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Based on the ASME Y14.5M-
1994 Dimensioning andTolerancing Standard
DIMENSIONALENGINEERING
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Tolerances
of Form
Straightness Flatness
Circularity Cylindricity
(ASME Y14.5M-1994, 6.4.1)
(ASME Y14.5M-1994, 6.4.3)
(ASME Y14.5M-1994, 6.4.2)
(ASME Y14.5M-1994, 6.4.4)
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Extreme Variations of FormAllowed By Size Tolerance
25.125
25(MMC)
25.1(LMC)
25.1(LMC)
25(MMC)
25.1(LMC)
MMC PerfectForm Boundary
Internal Feature of Size
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Extreme Variations of FormAllowed By Size Tolerance
2524.9
25(MMC)24.9
(LMC)
24.9(LMC)
MMC PerfectForm Boundary
25(MMC)
24.9(LMC)
External Feature of Size
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25+/-0.25
0.1 Tolerance
0.5 Tolerance
Straightness is the condition where an element of asurface or an axis is a straight line
Straightness(Flat Surfaces)
0.5 0.1
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Straightness(Flat Surfaces)
24.75 min
25.25 max
0.5 Tolerance Zone
0.1 Tolerance Zone
The straightness tolerance is applied in the view where theelements to be controlled are represented by a straight line
In this example each line element of the surface must liewithin a tolerance zone defined by two parallel linesseparated by the specified tolerance value applied to eachview. All points on the surface must lie within the limits ofsize and the applicable straightness limit.
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Straightness(Surface Elements)
MMC
0.1 Tolerance Zone
0.1
MMC
0.1 Tolerance Zone
MMC
0.1 Tolerance Zone
In this example each longitudinal element of the surface mustlie within a tolerance zone defined by two parallel linesseparated by the specified tolerance value. The feature mustbe within the limits of size and the boundary of perfect form at
MMC. Any barreling or waisting of the feature must notexceed the size limits of the feature.
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Straightness (RFS)
0.1
Outer Boundary (Max)
MMC
0.1 DiameterTolerance Zone
Outer Boundary = Actual Feature Size + Straightness Tolerance
n this example the derived median line of the features actual local sizemust lie within a tolerance zone defined by a cylinder whose diameter isqual to the specified tolerance value regardless of the feature size.
Each circular element of the feature must be within the specified limits ofize. However, the boundary of perfect form at MMC can be violated upo the maximum outer boundary or virtual condition diameter.
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Straightness (MMC)1514.85
15.1 Virtual Condition
15(MMC)
0.1 DiameterTolerance Zone
15.1 Virtual Condition
14.85
(LMC)
0.25 DiameterTolerance Zone
Virtual Condition = MMC Feature Size + Straightness Tolerance
this example the derived median line of the features actual local size
ust lie within a tolerance zone defined by a cylinder whose diameter isqual to the specified tolerance value at MMC. As each circular elementf the feature departs from MMC, the diameter of the tolerance cylinderallowed to increase by an amount equal to the departure from the local
MMC size. Each circular element of the feature must be within thepecified limits of size. However, the boundary of perfect form at MMCan be violated up to the virtual condition diameter.
0.1 M
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Flatness
Flatness is the condition of a surface having all elements inone plane. Flatness must fall within the limits of size. Theflatness tolerance must be less than the size tolerance.
25 +/-0.25
24.75 min25.25 max
0.1
0.1 Tolerance Zone
0.1 Tolerance Zone
In this example the entire surface must lie within a tolerancezone defined by two parallel planes separated by the specified
tolerance value. All points on the surface must lie within thelimits of size and the flatness limit.
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Circularity is the condition of a surface where all points of thesurface intersected by any plane perpendicular to a common
axis are equidistant from that axis. The circularity tolerancemust be less than the size tolerance
90
90
0.1
0.1 Wide Tolerance Zone
Circularity(Roundness)
In this example each circular element of the surface must lie within a
tolerance zone defined by two concentric circles separated by thespecified tolerance value. All points on the surface must lie within thelimits of size and the circularity limit.
0.1
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Cylindricity
Cylindricity is the condition of a surface of revolution in whichall points are equidistant from a common axis. Cylindricity is acomposite control of form which includes circularity
(roundness), straightness, and taper of a cylindrical feature.
0.1 Tolerance Zone
MMC
0.1
In this example the entire surface must lie within a tolerance zonedefined by two concentric cylinders separated by the specified
tolerance value. All points on the surface must lie within the limits ofsize and the cylindricity limit.
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____________ and___________ are individual line or circular
element (2-D) controls.
Form Control Quiz
The four form controls are____________,________,___________, and____________.
Rule #1 states that unless otherwise specified a feature of
size must have____________at MMC.
________ and____________are surface (3-D) controls.
Circularity can be applied to both________and_______ cylindricalparts.
1.
2.
3.
4.
5.
Form controls require a datum reference.
Form controls do not directly control a features size.
A features form tolerance must be less than its sizetolerance.
Flatness controls the orientation of a feature.
Size limits implicitly control a features form.
6.
7.
8.
9.
10.
Questions #1-5 Fill in blanks (choose from below)
straightnessflatness
circularity
cylindricity
perfect form
straight tapered profile
true position
angularity
Answer questions #6-10 True or False
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Tolerances of
Orientation
Angularity
Perpendicularity
Parallelism
(ASME Y14.5M-1994 ,6.6.2)
(ASME Y14.5M-1994 ,6.6.4)
(ASME Y14.5M-1994 ,6.6.3)
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Angularity(Feature Surface to Datum Surface)
Angularity is the condition of the planar feature surface at a
specified angle (other than 90 degrees) to the datumreference plane, within the specified tolerance zone.
