Random dynamics of a nonlinear spur gear pair in probabilistic domain

This paper investigates the response of a spur gear pair subjected to both deterministic and random loads. Backlash nonlinearity and time-varying mesh stiffness in gear systems are considered in the model. Path integration is adopted to capture the random response in probabilistic domain. In the path integration algorithm, the transition probability density function (PDF) within a short time interval is assumed as Gaussian. Then the mean and variance of the responses are calculated and expressed as closed forms for two different cases in gear systems, which are further used to construct the transition PDF. The simulation results are compared with that from Monte Carlo (MC) simulation and deterministic numerical integration. Good agreements are shown between these results. In addition, the multi-solutions feature characterizing the nonlinear gear system is also captured.