Complex dynamics of planetary gear systems

A full 2D dynamic model of a single-stage planetary gear system with backlash and time varying stiffness is considered here. This dynamic model is time variant and non-smooth, due to the presence of time varying meshing stiffness and backlash for all sun- planets and ring-planets meshes; moreover, bearing compliance is accounted for. The linear averaged equations of motion are solved to obtain the natural frequencies; conversely, the fully nonlinear equations of motion are analyzed numerically to study the effect of time varying stiffness and backlash and to point out the nonlinear dynamics of the system. The complex dynamics is deeply investigated over the meaningful mesh frequency ranges. The dynamic scenario is obtained by means of bifurcation analysis and completed with time spectral and topological properties of the response.