# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
## 2 Aerodynamic Simulation and Analysis of Pantograph
### Aerodynamic Load Analysis for a Single Pantograph Passing through a Tunnel
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Resistance [N]** & **Lateral Force [N]** & **Uplift Force [N]** \\ \hline Pantograph head & \(-\)710.62 & \(-\)0.7 & 202.98 \\ Pantograph head bracket & \(-\)640.19 & 0.85 & \(-\)55.3 \\ Upper arm & \(-\)132.61 & \(-\)0.72 & 153.07 \\ Link arm & \(-\)17.74 & \(-\)34.9 & 45.44 \\ Lower arm & \(-\)51.36 & 8.86 & \(-\)147.54 \\ Stabilizer & \(-\)9.18 & 0.89 & \(-\)22.75 \\ Whole & \(-\)2422.5 & \(-\)9.87 & 878.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The resistance, lateral force, and uplift force (average values) of the main components in the knuckle-downstream operating direction at 400 km/h. Figure 8: Pantograph knuckle-downstream and knuckle-upstream operation condition simulation and analysis diagram. (**a**) Knuckle-downstream operating direction. (**b**) Knuckle-upstream operating direction. condition or the knuckle-upstream operating condition, the bow head and the joints where the upper and lower arms connect experience significant negative pressure. The amplitude of surface pressure on the pantograph is similar in both conditions, with higher surface pressure values on the windward side of the base frame before entering and after exiting the tunnel, where the maximum positive pressure is about 4000 Pa, and the maximum negative pressure is approximately \(-\)3200 Pa. After the high-speed train enters the tunnel, the amplitude of the pressure experienced on the pantograph's surface significantly increases, with the maximum positive pressure reaching about 8000 Pa and the maximum negative pressure reaching \(-\)4500 Pa.  
Figure 9: Pantograph knuckle-downstream and knuckle-upstream operation condition simulation and analysis diagram. (**a**) Pantograph knuckle-downstream operating condition before entering the tunnel. (**b**) Pantograph knuckle-upstream operating condition before entering the tunnel. (**c**) Pantograph knuckle-downstream operating condition in the tunnel. (**d**) Pantograph knuckle-upstream operating condition in the tunnel. (**e**) Pantograph knuckle-downstream operating condition after exiting the tunnel. (**f**) Pantograph knuckle-upstream operating condition after exiting the tunnel. Table 2 presents the average values of drag, lateral force, and lift experienced by the main components of the structure during both knuckle-downstream and knuckle-upstream operating conditions. Through a comparative analysis of the three forces exerted on the entire pantograph, it was found that the drag forces in both knuckle-downstream and knuckle-upstream operating conditions are similar, with the drag in the knuckle-downstream condition slightly exceeding that in the closed condition. However, there are significant differences in the lateral forces experienced, with smaller lateral forces in the knuckle-downstream condition and larger ones in the closed condition. Additionally, in the closed condition, the pantograph experiences an upward lift, while in the knuckle-downstream condition, the lift exerted on the pantograph is downward. An analysis of the aerodynamic loads on the main components of the pantograph reveals differences primarily in the upper and lower arms and the upper and lower pull rods. In both the knuckle-downstream and closed operating modes, the direction of lift on these four rods is opposite, which is a major reason for the variance in lift forces experienced by the pantograph under the two operating conditions.