Geometric Dimensioning and Tolerancing

(1)

Based on the ASME

Y14.5M-1994 Dimensioning and

Tolerancing Standard

DIMENSIONAL

ENGINEERING

(2)

INTRODUCTION

Geometric dimensioning and tolerancing (GD&T) is an

international engineering language that is used on

engineering drawings (blue prints) to describe product in

three dimensions. GD&T uses a series of internationally

recognized symbols rather than words to describe the

product. These symbols are applied to the features of a

part and provide a very concise and clear definition of

design intent.

GD&T is a very precise mathematical language that

describes the form, orientation and location of part

features in zones of tolerance. These zones of tolerance

are then described relative to a Cartesian coordinate

system.

ASME Y14.5M-1994

American national Standards Institute/

American Society

of Mechanical Engineers

(3)

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)

(4)

Extreme Variations of Form

Allowed By Size Tolerance

25.1 25

25 (MMC)

25.1 (LMC)

25 (MMC)

25.1 (LMC)

MMC Perfect

Form Boundary

(5)

Extreme Variations of Form

Allowed By Size Tolerance

25 24.9

25 (MMC)

24.9 (LMC)

MMC Perfect

Form Boundary

25 (MMC)

24.9 (LMC)

(6)

25 +/-0.25

0.1 Tolerance

0.5 Tolerance

Straightness is the condition where an element of a

surface or an axis is a straight line

Straightness

(Flat Surfaces)

(7)

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 the

elements to be controlled are represented by a straight line

In this example each line element of the surface must lie

within a tolerance zone defined by two parallel lines

separated by the specified tolerance value applied to each

view. All points on the surface must lie within the limits of

size and the applicable straightness limit.

(8)

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 must

lie within a tolerance zone defined by two parallel lines

separated by the specified tolerance value. The feature must

be within the limits of size and the boundary of perfect form at

MMC. Any barreling or waisting of the feature must not

(9)

Straightness (RFS)

0.1

Outer Boundary (Max) MMC

0.1 Diameter Tolerance Zone

Outer Boundary = Actual Feature Size + Straightness Tolerance

In this example the derived median line of the feature’s actual local

size must lie within a tolerance zone defined by a cylinder whose

diameter is equal to the specified tolerance value regardless of the

feature size. Each circular element of the feature must be within

the specified limits of size. However, the boundary of perfect form

at MMC can be violated up to the maximum outer boundary or

(10)

Straightness (MMC)

15 14.85 15.1 Virtual Condition 15 (MMC) 0.1 Diameter Tolerance Zone 15.1 Virtual Condition 14.85 (LMC) 0.25 Diameter Tolerance Zone

Virtual Condition = MMC Feature Size + Straightness Tolerance

In this example the derived median line of the feature’s actual local size

must lie within a tolerance zone defined by a cylinder whose diameter is

equal to the specified tolerance value at MMC. As each circular element

of the feature departs from MMC, the diameter of the tolerance cylinder

is allowed to increase by an amount equal to the departure from the local

MMC size. Each circular element of the feature must be within the

specified limits of size. However, the boundary of perfect form at MMC

can be violated up to the virtual condition diameter.

(11)

Flatness

Flatness is the condition of a surface having all elements in

one plane. Flatness must fall within the limits of size. The

flatness tolerance must be less than the size tolerance.

25 +/-0.25

24.75 min 25.25 max

0.1

0.1 Tolerance Zone 0.1 Tolerance Zone

In this example the entire surface must lie within a tolerance

zone defined by two parallel planes separated by the specified

tolerance value. All points on the surface must lie within the

limits of size and the flatness limit.

(12)

Circularity is the condition of a surface where all points of the

surface intersected by any plane perpendicular to a common

axis are equidistant from that axis. The circularity tolerance

must 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 the

specified tolerance value. All points on the surface must lie within the

limits of size and the circularity limit.

(13)

Cylindricity

Cylindricity is the condition of a surface of revolution in which

all points are equidistant from a common axis. Cylindricity is a

composite 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 zone

defined by two concentric cylinders separated by the specified

tolerance value. All points on the surface must lie within the limits of

size and the cylindricity limit.

(14)

____________

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

_______

cylindrical parts.

1.

2.

3.

4.

5.

Form controls require a datum reference.

Form controls do not directly control a feature’s size. A feature’s form tolerance must be less than it’s size tolerance.

Flatness controls the orientation of a feature. Size limits implicitly control a feature’s form.

6.

7.

8.

9.

