Reliability analysis of a gear dynamic system based on Gamma degradation and an improved optimal squares approximation method

Abstract

Gear wear and fatigue often coexist under complex operating conditions. Their coex istence may bias reliability assessment and greatly increase the computational cost of time-varying reliability analysis. To address these issues, this paper proposes a dynamic multi-failure reliability analysis method for tooth surface wear, tooth surface contact fa tigue, and tooth root bending fatigue. First, the dynamic pressure angle is incorporated into the tooth surface wear model. A wear evolution model and a threshold limit-state function are then established by combining Archards wear law with Hertzian contact theory. Second, a Gamma stochastic process is used to describe the random strength degradation associated with contact fatigue and bending fatigue, and the degradation parameters are identified from the material probability-stress-life (P-S-N) curve. Third, Pearson correlation coefficients (PCCs) are introduced to describe the correlations among the basic random variables. Based on the moment information of the performance func tion obtained by second-order expansion, skewness and kurtosis are further used to construct an improved optimal squared approximation (OSA) probability density func tion for time-varying reliability computation. A high-speed stage gear of a belt-conveyor reducer is used as an example. The results show that the proposed method captures the reliability evolution of different failure modes and agrees well with Monte Carlo simulation (MCS) while reducing the computational cost.