Geometric Dimensioning and Tolerancing for Mechanical Design
Geometric Dimensioning and Tolerancing for Mechanical Design
Gene R. Cogorno
Contents
Preface ix
Acknowledgments xi
Chapter 1. Introduction to Geometric Dimensioning and Tolerancing 1
Chapter Objectives 2
What Is GD&T? 2
When Should GD&T Be Used? 3
Advantages of GD&T over Coordinate Dimensioning and Tolerancing 3
Summary 8
Chapter Review 8
Chapter 2. Dimensioning and Tolerancing Fundamentals 9
Chapter Objectives 9
Fundamental Drawing Rules 9
Units of Linear Measurement 10
Units of Angular Measurement 11
Types of Dimensions 11
Specifying Linear Tolerances 12
Specifying Angular Tolerances 13
Interpreting Dimensional Limits 14
Dimensioning and Tolerancing for CAD/CAM Database Models 14
Summary 15
Chapter Review 15
Chapter 3. Symbols, Terms, and Rules 17
Chapter Objectives 17
Symbols 17
Terms 30
Rules 33
Summary 38
Chapter Review 39
Problems 44
v
For more information about this title, click herevi Contents
Chapter 4. Datums 47
Chapter Objectives 47
Definition 48
Immobilization of a Part 48
Application of Datums 49
Datum Feature Selection 51
Datum Feature Identification 51
Inclined Datum Features 52
Cylindrical Datum Features 52
Establishing Datums 53
Multiple Datum Features 57
A Partial Surface as a Datum Feature 58
Datum Targets 59
Summary 62
Chapter Review 63
Problems 66
Chapter 5. Form 69
Chapter Objectives 69
Flatness 69
Straightness 72
Circularity 76
Cylindricity 78
Free-State Variation 78
Summary 80
Chapter Review 80
Problems 84
Chapter 6. Orientation 87
Chapter Objectives 87
Parallelism 88
Perpendicularity 90
Angularity 93
Summary 97
Chapter Review 97
Problems 100
Chapter 7. Position, General 103
Chapter Objectives 103
Definition 103
Specifying the Position Tolerance 104
Regardless of Feature Size 106
Maximum Material Condition 107
Shift Tolerance 109
Least Material Condition 112
Boundary Conditions 113Contents vii
Zero Positional Tolerance at MMC 115
Summary 118
Chapter Review 119
Problems 121
Chapter 8. Position, Location 125
Chapter Objectives 125
Floating Fasteners 126
Fixed Fasteners 128
Projected Tolerance Zones 130
Multiple Patterns of Features 132
Composite Positional Tolerancing 135
Two Single-Segment Feature Control Frames 138
Nonparallel Holes 139
Counterbored Holes 139
Noncircular Features at MMC 141
Symmetrical Features at MMC 142
Summary 146
Chapter Review 147
Problems 149
Chapter 9. Position, Coaxiality 157
Chapter Objectives 157
Definition 157
Comparison Between Position, Runout, and Concentricity 159
Specifying Coaxiality at MMC 159
Composite Positional Control of Coaxial Features 160
Tolerancing a Plug and Socket 162
Summary 162
Chapter Review 163
Problems 164
Chapter 10. Concentricity and Symmetry 167
Chapter Objectives 167
Concentricity 167
Symmetry 170
Summary 172
Chapter Review 173
Problems 175
Chapter 11. Runout 177
Chapter Objectives 177
Definition 177
Circular Runout 177
Total Runout 178
Specifying Runout and Partial Runout 179
Multiple Datum Features 179viii Contents
Face and Diameter Datums 179
Geometric Controls to Refine Datum Features 181
Surface Relationships Between Features 181
Inspecting Runout 182
Summary 183
Chapter Review 184
Problems 185
Chapter 12. Profile 187
Chapter Objectives 187
Definition 187
Specifying Profile 188
The Application of Datums 190
A Radius Refinement with Profile 190
Combing Profile Tolerances with Other Geometric Controls 191
Coplanarity 192
Profile of a Conical Feature 194
Composite Profile 195
Summary 199
Chapter Review 200
Problems 202
Chapter 13. Graphic Analysis 207
Chapter Objectives 207
Advantages of Graphic Analysis 207
The Accuracy of Graphic Analysis 208
Analysis of a Composite Geometric Tolerance 209
Analysis of a Pattern of Features Controlled to a Datum Feature of Size 213
Summary 217
Chapter Review 218
Problems 220
Chapter 14. A Strategy for Tolerancing Parts 225
Chapter Objectives 225
Size Features Located to Plane Surface Features 225
Size Features Located to Size Features 231
A Pattern of Features Located to a Second Pattern of Features 236
Summary 240
Chapter Review 241
Problems 244
Appendix 247
Index 253
Index
Actual mating envelope, 30
Advantages of GD&T, 3
All around symbol, 26, 189
ALL OVER note, 189
American National Standards Institute, 1
Angularity, 93
Application of datums, 49
Arc length symbol, 29
Basic dimension, 4, 26, 31, 188
Between symbol, 25, 189
Bonus tolerance, 6, 23, 108
Boundary, 141
Boundary conditions, 113
CAD/CAM database models, 14, 225
Calculation of wall thickness, 113, 114
Circular Runout, 177
Circularity, 76