10. Questions #1-5 Fill in blanks (choose from below)

straightness

flatness

circularity

cylindricity

perfect form

straight

tapered

profile

true position

angularity

(15)

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)

(16)

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 datum

reference plane, within the specified tolerance zone.

A

20 +/-0.5 30 o

A

19.5 min 0.3 Wide Tolerance Zone 30 o

A

20.5 max 0.3 Wide Tolerance Zone 30 o

The tolerance zone in this example is defined

by two parallel planes oriented at the

specified angle to the datum reference plane.

(17)

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 a

cylinder equal to the length of the feature, oriented

at the specified angle to the datum reference plane.

0.3 Circular Tolerance Zone

Angularity

(Feature Axis to Datum Surface)

NOTE: Tolerance applies

to feature at RFS

(18)

NOTE: Tolerance

applies 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.

A

Datum Axis A

Angularity

(Feature Axis to Datum Axis)

The tolerance zone in this example is defined by a

cylinder equal to the length of the feature, oriented

at the specified angle to the datum reference axis.

NOTE: Feature axis must lie

within tolerance zone cylinder

0.3 A

o

(19)

0.3 A

A

0.3 Wide

Tolerance Zone

A

Perpendicularity is the condition of the planar feature

surface at a right angle to the datum reference plane, within

the specified tolerance zone.

Perpendicularity

(Feature Surface to Datum Surface)

The tolerance zone in this example is

defined by two parallel planes oriented

perpendicular to the datum reference

plane.

(20)

C

Perpendicularity is the condition of the feature axis at a right

angle to the datum reference plane, within the specified

tolerance zone.

Perpendicularity

(Feature Axis to Datum Surface)

0.3 C 0.3 Circular Tolerance Zone 0.3 Diameter Tolerance Zone 0.3 Circular Tolerance Zone

NOTE: Tolerance applies

to feature at RFS

The tolerance zone in this example is

defined by a cylinder equal to the length of

the feature, oriented perpendicular to the

datum reference plane.

(21)

Perpendicularity

(Feature Axis to Datum Axis)

NOTE: Tolerance applies

to feature at RFS

The tolerance zone in this example is

defined by two parallel planes oriented

perpendicular to the datum reference axis.

Perpendicularity is the condition of the feature axis at a right

angle to the datum reference axis, within the specified

tolerance zone.

A

Datum Axis A

0.3 A

(22)

0.3 A

A

25 +/-0.5

25.5 max

A

24.5 min

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 example

is defined by two parallel planes

oriented parallel to the datum

reference plane.

(23)

A

Parallelism

(Feature Axis to Datum Surface)

0.3 A

A

NOTE: The specified tolerance

does not apply to the orientation

of the feature axis in this direction

Parallelism is the condition of the feature axis equidistant

along its length from the datum reference plane, within the

specified tolerance zone.

The tolerance zone in this example

is defined by two parallel planes

oriented parallel to the datum

reference plane.

NOTE: Tolerance applies

to feature at RFS

(24)

A

B

Parallelism

(Feature Axis to Datum Surfaces)

A

B

0.3 Circular Tolerance Zone 0.3 Circular Tolerance Zone 0.3 Circular Tolerance Zone

Parallelism is the condition of the feature axis equidistant

along its length from the two datum reference planes, within

the specified tolerance zone.

The tolerance zone in this example is

defined by a cylinder equal to the

length of the feature, oriented parallel

to the datum reference planes.

NOTE: Tolerance applies

to feature at RFS

(25)

Parallelism

(Feature Axis to Datum Axis)

Parallelism is the condition of the feature axis equidistant along

its length from the datum reference axis, within the specified

tolerance zone.

A

0.1 A 0.1 Circular Tolerance Zone 0.1 Circular Tolerance Zone

Datum Axis A

The tolerance zone in this example is

defined by a cylinder equal to the

length of the feature, oriented

parallel to the datum reference axis.

NOTE: Tolerance applies

to feature at RFS

(26)

Orientation Control Quiz

The three orientation controls are

__________

,

___________

, and

________________

.

1.

2.

3.

4.

5.

A

_______________

is always required when applying any of the orientation controls.

________________

is the appropriate geometric tolerance when controlling the orientation of a feature at right angles to a datum

reference.

