# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
## 5 Pantograph Flow-Induced Vibration Analysis
Additionally, prior to entering the tunnel (approximately 2 s), the displacement amplitudes of each component are noticeably smaller compared to after entering the tunnel, consistent with the phenomenon of a sharp increase in aerodynamic loads experienced by the pantograph after entering the tunnel. The displacement responses of the pantograph under the knuckle-upstream operating condition at speeds of 400 km/h, 500 km/h, and 600 km/h are depicted in Figures 22-24. Figure 21: Simulation and analysis diagram of displacement response of pantograph measuring points at 600 km/h (knuckle-downstream operating condition). Figure 20: Simulation and analysis diagram of displacement response of pantograph measuring points at 500 km/h (knuckle-downstream operating condition). It can be observed that with the increase in train operating speed, the displacement gradually increases under the closed-state condition of the pantograph. The maximum values reach 3.97 cm, 4.89 cm, 5.19 cm, and 7.33 cm, respectively, which align with the aerodynamic simulation results indicating that higher operating speeds result in greater aerodynamic lift forces acting on the pantograph. Additionally, prior to entering the tunnel (approximately 2 s), the displacement amplitudes of each component are noticeably smaller compared to after entering the tunnel, consistent with the phenomenon of a sharp increase in aerodynamic loads experienced by the pantograph after entering the tunnel. Figure 23: Simulation and analysis diagram of displacement response of pantograph measuring points at 500 km/h (knuckle-upstream operating condition). Figure 22: Simulation and analysis diagram of displacement response of pantograph measuring points at 400 km/h (knuckle-upstream operating condition). Compared to the knuckle-downstream operating condition, when the pantograph operates in the knuckle-upstream operating condition, the displacement of the pantograph head slightly increases. The increase in bow head displacement may have adverse effects on the stability of train operation, energy transmission efficiency, and bow net lifespan. Excessive displacement may cause instability and a decrease in the electrical energy transmission efficiency of trains during high-speed operation. Comparison of Contact Force Results of Flow-Induced Vibration Simulation at Different Speeds under Knuckle-Downstream and Knuckle-Upstream Operating Conditions  
The time-domain response of the contact force between the pantograph and the contact wire in the knuckle-downstream operating condition under operating speeds of 400 km/h, 500 km/h, and 600 km/h obtained from simulations is illustrated in Figures 25-27. Figure 24: Simulation and analysis diagram of displacement response of pantograph measuring points at 600 km/h (knuckle-upstream operating condition). Figure 25: Simulation and analysis diagram of time-domain response of pantograph-catenary contact force at 400 km/h (knuckle-downstream operating condition). Under various speed conditions in the knuckle-downstream operating condition, the contact forces between the pantograph and the contact wire are presented in Table 8. The average contact forces of the contact wire are all less than \(0.00097v^{2}+F_{0}\) (where \(F_{0}\) represents the static contact force of the contact wire), which complies with the requirements outlined in the referenced literature and standards [40]. Figure 19:0 Simulation and analysis diagram of time-domain response of pantograph-catenary contact force at 600 km/h (knuckle-downstream operating condition). \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Maximum Contact** & **Minimum Contact** & **Average Contact** & **Standard** & **Offine Rate [\%]** \\  & **Force [N]** & **Force [N]** & **Force [N]** & **Deviation of** & **Contact Force [N]** \\ \hline
400 km/h & 167.86 & 49.04 & 97.98 & 24.90 & 0 \\
450 km/h & 207.57 & 50.79 & 129.20 & 29.59 & 0 \\
500 km/h & 334.92 & 25.68 & 281.71 & 71.86 & 0 \\
600 km/h & 384.95 & 54.56 & 205.73 & 65.43 & 0 \\ \hline \end{tabular}
\end{table}