Model 13-12
13.5.5.1 Percent rejects 13-21
13.5.5.2 Percent Contribution Charts 13-22
13.5.5.3 Sensitivity Analysis 13-24
13.5.5.4 Modifying Geometry . 13-24
13.6 Summary 13-26
13.7 References . 13-27xiv Contents
Chapter 14: Minimum-Cost Tolerance Allocation Kenneth W. Chase, Ph.D.
14.1 Tolerance Allocation Using Least Cost Optimization . 14-1
14.2 1-D Tolerance Allocation 14-1
14.3 1-D Example: Shaft and Housing Assembly . 14-3
14.4 Advantages / Disadvantages of the Lagrange Multiplier Method . 14-7
14.6 2-D and 3-D Tolerance Allocation 14-8
14.5 True Cost and Optimum Acceptance Fraction 14-8
14.7 2-D Example: One-way Clutch Assembly . 14-9
14.7.1 Vector Loop Model and Assembly Function for the Clutch . 14-10
14.8 Allocation by Scaling, Weight Factors . 14-10
14.8.1 Proportional Scaling by Worst Case .14-11
14.8.2 Proportional Scaling by Root-Sum-Squares .14-11
14.8.3 Allocation by Weight Factors .14-11
14.9 Allocation by Cost Minimization . 14-12
14.9.1 Minimum Cost Tolerances by Worst Case 14-13
14.9.2 Minimum Cost Tolerances by RSS 14-14
14.10 Tolerance Allocation with Process Selection 14-15
14.11 Summary 14-16
14.12 References . 14-17
14.13 Appendix: Cost-Tolerance Functions for Metal Removal Processes . 14-18
Chapter 15: Automating the Tolerancing Process . Charles Glancy
James Stoddard
. Marvin Law
15.1 Background Information 15-2
15.1.1 Benefits of Automation 15-2
15.1.2 Overview of the Tolerancing Process 15-2
15.2 Automating the Creation of the Tolerance Model 15-3
15.2.1 Characterizing Critical Design Measurements . 15-3
15.2.2 Characterizing the Model Function . 15-4
15.2.2.1 Model Definition 15-4
15.2.2.2 Model Form 15-5
15.2.2.3 Model Scope 15-5
15.2.3 Characterizing Input Variables . 15-6
15.3 Automating Tolerance Analysis . 15-6
15.3.1 Method of System Moments 15-6
15.3.3 Distribution Fitting 15-8
15.3.2 Monte Carlo Simulation . 15-8
15.4 Automating Tolerance Optimization 15-9
15.5 Automating Communication Between Design and Manufacturing . 15-9
15.5.1 Manufacturing Process Capabilities . 15-10
15.5.1.1 Manufacturing Process Capability Database . 15-10
15.5.1.2 Database Administration 15-11
15.5.2 Design Requirements and Assumptions .15-11
15.6 CAT Automation Tools . 15-12
15.6.1 Tool Capability 15-12
15.6.2 Ease of Use . 15-12
15.6.3 Training . 15-13
15.6.4 Technical Support . 15-13
15.6.5 Data Management and CAD Integration 15-13
15.6.6 Reports and Records . 15-13
15.6.7 Tool Enhancement and Development . 15-14
15.6.8 Deployment 15-14
15.7 Summary 15-14
15.8 References . 15-14Contents xv
Chapter 16: Working in an Electronic Environment .Paul Matthews
16.1 Introduction 16-1
16.2 Paperless/Electronic Environment 16-2
16.2.1 Definition . 16-2
16.3 Development Information Tools 16-3
16.3.1 Product Development Automation Strategy 16-3
16.3.2 Master Model Theory . 16-4
16.3.3 Template Design . 16-7
16.3.3.1 Template Part and Assembly Databases . 16-7
16.3.3.2 Template Features 16-8
16.3.3.3 Templates for Analyses 16-9
16.3.3.4 Templates for Documentation 16-9
16.3.4 Component Libraries . 16-9
16.3.5 Information Verification . 16-10
16.4 Product Information Management .16-11
16.4.1 Configuration Management Techniques .16-11
16.4.2 Data Management Components 16-12
16.4.2.1 Workspace . 16-12
16.4.2.2 Product Vault 16-12
16.4.2.3 Company Vault . 16-12
16.4.3 Document Administrator . 16-13
16.4.4 File Cabinet Control 16-13
16.4.5 Software Automation . 16-13
16.5 Information Storage and Transfer . 16-13
16.5.1 Internet . 16-13
16.5.2 Electronic Mail 16-14
