Dynamics analysis of high-speed encased differential planetary Gear Trains with different load-sharing

Load-sharing measures are adopted to improve the load-sharing performance of planetary gear systems. However, the measures affect dynamic characteristics, especially at high speed. Encased differential planetary gear trains (EDPGTs) are used widely for a large load capacity. Thus, the dynamic characteristics of EDPGTs with different load-sharing mechanisms are studied. First, EDPGTs are divided into finite nodes. Second, dynamic equations for each component are structured by Timoshenko beam theory, considering gyroscopic coupling, gear error excitation, and time-varying mesh stiffness excitation. Then, meshing elements and supporting elements are incorporated into component models by connected nodes. Third, a finite element node model of the flexible pin is established. A simulation and experiment are implemented to verify the flexible pin model. Lastly, the overall dynamics model of EDPGTs is established and solved by the Newmark-β method. The commonly used floating sun gear, flexible pin, and flexible ring gear are considered separately and in different combinations, so eight combinations of load-sharing are proposed. Dynamics analysis demonstrates that rigid pins effectively suppress planetary gear vibration amplitudes in the x and y-direction, while a fixed sun gear configuration reduces the sun gear. Moreover, the rigid ring gear design attenuation the θ_z-direction vibrational displacement of each component. The analytical method provides theoretical support for optimizing high-speed planetary gear transmission systems.