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G E O M E T R I CD I M E N S I O N I N GA N DT O L E R A N C I N G

C H A P T E R O B J E C T I V E SUpon completion of this chapter students should be able to dothe following:

■ Describe what is meant by the term general t o l e r a n c i n g .

■ D e fine the concept geometric dimensioning and t o l e r a n c i n g .

■ Explain the purpose of a modifie r.

■ Distinguish between the concepts maximum materialcondition (MMC) and re g a rdless of feature size (RFS).

■ Explain the concept least material condition (LMC).

■ Describe what is meant by p rojected tolerance zone.

■ Make a sketch that illustrates the concept of datums.

■ Demonstrate how to establish datums.

■ Apply feature control symbols when dimensioningo b j e c t s .

■ Explain the concept of True position.

All around symbolA n g u l a r i t yBasic dimensionBetween symbolBilateral toleranceC i rc u l a r i t yC y l i n d r i c i t yD a t u mDatum featureDatum feature simulatorDatum feature symbolDatum planeDatum re f e rence frameDatum surf a c eDatum target symbolF e a t u re control symbolF l a t n e s sF ree-state variationGeometric dimensioningand tolerancingGeneral tolerancing Least material condition (LMC)Limit dimensioning

Maximum material condition (MMC)M o d i fie r sP a r a l l e l i s mP e r p e n d i c u l a r i t yPositional tolerancingP ro fil eP ro file of a lineP ro file of a surf a c eP rojected tolerancez o n eR e g a rdless of feature size (RFS)Rule #1R u n o u tSize toleranceStatistical tolerancings y m b o lS t r a i g h t n e s sTangent planeTo l e r a n c i n gTrue positionUnilateral toleranceVi rtual condition

C H A P T E R O U T L I N E Summary of geometric dimensioning and tolerancing

terms • Geometric dimensioning and tolerancingdefined • Modifiers • Feature control symbol

• True position • Circularity (roundness) • Cylindricity • Angularity • Parallelism • Perpendicularity

• Profile • Runout • Concentricity • Summary• Review questions • Problems

K E Y T E R M S

468

G e o m e t r i c D i m e n s i o n i n g a n d T o l e r a n c i n g 4 6 9

S u m m a ry of GeometricDimensioning and To l e r a n c i n gTe rm sActual Local Size. The value of any individual distanceat any cross section of a feature .

Actual Mating Size. The dimensional value of theactual mating envelope.

Actual Size. Actual measured size of a feature .

A l l o w a n c e . The diff e rence between the larger shaft sizelimit and the smallest hole size limit.

A n g u l a r i t y. Tolerancing of a feature at a specified angleother than 90 degrees from a re f e renced datum.

Basic Dimension. A theoretically “perfect” dimensionsimilar to a re f e rence or nominal dimension. It is used toidentify the exact location, size, shape, or orientation of af e a t u re. Associated tolerances are applied by notes, featurec o n t rol frame, or other methods, excluding tolerancewithin title blocks.

Bilateral To l e r a n c e s . Tolerances that are applied to anominal dimension in the positive and negative dire c t i o n s .

Bonus To l e r a n c e . The permitted allowable increase intolerance as the feature departs from the material conditioni d e n t i fied within the feature control frame.

C i rcular Runout. A tolerance that identifies an infin i t enumber of single circular elements measured at cro s ssections on a feature when the feature is rotated 360d e g rees for each cross section.

C i rc u l a r i t y. A tolerance that controls the circular cro s ssection of round features that is independent of otherf e a t u res. The tolerance zone boundary is formed by twoconcentric perfect circ l e s .

Clearance Fit. A condition between mating parts inwhich the internal part is always smaller than the extern a lp a rts it fits into.

C o a x i a l i t y. The condition of two or more feature shaving coincident axes.

Compound Datum Feature s . Two datum features usedto establish a datum or axis plane.

C o n c e n t r i c i t y. A tolerance in which the axis of a featuremust be coaxial to a specified datum re g a rdless of thed a t u m ’s and the feature ’s size. The lack of concentricity ise c c e n t r i c i t y.

C y l i n d r i c i t y. A tolerance that simultaneously contro l sa surface of revolution for straightness, parallelism, andc i rcularity of a feature, and is independent of any other fea-t u res on a part. The tolerance zone boundary is composedof two concentric perfect cylinders.

D a t u m . R e f e rence points, lines, planes, cylinders, andaxes which are assumed to be exact. They are establishedf rom datum feature s .

Datum Axis. The axis of a re f e renced datum feature suchas a hole or shaft.

Datum Feature . A feature which is used to establisha datum.

Datum Feature of Size. A feature that has size, such asa shaft, which is used to establish a datum.

Datum Identification Symbol. A special rectangular boxwhich contains the datum re f e rence letter and a dash oneither side of the letter. It is used to identify datum feature s .

Datum: Feature Simulator. A surface of adequatelyp recise form (such as a surface plate, a gage surface, or am a n d rel) contacting the datum feature(s) and used toestablish the simulated datum(s).

Datum: Refere n c e . Entering a datum re f e rence letter ina compartment of the feature control frame followingthe tolerance value.

Datum: Reference Frame. T h ree mutually perpendi-cular planes that establish a coordinate system. It is cre a t e dby datum re f e rences in a feature control frame or by a note.

Datum: Simulated. A point, axis, or plane established byp rocessing or inspection equipment, such as the following:s i m u l a t o r, surface plate, a gage surface, or a mandre l .

Datum Simulation. The use of a tool contacting adatum feature used to simulate a true geometric counter-p a rt of the feature .

Datum Simulator. A tool used to contact a datum feature .

Datum Ta rg e t . S p e c i fied points, lines, or areas on af e a t u re used to establish datums.

Datum Ta rget Are a . A specified area on a part that iscontacted to establish a datum.

Datum Ta rget Line. A line on a surface that is contactedto establish a datum.

Datum Ta rget Point. A specified point on a surface usedto establish a datum.

Datum Ta rget Symbol. A circle divided horizontallyinto halves containing a letter and number to identifydatum targ e t s .

Envelope, Actual Mating. The term is defined accord i n gto the type of features as follows:

( a ) For an External Feature. A similar perfect featurec o u n t e r p a rt of smallest size that can be circ u m-scribed about the features so that it just contacts thes u rface at the highest points. For example, a small-est cylinder of perfect form or two parallel planes

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of perfect form at minimum separation that justcontact(s) the highest points of the surf a c e ( s ) .

For features controlled by orientation or posi-tional tolerances, the actual mating envelope isorientated relative to the appropriate datum(s),for example, perpendicular to a primary datump l a n e .

( b ) For an Internal Feature. A similar perfect featurec o u n t e r p a rt of largest size that can be inscribedwithin the feature so that it just contacts the surf a c eat the highest points. For example, a largest cylin-der of perfect form or two parallel planes of perf e c tf o rm at maximum separation that just contact(s)the highest points of the surf a c e ( s ) .

For features controlled by orientation or posi-tional tolerance, the actual mating envelope is ori-ented relative to the appropriate datum(s).

F e a t u re . A component of a part such as a hole, slot,s u rface, pin, tab, or boss.

F e a t u re of Size. One cylindrical or spherical surface, ora set of two opposed elements or opposed parallel surf a c e s ,associated with a size dimension.

F e a t u re, Axis of. A straight line that coincides with theaxis of the true geometric counterpart of the specified fea-t u re .

F e a t u re, Center Plane of. A plane that coincides withthe center plane of the true geometric counterpart of thes p e c i fied feature .

F e a t u re, Derived Median Plane of. An imperfect plane(abstract) that passes through the center points of all linesegments bounded by the feature. These line segments aren o rmal to the actual mating envelope.

F e a t u re, Derived Median Line of. An imperfect line(abstract) that passes through the center points of all cro s ssections of the feature. These cross sections are normal tothe axis of the actual mating envelope. The cross sectioncenter points are determined as per ANSI B89.3.1.

F i t . A term used to describe the range of assembly thatresults from tolerances on two mating part s .

F l a t n e s s . A tolerance that controls the amount of vari-ation from the perfect plane on a feature independent ofany other features on the part .

F o rm To l e r a n c e . A tolerance that specifies the allowablevariation of a feature from its perfect form .

F ree-state Va r i a t i o n . The condition of a part that perm i t sits dimensional limits to vary after removal from manu-facturing or inspection equipment.

Least Material Condition (LMC). A condition of af e a t u re in which it contains the least amount of material

relative to the associated tolerances. Examples are maxi-mum hole diameter and minimum shaft diameter.

Limit Dimensions. A tolerancing method showingonly the maximum and minimum dimensions whichestablish the limits of a part size or location.

L i m i t s . The maximum and minimum allowable sizes ofa feature .

Location To l e r a n c e . A tolerance which specifies theallowable variation from the perfect location of a featurerelative to datums or other feature s .

Maximum Material Condition (MMC). A conditionin which the feature contains the maximum amount ofmaterial relative to the associated tolerances. Examples aremaximum shaft diameter and minimum hole diameter.

M o d i fie r. The application of MMC or LMC to alter then o rmally implied interpretation of a tolerance specific a t i o n .

P a r a l l e l i s m . A tolerance that controls the orientation ofi n t e rdependent surfaces and axes which must be of equaldistance from a datum plane or axis.

P e r p e n d i c u l a r i t y. A tolerance that controls surf a c e sand axes which must be at right angles with a re f e re n c e dd a t u m .

Position To l e r a n c e . A tolerance that controls the posi-tion of a feature relative to the true position specified forthe features, as related to a datum or datums.

P r i m a ry Datum. The first datum re f e rence in a featurec o n t rol frame. Normally is elected because it is mosti m p o rtant to the design criteria and function of thep a rt .

P ro file of a Line. A tolerance that controls the allow-able variation of line element in only one direction on as u rface along an elemental tolerance zone with re g a rd toa basic pro fil e .

