## 3 Multibody Simulations
### Security of Train Curve Passing at a Constant Speed  
Figure 10 shows the influence of curve radius \(R\) and wind speed (\(V_{w}\)) at different vehicle speeds (\(V_{c}\)) on the unloading factor. When \(V_{c}\) is less than 250 km/h, the unloading factor changes a little when the radius increases, and after \(V_{c}\) is greater than 250 km/h, the unloading factor slowly decreases as the radius increases. When the \(V_{w}\) is 15 m/s or less, the vehicle is safe in the range of 0-350 km/h. When the \(V_{w}\) reaches 30 m/s and the \(V_{c}\) reaches 200 km/h, the unloading factor has exceeded the safety limit value of 0.8, and the possibility of the train capsizing is greatly increased; when the \(V_{w}\) is 25 m/s, and when the \(V_{c}\) exceeds 250 km/h, there is a risk of overturning when the train curve passes; when the \(V_{w}\) is 20 m/s, when the \(V_{c}\) reaches 350 km/h, and the radius is less than 5000 m, the unloading factor has exceeded the safety limit value 0.8. When the \(V_{c}\) is greater than 250 km/h and the \(V_{w}\) is greater than 30 m/s, the train wheel sets have been derailed and should stop driving.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Track Radius(m)** & \(V\) **(km/h)** & **4500** & **5000** & **6000** & **7000** & **8000** & **9000** \\ \hline Spiral transition curve & & 340 & 300 & 250 & 220 & 190 & 170 \\ \begin{tabular}{c} \end{tabular} & 100–250 & 200 & 200 & 200 & 200 & 200 \\ \begin{tabular}{c} \end{tabular} & 105 & 105 & 105 & 105 & 105 & 105 \\ \hline Spiral transition curve & & 510 & 440 & 410 & 350 & 300 & 270 \\ \begin{tabular}{c} \end{tabular} & 300 & 200 & 200 & 200 & 200 & 200 \\ \begin{tabular}{c} \end{tabular} & 151 & 151 & 151 & 151 & 151 & 151 \\ \hline Spiral transition curve & & 590 & 590 & 590 & 590 & 530 & 470 \\ \
\begin{tabular}{c} \end{tabular} & 350 & 200 & 200 & 200 & 200 & 200 \\
\begin{tabular}{c} \end{tabular} & 175 & 175 & 175 & 175 & 175 & 175 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters for curve lines.  
As shown in Figures 11 and 12, the relationship between the safety vehicle speed and wind speed under the same radius can be obtained. The maximum vehicle speed does not exceed 350 km/h. As can be seen in Table 3, as the radius increases, the safe speed of vehicle curve passing increases, but the difference between R7000 and R9000 is not much. Additionally, the maximum safe speed is reduced when considering the IVS. For example, When the wind speed is 25 m/s and the radius is 9000 m, 7000 m, and 4500 m, considering the IVS will reduce the maximum safety speed by 14 km/h, 8 km/h, and 18 km/h, respectively. When the wind speed is 20 m/s and the radius is 4500 m, the case of fixed connection is safe, but considering the IVS will limit the safe speed to 330 km/h. Moreover, considering the IVS has little influence on the safety speed of the vehicle when the wind speed is 30 m/s, probably due to the safety speed being small in both cases.  
Figure 11: The relationship between the unloading factor with Vw and Vc at different radii in the case of considering the IVS. (**a**) R4500 m. (**b**) R7000 m. (**c**) R9000 m.  
Figure 10: The relationship between different curve radii and different wind speeds and unloading factor under 100–350 km/h.