# Influence of Metro Track Irregularities on Pantograph Vibration and Its Interaction with Catenary
## 2 Analysis of the Measured Excitations  
The analysis of the track irregularity of the whole line and the comparison with typical irregularities is given in this section to evaluate the track geometry. Figure 1 shows the whole line track irregularity measured by the inspection vehicle of Metro Line 1 in Z City (with the speed of 15\(\sim\)60 km/h; the average speed is approximately 43 km/h, and the sampling interval is 0.266 m/point).  
It can be observed from Figure 1c,d that there are periodic irregularities with wavelengths of 12.5 m and 25 m, and the amplitude of \(-\)6\(\sim\)7 mm existing in the level irregularity; there are periodic irregularities with wavelengths of 10-15 m, and the amplitude of \(-\)10-8 mm existing in the alignment irregularity. These characteristics are prevalent in the whole line of Metro Line 1 in Z City.  
To analyze the periodic characteristics of the track geometry more comprehensively, the track geometry power spectral density (PSD) is calculated, as shown in Figure 2.  
There are several spectral peaks in the level irregularities, indicating the existence of periodic irregularities. The wavelength range of the first spectral peak is 5.6-41.6 m with the largest component of 12.5-13.6 m, which may be caused by the periodic irregularities of the 25 m welded rail. The wavelength range of the second spectral peak is 2.5-4.5 m, and the peak wavelength is 3.6 m. The wavelength range of the third spectral peak is 1.78-2.38 m, and its peak value is located at the wavelength of 2.1 m. Considering that the irregularity with a shorter wavelength has less influence on the car body and pantograph, this manuscript does not focus on them.  
The PSD of the alignment irregularity is similar to that of the level irregularities. There are also several periodic irregularities. The frequency bands where the three largest peaks are located are 10-20 m, 2.7-4.5 m, and 1.78-2.38 m, which are basically the same as the level irregularities.  
Figure 1: The time-domain characteristics of the track geometries: (**a**) the time-history diagram of level irregularity; (**b**) the time-history diagram of alignment irregularity; (**c**) the feature of the level irregularity; (**d**) the feature of the alignment irregularity.  
Figure 2: Spectral characteristics of the track geometries: (**a**) the PSD of the level irregularity; (**b**) the PSD of the alignment irregularity.  
The track irregularity spectrum of Metro Line 1 in Z City is compared with other typical irregularity spectra, as shown in Figure 3, including the American 6-level spectrum [24], German high-interference spectrum [25], and the measured irregularity spectrum of the Beijing subway.  
The values of the track irregularity spectrum of Metro Line 1 in Z City are significantly higher than others, indicating that the overall track smoothness is poor. The positions where the larger spectral values exist are mainly the broadband peaks, which are also the reason for the deterioration in the smoothness of Metro Line 1 in Z City.  
Taking the measured irregularity spectrum of the Beijing subway as the comparison target, the deterioration wavelength range can be obtained: 6.5-18 m, 2.8-4 m, and 1.7-2.5 m. These medium- and long-wavelength irregularities may have a greater impact on vehicle vibration, leading to the vibration and wear increase of the pantograph. To verify the influence and determine the influencing degree of these abnormal irregularities, this manuscript establishes a pantograph-vehicle-track coupled dynamic model to study the influence of the measured irregularities on the vibration of vehicle and pantograph.