The Effects of Multi-Mesh Tooth Profile Modifications on Planetary Gear Vibration

Abstract

In this paper, the different effects of tooth profile modifications (TPMs) for the sun-planet and the ring-planet meshes on the first two rotational modes are investigated with the consideration of tooth thickness errors. A nonlinear model with multiple degree of freedoms is built to descript the rotational vibration of the planetary gears. In contrast to the majority of the models in the literature, the variable mesh stiffness, TPM, manufacturing error, and loss of contact in both of the sun-planet and ring-planet meshes are introduced in the analysis. Multiple scale method is used to analyze dynamic response and transmission errors. Numerical integrations are carried to verify the perturbation results and explore the nonlinear phenomena in the planetary gears. The frequency response curves of dynamic transmission error (DTE) obtained for different TPM with different tooth thickness errors are presented. Results indicate the TPM not only affects the amplitude of response but also results into the change of the margin of contact between sun gear and planet gears and the margin of contact between the ring gear and planet gears. In addition, the optimal TPM for the first mode may induce high level vibration on the second or higher order modes. These mean one need to consider the effects of TPM on the response amplitude and the margin of the loss of contact for both rotational modes to get an optimal TPM among the teeth of sun gear, planet gears, and ring gear. This provides guidance for practical design and tolerance standard for the planetary gears.