Geometric dimensioning and tolerancing for mechanical design

0 . ooo( m

4X R1.000

GEOMETRIC

DIMENSIONING

TOLERANCING

FOR MECHANICAL DESIGN

ThuVienDHKTCN-TN

KNV. 15002253 Section A -A

.XX = ±.01

.XXX = ± .005

ANGLES = ± 1°

Gene R. Cogorno

Geometrie Dimensioning

and Tolerancing for

Mechanical Design

Gene R. Cogorno

S e co n d E d itio n

Me

Gravu

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G eom etric D im ensioning and Tolerancing for M echanical D esign, Second Edition

Copyright © 2011, 2006 by Gene R. Cogorno. All rights reserved. Printed in the United States

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Contents

Preface .............................................................................................................................. ix

A ckn ow ledgm ents ..................................................................................................... xi

1 In trod u ctio n to G eo m etric D im en sio n in g and T oleran cin g ............... 1

C hapter O bjectives ..................................................................................................... 2

W hat Is G D & T? ............................................................................................................. 2

W hen Should G D & T Be U sed? ............................................................................. 2

A dvantages of G D & T O ver C oordinate D im ensioning

and T olerancing ..................................................................................................... 3

T he C ylindrical Tolerance Z one ............................................................ 4

T he M axim um M aterial Condition M odifier .................................... 5

D atum Featu res Specified in O rder of P receden ce ........................ 6

Sum m ary ......................................................................................................................... 7

C hapter R eview .......................................................................................................... 7

2 D im en sio n in g and T oleran cin g F u n d am en tals ....................................... 9

C hapter O bjectives ..................................................................................................... 9

Fundam ental D raw ing Rules ................................................................................ 9

U nits of Linear M easurem ent ................................................................................ 10

Specifyin g Linear D im ensions ............................................................................. 11

Specifyin g Linear T olerances ................................................................................ 11

Interpreting D im ensional Lim its ......................................................................... 13

Specifying A n gular D im ensions ......................................................................... 13

Specifying A n gular T olerances ........................................................................... 14

D im ensioning and T olerancing for C A D / C A M D atabase M odels . . 14

Sum m ary ........................................................................................................................ 15

C hapter R eview .......................................................................................................... 15

3 S y m b o ls, T erm s, and R u les .................................................................................. 17

C h apter O b jectives ..................................................................................................... 17

Sym bols ........................................................................................................................... 17

G eom etric C haracteristic Sym bols ....................................................... 17

T h e D atum Featu re Sym bol ...................................................................... 18

T h e Featu re C ontrol Fram e ...................................................................... 20

Reading the Feature C ontrol Fram e ..................................................... 20

O ther Sym bols U sed w ith G eom etric Tolerancing ........................ 23

T erm s ................................................................................................................................ 30

Ru les .................................................................................................................................. 36

Ru le #1: Lim its of Size Prescribe V ariations of Form ..................... 36

Rule #2: Applicability of M odifiers in Feature Control Frames . . . 38

T he Pitch D iam eter Rule ............................................................................. 39

iii

iv Contents

Sum m ary ...................................................................................................................... 39

Chapter Review ........................................................................................................ 40

Problem s ...................................................................................................................... 46

4 D atum s ........................................................................................................................... 49

Chapter Objectives ................................................................................................... 49

D efinition ...................................................................................................................... 49

A pplication of D atum s .......................................................................................... 50

Im m obilization of a Part ........................................................................................ 50

Datum Feature Selection ........................................................................................ 52

D atum Feature Identification .............................................................................. 53

Inclined D atum Features ....................................................................................... 54

Cylindrical D atum Features ................................................................................ 54

Establishing Datum Features .............................................................................. 54

Plane Flat Surfaces as D atum Features ............................................... 54

Datum Features of Size at RM B ............................................................. 56

Datum Features of Size at M M B ........................................................... 56

Plane Flat Surfaces versus Features of Size ...................................... 56

Irregular Features of Size ......................................................................... 57

M ultiple Datum Features ..................................................................................... 59

Partial Datum Features .......................................................................................... 59

Datum Targets .......................................................................................................... 59

Datum Targets Established on a C ylindrical Part .......................... 60

Step and M ovable Datum Target Sym bols ...................................... 61

