Dimensioning and Tolerancing Handbook The need to make more precise products, the requirements of mass production, and the desire for interchangeability have resulted in increased importance of clearly defining dimensions and tolerances. Major products such as aircraft and automobiles are assembled from parts produced by many companies. Only through clear definition of dimensional requirements is it possible for multiple companies to efficiently produce parts that will easily assemble and meet their functional requirements. The United States national standard on dimensioning and tolerancing has been revised periodically to include methods for defining dimensional requirements for increasingly complex applications. Recent standards include: USASI Y14.5-1966, ANSI Y14.5-1973, ANSI Y14.5M-1982, and ASME Y14.5M1994. This book is based on ASME Y14.5M-1994, but also includes some description of past practices for use by anyone who is required to maintain drawings created in compliance with a previous standard. Past practices are clearly identified when shown within the Handbook. Every attempt has been made to accurately describe the requirements of the current standard. The material in this book is intended to make the standardized practices easier to understand. Use of this publication will help ensure compliance with the related standard. However, should there be any conflict between this book and a standard, the standard would take precedence. This Dimensioning and Tolerancing Handbook contains information about the symbology used for dimensions and tolerances, general dimensioning, general tolerancing, form tolerances, datums, location tolerances, orientation tolerances, runout tolerances, and profile tolerances. Calculation methods and interpretation examples are included. A detailed table of contents makes location of any topic easy. A separate list of figures follows the table of contents to assist in locating a graphic example of any needed topic. There are over 250 figures to illustrate the concepts explained within the text. An index at the back of the book is provided to simplify location of specific information. About the Author Bruce A. Wilson, author and illustrator of the Dimensioning and Tolerancing Handbook, has established exceptional credentials in the field of dimensioning and tolerancing. He has lead implementation of Geometric Dimensioning and Tolerancing (GD&T) throughout the companies of a major corporation and served as the technical leader for GD&T implementation on aircraft development efforts that included multiple aircraft manufacturing corporations. Mr. Wilson’s industrial experience started with a position as a design drafter in an automated machine tool manufacturing company. He has subsequently held positions as design engineer, design manager, program manager, technology leader for dimensional management, and industrial consultant in the field of dimensional management. His dimensional management capabilities and technical leadership have had a strong influence on a range of products from the wheels for children’s tricycles to laser target designators used by military pilots. Tomahawk missiles, used at critical times like the Persian Gulf War, demonstrate the accuracy of Mr. Wilson’s designs, which all use GD&T to accurately define design requirements and the allowable variations. His other product applications have ranged from miniature gear drives to structural designs for large aircraft. A leader of multiple GD&T training programs for industry, Mr. Wilson has authored several other publications on this subject. Through his publications, training programs, and development of GD&T instructors, thousands of engineering, manufacturing, and inspection personnel have been trained. Currently a member of the American Society of Mechanical Engineers subcommittee on Dimensioning and Tolerancing (ASME Y14.5), Mr. Wilson is also a member of ASME Y14.1, ViceChairman of ASME Y14.2, Chairman of ASME Y14.3, and a member of the United States TAG/ISO/TC10/SC5 on Dimensioning and Tolerancing and the TAG/ISO/TC10/SC10 on Engineering Symbology.
