# A Fast Simulation Model of Pantograph-Stitched-Catenary Interaction in Long-Distance Travel
## 4 Influence of Train Overdesigned-Speed Operation on Pantograph-Catenary Interaction Dynamics  
After the validation and discussion of the present model, it is further applied to investigate the influence of train overdesign-speed operation on pantograph-catenary interaction dynamics, where the pantograph continuously interacting with the long stitched catenary in a short time is considered. The abovementioned experiment is chosen, where the vehicle operation speed (302 km/h) is higher than the designed top speed of the SYT7.0/9.8 catenary system (200 km/h). The operation time is considered to be 10 s, which corresponds to a 900 m long stitched catenary structure. Based on the present model, the pantograph-catenary interaction at 302 km/h is simulated, and the time histories of the pantograph-catenary contact forces and their corresponding spectral analysis results are shown in Figure 10. The simulation results are also compared with those from the measurement data. Both the measurement data and simulation results are adjusted through a low-pass filter at 0-20 Hz. The statistical results are also compared with those obtained at \(V\) = 200 km/h, as shown in Table 4. Figure 11 and Table 4 show that the pantograph-catenary interaction performance at \(V\) = 302 km/h remains sufficient. Although the present speed is almost 1.5 times greater than the catenary design speed and considering the influence of train-track interaction dynamics, both the simulation results and measurement data of the contact force are acceptable. The positive offset from measurement data is caused by the fact that the catenary in the real line is not idealized and the local irregularity of the catenary causes this offset. The statistical results of the contact force at \(V\) = 302 km/h show only a small increase compared to those at  
Figure 10: Mean contact force and standard deviation of the contact force in the leading pantograph with respect to different \(K^{\prime}_{S}\) values: (**a**) mean contact force and (**b**) standard deviation. Figure 9: Mean contact force and standard deviation of the contact force in the leading pantograph with respect to different \(d_{S}\): (**a**) mean contact force and (**b**) standard deviation. \(V\) = 200 km/h. The actual minimum contact force of the present results is slightly higher than that in standard EN 50318 at \(V\) = 300 km/h (59.2 N with [30 N, 55 N]); however, the actual maximum contact force of 151.2 N is much smaller than that in the standard, which should be [190 N, 225 N]. This is caused by the small tension of the contact wire, which decreases the stiffness of the catenary system. The spectral analysis results show that the contact force is mainly dominated by low-frequency components below 10 Hz. To better understand the stability of the present pantograph-catenary system in higher operation velocity, the influence of different vehicle velocities on the pantograph-catenary interaction above its design speed is then investigated. The time histories of the pantograph-catenary contact forces with respect to different train operation speeds and their minimum contact forces are shown in Figure 11, where the vehicle velocity \(V\) changes from 250 to 320 km/h. Figure 12 shows that the minimum contact forces quickly decrease with increasing \(V\) after \(V\) = 275 km/h. The minimum contact force even decreases from 59.2 N to 0 N with \(V\) increasing from 300 km/h to 312 km/h. This means that the stability of the present pantograph-catenary interaction system is decreased with \(V\) = 300 km/h, and it reaches a critical state at \(V\) = 312 km/h. At the critical state, the pantograph loses contact with the catenary, and the current collection performance obviously decreases. In addition, because \(V\) = 300 km/h is close to 312 km/h and the pantograph-catenary interaction system is highly nonlinear, a small change in the pantograph and catenary parameters can cause unstable dynamic behavior at \(V\) = 300 km/h, such as contact loss.