Sum m ary ...................................................................................................................... 63

Chapter Review ........................................................................................................ 64

Problems ..................................................................................................................... 66

5 Form ............................................................................................................................... 69

Chapter Objectives ................................................................................................... 69

Flatness .......................................................................................................................... 69

Definition ....................................................................................................... 69

Specifying Flatness Tolerance ................................................................ 70

Specifying Flatness of a M edian Plane ............................................... 71

Unit Flatness ................................................................................................... 73

Straightness ................................................................................................................. 73

Definition ....................................................................................................... 73

Specifying Straightness of a Surface Tolerance ............................... 73

Specifying Straightness of a M edian Line ........................................ 75

Circularity ................................................................................................................... 77

Definition ....................................................................................................... 77

Specifying Circularity Tolerance ........................................................... 77

Cylindricity ................................................................................................................ 78

Definition ....................................................................................................... 78

Specifying Cylindricity Tolerance ........................................................ 78

Free-State Variation ................................................................................................ 79

Summary ..................................................................................................................... 81

C h apter R eview ........................................................................................................... 82

Problem s ......................................................................................................................... 85

6 O rien ta tio n ..................................................................................................................... 89

C h ap ter O b jectives ...................................................................................................... 89

Perpen dicu larity ........................................................................................................... 90

D efinition ........................................................................................................... 90

Specifyin g P erpen dicu larity o f a F lat Su rface .................................. 90

T he T ang ent Plan e .......................................................................................... 91

Specifyin g th e Perpendicu larity o f an A xis to a

P lan e Su rface ............................................................................................... 91

Parallelism ....................................................................................................................... 93

D efinition ........................................................................................................... 93

Specifyin g P arallelism o f a Plan e Su rface ......................................... 93

Specifyin g P arallelism o f an A xis .......................................................... 94

A n gularity ....................................................................................................................... 95

D efin ition ........................................................................................................... 95

Specifyin g A ngularity o f a Plan e Su rface ............................................ 95

Specifyin g A ngularity o f an A xis .......................................................... 97

A ltern ative Practice ....................................................................................... 97

Sum m ary ......................................................................................................................... 98

C h ap ter Review .......................................................................................................... 98

P roblem s ......................................................................................................................... 101

7 P o sitio n , G en era l ........................................................................................................ 105

C hapter O bjectives ...................................................................................................... 105

D efinition ......................................................................................................................... 105

T he T oleran ce of Position ....................................................................................... 106

Specifying the Position Tolerance ...................................................................... 107

Specifying the Position T olerance at R FS ............................................ 107

Specifying the Position T olerance at M M C ....................................... 109

D atum Features o f Size Specified w ith a Regardless of M aterial

Boundary (RM B) M odifier ................................................................................ 112

D atum Features of Size Specified w ith a M axim um M aterial

Boundary (M M B) M odifier ............................................................................. 112

M M B M odifier Explained in M ore D etail ......................................... 113

Locating Features of Size w ith a Least M aterial C ondition (LM C)

M odifier ...................................................................................................................... 118

C alcu lation of W all T hickness ............................................................................. 119

B oundary C onditions ................................................................................................. 120

Z ero Positional T olerance at M M C .................................................................... 121

Sum m ary ......................................................................................................................... 124

C h ap ter R eview .......................................................................................................... 125

P roblem s ......................................................................................................................... 127

8 P o sitio n , L ocation ...................................................................................................... 131

C h ap ter O bjectives ...................................................................................................... 131

Contents y

vi Contents

Floating Fasteners ....................................................................................................... 131

C learance H ole LM C D iam eter .............................................................. 133

Clearance H ole Location Tolerance T .................................................. 133

Clearance H ole M M C D iam eter H ....................................................... 134

Fixed Fasteners ........................................................................................................... 134

Clearance H ole LM C D iam eter .............................................................. 136

Threaded H ole Location Tolerance tx .................................................. 136

Clearance H ole Location Tolerance t2 .................................................. 136

Clearance H ole M M C D iam eter H ....................................................... 137

Projected Tolerance Zones ................................................................................... 138

Through Holes ............................................................................................... 139

Blind H oles ...................................................................................................... 139

