Asme y14 5 1m 1994 (2012) scan (american society of mechanical engineers)

AN AMERICAN NATIONAL STANDARD ENGINEERING DRAWINGAND RELATED DOCUMENTATION PRACTICES Mathematical Definition of Dimensioning and Tolerancing Principles ASME Y14.5.1M-1994 REAFFIRMED 2012 FOR CURRENT COMMITTEE PERSONNEL PLEASE E-MAIL CS@asme.org The American Society of Mechanical Engineers ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS 345 East 47th Street, New York, N.Y 10017 Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT - Date of Issuance: January 31, 1995 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - This Standard will be revised when the Society approves the issuance of a new edition There will be no addenda or written interpretations of the requirements of this Standard issued to this Edition ASME is the registered trademark of The American Society of Mechanical Engineers This code or standard 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 individualsfrom competent and concerned interests have had an opportunity to participate The proposed code or standard was made available for public review and comment which provides an opportunity for additional public input from industry,academia, regulatory agencies, and the public-at-large ASME does not "approve," "rate," or "endorse" any item, construction, proprietary device, or activity ASME does not take any position with respect to the validity of any patent rights asserted in connection with any items mentionedin this document, and does not undertake to insure anyone utilizing a standard against liabilityfor infringement of any applicable Letters Patent, nor assume any such liability Users of a code or standard are expressly advised that determination of the validity of any such patent rights, andthe risk of infringement of such rights, is entirely their own responsibility Participation by federal agency representative(s1 or person(s) affiliated with industry is not to be interpreted as government or industry endorsementof this code or standard ASME accepts responsibilityfor only those interpretationsissued in accordance with governing ASMEproceduresandpolicies whichprecludetheissuanceofinterpretationsbyindividual volunteers No part of this document may be reproducedin any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher Copyright 1995 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Resewed Printed in U.S.A Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT The Y14 Committee created the Y14.5.1 Subcommittee in response to a need identified during a National Science Foundation (NSF) workshop The International Workshop on Mechanical Tolerancing was held in Orlando, Florida, in late 1988 The workshop report strongly identifiedaneed for amathematical definition for the current tolerancingstandards Tom Charlton coined the phrase “mathematization of tolerances.” The phrase meant to add mathematical rigor to the Y 14.5M standard.The response is the present standard, ASME Y 14.5.1M1994 This new standard creates explicit definitions for use in such areas as Computer Aided Design (CAD) and Computer Aided Manufacturing (CAM) The Committee has met three times a year since their first meeting af January of1989in Long Boat Key, Florida.Initial discussionscovered scope of the document, boundary definitions, size, and datums The Committee identified 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 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 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 crosssectional 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 appear to be for strength Yet, a two pointcross-sectional definition doesn’t 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 thatcan 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, presented in Section 4, were theresult 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 for reasons intent A fifth criterion, whetherthedefinitionwasmeasurable,wasnotused discussed above The end result of this work was based feedback on from the Y 14.5M Subcommittee