gd&t

Imperial Automotive Industries

Geometric Dimensioning and Tolerancing

Mark A. Morris

2

Contact Information

John Lindland (734) 369-3120 President – Consultant – Seminar Leader QualSAT, Inc. [email protected]

Mark A. Morris (734) 878-6569 Representing QualSAT, Inc. [email protected]

3

Geometric Characteristic Symbols

Form Tolerances

Profile Tolerances

Orientation Tolerances

Runout Tolerances

Location Tolerances

4

Section 1

Background, History, and the Importance of GD&T

5

Engineering Drawings

Engineering drawings are the vehicle used to communicate requirements for manufactured parts.

Graphic Representations Words Numbers Symbols

Engineering drawings are used to communicate contractual requirements.

6

We Need Operational Definitions

“Without an operational definition, investigations of a problem will be costly and ineffective, almost certain to lead to endless bickering and controversy.”

W. Edwards Deming, Ph.D.

Operational definitions provide three components:1. Specify Test to determine Compliance2. Set Criteria for Judgment3. Make Decisions based on the Criteria

7

Orthographic and Isometric Projection

8

Orthographic and Isometric Projection

9

1st vs. 3rd Angle Projection

Third Angle ProjectionFirst Angle Projection

Note: Third angle projection is more common in theUSA, first angle projection is more common in Europe.

10

ISO vs. ASME

Comparing the ISO and the ASME Approaches to GD&T

Issue or Topic ISO ASME

Approach

Explanation

Cost of Standards

Number of Standards

Theoretical Functional

Graphical, Few Words

700 – 1000 USD

10 - 16

Comprehensive

< 100 USD

1

Based on the work of Alex Kulikowski, 1998

11

ASME Y14.5M – 1994 Structure

1. Scope, Definitions, and General Dimensioning

2. General Tolerancing and Related Principles

3. Symbology

4. Datum Referencing

5. Tolerances of Location

6. Tolerances of Form, Profile, Orientation, and Runout

12

History of the Standard

ANSI Y14.5M 1964ANSI Y14.5M-1973ANSI Y14.5M-1982

ASME Y14.5M-1994 Dimensioning and Tolerancing

ASME Y14.5.1M-1994 Mathematical Definitions

Stanley Parker has been credited with bringing to light the problems that existed with limit dimensioning while working at the Royal Torpedo Factory in Scotland.

13

Identify the Standard Used

ASME Y14.5M-1994 requires the standard be identified on the drawing when it is applied.

Methods change as standards evolve.For example:

ANSI Y14.5-1982 ASME Y14.5-1994

A- A -

14

General Information

International System of Units (SI) have been used. U.S. Customary Units could have been used.

Figures are intended as illustrations to aid in understanding. They show one possible solution.

Capital letters on figures are intended to appear on finished drawings.

15

Foundations of Mechanical Accuracy

The Four Mechanical Arts

Geometry

Standards of Length

Dividing the Circle

Roundness Wayne R. Moore

16

Development of Flatness

Step 1 – Alternate between plates 1 and 2 until a relative match is achieved.

Plate 1 agrees with plate 2 None are known to be flat

Step 2 – Consider plate 1 as the master plate and work plate 3 to plate 1.

Plate 1 agrees with plate 2 Plate 1 agrees with plate 3 None are known to be flat

Based on the work of Sir Joseph Whitworth

17



Plate 2 agrees with plate 3 Plates 2 and 3 are known to be flatter that plate 1 None are known to be flat


Plate 1 agrees with plate 2 Plate 3 agrees with plate 2 None are known to be flat All are of nearly equal flatness

18



Plate 1 agrees with plate 3 Plates 1 and 3 are known to be flatter that plate 2 None are known to be flat


Plate 1 agrees with plate 3 Plate 2 agrees with plate 3 None are known to be flat All are of nearly equal flatness

Continue reducing the error until all three plates agree.

19

3 Documents for Product Quality

Product Drawing

Process Definition

Quality Control Plan

20

Section 2

Definitions, Rules, and Symbols

21

Key Definitions

Datum – Theoretically exact point, axis, or plane derived from the true geometric counterpart.

Datum Feature – Actual feature on a real part used to establish a datum.

Datum Feature Simulator – A surface of sufficient precision to establish a simulated datum.

Simulated Datum – A point, axis, or plane established by processing or inspection equipment.

Datum Target – A specified point, line, or area on a part used to establish the datum scheme.

22

Key Definitions

Feature of Size – A cylindrical or spherical surface, or two opposing elements or parallel surfaces.

Least Material Condition – This occurs where a feature of size contains the least material allowed by the stated limits of size.

Maximum Material Condition – This occurs where a feature of size contains the most material allowed by the stated limits of size.

Regardless of Feature Size – A term that indicates that a geometric tolerance or datum reference applies for any increment of size within its size tolerance.

23

Key Definitions

Tolerance – The total permissible variation in size for a specified dimension.

Bilateral Tolerance – A tolerance zone where the boundary conditions contain the specified dimension.

Geometric Tolerance – A general term that refers any of the 14 symbols used to control form, orientation, profile, runout, or location.

Unilateral Tolerance – A tolerance zone that only exists on one side of the specified dimension.

True Geometric Counterpart – The theoretically perfect boundary or best fit (tangent) plane of a specified datum feature.

24

Fundamental Rules

Each dimension shall have a tolerance.(except for those dimensions specifically identified as reference, maximum, minimum, or stock)

Ensure full understanding of each feature.

Show the detail needed and no more.

Serve function needs, no misinterpretation.

Manufacturing methods are not specified.

