Semantic Tolerance Modeling with Generalized Intervals

A significant amount of research has been performed to explore the mathematical basis for dimensional and geometric tolerance representation, analysis, and synthesis. However, tolerancing semantics such as logical dependency among variations and sequence of specifications is not maintained in these models. Consequently, their numerical results are not interpretable. In this paper, a semantic tolerance modeling scheme based on generalized intervals is proposed to improve the interpretability of tolerance modeling. Under certain optimality conditions, semantic tolerance models allow for true variation range estimations with simple computations. With the theoretical support of semantic tolerance modeling, a new dimension and tolerance specification scheme for semantic tolerancing is also proposed to better capture design intents and manufacturing implications, including flexible material selection, rigidity of specifications and constraints, component sorting in selective assembly, and assembly sequences.