gd&t form table of contents return to the previous slide slide 1quitmaster table of...

GD&T Form Table of ContentsReturn to the Previous Slide Slide 1 QuitMaster Table of ContentsGlossary

Chapter3 Form and Position TolerancesChapter3 Form and Position Tolerances 形位公差形位公差

TermsTerms术语术语Form toleranceForm tolerance形状公差Postion Postion tolerancetolerance位置公差位置公差


Form ToleranceForm Tolerance: : is the variation of the true form of is the variation of the true form of a single factor to its perfect form make a small shaft a single factor to its perfect form make a small shaft found to be distortion and not cylindrical, or the found to be distortion and not cylindrical, or the section is out of round, or the axes is bended, or section is out of round, or the axes is bended, or make a plane found to be warp.make a plane found to be warp.


Position Tolerance:Position Tolerance: is the variation of the actual position of is the variation of the actual position of related factors to its ideal position form. While machining a related factors to its ideal position form. While machining a stepped shaft, the axial cord of each step may not be the stepped shaft, the axial cord of each step may not be the same, namely, concentricity and coaxality error. Surfaces same, namely, concentricity and coaxality error. Surfaces expected to be perpendicular are not perpendicular after it expected to be perpendicular are not perpendicular after it machined. machined.


Symbols of Form and Position TolerancesSymbols of Form and Position Tolerances


A verification A verification setup, including a setup, including a dial indicator. dial indicator. This type of setup This type of setup is often used in is often used in the process of the process of verifying form verifying form during the during the production of production of parts.parts.

FORM TOLERANCESFORM TOLERANCES


Gages Used To Verify FormGages Used To Verify Form

Dial indicators are often used to measure Dial indicators are often used to measure variation from dimensional limits on form variation from dimensional limits on form tolerances. Note the spherical tipped probes tolerances. Note the spherical tipped probes of different size and flexibility.of different size and flexibility.


V blocks are often used to cradle cylindrical parts in the manufacturing and V blocks are often used to cradle cylindrical parts in the manufacturing and inspection processes.inspection processes.



A surface plate is vital in the processes of manufacturing and inspection. Made A surface plate is vital in the processes of manufacturing and inspection. Made from solid granite, they vary in size and thickness. The surfaces are processed to from solid granite, they vary in size and thickness. The surfaces are processed to a very smooth finish. They are used as datum plane simulators.a very smooth finish. They are used as datum plane simulators.



Additional tools and fixtures that are used in the inspection process.Additional tools and fixtures that are used in the inspection process.

Gages Used To Verify Dimensional AccuracyGages Used To Verify Dimensional Accuracy


FEATURE STRAIGHTNESSFEATURE STRAIGHTNESSFEATURE STRAIGHTNESSFEATURE STRAIGHTNESS

TOLERANCESOF FORMTOLERANCESOF FORM


Straightness Applied To A FeatureStraightness Applied To A Feature

In this example, the feature control frame, specifying straightness of line elements, is In this example, the feature control frame, specifying straightness of line elements, is applied to the top surface of the part. It is not associated with any dimension, therefore, applied to the top surface of the part. It is not associated with any dimension, therefore, it references its own true geometric counterpart—a perfectly straight line. This is the it references its own true geometric counterpart—a perfectly straight line. This is the case with case with all form tolerancesall form tolerances, datums are therefore , datums are therefore nevernever referenced in a feature control referenced in a feature control frame specifying form control.frame specifying form control.

16.015.4

0.2



The shape of the toleranceThe shape of the tolerance zonezone for surface element straightness is two parallel for surface element straightness is two parallel lineslines. Notice that the straightness specification is called out in the front view. . Notice that the straightness specification is called out in the front view. Therefore, the control applies in that view only (in the orientation of the front Therefore, the control applies in that view only (in the orientation of the front view, from left to right or right to left). The straightness control from front to view, from left to right or right to left). The straightness control from front to back (as shown in the side view) is equal to the size tolerance (0.6 mm).back (as shown in the side view) is equal to the size tolerance (0.6 mm).

0.2

16.015.4

0.2



0.2

0.2

Size limit tolerance Size limit tolerance 0.6 mm (allowed by0.6 mm (allowed byGeneral rule #1) General rule #1)

16.0

Remember, the straightness tolerance control applies Remember, the straightness tolerance control applies onlyonly in the orientation depicted in in the orientation depicted in the view where the straightness tolerance symbol is shown. Straightness in the other the view where the straightness tolerance symbol is shown. Straightness in the other (cross) orientation is controlled by the height (size) dimension tolerance.(cross) orientation is controlled by the height (size) dimension tolerance.

15.4


There is an infinite number of surface line elementsThere is an infinite number of surface line elements (in the orientation or direction of the (in the orientation or direction of the straightness control) that comprise the surface, and each line element must be verified straightness control) that comprise the surface, and each line element must be verified independent of all others. Each line is inspected separately (the inspection device is reset independent of all others. Each line is inspected separately (the inspection device is reset after each segment). Enough passes must be taken to satisfy the inspector that the surface after each segment). Enough passes must be taken to satisfy the inspector that the surface line elements are within the specified tolerance zone.line elements are within the specified tolerance zone.


0.2

0.6


Straightness Of Line ElementsStraightness Of Line Elements

To further illustrate the principle ofTo further illustrate the principle of orientation orientation, in relationship to straightness , in relationship to straightness control, consider the drawing above. Two separate geometric tolerances for control, consider the drawing above. Two separate geometric tolerances for straightness have been applied to the same surface, albeit in different orientations; straightness have been applied to the same surface, albeit in different orientations; the front view represents a cross-horizontal orientation—left to right, whereas the the front view represents a cross-horizontal orientation—left to right, whereas the right side view shows a longitudinal-horizontal orientation—front to back.right side view shows a longitudinal-horizontal orientation—front to back.

0.05 0.1



0.05 0.1

Each line element on the surfaceEach line element on the surfacemust lie between two parallel must lie between two parallel lineslines 0.05 apart in the orientation 0.05 apart in the orientationdepicted in the front view, and depicted in the front view, and 0.1 when oriented as shown in the 0.1 when oriented as shown in the right-side view of the drawing.right-side view of the drawing.



0.05 0.1

The illustration attempts to show the The illustration attempts to show the different tolerance zones that would different tolerance zones that would result from the two geometric tolerances result from the two geometric tolerances called out on the drawing.called out on the drawing.

