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tolerance stack up analysis
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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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