Analytical Solutions for Tolerance Optimization Model Considering the Influence of Product Service Life

In the service period of product, the deterioration may arise because of wear, corrosion, mechanical deformation, and other factors. The deterioration of components can result in dimensional deviations of the product. As a critical part in product design, the tolerance design must guarantee that the actual dimension remains within the specified limits. Considering the deterioration during the service life, two scenarios are investigated, and the corresponding models are established. In the first scenario, the service life is predetermined, and the objective function is to minimize the total cost. In the second scenario, the service life is treated as decision variables, and the objective function is to minimize the unit cost. Then, the Lagrangian multiplier method is adopted, and analytical solutions for the proposed method are derived. The analytical solutions show that it is necessary to consider the deterioration rate and product service life in the tolerance optimization model. And higher deterioration rate and longer product service life would result in tighter component tolerances and higher manufacturing costs. Comparing with numerical optimization solutions, the analytical solutions can be solved with high accuracy.