Analytical investigation on load sharing characteristics and speed difference of coaxial reverse closed differential herringbone gear transmission system with floating gear and errors

To investigate the influence of gear floating on the load sharing characteristics of the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) and the rotational speed difference between the upper and lower rotors, a dynamic Bending-Torsional-Axial-Pendular (BTAP) model of the CRCDHGTS was established using the centralized parameter method, which considers various excitation factors such as gear floating, errors, Time Varying Meshing Stiffness (TVMS), gyroscopic effect, and tooth friction. It considers the interaction between the closed-stage gear set and the differential-stage gear set, treating the herringbone gear as a symmetric helical gear connected through a receding slot. The dynamic model was solved using the Runge-Kutta method to obtain the dynamic meshing forces for each gear pair under single and combined floating modes. The Dynamic Load Sharing Coefficient (DLSC) of the system, which characterizes the Load Sharing Performance (LSP), was deduced. The load sharing characteristics of different floating modes were analyzed, as well as the influence of different floating displacement on the DLSC. The motion path of the gear floating was also determined. Additionally, the impact of manufacturing error and assembly error of each component on the DLSC under combined floating mode was analyzed. Finally, the influence of gear floating on the output rotation speeds of the upper and lower rotors of the system was investigated. The results indicate that both free-floating of the center gear and combined floating can effectively improve the LSP of the system. When the system adopts combined floating mode, the DLSC of inner and outer meshing changes between 0.91 and 1.09, demonstrating a significant improvement in the LSP. The DLSC of the system increases with the increase in error, with the eccentricity error having a greater impact on the DLSC compared to the assembly error. The optimal floating value for the sun gear is between 0.6 mm and 0.8 mm, while for the planetary gear, it is between 0.4 mm and 0.6 mm. The rotational speed difference between the upper and lower rotors can be controlled within 1r/min. These research findings provide a theoretical basis for further analysis of the dynamic stability and reliability of the system.