A
20 +/-0.5
30 o
A
19.5 min
0.3 WideTolerance
Zone
30o
A
20.5 max
0.3 WideTolerance
Zone
30o
The tolerance zone in this example is definedby two parallel planes oriented at thespecified angle to the datum reference plane.
0.3 A
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Angularity is the condition of the feature axis at a specified
angle (other than 90 degrees) to the datum reference plane,within the specified tolerance zone.
A
0.3 A
A
60 o
The tolerance zone in this example is defined by acylinder equal to the length of the feature, orientedat the specified angle to the datum reference plane.
0.3 CircularTolerance Zone
0.3 CircularTolerance Zone
Angularity(Feature Axis to Datum Surface)
NOTE: Tolerance appliesto feature at RFS
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0.3 CircularTolerance Zone
NOTE: Toleranceapplies to feature
at RFS
Angularity is the condition of the feature axis at a specified
angle (other than 90 degrees) to the datum reference axis,within the specified tolerance zone.
0.3 CircularTolerance Zone
A
Datum Axis A
Angularity(Feature Axis to Datum Axis)
The tolerance zone in this example is defined by acylinder equal to the length of the feature, orientedat the specified angle to the datum reference axis.
NOTE: Feature axis must liewithin tolerance zone cylinder
0.3 A
o45
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0.3 A
A
0.3 WideTolerance Zone
A A
Perpendicularity is the condition of the planar featuresurface at a right angle to the datum reference plane, within
the specified tolerance zone.
Perpendicularity(Feature Surface to Datum Surface)
0.3 Wide ToleranceZone
The tolerance zone in this example isdefined by two parallel planes orientedperpendicular to the datum referenceplane.
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C
Perpendicularity is the condition of the feature axis at a right
angle to the datum reference plane, within the specifiedtolerance zone.
Perpendicularity(Feature Axis to Datum Surface)
0.3 C
0.3 CircularTolerance Zone
0.3 DiameterTolerance Zone
0.3 CircularTolerance Zone
NOTE: Tolerance appliesto feature at RFS
The tolerance zone in this example isdefined by a cylinder equal to the length ofthe feature, oriented perpendicular to thedatum reference plane.
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Perpendicularity(Feature Axis to Datum Axis)
NOTE: Tolerance appliesto feature at RFS
The tolerance zone in this example isdefined by two parallel planes orientedperpendicular to the datum reference axis.
Perpendicularity is the condition of the feature axis at a right
angle to the datum reference axis, within the specifiedtolerance zone.
0.3 Wide ToleranceZone
A
Datum Axis A
0.3 A
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0.3 A
A
25 +/-0.5
5.5 max
0.3 Wide Tolerance Zone
A
24.5 min
0.3 Wide Tolerance Zone
A
Parallelism is the condition of the planar feature surface
equidistant at all points from the datum reference plane,within the specified tolerance zone.
Parallelism(Feature Surface to Datum Surface)
The tolerance zone in this exampleis defined by two parallel planesoriented parallel to the datumreference plane.
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A
0.3 Wide ToleranceZone
Parallelism(Feature Axis to Datum Surface)
0.3 A
A
NOTE: The specified tolerancedoes not apply to the orientationof the feature axis in this direction
Parallelism is the condition of the feature axis equidistant
along its length from the datum reference plane, within thespecified tolerance zone.
The tolerance zone in this exampleis defined by two parallel planesoriented parallel to the datumreference plane.
NOTE: Tolerance appliesto feature at RFS
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A
B
Parallelism(Feature Axis to Datum Surfaces)
A
B
0.3 CircularTolerance Zone
0.3 CircularTolerance Zone
0.3 CircularTolerance Zone
Parallelism is the condition of the feature axis equidistant
along its length from the two datum reference planes, withinthe specified tolerance zone.
The tolerance zone in this example isdefined by a cylinder equal to thelength of the feature, oriented parallelto the datum reference planes.
NOTE: Tolerance appliesto feature at RFS
0.3 A B
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Parallelism(Feature Axis to Datum Axis)
Parallelism is the condition of the feature axis equidistant alongits length from the datum reference axis, within the specified
tolerance zone.
A
0.1 A
0.1 CircularTolerance Zone
0.1 Circular
Tolerance Zone
Datum Axis A
The tolerance zone in this example is
defined by a cylinder equal to thelength of the feature, orientedparallel to the datum reference axis.
NOTE: Tolerance appliesto feature at RFS
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Orientation Control Quiz
The three orientation controls are__________,___________,and________________.
1.
2.
3.
4.
5.
A_______________ is always required when applying any ofthe orientation controls.
________________ is the appropriate geometric tolerance whencontrolling the orientation of a feature at right angles to a datumreference.
Orientation tolerances indirectly control a features form.
Mathematically all three orientation tolerances are_________.
Orientation tolerances do not control the________ of a feature.
6.
Orientation tolerance zones can be cylindrical.
Parallelism tolerances do not apply to features of size.
To apply an angularity tolerance the desired angle mustbe indicated as a basic dimension.
7.
8.
9.
10.
To apply a perpendicularity tolerance the desired angle
must be indicated as a basic dimension.
Questions #1-5 Fill in blanks (choose from below)
angularity
perpendicularityparallelism
datum reference
identical
location
profile
datum featuredatum target
Answer questions #6-10 True or False
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Tolerances
of Runout
Circular Runout
(ASME Y14.5M-1994, 6.7.1.2.1)
Total Runout(ASME Y14.5M-1994 ,6.7.1.2.2)
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Datum feature
Datum axis (establishedfrom datum feature
Angled surfacesconstructed arounda datum axis
External surfaces
constructed arounda datum axis
Internal surfacesconstructed around adatum axis
Surfaces constructedperpendicular to a
datum axis
Features Applicableto Runout Tolerancing
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0+ -
Full IndicatorMovement
Maximum Minimum
Total
Tolerance
MaximumReading
MinimumReading
Full PartRotation
Measuring position #1(circular element #1)
Circular Runout
When measuring circular runout, the indicator must be reset to zero at each measuring positionalong the feature surface. Each individual circular element of the surface is independentlyallowed the full specified tolerance. In this example, circular runout can be used to detect 2-dimensional wobble (orientation) and waviness (form), but not 3-dimensional characteristicssuch as surface profile (overall form) or surface wobble (overall orientation).