when Y14.5.1 presentedits analysis, and involved change a in its thinking aboutdatums The initial view of a datum was as something established before 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 andthe issues involvedwith datum features of size at MMC or LMC These apparently Ill Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - (This Foreword is not a part of ASME Y14.5.1M-1994.) dissimilar issues are unified mathematicallyin the concepts of “candidate datum” and “candidate 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 participation and contributions of Professor Ari Requicha of University of Rensselaer Polytechnic Institute, and Professor of Southern California, Professor Josh Turner Herb Voelcker of Cornell University Suggestions for improvement of this Standard are welcome They should be sent to the American 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 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT ASME STANDARDS COMMllTEE Y14 Engineering Drawing and Related Documentation Practices (The following is the 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 Corp 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 Associates, 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 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 MATHEMATICALDEFINITIONOF 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 Mechanical Engineers V ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT 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 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 Sharpe 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 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT CONTENTS Foreword Standards Committee Roster iii ScopeandDefinitions 1.1 General 1.2 References 1.3 Mathematical Notation 1.4 Definitions 1.5 Summary ofConventionalDesignations 1.6 Format 1 1 5 GeneralTolerancingandRelatedPrinciples 2.1 Feature Boundary 2.2 DimensionOrigin 2.3 Limits of Size 7 7 Symbology 11 DatumReferencing 4.1 General 4.2 Concepts 4.3 Establishing Datums 4.4 Establishing Datum ReferenceFrames 4.5 Datum Reference Frames for Composite Tolerances 4.6 Multiple Patterns of Features 4.7 Tabulation ofDatum Systems 13 13 13 13 16 17 17 18 TolerancesofLocation 5.1 General 5.2 Positional Tolerancing 5.3 Projected Tolerance Zone 5.4 Conical Tolerance Zone 5.5 Bidirectional Positional Tolerancing 5.6 Position Tolerancing atMMC for Boundaries of Elongated Holes 5.7 Concentricity andSymmetry 21 Tolerances of Form, Profile, Orientation, and Runout 6.1 General 6.2 Formand Orientation Control 6.3 Specifying Formand Orientation Tolerances 6.4 Form Tolerances 6.5 Profile Control 6.6 Orientation Tolerances 6.7 Runout Tolerance 6.8 Free State Variation 35 35 35 35 35 39 40 45 48 vii ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT V 21 22 24 25 27 32 32 Appendix AConsolidation of Parallelism.Perpendicularity.andAngularity 49 A1 General 49 A2 Planar Orientation 49 A3 Cylindrical Orientation 57 A4 Linear Orientation 66 Index ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - viii Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT 79 ASME Y14.5.1M-1994 ENGINEERINGDRAWINGANDRELATEDDOCUMENTATION PRACTICES MATHEMATICAL DEFINITION OF DIMENSIONING AND TOLERANCING PRINCIPLES SCOPE AND DEFINITIONS 1.1General ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - This Standard presents a mathematical definition of geometrical dimensioning and tolerancing consistentwiththeprinciplesandpracticesofASME Y14.5M-1994, enabling determination of actual values While the general format of this Standard parallels thatof ASMEY 14.5M- 1994, the latter document should be consulted for practices relating to dimensioning and tolerancing for use on engineering drawings and in related documentation Textualreferencesareincludedthroughout this StandardwhicharedirectquotationsfromASME Y14.5M-1994 All such quotations are identified by italicized type Any direct references to other documents are identified by an immediate citation The definitions established in this