Study on Wear Dynamic Reliability of Gear System Based on Markov Diffusive Process

Wear is one of the most common failure forms of gear transmission system. In this paper, a dynamic wear reliability evaluation method for gear system, which subjects to stochastic external load, is proposed on the basis of the Markov diffusive process. The stochastic load is considered as the combination of constant load and random noise. The failure is defined as the wear depth of the maximum wear point of gear under the constant load that exceeds a specific threshold. The maximum wear point and relative sliding velocity are obtained by deterministic wear analysis. The stochastic noise is assumed as Gaussian white noise; hence, the wear depth can be described as Markov diffusive process, and the transition probability is governed by Fokker–Planck–Kolmogorov (FPK) equation. With the transition probability function, the wear life and dynamic reliability of gear systems with different noise spectral densities are predicted. The results reveal that the wear depth obeys normal distribution and becomes more and more scattered with noise spectral density increases. The wear life does not obey normal distribution, and the effect of noise spectral density on mean life is neglectable while on a standard deviation of life is considerable.