0.1 Tolerance0.05 Tolerance


STRAIGHTNESS CONTROLLED STRAIGHTNESS CONTROLLED BY DEFAULT—RULE #1BY DEFAULT—RULE #1


Rule #1 (Default) Control of StraightnessRule #1 (Default) Control of Straightness

The dimension between the top and bottom of the object shown below, allows a The dimension between the top and bottom of the object shown below, allows a size tolerance of 0.5 mm. All line elements, across the entire surface, must be size tolerance of 0.5 mm. All line elements, across the entire surface, must be straight within 0.5 mm.straight within 0.5 mm.

12.512.0


12.5 12.0

Rule #1 (Default) Control of StraightnessRule #1 (Default) Control of Straightness

12.512.0

Straightness of Straightness of allall line elements (in line elements (in all directions) must fall within the all directions) must fall within the 0.5 mm tolerance zone defined by 0.5 mm tolerance zone defined by two parallel lines.two parallel lines.


STRAIGHTNESS CONTROLLED BY STRAIGHTNESS CONTROLLED BY RULE #1 COMBINED WITH A RULE #1 COMBINED WITH A

GEOMETRIC TOLERANCEGEOMETRIC TOLERANCE


Rule #1 is never overridden by a straightness control that is applied to surface Rule #1 is never overridden by a straightness control that is applied to surface elements. elements. The straightness control refines the allowable tolerance straightness The straightness control refines the allowable tolerance straightness error of the surface.error of the surface.

10.6 10.0

Straightness Controlled By Rule #1 Straightness Controlled By Rule #1 Combined With A Geometric ToleranceCombined With A Geometric Tolerance

0.3

10.610.0


Tolerance zone (2 parallelTolerance zone (2 parallellines, 0.3 apart) may floatlines, 0.3 apart) may floatinside Rule #1 limitsinside Rule #1 limits

The geometric tolerance controlling the straightness of the line elements on the The geometric tolerance controlling the straightness of the line elements on the top surface must be smaller, and be contained within the larger size tolerance. top surface must be smaller, and be contained within the larger size tolerance. However, the refining form tolerance may float within the larger size tolerance. However, the refining form tolerance may float within the larger size tolerance. Any line on the top surface (in the specified orientation) must be within 0.3 mm of Any line on the top surface (in the specified orientation) must be within 0.3 mm of perfect straightness. When form tolerances are called out on features, rule #1 is in perfect straightness. When form tolerances are called out on features, rule #1 is in effect, and all elements on the surface must be within the limits of size. effect, and all elements on the surface must be within the limits of size.


10.6 10.0

0.3

10.610.0


At this checking location. the full range of tolerance for straightness is available, At this checking location. the full range of tolerance for straightness is available, but remember, every line element is independent of all others.but remember, every line element is independent of all others.



10.6 10.0

0.3

10.610.0


At the lower range of the size limits, the full tolerance for straightness is available.At the lower range of the size limits, the full tolerance for straightness is available.



10.6 10.0

0.3

10.610.0


When departure from MMC is less than the straightness tolerance, as in this case, When departure from MMC is less than the straightness tolerance, as in this case, some of the tolerance for straightness is compromised, and therefore unavailable, some of the tolerance for straightness is compromised, and therefore unavailable,


Tolerance zone (2 parallel lines, 0.3 Tolerance zone (2 parallel lines, 0.3 apart) may float inside Rule #1 limits. apart) may float inside Rule #1 limits. Departure may be less than allowed, Departure may be less than allowed, but actual surface elements but actual surface elements cannot cannot violate size limitsviolate size limits..

10.6 10.0

0.3

10.610.0


Straightness of Surface ElementsStraightness of Surface Elements

0.04

14.93 - 15.00

Straightness of a feature is most often used to control the longitudinal surface elements of a cylinder or cone. Straightness of a feature is most often used to control the longitudinal surface elements of a cylinder or cone. An infinite number of longitudinal lines exist on the surface shown in the illustration above, and the An infinite number of longitudinal lines exist on the surface shown in the illustration above, and the specification implies that specification implies that allall surface line elements on the pin must be straight within a tolerance of 0.04 mm. surface line elements on the pin must be straight within a tolerance of 0.04 mm.


Straightness Of Surface ElementsStraightness Of Surface Elements

0.04

14.93 - 15.00

All longitudinal elements on the surface of the pin must lie between two parallel All longitudinal elements on the surface of the pin must lie between two parallel lines 0.04 mm apart. The two lines comprising the tolerance zone must also be in a lines 0.04 mm apart. The two lines comprising the tolerance zone must also be in a plane that is common with the axis of the cylindrical pin.plane that is common with the axis of the cylindrical pin.



There are infinite possibilities for resulting feature form in the drawing displayed, but in no There are infinite possibilities for resulting feature form in the drawing displayed, but in no case can the size limits be violated. Three extreme form possibilities will be illustrated.case can the size limits be violated. Three extreme form possibilities will be illustrated.

0.04

14.93 - 15.00


Straightness Of Surface Elements Combined With Rule #1Straightness Of Surface Elements Combined With Rule #1

The first example shows the pin curvature to the extent allowed by the geometric tolerance. The first example shows the pin curvature to the extent allowed by the geometric tolerance. Regardless of how much the diameter size varies, within the 14.93 – 15.00 mm diameter, the Regardless of how much the diameter size varies, within the 14.93 – 15.00 mm diameter, the surface line elements must be straight within the specified tolerance. Perfect form is required surface line elements must be straight within the specified tolerance. Perfect form is required at MMC. As departure from MMC occurs, out of straightness is allowed—up to 0.04 mm.at MMC. As departure from MMC occurs, out of straightness is allowed—up to 0.04 mm.

0.04 tolerance zone

0.04

14.93 - 15.00

15.00 MMC



““Waisting” can occur on the part, and if so, some of the tolerance may be compromised at Waisting” can occur on the part, and if so, some of the tolerance may be compromised at opposite points when at the lower limit of size. If the 0.04 tolerance was maximized all around opposite points when at the lower limit of size. If the 0.04 tolerance was maximized all around the diameter, 0.08 mm would have to be subtracted from the upper limit (15.00 mm), leaving a the diameter, 0.08 mm would have to be subtracted from the upper limit (15.00 mm), leaving a total minimum diameter of 14.92 mm. The part would be out of tolerance.total minimum diameter of 14.92 mm. The part would be out of tolerance.