Measuring position #2(circular element #2)
Circular runout can only be applied on an
RFS basis and cannot be modified toMMC or LMC.
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o360 PartRotation
50 +/- 2o o
As Shownon Drawing
Means This:
Datum axis A
Single circularelement
Circular Runout(Angled Surface to Datum Axis)
0.75 A
A
50 +/-0.25
0+-
NOTE: Circular runout in this example only
controls the 2-dimensional circular elements(circularity and coaxiality) of the angled featuresurface not the entire angled feature surface
Full IndicatorMovement( )
The tolerance zone for any individual circularelement is equal to the total allowable movement
of a dial indicator fixed in a position normal to thetrue geometric shape of the feature surface whenthe part is rotated 360 degrees about the datumaxis. The tolerance limit is applied independentlyto each individual measuring position along thefeature surface.
Allowable indicatorreading = 0.75 max.
When measuring circularrunout, the indicator must
be reset when repositionedalong the feature surface.
Collet or Chuck
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As Shownon Drawing
50 +/-0.25
0.75 A
Circular Runout(Surface Perpendicular to Datum Axis)
o360 PartRotation
0+-
Datum axis A
Single circularelement
NOTE: Circular runout in this example willonly control variation in the 2-dimensionalcircular elements of the planar surface (wobbleand waviness) not the entire feature surface
The tolerance zone for any individual circularelement is equal to the total allowable movement
of a dial indicator fixed in a position normal to thetrue geometric shape of the feature surface whenthe part is rotated 360 degrees about the datumaxis. The tolerance limit is applied independentlyto each individual measuring position along thefeature surface.
Means This:
Allowable indicatorreading = 0.75 max.
When measuring circular runout, the indicator mustbe reset when repositioned along the feature surface.
A
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0+ -
Allowable indicatorreading = 0.75 max.
Single circular element
o360 PartRotation
Means This:
As Shownon Drawing
50 +/-0.25
0.75 A
Datum axis A
When measuring circular runout,the indicator must be reset whenrepositioned along the featuresurface.
Circular Runout(Surface Coaxial to Datum Axis)
The tolerance zone for any individual circular element is equalto the total allowable movement of a dial indicator fixed in aposition normal to the true geometric shape of the feature
surface when the part is rotated 360 degrees about the datumaxis. The tolerance limit is applied independently to eachindividual measuring position along the feature surface.
NOTE: Circular runout in this example will
only control variation in the 2-dimensionalcircular elements of the surface (circularity andcoaxiality) not the entire feature surface
A
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0+ -
Allowable indicatorreading = 0.75 max.
Single circular element
o360 PartRotation
Means This:
As Shownon Drawing
0.75 A-B
Datum axis A-B
When measuring circular runout,the indicator must be reset whenrepositioned along the featuresurface.
Circular Runout(Surface Coaxial to Datum Axis)
The tolerance zone for any individual circular element is equalto the total allowable movement of a dial indicator fixed in aposition normal to the true geometric shape of the feature
surface when the part is rotated 360 degrees about the datumaxis. The tolerance limit is applied independently to eachindividual measuring position along the feature surface.
NOTE: Circular runout in this example will
only control variation in the 2-dimensionalcircular elements of the surface (circularity andcoaxiality) not the entire feature surface
Machine
center
Machinecenter
BA
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As Shownon Drawing
50 +/-0.25
Circular Runout(Surface Related to Datum Surface and Axis)
o360 PartRotation
0+ -
Datum axis B
Single circular element
The tolerance zone for any individual circular element isequal to the total allowable movement of a dial indicator fixedin a position normal to the true geometric shape of the
feature surface when the part is located against the datumsurface and rotated 360 degrees about the datum axis. Thetolerance limit is applied independently to each individualmeasuring position along the feature surface.
Means This:
A
Allowable indicatorreading = 0.75 max.
When measuring circular runout,
the indicator must be reset whenrepositioned along the featuresurface.
Collet or Chuck
Stop collar
0.75 A B
Datum plane A
B
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0+
Full IndicatorMovement
Total
Tolerance
MaximumReading
MinimumReading
Full PartRotation
-
0+ -
Total Runout
Maximum Minimum
When measuring total runout, the indicator is moved in a straight line along the feature surfacewhile the part is rotated about the datum axis. It is also acceptable to measure total runout byevaluating an appropriate number of individual circular elements along the surface while the paris rotated about the datum axis. Because the tolerance value is applied to the entire surface, theindicator must not be reset to zero when moved to each measuring position. In this example,total runout can be used to measure surface profile (overall form) and surface wobble (overallorientation).
IndicatorPath
Total runout can only be applied on an
RFS basis and cannot be modified toMMC or LMC.
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Full PartRotation
50 +/- 2o o
As Shownon Drawing
A
50 +/-0.25
0.75 A
Means This:
Datum axis A
0+-
The tolerance zone for the entire angled surface isequal to the total allowable movement of a dialindicator positioned normal to the true geometric
shape of the feature surface when the part isrotated about the datum axis and the indicator ismoved along the entire length of the featuresurface.0 +-
NOTE: Unlike circular runout, the use of total runout
will provide 3-dimensional composite control of thecumulative variations of circularity, coaxiality,angularity, taper and profile of the angled surface
Total Runout(Angled Surface to Datum Axis)
Collet or Chuck
When measuring total runout, theindicator must not be reset whenrepositioned along the featuresurface.