M ultiple Patterns of Features ............................................................................... 140

Com posite Positional Tolerancing ..................................................................... 142

M ultiple Single-Segm ent Positional Tolerancing ...................................... 147

Nonparallel H oles .................................................................................................... 148

Counterbored H oles ................................................................................................. 148

N oncircular Features at M M C ............................................................................ 150

Sym m etrical Features at M M C ............................................................................ 152

Sum m ary ....................................................................................................................... 152

Chapter Review ........................................................................................................ 153

Problem s ...................................................................................................................... 155

9 Position, C oaxiality ................................................................................................ 165

Chapter Objectives .................................................................................................... 165

Definition ...................................................................................................................... 165

Com parison Between Coaxiality Controls .................................................... 166

Specifying Coaxiality at M axim um M aterial Condition .......................... 167

Com posite Positional C ontrol of Coaxial Features .................................... 168

Coaxial Features Controlled W ithout D atum References ..................... 169

Tolerancing a Plug and Socket ............................................................................ 170

Sum m ary ...................................................................................................................... 170

Chapter Review ........................................................................................................ 171

Problem s ...................................................................................................................... 171

10 C oncentricity and Sym m etry ............................................................................... 175

Chapter Objectives .................................................................................................... 175

Concentricity ............................................................................................................... 175

Definition ........................................................................................................ 175

Specifying Concentricity ............................................................................ 175

Applications of Concentricity ................................................................ 177

Symmetry ...................................................................................................................... 177

Definition ........................................................................................................ 177

Specifying Sym m etry ................................................................................ 178

Applications of Sym m etry ....................................................................... 180

Sum m ary ...................................................................................................................... 180

C h apter R eview ........................................................................................................... 181

Problem s ......................................................................................................................... 182

11 R u n o u t ............................................................................................................................... 185

C h apter O bjectives ...................................................................................................... 185

D efin ition ......................................................................................................................... 185

C ircu lar R u nout ........................................................................................................... 185

T otal R u nout .................................................................................................................. 186

Specifyin g R u nout and P artial R u nout ............................................................. 186

M u ltiple D atum Featu res ....................................................................................... 187

Face and D iam eter D atum Features .................................................................. 188

G eom etric C ontrols to Refine D atum Featu res ............................................ 188

R elation sh ip Betw een Featu re Surfaces .......................................................... 189

Inspecting R u nout ...................................................................................................... 189

Sum m ary ......................................................................................................................... 190

C hapter Review ........................................................................................................... 191

Problem s ......................................................................................................................... 192

12 Profile ................................................................................................................................ 195

C h ap ter O bjectives ...................................................................................................... 195

D efinition ......................................................................................................................... 195

Specifying Profile Tolerance .................................................................................. 195

A pp lication of D atum Features ........................................................................... 198

A Radius R efinem ent w ith Profile ...................................................................... 199

C om bining Profile T olerances w ith O ther G eom etric C ontrols .......... 200

C op lanarity .................................................................................................................... 201

Profile o f a C onical Featu re ..................................................................................... 203

C o m p osite Profile T olerancing ............................................................................. 204

M u ltip le Single-Segm ent Profile T olerancing .............................................. 204

Inspection ...................................................................................................................... 208

Sum m ary ......................................................................................................................... 208

C hapter Review .......................................................................................................... 209

Problem s ......................................................................................................................... 210

13 G rap h ic A n aly sis ........................................................................................................ 215

C h ap ter O bjectives ..................................................................................................... 215

A dvantages of G raphic A nalysis ......................................................................... 215

A ccuracy of G raphic A nalysis ............................................................................. 216

A nalysis o f a C om posite G eom etric Tolerance ............................................ 216

A nalysis o f a Pattern of Features Controlled to a

D atum Feature of Size ......................................................................................... 220

Sum m ary ......................................................................................................................... 224

C h ap ter Review .......................................................................................................... 225

P roblem s ......................................................................................................................... 226

14 A S trateg y fo r Toleran cin g Parts ......................................................................... 231

C hapter O bjectives ..................................................................................................... 231

C o n t e n t s vii

viii Contents

Features of Size Located to Plane Surface Features .................................... 231

