Geometric+Tolerancing

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GEOME TRIC

DIMENSIONING

AND

TOLERANCING

C H A P T E R O B JE C T I V E S

Upon completion of this chapter students should be able to do

the following:

Describe what is meant by the termgeneraltolerancing.

Define the conceptgeometric dimensioning andtolerancing.

Explain the purpose of a modifier.

Distinguish between the conceptsmaximum material condition (MMC) and regardless of feature size (RFS) .

Explain the concept least material condition (LMC) .

Describe what is meant by projected tolerance zone .

Make a sketch that illustrates the concept of datums.

Demonstrate how to establish datums.

Apply feature control symbols when dimensioningob jects.

Explain the concept ofTrue posit ion .

All around symbol

Angularity

Basic dimension

Between symbol

Bilateral tolerance

Circularity

Cylindricity

Datum

Datum feature

Datum feature simulator

Datum feature symbol

Datum plane

Datum reference frame

Datum surface

Datum target symbol

Feature control symbol

FlatnessFree-state variation

Geometric dimensioningand tolerancing

General tolerancing

Least materialcondition (LMC)

Limit dimensioning

Maximum materialcondition (MMC)

Modifiers

Parallelism

Perpendicularity

Positional tolerancing

Profile

Profile of a line

Profile of a surface

Projected tolerancezone

Regardless of featuresize (RFS)

Rule #1

Runout

Size tolerance

Statistical tolerancing

symbolStraightness

Tangent plane

Tolerancing

True position

Unilateral tolerance

Virtual condition

C H AP T E R O U T L I N E

Summary of geometric dimensioning and tolerancing

terms • Geometric dimensioning and tolerancing

defined • 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

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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

Summary of Geometric Dimensioning and T olerancing Terms Actual 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.

Allowance. The difference between the larger shaft sizelimit and the smallest hole size limit.

Angularity. Tolerancing of a feature at a specified angleother than 90 degrees from a referenced datum.

Basic Dimension. A theoretically “perfect” dimensionsimi lar to a reference or nominal dimension. It is used toidenti fy the exact location, size, shape, or orientation of afeature. Associated tolerances are applied by notes, featurecontrol frame, or other methods, excluding tolerancewithin title blocks.

Bilateral Tolerances. Tolerances that are applied to anominal dimension in the positive and negative directions.

Bonus Tolerance. The permitted allowable increase intolerance as the feature departs from the material conditionidentified within the feature control frame.

Circular Runout. A tolerance that identifies an infinitenumber of single circular elements measured at crosssections on a feature when the feature is rotated 360degrees for each cross section.

Circularity. A tolerance that controls the circular crosssection of round features that is independent of otherfeatures. The tolerance zone boundary is formed by twoconcentric perfect circles.

Clearance Fit. A condition between mating parts inwhich the internal part is always smaller than the externalparts it fits into.

Coaxiality. The condition of two or more featureshaving coincident axes.

Compound Datum Features. Two datum features used

to establish a datum or axis plane.Concentricity. A tolerance in which the axis of a featuremust be coaxial to a specified datum regardless of thedatum’s and the feature’s size. The lack of concentricity iseccentricity.

Cylindricity. A tolerance that simultaneously controlsa surface of revolution for straightness, parallelism, andcircularity of a feature, and is independent of any other fea-tures on a part. The tolerance zone boundary is composedof two concentric perfect cylinders.

Datum. Reference points, lines, planes, cylinders, andaxes which are assumed to be exact. They are establishedfrom datum features.

Datum Axis. The axis of a referenced datum feature suchas a hole or shaft.

Datum Feature. A feature which is used to establish

a 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 reference letter and a dash oneither side of the letter. It is used to identify datum features.

Datum: Feature Simulator. A surface of adequatelyprecise form (such as a surface plate, a gage surface, or amandrel) contacting the datum feature(s) and used toestablish the simulated datum(s).

Datum: Reference. Entering a datum reference letter in

a compartment of the feature control frame followingthe tolerance value.

Datum: Reference Frame. Three mutually perpendi-cular planes that establish a coordinate system. It is createdby datum references in a feature control frame or by a note.

Datum: Simulated. A point, axis, or plane established byprocessing or inspection equipment, such as the following:simulator, surface plate, a gage surface, or a mandrel.

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

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

Datum Target. Specified points, lines, or areas on afeature used to establish datums.

Datum Target Area. A specified area on a part that iscontacted to establish a datum.

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

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

Datum Target Symbol. A circle divided horizontally

into halves containing a letter and number to identifydatum targets.

Envelope, Actual Mating. The term is defined accordingto the type of features as follows:

(a) For an External Feature . A similar perfect featurecounterpart of smallest size that can be circum-scribed about the features so that it just contacts thesurface 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 surface(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 datumplane.

(b) For an Internal Feature . A similar perfect featurecounterpart of largest size that can be inscribedwithin the feature so that it just contacts the surfaceat the highest points. For example, a largest cylin-der of perfect form or two parallel planes of perfectform at maximum separation that just contact(s)the highest points of the surface(s).

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

Feature. A component of a part such as a hole, slot,

surface, pin, tab, or boss.

Feature of Size. One cylindrical or spherical surface, ora set of two opposed elements or opposed parallel surfaces,associated with a size dimension.

Feature, Axis of. A straight line that coincides with theaxis of the true geometric counterpart of the specified fea-ture.

Feature, Center Plane of. A plane that coincides withthe center plane of the true geometric counterpart of thespecified feature.

Feature, Derived Median Plane of. An imperfect plane

(abstract) that passes through the center points of all linesegments bounded by the feature. These line segments arenormal to the actual mating envelope.

Feature, Derived Median Line of. An imperfect line(abstract) that passes through the center points of all crosssections 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.

Fit. A term used to describe the range of assembly thatresults from tolerances on two mating parts.

Flatness. A tolerance that controls the amount of vari -

ation from the perfect plane on a feature independent ofany other features on the part.

