# 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
Moreover, from the responses of the planetary carriers' angular velocities in Figure 11b,c after the hub motor input stabilized, it could be observed that the angular velocity amplitudes of both planetary carriers gradually decreased and eventually stabilized within a reasonable range of fluctuation. However, there was a noticeable difference: the fluctuations in the primary planetary carrier's angular velocity appeared more irregular, while those of the secondary planetary carrier were smoother, following a harmonic decreasing pattern. This difference arose mainly because the power transfer between the primary planetary carrier and the secondary sun gear occurred through the meshing of internal and external ring gears rather than through direct rigid coupling. On the one hand, the contact between the primary and secondary planetary carriers is more likely to be a more complex phenomenon. Figure 11: Angular velocity curves of the primary and secondary planetary carriers. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & \
\begin{tabular}{c} **Mean Angular Velocity** \\ **(Degree/s)** \\ \end{tabular} &
\begin{tabular}{c} **Theoretical Value** \\ **(Degree/s)** \\ \end{tabular} & **Error (\%)** \\ \hline Primary Planetary Carrier & 775.49 & 775.33 & 0.0206\% \\ Secondary Planetary Carrier & 137.32 & 137.33 & 0.0073\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of mean angular velocities and theoretical values. the internal and external ring gears was influenced by the precision of the gears. On the other hand, due to elastic deformation during gear meshing, the primary planetary carrier experienced shocks, vibrations, and uneven loads during operation. In contrast, the secondary planetary carrier was rigidly connected to the hub frame via bolts and nuts, eliminating the meshing-related shock and vibration issues. This indicates that the secondary planetary carrier's angular velocity was only affected by the secondary reduction system, while the primary planetary carrier was influenced not only by the primary reduction system but also by the contact shocks between it and the secondary sun gear. This interaction introduced negative feedback to the primary planetary carrier's angular velocity, explaining the difference in the smoothness of the angular velocity fluctuations between the two planetary carriers. From the figures, it can be observed that the angular velocities of the planetary carriers exhibited certain fluctuations, with the amplitude of these fluctuations gradually decreasing. The reasons for this are as follows: During the first second (0-1 s), the hub motor accelerates from 0 to 6000 degrees per second. After 1 s, the motor maintains a constant input speed of 6000 degrees per second. During this process, two types of excitations occur. The first is transient excitation caused by the motor's acceleration, and the second is steady-state excitation resulting from the motor maintaining a constant speed. The transient excitation introduced during the acceleration phase gradually diminishes due to the elastic deformation, contact stiffness, and damping effects within the gears during meshing. As a result, the transient response fades as the system dissipates energy. On the other hand, the steady-state excitation, which occurs once the motor speed stabilizes, induces a continuous steady-state response in the system. These phenomena were reflected in the fluctuations of the planetary carriers' angular velocities. Initially, the transient response corresponded to larger fluctuations in angular velocity. However, as the energy from the transient response dissipated, the fluctuations gradually decreased, eventually converging to the steady-state response. This explains the progressive reduction and eventual stabilization of the fluctuation amplitudes in the planetary carriers' angular velocities. Finally, as seen clearly in Figure 11c, the angular velocity curve exhibits a pattern of becoming dense initially and then more dispersed over time.