## 3 Comparison of the Models
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**No.** & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** & **S7** & **S8** & **S9** & **S10** \\ \hline \hline
\begin{tabular}{c} Yaw Stiffness \\ (kNm/rad) \\ \end{tabular} & 0 & 2 & 5 & 10 & 20 & 50 & 100 & 200 & 500 & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation conditions of yaw damping. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Definition** & **Value** \\ \hline \(m_{\text{C}}\) & Carrier mass & 200 kg \\ \(m_{\text{W}}\) & Wheel mass & 75 kg \\ \(J_{\text{C}x}\) & Carrier’s inertia moment in the \(x\) direction & 35 kg\(\cdot\)m\({}^{2}\) \\ \(J_{\text{C}y}\) & Carrier’s inertia moment in the \(y\) direction & 20 kg\(\cdot\)m\({}^{2}\) \\ \(J_{\text{C}z}\) & Carrier’s inertia moment in the \(z\) direction & 30 kg\(\cdot\)m\({}^{2}\) \\ \(J_{\text{W}x}\) & Wheel’s inertia moment in the \(x\) direction & 5 kg\(\cdot\)m\({}^{2}\) \\ \(J_{\text{W}y}\) & Wheel’s inertia moment in the \(y\) direction & 8 kg\(\cdot\)m\({}^{2}\) \\ \(J_{\text{W}z}\) & Wheel’s inertia moment in the \(z\) direction & 5 kg\(\cdot\)m\({}^{2}\) \\ \(b\) & Half lateral distance between the left and right wheels & 0.72 m \\ \(r_{0}\) & Nominal wheel radius & 0.4 m \\ \(\lambda\) & Equivalent wheel–rail tread conicity at the center position & 0.1 \\ \(k_{11}\) & Longitudinal Kalker’s creep coefficient & 4 \(\times\) 10\({}^{6}\) N \\ \(k_{22}\) & Lateral Kalker’s creep coefficient & 6 \(\times\) 10\({}^{6}\) N \\ \(g\) & Gravitational acceleration & 9.81 m/s\({}^{2}\) \\ \(F_{\text{L}z}\) & Extra vertical loads on the left wheel & 50 kN \\ \(F_{\text{R}z}\) & Extra vertical loads on the right wheel & 50 kN \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation conditions of longitudinal speed. Figure 7: Wheel–rail contact analysis. (**a**) Contact patches with connection lines; (**b**) number of contact patches. the yaw angle and the moment formed by gravitational restoring forces is positive feedback. Thus, a slight disturbance of the yaw angle can lead to a surging lateral deviation and divergent derailment. Figure 9 shows that at low speed and with a certain yaw suspension, the IRW slightly vibrates and finally converges. The vibrations of \(y\) and \(\Delta\omega\) gradually disappear with a tendency toward zero, but the speed of the lateral convergence toward 0 is quite slow. By contrast, \(\psi\) converges to zero much more quickly. As analyzed in Section 2.5 and shown in Equations (45)-(47), \(\psi\) is 0, while \(y\) slowly converges to 0 during the steady convergent process. Figure 10 shows the simulation results with large yaw suspension parameters, leading to a sharp vibration at the beginning and immediately entering the steady convergent process. Compared with condition V1-S6-C6, adopting large yaw suspension parameters does not result in an intuitively quicker lateral convergence but almost the same lateral  
Figure 8: Lateral dynamics simulation results (V1-S1-C1). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. Figure 9: Lateral dynamics simulation results (V1-S6-C6). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. convergence speed. That is because, in Equation (46), the steady convergent motion does not relate to the yaw suspension parameters. However, the large yaw suspension parameters affect the dynamic process at the beginning and shorten the vibration process before entering the steady convergent process. When the longitudinal speed increases to 20 m/s, the gyroscopic moment also increases and begins to gain the tendency to resist the derailment caused by the gravitational restoring moment. As shown in Figure 11, the yaw angle does not surge in one direction but bounces back after reaching the curve valley. The lateral displacement also tends to bounce back.