Form Tolerance. A tolerance that specifies the allowablevariation of a feature from its perfect form.

Free-state Variation. The condition of a part that permitsits dimensional limits to vary after removal from manu-facturing or inspection equipment.

Least Material Condition (LMC). A condition of afeature 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.

Limits. The maximum and minimum allowable sizes of

a feature.Location Tolerance. A tolerance which specifies theallowable variation from the perfect location of a featurerelative to datums or other features.

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.

Modifier. The application of MMC or LMC to alter thenormally implied interpretation of a tolerance specification.

Parallelism. A tolerance that controls the orientation of

interdependent surfaces and axes which must be of equaldistance from a datum plane or axis.

Perpendicularity. A tolerance that controls surfacesand axes which must be at right angles with a referenceddatum.

Position Tolerance. 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.

Primary Datum. The first datum reference in a featurecontrol frame. Normally is elected because it is mostimportant to the design criteria and function of the

part.

Profile of a Line. A tolerance that controls the allow-able variation of line element in only one direction on asurface along an elemental tolerance zone with regard toa basic profile.

Profile of a Surface. A tolerance that controls theallowable variation of a surface from a basic profile orconfiguration.

Profile Tolerance Zone. A tolerance zone that can con-trol the form of an individual feature and provide for acomposite control of form, orientation, and location.

Projected Tolerance Zone. A tolerance zone that appliesto the location of an axis beyond the surface of the featurebeing controlled.

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

Regardless of Feature Size (RFS). A condition of a tol-erance in which the tolerance must be met regardless of theproduced size of the feature.


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Runout. The composite surface variation from thedesired form of a part of revolution during full rotation ofthe part on a datum axis.

Secondary Datum. The second datum reference in afeature control frame. Established after the primarydatum, it has less design influence and functionally.

Size, Virtual Condition. The actual value of the virtualcondition boundary.

Straightness. A tolerance that controls the allowablevariation of a surface or an axis from a theoretically per-fect line.

Symmetry. A condition for which a feature (or features)is equally disposed or shaped about the center plane of adatum feature.

Tangent Plane. A theoretically exact plane derivedfrom the true geometric counterpart of the specified fea-ture surface by contacting the high points on the surface.

Tertiary Datum. The third datum reference in a featurecontrol frame. Established after the secondary datum, it hasthe least amount of design influence or functionality.

Tolerance. 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 360degrees about a datum axis.

Transition Fit. A condition in which the prescribedlimits of mating parts produce either a clearance or aninterference when the parts are assembled.

True Geometric Counterpart. The theoretically perfectboundary (virtual condition or actual mating envelope) orbest-fit (tangent) plane of a specified datum feature.

True Position. The theoretically exact location of a feature.

Unilateral Tolerance. A tolerance which allows variationsin only one direction.

Virtual Condition. A constant boundary produced bythe combined effects of the maximum material conditionsize and geometric tolerance. It represents the worst casecondit ion of assembly at MMC.

Zero Tolerance at MMC or LMC. A tolerancing methodwhere no tolerance is shown in the feature control frame.The tolerance allowed is totally dependent on the size ofthe feature departure from MMC or LMC.

GENERAL TOLERANCING

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 prod-uct. Interchangability of parts was the key. If a particular

product was composed of 100 parts, each individual partcould be produced in quantity, checked for accuracy,stored, and used as necessary.

Since it was humanly and technologically impossible tohave every individual part produced exactly alike (i t sti llis), the concept of geometric and positional tolerancing wasintroduced.Tolerancing 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",there is a tolerance of plus or minus .01",Figure 12-1 . Thistype of tolerance is called a size tolerance .

There are three different types of size tolerances: uni-lateral and bilateral, shown in Figure 12-2 , and limitdimensioning. When aunilateral 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 is

applied to a dimension, the tolerance applies in bothdirections, but not necessarily evenly distributed. In limit

FIGURE 12-2 Two types of tolerances

FIGURE 12-1 Size tolerance


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dimensioning , 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 compromisesin design, cuts down on unacceptable parts, decreasesmanufacturing 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 profile.

In order for parts to be acceptable, depending on theiruse, they need to be straight, round, cylindrical, flat, angu-lar, and so forth. This concept is illustrated in Figure 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 jected.

The need to tolerance more than just the size ofobjects led to the development of a more precise systemof tolerancing called geometric dimensioning and positional tolerancing . This new practice improved on con-ventional tolerancing significantly by allowing designersto tolerance size, form, orientation, profile, location,and runout, Figure 12-4 . In turn, these are the charac-

teristics that make it possible to achieve a high degree ofinterchangability.

Geometric Dimensioning and Tolerancing Defined Geometr ic 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 relation-ship to mating parts.

Figure 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 referencefor 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 properlyapply them. Figure 12-6 contains a chart of the buildingblocks of the geometric dimensioning and tolerancing sys-tem. In addition to the standard building blocks shown in

the figure, several modifying symbols are used whenapplying geometric tolerancing, as discussed in detail inupcoming paragraphs.

Another concept that must be understood in order toeffectively 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, theyare dealt with separately, and undertaken step-by-step asindividual concepts. They are presented now in the fol-lowing order: modifiers, datums, and geometric buildingblocks.

ANSI’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

INDIVIDUAL

FEATURES

FOR

INDIVIDUAL

OR RELATED

FEATURES

FORRELATED

FEATURES

FORM

PROFILE

ORIENTATIONLOCATION

RUNOUT


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tional tolerancing so they will be able to apply lateststandards set forth by ASME at any point in time and inaccordance with any edition of the manual that is spec-ified. Students should not use this chapter as a referencein place of the ASME standard. Always refer to the latestedition of the standard for specifics that go beyond thebasics covered herein.

Modifiers Modifiers are symbols that can be attached to the standardgeometric building blocks to alter their application orinterpretation. 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,Figure 12-7A,Figure 12-7B , andFigure 12-7C .

