Stationary Responses of Gear Systems With Combined Periodically Time-Varying Stiffness and Stochastic External Excitations

Abstract

The stationary dynamic response of a geared system with time-varying mesh stiffness subjected to stationary stochastic external excitation is examined in this paper. To this end, a spur gear pair model with periodical timevarying mesh stiffness is extended to include stochastic external force excitations. These random forces are introduced as second-order stationary and ergodic processes. In order to compute the stationary response, a very efficient method, called the iterative spectral method is used. This method is derived in the frequency domain and provides the explicit power spectral density of the response. The PSD response is expressed as a function of the bispectrum which is the bilinear Fourier transform of the bitemporal impulse response of the parametric system.