gd&t standard

STANDARD NO:A 00 0020REVISION : A

TITLE:- GUIDELINES FORGEOMETRIC DIMENSIONING &TOLERANCING EN03:00676N

PURPOSE:To provide guidel ines on use of Geometric Dimensioning & Tolerancing. System

convention to be mentioned on the drawing.

SCOPE :To define & i l lustrate the G D & T parameters on al l drawings made manually or on

computer for release.

REFERENCE :Reference is taken from ISO 1101-1983 / ISO 2692:1988 / ISO 5458:1987

/ ISO 5459:1981 & ASME Y14.5M-1994

TERMINOLOGY :Terms have been defined in the text at appropriate places.

Prepared By : Mayur Rajke Approved By : Nitin Ranade Released By : R.S.Shende Date : 24/4/02

Th is document shou ld no t be reproduced in any fo rm o r by any means w i thou t wr i t ten approva l f rommah ind ra & mah indra l td . (AS)

CONTENTS

PAGE NOGENERAL 1

GEOMETRIC CHARACTERISTIC 2

MODIFIERS 3

COMPOSITE FRAME 6

COMBINED FRAME 6

FEATURE CONTROL FRAME 7

BASIC DIMENSION 7

RULE # 1 8

RULE # 2 9

ABRIVATION 11

GEOMETRIC DIMENSIONS & TOLERANCING (GD&T) 12

FEATURES & FEATURES OF SIZE 12

FEATURES OF SIZE DIMENSIONS 13

INTERNAL AND EXTERNAL FEATURES OF SIZE 13

MAXIMUM MATERIAL CONDITION (MMC) 14

LEAST MATERIAL CONDITIONS (LMC) 14

REGARDLESS OF FEATURE SIZE (RFS) 14

MATERIAL CONDITION USAGE 15

RADIUS 16

CONTROL RADIUS 16

VIRTUAL CONDITION (VC) 17

INNER BOUNDARY (IB) 17

OUTER BOUNDARY (OB) 17

WORST-CASE BOUNDARY (WCB) 17

TOLERANCE OF POSITION (TOP) 22

PROJECTED TOLERANCE ZONE 28

CONCENTRICITY 30

SYMMETRY 34

PERPENDICULARITY 39

ANGULARITY 43

PARALLELISM 47

FLATNESS 52

STRAIGHTNESS 53

CIRCULARITY 63

CYLINDRICITY 67

IMPLIED DATUMS 71

PLANER DATUMS 72

INCLINED DATUM FEATURES 76

PROFILE 79

PROFILE OF A SURFACE 81

CIRCULAR RUNOUT 84

TOTAL RUNOUT 87

BACKGROUND OF GD&T 90

1

GENERALThis standard establishes uniform practices for stating and interpreting tolerancing and related

requirements for use on engineering drawings and in related documents. For a mathematical

explanation of many of the principles in this Standard, see ASME Y14.5.1M.

FIGURESThe figures in this Standard are intended only as illustration to aid the user in understanding the

principles and methods of tolerancing described in the text. The absence of a figure illustrating

the described application is neither reason to assume inapplicability, nor basis for drawing

rejection. In some instances, figures show added detail for emphasis. In other instances, figures

are incomplete by intent. Numerical values of tolerances are illustrative only.

(1) I t is desirable to make use of GD&T in place of coordinate tolerancing

practice.

(2) GD&T practice yield the fol lowing benefits

? Cyl indrical tolerance zones in place of rectangular tolerance zones.

? Addit ional manufacturing tolerance depending upon actual size of the

feature.

? I t is indicative of the references for sett ing required for inspection.

(3) The GD&T system of tolerancing uses a set of 14 symbols and 10

modif iers as shown in the fol lowing f igure 3.1 & 3.2

2

Geometric Characteristic SymbolsGeometric Characteristic Symbols are a set of fourteen symbols used in the

language of geometric tolerancing. They are shown in f igure 3.1 The symbols

are divided into f ive categories: form , prof i le, orientation , location & runout .

The chart in f igure 3.1 shows that certain geometric symbols never use a datum

reference and other geometric symbols always use a datum reference.

Furthermore, some geometric symbols may or may not use a datum reference.

3

MODIFIERSIn the language of geometric tolerancing there are set of symbols cal led

“modif iers.” Modifiers communicate addit ional information about the drawing or

tolerancing of an art.

5

(4) Feature Control FrameGeometric tolerances are specif ied on a drawing through the use of a feature

control frame. A feature control frame is a rectangular box that is divided into

compartments within which the geometr ic characterist ic symbol, tolerance

value, modif iers and datum references are placed. The compartments of a

feature control frame are shown in f igure 4.1.

The f irst compartment of the feature control frame is cal led the geometric

characterist ic port ion. I t contains one of the fourteen geometric characterist ic

symbols.

The second compartment of the feature control frame is referred to as the

tolerance port ion. The tolerance port ion of a feature control frame may contain

several bits of information .For example, i f the tolerance value is preceded by a

diameter symbol, the shape of the tolerance zone is a cyl inder. I f a diameter

symbol is not shown in the front of the tolerance value, the shape of the

tolerance zone is either paral lel planes, paral lel l ines or a uniform boundary in

the case of profi le. The tolerance value specif ied is always a total value.

The third, fourth and f i f th compartment of the feature control frame are referred

to as the datum reference port ion of the feature control frame, and these are

absent for form symbols and optional for profi le symbols.

6

Composite Feature Control FrameThe composite feature control frame contains a single entry of the geometric

characterist ic symbols fol lowed by each tolerance and datum requirement, one

above the other.

Combined Feature Control Frame and Datum Feature SymbolsWhere a feature or pattern of features control led by a geometric tolerance also

serves as a datum feature, the feature control frame and datum feature symbols

are combined.

Wherever a feature control frame and datum feature symbol are combined,

Data referenced in the feature control frame are not considered part of the

datum feature symbol. In the posit ional tolerance example, a feature is

control led for posit ion in relat ion to datum A and B, and identif ied as datum

feature C. Whenever datum C is referenced elsewhere on the drawing, the

reference applies to datum C, not to datum A and B.

7

Feature Control Frame With a Projected Tolerance ZoneWhere a posit ional or an orientation tolerance is specif ied as a projected

tolerance zone, the projected tolerance zone the projected tolerance zone

symbol is placed in the feature control frame, along with the dimension

indicating the minimum height of the tolerance zone. This is to fol low the stated

tolerance and any modif ier. Where necessary for clar if icat ion, the projected

tolerance zone is indicated with a chain l ine and the minimum height of the

tolerance zone is specif ied in a drawing view. The height dimension may then

be omitted from the feature control frame.

(5) GD&T tolerance for location, orientation and profile are

always related to a basic dimension as defined below.

Basic DimensionA basic dimension is a numerical value used to describe the theoretical ly

exact size, true profi le, or ientat ion or location of a feature or gauge information

(i.e. datum targets). On engineering drawings there are two uses for basic

dimensions. One is to define the theoret ical ly exact location, size, or ientat ion

or true profi le of a part feature the other use is to define gages information

(example: datum targets). When a basic dimension is used to define part

feature, i t provides the nominal locat ion from which permissible variat ions are

established by geometric tolerances.

8

(6) RULESThere are two general rules in ASME Y14.5m-1994. The f irst rule establ ishes

default condit ions for features of size. The second rule establishes a default

material condit ion for feature control frames.

DEFINITION

Rule#1 : Where only a tolerance of size is specif ied, the l imits of size of an

individual feature prescribe the extent to which variat ions in i ts form as well as

in i ts size are allowed.

For example, let’s look at how Rule #1 affects the diameter of a pin. When the

pin diameter is at MMC, the pin must have prefect from. For a pin diameter,

perfect from means perfect straightness and perfect roundness. This would

al low the pin to f i t through a boundary equal to i ts MMC. If the size of the pin

was less than i ts MMC, the pin could contain from error (straightness and

roundness error) equal to the amount the pin departed from MMC.

An example of the effects of Rule#1 on an external and an internal FOS is

shown in f igure 6.1

9

Rule #2Rule #2 is cal led “the al l appl icable geometr ic tolerances rule.”

Rule #2 : RFS applies, with respect to the individual tolerance, datum

reference or both, where no modifying symbol is specif ied. MMC or LMC

must be specif ied on the drawing where required.

Certain geometric tolerance always appl ies RFS and cannot be modif ied to

MMC or LMC.

Where a geometric tolerance is appl ied on an RFSS basis, the tolerance is

l imited to the specif ied value regardless of the actual size of the feature.

Rule #2a is an alternative practice of Rule #2. Rule #2a states that, for a

tolerance of posit ion, RFS may be specif ied in feature control frames if desired

and appl icable. In this case, the RFS symbol would be the symbol from the

1982 version of Y14.5 Figure 6.2 shows examples of Rule #2 and Rule#2a.

10

The from of a FOS is control led by i ts l imits of size, as described below:

- The surfaces of a feature of size shall not extend beyond a boundary

(Envelop) of perfect form at MMC.

- When the actual local size of a FOS has departed from MMC toward

LMC, the form is al lowed to vary by the same amount.

- The actual local size of an individual feature of size must be within the

specif ied tolerance of size.

- There is no requirement for a boundary of perfect form at LMC. If a

feature of size is produced at LMC, i t can vary from true form by the

amount al lowed by the MMC boundary.

How to override Rule #1Rule #1 dose not applies when in addit ion to the tolerance of size a form

tolerance is specif ied for the FOS.

Rule #1 Alternate definitionRule #1: For features of size, where only a tolerance of size is specif ied, the

surfaces shall not extend beyond a boundary (envelope) of perfect form at

MMC.

Rule #1 LimitationRule #1 dose not controls the location, orientat ion or relat ionship between

features of size.

11

(7) ABBREVIATIONS AND ACRONYMS USED IN THE TEXT

AME Actual Mating Envelope

CMM Coordinate Measuring Mac hine

CR Control led Radius

DIA Diameter

FIM Full Indicator Movement

FOS Feature of size

GD&T Geometr ic Dimensioning and Tolerancing

IB Inner Boundary

ID Inside Diameter

LMC Least Material Condit ion

MAX Maximum

MIN Minimum

MMC Maximum Mater ial Condit ion

OB Outer Boundary

OD Outside Diameter

RFS Regardless of Feature Size

TIR Total Indicator Reading

TOP Tolerance of Posit ion

VC Virtual Condit ion

WCB Worst-Case Boundary

Y14.5 ASME Y14.5M-1994

12

THE GEOMETRIC DIMENSIONING AND TOLERANCING SYMSTEM

DEFINITIONS

Geometric Dimensioning and Tolerancing (GD&T) is an international

language that is used on an engineering drawings to accurately describe a part.

The GD&T language consists of a well-defined set of symbols, rules,

definit ions and conventions. GD&T is a precise mathematical language that can

be used to describe the size, form, orientation and location of part features.

GD&T is also a design philosophy on how to design and dimension parts.

Features and Features of Size

A feature is a general term applied to a physical port ion of a part, such as a

surface, hole or slot. An easy Way to remember this term is to think of a feature

as a part surface. The part in Figure 7.1 contains seven features: the top and

bottom, the left and r ight sides, the front and back, and the hole surface.

13

Feature of Size Dimensions

A feature of size dimension i s a dimension that is associated with a feature

of size. A non - feature of size dimension is a dimension that is not associated

with a feature of size. In Figure 7.2 there are four feature of size dimensions

and three non-feature of size dimensions. Whether a dimension is or is not a

feature of size dimension is an important concept in geometric tolerancing.

Internal and External Features of size

There are two types of feature of size-external and internal . External feature of

size are comprised of part surfaces (or elements) that are external surfaces,

l ike a shaft diameter or the overal l width or height of a planar part. In Figure

7.2 the 34-36 dimension and the 24.0-24.2 dimension are size dimension for

external features of size. An internal FOS is comprised of part surface (or

elements) that are internal part surface, such as a hole diameter or the width of

a slot. In Figure 7.2, the 4.2-4.8-diameter hole and the 10.2-10.8-diameter hole

are size dimensions for internal features of size.

Length of feature of size length of the FOS is the actual span of the feature onthe part.