16.5.3 File Transfer Protocol . 16-14
16.5.4 Media Transfer 16-15
16.6 Manufacturing Guidelines . 16-15
16.6.1 Manufacturing Trust . 16-15
16.6.2 Dimensionless Prints 16-15
16.6.2.1 Sheetmetal . 16-16
16.6.2.2 Injection Molded Plastic . 16-17
16.6.2.3 Hog Out Parts . 16-17
16.6.2.4 Castings 16-18
16.6.2.5 Rapid Prototypes . 16-18
16.7 Database Format Standards 16-19
16.7.1 Native Database . 16-19
16.7.2 2-D Formats 16-19
16.7.2.1 Data eXchange Format (DXF) . 16-19
16.7.2.2 Hewlett-Packard Graphics Language (HPGL) 16-20
16.8 3-D Formats 16-20
16.8.1 Initial Graphics Exchange Specification (IGES) . 16-20
16.8.2 STandard for the Exchange of Product (STEP) 16-20
16.8.3 Virtual Reality Modeling Language (VRML) 16-20
16.8.4 STereoLithography (STL) 16-21
16.9 General Information Formats . 16-21
16.9.1 Hypertext Markup Language (HTML) 16-21
16.9.2 Portable Document Format (PDF) . 16-22
16.10 Graphics Formats . 16-22
16.10.1 Encapsulated PostScript (EPS) . 16-22
16.10.2 Joint Photographic Experts Group (JPEG) 16-22
16.10.3 Tagged Image File Format (TIFF) 16-22
16.11 Conclusion . 16-23
16.12 Appendix A IGES Entities 16-23xvi Contents
Part 4 Manufacturing
Chapter 17: Collecting and Developing Manufacturing Process Capability Models
. Michael D. King
17.1 Why Collect and Develop Process Capability Models? . 17-1
17.2 Developing Process Capability Models 17-2
17.3 Quality Prediction Models - Variable versus Attribute Information 17-3
17.3.1 Collecting and Modeling Variable Process Capability Models . 17-3
17.3.2 Collecting and Modeling Attribute Process Capability Models . 17-7
17.3.3 Feature Factoring Method . 17-7
17.3.4 Defect Weighting Methodology 17-7
17.4 Cost and Cycle Time Prediction Modeling Variations . 17-8
17.5 Validating and Checking the Results of Your Predictive Models 17-9
17.6 Summary .17-11
17.7 References 17-11
Part 5 Gaging
Chapter 18: Paper Gage Techniques .Martin P. Wright
18.1 What is Paper Gaging? . 18-1
18.2 Advantages and Disadvantages to Paper Gaging . 18-2
18.3 Discrimination Provided By a Paper Gage 18-3
18.4 Paper Gage Accuracy . 18-3
18.5 Plotting Paper Gage Data Points . 18-4
18.6 Paper Gage Applications . 18-4
18.6.1 Locational Verification 18-5
18.6.1.1 Simple Hole Pattern Verification 18-5
18.6.1.2 Three-Dimensional Hole Pattern Verification 18-8
18.6.1.3 Composite Positional Tolerance Verification 18-10
18.6.2 Capturing Tolerance From Datum Features Subject to Size Variation . 18-12
18.6.2.1 Datum Feature Applied on an RFS Basis . 18-12
18.6.2.2 Datum Feature Applied on an MMC Basis 18-12
18.6.2.3 Capturing Rotational Shift Tolerance from a Datum Feature
Applied on an MMC Basis 18-16
18.6.2.4 Determining the Datum from a Pattern of Features 18-19
18.6.3 Paper Gage Used as a Process Analysis Tool . 18-21
18.7 Summary 18-23
18.8 References . 18-23
Chapter 19: Receiver Gages — Go Gages and Functional Gages James D. Meadows
19.1 Introduction 19-1
19.2 Gaging Fundamentals 19-2
19.3 Gage Tolerancing Policies . 19-3
19.4 Examples of Gages . 19-4
19.4.1 Position Using Partial and Planar Datum Features . 19-4
19.4.2 Position Using Datum Features of Size at MMC 19-6
19.4.3 Position and Profile Using a Simultaneous Gaging Requirement . 19-9
19.4.4 Position Using Centerplane Datums . 19-12
19.4.5 Multiple Datum Structures 19-14
19.4.6 Secondary and Tertiary Datum Features of Size . 19-17Contents xvii
19.5 Push Pin vs. Fixed Pin Gaging . 19-20
19.6 Conclusion . 19-20
19.7 References . 19-20
Part 6 Precision Metrology
Chapter 20: Measurement Systems Analysis Gregory A. Hetland, Ph.D.
