PLANETARY GEAR PARAMETRIC INSTABILITY CAUSED BY MESH STIFFNESS VARIATION

Parametric instability is investigated for planetary gears where fluctuating stiffness results from the changing contact conditions at the multiple tooth meshes. The time-varying mesh stiffnesses of the sun–planet and ring–planet meshes are modelled as rectangular waveforms with different contact ratios and mesh phasing. The operating conditions leading to parametric instability are analytically identified. Using the well-defined properties of planetary gear vibration modes, the boundaries separating stable and unstable conditions are obtained as simple expressions in terms of mesh parameters. These expressions allow one to suppress particular instabilities by adjusting the contact ratios and mesh phasing. Tooth separation from parametric instability is numerically simulated to show the strong impact of this non-linearity on the response.