14

THE DEFINATIONS OF THE THREE COMMON MATERIAL

CONDITION USED IN GD&T

1) Maximum Material Condit ion (MMC)

Maximum Material Condition is the condit ion in which a feature of size

contains the maximum amount of material everywhere within the stated l imits of

size-for example, the largest shaft diameter or smallest hole diameter. Figure

7.3 shows examples of maximum material condit ion.

- the maximum material condit ion of an external feature of size

(i .e.shaft ) is i ts largest size l imit.

- The maximum material condit ion of an internal feature of size

(i .e.hole) is i ts smallest size l imit .

2) Least Material Condition (LMC)

Least material condition is the condit ion in which a feature of size contains

the least amount of material everywhere within the stated l imits of size –for

example, the smallest shaft diameter or the largest hole diameter. Figure 7.3

shows example of the material condit ion.

- The least material condit ion for an external feature of size

(i .e. shaft) is i ts smallest size l imit .

- The least material condit ion for an internal feature of size

(i . e. hole ) is i ts largest size l imit.

3) Regardless of Feature Size (RFS)

Regardless of feature size is the term that indicates a geometr ic tolerance

applies at any increment of the feature within i ts size tolerance. Another way to

visual ize RFS is that the geometric tolerance applies at whatever size the part

is produced. There is no symbol for RFS because it is the default condit ion for

al l geometric tolerances.

15

MATERIAL CONDITIONSA key concept in geometric Tolerancing is the abi l i ty to specify tolerances at

various part feature material condit ions. A geometric tolerance can be specif ied

to apply at the largest size, smallest size or actual size of a feature of size.

Material Condition Usage

Each material condit ion is used for different functional reasons. Geometric

tolerances are often specif ied to apply at MMC when the function of a FOS is

assembly. Geometric tolerances are often specif ied to apply at LMC to insure a

minimum distance on a part. Geometric tolerances are often specif ied to apply

at RFS to insure symmetrical relat ionships.

16

RADIUS AND CONTROLLED RADIUS

RadiusA radius is a straight l ine extending from the center of an arc or a circle to i ts

surface. The symbol for a radius is “R.” when the “R” symbol is used, i t creates

a zone defined by two arcs (the minimum and maximum radius). The part

surface must l ie within this zone. Figure 7.4 shows a radius tolerance zone.

The part surface may have f lats or reversals within the tolerance zone.

Controlled radiusA controlled radius is a radius with no f lats or reversals al lowed. The symbol

for a control led radius is “CR” when the “CR” symbol is used, i t creates a

tolerance zone defined by two arcs (the minimum and maximum radi i) . The part

surface must be within the crescent-shaped tolerance zone and be an arc

without f lats or reversals. Figure 7.5 shows a control led radius tolerance zone.

17

INTRODUCTION TO: VIRTUAL CONDITION AND BONUDARY

CONDITIONS

Depending upon its function, a FOS is control led by a size tolerance and one or

more geometr ic controls. Various material condit ions (MMC, LMC or RFS) may

also be appl ied. In each case, consideration must be given to the col lect ive

effects of the size, specif ied material condit ion and geometric tolerance of the

FOS. The terms that apply to these condit ions are virtual condit ion, inner

boundary and outer boundary.

Definit ions

Virtual condit ion (VC) is a worst-case boundary generated by col lect ive

effects of a feature of size at MMC or at LMC and the geometric tolerance for

that material condit ion. The VC of a FOS includes effects of the size,

orientat ion and location for the FOS. The virtual condit ion boundary is

related to the datum’s that are referenced in the geometric tolerance used to

determine the VC.

Inner boundary (IB) is a worst-case boundary generated by the smallest

feature of size minus the stated geometric tolerance (and any addit ional

tolerance, if applicable)

Outer boundary (OB) is a worst-case boundary generated by the largest

feature of size plus the stated geometric tolerance (and any addit ional

tolerance, i f applicable.)

Worst-case boundary (WCB) is a general term to refer to the extreme

boundary of a FOS that is the worst-case for assembly. Depending upon the

part dimensioning a worst-case boundary can be virtual condit ion, inner

boundary or outer boundary .

Virtual Condition Facts

Three important points about virtual condit ion are :

1. A virtual condit ion boundary (or WCB) is a constant value.

2. When a geometric tolerance is applied to a FOS, and the virtual

condit ion is calculated, the size tolerance requirements st i l l apply.

3. A FOS may have several virtual condit ions.

18

Feature of Size Boundary Conditions

I f there are no geometric controls applied to a FOS, the WCB is the outer or

inner boundary. The outer or inner boundary is equal to the MMC boundary as

defined by rule #1.see figure 7.6.

Whether a geometric control is appl ied to a feature, a surface or a FOS (an axis

or centerplane) can be determined by the location of the feature control frame

on the drawing. When a feature control frame is associated with a surface , i t

appl ies to the feature. See Figure7.7 A. When a feature control frame is

associated with a FOS dimension or placed beneath or behind the FOS

dimension, i t appl ies to the FOS. See Figure 7.7 B. i f a feature control frame is

applied to a FOS, then the WCB is affected.

Worst-case Boundary (WCB)

I f a feature control frame is appl ied to a feature (a surface), i t dose

not affect i ts WCB . I f a feature control frame is appl ied to a FOS (an

axis or centerplane), i t dose affect i ts WCB .

19

MMC Virtual Condit ionWhen a geometric tolerance that contains an MMC modif ier in the tolerance

port ion of the feature control frame is appl ied to a FOS, the virtual condit ion

(worst-case boundary)of the FOS is affected. The virtual condit ion (or WCB) is

the extreme boundary that represents the worst-case for functional

requirements, such as clearance or assembly with a mating part.

In the case of an external FOS such as a pin or a shaft, the VC(or WCB) is

determined by the fol lowing formula:

VC = MMC + Geometr ic Tolerance

In the case of an internal FOS, such as a hole, the VC (or WCB) is


VC = MMC – Geometr ic Tolerance

The virtual condit ion of an external FOS (at MMC) is a constant value, and can

also be referred to as the “ outer boundary" or “worst-case boundary" in

assembly calculat ions. The vir tual condit ion of an internal FOS (at MMC) is a

constant value and can also be referred to as the “inner boundary” or “worst-

case boundary” in assembly calculat ions. Figure 7.8 shows examples of vir tual

condit ion calculat ions (as MMC).

20

LMC Virtual Condition

When a geometrical tolerance that contains an LMC modif ier in the tolerance

port ion of the feature control frame is applied to a FOS, the virtual condit ion of

the FOS is affected. The virtual condit ion is the extreme boundary that

represents the worst-case for functional requirement, such as wall thickness,

al ignment or minimum machine stock on a part.

In the case of an external FOS, such as a pin or a shaft, the VC is


VC = LMC - Geometr ic Tolerance

In the case of an internal FOS, such as a hole, the VC is determined by the

fol lowing formula:

VC = LMC + Geometr ic Tolerance

The virtual condit ion of an external FOS (at LMC) is always a constant value

and can also be referred to as the “inner boundary” in calculat ion. The virtual

condit ion of an internal FOS (at LMC) is always a constant boundary and can

also be referred to as the “outer boundary” in calculat ion. Figure 7.9 shows

examples of vir tual condit ion calculat ion (at LMC).

21

Multiple Virtual Condit ionsOn complex industr ia l drawings, i t is common to have mult ip le geometr ic controls

appl ied to a FOS. When this happens, the feature of size may have several v ir tual

condit ions. Figure 7.10 shows an example of a FOS with two vir tual condit ions. Panel

A shows the size tolerance requirements. of rules # 1. panel B shows the vir tual

condit ion that resul t f rom the perpendicular i ty control . This control produces a 10.3

dia. boundary relat ive to datum plane A . Panel C shows the vir tual condit ion that

resul ts f rom the posi t ional control . This control produces a 10.4 dia. boundary relat ive

to datums A, B & C. When a Geometr ic tolerance is appl ied to a FOS – other than a

straightness control – the requirements of Rule # 1 st i l l apply.

22

(8) Examples for common use are given below

LOCATION TOLERANCES

TOP GENERAL INFORMATION

Definitions and ConventionsTrue position is the theoretical ly exact location of a FOS as defined by basic

dimensions. A tolerance of position (TOP) control is a geometric tolerance

that defines the location tolerance of a FOS from its true posit ion. When

specif ied on RFS basis, a TOP control defines a tolerance zone that the center,

axis or centerplane of the AME of a FOS must be within. When specif ied on an

MMC or LMC basis, a TOP control defines a boundary – often referred to as the

virtual condit ion – that may not be violated by the surface or surfaces of the

considered feature.

Where i t is desired to specify a TOP on RFS basis, the feature control frame

does not show any modif iers. RFS is the default condit ion for al l geometric

tolerances. Where i t is desired to specify a TOP on MMC or LMC basis, the

appropriate modif ier is shown in the tolerance posit ion of the feature control

frame. MMC and LMC modif iers may also be specif ied in the datum port ion of

the feature control frame where desired and appropriate. See f igure 8.1.

23

Whenever a TOP control is specif ied, the theoretical ly exact location of the axis

or centerplane of the feature of size must be defined with basic dimensions. The

theoretical ly exact location of a FOS as defined by basic dimensions is cal led

the true posit ion of the FOS. An example of a TOP tolerance zone and its true

posit ion are shown in f igure 8.2.

True Position

When a TOP cal lout is specif ied, the true posit ion of the FOS is the

theoret ical ly exact locat ion as defined by the basic dimensions.

Whenever a geometr ic control with datum reference is used, i t controls the

orientat ion of the toleranced feature relat ive to the primary datum referenced.

24

Types of Part Relationships that can be Controlled with TOP

TOP is commonly used to control four types of part relat ionships:

1) The distance between features of s ize, such as holes, bosses, s lots,

tabs, etc.

2) The locat ion of feature of s ize (or patterns of features of s ize) such as

holes, bosses, s lots, tabs, etc.

3) The coaxial i ty between features of size.

4) The symmetr ical relat ionship between feature of size.

With coordinate tolerancing, i t is not stated whether the holes are def ined from

surface are defined from the holes.

25

Advantages of TOPIn comparison with coordinate tolerancing, TOP offers may advantages Six

important advantages are :

1. Provides larger tolerance zones, cyl indr ical tolerance zones are larger than

square zones.

2. Permits addit ional tolerances – bonus and datum Shift .

3. Prevents tolerance accumulat ion.

4. Permits the use of funct ional gauges.

5. Protects the part funct ion.

6. Lowers manufactur ing costs.

Guide to TOP Modifier Usage

When specify ing TOP controls, the designer must specify under which mater ial

condit ion the control is to apply. Figure 8.4 provides a guide for determining

when the MMC or LMC condit ion should be specif ied or when the RFS condit ion

should be invoked. Note that the funct ion of the FOS being toleranced is the

primary cr i ter ia for material condit ion select ion. Also, the relat ive cost to

produce and verify a FOS is most favorable when the MMC modif ier is used.

Modi f ie rs Commonly used In these funct iona l

app l ica t ions

Bonus or da tum

sh i f t permiss ib le

Re la t i ve cos t to

produce & ver i fy

M? Assemb ly

? Loca t ion o f a non-c r i t i ca l

FOS

Yes L o w e s t

L

? Min imum wa l l th i ckness

? Min imum pa r t d i s tance

? Min imum mach ine s tock

? Al ignment

Yes

Grea te r t han MMC;

less than RFS

RFS

Invoked

b y

show ing

n o

modif ier

? To con t ro l a symmet r i ca l

re la t i onsh ip

? When the e f fec ts o f bonus o r da tum

sh i f t w i l l be de t r imen ta l to the

func t ion o f the par t

? To con t ro l m in imum mach ine s tock

? Cente r i ng

? Al ignment

N o H ighes t

F IGURE 8 .4 Gu ide fo r Se lec t i ng Mod i f i e r s i n TOP Con t ro l s Based on P roduc t Func t i on

When considering the funct ions of a FOS, i t is often found that assembly with

other parts is required; therefore, the MMC modif ier is the most commonly used

modif ier in TOP controls. Also, the MMC modif ier is the least expensive option

for producing and verifying a FOS.

26

Where TOP is Used on RFS BasisIn certain cases, the funct ion of a part may require a TOP to be appl ied on RFS

basis .The chart in f igure 8.5 descr ibes several appl icat ion where the RFS

modif ier is recommended. When a TOP is appl ied on a RFS basis, a closer

control is imposed on the part when compared to MMC appl icat ion. Also the

inspection of the TOP requirement becomes more complex.

