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Understanding the Accuracy of Assembly Variation Analysis Methods

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Monte Carlo (MC) RSS linear (RSS) ... 10,000 Sample Monte Carlo. There is significant variability even using. Monte Carlo with 10,000 samples. June 2000. ADCATS ... – PowerPoint PPT presentation

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Title: Understanding the Accuracy of Assembly Variation Analysis Methods


1
Understanding the Accuracy of Assembly Variation
Analysis Methods
  • ADCATS 2000
  • Robert Cvetko
  • June 2000

2
Problem Statement
  • There are several different analysis methods
  • An engineer will often use one method for all
    situations
  • The confidence level of the results is seldom
    estimated

3
Outline of Presentation
  • New metrics to help estimate accuracy
  • Estimating accuracy (one-way clutch)
  • Monte Carlo (MC)
  • RSS linear (RSS)
  • Method selection technique to match the error of
    input information with the analysis

4
Sample Problem
  • One-way Clutch Assembly

5
Clutch Assembly Problem
?
  • Contact angle important for performance
  • Known to be quite non-quadratic
  • Easily represented in explicit and implicit form

c
c
b
a
e
6
Details for the Clutch Assembly
  • Cost of bad clutch is 20
  • Optimum point is the nominal angle

7
Monte Carlo Benchmark
(One Billion Samples)
8
10,000 Sample Monte Carlo
There is significant variability even using
Monte Carlo with 10,000 samples.
9
One-Sigma Bound on the Mean
Estimate of the Mean versus Sample Size
1.6
1.4
16 samples
1.2
s
0.25 s
1.0
4 samples
Probability Density for the
Estimate of the Mean
0.8
s
0.5 s
0.6
1 sample
0.4
s
1 s
0.2
0.0
-3
-2
-1
0
1
2
3
Estimate of the Mean
10
New Metric Standard Moment Error
  • Dimensionless measure of error in a distribution
    moment
  • All moments scaled by the standard deviation

11
sSER1 for Monte Carlo
12
sSER2 for Monte Carlo
13
sSER3-4 for Monte Carlo
14
Standard Moment Errors
15
10,000 Sample Monte Carlo
You dont have to do multiple Monte
Carlo Simulations to estimate the error!
16
Application Quality Loss Function
17
Estimating Quality Loss with MC
18
RSS Linear Analysis
  • Using First-Order Sensitivities

19
New Metric Quadratic Ratio
  • Dimensionless ratio of quadratic to linear effect
  • Function of derivatives and standard deviation of
    one input variable

20
Calculating the QR
  • The variables that have the largest contribution
    to variance or standard deviations
  • The hub radius a contributes over 80 of the
    variance and has the largest standard deviation

21
Linearization Error
  • First and second-order moments as function of one
    variable
  • Simplified SER estimates for normal input
    variables

22
Linearization of Clutch
Error Estimates Obtained From
RSS vs.
RSS vs.
Quadratic
Method of System Moments
a
Benchmark
Ratio of
SER1
0.0141
0.0156
0.0157
SER2
-0.0004
-0.0004
-0.0034
SER3
0.0844
0.0936
0.0944
SER4
-0.0119
-0.0144
-0.0441
  • The QR is effective at estimating the reduction
    in error that could be achieved by using a
    second-order method
  • If the accuracy of the linear method is not
    enough, a more complex model could be used

23
Method Selection
  • Matching Input and Analysis Error and Matching
    Method with Objective

24
Error Matching
  • Things should be made as simple as possible, but
    not any simpler-Albert Einstein
  • Method complexity increases with accuracy
  • Simplicity
  • Reduce computation error
  • Design iteration
  • Presenting results

25
Converting Input Errors to sSER2
  • Incomplete assembly model
  • Input variable
  • Specification limits
  • Loss constant

26
Design Iteration Efficiency
RSS
DOE
Design Iteration Efficiency
MSM
MC
Accuracy
27
Conclusions
  • Confidence of analysis method should be estimated
  • Confidence of model inputs should be estimated
  • New metrics - SER and QR help to estimate the
    error analysis method and input errors
  • Error matching can help keep analysis models
    simple and increase efficiency
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