Standard apply to product specifications in any representation, includingdrawings,electronicexchangeformats,or data bases When reference is made in this Standard to a part drawing, it applies to any form of product specification 1.1.4 Referenceto Gaging This Standard is not intended as a gaging standard Any reference to gaging is included for explanatory purposes only 1.2References When the following American National Standards referred to inthis Standard are superseded by a revision approved by the American National Standards Institute, the revision shall apply ANSI B46.1-1985, Surface Texture Dimensioning and ASME Y 14.5M-1994, Tolerancing 1.3 Mathematical Notation This Subsection describes the mathematical notation used throughout this Standard, including symbology (typographic conventions) and algebraic notation 1.3.1 Symbology.All mathematical equations in this Standard are relationships between real numbers, three-dimensional vectors, coordinate systems associated 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 not 1.1.2 Figures Thefiguresin this Standardare intended only as illustrations to aid the user in under-change the nature of the designated quantity Technically, thereis a difference between a vector standing the principles and methods described in the this Stantext In some instances figures show added detail for and a vector with position Generally in dard, vectors not have location In particular, diemphasis; in other instances figures are incomplete rection vectors, which are often defined for specific by intent Any numerical values of dimensions and points on curves or surfaces, are functions of position tolerances are illustrative only on the geometry, but are not located at those points (Anotherconventionalview is thatallvectorsare 1.1.3 Notes Notesshownincapitallettersare located at the origin.) Throughoutthis Standard, pointended to appear on finished drawings Notes in sitionvectorsareusedtodenotepointsinspace lower case letters are explanatory only and are not While thereis a technical difference between a vector intended to appear on drawings 1.1.1 Units TheInternationalSystem ofUnits (SI) is featured in the Standard because SI units are expected to supersede United States (U.S.) customary units specified on engineering drawings Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT MATHEMATICAL DEFINITION OF DIMENSIONING AND TOLERANCINGPRINCIPLES ASME Y14.5.1M-1994 I I Quantity TABLE 1.3.1 SYMBOLOGY Symbol Plain-face, italic, lower-case English or lower-case Greek letters ( t ,r , 8, etc.) Real Numbers Bold-face, italic English letters with an arrow diacritical mark (7,etc.) Vectors Unit Vectors Bold-face, italic English letters with a carat diacritical mark @, etc.) Functions (real or vector-valued) Datum Reference Frames (coordinate systems) Sets A real number or vector symbol (depending on the kind of value of the function) followed etc.] by the parameters of the function in parentheses [r (3, Plain-face, upper case Greek letter (r,etc.) Plain-face, italic, upper-case English letters (S, F , etc.) and a point in space, the equivalence used in Standard should not cause confusion this ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - The magnitudeof the cross productis equal in value two vectors times to the product of the lengths of the the sine of the angle between them For a given feature, the notagon r($, r ) will de1.3.2 Algebraic Notation A vector can be exP to true position (see panded into scalar components (with the components note the distance from a point Subsection 1.4) in datum reference frame r When 0, j', distinguished by subscripts, if necessary) Let thedatumreference f r q e is understoodfromthe and k be the unit vectors along the x, y, andz axes, context, the notation r(P) will be used Figure 1-1 qspectively, of a coordinate system Then a vector shows a case of a true-position axis If the axis is V can be uniquely expanded as: represented by a point Po on the axis and a direction (a unit vector), then r($) can be evaluated by either of the following formulas: + -+ The vector can be written V = (u,b,c).The magnitude (length) of vector ? is denoted by I? I and can be evaluated by: Iv'l = d m r(P)= - - [(P' - z0) l0]2 r$) = I ($-$o) -3 + - + s0t2 or A unit vector9 is any vector with magnitude equal to one The scalar pr2duct (dot product; innzr product) of two vectors V , = (?, b,, c , ) and V , = (u,, b,, c,) is denoted by V , V, The scalar product is a real number given by: VI * V2= ala2+ b,b, 41.'