# Dynamic Modeling and Output Characteristics Analysis of the Hub-Drive Reduction System
## 5 Full-System Load Test and Validation of the Hub Drive System
### Output Characteristics Analysis of the Hub Transmission Reduction System
#### 5.3.2 Analysis of Contact Force Characteristics During Gear Meshing
On the other hand, the modified tooth profile introduces tooth clearance during meshing. The existence of tooth clearance increased the impact during engagement, which also contributes to vibrations between the gears. The harmonic oscillation of the contact force curves is attributed to the fact that both the fundamental frequency of the input shaft and the meshing frequency exhibit periodic variations during gear meshing. This periodicity leads to the oscillating behavior of the contact forces. As the system continues to operate, the amplitude of these oscillations gradually decreases and eventually stabilizes. As discussed earlier, the gear reduction system is subjected to two types of excitation: transient shock from the motor's acceleration and forced vibration from the stabilized motor input. While the forced vibration persists throughout the operation, the vibrations caused by the acceleration shock gradually dissipate due to the system's damping. Consequently, the contact forces eventually stabilize and oscillate within a certain range. Based on the zoomed-in views of the contact force curves during gear meshing, a further analysis of the contact forces between the sun gears and planetary gears at each stage reveals the following: During the meshing of the sun gears and planetary gears, the contact force periodically dropped to zero. This occurred because the gears in the reduction  
Figure 15: Contact force between the secondary sun gear and the planetary gears, along with a zoomed-in view. system underwent tooth profile modification and had certain displacement coefficients. In actual meshing, excessive impact can cause significant tooth clearance when the sun gear and planetary gear rotate to a specific position. The presence of tooth clearance resulted in temporary disengagement of the gears, during which the contact force became zero, accompanied by some impact and vibration, as illustrated in Figure 14c. A comparison of Figures 14 and 15 reveals that although disengagement occurred in the contact between the sun gears and planetary gears at both stages, the duration of disengagement differed. In the contact between the primary sun gear and the planetary gears, disengagement persisted throughout the entire simulation. However, in the contact between the secondary sun gear and the planetary gears, disengagement only occurred at the beginning, and as the contact force fluctuations stabilized, disengagement no longer occurred. The reasons for this difference can be attributed to the following two factors:  
Difference in the number of planetary gears: The secondary planetary gear set contains four gears, compared with three in the primary planetary gear set. With more planetary gears, the system absorbs energy from impacts more quickly, restoring stability faster. Difference in the degree of excitation impact: The primary reduction stage is directly exposed to the shock caused by the hub motor's acceleration, while the secondary reduction stage experiences significantly reduced impact. First, the shock is attenuated by passing through the primary reducer. Second, the contact between the primary planetary carrier and the secondary sun gear's internal and external ring gears provides additional damping. As a result, the shock from the motor's acceleration undergoes two stages of isolation before reaching the secondary reducer, further reducing its intensity. During the process described above, the contact force curve between the primary planetary carrier and the secondary sun gear is shown in Figure 16. The contact force fluctuated within a certain range, with the amplitude gradually decreasing until it stabilized. This curve indicates that the power transmission between the primary and secondary reducers is not an ideal linear relationship. It also confirms the earlier discussion regarding the influence of these contact force variations on the angular velocity output of the primary planetary carrier.