## 2 System Dynamics Model of Vehicle-Curved Switch Rail
### Vehicle and Curved Switch Rail System Dynamics Model  
The vehicle and curved switch rail are connected by the wheel-rail relationship. As shown in Figure 5, the dynamic model of the vehicle-curved switch rail system has been established.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Value** \\ \hline Car body mass (kg) & 41,190 \\ Car body rolling moment of inertia (kg:m\({}^{2}\)) & 79,600 \\ Car body pitching moment of inertia (kg:m\({}^{2}\)) & 2,105,000 \\ Car body yawing moment of inertia (kg:m\({}^{2}\)) & 2,093,000 \\ Bogie frame mass (kg) & 2920 \\ Bogie frame rolling moment of inertia (kg:m\({}^{2}\)) & 2247 \\ Bogie frame pitching moment of inertia (kg:m\({}^{2}\)) & 2860 \\ Bogie frame yawing moment of inertia (kg:m\({}^{2}\)) & 5040 \\ Wheelset mass (kg) & 1523 \\ Wheelset rolling moment of inertia (kg:m\({}^{2}\)) & 708 \\ Wheelset pitching moment of inertia (kg:m\({}^{2}\)) & 100 \\ Wheelset yawing moment of inertia (kg:m\({}^{2}\)) & 708 \\ Vertical stiffness of primary spring (N/m) & 1,500,000 \\ Longitudinal stiffness of primary spring (N/m) & 980,000 \\ Lateral stiffness of primary spring (N/m) & 980,000 \\ Vertical damping of primary vertical shock absorber (N\(\cdot\)s/m) & 10,000 \\ Vertical stiffness of secondary suspension (N/m) & 450,000 \\ Longitudinal stiffness of secondary spring (N/m) & 20,0000 \\ Lateral stiffness of secondary spring (N/m) & 200,000 \\ Vertical damping of secondary vertical shock absorber (N\(\cdot\)s/m) & 20,000 \\ Longitudinal damping of secondary longitudinal shock absorber (N\(\cdot\)s/m) & 360,000 \\ Lateral damping of secondary lateral shock absorber (N\(\cdot\)s/m) & 22,000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Part parameters of CRH5 EMU.  
Figure 4: Multibody dynamics model of CRH5.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Dynamic Index** & **Specified Limit Value** \\ \hline Wheel–rail vertical force & \(\leq\)170 kN \\ Wheel–rail lateral force & \(\leq\)48.4 kN \\ Derailment coefficient & \(<\)0.8 \\ Vertical acceleration & \(<\)2.5 m/s\({}^{2}\) \\ Lateral acceleration & \(<\)2.5 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The limit of each dynamic index of CRH5.  
The curved switch rail has a variable section structure. Multiple contact modes occur between the wheels and rails when the vehicle passes through this area. The hypothetical conditions of the traditional Hertz theory are idealized. The calculation of the multi-point contact relationship between the wheels and rails will have errors, and the calculation results will be quite different from the actual situation [46]. The Kalker non-Hertzian contact theory, which takes into account the actual wheel-rail contact shape, can be used to compute the precise solution of three-dimensional rolling contact. However, the rate of calculation is rather slow [37]. The Kik-Piotrowski method solves the problem of slow calculation speed and ensures the accuracy and efficiency of calculation. The Universal Mechanism uses the non-Hertzian contact Kik-Piotrowski method based on virtual penetration as a contact algorithm for the Archard wear model. It predicts realistic wheel-rail profiles and takes into account the efficiency of the calculation. Therefore, this paper uses it to predict the wear on key sections of curved switch rails.