# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
## 5 Pantograph Flow-Induced Vibration Analysis

Table 8: Contact force and offline rate of pantographs under different speed conditions when the pantograph is in the knuckle-downstream operating condition. Figure 26: Simulation and analysis diagram of time-domain response of pantograph-catenary contact force at 500 km/h (knuckle-downstream operating condition). Analysis reveals that the contact force between the pantograph and the contact wire significantly increases after entering the tunnel compared to before (approximately 2 s prior). With the increase in operating speed, the contact force of the pantograph with the contact wire (maximum contact force, average contact force, and standard deviation of contact force) increases. Additionally, significant mechanical wear occurs between the pantograph carbon slide and the contact wire. The time-domain responses 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 are illustrated in Figures 28-30. In the knuckle-upstream operating condition, the contact forces between the pantograph and the contact wire are presented in Table 9. 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). Figure 28: Simulation and analysis diagram of time-domain response of pantograph-catenary contact force at 400 km/h (knuckle-upstream operating condition). Figure 29: Simulation and analysis diagram of time-domain response of pantograph-catenary contact force at 500 km/h (knuckle-upstream operating condition). Analysis reveals that the contact force between the pantograph and the contact wire significantly increases after entering the tunnel compared to before (approximately 2 s prior). With the increase in operating speed, the contact force of the pantograph with the contact wire (maximum contact force, average contact force, and contact force standard deviation) increases. Additionally, significant mechanical wear occurs between the pantograph carbon slide and the contact wire. Compared to the knuckle-upstream operating condition, the pantograph experiences upward aerodynamic forces, leading to an increase in the maximum contact force, average contact force, and contact force standard deviation of the contact wire in the knuckle-upstream operating condition. This results in an increase in the offline rate, thereby affecting the stability of the current collection. Analysis using simulation software reveals that adjusting the stiffness of the equivalent spring of the pneumatic cushion and the mass of the pantograph head can reduce the contact force between the pantograph and the contact wire during high-speed operation. The larger the stiffness of the equivalent spring of the pneumatic cushion and the mass of the pantograph head, the smaller is the contact force between the pantograph and the contact wire, as shown in Figure 31 (where the X-axis units 1 represent the pantograph head density and spring stiffness in the knuckle-downstream operating condition with a speed of 400 km/h). Figure 30: Simulation and analysis diagram of time-domain response of pantograph-catenary contact force at 600 km/h (knuckle-upstream operating condition). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Maximum Contact** & **Minimum Contact** & **Average Contact** & **Standard** \\  & **Force [N]** & **Force [N]** & **Force [N]** & **Deviation of** \\  & & & **Contact Force [N]** & **Offline Rate [\%]** \\ \hline
400 km/h & 248.87 & 0 & 115.85 & 63.85 & 0.4 \\
450 km/h & 290.12 & 0 & 133.44 & 77.53 & 1.45 \\
500 km/h & 303.67 & 0 & 153.38 & 76.61 & 0.64 \\
600 km/h & 399.85 & 0 & 171.63 & 112.59 & 3.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Contact force and offline rate of pantographs under different speed conditions when the pantograph is in the knuckle-upstream operating condition.