Optimal geometric tolerance design framework for rigid parts with assembly function requirements using evolutionary algorithms

Tolerance design is always a challenging task for engineers, since it need to satisfy multidisciplinary functions. Engineering design is done in two stages: assembly design and detail design. In the first stage, an assembly is designed considering certain system level functions and in secondary detail design stage; decomposition of the assembly is done and process tolerancing is employed for the parts. At the secondary detail design stage, designer adopts geometrical dimensioning and tolerancing (GD&T) concepts for process tolerancing. Hence, assembly and detail design are done in different phases with dissimilar perspectives. As a result, geometric tolerance design often lands in conflict, redesign, and in the case of concurrent engineering, costly reiterations are performed. This conflict occurs because of two vital reasons: (1) a gap exists between these two design stages and no common relation between them; (2) GD&T is adopted in the secondary stage, which is not available in primary stage. This paper offers a framework for a design engineer to bridge the gap and to establish the relation between these stages. A nonlinear combinatorial optimization problem is framed based on assembly function requirement (AFR), and tolerance values are optimized with appropriate constraints. Nontraditional Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and differential evolution (DE) algorithms are used to solve the problem. For the allocated position tolerances, appropriate sensitive factors are indicated to facilitate design improvement. Finally, a case study is used to illustrate the complete framework.