Whenever a TOP control is appl ied at RFS, three condit ions are presents:

1. The tolerance zone appl ies to the axis(or centerplane) of the FOS.

2. The tolerance value appl ies regardless of the size of the tolerance feature

of size.

3. The requirement must be verif ied with a variable gauge.

Coaxial Diameter ApplicationFigure 8.5 i l lustrates the amount of bonus and/or datum shif t permissible in

coaxial diameter appl icat ion. In example one, the tolerance diameter and the

datum feature diameter are different diameters. The bonus tolerance

permissible comes from the toleranced diameter. The datum shif t permissible

Comes from the datum feature diameter.

27

Specification Test for TOPFor the top contro l to be a speci f icat ion, i t must sat is fy the fo l lowing

condit ions:

- The TOP must be appl ied to a FOS.

- Datum references are required. The datum references must ensure

repeatab le measurements of the to leranced FOS.

- Basic d imensions must be used to establ ish the t rue posi t ion of the

to leranced FOS f rom the datums referenced (and between features of

s ize in a pat tern).

I f any of these condi t ions are not fu l f i l led, the TOP speci f icat ion is incorrect or

incomplete. F igure 8.6 shows a speci f icat ion f lowchart for a TOP speci f icat ion.

*Except for coax ia l non-opposed d iameters, as shown in F igure 8.5

The defaul t condi t ion for a TOP contro l is RFS, which is very expensive

and of ten not requi red. For each TOP contro l , considerat ion should be

given to us ing the MMC or LMC modif ier .

28

Top Using a Projected Tolerance Zone

When dimensioning threaded holes (or press – f i t holes) , considerat ion must be

g iven to the var ia t ion in perpendicu lar ly of the ax is of the ho le re la t ive to the

mat ing face of the assembly. The squareness error of the fastener (or press –

f i t p in) may resul t in an in ter ference condi t ion wi th the mat ing par t . F igure 8.7

shows as example. An in ter ference condi t ion can occur where a pos i t ion

to lerance is speci f ied for the hole, and the hole is t ipped wi th in the posi t ion

to lerance zone. When the fastener is p laced in the hole, the or ientat ion of the

fastener may resul t in an in ter ference condi t ion near the head of the fastener .

This condi t ion is common wi th f ixed fastener appl icat ions. Where there is

concern that an in ter ference condi t ion may ex is t , due to the or ientat ion of the

fastener , a pro jected to lerance zone modi f ier should be used.

TOP Using a projected Tolerance Zone

- Where a pro jected to lerance zone is used, the to lerance zone is

pro jected above the par t sur face.

- The symbol for the pro jected to lerance zone modi f ier is P .

- A pro jected to lerance zone is used to l imi t the perpendicu lar i ty of a

hole to ensure assembly wi th the mat ing par t .

A ru le of thumb in bo l ted jo in t appl icat ion whenever the height of the

c learance ho le is greater than the depth of the threaded ho le, a pro jected

to lerance zone modi f ier should be speci f ied.

29

A projected to lerance zone i s a to lerance zone that is pro jec ted above the par t

sur face. A pro jected to lerance zone ex is ts whenever the pro jected to lerance

zone modi f ier is speci f ied. The pro jected to lerance zone symbol is a "p"

enclosed in a c i rc le. Where a pro jected to lerance zone is speci f ied, the

to lerance zone is pro jected above the par t sur face.

Figure 8.8 i l lust rates the appl icat ion of a TOP using a pro jected to lerance zone.

The symbol for pro jected to lerance zone is shown, then the height for the

pro jected to lerance zone is speci f ied. The height for the pro jected to lerance

zone is a min imum and should be equal to the max. th ickness of the mat ing

par t . The d i rect ion and height of the pro jected to leranced zone are i l lus t rated.

By us ing a pro jected to lerance zone, the or ientat ion of the fasteners is l imi ted,

which ensure assembly of the mat ing par t . When us ing the f ixed fastener

formula, spec i fy ing a pro jected to lerance zone wi l l ensure that f ixed fasteners

wi l l not in ter fere wi th the c learance holes of mat ing par t .

The use of the pro jected to lerance zone modi f ier is not necessary when the

height of the mat ing par t is th in , as in sheet meta l .

30

CONCENTRICITY

DefinitionConcentricity is the condi t ion where the median points of a l l d iametr ica l ly

opposed e lements of a cy l inder (or a sur face of revolut ion) are congruent wi th

the ax is of a datum feature. A median point is the midpoint of a two-point

measurement .

A concentricity control is a geometr ic to lerance that l imi ts the concentr ic i ty

er ror of a par t feature. The to lerance zone for a concentr ic i ty cont ro l is three-

d imensional ; i t is a cy l inder that is coax ia l w i th the datum ax is . The d iameter of

the cy l inder is equal to the concent r ic i ty cont ro l to lerance va lue. The median

points of cor respondingly located e lements of the feature being cont ro l led,

regard less of feature s ize, must l ie wi th in the cy l indr ica l to lerance zone. When

using a concentr ic i ty contro l , the speci f ied to lerance and the datum references

always apply on RFS basis .

An example of a concentr ic i ty to lerance zone is shown in F igure 8.9.

Concentricity

- The to lerance zone is a cy l inder centered about the datum ax is .

- The median points of the to leranced feature must be wi th in the

to lerance zone.

31

Concentricity Application

In industry concentr ic i ty contro ls are only used in a few unique appl icat ions.

Concentr ic i ty is used when a pr imary considerat ion is prec ise balance of the

part , equal wal l th ickness or another funct ional requi rement that ca l ls for equal

d is t r ibut ion of mass. The to lerance FOS may conta in f la ts or be lobed and st i l l

be perfect ly concentr ic . Before us ing a concentr ic i ty contro l , the use of

to lerance of posi t ion or runout should be considered. When speci fy ing

concentr ic i ty , the form of the to leranced d iameter is a l lowed to vary to a

greater extent than i f a runout contro l was used. In F igure 8.10, a concentr ic i ty

cont ro l is appl ied to a d iameter .

When concentr ic i ty is appl ied to a d iameter , the fo l lowing condi t ions apply :

- The d iameter must meet i ts s ize and Rule # 1 requi rements.

- The concentr ic i ty contro l to lerance zone is a cy l inder that is coaxia l wi th a

datum ax is .

- The to lerance va lue def ines the d iameter of the to lerance zone.

- A l l median points of the to leranced d iameter must be wi th in the to lerance

zone.

The maximum poss ib le d is tance between the median points of the to leranced

diameter and the datum ax is is ha l f the concent r ic i ty to lerance va lue.

Fi rs t consider us ing TOP at MMC to def ine a coaxia l re lat ionship on a par t .

TOP is less expensive to produce and to inspect .

32

Differences Between Concentricity, Runout and TOP (RFS)

When d imensioning coaxia l d iameters, severa l geometr ic contro ls can be used.

On a par t that ro tates around and ax is , three geometr ic cont ro ls are common.

The designer can choose between concentr ic i ty , tota l rubout and TOP (RFS).

The chart in f igure 8.11 shows a compar ison between th is contro l .

GEOMETRIC CONTROLCONCEPT

CONCENTRICITY TOTAL RUNOUT TOP(RFS )

Tolerance zone Cyl inder Two coaxia lcy l inders

Cyl inder

Tolerance zoneappl ies to…

Median points ofto leranceddiameter

Surface e lementsof a to leranced

diameter

Axis of theAME of theto leranceddiameter

Relat ive cost toproduce

## ### #

Relat ive cost toinspect

### ## #

Part character ist icsbeing control led

Locat ion andor ientat ion

Locat ion,or ientat ion and

form

Locat ionand

or ientat ion

F IGURE 8 .11 D i f f e rences Be tween Concen t r i c i t y , Runou t , and TOP

Differences Between concentricity and runout

Two d i f ferences between rubout and concentr ic i ty are:

1. The shape of the to lerance zone

2. Runout affects form

One di f ference between TOP (RFS) and concentr ic i ty is :

- With TOP the ax is of the AME must be wi th in the to lerance Zone. With

concentr ic i ty , the median points of the Toleranced d iameter must be

wi th in the to lerance zone.

AS a ru le of thumb, Runout and Concentr ic i ty should only be considered onpar ts that ro tate.

33

Specification Test for a Concentricity Control.For a concentr ic i ty contro l to be a speci f icat ion, i t must sat is fy the fo l lowing

condit ions:

- The feature cont ro l f rame must be appl ied to a sur face revolut ion that

is coax ia l to the datum ax is .

- Datum references are requi red. The datum references must ensure that a

legal datum ax is is establ ished.

- The DIA. Symbol must be shown in the to lerance por t ion of the feature

contro l f rame.

- The M L T P modi f iers may not be used in the feature cont ro l f rame.

I f any of these condi t ions are not fu l f i l led, the concentr ic i ty speci f icat ion is

incorrect or incomplete. F igure 8.12 shows a speci f icat ion f lowchart for a

concentr ic i ty contro l .

34

SYMMETRY CONTROL

Symmetry is s imi lar to concentr ic i ty . The d i f ference is that , whi le concentr ic i ty

is used on surface of revolut ion, symmetry is used on p lanar features of s ize.

DefinitionSymmetry i s the condi t ion where the median po ints of a l l opposed e lements of

two or more feature sur faces are congruent wi th the ax is or centerp lane of a

datum feature. A summitry control is a geometr ic to lerance that l imi ts the

symmetry er ror of a par t feature. A symmetry cont ro l may on ly be appl ied to

par t features that are shown symmetr ica l to the datum centerp lane. The

to lerance zone is centered about the datum centerp lane. The width between the

p lanes is equal to the symmetry cont ro l to lerance va lue. The median po in ts

must l ie wi th in the para l le l p lane to lerance zone, regard less of feature s ize.

When using a symmetry contro l , the speci f ied to lerance and the datum

references must a lways be appl ied on RFS basis . An example of a symmetry

contro l to lerance zone is shown in f igure 8.13.

Symmetry Control

- The to lerance zone is two para l le l p lanes centered about a datum ax is or

centerp lane.

- The median points of the to lerance feature must be wi th in the to lerance

zone.

35

Symmetry Application

Symmetry contro ls are only used in a few unique appl icat ions in indust ry .

Symmetry is used when a pr imary cons iderat ion of symmetr ica l feature is

prec ise balance of the par t , equal wal l th ickness or another funct ional

requi rement that ca l ls for equal d is t r ibut ion of par t mass. Otherwise, TOP is

recommended to contro l symmetr ica l re lat ionships. In F igure 8.14, a symmetry

contro l is appl ied to a s lo t . When symmetry is appl ied to a s lo t , the fo l lowing

condi t ions apply :

- The s lot must meet i ts s ize and Rule # 1 requirements.

- The symmetry cont ro l to lerance zone is two para l le l p lanes that are

centered about the datum centerp lane.

- The to lerance va lve of the symmetry cont ro l def ines the d is tance between

the para l le l p lanes.

- Al l the median points of the to lerance s lot must be wi th in the to lerance

zone.

The maximum poss ib le d is tance between the median points of the to lerance

feature and the datum centerp lane is ha l f the symmetry to lerance va lue.

36

Differences Between Symmetry and TOP (RFS)

Symmetry and to lerance of pos i t ion (RFS) are two geometr ic cont ro ls that can

be used to to lerance symmetr ica l par t features. Of ten confus ion ex is ts over

which contro l is best to use in a g iven s i tuat ion. Understanding d i f ferences

between these contro ls wi l l he lp to e l iminate the confus ion over choosing a

symbol in a par t appl icat ion.

Symmetry cont ro ls the locat ion of the median points of a par t feature. TOP

contro ls the locat ion of the centerp lane of the actua l mat ing envelope of a par t

feature. IN genera l , TOP is considered a more economical to lerance to produce

and to ver i fy . F igure 8.15 shows a compar ison between symmetry and TOP

(RFS).

