The multi-power face gear split flow system is a new type of transmission system, which has the advantages of stable and reliable transmission and strong carrying capacity. And it has great potential in the application of helicopter transmission systems. In this paper, the multi-power face gear split flow system was taken as the research object. Based on the lumped parameter method and Newton’s second law, the translational-torsional dynamic model of the system was established considering the translational vibration and the torsional vibration of the gears, and the meshing force curves and load-sharing coefficient curves were drawn. At the same time, the factors affecting the load-sharing characteristics of the transmission system were studied. The impacts of manufacturing errors, assembly errors, manufacturing error phases, assembly error phases, meshing damping, support stiffness, and the input power on the load-sharing coefficients were analyzed. The research shows that the errors and error phases of spur gears have small impacts on the load-sharing coefficients, while the support stiffness of spur gears has a great impact on the load-sharing coefficients. The errors and error phases of face gears have small impacts on the load-sharing coefficients, while the support stiffness of spur gears has a great impact on the load-sharing coefficients. The load-sharing coefficients increase constantly with the increase in the meshing damping between face gears and spur gears, whereas the load-sharing coefficients decrease constantly with the increase in the input power.

This paper presents a coaxial counter-rotating planetary transmission system. The transmission system under study is a two-stage planetary gear train (PGT) comprising a fixed-axes PGT and a differential PGT. A dynamic model of the transmission system is established, considering both the excitations caused by the time-varying mesh stiffness (TMS) and the transmission errors, respectively. The Runge–Kutta algorithm is used to calculate and analyze the dynamic characteristics of the system. This includes studying dynamic meshing forces, planet gear displacements, and load-sharing coefficients (LSCs) under both internal and external excitations, as well as different input torques. The results indicate that when considering external excitations, the variations in the meshing force curves become more pronounced. The radial displacements of the planet gears in the differential PGT are greater than that in the fixed-axes PGT. With increasing input torque, the average displacements of the planet gears in all directions tend to increase. The differential PGT, transmitting a higher power, demonstrates a better load-sharing performance compared to the fixed-axes PGT.

This study focuses on a marine two-stage tandem hybrid planetary system. Natural frequencies and vibration modes are determined using a translational–torsional coupled dynamic model. Based on the motion characteristics of the transmission system, free vibration is categorized into three typical modes. The parameter sensitivity of natural frequencies is computed, and the effects of structural parameters such as unequally spaced planet, mesh stiffness, planet mass and rotational inertia on the natural frequencies are analyzed. Utilizing the coupling factor, the mode transition criterion for the natural frequencies response to parameters is formulated. The results demonstrate that the vibration modes of the two-stage tandem hybrid planetary system can be classified as the fixed-axis train vibration mode, the differential train vibration mode, and the coupled vibration mode. Unequally spaced planet primarily disrupts vibration modes without significantly affecting natural frequencies. In contrast, the effects of mesh stiffness, planet mass and rotational inertia on the modes are opposite to those of unequally spaced planets. The validity of the parameter sensitivity and mode transition criterion is substantiated through illustrative examples.