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TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I. GENERAL ............................................................................ 3 II. COMPLETION LEVEL OF FIGURES....................................... 4 III. BASIS FOR GUIDELINES ...................................................... 4 IV. GAGING EXAMPLES ............................................................ 5 V. UNITS OF MEASURE............................................................ 6 CHAPTER 2 SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 I. GENERAL ............................................................................. 9 II. GENERAL SYMBOLS............................................................10 Diameter............................................................................10 Counterbore Symbol............................................................11 Countersink .......................................................................11 Depth................................................................................12 Dimension Origin ...............................................................12 Square...............................................................................13 Reference ...........................................................................13 Arc Length.........................................................................14 Slope................................................................................14 Conical Taper .....................................................................15 LETTERS ............................................................................15 Letter X.............................................................................15 Radius...............................................................................15 Controlled Radius................................................................16 Spherical Radius .................................................................16 Spherical Diameter ..............................................................16 III. TOLERANCING SYMBOLS...................................................17 DATUM IDENTIFICATION SYMBOLS ...................................17 1994 Datum Feature Symbol.................................................17 1982 Datum Feature Symbol.................................................17 Datum Target Symbol..........................................................18 Target Point Symbol ...........................................................19 FORM.................................................................................20 Straightness .......................................................................20 Flatness.............................................................................20 Circularity .........................................................................21 Cylindricity........................................................................21 ORIENTATION.....................................................................22 Genium Publishing
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Dimensioning and Tolerancing Handbook Parallelism.........................................................................22 Perpendicularity ..................................................................22 Angularity .........................................................................23 LOCATION ..........................................................................23 Position ............................................................................23 Concentricity......................................................................24 Symmetry..........................................................................24 PROFILE .............................................................................25 Line Profile........................................................................25 Surface Profile....................................................................26 RUNOUT.............................................................................26 Circular Runout ..................................................................26 Total Runout......................................................................27 MODIFIERS.........................................................................28 Maximum Material Condition ...............................................28 Least Material Condition ......................................................28 Regardless of Feature Size.....................................................29 Projected Tolerance..............................................................30 Statistical Value..................................................................30 Tangent Plane.....................................................................30 Free State ..........................................................................31 BETWEEN ...........................................................................31 IV. FEATURE CONTROL FRAMES ............................................32 Feature Control Frame Lines .................................................33
CHAPTER 3 GENERAL DIMENSION APPLICATION. . . . . . . . . . . . . . . . . . . . . . . . 3 7 I. GENERAL ...........................................................................37 DIMENSION VALUES ..........................................................37 Rounding Numbers..............................................................37 Fractions ...........................................................................38 LINE TYPES AND ARROWS.................................................38 Extension Lines ..................................................................38 Dimension Line ..................................................................39 Leader Lines.......................................................................39 Arrow and Number Placement................................................39 Arrow and Number Arrangements...........................................39 Line Uses for Clarity ...........................................................40 APPLICABLE LINEAR UNITS...............................................40 Linear Unit Notation............................................................40 Linear Unit Application........................................................40 Linear Unit Exceptions.........................................................41 Foot Dimensions ................................................................41 ANGULAR UNITS ................................................................41 Arc Minutes and Seconds......................................................41 II. FUNDAMENTAL RULES ......................................................41 SIZE AND LOCATION..........................................................41 Genium Publishing
