# A Fast Simulation Model of Pantograph-Stitched-Catenary Interaction in Long-Distance Travel
## 5 Conclusions  
In this study, a reduced pantograph-stitched-catenary interaction model is developed based on the existing reduced catenary model to efficiently investigate the dynamic characteristics of pantograph-stitched-catenary interactions during long-distance travel. Note that the function of the stitch wire is similar to that of the messenger wire, which also has tension and carries the contact wire through the dropper. The stitch wire is also supported by the messenger wire through the clamp. Therefore, in the present model, the stitch wire and catenary suspension are simplified into a part of the messenger wire supported by a couple of spring-damper elements, where the distance of these two spring-damper elements and the stiffness and damping of each spring-damping element are chosen to ensure  
Figure 14: Minimum contact forces with respect to different contact wire tensions and vehicle velocities. Figure 13: Time histories of the pantograph–catenary contact force and its minimum contact force with respect to different contact wire tensions and \(V\): (**a**) \(V=320\) km/h and (**b**) \(V=350\) km/h. that the stiffness of the stitch wire model is equal to the original stiffness. Because only a small area instead of the whole long stitched catenary needs to be modeled, the number of DOFs of the pantograph-catenary interaction system decreases, and the dynamic responses of the pantograph-catenary interaction can be efficiently calculated. The present model is validated with measurement data from an on-track test of the Swedish Regina train and EN 50318 standard, and then, it is used to investigate the dynamic response of the existing pantograph-catenary interaction system under train overdesigned-speed operation. Based on the obtained calculation results, the following conclusions are drawn:  
1. The proposed reduced pantograph-stitched-catenary model can efficiently and accurately investigate the dynamic behavior of pantograph-stitched-catenary interactions. When calculating the pantograph-catenary-interaction dynamic responses, the calculation time of the present model is only 1/7 of that of the MSM with a train operation distance of 1200 m. This greatly benefits the investigation of the long-term service evolution of the pantograph-stitched-catenary system, such as the wear rate calculation in pantograph contact strip wear investigations. 2. When the train operation speed is higher than the designed top speed of the SYT7.0/9.8 catenary system and up to 300 km/h, the pantograph-catenary interaction dynamic performance of the present pantograph-catenary system is still acceptable, and the risk of contact loss is small. However, when \(V\) = 300 km/h, the present pantograph-catenary system is not stable and is close to its critical state, which means that it can result in contact loss with a small change in the pantograph-catenary system parameters. Thus, it cannot operate at \(V\) = 300 km/h in the long term. To increase the maximum operation speed of the existing SYT7.0/9.8 catenary system to 300 km/h, the contact wire tension should be increased to 15.8 kN. Finally, the limitations of the proposed dynamic model are that only the main dynamic characteristics of the pantograph-catenary interaction can be simulated and investigated, and the detailed dynamic responses of the components in the catenary system cannot be fully presented, especially those of the stitch wire. In our future works, a FEM-based reduced catenary model will be formulated to accurately and efficiently investigate both the main dynamic characteristics of the pantograph-catenary interaction and the dynamics of key components. Software, C.X. ; Validation, Y.X., Z.L. and C.X. ; Formal analysis, Y.X. ; Investigation, L.P.; Resources, Z.L. ; Data curation, Z.L. ; Writing--original draft, L.P.; Writing--review & editing, Y.X. ; Project administration, J.L. ; Funding acquisition, L.P. and J.L. All authors have read and agreed to the published version of the manuscript.