# A Fast Simulation Model of Pantograph-Stitched-Catenary Interaction in Long-Distance Travel  
Like Pan  
1 China Academy of Railway Sciences Co., Ltd., Beijing 100081, China; [EMAIL_ADDRESS]  
[PERSON]  
2 Faculty of Transportation Engineering, Kunming University of Science and Technology, Kunming 650504, China; [EMAIL_ADDRESS] (C.X. ); le  
Many scholars have contributed to pantograph-catenary dynamic studies with low vehicle operation speed and a short catenary model, including the basic pantograph-catenary interaction modeling and simulation [6; 7; 8; 9], the influence of multi-pantograph operation on system dynamic responses [10; 11; 12; 13], pantograph and catenary fatigue problem [14; 15; 16], and the system's stability under environmental influences (like wind and ice) [4; 17; 18]. In these studies, the finite element method (FEM) [19; 20; 21; 22; 23] and modal superposition method (MSM) [1; 24; 25; 26; 27] are mainly used, and they are proven to be accurate in studying these problems. However, as mentioned before, in the high-speed operation case, the catenary can be very long, and both the MSM and FEM must model this very long catenary system. This will greatly increase the degrees of freedom (DOF) of the whole model and decrease the computational efficiency. In 2017, [PERSON] and [PERSON] [1] found that the vibration of the catenary structure caused by the pantograph-catenary interaction mainly concentrates in about 2-3 spans due to structural damping, and they developed a real-time catenary model to efficiently simulate the pantograph-catenary interaction in the hardware-in-the-loop case. In this model, the long catenary is reduced to 3-5 spans around the pantograph, and this small reduced catenary becomes the basis of the real-time catenary model. [PERSON] et al. [28] also developed a reduced catenary model to efficiently simulate the pantograph-catenary interaction, where the long catenary systems are reduced to small regions around the moving pantograph. The pantograph and the small area around the pantograph where most of the vibration is located are moving, and the catenary itself keeps the longitude static. Thus, there is a relative movement between the small certain area and the catenary structure, and the arbitrary Lagrange-Eulerian method (ALE method) is used to describe the movement of the catenary in this small moving area. The MSM is further used to model this small area, and the reduced catenary model is finally formulated. Based on this model, the influence of track structure maintenance on pantograph-catenary interaction dynamics is analyzed. [PERSON] et al. [29] further developed a mesh moving method to efficiently solve the pantograph-catenary interaction dynamic responses, where only the abovementioned small area of the catenary around the pantograph needs to be meshed in detail and coupled with a coarser fixed mesh domain of the whole catenary structure. [PERSON] et al. [30] further investigated the length of the effective vibration area of the catenary to decide the length of the reduced catenary model, where the traditional MSM was used to model the pantograph-catenary interaction system, and the vibration energy of the catenary was calculated to determine the length of the effective vibration area. The abovementioned new methods greatly decrease the number of DOFs of the catenary model and have proven to be highly efficient and accurate in solving pantograph-catenary interaction dynamic responses with long catenary structures. However, the existing methods only consider simple catenary systems, and stitched catenary systems are ignored. This is mainly caused by the application of the MSM, where the stitch wire connects with the messenger wire at the end of every two neighboring spans, and the shape function of this structure is difficult to express. While the FEM can be used to model a stitched catenary system, it is difficult to combine it with the abovementioned new  
Figure 1: Schematic of the pantograph–catenary interaction with a long travel distance. modeling methods.