MAXIMUMMATERIAL CONDITION

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

FIGURE 12-5 Geometr icall y dimensioned and toleranced drawing (From ASME Y14.5M–1994)

FIGURE 12-6Building blocks

S YMBO L C HA RA CT ER IS TIC GEOMETRIC

TOLERANCE

STRAIGHTNESS

FLATNESSFORM

CIRCULARITY

CYLINDRICITYPROFILE OF A LINE

PROFILEPROFILE OF A SURFACE

ANGULARITY

PERPENDICULARITY ORIENTATION

PARALLELISM

TRUE POSITION

CONCENTRICITY LOCATION

SYMMETRY

* CIRCULAR RUNOUTRUNOUT

* TOTALRUNOUT

* MAY BEFILLEDIN

FIGURE 12-7A Modifiers used when applying geometr ic tolerancing

MAXIMUM MATERIALCONDITION

LEASTMATERIALCONDITION

PROJECTED TOLERANCE ZONE

FREE STATE VARIATION

TANGENTPLANE

ALLAROUND

BETWEEN SYMBOL

STATISTICALTOLERANCE

THE RFS SYMBOL CAN STILLBE USED BUTTHE

PREFERRED PRACTICE IS TO OMITIT.


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ple, MMC of the external feature in Figure 12-8 is .77inch. This is the MMC because it represents the condi-tion where the most material exists on the part beingmanufactured. The MMC of the internal feature in the fig-ure 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 ruleof thumb to remember is that MMC means most material.

REGARDLESSOFFEATURESIZE

Regardless of feature size (RFS) , tells machinists that atolerance of form or position or any characteristic must bemaintained regardless of the actual produced size of theobject. Geometric tolerances are understood to applyregardless of feature size where the modifiers Mor L are

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FIGURE 12-7B Form and proportion of geometr ic tolerancing symbols


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not used. It is permissible to show the RFS modifier;however, it is redundant and the preferred practice is toomit it. The RFS concept is illustrated in Figure 12-9 . Inthe RFS example, the object is acceptable if produced insizes from 1.002 inches to .998 inch inclusive. The formcontrol is axis straightness to a tolerance of .002 inchregardless of feature size. This means that the .002-inchaxis straightness tolerance must be adhered to, regardless

of 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.However, because of the MMC modifier, the .002 inch axisstraightness tolerance applies only at MMC or 1.002inches.

If the produced size is smaller, the straightness toler-ance can be increased proportionally. Of course, thismakes the MMC modifier more popular with machinistsfor several reasons: 1) it allows them greater room for error


FIGURE 12-7C Form and proportion of dimensioning symbols and letters

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


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without actually increasing the tolerance, 2) it decreasesthe number of parts rejected, 3) it cuts down on unac-ceptable parts, 4) it decreases the number of inspectionsrequired, 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 produceinterchangeable parts at minimum expense.

LEAST MATERIAL CONDITION

Least material condition (LMC) , is the opposite of MMC.It refers to the condition in which the least material exists.This concept is il lustrated in Figure 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.Consequently, .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 represents the LMC.

PRO JECTEDTOLERANCEZONEProjected 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.”

FREE-STATEVARIATIONFree-state variation is the concept that some parts cannotbe expected to be contained within a boundary of perfectform. Some parts may vary in form beyond the MMC size

limits after forces applied during manufacture are removed.For example, a thin-walled part shape may vary in its freestate due to stresses being released in the part. This vari-ation may require that the part meet its tolerance require-ments while in its free state.

Parts that are subject to free-state variation do nothave to meet the Rule #1 requirement 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 standards.The appropriate standard would govern the limits ofform variation allowed after manufacture.

The free-state symbol specifies the maximum allow-able free-state variation. It is placed within a featurecontrol frame, following the tolerance and any modifiers,Figure 12-11.

TANGENT PLANEThe tangent plane concept uses a modifying symbol withan orientation tolerance to modify the intended control ofthe surface. When an orientation tolerance is applied to asurface, 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, flat-ness, and other imperfections as well.

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

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FIGURE 12-9 Regardless of feature size (RFS)

FIGURE 12-10 Least materi al condit ion (LMC)


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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-trols the form of the surface. The surface of the con-trolled feature must be within the specified limits of size,but is not required 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, Figure 12-12.

ALL AROUNDS YMBOL

The all around symbol is the symbolic means of indi-cating that the specified tolerance applies all around thepart. 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 extends

the tolerance zone all around the feature to includeabrupt surface variations, Fi gure 12-13. This conceptwill be discussed further later in this chapter under theheading “Profile.”

BETWEENS YMBOL

Thebetween 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-ture 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 profile tolerance when it isnot clearly visible due to surface variations. Figure 12-14 illustrates the use of this symbol.

STATISTICALTOLERANCINGS YMBOL

The statistical tolerancing symbol is a symbolic means ofindicating that the stated tolerance is based on statisticalprocess 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 Figure 12-15 . When the tolerance is a statisticalgeometric tolerance, the symbol is placed in the featurecontrol frame as shown in Figure 12-16.

FIGURE 12-11 Feature control frame with free-state symbol

FIGURE 12-12 Specify ing a tangent plane

FIGURE 12-14 Between symbol

FIGURE 12-13 All around symbol

FIGURE 12-15 Statistical tolerance symbol


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DATUMS

Datums are theoretically perfect points, lines, axes, surfaces,or planes used for referencing features of an object. Theyare established by the physical datum features that are iden-tified on the drawing. Identification of datum features isdone by using adatum 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 theappropriate way to indicate a datum feature. The symbolsshould only be applied to physical features. They shouldnot be attached to centerlines, axes, center planes, or

other theoretical entities. Figure 12-17 shows two ways inwhich datum feature symbols are placed on drawings. Thedatum symbol is attached to an extension l ine of the fea-ture outline, clearly separated from the dimension linewhen the datum feature is a surface or placed on the vis-ible outline of a feature surface.