GEOMETRIC CONTROLCONCEPT

SYMMETRY TOP(RFS)

Tolerance zone Two para l le l p lanes Two para l le l p lanes

Tolerance zone

appl ies to…

Median points of

to leranced FOS

The centerplane of the

AME

Types of part

character ist ics

being control led

Orientat ion and

locat ion

Orientat ion and

locat ion

Relat ive cost to

produce

### ##

Relat ive cost to

inspect

### ##

F I G U R E 8 . 1 5 D i f f e r e n c e B e t w e e n S y m m e t r y a n d T O P

37

Specification Test for a Symmetry ControlFor a symmetry contro l to be a legal speci f icat ion, i t must sat is fy the fo l lowing

condit ions:

- The feature cont ro l f rame must be appl ied to a p laner FOS that is

symmetr ica l about the datum centerp lane.

- Datum references are requi red. The datum references must ensure that a

legal datum centerp lane is establ ished.

- No modi f iers may be used in the feature contro l f rame.

I f any of these condi t ions are not fu l f i l led, the symmetry speci f icat ion is

incorrect or incomplete. F igure 8.16 shows a legal speci f icat ion f lowchart for a

symmetry cont ro l .

39

PERPENDICULARITY

DefinitionPerpendicularity is the condi t ion that resul ts when a surface, ax is or

centerp lane is exact ly 90 degree to a datum. A perpendicularity control is a

geometr ic to lerance that l imi ts the amount a sur face, ax is or centerp lane is

permi t ted to vary f rom being perpendicu lar to the datum.

Perpendicularity Tolerance Zones

The two common to lerance zones for a perpendicu lar i ty cont ro l are:

1. The para l le l p lanes.

2. A cyl inder.

Perpendicularity Applications

Most perpendicu lar i ty appl icat ions fa l l in to one of three genera l cases:

1. Perpendicu lar i ty appl ied to a sur face.

2. Perpendicu lar i ty appl ied to a p laner FOS.

3. Perpendicu lar i ty appl ied to a cy l indr ica l FOS.

In F igure 8.17, a perpendicular i ty contro l is appl ied to a sur face. In th is

appl icat ion, the perpendicu lar i ty contro l conta ins two datum references. When

two datum references are used in a perpendicu lar i ty contro l , the to lerance zone

is perpendicu lar to two datum planes.

40

In FIGURE 8.18, a perpendicular i ty contro l is appl ied to a surface. This is the

most common appl icat ion of perpendicu lar i ty . When perpendicu lar i ty is appl ied

to a sur face, the fo l lowing four condi t ion apply :

1. The shape of the to lerance zone is two para l le ls p lanes that are

perpendicu lar to the datum p lane.

2. The to lerance value of the perpendicu lar i ty contro l def ines the d is tance

between the to lerance zone p lanes.

3. A l l the e lements of the sur face must be wi th in the to lerance zone.

4. The Perpendicular i ty to lerance zone l imi ts the f la tness of the

to leranced feature.

Perpendicularity Applied to a Surface

- The shape of the to lerance zone is two para l le l p lanes that are

perpendicu lar to the datum p lane.

- The d is tance between the p lanes is equal to the perpendicu lar i ty

to lerance zone.

- A l l e lements of the to leranced surface must be wi th in the to lerance

zone.

- The Perpendicular i ty to lerance zone l imi ts the f la tness of the

to leranced feature.

41

In FIGURE 8.19, a perpendicular i ty contro l that conta ins the MMC modi f ier is

appl ied to a p laner FOS. This type of geometr ic contro l is of ten used to ensure

the funct ion of assembly. When perpendicu lar i ty is appl ied to a p laner FOS and

conta ins the MMC modi f ier , the fo l lowing condi t ions apply :

- The shape of the to lerance zone is two para l le l p lanes that are perpendicu lar

to the datum p lanes.

- The to lerance value of the perpendicu lar i ty contro l def ines the d is tance


- The center p lane of the AME of the FOS must be wi th in the to lerance zone.

- A bonus to lerance is permissib le.

- A f ixed gauge may be used to ver i fy the perpendicu lar i ty cont ro l .

42

Figure 8.20 shows a speci f icat ion f lowchart for a perpendicular i ty speci f icat ion.

This chart appl ies to RFS datum references only.

43

ANGULARITY

DefinitionAngularity is the condi t ion of a sur face, center p lane or ax is being exact ly at a

speci f ied angle. An angularity control is a geometr ic to lerance that l imi ts the

amount a sur face, ax is or centerp lane is permi t ted to very f rom i ts spec i f ied

angle .

Angularity Tolerance Zones

The two common to lerance zone shapes for an angular i ty cont ro l are:

1) Two para l le l p lanes

2) A cy l inder

Angularity Applications

Most angular i ty appl icat ions fa l l in to one of two genera l cases:

1) Angular i ty appl ied to a sur face, or

2) Angular i ty appl ied to a cy l indr ica l FOS

Angularity Applied To A Surface

- The shape of the to lerance zone is two para l le l p lanes.

- The to lerance zone is or iented re la t ive to the datum p lane wi th a bas ic

angle .

- Al l of the e lements of the surface must be wi th in the to lerance zone.

- The angular i ty to lerance zone a lso l imi ts the f la tness of the to lerance

surface.

When an angular i ty contro l is appl ied to a surface, the WCB of the to leranced

surface is not af fected. When an angular i ty contro l is appl ied to a FOS, the

WCB of the FOS is affected. The WCB of a FOS that is to leranced with an

or ientat ion cont ro l is or iented re la t ive to the datums spec i f ied.

44

In F igure 8.21, an angular i ty contro l is appl ied to a surface; th is is the most

common appl icat ion of angular i ty . In angular i ty appl icat ions, the par t feature

being cont ro l led must be d imensioned wi th a bas ic angle re la t ive to the datum

speci f ied. When angular i ty is appl ied to a sur face, the fo l lowing condi t ions

app ly :

- The shape of the to lerance zone is two para l le l p lanes.

- The angular i ty cont ro l to lerance va lue def ines the d is tance between the

to lerance zone p lanes.

- A l l the e lements of the sur face must be wi th in the to lerance zone.

- The to lerance zone is or iented re la t ive to the datum p lane by a bas ic

angle .

- The angular i ty to lerance zone a lso l imi ts the f la tness of the to leranced

surface.

45

In F igure 8.22, an angular i ty contro l is appl ied to a d iametr ica l FOS. Note the

use of the d iameter modi f ier in the to lerance por t ion of the feature cont ro l

f rame. When angular i ty is appl ied to a d iameter , i t cont ro ls the or ientat ion of

the ax is of the d iameter . In F igure 8.22, the fo l lowing condi t ions apply :

- The to lerance zone is a cy l inder .

- The angular i ty cont ro l to lerance va lue def ines the d iameter of the

to lerance cy l inder .

- The ax is of the to leranced feature must be wi th in the to lerance zone.

- The to lerance zone is or iented re la t ive to the datum p lane by a bas ic

angle .

- An impl ied 90 degree bas ic angle ex is ts in the other d i rect ion.

When angular i ty is appl ied to a hole, i t is usual ly used wi th two datum

references.

46

Specification Test for an Angularity ControlFor an angular i ty contro l to be a speci f icat ion, i t must sat is fy the fo l lowing

condi t ion:

- One or more datum planes, a datum ax is or centerp lane must be

referenced in the feature cont ro l f rame.

- I f i t is appl ied to a sur face, the pro jected to leranced zone, d iameter , MMC

and LMC modi f iers may not be used in the to lerance por t ion of the feature

contro l f rame. ( I f i t is appl ied to a FOS, modi f iers may be used.)

- A basic angle must be speci f ied re lat ive to the datums referenced.

- The to lerance va lue spec i f ied must be a ref inement of any other geometr ic

to lerances that cont ro l the angular i ty of the feature ( for example,

to lerance of pos i t ion, runout and prof i le) .

-

F igure 8.23 shows a speci f icat ion f lowchart for an angular i ty contro l . The chart

appl ies to RFS datum references only .

47

ParallelismThe two common to lerance zones for a para l le l ism cont ro l are:

1) Two para l le l p lanes

2) A cy l inder

The fo l lowing appl icat ions show th is to lerance zones and discuss thei r use.

Parallelism Applications

Most para l le l ism appl icat ions fa l l in to one of two genera l cases:

1) Para l le l ism appl ied to a sur face or

2) Para l le l ism appl ied to a d iameter (MMC)

In Figure 8.24, a paral le l ism contro l is appl ied to a surface. This is the most

common appl icat ion of para l le l ism. When paral le l ism is appl ied to a surface,

the fo l lowing condi t ions apply :

- The to lerance zone is two para l le l p lanes that are para l le l to the datum

plane.

- The to lerance zone is located wi th in the l imi ts of the s ize d imension.

- The to lerance value of the para l le l ism contro l def ines the d is tance


- A l l the e lements of the sur face must be wi th in the to lerance zone.

- The para l le l ism to lerance zone l imi ts the f la tness of the to leranced

feature.

48

Parallelism (at MMC) Applied to a FOS

- The to lerance zone is a cy l inder (or two para l le l p lanes) .

- The ax is (or centerp lane ) must be wi th in the to lerance zone.


- A f ixed gauge may be used to ver i fy the para l le l ism cont ro l .

The WCB of the FOS is affected.

49

Parallelism with the Tangent plane ModifierAnother use for a para l le l ism appl icat ion is wi th the tangent p lane modi f ier . The

tangent p lane modi f ier denotes that on ly the tangent p lane estab l ished by the

high points of the contro l led surfaces must be wi th in the paral le l ism to lerance

zone. When the tangent p lane modi f ier is used in para l le l ism cal louts, the

f latness of the to leranced surface is not contro l led. FIGURE 8.26 shows a

para l le l ism appl icat ion that uses the tangent p lane modi f ier . The fo l lowing


- The to lerance zone is two para l le l p lanes.

- The tangent p lane establ ished by the h igh points of the surface(s) must be

wi th in the 0.1 para l le l ism to lerance zone.

- The f la tness of the to leranced surface is not contro l led by the para l le l ism

control .

Parallelism with the Tangent Plane Modifier

When the tangent p lane modi f ier is used in a para l le l ism contro l :

- Only the tangent p lane of the to lerance surface must be wi th in the

para l le l ism to lerance zone.

- The f la tness of the surface is not contro l led by the paral le l ism cal lout .

In many cases, us ing the tangent p lane modi f ier can reduce manufactur ing

costs. When us ing an or ientat ion contro l , evaluate the requi rements for the

form of the surface. I f the f la tness to lerance could be greater than the

or ientat ion to lerance, cons ider us ing the tangent p lane modi f ier .

50

Specification Test for a Parallelism ControlFor a para l le l ism contro l to be a speci f icat ion, i t must sat is fy the fo l lowing

condi t ion:

- One or more datum planes, a datum ax is or centerp lane must be

referenced in the feature cont ro l f rame.

- I f i t is appl ied to a surface, the LMC or MMC modi f iers may not be used in

the to lerance por t ion of the feature cont ro l f rame.

- The to lerance va lue spec i f ied must be less than any other geometr ic

to lerances that cont ro l the para l le l ism of the feature ( for example,

to lerance of pos i t ion, runout and prof i le) .

F igure 8.27 shows a speci f icat ion f lowchart for a paral le l ism contro l .

51

FORM TOLERANCES

52

FLATNESS

DefinitionFlatness is the condi t ion of a sur face hav ing a l l o f i ts e lements in one p lane. A

f latness control is a geometr ic to lerance that l imi ts the amount of f la tness

error a sur face is a l lowed. The to lerance zone for a f la tness contro l is three-

dimensional . I t consists of two paral le l p lanes wi th in which a l l the surface

elements must l ie . The d is tance between the para l le l p lanes is equal to the

f la tness contro l to lerance value. F latness (as wel l as other form contro ls) is

measured by compar ing a sur face to i ts own t rue counter par t . In the case of

f la tness, the f i rs t p lane of the to lerance zone (a theoret ica l reference p lane) is

establ ished by contact ing the three h igh points of the contro l led surface. The

second p lane of the to lerance zone is para l le l to the f i rs t p lane and of fset by

the f la tness to lerance value. Al l the points of the contro l led sur face must l ie

wi th in the to lerance zone. An example of a f la tness to lerance zone is shown in

Figure 8.28

A f la tness contro l is a lways appl ied to a p lanar sur face. Therefore, a f la tness

contro l can never use an MMC or LMC modi f ier . These modi f iers can only be

used when a geometr ic contro l is appl ied to a feature of s ize. A lso, f la tness

cannot overr ide Rule#1. F la tness is a separate requi rement and ver i f ied

separate ly f rom the s ize to lerance and Rule#1 requi rements.