Features of Size Located to Features o f Size .................................................. 237

A Pattern of Features Located to a Second Pattern of Features ............ 241

Sum m ary ....................................................................................................................... 245

Chapter Review ......................................................................................................... 246

Problem s ....................................................................................................................... 249

A ppendix ....................................................................................................................... 253

Index .............................................................................................................................. 259

Preface

Ihis book is w ritten prim arily for the learner w ho is new to the subject of

geom etric dim ensioning and tolerancing (GD&T). The purpose of this

-1 - book is to teach the graphic language of G D & T in a w ay that the learner

can easily understand and use in practical applications. This w ork is intended

as a textbook to be used in colleges, universities, technical schools, and corporate

training program s. It is intended for use in engineering, design, manufacturing,

inspection, and drafting curriculums. This book is also appropriate for a self-study

The m aterial in this book is w ritten in accordance with the latest revision of the

geometric dimensioning and tolerancing standard, ASME Y14.5-2009. GD&T is a graphic

language; in order to facilitate understanding of this subject, there is at least one drawing

to illustrate each concept discussed. Drawings in this text are for illustration purposes

only. In order to avoid confusion, only the concepts being discussed are com pletely

toleranced. All the draw ings in this book are dimensioned and toleranced with the inch

system of m easurem ent because m ost drawings produced in the United States are

dim ensioned and toleranced with this system. The reader is expected to know how to

read engineering drawings.

The discussion of each control starts with a definition and continues with how the

control is specified, interpreted, and inspected. There is a sequential review and a series

of study questions and problem s at the end of each chapter to em phasize key concepts

and to serve as a self-test. This book is logically ordered so that it can easily be used

as a reference text.

To optim ize the learning process, it is im portant for the learner to

1. Preview the chapter objectives, headings, drawing captions, and summary.

2. Preview the chapter once again, focusing attention on the drawings and, at the

sam e time, form ulating questions about the material.

3. Read the chapter com pletely, searching for answers to your questions.

program .

Organization

A Note to the Learner

ix

About the Author

G ene R. Cogom o is a professional educator, speaker,

and author with more than 30 years of experience in

education and training. He earned both his Bachelor's

and Master's degrees in Industrial Education from

San Jose State University. In 1984, he joined FMC

Corporation as a Senior Technical Trainer. In 1992,

Mr. Cogorno founded Technical Training Consultants,

where he teaches courses in geometric dimensioning

and tolerancing, tolerance analysis, and blueprint

reading.

________________CHAPTER 1

Introduction to Geometric

Dimensioning and Tolerancing

F

or many in the m anufacturing sector, geom etric dim ensioning and tolerancing is

a new subject. During W orld W ar II, the United States m anufactured and shipped

spare parts overseas for the war effort. Many of these parts, even though they

were made to specifications, would not assem ble. The military recognized that defec￾tive parts caused serious problem s for military personnel. After the war, a com m ittee

representing governm ent, industry, and education spent considerable time and effort

investigating this defective parts problem; this group needed to find a way to ensure

that parts would fit and function properly every time. The result was the developm ent

of geom etric dim ensioning and tolerancing (GD&T).

Ultim ately, the USASI Y 14.5-1966 [United States of Am erica Standards Institute—

predecessor to the American National Standards Institute (ANSI)] docum ent was pro￾duced based on earlier standards and industry practices. The following are revisions to

that standard:

• ANSI Y 14.5-1973 (American National Standards Institute)

• ANSI Y 14.5M -1982

• ASM E Y 14.5M -1994 (Am erican Society o f Mechanical Engineers)

• ASM E Y 14.5-2009

The 2009 revision is the current, authoritative reference docum ent that specifies the

proper application of GD&T.

Most governm ent contractors are now required to generate drawings that are toler￾anced with GD&T. Because of tighter tolerancing requirem ents, shorter time to produc￾tion, and the need to com m unicate design intent m ore accurately, many com panies

other than military suppliers are recognizing the importance of tolerancing their draw ­

ings with GD&T.

Conventional tolerancing m ethods have been in use since the m iddle o f the 1800s.

