Reliability-based optimal tolerance design of mechanical systems including epistemic uncertainty

Abstract

As an essential step of product design, tolerance design plays a critical role in reducing manufacturing costs while ensuring mechanical assemblies’ quality and reliability. However, existing tolerance allocation approaches only are concentrated on design specification constraints during the design stage, although component degradation caused by environmental and operating conditions increases the probability of product failure during the service life. To deal with the degradation effect arising over the service life of mechanical assemblies, this paper proposes a reliability-based tolerance design approach to allocate optimal, reliable tolerances to mechanical systems. The proposed approach rewrites the tolerance allocation problem as a two-objective optimization problem with probabilistic constraints, where time-dependent reliability is incorporated to ensure the product’s reliable and consistent operation during the specified service life. Then, the proposed approach applies the non-dominated sorting genetic algorithm II and an entropy-based TOPSIS method to obtain the non-dominated optimal tolerances and the best solution, respectively. In addition, unlike previous methods, epistemic uncertainty effects are considered in this work. A modified linear degradation model is developed to include the epistemic uncertainty in the degradation model’s parameters and investigate the effects of uncertainties on reliability.Accordingly, the proposed approach employs a single-loop sampling procedure to incorporate the effects of epistemic uncertainty on the obtained optimal tolerances. Finally, to illustrate the capability of the proposed method, an industrial case study is considered, and the obtained results and performances are compared and discussed.