Orientation tolerances indirectly control a feature’s 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 must be 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

perpendicularity

parallelism

datum reference

identical

location

profile

datum feature

datum target

(27)

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)

(28)

Datum feature

Datum axis (established

from datum feature

Angled surfaces

constructed around

a datum axis

External surfaces

constructed around

a datum axis

Internal surfaces

constructed around a

datum axis

Surfaces constructed

perpendicular to a

datum axis

Features Applicable

to Runout Tolerancing

(29)

0

+

-Full Indicator Movement Maximum Minimum Total Tolerance Maximum Reading Minimum Reading Full Part Rotation Measuring position #1 (circular element #1)

Circular Runout

When measuring circular runout, the indicator must be reset to zero at each measuring position along the feature surface. Each individual circular element of the surface is independently allowed the full specified tolerance. In this example, circular runout can be used to detect 2-dimensional wobble (orientation) and waviness (form), but not 3-2-dimensional characteristics such 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 to MMC or LMC.

(30)

o 360 Part Rotation 50 o +/- 2o

As Shown

on Drawing

Means This:

Datum axis A Single circular element

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 feature surface not the entire angled feature surface

Full Indicator Movement

(

)

The tolerance zone for any individual circular element is equal to the total allowable movement of a dial indicator fixed in a position normal to the true geometric shape of the feature surface when the part is rotated 360 degrees about the datum axis. The tolerance limit is applied independently to each individual measuring position along the feature surface.

Allowable indicator reading = 0.75 max.

When measuring circular runout, the indicator must be reset when repositioned along the feature surface.

(31)

As Shown

on Drawing

50 +/-0.25

0.75 A

Circular Runout

(Surface Perpendicular to Datum Axis)

o 360 Part Rotation 0 + -Datum axis A Single circular element

NOTE: Circular runout in this example will only control variation in the 2-dimensional circular elements of the planar surface (wobble and waviness) not the entire feature surface The tolerance zone for any individual circular element is equal to the total allowable movement of a dial indicator fixed in a position normal to the true geometric shape of the feature surface when the part is rotated 360 degrees about the datum axis. The tolerance limit is applied independently to each individual measuring position along the feature surface.

Means This:

(32)

0

+

-Allowable indicator reading = 0.75 max.

Single circular element o 360 Part Rotation

Means This:

As Shown

on Drawing

50 +/-0.25 0.75 A Datum axis A

Circular Runout

(Surface Coaxial to Datum Axis)

The tolerance zone for any individual circular element is equal to the total allowable movement of a dial indicator fixed in a position normal to the true geometric shape of the feature surface when the part is rotated 360 degrees about the datum axis. The tolerance limit is applied independently to each individual measuring position along the feature surface.

NOTE: Circular runout in this example will only control variation in the 2-dimensional circular elements of the surface (circularity and coaxiality) not the entire feature surface

(33)

0

+

-Allowable indicator reading = 0.75 max.

Single circular element

o 360 Part Rotation

Means This:

As Shown

on Drawing

0.75 A-B

Datum axis A-B

Circular Runout

(Surface Coaxial to Datum Axis)

The tolerance zone for any individual circular element is equal to the total allowable movement of a dial indicator fixed in a position normal to the true geometric shape of the feature surface when the part is rotated 360 degrees about the datum axis. The tolerance limit is applied independently to each individual measuring position along the feature surface.

NOTE: Circular runout in this example will only control variation in the 2-dimensional circular elements of the surface (circularity and coaxiality) not the entire feature surface

Machine center Machine center B A

(34)

As Shown

on Drawing

50 +/-0.25

Circular Runout

(Surface Related to Datum Surface and Axis)

o 360 Part Rotation 0 + -Datum axis B Single circular element

The tolerance zone for any individual circular element is equal to the total allowable movement of a dial indicator fixed in a position normal to the true geometric shape of the

feature surface when the part is located against the datum surface and rotated 360 degrees about the datum axis. The tolerance limit is applied independently to each individual measuring position along the feature surface.

Means This:

A

When measuring circular runout, the indicator must be reset when repositioned along the feature surface. Collet or Chuck Stop collar 0.75 A B Datum plane A B

(35)

0

+

Full Indicator Movement Total Tolerance Maximum Reading Minimum Reading Full Part Rotation

-0

+

-Total Runout

Maximum Minimum

When measuring total runout, the indicator is moved in a straight line along the feature surface while the part is rotated about the datum axis. It is also acceptable to measure total runout by evaluating an appropriate number of individual circular elements along the surface while the part is rotated about the datum axis. Because the tolerance value is applied to the entire surface, the indicator 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 (overall orientation).

Indicator Path

Total runout can only be applied on an RFS basis and cannot be modified to MMC or LMC.