Clearance hole size at least material
condition, 127
Clocking, 234, 238
Coaxiality, 157
Coaxiality at maximum material condition,
159
Composite feature control frame, 21, 135, 195
Composite positional control of coaxial
features, 160
Composite positional tolerancing, 135
Composite profile, 195
Conical taper, 28
Controlled radius symbol (CR), 28
Coordinate conversion diagram, 251
Coordinate conversion table, 252
Coordinate dimensioning and tolerancing, 3
Coplanarity, 192
Counterbore symbol, 26
Counterbored holes, 139
Countersink symbol, 26
Cylindrical datum features, 52
Cylindrical tolerance zone, 4
Cylindricity, 78
Data graph, 210, 213
Datum, 31, 47
Datum feature, 31
Datum feature identification, 51
Datum feature of size, 54
Datum feature of size specified at MMC &
RFS, 55
Datum feature selection, 51
Datum feature simulator, 31
Datum Feature Symbol, 19
Datum reference frame, 48, 105
Datum targets, 25, 59
Datum target areas, 59, 61
Datum target lines, 59, 61
Datum target points, 59
Equalizing datums, 61
Step datums, 61
Datum targets established on a cylindrical
part, 60
Datums specified in order of precedence,
6, 48
Definition of coaxiality, 157
Depth symbol, 27
Diamond shaped pin, 239
Dimension origin symbol, 27
Dimensional limits, 14
Drill sizes chart, 249
Face and diameter datums, 179
Fasteners 126, 128
Feature, 31
Feature control frame, 20
Feature control frames specified with MMC,
23
Feature control frames specified with
RFS, 22
Feature of size, 31
Feature subject to size variations, 31
Features controlled to datum features of size,
54, 55
Features not subject to size variations, 54
Features subject to size variations,
54, 55
Fixed and double fixed fasteners, 128
Fixed fastener formula, 129
Flatness, 69
Unit flatness, 71
Floating fastener formula, 126
Form, 18, 69
Free state variation symbol, 25
Free state variation, 78
Full indicator movement (FIM), 169, 183
Functional gage, 109, 238, 239
Gage sketch (cartoon gage), 236
Geometric Characteristic Symbols, 18
Geometric controls to refine datum features,
229, 232, 235
Geometric Dimensioning and Tolerancing, 2
Geometric form, 69
Graphic analysis, 207
Immobilization of a part, 48
Implied datums, 3
Inch and millimeter dimensions, 10
Inclined datum features, 52
Inspecting a hole location, 105
Least material condition (LMC), 32, 112
Least material condition modifier (circle L),
24, 32, 112
Location, 18
Material conditions, 22
Maximum material condition (MMC), 32, 55,
108, 226
Maximum material condition modifier
(circle M), 23, 107
Measurement
Angular, 11
Linear, 11
Multiple datum features, 57, 179
Multiple patterns of features, 132
Noncircular features at MMC, 141
Nonparallel holes, 139
Orientation, 18, 87
Oversize diameters in drilling, 247
Paper gaging. See Graphic analysis
Parallelism, 88
Partial runout, 179
Partial surface as a datum feature, 58
Pattern of features controlled to datums,
230
Pattern of features located to a second
Pattern of features, 236
Perpendicularity, 90
Perpendicularity refinement, 229
Pitch diameter rule, 36
Plug and Socket, 162
Position tolerance, 103, 125, 157
Position tolerance at MMC, 107
Profile, 18
Profile of a conical feature, 194
Projected tolerance zone, 28, 131
Radius, 27
Radius refinement with profile, 190
Radius symbol (R), 27
Reference dimension, 29
Regardless of feature size (RFS), 32, 35, 54,
106
Restrained condition, 79
Resultant condition, 32, 113
Rule #1, 33
Rule #2, 35
Rules, fundamental drawing, 10
Runout, 18, 177
Screw sizes, 248
Shift tolerance, 55, 109
Shift tolerance, special case, 142, 159
Size feature, 31
Size feature located to specified datums,
225
Size features located to a size feature, 231
Slope, 29
Specifying profile of a surface, 188
Spherical diameter (SØ), 28
Spherical radius (SR), 28
Spotface, 27
Square symbol, 28
Statistical tolerance, 28
Straightness of a median line and median
plane, 74
Straightness of a surface, 72
Symbols used with geometric tolerancing,
25
Symmetrical features at MMC, 142
Tangent plane, 28, 91
Theoretical tolerance zone, 104
Tolerance
Angular, 13
Linear, 12
Tolerance zone overlay gage, 211,
215
Total runout, 178
True position, 32, 104
Two single-segment feature control frames,
138Index 255
Two single-segment profile control,
198
Types of dimensions, 11
Virtual condition, 32
Virtual condition boundary, 110
Virtual condition rule, 36, 110
Worst-case boundary, 33
Zero dimensions, 157
Zero positional tolerance at maximum
material condition, 115
Zero positional tolerance for a pattern of
features, 233
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