0.04 tolerance zone

0.04 tolerance zone

0.04

14.93 - 15.00

15.00 MMC

15.00 MMC



Feature “barreling” could also result. But once again, some of the tolerance could be Feature “barreling” could also result. But once again, some of the tolerance could be compromised at opposite points inasmuch as the full 0.04 mm tolerance could not be in compromised at opposite points inasmuch as the full 0.04 mm tolerance could not be in effect all around the object without violating the overall size tolerance.effect all around the object without violating the overall size tolerance.

0.04 tolerance zone

0.04 tolerance zone

0.04

14.93 - 15.00

15.00 MMC

15.00 MMC

15.00 MMC



0.04

14.93 - 15.00

15.00 MMC

15.00 MMC

15.00 MMC

0.04 tolerance zone

0.04 tolerance zone

In a feature-control application, the straightness tolerance must be less than the size tolerance.* In the In a feature-control application, the straightness tolerance must be less than the size tolerance.* In the case of barreling or waisting of the surface, the full straightness tolerance may not be available for case of barreling or waisting of the surface, the full straightness tolerance may not be available for opposite elements because the limits of size cannot be violated.opposite elements because the limits of size cannot be violated.

REMEMBERREMEMBER

**This general rule can be This general rule can be overridden by a note overridden by a note specifying that perfect form is specifying that perfect form is not required at MMC.not required at MMC.


0.3

10.810.0

0.3

10.610.0

•The application of the feature control frame—whether associated with a feature or a feature The application of the feature control frame—whether associated with a feature or a feature of size—makes a significant difference in the interpretation of the control. of size—makes a significant difference in the interpretation of the control.

•In the illustration on the left, the control is on a feature; notice the resulting tolerance zone, In the illustration on the left, the control is on a feature; notice the resulting tolerance zone, controlling the surface line elements. controlling the surface line elements.

•The drawing on the right shows the application of the geometric tolerance in conjunction The drawing on the right shows the application of the geometric tolerance in conjunction with the feature of size, thus controlling the median line or axis of the part.with the feature of size, thus controlling the median line or axis of the part.

Feature Control Frame ApplicationsFeature Control Frame Applications


Rule #1 Default Straightness ControlRule #1 Default Straightness Control

In this example, the maximum possible diameter the pin could be, within its size In this example, the maximum possible diameter the pin could be, within its size limits, is 10.6 mm. limits, is 10.6 mm. At that size (maximum material condition), the cylindrical At that size (maximum material condition), the cylindrical form of the pin would have to be perfectform of the pin would have to be perfect, the axis would be perfectly straight, as , the axis would be perfectly straight, as would all the longitudinal line elements on the surface. As the pin diameter gets would all the longitudinal line elements on the surface. As the pin diameter gets smaller in size, moving away from maximum material condition towards least smaller in size, moving away from maximum material condition towards least material condition (LMC)—but still within the size tolerance limits—the axis of material condition (LMC)—but still within the size tolerance limits—the axis of the pin is allowed to bow or deform in the same amount. the pin is allowed to bow or deform in the same amount.

10.610.0


Pin diameter Pin diameter smaller than MMCsmaller than MMC, , but within size tolerance.but within size tolerance.

Rule #1 BoundaryRule #1 Boundary(Mating Envelope)(Mating Envelope)

10.6 MMC

Because rule #1 is in Because rule #1 is in effect, the size envelope effect, the size envelope cannot be violated, and cannot be violated, and where there is no where there is no geometric tolerance geometric tolerance applied to the dimension, applied to the dimension, the virtual condition is the virtual condition is equal to the MMC of the equal to the MMC of the pin, which in this case, is pin, which in this case, is 10.6 mm. As the pin 10.6 mm. As the pin diameter decreases in diameter decreases in size, but remains within size, but remains within the size tolerance, the the size tolerance, the straightness of the pin’s straightness of the pin’s axis may be affected in an axis may be affected in an amount equal to the amount equal to the departure.departure.

Rule #1 Straightness ControlRule #1 Straightness Control10.610.0


Tolerance Zone Diameter = 0.6

Pin Diameter at 10.0

10.6 MMC

Rule #1 Straightness ControlRule #1 Straightness Control

Shown at the worst case—the Shown at the worst case—the smallest diameter allowed by smallest diameter allowed by the size tolerance or least the size tolerance or least material condition—the material condition—the tolerance zone for the axis tolerance zone for the axis would be equal to would be equal to 0.6 mm, 0.6 mm, thus permitting the axis to be thus permitting the axis to be out of straightness by the same out of straightness by the same amount—the part could be amount—the part could be cylindrical but bowed.cylindrical but bowed.

Rule #1 BoundaryRule #1 Boundary(Mating Envelope)(Mating Envelope)

10.610.0


FEATURE OF SIZE FEATURE OF SIZE STRAIGHTNESS AT RFSSTRAIGHTNESS AT RFS


12.612.0

0.2

Feature Axis Control RFSFeature Axis Control RFS

In this illustration, the feature control frame is associated with the size dimension—the In this illustration, the feature control frame is associated with the size dimension—the diameter of the pin. Thus, the control is on the axis of the part, and applies at diameter of the pin. Thus, the control is on the axis of the part, and applies at any any increment of sizeincrement of size within the specified diameter size tolerance. Because the geometric within the specified diameter size tolerance. Because the geometric tolerance is applied to a feature of size, Rule #1 is overridden. The tolerance is applied to a feature of size, Rule #1 is overridden. The virtual condition, virtual condition, oror mating part envelopemating part envelope of the pin is equal to the MMC of the pin, of the pin is equal to the MMC of the pin, plus the geometric plus the geometric tolerancetolerance, or , or 12.8 mm.12.8 mm.


Pin Diameter--at any cross section, must Pin Diameter--at any cross section, must be within the limits of size (be within the limits of size (12.0-12.6 mm).12.0-12.6 mm).

0.2 tolerance 0.2 tolerance zone, regardless of zone, regardless of feature size.feature size.The smallest true cylinder (an adjustable gage), in contact The smallest true cylinder (an adjustable gage), in contact

with the high points on the surface. The maximum with the high points on the surface. The maximum acceptableacceptable diameter would be equal to the virtual condition— diameter would be equal to the virtual condition—the pin’s MMC the pin’s MMC plusplus the geometric tolerance ( the geometric tolerance (12.8 mm).12.8 mm).