P ro file of a Surf a c e . A tolerance that controls theallowable variation of a surface from a basic pro file orc o n fig u r a t i o n .

P ro file Tolerance Zone. A tolerance zone that can con-t rol the form of an individual feature and provide for acomposite control of form, orientation, and location.

P rojected Tolerance Zone. A tolerance zone that appliesto the location of an axis beyond the surface of the featurebeing contro l l e d .

R e f e rence Dimension. A non-tolerance zone or locationdimension used for information purposes only and doesnot govern production or inspection operations.

R e g a rdless of Feature Size (RFS). A condition of a tol-erance in which the tolerance must be met re g a rdless of thep roduced size of the feature .


R u n o u t . The composite surface variation from thed e s i red form of a part of revolution during full rotation ofthe part on a datum axis.

S e c o n d a ry Datum. The second datum re f e rence in af e a t u re control frame. Established after the primarydatum, it has less design influence and functionally.

Size, Vi rtual Condition. The actual value of the virt u a lcondition boundary.

S t r a i g h t n e s s . A tolerance that controls the allowablevariation of a surface or an axis from a theoretically per-fect line.

S y m m e t ry. A condition for which a feature (or feature s )is equally disposed or shaped about the center plane of adatum feature .

Tangent Plane. A theoretically exact plane derivedf rom the true geometric counterpart of the specified fea-t u re surface by contacting the high points on the surf a c e .

Te rt i a ry Datum. The third datum re f e rence in a featurec o n t rol frame. Established after the secondary datum, it hasthe least amount of design influence or functionality.

To l e r a n c e . The acceptable dimensional variation orallowance of a part .

Total Runout. A tolerance that provides for a compos-ite control of all surface elements as the part is rotated 360d e g rees about a datum axis.

Transition Fit. A condition in which the pre s c r i b e dlimits of mating parts produce either a clearance or ani n t e rf e rence when the parts are assembled.

True Geometric Counterpart . The theoretically perf e c tb o u n d a ry (virtual condition or actual mating envelope) orb e s t - fit (tangent) plane of a specified datum feature .

True Position. The theoretically exact location of a feature .

Unilateral To l e r a n c e . A tolerance which allows variationsin only one dire c t i o n .

Vi rtual Condition. A constant boundary produced bythe combined effects of the maximum material conditionsize and geometric tolerance. It re p resents the worst casecondition of assembly at MMC.

Z e ro Tolerance at MMC or LMC. A tolerancing methodw h e re no tolerance is shown in the feature control frame.The tolerance allowed is totally dependent on the size ofthe feature depart u re from MMC or LMC.

GE N E R A L TO L E R A N C I N G

The industrial revolution created a need for mass pro-duction; assembling interchangeable parts on an assemblyline to turn out great quantities of a given finished pro d-uct. Interchangability of parts was the key. If a part i c u l a r

p roduct was composed of 100 parts, each individual partcould be produced in quantity, checked for accuracy,s t o red, and used as necessary.

Since it was humanly and technologically impossible tohave every individual part produced exactly alike (it stillis), the concept of geometric and positional tolerancing wasi n t roduced. To l e r a n c i n g means setting acceptable limits ofdeviation. For example, if a mass produced part is to be 4"in length under ideal conditions, but is acceptable aslong as it is not less than 3.99" and not longer than 4.01",t h e re is a tolerance of plus or minus .01", F i g u re 12-1. Thistype of tolerance is called a size tolerance.

T h e re are three diff e rent types of size tolerances: uni-lateral and bilateral, shown in F i g u re 12-2, and limitdimensioning. When a unilateral tolerance is applied to adimension, the tolerance applies in one direction only (forexample, the object may be larger but not smaller, or it maybe smaller but not larger). When a bilateral tolerance i sapplied to a dimension, the tolerance applies in bothd i rections, but not necessarily evenly distributed. In l i m i t

FIGURE 12-2 Two types of tolerances

FIGURE 12-1 Size tolerance

d i m e n s i o n i n g, the high limit is placed above the low value.When placed in a single line, the low limit precedes thehigh limit and the two are separated by a dash.

Tolerancing size dimensions offers a number of advan-tages. It allows for acceptable error without compro m i s e sin design, cuts down on unacceptable parts, decre a s e smanufacturing time, and makes the product less expensiveto produce. However, it soon became apparent that inspite of advantages gained from size tolerances, tolerancingonly the size of an object was not enough. Other charac-teristics of objects also needed to be toleranced, such as loca-tion of features, orientation, form, runout, and pro fil e .

In order for parts to be acceptable, depending on theiruse, they need to be straight, round, cylindrical, flat, angu-l a r, and so forth. This concept is illustrated in F i g u re 12-3.The object depicted is a shaft that is to be manufactured towithin plus or minus .01 of 1.00 inch in diameter. The fin-ished product meets the size specifications but, since it isnot straight, the part might be re j e c t e d .

The need to tolerance more than just the size ofobjects led to the development of a more precise systemof tolerancing called geometric dimensioning and p o s i-tional tolerancing. This new practice improved on con-ventional tolerancing significantly by allowing designersto tolerance size, form, orientation, pro file, location,and runout, F i g u re 12-4. In turn, these are the charac-teristics that make it possible to achieve a high degree ofi n t e rc h a n g a b i l i t y.

Geometric Dimensioning andTolerancing Defin e dGeometric dimensioning and tolerancing is a dimensioningpractice which allows designers to set tolerance limitsnot just for the size of an object, but for all of the variouscritical characteristics of a part. In applying geometric

dimensioning and tolerancing to a part, the designermust examine it in terms of its function and its re l a t i o n-ship to mating part s .

F i g u re 12-5 is an example of a drawing of an object thathas been geometrically dimensioned and toleranced. It istaken from the dimensioning standards as defined by theAmerican National Standards Institute (ANSI), written bythe American Society of Mechanical Engineers (ASME) orASME Y14.5M–1994. This manual is a necessary re f e re n c efor drafters and designers involved in geometric dimen-sioning and positional tolerancing.

The key to learning geometric dimensioning and posi-tional tolerancing is to learn the various building blockswhich make up the system, as well as how to pro p e r l yapply them. F i g u re 12-6 contains a chart of the buildingblocks of the geometric dimensioning and tolerancing sys-tem. In addition to the standard building blocks shown inthe fig u re, several modifying symbols are used whenapplying geometric tolerancing, as discussed in detail inupcoming paragraphs.

Another concept that must be understood in order toe ffectively apply geometric tolerancing is the concept ofdatums. For skilled, experienced designers, the geometricbuilding blocks, modifiers, and datums blend together asa single concept. However, for the purpose of learning, theya re dealt with separately, and undertaken step-by-step asindividual concepts. They are presented now in the fol-lowing order: modifiers, datums, and geometric buildingb l o c k s .

A N S I ’s dimensioning standards manual (Y14.5 series)changes from time to time as standards are updated. Forexample, the Y14.5 manual became Y14.5M in 1982 toaccommodate metric dimensioning. Revised again in1988, it became Y14.5M-R1988. In the latest edition,the standard takes on the name of the developing agency,the American Society of Mechanical Engineers (ASME).ASME Y14.5M–1994 is the latest edition in the ongoingrevision process of the standard. This chapter helps stu-dents learn the basics of geometric dimensioning and posi-

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FIGURE 12-3 Tolerance of form

FIGURE 12-4 Types of tolerances

FOR INDIVIDUALFEATURES

FORINDIVIDUALOR RELATEDFEATURES

FOR RELATEDFEATURES

FORM

PROFILE

ORIENTATIONLOCATIONRUNOUT


tional tolerancing so they will be able to apply latests t a n d a rds set forth by ASME at any point in time and ina c c o rdance with any edition of the manual that is spec-i fied. Students should not use this chapter as a re f e re n c ein place of the ASME standard. Always refer to the latestedition of the standard for specifics that go beyond thebasics covered here i n .

M o d i fie r sM o d i fie r s a re symbols that can be attached to the standardgeometric building blocks to alter their application ori n t e r p retation. The proper use of modifiers is fundamen-tal to effective geometric tolerancing. Various modifiers areoften used: maximum material condition, least materialcondition, projected tolerance zone, free-state variation, tan-gent plane, all around, between symbol, and statisticaltolerance, F i g u re 12-7A, F i g u re 12-7B, and F i g u re 12-7C.

MA X I M U M MAT E R I A L CO N D I T I O N

Maximum material condition (MMC), is the condition ofa characteristic when the most material exists. For exam-

FIGURE 12-5 Geometrically dimensioned and toleranced drawing ( F rom ASME Y14.5M–1994)

FIGURE 12-6 Building blocks

SYMBOL CHARACTERISTIC GEOMETRICTOLERANCE

STRAIGHTNESS

FLATNESSFORM

CIRCULARITY

CYLINDRICITY

PROFILE OF A LINEPROFILE

PROFILE OF A SURFACE

ANGULARITY

PERPENDICULARITY ORIENTATION

PARALLELISM

TRUE POSITION

CONCENTRICITY LOCATION

SYMMETRY

* CIRCULAR RUNOUTRUNOUT

* TOTALRUNOUT

* MAY BEFILLEDIN

FIGURE 12-7A M o d i fiers used when applying geometric tolerancing

MAXIMUM MATERIALCONDITION

LEASTMATERIALCONDITION

PROJECTED TOLERANCE ZONE

FREE STATE VARIATION

TANGENTPLANE

ALLAROUND

BETWEEN SYMBOL

STATISTICAL TOLERANCE

THE RFS SYMBOL CAN STILLBE USED BUTTHEPREFERRED PRACTICE IS TO OMITIT.

ple, MMC of the external feature in F i g u re 12-8 is .77inch. This is the MMC because it re p resents the condi-tion where the most material exists on the part beingm a n u f a c t u red. The MMC of the internal feature in the fig-u re is .73 inch. This is the MMC because the most mate-rial exists when the hole is produced at the smallestallowable size.

