Nonlinear dynamics of idler gear systems

This work examines the nonlinear, parametrically excited dynamics of idler gearsets. The two gear tooth meshes provide two interacting parametric excitation sources and two possible tooth separations. The periodic steady state solutions are obtained using analytical and numerical approaches. Asymptotic perturbation analysis gives the solution branches and their stabilities near primary, secondary, and subharmonic resonances. The ratio of mesh stiffness variation to its mean value is the small parameter. The time of tooth separation is assumed to be a small fraction of the mesh period. With these stipulations, the nonsmooth separation function that determines contact loss and the variable mesh stiffness are reformulated into a form suitable for perturbation. Perturbation yields closed-form expressions that expose the impact of key parameters on the nonlinear response. The asymptotic analysis for this strongly nonlinear system compares well to separate harmonic balance/arclength continuation and numerical integration solutions. The expressions in terms of fundamental design quantities have natural practical application.