Flatness Tolerance Zone

A f la tness contro l to lerance zone is two para l le l p lanes spaced apar t by the

f la tness to lerance value. The f i rs t p lane of the to lerance zone is establ ished by

contact ing the three h igh points of the to leranced surface.

53

Rule#1’s Effects on Flatness

Whenever Rule#1 appl ies to a feature of s ize that consis ts of two para l le l

p lanes ( i .e . Tab or s lot ) , an automat ic ind i rect f la tness contro l ex is ts for both

surfaces. This indi rect contro l is a resul t of the interre lat ionship between

Rule#1(perfect form at MMC) and the s ize d imension. When the feature of s ize

is at MMC, Both surfaces must be perfect ly f lat . As the feature departs f rom

MMC, a f la tness error equal to the amount of the depar ture is a l lowed. Since

Rule#1 prov ides an automat ic ind i rect f la tness contro l , a f la tness contro l should

not be used unless i t is a ref inement of the d imensional l imi ts of the surface.

FIGURE 8.29 shows an example of the effects of Rule#1 on f latness.

Rule#1’s Effects on Flatness

Whenever Rule#1 appl ies to a p lanar FOS… …

- I t provides an automat ic indi rect f la tness contro l for both surfaces.

54

Indirect Flatness Controls

There are severa l geometr ic contro ls that can indi rect ly af fect the f la tness of a

sur face; they are Rule#1, perpendicu lar i ty , para l le l ism, angular i ty , to ta l runout ,

and prof i le of a surface. When any of these contro ls are used on a surface,

they a lso l imi t the f la tness of the surface. However, ind i rect form contro ls are

not inspected. I f i t is desi red to have the f la tness of a surface inspected, a

f latness contro l should be speci f ied on the drawing. I f a f la tness contro l is

spec i f ied, i ts to lerance va lue must be less than the to lerance va lue of any

indirect f latness controls that affect the surface.

Specification Test for a Flatness Control

For a f la tness contro l to be a legal speci f icat ion, i t must sat is fy the fo l lowing

condit ions:

- No datum references can be speci f ied in the feature contro l f rame.

- No modi f iers can be speci f ied in the feature contro l f rame.

- The contro l must be appl ied to a p lanar surface.

- The f la tness cont ro l to lerance va lue must be less than any other

geometr ic contro l that l imi ts the f latness of the surface.

- The f la tness contro l to lerance value must be less than the s ize to lerance

associated wi th the surface.

-

F igure 8.30 shows a speci f icat ion f lowchart for a f latness contro l .

55

STRAIGHTNESS AS A SURFACE ELEMENT CONTROL

Definition

Straightness of a l ine element i s the condi t ion where each l ine e lement (or ax is

or centerp lane) is a s t ra ight l ine. A straightness control d irected to a surface i s

a geometr ic to lerance that l imi ts the amount of s t ra ightness er ror a l lowed in

each surface l ine e lement. The to lerance zone for a st ra ightness contro l (as a

surface l ine e lement contro l ) is two-d imensional ; i t consis ts of two para l le l l ines

for each l ine e lement of the sur face. The d is tance between the para l le l l ines is

equal to the s t ra ightness to lerance va lue. The f i rs t l ine e lement of the to lerance

zone is establ ished by the two h igh points of a l ine e lement of a sur face. The

second l ine e lement of the to lerance zone is para l le l to the f i rs t l ine e lement

and of fset by the st ra ightness to lerance value. A st ra ightness to lerance zone

may be located anywhere between the d imensional l imi ts of the sur face. A l l the

points of each cont ro l led l ine e lement must l ie wi th in the to lerance zone.

When st ra ightness is appl ied to surface e lements, the MMC or LMC modif iers

are not used. An example of s t ra ightness as a sur face l ine e lement’s contro l is

shown in F igure 8.31

Straightness of a Line Element

The to lerance zone for a s t ra ightness contro l appl ied to sur face e lements is

two para l le l l ines spaced apar t a d is tance equal to the s t ra ightness

to le rance va lue.

56

In F igure 8.32 , the st ra ightness contro l is appl ied to the surface e lement of the

pin. When st ra ightness is appl ied as a surface e lement contro l the fo l lowing


- The to lerance zone appl ies to the sur face e lements.

- The to lerance zone is two para l le l l ines.

- Rule #1 appl ies.

- The outer / inner boundary is not af fected.

- No modif iers may be speci f ied.

- The to lerance va lue speci f ied must be less than the s ize to lerance.

Rule #1’s Effects on Surface Straightness

Whenever Rule #1 is in ef fect , an automat ic indi rect s t ra ightness contro l ex is ts

for the surface l ine e lements. This indi rect contro l is a resul t of the

inter re lat ionship between Rule #1 and the s ize d imension. When the feature of

s ize is at MMC, the l ine e lements must be perfect ly s t ra ight . As the FOS

departs f rom MMC, a s t ra ightness er ror equal to the amount of the depar ture is

a l lowed (see F igure 8.35) . S ince Rule #1 prov ides an automat ic ind i rect

st ra ightness contro l , a st ra ightness contro l should not be used unless i ts

to lerance va lue is less than the tota l s ize to lerance. F igure 8.32 shows an

example of the effects of Rule #1 on st ra ightness.

Rule #1’s Effects on Straightness

Whenever Rule #1 appl ies to a Fos:

- I t provides an automat ic indi rect st ra ightness contro l for i ts surface

elements .

57

Specification Test for a Straightness Control Applied to Surface

ElementsFor a s t ra ightness contro l appl ied to sur face e lements to be a legal

speci f icat ion, i t must sat isfy the fo l lowing condi t ions:


- The contro l must be d i rected to the surface e lements.


- The st ra ightness contro l must be appl ied in the v iew where the contro l led

elements are shown as a l ine.

- The to lerance va lue spec i f ied must be less than any other geometr ic

contro ls that l imi t the form of the surface.

- The to lerance va lue speci f ied must be less than the s ize to lerance.

Figure 8.33 shows a speci f icat ion f lowchart for a st ra ightness contro l appl ied to

surface elements.

58

STRAIGHTNESS AS AN AXIS OR CENTERPLANE CONTROL

How to Determine When a Straightness Control Applies to a FOS

A st ra ightness contro l is the only form contro l that can be appl ied to e i ther a

surface or a feature of s ize. The interpretat ion of a s t ra ightness contro l appl ied

to a FOS is s igni f f icant ly d i f ferent f rom a st ra ightness contro l appl ied to a

surface. When a st ra ightness contro l is appl ied to a FOS, the fo l lowing


- The to lerance zone appl ies to the ax is or centerp lane of the FOS.

- Rule #1 is overr idden.

- The v i r tua l condi t ion or outer / inner boundary of the FOS is af fected.

- The MMC or LMC modif iers may be used.

- The to lerance va lue spec i f ied may be greater than the s ize to lerance.

You can te l l i f a s t ra ightness contro l is appl ied to a feature or to a FOS by the

locat ion of the feature contro l f rame on the drawing. In F igure 8.34 A , the

stra ightness contro l is located so that i t is d i rected to the p in surface. The pin

surface is a feature; therefore, the symbol appl ies to the ( feature) surface

elements of the p in. In FIGURE 8.34 B , the stra ightness contro l is located so

that i t is re lated to a FOS dimension. In th is case, the symbol appl ies to a FOS.

Straightness of a FOS

Whenever a st ra ightness contro l is associated wi th a FOS dimension, i t

appl ies to the ax is or centerp lane of the FOS.

Definition of Straightness of as an Axis/Centerplane Control

59

Stra ightness of an ax is is the condi t ion where an ax is is a st ra ight l ine.

Stra ightness of a centerp lane is the condi t ion where each l ine e lement is a

st ra ight l ine. A st ra ightness contro l appl ied to a FOS is a geometr ic to lerance

that l imi ts the amount of s t ra ightness er ror a l lowed in the ax is or centerp lane.

When a st ra ightness contro l is appl ied to a d iameter , a d iameter symbol

modi f ier is shown in the to lerance por t ion of the feature contro l f rame, and the

to lerance zone is a cy l inder . The d iameter of the cy l inder is equal to the

stra ightness to lerance value. The ax is of the FOS must l ie wi th in the cy l indr ica l

to lerance zone. When a st ra ightness contro l is appl ied to a p lanar FOS, the

to lerance zone is two para l le l p lanes. Each l ine e lement of the centerp lane

must l ie wi th in the to lerance zone.

When a st ra ightness contro l is appl ied to a FOS, i t can be speci f ied at RFS (by

defaul t ) , a t MMC, or at LMC. Remember, RFS is automat ic when no modi f ier is

shown.

Straightness of a FOS

Whenever a st ra ightness contro l is associated wi th the s ize d imension of a

FOS, the fo l lowing condi t ions apply:

- The to lerance zone appl ies to the ax is or centerp lane.


- The v i r tua l condi t ion (outer or inner boundary) is af fected.

- MMC or LMC modif iers may be speci f ied.

- The to lerance va lue may be greater than the spec i f ied s ize to lerance.

Rule #1’s Effects on Straightness of a FOS

Whenever Rule #1 appl ies to a FOS, an automat ic s t ra ightness contro l ex is ts

for the ax is (or centerp lane) of the FOS. This automat ic contro l is a resul t of

the in ter re lat ionship between Rule #1 and the s ize d imension. When the FOS is

at MMC, the ax is (or centerp lane) must be perfect ly s t ra ight . As the FOS

departs f rom MMC, a s t ra ightness er ror equal to the amount of the depar ture is

a l lowed. F igure 8.35 shows an example of Rule #1’s effects on the axis of a

FOS. I f the st ra ightness provided by Rule #1 is suff ic ient for the appl icat ion,

there is no need to add a st ra ightness contro l .

60

Rule #1’s Effects on Straightness of a FOS

Whenever Rule #1 appl ies to a FOS… …

- I t prov ides an automat ic s t ra ightness contro l for the ax is or

centerp lane.

Straightness at MMC Application

A common reason for apply ing a st ra ightness contro l at MMC to a FOS on a

drawing is to insure the funct ion of assembly. Whenever the MMC modi f ier is

used in a st ra ightness contro l , i t means the stated to lerance appl ies when the

FOS is produced at MMC: ext ra to lerance is permiss ib le. As the FOS departs

f rom MMC towards LMC, a bonus to lerance becomes avai lab le . An example is

shown in Figure 8.36.

Straightness Effects of Rule #1

Stra ightness is the only geometr ic contro l that can overr ide Rule #1.

61

Whenever a s t ra ightness contro l is appl ied to a FOS at MMC, the fo l lowing


- The FOS must a lso be wi th in i ts s ize to lerance.

- St ra ightness contro l speci f ies a to lerance zone wi th in which the ax is or

centerp lane must l ie .



- The v i r tual condi t ion of the FOS is af fected.

- A f ixed gauge may be used to ver i fy the s t ra ightness.

An example of s t ra ightness appl ied to a centerp lane is shown in F igure 8.36

Straightness of a FOS at MMC

Whenever s t ra ightness is appl ied to a FOS at MMC, a bonus to lerance is

permissible.

62

Specification Test for Straightness Applied to a FOS

For a st ra ightness contro l appl ied to a FOS to be a speci f icat ion, i t must sat isfy

the fo l lowing condi t ions:


- The contro l must be associated wi th a feature of s ize d imension.

- I f appl ied to a cy l indr ica l FOS, a d iameter symbol should be speci f ied in

the to lerance por t ion of the feature cont ro l f rame.

- The contro l can not conta in the pro jected to lerance zone or tangent p lane

modi f ier .

- The to lerance va lue should be a ref inement of o ther geometr ic to lerances

that contro l the st ra ightness of the feature.

Figure 8.37 shows a speci f icat ion f lowchart for st ra ightness appl ied to a FOS.

63

CIRCULARITY

DefinitionCircularity is a condi t ion where a l l po ints of a sur face of revolut ion, at any

sect ion perpendicu lar to a common ax is , are equid is tant f rom that ax is .