20.1 Introduction 20-1
20.2 Measurement Methods Analysis 20-2
20.2.1 Measurement System Definition (Phase 1) . 20-2
20.2.1.1 Identification of Variables 20-2
20.2.1.2 Specifications of Conformance 20-3
20.2.1.3 Measurement System Capability Requirements . 20-3
20.2.2 Identification of Sources of Uncertainty (Phase 2) . 20-3
20.2.2.1 Machine Sources of Uncertainty 20-4
20.2.2.2 Software Sources of Uncertainty . 20-4
20.2.2.3 Environmental Sources of Uncertainty . 20-5
20.2.2.4 Part Sources of Uncertainty 20-5
20.2.2.5 Fixturing Sources of Uncertainty . 20-5
20.2.2.6 Operator Sources of Uncertainty . 20-6
20.2.3 Measurement System Qualification (Phase 3) 20-6
20.2.3.1 Plan the Capabilities Studies 20-6
20.2.3.2 Production Systems . 20-7
20.2.3.3 Calibrate the System 20-7
20.2.3.4 Conduct Studies and Define Capabilities . 20-8
20.2.4 Quantify the Error Budget (Phase 4) 20-8
20.2.4.1 Plan Testing (Isolate Error Sources) . 20-8
20.2.4.2 Analyze Uncertainty 20-9
20.2.5 Optimize Measurement System (Phase 5) 20-9
20.2.5.1 Identify Opportunities 20-9
20.2.5.2 Attempt Improvements and Revisit Testing . 20-9
20.2.5.3 Revisit Qualification 20-10
20.2.6 Implement and Control Measurement System (Phase 6) 20-10
20.2.6.1 Plan Performance Criteria . 20-10
20.2.6.2 Plan Calibration and Maintenance Requirements .20-11
20.2.6.3 Implement System and Initiate Control 20-11
20.2.6.4 CMM Operator Competencies 20-11
20.2.6.5 Business Issue . 20-12
20.3 CMM Performance Test Overview 20-17
20.3.1 Environmental Tests (Section 1) 20-17
20.3.1.1 Temperature Parameters . 20-17
20.3.1.2 Other Environmental Parameters 20-20
20.3.2 Machine Tests (Section 2) . 20-21
20.3.2.1 Probe Settling Time 20-21
20.3.2.2 Probe Deflection 20-24
20.3.2.3 Other Machine Parameters . 20-27
20.3.2.4 Multiple Probes . 20-27
20.3.3 Feature Based Measurement Tests (Section 3) . 20-28
20.3.3.1 Number of Points Per Feature 20-30
20.3.3.2 Other Geometric Features 20-34
20.3.3.3 Contact Scanning 20-34
20.3.3.4 Surface Roughness 20-35
20.4 CMM Capability Matrix 20-35
20.5 References . 20-38xviii Contents
Part 7 Applications
Chapter 21: Predicting Piecepart Quality . Dan A. Watson, Ph.D.
21.1 Introduction 21-1
21.2 The Problem 21-2
21.3 Statistical Framework 21-3
21.3.1 Assumptions . 21-3
21.3.2 Internal Feature at MMC 21-5
21.3.3 Internal Feature at LMC . 21-7
21.3.4 External Features 21-8
21.3.5 Alternate Distribution Assumptions . 21-8
21.4 Non-Size Feature Applications . 21-9
21.5 Example . 21-9
21.6 Summary 21-10
21.7 References 21-11
Chapter 22: Floating and Fixed Fasteners .Paul Zimmermann
22.1 Introduction 22-1
22.2 Floating and Fixed Fasteners 22-1
22.2.1 What is a Floating Fastener? . 22-4
22.2.2 What is a Fixed Fastener? . 22-4
22.2.3 What is a Double-Fixed Fastener? . 22-4
22.3 Geometric Dimensioning and Tolerancing (Cylindrical Tolerance Zone
Versus +/- Tolerancing) 22-5
22.4 Calculations for Fixed, Floating and Double-fixed Fasteners . 22-8
22.5 Geometric Dimensioning and Tolerancing Rules/Formulas for Floating Fastener 22-8
22.5.1 How to Calculate Clearance Hole Diameter for a Floating Fastener Application 22-8
22.5.2 How to Calculate Counterbore Diameter for a Floating Fastener Application 22-9
22.5.3 Why Floating Fasteners are Not Recommended 22-10
22.6 Geometric Dimensioning and Tolerancing Rules/Formulas for Fixed Fasteners 22-10
22.6.1 How to Calculate Fixed Fastener Applications 22-10
22.6.2 How to Calculate Counterbore Diameter for a Fixed Fastener Application . 22-10