In Figures 12-18A, 12-18B , and12-18C , the datum fea-ture symbol is placed on an extension of the dimension lineof a feature of size when the datum is an axis or centerplane. In Figures 12-18D , 12-18E , and12-18F , 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 12-18Fshows one arrow of the dimension line being replaced bythe datum feature triangle when space is limited. If no fea-ture control frame is used, the symbol is placed on a

dimension leader line to the feature size dimension as seenby the example of Datum B in Figure 12-19 . In Figure 12-20 the symbol is attached to the feature control framebelow (or above) when the feature(s) controlled is adatum center plane.

ESTABLISHINGDATUMS

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 statistical geometric tolerance

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

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


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be used in producing the part, how the part will be

inspected, and the part’s relationship to other parts afterassembly. Designers and drafters must also understand thedifference between a datum, datum feature, datum featuresimulator, datum surface, datum plane, and a datumfeature 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 references to which

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

A datum feature simulator is a surface, the form of

which 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 datumfeature(s) and simulates the theoretical datum. Simulationis necessary since measurements cannot be made from thetheoretical true geometric counterpart. I t is therefore nec-essary 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.Figures 12-23 and 12-24 illustrate this concept withrespect to a surface and a feature of size.

A datum surface (feature) is the inexact surface of the

object used to establish a datum plane. Adatum plane is atheoretically perfect plane from which measurements aremade. Since inaccuracies and variations in the surface con-dition of the datum surface make it impractical to takemeasurements 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, asurface plate, which simulates the datum plane. Thisconcept is illustrated in Figure 12-21.


FIGURE 12-20 Placement of datum feature symbol in conjuncti on wi th a feature control frame

FIGURE 12-19 Datum reference on dimension leader l ine


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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 referenced toDATUM A are measured from the theoretically perfectdatum plane. High point contact is used for establishing

datums when the entire surface in question will be amachined surface.

A datum feature of size is established by associating thedatum feature symbol with the size dimension of theselected feature size. When identified, the theoreticaldatum is the axis, centerline, or center plane of the truegeometric counterpart. it is simulated by the processing

equipment (such as a chuck, vise, or centering device).The datum feature simulator establishes the datum axis,centerline, or center plane from which measurements canbe referenced. This concept is illustrated in Figures 12-23and 12-24.

DATUMTARGETS

On rougher, more irregular surfaces, such as those asso-ciated with castings, specified points, lines, or area con-tacts are used for establishing datums. Datum targets

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

FIGURE 12-22 Datum feature symbol


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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 surfaceas a datum feature.

Adatum target symbol is used to identify datum targets.It consists of a circle divided in half with a horizontal l ine.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 normallyempty except when using a diameter symbol followed bya value to identi fy the shape and size of the target area,Figure 12-25 .Figure 12-26 shows a part using datum’s tar-get areas to establish a datum plane.

Dimensions used to locate targets may bebasic dimensions or toleranced dimensions. A basic dimension is a theoret-ically perfect dimension, much like a nominal or design

FIGURE 12-23 Primary external datum diameter with datum feature simulator

FIGURE 12-24 Primary i nternal datum diameter with datum feature simulator

FIGURE 12-25 Datum target symbol

FIGURE 12-26 Primary datum plane established by three datum target areas


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

When specific datum target points are used for estab-lishing datums, a minimum of three points, not in astraight line, are required for the primary datum, a mini-mum of two for the secondary, and a minimum of one forthe tertiary, 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 tertiary datum plane C is the right side. Thedatum feature symbol is placed on a drawing in the viewwhere the surface in question appears as an edge.

Notice also that the secondary datum must be perpen-dicular to the first, and the tertiary 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 reference frame. The datum reference frame ia a hypothetical, three-dimensional framethat establishes the three axes of an X, Y, and Z coordinatesystem into which the object being produced fits andfrom which measurements can be made. Figure 12-29 shows an object located within a datum reference frame.For features that have sides (for example, rectangularand square objects), it takes three datums to establish adatum reference frame.

For cylindrical features, a complete reference frame isestablished with two datum references. Figure 12-30

shows an object within a reference frame. Datum D is the

C h a p t e r 1 2

FIGURE 12-27 Basic dimension symbol

FIGURE 12-28 Dimensioning datum targets

FIGURE 12-29 Datum reference frame


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primary 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. Thereference frame is thus established using two datums.

Figure 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.

Feature Contro l Symbol

The feature control symbol is a rectangular box in which alldata referring to the subject feature control are placed,including: the symbol, datum references, the featurecontrol tolerance, and modifiers. These various feature con-trol elements are separated by vertical lines. (Figure 12-5contains a drawing showing how feature control symbolsare 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 symbolwhere applicable. Then, there is the feature control toler-ance, modifiers when used, and datum references listed in

order from left to right, Figure 12-32 .Figures 12-33 through 12-37 illustrate how feature con-

trol symbols are developed for a variety of design situa-tions. Figure 12-33 is a feature control symbol whichspecifies a .005 tolerance for symmetry and no datum ref-erence. Figure 12-34 specifies a tolerance of .005 for thetrue position of a feature relative to Datum A. Figures12-35 and 12-36 show the proper methods for con-structing feature control symbols with two and threedatum references, respectively. Figure 12-37 illustrates afeatur control symbol with a modifier and a controlleddatum added.

True Posit ion True positi on 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 imaginarycylinder, the diameter of which is equal to the statedposition tolerance. The dimensions used to locate a fea-ture, that is to have a position tolerance, must be basicdimensions.

FIGURE 12-30 Part with cylindrical datum feature

FIGURE 12-32 Order of elements in a feature control symbol

GEOMETRIC CHARACTERISTIC

SYMBOL

ZONE DESCRIPTOR

FEATURE TOLERANCE

MODIFIER

PRIMARY DATUM

REFERENCE

SECONDARY DATUM

REFERENCE

TERTIARY DATUM

REFERENCE

.001 A B C

FIGURE 12-31 Basic dimensions

3.625

BASIC DIMENSIONEXACT DIMENSION


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C h a p t e r 1 2

Figure 12-38 contains an example of a part with twoholes dri ll ed 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 holes

must 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 largerthan MMC, the diameter of the tolerance zones can beincreased correspondingly.

