Unified dimension and tolerance modeling for mechanical precision predicting

Precision predicting is significant for quality qualification of complicated product, and it is one of the fundamental applications for virtual assembly system. For most predicting methodologies, functional precision is propagated by both dimension and geometric tolerance; however, dimension and geometric tolerance have different manifestation patterns that relay on traditional GD&T standard, and it brings difficulty in considering dimension and geometric tolerance simultaneously; hence, a uniform model called maximum compatible constraint model (MCCM) is proposed. Dimension and geometric tolerance are clustered into three types: deterministic constraint, micro-degree constraint, and release constraint. The MCCM model explains these multiform constraints with unified constraint matrix, dimension torsor (D _mT ), and deviation torsor (D _vT ). D _mT is introduced to record the ideal position of functional geometry referring to geometry coordinate system. D _vT and micro-degree variational zone are discussed for explaining variational information of precision; in addition, topological structure related to functional and datum surfaces are extracted. By compatible structure, MCCM is not only adaptable for explaining dimension and geometric tolerance, but also for modeling geometric and assembly constraints that are meaningful for variation propagation during assembly process. With all constraints, dimension and tolerances are modeled, and then MCCM set is attained. Within the MCCM set, dimension cumulative, variation, and error propagation are facilitated by constraint and direction discussion, and precision predicting is conducted more specifically.