22.6.3 Why Fixed Fasteners are Recommended .22-11
22.7 Geometric Dimensioning and Tolerancing Rules/Formulas for Double-fixed
Fastener .22-11
22.7.1 How to Calculate a Clearance Hole .22-11
22.7.2 How to Calculate the Countersink Diameter, Head Height Above and Head
Height Below the Surface .22-11
22.7.3 What Are the Problems Associated with Double-fixed Fasteners? . 22-13
22.8 Nut Plates: Floating and Nonfloating (see Fig. 22-14) 22-14
22.9 Projected Tolerance Zone . 22-15
22.9.1 Comparison of Positional Tolerancing With and Without a Projected Tolerance
Zone . 22-16
22.9.2 Percent of Actual Orientation Versus Lost Functional Tolerance . 22-18
22.10 Hardware Pages 22-18
22.10.1 Floating Fastener Hardware Pages . 22-20
22.10.2 Fixed Fastener Hardware Pages 22-21
22.10.3 Double-fixed Fastener Hardware Pages . 22-23
22.10.4 Counterbore Depths - Pan Head and Socket Head Cap Screws 22-25
22.10.5 Flat Head Screw Head Height - Above and Below the Surface . 22-26
22.11 References . 22-26Contents xix
Chapter 23: Fixed and Floating Fastener Variation .Chris Cuba
23.1 Introduction 23-1
23.2 Hole Variation . 23-2
23.3 Assembly Variation 23-4
23.4 Fixed and Floating Fasteners 23-4
23.4.1 Fixed Fastener Assembly Shift 23-5
23.4.2 Fixed Fastener Assembly Shift Using One Equation and Dimension Loop . 23-6
23.4.3 Fixed Fastener Equation 23-7
23.4.4 Fixed Fastener Gap Analysis Steps . 23-7
23.4.5 Floating Fastener Gap Analysis Steps 23-8
23.5 Summary 23-9
23.6 References . 23-10
Chapter 24: Pinned Interfaces . Stephen Harry Werst
24.1 List of Symbols (Definitions and Terminology) 24-1
24.2 Introduction 24-2
24.3 Performance Considerations . 24-2
24.4 Variation Components of Pinned Interfaces . 24-3
24.4.1 Type I Error . 24-3
24.4.2 Type II Error 24-3
24.5 Types of Alignment Pins . 24-4
24.6 Tolerance Allocation Methods - Worst Case vs. Statistical 24-6
24.7 Processes and Capabilities 24-6
24.8 Design Methodology 24-7
24.9 Proper Use of Material Modifiers 24-10
24.10 Temperature Considerations 24-11
24.11 Two Round Pins with Two Holes .24-11
24.11.1 Fit 24-12
24.11.2 Rotation Errors 24-12
24.11.3 Translation Errors . 24-13
24.11.4 Performance Constants 24-13
24.11.5 Dimensioning Methodology 24-14
24.12 Round Pins with a Hole and a Slot 24-14
24.12.1 Fit 24-14
24.12.2 Rotation Errors 24-16
24.12.3 Translation Errors . 24-17
24.12.4 Performance Constants 24-17
24.12.5 Dimensioning Methodology 24-17
24.13 Round Pins with One Hole and Edge Contact 24-18
24.13.1 Fit 24-19
24.13.2 Rotation Errors 24-20
24.13.3 Translation errors . 24-20
24.13.4 Performance Constants 24-20
24.13.5 Dimensioning Methodology 24-20
24.14 One Diamond Pin and One Round Pin with Two Holes . 24-23
24.14.1 Fit 24-23
24.14.2 Rotation and Translation Errors . 24-24
24.14.3 Performance Constants 24-24
24.14.4 Dimensioning Methodology 24-24
24.15 One Parallel-Flats Pin and One Round Pin with Two Holes . 24-26
24.15.1 Fit 24-26
24.15.2 Rotation and Translation Errors . 24-27
24.15.3 Performance Constants 24-27
24.15.4 Dimensioning Methodology 24-28
24.16 References . 24-29xx Contents
Chapter 25: Gage Repeatability and Reproducibility (GR&R) Calculations .
. Gregory A. Hetland, Ph.D.
25.1 Introduction 25-1
25.2 Standard GR&R Procedure 25-1
25.3 Summary 25-7
25.4 References . 25-7
Part 8 The Future
Chapter 26: The Future . Several contributors
Figures . F-1
Tables . T-1
Index I-1
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