Mathematical formulation of tolerance synthesis taking into account the assembly process

For automotive and aircraft industries, produtibility has to go through a better product assemblability. To do so, effects of manufacturing variations have to be reduced. Therefore, the tolerance synthesis has become an important issue in product design process. A mathematical formulation of tolerance synthesis is described in this paper. This mathematical formulation is based on variational geometry, and takes into account not only manufacturing variations and gaps, but also the assembly sequences and nature of contacts between parts. This formulation integrates the quantifier notion (existential quantifier "there exists", universal quantifier "for all"). This notion modelizes the concept that an assembly requirement must be respected in at least one acceptable configuration of gaps (∃), or that an assembly requirement must be respected for all acceptable configurations of gaps (∀).