(36)

Full Part Rotation 50 o +/- 2o

As Shown

on Drawing

A 50 +/-0.25 0.75 A

Means This:

Datum axis A 0 +

-The tolerance zone for the entire angled surface is equal to the total allowable movement of a dial indicator positioned normal to the true geometric shape of the feature surface when the part is rotated about the datum axis and the indicator is moved along the entire length of the feature surface.

0

+

-NOTE: Unlike circular runout, the use of total runout will provide 3-dimensional composite control of the cumulative 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, the indicator must not be reset when repositioned along the feature surface.

(applies to the entire feature surface) Allowable indicator reading = 0.75 max.

(37)

0

+

-Total Runout

(Surface Perpendicular to Datum Axis)

As Shown

on Drawing

A 50 +/-0.25 0.75 A 35 10 0 + -Datum axis A Full Part Rotation 35 10

Means This:

NOTE: The use of total runout in this example will provide composite control of the cumulative variations of perpendicularity (wobble) and flatness (concavity or convexity) of the feature surface.

The tolerance zone for the portion of the feature surface indicated is equal to the total allowable movement of a dial indicator positioned normal to the true geometric shape of the feature surface when the part is rotated about the datum axis and the indicator is moved along the portion of the feature surface within the area described by the basic dimensions.

When measuring total runout, the indicator must not be reset when repositioned along the feature surface.

(applies to portion of feature surface indicated) Allowable indicator reading = 0.75 max.

(38)

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 right angles to the datum reference.

2.

3.

4.

5.

Circular runout tolerances apply to single elements .

6.

Circular runout tolerances are used to control an entire feature surface.

Runout tolerances always require a datum reference.

7.

Circular runout and total runout both control axis to surface relationships.

8.

Circular runout can be applied to control taper of a part.

9.

Total runout tolerances are an appropriate way to limit “wobble” of a rotating surface.

10.

Runout tolerances are used to control a feature’s size.

11.

Total runout can control circularity, straightness, taper, coaxiality, angularity and any other surface variation.

(39)

Tolerances

of Profile

Profile of a Line

Profile of a Surface (ASME Y14.5M-1994, 6.5.2b)

(40)

18 Max

Profile of a Line

2 Wide Size Tolerance Zone 1 A B C A 17 +/- 1 1 Wide Profile Tolerance 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 two

parallel lines oriented with respect to the datum reference

frame. The profile tolerance zone is free to float within the

larger size tolerance and applies only to the form and

orientation of any individual line element along the entire

surface.

Profile of a Line is a two-dimensional tolerance that can be applied to a

part feature in situations where the control of the entire feature surface as

a single entity is not required or desired. The tolerance applies to the line

element of the surface at each individual cross section indicated on the

drawing.

(41)

Profile of a Surface is a three-dimensional tolerance that can be applied

to a part feature in situations where the control of the entire feature

surface as a single entity is desired. The tolerance applies to the entire

surface and can be used to control size, location, form and/or orientation

of a feature surface.

Profile of a Surface

2 Wide Tolerance Zone

Size, Form and Orientation

A A1 20 X 20 A2 20 X 20 A3 20 X 20 C 2 A B C 23.5 23.5 Nominal Location

The profile tolerance zone in this example is defined by two parallel planes oriented with respect to the datum reference frame. The profile tolerance zone is located and aligned in a way that enables the part surface to vary equally about the true profile of the feature.

(42)

Profile of a Surface

A1 20 X 20 A2 20 X 20 A3 20 X 20 B C 50 B C 50 1 Wide Total Tolerance Zone

(Bilateral Tolerance)

The tolerance zone in this example is defined by two parallel planes oriented with respect to the datum reference frame. The profile tolerance zone is located and aligned in a way that enables the part surface to vary equally about the true profile of the trim.

1 A B C

Nominal Location 0.5 Inboard

0.5 Outboard

Profile of a Surface when applied to trim edges of sheet metal parts will control the location, form and orientation of the entire trimmed surface. When a

bilateral value is specified, the tolerance zone allows the trim edge variation and/or locational error to be on both sides of the true profile. The tolerance applies to the entire edge surface.

(43)

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 Total Tolerance Zone

(Unilateral Tolerance)

Profile of a Surface when applied to trim edges of sheet metal parts will control the location, form and orientation of the entire trimmed surface. When a

unilateral value is specified, the tolerance zone limits the trim edge variation and/or locational error to one side of the true profile. The tolerance applies to the entire edge surface.

