## 1 Introduction
[15] studied the load distribution between star gears in a two-stage star gear transmission system, built a mathematical model for calculating the load-sharing coefficient considering the displacement coordination, and obtained the curve of the load-sharing coefficient. Then, [PERSON] et al. [16] analyzed the load distribution mechanism of the star gear reducer, established a calculation model of the load-sharing coefficient accounting for the comprehensive meshing errors, and obtained the curves of the influences of the errors on the load-sharing coefficient. [PERSON] et al. [17] established a load distribution analysis model for a two-stage star gear transmission and systematically investigated its load distribution behavior. [PERSON] et al. [18] established a static-load-sharing calculation model of a two-stage five-branch planetary gear train and introduced the loading tooth contact analysis method to analyze the effects of manufacturing errors, installation errors, and the floating amount on the load-sharing coefficient. [PERSON] et al. [19] developed a dynamic model of a multi-stage planetary gear transmission system of a wind turbine by employing the lumped parameter method and explored the load-sharing behavior under the action of time-varying input speed and internal excitation. In addition to the studies on the load sharing of planetary gears, according to the collected literature, a few scholars have also studied load sharing for systems containing face gears in earlier times. In 2002, [PERSON] [20] set up a complex load-sharing test platform for a face gear split-torque drive and the test results showed that the load-sharing coefficient between the two face gears at the input gear was 1.083 and the load-sharing coefficient between the two idle gears was 1.33, which verified the feasibility of using a face gear in the torque-sharing systems. [PERSON] [21] studied the load distribution and sharing of a face gear split-torque transmission system using both the classic method and the finite element method. [PERSON] et al. [22] established the analysis model of a helicopter face gear split-torque transmission system and the results showed that the load-sharing performance can be improved using floating supports. Coaxial face gear split-torque transmission systems have become a hot research topic recently. [PERSON] et al. [23; 24] analyzed the uneven load mechanism for the concentric face gear split-torque transmission and investigated the influence of system parameters on the load-sharing performance. [PERSON] et al. [25] combined the finite element method (FEM) and the analytical method (AM) to investigate the effects of the distribution angle of opinions and the load conditions on the meshing stiffness of the gear pairs in the CFGSTTS. Subsequently, [PERSON] et al. [26; 27] determined the power direction of the CFGSTTS using the finite element method; investigated the effect of system parameters on the power direction; and discussed the influences of torsional stiffness, backlash, and time-varying meshing stiffness on the dynamic load distribution through the lumped parameter model. [PERSON] et al. [28] analyzed the main factors that affect the load distribution of the concentric face gear split-torque transmission, established a bending-torsion-shaft coupling centralized parametric dynamic model, and investigated the influence of support stiffness and no-load transmission errors on the dynamic-load-sharing performance. [PERSON] et al. [29; 30] developed a translation-torsion dynamic model of a coaxial face gear split-torque transmission system, obtained the meshing force curve and load distribution coefficient curve, and then analyzed the effects of various factors on the load distribution coefficient. Due to manufacturing and assembly errors, as well as the structural differences between the upper and the lower face gears, the loads on each branch gear of the concentric face gear split-torque transmission system vary.