Configuration Space Based Analysis of Position Uncertainties of Toleranced Parts in an Assembly

A new method for analyzing position uncertainties of two parts in an assembly is proposed if certain shape deviations of individual parts are allowed by tolerances. Assembling of a mechanical product is usually achieved by mating some face pairs of the component parts. Realization of the proper surface contact is important for precisely achieving the machine function. Based on this concept, the authors derive three necessary conditions on the configuration of two non-nominal parts in an assembly, which are non-penetration condition, contacting condition of mating faces, and optimization condition concerning their assembling method. Proposed method achieves the tolerance analysis by computing a variation bound of the configuration of two toleranced parts if some non-nominal parts allowed by tolerances satisfy the necessary conditions. Since rotations are linearized by assuming small positional variations, the conditions can be described by a set of linear inequalities on configura-tion parameters of the parts. The variation bound thus becomes a union of some polytopes in the configuration space. An experimental program for computing the variation bound is implemented and demonstrated.