In using this concept, the designer must remember thatthe MMC of an internal feature is the smallest allowablesize. The MMC of an external feature is the largest allow-

able size within specified tolerance limits inclusive. A ru l eof thumb to remember is that MMC means most material.

RE G A R D L E S S O F FE AT U R E SI Z E

R e g a rdless of feature size (RFS), tells machinists that atolerance of form or position or any characteristic must bemaintained re g a rdless of the actual produced size of theobject. Geometric tolerances are understood to applyre g a rdless of feature size where the modifiers M or L a re

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FIGURE 12-7B F o rm and pro p o rtion of geometric tolerancing symbols

not used. It is permissible to show the RFS modifie r ;h o w e v e r, it is redundant and the pre f e rred practice is toomit it. The RFS concept is illustrated in F i g u re 12-9. Inthe RFS example, the object is acceptable if produced insizes from 1.002 inches to .998 inch inclusive. The formc o n t rol is axis straightness to a tolerance of .002 inchre g a rdless of feature size. This means that the .002-inchaxis straightness tolerance must be adhered to, re g a rd l e s sof the produced size of the part .

Contrast this with the MMC example. In this case,the produced sizes are still 1.002 inches to .998 inch.H o w e v e r, because of the MMC modifie r, the .002 inch axisstraightness tolerance applies only at MMC or 1.002i n c h e s .

If the produced size is smaller, the straightness toler-ance can be increased pro p o rt i o n a l l y. Of course, thismakes the MMC modifier more popular with machinistsfor several reasons: 1) it allows them greater room for erro r


FIGURE 12-7C F o rm and pro p o rtion of dimensioning symbols and letters

FIGURE 12-8 MMC of an external and an internal feature

without actually increasing the tolerance, 2) it decre a s e sthe number of parts rejected, 3) it cuts down on unac-ceptable parts, 4) it decreases the number of inspectionsre q u i red, and 5) it allows the use of functional gaging. Allof these advantages translate into substantial financial sav-ings while, at the same time, making it possible to pro d u c ei n t e rchangeable parts at minimum expense.

LE A S T MAT E R I A L CO N D I T I O N

Least material condition (LMC), is the opposite of MMC.It refers to the condition in which the least material exists.This concept is illustrated in F i g u re 12-10.

In the top example, the external feature of the part isacceptable if produced in sizes ranging from .98 inch to

1.02 inches inclusive. The least material exists at .98 inch.C o n s e q u e n t l y, .98 inch is the LMC.

In the bottom example, the internal feature (hole) isacceptable if produced in sizes ranging from .98 inch to1.02 inches inclusive. The least material exists at 1.02inches. Consequently, 1.02 re p resents the LMC.

PR O J E C T E D TO L E R A N C E ZO N E

P rojected tolerance zone is a modifier that allows a tolerancezone established by a locational tolerance to be extendeda specified distance beyond a given surface. This conceptis discussed further later in this chapter under the heading“ True Position.”

FR E E- STAT E VA R I AT I O N

F ree-state variation is the concept that some parts cannotbe expected to be contained within a boundary of perf e c tf o rm. Some parts may vary in form beyond the MMC sizelimits after forces applied during manufacture are re m o v e d .For example, a thin-walled part shape may vary in its fre estate due to stresses being released in the part. This vari-ation may re q u i re that the part meet its tolerance re q u i re-ments while in its free state.

P a rts that are subject to free-state variation do nothave to meet the Rule #1 re q u i rement of perfect form atMMC. These parts are standard stock such as bars, sheets,tubes, extrusions, structural shapes, or other items pro-duced to established industry or government standard s .The appropriate standard would govern the limits off o rm variation allowed after manufacture .

The free-state symbol specifies the maximum allow-able free-state variation. It is placed within a featurec o n t rol frame, following the tolerance and any modifie r s ,F i g u re 12-1 1 .

TA N G E N T PL A N E

The tangent plane concept uses a modifying symbol withan orientation tolerance to modify the intended control ofthe surface. When an orientation tolerance is applied to as u rface, the primary control is equivalent to the symbol-ogy used. An example is the primary control of a parallelcallout is parallelism. However, when applied, the speci-fied symbol controls not only parallelism but other formvariations such as concavity, convexity, waviness, fla t-ness, and other imperfections as well.

If two such controlled surfaces are assembled, thea b rupt variation in the surfaces can cause diff e rent mat-ing effects and assembly conditions. There are severalways to control the effects of surface conditions whenapplying orientation tolerances. The obvious method isto re fine the surface control with a form tolerance suchas flatness. This is permissible because the orientation tol-

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FIGURE 12-9 R e g a rdless of feature size (RFS)

FIGURE 12-10 Least material condition (LMC)


erance controls flatness to the extent of the specified tol-erance value.

Another method is to modify the orientation toler-ance to apply a tangent plane. When the modifier isapplied, the orientation tolerance zone for a tangent planeis identical to any other orientation tolerance zones withone exception. The orientation tolerance no longer con-t rols the form of the surface. The surface of the con-t rolled feature must be within the specified limits of size,but is not re q u i red to fall within the parallelism tolerancezone boundary. Only a plane tangent to the high points onthe surface must be within the tolerance zone boundary.The symbol is placed within the feature control frame fol-lowing the stated tolerance, F i g u re 12-12.

AL L AR O U N D SY M B O L

The all around symbol is the symbolic means of indi-cating that the specified tolerance applies all around thep a rt. The normal tolerance zone of a geometric calloutextends the length of the feature in question. If there isan abrupt change in surface condition, such as an off-set, the tolerance zone would conclude at the beginningof the offset. Applying the all around symbol extendsthe tolerance zone all around the feature to includea b rupt surface variations, F i g u re 12-13. This conceptwill be discussed further later in this chapter under theheading “Pro file.”

BE T W E E N SY M B O L

The between symbol is a symbolic means of indicating thatthe stated tolerance applies to a specified segment of a sur-face between designated points. The normal tolerance

zone of a geometric callout extends the length of the fea-t u re in question. Application of this symbol can be used tolimit the tolerance zone to a specified area. It can also beused to clarify the extent of the pro file tolerance when it isnot clearly visible due to surface variations. F i g u re 12-14illustrates the use of this symbol.

STAT I S T I C A L TO L E R A N C I N G SY M B O L

The statistical tolerancing symbol is a symbolic means ofindicating that the stated tolerance is based on statisticalp rocess control (SPC). The symbol can be applied in oneof two ways. When the tolerance is a statistical size toler-ance, the symbol is placed next to the size dimension asshown in F i g u re 12-15. When the tolerance is a statisticalgeometric tolerance, the symbol is placed in the featurec o n t rol frame as shown in F i g u re 12-16.

FIGURE 12-11 F e a t u re control frame with free-state symbol

FIGURE 12-12 Specifying a tangent plane

FIGURE 12-14 Between symbol

FIGURE 12-13 All around symbol

FIGURE 12-15 Statistical tolerance symbol

DAT U M S

D a t u m s a re theoretically perfect points, lines, axes, surf a c e s ,or planes used for re f e rencing features of an object. Theya re established by the physical datum features that are iden-t i fied on the drawing. Identification of datum features isdone by using a datum feature symbol. This symbol consistsof a capital letter enclosed in a square frame. A leader lineextends from the frame to the selected feature. A triangleis attached to the end of the leader and is applied in thea p p ropriate way to indicate a datum feature. The symbolsshould only be applied to physical features. They shouldnot be attached to centerlines, axes, center planes, orother theoretical entities. F i g u re 12-17shows two ways inwhich datum feature symbols are placed on drawings. Thedatum symbol is attached to an extension line of the fea-t u re outline, clearly separated from the dimension linewhen the datum feature is a surface or placed on the vis-ible outline of a feature surf a c e .

In F i g u res 12-18A, 1 2 - 1 8 B, and 1 2 - 1 8 C, the datum fea-t u re symbol is placed on an extension of the dimension lineof a feature of size when the datum is an axis or centerplane. In F i g u res 12-18D, 1 2 - 1 8 E, and 1 2 - 1 8 F, the datum

is an axis. The symbol can be placed on the outline of acylindrical surface or an extension line of the feature out-line, separated from the size dimension. Figure 12-1 8 Fshows one arrow of the dimension line being replaced bythe datum feature triangle when space is limited. If no fea-t u re control frame is used, the symbol is placed on adimension leader line to the feature size dimension as seenby the example of Datum B in F i g u re 12-19. In F i g u re1 2-2 0 the symbol is attached to the feature control framebelow (or above) when the feature(s) controlled is adatum center plane.

ES TA B L I S H I N G DAT U M S

In establishing datums, designers must consider thefunction of the part, the manufacturing processes that will

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FIGURE 12-16 Symbol indicating the specified tolerance is a sta-tistical geometric tolerance

FIGURE 12-17 Datum feature symbols on a feature surface and anextension line

FIGURE 12-18 Placement of datum feature symbols on features of size

be used in producing the part, how the part will beinspected, and the part ’s relationship to other parts aftera s s e m b l y. Designers and drafters must also understand thed i ff e rence between a datum, datum feature, datum features i m u l a t o r, datum surface, datum plane, and a datumf e a t u re of size.

A datum is theoretical in nature and is located by thephysical datum features identified on the drawing. Adatum is considered to be the true geometric counterpartof the feature. It is the origin from which measurements aremade, or which provides geometrical re f e rences to which

other features are established. A datum feature is the actualphysical feature on a part used to establish a datum,F i g u re 12-21. It is identified on a drawing by use of adatum feature symbol, F i g u re 12-22.