Figure 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 12-38provides the interpretation. The cylindrical tolerancezone is shown in phantom lines. The centerline of the hole

is acceptable as long as it falls anywhere within the hypo-thetical cylinder.

USING THEPRO JECTEDTOLERANCEZONEMODIFIER

ASME recommends the use of the projected tolerance zoneconcept when the variation in perpendiculars of threaded

FIGURE 12-34 Feature control symbol wit h one datum reference

.005 A

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARY DATUM

REFERENCE

FIGURE 12-35 Feature control symbol with two datum references

FIGURE 12-36 Feature control symbol wi th three datum references

FIGURE 12-37 Feature control symbol with a modifier

FIGURE 12-33 Feature control symbol wi th no datum reference

.005

GEOMETRIC SYMBOL

FEATURE TOLERANCE

.002 A B

GEOMETRIC SYMBOL

FEATURETOLERANCE

PRIMARY DATUM

REFERENCE

SECONDARY DATUM

REFERENCE

.003 A B C

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARY DATUM REFERENCE

SECONDARY DATUM

TERTIARY DATUM

.002 A

GEOMETRIC SYMBOL

FEATURETOLERANCE

MODIFIER

PRIMARY DATUM

REFERENCE

– B –

THIS DATUM IS CONTROLLED BY THE ABOVE GEOMETRIC SYMBOL

FIGURE 12-38 True position

FIGURE 12-39 Cylindr ical tolerance zone


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or press-fit holes could cause fasteners, such as screws,studs, or pins, to interfere with mating parts.

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 interferes with the matingfeature. 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 extendsthrough 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-trolled. The height of the zone is equal to the valuespecified within the feature control frame. Figure 12-40 illustrates this concept.

The projected tolerance zone symbol is a capital Penclosed with a circle. It is placed within the feature con-trol frame following the tolerance value or modifier whereapplicable. The projection height is placed after the projected tolerance zone symbol, as illustrated in Figure12-40. When a projected tolerance zone modifier is used,the surface from which the tolerance is projected is iden-tified as a datum and the length of the projected tolerancezone is specified. In cases where it is not clear from whichsurface the projection extends, such as a through hole, aheavy chain line is used with a dimension applied to it, asillustrated inFigure 12-41 . The resultant tolerance zone lies

totally outside the feature being controlled.

FLATNESS

Flatness is a feature control of a surface which requires allelements of the surface to lie within two hypotheticalparallel planes. When flatness is the feature control, adatum reference is neither required nor proper.

Flatness is applied by means of a leader pointing to thesurface or by an extension line of the surface. It cannotbe attached to the size dimension. The modifiers Mor L

cannot be used with flatness because it is a surface con-trol only. The flatness tolerance is not additive and mustbe less than the tolerance of size of the part unless theappropriate note is added exempting it from Rule #1requirements.

Figure 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 surfaceand 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 needlefrom one extreme to the other cannot exceed the amountof the specified tolerance. The dial indicator is set to runparallel to a surface table which is a theoretically perfectsurface. The dial indicator is mounted on a stand orheight gauge. The machined surface is run under it,FIGURE 12-40 Specified projected tolerance zone

FIGURE 12-41 Projected tolerance zone using chain l ine


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

STRAIGHTNESS

A straightness tolerance can be used to control surfaceelements, an axis or a center plane. When used to controlsingle elements for a flat surface, it is applied in the viewwhere the element to be controlled is a straight line. When

applied, it controls line elements in only one direction. Itdiffers from flatness in that flatness covers an entire surfacerather 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 difference between straightness and flatnessconcerns the application of the feature control frame.The method in which the feature control frame is applieddetermines the intended control. If the feature controlframe is attached to an extension line of the surface or

attached to a leader pointing to the surface, the intendedcontrol is to the surface,Figure 12-43A. However, if the fea-ture control frame is attached to a dimension line or adja-cent to a dimension, the intended control is an axis orcenter plane,Figure 12-43B . Drastically different results arerealized based on the application method.

STRAIGHTNESS OF A FLAT SURFACE

Figure 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 bottomsurface straightness error is controlled by the limits of size.In this case, the straightness tolerance is used as a refine-ment for the top surface only. The feature control framestates that any longitudinal element for the referenced sur-face, in the direction indicated, must lie between twoparallel straight lines that are .002 inch apart.

STRAIGHTNESS OF A CYLINDRICAL SURFACE

Straightness applied to the surface of a cylindrical featureis shown inFigure 12-45 . It is similar to that of a flat sur-

C h a p t e r 1 2

FIGURE 12-42 Flatness

FIGURE 12-43 Dimensioning and tolerancing


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face, with one exception. Since the surface is round,opposing surface line elements must also be consideredwhen 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 surfacestraightness would cause the part to exceed the MMCboundary of size.Figure 12-46 il lustrates the relationshipbetween a straightness tolerance and a size tolerance of apart. Remember, each element of the surface must staywithin the specified straightness tolerance zone and withinthe size tolerance envelope. Straightness is affected by run-ning the single-line elements of a surface under a dial indi-cator for a full indicator movement (FIM).

Figures 12-47 through 12-52 further illustrate the

concept of straightness. Figure 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 difference between maximum andminimum limits defines the maximum form variation thatis allowed. ASME Y14.5M outlines the requirements ofform control for individual features controlled only witha size dimension. This requirement is known as Rule #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 means

that the size limitsof 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 surface

FIGURE 12-46 Str aightness interpreted FIGURE 12-45 Str aightness of surface elements


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C h a p t e r 1 2

from MMC. When the part is made at LMC, the form vari-ation is equal to the difference between the MMC andLMC sizes as illustrated in Figure 12-47.

