## 4 Comparison of Different Wheel-Rail Contact Models  
To analyze the impact of different algorithms on wheel-rail contact dynamics, different wheel-rail contact models were established based on the corresponding algorithms. By considering single-point contact, calculating normal compression amount based on vertical penetration and adopting the empirical formula for normal contact stiffness calculation, the corresponding wheel-rail contact model was established. This model was designated as Model 1. Similarly, different wheel-rail contact models were established, as listed in Table 1. The effect of considering multipoint contact versus single-point contact can be clarified by comparing Models 1 and 2. The effect of different algorithms for wheel-rail normal compression amount can be clarified by comparing Models 2 and 3, while the effect of different calculation formulae for the normal contact stiffness can be clarified by comparing Models 3 and 4.  
A single CRH2 motor vehicle passing through the CRTS II slab ballastless track was taken as the example. The train running speed was set to 300 km/h. LM\({}_{\rm A}\) and CHN60 were adopted as the wheel and rail profiles, respectively, as presented in Figure 10.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wheel-Rail Contact Model** & \begin{tabular}{c} **Consideration of Contact** \\ **Point** \\ \end{tabular} & \
\begin{tabular}{c} **Calculation Basis for Normal** \\ **Compression Amount** \\ \end{tabular} &
\begin{tabular}{c} **Algorithm for Normal** \\ **Contact Stiffness** \\ \end{tabular} \\ \hline Model 1 & Single-point contact & Vertical penetration & Empirical formula \\ Model 2 & Multipoint contact & Vertical penetration & Empirical formula \\ Model 3 & Multipoint contact & Normal penetration & Empirical formula \\ Model 4 & Multipoint contact & Normal penetration & Theoretical formula \\ \hline \hline \end{tabular}
\end{table}
Table 1: Setting of different wheel-rail contact models.  
A comparative analysis under ordinary and seismic conditions was conducted. Under the seismic condition, the track irregularity excitation was considered; Figure 11 shows the irregularity samples. Since the wheel-rail dynamic response is mainly influenced by transverse excitations of earthquakes [36], only the transverse excitations were considered in this study. The El-Centro wave, generated by the 6.5 magnitude earthquake that took place in California, United States on 18 May 1957, has distinctive waveform characteristics that make it one of the frequently utilized seismic waves in the field of train-running safety under earthquakes [37; 38]. The acceleration time history of this earthquake wave was obtained from the Pacific Earthquake Engineering Research (PEER) Ground Motion Database, and the peak acceleration was adjusted to 0.3 g as the ground motion input, as shown in Figure 12. For ordinary conditions, only track irregularity excitation was considered.  
Figure 11: Samples of rail irregularities: (**a**) Lateral irregularities; (**b**) Vertical irregularities; (**c**) Torsional irregularities.  
Figure 10: Profiles of the wheel and rail (units: mm): (**a**) wheel profile; (**b**) rail profile.