Ci rcu lar i ty can be appl ied to any par t feature wi th a d iametr ica l ( round) cross

section.

A circularity control is a geometr ic to lerance that l imi ts the amount of

c i rcular i ty on a part surface. I t speci f ies that each c i rcular e lement of a

feature’s surface must l ie wi th in a to lerance zone of two coaxia l c i rc les. I t a lso

appl ies independent ly at each cross sect ion e lement and at a r ight angle to the

feature ax is . The radia l d is tance between the c i rc les is equal to the c i rcu lar i ty

cont ro l to lerance va lue. See F igure 8.38

A c i rcu lar i ty contro l can only be appl ied to a surface; therefore, MMC, LMC,

d iameter , pro jected to lerance zone or tangent p lane modi f iers are not used.

64

Rule #1’s Effects on CircularityWhenever Rule #1 appl ies to a FOS wi th a d iametr ica l cross sect ion, an

automat ic indi rect c i rcular i ty contro l ex ists for i ts surface. This indi rect contro l

is the resul t of the in ter re lat ionship between Rule #1 and the s ize d imension.

When a diameter is at MMC, i ts cross sect ion elements must be perfect ly

c i rcular . As a d iameter departs f rom MMC, a c i rcular i ty error is permiss ib le.

F igure 8.39 i l lust rates an example of how Rule #1 indi rect ly af fects c i rcu lar i ty .

F igure 8.39 i l lust rates that whenever a d iameter is cont ro l led by Rule #1, i ts

cross sect ion e lements must l ie between two coaxia l c i rc les, one equal to the

MMC of the d iameter , the second rad ia l ly smal ler by the s ize to lerance.

Therefore, a d iametr ica l d imension automat ica l ly rest r ic ts the c i rcu lar i ty of a

d iameter to be equal to i ts s ize to lerance.

Rule #1 as a Circularity Control

Whenever Rule #1 appl ies to a FOS wi th a d iametr ica l cross sect ion, i ts

c i rcu lar i ty is automat ica l ly rest r ic ted to be equal to be equal to i ts s ize

to lerance.

65

Circularity ApplicationA common reason for us ing a c i rcu lar i ty contro l on a drawing is to l imi t the

lobing (out of round) of a shaf t d iameter . In cer ta in cases, lobing of a shaf t

d iameter wi l l cause bear ings or bushings to fa i l premature ly . In F igure 8.40, the

c i rcu lar i ty cont ro l l imi ts the maximum al lowable amount of c i rcu lar i ty er ror of

the shaf t d iameter . In th is appl icat ion, the fo l lowing statements apply ;

- The d iameter must be wi th in i ts s ize to lerance.

- The c i rcu lar i ty contro l does not overr ide Rule #1.

- The c i rcu lar i ty contro l to lerance must be less than the s ize to lerance.

- The c i rcular i ty contro l does not af fect the outer boundary of the FOS.

66

Specification Test for a Circularity ControlFor a c i rcu lar i ty contro l to be a speci f icat ion, i t must sat is fy the fo l lowing

condit ions:



- The cont ro l must be appl ied to a d iametr ica l feature.

- The c i rcu lar i ty cont ro l to lerance va lue must be less than any other

geometr ic contro l that l imi ts the c i rcu lar i ty of the feature.

Figure 8.41 shows a speci f icat ion f lowchart for a c i rcular i ty contro l .

67

CYLINDRICITY

DefinitionCyl indr ic i ty is a condi t ion of a surface of revolut ion in which a l l points of the

surface are equid is tant f rom a common axis. A cy l indr ic i ty contro l is a

geometr ic to lerance that l imi ts the amount of cy l indr ic i ty er ror permi t ted on a

par t sur face. I t speci f ies a to lerance zone of two coaxia l cy l inders wi th in which

al l points of the surface must l ie . A cy l indr ic i ty contro l appl ies s imul taneously

to the ent i re sur face. The rad ia l d is tance between the two coax ia l cy l inders is

equal to the cy l indr ic i ty contro l to lerance va lue. A cy l indr ic i ty contro l is a

composi te contro l that l imi ts the c i rcular i ty , s t ra ightness and taper of a

d iameter s imul taneously . See F igure 8.42

A cy l indr ic i ty contro l can only be appl ied to a sur face; therefore, the MMC,

LMC, d iameter , pro jected to lerance zone or tangent p lane modi f iers are not

used.

68

Rule #1’s Effects on Cylindricity

Whenever Rule #1 appl ies to a cy l indr ica l FOS, an automat ic ind i rect

cy l indr ic i ty contro l ex ists for i ts surface. This indi rect contro l is the resul t of the

inter re la t ionship between Rule #1 and the s ize d imension. When the d iameter is

at MMC, i ts surface must be perfect ly cy l indr ical . As the d iameter departs f rom

MMC, a cy l indr ic i ty er ror is permiss ib le. F igure 8.43 i l lust rates an example of

how Rule #1 indi rect ly af fects cy l indr ic i ty .

F igure 8.43 i l lust rates that whenever a d iameter is cont ro l led by Rule #1, i ts

sur face must l ie between two coaxia l cy l inders, one equal to the MMC of the

diameter and the second rad ia l ly smal ler by the s ize to lerance. Therefore, a

d iametr ica l d imension automat ica l ly rest r ic ts the cy l indr ic i ty of a d iameter to be

equal to i ts s ize to lerance.

Rule #1 as Cylindricity Control

Whenever Rule #1 appl ies to a cy l indr ica l FOS, i ts cy l indr ic i ty is

automat ica l ly rest r ic ted to be equal to i ts s ize to lerance.

69

Cylindricity ApplicationA common reason for a cy l indr ic i ty contro l to be used on a drawing is to l imi t

the surface condi t ions (out of round, taper and stra ightness ) of a shaft

d iameter. In cer ta in cases, surface condi t ions of a shaft d iameter wi l l cause

bear ings or bushings to fa i l premature ly . In F igure 8.44, the cy l indr ic i ty contro l

l imi ts the maximum al lowable cy l indr ic i ty er ror of the shaf t d iameter . In th is

appl icat ion, the fo l lowing s tatements apply :

- The d iameter must a lso be wi th in i ts s ize to lerance.

- The cy l indr ic i ty cont ro l does not overr ide Rule #1.

- The cy l indr ic i ty contro l to lerance must be less than the tota l s ize

to lerance.

- The cy l indr ic i ty contro l does not af fect the outer boundary of the FOS.

Indirect Cylindricity Controls

There are severa l geometr ic contro ls that can ind i rect ly af fect the cy l indr ic i ty of

a d iameter ; they are Rule #1, prof i le of a sur face and tota l runout . When any of

these contro ls are used on a d iameter , they a lso l imi t the cy l indr ic i ty of the

diameter . However , ind i rect cy l indr ic i ty contro ls are not inspected. I f i t is

des i red to have cy l indr ic i ty of a d iameter inspected, a cy l indr ic i ty cont ro l should

be speci f ied. I f a cy l indr ic i ty contro l is speci f ied, i ts to lerance value must be

less than the to lerance value of any ind i rect cy l indr ic i ty contro ls that af fect the

d iameter .

70

Specification Test for a Cylindricity ControlFor a cy l indr ic i ty contro l to be a speci f icat ion, i t must sat is fy the fo l lowing

condit ions:



- The contro l must be appl ied to a cy l indr ica l feature.

- The cy l indr ic i ty cont ro l to lerance va lue must be less than any other

geometr ic contro l that l imi ts the cy l indr ic i ty of the feature.

Figure 8.45 shows a speci f icat ion f lowchart for a cy l indr ic i ty contro l .

71

IMPLIED DATUMS

DefinitionAn impl ied datum is an assumed p lane, ax is or point f rom which a d imensional

measurement is made. Impl ied datums are an o ld concept f rom coord inate

to lerancing. An example of impl ied datums is shown in F igure 8.46. In th is

f igure, the bot tom and lef t s ides of the b lock are considered impl ied datums.

Shortcomings of Implied Datums

Impl ied datums have two major shor tcomings. F i rs t , they do not c lear ly

communicate to the drawing user which surface should contact the inspect ion

equipment. When the drawing does not c lear ly speci fy which surfaces are to

contact the inspect ion equipment, the inspector must make an assumpt ion.

Second, impl ied datums do not communicate to the drawing user in which

sequence the par t should be brought in to contact wi th the inspect ion

equipment. I f the order is not c lear ly speci f ied, each inspector could assume a

di f ferent sequence. Each sequence would then produce di f ferent resul ts for the

part measurements. F igure 8.46 i l lust rates th is problem.

72

Consequences of Implied Datums

The use of impl ied datums resul ts in two consequences:

- Good par ts are re jected.

- Bad parts are accepted.

The use of impl ied datums requi res the inspector to assume which par t surfaces

should contact the inspect ion equipment and in what sequence. A par t that is to

speci f icat ion when measured proper ly may be re jected when measured f rom the

wrong surfaces or when using the wrong sequence. Also, a part that would be

out of speci f icat ion when measured proper ly may pass inspect ion when

measured f rom the wrong surfaces or using the wrong sequence.

PLANAR DATUMS

General Information on Datums

A datum is a theoret ica l ly exact p lane, po int or ax is f rom which a d imensional

measurement is made. A datum feature is a par t feature that contacts a datum.

A planar datum i s the t rue geometr ic counterpar t of a p lanar datum feature. A

t rue geometr ic counterpart i s the theoret ica l per fect boundary or best f i t

tangent p lane of a spec i f ied datum feature.

Depending upon the type of datum feature, a t rue geometr ic counterpar t may

be:

- A tangent p lane contact ing the h igh points of a surface.

- A maximum mater ia l condi t ion boundary.

- A least mater ia l condi t ion boundary.

- A v i r tua l condi t ion boundary.

- An actua l mat ing enve lope.

- A mathemat ica l ly def ined contour .

- A worst-case boundary.

Datum Features and Datum

- Datum features are par t features and they ex is t on the par t .

- A datum feature s imulator is the inspect ion equipment that inc ludes the

gauge e lements used to estab l ish a s imulated datum.

- Datums are theoret ica l reference p lanes, po ints or axes and are

s imulated by the inspect ion equipment .

- For pract ica l purpose, a s imulated datum is considered a datum.

Datum Feature Symbol

73

The symbol used to speci fy a datum feature on a drawing is shown in F igure

8.47. I t is ca l led the datum feature symbol . The method of at taching th is symbol

to a par t feature determines i f i t des ignates a p lanar datum or a FOS datum.

Figure 8.47 shows four ways of d isp lay ing the datum feature symbol to denote a

p lanar datum.

74

Referencing Datums in Feature Control Frames

After datums are speci f ied, the drawing must a lso communicate when and how

the datum should be used. This is typ ica l ly done through the use of feature

contro l f rames. When feature contro l f rames are speci f ied, they reference the

datums to be used for the i r measurement . For example, in F igure 8.48, the bo l t

ho les are to leranced re la t ive to the Datums through the use of a geometr ic

to lerance. Since the par t is c lamped against surface A, surface A wi l l establ ish

the or ientat ion of the par t in space and is referenced as the pr imary datum. The

part is located by the p i lo t d iameter ; therefore, i t is referenced as the

secondary datum.

When feature contro l f rames reference datums, they a lso speci fy the sequence

for contact ing the par t to the datums referenced. The sequence is determined

by reading the feature contro l f rame f rom the lef t . The f i rs t compartment that

conta ins a datum reference denotes the datum feature that is to contact the

inspect ion equipment f i rs t . The second compartment that conta ins a datum

reference denotes the datum feature that is to contact the inspect ion equipment

th i rd. F igure 8.48 shows an example of how to in terpret the datum sequence in

a feature cont ro l f rame.

75

Datum-Related Versus FOS Dimensions

Only d imensions that are re la ted to a datum reference f rame through geometr ic

to lerances should be measured in a datum reference f rame. I f a d imension is

not assoc iated to a datum reference f rame wi th a geometr ic to lerance, then

there is no spec i f icat ion on how to locate the par t in the datum reference f rame.

In F igure 8.49, the ho le locat ions are re la ted to the datum reference f rame, D

pr imary, E secondary and F ter t iary . Dur ing inspect ion of the ho le locat ion

dimensions, the par t should be mounted in datum reference f rame. The overa l l

d imensions are FOS dimensions. Dur ing inspect ion of the overal l d imension,

the par t should not be mounted in the datum reference f rame.