Non-mandatory dimensions are OK.

Designed of optimal readability.

25

Fundamental Rules

Dimension materials made to gage numbers.

90o apply when features are shown as .

90o apply when centerlines are shown .

Dimensions apply at 20oC (68oF).

Dimensions apply in a free state.

Tolerances apply for full size of feature.

Dimensions and tolerances only apply at the drawing level where they were specified.

26

Limits of Size

Actual Size is a general term for the size of a feature as produced. It has two interpretations.

Actual Local Size is the value of the individual distance at any cross section of any feature of size.

Actual Mating Size is the dimensional value of the actual mating envelope.

Limits of Size are the specified minimum and maximum values for a feature of size.

27

Rule #1 – The Taylor Principle

“Where only a tolerance of size is specified, the limits of size of an individual feature prescribe the extent to which variations in its geometric form, as well as size, are allowed.”

ASME Y14.5M-1994

Simply put:Limits of size for an individual feature control the allowable variation to its form and its size.

28

Size Controls FormThis on a drawing

Allows this Or this25.4 (LMC)

25.0 (MMC)

25.4(LMC)

25.4(LMC)

25.0(MMC)

25.425.0

According to Rule #1, a true geometric counterpart at MMC must pass through the hole.

29

Size Controls Form

12.212.0

12.0 (LMC)

12.2 (MMC) 12.2 (MMC)

12.0 (LMC)

This on a drawing

Allows this Or this

According to Rule #1, a true geometric counterpart at MMC must pass over the pin.

30

Features with and without Size

Definition: A feature is a physical portion of a part such as a surface, hole, tab, slot, pin, etc.

Features Without Size: Any Plane Surface

Features With Size: Cylindrical Surface Spherical Surface A Set of 2 Opposing Elements or Parallel Planes

31

Features With & Without Size

32

MMC & LMC Workshop

.752

.750.375+.001-.000

2.7422.748

.375+.0002-.0002

Determine MMC and LMC for each feature of size below.

33

Rule #2

RFS applies to geometric tolerances defining individual tolerance, datum reference, or both, where no modifying symbol has been specified. MMC and LMC must be specified where required.

34

Angular Units

Angular Dimensioning

Either degrees, minutes, and seconds or decimal degrees may be used.

Precede small angles with zeros for degrees and minutes as place holders.

25o 30’ 45”or

25.5125o

0o 0’ 55’’

35

Millimeter Dimensioning

Use a single 0 to describe unilateral tolerances where the intended value is nil.

For bilateral tolerances, use the same number of significant digits in both limits of size.

For limit dimensioning, use the same number of significant digits both limits of size.

For basic dimensions, tolerance control is accomplished by the feature control frame. Follow rules for millimeter dimensions.

25+ 0-0.25

25+ 0.10 -0.25

25.1024.75

25

36

Decimal Inch Dimensioning

For unilateral tolerances, use the same number of zeros when the intended value is nil.

For bilateral tolerances, use the same number of significant digits in dimension and limits.

For limit dimensioning, use the same number of significant digits both limits of size.

For basic dimensions, use the same number of significant digits as in the feature control frame.

1.000+ .000 - .010

1.000+ .004 - .010

1.004.990

1.000

37

Location of Features

Rectangular Coordinate Dimensioning

Rectangular Coordinates w/o Dimension Lines

Tabular Dimensioning

Polar Coordinate Dimensioning

Repetitive Features or Dimensions

Use of “X” to indicate “by”

38

Tolerancing and Related Principles

General PracticesDirect Tolerancing MethodsTolerance ExpressionInterpretation of LimitsSingle LimitsTolerance Accumulation Chain Dimensioning Base Line Dimensioning Direct Dimensioning

39

Chain Dimensioning

- + +/- Tol Description

Totals

10.05 9.95

7.557.45

12.5512.45

13.3513.25

X

Y

What are the min and max values between surfaces X and Y?

40

Base Line DimensioningWhat are the min and max values between surfaces X and Y?


Totals

10.05 9.95

X

Y

17.5517.45

30.0529.95

43.3543.25

41

Direct Dimensioning

What are the min and max values between surfaces X and Y?


Totals

10.05 9.95

X

Y

17.5517.45

30.0529.95

23.3523.25

42

Use of Basic Dimensions

Basic dimensions define the perfect location of features with respect to the datum reference frame.

Basic dimensions define the theoretical exact size and location for features.

Feature control frames define the intended tolerance for features.

43

Understand Perfect Geometry

Perhaps the best way to comprehend GD&T is first to envision the geometry of the perfect part defined by basic dimensions.

Then we can apply the tolerances given in the feature control frames to define the allowable variation from the perfect part.

44

Using Tables to Define Basic Dimensions

Paragraph 1.9 discusses locations of features.

Paragraph 1.9.3 allows the use of tables that list the location of features as rectangular coordinates from mutually perpendicular planes.

Tables may be prepared in any suitable manner that adequately locates features.

45

Feature Control Frame Symbols

Description SymbolFeature Control Frame

Diameter

Spherical Diameter

Maximum Material Condition

Least Material Condition

Projected Tolerance Zone

Free State

Tangent Plane

Statistical Tolerance

.010 A B C

S

M

L

P

F

TST

46

Feature Control Frame Elements

M.014 A B CM

Label the elements of the feature control frame using the following terms:Datum Modifier Geometric CharacteristicDiameter Symbol Primary DatumFeature Modifier Secondary DatumFeature Tolerance Tertiary Datum

47

Feature Control Frames Example

B

C

A

48


.005

A

A.005

.005

A

A.005

B

.005 BA

49

Feature Control Frame Placement

Locate the Feature Control Frame below or attached to the leader-directed dimension or callout.

