# 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
From the figure, it can also be observed that the overall contact force curves during gear meshing exhibited a pattern of becoming dense initially and then more dispersed over time. From the perspective of excitation changes and frequency analysis, as the shock from the hub motor's acceleration gradually dissipated, the system's frequency components increasingly converged towards the motor's stable input rotational frequency and the respective meshing frequencies of the gears. Figure 16: Contact force between the primary planetary carrier and the secondary sun gear’s internal and external ring gears. An analysis of the frequency-domain curves of the contact forces during the 19-20 s interval, as shown in Figures 17 and 18, reveals the following: The primary frequency component of the contact force between the primary sun gear and the planetary gears was 14.56 Hz along with its second harmonic. The fundamental frequency tended towards the rotational frequency of the primary sun gear. The discrepancy between the theoretical and actual rotational frequencies was due to the system not yet having reached a stable operating state, with residual effects from the hub motor's acceleration shock still present. Similar to the frequency-domain curve of the primary planetary carrier's acceleration, the high-frequency components were relatively complex, although the primary meshing frequency still made a noticeable contribution. In contrast, the frequency-domain curve of the contact force between the secondary sun gear and planetary gears contains fewer high-frequency components, reflecting the smoother nature of the contact force curve. The primary frequency component was 3.119 Hz, which slightly deviated from the secondary sun gear's rotational frequency, likely because the system had not yet fully stabilized. Moreover, both the rotational frequency of the primary sun gear and the secondary meshing frequency are clearly identifiable in the system's frequency components, indicating their contribution to the system's behavior. This aligns with real-world expectations. Finally, by comparing the time-domain and frequency-domain curves of the contact force variations discussed in this section with the corresponding angular velocity curves of the planetary carriers, it can be observed that the fluctuations in the contact force during gear meshing were synchronized with the fluctuations in the angular velocity of the planetary carriers. Furthermore, the frequency components were consistent across both. The contact force variations caused by gear meshing can be considered as the input to the respective reduction stages, while the angular velocity of the planetary carriers  
Figure 17: Frequency-domain curve of the contact force between the primary planetary gear and the sun gear during the 19–20 s interval. Figure 18: Frequency-domain curve of the contact force between the secondary planetary gear and the sun gear during the 19–20 s interval. represents the output of the reducer. This relationship indicates that the fluctuations in the contact force during gear meshing are the underlying cause of the angular velocity fluctuations in the planetary carriers. It also provides a deeper understanding of the dynamic performance of the two-stage planetary gear reduction system.