Dynamic analysis and modeling simulation of 4K planetary gear systems based on bond graph theory

Studies on the dynamic performance of 4K planetary gear trains remain limited. This study proposes a bond-graph-based method for the dynamic analysis of complex 4K planetary gear trains. The method decomposes a complex planetary gear train into several independent single-stage planetary gear train systems, thereby simplifying the modeling process and providing a new modeling approach for complex planetary gear trains containing compound members. Subsequently, a complete bond graph model is established, and the corresponding state equations are derived and solved numerically to obtain the time histories of the rotational speeds of the individual members, the dynamic mesh torques, and the vibration responses along the lines of action. The predicted speed ratios of the individual members agree well with the corresponding theoretical values, with all relative errors remaining below 1%, thereby validating the accuracy of the proposed model. Furthermore, a sensitivity analysis is conducted to investigate the effects of the I-, C-, and R-element parameters on the output-speed response under different operating conditions, providing practical guidance for engineering design. Finally, a virtual prototype of the 4K planetary gear train is developed in RecurDyn. The steady-state rotational speeds predicted by the RecurDyn model agree well with those obtained from the bond graph model. A comparison among the theoretical values, bond graph predictions, and RecurDyn simulation results shows that all relative errors remain below 1%. The results demonstrate the effectiveness of the proposed bond graph method for the dynamic simulation of 4K planetary gear trains and provide a theoretical foundation for their engineering design and application.