Dynamics and Parametric Identification of Geared Rotordynamic Systems

In the first part of this study, dynamic response and stability characteristics of gear-pair systems supported on bearings with rolling elements is investigated. The resulting mechanical models possess strongly nonlinear characteristics, accounting for gear backlash and bearing stiffness nonlinearities. The emphasis is first put on obtaining periodic steady state motions and the results illustrate the effect of selected system parameters on the dynamics. The results obtained indicate that for some parameter combinations, there appear frequency intervals where only branches of unstable periodic motions are captured, generated through a Hopf bifurcation. By performing direct integration of the equations of motion, it is demonstrated that quasiperiodic and chaotic responses emerge inside these intervals. Finally, the attention is focused on issues related to parametric identification. In particular, a Bayesian statistical framework is adopted to estimate the optimal values of the gear and bearing model parameters. This is achieved by combining experimental information from vibration measurements with theoretical information built into a parametric mathematical model of the system.