Reliability Analysis for Rotate Vector Reducer by Combining Polynomial Chaos Expansion and Saddlepoint Approximation Considering Multi-Failure Modes

Abstract

Abstract Rotate vector (RV) reducer is an essential mechanical transmission device in industrial machinery, robotics, aerospace, and other fields. The dynamic transmission characteristics and strength of the cycloidal pin gear and turning-arm bearing significantly affect the motion accuracy and reliability of RV reducer. Uncertainties from manufacturing and assembly errors and working loads add complexity to these effects. Developing effective methods for uncertainty propagation and reliability analysis for the RV reducer is crucial. In this work, the mail failure modes of RV reducer are studied, and an effective reliability analysis method for RV reducer considering the correlation between multi-failure modes is proposed by combining polynomial chaos expansion (PCE) and saddlepoint approximation method (SPA). This paper develops an uncertainty propagation strategy for RV reducer based on dynamic simulation and PCE method with high accuracy. On this basis, a surrogated cumulant generating function (CGF) and SPA are combined to analyze the stochastic characteristics of the failure behaviors. Then, based on the probability density function (PDF) and cumulative distribution function (CDF) calculated by SPA, the copula function is employed to quantify the correlations between the multi-failure modes. Further, the system reliability with multi-failure modes is estimated by SPA and optimal copula function. The validity of the proposed approach is illustrated by RV-320E reducer reliability estimation, and the results show that the proposed method can provide an effective reliability assessment technology for complex system under unknown physical model and distribution characteristics.