- x i The first equationis a version of the Pythagorean Theorem The second equationis based on the properties of the cross product 1.4DEFINITIONS The following terms are defined as their use applies to this Standard ASME Y14.5M-1994 should be consulted for definitions applying to dimensioning and tolerancing + clc2 and is equal in value to the product of the lengthsof the two vectors times the cosine of the angle between 1.4.1 Actualmating surface A surface of perthem The vector product (cross product; outer prod+ fect form which corresponds to an actual part feature uct) of two vectorsand ?, is denoted by V , x -+ + For a cylindrical or spherical feature, the actual matV , The cross product is a vector V, = (a,, b,, c,) ing surface is the actual mating envelope For a plawith components given by: nar feature, it is defined by the procedures defining a primary datum plane a3 = b, c2 - b2c, b3 = a2 ~1 - ~2 1.4.2 Actual value A uniquenumericalvalue c3 = a, b, - a2b, representingageometriccharacteristicassociated Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT T Y CUTTING PLANE ORIENTATION EACH ELEMENT FIG.A-19aLINEARANGULARITYOFRADIALSURFACELINEELEMENTS;PRIMARY DATUM AXIS; NOSECONDARY DATUM SPECIFIED FIG.A-19bLINEARANGULARITYOFSURFACELINEELEMENTS;PRIMARY NOSECONDARY DATUM SPECIFIED DATUM AXIS; 67 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT b/ 7’g EACH ELEMENT CUTTING PLANE ORIENTATION CUTTING PLANE ORIENTATION FIG.A-19cLINEARANGULARITYOFSURFACELINEELEMENTS;PRIMARY SECONDARY DATUM AXES AND ONE POSSIBLE SET OF CUTTING PLANE ORIENTATIONS FIG A-19d LINEARANGULARITYOFSURFACELINEELEMENTS;PRIMARY NO SECONDARY DATUM SPECIFIED DATUM AXIS; 68 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT CUTTING PLANE ORIENTATIONS FIG.A-20aLINEARPARALLELISMOFSURFACELINEELEMENTS;PRIMARY DATUM AXIS; NOSECONDARY DATUM SPECIFIED; CUlTING PLANESCONTAINTHEPRIMARY DATUM AXIS ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - planes whoseorientation is controlled by the primary datum axis For each cutting plane the tolerance zone is bounded by two parallel lines oriented at the basic angle with respect to the primary datum axis Application of a secondary datum would provide no further control Figure A-20b depicts a cylindrical part with a flat surface.A parallelism control is specified for the elements of the flat surface with respect to both the primary datum axis and the secondary datum plane The surface line elements are determined by cutting planes whoseorientation is controlled by the primary datum axis and the secondary datum axis Since a secondary datum is specified, the cutting planes are not allowed to rotate about the primary datum axis For each cutting plane the tolerance zone is bounded by two parallel lines oriented parallel to the primary datum axis Figure A-20c is the same as Fig A-20b except that the flat surface has been replaced by acontoured surface and no secondary datum has been specified The surface line elements are determined by cutting planes whose orientation is controlled by the primary datum axis Since no secondary datum is specified, the cutting planesmay have any orientation about the datum axis For each cutting plane the tolerance zone is bounded by two parallel lines parallel to the primarydatum axis A secondary datum could be specified to further restrict the orientation of the cutting planes fied for the elements of the annular surface relative to a primarydatum axis The radial line elements are determined by cutting planeswhose orientation is controlled by the primary datum axis For each cutting plane the