Elasto-dynamic modeling and modal analysis of spider reducer with small tooth number difference

In order to solve the problems of teeth breakage and premature fatigue of planetary bearings in spider reducers, a methodology of dynamic modeling for spider reducers was proposed and its dynamic characteristics were analyzed. With the substructure synthesis technique, a lumped parameter elasto-dynamic model of the spider reducer was established. The transmission system was divided into four subsystems as the input shaft subsystem, output shaft subsystem, spider shaft subsystem and translational spider gear subsystem. The differential motion equations of the four subsystems were derived by using the Newtonian method. The compatibility conditions of the reducer were derived with considering the deflections of bearings and gear pairs and the index and eccentric errors of eccentric sleeves. By combining the compatibility conditions with subsystem motion equations, the governing motion equations of the reducer were formulated. Through the eigenvalue decomposition, the modal properties of the transmission system were analyzed and the lower orders of natural frequencies and corresponding vibration modes were classified. The results show that the lower orders of natural frequencies are far above the rated input rotation frequency of the reducer, so it is not possible to cause structural resonances. Meanwhile, the corresponding vibration modes behave as complicated compound vibration modes of the four subsystems. To verify the correctness of theoretical analysis, an impact modal test was carried out. The comparison of lower orders of natural frequencies reveals a good match between theoretical and experimental results. From this point of view, it can be concluded that the proposed elasto-dynamic model si of satisfactory accuracy, and hence can be used to predict the steady-state dynamic responses of the system. The present research provides a solid fundament for further dynamic design and structural optimization of spider reducers. ©, 2015, Chinese Vibration Engineering Society. All right reserved.