A datum feature simulator is a surface, the form ofwhich is of such precise accuracy (such as a surface plate,a gage surface, or a mandrel), that it is used to simulate thedatum. The datum feature simulator contacts the datumf e a t u re(s) and simulates the theoretical datum. Simulationis necessary since measurements cannot be made from thet h e o retical true geometric counterpart. It is there f o re nec-e s s a ry to use high-quality geometric features to simulatedatums. Although the features are not perfect, they are ofsuch a quality that they can be used for that purpose.F i g u res 12-23 and 1 2 - 2 4 illustrate this concept withrespect to a surface and a feature of size.

A datum surf a c e ( f e a t u re) is the inexact surface of theobject used to establish a datum plane. A datum plane is at h e o retically perfect plane from which measurements aremade. Since inaccuracies and variations in the surface con-dition of the datum surface make it impractical to takem e a s u rements from, then a theoretically perfect planemust be established from which measurements are made.To establish this datum plane, the high points of thedatum surface are brought in contact with, in this case, as u rface plate, which simulates the datum plane. Thisconcept is illustrated in Figure 12-21.


FIGURE 12-20 Placement of datum feature symbol in conjunctionwith a feature control frame

FIGURE 12-19 Datum re f e rence on dimension leader line

Notice the irregularities on the datum surface. Thehigh points on the datum surface actually establish thedatum plane, which, in this case, is the top of the manu-facturing equipment. All measurements re f e renced toD ATUM A are measured from the theoretically perf e c tdatum plane. High point contact is used for establishing

datums when the entire surface in question will be amachined surf a c e .

A datum feature of size is established by associating thedatum feature symbol with the size dimension of theselected feature size. When identified, the theore t i c a ldatum is the axis, centerline, or center plane of the tru egeometric counterpart. it is simulated by the pro c e s s i n gequipment (such as a chuck, vise, or centering device).The datum feature simulator establishes the datum axis,centerline, or center plane from which measurements canbe re f e renced. This concept is illustrated in Figures 12-23and 12-24.

DAT U M TA R G E T S

On ro u g h e r, more irregular surfaces, such as those a s s o-ciated with castings, specified points, lines, or area con-tacts are used for establishing datums. Datum targ e t s

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FIGURE 12-21 Datum feature, simulated datum, and theoretical datum plane

FIGURE 12-22 Datum feature symbol


designate specific points, lines, or areas of contact on a partthat are used in establishing a datum. They are usedwhen it is not always practical to identify an entire surf a c eas a datum feature .

A datum target symbol is used to identify datum targ e t s .It consists of a circle divided in half with a horizontal line.The lower portion contains the datum identifying letter fol-

lowed by a datum target number. The numbers are sequen-tial, starting with one for each datum. The letter andnumber establish a target label to identify planes or axesas datums. The upper half of the symbol is norm a l l yempty except when using a diameter symbol followed bya value to identify the shape and size of the target are a ,F i g u re 12-25. F i g u re 12-26 shows a part using datum’s tar-get areas to establish a datum plane.

Dimensions used to locate targets may be basic dimensionsor toleranced dimensions. A basic dimension is a theore t-ically perfect dimension, much like a nominal or design

FIGURE 12-23 P r i m a ry external datum diameter with datum features i m u l a t o r

FIGURE 12-24 P r i m a ry internal datum diameter with datum features i m u l a t o r

FIGURE 12-25 Datum target symbol

FIGURE 12-26 P r i m a ry datum plane established by three datum tar-get are a s

dimension. The dimension is identified by enclosing thevalue in a rectangular box as shown in F i g u re 12-27.Tolerances placed in general notes or within the title blockdo not apply to basic dimensions. In F i g u re 12-28, thedatum targets are located using basic dimensions. Points arelocated relative to one another and dimensioned to showthe relationship between targ e t s .

When specific datum target points are used for estab-lishing datums, a minimum of three points, not in astraight line, are re q u i red for the primary datum, a mini-mum of two for the secondary, and a minimum of one forthe tert i a ry, Figure 12-28. In Figure 12-28, primary datumplane A is the top of the object and it is established by pointsA1, A2, and A3. Secondary datum plane B is the front of the

object and tert i a ry datum plane C is the right side. Thedatum feature symbol is placed on a drawing in the vieww h e re the surface in question appears as an edge.

Notice also that the secondary datum must be perpen-d i c u l a r to the first, and the tert i a ry datum must be per-pendicular to both the primary and secondary datums.These three mutually perpendicular datum planes estab-lish what is called the datum re f e rence frame. The d a t u mre f e rence frame ia a hypothetical, three-dimensional framethat establishes the three axes of an X, Y, and Z coord i n a t esystem into which the object being produced fits andf rom which measurements can be made. F i g u re 12-29shows an object located within a datum re f e rence frame.For features that have sides (for example, re c t a n g u l a rand square objects), it takes three datums to establish adatum re f e rence frame.

For cylindrical features, a complete re f e rence frame isestablished with two datum re f e rences. F i g u re 12-30shows an object within a re f e rence frame. Datum D is the

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FIGURE 12-27 Basic dimension symbol

FIGURE 12-28 Dimensioning datum targ e t s

FIGURE 12-29 Datum re f e rence frame


p r i m a ry datum feature and is used to establish datum planeK. Notice that datum feature E is established by two theo-retical planes intersecting at right angles on the datum axis.The datum axis becomes the origin of measurements tolocate other features on the object. Datum feature E usesthe second and third plane to locate the datum axis. There f e rence frame is thus established using two datums.

F i g u re 12-31 is an example of a “basic dimension.” Abasic dimension is a theoretically perfect dimension,much like a nominal or design dimension, that is used tolocate or specify the size of a feature. Basic dimensions areenclosed in rectangular boxes, as shown in Figure 12-31.

F e a t u re Control SymbolThe f e a t u re control symbol is a rectangular box in which alldata re f e rring to the subject feature control are placed,including: the symbol, datum references, the featurec o nt rol tolerance, and modifiers. These various feature c o n-t rol elements are separated by vertical lines. (Figure 12-5contains a drawing showing how feature control symbolsa re actually composed.)

The order of the data contained in a feature control frameis important. The first element is the feature control sym-bol. Next is the zone descriptor, such as a diameter symbolw h e re applicable. Then, there is the feature control toler-ance, modifiers when used, and datum re f e rences listed ino rder from left to right, F i g u re 12-32.

F i g u res 12-33 t h rough 1 2 - 3 7 illustrate how feature con-t rol symbols are developed for a variety of design situa-tions. Figure 12-33 is a feature control symbol whichs p e c i fies a .005 tolerance for symmetry and no datum re f-e rence. Figure 12-34 specifies a tolerance of .005 for thet rue position of a feature relative to Datum A. Figure s1 2-35 and 12-36 show the proper methods for con-s t ructing feature control symbols with two and thre edatum re f e rences, re s p e c t i v e l y. Figure 12-37 illustrates afeatur control symbol with a modifier and a contro l l e ddatum added.

True PositionTrue position is the theoretically exact location of thecenterline of a product feature such as a hole. The toler-ance zone created by a position tolerance is an imaginaryc y l i n d e r, the diameter of which is equal to the statedposition tolerance. The dimensions used to locate a fea-t u re, that is to have a position tolerance, must be basicd i m e n s i o n s .

FIGURE 12-30 P a rt with cylindrical datum feature

FIGURE 12-32 O rder of elements in a feature control symbol

GEOMETRIC CHARACTERISTICSYMBOL

ZONE DESCRIPTOR

FEATURE TOLERANCE

MODIFIER

PRIMARY DATUMREFERENCE

SECONDARY DATUM REFERENCE

TERTIARY DATUMREFERENCE

.001 A B C

FIGURE 12-31 Basic dimensions

3.625

BASIC DIMENSIONEXACT DIMENSION

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F i g u re 12-38 contains an example of a part with twoholes drilled through it. The holes have a position toler-ance relative to three datums: A, B, and C. The holes arelocated by basic dimensions. The feature control frame

states that the positions of the centerlines of the holesmust fall within cylindrical tolerance zones having diam-eters of .030 inch at MMC relative to DATUMS A, B, andC. The modifier indicates that the .030 inch toleranceapplies only at MMC. As the holes are produced larg e rthan MMC, the diameter of the tolerance zones can bei n c reased corre s p o n d i n g l y.

F i g u re 12-39 illustrates the concept of the cylindrical tol-erance zone from Figure 12-38. The feature control frameis repeated showing a .030 inch diameter tolerance zone.The broken-out section of the object from Figure 12-38p rovides the interpretation. The cylindrical tolerancezone is shown in phantom lines. The centerline of the holeis acceptable as long as it falls anywhere within the hypo-thetical cylinder.

US I N G T H E PR O J E C T E D TO L E R A N C E ZO N E

MO D I F I E R

ASME recommends the use of the projected tolerance zoneconcept when the variation in perpendiculars of thre a d e d

FIGURE 12-34 F e a t u re control symbol with one datum re f e re n c e

.005 A

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARYDATUM

REFERENCE

FIGURE 12-35 F e a t u re control symbol with two datum re f e re n c e s

FIGURE 12-36 F e a t u re control symbol with three datum re f e re n c e s

FIGURE 12-37 F e a t u re control symbol with a modifie r

FIGURE 12-33 F e a t u re control symbol with no datum re f e re n c e

.005

GEOMETRIC SYMBOL

FEATURE TOLERANCE

.002 A B

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARYDATUMREFERENCE

SECONDARYDATUMREFERENCE

.003 A B C

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARY DATUM REFERENCE

SECONDARY DATUM

TERTIARY DATUM

.002 A

GEOMETRIC SYMBOL

FEATURE TOLERANCE

MODIFIER

PRIMARY DATUM REFERENCE

– B –

THIS DATUM IS CONTROLLED BYTHE ABOVE GEOMETRIC SYMBOL

FIGURE 12-38 True position

FIGURE 12-39 Cylindrical tolerance zone


or pre s s - fit holes could cause fasteners, such as scre w s ,studs, or pins, to interf e re with mating part s .

