Analytical investigation of tooth profile modification effects on planetary gear dynamics

• Develop an analytical tooth profile model (TPM) for planetary gear dynamics
• Find an optimal TPM for minimal vibration using a closed-form perturbation solution
• Demonstrate the importance of dynamic analysis by comparing STE and dynamic response
• Examine the combined use of sun–planet and ring–planet mesh TPM
• System parameters and vibration modes change the effects of TPM on dynamic response.

This study investigates the impact of tooth profile modification on spur planetary gear vibration. An analytical model is proposed to capture the excitation from tooth profile modifications at the sun–planet and ring–planet meshes. The accuracy of the proposed model for dynamic analysis is correlated against a benchmark finite element analysis. Perturbation analysis yields a closed-form approximation of the vibration response with tooth profile modifications. The perturbation solution is used to investigate the effects of tooth profile modification. The tooth profile modification parameters that minimize response are readily obtained. Static transmission error and dynamic response are minimized at different amounts of profile modification, which contradicts common practical thinking regarding the correlation between static transmission error and dynamic response. Contrary to expectations, the optimal sun–planet and ring–planet tooth profile modifications that minimize response when applied individually may increase dynamic response when applied simultaneously. System parameters such as mesh stiffness and mesh phase significantly affect the influence of tooth profile modification.