(applies to the entire feature surface)Allowable indicator reading = 0.75 max.
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0+-
Total Runout(Surface Perpendicular to Datum Axis)
As Shownon Drawing
A
50 +/-0.25
0.75 A
35
10
0+-
Datum axis AFull PartRotation
35
10
Means This:
NOTE: The use of total runout in this examplewill provide composite control of the cumulative
variations of perpendicularity (wobble) andflatness (concavity or convexity) of the featuresurface.
The tolerance zone for the portion of the feature surfaceindicated is equal to the total allowable movement of a dial
indicator positioned normal to the true geometric shape of thefeature surface when the part is rotated about the datum axisand the indicator is moved along the portion of the featuresurface within the area described by the basic dimensions.
When measuring total runout, the indicatormust not be reset when repositioned along thefeature surface.
(applies to portion of feature surface indicated)Allowable indicator reading = 0.75 max.
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Runout Control Quiz
Answer questions #1-12 True or False
Total runout is a 2-dimensional control.1.
Runout tolerances are used on rotating parts.
Total runout tolerances should be applied at MMC.
Runout tolerances can be applied to surfaces at rightangles to the datum reference.
2.
3.
4.
5.
Circular runout tolerances apply to single elements .
6. Circular runout tolerances are used to control an entirefeature surface.
Runout tolerances always require a datum reference.7.
Circular runout and total runout both control axis tosurface relationships.
8.
Circular runout can be applied to control taper of a part.9.
Total runout tolerances are an appropriate way to limitwobble of a rotating surface.
10.
Runout tolerances are used to control a features size. 11.
Total runout can control circularity, straightness, taper,coaxiality, angularity and any other surface variation.
12.
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Tolerancesof Profile
Profile of a Line
Profile of a Surface
(ASME Y14.5M-1994, 6.5.2b)
(ASME Y14.5M-1994, 6.5.2a)
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18 Max
Profile of a Line
2 Wide SizeTolerance Zone
1 A B C
A
17 +/- 1
1 Wide ProfileTolerance Zone
C
A1
20 X 20
A2
20 X 20
A3
20 X 20
B
The profile tolerance zone in this example is defined by twoparallel lines oriented with respect to the datum referenceframe. The profile tolerance zone is free to float within the
larger size tolerance and applies only to the form andorientation of any individual line element along the entiresurface.
rofile of a Line is a two-dimensional tolerance that can be applied to aart feature in situations where the control of the entire feature surface assingle entity is not required or desired. The tolerance applies to the lineement of the surface at each individual cross section indicated on therawing.
16 Min.
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rofile of a Surface is a three-dimensional tolerance that can be applieda part feature in situations where the control of the entire feature
urface as a single entity is desired. The tolerance applies to the entireurface and can be used to control size, location, form and/or orientation
a feature surface.
Profile of a Surface
2 Wide Tolerance ZoneSize, Form and Orientation
A
A1
20 X 20
A2
20 X 20
A3
20 X 20
C 2 A B C
23.5
23.5NominalLocation
The profile tolerance zone in this example is defined by two parallelplanes oriented with respect to the datum reference frame. The profiletolerance zone is located and aligned in a way that enables the part
surface to vary equally about the true profile of the feature.
B
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Profile of a Surface
A1
20 X 20
A2
20 X 20
A3
20 X 20
B
C
50
B
C
50
1 Wide TotalTolerance Zone
(Bilateral Tolerance)
The tolerance zone in this example is defined by two parallel planesoriented with respect to the datum reference frame. The profile tolerancezone is located and aligned in a way that enables the part surface tovary equally about the true profile of the trim.
1 A B C
Nominal Location
0.5 Inboard
0.5 Outboard
rofile of a Surface when applied to trim edges of sheet metal parts will controe location, form and orientation of the entire trimmed surface. When a
lateral value is specified, the tolerance zone allows the trim edge variationnd/or locational error to be on both sides of the true profile. The tolerancepplies to the entire edge surface.
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Profile of a Surface
A1
20 X 20
A2
20 X 20
A3
20 X 20
B
C
50
B
C
50
0.5 Wide TotalTolerance Zone
(Unilateral Tolerance)
rofile of a Surface when applied to trim edges of sheet metal parts will controe location, form and orientation of the entire trimmed surface. When a
nilateral value is specified, the tolerance zone limits the trim edge variationnd/or locational error to one side of the true profile. The tolerance applies toe entire edge surface.
The tolerance zone in this example is defined by two parallel planesoriented with respect to the datum reference frame. The profile tolerancezone is located and aligned in a way that allows the trim surface to varyfrom the true profile only in the inboard direction.
0.5 A B C
Nominal Location
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Profile of a Surface
A1
20 X 20
A2
20 X 20
A3
20 X 20
B
C
50
1.2 A B C
B
C
50
0.5 Inboard
0.7 Outboard
1.2 Wide TotalTolerance Zone
(Unequal Bilateral Tolerance)
rofile of a Surface when applied to trim edges of sheet metal parts will controe location, form and orientation of the entire trimmed surface. Typically when
nequal values are specified, the tolerance zone will represent the actualeasured trim edge variation and/or locational error. The tolerance applies toe entire edge surface.
The tolerance zone in this example is defined by two parallel planesoriented with respect to the datum reference frame. The profile tolerancezone is located and aligned in a way that enables the part surface tovary from the true profile more in one direction (outboard) than in theother (inboard).
0.5
Nominal Location
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A
25
A0.5
0.1
25.2524.75
0.1 Wide Tolerance Zone
A
Composite Profile of Two CoplanarSurfaces w/o Orientation Refinement
Profile of a Surface
Form Only
Location &Orientation
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0.1 Wide Tolerance Zone
0.1 Wide Tolerance Zone
25.25
24.75
A
A
A
25
A0.5A0.1 Form & Orientation
Composite Profile of Two CoplanarSurfaces With Orientation Refinement
Profile of a Surface
Location
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6.