tolerance zone is bounded by two parallel lines oriented perpendicular to the primary datum axis Application of a secondary datum would provide no further control Figure A-21b depicts a cylindrical part A perpendicularity control is specified for the elements of an end surface with respect to the primary datum axis The surface line elements are determined by cutting planes whose orientation is controlled by the primary datum axis For each cutting plane the tolerance zone is bounded by two parallel lines oriented at the basic angle with respect to the primary datum axis If no secondary datum hadbeen specified, the cutting planes would have been free to rotate about the primary datum axis Figure A-21c is the same as Fig.A-21b except that theend surface has beenreplaced by acontoured surface The surface line elements are determined by cutting planes whose orientation is controlled by the primary datum axis and the secondary datum axis For each cutting plane the tolerance zone is bounded by two parallel lines perpendicular to the datum axis A.4.4 Case 22 Figure A-22a depicts a disk with an angularity control specified for the elements of a beveled surface relative to a primary datum plane The surface line elements are determined by cutting planes whose orientation is controlled by the primary datum plane For each cutting plane the tolerance A.4.3 Case 21 Figure A-21a depicts a stepped cylindrical part with aperpendicularity control speci- Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS 69 Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT CUlTlNG PLANE ORIENTATIONS I FIG A-20b LINEARPARALLELISMOFSURFACELINEELEMENTS;PRIMARY SECONDARY DATUM AXES AND / / I 0.0 I A EACH ELEMENT ONE POSSIBLE SET OF CUTTING PLANE ORIENTATONS -d - - FIG A - ~ LINEARPARALLELISMOFSURFACELINEELEMENTS;PRIMARY NO SECONDARY DATUM SPECIFIED DATUM AXIS; 70 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT 1 0.01 [A] - FIG A-21a LINEAR PERPENDICULARITY OF RADIAL SURFACE LINE ELEMENTS; PRIMARY DATUM AXIS; NO SECONDARY DATUM SPECIFIED CUTTING PLANE ORIENTATION FIG A-21b LINEAR PERPENDICULARITY OF SURFACE LINE ELEMENTS; PRIMARY AND SECONDARY DATUM AXES 71 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT CUTTING PLANE ORIENTATION FIG A - ~ LINEARPERPENDICULARITY OF SURFACELINEELEMENTS ON ACONTOURED SURFACE;PRIMARY AND SECONDARY DATUM AXES ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - zone is bounded by two parallel lines oriented at the A.4.5 Case 23 Figure A-23a depicts a part with basic angle with respect to the primary datum plane a parallelism contiol specified for the elements of a Application of a secondary datum would further replanar surface relative to both a primary datum plane strict the orientationof the cutting planes As can be and a secondary datum axis The radial line elements seen in Table A-1, Note applies to this figure A are determined by cutting planes whose orientation perfectly flat actual surface cut at a sharper (smaller) is controlled by theprimarydatumaxis.Foreach cutting plane the tolerance zone is bounded by two angle to the datum plane would pass the angularity tolerancewithaproperlyorientedset of cutting parallel lines oriented at the basic angle with respect to the primary datum plane planes Figure A-22b depicts a rectangular part with a bev- Figure A-23b depicts a cylindrical part with a pareled surface An angularity control is specified for allelismcontrolspecifiedfortheelements of one end surface with respect to the primary datum plane the elements of the beveled surface with respect to defined by the opposite end The surface line elethe primary datum plane The surface line elements mentsaredeterminedbycuttingplaneswhichare are determined by cutting planes whose orientation perpendicular to the primary datum plane Since no is controlledbytheprimarydatumplaneandthe secondary datum is specified, the cutting planes are secondary datum plane A secondary datum is speciallowed to rotate about the direction vector fied to fully constrain the orientation of the cutting of