These m ethods do a good job of dim ensioning and tolerancing the size of features and

are still used in that capacity today, but they do a poor job o f locating and orienting

features o f size. GD& T is used extensively for tolerancing the size, form, orientation,

and location of features. Tolerancing with GD& T has a num ber of advantages over

conventional tolerancing methods; three dram atic advantages are illustrated in this

chapter.

l

2 C h a pt e r One

The purpose of this introductory chapter is to provide an understanding o f what

GD&T is, why it was developed, when to use it, and what advantages it has over con￾ventional tolerancing methods. With an understanding of this subject, technical practi￾tioners will be likely to learn the skill of tolerancing with GD&T more effectively; with

this new skill, engineers will have a greater understanding of how parts assemble, do a

better job of communicating design requirements, and ultimately be able to make a

greater contribution to their com panies' bottom line.

Chapter Objectives

After completing this chapter, the learner will be able to

• Define GD&T

• Explain when to use GD&T

• Identify three advantages of GD&T over coordinate tolerancing

What Is GD&T?

GD&T is a symbolic language used to specify the size, shape, form, orientation, and

location of features on a part. Features toleranced with GD&T reflect the actual relation￾ship between mating parts. Drawings with properly applied geometric tolerancing pro￾vide the best opportunity for uniform interpretation and cost-effective assembly. GD&T

was created to ensure the proper assembly of mating parts, to improve quality, and to

reduce cost.

GD&T is a design tool. Before designers can apply geometric tolerancing properly,

they must carefully consider the fit and function of each feature of every part. GD&T, in

effect, serves as a checklist to remind the designer to consider all aspects of each feature.

Properly applied geometric tolerancing ensures that every part will assemble every

time. Geometric tolerancing allows the designer to specify the maximum available tol￾erance and, consequently, design the most economical parts.

GD&T communicates design requirements. This tolerancing scheme identifies all

applicable datum features, which are reference surfaces, and the features being con￾trolled to these datum features. A properly toleranced drawing is a picture that not only

communicates the size and shape of the part but also tells a story that explains the toler￾ance relationships between features.

When Should GD&T Be Used?

Many designers ask, "W hen should I use G D&T?" Because GD&T was designed to

position features of size, the simplest answer is to locate all features of size with GD&T

controls. Designers should tolerance parts with GD&T when

• Drawing delineation and interpretation need to be the same

• Features are critical to function or interchangeability

• It is important to stop scrapping perfectly good parts

• It is important to reduce drawing changes

V ^ I

I ntroducti on to Geometric Dimensioning and Tolerancing 3

• Autom ated equipm ent is used

• Functional gaging is required

• It is im portant to increase productivity

• Com panies want across the board savings

Advantages of GD&T Over Coordinate Dimensioning and Tolerancing

Since the m iddle of the nineteenth century, industry has been using the plus or minus

tolerancing system for tolerancing drawings. This system has several limitations:

• The plus or minus tolerancing system generates rectangular tolerance zones. A

tolerance zone, show n in the exam ple in Fig. 1-1, is a rectangular boundary within

which the axis of a feature that is in tolerance must lie. Rectangular tolerance

zones do not have a uniform distance from the center to the outer edge. In the

figure, from left to right and top to bottom , the tolerance is ± .005; across the

diagonals, the tolerance is ± .007. Therefore, when designers tolerance features

with a plus or minus .005 tolerance, they m ust tolerance the mating parts to

accept a ± .007 tolerance, which exists across the diagonals of the tolerance

zones.

• Size features can be specified only at the regardless of feature size condition.

Regardless o f featu re size means that the location tolerance remains the sam e no

m atter w hat size the feature happens to be within its size tolerance. If a hole

such as the one in Fig. 1-1 increases in size, it has m ore location tolerance, but

with the plus and minus tolerancing system , there is no way to take advantage

of that additional tolerance.

• Datum features usually are not specified where the plus or minus tolerancing

system is used. Consequently, machinists and inspectors don't know which

datum features apply or in what order they apply. In Fig. 1-1, m easurements are

taken from the lower and left sides of the part. The fact that m easurements are

taken from these sides indicates that they are datum features. However, since

these datum features are not specified, they are called implied datum features.

Figure 1-1 The traditional plus or minus tolerancing system. The axis of the 3-inch hole must fall

inside the .010-square tolerance zone.