A Bayesian-reliability based multi-objective optimization for tolerance design of mechanical assemblies

Tolerances significantly affect the assemblability of components, the product's performance, and manufacturing cost in mechanical assemblies. Despite the importance of product reliability assessment, the reliability-based tolerance design of mechanical assemblies has not been previously considered in the literature. In this paper, a novel method based on Bayesian modeling is proposed for the tolerance-reliability analysis and allocation of complex assemblies where the explicit assembly functions are difficult or impossible to extract. To reach this aim, a Bayesian model is developed for tolerance-reliability analysis. Then, a multi-objective optimization formulation is proposed for obtaining the optimum tolerances of components to minimize cost and maximize product performance. Subsequently, Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed for solving multi-objective optimization. Then, the enhanced TOPSIS is used to find the best optimum tolerances from the optimum Pareto solutions. Using the importance vector concept, a sensitivity analysis approach is used to determine the effects of design variables on the product reliability level and improve assembly reliability to the desired level. Finally, to exhibit the applicability of the proposed method, a transmission planetary gear system is considered, and the obtained results are compared and discussed for verification.