Semantic Tolerance Modeling

Abstract

A significant amount of research efforts has been given to explore the mathematical basis for 3D dimensional and geometric tolerance representation, analysis, and synthesis. However, engineering semantics is not maintained in these mathematic models. It is hard to interpret calculated numerical results in a meaningful way. In this paper, a new semantic tolerance modeling scheme based on modal interval is introduced to improve interpretability of tolerance modeling. With logical quantifiers, semantic relations between tolerance specifications and implications of tolerance stacking are embedded in the mathematic model. The model captures the semantics of physical property difference between rigid and flexible materials as well as tolerancing intents such as sequence of specification, measurement, and assembly. Compared to traditional methods, the semantic tolerancing allows us to estimate true variation ranges such that feasible and complete solutions can be obtained.

Assembly variation analysis of compliant mechanisms by combining direct linearization method and Lagrange’s equations

“…Mainstream tolerance analysis methods (Cao et al, 2018) include tolerance-map (T-Map) (Davidson et al, 2002), topologically and technologically related surfaces (TTRS) method (Desrochers, 2003;Desrochers and Clément, 1994), matrix model (Desrochers and Rivière, 1997), polytopes model (Teissandier et al, 1999), semantic model (Wang, 2006), Jacobian model (Laperriere and ElMaraghy, 2000), Torsor model (Clément et al, 1998;Desrochers, 2003), Unified Jacobian-Torsor model (Ghie et al, 2003;Laperrière et al, 2002), skin model (Mathieu and Ballu, 2007;Schleich et al, 2012;Zhang, 2011) and direct linearization method (DLM) (Marler, 1988). Among these methods, DLM is a typical vector-loop based method which is good at deviation propagation analysis for closed-loop structures (Gao et al, 1998).…”

Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation

“…Dantan et al [9] proposed a statistical method for tolerance analysis and used genetic algorithm for tolerance synthesis. Wang [10] presented a new semantic tolerance modeling scheme based on modal interval to develop the interpretability of tolerance modeling. Wu and Rao [11] proposed a fuzzy based approach using vector loops for modeling and analysis of mechanical errors caused by various geometric and dimensional tolerances in a mechanical assembly.…”

Closed-Loop Analysis in Semantic Tolerance Modeling

“…The attention of interpretability needs to be given in tolerance analysis. Recently, we proposed a new semantic tolerance modeling scheme [2,3,4,5] based on generalized intervals to enhance the interpretability of tolerance modeling. The purpose of semantic tolerance modeling is to embed logic relationships and engineering implications into the mathematical representation.…”