Run the leader from the frame to the feature.

Attach a side or an end of the frame to an extension line from the feature.

Attach a side or an end of the frame to an extension of the dimension line related to the feature in question.

50

Other Common SymbolsDescription Symbol

Radius R

Spherical Radius SR

Controlled Radius CR

Reference ( )

Between

All Around

Number of Places 8X

Counter Bore or Spot Face

CountersinkDepth or Deep

51


2.000

30o

5.000

1.750

1.500

3.000

C

B

1.0101.000

M.010 A B C

.020 BA C

A BA

BA.005

.005 BA

.005

A

52

Geometric Characteristic Symbols

ApplicationType of

Tolerance Characteristic Symbol 2D or 3D

FlatnessStraightnessCircularityCylindricityPerpendicularityParallelismAngularityPositionSymmetryConcentricityCircular RunoutTotal RunoutProfile of a LineProfile of a Surface

IndividualFeatures

RelatedFeatures

Either Individual orRelated Features

53

Some Other General Rules

Statistical Tolerancing – Assignment of component tolerances to meet assembly needs of statistical stacks.

Radius and Diameter Callouts – R, CR, SR, , and S .

Non-Rigid Parts – Method of restraint must be specified.

Screw Threads, Gears and Splines – Screw threads are evaluated at their pitch diameter unless otherwise specified. Gears and splines must be specified.

54

Section 3

Applications of Tolerance Zones

55

Form Tolerances

Flatness

Straightness

Circularity

Cylindricity

56

Form Tolerances

Datum references are never made for form tolerances.Rule #1 says that limits of size control variation in form.Generally, form tolerances are only necessary to refine (require a tighter tolerance) limits of size.Form tolerances are often applied to features to qualify them as acceptable datum features.

57

Flatness

Definition Flatness exists when a surface has all of its elements in one plane.

Tolerance Zone Two parallel planes within which the surface must lie.

58

Checking for Flatness

59

Proper Application of Flatness

No datum is referenced.

It is applied to a single planar feature.

No modifiers are specified.

Tolerance value is a refinement of other geometric tolerances or Rule #1.

60

Straightness

Definition Straightness exists when an element of a surface or an axis is a straight line.

Tolerance Zone Two parallel lines in the same plane for two-dimensional applications. A cylindrical tolerance zone that contains an axis for three-dimensional applications.

61

Checking for Straightness

62

Proper Application of Straightnessapplied to a Surface Element


It is applied to a surface element.

It is applied in a view where the element to be controlled is shown as a line.


Tolerance value is a refinement of other geometric tolerances or Rule #1.

63

Straightness of a Feature of Size

When straightness is applied to a feature of size:

Tolerance zone applies to the axis or centerplane.

Rule #1 does not apply. The tolerance value may be larger

that the limits of size for the feature of size.

64

Proper Application of Straightness applied to a Feature of Size


It is applied to a planar or cylindrical feature of size.

If a planar feature of size, the diameter symbol is not used.

If a cylindrical feature of size, the diameter symbol is used.

, T , and L modifiers are not specified.

Tolerance value is a refinement of other geometric tolerances.

P

65

Circularity (roundness)

Definition Circularity exists when all of the points on a perpendicular cross section of a cylinder or a cone are equidistant to its axis.

Tolerance Zone Two concentric circles that contain each circular element of the surface.

Note: Circularity also applies to spheres.

66

Checking for Circularity

67

Proper Application of Circularity


It is applied to a circular feature.


Tolerance value is a refinement of limits of size on the diameter or of other specified geometric tolerances.

68

Cylindricity

Definition Cylindricity exists when all of the points on the surface of a cylinder are equidistant to a common axis.

Tolerance Zone Two concentric cylinders that contain the entire cylindrical surface.

69

Checking for Cylindricity

70

Proper Application of Cylindricity


It is applied to a cylindrical feature.


Tolerance value is a refinement of limits of size on the diameter or of other specified geometric tolerances.

71

Decisions for Form Tolerances

FormTolerances

Consider Limits of Size

Flatness Straightness Circularity Cylindricity

SurfaceElements

Axis or Center Plane

Consider Material Condition

MMCRFS

72


Angularity

Perpendicularity

Parallelism

73


Datum references are always used for orientation tolerances.Orientation tolerances applied to a surface control the form of toleranced surface.Only a tangent plane may need control.Orientation tolerances may be applied to control both features of size and features without size.Orientation tolerances do not control size or location.Generally, profile tolerances are used to locate features without size and position tolerances are used to locate features of size.

74

Angularity

Definition Angularity exists when all of the points on a surface create a plane or a feature axis is at the specified angle, when compared to a reference plane or axis.

Tolerance Zone Two parallel planes at the true angle to a reference plane and contain the entire surface surface.

Note: Applies to median planes and axes too.Datum Plane

Datum Feature

75

Checking for Angularity

76

Proper Application of Angularity

Datum reference is specified.

Surface applications may use tangent plane modifier.

Feature of size applications may use MMC, LMC, diameter, of projected tolerance zone modifiers.

Basic angle defines perfect geometry between the datum reference and the toleranced feature.

Specified tolerance is a refinement of other geometric tolerances that control angularity of the toleranced feature.

77

Perpendicularity

Definition Perpendicularity exists when all of the points on a surface, median plane, or axis are at a right angle to a reference plane or axis.

Tolerance Zone Two parallel planes that are perpendicular to a reference plane and contain the entire surface surface.


