Constructing a meta-model for assembly tolerance types with a description logic based approach

• Constraint relations are formalized by assertional axioms.
• Assembly tolerance types are defined with terminological axioms.
• Assembly tolerance types are generated automatically in the meta-model.
• The meta-model has rigorous logic-based semantics.
• The meta-model lays a good foundation for realizing semantic interoperability.

There is a critical requirement for semantic interoperability among heterogeneous computer-aided tolerancing (CAT) systems with the sustainable growing demand of collaborative product design. But current data exchange standard for exchanging tolerance information among these systems can only exchange syntaxes and cannot exchange semantics. Semantic interoperability among heterogeneous CAT systems is difficult to be implemented only with this standard. To address this problem, some meta-models of tolerance information supporting semantic interoperability and an interoperability platform based on these meta-models should be constructed and developed, respectively. This paper mainly focuses on the construction of a meta-model for assembly tolerance types with a description logic ALC(D)ALC(D) based approach. Description logics, a family of knowledge representation languages for authoring ontologies, are well-known for having rigorous logic-based semantics which supports semantic interoperability. ALC(D)ALC(D) can provide a formal method to describe the research objects and the relations among them. In this formal method, constraint relations among parts, assembly feature surfaces and geometrical features are defined with some ALC(D)ALC(D) assertional axioms, and the meta-model of assembly tolerance types is constructed through describing the spatial relations between geometrical features with some ALC(D)ALC(D) terminological axioms. Besides, ALC(D)ALC(D) can also provide a highly efficient reasoning algorithm to automatically detect the inconsistency of the knowledge base, a finite set of assertional and terminological axioms. With this reasoning algorithm, assembly tolerance types for each pair of geometrical features are generated automatically through detecting the inconsistencies of the knowledge base. An application example is provided to illustrate the process of generating assembly tolerance types.