Nonlinear dynamic analysis of a cycloidal ball planetary transmission considering tooth undercutting

A cycloidal ball planetary transmission (CBPT) is a new type of transmission system with a large transmission ratio and a phenomenon of tooth undercutting. Nonlinear dynamic differential equations of the CBPT in the undercutting state are constructed. Firstly, the complete tooth profile equations of cycloidal grooves are established. With the increase of the radius of the deceleration balls, the tooth undercutting is firstly occurred in the inner part, and then in the outer part of the epicycloid grooves. Secondly, considering time-varying meshing stiffness, damping, meshing state, pre-tightening and external excitation, a strong nonlinear coupling dynamic model (70-DOF) of translation-torsion is established to further construct the nonlinear differential equations of the CBPT according to Lagrange equation. Thirdly, the response signal of the system is decomposed into low frequency and high frequency response signals. Fourthly, the nonlinear dynamic characteristics with three parameters (the damping, radius of rolling circle, short amplitude coefficient) are investigated. Finally, the effectiveness of the proposed model has been validated in part by testing vibration signals of CBPT. The stability of the system is affected by the damping, radius of rolling circle and short amplitude coefficient, which will provide useful support for the design of CBPT. (C) 2019 Elsevier Ltd. All rights reserved.