Stochastic spur gear dynamics by numerical path integration

In this paper the method of numerical path integration is applied to investigate the dynamics of a model of a pair of meshing spur gears. Our approach is based on the observation that the dynamics of a nonlinear mechanical system excited by a deterministic loading process can, to a large extent, be characterized by the response obtained by adding a small white noise to the loading. By this, the response can be expressed as a Markov diffusion process, which makes available the powerful toolbox of stochastic analysis, in particular the path integration method.