Figure 12-48 is the same part with a straightness tol-erance of .002 regardless of feature size tolerance. Theimplied regardless of feature size tolerance limits the

amount the surface can be out of straightness to a maxi-mum of .002 regardless of the produced size of the part.However, 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 thefigure illustrates how the part would be drawn. The fiveillustrations 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 PLANE

To locate the axis of a part, the size of the part must beknown. To locate the center plane of two parallel features,

the distance between the features must be known. Theseare two examples of what is known as features of size.Logically, then, to control the axis of a part the feature con-trol frame must be applied to the size dimension of thatpart, 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-ture, the tolerance zone is cylindrical and extends the fulllength of the controlled feature. Straightness applied to con-trol the center plane of a noncylindrical feature is shown

in Figure 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 featurecontrol frame.

Straightness applied to the axis or center plane of a

feature creates a boundary condition known as vir tual condition . Virtual condition in ASME Y14.5 is defined as fol-lows: “A constant boundary generated by the collectiveeffects 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 straightnesstolerance from the MMC size for a hole. The resultantboundary represents the extreme form variation allowed forthe part. Although this boundary is theoretical, it representsthe 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 Straightness

FIGURE 12-47 Object with no feature control symbol (Rule #1 applies )


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ter plane allows for the availability of straightness toleranceeven when the part is made at MMC. Axis or center planecontrol of a feature becomes more desirable because of theincreased availability of tolerance and better control ofmating features.

Figure 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 features.It specifies the tolerance allowed when part is produced atMMC. The drawing at the top of the figure 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, the

amount that the part can be out of straightness increasescorrespondingly as the produced size decreases. The tableat the bottom of Figure 12-50 summarizes the manufac-tured sizes and the corresponding amounts that the partcan be out of straightness for each size.

Figure 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 producedat LMC. This results in the opposite effect of what occurred

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 correspondingly.

Figure 12-52 illustrates the same part from a .002

straightness tolerance and a regardless of feature sizetolerance. Notice in this example that the .002 straight-ness tolerance appl ies regardless of the actual producedsize of the part.

Circularity (Roundness) Circularity , sometimes referred to as roundness, is a featurecontrol 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 by

two concentric and coplanar circles between which allpoints on the surface of revolution must lie.

Figures 12-53 and 12-54 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 surfacemust 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 reference.FIGURE 12-50 Straightness of an axis at MMC

FIGURE 12-51 Straightness of an axis at LMC


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C h a p t e r 1 2

Circulari ty establishes elemental single-line tolerancezones that may be located anywhere along a surface. Thetolerance zones are taken at any cross section of the feature.Therefore, the object may be spherical, cylindrical, tapered,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-ture. In measuring a circularity tolerance, the full indicatormovement (FIM) of the dial indicator should not be anylarger than the size tolerance, and there should be severalmeasurements made at different points along the surfaceof the diameter. All measurements taken must fall withinthe circularity tolerance.

Cylindricit y Cylindricity is a feature control in which all elements of

a surface of revolution form a cylinder. It gives theeffect of circularity extended the entire length of theobject, rather than just a specified cross section. The tol-erance zone is formed by two hypothetical concentriccylinders.

Figure 12-55 illustrates how cylindricity is called-out ona drawing. Notice that a cylindricity tolerance does notrequire a datum reference.

Figure 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 l imits of the object at

its produced size within specified size limits. The innercylinder is smaller (on radius) by a distance equal to thecylindricity tolerance.

Cylindricity requires that all elements on the surface fallwithin the size tolerance and the tolerance established bythe feature control.

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 Circulari ty for a cylinder or cone

FIGURE 12-54 Circularity for a sphere

FIGURE 12-52 Straightness of an axis at RFS


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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.

Angular it y

Angularity is a feature control in which a given surface,axis, or center plane must form a specified angle otherthan 90°with a datum. Consequently, an angularity tol-erance requires one or more datum references. The tol-

erance zone formed by an angularity callout consists oftwo hypothetical parallel planes which form the specifiedangle with the datum. All points on the angular surface oralong the angular axis must lie between these parallelplanes.

ANGULARIT YOFASURFACE

Figure 12-56 il lustrates how an angularity tolerance on asurface is called out on a drawing. Notice that the specifiedangle is basic. This is required when applying an angular-ity tolerance. Figure 12-56 also provides an interpreta-

tion of what the angularity tolerance actually means. Thesurface 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 required that the flatness of the feature be lessthan the orientation, a flatness callout can be used as arefinement of the orientation callout. When using flatnessas a refinement, the tolerance is less than the orientationtolerance. The feature control frame is normall y placed

on an extension line below the orientation control,Figure 12-57 .

ANGULARIT YOFANAXISORCENTERPLANEAn angularity callout can also be used to control the axisor center plane of a feature. This is done by placing the fea-ture control frame with the size dimension in an appro-priate manner as seen in Figure 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, Figure 12-59 .

FIGURE 12-55 Specifying cylindricity

FIGURE 12-56 Specifying angulari ty for a surface

FIGURE 12-57 Angularity with flatness refinement


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C h a p t e r 1 2

Parallelism

Parallelism 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 tolerancerequires one or more datum references. 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.

PARALLELISMOF ASURFACE

Figure 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 required 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 required that the flatness of the feature be less than theorientation, a flatness callout can be used as a refinement

of the orientation callout. When using flatness as arefinement, the tolerance is less than the orientationtolerance. The feature control frame is normally placedon an extension line below the orientation control,Figure 12-61 .

