Stochastic dynamical response of a gear pair under filtered noise excitation

Abstract

In this study, the stochastic dynamic response of a spur gear pair model under the excitation of filtered noise is investigated. The spur gear pair is modeled as a single degree of freedom (SDOF) system in which nonlinear and non-smooth backlash and time-varying mesh stiffness as well as stochastic excitation are concurrently considered. Four cases are addressed, based on how the noise is incorporated in the loading terms. A first order filter is employed to generate various filtered noises with the same energy but different power spectrum. The combination of the SDOF gear model and the shaping filter leads to a (3D) Markov model. The numerical path integration (PI) technique is adopted to obtain the probabilistic response of the gear model using an adaptive time-stepping method in order to increase the accuracy of the time integration. A 4D system is also considered by applying a second order filter to model a narrow-band noise. The results are verified by comparing with Monte Carlo simulations. The effect of the noise spectrum on the probabilistic response is evaluated for different loading cases. The response PDF is of key importance in relation to reliability assessment of gear systems.