# Influence of Metro Track Irregularities on Pantograph Vibration and Its Interaction with Catenary
## 3 Establishment and Validation of the Analysis Model
### Model Validation  
First, to verify the accuracy of the vehicle dynamics model, the track irregularity measured by the inspection vehicle and the actual operating speed were used for simulation calculation. The vertical acceleration of the car body was extracted and compared with the vibration acceleration of the inspection vehicle, as shown in Figure 6.  
As can be seen from Figure 6, the car body acceleration obtained by the simulation is in good agreement with the measured acceleration of the inspection car, and both are in the range of \(-\)0.6\(\sim\)0.6 m/s\({}^{2}\). It can also be seen from the detailed diagram that the simulated results are consistent with the measured result in the trend and the values of the curve, which indicates that the vehicle dynamics model established in the manuscript is reliable.  
Secondly, to verify the accuracy of the model in the calculation of the PC contact, the contact forces during the operation of the vehicle were extracted, as shown in Figure 7. It can be observed that the contact normal forces are basically around 100 N, and the maximum value is around 200 N. The statistical analysis was carried out, and the results were compared with the on-site test data, as shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Vehicle mass & 33.86 t \\ Bogie mass & 3.73 t \\ Wheelset mass & 1.731 t \\ Longitudinal stiffness of the primary suspension & 17.2277 MN/m \\ Lateral stiffness of the primary suspension & 9.2277 MN/m \\ Vertical stiffness of the primary suspension & 0.347 MN/m \\ Longitudinal stiffness of the air spring & 0.162 MN/m \\ Lateral stiffness of the air spring & 0.162 MN/m \\ Vertical stiffness of the air spring & 0.349 MN/m \\ The connection stiffness of the pantograph strip and the & 19.7 kN/m \\ upper frame & 10.6 kN/m \\ The connection stiffness of the upper frame and the & 10.6 kN/m \\ lower frame & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model parameters of the type B metro vehicle operating on Z City Metro Line 1.  
Figure 5: Nonlinear characteristics of the vehicle suspension system. (**a**) Nonlinear characteristics of the primary vertical dampers; (**b**) Nonlinear characteristics of the secondary lateral bumptstop focce.  
It can be observed from Table 2 that the model established in the manuscript is close to the field test results. The deviation is basically within 5%, especially in the average, standard deviation, and maximum contact force of PC.  
The model validation part shows that the pantograph-vehicle-track coupling dynamics model established in the manuscript has high accuracy in the calculation of vehicle dynamics and PC contact, which can provide a basis for subsequent theoretical calculations and analysis.  
In summary, the track-vehicle-pantograph-catenary contact dynamics model was established based on the wheel-rail, vehicle, and pantograph-catenary parameters of the actual vehicle running on Z City Metro Line 1. The nonlinear characteristics of the suspension system were fully considered in the model, and the measured data of the line were used for verification, which can accurately reflect the relationship between the track irregularity, vehicle response, and pantograph-catenary interaction.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Field Test/N** & **Model Results/N** \\ \hline Mean Contact Force & 115.90 & 109.21 \\ Standard Deviation & 18.90 & 18.50 \\ Max. Value & 207.70 & 200.76 \\ Min. Value & 67.88 & 52.77 \\ \hline \hline \end{tabular}
\end{table}
Table 2: PC contact force validation [28].  
Figure 6: Validation of the vehicle dynamics model.  
Figure 7: PC contact force.