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ASME Y14.5.1-2019: Mathematical Definition of Dimensioning and Tolerancing Principles, 2019

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ASME Y14.5.1-2019: Mathematical Definition of Dimensioning and Tolerancing Principles, 2019

CONTENTS
FOREWORD
ASME Y14 COMMITTEE ROSTER
CORRESPONDENCE WITH THE Y14 COMMITTEE
Section 1 Scope and Definitions [Go to Page]
1.1 SCOPE [Go to Page]
1.1.1 Reference to Gaging
1.2 ASME Y14 SERIES CONVENTIONS [Go to Page]
1.2.1 Mandatory, Recommended, Guidance, and Optional Words
1.2.2 Cross-Reference of Standards
1.2.3 Invocation of Referenced Standards
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 [Go to Page]
1.4.1 Symbology
1.4.2 Algebraic Notation
1.5 DEFINITIONS [Go to Page]
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
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
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
1.7 FORMAT
Section 2 General Tolerancing and Related Principles [Go to Page]
2.1 SURFACE POINTS
2.2 DIMENSION ORIGIN
2.3 FEATURES OF SIZE [Go to Page]
2.3.1 Limits of Size
2.3.2 Variation of Size
2.3.3 Actual Local Size Limits
2.3.4 Continuous Features of Size
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
Section 3 Symbology
Section 4 Datum Reference Frames [Go to Page]
4.1 GENERAL
4.2 CONCEPTS
4.3 DEGREES OF FREEDOM
4.4 DATUM FEATURE SIMULATORS (THEORETICAL) [Go to Page]
4.4.1 Datum Feature Simulator Requirements
4.5 CONSTRAINING DEGREES OF FREEDOM [Go to Page]
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
4.7 CANDIDATE DATUM SETS AND CANDIDATE REFERENCE FRAME SETS [Go to Page]
4.7.1 Establishing a Candidate Datum Set
4.7.2 Types of Datum Features
4.7.3 Planar Datum Features
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
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
Section 5 Tolerances of Form [Go to Page]
5.1 GENERAL
5.2 FORM CONTROL
5.3 SPECIFYING FORM TOLERANCES
5.4 FORM TOLERANCES [Go to Page]
5.4.1 Straightness
5.4.2 Flatness
5.4.3 Circularity (Roundness)
5.4.4 Cylindricity
Section 6 Tolerances of Orientation [Go to Page]
6.1 GENERAL
6.2 ORIENTATION CONTROL
6.3 SPECIFYING ORIENTATION TOLERANCES
6.4 ORIENTATION TOLERANCE [Go to Page]
6.4.1 Planar Orientation Tolerance Zone
6.4.2 Cylindrical Orientation Tolerance Zone
6.4.3 Linear Orientation Tolerance Zone
Section 7 Tolerances of Location [Go to Page]
7.1 GENERAL [Go to Page]
7.1.1 Material Condition Basis
7.1.2 Patterns of Features
7.2 POSITION TOLERANCING [Go to Page]
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
7.4 CONICAL TOLERANCE ZONE [Go to Page]
7.4.1 In Terms of the Surface of the Feature
7.4.2 In Terms of the Resolved Geometry (Axis) of the Feature
7.5 BIDIRECTIONAL POSITION TOLERANCING [Go to Page]
7.5.1 In Terms of the Surface of the Feature
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
7.6 POSITION TOLERANCING AT MMC FOR BOUNDARIES OF ELONGATED HOLES
7.7 CONCENTRICITY AND SYMMETRY
Section 8 Tolerances of Profile [Go to Page]
8.1 GENERAL
8.2 PROFILE [Go to Page]
8.2.1 Types of Profile Tolerances
8.3 TOLERANCE ZONE BOUNDARIES [Go to Page]
8.3.1 Uniform Tolerance Zones
8.4 PROFILE APPLICATIONS [Go to Page]
8.4.1 Optimization of Profile Tolerance Systems
8.4.2 Constraint Properties of Profile Tolerance Zones
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
8.6 NONUNIFORM TOLERANCE ZONE
Section 9 Tolerances of Runout [Go to Page]
9.1 RUNOUT TOLERANCE [Go to Page]
9.1.1 Circular Runout
9.1.2 Total Runout
Figures [Go to Page]
Figure 1-1 Example: Distance From a Point to a True Position Axis
Figure 1-2 Example: Cutting Surfaces to Evaluate Circular Runout
Figure 1-3 Examples of a Planar Surface of Support
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
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
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
Figure 4-3 Tertiary Datum Feature Simulator Is Basically Located and Oriented
Figure 4-4 Example of Translation Modifier
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
Figure 6-1 Planar Orientation Zone With Primary and Secondary Datum Planes Specified
Figure 6-2 Projection of Tolerance Vector Onto Primary Datum Plane
Figure 6-3 Cylindrical Orientation Zone With Respect to a Primary Datum Plane
Figure 6-4 Linear Orientation Zone Bounded by Parallel Lines