Profile Control Quiz
Profile tolerances always require a datum reference.
Answer questions #1-13 True or False
1.
Profile of a surface tolerance is a 2-dimensional control.
Profile of a line tolerances should be applied at MMC.
Profile tolerances can be applied to features of size.
2.
3.
4.
5.
Profile of a surface tolerance should be used to controltrim edges on sheet metal parts.
Profile tolerances can be combined with other geometriccontrols such as flatness to control a feature.
Profile of a line tolerances apply to an entire surface.7.
Profile of a line controls apply to individual line elements.8.
Profile tolerances only control the location of a surface.9.
Composite profile controls should be avoided becausethey are more restrictive and very difficult to check.
10.
Profile tolerances can be applied either bilateral orunilateral to a feature.
11.
Profile tolerances can be applied in both freestate andrestrained datum conditions.
12.
Tolerances shown in the lower segment of a compositeprofile feature control frame control the location of a
feature to the specified datums.
13.
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In composite profile applications, the tolerance shown in the upper
segment of the feature control frame applies only to the________ ofthe feature.
Profile Control Quiz
The two types of profile tolerances are_________________,and____________________.
1.
2.
3.4.
5.
Profile tolerances can be used to control the________,____,___________ , and sometimes size of a feature.
Profile tolerances can be applied_________ or__________._________________ tolerances are 2-dimensional controls.
____________________ tolerances are 3-dimensional controls.
Questions #1-9 Fill in blanks (choose from below)
6._________________ can be used when different tolerances arerequired for location and form and/or orientation.
7. When using profile tolerances to control the location and/or orientation ofa feature, a_______________ must be includedin the feature control frame.
8. When using profile tolerances to control form only, a________________ is not required in the feature control frame.
9.
profile of a linedatum reference
composite profile bilateral
location form
primary datum
true geometric counterpart
orientationprofile of a surface
unilateral
virtual condition
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Tolerances
of Location
True Position
Concentricity
Symmetry
(ASME Y14.5M-1994, 5.2)
(ASME Y14.5M-1994, 5.12)
(ASME Y14.5M-1994, 5.13)
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Notes
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10.25 +/- 0.5
10.25 +/- 0.5
8.5 +/- 0.1
RectangularTolerance Zone
10.25
10.25
8.5 +/- 0.1
Circular ToleranceZone
B
A
C
Coordinate vs GeometricTolerancing Methods
Coordinate Dimensioning Geometric Dimensioning
Rectangular Tolerance Zone Circular Tolerance Zone
1.4
+/- 0.5
+/- 0.5
57% LargerTolerance Zone
Circular Tolerance Zone
Rectangular Tolerance Zone
Increased Effective Tolerance
1.4 A B C
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Formula to determine the actual radialposition of a feature using measuredcoordinate values (RFS)
Z positional tolerance /2
X2 Y2+Z =
X =2
Y =2
X
Y
ZFeature axis actual
location (measured)
Positionaltolerance zonecylinder
Feature axis trueposition (designed)
Positional Tolerance Verification
Z = total radial deviation
X measured deviation
Y measured deviation
Actual featureboundary
(Applies when a circular tolerance is indicated)
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Formula to determine the actual radialposition of a feature using measuredcoordinate values (MMC)
Z
X2 Y2+Z =
X =2
Y =2
X
Y
ZFeature axis actual
location (measured)
Positionaltolerance zonecylinder
Feature axis trueposition (designed)
Positional Tolerance Verification
Z = total radial deviation
X measured deviationY measured deviation
Actual featureboundary
+( actual - MMC)2
= positional tolerance
(Applies when a circular tolerance is indicated)
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Bi-directional True PositionRectangular Coordinate Method
3510
10
AC
B
1.5 A B C
0.5 A B C2X
2X
10 35
1.5 WideTolerance
Zone
0.5 WideTolerance Zone
True Position Relatedto Datum Reference Frame
10B
C
Each axis must lie within the 1.5 X 0.5 rectangular tolerance zonebasically located to the datum reference frame
As Shownon Drawing
Means This:
2X 6 +/-0.25
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Bi-directional True PositionMultiple Single-Segment Method
3510
10
AC
B
10 35
1.5 WideTolerance
Zone
0.5 WideTolerance Zone
True Position Relatedto Datum Reference Frame
10B
C
Each axis must lie within the 1.5 X 0.5 rectangular tolerance zonebasically located to the datum reference frame
As Shownon Drawing
Means This:
2X 6 +/-0.25
1.5 A B C0.5 A B
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3510
10
AC
B As Shownon Drawing
Means This:
1.5 A B C 0.5 A B CBOUNDARY BOUNDARY
10 3510 B
C
2X 13 +/-0.25 2X 6 +/-0.25
12.75 MMC width of slot-1.50 Position tolerance
11.25 Maximum boundary
Both holes must be within the size limits and noportion of their surfaces may lie within the areadescribed by the 11.25 x 5.25 maximumboundaries when the part is positioned withrespect to the datum reference frame. Theboundary concept can only be applied on an
MMC basis.
