Geometric Dimensioning and Tolerancing Applicati Appli cations, ons, Analy Analysis sis & Measu Measuremen rementt [per ASME Y14.5-2009]
©
James D. Meadows
James Jame s D. Meado ws & Associates. Inc.
ASME Pres s
© 2009 James D. Meadows ALL RIGHTS RESERVED including those of translation. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means--graphic, electronic, mechanical, including photocopying, recording, taping, Web distribution, or otherwise--without written permission of the publisher. Some illustrations in this book are copyrighted by and are the property of SolidWorks Corporation. Published and distributed by: James D. Meadows & Associates, Inc. 170 E. Main, D-137 Hendersonville, TN 37075 Phone: (615) 824-8644 FAX: (615) 824-5262 www.geotolmeadows.com Co-Published and co-distributed by: ASME Press Three Park Avenue New York, NY 10016-5990 1-800-THE-ASME (1-800-843-2763) www asme.org ISBN: 978-0-9714401-6-6
ASME Order No. 802166 Library of Congress Number: PRE000002062 Printed in the United States of America 1 2 3 4 5 6 7 8 9 10 Printing No liability is assumed by the publisher James D. Meadows & Associates, Inc., nor its author with respect to the use of the information contained herein. Information contained in this work has been obtained from sources believed to be reliable. While every precaution has been taken in the preparation of this book, neither James D. Meadows & Associates, Inc., nor its author guarantee the accuracy or completeness of any information published herein and neither James D. Meadows & Associates, Inc., nor its author shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that James D. Meadows & Associates, Inc., and its author are supplying information but are not attempting to render engineering or other professional services. The publisher and its author shall not be liable for any special, consequential, or exemplary damages resulting in whole or part, from the readers’ use of, or reliance upon, this material.
Foreword This textbook has been written for anyone whose work requires them to communicate, interpret or manufacture products through the use of engineering drawings and/or CAD models that use Geometric Dimensioning and Tolerancing. Readers will specifically learn the new ASME Y14.5-2009 standard on Dimensioning and Tolerancing. It teaches the new Y14.5 symbology, rules and basic principle revisions that took the Y14.5 committee 15 years to complete. The result of attaining this knowledge is that: product representations are able to be more specific in conveying tolerancing needs, products can be more easily manufactured, and appropriate inspection techniques are clarified. Product designers, manufacturing engineers, quality engineers, inspectors, product engineers and process engineers are just a few of the job categories that can benefit from the material. Even those who have been trained in GD&T will need to be trained in these vast and sweeping changes that have been instituted into this latest Y14.5 revision. This book covers all of the basics on how to interpret, apply and measure GD&T per ASME Y14.5-2009. Books, such as this one, are evolutions of explanations given hundreds of times by teachers and consultants trying to find the optimal way of giving our knowledge to others. The topics to be covered are refined, and our ways of conveying them to our students and readers get better over time. I’ve been teaching and consulting on this material for about 25 years now. This is my twelfth technical book on the subject of dimensioning and tolerancing. At first, I believed that knowing a thing and being able to explain a thing were synonymous. But after more than a few blank stares, and a ton of questions, one realizes that just isn’t true. So, you try to think like a student again and anticipate the questions they would have and then answer them before i t becomes necessary for them to be asked. I used to believe that the most difficult topics were the ones that the most time should be spent on. Then I learned that the topics that were most beneficial to allowing professionals to do their jobs more efficiently were those that were most worthy of study and explanation. Writers and teachers learn over time. I’ve learned short, simple books sell better than long, comprehensive books. But I’ve also learned that the reader of a short book is cheated with just a little bit of knowledge and lulled into a false sense of security about their ability to apply what they have learned. So, I write long books. I want the readers to have all of