Computer-aided tolerance chain and stability analysis

The present paper describes a methodology and a software tool that allow assemblies to be evaluated and analysed with respect to degree of geometrical coupling and robustness on any hierarchical level of the assembly structure. Based on the assembly sequence and the mating conditions of a number of components fulfilling a number of functional requirements, a function means hierarchy with a pertinent set of relations between sub-assemblies, components and features is automatically generated and used for tolerance chain and stability analysis. Based on mating conditions and specified geometrical constraints, tolerance chains are automatically detected and presented in the structure. Geometrical couplings between sub-systems, components and individual features are detected and presented in stability matrices. The analysis tools assist in the iterative work of concept improvement and the decomposition of top-level geometrical constraints (tolerances on critical product dimensions) into bottom level feature constraints (tolerances on individual surfaces). The two analysis toots utilize the basic ideas in robust design and axiomatic design (the independence axiom), and can be used to compare and evaluate assembly concept solutions including different assembly fixturing solutions. The similarities between uncoupled robust assembly design and uncoupled robust tolerancing of individual parts are discussed and illustrated. Two examples are used to describe the methodology and the software tool.