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DIMENSION TOLERANCES..................................................41 Dimension Tolerance Exceptions............................................41 Tolerance Accumulation .......................................................42 FUNCTIONALITY ................................................................42 PROCESS SPECIFICATION..................................................42 READABILITY.....................................................................42 Application to the Profile .....................................................42 Placement Between Views.....................................................43 Dimension Vsible Features ...................................................43 Placement..........................................................................43 90° ANGLES ........................................................................43 90° Angle Tolerances ...........................................................43 Basic 90° Angles.................................................................43 TEMPERATURE ..................................................................43 DOUBLE DIMENSIONING.....................................................43 REFERENCE DIMENSION....................................................44 STOCK SIZE........................................................................44 III. APPLICATION GUIDELINES.................................................44 SPACING ............................................................................44 Object to First Dimension ....................................................44 Between Dimension Lines.....................................................44 Extension Line Spaces .........................................................45 DIRECTION OF APPLICATION .............................................45 ANGLE DIMENSIONS ..........................................................46 DIMENSIONS APPLIED TO SMALL FEATURES....................46 Oblique Extension Lines.......................................................46 Offset Extension Lines.........................................................47 Extension Line Intersections..................................................47 DIMENSION VALUE LOCATION...........................................48 READING DIRECTION .........................................................49 OUTSIDE THE VIEW ............................................................49 NOT TO SCALE ...................................................................50 Scaling Drawings................................................................50 EXTENDED INTERSECTIONS...............................................50 LIMITED APPLICATION.......................................................51 IV. APPLICATION TO FEATURES..............................................51 DIAMETER..........................................................................51 RADII..................................................................................52 Located by Tangents ............................................................53 Located by arc centers...........................................................54 Foreshortened Radii .............................................................54 Spherical Radii ...................................................................54 True Radius........................................................................55 Radius Note .......................................................................55 CHORDS AND ARC LENGTHS .............................................55 ROUNDED ENDS.................................................................56 Genium Publishing
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Fully Rounded Ends.............................................................57 Partially Rounded Ends.........................................................57 IRREGULAR OUTLINE.........................................................57 SYMMETRICAL FEATURES ................................................57 HOLES................................................................................58 Hole Diameter and Depth......................................................59 Countersinks......................................................................60 Counterdrills ......................................................................60 Counterbores ......................................................................61 Spotfaces...........................................................................62 Slotted holes ......................................................................62 CHAMFERS ........................................................................63 Chamfered holes and shafts....................................................64 MACHINE CENTERS ...........................................................64 KEYSEATS..........................................................................64 KNURLS .............................................................................65 THREADS ...........................................................................66 SURFACE TEXTURE ...........................................................66 GEARS AND SPLINES .........................................................67 ROD AND TUBING DETAILS................................................67 V. LOCATION DIMENSIONS ......................................................68 RECTANGULAR COORDINATES..........................................68 Rectangular Coordinate Dimensions........................................69 Excluding Dimension Lines ..................................................69 Tabular Dimensions.............................................................70 POLAR COORDINATES .......................................................71 REPEATED DIMENSIONS ....................................................72 NUMBER OF TIMES ............................................................73 X TO INDICATE BY .............................................................73 CHAPTER 4 GENERAL TOLERANCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 I. GENERAL ...........................................................................77 II. TOLERANCE APPLICATION METHODS ...............................77 NOTED TOLERANCES.........................................................77 DIRECT APPLICATION TO DIMENSIONS .............................78 Plus and Minus Tolerances....................................................78 Bilateral.............................................................................78 Unilateral...........................................................................79 Limit Dimensions...............................................................79 Single Limits .....................................................................79 LIMITS AND FITS................................................................80 Metric Limits and Fits .........................................................80 Inch Limits and Fits ............................................................81 DIRECT APPLICATION TO A FEATURE ...............................81 REFERENCED DOCUMENTS ...............................................81 PLATED PARTS ..................................................................81 Genium Publishing
