Primary resonances of gear systems with parametric and internal excitations solved by homotopy analysis method

An analytical technique, namely the Homotopy Analysis Method (HAM), has been applied to solve periodic solutions for primary resonances of a gear system with both parametric and internal excitations. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all. Thus it is valid for both weakly and strongly nonlinear problems. In the meantime, the analytical technique can provide a simple way to adjust and control the convergence regions of the series solutions by means of an auxiliary parameter. In this paper, the nonlinear frequency response characteristics of a parametricly excited spur gear pair with backlash are presented. The influence of internal excitation on the primary resonances is analyzed and the frequency-response curves are obtained by using HAM.