PARALLELISMOFANAXISORCENTERPLANE

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 Angulari ty for an axis (cyl indrical tolerance zone)

FIGURE 12-59 Angulari ty for an axis (two paral lel planes) (FromASME Y14.5M – 1994)


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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 rel-ative to the specified datum surface, Figure 12-62 . Virtualcondition exists for the controlled feature, which allows foravailability of additional tolerance. The MandLmodifierscan 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-trol is three-dimensional, allowing the axis to float relativeto orientation of the datum, Figure 12-63 . Virtual conditionexists for the controlled feature, which allows for the avail-abil ity of additional tolerance. TheMandLmodifiers 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 two

parallel planes separated by the amount of the stated tol-erance. Virtual condition exists for the controlled feature,which allows for availability of additional tolerance. The MandLmodifiers can be used as a result of controlling a fea-ture of size.

Perpendicularit y Perpendicularity 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 Paralleli sm for a surface to datum plane

FIGURE 12-61 Parallelism wi th flatness refinement

FIGURE 12-62 Paralleli sm for an axis to datum plane


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C h a p t e r 1 2

tolerance requires a datum reference. A perpendicularitytolerance is formed by two hypothetical parallel planes thatare at 90°to a specified datum. They are spaced apart at adistance equal to the perpendicularity tolerance.

PERPENDICULARIT YOF ASURFACE

Figure 12-64 illustrates how a perpendicularity toler-ance is called out on a drawing and provides an inter-pretation of what the perpendicularity tolerance actuallymeans. The elements of the toleranced surface must fall

within 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 restagainst 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 required that the flatness of the feature be less than theorientation, a flatness callout can be used as a refinementof the orientation callout. When using flatness as arefinement, the tolerance is less than the orientationtolerance. The feature control frame is normally placedon an extension line below the orientation control,Figure 12-65 .

PERPENDICULARIT YOFANAXISORCENTERPLANE

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 Parall eli sm for an axis to datum axis

FIGURE 12-64 Perpendiculari ty for a surface to a datum plane

FIGURE 12-65 Perpendicular ity with flatness refinement


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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 zone

shape is cylindrical, and its diameter equals the amount ofthe stated tolerance. The tolerance control is three-dimensional, allowing the axis to be at any orientation rel-ative to the specified datum surface,Figure 12-66 . Virtualcondition exists for the controlled feature, which allows foravailability of additional tolerance. The M and L modi-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 relativeto orientation of the datum, Figure 12-67 . Virtual condi-

tion exists for the controlled feature, which allows for avail-abil ity of additional tolerance. TheMandLmodifiers 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. Virtual condition exists for the controlled fea-ture, which allows for availability of additional tolerance.

The Mand L modifiers can be used as a result of con-trolling a feature of size.

Profile

Profile is a feature control that specifies the amount ofallowable variance of a surface or line elements on a surface.There are three different variations of the profile tolerance:unilateral (inside), unilateral (outside), and bilateral (unequaldistribution), Figure 12-68 . A profile tolerance is normallyused for controlling arcs, curves, and other unusual profilesnot covered by the other feature controls. It is a valuable fea-ture control for use on objects that are so irregular that otherfeature controls do not easily apply.

When applying a profile tolerance, the symbol usedindicates whether the designer intends profile of a line orprofile of a surface, Figures 12-69 and 12-70 (page 498).

Profile of a line establishes a tolerance for a given single ele-ment of a surface.Profile of a surface applies to the entire sur-face. The difference between profile of a line and profile ofa surface is similar to the difference between circularityand cylindricity.

When using a profile tolerance, drafters and designersshould remember to use phantom lines to indicate whetherthe tolerance is applied unilaterally up or unilaterallydown. A bilateral profile tolerance requires no phantomlines. An ALL AROUND symbol should also be placed on

FIGURE 12-67 Perpendiculari ty for an axis to a datum axis FIGURE 12-66 Perpendicular ity for an axis to a datum plane


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the leader line of the feature control frame to specifywhether the tolerance applies ALL AROUND or betweenspecific points on the object,Figure 12-71 .

Figure 12-72 provides an interpretation of what theBETWEEN A & B profile 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. Figure 12-73 provides an interpretation of whatthe ALL AROUND profile tolerance in Figure 12-71 actu-ally means. The entire surface of the object, all around theobject, must fall within the specified tolerance zone.

Profile tolerances may be inspected using a dial indi-cator. However, because the tolerance zone must bemeasured at right angles to the basic true profile and per-

C h a p t e r 1 2

FIGURE 12-68 Application of profile of a surface


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pendicular to the datum, the dial indicator must be set upto move and read in both directions. Other methods ofinspecting profile tolerances are becoming more popular,however. Optical comparators are becoming widely usedfor inspecting profile tolerances. An optical comparatormagnifies the silhouette of the part and projects it onto ascreen where it is compared to a calibrated grid or tem-plate so that the profile and size tolerances may beinspected visually.

Runout Runout is a feature control that limits the amount of devi-ation from perfect form allowed on surfaces or rotationthrough one full rotation of the object about its axis.Revolution of the object is around a datum axis. Conseq-uently, a runout tolerance does require a datum reference.

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

types of objects manufactured on lathes, Figures 12-74 and 12-75 .

Notice in Figures 12-74 and 12-75 that there are twotypes of runout: circular runout and total runout. Thecircular 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 inFigure 12-75. Runout is most frequently used when theactual produced size of the feature is not as important as theform, and the quality of the feature must be related to some

other feature. Circular runout is inspected using a dialindicator along a single fixed position so that errors are readonly along a single line. Total runout requires that thedial indicator move in both directions along the entiresurface being toleranced.

Concent r icit y It is not uncommon in manufacturing to have a partmade up of several subparts all sharing the same cen-

FIGURE 12-69 Profile of a l ine wi th size control


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terline or axis. Such a part is illustrated in Figure 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 the

axis of a feature relative to the axis of a datum. A con-centricity tolerance deals only with the centerline rela-tionship. It does not affect the size, form, or surfacequality of the part. Concentricity deals only with axialrelationships. It is applied only on a regardless-of-feature-size basis. Regardless of how large or small the variouss ubpa rt s of an overall part are, only their axes arerequired 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 Profile of a surface

FIGURE 12-71 Profile “ALL AROUND”

FIGURE 12-73 Interpretation of “ALL AROUND”

FIGURE 12-72 Interpretati on of “BETWEEN A & B”


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fall. This concept is illustrated in Figure 12-77 . A con-centricity tolerance is inspected by a full indicator move-ment of a dial indicator.