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III. NUMERICAL FORMAT........................................................81 METRIC VALUES ................................................................82 Bilateral Tolerance...............................................................82 Unilateral Tolerance.............................................................82 Limit Dimensions...............................................................82 INCH VALUES.....................................................................83 ANGLE VALUES..................................................................83 Angles on Metric Drawings...................................................83 Angles on Inch Drawings......................................................83 Angle Units .......................................................................84 IV. TOLERANCE ACCUMULATION ...........................................84 DIRECT APPLICATION ........................................................84 BASE LINE DIMENSIONING.................................................85 CHAIN DIMENSIONING .......................................................86 REFERENCE DIMENSION....................................................86 Using Reference Dimensions .................................................87 V. SPECIFIED ORIGIN..............................................................88 DIMENSIONING FROM AN ORIGIN......................................88 Measurement From an Origin ................................................88 VI. MATERIAL CONDITIONS.....................................................89 PERFECT FORM AT MMC...................................................89 Perfect Form Example..........................................................89 Variations of Form Within the MMC Envelope ........................90 Specified Exceptions............................................................90 Relationships Between Features Not Controlled by MMC...........90 FREE STATE VARIATION....................................................91 MATERIAL CONDITION EFFECTS .......................................91 MMC Effect.......................................................................92 Zero Tolerance at MMC .......................................................92 LMC Effect........................................................................93 RFS Effect.........................................................................94 Assumed and Specified Material Conditions..............................94 United States (1994) ............................................................95 International.......................................................................95 VII. VIRTUAL CONDITION .........................................................96 VIRTUAL CONDITION OF A HOLE.......................................96 VIII. GEARS AND SPLINES .........................................................96 IX. THREADS ...........................................................................96 X. ANGULAR SURFACES ........................................................98 ANGULAR TOLERANCE......................................................98 BASIC ANGLES...................................................................99 XI. TAPERS..............................................................................99 CONICAL TAPERS ............................................................ 100 Conical Taper Calculation................................................... 100 Basic Taper, Basic Diameter, Toleranced Location.................... 100 Toleranced Taper, Toleranced Diameter .................................. 100 Genium Publishing
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Two Diameters and Length.................................................. 101 FLAT TAPERS................................................................... 102 Slope Calculation.............................................................. 103 XII. RADII................................................................................ 103 Controlled Radius.............................................................. 104 Radius............................................................................. 104 Previous Practice............................................................... 104 CHAPTER 5 DATUMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 7 I. GENERAL ......................................................................... 107 TERMINOLOGY................................................................. 107 Datum............................................................................. 107 Datum Feature .................................................................. 107 Datum Simulator .............................................................. 107 Datum Reference............................................................... 109 Datum Feature Symbol ...................................................... 109 Datum Reference Frame...................................................... 109 DATUM IDENTIFICATION LETTERS .................................. 109 TEMPORARY AND PERMANENT DATUM FEATURES........ 110 II. DATUM REFERENCE FRAME............................................ 110 III. ORDER OF PRECEDENCE ................................................. 112 SURFACES TO ESTABLISH DATUMS ................................ 113 Primary Surface ................................................................ 113 Tertiary Surface................................................................. 117 FEATURES OF SIZE TO ESTABLISH DATUMS ................... 117 Primary Axis.................................................................... 117 Primary Plane, Secondary Axis ............................................ 118 Primary Axis, Secondary Plane ............................................ 120 Primary Plane, Secondary Axis, Tertiary Plane ....................... 121 Primary Plane, Secondary Axis, Tertiary Axis ........................ 122 MULTIPLE DATUM REFERENCE FRAMES ........................ 123 IV. IDENTIFICATION OF DATUM FEATURES .......................... 123 IDENTIFICATION OF DATUM SURFACES.......................... 123 On Extension Lines ........................................................... 124 Application Using ASME Y14.5M-1994 Symbols.................. 124 Application Using ANSI Y14.5M-1982 Symbols ................... 125 Application on a Surface..................................................... 125 IDENTIFICATION OF DATUM FEATURES OF SIZE............. 125 Section View of a Hole ...................................................... 125 Applied to a Shaft ............................................................. 126 Applied to a Slot or Tab ..................................................... 127 Applied to One Hole in a Pattern.......................................... 128 Applied to a Feature Control Frame...................................... 128 V. DATUM REFERENCES AND DATUM SIMULATION ............ 129 SPECIFIED ORDER OF PRECEDENCE................................ 130 SIMULATION OF SURFACES............................................. 131 Genium Publishing
