## 4 Discussion
### Support Stiffness  
Figure 8 shows the variation in the system's load-sharing coefficient, contact area, and meshing force with the support stiffness factor of the idler gear. \(F_{m}\) and \(F_{p}\) in Figure 8g are the mean values of the meshing force and the fluctuation amplitude, respectively. As shown in Figure 8a, the load-sharing coefficient of the idler gear slowly increased from 1.04 at 0.1 times the support stiffness to 1.13 at 10 times the support stiffness, and the load-sharing coefficient of the input gear rapidly decreased from 1.52 at 0.1 times the support stiffness to 1.23 at 10 times the support stiffness. Moreover, both load-sharing coefficients changed rapidly in the range of (0.1, 1). Furthermore, the influence trend of the support stiffness of the idler gear on the load-sharing coefficient of the input gear was consistent with Figure 6 in reference [28]. Figure 8b-f clearly indicate that the idler support stiffness had little effect on the contact area of the input-face gear pair. In contrast, it had an obvious influence on the contact area of the idler face gear pair and the tail face gear pair. As seen in Figure 8g, as the stiffness increased, the power transmitted from the input gear to the lower face gear increased, while the power transmitted to the upper face gear through the tail gear decreased, and the changed power of these two parts was transmitted to the upper face gear through the idler gear. Therefore, not only could the contact characteristics of the idler gear pair be adjusted by changing the support stiffness of the idler gear but the power transmitted by each gear pair could be adjusted to make the load more balanced. The influences of the support stiffness of the input gear on the load-sharing coefficient, contact area, and meshing force are explored in Figure 9. It can be seen in Figure 9a that increasing the support stiffness of the input gear significantly increased the load-sharing coefficient of the idler gear and the input gear, where the load-sharing coefficient of the input gear rapidly increased from 1.07 to 1.60. Furthermore, both load-sharing coefficients varied quickly in the range of (0.1, 1). Similar to Figure 6 of [28], the input gear stiffness had a greater effect on the load-sharing performance of the input gear. As shown in Figure 9b-f, the input gear support stiffness had little effect on the contact area of the input-upper face gear pair. However, the contact area of other gear pairs clearly decreased when the stiffness increased. Figure 9g shows that as the stiffness decreased, the power transmitted by the input gear to the lower face gear increased and then transmitted to the upper face gear through the idler gear. In summary, a smaller input gear support stiffness was more conducive to the control of the load-sharing coefficient and contact area. Figure 10 shows the influence of the support stiffness of the tail transmission gear on the load-sharing coefficient, contact area, and meshing force of each gear pair. As can be seen in Figure 10a, with an increase in the support stiffness of the tail transmission gear, the load-sharing coefficient of the input gear changed significantly compared to that of the idler gear, and the greater the stiffness coefficient, the gentler the change was. In Figure 6 of [28], the load-sharing coefficient of the input gear decreases with the increase of the tail gear support stiffness, which is consistent with the conclusion of this study. As can be seen in Figure 10b-g, with the increase in the stiffness factor, the contact area of the tail gear pair increased significantly such that the tail gear bore more load. This also reduced the maximum load transmitted in the idler gear and the input gear meshing pair. Therefore, the large tail support stiffness was more conducive to a balanced bearing. Figure 11 shows the influence of the support stiffness of the upper gear on the load-sharing coefficient, the contact area, the mean value of the meshing force, and the fluctuation amplitude of the meshing force.