The tolerance zone in this example is defined by two parallel planes oriented with respect to the datum reference frame. The profile tolerance zone is located and aligned in a way that allows the trim surface to vary from the true profile only in the inboard direction.

0.5 A B C

(44)

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 Total Tolerance Zone

(Unequal Bilateral Tolerance)

Profile of a Surface when applied to trim edges of sheet metal parts will control the location, form and orientation of the entire trimmed surface. Typically when unequal values are specified, the tolerance zone will represent the actual

measured trim edge variation and/or locational error. The tolerance applies to the entire edge surface.

The tolerance zone in this example is defined by two parallel planes oriented with respect to the datum reference frame. The profile tolerance zone is located and aligned in a way that enables the part surface to vary from the true profile more in one direction (outboard) than in the other (inboard).

0.5

(45)

A 25 A 0.5 0.1 25.25 24.75 0.1 Wide Tolerance Zone

A

Composite Profile of Two Coplanar

Surfaces w/o Orientation Refinement

Profile of a Surface

Form Only Location & Orientation

(46)

0.1 Wide Tolerance Zone 25.25 24.75 A A A 25 A 0.5 A

0.1 _{Form & Orientation}

Composite Profile of Two Coplanar

Surfaces With Orientation Refinement

Profile of a Surface

(47)

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 control trim edges on sheet metal parts.

Profile tolerances can be combined with other geometric controls 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 because they are more restrictive and very difficult to check.

10.

Profile tolerances can be applied either bilateral or unilateral to a feature.

11.

Profile tolerances can be applied in both freestate and restrained datum conditions.

12.

Tolerances shown in the lower segment of a composite profile feature control frame control the location of a feature to the specified datums.

(48)

In composite profile applications, the tolerance shown in the upper segment of the feature control frame applies only to the

________

of the 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 are

required for location and form and/or orientation.

7.

When using profile tolerances to control the location and/or orientation of a feature, a

_______________

must be included

in 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 line

datum reference

composite profile

bilateral

location

form

primary datum

true geometric counterpart

orientation

profile of a surface

unilateral

(49)

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)

(50)

(51)

10.25 +/- 0.5 10.25 +/- 0.5 8.5 +/- 0.1 Rectangular Tolerance Zone 10.25 10.25 8.5 +/- 0.1 Circular Tolerance Zone B A C

Coordinate vs Geometric

Tolerancing Methods

Coordinate Dimensioning

Geometric Dimensioning

Rectangular Tolerance Zone Circular Tolerance Zone 1.4 +/- 0.5

+/- 0.5

57% Larger

Tolerance Zone

Circular Tolerance Zone

Rectangular Tolerance Zone

Increased Effective Tolerance

(52)

Formula to determine the actual radial

position of a feature using measured

coordinate values (RFS)

Z

positional tolerance /2

X

2 +

Y

2 Z =

X =

2 Y =

2 X

Y

Z

Feature axis actual

location (measured)

Positional

tolerance zone

cylinder

Feature axis true

position (designed)

Positional Tolerance Verification

Z = total radial deviation

“X” measured deviation

“Y” measured deviation

Actual feature

boundary

(53)

Formula to determine the actual radial

position of a feature using measured

coordinate values (MMC)

Z

X

2 +

Y

2 Z =

X =

2 Y =

2 X

Y

Z

Feature axis actual

location (measured)

Positional

tolerance zone

cylinder

Feature axis true

position (designed)

Positional Tolerance Verification

Z = total radial deviation

“X” measured deviation

“Y” measured deviation

Actual feature

boundary

+( actual -

MMC)

2 = positional tolerance

(54)

Bi-directional True Position

Rectangular Coordinate Method

35 10 10

A

C

B

1.5 A B C 0.5 A B C

2X

10 35 1.5 Wide Tolerance Zone 0.5 Wide Tolerance Zone True Position Related

to Datum Reference Frame

10

B

C

Each axis must lie within the 1.5 X 0.5 rectangular tolerance zone

basically located to the datum reference frame

As Shown

on Drawing

Means This:

(55)

Bi-directional True Position

Multiple Single-Segment Method

35 10 10

A

C

B

10 35 1.5 Wide Tolerance Zone 0.5 Wide Tolerance Zone True Position Related

to Datum Reference Frame

10

B

C

Each axis must lie within the 1.5 X 0.5 rectangular tolerance zone

basically located to the datum reference frame

As Shown

on Drawing

Means This:

2X 6 +/-0.25

1.5 A B C 0.5 A B

(56)