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Surface as a Primary Datum ................................................ 131 Surface as a Secondary Datum.............................................. 132 Surface as a Tertiary Datum................................................. 134 SIMULATION OF FEATURES OF SIZE................................ 136 Hole as Primary Datum (MMC)........................................... 136 Hole as Secondary Datum (MMC) ........................................ 138 Hole as Primary Datum (RFS)............................................. 139 Hole as Secondary Datum (RFS).......................................... 140 TERTIARY DATUMS FOR CLOCKING................................ 141 VI. DATUM TARGETS............................................................. 143 Target Types .................................................................... 143 Identification .................................................................... 143 Near Side, Far Side............................................................ 143 POINTS............................................................................. 143 Number Needed ................................................................. 144 Simulation....................................................................... 144 LINES ............................................................................... 144 Simulation....................................................................... 145 AREAS.............................................................................. 145 Simulation....................................................................... 146 TARGET LOCATIONS........................................................ 146 TARGET TYPE COMBINATIONS ........................................ 147 VII. COMPLEX DATUMS.......................................................... 148 COMPOUND DATUMS....................................................... 149 Two on Axis.................................................................... 149 Modifiers......................................................................... 149 Two Surfaces.................................................................... 150 PATTERNS OF FEATURES AS DATUMS ............................ 151 Datum Identification and Reference ....................................... 151 PARTIAL SURFACE (Limited Zone) ..................................... 151 STEPPED DATUMS ........................................................... 151 Datum Plane Identification.................................................. 152 THREADS AS DATUM FEATURES..................................... 152 SPLINES AND GEARS AS DATUM FEATURES ................... 152 INCLINED DATUM FEATURES .......................................... 152 Simulating Inclined Datum Features ..................................... 153 EQUALIZING DATUMS...................................................... 153 Equalizing Target Location.................................................. 154 REPEATING DATUMS ....................................................... 154 Individually Notation ......................................................... 154 CHAPTER 6 FORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 7 I. GENERAL ......................................................................... 157 II. FORM ............................................................................... 157 Size Limits...................................................................... 157 Genium Publishing
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Dimensioning and Tolerancing Handbook Maximum Material Condition ............................................. 157 Maximum Material Condition of a Shaft ............................... 157 Maximum Material Condition of a Hole................................ 158 Perfect Form Boundary at MMC .......................................... 158 Least Material Condition .................................................... 159 Least Material Condition of a Shaft ...................................... 159 Least Material Condition of a Hole ....................................... 159 No Perfect Form Boundary at LMC ...................................... 159 Form Controlled by Size .................................................... 159 Exceptions to Rule #1........................................................ 159 STRAIGHTNESS ................................................................ 160 Straightness Applied to Control Surface Errors ....................... 161 Straightness Applied to Control an Axis or Center Plane .......... 161 Straightness of a Flat Surface .............................................. 161 Straightness of Line Elements on a Cylinder .......................... 162 Straightness of Line Elements on a Shaft............................... 162 Straightness of Line Elements on a Hole ............................... 163 Axis Straightness.............................................................. 165 Axis Straightness of A Shaft ............................................... 165 Axis Straightness of A Hole................................................ 166 Applied RFS .................................................................... 166 Applied MMC .................................................................. 167 Straightness of A Center Plane ............................................ 169 Straightness Per Unit Length............................................... 169 FLATNESS........................................................................ 170 Flatness Control By Size Tolerance ...................................... 170 Flatness Specification ........................................................ 170 Flatness Interpretation........................................................ 171 Flatness Per Unit Area ....................................................... 171 CIRCULARITY .................................................................. 172 Circularity Control by Size Dimensions................................ 172 Specification of Circularity ................................................. 172 Circularity Interpretation..................................................... 173 CYLINDRICITY ................................................................. 174 Cylindricity Control By Size Dimensions.............................. 174 Specification Of Cylindricity............................................... 174 Cylindricity Interpretation ................................................... 174 EXCEPTION TO PERFECT FORM BOUNDARY ................... 176 Stock Shapes.................................................................... 176 Free State Variation ........................................................... 176 Noted Exception................................................................ 176
CHAPTER 7 ORIENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 9 ANGULARITY ................................................................... 179 Angularity Applied to A Surface .......................................... 179 Angularity Interpretation..................................................... 180 Genium Publishing
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PERPENDICULARITY........................................................ 180 Perpendicularity of A Surface............................................... 180 Perpendicularity of A Surface Interpretation............................ 181 Perpendicularity of A Feature of Size .................................... 181 Perpendicularity on A Pin ................................................... 182 Interpretation of Perpendicularity on A Pin............................. 184 Virtual Condition of A Pin ................................................. 184 Bonus Tolerance on Perpendicularity..................................... 184 Perpendicularity on A Hole ................................................. 184 Interpretation of Perpendicularity on A Hole ........................... 185 Virtual Condition of A Hole................................................ 185 Bonus Tolerance on Perpendicularity..................................... 186 Perpendicularity At Regardless of Feature Size ........................ 186 Perpendicularity on A Rectangular Feature of Size................... 188 PARALLELISM.................................................................. 189 Parallelism of Surfaces....................................................... 189 Parallelism of a Surface Interpretation ................................... 