Datum Feature

78

Checking for Perpendicularity

79

Proper Application of Perpendicularity





Specified tolerance is a refinement of other geometric tolerances that control the perpendicularity of the toleranced feature.

80

Parallelism

Definition Parallelism exists when all of the points on a surface, median plane, or axis are equidistant to a reference plane or axis.

Tolerance Zone Two parallel planes that are parallel to a reference plane and contain the entire surface surface.


Datum Feature

81

Checking for Parallelism

82

Proper Application of Parallelism





Specified tolerance is a refinement of other geometric tolerances that control parallelism of the toleranced feature.

83

Decisions for Orientation Tolerances

OrientationTolerances

ParallelismAngularity Perpendicularity


Consider LimitsOf Location

Featureof Size

PlaneSurface


MMCRFS LMC

84

Location Tolerances

True Position

Symmetry

Concentricity

85

Location Tolerances

Datum references are always used for location tolerances.Location tolerances are reserved for tolerancing applications on features of size.They are always located by basic dimensions back to the datum scheme.Location tolerances shown on the same centerline are assumed to have a basic dimension of zero.Symmetry and concentricity application are centered about the datum scheme specified for the controlled feature.

86

True Position

Definition True position is the exact intended location of a feature relative to a specified datum scheme.

Tolerance Zone Most frequently, the tolerance zone is a cylinder of specified diameter within which the true axis of the feature must lie.

Note: True position can also be applied to median planes relative to specified datums.

87

Positional Tolerancing

Traditional tolerancing (say + .005”) consist of 2-D rectangular boundaries.

A circular boundary with the same worst-case conditions increases the area of the tolerance zone by 57%, prior to any bonus tolerance.

88

Traditional Fastener Tolerances

Threaded Fastener 3/8 – 16Clearance Hole 13/32

Perfect Condition

1/64 = .0156

Worst-Case Condition

.0015Clearance

89

Bonus Tolerances

When tolerancing features of size, bonus tolerances may be applicable.

With MMC, as the size of a hole increases, so does the acceptable tolerance zone, provided the hole does not exceed its limits of size.Hole at

MMC

OriginalToleranceZone

Larger Hole

Larger Tolerance Zone

Larger Hole

90

Maximum Material Condition (MMC)

Largest permissible external feature. Outside Diameter External Feature Size Key

Smallest permissible internal feature. Holes Slots Key Way

91

Maximum Material Condition

B

C

M.014 A B C

.760

.750

Size ToleranceMMC

4X

Note: Datum feature A is the back surface.

92

Least Material Condition (LMC)

Smallest permissible external feature. Outside Diameter External Feature Size Key

Largest permissible internal feature. Holes Slots Key Way

93

Least Material Condition

B

C

L.014 A B C

.760

.750

Size ToleranceLMC

4X


94

Regardless of Feature Size (RFS)

RFS is no longer documented except in rare cases where it is required for clarity.

RFS is assumed for features of size when neither MMC nor LMC are specified.

95

Regardless of Feature Size

B

C

.014 A B C

.760

.750

Size Tolerance

4X


96

Applications of Material Condition Modifiers

Maximum Material Condition Used for clearance application.

Least Material Condition Used for location applications. Used to protect wall thickness.

Regardless of Feature Size Used when size and location do not interact.

M

L

97

Applications for Least Material Condition

.503

.501 .002 L

.500

.499

The purpose of the hole is to locate the PLP pin below.

Worst Case Scenario

Hole diameter at .503 (LMC)Pin diameter at .499 (LMC)Clearance is .004Pin can shift .002 in any directionTolerance for hole location is Ø .002 at LMCHole can be off location .001 in any directionPin can be off location .003 in any direction

98


.503

.501 .002 L

.500

.499


Hole at MMC – Pin at LMC

Hole diameter at .501 (MMC)Pin diameter at .499 (LMC)Clearance is .002Pin can shift .001 in any directionTolerance for hole location is Ø .004 at MMCHole can be off location .002 in any directionPin can be off location .003 in any direction

99


.503

.501 .002 L

.500

.499


Hole at MMC – Pin at MMC

Hole diameter at .501 (MMC)Pin diameter at .500 (MMC)Clearance is .001Pin can shift .0005 in any directionTolerance for hole location is Ø .004 at MMCHole can be off location .002 in any directionPin can be off location .0025 in any direction

100

Virtual and Resultant Conditions

Virtual Condition is the constant boundary generated by the collective effects of a feature’s specified MMC or LMC and the geometric tolerance for that material condition (i.e, the premise for functional gaging).

Resultant Condition is the variable boundary generated by the collective effects of a feature’s specified MMC or LMC, its geometric tolerance for that material condition, the size tolerance, and any additional geometric tolerance derived from the feature’s departure from its specified material condition (e.g., extreme boundary allowed for a given situation).