o90
True position boundary relatedto datum reference frame
A
Bi-directional True PositionNoncylndrical Features (Boundary Concept)
MM
5.75 MMC length of slot-0.50 Position tolerance
5.25 maximum boundary
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Composite True PositionWithout Pattern Orientation Control
3510
10
AC
B
10 35
True Position Relatedto Datum ReferenceFrame
10B
C
Each axis must lie within each tolerance zone simultaneously
As Shownon Drawing
Means This:
2X 6 +/-0.25
1.5 A B C0.5 A
0.5 Feature-RelatingTolerance Zone Cylinder
1.5 Pattern-LocatingTolerance Zone Cylinder
patternlocationrelativeto Datums A, B, and Cpatternorientationrelative to
Datum A only (perpendicularity)
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Composite True PositionWith Pattern Orientation Control
3510
10
AC
B
10 35
True Position Relatedto Datum ReferenceFrame
10B
C
Each axis must lie within each tolerance zone simultaneously
As Shownon Drawing
Means This:
2X 6 +/-0.25
0.5 Feature-RelatingTolerance Zone Cylinder
1.5 Pattern-LocatingTolerance Zone Cylinder
patternlocationrelativeto Datums A, B, and C
patternorientationrelative toDatums A and B
1.5 A B C0.5 A B
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Location (Concentricity)Datum Features at RFS
A
15.9515.90
As Shown on Drawing
Derived Median Points ofDiametrically Opposed Elements
Axis of DatumFeature A
Means This:
Within the limits of size and regardless of feature size, all median points ofdiametrically opposed elements must lie within a 0.5 cylindrical
tolerance zone. The axis of the tolerance zone coincides with the axis ofdatum feature A. Concentricity can only be applied on an RFS basis.
0.5 A6.35 +/- 0.05
0.5 CoaxialTolerance Zone
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Location (Symmetry)Datum Features at RFS
A
15.9515.90
0.5 A6.35 +/- 0.05
Derived MedianPoints
Center Plane ofDatum Feature A
0.5 WideTolerance Zone
Means This:
Within the limits of size and regardless of feature size, all median pointsof opposed elements must lie between two parallel planes equally
disposed about datum plane A, 0.5 apart. Symmetry can only beapplied on an RFS basis.
As Shown on Drawing
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True Position Quiz
Answer questions #1-11 True or False
Positional tolerances are applied to individual or patternsof features of size.
1.
Cylindrical tolerance zones more closely represent thefunctional requirements of a pattern of clearance holes.
True position tolerances can control a features size.
Positional tolerances are applied on an MMC, LMC, orRFS basis.
2.
3.
4.
5.
True position tolerance values are used to calculate theminimum size of a feature required for assembly.
6. Composite true position tolerances should be avoided
because it is overly restrictive and difficult to check.
Composite true position tolerances can only be appliedto patterns of related features.
7.
The tolerance value shown in the upper segment of acomposite true position feature control frame appliesto the location of a pattern of features to the specifieddatums.
8.
Positional tolerances can be used to control circularity
9.
10.
11.
The tolerance value shown in the lower segment of acomposite true position feature control frame appliesto the location of a pattern of features to the specified
datums.
True position tolerances can be used to control center
distance relationships between features of size.
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Positional tolerance zones can be___________,___________,or spherical
1.
2.
3.
4.
5.
________________ are used to establish the true (theoreticallyexact) position of a feature from specified datums.
Positional tolerancing is a_____________ control.
Positional tolerance can apply to the____ or________________ ofa feature.
_____ and________ fastener equations are used to determineappropriate clearance hole sizes for mating details
6.
7.
_________ tolerance zones are recommended to prevent fastenerinterference in mating details.
8.
projected3-dimensional
surface boundary floating
location fixed
basic dimensions
maximum material
cylindricalpattern-locating rectangular
feature-relating
True Position Quiz
Questions #1-9 Fill in blanks (choose from below)
The tolerance shown in the upper segment of a composite true
position feature control frame is called the________________tolerance zone.
The tolerance shown in the lower segment of a composite true
position feature control frame is called the________________tolerance zone.
9. Functional gaging principles can be applied when__________________ condition is specified
axis
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Fixed andFloatingFastener
Exercises
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2x M10 X 1.5(Reference)
B
A
?.?
2x 10.50 +/- 0.25
M Calculate RequiredPositional Tolerance
0.52x ??.?? +/- 0.25
M
CalculateNominal Size
A
B
T = H - FH = Minimum Hole Size = 10.25F = Max. Fastener Size = 10
T = 10.25 -10T = ______
Floating Fasteners
H = F +TF = Max. Fastener Size = 10T = Positional Tolerance = 0.50
H = 10 + 0.50
H = ______
n applications where two or more mating details are assembled, and all partsave clearance holes for the fasteners, the floating fastener formulashownelow can be used to calculate the appropriate hole sizes or positional toleranceequirements to ensure assembly. The formula will provide a zero-interference fit
when the features are at MMC and at their extreme of positional tolerance
H= Min. diameter of clearance holeF= Maximum diameter of fastenerT= Positional tolerance diameter
H=F+T or T=H-F
General Equation Applies toEach Part Individually
remember: the size tolerance must be
added to the calculated MMC hole size toobtain the correct nominal value.
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2x M10 X 1.5(Reference)
B
A
0.25
2x 10.50 +/- 0.25
M
0.52x 10.75 +/- 0.25
M
A
B
Floating Fasteners
REMEMBER!!! All Calculations Apply at MMC
H= Min. diameter of clearance holeF= Maximum diameter of fastenerT= Positional tolerance diameter
H=F+T or T=H-F
General Equation Applies toEach Part Individually
T = H - FH = Minimum Hole Size = 10.25F = Max. Fastener Size = 10
T = 10.25 -10T = 0.25
Calculate RequiredPositional Tolerance
F = Max. Fastener Size = 10T = Positional Tolerance = 0.5
H = 10 + .5
H = 10.5 Minimum
H = F +T
n applications where two or more mating details are assembled, and all partsave clearance holes for the fasteners, the floating fastener formulashownelow can be used to calculate the appropriate hole sizes or positional toleranceequirements to ensure assembly. The formula will provide a zero-interference fit
when the features are at MMC and at their extreme of positional tolerance
remember: the size tolerance must be
added to the calculated MMC hole size toobtain the correct nominal value.CalculateNominal Size
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F = Max. Fastener Size = 10.00T = Positional Tolerance = 0.80
2x M10 X 1.5(Reference)
B
A
0.82x ??.?? +/- 0.25
M
Calculate Required
Clearance Hole Size.
