Experimental measurement and numerical computation of parametric instabilities in a planetary gearbox

This article experimentally and numerically investigates the vibration behavior of a high-speed planetary gearbox. The subject planetary gear is a system in practical use. The focus is on parametrically excited vibrations and parametric instabilities that arise from time-varying gear mesh stiffness and may lead to gear whine. An example gearbox is deliberately subjected to poor profile modification in order to increase the dynamic excitation. Experiments reveal that this non-optimized version generates gear whine, where the same system with appropriate profile modifications does not. The measurements show a broadband frequency spectrum at certain operating conditions. A rotational lumped-parameter model with a linear implementation of the time-varying gear mesh stiffnesses is used to investigate the instability phenomena from a theoretical point of view. The model is analyzed in the time (numerical integration) and frequency (harmonic balance) domains. The computational approach clearly identifies that the large vibration results from parametric instability. The calculations explain the measurements and confirm the occurrence of parametric instabilities in a planetary gearbox by experiments.