The attitude of a threaded fastener is controlled by theinclination of the threaded hole into which it willassemble. There are instances where the inclinationcan be such that the fastener interf e res with the matingf e a t u re. One method of overcoming this problem is touse a projected tolerance zone. When projected, the tol-erance zone’s intended outcome is to decrease the incli-nation of the fastener passing through the mating part .It is often thought that the tolerance zone extendst h rough the feature being controlled to a point beyondthe part equal to the projection, but this is not the case.Instead, the controlled feature has no internal toler-ance; the zone is totally outside of the feature being con-t rolled. The height of the zone is equal to the values p e c i fied within the feature control frame. F i g u re 12-40illustrates this concept.

The projected tolerance zone symbol is a capital Penclosed with a circle. It is placed within the feature con-t rol frame following the tolerance value or modifier whereapplicable. The projection height is placed after the pro-jected tolerance zone symbol, as illustrated in Figure1 2-40. When a projected tolerance zone modifier is used,the surface from which the tolerance is projected is iden-t i fied as a datum and the length of the projected tolerancezone is specified. In cases where it is not clear from whichs u rface the projection extends, such as a through hole, aheavy chain line is used with a dimension applied to it, asillustrated in F i g u re 12-41. The resultant tolerance zone liestotally outside the feature being contro l l e d .

FL AT N E S S

F l a t n e s s is a feature control of a surface which re q u i res allelements of the surface to lie within two hypotheticalparallel planes. When flatness is the feature control, adatum re f e rence is neither re q u i red nor pro p e r.

Flatness is applied by means of a leader pointing to thes u rface or by an extension line of the surface. It cannotbe attached to the size dimension. The modifiers M or Lcannot be used with flatness because it is a surface con-t rol only. The flatness tolerance is not additive and mustbe less than the tolerance of size of the part unless thea p p ropriate note is added exempting it from Rule #1re q u i re m e n t s .

F i g u re 12-42 shows how flatness is called out in adrawing and the effect such a callout has on the pro-duced part. The surface indicated must be flat within a tol-erance zone of .010, as shown in Figure 12-42.

Flatness is specified when size tolerances alone arenot sufficient to control the form and quality of the surf a c eand when a surface must be flat enough to provide a sta-ble base or a smooth interface with a mating part .

Flatness is inspected for a full indicator movement(FIM) using a dial indicator. FIM is the newer term whichhas replaced the older “total indicator movement” orTIR. FIM means that the swing of the indicator needlef rom one extreme to the other cannot exceed the amountof the specified tolerance. The dial indicator is set to ru nparallel to a surface table which is a theoretically perf e c ts u rface. The dial indicator is mounted on a stand orheight gauge. The machined surface is run under it,FIGURE 12-40 S p e c i fied projected tolerance zone

FIGURE 12-41 P rojected tolerance zone using chain line

allowing the dial indicator to detect irregularities that falloutside of the tolerance zone.

ST R A I G H T N E S S

A s t r a i g h t n e s s tolerance can be used to control surf a c eelements, an axis or a center plane. When used to contro lsingle elements for a flat surface, it is applied in the vieww h e re the element to be controlled is a straight line. Whenapplied, it controls line elements in only one direction. Itd i ffers from flatness in that flatness covers an entire surf a c erather than just single elements on a surface. A straightnesstolerance yields a tolerance zone of a specified width,within which all points on the line in question must lie.Straightness is generally applied to longitudinal elements.

Another diff e rence between straightness and fla t n e s sc o n c e rns the application of the feature control frame.The method in which the feature control frame is appliedd e t e rmines the intended control. If the feature contro lframe is attached to an extension line of the surface or

attached to a leader pointing to the surface, the intendedc o n t rol is to the surface, F i g u re 12-43A. However, if the fea-t u re control frame is attached to a dimension line or adja-cent to a dimension, the intended control is an axis orcenter plane, F i g u re 12-43B. Drastically diff e rent results arerealized based on the application method.

STRAIGHTNESS OF A FLAT SURFACEF i g u re 12-44 shows how a straightness tolerance is appliedon a drawing to the elements of a flat surface. The straight-ness tolerance applies only to the top surface. The bottoms u rface straightness error is controlled by the limits of size.In this case, the straightness tolerance is used as a re fin e-ment for the top surface only. The feature control framestates that any longitudinal element for the re f e renced sur-face, in the direction indicated, must lie between twoparallel straight lines that are .002 inch apart .

STRAIGHTNESS OF A CYLINDRICAL SURFACEStraightness applied to the surface of a cylindrical featureis shown in F i g u re 12-45. It is similar to that of a flat sur-

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FIGURE 12-42 F l a t n e s s

FIGURE 12-43 Dimensioning and tolerancing


face, with one exception. Since the surface is ro u n d ,opposing surface line elements must also be considere dwhen verifying straightness. The full straightness tolerancemay not be available for these elements due to conditionssuch as wasting or barreling of the surface. Additionally, thestraightness tolerance is not additive to the size toler-ance and must be contained within the limits of size.This means that if the part is made at MMC, no straight-ness tolerance is available because any variation in surf a c estraightness would cause the part to exceed the MMCb o u n d a ry of size. F i g u re 12-46 illustrates the re l a t i o n s h i pbetween a straightness tolerance and a size tolerance of ap a rt. Remember, each element of the surface must staywithin the specified straightness tolerance zone and withinthe size tolerance envelope. Straightness is affected by ru n-ning the single-line elements of a surface under a dial indi-cator for a full indicator movement (FIM).

F i g u res 12-47 through 12-52 further illustrate theconcept of straightness. F i g u re 12-47 shows a part witha size tolerance, but no feature control tolerance. In thisexample, the form of the feature is controlled by thesize tolerance. The diff e rence between maximum andminimum limits defines the maximum form variation thatis allowed. ASME Y14.5M outlines the re q u i rements off o rm control for individual features controlled only witha size dimension. This re q u i rement is known as R u l e# 1. According to the standard, Rule #1 states: “Where onlya tolerance size is specified, the limits of size of an indi-vidual feature define the extent to which variations in itsgeometric form, as well as size, are allowed.” This meansthat the size limits of a part determine the maximum andminimum limits (boundaries) for that part. The MMClimit establishes a boundary limit of perfect form. If a partis at MMC, it must have perfect form. No variation in formis allowed. As the part varies in size toward LMC, the formof the part is allowed to vary equal to the variation in size

FIGURE 12-44 Straightness of a flat surf a c e

FIGURE 12-46 Straightness interpre t e dFIGURE 12-45 Straightness of surface elements

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f rom MMC. When the part is made at LMC, the form vari-ation is equal to the diff e rence between the MMC andLMC sizes as illustrated in Figure 12-47.

F i g u re 12-48 is the same part with a straightness tol-erance of .002 re g a rdless of feature size tolerance. Theimplied re g a rdless of feature size tolerance limits theamount the surface can be out of straightness to a maxi-mum of .002 re g a rdless of the produced size of the part .H o w e v e r, because the straightness control is on a cylin-drical surface, the .002 tolerance might not be available asthe part approaches MMC. The drawing at the top of thefig u re illustrates how the part would be drawn. The fiv eillustrations below the part as drawn illustrate the actualshape of the object with each corresponding produced sizeand the available tolerance.

STRAIGHTNESS OF AN AXIS OR CENTER PLANETo locate the axis of a part, the size of the part must beknown. To locate the center plane of two parallel feature s ,the distance between the features must be known. Thesea re two examples of what is known as features of size.L o g i c a l l y, then, to control the axis of a part the feature con-t rol frame must be applied to the size dimension of thatp a rt, or to control the center plane of a rectangular part itmust be applied to the size dimension, Figure 12-43B.When straightness is applied to control the axis of the fea-t u re, the tolerance zone is cylindrical and extends the fulllength of the controlled feature. Straightness applied to con-t rol the center plane of a noncylindrical feature is shown

in F i g u re 12-49. It is similar to that of straightness of acylindrical feature, except that the tolerance zone is awidth and no diameter symbol is used within the featurec o n t rol frame.

Straightness applied to the axis or center plane of af e a t u re creates a boundary condition known as v i rt u a lc o n d i t i o n. Vi rtual condition in ASME Y14.5 is defined as fol-lows: “A constant boundary generated by the collectivee ffects of a size feature ’s specified MMC or LMC and thegeometric tolerance for that material condition.” Thismeans that you are allowed to add the straightness toleranceto the MMC size for a shaft and subtract the straightnesst o lerance from the MMC size for a hole. The re s u l t a n tb o u n d a ry re p resents the extreme form variation allowed forthe part. Although this boundary is theoretical, it re p re s e n t sthe size boundary of mating features. Unlike straightnessof a feature control, a straightness control of an axis or cen-

FIGURE 12-48 Straightness at RFS

FIGURE 12-49 S t r a i g h t n e s s

FIGURE 12-47 Object with no feature control symbol (Rule #1a p p l i e s )


ter plane allows for the availability of straightness toleranceeven when the part is made at MMC. Axis or center planec o n t rol of a feature becomes more desirable because of thei n c reased availability of tolerance and better control ofmating feature s .

F i g u re 12-50 is the same part in the previous exampleswith a straightness tolerance of .002 at maximum materialcondition applied. The use of the MMC modifier is limitedto tolerances controlling the axis or center plane of feature s .It specifies the tolerance allowed when part is produced atMMC. The drawing at the top of the fig u re illustrates howthe part would be drawn. The five illustrations belowthe part as drawn illustrate the actual shape of the objectwith each corresponding produced size. A virtual condi-tion boundary of .506 is created. When the part is at.504, the .506 virtual condition boundary allows forstraightness of .002 at MMC. Since the .002 straightnesstolerance applies at maximum material condition, theamount that the part can be out of straightness incre a s e sc o rrespondingly as the produced size decreases. The tableat the bottom of Figure 12-50 summarizes the manufac-t u red sizes and the corresponding amounts that the partcan be out of straightness for each size.

