## 4 Discussion
### Support Stiffness
Figure 11a shows that increasing the support stiffness of the upper face gear slightly increased the load-sharing coefficient of the input gear. However, the load-sharing coefficient of the idler gear reduced significantly, from 1.33 when the supporting stiffness was 0.1 to 1.004 when the supporting stiffness was 10 and decreased rapidly in the range of (0.1, 1). As can be seen in Figure 11b-f, with an increase in  
Figure 8: Influence of the support stiffness of the idler gear on the load-sharing and contact characteristics. the support stiffness of the upper face gear, the contact area of the idler gear 1-upper face gear pair expanded and the contact spot was offset to the outer end. The related conclusion can be obtained from Figure 11g, where increasing the upper face gear support stiffness increased the mean value of the contact force of idler gear 1 and minimized the difference with the mean value of the contact force of idler gear 2. Hence, the load equalization factor of the idler gear was reduced. The large stiffness coefficient reduced the contact area of the meshing pairs M56 and M57, and the average meshing force slowly decreased. This meant that the power transmitted to the upper face gear through the tail gear became smaller, and more power was transmitted through idler gear 1. Consequently, the load-sharing coefficient and power transmission path could be controlled to a certain extent by adjusting the support stiffness of the upper face gear. As can be seen in Figure 12a, increasing the support stiffness of the lower face gear significantly reduced the load-sharing coefficient of the input gear. However, the load-sharing coefficient of the idler gear first decreased and then increased. When the stiffness coefficient was about 0.9, the load-sharing coefficient was the smallest. It can be seen in Figure 12b-f that changing the support stiffness of the lower face gear had the greatest impact on the contact characteristics of the idler gear-face gear pair. Similarly, increasing  
Figure 9: Influence of the support stiffness of the input gear on the load-sharing and contact characteristics. the lower face gear support stiffness significantly increased the average contact force of idler gear 2 and gradually exceeded that of idler gear 1. Therefore, the load-sharing coefficient decreased first and then increased. In general, increasing the support stiffness of the lower face gear increased the power transmitted from the input gear to the lower gear and output this power to the upper face gear through idler gear 2. To further investigate the effects of the angular, axial, and radial components of the upper and lower face gear support stiffness on the load-sharing characteristics, the results obtained using quasi-static analysis are shown in Figures 13 and 14. In these figures, subfigures (a), (b), and (c) show the effects of the angular, axial, and radial stiffness on the load sharing, respectively. It can be seen that the angular stiffness of the upper face gear had a great impact on the load sharing of the idler gear. When the stiffness factor exceeded 1, the influence on load sharing gradually decreased.