Assembly Tolerance Modeling Based on Generalized Directed Graph

Abstract

Tolerance greatly influences the quality, process planning, measurement, cost, and assembly of products. How to use an effective method to interpret tolerance semantics is becoming more and more important. Traditional directed graph theory cannot interpret the assembly relationship clearly. This paper presents an assembly tolerance modeling method based on generalized directed graph. The construction process of tolerance model, reference frame and key features related to geometric shape and dimension were defined. Then assembly tolerance relationship between key features by generalized directed graph was described and a unit vector was used to represent assembly tolerance model. The elements of the vectors denote the assembly relationship between function vertexes. Therefore, generalized chain and generalized adjacent matrix were defined, all of which formed the concept of generalized directed graph. The assembly tolerance model structure was formalized by generalized adjacent matrix. Finally, the effectiveness of the proposed method is tested using an example. The result indicates that the method is a reasonable way to interpret the assembly tolerance semantics and the proposed method has very important applications for assembly plan.