Application of Quasi-Monte Carlo Method Based on Good Point Set in Tolerance Analysis

Abstract

Tolerance analysis is increasingly becoming an important tool for mechanical design, process planning, manufacturing, and inspection. It provides a quantitative analysis tool for evaluating the effects of manufacturing variations on performance and overall cost of the final assembly. It boosts concurrent engineering by bringing engineering design requirements and manufacturing capabilities together in a common model. It can be either worst-case or statistical. It may involve linear or nonlinear behavior. Monte Carlo simulation is the simplest and the most popular method for nonlinear statistical tolerance analysis. Monte Carlo simulation offers a powerful analytical method for predicting the effects of manufacturing variations on design performance and production cost. However, the main drawbacks of this method are that it is necessary to generate very large samples to assure calculation accuracy, and that the results of analysis contain errors of probability. In this paper, a quasi-Monte Carlo method based on good point (GP) set is proposed. The difference between the method proposed and Monte Carlo simulation lies in that the quasi-random numbers generated by Monte Carlo simulation method are replaced by ones generated by the method proposed in this paper. Compared with Monte Carlo simulation method, the proposed method provides analysis results with less calculation amount and higher precision.