the planes For each cutting plane the tolerance zone is primary datum plane For each cutting plane the tolbounded by two parallel lines oriented at the basic erance zone is bounded by two parallel lines parallel angle with respect to the primary datum plane to the primary datum plane For conformance, a set Figure A-22cis the same as Fig A-22b except that of cutting planes must be found such that the rethe beveled surface has been replaced by a contoured sulting surface elements satisfy the specification surface The surface line elements &e determined by Figure A-23c depicts a rectangular part with a parcutting planes whose orientation is controlledby the of one end allelism control specified for the elements primary datum plane and the secondary datum plane surface with respect to the primary datum plane The For each cutting plane the tolerance zone is bounded surfacelineelementsaredeterminedbycutting by two parallel lines oriented at the basic angle with planes which are controlled by the primary datum respect to the primary datum plane and parallel to plane and the secondary datum plane For each cutting plane the tolerance zone is bounded,by two parthe secondary datum plane 72 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT ONE POSSIBLE SET OF CUTTING PLANE ORIENTATIONS I WARNING: WITHOUT THE ADDITION OF A SECONDARY DATUM TO CONTROL THE ORIENTATION OF THE CUlTING PLANE SETS, THIS CALLOUT DOES NOT PROVIDE ADEQUATE CONTROL OF THE BASIC ANGLE FIG.A-22aLINEARANGULARITYOFSURFACELINEELEMENTS;PRIMARY PLANE;NOSECONDARY DATUM SPECIFIED ox AIR^ -1L10.01 FIG A-22b DATUM EACH ELEMENT CUTTING PLANE ORIENTATKIN LINEARANGULARITYOFSURFACELINEELEMENTS;.PRIMARY SECONDARY DATUM PLANES AND 73 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT CUTTING PLANE ORIENTATION FIG.A-22cLINEARANGULARITY OF SURFACELINEELEMENTS;PRIMARY PLANE; NOSECONDARY DATUM SPECIFIED DATUM b ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - CUlTlNG PLANE ORIENTATION FIG.A-23aLINEARPARALLELISMOFRADIALSURFACELINEELEMENTS;PRIMARY DATUM PLANE;SECONDARY DATUM AXIS 74 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT ONE POSSIBLE SET OF CUlTING PLANE ORIENTATIONS FIG A-23b LINEARPARALLELISMOFSURFACELINEELEMENTS;PRIMARY PLANE; NO SECONDARY DATUM SPECIFIED DATUM allel lines parallel to the primary datum plane and plane and the secondary datum plane For each cutperpendicular to the secondary datum plane ting plane the tolerance zoneis bounded by two parFigure A-23d is the same as Fig A-23c except that allel lines oriented perpendicular to the primary dathe planar surface has been replaced by a contoured tum plane and parallel to the secondary datum plane surface The surface line elements are determined by Figure A-24b depicts a rectangular part with a concutting planes which are controlled by the primary touredendsurface.Aperpendicularitycontrol is datum plane and the secondary datum plane For eachspecified for the elements of the contoured surface cutting plane the tolerance zone is bounded by two with respect to the primary datum plane and the secparallel lines parallel to the primary datum plane and ondary datum plane The surface line elements are perpendicular to the secondary datum plane determined by cuttingplaneswhoseorientationis controlled by the primary d a m plane and the secA.4.6 Case 24 Figure A-24a depicts a part with ondary datum plane a perpendicularity control specified for the elements Foreachcuttingplanethetolerancezone is of a flat surface relative to a datum plane The surbounded by two parallel lines oriented perpendicular face line elements are determined by cutting planes to the primary datum plane and parallel to the secondary plane whose orientationis controlled by the primary datum 75 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT CUTTING PLANE ORIENTATION I FIG.A-23cLINEARPARALLELISMOFSURFACELINEELEMENTS;PRIMARY SECONDARY DATUM PLANES AND FIG A-23d LINEARPARALLELISMOFSURFACELINEELEMENTS;PRIMARY SECONDARY DATUM PLANES 76 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT AND ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - CUTTING PLANE ORIENTATION CLJllffi PUNE ORIENTATON FIG.A-24aLINEARPERPENDICULARITYOFSURFACELINEELEMENTS;PRIMARY SECONDARY DATUM PLANES P 11 0.01 AND ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - rn"\ IA~B] EACH ELEMENT I I + I I CUlTING PLANE ORIENTATION FIG A-24b LINEARPERPENDICULARITY OF SURFACELINEELEMENTS;PRIMARY PLANE; NO SECONDARY DATUM SPECIFIED DATUM 77 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT r 1.5CompositePattern 4.6 Composite Tolerance 4.5 4.6, 5.1.2 A Concentricity 5.7 n Conformance see individual tolerance types ActualMatingEnvelope Definition 1.4.7 Definition 1.4.13 5.4 Conical Tolerance Zone Position Tolerance 5.2.2 Actual Value 5.4.l(c), 5.4.2(c) ActualMatingSize.Definition 1.4.19 Conformance 5.4.1 (b), 5.4.2(b) ActualMatingSurface.Definition 1.4.1 Definition 5.4.l(a), 5.4.2(a) ActualMinimumMaterialEnvelope Consolidation of Parallelism Perpendicularity Position Tolerance 5.2.2 and Angularity Appendix A Definition 1.4.14 Coordinate Systems 4.1 ActualMinimumMaterialSize.Definition 1.4.20 CuttingPlane 6.4.1,6.4.2,6.6.3,A.4 Actual Value see individual tolerance types Definition 1.4.8 Definition 1.4.2 Cutting Vector Definition 1.4.9 Angularity 6.6,Appendix A Cylinder Datums 4.3.3(a), 4.3.4(a), 4.3.5(a) Cylindrical Tolerance Zone .A.3.1 A.3.4 Cylindrical Orientation Tolerance Zone 6.6.2, A.3 Linear Tolerance Zone A.4.1 A.4.4 Cylindricity .6.2 6.4.4 Planar Tolerance Zone A.2.1,A.2.4,A.2.7,A.2.10 6.8 Assembly B Bilateral Profile Tolerance 6.5 Datum Features Cylinders 4.3.3(a) 4.3.4(a), 4.3.5(a) Planes 3.2 Spheres 4.3.3(c) 4.3.4(c), 3 ~ ) Widths .4.3.3(b) 4.3.4(b), 4.3.5(b) Datum Precedence 4.3 4.4.2 Datum Reference Frames 4.1, 4.4 Composite Tolerance 4.5 Degrees of Freedom 4.1 Free Transformations 4.7 Invariants 4.1 Tabulation of Datum Systems 4.7 Datum Referencing Definitions Actual Mating Envelope 1.4.13 Actual Mating Size 1.4.19 Actual Mating Surface 1.4.1 Actual Minimum Material Size .1.4.20 Actual Minimum Material Envelope 1.4.14 Actual Value 1.4.2 C e, 1.5 1.5 Candidate Datum.Definition 1.4.3 Candidate Datum Reference Frame Set 4.2 Definition 1.4.5 Candidate Datum Reference Frame Definition 1.4.4 Candidate Datum Set 4.2 Definition 1.4.6 Circular Surface Element Circularity .6.4.3 Definition 1.4.1 Roundness 6.4.3 Runout 7.1 Circular Runout 6.7.1 Circularity 6.2 6.4.3 Conical Feature 4.3(b) Cylindrical or Conical Feature .6 4.3(b) Composite Control 6.4.4 6.7 e p 79 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS 1.5 1.5 1.5 Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - D 8s Form Tolerance 6.4 Circularity 6.4.3 Cylindricity 6.4.4 Flatness .6.4.2 Straightness 4.1 Format Actual Value 1.6 Conformance 1.6 Definitions 1.6 Free State Variation 6.8 ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Definitions (Cont'd) Candidate Datum 1.4.3 Candidate Datum Reference Frame 1.4.4 Candidate Datum Reference Frame Set 1.4.5 Candidate Datum Set 1.4.6 Circular Surface Element 1.4.11 Conformance 1.4.7 Cutting Plane 1.4.8 Cutting Vector 1.4.9 Direction Vector 1.4.10 Mating Surface Normal 1.4.15 Perfect Form 1.4.16 Resolved Geometry 1.4.17 Set of Support 1.4.18 Spine 1.4.23 Surface Line Element 1.4.12 Tolerance Zone see individual tolerance types True Position 1.4.24 True Position Mating Size 1.4.21 True Position Minimum Material Size 1.4.22 Derived Median Line Straightness 6.4.1 Designations 6, b,, ba b3 fl, r ( + r(P, TAM, rA", rTp rTPMM, t to, 1.5 Dimension Origin 2.2 Direction Vector, Definition 1.4.10 r), e, ep, G Gaging I Imperfectly-Formed Features 4.2 L Lirpits of Size 2.3 also see SizeLimits Elongated Holes 5.6 Linear Orientation Tolerance Zone 6.6.3, A.4 f M MathematicalNotation (also see Designations) Algebraic Notation Cross Product Datum Reference Frames Dot Product Functions Real Numbers Scalar Product Sets Symbology Unit Vectors 1.3.1, Vector Product Vectors Mating Surface Normal 1.4.15.1.5,6.4.1,6.5, E EACH ELEMENT 6.6 EACH RADIAL ELEMENT 6.6 Elongated Holes Feature of Size 5.6 Limits of