ASME Y14.5.1 2019
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ASME Y14.5.1-2019: Mathematical Definition of Dimensioning and Tolerancing Principles
| Published By | Publication Date | Number of Pages |
| ASME | 2019 | 101 |
This Standard presents a mathematical definition of geometrical dimensioning and tolerancing consistent with the principles and practices of ASME Y14.5-2009, enabling determination of actual values. While the general format of this Standard parallels that of ASME Y14.5-2009, the latter document should be consulted for practices relating to dimensioning and tolerancing for use on engineering product definition and in related documentation.
PDF Catalog
| PDF Pages | PDF Title |
|---|---|
| 4 | CONTENTS |
| 9 | FOREWORD |
| 10 | ASME Y14 COMMITTEE ROSTER |
| 11 | CORRESPONDENCE WITH THE Y14 COMMITTEE |
| 12 | Section 1 Scope and Definitions 1.1 SCOPE 1.1.1 Reference to Gaging 1.2 ASME Y14 SERIES CONVENTIONS 1.2.1 Mandatory, Recommended, Guidance, and Optional Words 1.2.2 Cross-Reference of Standards 1.2.3 Invocation of Referenced Standards |
| 13 | 1.2.4 Parentheses Following a Definition 1.2.5 Notes 1.2.6 Acronyms and Abbreviations 1.2.7 Units 1.2.8 Figures 1.2.9 Precedence of Standards 1.3 REFERENCES 1.4 MATHEMATICAL NOTATION 1.4.1 Symbology |
| 14 | 1.4.2 Algebraic Notation 1.5 DEFINITIONS 1.5.1 Actual Value 1.5.2 Candidate Datum 1.5.3 Candidate Datum Reference Frame 1.5.4 Candidate Datum Reference Frame Set |
| 15 | 1.5.5 Candidate Datum Set 1.5.6 Conformance to a Geometric Tolerance 1.5.7 Cutting Surface 1.5.8 Derived Median Line 1.5.9 Derived Median Plane 1.5.10 Design Geometry 1.5.11 Direction Vector 1.5.12 Element, Circular 1.5.13 Element, Line 1.5.14 Engineering Data 1.5.15 Envelope, Actual Mating 1.5.16 Envelope, Actual Minimum Material 1.5.17 Feature 1.5.18 Feature of Size, External 1.5.19 Feature of Size, Internal 1.5.20 Half-Space |
| 16 | 1.5.21 Perfect Form 1.5.22 Resolved Geometry 1.5.23 Size, Actual Mating 1.5.24 Size, Actual Minimum Material 1.5.25 Spine 1.5.26 Spine, Local Size 1.5.27 Surface of Support 1.5.28 Tolerance Zone 1.5.29 True Position 1.5.30 True Profile 1.6 SUMMARY OF CONVENTIONAL DESIGNATIONS |
| 17 | 1.7 FORMAT Figures Figure 1-1 Example: Distance From a Point to a True Position Axis Figure 1-2 Example: Cutting Surfaces to Evaluate Circular Runout Tables Table 1-1 Mathematical Symbology |
| 18 | Figure 1-3 Examples of a Planar Surface of Support |
| 19 | Section 2 General Tolerancing and Related Principles 2.1 SURFACE POINTS 2.2 DIMENSION ORIGIN 2.3 FEATURES OF SIZE 2.3.1 Limits of Size |
| 20 | 2.3.2 Variation of Size 2.3.3 Actual Local Size Limits |
| 21 | 2.3.4 Continuous Features of Size |
| 22 | 2.3.5 Limits for Irregular Feature of Size (Type b) 2.3.6 Variation of Size Under Rule #1 for Irregular Features of Size Figure 2-1 Irregular Features of Size (Type a), Collection of Features Figure 2-2 Symbols Used in the Definition of Size Figure 2-3 Conformance to Limits of Size, Internal Feature of Size |
| 23 | Figure 2-4 Examples of Surface Attributes Leading to Variations in the Derived Median Line Figure 2-5 The Cutting Plane at a Point on a Local Size Spine, and Some of the Evaluation Lines in That Cutting Plane Figure 2-6 Profile of a Surface Tolerance Describing an External IFOSb |
