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Statistical Tolerance Analysis of Flexible Assemblies

Michael Tonks, Brigham Young University
Presented June 16, 2001 at the ADCATS 2001 Conference

Traditional methods of statistical tolerance analysis cannot account for deformations or stresses due to assembly of flexible parts.  A flexible tolerance analysis method that combines statistical tolerance analysis with finite element analysis is being developed at BYU.  It features a statistical finite element solution, which can predict the range of internal displacements, forces, and stresses due to assembly. 

The statistical solution involves determining a covariance matrix that describes the interdependence of any two nodes in the FEA model.  Three methods for determining the covariance matrix have been developed.  Each of these methods characterizes the surface variation in a different form and they differ in their ability to model the wavelength of surface variations.  The results given by each of these methods compare favorably with the results given from a Monte Carlo simulation.  Additionally, while the Monte Carlo method takes thousands of calls to the FEA model, these methods take only two FEA calls.

Currently the method that best characterizes the wavelength variation cannot accurately analyze wavelengths longer then the part length.  Current research is being done to create a hybrid method that can characterize wavelength variation and handle long wavelengths.  Research is also being done to verify these methods on actual production assemblies.

Michael Tonks is a graduate student at Brigham Young University.  He is working under the direction of Dr. Ken Chase to create a comprehensive method for tolerance analysis of flexible assemblies.  He has worked as a summer intern at Los Alamos National Lab for 3 years, assisting in finite element research and in high impact material testing.


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