12.612.0

0.2

Feature Axis Control RFSFeature Axis Control RFSThe feature The feature axisaxis straightness is maintained straightness is maintained regardless of feature size regardless of feature size (RFS). The 0.2 axis (RFS). The 0.2 axis tolerance applies at tolerance applies at anyany increment of size within the increment of size within the stated diameter size stated diameter size tolerance. Rule #1 is tolerance. Rule #1 is overridden, and the virtual overridden, and the virtual condition is condition is 12.8 mm.12.8 mm.


Pin Diameter Straightness Tolerance Zone Diameter

12.612.412.212.0

0.20.20.20.2

12.612.0

0.2

Straightness Tolerance Applied to a Straightness Tolerance Applied to a Feature of Size RFSFeature of Size RFS

At any increment of size, At any increment of size, within the size limits, the within the size limits, the tolerance for straightness tolerance for straightness of the median line or axis of the median line or axis is constant. Rule #1 is is constant. Rule #1 is overridden because the overridden because the control is applied to a control is applied to a feature of size.feature of size.


12.0 - 12.6

0.2

Straightness Tolerance Applied to a Feature of Size MMCStraightness Tolerance Applied to a Feature of Size MMC

When it is important to modify a straightness control to a condition of MMC, the When it is important to modify a straightness control to a condition of MMC, the tolerance portion of the feature control frame must include the appropriate tolerance portion of the feature control frame must include the appropriate material condition modifiermaterial condition modifier..


Straightness Bonus Total DiametralPin Tolerance Tolerance Tolerance Zone

12.6 0.2 0.0 0.2

ToleranceToleranceZoneZone

VirtualVirtualConditionCondition 12.812.8

0.2 M12.0 -12.6

Pin Diameter, at Pin Diameter, at anyany cross section, must be cross section, must be within the limits of size (within the limits of size (12.0-12.6).12.0-12.6).

This series of visuals illustrate the concept of This series of visuals illustrate the concept of bonus bonus tolerancetolerance applied as the object departs from MMC. applied as the object departs from MMC.






0.2 M12.0 -12.6


This series of visuals illustrate the concept of This series of visuals illustrate the concept of bonus bonus tolerancetolerance applied as the object departs from MMC. applied as the object departs from MMC.


12.4 0.2 0.2 0.4





0.2 M12.0 -12.6


This series of visuals illustrate the concept of bonus This series of visuals illustrate the concept of bonus tolerance applied as the object departs from MMC.tolerance applied as the object departs from MMC.


12.2 0.2 0.4 0.6





0.2 M12.0 -12.6


This series of visuals illustrate the concept of bonus This series of visuals illustrate the concept of bonus tolerance applied as the object departs from MMC.tolerance applied as the object departs from MMC.


12.0 0.2 0.6 0.8


Advantages of Straightness Tolerance Advantages of Straightness Tolerance Applied to a Feature of Size MMCApplied to a Feature of Size MMC

Applying straightness to a feature of size—especially if the control is modified to Applying straightness to a feature of size—especially if the control is modified to apply at maximum material condition—allows for additional tolerance as apply at maximum material condition—allows for additional tolerance as departure from MMC occurs. This added or departure from MMC occurs. This added or bonusbonus tolerance provides greater tolerance provides greater flexibility to manufacturing, and can have a positive affect on production costs. In flexibility to manufacturing, and can have a positive affect on production costs. In those instances where the conditions are as described above, fixed gages that those instances where the conditions are as described above, fixed gages that represent the worst case for assembly can also be used for verification, thus represent the worst case for assembly can also be used for verification, thus impacting overall costs. impacting overall costs.

The next series of screens will illustrate this concept. The advantages of MMC The next series of screens will illustrate this concept. The advantages of MMC control will be illustrated through the use of sketched parts in various control will be illustrated through the use of sketched parts in various configurations, in their respective receiver gages.configurations, in their respective receiver gages.


Mating Part Boundary VerificationMating Part Boundary Verification

The dimension and control frame are The dimension and control frame are shown in the lower left corner of the shown in the lower left corner of the screen. In the illustration, the part is screen. In the illustration, the part is shown at the maximum material shown at the maximum material condition. It is in the receiver gage is condition. It is in the receiver gage is shown at the mating part boundary shown at the mating part boundary limits or virtual condition. There is limits or virtual condition. There is adequate clearance for the parts to adequate clearance for the parts to assemble without interference.assemble without interference.

12.8 (VC)

12.6

(1)

0.2 M12.0 -12.6


(1)

12.8 (VC)

12.6

(1)

0.2 M12.0 -12.6


Pin Diameter at MMC & perfectly straight.Gage at Virtual Condition



(1)

12.8

0.2

12.6

(2)

(2)

12.8 (VC)

12.6

(1)

0.2 M12.0 -12.6


Pin Diameter at MMC.Gage will accept with0.2 variation in straightness


0.8

12.8

12.0

(3)(3)


(1)

12.8

0.2

12.6


(2)

(2)

12.8 (VC)

12.6

(1)

0.2 M12.0 -12.6


Pin Diameter at LMC.Gage will accept with0.8 variation in straightness


0.8

12.8

12.0

(3)


(1)

12.8 (VC)

12.6

(1)

12.8

0.2

12.6


(2)

0.2 M12.0 -12.6

Mating Part Boundary VerificationMating Part Boundary VerificationCarefully review these concepts. Carefully review these concepts.

(2)

(3) Pin Diameter at LMC.Gage will accept with0.8 variation in straightness


TOLERANCES OF FORMTOLERANCES OF FORMTOLERANCES OF FORMTOLERANCES OF FORM

FLATNESSFLATNESS


TERMS AND DEFINITIONSTERMS AND DEFINITIONS

•Flatness:Flatness: A condition where all of the elements of a given surface are in a single A condition where all of the elements of a given surface are in a single plane.plane.

•Flatness tolerance:Flatness tolerance: The total amount surface elements are permitted to vary The total amount surface elements are permitted to vary from a true plane.from a true plane.

