1、AN AMERICAN NATIONAL STANDARD ENGINEERING DRAWING AND RELATED DOCUMENTATION PRACTICES Mathematical Definition of Dimensioning and Tolerancing Principles ASME Y14.5.1M-1994 The American Society of Mechanical Engineers 345 East 47th Street, New York, N.Y. 1001 7 - Date of Issuance: January 31, 1995 Th
2、is Standard will be revised when the Society approves the issuance of a new edition. There will be no addenda or written interpretations of the require- ments of this Standard issued to this Edition. ASME is the registered trademark of The American Society of Mechanical Engineers. This code or stand
3、ard was developed under procedures accredited as meeting the criteria for American National Standards. The Consensus Committee that approved the code or standard was balanced to assure that individuals from competent and concerned interests have had an opportu- nity to participate. The proposed code
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8、 be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. Copyright 0 1995 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Resewed Printed in U.S.A (This Foreword is not a part of ASME Y14.5.1M-1994.) The Y14 Committ
9、ee created the Y14.5.1 Subcommittee in response to a need identified during a National Science Foundation (NSF) workshop. The International Workshop on Me- chanical Tolerancing was held in Orlando, Florida, in late 1988. The workshop report strongly identified a need for a mathematical definition fo
10、r the current tolerancing standards. Tom Charlton coined the phrase “mathematization of tolerances.” The phrase meant to add mathe- matical rigor to the Y 14.5M standard. The response is the present standard, ASME Y 14.5.1M- 1994. This new standard creates explicit definitions for use in such areas
11、as Computer Aided Design (CAD) and Computer Aided Manufacturing (CAM). The Committee has met three times a year since their first meeting af January of 1989 in Long Boat Key, Florida. Initial discussions covered scope of the document, boundary definitions, size, and datums. The Committee identified
12、four major divisions of a tolerance: 1) the mathematical definition of the tolerance zone; 2) the mathematical definition of conformance to the tolerance; 3) the mathematical definition of the actual value; 4) the mathematical definition of the measured value. The Subcommittee later decided that the
13、 measured value was beyond the scope of this Standard. When this Standard defines part conformance, it consists of the infinite set of points that make up all the surfaces of the part, and it is addressing imperfect form semantics. This Standard does not fully address the issue of boundary, that is
14、where one surface stops and the other surface starts. The Subcommittee hopes to define this in the next edition of this Standard. The definition of size took up many days of discussions and interaction with the Y14.5 Subcommittee. It always came back to the statement of a micrometer-type two point c
15、ross- sectional measurement. The difficulty comes from the method of defining the cross-section. Consider a figure such as an imperfectly formed cylinder. When considering the infinite set of points that make up the surface, what is the intent behind a two point measurement? Most of the reasons appe
16、ar to be for strength. Yet, a two point cross-sectional definition doesnt define strength on, for instance, a three-lobed part. These and other considerations led to the existing definition. The pictorial definition, presented in Section 2, is the smallest of the largest elastic perfect spheres that
17、 can be passed through the part without breaking the surface. ws Standard does not address measurement, yet often a two point cross-sectional measurement is adequate for form, fit, and function. The subject of datums also led to many hours of work by the Subcommittee. The current definitions, presen
18、ted in Section 4, were the result of evaluating a number of approaches against four criteria: 1) conformance to Y14.5M; 2) whether a unique datum is defined; 3) whether the definition is mathematically unambiguous; and 4) whether the definition conveys design intent. A fifth criterion, whether the d
