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2011 Edition, October 1, 2011

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A Comprehensive System for Predicting Assembly Variation with Potential Application to Transmission Design

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Description / Abstract:

Recent advances in tolerance analysis of assemblies allow designers to: predict tolerance stack-up due to process variations; examine variation in clearances and fits critical to performance; use actual production variation data or estimates from prior experience; and use engineering design limits to predict the percent rejects in production runs. A comprehensive system has been developed for modeling 1D, 2D, and 3D assemblies, which includes three sources of variation: dimensional (lengths and angles), geometric (GD&T), and kinematic (small internal adjustments due to dimensional variations). Once the assembly has been described, an algebraic model is created, in which each dimension is represented by a vector, with a nominal +/- tolerance. The vectors are linked into chains or loops, describing each critical clearance or assembly feature in terms of the contributing dimensions. The chains form vector loops describing the interaction and accumulation of the three sources of variation in the assembly. Small variations are applied to each source and analyzed statistically to predict the resulting variation in the critical assembly features. Solutions for the mean and standard deviations are obtained by matrix algebra. Only two assemblies are analyzed: one for the mean and another for the variance of the assembly features. The same modeling elements may be used to model complex assemblies. Benefits of tolerance analysis include reduced reject rates, fewer problems on the assembly floor, reduced costs, and shorter time to market. Critical requirements of shaft alignment, gear meshing and controls in transmissions and gear trains are ideally suited for this efficient, comprehensive system.