35 10 10

A

C

B

_{As Shown}

on Drawing

Means This:

1.5 A B C _{0.5 A B C} BOUNDARY _BOUNDARY 10 35 10

B

C

2X 13 +/-0.25 _{2X 6}_+/-0.25 12.75MMC width of slot -1.50Position tolerance 11.25 Maximum boundary

Both holes must be within the size limits and no portion of their surfaces may lie within the area described by the 11.25 x 5.25 maximum

boundaries when the part is positioned with respect to the datum reference frame. The boundary concept can only be applied on an MMC basis.

o

90 True position boundary related

to datum reference frame

A

Bi-directional True Position

Noncylndrical Features (Boundary Concept)

M M

5.75 MMC length of slot

-0.50Position tolerance

(57)

Composite True Position

Without Pattern Orientation Control

35 10 10

A

C

B

10 35

True Position Related to Datum Reference Frame

10

B

C

Each axis must lie within each tolerance zone simultaneously

As Shown

on Drawing

Means This:

2X 6 +/-0.25

1.5 A B C 0.5 A 0.5 Feature-Relating Tolerance Zone Cylinder

1.5 Pattern-Locating Tolerance Zone Cylinder

pattern location relative to Datums A, B, and C pattern orientation relative to

(58)

Composite True Position

With Pattern Orientation Control

35 10 10

A

C

B

10 35

True Position Related to Datum Reference Frame

10

B

C

Each axis must lie within each tolerance zone simultaneously

As Shown

on Drawing

Means This:

2X 6 +/-0.25

0.5 Feature-Relating Tolerance Zone Cylinder

1.5 Pattern-Locating Tolerance Zone Cylinder

pattern location relative to Datums A, B, and C

pattern orientation relative to Datums A and B

1.5 A B C 0.5 A B

(59)

Location (Concentricity)

Datum Features at RFS

A

15.95

15.90 As Shown on Drawing

Derived Median Points of Diametrically Opposed Elements

Axis of Datum Feature A

Means This:

Within the limits of size and regardless of feature size, all median points of diametrically opposed elements must lie within a 0.5 cylindrical

tolerance zone. The axis of the tolerance zone coincides with the axis of datum feature A. Concentricity can only be applied on an RFS basis.

0.5 A

6.35 +/- 0.05

0.5 Coaxial Tolerance Zone

(60)

Location (Symmetry)

Datum Features at RFS

A

15.95

15.90 0.5 A

6.35 +/- 0.05

Derived Median Points Center Plane of Datum Feature A 0.5 Wide Tolerance Zone

Means This:

Within the limits of size and regardless of feature size, all median points of opposed elements must lie between two parallel planes equally

disposed about datum plane A, 0.5 apart. Symmetry can only be applied on an RFS basis.

(61)

True Position Quiz

Answer questions #1-11 True or False

Positional tolerances are applied to individual or patterns of features of size.

1.

Cylindrical tolerance zones more closely represent the functional requirements of a pattern of clearance holes.

True position tolerances can control a feature’s size. Positional tolerances are applied on an MMC, LMC, or RFS basis.

2.

3.

4.

5.

True position tolerance values are used to calculate the minimum 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 applied to patterns of related features.

7.

The tolerance value shown in the upper segment of a composite true position feature control frame applies to the location of a pattern of features to the specified datums.

8.

Positional tolerances can be used to control circularity

9.

10.

11.

The tolerance value shown in the lower segment of a composite true position feature control frame applies to 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.

(62)

Positional tolerance zones can be

___________

,

___________

, or spherical

1.

2.

3.

4.

5. ________________

are used to establish the true (theoretically exact) position of a feature from specified datums.

Positional tolerancing is a

_____________

control.

Positional tolerance can apply to the

____

or

________________

of a feature.

_____

and

________

fastener equations are used to determine appropriate clearance hole sizes for mating details

6.

7. _________

tolerance zones are recommended to prevent fastener interference in mating details.