19、efinition was measurable, was not used for reasons discussed above. The end result of this work was based on feedback from the Y 14.5M Subcom- mittee when Y14.5.1 presented its analysis, and involved a change in its thinking about datums. The initial view of a datum was as something established befo
20、re a part feature is evaluated. The current definitions involve a different view that a datum existsfor the sake ofthe features related to it. The result was a consolidation of the issues involved with “wobbling” datums and the issues involved with datum features of size at MMC or LMC. These apparen
21、tly Ill . dissimilar issues are unified mathematically in the concepts of “candidate datum” and “candi- date datum reference frame.” A special thanks to the Y14 Main Committee and Y14.5 Subcommittee members in their support and encouragement in the development of this Standard. Also of note are the
22、participation and contributions of Professor Ari Requicha of University of Southern California, Professor Josh Turner of Rensselaer Polytechnic Institute, and Professor Herb Voelcker of Cornell University. Suggestions for improvement of this Standard are welcome. They should be sent to the American
23、Society of Mechanical Engineers, Att: Secretary, Y14 Main Committee, 345 East 47th Street, New York, NY 10017. This Standard was approved as an American National Standard on November 14, 1994. iv ASME STANDARDS COMMllTEE Y14 Engineering Drawing and Related Documentation Practices (The following is t
24、he roster of the Committee at the time of approval of this Standard.) OFFICERS P. E. McKim, Chair F. Bakos, Jr., Vice-Chair C. J. Gomez, Secretary COMMIITEE PERSONNEL A. R. Anderson, Trikon Corp. F. Bakos, Jr., Eastman Kodak Co. T. D. Benoit, Alternate, Pratt b Whitney CEB D. E. Bowerman, Copeland C
25、orp. J. V. Burleigh, The Boeing Co. L. Burns R. A. Chaddedon, Southwest Consultants F. A. Christiana, ASEA Brown Boveri, Combustion Engineering Systems M. E. Curtis, Jr., Rexnord Corp. R. W. DeBolt, Motorola, Inc., Government and Space Technology Group H. L. Dubocq L. W. Foster, L. W. Foster Associa
26、tes, Inc. C. J. Gomez, The American Society of Mechanical Engineers D. Hagler, E-Systems, Inc., Garland Div. E. L. Kardas, Pratt b Whitney CEB C. G. Lance, Santa Cruz Technology Center P. E. McKim, Caterpillar, Inc. C. D. Merkley, IBM Corp. E. Niemiec, Westinghouse Electric Corp. R. J. Poliui D. L.
27、Ragon, Deere b Company, John Deere Dubuque Works R. L. Tennis, Caterpillar, Inc. R. P. Tremblay, US. Department of the Army, ARDEC R. K. Walker, Westinghouse Marine Division G. H. Whitmire, TEC/TREND K. E. Wiegandt, Sandia National Laboratory P. Wreede, E-Systems, Inc. SUBCOMMllTEE 5.1 MATHEMATICAL
28、DEFINITION OF DIMENSIONING AND TOLERANCING PRINCIPLES R. K. Walker, Chair, Westinghouse Marine Division T. H. Hopp, Vice-Chair, National Institute of Standards and Technology M. A. Nasson, Vice-Chair, The Charles Stark Draper Laboratory, Inc. A. M. Nickles, Secretary, The American Society of Mechani
29、cal Engineers V M. E. Algeo, National Institute of Standards and Technology R. E. Coombes, Caterpillar Inc. L. W. Foster, Lowell W. Foster Associates Inc. M. T. Gale, Giddings b Lewis Measurement Systems J. D. Guilford, Rensselaer Design Research Center R. J. Hocken, University of North Carolina R.
30、K. Hook, Metcon J. Hurt, SDRC D. P. Karl, Ford Motor Co. C. G. Lance, Santa Cruz Technology Center J. D. Meadows, Institute for Engineering and Design A. G. Neumann, Technical Consultants, Inc. R. W. Nickey, Naval Warfare Assessment Center F. G. Parsons, Federal Products Co. K. L. Sheehan, Brown b S
31、harpe V. Srinivasan, IBM, Research Division B. R. Taylor, Renishaw PLC W. B. Taylor, Westinghouse Electric Corp. S. Thompson, Lawrence Livermore National Laboratory T. Woo, National Science Foundation vi CONTENTS Foreword Standards Committee Roster 1 Scope and Definitions 1.1 General . 1.2 Reference
32、s . 1.3 Mathematical Notation . 1.4 Definitions 1.5 Summary of Conventional Designations . 1.6 Format 2 General Tolerancing and Related Principles . 2.1 Feature Boundary 2.2 Dimension Origin 2.3 Limits of Size . 3 Symbology . 4 Datum Referencing . 4.1 General . 4.2 Concepts 4.3 Establishing Datums .
