Planetary gear vibration causes undesirable noise. It may also excite structural resonances or shorten the life of bearings and other drivetrain components. Extensive theoretical research highlights the interest in this topic, but limited experimental data is available to direct and improve these analytical tools or provide practical design guidance to engineers who face increased pressure to reduce transmission noise. This research provides experimental data that has already confirmed, improved, and suggested new directions for analytical modeling. It is hoped that this intentionally broad effort will continue to show its usefulness in the literature.
Experimental methods--including stationary modal analysis and spinning vibration tests--are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Natural frequencies, mode shapes, and dynamic response obtained by modal vibration testing are compared to the results from lumped-parameter and finite element models. Both models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally.
Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures to capture all of the natural frequencies and modes. The natural frequencies in the high-frequency range tend to gather into clusters (or groups). This behavior is first observed in the experiments and studied in further detail with numerical analysis. There are three natural frequency clusters. Each cluster contains one rotational, one translational, and one planet mode type. The clustering phenomenon is robust, continuing through parameter variations of several orders of magnitude. There are two conditions that disrupt the clustering effect or diminish its prominence.
The experiments are also used to improve the existing models, particularly among high-frequency modes with significant tooth mesh deflection. Current lumped-parameter models do not consider the anisotropic nature of planet bearing stiffnesses, but these experiments show that all natural frequencies increase with higher torque. The accuracy of natural frequency prediction is improved when the planet bearings have different stiffness values in the tangential and radial directions, consistent with the bearing load direction. Experiments at different applied torque values demonstrate this behavior and give increased understanding about the influence of torque on system parameters and dynamic response. A finite element/contact mechanics model provides accurate calculation of the anisotropic planet bearing stiffnesses and the load-dependent mesh stiffnesses. An analytical model using these values accurately predicts changes in the experimental natural frequencies of the modes with high strain energy in the planet bearings for changing torque. Experiments also show changes in the mode shapes and damping ratios with increased torque.
Elastic vibration of the ring gear and planet gears is also studied. Continuous vibration modes occur in the range of the high-frequency lumped-parameter modes and beyond. A finite element model confirms the vibration mode shape in the planet gears, which is elastically coupled to the ring gear. Two elastic modes are also observed in the ring gear: a two nodal diameter mode and a three nodal diameter model. The modes and their natural frequencies are insensitive to the number of planets, as seen in experiments on systems with three, four, and five planet gears.
Finally, spinning tests give the vibration response of each individual planetary gear component under operating conditions. The measured natural frequencies and vibration modes agree with the stationary modal vibration tests. The modes are separated into discrete categories, agreeing with the analytical literature. The effect of mean torque on vibration response is shown. Theoretical predictions of vibration suppression due to mesh phasing are compared against the experiments.