Dynamic responses of electromechanical transmission system based on a nonlinear hybrid model

A nonlinear hybrid model of electromechanical transmission system is proposed by combining finite element method and lumped parameter method, in which the flexible shaft model is established by using three-dimension nonlinear beam element based on the absolute node coordinate formulation and the gear mesh model is calculated by using nonlinear time-varying lumped parameter model. In the hybrid model, the coupling between the nonlinear deformation of shafts and excitation of gears is considered. The generalized-α implicit time stepping algorithm is used to study the dynamic responses of system. Then, comparisons and analyses are made of the dynamic responses of system between the hybrid model and previous lumped parameter model. Finally, the effects of flexibility of shafts, the geometrical parameters of shaft, the mounting position of the gear on the shaft and the operation conditions on the dynamic responses of system are analyzed. The results show that the presented nonlinear hybrid model is valid and effective in predicting the dynamic behavior of electromechanical transmission system. The gear meshing force is increased by 14.3% and new coupling frequencies are observed due to the effect of the shaft flexibility. Moreover, since the shaft radius of 0.05 m is the critical value for the accurate calculation of the proposed nonlinear hybrid model, the nonlinearity caused by the shaft vibration cannot be ignored. When the gear is installed at the midpoint of the shaft, the maximum von Mises stress of the shaft of 1.8 × 10⁷ Pa is achieved and located at the connected point on the shaft. This study plays an important role in the field of electromechanical transmission design.