| 24 | Section 3 Symbology |
| 25 | Section 4 Datum Reference Frames 4.1 GENERAL 4.2 CONCEPTS 4.3 DEGREES OF FREEDOM 4.4 DATUM FEATURE SIMULATORS (THEORETICAL) 4.4.1 Datum Feature Simulator Requirements |
| 26 | 4.5 CONSTRAINING DEGREES OF FREEDOM 4.5.1 Primary Datum Feature Types and Constrained Degrees of Freedom 4.5.2 Datum Feature Order of Precedence in a Datum Reference Frame 4.5.3 Partially Constrained Datum Reference Frame 4.5.4 Datum Reference Frames for Composite Tolerances 4.5.5 Customized Datum Reference Frames 4.6 TABULATION OF DATUM REFERENCE FRAMES |
| 27 | 4.7 CANDIDATE DATUM SETS AND CANDIDATE REFERENCE FRAME SETS 4.7.1 Establishing a Candidate Datum Set 4.7.2 Types of Datum Features 4.7.3 Planar Datum Features |
| 28 | 4.7.4 Datum Features of Size Referenced at RMB 4.7.5 Datum Features of Size Referenced at MMB 4.7.6 Datum Features of Size Referenced at LMB |
| 29 | 4.7.7 Translation Modifier 4.7.8 Establishing a Candidate Datum Reference Frame Set 4.7.9 Conformance and Actual Value 4.7.10 Simultaneous Requirements 4.7.11 Alternate Stabilization Procedures Table 4-1 Symbols for Datum Reference Frame Tables |
| 30 | Table 4-2 Point as Primary Datum (Spherical Datum Feature) Table 4-3 Axis as Primary Datum (Cylindical Datum Feature) |
| 31 | Table 4-4 Plane as Primary Datum (Planar or Width Datum Feature) Table 4-5 Coincident Axis and Point as Primary Datum (Conical Datum Feature) Table 4-6 Axis and Plane as Primary Datum (Linear Extruded Shape Datum Feature) Table 4-7 Axis Point and Plane as Primary Datum (Complex Datum Feature) Table 4-8 Generic Invariant Cases |
| 32 | Figure 4-1 Example From Table 4-3 — Axis as Primary Datum Figure 4-2 Example of Testing Whether a Plane Is a Valid Datum Plane |
| 33 | Figure 4-3 Tertiary Datum Feature Simulator Is Basically Located and Oriented Figure 4-4 Example of Translation Modifier |
| 34 | Section 5 Tolerances of Form 5.1 GENERAL 5.2 FORM CONTROL 5.3 SPECIFYING FORM TOLERANCES 5.4 FORM TOLERANCES 5.4.1 Straightness |
| 35 | 5.4.2 Flatness |
| 36 | 5.4.3 Circularity (Roundness) |
| 37 | 5.4.4 Cylindricity |
| 38 | Figure 5-1 Evaluation of Straightness of a Cylindrical Surface Figure 5-2 Evaluation of Straightness of a Planar Surface Figure 5-3 Illustration of Circularity Tolerance Zone for a Cylindrical or Conical Feature |
| 39 | Section 6 Tolerances of Orientation 6.1 GENERAL 6.2 ORIENTATION CONTROL 6.3 SPECIFYING ORIENTATION TOLERANCES 6.4 ORIENTATION TOLERANCE |
| 40 | 6.4.1 Planar Orientation Tolerance Zone |
| 41 | 6.4.2 Cylindrical Orientation Tolerance Zone 6.4.3 Linear Orientation Tolerance Zone |
| 42 | Figure 6-1 Planar Orientation Zone With Primary and Secondary Datum Planes Specified Figure 6-2 Projection of Tolerance Vector Onto Primary Datum Plane |
| 43 | Figure 6-3 Cylindrical Orientation Zone With Respect to a Primary Datum Plane Figure 6-4 Linear Orientation Zone Bounded by Parallel Lines |
| 44 | Section 7 Tolerances of Location 7.1 GENERAL 7.1.1 Material Condition Basis 7.1.2 Patterns of Features 7.2 POSITION TOLERANCING |
| 45 | 7.2.1 In Terms of the Surface of a Feature 7.2.2 In Terms of the Resolved Geometry of a Feature 7.3 PROJECTED TOLERANCE ZONE |
| 46 | 7.4 CONICAL TOLERANCE ZONE 7.4.1 In Terms of the Surface of the Feature |