•Flatness tolerance zone:Flatness tolerance zone: The distance between two parallel planes within which The distance between two parallel planes within which all of the elements of the controlled surface must lie.all of the elements of the controlled surface must lie.


Flatness VerificationFlatness Verification

•Flatness Flatness (A 3D tolerance zone)(A 3D tolerance zone) may be may be determined by adetermined by a theoretical plane, theoretical plane, established by the high points of the controlled surfaceestablished by the high points of the controlled surface in contact with a surface in contact with a surface plate or gage. plate or gage.

•From the theoretical plane, From the theoretical plane, a second plane is offset and parallel by a distance a second plane is offset and parallel by a distance equal to the tolerance value.equal to the tolerance value. All elements of the controlled surface must lie All elements of the controlled surface must lie between the two parallel planes. between the two parallel planes.


Second PlaneSecond Plane

FlatnessFlatnessTolerance ZoneTolerance Zone

Primary PlanePrimary Plane

Surface PlateSurface Plate

Flatness VerificationFlatness VerificationNeither the object nor the gage is perfectly flat. They will position themselves on the high Neither the object nor the gage is perfectly flat. They will position themselves on the high points of contact. Once that is done, the second plane, parallel to the first, is established a points of contact. Once that is done, the second plane, parallel to the first, is established a linear distance—equal to the tolerance value—away from the theoretical plane. All of the linear distance—equal to the tolerance value—away from the theoretical plane. All of the elements on the controlled surface must lie between the two planes.elements on the controlled surface must lie between the two planes.


Second PlaneSecond Plane

FlatnessFlatnessTolerance ZoneTolerance Zone

Primary PlanePrimary Plane

Surface PlateSurface Plate

Flatness VerificationFlatness VerificationFlatness may be verified with a dial indicator that extends through a hole in a surface plate. Flatness may be verified with a dial indicator that extends through a hole in a surface plate. The indicator is made stationary, and the part is moved around on the surface plate to The indicator is made stationary, and the part is moved around on the surface plate to ensure that all elements of the controlled surface are checked.ensure that all elements of the controlled surface are checked.


Feature FlatnessFeature Flatness

0.2

0.2

Size limit tolerance Size limit tolerance 0.6mm (allowed by0.6mm (allowed byGeneral rule #1) General rule #1)

16.015.4

The flatness tolerance control applies toThe flatness tolerance control applies to all elements all elements on the surface to which the tolerance on the surface to which the tolerance is applied. The flatness tolerance is allowed to float within the larger size tolerance. It can is applied. The flatness tolerance is allowed to float within the larger size tolerance. It can be oriented in any location or direction as long as it does not violate the size tolerance.be oriented in any location or direction as long as it does not violate the size tolerance.


All surface elements must be within the tolerance zone defined by two parallel All surface elements must be within the tolerance zone defined by two parallel planes, 0.2 apart. Enough passes in random directions must be taken to satisfy the planes, 0.2 apart. Enough passes in random directions must be taken to satisfy the inspector that all of the surface elements are within the specified tolerance zone.inspector that all of the surface elements are within the specified tolerance zone.

Feature Flatness Feature Flatness

0.2



Flatness being verified using a surface plate, a height stand, and a Flatness being verified using a surface plate, a height stand, and a dial indicator.dial indicator.



Inspection/verification setup, comprised of a rotational surface Inspection/verification setup, comprised of a rotational surface plate, a height stand, and a digital indicator.plate, a height stand, and a digital indicator.


Coordinate tolerances combined with the first fundamental rule, when applied to a Coordinate tolerances combined with the first fundamental rule, when applied to a feature of size (a distance between two parallel surfaces), provides an automatic feature of size (a distance between two parallel surfaces), provides an automatic flatness control for flatness control for bothboth surfaces. At MMC, both surfaces would have to be surfaces. At MMC, both surfaces would have to be perfectly flat. As departure from MMC occurs, however, form variation equal in perfectly flat. As departure from MMC occurs, however, form variation equal in amount to that departure is allowed. (Form variation limits are equal to the amount to that departure is allowed. (Form variation limits are equal to the difference between the upper and lower size tolerance, and apply equally for difference between the upper and lower size tolerance, and apply equally for bothboth surfaces). Because rule #1 is in effect, the size limits surfaces). Because rule #1 is in effect, the size limits cannotcannot be violated. be violated.

Default Flatness Controlled By The First Fundamental RuleDefault Flatness Controlled By The First Fundamental Rule


Flatness ApplicationFlatness Application

The feature control frame can be attached to an extension line as shown here. It The feature control frame can be attached to an extension line as shown here. It may also be attached to a leader, with its arrow touching the surface (as shown on may also be attached to a leader, with its arrow touching the surface (as shown on the next slide). However, it must the next slide). However, it must alwaysalways be associated with a view where the be associated with a view where the surface being controlled for flatness appears as a single line—an edge view.surface being controlled for flatness appears as a single line—an edge view.

0.2

14.0 - 14.6


0.2

14.0 - 14.6

The top surface is specified to be flat within The top surface is specified to be flat within a tolerance zone defined by two parallel a tolerance zone defined by two parallel planes 0.2 mm apart. The size dimension planes 0.2 mm apart. The size dimension allows 0.6 mm of tolerance between the allows 0.6 mm of tolerance between the two surfaces. two surfaces.



14.6 MMC14.0 LMC

14.0 - 14.6


The limits of size are illustrated on the The limits of size are illustrated on the drawing. Clearly, the part is within the drawing. Clearly, the part is within the size tolerance range. But the flatness size tolerance range. But the flatness tolerance must also be within the size tolerance must also be within the size tolerance, and contain all of the surface tolerance, and contain all of the surface elements.elements.

0.2


0.2 Tolerance Zone

14.6 MMC14.0 LMC

14.0 - 14.6

0.2 The surface elements are within the size The surface elements are within the size tolerance but fall outside the prescribed tolerance but fall outside the prescribed flatness tolerance.flatness tolerance.



0.2 Tolerance Zone

14.6 MMC14.0 LMC

14.0 - 14.6

0.2As long as the tolerance zone for flatness As long as the tolerance zone for flatness is parallel to the theoretical plane is parallel to the theoretical plane established at the bottom, the elements established at the bottom, the elements will not fit within the tolerance zone. will not fit within the tolerance zone. However, what has been stipulated is However, what has been stipulated is that the top has to be flat. There is no that the top has to be flat. There is no relationship to the bottom, other than the relationship to the bottom, other than the size dimension. So. . .size dimension. So. . .



