# Influence of Metro Track Irregularities on Pantograph Vibration and Its Interaction with Catenary
## 5 Optimization Suggestions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Maximum Value (N)**} & \multicolumn{2}{c}{**Effective Value (N)**} & \multicolumn{2}{c}{**Standard Deviation**} \\ \cline{2-7}  & **Normal** & **Friction** & **Normal** & **Friction** & **Normal** & **Friction** \\ \hline Before & 201.5 & 48.72 & 95.35 & 9.68 & 13.40 & 6.70 \\ Maintenance & 163.2 & 20.73 & 95.79 & 4.05 & 8.67 & 2.54 \\ Maintenance 2 & 151.2 & 11.42 & 96.70 & 1.90 & 6.34 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical values of the acceleration of pantograph strip. Figure 14: The effect of the maintenance suggestions (on vibration): (**a**) vertical vibration; (**b**) lateral vibration. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{2}{c}{**Maximum Value**} & \multicolumn{2}{c}{**Effective Value**} \\ \cline{2-5}  & \multicolumn{2}{c}{**(m/s\({}^{2}\))**} & \multicolumn{2}{c}{**(m/s\({}^{2}\))**} \\ \cline{2-5}  & **Vertical** & **Lateral** & **Vertical** & **Lateral** \\ \hline Before & 0.57 & _7.77_ & 0.096 & 1.03 \\ Maintenance & 0.51 & 2.92 & 0.073 & 0.51 \\ Maintenance 2 & 0.49 & 2.84 & 0.058 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical values of the acceleration of pantograph strip. It can be observed from Figure 15 that after controlling the irregularity with specific wavelengths, the PC normal contact forces are more concentrated at their mean value of 110 N, and the lateral forces are more concentrated at 0. The maximum and minimum values are both improved, indicating that the PC contact is more stable. The statistical values in Table 4 show that the maintenance suggestions have a great influence on the PC lateral friction. In the case of maintenance 1, the maximum lateral friction force can be reduced by 57%, the effective value can be reduced by 58%, and the standard deviation can be reduced by 62%. Considering that the operation problem is the rapid wear of the pantograph strip, the friction work is used to approximate the wear of the pantograph in the manuscript. The PC friction work of the whole section under the three calculation conditions is compared, as shown in Figure 16.  
According to Figure 16, it can be seen that under the initial condition, the friction work has many sharp peaks; however, these peaks are significantly reduced under the maintenance conditions. For example, when t = 79 s, the friction work is 1.14 J under the initial condition, while that under the maintenance 1 and 2 conditions is 0.26 J and 0.10 J, respectively. It can be observed from Figure 16 that under the maintenance conditions, the friction work decreases in the whole frequency domain, especially at the two peaks. The statistical values of friction work are shown in Table 5.  
Figure 16: The effect of the maintenance suggestions (frictional work). (**a**) In time domain; (**b**) In frequency domain. Figure 15: The effect of the maintenance suggestions (on contact force): (**a**) normal contact force; (**b**) friction force. The PC friction work can be reduced to the degree of 90% or more in the parameter of maximum value and the mean value under the maintenance condition, and the overall value of the friction work is closer to 0, indicating that the suggestions proposed in this paper can have a positive effect on the friction control of the pantograph strip.