| 47 | 7.4.2 In Terms of the Resolved Geometry (Axis) of the Feature 7.5 BIDIRECTIONAL POSITION TOLERANCING 7.5.1 In Terms of the Surface of the Feature |
| 48 | 7.5.2 In Terms of the Resolved Geometry (Axis) of the Feature 7.5.3 Polar Bidirectional Tolerancing in Terms of the Resolved Geometry (Axis) of the Feature |
| 49 | 7.6 POSITION TOLERANCING AT MMC FOR BOUNDARIES OF ELONGATED HOLES 7.7 CONCENTRICITY AND SYMMETRY |
| 50 | Figure 7-1 First Illustration of the Difference Between Surface and Resolved Geometry Interpretations of Position Tolerancing Figure 7-2 Second Illustration of the Difference Between Surface and Resolved Geometry Interpretations of Position Tolerancing Figure 7-3 Tolerance Zone and Conformance: Holes at MMC or RFS, Shafts at LMC — Surface Interpretation Figure 7-4 Tolerance Zone and Conformance: Tabs at MMC or RFS, Slots at LMC — Surface Interpretation Table 7-1 Definition of Position Tolerance Zone — Surface Interpretation |
| 51 | Figure 7-5 Tolerance Zone and Conformance: Holes at MMC or RFS, Shafts at LMC — Resolved Geometry Interpretation Table 7-2 Size of Position Tolerance Zone — Surface Interpretation Table 7-3 Size of Position Tolerance Zone — Resolved Geometry Interpretation Table 7-4 Definition of Verifying Volume for Projected Tolerance Zone |
| 52 | Figure 7-6 Projected Tolerance Zone for a Hole Figure 7-7 Surface Interpretation of Conical Tolerance Zone for Holes at MMC or RFS Figure 7-8 Resolved Geometry (Axis) Interpretation of Conical Tolerance Zone for Holes at MMC or RFS Table 7-5 Definition of Conical Tolerance Zone — Surface Interpretation Table 7-6 Size of Conical Tolerance Zone — Surface Interpretation |
| 53 | Table 7-7 Size of Conical Tolerance Zone — Resolved Geometry (Axis) Interpretation Table 7-8 Definition of Bidirectional Tolerance Zone — Surface Interpretation Table 7-9 Size of Bidirectional Tolerance Zone — Surface Interpretation |
| 54 | Figure 7-9 Bidirectional Hole Tolerance at MMC With Cylindrical Tolerance Zones — Surface Interpretation Figure 7-10 Bidirectional Shaft Tolerance at MMC With Parallel Plane Tolerance Zones — Surface Interpretation Table 7-10 Size of Bidirectional Tolerance Zone — Resolved Geometry (Axis) Interpretation |
| 55 | Figure 7-11 Definition of the Tolerance Zone for Polar Bidirectional Tolerancing Figure 7-12 Tolerance Zone and Conformance, Elongated Hole at MMC — Tolerance Zone is the Right Cylinder Shown in Cross Section Table 7-11 Size of Polar Bidirectional Tolerance Zone — Resolved Geometry (Axis) Interpretation |
| 56 | Figure 7-13 Rays Are Arranged in the Lowest Order of Symmetry About an Axis or a Point Table 7-12 Symmetry Elements for ObtainingCorresponding Feature Elements |
| 57 | Section 8 Tolerances of Profile 8.1 GENERAL 8.2 PROFILE 8.2.1 Types of Profile Tolerances 8.3 TOLERANCE ZONE BOUNDARIES 8.3.1 Uniform Tolerance Zones |
| 58 | 8.4 PROFILE APPLICATIONS 8.4.1 Optimization of Profile Tolerance Systems 8.4.2 Constraint Properties of Profile Tolerance Zones |
| 59 | 8.4.3 Effect of Pattern Creation (Grouping) Mechanisms 8.4.4 Effect of Individual Profile Specifications 8.4.5 Datum Feature References 8.4.6 Effect of Simultaneous Requirements 8.4.7 Composite Profile 8.5 EXTENSION OF TOLERANCE ZONE BOUNDARIES FOR SHARP CORNERS |
| 60 | 8.6 NONUNIFORM TOLERANCE ZONE Table 8-1 Table of Profile Tolerance Dispositions |