the information they might need in one book. I want to give them all of the basic information, but also to provide them with the more complex information for them to use when they realize that a little bit of knowledge is simply not enough to do a good job. This book combines basic and advanced information about the principles and applications of plus and minus tolerancing, geometric tolerancing, tolerance stack-up analysis, statistical tolerancing, inspection, gage and fixture design and how to read geometric controls as though the symbology was a group of sentences trying to describe how a part functions. It is the most comprehensive book I could have written within the shortest number of pages. Given the fact that I’ve trained tens-of-thousands of people and consulted on thousands of projects, I believe it anticipates the questions students most often worry over and wonder about and gives them clear answers to those questions. I would like to thank my trusted colleagues Michael Gay, Patty Hastie and Jeannie Winchell for their help in putting this book into its present form. Michael takes my crude drawings and turns them into fine illustrations. He puts up with countless changes, many so minor few would notice the difference. But each change makes the illustration a little better and the explanation clearer. I would like to thank Michael for his great work, but also for his great patience. Patty Hastie is a subject matter expert and a friend. When she proof reads a book, she saves me from a lot of embarrassment. Her critiques span a wide variety of ills from bad grammar to illustrations pasted into the wrong places. She also improves the
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text and the illustrations with her knowledgeable suggestions. She constantly proves to me that no one should ever count solely on themselves to proof their own work. This book has been greatly improved by her, and if there are still things that could be better, it’s probably because she told me to change something and I chose not to. Jeannie Winchell is the one who takes my hand-scribbled pages and turns them into a book. She coordinates the entire project and works closely with Michael and Patty to merge illustrations and text. I sincerely hope the information contained in this book helps you. James D. Meadows
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Table Chapter Number 1
of Contents
Chapter Title
Pages
Symbols, Rules, Charts -Geometric Characteristics -Symbols -New Symbols -Old Symbols, New Meanings -Charts-Food Chains of Symbology -A Few Basic Definitions, Formulas and Guidelines -New Rule Regarding the Use of Regardless of Feature Size -Maximum Material Boundary, Least Material Boundary and Regardless of Material Boundary -Actual Minimum Material Envelope vs. Actual Mating Envelope -Flatness of the Derived Median Plane -Types of Controls -Tolerances -General Rules for Tolerances Selecting a Tolerancing Approach -Datums and Datum Features -Defining, Tolerancing and Qualifying Datum Features -Fixed Fastener Assembly Tolerancing Formula -Simultaneous Requirement Rule -Reading a Feature Control Frame
10 11 12 13 13 15 20 21 23 24 25 28
3
Datum Feature Simulators -Datum Feature Simulators: Physical and Imaginary -Fixtures, Gages and Virtual Condition Boundaries
29 30 31
4
Boundaries and Material Condition Symbols, MMC, LMC & RFS -Dimensioning and Tolerancing Overview -Rule #1: Size Tolerance and Form Tolerance are Interdependent -Exceptions to Rule #1 -New Principle of Independency Symbol -GO Gages -Brief Comparison of Concentricity, Circular Runout, Total Runout and Position Tolerancing -Introduction of Orientation on Mating Parts -Material Condition Symbols and Concepts Explained -Regardless of Feature Size -Least Material Condition -Maximum Material Condition -Inner and Outer Boundary Calculations
35 36 37 38 38 40
2
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1 2 3 5 5 6 8 10
42 42 45 45 48 49 50
Table of Contents
5
Major Concepts of Geometric Dimensioning and Tolerancing --Converting from Plus and Minus Tolerance to Geometric Tolerance -Position -Profile -Selecting Datum Features -Size Tolerance Controls Form Tolerance (Rule #1), GO Gages -Flatness -Perpendicularity -Mating Part Tolerancing -Reading the Feature Control Frames as a Language -Functional Gages -Calculating Inner and Outer Boundaries -Virtual Condition -Resultant Condition -Practical Absolute Gage Tolerancing -Bonus Tolerancing Formulas -Allowed vs. Actual Deviation from True Position Calculations -Conversion Chart Inches -Conversion Chart Millimeters -Tolerance Zone vs. Boundary Verification -Another Difference between Bonus Tolerance (Growth) and Datum Shift (Movement) of Tolerance Zones
