Dynamic Modeling and Analysis of a Star-wheel Reducer

The star-wheel reducer has been regarded as a promising alternative solution for industrial power transmission where large transmission ratio and high power density are required. As one of the most overwhelming concerns in the early design stage of such kind of transmission device, its dynamic performance must be evaluated in advance to provide guidelines for vibration suppression and tolerance control. For this purpose, this paper proposes a methodology of dynamic modeling for the star-wheel reducer and analyzes the dynamic behaviors of the transmission system. By using the technique of substructure synthesis, an analytical elasto-dynamic model is established in which the effects of component compliances and manufacturing/assembling errors are included. The differential motion equations of each subsystem are derived with the 2nd Newtonian law. These differential motion equations are further assembled by the compatibility conditions among the subsystems to formulate a governing equation of the overall transmission system. Based on the established dynamic model, a modal analysis and a dynamic analysis are carried out to reveal the modal characteristics and the steady-state responses of the star-wheel reducer. The results show that the first 6 orders natural frequencies are ranging from 66.2 to 197 Hz and are much higher than the reducer’s input frequency of 16.7 Hz under input speed of 1000 r/min. In addition, the meshing forces of the two phases of star-wheel are similar only with a phase difference of 180°. Finally, a test-rig is set up to perform an experimental modal test and a vibration test. The satisfactory agreement between the experimental data and the theoretical simulation results proves the correctness and accuracy of the proposed dynamic model. The present study is expected to provide a fundamental framework for error controlling and performance enhancement of the star-wheel reducer.