Statistical Tolerancing based on Variation of Point-set

Abstract Functional tolerancing of mechanisms has now been well accepted in industry and become a major concern for academia. After a brief comparison of existing 3D functional tolerance analysis models, a statistical tolerancing approach based on variation of point- set is proposed in this paper. The toleranced surface is represented by a point-set which is consistent with its parametric equations, the semantics of geometrical tolerances are parameterized with respect to variation of point-set and associated mathematical interpretations of tolerance zone are formalized. Three methods are presented to extract individual points from point-set: characteristic points of MGRE, characteristic points of geometrical surface and discrete points of geometrical surface. The tolerance chains through key assembly features are analyzed and represented by homogenous transform matrix. The over-constrained degrees of freedom of a complex junction with multiple mating features are taken into account in accordance with datum precedence. The approach is applied to statistical tolerance analysis of a coordinate measuring machine to analyze deviation distribution of a geometrical functional requirement on the ending geometric feature.