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2000 Conference Presentations
|Tolerance Analysis of Flexible Assemblies Using Finite Element and Spectral Analysis
Bryan F. Bihlmaier,
Traditional statistical tolerance analysis assumes rigid parts. Rigid body tolerance analysis over-estimates variations in flexible assemblies, because flexible parts deform under assembly loads to compensate for manufacturing variations. Traditional methods can not account for deformations or stresses due to assembly. This paper describes a new method for modeling flexible assemblies, called the Flexible Assembly Spectral Tolerance Analysis (FASTA) method, which uses the autocorrelation function from frequency spectrum analysis to model random surface variations.
Finite element models are used to predict assembly forces, stresses and deformations from known surface variations. However, variations at surface nodes are not independent variables. Therefore, covariance must be included in the statistical analysis of flexible assemblies. Covariance between nodes arises from both material elastic coupling and surface continuity constraints. This paper shows how covariance is included in statistical predictions, and how to calculate the covariance matrix from autocorrelation functions of mating part surfaces. The autocorrelation function includes the effects of surface waviness wavelength. Deterministic variations, such as part warping, are separated from random variations.
The proposed method agrees well with Monte Carlo simulations, but greatly reduces computation times. Only two finite element solutions are required: for the mean and for the variance. The FASTA method is especially useful as a design and tolerance allocation tool. The expected range of stresses and deformations from assembly processes may be statistically predicted before parts are manufactured, based on surface tolerances.
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