8. projected

3-dimensional

surface boundary

floating

location

fixed

basic dimensions

maximum material

cylindrical

pattern-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

(63)

(64)

(65)

Fixed and

Floating

Fastener

Exercises

(66)

2x M10 X 1.5 (Reference)

B

A

?.? 2x 10.50 +/- 0.25 M Calculate Required Positional Tolerance 0.5 2x ??.?? +/- 0.25 M Calculate Nominal Size

A

B

T = H - F

H = Minimum Hole Size = 10.25 F = Max. Fastener Size = 10

T = 10.25 -10

T = ______

Floating Fasteners

H = F +T

F = Max. Fastener Size = 10 T = Positional Tolerance = 0.50

H = 10 + 0.50

H = ______

In applications where two or more mating details are assembled, and all parts have clearance holes for the fasteners, the floating fastener formula shown below can be used to calculate the appropriate hole sizes or positional tolerance requirements 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 hole F= Maximum diameter of fastener T= Positional tolerance diameter

H=F+T or T=H-F

General Equation Applies to Each Part Individually

remember: the size tolerance must be added to the calculated MMC hole size to obtain the correct nominal value.

(67)

B

A

0.25 2x 10.50 +/- 0.25 M 0.5 2x 10.75 +/- 0.25 M

A

B

Floating Fasteners

REMEMBER!!! All Calculations Apply at MMC

H=F+T or T=H-F

General Equation Applies to Each Part Individually

T = H - F

H = Minimum Hole Size = 10.25 F = Max. Fastener Size = 10

T = 10.25 -10

T = 0.25

Calculate Required Positional Tolerance

H = 10 + .5

H = 10.5 Minimum

H = F +T

In applications where two or more mating details are assembled, and all parts have clearance holes for the fasteners, the floating fastener formula shown below can be used to calculate the appropriate hole sizes or positional tolerance requirements to ensure assembly. The formula will provide a “zero-interference” fit when the features are at MMC and at their extreme of positional tolerance

Calculate Nominal Size

(68)

F = Max. Fastener Size = 10.00 T = Positional Tolerance = 0.80 2x M10 X 1.5 (Reference)

B

A

0.8 2x ??.?? +/- 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=F+2T or T=(H-F)/2

General Equation Used When Positional Tolerances Are Equal

In fixed fastener applications where two mating details have equal positional

tolerances, the fixed fastener formula shown below can be used to calculate the appropriate minimum clearance hole size and/or positional tolerance required to ensure 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 example the positional tolerances indicated are the same for both parts.)

0.8 M P10

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 calculated MMC size to obtain the correct nominal value.

(69)

B

A

2x 11.85 +/- 0.25 0.8 M Calculate Required Clearance Hole Size.

A

B

Fixed Fasteners

H = F + 2T

F = Max. Fastener Size = 10.00 T = Positional Tolerance = 0.80

H = 10.00 + 2(0.8)

H = 11.60 Minimum

H=F+2T or T=(H-F)/2

0.8 M P10

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED

2X M10 X 1.5 _{(MMC For Calculations)}Nominal Size

REMEMBER!!! All Calculations Apply at MMC

(70)

B

A

2x 11.85 +/- 0.25 0.8 M Calculate Required Clearance Hole Size.

A

B

Fixed Fasteners

H = F + 2T

H = 10 + 2(0.8)

H = 11.6 Minimum

H=F+2T or T=(H-F)/2

0.8 M P₁₀

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED

REMEMBER!!! All Calculations Apply at MMC

(71)

B

A

0.5 2x 11.25 +/- 0.25

M Calculate Required _{Positional Tolerance .}

(Both Parts)

A

B

In applications where two mating details are assembled, and one part has restrained fasteners, the fixed fastener formula shown below can be used to calculate appropriate hole sizes and/or positional tolerances required to ensure assembly. 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 the resultant positional tolerance is applied to both parts equally.)

Fixed Fasteners

T = (H - F)/2

H = Minimum Hole Size = 11 F = Max. Fastener Size = 10

T = (11 - 10)/2

T = 0.50

H=F+2T or T=(H-F)/2

2X M10 X 1.5 0.5 M P ₁₀

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED

Nominal Size (MMC For Calculations)

REMEMBER!!! All Calculations Apply at MMC

(72)

B

A

0.5 2x ??.?? +/- 0.25 M Calculate Required Clearance Hole Size.

A

B

Fixed Fasteners

H = Min. diameter of clearance hole F = Maximum diameter of fastener T1= Positional tolerance (Part A) T2=

Positional tolerance (Part B)

H=F+(T

1

+ T

2

)

General Equation Used When Positional Tolerances Are Not Equal

F = Max. Fastener Size = 10 T1= Positional Tol. (A) = 0.50

T2= Positional Tol. (B) = 1

H = 10+ (0.5 + 1)

H = ____

H=F+(T

1

+ T

2

)

In fixed fastener applications where two mating details have unequal positional tolerances, the fixed fastener formula shown below can be used to calculate the appropriate minimum clearance hole size and/or positional tolerances required to ensure 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 example the positional tolerances indicated are not equal.)

