## 3 Results
### Case 1--Effect of OOR Amplitude on Track Dynamics  
Figure 5 illustrates the von Mises equivalent stress in track components derived from the simulation for the case of a sixth-order polygonal wheel with an OOR amplitude of 0.09 mm passing the midsection of the track at 300 km/h. In this figure, panel 1 depicts the von Mises equivalent stress in the rail between two adjacent rail fastenings with a constant spacing of 0.65 m. Panels 2, 3, and 4 illustrate the von Mises equivalent stress in the concrete slab, CA layer, and support layer, respectively. Figure 5 serves as an example of typical results obtained from the FE analysis. It can be seen from Figure 5 that the peak von Mises equivalent stress in the rail occurs midway between two adjacent rail fastenings. Therefore, only the track responses from the middle cross-section between two rail fastenings are displayed; the position of the track fasteners is not displayed, due to space limitations. The track dynamics, namely, the stresses, displacements, and acceleration, were extracted at the time of maximum acceleration, and were measured from the FE-nodes between two adjacent rail fastenings on the slab, CA, and support top layer. Five selected positions over a rail cross-section are denoted as A, B, C, D, and E in Figure 6. The responses of the rail vibration acceleration at a train speed of 300 km/h in Case 1 are illustrated \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Case**} & **OOR Amplitude** & **Harmonic** & **Running Speed** \\  & **(mm)** & **Order** & **(km-h\({}^{-1}\))** \\ \hline Case 1: Effect of OOR amplitude on track dynamics & 0.01–0.12 & 6 & 300 \\ Case 2: Effect of harmonic order on track dynamics & 0.03 & 3–21 & 300 \\ Case 3: Effect of running speed on track dynamics & 0.03 & 6 & 200–350 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation cases. Figure 5: Von Mises equivalent stresses in structural components of the track (Pa): (**a**) von Mises equivalent stress in the rail; (**b**) von Mises equivalent stressin the concrete slab layer; (**c**) von Mises equivalent stress in the CA layer; (**d**) von Mises equivalent stress in the support layer. in Figure 7. The time histories of the vertical acceleration at A, B, C, D, and E generally exhibit a sinusoidal shape, similar to the periodic radial deviation from the nominal radius. Figure 6: Selected positions on rail cross-section. Figure 7: Time history of vertical vibration acceleration at points A–E on the rail for various out-of-roundness (OOR) amplitudes at a train speed of 300 km/h. Figure 8 shows the differences in acceleration, displacement, and von Mises equivalent stress between positions A-E on the rail cross-section. Figure 8a indicates that the vertical rail acceleration increases proportionately as the OOR amplitude of the polygonal wheel increases from 0.01 to 0.12 mm. The rail acceleration at A, B, C, D, and E for an OOR amplitude of 0.12 mm is approximately 5.24, 6.94, 7.59, 6.73, and 4.49 times greater, respectively, than those for an OOR amplitude of 0.01 mm. This is because the impact load caused by polygonized wheels with an OOR amplitude of 0.12 mm can reach up to 120 kN, which is significant. This amount of load can increase the amplitude of acceleration, resulting in the collision of the edge of the polygon with the crown of the rail, so considerable attention should be paid to such wheels. From Figure 8b, we can see that there are only small differences between the displacement responses at different positions on the rail cross-section. As the OOR amplitude varies from 0.01 to 0.12 mm, the displacement at A, B, C, D, and E increases by 52.26%, 52.32%, 52.43%, 52.52%, and 52.56%, respectively. There seems to be a linear relationship between the displacement and the OOR amplitude. In Figure 8c, the same trend is observed: The stress at A, B, C, D, and E increases by 49.80%, 38.16%, 34.86%, 39.22%, and 47.02%, respectively, as the OOR amplitude of the polygonal wheel increases from 0.01 to 0.12 mm.