F i g u re 12-51 is an example of the same part with a .002straightness tolerance at least material condition (LMC).It specifies the tolerance allowed when the part is pro d u c e dat LMC. This results in the opposite effect of what occurre d

in Figure 12-49. Notice that the .002 straightness toleranceapplies at the least material condition. As the actual pro-duced size increases, the amount of out of straightnessallowed increases corre s p o n d i n g l y.

F i g u re 12-52 illustrates the same part from a .002straightness tolerance and a re g a rdless of feature sizetolerance. Notice in this example that the .002 straight-ness tolerance applies re g a rdless of the actual pro d u c e dsize of the part .

C i rcularity (Roundness)C i rc u l a r i t y, sometimes re f e rred to as roundness, is a featurec o n t rol for a surface of revolution (cylinder, sphere, cone,and so forth). It specifies that all points of a surface mustbe equidistant from the centerline or axis of the object inquestion. The tolerance zone for circularity is formed bytwo concentric and coplanar circles between which allpoints on the surface of revolution must lie.

F i g u res 12-53 a n d 1 2 - 5 4 illustrate how circularity iscalled-out on a drawing and provides an interpretation ofwhat the circularity tolerance actually means. At anyselected cross section of the part, all points on the surf a c emust fall within the zone created by the two concentric cir-cles. At any point where circularity is measured, it must fallwithin the size tolerance. Notice that a circularity tolerancecannot specify a datum re f e re n c e .FIGURE 12-50 Straightness of an axis at MMC

FIGURE 12-51 Straightness of an axis at LMC

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C i rcularity establishes elemental single-line tolerancezones that may be located anywhere along a surface. Thetolerance zones are taken at any cross section of the feature .T h e re f o re, the object may be spherical, cylindrical, tapere d ,or even hourglass shaped so long as the cross-section forinspection is taken at 90° to the nominal axis of the

object. A circularity tolerance is inspected using a dial indi-cator and making readings relative to the axis of the fea-t u re. In measuring a circularity tolerance, the full indicatormovement (FIM) of the dial indicator should not be anyl a rger than the size tolerance, and there should be severalm e a s u rements made at diff e rent points along the surf a c eof the diameter. All measurements taken must fall withinthe circularity tolerance.

C y l i n d r i c i t yC y l i n d r i c i t y is a feature control in which all elements ofa surface of revolution form a cylinder. It gives thee ffect of circularity extended the entire length of theobject, rather than just a specified cross section. The tol-erance zone is formed by two hypothetical concentricc y l i n d e r s .

F i g u re 12-55 illustrates how cylindricity is called-out ona drawing. Notice that a cylindricity tolerance does notre q u i re a datum re f e re n c e .

F i g u re 12-55 also provides an illustration of what thecylindricity tolerance actually means. Two hypotheticalconcentric cylinders form the tolerance zone. The outsidecylinder is established by the outer limits of the object atits produced size within specified size limits. The innercylinder is smaller (on radius) by a distance equal to thecylindricity tolerance.

Cylindricity re q u i res that all elements on the surface fallwithin the size tolerance and the tolerance established bythe feature contro l .

A cylindricity tolerance must be less than the size tol-erance and is not additive to the maximum material con-dition of the feature. Cylindricity is inspected by passingthe tolerance object through a gauge. The object should

FIGURE 12-53 C i rcularity for a cylinder or cone

FIGURE 12-54 C i rcularity for a sphere

FIGURE 12-52 Straightness of an axis at RFS


pass through a gauge that is equal to or greater than thediameter of the external envelope establishing the cylin-drical tolerance zone. It should not pass through a gaugethat is slightly smaller than the internal envelope, whichestablishes the cylindrical tolerance zone.

A n g u l a r i t yA n g u l a r i t y is a feature control in which a given surf a c e ,axis, or center plane must form a specified angle otherthan 90° with a datum. Consequently, an angularity tol-erance re q u i res one or more datum re f e rences. The tol-erance zone formed by an angularity callout consists oftwo hypothetical parallel planes which form the specifie dangle with the datum. All points on the angular surface oralong the angular axis must lie between these parallelp l a n e s .

AN G U L A R I T Y O F A SU R FA C E

F i g u re 12-56 illustrates how an angularity tolerance on as u rface is called out on a drawing. Notice that the specifie dangle is basic. This is re q u i red when applying an angular-ity tolerance. Figure 12-56 also provides an interpre t a-tion of what the angularity tolerance actually means. Thes u rface must lie between two parallel planes of 0.4 apartwhich are inclined at 30° basic angle to datum plane A.

Angularity also controls the flatness of the surface tothe same extent it controls the angular orientation.When it is re q u i red that the flatness of the feature be lessthan the orientation, a flatness callout can be used as are finement of the orientation callout. When using fla t n e s sas a re finement, the tolerance is less than the orientationtolerance. The feature control frame is normally placed

on an extension line below the orientation contro l ,F i g u re 12-57.

AN G U L A R I T Y O F A N AX I S O R CE N T E R PL A N E

An angularity callout can also be used to control the axisor center plane of a feature. This is done by placing the fea-t u re control frame with the size dimension in an appro-priate manner as seen in F i g u re 12-58. The tolerancezone for an axis control can be cylindrical in shape or twoparallel planes. When the diameter symbol is used withinthe feature control frame, the tolerance zone is cylindrical.When no diameter is used, the tolerance zone shape is twoparallel planes, F i g u re 12-59.

FIGURE 12-55 Specifying cylindricity

FIGURE 12-56 Specifying angularity for a surf a c e

FIGURE 12-57 Angularity with flatness re fin e m e n t

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P a r a l l e l i s mP a r a l l e l i s m is a feature control that specifies that all pointson a given surface, axis, line, or center plane must be equi-distant from a datum. Consequently, a parallelism tolerancere q u i res one or more datum re f e rences. A parallelism tol-erance zone is formed by two hypothetical parallel planesthat are parallel to a specified datum. They are spaced apartat a distance equal to the parallelism tolerance.

PA R A L L E L I S M O F A SU R FA C E

F i g u re 12-60 illustrates how a parallelism is called out ona drawing and provides an interpretation of what the par-allelism tolerance actually means. Notice that all elementsof the toleranced surface must fall within the size limits.

Notice in Figure 12-60 that the 0.12 parallelism toler-ance is called out relative to Datum A. You must specify adatum when calling out a parallelism tolerance. Parallelismshould be specified when features such as surfaces, axes,and planes are re q u i red to lie in a common orientation.

Parallelism is inspected by placing the part on an inspec-tion table and running a dial indicator a full indicatormovement across the surface of the part .

Parallelism also controls the flatness of the surface tothe same extent it controls parallel orientation. When itis re q u i red that the flatness of the feature be less than theorientation, a flatness callout can be used as a re fin e m e n tof the orientation callout. When using flatness as are finement, the tolerance is less than the orientationtolerance. The feature control frame is normally placedon an extension line below the orientation contro l ,F i g u re 12-61.

PA R A L L E L I S M O F A N AX I S O R CE N T E R PL A N E

Parallelism can be used to control the orientation of an axisto a datum plane, an axis to an axis, or the center plane ofnoncylindrical parts. When applied to control the axis or

FIGURE 12-58 Angularity for an axis (cylindrical tolerance zone)

FIGURE 12-59 Angularity for an axis (two parallel planes) ( F ro mASME Y14.5M – 1994)


center plane, the feature control frame must be placedwith the size dimension in the appropriate fashion. Whenused to control an axis to a datum plane, the tolerance zoneshape is two parallel planes separated by the amount of thestated tolerance. The tolerance control is only applicable re l-ative to the specified datum surface, F i g u re 12-62. Vi rt u a lcondition exists for the controlled feature, which allows foravailability of additional tolerance. The M and L m o d i fie r scan be used as a result of controlling a feature of size.

When used to control an axis to a datum axis, the tol-erance zone shape is cylindrical and the diameter is equalto the amount of the stated tolerance. The tolerance con-t rol is three-dimensional, allowing the axis to float re l a t i v eto orientation of the datum, F i g u re 12-63. Vi rtual conditionexists for the controlled feature, which allows for the avail-ability of additional tolerance. The M and L m o d i fiers canbe used as a result of controlling a feature of size.

When used to control a center plane to a datum planeor a center plane to a center plane, the similarity is that ofan axis to a surface or an axis to a datum axis. However, thetolerance zone shape is never cylindrical. The shape is twoparallel planes separated by the amount of the stated tol-erance. Vi rtual condition exists for the controlled feature ,which allows for availability of additional tolerance. The Mand L m o d i fiers can be used as a result of controlling a fea-t u re of size.

P e r p e n d i c u l a r i t yP e r p e n d i c u l a r i t y is a feature control that specifies that allelements of a surface, axis, center plane, or line form a 90°angle with a datum. Consequently, a perpendicularity

FIGURE 12-60 Parallelism for a surface to datum plane

FIGURE 12-61 Parallelism with flatness re fin e m e n t

FIGURE 12-62 Parallelism for an axis to datum plane

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tolerance re q u i res a datum re f e rence. A perpendicularitytolerance is formed by two hypothetical parallel planes thata re at 90° to a specified datum. They are spaced apart at adistance equal to the perpendicularity tolerance.

PE R P E N D I C U L A R I T Y O F A SU R FA C E

F i g u re 12-64 illustrates how a perpendicularity toler-ance is called out on a drawing and provides an inter-p retation of what the perpendicularity tolerance actuallymeans. The elements of the toleranced surface must fallwithin the size limits and between two hypothetical par-allel planes that are a distance apart equal to the perpen-dicularity tolerance.