190 Parallelism of Holes .......................................................... 190 Parallelism Effect at MMC ................................................. 191 MMC Departure Effect on Parallelism................................... 191 Parallelism Applied to Multiple Features............................... 191 Referenced Datums Effect on Orientation Tolerances ................ 191 One Datum Reference......................................................... 191 Two Datum References....................................................... 193 DIMENSIONS RELATED TO A DATUM REFERENCE FRAME............................................................................. 195 Noted Datum Reference Frame............................................. 195 Measurements from a Noted Datum Reference Frame ............... 195 CHAPTER 8 POSITION, CONCENTRICITY, AND SYMMETRY. . . . . . . . . . 1 9 9 I. GENERAL ......................................................................... 199 LOCATION TOLERANCES ................................................. 199 II. POSITION TOLERANCES ................................................... 200 Feature Control Frame ....................................................... 201 Position Tolerance Symbol................................................. 201 Tolerance Value ................................................................ 201 Material Condition Modifier (1994) ...................................... 201 Material Condition Modifier (1982) ...................................... 201 Datum References.............................................................. 202 Basic Location Dimensions................................................. 202 Locations From Referenced Datums...................................... 202 True Positions .................................................................. 202 Hole Locations ................................................................. 204 Comparison of Coordinate and Position Tolerances.................. 204 Coordinate (plus or minus) Tolerances................................... 204 Genium Publishing
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Dimensioning and Tolerancing Handbook Position Tolerances ........................................................... 206 Round vs. Square Tolerance Zones........................................ 208 Calculated Tolerance Zone Comparison ................................. 208 Square Tolerance Zones ...................................................... 208 Round Tolerance Zone........................................................ 209 CALCULATION OF POSITION TOLERANCES FOR HOLES.............................................................................. 210 Floating Fastener .............................................................. 210 Calculations for a Floating Fastener Application..................... 211 One Clearance Hole Diameter .............................................. 211 Two Clearance Hole Diameters ............................................ 212 Unequal Distribution for Floating Fastener Applications........... 213 Fixed Fastener .................................................................. 213 Press Fit and Threaded Holes ............................................... 213 Fixed Fastener Assembly.................................................... 214 Single Fixed Condition ...................................................... 214 Permitted Location Tolerance............................................... 214 Calculations for a Fixed Fastener Application......................... 214 Clearance Hole Diameter Effect............................................ 215 Position Tolerance for a Dowel Pin ...................................... 215 Position Tolerance for a Screw............................................. 217 Unequal Distribution for Fixed Fastener Applications............... 217 Plus or Minus (±) Location Tolerances for Holes .................... 217 MATERIAL CONDITION MODIFIERS ON POSITION TOLERANCES................................................................... 218 Material Condition Modifier Application, 1994....................... 218 Material Condition Modifier Application, ISO ........................ 218 Material Condition Modifier Application, 1982....................... 218 Material Condition Modifier Application, 1973....................... 218 Material Condition Basis of Positioned Feature....................... 219 Maximum Material Condition (MMC) .................................. 219 Departure from MMC ........................................................ 220 MMC Applications ........................................................... 221 Allowable Error at MMC.................................................... 221 Allowable Error Due to Departure from MMC ........................ 222 Regardless of Feature Size (RFS) ......................................... 222 RFS Applications ............................................................. 223 Least Material Condition (LMC).......................................... 224 Departure from LMC ......................................................... 225 LMC Applications ............................................................ 225 Material Condition Basis of Datum Features........................... 227 Material Condition Modifier Application on Datum References, 1994 .......................................................... 227 Material Condition Modifier Application on Datum References, ISO ........................................................... 227 Material Condition Modifier Application on Datum References, 1982 .......................................................... 227 Genium Publishing
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Material Condition Modifier Application on Datum References, 1973 .......................................................... 227 Datum Reference at MMC .................................................. 227 Datum Reference at RFS .................................................... 228 Datum Reference at LMC ................................................... 229 ZERO POSITION TOLERANCE AT MMC............................. 229 Limited Position Tolerance Advantage................................... 229 Zero Position Tolerance at MMC Specification....................... 230 Calculating a Zero Position Tolerance at MMC ...................... 232 PROJECTED TOLERANCE ZONE........................................ 232 Projection Distance............................................................ 232 Application of the Projected Tolerance Zone Symbol ............... 232 Projected Tolerance Zone .................................................... 234 Interference Conditions When Projected Zones are Not Used ...... 234 Clearance Conditions When Projected Zones are Used............... 234 APPLICABLE FEATURES................................................... 235 Threads............................................................................ 236 Gears and Splines .............................................................. 236 SIMULTANEOUS REQUIREMENTS .................................... 236 Simultaneous Requirements Referenced to Datum Surfaces........ 236 Simultaneous Requirements Referenced to Datum Features of Size ....................................................................... 237 Applicability of Simultaneous Requirements.......................... 237 Noted Separate Requirements............................................... 