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Assembly Model
Distribution of Tolerance
Explicit: Linearized Sensitivity Mechanistic Model Non-linear Model
Implicit:
Worst Case
Statistical: Root sum squares Monte Carlo
4
3
2
1
0
-1
-2
-3
-4 -3 -2 -1 0 1 2 3 4
-4
Central tendency or mean: Spread or variation
xE[x]x1x2...xn n
n
(xi x)2
Var[x] i1 n1
Leabharlann Baidu
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上汽通用五菱—上海交通大学现代车身技术联合研究中心
车身质量控制系列讲座
公差分析和车身尺寸链方法
Tolerance Analysis & Auto-body Dimension Chain Method
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1
Contents
➢ 1-D Tolerance analysis
• Variation vs. Tolerance • Variation Simulation Methods • Advantages and Limitations of Each Method
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Variation Simulation Methods
Two things are essential in order to perform variation analysis. One is an assembly model or input-output model. The other is the distribution of variables.
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Worst Case Analysis
In worst case analysis, it is assumed that the contributing dimensions are always within tolerance. By making this assumption worst case limits can be found within which the measured dimension must always fall.
100 +/- 0.1 (C)
49.9 +/-0.1
(A)
49.9 +/-0.1
(B)
? +/- ?
Given component tolerances, determine the variation in the measured dimension (the gap between the blocks and the base).
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Part I 1-D Tolerance analysis
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Deviation
Characterizing the performance of a process
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Commonly Used Variation Simulation Methods
1
x
± 1
a
2
x2± b
2
3
1
y± t
3
x
± 3
c
Worst Case:
(Conway, 1948; Chase and Parkinson, 1991)
1
x
± 1
a
2
x2± b
2
3
1
y± t
3
x
± 3
c
But the method can applied more widely than mechanical assembly. The general form is: given a function Y=f(x1, x2, …), and the distributions of xi, What is the distribution of y ?
But the techniques for predicting variation or tolerance for an assembly is the same.
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Variation Simulation
Given individual part dimensions and their distribution, what are the assembly dimensions ?
4
Variation vs. Tolerance
LSL
USL
Variation: • is what the process gives us, • may be quite different from the tolerance.
Tolerance or Specification is • the allowable level of variation, • based on functional consideration, • used to establish a part's conformability to design.
Root Sum Squares (RSS):
(Spotts, 1978, Lee and Woo, 1990)
Monte Carlo Simulation:
(Craig, 1989)
yx1x2x3
tabc
t a2b2c2
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Simple Variation Simulation Example
➢ Auto-body Dimension Chain Method
• Integration of Key Characteristic of Product & Process
• Assembly Constraints • Tolerance and Solving of Dimension Chain
