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Understanding the Accuracy of Assembly Variation Analysis Methods

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

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Understanding the Accuracy of Assembly Variation Analysis Methods

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  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 ADCATS 2000

  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 ADCATS 2000

  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 ADCATS 2000

  6. Details for the Clutch Assembly • Cost of “bad” clutch is $20 • Optimum point is the nominal angle ADCATS 2000

  7. Monte Carlo Benchmark (One Billion Samples) ADCATS 2000

  8. 10,000 Sample Monte Carlo Monte Carlo - 1,000 Runs Run #1(10,000 Samples) Max/Min Std Dev 7.01111 7.02288/ 7.00846 .002203 m 1 0.04893 0.05036/0.04598 .000717 m 2 -.00086 -.00011/-.00184 .000263 m 3 0.00732 0.00788/ 0.00628 .000251 m 4 There is significant variability even using Monte Carlo with 10,000 samples. ADCATS 2000

  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 ADCATS 2000

  10. New Metric: Standard Moment Error Estimate True • Dimensionless measure of error in a distribution moment • All moments scaled by the standard deviation ADCATS 2000

  11. sSER1 for Monte Carlo ADCATS 2000

  12. sSER2 for Monte Carlo ADCATS 2000

  13. sSER3-4 for Monte Carlo ADCATS 2000

  14. Standard Moment Errors ADCATS 2000

  15. 10,000 Sample Monte Carlo Monte Carlo - 1,000 Runs Est 68% Run #1(10,000 Samples) Max/Min Std Dev Conf Int 7.01111 7.02288/ 7.00846 .002203 ± .002212 m 1 0.04893 0.05036/0.04598 .000717 ± .000692 m 2 -.00086 -.00011/-.00184 .000263 ± .000212 m 3 0.00732 0.00788/ 0.00628 .000251 ± .000233 m 4 You don’t have to do multiple Monte CarloSimulations to estimate the error! ADCATS 2000

  16. Application: Quality Loss Function ADCATS 2000

  17. Estimating Quality Loss with MC ADCATS 2000

  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 ADCATS 2000

  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 ADCATS 2000

  21. Linearization Error • First and second-order moments as function of one variable • Simplified SER estimates for normal input variables ADCATS 2000

  22. Linearization of Clutch Error Estimates Obtained From: RSS vs. RSS vs. Quadratic Method of System Moments Benchmark a 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 ADCATS 2000

  23. Method Selection Matching Input and Analysis Errorand Matching Method with Objective

  24. Error Matching Input Error Analysis Error • “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 ADCATS 2000

  25. Converting Input Errors to sSER2 • Incomplete assembly model • Input variable • Specification limits • Loss constant ADCATS 2000

  26. Design Iteration Efficiency RSS DOE Design Iteration Efficiency MSM MC Accuracy ADCATS 2000

  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 ADCATS 2000

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