The perpendicularity of a part such as the one shownin Figure 12-64 could be inspected by clamping the partto an inspection angle. The datum surface should re s tagainst the inspection angle. Then a dial indicator shouldbe passed over the entire surface for a full indicator move-ment to determine if the perpendicularity tolerance hasbeen complied with.

Perpendicularity also controls the flatness of the sur-face to the same extent it controls orientation. When itis re q u i red that the flatness of the feature be less than theorientation, a flatness callout can be used as a re fin e m e n tof the orientation callout. When using flatness as are finement, the tolerance is less than the orientationtolerance. The feature control frame is normally placedon an extension line below the orientation contro l ,F i g u re 12-65.

PE R P E N D I C U L A R I T Y O F A N AX I S O R

CE N T E R PL A N E

Perpendicularity can be used to control the orientation of anaxis to a datum plane, an axis to an axis, or the center plane

FIGURE 12-63 Parallelism for an axis to datum axis

FIGURE 12-64 Perpendicularity for a surface to a datum plane

FIGURE 12-65 Perpendicularity with flatness re fin e m e n t


of noncylindrical parts. When applied to control the axis orcenter plane, the feature control frame must be placedwith the size dimension in the appropriate fashion. Whenused to control an axis to a datum plane, the tolerance zoneshape is cylindrical, and its diameter equals the amount ofthe stated tolerance. The tolerance control is thre e-dimensional, allowing the axis to be at any orientation re l-ative to the specified datum surface, F i g u re 12-66. Vi rt u a lcondition exists for the controlled feature, which allows foravailability of additional tolerance. The M and L m o d i-fiers can be used as a result of controlling a feature of size.

When used to control an axis to a datum axis, the tol-erance zone shape is two parallel planes which are sepa-rated by a distance equal to the amount of the statedtolerance. The tolerance control is only applicable re l a t i v eto orientation of the datum, F i g u re 12-67. Vi rtual condi-tion exists for the controlled feature, which allows for avail-ability of additional tolerance. The M and L m o d i fiers canbe used as a result of controlling a feature of size.

When used to control a center plane to a datum planeor a center plane to a center plane, the similarity is that ofan axis to a surface or an axis to a datum axis. However, thetolerance zone shape is never cylindrical. The shape is twoparallel planes separated by the amount of the stated tol-erance. Vi rtual condition exists for the controlled fea-t u re, which allows for availability of additional tolerance.

The M and L m o d i fiers can be used as a result of con-t rolling a feature of size.

P ro fil eP ro fil e is a feature control that specifies the amount ofallowable variance of a surface or line elements on a surf a c e .T h e re are three diff e rent variations of the pro file tolerance:unilateral (inside), unilateral (outside), and bilateral (unequaldistribution), F i g u re 12-68. A pro file tolerance is norm a l l yused for controlling arcs, curves, and other unusual pro fil e snot covered by the other feature controls. It is a valuable fea-t u re control for use on objects that are so irregular that otherf e a t u re controls do not easily apply.

When applying a pro file tolerance, the symbol usedindicates whether the designer intends pro file of a line orp ro file of a surface, F i g u res 12-69 and 12-70 (page 498).P ro file of a line establishes a tolerance for a given single ele-ment of a surface. P ro file of a surf a c e applies to the entire sur-face. The diff e rence between pro file of a line and pro file ofa surface is similar to the diff e rence between circ u l a r i t yand cylindricity.

When using a pro file tolerance, drafters and designersshould remember to use phantom lines to indicate whetherthe tolerance is applied unilaterally up or unilaterallydown. A bilateral pro file tolerance re q u i res no phantomlines. An ALL AROUND symbol should also be placed on

FIGURE 12-67 Perpendicularity for an axis to a datum axisFIGURE 12-66 Perpendicularity for an axis to a datum plane

the leader line of the feature control frame to specifywhether the tolerance applies ALL AROUND or betweens p e c i fic points on the object, F i g u re 12-71.

F i g u re 12-72 p rovides an interpretation of what theBETWEEN A & B pro file tolerance in Figure 12-71 actu-ally means. The rounded top surface, and only the top sur-face, of the object must fall within the specified tolerance

zone. F i g u re 12-73 p rovides an interpretation of whatthe ALL AROUND pro file tolerance in Figure 12-71 actu-ally means. The entire surface of the object, all around theobject, must fall within the specified tolerance zone.

P ro file tolerances may be inspected using a dial indi-c a t o r. However, because the tolerance zone must bem e a s u red at right angles to the basic true pro file and per-

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FIGURE 12-68 Application of pro file of a surf a c e


pendicular to the datum, the dial indicator must be set upto move and read in both directions. Other methods ofinspecting pro file tolerances are becoming more popular,h o w e v e r. Optical comparators are becoming widely usedfor inspecting pro file tolerances. An optical comparatorm a g n i fies the silhouette of the part and projects it onto as c reen where it is compared to a calibrated grid or tem-plate so that the pro file and size tolerances may beinspected visually.

R u n o u tR u n o u t is a feature control that limits the amount of devi-ation from perfect form allowed on surfaces or ro t a t i o nt h rough one full rotation of the object about its axis.Revolution of the object is around a datum axis. Conseq-u e n t l y, a runout tolerance does re q u i re a datum re f e re n c e .

Runout is most frequently used on objects consistingof a series of concentric cylinders and other shapes of re v-olution that have circular cross sections; usually, the

types of objects manufactured on lathes, F i g u res 12-74and 1 2 - 7 5.

Notice in Figures 12-74 and 12-75 that there are twotypes of runout: circular runout and total runout. Thec i rcular runout tolerance applies at any single-line ele-ment through which a section passes. The total runout tol-erance applies along an entire surface, as illustrated inF i g u re 12-75. Runout is most frequently used when theactual produced size of the feature is not as important as thef o rm, and the quality of the feature must be related to someother feature. Circular runout is inspected using a dialindicator along a single fixed position so that errors are re a donly along a single line. Total runout re q u i res that thedial indicator move in both directions along the entires u rface being toleranced.

C o n c e n t r i c i t yIt is not uncommon in manufacturing to have a partmade up of several subparts all sharing the same cen-

FIGURE 12-69 P ro file of a line with size contro l

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terline or axis. Such a part is illustrated in F i g u re 12-76.In such a part it is critical that the centerline for each sub-sequent subpart be concentric with the centerlines of theother subparts. When this is the case, a concentricity tol-erance is applied. A concentricity tolerance locates theaxis of a feature relative to the axis of a datum. A con-centricity tolerance deals only with the centerline re l a-tionship. It does not affect the size, form, or surf a c equality of the part. Concentricity deals only with axialrelationships. It is applied only on a re g a rd l e s s - o f - f e a t u re -size basis. Regardless of how large or small the variouss u b p a rts of an overall part are, only their axes arere q u i red to be concentric. A concentricity tolerance cre-ates a cylindrical tolerance zone in which all center-lines for each successive subpart of an overall part must

FIGURE 12-70 P ro file of a surf a c e

FIGURE 12-71 P ro file “ALL AROUND”

FIGURE 12-73 I n t e r p retation of “ALL AROUND”

FIGURE 12-72 I n t e r p retation of “BETWEEN A & B”


fall. This concept is illustrated in F i g u re 12-77. A con-centricity tolerance is inspected by a full indicator move-ment of a dial indicator.

SY M M E T RY

P a rts that are symmetrically disposed about the centerplane of a datum feature are common in manufacturingsettings. If it is necessary that a feature be located sym-metrically with re g a rd to the center plane of a datum fea-t u re, a symmetry tolerance may be applied, F i g u re 12-78.The part in Figure 12-78 is symmetrical about a centerplane. To ensure that the part is located symmetrically withrespect to the center plane, a .030 symmetry tolerance isapplied. This creates a .030 tolerance zone within whichthe center plane in question must fall, as illustrated in thebottom portion of Figure 12-78.

TR U E PO S I T I O N I N G

True position tolerancing is used to locate features ofp a rts that are to be assembled and mated. True position issymbolized by a circle overlaid by a large plus sign orc ross. This symbol is followed by the tolerance, a modifie rwhen appropriate, and a re f e rence datum, F i g u re 12-79.F i g u res 12-80and 1 2 - 8 1 illustrate the diff e rence betweenconventional and true position dimensioning. The toler-

FIGURE 12-75 Specifying total runout relative to a datum diameter

FIGURE 12-76 P a rt with concentric subpart s

FIGURE 12-74 Specifying circular runout relative to a datum diameter

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ance dimensions shown in Figure 12-80 create a square tol-erance zone. This means that the zone within which thecenterline being located by the dimensions must fall t a k e sthe shape of a square. As you can see in Figure 12-81, thetolerancing zone is round when true position dimen-sioning is used. The effect of this on manufacturing is thatthe round tolerancing zone with true position dimen-sioning increases the size of the tolerance zone by 57%,F i g u re 12-82. This means that for the same tolerance themachinist has 57% more room for error without pro d u c-ing an out-of-tolerance part .

When using true position dimensioning, the toleranceis assumed to apply re g a rdless of the feature size unlessm o d i fied otherwise. F i g u re 12-83 illustrates the effect ofmodifying a true position tolerance with a maximummaterial condition modifie r. In this example, a hole is tobe drilled through a plate. The maximum diameter is .254and the minimum diameter is .250. There f o re, the max-imum material condition of the part occurs when thehole is drilled to a diameter of .250. Notice from thisexample that as the hole increases, the positional toler-ance increases. At maximum material condition (.250diameter), the tolerance zone has a diameter of .042. Atleast material condition (.254 diameter), the tolerancezone increases to .046 diameter. The tolerance zonediameter increases correspondingly as the hole sizei n c re a s e s .