| 61 | Figure 8-1 Tolerance Zone Derivation — Equally Disposed Profile Figure 8-2 Tolerance Zone Derivation — Unequally Disposed Profile |
| 62 | Figure 8-3 Tolerance Zone Derivation — Unilaterally Disposed Profile (Outside) Figure 8-4 Tolerance Zone Derivation — Unilaterally Disposed Profile (Inside) |
| 63 | Figure 8-5 Actual Zone Definition for Equally Disposed Profile — Example of Conformance Figure 8-6 Actual Zone Definition for Unequally Disposed Profile — Example of Conformance Figure 8-7 Actual Zone for Unilateral (Outside) Profile — Example of Nonconformance |
| 64 | Figure 8-8 Actual Zone for Unilateral (Inside) Profile — Example of Nonconformance Figure 8-9 Profile Tolerance for a Single Feature Without a Datum Reference Frame Figure 8-10 Profile Tolerance Zone for a Single Feature Without a Datum Reference Frame |
| 65 | Figure 8-11 Candidate Configuration #1 (System Not Optimized) Figure 8-12 Candidate Configuration #2 (System Optimized) Figure 8-13 Actual Values in a Multi-Feature Profile Tolerance System — Specification |
| 66 | Figure 8-14 Actual Values in a Multi-Feature Profile Tolerance System — Basically Related Profile Tolerance Zones Figure 8-15 Actual Values in a Multi-Feature Profile Tolerance System — Candidate Configuration #1 (System Not Optimized) Figure 8-16 Actual Values in a Multi-Feature Profile Tolerance System — Candidate Configuration #2 (System Optimized) |
| 67 | Figure 8-17 Individual Requirements for Profile — Specification Figure 8-18 Individual Requirements for Profile — Tolerance Zones Figure 8-19 Individual Requirements for Profile — Individual Requirement 1 |
| 68 | Figure 8-20 Individual Requirements for Profile — Individual Requirement 2 Figure 8-21 Datum Feature References With Profile — Specification Figure 8-22 Datum Feature References With Profile — Tolerance Zones and Simulators |
| 69 | Figure 8-23 Datum Feature References With Profile — Invalid Candidate Configuration Figure 8-24 Datum Feature References With Profile — Valid Candidate Configuration Figure 8-25 Simultaneous Requirements for Profile — Specification |
| 70 | Figure 8-26 Simultaneous Requirements for Profile — Tolerance Zones Figure 8-27 Simultaneous Requirements for Profile (System Not Optimized) Figure 8-28 Simultaneous Requirements for Profile (System Optimized) |
| 71 | Figure 8-29 Composite Profile Lower Segment — Specification Figure 8-30 Composite Profile Lower Segment —Tolerance Zones (FRTZF) Figure 8-31 Composite Profile Lower Segment (System Not Optimized) |
| 72 | Figure 8-32 Composite Profile Lower Segment (System Optimized) Figure 8-33 Tolerance Zone Derivation — Profile With Sharp Corner Figure 8-34 Actual Zone Definition — Profile With Sharp Corner |
| 73 | Section 9 Tolerances of Runout 9.1 RUNOUT TOLERANCE 9.1.1 Circular Runout |
| 74 | 9.1.2 Total Runout |
| 75 | Figure 9-1 Circular Runout Zone |
| 76 | NONMANDATORY APPENDICES NONMANDATORY APPENDIX A PRINCIPAL CHANGES AND IMPROVEMENTS A-1 GENERAL A-2 STANDARD Y14 FORMAT A-3 SECTION 1, SCOPE AND DEFINITIONS A-4 SECTION 2, GENERAL TOLERANCING AND RELATED PRINCIPLES A-5 SECTION 3, SYMBOLOGY A-6 SECTION 4, DATUM REFERENCE FRAMES A-7 SECTION 5, TOLERANCES OF FORM |
| 77 | A-8 SECTION 6, TOLERANCES OF ORIENTATION A-9 SECTION 7, TOLERANCES OF LOCATION A-10 SECTION 8, TOLERANCES OF PROFILE |
