Assembly Model
Distribution of Tolerance
Explicit: Linearized Sensitivity Mechanistic Model Non-linear Model
Implicit:
Worst Case
Statistical: Root sum squares Monte Carlo
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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Contents
➢ 1-D Tolerance analysis
• Variation vs. Tolerance • Variation Simulation Methods • Advantages and Limitations of Each Method
➢ Auto-body Dimension Chain Method
• Integration of Key Characteristic of Product & Process
• Assembly Constraints • Tolerance and Solving of Dimension Chain
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 ?
Root Sum Squares (RSS):
(Spotts, 1978, Lee and Woo, 1990)
Monte Carlo Simulation:
(Craig, 1989)
y x1 x2 x3
t abc t a2 b2 c2
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Simple Variation Simulation Example
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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Commonly Used Variation Simulation Methods
1
x
± 1
a
2
x2± b
2
3
1
y ±t
3 x ±c
3
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 ?
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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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Variation vs. Tolerance
LSL
US L
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.
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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.
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
x E[x] x1 x2 ... xn n
n
(xi x)2
Var[x] i1 n 1
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Part I 1-D Tolerance analysis
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Deviation
Characterizing the performance of a process