Size 5.6(b) Position Tolerancing 5.6 Envelope ActualMating 1.4.13,5.2.2 Actual Minimum Material 1.4.14, 5.2.2 Envelope Principle 2.3.2 Establishing Datums 4.3 N 19 F Feature Boundary 2.1 Establishing Feature Boundaries 1.2 Surface Points 2.1.1 Feature Control Frame 4.2 Flatness., 6.2, 6.4.4 Form Actual Feature Surface 6.3(b) Length of the Surface 6.3(a) Limited Area 6.3(a) 1.3.2 1.3.2 1.3.1 1.3.2 1.3.1 1.3.1 1.3.2 1.3.1 1.3.1 1.3.2 1.3.2 1.3.1 6.7.1 1.5 Orientation Cylindrical Tolerance Zone 6.6.2,A.3 Linear Tolerance Zone 6.6.3,A.4 Planar Tolerance Zone 6.6.1, A.2 Secondary Datums .AppendixA.A.1 Orientation Tolerance 6.6 80 Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS 1.1.4 Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT P + 1.5 P Parallelism 6.6 Appendix A Cylindrical Tolerance Zone A.3.2,A.3.5 Linear Tolerance Zone A.4.2,A.4.5 Planar Tolerance Zone A.2.2, A.2.5, A.2.8, A.2.11 Patterns of Features 4.6 5.1.2 Perfect Form 1.4.1, 1.4.13, 1.4.17, 2.3.2,5.1.1, 5.3(a), 5.4.l(a), 5.6(a), 6.7 1.4.16 Definition Perpendicularity .6.6, Appendix A Cylindrical Tolerance Zone A.3.3,A.3.6 Linear Tolerance Zone A.4.3,A.4.6 Planar Tolerance Zone A.2.3, A.2.6, A.2.9, A.2.12 Planar Datum Features .4 3.2 Primary Datum .4.3.2(a) Rocking 3.2 Secondary Datum 3.2(b) Tertiary Datum .4.3.2(c) Planar Orientation Tolerance Zone 6.6.1, A.2 Positional Tolerancing Bidirectional 5.5 Conical Zone 5.4 Conventional 5.2 Elongated Holes 5.6 Projected 5.3 Surface Interpretation 5.2.1 Tolerance Zone 5.2.1 Profile Profile Tolerance 6.5 Projected Tolerance Zone 5.3 R r(P+) r ( P r ) -9 rAMM 1.5 1.5 1.5 1.5 1.5 1.5 rAM rTp r,,,, Resolved Geometry Axis 5.4, 5.5 Bidirection Position Tolerance 5.5.2 Conical Position Tolerance 5.4.2 Definition 1.4.17 Interpretation 5.1.1 Polar Tolerancing 5.5.3 Position Tolerance 5.2.2 Roundness 6.4.3, also see Circularity Runout Runout Tolerance 6.7 Circular .6 7.1 Total 7.2 S Scope and Definitions Figures 1.1.2 Scope and Definitions Notes 1.1.3 Scope and Definitions Units 1.1.1 Set of Support Definition 1.4.18 Simultaneous 2.1.2, 4.6, 5.1, 6.4.3, 6.4.4, 6.6.3(b) Size 2.3 and Envelope Principle 2.3.2 Size Limits (also see Limits of Size) Conformance 2.3.l(b) 2.3.2(b) Need to Conform 5.2.l(b), 5.2.2(b), 5.4.l(b), 5.4.2(b), 5.5.l(b) Sphere Datums .4.3.3(c).4.3.4(c), 4.3.5(~) Spherical Feature 1.4.1.1.4.17,1.4.19, 1.4.20,2.3,2.3.1,5.2,5.7,6.4.3 Spine Definition 1.4.23 Straightness .6.2 6.4.1 Derived Median Line 4.1 Surface Line Elements 6.4.1 Surface Interpretation 5.1.1 Position Tolerance 5.2.1 Projected Tolerance 5.3 Surface Line Elements Definition 1.4.12 4.1 Straightness 1.2 Surface Texture Surround 2.3.l(b) 5.2.l(b), 5.4.l(b) Symmetry 5.7 Patterns 5.7 Symmetry Axis 5.7 Symmetry Plane 5.7 5.7 SymmetryPoint t T to P 1.5 Tangent Plane 6.6 Thin Walls 6.8 Tolerance of Location Material Condition Basis 5.1.1 Tolerance Zone Bidirectional Positional 5.5 Circularity .6.4.3 conical 5.4 Cylindrical Orientation 6.2 Cylindricity 6.4.4 Definition see individual tolerance types Flatness 6.4.2 Fully Restrained A.l Linear Orientation 6.3 Orientation .6.6 A.l ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS 1.5 1.5 Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT v Tolerance Zone (Cont’d) Planar Orientation 6.1 Position 5.2.1, 5.2.2 Profile 6.5 Projected 5.3 Roundness 6.4.3 Straightness 4.1 Total Runout 7.2 True Position 5.2 Definition 1.4.24 TruePositionMating Size, Definition 1.4.21 TruePositionMinimumMaterial Size Definition 1.4.22 Unilateral Profile Tolerance ``,,``,`,,`,`,`,,,,`,```,`-`-`,,`,,`,`,,` - Copyright ASME International Provided by IHS under license with ASME No reproduction or networking permitted without license from IHS U Variation of Size 2.3.1 Verifying Boundary 5.3 Verifying Volume 5.3 Virtual Condition 5.2.1 W Width Datums 4.3.3(b) 4.3.4(b), 4.3.5(b) Features .1.4.17 1.4.19,1.4.20, 4.3, 5.2, 5.3, 5.7 of Bidirectional Tolerance Zone 5.5.1 of Elongated Holes 5.6 6.5 82 Licensee=University of Texas Revised Sub Account/5620001114 Not for Resale, 08/20/2013 21:07:10 MDT