0.2 Tolerance Zone

14.6 MMC14.0 LMC

14.0 - 14.6

0.2Placing gage blocks under one end of the part creates Placing gage blocks under one end of the part creates an equalizing effect on the object. We can now an equalizing effect on the object. We can now verify whether or not, under such circumstances, the verify whether or not, under such circumstances, the elements of the surface are within the prescribed elements of the surface are within the prescribed tolerance zone. As can be seen in the illustration, tolerance zone. As can be seen in the illustration, with this adjustment, all of the elements fall within with this adjustment, all of the elements fall within the tolerance for the tolerance for size size andand form. form.


Gage BlockGage Block


0.4 Tolerance Zone

7.2 MMC6.0 LMC

6.0 – 7.2

0.4The full range of the tolerance zone for flatness The full range of the tolerance zone for flatness becomes available only after the departure becomes available only after the departure from MMC exceeds the width of the tolerance from MMC exceeds the width of the tolerance zone for flatness. This is because the size zone for flatness. This is because the size limits cannot be violated. When the part is at limits cannot be violated. When the part is at the upper limit of the size tolerance, some of the upper limit of the size tolerance, some of the form tolerance zone must be compromised.the form tolerance zone must be compromised.



This blown up view may help solidify the concept. When nearly at maximum material This blown up view may help solidify the concept. When nearly at maximum material condition, there may not be sufficient space to accommodate the entire form tolerance. condition, there may not be sufficient space to accommodate the entire form tolerance. The 0.4 tolerance range is compromised in this illustration because its limits extend The 0.4 tolerance range is compromised in this illustration because its limits extend beyond the size limits. At MMC the surface would have to be perfectly flat. All surface beyond the size limits. At MMC the surface would have to be perfectly flat. All surface elements must be within the size tolerance zone, indicated by yellow phantom lines.elements must be within the size tolerance zone, indicated by yellow phantom lines.


0.41.2


GEOMETRIC TOLERANCESGEOMETRIC TOLERANCESGEOMETRIC TOLERANCESGEOMETRIC TOLERANCES

CIRCULARITYCIRCULARITYCIRCULARITYCIRCULARITY


DEFINITIONSDEFINITIONS

•CircularityCircularity for a feature other than a sphere is a condition where all points of the for a feature other than a sphere is a condition where all points of the surface intersected by any plane perpendicular to an axis are equidistant from that surface intersected by any plane perpendicular to an axis are equidistant from that axis.axis.

•CircularityCircularity for a sphere is a condition where all points of the surface intersected by for a sphere is a condition where all points of the surface intersected by any plane passing through a common center are equidistant from that center.any plane passing through a common center are equidistant from that center.

•Circular tolerance:Circular tolerance: The amount which surface elements of a controlled diameter The amount which surface elements of a controlled diameter may vary from a theoretically perfect circle.may vary from a theoretically perfect circle.

•Circularity tolerance zone:Circularity tolerance zone: Two concentric circles which are perpendicular to the Two concentric circles which are perpendicular to the diameter axis, or in a plane that passes through the center of a sphere, and separated diameter axis, or in a plane that passes through the center of a sphere, and separated by a radial distance equal to the tolerance value, and within which, at by a radial distance equal to the tolerance value, and within which, at anyany cross cross section, each circular element of the surface must lie.section, each circular element of the surface must lie.


DEFINITIONSDEFINITIONS

CircularityCircularity for a feature other than a sphere is a condition where all points of the surface for a feature other than a sphere is a condition where all points of the surface intersected by any plane perpendicular to an axis are equidistant from that axis.intersected by any plane perpendicular to an axis are equidistant from that axis.

CircularityCircularity for a sphere is a condition where all points of the surface intersected by any plane for a sphere is a condition where all points of the surface intersected by any plane passing through a common center are equidistant from that center.passing through a common center are equidistant from that center.

Circular tolerance:Circular tolerance: The amount which surface elements of a controlled diameter may vary from The amount which surface elements of a controlled diameter may vary from a theoretically perfect circle.a theoretically perfect circle.

Circularity tolerance zone:Circularity tolerance zone: Two concentric circles which are perpendicular to the diameter Two concentric circles which are perpendicular to the diameter axis, or in a plane that passes through the center of a sphere, and separated by a radial axis, or in a plane that passes through the center of a sphere, and separated by a radial distance equal to the tolerance value, and within which, at any cross section, each circular distance equal to the tolerance value, and within which, at any cross section, each circular element of the surface must lie. (Many cross sections must be inspected)element of the surface must lie. (Many cross sections must be inspected)

Note:Note: A circularity tolerance zone—two concentric circles—is conceptually easy to visualize. A circularity tolerance zone—two concentric circles—is conceptually easy to visualize. However, verification of a circularity form control is complicated enough that a separate ANSI However, verification of a circularity form control is complicated enough that a separate ANSI standard (ANSI B89.3.1) is required to provide an expanded explanation of standard (ANSI B89.3.1) is required to provide an expanded explanation of specificationspecification and and inspectioninspection requirements. For example, the specification requirements. For example, the specification .005 LSC 150 .010 means that means that the roundness of the controlled surface shall be within .005 inches as determined by the least the roundness of the controlled surface shall be within .005 inches as determined by the least squares circle method with 150 cycles per revolution, using a .010 radius stylus tip.squares circle method with 150 cycles per revolution, using a .010 radius stylus tip.


GEOMETRIC TOLERANCESGEOMETRIC TOLERANCESGEOMETRIC TOLERANCESGEOMETRIC TOLERANCES

Circularity being gauged in process of part production. Circularity being gauged in process of part production.


CircularityCircularity

•Circularity is a (2D tolerance Zone ) surface feature form control.Circularity is a (2D tolerance Zone ) surface feature form control. When When circularity is applied to an circularity is applied to an external featureexternal feature such as the diameter of a pin or shaft, such as the diameter of a pin or shaft, the the outerouter boundary (larger tolerance band or circle) is first established by boundary (larger tolerance band or circle) is first established by circumscribing the high points of the surface using a variable gage—one that will circumscribing the high points of the surface using a variable gage—one that will collapse around the external diameter while maintaining its circular shape. collapse around the external diameter while maintaining its circular shape.