101

Virtual and Resultant ConditionsGiven MMC

VirtualCondition

Constant Value

VariableValue

ResultantCondition

InnerBoundary

OuterBoundary

Internal Feature of SizeØ 25.5

25.1

Ø 0.1 M

Ø Hole Ø Tol V Cond R Cond

25.1

25.2

25.3

25.4

25.5

0.1

0.2

0.3

0.4

0.5

25.2

25.4

25.6

25.8

26.0

25.0

102

Inner and Outer Boundary Conditions

Ø 25.525.1

Ø 0.1 M

Tolerance ZoneAt MMC

Virtual ConditionSize

Bonus ToleranceAt LMC

Hole at LMCOuterBoundary

Inner Boundary

103

Virtual and Resultant ConditionsGiven MMC

VirtualCondition

Constant Value

VariableValue

ResultantCondition

OuterBoundary

InnerBoundary

External Feature of SizeØ 24.9

24.5

Ø 0.1 M

Ø Pin Ø Tol V Cond R Cond

24.9

24.8

24.7

24.6

24.5

0.1

0.2

0.3

0.4

0.5

24.8

24.6

24.4

24.2

24.0

25.0

104

Virtual and Resultant ConditionsGiven LMC

VirtualCondition

Constant Value

VariableValue

ResultantCondition

OuterBoundary

InnerBoundary


25.1

Ø 0.1 L

Ø Hole Ø Tol V Cond R Cond

25.1

25.2

25.3

25.4

25.5

0.5

0.4

0.3

0.2

0.1

24.6

24.8

25.0

25.2

25.4

25.6

105

Virtual and Resultant ConditionsGiven LMC

VirtualCondition

Constant Value

VariableValue

ResultantCondition

InnerBoundary

OuterBoundary


24.5

Ø 0.1 L

Ø Pin Ø Tol V Cond R Cond

24.9

24.8

24.7

24.6

24.5

0.5

0.4

0.3

0.2

0.1

25.4

25.2

25.0

24.8

24.6

24.4

106

Inner and Outer BoundariesGiven RFS

VariableValue

VariableValue

InnerBoundary

OuterBoundary


25.1

Ø 0.1

Ø Hole Ø Tol I. B. O. B.

25.1

25.2

25.3

25.4

25.5

0.1

0.1

0.1

0.1

0.1 25.6

25.0

107

Inner and Outer Boundaries Given MMC

Variable Value

VariableValue

OuterBoundary

InnerBoundary


24.5

Ø 0.1

Ø Pin Ø Tol O. B. I. B.

24.9

24.8

24.7

24.6

24.5

0.1

0.2

0.3

0.4

0.5 24.4

25.0

108

Zero Tolerance at MMC

Where zero tolerance is specified at MMC, the tolerance is totally based on the actual mating size of the feature specified.

Location and orientation must be perfect when the feature is at MMC.

As the feature departs from MMC the allowable tolerance is based on the size the feature compared to its MMC.

109

Logic for Zero Tolerance at MMC

A

Ø 1.006 + .003

Ø .004 M A

BØ .514 + .003

Ø .005 M A B M

A

Ø .994 + .003

Ø .002 M A

BØ .500 + .001

Ø .005 M A B M

110


Ø .506VirtualConditionBoundary

Ø .999VirtualConditionBoundary

FunctionalExtremes areØ .991 and Ø .999

111


Ø .994 + .003

Ø .002 M A

B

Based on assumptions about process variation, we may have arbitrarilydivided the total tolerance of Ø .008 into Ø .006 for size and Ø .002 fororientation. We could have divided the tolerance into Ø .004 + Ø.004, or Ø .002 + Ø .006, or even Ø .008 + Ø .000.

112


Ø .995 + .004

Ø .000 M A

B

Why not give the entire tolerance to the manufacturing process and letthe process divide it up as needed? This is what happens when we specify zero tolerance at MMC.

113

Verification of Position at MMC

1. Determine tolerance at MMC.

2. Determine actual mating size.

3. Calculate positional tolerance allowed.

4. Determine positional error in location.

5. Compare positional error in location to positional tolerance allowed.

6. Decide to accept or reject.

114

Specification of Position at MMC

B

C

M.010 A B C

.760

.750

1.250 3.000

1.000

2.000

115

Verification of Position at MMC

Hole #1 Hole #2 Hole #3 Hole #4

Hole Size at MMC

Actual Mating Size of Hole

Positional Tolerance Allowed

Actual Location in the X Axis

Actual Location in the Y Axis

Actual Positional Tolerance

Accept or Reject

.752 .756 .758 .762

.996

1.255 4.248

1.007 3.010

4.249 1.252

3.003

116

Verification of Position at LMC

1. Determine tolerance at LMC.

2. Determine actual mating size.

3. Calculate positional tolerance allowed.

4. Determine positional error in location.

5. Compare positional error in location to positional tolerance allowed.

6. Decide to accept or reject.

117

Specification of Position at LMC

B

C

L.010 A B C

.760

.750

1.250 3.000

1.000

2.000

118

Verification of Position at LMC

Hole #1 Hole #2 Hole #3 Hole #4

Hole Size at LMC

Actual Mating Size of Hole

Positional Tolerance Allowed

Actual Location in the X Axis

Actual Location in the Y Axis

Actual Positional Tolerance

Accept or Reject

.752 .756 .758 .760

.996

1.255 4.248

1.007 3.010

4.249 1.252

3.003

119

Proper Application of Position

Position control is applied to a feature of size.Datum references are specified and logical for the application.Basic dimensions establish the desired true position of the feature of size.Tangent plane modifier is not used.Diameter symbol is used to specify axis control.Diameter symbol is not used to specify center plane control.MMC, LMC, or RFS may be specified.

120

Symmetry

Definition Symmetry defines the location of non-cylindrical features about a derived median plane.

Tolerance Zone The tolerance zone is defined by two planes, equidistant to a datum center plane. The derived median points must fall within these two planes.

A

121

Set Up for Symmetry

122

Proper Application of Symmetry

A planar feature of size to be controlled uses the same center plane as the datum scheme.

Diameter symbol is never used to specify the symmetry tolerance.

MMC, LMC, tangent plane, and projected tolerance zone modifiers may not be specified.

123

Concentricity

Definition Concentricity defines the location of cylindrical features about an axis of rotation.