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
Figure 7-5 Tolerance Zone and Conformance: Holes at MMC or RFS, Shafts at LMC — Resolved Geometry Interpretation
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
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
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
Figure 7-13 Rays Are Arranged in the Lowest Order of Symmetry About an Axis or a Point
Figure 8-1 Tolerance Zone Derivation — Equally Disposed Profile
Figure 8-2 Tolerance Zone Derivation — Unequally Disposed Profile
Figure 8-3 Tolerance Zone Derivation — Unilaterally Disposed Profile (Outside)
Figure 8-4 Tolerance Zone Derivation — Unilaterally Disposed Profile (Inside)
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
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
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
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)
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
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
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
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)
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)
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
Figure 9-1 Circular Runout Zone
Figure B-1 Signed Distances
Figure B-2 Least Squares Simulators
Figure B-3 Min–Max Simulators
Figure B-4 L1 Simulators
Figure B-5 Progressed Least Squares Simulators
Figure B-6 Mating of Actual Parts
Figure B-7 Mostly Progressed Least Squares Simulators
Figure B-8 Constrained L1 Simulators
Figure B-9 Constrained Min–Max Simulators
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
Figure B-13 Constrained Simulators for an Hourglass-Shaped Opposed Lines Feature
Figure B-14 Constrained Simulators for a Skew-Convex Linear Feature
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
Figure B-18 Void-Filling Can Improve Constrained Simulators
Figure B-19 Void-Filling Can Degrade the Constrained Min-Max Simulator
Figure D-1 Size Ordering for Perfect and Imperfect Features of Size
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
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
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
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
Tables [Go to Page]
Table 1-1 Mathematical Symbology
Table 4-1 Symbols for Datum Reference Frame Tables
Table 4-2 Point as Primary Datum (Spherical Datum Feature)
Table 4-3 Axis as Primary Datum (Cylindical Datum Feature)
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
Table 7-1 Definition of Position Tolerance Zone — Surface 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
Table 7-5 Definition of Conical Tolerance Zone — Surface Interpretation
Table 7-6 Size of Conical Tolerance Zone — Surface Interpretation
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
Table 7-10 Size of Bidirectional Tolerance Zone — Resolved Geometry (Axis) Interpretation
Table 7-11 Size of Polar Bidirectional Tolerance Zone — Resolved Geometry (Axis) Interpretation
Table 7-12 Symmetry Elements for ObtainingCorresponding Feature Elements
Table 8-1 Table of Profile Tolerance Dispositions
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
NONMANDATORY APPENDICES [Go to Page]
NONMANDATORY APPENDIX A PRINCIPAL CHANGES AND IMPROVEMENTS [Go to Page]
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
A-8 SECTION 6, TOLERANCES OF ORIENTATION
A-9 SECTION 7, TOLERANCES OF LOCATION
A-10 SECTION 8, TOLERANCES OF PROFILE
A-11 SECTION 9, TOLERANCES OF RUNOUT
A-12 NONMANDATORY APPENDICES
NONMANDATORY APPENDIX B MATHEMATICAL DATUM SIMULATORS REFERENCED AT RMB: DEFINITIONS AND PROPERTIES [Go to Page]
B-1 INTRODUCTION
B-2 REQUIREMENTS FOR A SINGLE SIMULATOR
NONMANDATORY APPENDIX C FORMER PRACTICES [Go to Page]
C-1 PROFILE CONTROL
NONMANDATORY APPENDIX D CONCEPTS RELATED TO SIZE [Go to Page]
D-1 GENERAL
D-2 ORDERING OF SIZE VALUES
NONMANDATORY APPENDIX E A SELECTION OF MATHEMATICAL CONCEPTS [Go to Page]
E-1 WHY THIS APPENDIX?
E-2 MANIFOLDS
E-3 CONTINUITY
E-4 SUPPORT
E-5 REGULARIZED SETS
NONMANDATORY APPENDIX F POTENTIAL MISUSE OF THE SWEPT-SPHERE DEFINITION OF SIZE [Go to Page]
F-1 GENERAL
F-2 THE SHORT SPINE
F-3 THE SPACE-FILLING SPINE
F-4 THE NONSURROUND CASE
F-5 POSSIBLE REMEDIES [Go to Page]

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