tolerance stack up analysis

TOLERANCE STACK UP ANALYSIS

Introduction

Tolerance analysis : Study of individual tolerances Process of determining the cumulative variation possible

between two or more features. Tolerance stack up analysis is one part of tolerance

analysis. Analyzes and predicts the variation between the

parts. Determines the maximum possible variation between

two components in an assembly.

Merits of Tolerance Stack Up Analysis

Optimize the tolerances of parts and assemblies in a new design

Balance accuracy , precision and cost with manufacturing process

Determine the part tolerance required to satisfy a final assembly condition

Determine allowable part tolerance if assembly tolerance is known

Determine the effect changing a tolerance will have on assembly component

Steps in Tolerance Stack Up Analysis

The Distance to be studied is identified and labeled The positive and negative directions are identified A tolerance stack up sketch is created The dimensions in positive direction and negative

directions are added individually The nominal distance is found out by subtracting negative

direction total from the positive direction total The total possible variation is obtained by adding all

tolerances The maximum and minimum variations are obtained from

the nominal distance and total variation values.

Problem

For an inseparable assembly using tolerance stack up analysis find the maximum and minimum distance between the part 5 and 6 in assembly.

Tolerance Stack Up Sketch

Tolerance Stack Up Report

Dimensional Chain Analysis

Dimensional Chain is a consecutive series of interrelated dimensions that contribute to the tolerance of a dimension and form a closed loop.

Two Basic tasks in tolerance design process : Dimensional Chain analysis Dimensional Chain synthesis

In Dimensional analysis component tolerance are specified and resulting assembly variation is calculated.

Dimensional Synthesis involves allocation of specified assembly tolerance between component dimension of the assembly.

Equivalent tolerance method

All independent dimensions have same tolerance Tx1=Tx2=.........=Txn=T

Used when all independent dimensions in the analysed dimensional chain have same nominal value.

Deterministic approach formula is

Stochastic approach formula is

Equivalent Standard tolerance grade method

All independent dimensions are assigned tolerance values from the same tolerance grade.

Value of dimension tolerance is :

Txi = tolerance of ith independent dimension

Xi = nominal value of ith independent dimension

K =unknown tolerance grade factor

Deterministic Approach:

Stochastic Approach:

Problem

Two holes are drilled in a plate. What are the required tolerances of dimensions A,B,C,D if the tolerance of the dependent dimension Z is required as not greater than 140 µm and the nominal values of the independent dimensions are A=124mm, B=56mm,C=87mm,D=25.5mm

Solution

Solution

Equivalent tolerance method

TA=TB=TC=TD=TW

Tz = 140 µm

=0.75*T A +0.66*TB +0.75*TC +0.66*TD =2.82*TW

TA=TB=TC=TD=TW = 50 µm

Equivalent standard tolerance grade method

Tz = 140 µm

=K*(0.75* A 1/3 +0.66*B 1/3+0.75*C 1/3 +0.66* D 1/3)

K=12.11

TA=60 µm TB=47 µm TC=54 µm TD=35 µm

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