58 58 63 64 64 66 67 68 71 74 74 75 75 75 76 78 82 84 85 88
89
6
Form -Flatness -Straightness -Cylindricity -Circularity (Roundness) -Spherical Diameters Controlled with Circularity -Average Dimensions
93 95 100 109 113 118 119
7
Orientation -Parallelism -Parallelism of a Tangent Plane -Perpendicularity -Angularity -Angularity of a Tangent Plane -Angularity as a Refinement of Position -Shifting vs. Growing Tolerance Zones
120 122 128 129 136 138 140 142
8
Profile -Profile of a Surface -New Symbol for Unequal or Unilateral Profile Tolerancing -Profile of a Line -The Power and Versatility of Profile (Mating Parts)
146 147 151 160 163
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Table of Contents
9
-Tolerancing Mating Part Profiles -Composite Profile -Composite vs. Two Single Segment Profile Controls -Profiling Patterns of Features Using 3 Levels of Profile Tolerances -Coplanarity -Continuous Feature of Size Symbol -Dimension Origin Symbol -Locating Offset Surface with Profile of a Surface -Conicity
163 168 173 176 177 177 180 184 187
Runout -Circular Runout -Total Runout -Comparison of Perpendicularity and Total Runout on a Planar Surface
191 192 195 203
10 Concentricity and Symmetry -Concentricity -Comparison of Coaxiality Controls -Symmetry
207 208 210 215
11 Datums -How They are Selected and What They Mean -Specifying Degrees of Freedom -Datum Feature Simulation -Designating Degrees of Freedom on the Part Drawing -Establishing a Valid Datum Plane -Effects of Differing Datum Precedence on Part Acceptance -Curved Surface as a Datum Feature -Conical Datum Features -Datum Feature Pattern Referenced Regardless of Material Boundary -Inclined Datum Feature -Constant Cross-Sections and Complex Datum Features -Specifying Degrees of Freedom in the Feature Control Frame -Multiple Datum Reference Frame Identification -Correct Material Boundary Size Specified Next to the Datum Feature -Correct Material Boundary Calculations -Using the Translation Modifier -Basic or BSC Spelled Out in a Feature Control Frame -Planar Datum Feature Simulated at Regardless of Material Boundary (RMB) -Planar Datum Feature Simulated at Maximum Material Boundary (MMB) -Offset Datum Features of Size Simulated at RMB and MMB -Profiled Datum Features Simulated at RMB and MMB -Irregular Datum Features of Size
217 219 223 224 227 232 237 238 239 240 241 242 243 245 246 247 248 250 252 253 255 256 263
12 Centerplane Datums -An Overview
264 265
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Table of Contents
-Centerplane Datu ms on Mating Parts in a Fixed Fastener Assembly
267
13 Position with Fixed Fastener Assemblies and Projected Tolerance Zones -Tolerancing Mating Parts in a Fixed Fastener Assembly -Projected Toleran ce Zones and How they are Measured -Datum Feature Shift/Pattern Shift -Alternate Method Using Chain Lines to Show Projected Tolerance Zones -Calculating Clearance Hole Sizes Needed Without Projected Tolerance Zones
279 280 286 289 292 293
14 Tolerancing Mating Parts in a Floating Fastener Assembly -Floating Fastener Assembly Condition (Radial Hole Patterns) -Assigning Datum Features t o Mating Parts with Radial Hole Patterns -Calculating Position Tolerance -Two Single Segment Position Tolerancing -Calculating Minimum Wall Thicknesses -Accumulative Datum Shift on Mating Parts in an Assembly -Tolerance Zones and Their Movement wi th Two Single Segment Position
294 295 296 298 300 301 303 304
15 Direct vs. Indirect Relationships -Overview -Tolerancing Mating Parts Holding Function Directly and Indirectly -Switching Datums in Mid-Stream -Unique Effects of Utilizing the LMC and LMB Concepts -Wall Thickness Calculations
305 306 308 311 311 314
16 Datum Targets -Flexible Parts, Datum Target s and Partial Datum Features -Sheet Metal Panels and GD&T Sheets -Equalizing Datums -Moveable Targets, Finding the Datum Planes and Fixturing -Datum Target Symbols for Spherical Diameters -Centerplane Datums -Spherical Tolerance Zones
321 322 327 329 333 335 336 337
17 Datum Feature Scheme Choices -Datum Feature Patterns and Profile -Simultaneous Requirements -Compound Datum Features of Size -Secondary and Tert iary Datum Features of Size -Finished Machining Requirements for a Cast Part
338 339 342 345 347 350
18 Flexible Parts -Flexible Parts and Inspecting Them in the Way They Work -Temporary Datum Features -Common Misconceptions -Free State Variation in Sheet Metal Parts