33、 4.4 Establishing Datum Reference Frames . 4.5 Datum Reference Frames for Composite Tolerances 4.6 Multiple Patterns of Features . 4.7 Tabulation of Datum Systems . 5 Tolerances of Location 5.1 General . 5.2 Positional Tolerancing 5.3 Projected Tolerance Zone . 5.4 Conical Tolerance Zone 5.5 Bidirec
34、tional Positional Tolerancing . 5.6 Position Tolerancing at MMC for Boundaries of Elongated Holes . 5.7 Concentricity and Symmetry 6 Tolerances of Form, Profile, Orientation, and Runout . 6.1 General . 6.2 Form and Orientation Control . 6.3 Specifying Form and Orientation Tolerances . 6.4 Form Toler
35、ances . 6.5 Profile Control . 6.6 Orientation Tolerances . 6.7 Runout Tolerance 6.8 Free State Variation iii V 1 1 1 1 2 5 5 7 7 7 7 11 13 13 13 13 16 17 17 18 21 21 22 24 25 27 32 32 35 35 35 35 35 39 40 45 48 vii Appendix A Consolidation of Parallelism. Perpendicularity. and Angularity . 49 A1 Gen
36、eral . 49 A2 Planar Orientation 49 A3 Cylindrical Orientation . 57 A4 Linear Orientation 66 Index . 79 viii ASME Y14.5.1M-1994 ENGINEERING DRAWING AND RELATED DOCUMENTATION PRACTICES MATHEMATICAL DEFINITION OF DIMENSIONING AND TOLERANCING PRINCIPLES 1 SCOPE AND DEFINITIONS 1.1 General This Standard
37、presents a mathematical definition of geometrical dimensioning and tolerancing consist- ent with the principles and practices of ASME Y14.5M-1994, enabling determination of actual val- ues. While the general format of this Standard paral- lels that of ASME Y 14.5M- 1994, the latter document should b
38、e consulted for practices relating to dimen- sioning and tolerancing for use on engineering draw- ings and in related documentation. Textual references are included throughout this Standard which are direct quotations from ASME Y14.5M-1994. All such quotations are identified by italicized type. Any
39、direct references to other docu- ments are identified by an immediate citation. The definitions established in this Standard apply to product specifications in any representation, in- cluding drawings, electronic exchange formats, or data bases. When reference is made in this Standard to a part draw
40、ing, it applies to any form of product specification. 1.1.1 Units. The International System of Units (SI) is featured in the Standard because SI units are expected to supersede United States (U.S.) custom- ary units specified on engineering drawings. 1.1.2 Figures. The figures in this Standard are i
41、ntended only as illustrations to aid the user in under- standing the principles and methods described in the text. In some instances figures show added detail for emphasis; in other instances figures are incomplete by intent. Any numerical values of dimensions and tolerances are illustrative only. 1
42、.1.3 Notes. Notes shown in capital letters are intended to appear on finished drawings. Notes in lower case letters are explanatory only and are not intended to appear on drawings. 1 1.1.4 Reference to Gaging. This Standard is not intended as a gaging standard. Any reference to gag- ing is included
43、for explanatory purposes only. 1.2 References When the following American National Standards referred to in this Standard are superseded by a revi- sion approved by the American National Standards Institute, the revision shall apply. ANSI B46.1-1985, Surface Texture ASME Y 14.5M-1994, Dimensioning a
44、nd Tolerancing 1.3 Mathematical Notation This Subsection describes the mathematical nota- tion used throughout this Standard, including sym- bology (typographic conventions) and algebraic notation. 1.3.1 Symbology. All mathematical equations in this Standard are relationships between real numbers, t
45、hree-dimensional vectors, coordinate systems asso- ciated with datum reference frames, and sets of these quantities. The symbol conventions shown in Table 1.3 are used for these quantities. These symbols may be subscripted to distinguish between distinct quantities. Such subscripts do not change the
46、 nature of the designated quantity. Technically, there is a difference between a vector and a vector with position. Generally in this Stan- dard, vectors do not have location. In particular, di- rection vectors, which are often defined for specific points on curves or surfaces, are functions of posi
47、tion on the geometry, but are not located at those points. (Another conventional view is that all vectors are located at the origin.) Throughout this Standard, po- sition vectors are used to denote points in space. While there is a technical difference between a vector ASME Y14.5.1M-1994 MATHEMATICA
48、L DEFINITION OF DIMENSIONING AND TOLERANCING PRINCIPLES TABLE 1.3.1 SYMBOLOGY I Quantity I Symbol Real Numbers Plain-face, italic, upper-case English letters (S, F, etc.) Sets Plain-face, upper case Greek letter (r, etc.) (coordinate systems) Datum Reference Frames by the parameters of the function
49、in parentheses r (3, etc. (real or vector-valued) A real number or vector symbol (depending on the kind of value of the function) followed Functions Bold-face, italic English letters with a carat diacritical mark , etc.) Unit Vectors Bold-face, italic English letters with an arrow diacritical mark (7, etc.) Vectors Plain-face, italic, lower-case English or lower-case Greek letters (t, r, 8, etc.) and a point in space, the equivalence used in this Standard should not cause confusion. 1.3.2 Algebraic Notation. A vector can be ex- panded into scalar components (with the components distinguish