239 SINGLE SEGMENT FEATURE CONTROL FRAMES............. 240 COMPOSITE POSITION TOLERANCES............................... 240 Datum references ............................................................... 241 Levels of Control .............................................................. 241 Composite Position Tolerances on Flat Hole Patterns.............. 241 Pattern-Locating Tolerances................................................. 242 Pattern-Locating Tolerance Zone Framework .......................... 242 Feature-Relating Tolerance .................................................. 243 Feature-Relating Tolerance Zone Framework .......................... 243 Two Datum References on the Feature-Relating Tolerance......... 244 Composite Position Tolerances on Radial Hole Patterns ........... 246 Pattern-Locating Tolerance .................................................. 247 Feature-Relating Tolerance .................................................. 247 Hole Locations ................................................................. 248 Simultaneous Vs Separate Requirements on Composite Position Tolerances ....................................................... 248 Simultaneous and Separate Requirement for Composite Position Tolerances ....................................................... 249 Simultaneous Pattern and Simultaneous Feature-Relating Tolerance Requirements.................................................. 251 MULTIPLE SINGLE SEGMENT FEATURE CONTROL FRAMES........................................................................... 252 Genium Publishing
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Levels of Control .............................................................. 253 Two Single Segment Position Tolerances on a Flat Hole Pattern ........................................................................ 253 Two Single-Segment Position Tolerances on a Radial Hole Pattern ........................................................................ 255 BILATERAL POSITION TOLERANCES ................................ 257 Rectangular Bilateral Position Tolerance................................ 257 Material Condition Modifiers on Bilateral Position Tolerances.................................................................... 258 Curved Bilateral Position Tolerance ...................................... 258 COUNTERBORED HOLES .................................................. 259 One Position Tolerance for Hole and Counterbore.................... 259 Separate Position Tolerances for the Hole and Counterbore........ 259 Counterbore Position Referenced to Hole Location .................. 259 TAPERED TOLERANCE ZONES ......................................... 261 POSITION OF NONCIRCULAR FEATURES ......................... 261 Rectangular Slots and Rails................................................. 261 Irregular Features (combined with profile) .............................. 263 Profile Tolerance Effect ...................................................... 264 Position Tolerance Effect .................................................... 265 COAXIAL FEATURES CONTROLLED WITH POSITION TOLERANCES................................................................... 266 Single Line Position Tolerance on In-Line Holes .................... 266 Two Line Composite Tolerance on In-Line Holes.................... 268 Three Line Composite Tolerance on In-Line Holes .................. 270 Multiple Hole Sizes on Coaxial Holes .................................. 272 III. SYMMETRY...................................................................... 272 Symmetrical Applications................................................... 272 SYMMETRY AT MMC (Position)......................................... 272 Creating a Plane of Symmetry ............................................. 274 Locating Symmetrical Features ............................................ 274 Position Tolerance for Symmetry......................................... 274 SYMMETRY AT RFS WITH POSITION................................ 274 SYMMETRY TOLERANCE SPECIFICATION ....................... 275 IV. CONCENTRICITY .............................................................. 275 Caution Regarding Usage of Concentricity ............................. 275 CONCENTRICITY APPLICATION ....................................... 276 Concentricity Interpretation................................................. 276 CHAPTER 9 PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 1 I. PROFILE ........................................................................... 281 BILATERAL AND UNILATERAL......................................... 281 Bilateral Profile Tolerance................................................... 281 Unilateral Tolerance Zone, Outside ....................................... 281 Unilateral Tolerance Zone, Inside.......................................... 282 Offset Tolerance Zone ........................................................ 283 Genium Publishing
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LINE PROFILE................................................................... 284 SURFACE PROFILE........................................................... 285 LEVELS OF CONTROL ...................................................... 286 No Datum References......................................................... 286 Datum References.............................................................. 287 Datum References and Basic Dimensions For Location............. 288 LIMITS OF APPLICATION.................................................. 290 Default Limits of Application.............................................. 290 Restricted Limits of Application .......................................... 290 Extended Limits Of Application........................................... 291 All Around....................................................................... 291 CONE PROFILE ................................................................. 293 COPLANARITY ................................................................. 293 Coplanarity and Orientation................................................. 294 Coplanarity, Orientation, and Location .................................. 294 CHAPTER 1 0 RUNOUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 7 I. RUNOUT........................................................................... 297 CIRCULAR RUNOUT ......................................................... 297 Circular Runout Tolerance Application.................................. 297 Circular Runout Interpretation ............................................. 298 TOTAL RUNOUT ............................................................... 298 Total Runout Tolerance Application ..................................... 299 Total Runout Interpretation ................................................. 299 RUNOUT REFERENCED TO COMPOUND DATUMS ............ 300 RUNOUT REFERENCED TO TWO DATUMS........................ 301 CHAPTER 1 1 VERIFYING DIMENSIONAL REQUIREMENTS. . . . . . . . . . . . . . 3 0 5 I. GENERAL ......................................................................... 305 II. VERIFYING FORM TOLERANCES...................................... 306 STRAIGHTNESS OF A SURFACE ELEMENT....................... 306 Straightness Measured Using a Surface Plate .......................... 306 Straightness Measured with Hand Tools................................. 307 STRAIGHTNESS ON AN AXIS............................................ 308 Straightness of a Shaft Axis at MMC ................................... 308 Functional Gaging Shaft Axis Straightness at MMC ............... 308 Alternate Method for Verifying Shaft Axis Straightness at MMC...................................................................... 308 Alternate Method #2 for Verifying Shaft Axis Straightness at MMC...................................................................... 308 Straightness of a Shaft Axis at RFS ..................................... 309 Axis Error Determined from Surface Errors............................. 310 Round, Constant Diameter, Curved Axis ............................... 310 Irregular Surface, Irregular Axis............................................ 310 Genium Publishing