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED

10

(73)

B

A

0.5 2x 11.75 +/- 0.25 M Calculate Required Clearance Hole Size.

A

B

In fixed fastener applications where two mating details have unequal positional tolerances, the fixed fastener formula shown below can be used to calculate the appropriate minimum clearance hole size and/or positional tolerances required to ensure 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 example the positional tolerances indicated are not equal.)

Fixed Fasteners

F = Max. Fastener Size = 10 T1= Positional Tol. (A) = 0.5

T2= 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 hole F = Maximum diameter of fastener T1= Positional tolerance (Part A) T2=

Positional tolerance (Part B)

H= F+(T

1

+ T

2

)

General Equation Used When Positional Tolerances Are Not Equal

H=F+(T

1

+ T

2

)

1 M P 10

REMEMBER!!! All Calculations Apply at MMC

(74)

D P

H F

A

B

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS NOT USED

2x 10.05 +/-0.05

B

A

0.5 M 2x ??.?? +/-0.25 Calculate Nominal Size 0.5 M

In applications where a projected tolerance zone is not indicated, it is necessary to select a positional tolerance and minimum clearance hole size

combination that will allow for any out-of-squareness of the feature containing the fastener. The modified fixed fastener formula shown below can be used to

calculate the appropriate minimum clearance hole size required to ensure

assembly. The formula provides a “zero-interference” fit when the features are at MMC and at the extreme positional tolerance.

Fixed Fasteners

H =

10.00 + 0.5 + 0.5(1 + 2(15/20))

H = __________

H= F + T

1

+ T

2

(1+(2P/D))

H= Min. diameter of clearance hole F= Maximum diameter of pin T1= 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) = 0.5

T2= Positional Tol. (B) = 0.5 D

= Min. pin depth = 20. P = Max. pin projection = 15

(75)

D P

H F

A

B

H= Min. diameter of clearance hole F= Maximum diameter of pin T1= 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 M 2x 12 +/-0.25 Calculate Nominal Size 0.5 M

F = Max. pin size = 10 T1= Positional tol. (A) = 0.5

T2= Positional tol. (B) = 0.5 D

= Min. pin depth = 20 P = Max. pin projection = 15

H= F + T

1

+ T

2

(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 not indicated, it is necessary to select a positional tolerance and minimum clearance hole size

combination that will allow for any out-of-squareness of the feature containing the fastener. The modified fixed fastener formula shown below can be used to

calculate the appropriate minimum clearance hole size required to ensure

assembly. The formula provides a “zero-interference” fit when the features are at MMC and at the extreme positional tolerance.

Fixed Fasteners

H= F + T

1

+ T

2

(1+(2P/D))

REMEMBER!!! All Calculations Apply at MMC

(76)

Answers to Quizzes

and Exercises

(77)

Rules and Definitions Quiz

1. Tight tolerances ensure high quality and performance. 2. The use of GD&T improves productivity.

3. Size tolerances control both orientation and position. 4. Unless otherwise specified size tolerances control form. 5. A material modifier symbol is not required for RFS. 6. A material modifier symbol is not required for MMC. 7. Title block default tolerances apply to basic dimensions. 8. A surface on a part is considered a feature.

9. Bilateral tolerances allow variation in two directions. 10. A free state modifier can only be applied to a tolerance. 11. A free state datum modifier applies to “assists” & “rests”. 12. Virtual condition applies regardless of feature size.

FALSE

TRUE

FALSE

TRUE

FALSE

TRUE

FALSE

(78)

Material Condition Quiz

Internal Features

MMC LMC

External Features

MMC LMC

.890

.885

.895

.890

23.45 +0.05/-0.25

10.75 +0.25/-0

123. 5 +/-0.1

23.45 +0.05/-0.25

10.75 +0/-0.25

123. 5 +/-0.1

Calculate appropriate values

Fill in blanks

10.75 11

23.2 23.5

123.4 123.6

.890 .895

10.75 10.5

23.5 23.2

123.6 123.4

.890 .885

(79)

1. Datum target areas are theoretically exact. 2. Datum features are imaginary.

3. Primary datums have only three points of contact. 4. The 6 Degrees of Freedom are U/D, F/A, & C/C. 5. Datum simulators are part of the gage or tool. 6. Datum simulators are used to represent datums.

8. All datum features must be dimensionally stable. 9. Datum planes constrain degrees of freedom. 10. Tertiary datums are not always required.