2004-12-05 geometric dimension ing and tolerancing

7/31/2019 2004-12-05 Geometric Dimension Ing and Tolerancing

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Tolerance Analysis

TQM - University of Michigan1

Pat Hammett

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Geometric Dimensioningand Tolerancing (GD&T)

Tolerance Analysis Methods

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Example: Joining Partsn Suppose you want to join the following two parts.

n They need to be properly aligned and dimensionallyacceptable to insure a good assembly.

weldAssembly

OK

Height

weld weld

PoorAlign

ExcessDeviation

NOK NOK


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What is GD&T?n Symbolized notation system to communicate

tolerances through the use of datums (references).

n GD&T is used whenever the location of a part is ascritical or more critical than its size. It insures thattwo parts can mate or join properly.

n Thus, GD&T communicates 2 key issues:

n Datum Reference System (how part is held).

n Tolerances for Part Characteristics.

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Datums

n Datums define the reference system for a partto measure or assemble it.n reference systems may be absolute (XYZ) or relative (XY).

n Use pins ~ part holes or slots & clamps ~ part surfaces

Slot: B2

(2-way locator)

Hole:

(4-way locator)

A1 Clamp surface

to locator block

A2

A3Clamp

Clamp


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Symbols and Characteristics

Type of Tolerance Characteristic Symbol

Individual Feature Flatness

Diameter

Individual orRelated Features

Profile

Related Features Position

Parallelism

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GD&T Drawing Examplen Dimension may deviate up to 1mm any direction draw

circle with a radius = 1 (profile = 2 -> tol.+/- 1)

(2mm total tolerance band relative to datums)

Geometric Tolerance

Allows deviation of

1mm in any direction

Square Tolerance

for T @45 = +/- 1

tX = 0.7; tY = 0.7

Dimension


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Interchangeability & Tolerancesn Interchangeability -- given the assembly of two

or more components, manufacturers mayrandomly select any sample for each componentand produce an acceptable assembly.

n To insure interchangeability, manufacturersassign tolerances to each component.

n

With interchangeability, a part dimension,d,may deviate from its nominal specification, N,

by some tolerance, t , and still produce anacceptable assembly.

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Types of Tolerances

n Bi-lateral tolerance: Nominal +/- 1mm

n Most common in manufacturing

n Unilateral tolerance: Nominal + 1 mm

n Example: material thickness specification are oftenone-sided because the goal is to use the least

amount of material (lower cost).


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Tolerance Analysis Approaches

n Tolerance Allocation - (top-down)n assign tolerances of final assembly based on customer needs

n work backward from assembly to components

n Tolerance Synthesis - (bottom-up)n assign tolerances of components based on process capability.

n work forward from components to assembly

n Hybrid Systems (most common approach)n

Assign initial tolerances from bottom-up -- if final assemblytolerances are too large, - work top-down until componenttolerances are capable of meeting final assembly tolerances

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Tolerance Analysis Methods

Linear Stack-Up Analysis:

1. Worst Case Stacking

2. Statistical Stacking - Root Mean Square Method

Non-Linear Stack-Up Analysis

3. Simulation

I n t his class, w e w ill focus on linear stack-upanalysis.


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1. Worst Case Stacking

Worst Case Stacking -- assumes assembly AB must joinextreme values for A & B.

Specification for Part A and B: 20 +/- 0.5mmBottom-Up: if tA= tB = 0.5, then

tAB = tA+ tB = 0.5 + 0.5 = 1 >> tAB +/- 1mm

==

+=N

i

iASMtAB

1

N

1i

iNominal

Part A Part BJoin A & B

ASM AB = overall length

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Worst Case Top Down Example

Worst Case Stacking -- assumes assembly AB must joinextreme values for A & B.

Specification for AB: 40 +/- 1 mm

Top-Down: if tAB = 1 then

tAB/ 2 = 1/2 >> tA = tB = +/- 0.5 mm

==

+=N

i

iASM tAB1

N

1i

iNominal




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Statistical Tolerance Analysisn If two parts follow a probabilistic distribution,

then worst case stacking may be inappropriate.

n For example, if the dimensions of part A and Bboth follow a normal distribution, then the jointprobability of selecting the extremes is quitesmall.

n So, rather than using worst case, statisticaltolerance analysis is used.

