# The Influence of Track Irregularity in Front of the Turnout on the Dynamic Performance of Vehicles
## 2 Numerical Approach
### Turnout Model  
The turnout model is an elastic track model based on the standard CHN60-1100-1:18 turnout design for high-speed railways (the curve radius is 1100 m, and the turnout angle is 1:18). The total length of the turnout is 69 m, and a straight line of 100 m is established in front of the turnout.  
The nominal rail profile changes continuously along the turnout. Based on the critical rail sections of the turnout, as shown in Figure 4a,b, longitudinal interpolation is performed along the rail, which interpolates variable rail cross-sections between the various profiles in the longitudinal direction employing Bezier curves [29]. The numbers of cross-sections in the switch and crossing panels are 72 and 48, respectively, and the variable cross-section lengths of the switch and crossing panels are 21.3 and 14.1 m, respectively [30]. This ensures a smooth transition from one rail profile to the next profile.  
Figure 2: The topological graph of the vehicle model.  
The switch and the stock rails are modeled as two separate bodies, obtained by defining separate sets of wheel-rail pairs. The position and angle of the switch and stock rail in the lateral and longitudinal directions can be set independently, so the relative position between the two rails can be simulated. The stock rail and switch rail models are shown in Figure 4c.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Vehicle mass (kg) & \(3.376\times 10^{4}\) \\ The rolling moment of inertia of the car body (kg\(\cdot\)m\({}^{2}\)) & \(1.094\times 10^{5}\) \\ The nodding moment of inertia of the car body (kg\(\cdot\)m\({}^{2}\)) & \(1.655\times 10^{6}\) \\ The yawing moment of inertia of the car body (kg\(\cdot\)m\({}^{2}\)) & \(1.561\times 10^{6}\) \\ \multicolumn{2}{c}{Bogie frame mass (kg)} & \(2.400\times 10^{3}\) \\ The rolling moment of inertia of the bogie (kg\(\cdot\)m\({}^{2}\)) & \(1.944\times 10^{3}\) \\ The nodding moment of inertia of the bogie (kg\(\cdot\)m\({}^{2}\)) & \(1.314\times 10^{3}\) \\ The yawing moment of inertia of the bogie (kg\(\cdot\)m\({}^{2}\)) & \(2.400\times 10^{3}\) \\ Wheelset mass (kg) & \(1.850\times 10^{3}\) \\ The rolling moment of inertia of the wheelset (kg\(\cdot\)m\({}^{2}\)) & \(0.967\times 10^{3}\) \\ The nodding moment of inertia of the wheelset (kg\(\cdot\)m\({}^{2}\)) & \(0.123\times 10^{3}\) \\ The yawing moment of inertia of the wheelset (kg\(\cdot\)m\({}^{2}\)) & \(0.967\times 10^{3}\) \\ Longitudinal stiffness of primary spring (N/m) & \(9.800\times 10^{5}\) \\ Lateral stiffness of primary spring (N/m) & \(9.800\times 10^{5}\) \\ Vertical stiffness of primary spring (N/m) & \(1.176\times 10^{6}\) \\ Vertical damping of primary spring (N\(\cdot\)s/m) & \(1.000\times 10^{4}\) \\ Longitudinal stiffness of secondary spring (N/m) & \(1.600\times 10^{5}\) \\ Lateral stiffness of secondary spring (N/m) & \(1.600\times 10^{5}\) \\ Vertical stiffness of secondary spring (N/m) & \(2.400\times 10^{5}\) \\ Lateral damping of secondary spring (N\(\cdot\)s/m) & \(4.000\times 10^{4}\) \\ Vertical damping of secondary spring (N\(\cdot\)s/m) & \(2.000\times 10^{4}\) \\ Nominal rolling radius of the wheel (m) & \(0.43\) \\ Distance between the mass centers of the bogies (m) & \(17.50\) \\ Distance of bogie fixed axes (m) & \(2.50\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Vehicle parameters.  
Figure 3: Nonlinear suspension stiffness: (**a**) the anti-yaw damper and (**b**) the lateral stop.