# 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
#### 5.3.1 Angular Velocity Output Characteristics of Planetary Carriers  
To understand the dynamic characteristics of the high-torque hub transmission reduction system, a detailed analysis was conducted on the input, transmission, and output of power. Without external disturbances, the only power input was the angular speed provided by the hub motor, with the input curve shown previously in Figure 4.  
The motor drives the primary sun gear through the drive shaft, which transmits power to the primary planetary carrier and onward to the secondary sun gear. The secondary planetary carrier, which is rigidly connected to the wheel hub, outputs power to the wheel. Figure 8: Acceleration signal results of vibration test. Figure 9: Acceleration signals in the dynamic model. The entire wheel hub system drives the vehicle, with four independently driven hub systems propelling the vehicle. The power transmission path is illustrated in Figure 10.  
As shown in Figure 10, the two-stage planetary gear reducer plays a critical role in the power transmission process of the entire system. In this planetary gear reducer, the primary sun gear is rigidly connected to the drive shaft. Assuming no torque loss during transmission through the drive shaft, the input power directly corresponds to the initial input speed of the hub motor. Simultaneously, the wheel hub is rigidly connected to the secondary planetary carrier, making the output speed of the secondary planetary carrier the system's output speed. It is important to note that the connection between the first-stage and second-stage gear reducers is not achieved through rigid coupling but through meshing contact between the primary planetary carrier and the secondary sun gear via internal and external ring gears. Due to the contact-based transmission, the power transfer between the primary planetary carrier and the secondary sun gear involves efficiency losses. Since the dynamics of the primary planetary carrier directly influence the overall output of the system as the input to the second-stage reducer, analyzing the angular velocity variations of both the primary and secondary planetary carriers becomes essential for understanding the dynamic behavior of the high-torque wheel hub transmission reduction system. Based on the dynamic model developed earlier in the multi-body dynamics simulation software ADAMS and given the initial inputs and boundary conditions, an analysis of the output characteristics of the wheel hub transmission reduction system was conducted. Numerical simulations were performed, and the resulting output angular velocity curves of the primary and secondary planetary carriers are presented in Figure 11. Subfigures (b) and (c) provide zoomed-in views of the corresponding curves in (a) over the 1-20 s interval, offering a more detailed illustration of the system's response after the hub motor input stabilized. The results in Figure 11 show that the angular velocities of both planetary carriers followed similar trends. During the first second, their angular velocities increased in response to the input from the hub motor. Afterward, the system stabilized, indicating that the two-stage planetary gear reducer responded quickly to the input and exhibited stable output once the input became steady. This demonstrated a linear relationship between the input from the hub motor and the output from the planetary carriers, aligning with the theoretical motion mechanism; additionally, the mean angular velocities of the planetary carriers during stable operation were calculated and compared with theoretical values. The comparison is provided in Table 5. The small errors between the simulated and theoretical values confirm the reliability and accuracy of the dynamic model. Figure 10: Power transmission path of the hub transmission reduction system.