Tolerance Zone The tolerance zone is defined as a cylinder about the datum axis that must contain the median points of diametrically opposed elements of a feature.

A

124

Checking for Concentricity

125

Proper Application of Concentricity

The surface of revolution to be controlled is coaxial to the axis of the datum scheme.

Diameter symbol is used to specify the concentricity tolerance.

MMC, LMC, tangent plane, and projected tolerance zone modifiers may not be specified.

126

Decision Matrix for Coaxial Features

Position(RFS)

Total Runout Concentricity

Cost to

Produce$ $$$ $$

Cost to

Inspect$ $$ $$$

Characteristics

underControl

Location and

Orientation

Location Orientation and Form

Location and

Orientation

127

Decisions for Location Tolerances

LocationTolerances

PositionConcentricity Symmetry

CenterPlane

Axis

DetermineTolerance

For Position OnlyConsider Material Condition

MMCRFS LMC

128

Profile Tolerances

Profile of a Line

Profile of a Surface

2-D Application

3-D Application

129

Profile Tolerances

Profile tolerances are used to control multiple coplanar surfaces.Perfect geometry must be defined via basic dimensions.The default interpretation for the tolerance zone is bilateral and equal about the true perfect geometry.Profile tolerances are not used to control features of size so MMC, LMC, and RFS do not apply.Profile features can be used as datum features or they must be related to a defined datum scheme.

130

Profile

Definition Profile defines the theoretically exact position of a surface (3-D) or the cross section of a surface (2-D).

Tolerance Zone A uniform boundary on either side of the true profile that must contain either the surface or line.

3-D Application 2-D Application

131

Profile for Cam Application

132

Functional Gaging of Profile

133

Proper Application of Profile Tolerances

Profile features are used as datum features or related to a defined datum scheme.

andBasic dimensions relate the true profile back to the datum scheme.

orThe profile tolerance value must be a refinement of dimensions used to locate the true profile.

134

Decisions for Profile Tolerances

ProfileTolerances


Profile of a Surface

Profile of aLine

Consider Tolerance Zone

BilateralUnilateral

Inside Outside Equal Unequal

135

Runout Tolerances

Circular Runout

Total Runout

2-D Application

3-D Application

136

Runout

Definition Runout is a composite control used to specify functional relationships between part features and a datum axis.

Tolerance Zone Circular runout is a 2-D application that evaluates full indicator movement on a perpendicular cross section rotating about a datum axis. Total runout evaluates full indicator movement of the full surface rotating about a datum axis.

3-D Application 2-D Application

137

Checking for Runout

138

Proper Application of Runout

The surface to be controlled is either coaxial or perpendicular to the axis of the datum scheme.

Diameter symbol is never used to specify a runout tolerance.

MMC, LMC, tangent plane, and projected tolerance zone modifiers may not be specified for a runout tolerance.

139

Decisions for Runout Tolerances

RunoutTolerances


TotalRunout

CircularRunout

140

Geometric Characteristics for Round Features

Circularity (roundness) Evaluates cross section of surface to its own axis

Cylindricity Evaluates entire surface to its own axis

Runout Evaluates cross section of surface to a defined axis

Total Runout Evaluates entire surface to a defined axis

Concentricity Evaluates best fit axis of feature to a defined axis

141

Tolerance Design Flow Chart

DesignRequirements

EstablishDatums

IndividualFeatures Related

FeaturesIndividual or

Related Features

FormTolerances Profile

Tolerances

LocationTolerances

RunoutTolerances

OrientationTolerances

142

Section 4

Datums and Datum Schemes

143

Reference Planes(The Point of Known Return) Ted Busch, 1962

Define the datum reference frame.

Use of mutually perpendicular planes.

The goal is the replication of measurements.

Immobilize the part in up to six degrees of freedom.

144

Theoretically Perfect Geometry

Three mutually perpendicular planes.

DatumPoint

3 Datum Planesdefine the Originof Measurement

145

Criteria for Selecting Datum Features

Geometric Relationship to Toleranced Feature

Geometric Relationship to Design Requirements

Accessibility of the Feature

Sufficient in Size to be Useful

Readily Discernable on the Part

146

Designating Precedence of Datums

Alphabetical order is not relevant.

Order of precedence is shown in the feature control frame.

Consider function first.

Then, consider the process next.

Finally, consider measurement processes.

147

Datum Features of Size

MMC callouts on a datum features of size can allow a datum shift on the exact location of the datum feature.

This applies to: Cylindrical Surfaces (internal or external) Spherical Surfaces A Set of 2 Opposing Elements or Parallel

Planes A Pattern of Features such as a Bolt Hole

Pattern

148

Decisions for Datum Selection

SelectDatum Feature

Featureof Size

Surface

AxisCenterPlane


MMCRFS LMC

Are Other Datums Required?

149

Rational Strategyfor Datum Selection

It is reasonable to prioritize the datum selection process as follows:

1. Functional Requirements

1. Production Requirements

1. Measurement Requirements

150

What Are We Really Interested In?

1. Error in Geometric Forms

2. Size for Features of Size

3. Location of Features

151

Introduction to Datum Workshop

Select datums based on function.Some features are leaders, others are followers.Sequence of considerations:

Establish the datum reference frame (DRF). Qualify the datum features to the DRF. Relate remaining features to the DRF.

For consistency, assume .005” tolerance zones unless otherwise specified.Select and qualify the datum features and identify the datum point as specified in the following examples.

152

Datum WorkshopLocate the part on the back surface first, then the bottomedge, then the left side.