| 78 | A-11 SECTION 9, TOLERANCES OF RUNOUT A-12 NONMANDATORY APPENDICES |
| 79 | NONMANDATORY APPENDIX B MATHEMATICAL DATUM SIMULATORS REFERENCED AT RMB: DEFINITIONS AND PROPERTIES B-1 INTRODUCTION B-2 REQUIREMENTS FOR A SINGLE SIMULATOR |
| 83 | Figure B-1 Signed Distances Figure B-2 Least Squares Simulators Figure B-3 Min–Max Simulators |
| 84 | Figure B-4 L1 Simulators Figure B-5 Progressed Least Squares Simulators Figure B-6 Mating of Actual Parts |
| 85 | Figure B-7 Mostly Progressed Least Squares Simulators Figure B-8 Constrained L1 Simulators Figure B-9 Constrained Min–Max Simulators |
| 86 | Figure B-10 Constrained Least Squares Simulators Figure B-11 Constrained Simulators for a V-Shaped Feature Figure B-12 Constrained Simulators for a Peanut-Shaped Circular Feature |
| 87 | Figure B-13 Constrained Simulators for an Hourglass-Shaped Opposed Lines Feature Figure B-14 Constrained Simulators for a Skew-Convex Linear Feature |
| 88 | Figure B-15 Constrained Simulators for a Dented Circular Feature Figure B-16 Constrained Simulators for a Skew-Convex Opposed Lines Feature Figure B-17 Large Voids Can Harm Constrained Simulators |
| 89 | Figure B-18 Void-Filling Can Improve Constrained Simulators Figure B-19 Void-Filling Can Degrade the Constrained Min-Max Simulator |
| 90 | NONMANDATORY APPENDIX C FORMER PRACTICES C-1 PROFILE CONTROL |
| 91 | Figure D-1 Size Ordering for Perfect and Imperfect Features of Size NONMANDATORY APPENDIX D CONCEPTS RELATED TO SIZE D-1 GENERAL D-2 ORDERING OF SIZE VALUES |
| 92 | Table D-1 Uniqueness and Containment Relationships for Features of Size — Part 1 Table D-2 Uniqueness and Containment Relationships for Features of Size — Part 2 |
| 93 | NONMANDATORY APPENDIX E A SELECTION OF MATHEMATICAL CONCEPTS E-1 WHY THIS APPENDIX? E-2 MANIFOLDS E-3 CONTINUITY E-4 SUPPORT E-5 REGULARIZED SETS |
| 94 | Figure E-1 Examples of One-Dimensional Manifold (Left) and Not (Right) Figure E-2 A Line Which Is Continuous (Left) and Not (Right) Figure E-3 A Line Which Is Tangent Continuous (Left) and Not (Right) Figure E-4 An Object, Its Interior, and Its Boundary |
| 95 | Figure E-5 The Result of Union Between Two Objects, and the Non-Manifold Boundary Figure E-6 The Interior of Two Objects, and Their Union With a Manifold Boundary |
| 96 | NONMANDATORY APPENDIX F POTENTIAL MISUSE OF THE SWEPT-SPHERE DEFINITION OF SIZE F-1 GENERAL F-2 THE SHORT SPINE F-3 THE SPACE-FILLING SPINE |
| 97 | Figure F-1 MMC and LMC Spheres, and a Part to Be Tested for Conformance Figure F-2 LMC and MMC Spines Figure F-3 LMC and MMC Swept Regions Figure F-4 Conformance to the Size Tolerance Figure F-5 MMC and LMC Spheres, and a Part to Be Tested for Conformance Figure F-6 LMC and MMC Spines F-4 THE NONSURROUND CASE F-5 POSSIBLE REMEDIES |
| 98 | Figure F-7 LMC and MMC Swept Regions Figure F-8 Incorrect Determination of Conformance to the Size Tolerance Figure F-9 MMC and LMC Spheres, and a Part to Be Tested for Conformance Figure F-10 LMC and MMC Spines Figure F-11 LMC and MMC Swept Regions Figure F-12 Incorrect Determination of Conformance to the Size Tolerance Figure F-13 MMC and LMC Spheres, and a Part to Be Tested for Conformance Figure F-14 Incorrect Determination of Conformance tothe Size Tolerance |
