# A Fast Simulation Model of Pantograph-Stitched-Catenary Interaction in Long-Distance Travel
## 3 Validation and Discussion  
### Validation  
#### 3.1.1 Validation Based on the Measurement Data  
The test results are first compared to validate the present model. In 2020, Trafikverket (The Swedish Transport Administration) initiated a project to test whether the SYT7.0/9.8 catenary system (designed train speed 200 km/h, messenger wire tension 7 kN, contact wire tension 9.8 kN) can support high-speed trains running at a maximum speed of 300 km/h, as shown in Figure 3. The railway between Falkoping and Toreboda in Sweden was chosen, and a Swedish Regina train (top speed 300 km/h) with a high-speed pantograph was used for the field test. The test results indicated that the SYT7.0/9.8 catenary system can run the high-speed train at a maximum speed of 302 km/h for only a short time (time of the field test) while maintaining the resulting contact forces at acceptable levels.  
The measurement data from this test are used for validation purposes, acquired from the [PERSON] group in Sweden. The date sample frequency is 500 Hz, and the measurement data are filtered in 0-20 Hz. Parameters of the pantograph-catenary interaction model are listed in [27]. Structural damping is also considered, and the damping ratio of the catenary is 0.02, as used in [27]. Based on the pre-analysis method [28], the reduced stitched catenary model is 180 m long with three spans, \(d_{S}\) is 12 m, and \(K_{S}^{\prime}\) is \(3\times 10^{5}\) N/m. The constant operational speed of 222 km/h is taken from the on-track test for model validation, which corresponds to the designed operation speed of SYT7.0/9.8. Based on the test conditions, the train is considered to run on a straight track. The first 120 modes of the messenger and contact wires are considered, and the number of DOFs of the entire pantograph-catenary interaction model is 722. Based on the key parameters from the experiment, the pantograph uplift force considered in the pantograph model is calculated by  
\[F_{up}=50+0.097V^{2} \tag{9}\]  
The key dynamic characteristic of the pantograph-catenary system is the contact force [11]; thus, it is calculated here to validate the reduced catenary model. The time histories of the contact forces of the pantograph-catenary system and their corresponding spectral analyses at 222 km/h are shown in Figure 4, where the calculation results from the present model are compared with those from the experiment. The measurement data of the contact force are obtained based on the acceleration of the contact strips on the pantograph, and the contact force from both the present model and the measurement data are filtered in a 0-20 Hz span. As shown in Figure 4, the calculation results from the present model are similar to the measurement data at 222 km/h, and the amplitudes of the contact force from the present model are close to those of the measurement data. The spectral analysis  
Figure 3: Schematic of the present pantograph–catenary dynamics test in Sweden: (**a**) test line; (**b**) Swedish Regina train; (**c**) high-speed pantograph with accelerometers and (**d**) installation of the accelerometers.  
results show that the peak frequencies of the spectrum from both the measurement data and the reduced stitched catenary model are in good agreement with each other in the three frequency spans considered (0-2 Hz, 0-5 Hz and 5-20 Hz). The spectral analysis results are further sorted and presented in Table 1. Table 1 shows that the spectral analysis results from the present model are in good agreement at both low frequencies (0-5 Hz) and high frequencies (5-20 Hz).