153

Datum WorkshopLocate the part on the backsurface first, then the bottom edge, then the right hand sideof the bottom slot.

154

Datum Workshop

1.0001.005

Locate the part on the back surface first, then the bottom edge, then centrally to the bottom slot with a .998 virtualsize key.

155

Datum Workshop

1.0001.004

1.5001.502

Locate the part on the frontsurface first, then by a 1.504virtual size hole for the large boss, then by a .996 virtual size key for the right hand slot.

156

Datum Workshop

1.5001.502

2.500

Locate the part on the front surface first, then by a 1.502virtual size hole for the large boss, then by the bottom edge.The bottom edge must lie in a tolerance zone from 2.490 to 2.510 from the large boss.

157

Section 5

Tolerancing Strategies

158

Process for Tolerance Analysis

Establish Performance Requirements

Develop a Loop Diagram

Convert Dimensional Requirements to Target Values with Equal Bilateral Tolerances

Calculate Variation for Performance Requirement

Select the Method of Analysis

Determine the Target Value for Requirement

159

Statement of the Problem

A problem well defined is half solved.John Dewey

Thorough problem definition may lead directly to its solution.

Hans Bajaria

The formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill.

Albert Einstein

160

Assembly Stack-Up Analysis

StartEnd


Totals

What is the minimum and maximum gap between the bottom of the collar and the upper bearing?

161

Component Tolerances

2.9062.896

3.1163.096

.227

.217

.070

.060

.080

.077

2.8052.795

.050

.045

.055

.045

162

Stack Analysis Result

StartEnd

+ +/- Tol Description

Totals

.0785.050

2.800

.0475

.0785

3.106.222

3.179 3.2035 .0305

.0015

.005

.005

.0025

.0015

.010

.005

Bottom of Bearing

Hub Upper Lip

Hub Lower Lip

Datum A of Valve

Top of Valve

Bottom of Collar

Top of Lower Bearing

-

What is the minimum and maximum gap between the bottom of the collar and the upper bearing?

163

Worst Case Evaluation

Nominal Assembly Length = 1.000 + .500 + 2.000 = 3.500

Tolerance of Assembly Length = .002 + .001 + .004 = + .007

While this approach of adding component tolerances is mathematically correct, in practical application it is often too conservative.

A B C

Assembly Length

1.000+ .002

.500+ .001

2.000+ .004

164

Worst Case Pros and Cons

Pros No risk of components not interacting properly. 100% interchangeability of components.

Cons Method is conservative. Underutilization of full tolerance range. Tolerances for interacting dimensions are

smaller than necessary, which may increase cost.

165

Statistical Method of Linear Evaluation

Nominal Assembly Length = 1.000 + .500 + 2.000 = 3.500

Tolerance of Assembly Length = .0022 + .0012 + .0042 = + .0046

To statistically calculate the tolerance we take the root of the sum of the squared values of the individual tolerances (RSS).

A B C

Assembly Length

1.000+ .002

.500+ .001

2.000+ .004

166

Some Critical Assumptions

Component dimensions are independent.

Components are assembled randomly.

Component should be normally distributed.

The actual average value for each component is equal to the nominal value specified for that component. (Otherwise, the nominal value for the assembly will not be met and the tolerances will not be realistic.) Process control is needed.

167

From Part Tolerances to an Assembly Tolerance

A

B

C

Assembly

Variances are additive while standard deviations are not.

168

Statistical Tolerancing Pros and Cons

Pros Larger tolerances on interacting dimensions.

Cons Small percent of final assemblies fall outside

limits.

Special Considerations Averages of interacting dimensions must be

controlled via variables measurements. Interacting dimensions must be independent

and normally distributed. Lot size should be moderately large.

169

From an Assembly Tolerance back to Component Tolerances

In practice, we are often required to begin with a defined end result and determine appropriate tolerances for the components.

A

B

CAssembly

170

Two Theorems of Relevance

Two theorems hold great importance in the interrelationship of tolerances.The first is similar to the Pythagorean Theorem

The second theorem appears less obvious:

)...( 223

22

21sum n

)( 22

2121

AB

171

Composite Tolerances and Single Segment Tolerances

There are times when it is more important to control the relationships between features than to control their locations to the datums.

M.030 A B CM.030 A B C

M.010 A

M.030 A B C

M.010 A B

M.030 A B C

M.010 A B

172

Standard Positional Tolerance

B

C

.760

.750

1.250 3.000

1.000

2.000

4X

M.030 A B C

A

173

Functional Gage for Virtual Condition of Holes to Datums

B

C

.720

1.250 3.000

1.000

2.000

4X

Datum Surface A

174

Composite Tolerance with One Datum in the Lower Segment

B

C

.760

.750

1.250 3.000

1.000

2.000

4X

A

M.030 A B C

M.010 A

175

Composite Tolerance Feature Control Frame

PLTZF locates and orients features to the specified datums via basic dimensions.

FRTZF locates the features within the pattern via basic dimensions to each other and controls their orientation relative to the specified datum(s).

FRTZF releases the pattern from the requirements given by basic dimensions to their datum features.

