# Influence of Metro Track Irregularities on Pantograph Vibration and Its Interaction with Catenary
## 6 Conclusions  
In this manuscript, aiming at the problem of rapid wear of the pantograph strip in Z City, a vehicle-track-pantograph coupling dynamic model was established to carry out the dynamic calculation and simulation, and the transmission of the vibration in the track irregularity-vehicle vibration-pantograph sequence was studied and analyzed. Then, optimization suggestions for the maintenance of the track irregularity were put forward. Finally, by evaluating the optimization suggestions, their rationality and effectiveness were confirmed. The main conclusions are as follows:  
1. The track spectrum values of Metro Line 1 in Z City are significantly higher than those of the American level 6 spectra, the German high-interference spectrum, and the Beijing Metro spectrum, indicating that the overall track smoothness is poor. There are multiple broadband peaks in the irregularity, such as three wavelengths of 3-4 m, 6-8 m, and 9-16 m, indicating that the irregularities of the specific wavelengths are the main reasons for the deterioration of the track geometry.
2. The two-stage suspension system of the vehicle can attenuate the vibration caused by some short-wavelength irregularities, but the irregularities of the 3-4 m and 9-16 m wavelengths can have a significant impact on the vehicle, aggravating pantograph vibration and PC contact force.
3. The vertical and lateral contact force of the pantograph and catenary is larger in the three wavelength ranges of 3-4 m, 6-8 m, and 9-16 m, and the track irregularity is larger in the two wavelength ranges of 3-4 m and 9-16 m. There is a direct mapping relationship between the spectra.
4. Comparing the spectral characteristics and pantograph contact force under the irregularities of Z City Metro Line 1 and the Beijing Metro, it is further determined that the vibration and friction of the pantograph are exacerbated due to the excessive amplitudes of the wavelengths of 3-4 m and 9-16 m.
5. Optimization suggestions for controlling the irregularity in the wavelengths of 3-4 m and 9-16 m were proposed, and the dynamic calculation was carried out. The results show that the PC contact force and friction work can be significantly reduced by using the optimization measures, which can contribute to the reduction in the wear of the pantograph strip.  
B.A.: conceptualization, software, methodology, writing--original draft preparation, validation; P.W.: conceptualization, writing--review and editing; S.M.: investigation, formal analysis; Z.M.: software, formal analysis, investigation; Y.Z.: supervision, writing--review and editing; W.Z.: validation, investigation. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Project 2021 YFB2601000, the National Natural Science Foundation of China, grant number 51878661, 51908031, and the Science and Technology Program of Zhejiang Communications Investment Group Co., Ltd. (202102).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Maximum Value (J)** & **Mean Value (J)** & **Standard Deviation** \\ \hline Before Maintenance & 1.139 & 0.052 & 0.103 \\ Maintenance 1 & 0.258 & 0.009 & 0.024 \\ Maintenance 2 & 0.100 & 0.002 & 0.006 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical values of the acceleration of pantograph strip.