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2. Statistical Tolerance Analysis

If assume A & B follow probabilistic distributions such thattAB = f(variation of A & B).

1.7.722

22

=+=

+=

AB

BAAB

t

ttt

==

=N

ii

tX1

2N

1iiNominal



Bottom-upTolerancing

So if tA= tB = +/- 0.7


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Additive Theorem of Variance

n Statistical tolerance: based on additive theorem of2.

222

AASM

BAASM

XXX

XXX

BAASM

B

+=

+=

+=



Linear Stack-Up:

Mean Stack-Up:

Variance Stack-Up:

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Example: Statistical Stacking

If Part A ~N(21, 0.202) and Part B ~N(19, 0.152)What is the predicted assembly mean?

What is the predicted assembly sigma?

What are necessary tolerances for Part A and B to achieve 6?(Hint: Suppose you need to achieve a Cp = 2.0.)




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Tolerances and Six Sigma

n Suppose specification for ASM AB is 40 +/- 1 mm

n What sigma must be achieved for each component toinsure the assembly achieves a Cp = 2.0, Cpk > 1.5?

Part APart BJoin A & B


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Worst Case Vs. Statisticaln Suppose ASM tolerance +/1 mm

n Worst Case Top Down: tA= tB = +/- 0.5 mm

n Statistical Top-Down: tA= tB = +/- 0.7 mm

n

For the same assembly tolerance, statisticalstatistical allows greater variation in thecomponents.


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3. Tolerance Simulation Modelsn The prior statistical stack-up analysis is based on root-

mean-squared method (additive variance theorem).

n Alternatively, we could write a simulation model andrandomly generate combinations of components fromtheir distributions (e.g., normal, uniform, etc).

n Then, compute the expected variance of the assembly.

Typically, you would then assign tolerances of say +/-4assy or 6assy

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Bender Correction - Statistical

n if more than 2 components are assembledwith statistical, we sometimes use correctionfactors because components may becomeunnecessarily wide.

n Bender Factor, B = 1.5

==22

5.1 iiassy ttBt


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Gilson Correction Worst Casen If using worst case stacking, the Gilson

correction factor allows loosening ofcomponent tolerances.

N 2 3 4 5

K 1* 0.92 0.80 0.72

if N=2; K (Gilson = 1.0)

NK 6.1=

=

=N

iiassy tKt

1

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Tolerance Analysis Examples

n Bottom-Up Tolerance Stack-Upn If each block can be held to 20 +/- 0.5 mm, what is the

expected tolerance for the assembly?

n Worst Case - Linear Stackn No Correction:

n tABC = +/- (.5+.5+.5+.5) = +/- 2.0 mm

n With Correction:

n tABC = +/- K(4*0.5) = .80(2.0) = +/- 1.6 mm

A B C

overall length: ABCD = tolerance??

D


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Non-Traditional Methodsn Both worst case and statistical tolerance models

assume rigid parts and additive theorem of variance.(often resulting in unnecessarily tight tolerances forcomponents within assembly)

n Tolerance Adjustments:n Additional Factors: some models include assembly processing

variation in addition to the variation of joining components.

n Weighted Tolerance Models: some models assign contributionfactors if one variable dominates the assembly.

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Example: Non-Rigid to Rigid Part

n A 2 mm thick center pillar is attached to an 0.7 mm thickbody side is 0.7mm thick with the following results:

Why might you assign a tightertolerance to the center pillar and a

looser tolerance for body side?

VariablePart A -

Body Side

Part B - Center

Pillar

Predicted

Stack-Up

Actual

Assembly

Mean -0.70 0.20 -0.50 0.30

Std Deviation 0.33 0.11 0.35 0.12

222

AASM

XXX

BAASM

B

+=

+=

Predicted Stack-Up

2004-12-05 geometric dimension ing and tolerancing

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