Optimum tolerance allocation in mechanical assemblies using an interval method

Tolerance allocation methods serve as effective tools for design engineers to reduce the overall manufacturing cost of products. In every mechanical design, it is the design engineer's task to assign tolerances to all dimensions and clearances to all joints in an assembly. This paper presents an optimum allocation method, based on interval analysis, for finding the optimum values of tolerances and clearances in mechanical assemblies that will not only minimize a stated objective function, but also satisfy the required functional and design constraints. The design constraints include dimensional requirements that the related parts must match relative to each other with a specified precision. Given a set of trial values of component tolerances and joint clearances, the present method utilizes the sequential quadratic programming method, Broyden–Fletcher–Goldfarb–Shanno quasi-Newton method and line search approaches to find the optimum values of tolerances and clearances. The effects of different cost function models on the manufacturing cost are also compared and discussed. Numerical examples are presented to illustrate the application of the method.