Nonlinear Assembly Tolerance Design for Spatial Mechanisms Based on Reliability Methods

Abstract

Assembly tolerance design for spatial mechanisms is a complex engineering problem that involves a highly nonlinear dimension chain equation and challenges in simplifying the spatial mechanism matrix equation. To address the nonlinearity of the problem and the difficulty of simplifying the dimension chain equation, this paper investigates the use of the Rackwitz–Fiessler (R–F) reliability analysis method and several surrogate model methods, respectively. The tolerance analysis results obtained for a landing gear assembly problem using the R–F method and the surrogate model methods indicate that compared with the extremum method and the probability method, the R–F method allows more accurate and efficient computation of the successful assembly rate, a reasonable tolerance allocation design, and cost reductions of 37% and 16%, respectively. Moreover, the surrogate-model-based computation results show that the support vector machine (SVM) method offers the highest computational accuracy among the three investigated surrogate methods but is more time consuming, whereas the response surface method and the back propagation (BP) neural network method offer relatively low accuracy but higher calculation efficiency. Overall, all of the surrogate model methods provide good computational accuracy while requiring far less time for analysis and computation compared with the simplification of the dimension chain equation or the Monte Carlo method.