# Dynamic Modeling and Output Characteristics Analysis of the Hub-Drive Reduction System
## 3 Dynamic Modeling of the Wheel Hub Transmission Reduction System  
The wheel hub transmission reduction system is a core functional component of large mining vehicles, and its dynamic performance directly determines the stability and smoothness of a vehicle. For this reason, the system's dynamic modeling and numerical simulation were conducted using ADAMS, multi-body dynamics simulation software, to explore the intricate dynamic behavior and influencing factors. As shown in Figure 1, the model of the wheel hub transmission reduction system contained many parts, including numerous nuts, bolts, bearings, and seals. To reduce the computational time and memory usage during dynamic simulations, these connectors were replaced by fixed and revolute joints where appropriate. Additionally, non-essential features such as oil holes, washers, and seals were excluded from the model to simplify calculations without affecting the system's movement. Material properties were assigned to the model according to the parameters listed in Table 1, ensuring consistency between the planetary gear carrier and the hub frame, as well as between planetary and sun gears. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Material** & **E/GPa** & **Density/(kg/m3)** &
\begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} \\ \hline Frame & AS1444-4320M & 206 & 7850 & 0.29 \\ Wheel hub & GS-25 CrMo4 & 211 & 7850 & 0.29 \\ Drive shaft & 40 Cr & 211 & 7870 & 0.28 \\ Sun gear & 18 CrNiMo7-6 & 202 & 7910 & 0.27 \\ Ring gear & 40 CrNiMo & 190 & 7700 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters of the system components. Figure 2: Exploded view of the two-stage planetary gear reducer. Based on the motion relationships and contact modes among the components of the wheel hub transmission reduction system, the types of connections and constraints were carefully defined. Since the hub frame remains stationary relative to the vehicle chassis, a fixed joint was defined between the hub frame and the ground. As the drive shaft serves as the power transmission element, one end of the shaft was defined with a revolute joint connected to the ground while the other end was rigidly connected to the primary sun gear. The hub and the secondary planet carrier were rigidly connected to act as the system's output. For a two-stage planetary gear system, the primary sun gear provides the power input and the planetary carriers serve as intermediate components to transmit power. The power flows from the primary planet carrier to the secondary sun gear and finally to the secondary planet carrier, which outputs the power to the wheels. The rotational joints between planetary gears and their respective planet carriers were defined accordingly. Similarly, rotational joints were established between each planet carrier and its central sun gear, with fixed joints applied between the planetary gears and their respective shafts. The contact and friction constraints were defined between the planetary gears, the sun gears, and the ring gears to accurately model the dynamic interactions. And a fixed connection was defined between the primary and secondary ring gears, while a coplanar constraint and contact were established between the primary ring gear and the hub frame to restrict axial movement. The relevant contact and friction parameters were determined such that the contact stiffness k was 3.78 \(\times\) 109 with a damping coefficient of 30 N\(\cdot\)s/mm, the maximum penetration depth was 0.01 mm, and the exponential factor was 1.5. The dynamic friction coefficient was set as 0.05, and a static friction coefficient of 0.08, dynamic friction relative velocity of 1.0 mm/s, and static friction velocity of 0.1 mm/s were also defined to reflect real-world conditions. The system's initial input parameters were derived from the specifications of a 400-ton mining dump truck, which uses this wheel hub transmission reduction system as a critical component.