•The The innerinner boundary of the external feature can then be established as radially boundary of the external feature can then be established as radially smaller than the upper limit of the size tolerance by the amount of the specified smaller than the upper limit of the size tolerance by the amount of the specified form tolerance. However, the actual feature, at any point of measurement, must form tolerance. However, the actual feature, at any point of measurement, must be within the size envelope allowed by rule #1. be within the size envelope allowed by rule #1.



•When circularity control is applied to an When circularity control is applied to an internalinternal feature, such as a hole, the feature, such as a hole, the innerinner boundary (smaller tolerance band or circle) is established by gage contact of the high boundary (smaller tolerance band or circle) is established by gage contact of the high points of the surface. points of the surface.

•The The outerouter boundary is radially larger than the smaller size tolerance limit by the amount boundary is radially larger than the smaller size tolerance limit by the amount of the specified form tolerance. In this case also, the feature, at any point of of the specified form tolerance. In this case also, the feature, at any point of measurement (perpendicular to the axis), must be within the limits of size. measurement (perpendicular to the axis), must be within the limits of size.



The specified circularity requires that within the tolerance limits established by The specified circularity requires that within the tolerance limits established by the size dimension, the form tolerance (the size dimension, the form tolerance (all circular cross-sections on the partall circular cross-sections on the part) ) must not vary from true circularity beyond the amount permitted by the circularity must not vary from true circularity beyond the amount permitted by the circularity tolerance, which consists of two concentric circles spaced apart by 0.4 mm tolerance, which consists of two concentric circles spaced apart by 0.4 mm radialradial distance.distance.

0.4


Two concentric circles establish the circularity tolerance zone.Two concentric circles establish the circularity tolerance zone.


0.4



Smallest true circleSmallest true circle that circumscribesthat circumscribes the high pointsthe high points of the featureof the feature diameter—within diameter—within tolerancetolerance

0.4


Smallest true circleSmallest true circle that circumscribesthat circumscribes the high pointsthe high points of the featureof the feature diameter—within diameter—within

tolerance.tolerance.


The outline of the actual part and its cross The outline of the actual part and its cross section are shown. section are shown. After a measurement is After a measurement is taken at a specific location, the part is taken at a specific location, the part is rotated slowly approx 30 deg. where another rotated slowly approx 30 deg. where another measurement is taken. This procedure measurement is taken. This procedure continues all around the part.continues all around the part.

Note that all elements of the circular section Note that all elements of the circular section are within the boundaries of the tolerance are within the boundaries of the tolerance limits.limits.

0.4

0.4 Offset of 0.4 Offset of concentric circlesconcentric circles


Smallest true circleSmallest true circle that circumscribesthat circumscribes the high pointsthe high points of the featureof the feature diameter—within diameter—within

tolerance.tolerance.


Measurements are taken at many section Measurements are taken at many section locations along the part.locations along the part.

The gauge is reset between each The gauge is reset between each measurement. measurement.

0.4

0.4 Offset of 0.4 Offset of concentric circlesconcentric circles


•Diametrical features such as cylinders, cones, and spheres are the only features Diametrical features such as cylinders, cones, and spheres are the only features that circularity can appropriately be applied to.that circularity can appropriately be applied to.

•Circularity cannot be modified to apply at MMC or LMCCircularity cannot be modified to apply at MMC or LMC . It comes under the . It comes under the control of size tolerances and general rule #1, which stipulates that the form must control of size tolerances and general rule #1, which stipulates that the form must be perfect when the part is at MMC. Circularity, therefore, always applies be perfect when the part is at MMC. Circularity, therefore, always applies regardless of feature size, and must be contained within the boundaries of the size regardless of feature size, and must be contained within the boundaries of the size limits.limits.



Circularity Indirectly Controlled byCircularity Indirectly Controlled byOther Geometric TolerancesOther Geometric Tolerances

If circularity is determined to be a necessary specification, care should be taken If circularity is determined to be a necessary specification, care should be taken to ascertain the effects of other geometric tolerances that may also influence or to ascertain the effects of other geometric tolerances that may also influence or indirectly control circularity. indirectly control circularity. In addition to circularity, geometric tolerances In addition to circularity, geometric tolerances controlling cylindricity, profile, and runout also influence the circular form of controlling cylindricity, profile, and runout also influence the circular form of features. features.


FORM CONTROLSFORM CONTROLSFORM CONTROLSFORM CONTROLS

CYLINDRICITYCYLINDRICITYCYLINDRICITYCYLINDRICITY


CYLINDRICITYCYLINDRICITY

CylindricityCylindricity: : A condition of a surface of revolution in which all points on the surface are A condition of a surface of revolution in which all points on the surface are perpendicular and equidistantperpendicular and equidistant from a common axis. from a common axis. Cylindricity can control Cylindricity can control straightness and circularitystraightness and circularity

Cylindricity ToleranceCylindricity Tolerance:: A 3D boundaryA 3D boundary defined by two theoretically perfect coaxial defined by two theoretically perfect coaxial cylinderscylinders within which all the elements of the specified surface must lie. within which all the elements of the specified surface must lie.

Cylindricity (3D) Tolerance ZoneCylindricity (3D) Tolerance Zone:: The radial distance between the two coaxial cylinders The radial distance between the two coaxial cylinders defines the tolerance zone and represents the amount that surface elements are allowed defines the tolerance zone and represents the amount that surface elements are allowed to vary from a perfect cylinder. This numerical value (always less than one-half of the to vary from a perfect cylinder. This numerical value (always less than one-half of the diametrical tolerance) is specified in the tolerance cell of the feature control frame. diametrical tolerance) is specified in the tolerance cell of the feature control frame.

Note:Note: As a surface form control, cylindricity is As a surface form control, cylindricity is always considered RFSalways considered RFS, and the physical , and the physical limits imposed by size dimensions cannot be violated. Datums are neither proper nor limits imposed by size dimensions cannot be violated. Datums are neither proper nor allowed in the feature control frame, and the tolerance cannot be modified to consider allowed in the feature control frame, and the tolerance cannot be modified to consider additional tolerance as departure from MMC occurs. A diameter symbol zone additional tolerance as departure from MMC occurs. A diameter symbol zone descriptor cannot be used in the feature control frame. descriptor cannot be used in the feature control frame.