Datum-Related Dimensions

Only d imensions re lated to a datum reference f rame through the use of

geometr ic to lerances are to be measured in a datum reference f rame.

76

Inclined Datum Features

An inc l ined datum feature i s a datum feature that is a t an angle other than 90

degree, re la t ive to the other datum features. On par ts wi th datum features

(sur faces) at angles other than 90 deg. The datum reference f rame wi l l conta in

planes at the basic angle of the par t sur face. The par t shown in F igure 8.50 has

a sur face 60 deg. f rom datum feature A : th is surface is designated as datum

feature C . The datum reference f rame would have three perpendicu lar p lanes.

However , the inc l ined datum feature would have i ts datum feature s imulator

or iented at the basic angles shown on the drawing. For th is type of datum

reference f rame, the angle of the surface must be speci f ied as basic and the

surface is cont ro l led by a geometr ic to lerance.

Multiple Datum Reference Frames

In cer ta in cases, the funct ional requi rements of a par t ca l l for the par t to

conta in more than one datum reference f rame. A par t may have as many datum

references f rames as needed to def ine i ts funct ional re lat ionships. The datum

reference f rames may be at r ight angles or at angles other than 90 deg. Also, a

datum p lane may be used in more than one datum reference f rame. F igure 8.51

shows a par t wi th three datum reference f rames.

78

FOS DATUM FEATURES

Specifying an Axis or Centerplane as a Datum

A FOS is speci f ied as a datum feature by associat ing the datum ident i f icat ion

symbol wi th the FOS. When a FOS is speci f ied as a datum feature, i t resul ts in

an ax is or centerp lane as a datum. There are f ive common ways to spec i fy an

ax is or centerp lane as a datum. They are:

1. The datum ident i f icat ion symbol can be touching the sur face of a d iameter

to speci fy the ax is as a datum.(See Figure 8.52A)

2. The datum ident i f icat ion symbol can be touching the beginning of a leader

l ine of a FOS to speci fy an ax is datum. (See Figure 8.52B)

3. The datum ident i f icat ion symbol can be touching a feature contro l f rame to

speci fy an ax is or centerp lane as a datum. (See F igure 8.52 C)

4. The datum ident i f icat ion symbol can be in l ine wi th a d imension l ine and

touching the extens ion l ine on the opposi te s ide of the d imension l ine

arrowhead of a FOS to spec i fy an ax is or a centerp lane as a datum. (See

Figure 8.52 D)

5. The datum ident i f icat ion symbol can replace one s ide of the d imension l ine

and ar rowhead. When the d imension l ine is p laced outs ide the extens ion

l ines of a FOS dimension, i t speci f ies an ax is or centerp lane as a datum.

(See Figure 8.52 E)

79

PROFILE

A profi le i s the out l ine of a par t feature in a g iven p lane. A true profi le is the

exact prof i le of a par t feature as descr ibed by basic d imensions. A prof i le

control is a geometr ic to lerance that speci f ies a uni form boundary a long the

true prof i le that the e lements of the surface must l ie wi th in. A prof i le of a l ine

contro l is a type of prof i le cont ro l that appl ies to l ine e lements of the to leranced

surface. F igure 8.53 i l lust rates these terms. Whenever a prof i le contro l is used,

i t is associated wi th a t rue prof i le (a surface def ined wi th basic d imension). The

t rue prof i le may be located wi th bas ic or to leranced d imensions re la t ive to the

datums referenced in the prof i le contro l .

Profile Tolerance Zone Coverage

- A prof i le contro l to lerance zone (sur face or l ine) appl ies only to the

surface to which the contro l is d i rected, unless extended by one of

the three methods shown below.

- The to lerance zone can be extended to cover addi t iona l sur faces by:

1 . the between symbol

2 . the a l l around symbol ; or

3. a note

81

PROFILE OF A SURFACEA prof i le of a surface control is a geometr ic to lerance that l imi ts the amount of

er ror a sur face can have re la t ive to i ts t rue prof i le . Common appl icat ions for

prof i le of a sur face contro ls inc lude contro l l ing--e i ther independent ly or in

combinat ion-- the s ize, locat ion, or ientat ion and form of :

- P lanar , curved or i r regular sur faces

- Po lygons

- Cy l inders, sur faces of revolut ion or cones

- Coplanar surfaces

Profile used to Tolerance a Surface Location

Figure 8.55 shows an example of prof i le cont ro ls used to to lerance the locat ion,

or ientat ion and form of a p lanar sur face. This is the most common appl icat ion

of prof i le . In th is appl icat ion, prof i le is appl ied to a p lanar surface, and the

fo l lowing condi t ions apply :

- The prof i le ca l lout is appl ied to a t rue prof i le .

- The t rue prof i le is re lated to the datums referenced wi th basic

dimensions.

- The to lerance zone is a uni form boundary centered around the t rue

prof i le .

- A l l e lements of the surface must be wi th in the to lerance zone

simul taneously .

- The to lerance zone l imi ts the locat ion, or ientat ion and form of the

surface.

82

Profile Used to Tolerance Coplanar Surfaces

A prof i le cont ro l may be used when i t is in tended to t reat two or more coplanar

surfaces as a s ingle surface. In th is type of appl icat ion, the prof i le contro l is a

form contro l and does not use datum references; i t s imulates a f la tness contro l .

When prof i le is used as a form contro l , the to lerance zone is uni la tera l (away

from the impl ied sel f -datum).

When prof i le of a surface (as a form contro l ) is appl ied to coplanar surfaces, i t

contro ls the form of the surfaces as i f they were a s ingle surface. F igure 8.56

shows an example of prof i le appl ied to coplanar sur face. In th is appl icat ion, the


- The prof i le ca l lout is appl ied to a t rue prof i le . (An impl ied basic zero

between the sur faces establ ishes the t rue prof i le . )

- The number of sur faces being contro l led is designated next to the prof i le

ca l lout .

- The to lerance zone is a un i la tera l boundary extending away f rom the

impl ied datum. (The un i la tera l to lerance zone is automat ic wi th an

impl ied se l f -datum.)

- A l l e lements of the surfaces to which the to lerance appl ies must be wi th in

the prof i le to lerance zone.

- The prof i le to lerance zone l imi ts the form and coplanar i ty of the surfaces.

83

Specification Test for Profile of a SurfaceFor a prof i le of a surface contro l to be a speci f icat ion i t must sat isfy the

fol lowing condi t ions:

- The t rue prof i le must be def ined wi th basic d imensions or be a p lanar

surface ( or coplanar surfaces).

- No modi f iers may be d isp layed in the to lerance por t ion of the feature

contro l f rame.

- I f the t rue prof i le is located wi th to leranced d imension, the prof i le

to lerance must be a ref inement of the to lerance va lue of the d imensions.

Figure 8.57 shows a speci f icat ion f lowchart for a prof i le of a surface contro l .

* The MMC or LMC modif iers may be speci f ied in the datum references of a

prof i le contro l .

84

RUNOUT TOLERANCES

Definition of Circular RunoutCircular runout i s a composi te contro l that af fects the form, or ientat ion and

locat ion of c i rcu lar e lements ( ind iv idual ly ) of a par t feature re la t ive to a datum

axis . A circular runout control i s a geometr ic to lerance that l imi ts the amount of

c i rcu lar runout of a par t sur face. Ci rcu lar runout appl ies independent ly to each

ci rcu lar e lement of a d iameter . I t is refer red to as a composite control because

i t cont ro ls the form, locat ion and or ientat ion of a par t feature s imul taneously ( in

a s ingle gauge reading) . Ci rcu lar runout is f requent ly used to contro l the

locat ion of c i rcu lar e lements of a d iameter . When appl ied to a d iameter , i t

cont ro ls the form (c i rcu lar i ty ) and locat ion of the d iameter to a datum ax is .

Establishing A Datum Axis For Runout

There are three ways to estab l ish a datum ax is for a runout cont ro l .

They are:

1. A s ingle d iameter of suf f ic ient length

2. Two coaxia l d iameters a suf f ic ient d is tance apart to create a s ingle da tum ax is3. Sur face and a d iameter a t r ight angles

85

I f a d iameter is too shor t to establ ish an ax is for inspect ion the d iameter wi l l

not serve wel l as a pr imary datum feature in the funct ion of the par t .

Circular Runout Tolerance Zone

The to lerance zone for c i rcu lar runout is two coaxia l c i rc les that are located

on the datum ax is .

Verifying Circular RunoutIn F igure 8.59, a c i rcu lar runout contro l is appl ied to a d iameter . When ver i fy ing

th is d iameter , three separate checks should be made: the s ize of the d iameter ,

the Rule #1 boundary, and the runout of the d iameter . Chapter Two expla ins

how to check the s ize and Rule #1 boundary. Now we wi l l look at how to ver i fy

the runout requi rement .

One way a c i rcu lar runout contro l could be ver i f ied is shown in the lower hal f of

Figure 8.59. F i rs t , the part is mounted in a chuck or col let to establ ish datum

axis A, then a d ia l ind icator is p laced perpendicular to the surface of the

diameter being inspected. The par t is rotated 360 degree, and the tota l

ind icator reading (TIR) is the runout to lerance va lue for that c i rcu lar e lement .

The d ia l ind icator is moved to another locat ion on the d iameter , and another

ind icator reading is obta ined. The number of c i rcu lar e lements to be checked is

usual ly lef t to the inspector 's judgment.

86

Verifying Circular Runout

When ver i fy ing c i rcu lar runout , the runout to lerance va lue is the maximum dia l

indicator reading for the c i rcu lar e lement being checked.

Specification Test for a Runout Control

For a runout contro l appl ied to a d iameter to be a speci f icat ion, i t must sat is fy

the fo l lowing condi t ions:

- A datum must be referenced in the feature contro l f rame.

- Datums referenced must speci fy a proper datum axis.

- A runout contro l must be appl ied to a surface e lement that surrounds the

datum ax is .

- The runout contro l must be appl ied on an RFS basis.

- The runout contro l must not inc lude any modif iers.

F igure 8.60 shows a speci f icat ion f lowchart for a runout contro l appl ied to a

d iameter .

87

DefinitionTotal runout i s a composi te contro l af fect ing the form, or ientat ion, and locat ion

of a l l sur face e lements (s imul taneously) of a d iameter (or sur face) re lat ive to a

datum ax is . A total runout control is a geometr ic to lerance that l imi ts the

amount of to ta l runout of a sur face. I t appl ies to the ent i re length of a d iameter

s imul taneously. I t is referred to as a composi te contro l because i t af fects the

form, or ientat ion, and locat ion of a par t feature s imul taneously . Tota l runout is

f requent ly used to cont ro l the locat ion of a d iameter . when appl ied to a

diameter , i t contro ls the form (cy l indr ic i ty) , or ientat ion, and locat ion of the

d iameter re la t ive to a datum ax is .

When appl ied to a d iameter , the to lerance zone shape for a to ta l runout contro l

is eas i ly v isual ized; i t is two coaxia l cy l inders whose centers are located on the

datum ax is . The rad ia l d is tance between the cy l inders is equal to the runout

to lerance va lue. F igure 8.61 i l lus t ra tes the to lerance zone for to ta l runout .

88

Total Runout ApplicationFigure 8.62 i l lust rates a tota l runout appl icat ion. In th is appl icat ion, the


- The d iameter must meet i ts s ize requi rements.

- The WCB is affected (24.6+0.2=24.8).

- The runout contro l appl ies RFS.

- The runout appl ies s imul taneously to a l l e lements of the d iameter .

- The to lerance zone is two coax ia l cy l inders 0.2 apar t .

- The maximum possib le ax is of fset is 0.1

89

Figure 8.63 i l lust rates an appl icat ion of to ta l runout appl ied to a sur face that is

perpendicular to the datum axis . This type of appl icat ion is used to contro l the

squareness of a sur face to a datum axis . In th is appl icat ion, the fo l lowing


- The runout contro l appl ies RFS.

- The runout appl ies to a l l e lements of the sur face s imul taneously .

- The shape of the to lerance zone is two para l le l p lanes perpendicu lar to

the datum ax is .

- The runout symbol contro ls the angular re lat ionship (or ientat ion) of the

surface to the datum ax is .