2X M10 X 1.5
A
B
Fixed Fasteners
H = 10.00 + 2(0.8)H = _____
H= Min. diameter of clearance holeF= Maximum diameter of fastenerT= Positional tolerance diameter
H=F+2T or T=(H-F)/2
General Equation Used When
Positional Tolerances Are Equal
In fixed fastenerapplications where two mating details have equal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerance required toensure assembly. The formula provides a zero-interference fit when the features
are at MMC and at their extreme of positional tolerance. (Note that in this examplethe positional tolerances indicated are the same for both parts.)
0.8 M 10P
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED
Nominal Size
(MMC For Calculations)
H = F + 2T
remember: the size tolerance
must be added to the calculatedMMC size to obtain the correct
nominal value.
10
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2x M10 X 1.5(Reference)
B
A
2x 11.85 +/- 0.250.8 M
Calculate Required
Clearance Hole Size.
A
B
In fixed fastenerapplications where two mating details have equal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerance required toensure assembly. The formula provides a zero-interference fit when the features
are at MMC and at their extreme of positional tolerance. (Note that in this examplethe positional tolerances indicated are the same for both parts.)
Fixed Fasteners
H = F + 2TF = Max. Fastener Size = 10.00T = Positional Tolerance = 0.80
H = 10.00 + 2(0.8)H = 11.60 Minimum
H= Min. diameter of clearance holeF= Maximum diameter of fastenerT= Positional tolerance diameter
H=F+2T or T=(H-F)/2
General Equation Used When
Positional Tolerances Are Equal
0.8 M 10P
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED
2X M10 X 1.5Nominal Size
(MMC For Calculations)
remember: the size tolerance
must be added to the calculated
MMC size to obtain the correct
nominal value.
REMEMBER!!! All Calculations Apply at MMC
10
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2x M10 X 1.5(Reference)
B
A
2x 11.85 +/- 0.250.8 M
Calculate Required
Clearance Hole Size.
A
B
In fixed fastenerapplications where two mating details have equal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerance required toensure assembly. The formula provides a zero-interference fit when the features
are at MMC and at their extreme of positional tolerance. (Note that in this examplethe positional tolerances indicated are the same for both parts.)
Fixed Fasteners
H = F + 2TF = Max. Fastener Size = 10T = Positional Tolerance = 0.8
H = 10 + 2(0.8)H = 11.6 Minimum
H= Min. diameter of clearance holeF= Maximum diameter of fastenerT= Positional tolerance diameter
H=F+2T or T=(H-F)/2
General Equation Used When
Positional Tolerances Are Equal
0.8 M 10P
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED
2X M10 X 1.5Nominal Size
(MMC For Calculations)
remember: the size tolerance
must be added to the calculated
MMC size to obtain the correct
nominal value.
REMEMBER!!! All Calculations Apply at MMC
10
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2x M10 X 1.5(Reference)
B
A
0.52x 11.25 +/- 0.25
MCalculate Required
Positional Tolerance .
(Both Parts)
A
B
In applications where two mating details are assembled, and one part hasrestrained fasteners, the fixed fastener formulashown below can be used tocalculate appropriate hole sizes and/or positional tolerances required to ensureassembly. The formula will provide a zero-interference fit when the features are
at MMC and at their extreme of positional tolerance. (Note: in this example theresultant positional tolerance is applied to both parts equally.)
Fixed Fasteners
T = (H - F)/2H = Minimum Hole Size = 11F = Max. Fastener Size = 10
T = (11 - 10)/2T = 0.50
H= Min. diameter of clearance holeF= Maximum diameter of fastenerT= Positional tolerance diameter
H=F+2T or T=(H-F)/2
General Equation Used When
Positional Tolerances Are Equal
2X M10 X 1.5
0.5 M 10P
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED
Nominal Size
(MMC For Calculations)
REMEMBER!!! All Calculations Apply at MMC
10
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2x M10 X 1.5(Reference)
B
A
0.52x ??.?? +/- 0.25
M
Calculate Required
Clearance Hole Size.
A
B
Fixed Fasteners
H = Min. diameter of clearance holeF = Maximum diameter of fastenerT1= Positional tolerance (Part A) T2=Positional tolerance (Part B)
H=F+(T1 + T2)
General Equation Used WhenPositional Tolerances Are Not Equal
F = Max. Fastener Size = 10T1 = Positional Tol. (A) = 0.50T2 = Positional Tol. (B) = 1
H = 10+ (0.5 + 1)H = ____
H=F+(T1 + T2)
In fixed fastener applications where two mating details have unequal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerances required toensure assembly. The formula provides a zero-interference fit when the features
are at MMC and at their extreme of positional tolerance. (Note that in this examplethe positional tolerances indicated are not equal.)
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED
2X M10 X 1.5Nominal Size
(MMC For Calculations)
remember: the size tolerance must be
added to the calculated MMC hole size toobtain the correct nominal value.
10
1 M 10P
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2x M10 X 1.5(Reference)
B
A
0.52x 11.75 +/- 0.25
M
Calculate Required
Clearance Hole Size.
A
B
In fixed fastener applications where two mating details have unequal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerances required toensure assembly. The formula provides a zero-interference fit when the features
are at MMC and at their extreme of positional tolerance. (Note that in this examplethe positional tolerances indicated are not equal.)