Tolerances Of Form—CylindricityTolerances Of Form—CylindricityDefinitions of TermsDefinitions of Terms


•When cylindricity control is applied to an When cylindricity control is applied to an externalexternal feature, the outer boundary feature, the outer boundary (larger cylinder) is typically established by circumscribing the high points of the (larger cylinder) is typically established by circumscribing the high points of the surface. The inner boundary is radially smaller by the amount of the specified surface. The inner boundary is radially smaller by the amount of the specified tolerance. The feature, at any point of measurement (a plane, perpendicular to the tolerance. The feature, at any point of measurement (a plane, perpendicular to the axis), must be within the limits of size. axis), must be within the limits of size.

Tolerances Of Form - CylindricityTolerances Of Form - Cylindricity



When cylindricity control is applied to an When cylindricity control is applied to an internalinternal feature, the inner boundary (smaller feature, the inner boundary (smaller cylinder) is typically established by gage contact with the high points of the surface. cylinder) is typically established by gage contact with the high points of the surface. The outer boundary is radially larger by the amount of the specified tolerance. The The outer boundary is radially larger by the amount of the specified tolerance. The feature, at any point of measurement, must be within the limits of size. feature, at any point of measurement, must be within the limits of size.


GEOMETRIC CONTROLGEOMETRIC CONTROLFOR CYLINDRICITYFOR CYLINDRICITY


•The geometric control for cylindricity is a feature The geometric control for cylindricity is a feature formform tolerance which controls tolerance which controls circular, longitudinal, and parallel elements of the feature circular, longitudinal, and parallel elements of the feature surface elementssurface elements only. only. Because it is strictly a surface element control, datums are neither proper nor allowed. Because it is strictly a surface element control, datums are neither proper nor allowed. As is the case with all surface controls, cylindricity always applies regardless of feature As is the case with all surface controls, cylindricity always applies regardless of feature size.size.

•Because cylindricity can Because cylindricity can onlyonly be applied to features and cannot be applied to features be applied to features and cannot be applied to features of size, material condition modifiers of size, material condition modifiers cannotcannot be used with a cylindricity specification. be used with a cylindricity specification.

•The size envelope imposed by dimensional limits and Rule #1 are never overridden by The size envelope imposed by dimensional limits and Rule #1 are never overridden by a geometric tolerance for cylindricity, and the geometric tolerance becomes the a geometric tolerance for cylindricity, and the geometric tolerance becomes the controlling factor only when departure from MMC exceeds the cylindricity tolerance controlling factor only when departure from MMC exceeds the cylindricity tolerance value. Therefore, the value. Therefore, the virtual conditionvirtual condition of the controlled feature is of the controlled feature is notnot affected. affected.


OVERVIEW


0.4

A feature control frame describing cylindricity control may be called out in either A feature control frame describing cylindricity control may be called out in either view and is applied by using a leader line, as shown.view and is applied by using a leader line, as shown.

0.4OR

Verifying Cylindricity Geometric ToleranceVerifying Cylindricity Geometric Tolerance


0.4

Tolerance zone is twoTolerance zone is twocoaxialcoaxial cylinderscylinders


Multiple-section measurements are taken Multiple-section measurements are taken just like the measurements for just like the measurements for circularity, except circularity, except the gauge is NOT the gauge is NOT reset between sections.reset between sections.


0.4

Smallest true cylinderSmallest true cylinder that circumscribesthat circumscribes the high pointsthe high points of the featureof the feature diameter.diameter.

0.4 Radial Distance0.4 Radial Distance

Tolerance zone is twoTolerance zone is twocoaxialcoaxial cylinders cylinders



0.2

10.5 9.5

The size tolerance zone consists of two coaxial The size tolerance zone consists of two coaxial cylinders, 0.5 mm apart. This tolerance defines cylinders, 0.5 mm apart. This tolerance defines the actual local size limits.the actual local size limits.

Cylindricity Geometric Tolerance—Always RFS Cylindricity Geometric Tolerance—Always RFS


0.2

10.5 9.5

The cylindricity tolerance zone consists of two The cylindricity tolerance zone consists of two coaxial cylinders, 0.2 mm apart. This tolerance coaxial cylinders, 0.2 mm apart. This tolerance can “float” within the larger size tolerance.can “float” within the larger size tolerance.


The size tolerance zone consists of two coaxial The size tolerance zone consists of two coaxial cylinders, 0.5 mm apart. This tolerance defines cylinders, 0.5 mm apart. This tolerance defines the actual local size limits.the actual local size limits.


Coaxial cylinders establish the Coaxial cylinders establish the tolerance zone for feature cylindricity.tolerance zone for feature cylindricity.


Feature size tolerance.Feature size tolerance. (While (While surface elements are restricted surface elements are restricted to the refined tolerance zone, the to the refined tolerance zone, the actual local [measured] sizeactual local [measured] size of of the cylindrical feature may vary the cylindrical feature may vary within the larger boundaries.)within the larger boundaries.)

0.2


Coaxial cylinders establish the Coaxial cylinders establish the tolerance zone for feature cylindricity tolerance zone for feature cylindricity (RFS). (RFS).

At any measuring position, all At any measuring position, all surface elements must be within surface elements must be within the cylindricity tolerance zone. the cylindricity tolerance zone. They may vary within the zone, They may vary within the zone, and the entire zone may expand and the entire zone may expand or contract within the larger size or contract within the larger size tolerance. tolerance.


0.2

Feature size tolerance. (While Feature size tolerance. (While surface elements are restricted surface elements are restricted to the refined tolerance zone, the to the refined tolerance zone, the actual local [measured] sizeactual local [measured] size of of the cylindrical feature may vary the cylindrical feature may vary within the larger boundaries.)within the larger boundaries.)


The cylindricity tolerance zone The cylindricity tolerance zone may extend beyond the lower may extend beyond the lower limit of the size tolerance, but limit of the size tolerance, but no elements on the surface can no elements on the surface can be located outside of those be located outside of those limits. That part of the limits. That part of the tolerance would be sacrificed.tolerance would be sacrificed.


0.2



The geometric tolerance for The geometric tolerance for cylindricity becomes the cylindricity becomes the controlling factor only when controlling factor only when departure from MMC exceeds departure from MMC exceeds the cylindricity tolerance value.the cylindricity tolerance value.


0.2


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