## 3 Coupling between Aerodynamics and Structural Dynamics
### Verification  
The contact forces between pantograph and catenary at various train speeds were tested on Beijing-Shenyang line, and fitted. The fitted maximum, minimum and mean values at 100 m/s are shown in Table 1. The train was in a stable state during this test, that is, the processes of starting (acceleration) and braking (deceleration) were not included and the line was considered to be sufficiently long. The pantograph simulation was analyzed to verify the proposed coupling method under 360 km/h speed and open-air conditions while considering the influence of the car body on the flow field.  
The contact forces between the pantograph and catenary with coupled aerodynamics and multi-body dynamics (i.e., \"bidirectional coupling\"), aerodynamics loads being taken as known loads and aerodynamics loads being not considered are shown in Figure 10. The initial stage at which contact forces between the pantograph and catenary were calculated was removed to maintain accordance with the test results. The results are shown in Table 1; all proportions listed in the table are based on the fitted results.  
As shown in Figure 10 and Table 1, in the three cases examined here, the change laws of the contact force between the pantograph and catenary are consistent; thus, only the aerodynamic loads change the values. When aerodynamics loads are not considered, the contact forces between the pantograph and catenary are much smaller compared to the other two cases. Aerodynamics loads on the pantograph appear to significantly affect current collection when the train runs at high speed. In the case of open air, compared with aerodynamic loads as known loads, the standard deviation of the contact force is larger when aerodynamics and multi-body dynamics are coupled. This indicates that contact force fluctuates substantially and the current collection quality is poor. The coupling calculation results are closer to the test results than the non-coupling results regardless of the maximum, minimum, or mean.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Maximum** & **Minimum** & **Mean** & **Standard Deviation** & \
\begin{tabular}{c} **Mean** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Minimum** \\ **Error** \\ \end{tabular} \\ \hline Bidirectional coupling & 254.264 & 126.475 & 183.55598 & 25.55415 & \(-\)0.05\% & 3.92\% \\ Wind loads as known loads & 255.9772 & 129.57878 & 182.58699 & 25.02823 & \(-\)0.58\% & 6.47\% \\ No wind loads & 216.15146 & 119.43517 & 162.41813 & 21.661 & 11.56\% & \(-\)11.56\% \\ Fitted results & 242.667 & 121.704 & 183.65 & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical results of contact force between pantograph and catenary simulated and fitted under open air at 360 km/h.  
Figure 9: Hybrid meshing and grid motion method.  
According to EN50318, the verification standard of the dynamic coupling simulation between the pantograph and catenary, the mean of contact force \(F_{\rm m}\leq 0.00097\times 360^{2}+70=195.712N\) and the standard deviation of contact force \(\sigma_{\rm max}<0.3F_{\rm m}=0.3\times 195.712=58.7136N\). Accordingly, the fitted simulation results and experimental results satisfy the relevant requirements.