# 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  
Given the initial inputs and boundary conditions, the overall dynamic characteristics of the wheel hub transmission reduction system were primarily focused on the system's response to the input. Based on the system's motion mechanism and the analysis of connection and contact methods, the system's response to the hub motor input was reflected in two key aspects: the angular velocity output of the two-stage planetary gear system and the contact forces generated during gear meshing. While the previous section focused on the angular velocity output curves of the planetary carriers and their dynamic characteristics, this section provides a detailed discussion of the contact force variations during gear meshing. In the operation of the wheel hub transmission reduction system, the primary sun gear meshes with three planetary gears, which also engage with the primary ring gear to transmit power and achieve speed reduction. During the system design phase, the material properties, tooth profile modifications, and displacement coefficients of the three planetary gears are kept identical. Therefore, it can be assumed that the contact conditions between the three planetary gears, the sun gear, and the ring gear are consistent. Similarly, the four secondary planetary gears exhibit consistent contact conditions with the secondary sun gear and the secondary ring gear. From a force analysis perspective, each planetary gear is subject to forces from the sun gear, the ring gear, and the outer race of the bearing. During steady-state operation, the bearing primarily supports the axial rotation of the planetary gears, while the radial load from the bearing is negligible compared with the contact forces during gear meshing. As a result, it can be assumed that the planetary gears maintain force equilibrium under the influence of the sun gear and the ring gear, with synchronized variations in the meshing contact forces between them. Therefore, the following analysis of the dynamics of the  
Figure 12: Angular velocity variation of the primary planetary carrier during the 19–20 s interval. Figure 13: Frequency-domain curve of the angular velocity variation of the primary planetary carrier during the 19–20 s interval. planetary gear system specifically focuses on the contact forces between the planetary gears and the sun gear. Using the previously established dynamic model of the wheel hub transmission reduction system, numerical simulations were performed with ADAMS multibody dynamics software. The parameter settings and boundary conditions were consistent with those described earlier. After extracting and processing the simulation results, the contact force variation curves for the gears at different stages were obtained, as shown in the following figures. Figure 14 presents the contact force variation curve between the primary sun gear and the planetary gears. Subfigures (b) and (c) provide zoomed-in views of (a), showing finer details of the contact force variations. Similarly, Figure 15 illustrates the contact force variation curve between the secondary sun gear and the planetary gears, with subfigures (b) providing detailed views of the corresponding curves. Figure 14: Contact force between primary sun gear and planetary gears, along with zoomed-in views. From the analysis of Figures 14 and 15, it can be observed that the contact force curves between the sun gears and the planetary gears at both stages exhibit similar trends. Initially, the contact forces increased with the rise in input power from the hub motor. Once the motor input stabilized, the contact forces displayed harmonic oscillations, with the amplitude gradually decreasing until they stabilized. The reasons for these fluctuations in the contact force curves are as follows: On one hand, the contact between the sun gear and the planetary gears involves the elastic deformation of the gears themselves. Additionally, the contact stiffness and damping within the system introduce vibrations.