- The runout contro l a lso l imi ts the f latness of the surface.

Legal Specification Test for Total RunoutThe legal speci f icat ion test for tota l runout is the same as the test for c i rcu lar

runout. The legal speci f icat ion f lowchart for c i rcular runout is shown Figure

8.60

90

(9) BACKGROUND OF GD&T

For about one hundred f i f ty years, a to leranc ing approach ca l led "coord inate

to leranc ing" was the predominant to leranc ing system used on engineer ing

drawings. Coordinate to lerancing is a d imensioning system where a par t feature

is located (or def ined)by means of rectangular d imensions wi th g iven

to lerances. An example of coord inate to leranc ing is shown in F igure 9.1.

SHORTCOMINGS OF COORDINATE TOLERANCINGCoordinate to leranc ing was very successfu l when companies were smal l ,

because i t was easy to ta lk to the machin is t to exp la in what the drawing in tent

was. Over the years, as companies grew in s ize, par ts were obta ined f rom

many sources. The abi l i ty for the designer and machin is t to communicate

di rect ly had d imin ished, and the shor tcomings of the coord inate to lerancing

sy stem became ev ident . Coord inate to leranc ing s imply does not have the

completeness to prec ise ly communicate the par t requi rements.

Coord inate to leranc ing conta ins three major shor tcomings. They are:

1. Square or rectangular to lerance zones.

2. F ixed-s ize to lerance zones

3. Ambiguous instruct ions for inspect ion

91

Coordinate Tolerancing and Square (or I l logical) Tolerance Zones

Let 's look at the coord inate to leranc ing shor tcomings in more depth. F i rs t , le t 's

examine the to lerance zone for the 8.0-8.4 d ia . ho le locat ions f rom the par t in

F igure 9.1. The hole locat ion to lerance zone is formed by the max. and min. of

the ver t ica l hor izonta l locat ion d imensions.

Figure 9.2 shows that a 0.5 square to lerance zone would be formed. The

i l log ica l aspect of a square to lerance zone is that the hole can be of f i ts

nominal locat ion in the d iagonal d i rect ions a greater d is tance than in the

ver t ica l and hor izonta l d i rect ions. A more log ica l and funct ional approach is to

a l low the same to lerance for a hole locat ion in a l l d i rect ions, creat ing a

cy l indr ica l to lerance zone.

Coordinate Tolerancing and Fixed-Size Tolerance Zones

Next , le t 's d iscuss how coordinate to lerancing uses f ixed-s ize to lerance zones.

The pr int speci f icat ion requi res the center of the hole to be wi th in a 0.5 square

to lerance zone, whether the hole is at i ts smal lest s ize l imi t or i ts largest s ize

l imi t . When the important funct ion of the holes is assembly, the hole locat ion is

most cr i t ica l when the hole is at i ts min imum l imi t of s ize. I f the actual hole s ize

larger than i ts min imum s ize l imi t , i ts locat ion to lerance can be correspondingly

larger wi thout af fect ing the part funct ion.

Square and f ixed-s ize to lerance zones can cause funct ional par ts to be

scrapped. Since coord inate to lerancing does not a l low for cy l indr ica l to lerance

zones or to lerance zones that increase wi th the ho le s ize, lengthy notes would

have to be added to a drawing to a l low for these condi t ions.

92

Coordinate Tolerancing andAmbiguous Instruction for Inspection

A th i rd major shor tcoming of coord inate to lerancing is that i t has ambiguous

instruct ion for inspect ion. F igure 9.3 shows two logical methods and inspector

could use to set up the part f rom Figure 9.1 for inspect ing the holes. The

inspector could rest the part on the face f i rs t , long s ide second and the short

s ide th i rd or the inspector could rest the part on the face f i rs t , the short s ide

second and the long s ide th i rd.

Because there are d i f ferent ways to hold the par t for inspect ion, two inspectors

could get d i f ferent measurements f rom the same part . This can resul t in two

problems: good par ts may be re jected or worse yet , bad par ts could be

accepted as good parts.

The problem is that the drawing does not communicate to the inspector which

surfaces should touch the gauging equipment f i rs t , second and th i rd. When

using coord inate to lerancing, addi t ional notes would be requi red to

communicate th is important informat ion to the inspector .

As you can see, coordinate to lerancing has some very s igni f icant shor tcomings.

That 's why i ts use is rapid ly d imin ishing in industry. However, coordinate

to leranc ing is not to ta l ly obsolete; i t does have some usefu l appl icat ions on

engineer ing drawings. The chart in F igure 9.4 shows appropr iate uses for

coord inate to lerances on engineer ing drawings.

Coordinate Dimension Usage

Type of Dimension Appropriate Use Poor Use

Size XChamfer XRadius XLocat ing Part Feature XContro l l ing AngularRelat ionship XDefin ing the Form of PartFeatures X

Figure 9.4 Appropr iate User for Coordinate Tolerancing.

93

THE GEOMETRIC DIMENSIONING ANDTOLERANCING SYSTEM

Definition

Geometr ic Dimensioning and Tolerancing (GD&T) i s an in ternat ional language

that is used on engineer ing drawings to accurate ly descr ibe a par t . The GD&T

language consists of a wel l -def ined set of symbols, ru les, def in i t ions and

convent ions. GD&T is a prec ise mathemat ica l language that can be used to

descr ibe the s ize, form, or ientat ion and locat ion of par t features. GD&T is a lso

a des ign phi losophy on how to des ign and d imension par ts . F igure 9.5 shows

an example of an engineer ing drawing that is to leranced wi th GD&T.

Design Philosophy of Geometric TolerancingGeometr ic to lerancing encourages a d imensioning phi losophy cal led " funct ional

d imensioning." Funct ional d imensioning i s a d imensioning phi losophy that

def ines a part based on how i t funct ions in the f inal product . The funct ional

d imensioning phi losophy is encouraged in many p laces throughout the Y14.5

standard. A l though funct ional d imensioning is the phi losophy, i t does not mean

the designer should design the component wi thout tak ing other factors in to

cons iderat ion. Many companies f ind i t a great advantages to use a process

cal led "s imul taneous engineer ing." Simultaneous engineer ing is a process

where design is a resul t of input f rom market ing, engineer ing, manufactur ing,

inspect ion, assembly and serv ice. S imul taneous engineer ing of ten resul ts in

bet ter product at lower cost .

94

GD&T BENEFITS

- Improves Communication

GD&T can provide uni formi ty in drawing speci f icat ions and interpretat ion,

thereby reducing controversy, guesswork and assumpt ions. Design,

product ion and inspect ion a l l work in the same language.

- Provides Better Product Design

The use of GD&T can improve your product designs by prov id ing

designers wi th the too ls to "say what they mean," and by fo l lowing the

funct ional d imensioning phi losophy.

- Increases Production Tolerances

There are two ways to lerances are increased through the use of GD&T.

First , under certa in condi t ions, GD&T prov ides "bonus" or ext ra to lerance

for manufactur ing. This addi t ional to lerance can make a s igni f icant

savings in product ion costs. Second, by the use of funct ional

d imensioning, the to lerances are ass igned to the par t based upon i ts

funct ional requi rements. This of ten resul ts in a larger to lerance for

manufactur ing. I t e l iminates the problems that resul t when designers

copy ex is t ing to lerances or ass ign t ight to lerances, because they don' t

know how to determine a reasonable ( funct iona l ) to lerance.

COMPARISON BETWEEN GD&T AND

COORDINATE TOLERANCINGSomet imes designers th ink that i t is faster to d imension a par t wi th coord inate

to lerancing than by us ing geometr ic to lerancing. This is not t rue. Let 's take the

drawing f rom Figure 9.1 and add geometr ic to lerances to e l iminate the major

shortcomings of the coordinate d imensions.

The f i rs t major shortcoming of coordinate to lerancing is "square to lerance

zones." Let 's look at how geometr ic to leranc ing e l iminates th is shor t coming. In

Figure 9.6, the arrow labeled "A" points to a GD&T symbol . This symbol

speci f ies a cy l indr ica l to lerance zone. The square to lerance zone f rom the

coord inate to leranced vers ion (F igure 9.1) is conver ted in to a cy l indr ica l

to lerance zone. Not ice that the to lerance va lue is larger than the 0.5 to lerance

al lowed in F igure 9.1.F igure 9.7 shows how the cy l indr ica l zone prov ides

addi t ional to lerance in compar ison wi th the square to lerance zone. The

addi t ional to lerance gained f rom us ing cy l indr ica l to lerance zones can reduce

manufactur ing costs.

95

The second major shor tcoming of coord inate to lerancing is " f ixed-s ize to lerance

zones." Let 's look at how geometr ic to leranc ing e l iminates th is shor tcoming. In

Figure 9.6 the arrow labeled "B" points to a GD&T symbol . This symbol

spec i f ies a to lerance zone that appl ies when the holes are the i r smal lest

d iameter . When the holes are larger , th is GD&T symbol a l lows the hole locat ion

to have addi t iona l to lerance. Th is addi t iona l to lerance a l lowed by the GD&T

symbol can reduce manufactur ing costs.

96

The th i rd major shor tcoming of coord inate to lerancing is that i t has "ambiguous

inst ruct ions for inspect ion." Let 's look at how geometr ic to leranc ing e l iminates

th is shortcoming. Geometr ic to lerancing conta ins a concept cal led the "datum

sy stem." The datum system al lows the designer to communicate the appropr iate

method of par t setup to the inspector . F i rs t , symbols are added to the drawing

to denote which surfaces touch the gauge. See Figure 9.6, ar rows labeled "C"

and "D." Then, ins ide the feature contro l f rame (see arrow labeled "E") , the

sequence is g iven for the inspector to address the par t to gage surfaces. Using

the geometr ic to lerancing speci f icat ions f rom Figure 9.6, the inspect ion method

would be the one shown in F igure 9.3A .

Now, through the use of geometr ic to lerancing, the d imensioning shor tcomings

are e l iminated. Let 's take a look at what the drawing would look l ike i f we t r ied

to accompl ish the same level of drawing completeness wi th coord inate

to lerancing. F igure 9.8 shows the v ise pad drawing f rom Figure 9.6. This t ime

the par t is d imensioned wi th coord inate d imensions to the same leve l of

completeness as the GD&T vers ion, but us ing words instead of symbols. Now,

which drawing do you th ink would be easier to create? When the goal is to

dimension both drawings to the same degree of completeness, i t is faster to

use geometr ic to lerances.

97

The d i f ferences between coord inate to leranc ing and geometr ic to leranc ing are

summar ized in F igure 9.9. When compar ing these to lerancing methods, i t is

easy to understand why geometr ic to lerancing is rep lac ing coord inate

to leranc ing.

DRAWING

CONCEPT

COORDINATE

TOLERANCING

GEOMETRIC

TOLERANCING

TOLERANCE

ZONE SHAPE

CONDITION

? Square or rec tangu lar to le rance

zones fo r ho le loca t ions

RESULTS

? Less to le rance ava i lab le fo r

ho le

? H igher manufactur ing costs

CONDITION

? Can use d iameter symbol to

a l low round to le rance zones

RESULTS

? 57% more to le rance fo r ho le

loca t ion

? Lower manufactur ing costs

TOLERANCE

ZONE

FLEXIBILITY

CONDITION

? To lerance zone is f ixed in s ize

RESULTS

? Funct iona l par ts scrapped

? H igher opera t ing costs

CONDITION

? Use of MMC modi f ie rs a l lows

to le rance zones to inc rease

under cer ta in cond i t ions

RESULTS

? Funct iona l par ts used

? Lower opera t ing cos ts

EASE OF

INSPECTION

CONDITION

? Imp l ied datum a l lows cho ices

for set up when inspect ing the

par t

RESULTS

? Mul t ip le inspectors may get

d i f ferent resu l ts

? Good par ts scrapped

? Bad par ts accepted

CONDITION

? The datum system communi -

cates one up for inspect ion

RESULTS

? C lear inst ruct ions for inspect ion

? E l iminates d isputes over par t

acceptance

Fig 9.9 Compar ison Between Coord inate Toleranc ing & Geometr ic Toleranc ing.

gd&t standard

Documents

combined feature control

feature o

tolerance value

tolerance portion

certain geometric symbols

datum feature symbolswhere

profile symbols

form symbols