Statistical Tolerance Analysis with T-Maps for Assemblies

The T-Map® (Tolerance-Map®) model for representing geometric variations of planar surfaces is extended to include probabilistic representations of variations of those surfaces. T-Maps are hypothetical volume of points, which can arise from tolerances on size, position, orientation, and form. The variations of a planar surface are decomposed into manufacturing and geometric bias. Statistical accumulation of variation in an assembly is computed using convolution of T-Maps. The dimension of interest is mapped to a surface Sc in the hypothetical Euclidean space. Probability distribution is then computed as weighted surface area of intersection of the surface Sc with the convolved accumulation T-Map.