Dimensioning and Tolerancing

Design representation:

enough information to

manufacture the part precisely

inspect the manufactured part

[geomtery, dimensions, tolerances]

ProjectionsTheoretical technique to map 3D objects to

2D

DimensionsTo assist machinist:e.g. distance between centers of holes

Tolerancesimprecision in machining

must specify the tolerance range,

What is a ‘good level of tolerance’?

Designer: tight tolerance is better

(less vibration, less wear, less noise)

Machinist: large tolerances is better

(easier to machine, faster to produce, easier to assemble)

Tolerances interchangeability

Tolerance and Concurrent Engineering

Why ?

Tolerance specification needs knowledge of

accuracy, repeatability of machines

process capability

…

Part 1. Projections.

3D models: expensive, difficult to make

=> need 2D representaitons

Images must convey feasible 3D objects

Albrecht Durer’s machine [14??AD] (perspective map)

1. Renaissance architects

2. Modern CAD systems

(a) 3D rendering, image processing

(b) Mathematics of free-form surfaces (NURBS)

Importance of perspective maps

Why perspective maps ?

larger, farther same image size

same size, farther smaller image

Human sight and perception

parallel lines converge to a point

The vanishing point (or station point)

Effect of vanishing point on perspective map

Image on the ‘picture plane’ is a perspective of the 3D object

[Is the object behind in perspective view ?]

para

llel

parallel

para

llel

converge:

finite vanishing point

converge:finite vanishing pointpa

ralle

l

parallel

para

llel

parallel

para

llel

converge:

finite vanishing point

converge:finite vanishing point

para

llel

converge:

finite vanishing point

converge:finite vanishing point

Perspectives and vanishing points

Perspectives in mechanical drafting Not good !

(1) parallel lines converge misinterpreted by the machinist

(2) Views have too many lines

Orthographic views

A mapping where parallel lines remain parallel

How ?Set the vanishing point at infinity

Another problem:

Back, Sides of object not visible (hidden surfaces)

Solution: Multiple views

Orthographic views:Language of engineering communication

View direction selection in orthographics

Maximize true-size view of most faces

FRONT

TOP

RIGHTFRONT

TOP

RIGHT

Isometric view: gives a ‘3D image’

each side has equal length

(a) orthograhic (b) top view rotated by 45° (c) Isometric projection

each side has equal length

(a) orthograhic (b) top view rotated by 45° (c) Isometric projection

Different types of projections

All engineering drawings must be made to scale

Datum: A theoretical geometric object (point, line, axis, or plane) derived from a specific part/feature of a datum feature on the part.

Uses:

(1) specify distance of a feature from the datum

(2) specify a geometric characteristic (e.g. straightness) of a feature

Part 2. ANSI dimensioning

Basic Dimension:The theoretically exact size of a feature or datum

Feature:A geometric entity on the part, (hole, axis, plane, edge)

Datum feature:An actual feature of a part, that is used to establish a datum.

Limits: The max/min allowable sizes

Largest allowable size: upper limit

Least allowable size: lower limit.

LMC (Least Material Condition)

MMC (Maximum material Condition)

Conventions for dimensioning

(a) Specify tolerance for all dimensions

(b) All necessary , sufficient dimensionsX over-dimensioned XX under-dimensioned X

Reference dimensions:Redundant dimensions, in ( …)

(c) Dimensions should be (i) marked off the datum feature (ii) shown in true-size view (iii) shown in visible view

(a) Size of a featureSpecified by a basic size, and tolerance: 2.50±0.03

upper limit =

lower limit =

No of digits after decimal precision

Part 3. Mechanical Tolerancing

Conventional Tolerancing:

Unilateral and Bilateral Tolerances:

2.50+0.03- 0.03

+0.06+ 0.002.47

-0.00-0.062.532.49

+0.04- 0.02

bilateral unilateral-0.03-0.092.562.50

+0.03- 0.032.50+0.03- 0.03

+0.06+ 0.002.47+0.06+ 0.002.47

-0.00-0.062.53-0.00-0.062.532.49

+0.04- 0.022.49+0.04- 0.02

bilateral unilateral-0.03-0.092.56-0.03-0.092.56

(b) The type of fit between mating features

Designer needs to specify

basic dia, tol of shaft: S±s/2

basic dia, tol of hole: H±h/2

Allowance: a = Dhmin – Dsmax.

Conventional Tolerancing..

