This document discusses tolerance stack up analysis which determines the maximum possible variation between components in an assembly. It describes the merits of tolerance stack up analysis such as optimizing part tolerances. The key steps are identified including labeling dimensions, creating a sketch, adding dimensions, finding nominal and total variation. An example problem is provided to find the maximum and minimum distance between parts using a tolerance stack up report and sketch. Dimensional chain analysis and synthesis are also overviewed. Equivalent tolerance and standard tolerance grade methods are explained for solving tolerance allocation problems.

1. TOLERANCE STACK UP ANALYSIS

2. 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.

3. 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

4. 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.

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

6. Tolerance Stack Up Sketch

7. Tolerance Stack Up Report

8. 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.

9. 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

10. 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:

11. 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

12. Solution

13. 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

14. THANK YOU