S YMMETRY

Parts that are symmetrically disposed about the center

plane of a datum feature are common in manufacturingsettings. If it is necessary that a feature be located sym-metrically with regard to the center plane of a datum fea-ture, a symmetry tolerance may be applied,Figure 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.

TRUEPOSITIONING

True position tolerancing is used to locate features ofparts that are to be assembled and mated. True position issymbolized by a circle overlaid by a large plus sign orcross. This symbol is followed by the tolerance, a modifierwhen appropriate, and a reference datum, Figure 12-79 .Figures 12-80 and12-81 il lustrate the difference betweenconventional and true position dimensioning. The toler-

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

FIGURE 12-76 Part with concentric subparts

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 takesthe 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%,Figure 12-82 . This means that for the same tolerance themachinist has 57% more room for error without produc-ing an out-of-tolerance part.

When using true position dimensioning, the toleranceis assumed to apply regardless of the feature size unlessmodified otherwise.Figure 12-83 illustrates the effect ofmodifying a true position tolerance with a maximummaterial condition modifier. In this example, a hole is tobe dril led through a plate. The maximum diameter is .254

and the minimum diameter is .250. Therefore, 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 sizeincreases.

REVIEWOFDATUMS

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 represent the starting point for ref-erencing dimensions to various features on parts and formaking calculations relative to those dimensions. Datumsare usually physical components. However, they can alsobe invisible lines, planes, axes, or points that are located bycalculations or as they relate to other features. Featuressuch as diameters, widths, holes, and slots are frequentlyspecified as datum features.

Datums are classified as being a primary, secondary, ortertiary datum, Figure 12-84 . Three points are required to

establish a primary datum. Two points are requiredto establish a secondary datum. One point is required toestablish a tertiary datum, Figure 12-85 . Each point usedto establish a datum is called off by a datum target symbol,Figure 12-86 . The letter designation in the datum targetsymbol is the datum identifier. For example, the letter Ain Figure 12-87 is the datum designator for Datum A. Thenumber 2 in Figure 12-88 is the point designator forPoint 2. Therefore, the complete designation of “A2”means Datum A-Point 2.

FIGURE 12-77 Concentr icity tolerancing


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FIGURE 12-78 Symmetry tolerancing

FIGURE 12-81 True positi on dimensioning

FIGURE 12-82 Comparison of tolerance zones

FIGURE 12-83 True posit ioning at MMC

FIGURE 12-79 True positi on symbology

FIGURE 12-80 Conventional dimensioning

.042 A B C

MODIFIER ADDED


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Figure 12-89 illustrates how the points which establishdatums should be dimensioned on a drawing. In thisil lustration, the three points which establish Datum A aredimensioned in the top view and labeled using the datumtarget symbol. The two points that establish Datum B

are dimensioned in the front view. The one point that estab-lishes Datum C is dimensioned in the right-side view.Figure 12-90 illustrates the concept of datum plane anddatum surface. The theoretically perfect plane is repre-sented by the top of the machine table. The less perfectactual datum surface is the bottom surface of the part.Figure 12-91 shows how the differences between the per-fect datum plane and the actual datum surface are recon-ciled. The three points protruding from the machine tablecorrespond with the three points which establish Datum

A. Once this difference has been reconciled, inspections ofthe part can be carried out.

FIGURE 12-84 Datums

FIGURE 12-85 Establ ishing 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 surface

FIGURE 12-91 Reconcil ing the datum surface to the datum plane

EACH POINT IS CALLED OFFBYADATUM

TARGET SYMBOL

A2

THE ‘2’INDICATES THE POINT

2

THE ‘A’INDICATES THEDATUM

A


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Summary • General tolerancing involves setting acceptable limits of

deviation for manufactured parts.

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

• Modifiers are symbols that can be attached to the stan-dard geometric building blocks to alter their applicationor interpretation.

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

• Projected tolerance zone is a modifier that allows atolerance zone established by a locational tolerance tobe extended a specified distance beyond a given surface.

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

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

Review Quest ions Answer 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 runout.

3. The need to tolerance more than just the size of an

object 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 regardless of feature size is a modifier whichtells machinists that a tolerance of form or position orany characteristic must be maintained, regardless of theactual produced size of the object.

6. Datums are components of a part such as a hole, slot,surface, or boss.

7. A datum is established on a cast surface by a “flag” or asymbol.

Answer the following questions by selecting the bestanswer.

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. Circularity

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 nottrue regardingflatness ?a. It differs from straightness.b. The term flatness is interchangeable with the term

straightness.c. When flatness is the feature control, a datum refer-

ence is neither required nor proper.d. Flatness is specified when size tolerances alone are

not sufficient to control the form and quality of thesurface.

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 isnottrue regarding feature con-trol symbols?a. The order of data in a feature control frame is

important.b. The first element is the feature control symbol.c. Various feature control elements are separated by //.d. Datum references are listed in order from left to

right.

7. Which of the following feature controls musthave adatum reference?a. Flatnessb. Straightnessc. Cylindricityd. Parallelism

Chapter Twelve Pr ob lems The 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 carefully.

STEP 2 Make a checklist of tasks you will need tocomplete.


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STEP 3 Center the required view or views in the workarea.

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 free-

hand lettering.NOTE: These problems do not follow current draft ing standards.

You are to use the informati on shown here to develop properly drawn, dimensioned, and toleranced drawings.

Problem12-1

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

Problem12-2

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

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

Problem12-4

Apply tolerances to locate the holes using trueposition and basic dimensions relative to

datums A-B-C.

Problem12-3

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 to

the axis of the part to within .002.


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