## 4 Results and Discussion
### Time-Domain Characteristics
#### 4.1.2 Contact Force between Pantograph and Catenary  
Figure 12 and Table 3 show comparison curves of the contact force between the pantograph and catenary and their statistical results, respectively, as the train passes through the tunnel at different speeds. The maximum contact force appears at 360 km/h and minimum contact force at 400 km/h appears. This disparity is obvious especially near the tunnel exit, e.g., where the contact force is 272.87 N near 627.4 m at 360 km/h and is 92.72 N near 636 m at 400 km/h. The differences among different speeds inside the tunnel are larger than those outside the tunnel, which indicates that the tunnel effect is significant and consistent with the objective fact.  
Compared with that at 280 km/h, the maximum, minimum, and mean values of the contact force between the pantograph and catenary at 320 km/h increase and the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Maximum** & **Minimum** & **Mean** & **Standard** & **Standard** & **Mean** \\  & **(N)** & **(N)** & **(N)** & **Deviation** & **Deviation** & **Difference** \\ \hline
280 km/h & 259.666 & \(117.859\) & \(178.09312\) & \(26.84069\) & - \\
320 km/h & 264.556 & \(122.616\) & \(184.08905\) & \(26.12482\) & \(-2.67\%\) & 3.37\% \\
360 km/h & 293.885 & \(127.550\) & \(196.55243\) & \(28.08317\) & \(4.63\%\) & \(10.36\%\) \\
400 km/h & 290.781 & \(92.366\) & \(173.37707\) & \(29.66925\) & \(10.54\%\) & \(-2.65\%\) \\
420 km/h & 292.640 & \(110.554\) & \(186.40273\) & \(29.76878\) & \(10.91\%\) & \(4.67\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical results of contact force between pantograph and catenary passing through tunnel at different speeds.  
Figure 12: Comparison curves of contact force between pantograph and catenary passing through tunnel at different speeds.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Maximum** & **Minimum** & **Mean** & **Standard** & **Standard** & **Mean** \\  & **(N)** & **(N)** & **(N)** & **Deviation** & **Deviation** & **Difference** \\ \hline
280 km/h & 259.666 & \(117.859\) & \(178.09312\) & \(26.84069\) & - \\
320 km/h & 264.556 & \(122.616\) & \(184.08905\) & \(26.12482\) & \(-2.67\%\) & 3.37\% \\
360 km/h & 293.885 & \(127.550\) & \(196.55243\) & \(28.08317\) & \(4.63\%\) & \(10.36\%\) \\
400 km/h & 290.781 & \(92.366\) & \(173.37707\) & \(29.66925\) & \(10.54\%\) & \(-2.65\%\) \\
420 km/h & 292.640 & \(110.554\) & \(186.40273\) & \(29.76878\) & \(10.91\%\) & \(4.67\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical results of contact force between pantograph and catenary passing through tunnel at different speeds.  
standard deviation slightly decreases at a ratio of 2.67%. These changes are beneficial in terms of the stable contact between the pantograph and catenary. Compared with that at 360 km/h, the maximum, minimum, and mean values of the contact force between the pantograph and catenary decrease at 400 km/h and 420 km/h, but the standard deviations increase. Taking 280 km/h as the benchmark, the ratios are 5.91% and 6.28%, respectively; the minimum values decrease to greater extent at ratios of 29.85% and 13.32%, respectively. These changes are detrimental to the stable contact between the pantograph and catenary and in practice could easily separate them. This is the fundamental reason for restricting the speed of the train. When the speed increases from 320 km/h to 360 km/h, the standard deviation increases rapidly from 26.12482 N to 28.08317 N at a ratio of 7.5%. According to the corresponding aerodynamic lift and contact force values, the aerodynamic lift critically affects the contact force between the pantograph and catenary, but it is not the only influencing factor.