Efficient response determination of a M-D-O-F gear model subject to combined periodic and stochastic excitations

Abstract

The nonlinear response of a multi-degree-of-freedom (M-D-O-F) gear model subject to combined periodic and stochastic excitations is investigated by an efficient linearization scheme, accounting for the time-variant stiffness, and the backlash feature involved in the model. The steady-state response of the model is expressed as the sum of a periodic (deterministic) part, and of a zero-mean stochastic part. Further, the piecewise linear term accounting for the teeth backlash in the gear model is approximated by a 5-th order polynomial expression. Harmonic balance and statistical linearization schemes are used to derive a set of coupled nonlinear algebraic equations involving the amplitudes of the periodic part, and the statistical moments of the stochastic part of the solution. These equations can be solved iteratively by any of the apropos standard numerical algorithms. Examples of a two-stage gear system under combined excitations with wide-band spectrum stochastic excitation, and narrow-band spectrum stochastic excitation are considered. The derived numerical results demonstrate the reliability and efficiency of the proposed scheme by juxtaposition with data from pertinent Monte Carlo simulations.