Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 513958, 26 pages
Research Article

A Method for Designing Assembly Tolerance Networks of Mechanical Assemblies

1School of Mechanical Engineering, Xi'an Jiaotong University, Shaanxi 710049, China
2State Key Laboratory for Manufacturing Systems Engineering of China, Shaanxi 710049, China
3Department of Industrial Engineering, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 16 May 2011; Accepted 16 July 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Yi Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


When designing mechanical assemblies, assembly tolerance design is an important issue which must be seriously considered by designers. Assembly tolerances reflect functional requirements of assembling, which can be used to control assembling qualities and production costs. This paper proposes a new method for designing assembly tolerance networks of mechanical assemblies. The method establishes the assembly structure tree model of an assembly based on its product structure tree model. On this basis, assembly information model and assembly relation model are set up based on polychromatic sets (PS) theory. According to the two models, the systems of location relation equations and interference relation equations are established. Then, using methods of topologically related surfaces (TTRS) theory and variational geometric constraints (VGC) theory, three VGC reasoning matrices are constructed. According to corresponding relations between VGCs and assembly tolerance types, the reasoning matrices of tolerance types are also established by using contour matrices of PS. Finally, an exemplary product is used to construct its assembly tolerance networks and meanwhile to verify the feasibility and effectiveness of the proposed method.