# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
## 2 Aerodynamic Simulation and Analysis of Pantograph
### Comparison of Aerodynamic Loads on Pantographs at Different Operating Speeds  
This section is dedicated to comparing the aerodynamic characteristics of the airflow around the pantograph under the knuckle-upstream operating condition at different speeds of 400 km/h, 450 km/h, 500 km/h, and 600 km/h, analyzing the aerodynamic properties of the pantograph across these four scenarios.  
Figure 10 presents the surface pressure distribution on both the windward and leeward sides of the pantograph under the knuckle-upstream operating condition as it passes through a tunnel at speeds of 400 km/h, 450 km/h, 500 km/h, and 600 km/h, capturing the surface pressure contour maps of the pantograph at the same moment in time. It is observed that with the increase in operating speed, the pressure experienced on the surface of the pantograph significantly increases, although the distribution of surface pressure on the pantograph does not undergo substantial changes.  
Tables 3-5, along with Figure 11, provide the average values of drag, lateral force, and lift experienced by the main components of the pantograph at the same moment during operation at different speeds. It is observed that as the operating speed increases, the drag force exerted on the structure significantly increases. The lateral forces on the pantograph also increase with speed, but since lateral forces are relatively small, they do not have a substantial impact on the overall displacement of the pantograph structure. However, the lift experienced by the components of the pantograph shows a notable increase with higher operating speeds, which has a considerable effect on the vertical displacement of the structure.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{2}{c}{**Resistance [N]**} & \multicolumn{2}{c}{**Lateral Force [N]**} & \multicolumn{2}{c}{**Uplift Force [N]**} \\ \cline{2-7}  & **Knuckle-Downstream** & **Knuckle-Upstream** & **Knuckle-Downstream** & **Knuckle-Upstream** & **Knuckle-Downstream** & **Knuckle-Upstream** \\ \hline Pantograph head & \(-697.92\) & \(-647.63\) & \(-18.34\) & \(-3.3\) & \(212.89\) & \(156.89\) \\ Pantograph Head bracket & \(-618.06\) & \(-627.06\) & \(13.22\) & \(5.96\) & \(-39.81\) & \(58.11\) \\ Upper arm & \(-136.2\) & \(-138.72\) & \(-0.97\) & \(-30.38\) & \(154.03\) & \(-43.16\) \\ Link arm & \(-21.47\) & \(-15.49\) & \(-45.01\) & \(-26.03\) & \(52.93\) & \(-39.73\) \\ Lower arm & \(-31.01\) & \(-29.94\) & \(3.35\) & \(-68.5\) & \(-86.26\) & \(89.45\) \\ Stabilizer & \(-8.01\) & \(-53.5\) & \(1.59\) & \(-0.12\) & \(-4.72\) & \(40.39\) \\ Whole & \(-2785.67\) & \(-2722.62\) & \(2.66\) & \(-145.58\) & \(-386.01\) & \(264.73\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The resistance, lateral force, and uplift force (average values) of the main components under the knuckle-upstream and knuckle-downstream operating conditions at 400 km/h.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{4}{c}{**Lateral Force [N]**} \\ \cline{2-5}  & **400 km/h** & **450 km/h** & **500 km/h** & **600 km/h** \\ \hline Pantograph head & \(-3.3\) & \(-4.57\) & \(-8.13\) & \(-11.92\) \\ Pantograph head bracket & \(5.96\) & \(7.59\) & \(8.95\) & \(11.9\) \\ Upper arm & \(-30.38\) & \(-36.55\) & \(-46.01\) & \(-74.06\) \\ Link arm & \(-26.03\) & \(-32.76\) & \(-40.01\) & \(-55.54\) \\ Lower arm & \(-68.5\) & \(-87.57\) & \(-107.75\) & \(-145.36\) \\ Stabilizer & \(-0.12\) & \(-0.18\) & \(-0.45\) & \(-2.88\) \\ Whole & \(-145.58\) & \(-183.73\) & \(-231.32\) & \(-332.04\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The average lateral force of pantograph under the knuckle-upstream operating condition at different running speeds.  
Figure 10: Pressure cloud image of train pantograph section at different operating speeds. (**a**) 400 km/h. (**b**) 450 km/h. (**c**) 500 km/h. (**d**) 600 km/h.