352 353 354 355 356
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Table of Contents
-Specifying Restrained State Inspection -Fixturing Sheet Metal Parts -Profile ALL OVER Controls and What They Mean
358 359 363
19 Position Boundary Concept -Position Boundary -Elongated Holes -Functional Gages and Virtual Condition Boundaries -Tolerancing Hoses, Pipes and Tubing with Positional Boundary -Tolerancing Oddly Configured Features with Positional Boundary -Oddly Configured Datum Features and How to Represent them in Gages -Tolerance Zones vs. Boundary Concept Explanation -Rectangular Tolerance Zones for Round Holes -Bi-directional Position Tolerancing, Polar Coordinate Method
366 367 367 370 371 373 374 376 378 379
20 Why Use GD&T -Multiple Interpretations of Simple Plus and Minus Tolerances -Converting from Plus and Minus to Composite Position Tolerancing -Calculating the Position Tolerance for a Composite Position Control -Minimum Wall Thickness Calculation for Composite Position Tolerances -Composite Tolerancing for Coaxial Hole Patterns -Minimum Wall Thickness Calculations for Coaxial Hole Patterns -Composite Position Tolerancing with 3 Levels of Control -Differentiating Between Features of Similar Size and Shape
381 383 386 387 391 393 393 396 397
21 Composite vs. Two Single Segment Positional Tolerancing -Composite vs. Two Single Segment Positional Tolerancing -Similarities -Differences -One Level Tolerancing vs. Composite Tol. and Simultaneous Requirements -Two Single Segment Position Controls -Refining Geometric Controls to be More Cost Effective
398 399 401 402 405 411 414
22 Dimensioning and Tolerancing of Gages -Dimensioning and Tolerancing of Gages per ASME Y14.43-2003 -GO Gages -NOGO Gages -Functional Gages -Calculating to Determine Good Parts Rejected or Bad Parts Accepted -Steps in the Development of a Dimensional Inspection Plan
423 424 424 426 427 430 436
23 Tolerance Stack-Up Analysis -Tolerance Stack-Up Analysis for a Fixed Fastener Assembly -Rules -Calculating Gaps; Working the Route -Calculating Inner and Outer Boundary Means and Their Tolerances
442 443 444 445 448
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Table of Contents
-Calculating Statistical Toleranclng -Root Sum Squares -Bender Factor -Reintegrating the Statistical Tolerancing into the Assembly -A Simpler Way to Reintegrate the Statistical Tolerance -More Statistical Formulas and Symbols -Glossary of Statistical Terms
451 451 457 458 461 462 464
24 How to be Specific in Calculating and Specifying Statistical Requirements for Size and Geometric Tolerancing -Some Useful Definitions When Geometric Tolerances are Used -Symbology for SPC Formulas -Arithmetic Mean; Normal Distribution of Tolerance and the Standard Deviation; Statistical Probability for Tolerance Stack-Up Analysis for Positional Geometric Tolerances -Calculating a Standard Deviation -Predicting the Amount of Tolerance to be Consumed by Manufacturing -Charts and Tables
474 476 477 478
25 Tolerance Stack-Up Analysis in a 5-Part Assembly -Determining a MIN GAP in a Rotating Assembly -Factors vs. Non-factors -Alignment -Dealing with Threaded Features -Calculating the Pertinent Numbers -Simplifying the Assembly Drawing -Creating a Line Graph with Numbers to Calculate the Minimum Clearance -Adding the Negative and Positive Designations -Wall Thickness Calculations and Choosing the Pertinent Tolerances -Single Part Analysis -Using Profile Tol. and Separate Requirements for Accumulated Error
481 482 483 485 486 490 491 492 492 493 496 499
26 Tolerance Stack-Up Created during Manufacture due to Changing Set Ups -Where the Tolerance Accumulation Comes From -Proportions and Trigonomet ry
502 503 504
27 GD&T as a Language -To Properly Read a Drawing -Reading the Feature Control Frames as Sentences -Profile -Tolerance Zones and Pattern Shift Zones -Reading Two Single Segment Controls -Using Gages to Visualize a Geometric Tolerance’s Meaning -Reading a GD&T Sheet -Optional Tolerancing Approaches for Similar Results -Gears
507 508 512 513 513 514 517 526 529 530
viii
466 469 471
Table of Contents
-Pattern Shift, Where it Comes From and How it Effects the Workpiece -Bonus Tolerance, Virtual Condition and Zero Positional Tolerances -Threads, Gears and Splines -Sequential Tolerancing Using the Simultaneous Requirement Rule 28 Definitions
532 535 536 537 539
Index
568
Bibliography
573
Other GD&T Course Materials Written by James D. Meadows
574
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