M.030 A B C

M.010 A

Pattern LocatingTolerance Zone

Framework(PLTZF)One Tolerance

Zone Symbol

Feature RelatingTolerance Zone

Framework(FRTZF)

176

Two Functional Gages for the Composite Tolerance

.740

3.000

2.000

4X

Datum Surface A

B

C

.720

1.250 3.000

1.000

2.000

4X

Datum Surface A

M.030 A B C

M.010 A

177

Composite Tolerance with Two Datums in the Lower Segment

B

C

.760

.750

1.250 3.000

1.000

2.000

4X

A

M.030 A B C

M.010 A B

178

Two Functional Gages for the Composite Tolerance

B

C

.720

1.250 3.000

1.000

2.000

4X

Datum Surface A

M.030 A B C

M.010 A B

.740

3.000

2.000

4X

Datum Surface A

Orientation of Datum B remains parallel to thehole pattern as it moves up or down on two rails. B

179

Two Single Segments with Two Datums in the Lower Segment

B

C

.760

.750

1.250 3.000

1.000

2.000

4X

A

M.030 A B C

M.010 A B

180

Two Functional Gages for the Two Single Segment Tolerances

.740

3.000

2.000

4X

Datum Surface A

B

1.000

B

C

.720

1.250 3.000

1.000

2.000

4X

Datum Surface A

M.030 A B C

M.010 A B

181

Fixed and Floating Fastener Calculations

Floating Fastener scenario exists when the fastener must pass through two clearance holes in mating parts.

Fixed Fastener scenario exists when one of the parts has threaded holes and the other part has clearance holes.

Projected Tolerance Zone should be used to specify the height out of the threaded hole that the tolerance zone applies.

182

Threaded Holes

“Threaded holes aren’t really holes. They are a vehicle to locate and orientate mating parts.”

Carl Lance

Nubs on a shower head behave the same as a threaded hole.

183

Two Clearance Holes –Floating Formula ApplicationWhat should we use as the positional tolerance for each of these two mating parts?

MMC of clearance holes minus MMC of fastener is given to the positional tolerance of both pieces.

Two Pieces Required

.404- .375

.029

Assuming a 3/8 – 16 threaded fastener…

M.029 A B C

B

C

.406

1.250 3.000

1.000

2.000

4X

M.XXX A B C

A

+ .007 - .002

.502

.500

184

Threaded Hole with Clearance Hole – Fixed Fastener Application

B

C

4X3/8 - 16 2B UNC thru

1.250 3.000

1.000

2.000

M.XXX A B C

A

.502

.500

P .502

B

C

.406

1.250 3.000

1.000

2.000

4X

M.XXX A B C

A

+ .007 - .002

.502

.500M.015 A B CP .502

What tolerances should we use for positional tolerances for these two mating parts?

MMC of clearance hole minus MMC of fastener must be shared between the two positional tolerance of the two pieces.

.404-.375.029

M.014 A B C

185

Topics Worthy of Discussion

Definition of Functional Requirements

Failure Mode and Effects Analysis

Consistent Tooling and Gaging Locators

Communication with Suppliers

Developing Optimal Specifications

186

Sources of Variation

The following primary contributors to body-in-white variability were identified as part of the Auto Body Consortium’s 2mm Program for Variation Reduction:

Locator Pins 28.4% Incoming Material 21.3% Welding 19.1% Clamping 13.5% Robot Programming 5.0% Carriers 3.5% Rough Locators 2.8% NC Blocks 2.8%

187

Sources of Variation

A summary of the sources of locator pin problems: Size 22.5% Pin Interference with Panel 17.5% Loose Pins 12.5% Pin Too Short 7.5% PLP Quantity 7.5% Pin PLP Selection 7.5% Pins Needed Rotating 5.0% Worn Pins 5.0% Missing Pins 5.0% Pin Shape 2.5% Pin Too Long 2.5%

188

Other Sources of Variation

GravityClamp SequenceTool InterferenceTool RepeatabilityMeasurement ErrorIncoming Part Quality Uncoordinated Datum SchemeClearance from Clamp Finger to Net Block

Environment

Equipment

Material

Methods

People

189

Section 6

Functional Gaging

190

Merits of Functional Gaging

Simple Functional Checks for Conformity

Takes Advantage of Bonus Tolerances

Checks Parts for their Virtual Condition

Allows for Best-Fit Solutions

Rejects Less Functionally Good Parts

191

Functional GagingPros and Cons

Pros Reduces risk of shipping bad product. Reduces risk of scrapping good product. Reduces inspection costs. Provides attribute data.

Cons Doesn’t provide variables data. Usually won’t qualify for PPAP submission. May not correlate with CMM data.

192

Functional Gaging of Profile

193

What to Do About Design Errors…

The first thing you want to do about design error is to find them early.

As human nature would have it, most designers seem to want to focus on the next design, rather than spending their time on past mistakes.

If you can identify design errors early in the design review process, the potential of actually getting the drawings corrected is often much greater.

194

Some things to Look for in Design Reviews

Datum schemes that don’t make sense.

Datum schemes that don’t match the physics of assembly.

Datum schemes that are in conflict with themselves.

Datum schemes that will be difficult to manufacture.

Datum schemes that will be difficult to inspect.

195


Geometric tolerances that aren’t referenced to a datum scheme when they should be.

Geometric tolerances that are referenced to a datum scheme when they shouldn’t be.

Diameter symbols used where they shouldn’t be used.

Diameter symbols not used where they should be.

196


Use of geometric tolerances that don’t refine either the limits of size or other tolerances.

Patterns of holes where the quantity of holes has not been specified.

Dimensional requirements that can’t be made.

Dimensional requirements that can’t be checked.

197

Process for Design Change

Quality management systems require a defined process for design changes within the scope of design control.

Designers need explicit and accurate feedback to improve both current and future designs.

If drawings aren’t updated to eliminate design flaws, the odds are pretty good that you’ll see that problem again in the future.

gd&t

Art & Photos

drawingallows

010abtwo functional

datum planedatum

axisactual

compare positional

true geometric

determine

tangent plane