# 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  
This section analyzes the aerodynamic pressure distribution and the aerodynamic loads on various components of the pantograph under the knuckle-upstream operating condition at a speed of 400 km/h as it passes through a tunnel on a single track. Figure 7 presents the surface pressure contours of the pantograph at three different moments: before entering the tunnel, inside the tunnel, and upon exiting the tunnel. It is observed that when the high-speed train operates at a speed of 400 km/h, the windward side of the pantograph primarily experiences positive pressure, while the leeward side is subjected to negative pressure. The pressure difference between these two sides is a significant source of aerodynamic drag on the high-speed pantograph. It is evident that before entering and after exiting the tunnel, the windward surface of the pantograph's base frame experiences higher surface pressure values, with the maximum positive pressure being approximately 4000 Pa and the maximum negative pressure being around \(-\)3200 Pa. Upon entering the tunnel, the amplitude of the pressure experienced on the surface of the pantograph significantly increases, with the maximum positive pressure reaching about 8000 Pa and the maximum negative pressure reaching \(-\)4500 Pa. Through the computational simulation of the flow field, the average values of drag, lateral force, and lift experienced by the main components of the structure during operation can be obtained, as shown in Table 1. It is observed that the drag forces exerted on all structures are primarily concentrated on the bow head and the balancing beam, with the pull rods experiencing smaller forces due to their smaller windward surface area. Figure 7: Pressure cloud image of train pantograph section at 400 km/h under the knuckle-downstream operating condition. (**a**) Before entering the tunnel. (**b**) In the tunnel. (**c**) After exiting the tunnel. The lateral forces on all components are minor, having negligible impact on the overall displacement of the pantograph structure. Among the components, aside from the bow head, upper arm, and upper pull rod, which experience upward lift forces, other structures are subjected to downward lift forces. The bow head, in particular, experiences significant lift, substantially affecting the vertical displacement of the structure. This indicates that the aerodynamic loads on the pantograph are mainly manifested on the bow head. Comparison of Aerodynamic Loads on Low-Carbon High-Speed Pantographs under the Knuckle-Upstream and Knuckle-Downstream Operating Conditions  
This section focuses on comparing the aerodynamic characteristics of the airflow around the pantograph when operating at a speed of 400 km/h in the knuckle-downstream and knuckle-upstream operating conditions, as shown in Figure 8. The analysis aims to highlight the differences in aerodynamic properties of the pantograph under these two operational conditions. Figure 8 presents simulation and analysis diagrams in both the knuckle-downstream and knuckle-upstream operating conditions, along with the coordinate system, where the positive direction of the X-axis is aligned with the direction of the train's movement, and the positive direction of the Z-axis corresponds to the vertical direction of the train. Figure 9 presents the distribution of surface pressure on the windward and leeward sides of the pantograph when operating at a speed of 400 km/h through a tunnel in both knuckle-downstream and knuckle-upstream operating conditions. Surface pressure contour maps are captured at three moments: before entering the tunnel, inside the tunnel, and upon exiting the tunnel. Regardless of whether the knuckle-downstream operating