# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
## 5 Pantograph Flow-Induced Vibration Analysis  
During the operation of high-speed trains, the vibration of the pantograph structure has a significant impact on the stable current collection of high-speed trains and is also affected by the air. Flow-induced vibration is also an important factor affecting the stability of pantograph current collection. In this chapter, the aerodynamic load characteristics obtained above are combined with the results of modal analysis. The modal superposition method is used to analyze the time-domain response of the pantograph of a high-speed train under the action of aerodynamic loads. This article maps the fluid forces obtained from pneumatic simulation to the components of a fully flexible pantograph model, and studies the flow induced vibration effect of high-speed trains during operation due to the action of fluid forces. Selected typical measurement points of the pantograph are analyzed for the characteristics of flow-induced vibration response at different operating speeds. The selected measurement points include: the middle part of the pantograph head, the middle part of the head support bracket, the middle part of the upper arm rod, the middle part of the pull rod, the connection part of the upper and lower arm rods, the middle part of the lower arm rod, and the middle part of the balance rod, as illustrated in Figure 18.  
The modal superposition method is utilized to analyze the time-domain displacement response of multiple measurement points on the pantograph under external aerodynamic loads. During the simulation process, the contact wire is equivalently represented as a spring. The time-domain response of the contact force between the pantograph and the contact wire under different conditions can be considered as the product of the spring stiffness and the displacement response of the pantograph head. We analyze the maximum, minimum, average values, and standard deviation of the contact force, as well as assess the offline rate of the pantograph during train operation. Comparison of Displacement Results of Flow-Induced Vibration Simulation at Different Speeds under Knuckle-Downstream and Knuckle-Upstream Operating Condition  
The displacement of the pantograph represents the contact state between the pantograph head and the overhead contact system. The stability of the bow displacement is crucial for the normal operation of the pantograph. If the displacement is unstable, it may lead to poor contact or even circuit disconnection. Stable displacement helps improve the efficiency of electrical energy transmission. Abnormal displacement may cause poor contact between the pantograph and the overhead contact line, thereby affecting the safety of train operation. Therefore, the simulation of pantograph displacement is of great significance. The displacement responses of the pantograph under knuckle-downstream operating condition at speeds of 400 km/h, 500 km/h, and 600 km/h are depicted in Figures 19-21. Figure 19: Simulation and analysis diagram of displacement response of pantograph measuring points at 400 km/h (knuckle-downstream operating condition). Figure 18: Simulation and analysis diagram of displacement response measurement point selection (Points 1–7 represent respectively carbon contact strips, pantograph head bracket, upper arm, hinge point, link arm, lower arm and stabilizer). It can be observed that with the increase in train operating speed, the displacement gradually increases under knuckle-downstream operating condition of the pantograph. The maximum values reach 2.17 cm, 3.06 cm, 5.89 cm, and 7.00 cm, respectively, which align with the aerodynamic simulation results, indicating that higher operating speeds result in greater aerodynamic lift forces acting on the pantograph.