RE V I E W O F DAT U M S

Fundamental to an understanding of geometric dimen-sioning and tolerancing is an understanding of datums.Since many engineering and drafting students find the con-cept of datums difficult to understand, this section willreview the concept in depth. It is important to understanddatums because they re p resent the starting point for re f-e rencing dimensions to various features on parts and formaking calculations relative to those dimensions. Datumsa re usually physical components. However, they can alsobe invisible lines, planes, axes, or points that are located bycalculations or as they relate to other features. Feature ssuch as diameters, widths, holes, and slots are fre q u e n t l ys p e c i fied as datum feature s .

Datums are classified as being a primary, secondary, ort e rt i a ry datum, F i g u re 12-84. Three points are re q u i red toestablish a primary datum. Two points are re q u i red to establish a secondary datum. One point is re q u i red toestablish a tert i a ry datum, F i g u re 12-85. Each point usedto establish a datum is called off by a datum target symbol,F i g u re 12-86. The letter designation in the datum targ e tsymbol is the datum identifie r. For example, the letter Ain F i g u re 12-87 is the datum designator for Datum A. Thenumber 2 in F i g u re 12-88 is the point designator forPoint 2. There f o re, the complete designation of “A2”means Datum A-Point 2.

FIGURE 12-77 Concentricity tolerancing


FIGURE 12-78 S y m m e t ry tolerancing

FIGURE 12-81 True position dimensioning

FIGURE 12-82 Comparison of tolerance zones

FIGURE 12-83 True positioning at MMC

FIGURE 12-79 True position symbology

FIGURE 12-80 Conventional dimensioning

.042 A B C

MODIFIER ADDED

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F i g u re 12-89 illustrates how the points which establishdatums should be dimensioned on a drawing. In thisillustration, the three points which establish Datum A aredimensioned in the top view and labeled using the datumt a rget symbol. The two points that establish Datum B

a re dimensioned in the front view. The one point that estab-lishes Datum C is dimensioned in the right-side view.F i g u re 12-90 illustrates the concept of datum plane anddatum surface. The theoretically perfect plane is re p re-sented by the top of the machine table. The less perf e c tactual datum surface is the bottom surface of the part .F i g u re 12-91shows how the diff e rences between the per-fect datum plane and the actual datum surface are re c o n-ciled. The three points pro t ruding from the machine tablec o rrespond with the three points which establish DatumA. Once this diff e rence has been reconciled, inspections ofthe part can be carried out.

FIGURE 12-84 D a t u m s

FIGURE 12-85 Establishing datums

FIGURE 12-86 Datum target symbol

FIGURE 12-87 Datum designation

FIGURE 12-88 Point designator

FIGURE 12-89 Dimensioning datum points

FIGURE 12-90 Datum plane versus datum surf a c e

FIGURE 12-91 Reconciling the datum surface to the datum plane

EACH POINT IS CALLED OFFBY A DATUM TARGET SYMBOL

A2

THE ‘2’INDICATES THE POINT

2

THE ‘A’ INDICATES THE DATUM

A


S u m m a ry• General tolerancing involves setting acceptable limits of

deviation for manufactured part s .

• Geometric dimensioning and tolerancing involves set-ting tolerance limits for all characteristics of a part .

• M o d i fiers are symbols that can be attached to the stan-d a rd geometric building blocks to alter their applicationor interpre t a t i o n .

• MMC is when the most material exists in the part .RFS means that a tolerance of form or position or anycharacteristic must be maintained re g a rdless of theactual produced size of the object.

• P rojected tolerance zone is a modifier that allows atolerance zone established by a locational tolerance tobe extended a specified distance beyond a given surf a c e .

• Datums are theoretically perfect points, lines, axes, sur-faces, or planes used for re f e rencing features of an object.

• True position is the theoretically exact location of thecenterline of a product feature such as hole.

Review QuestionsAnswer the following questions either true or false.

1. Tolerancing means setting acceptable limits of deviation.

2. The three types of size tolerances are unilateral, location,and ru n o u t .

3. The need to tolerance more than just the size of anobject led to the development of geometric dimen-sioning and tolerancing.

4. Geometric dimensioning specifies the allowable varia-tion of a feature from perfect form .

5. The term re g a rdless of feature size is a modifier whichtells machinists that a tolerance of form or position orany characteristic must be maintained, re g a rdless of theactual produced size of the object.

6. Datums are components of a part such as a hole, slot,s u rface, or boss.

7. A datum is established on a cast surface by a “flag” or as y m b o l .

Answer the following questions by selecting the besta n s w e r.

1. Which of the following is the identification for theASME standard on dimensioning?a. ASME Y14.5 M – 1994b. ASME Y24.5 M – 1992c. ASME Y34.5 M – 1990d. ASME Y44.5 M – 1988

2. Which of the following has the incorrect symbol? a. Flatnessb. Circ u l a r i t y •c. Straightness —d. True position ♦

3. Which of the following has the incorrect symbol?a. Perpendicularity ==b. Straightness —c. Parallelism / /d. Angularity

4. Which of the following is n o t t rue re g a rding fla t n e s s? a. It differs from straightness. b. The term flatness is interchangeable with the term

s t r a i g h t n e s s .c. When flatness is the feature control, a datum re f e r-

ence is neither re q u i red nor pro p e r. d. Flatness is specified when size tolerances alone are

not sufficient to control the form and quality of thes u rface.

5. The term least material condition means:a. The opposite of MMC.b. A condition of a feature in which it contains the

least amount of material. c. The theoretically exact location of a feature .d. Both a and b

6. Which of the following is n o t t rue re g a rding feature con-t rol symbols?a. The order of data in a feature control frame is

i m p o rtant. b. The first element is the feature control symbol.c. Various feature control elements are separated by //.d. Datum re f e rences are listed in order from left to

right.

7. Which of the following feature controls m u s t have adatum re f e re n c e ?a. Flatness b. Straightness c. Cylindricity d. Parallelism

Chapter Twelve Pro b l e m sThe following problems are intended to give beginningdrafters practice in applying the principles of geometricdimensioning and tolerancing.

The steps to follow in completing the problems are :

STEP 1 Study the problem care f u l l y.

STEP 2 Make a checklist of tasks you will need toc o m p l e t e .

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STEP 3 Center the re q u i red view or views in the worka re a .

STEP 4 Include all dimensions according to ASMEY14.5M – 1994.

STEP 5 Re-check all work. If it’s correct, neatly fill outthe title block using light guidelines and fre e-hand lettering.

NOTE: These problems do not follow current drafting standard s .You are to use the information shown here to developp roperly drawn, dimensioned, and toleranced drawings.

Problem 12-1

Apply tolerances so that this part is straight towithin .004 at MMC.

Problem 12-2

Apply tolerances so that the top surface ofthis part is flat to within .001 and the two

sides of the slot are parallel to each other within .002 RFS.

Problem 12-4

Apply tolerances to locate the holes using tru eposition and basic dimensions relative to

datums A-B-C.

Problem 12-3

Apply tolerances so that the smaller diameterhas a cylindricity tolerance of .005 and the

smaller diameter is concentric to the larger diameter towithin .002. The shoulder must be perpendicular tothe axis of the part to within .002.


Problem 12-5

Apply angularity, true position, and parallelismtolerances of .001 to this part. Select the

a p p ropriate datums. The parallelism tolerances should beapplied to the sides of the slot.

Problem 12-6

Apply tolerances so that the outside diameterof the part is round to within .004 and the

ends are parallel to within .001 at maximum materialcondition.

Problem 12-7

Apply a line pro file tolerance to the top ofthe part between points X and Y of .004.

Apply true position tolerances to the holes of .021, andparallelism tolerances of .001 to the two finished sides.

Problem 12-8

Use the bottom of the part as Datum A and theright side of the part as Datum B. Apply surf a c e

p ro file tolerances of .001 to the top of the part betweenpoints X and Y.

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Problem 12-9

Select datums and apply tolerances in such away as to ensure that the slot is symmetrical to

within .002 with the .50 diameter hole, and the bottomsurface is parallel to the top surface to within .004.

Problem 12-10

Apply tolerances to this part so that thetapered end has a total runout of .002.

Problem 12-11

Apply tolerances to this part so that diametersX and Z have a total runout of .02 relative to

Datum A (the large diameter of the part) and line ru n o u tof .004 to the two tapered surfaces.

Problem 12-12

Select datums and apply a positional toler-ance of .001 at MMC to the holes, and a per-

pendicularity tolerance of .003 to the vertical leg ofthe angle.


Problem 12-13

Problem 12-14

PROBLEMS 12-13 THROUGH 12-30For each of the remaining geometric dimensioning andtolerancing problems, examine the problem closelywith an eye to the purpose that will be served by thep a rt. Then select datums, tolerances, and feature contro l sas appropriate, and apply them properly to the parts. Inthis way you will begin to develop the skills re q u i red of

a mechanical designer. Do not overdesign. Remember,the closer the tolerances, and the more feature controlapplied, the more expensive the part. Try to use the ru l eof thumb that says: “Apply only as many feature contro l sand tolerances as absolutely necessary to ensure that thepart will properly serve its purpose after assembly.”

Problem 12-15

Problem 12-16

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Problem 12-17

Problem 12-18

Problem 12-19

Problem 12-20


Problem 12-21

Problem 12-22

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Problem 12-25

Problem 12-23 Problem 12-24


Problem 12-26

Problem 12-27 Problem 12-28

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PROBLEM 12-31Problem 12-29

Problem 12-30

This problem deals with feature control symbols. Initems 1–19 explain what each symbol means. In items20–30, draw the required symbols.

.005 A B C1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11)

12)

13)

20)

21)

22)

23)

24)

25)

26)

27)

28)

29)

30)

ANGULARITY

TRUE POSITION

FLATNESS

PROFILE OF A SURFACE

PERPENDICULARITY

CIRCULAR RUNOUT

STRAIGHTNESS

TOTALRUNOUT

PROFILE OF A LINE

CYLINDRICITY

CIRCULARITY

SYMBOL MEANS SYMBOL MEANS14)

15)

16)

17)

18)

19)

MEANS

SYMBOL

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