0.0006d1/30.0006d1/3-0.001dShrink

0.0006d1/30.0006d1/3-0.0005dMedium Force

0.0006d1/30.0006d1/3-0.00025dTightInterference

[difficult assembly

can transmit torque]

0.0004d1/30.0006d1/30Wringing

0.0004d1/30.0006d1/30SnugTransition

[difficult to mfg

precision fit

0.0018d1/30.0018d1/30.0009d2/3Medium

0.0013d1/30.0013d1/30.0014d2/3Free

0.0025d1/30.0025d1/30.0025d2/3LooseClearance

[easy assembly,

may vibrate in use]

s (shaft tolerance)h (hole tolerance)a (allowance)Sub-TypeFIT

0.0006d1/30.0006d1/3-0.001dShrink

0.0006d1/30.0006d1/3-0.0005dMedium Force

0.0006d1/30.0006d1/3-0.00025dTightInterference

[difficult assembly

can transmit torque]

0.0004d1/30.0006d1/30Wringing

0.0004d1/30.0006d1/30SnugTransition

[difficult to mfg

precision fit

0.0018d1/30.0018d1/30.0009d2/3Medium

0.0013d1/30.0013d1/30.0014d2/3Free

0.0025d1/30.0025d1/30.0025d2/3LooseClearance

[easy assembly,

may vibrate in use]

s (shaft tolerance)h (hole tolerance)a (allowance)Sub-TypeFIT

Standard fits

The hole-basic specification convention

shaft hole

2.00

0+-

h

a

s

basicsize

hole basicunilateral toleranceclearance fit

+-

h

a

s

basicsize

hole basicbilateral toleranceclearance fit

meansize

+- h

a

s

basicsize

hole basicunilateral toleranceinterference fit

+-

h

a

sbasic

size

shaft basicbilateral toleranceinterference fit

meansize

+-

shaft hole

2.00

0+-

h

a

s

basicsize

hole basicunilateral toleranceclearance fit

+-

h

a

s

basicsize

hole basicbilateral toleranceclearance fit

meansize

+- h

a

s

basicsize

hole basicunilateral toleranceinterference fit

+-

h

a

sbasic

size

shaft basicbilateral toleranceinterference fit

meansize

+-

[Holes are made by drills]

Generalization of hole-basic/shaft-basic

MMC: Maximum material condition

LMC: Least material condition

Hole at MMC at the lower limit

Hole at LMC at the upper limit

Geometric Tolerancing

Y

X

t

t

max tol = t 2

Y

X

t

t

max tol = t 2

Problems in Conventional tolerancing:

(a) Assumes perfect surfaces

(b) No use of Datums

(c) No specification of form tolerances

(d) X±t/2, Y±t/2 rectangular tolerance zone (cylindrical preferred)

Datums

A theoretical feature (e.g. plane, line)

Serves as a global coordinate frame for the part

during different activities such as

design, manufacturing and inspection.

Each design must specify the datum planes(or other datums)

Datum feature The actual plane on the part (imperfect) corresponding to a (perfect) datum plane

datum feature A

datum plane A

datum feature B

datum plane B

datum A

datum B datum C

datum feature A

datum plane A

datum feature B

datum plane B

datum feature B

datum plane B

datum A

datum B datum C

datum A

datum B datum C

Sequence of establishing datums:PRIMARY (3 points) SECONDARY (2 points) TERTIARY (1 point)

ANSI symbols for geometric tolerancing

True Position

Location

Total runout

Circular runout

Runout

Concentricity

Parallel

Perpendicular

Angle

Orientation

Surface profile

Line profile

Profile

Cylindricity

Circularity

Flatness

Straightness

Form

SymbolCharacteristicType of Tolerance

True Position

Location

Total runout

Circular runout

Runout

Concentricity

Parallel

Perpendicular

Angle

Orientation

Surface profile

Line profile

Profile

Cylindricity

Circularity

Flatness

Straightness

Form

SymbolCharacteristicType of Tolerance

MMC

Arc length

Reference size

Spherical Radius

Radius

Spherical Diameter

Diameter

Projected Tol Zone

LMC

Regardless of feature size

ANSI modification symbols

MMC

Arc length

Reference size

Spherical Radius

Radius

Spherical Diameter

Diameter

Projected Tol Zone

LMC

Regardless of feature size

ANSI modification symbols

MM

SS

LL

PP

SS

R

SR

( )

3.00

-A-

symbol tolerance modifier datum modifier

0.001 M MA

datum

basic size

symbol tolerance primary- secondary- tertiary datum

0.001 A B C

3.00

-A-

symbol tolerance modifier datum modifier

0.001 M MA

symbol tolerance modifier datum modifier

0.001 M MA0.001 MM MMA

datum

basic size

symbol tolerance primary- secondary- tertiary datum

0.001 A B C

symbol tolerance primary- secondary- tertiary datum

0.001 A B C

Different allowed notations (ANSI)

Location tolerances:

Conventional system:rectangular tolerance zones

True Position Tolerancingcircular (cylindrical) tolerance zone

Form Tolerances

Form Tolerances

Form Tolerances