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Dimensioning and Tolerancing Handbook
Straightness of a Hole Axis at MMC .................................... 310 Functional Gaging Hole Axis Straightness at MMC................ 311 Alternate Methods for Verifying Hole Axis Straightness at MMC ......................................................................... 312 Straightness of a Hole Axis at RFS ...................................... 312 FLATNESS........................................................................ 312 Verifying Flatness with a Dial Indicator and Height Stand ......... 312 Adjustment of Part Orientation Permitted............................... 314 Alternate Flatness Check Method ......................................... 314 Quick Check Flatness Approximation................................... 315 CIRCULARITY .................................................................. 315 Dial Indicator Measurement of Circularity.............................. 316 CYLINDRICITY ................................................................. 317 III. VERIFYING ORIENTATION TOLERANCES ......................... 317 PERPENDICULARITY OF A SURFACE............................... 317 Two Datum References....................................................... 317 Simulation of the Datums................................................... 319 Measurement of the Perpendicularity Variations ...................... 319 One Datum Reference......................................................... 319 Simulation of the Datum.................................................... 319 Measurement of the Perpendicularity Variations ...................... 319 PERPENDICULARITY OF A FEATURE OF SIZE.................. 321 Perpendicularity of a Hole (MMC)........................................ 321 Datum Surface.................................................................. 321 Gage Pin Diameter ............................................................ 321 Datum Axis ..................................................................... 322 Datum Axis Simulation ..................................................... 322 Verifying Perpendicularity of the Hole................................... 323 Perpendicularity of a Hole (RFS).......................................... 324 Perpendicularity of a Pin (MMC) ......................................... 324 ANGULARITY OF A SURFACE .......................................... 325 Two Datum References....................................................... 326 Datum Simulation............................................................. 326 Angularity Error Measuring................................................. 327 One Datum Reference......................................................... 327 Datum Simulation and Angularity Measurement ..................... 328 PARALLELISM.................................................................. 328 Parallelism on a Surface ..................................................... 329 Measurement of Parallelism on a Flat Surface......................... 329 Parallelism of Holes at MMC.............................................. 329 Functional Gaging Parallel Holes......................................... 329 Parallelism of Pins at RFS ................................................. 330 IV. VERIFYING LOCATION TOLERANCES............................... 331 Evaluating Measured Locations ............................................ 332 Functional Gages .............................................................. 332 Coordinate Measuring Machines (CMM) ............................... 332 SINGLE LINE POSITION TOLERANCE ................................ 333 Genium Publishing
Table of Contents
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Position Tolerance On Holes (MMC) From Datum Surfaces ..... 333 Functional Gage................................................................ 333 Paper Gage....................................................................... 335 Location Measurements ...................................................... 335 Plotting X and Y Errors...................................................... 335 Checking Diameter Position Error ........................................ 335 Consideration of MMC ...................................................... 337 Calculated Position Errors................................................... 337 Position Tolerance RFS ..................................................... 337 Position Tolerance on Holes at MMC Relative to Datum Feature of Size at MMC ................................................. 338 Functional Gaging Separate Requirements.............................. 340 Functional Gage Requirements............................................. 340 Simultaneous Requirement.................................................. 341 COMPOSITE POSITION TOLERANCE (MMC)...................... 341 Composite Position from Datum Surfaces ............................. 342 First Line Functional Gage ................................................. 342 Second Line Functional Gage .............................................. 342 Paper Gage....................................................................... 343 Paper Gaging the PLTZF.................................................... 343 Paper Gaging the FRTZF ................................................... 343 Plotting Location Errors..................................................... 345 TWO SINGLE SEGMENT POSITION TOLERANCES ............. 346 Gaging the First Line......................................................... 346 Gaging the Second Line...................................................... 347 CONCENTRICITY .............................................................. 348 Establish the Datum Axis................................................... 348 Axis Error Determined from Surface Errors............................. 348 V. VERIFYING RUNOUT TOLERANCES.................................. 350 CIRCULAR RUNOUT ......................................................... 350 TOTAL RUNOUT ............................................................... 351 APPENDICES APPENDIX A Tolerancing Symbols..............................................................353 General Dimension Symbols....................................................356 APPENDIX B Feature Control Frames ...........................................................357 APPENDIX C Datum Feature Symbol Application...........................................361 APPENDIX D Formulas ..............................................................................365 INDEX Index....................................................................................369 ABOUT THE AUTHOR................................................................381 Genium Publishing