Fixed Fasteners
F = Max. Fastener Size = 10T1 = Positional Tol. (A) = 0.5T2 = Positional Tol. (B) = 1
H = 10 + (0.5 + 1)H = 11.5 Minimum
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED
H = Min. diameter of clearance holeF = Maximum diameter of fastenerT1= Positional tolerance (Part A) T2=Positional tolerance (Part B)
H= F+(T1 + T2)
General Equation Used WhenPositional Tolerances Are Not Equal
H=F+(T1 + T2)
1 M 10P
2X M10 X 1.5Nominal Size
(MMC For Calculations)
remember: the size tolerance must be
added to the calculated MMC hole size toobtain the correct nominal value.
REMEMBER!!! All Calculations Apply at MMC
10
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D
P
H F
A
B
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS NOT USED
2x 10.05 +/-0.05
B
A
0.5 M2x ??.?? +/-0.25Calculate
Nominal Size
0.5 M
In applications where a projected tolerance zone is notindicated, it isnecessary to select a positional tolerance and minimum clearance hole sizecombination that will allow for any out-of-squareness of the feature containing thefastener. The modified fixed fastener formulashown below can be used to
calculate the appropriate minimum clearance hole size required to ensureassembly. The formula provides a zero-interference fit when the features are atMMC and at the extreme positional tolerance.
Fixed Fasteners
H = 10.00 + 0.5 + 0.5(1 + 2(15/20))H = __________
H= F + T1 + T2 (1+(2P/D))
remember: the size tolerance must be
added to the calculated MMC hole size to
obtain the correct nominal value.
H= Min. diameter of clearance holeF= Maximum diameter of pinT1= Positional tolerance (Part A)T2= Positional tolerance (Part B)D= Min. depth of pin (Part A)P= Maximum projection of pin
F = Max. pin size = 10
T1 = Positional Tol. (A) = 0.5T2 = Positional Tol. (B) = 0.5 D= Min. pin depth = 20. P= Max. pin projection = 15
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D
P
H F
A
B
H= Min. diameter of clearance holeF= Maximum diameter of pinT1= Positional tolerance (Part A)T2= Positional tolerance (Part B)D= Min. depth of pin (Part A)P= Maximum projection of pin
APPLIES WHEN A PROJECTED TOLERANCE ZONE IS NOT USED
2x 10.05 +/-0.05
B
A
0.5 M2x 12 +/-0.25Calculate
Nominal Size
0.5 M
F = Max. pin size = 10
T1 = Positional tol. (A) = 0.5T2 = Positional tol. (B) = 0.5 D= Min. pin depth = 20 P= Max. pin projection = 15
H= F + T1 + T2 (1+(2P/D))
H = 10 + 0.5 + 0.5(1 + 2(15/20))H = 11.75 Minimum
In applications where a projected tolerance zone is notindicated, it isnecessary to select a positional tolerance and minimum clearance hole sizecombination that will allow for any out-of-squareness of the feature containing thefastener. The modified fixed fastener formulashown below can be used to
calculate the appropriate minimum clearance hole size required to ensureassembly. The formula provides a zero-interference fit when the features are atMMC and at the extreme positional tolerance.
Fixed Fasteners
H= F + T1 + T2 (1+(2P/D))
REMEMBER!!! All Calculations Apply at MMC
remember: the size tolerance must be
added to the calculated MMC hole size to
obtain the correct nominal value.
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Extreme Variations of FormAllowed By Size Tolerance
25.1
25
25
24.9
25(MMC)
25.1(LMC)
25.1(LMC)
25(MMC)24.9
(LMC)
24.9(LMC)
25
(MMC)
25.1(LMC)
MMC PerfectForm Boundary
25
(MMC)
24.9(LMC)
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Virtual Condition BoundaryInternal Feature (MMC Concept)
12.5 Virtual Condition Boundary
13.5 MMC Size of Feature
1 Applicable Geometric Tolerance
Calculating Virtual Condition
1 A B CM
14 +/- 0.5
C
BXX.X
XX.X
A
As Shown on Drawing
Axis Location ofMMC Hole Shownat Extreme Limit
Boundary of MMC HoleShown at Extreme Limit
1 Positional
Tolerance Zone atMMC
True (Basic)Position of Hole
True (Basic)Position of Hole
Other PossibleExtreme Locations
Virtual ConditionInner Boundary
Maximum InscribedDiameter( )
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Resultant Condition BoundaryInternal Feature (MMC Concept)
1 A B CM
14 +/- 0.5
C
BXX.X
XX.X
A
16.5 Resultant Condition Boundary
14.5 LMC Size of Feature
2 Geometric Tolerance (at LMC)
Calculating Resultant Condition (Internal Feature)
As Shown on Drawing
Axis Location ofLMC Hole Shownat Extreme Limit
Boundary of LMC HoleShown at Extreme Limit
2 Positional
Tolerance Zone atLMC
True (Basic)Position of Hole
True (Basic)Position of Hole
Other PossibleExtreme Locations
Resultant ConditionOuter Boundary
Minimum CircumscribedDiameter( )
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Virtual Condition BoundaryExternal Feature (MMC Concept)
15.5 Virtual Condition Boundary
14.5 MMC Size of Feature
1 Applicable Geometric Tolerance
Calculating Virtual Condition
1 A B CM
14 +/- 0.5
C
BXX.X
XX.XX
A
As Shown on Drawing
Axis Location ofMMC Feature Shownat Extreme Limit
Boundary of MMC FeatureShown at Extreme Limit
1 Positional
Tolerance Zone atMMC
True (Basic)Position of Feature
True (Basic)Position of Feature
Other PossibleExtreme Locations
Virtual Condition
Outer BoundaryMinimum Circumscribed
Diameter( )
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Resultant Condition BoundaryExternal Feature (MMC Concept)
1 A B CM
14 +/- 0.5
C
BXX.X
XX.X
A
As Shown on Drawing
Boundary of LMC feature
2 PositionalTolerance Zone at
LMC
True (Basic)Position of Feature
True (Basic)
Other PossibleExtreme Locations
Resultant ConditionInner Boundary
Maximum InscribedDiameter( )