The pantograph strip interface involves many physical phenomena. Temperature evolution is one of them. This problem includes various thermal flux and sources. More specifically, due to the train motion, a moving zigzag heat source occurs. This paper deals with a thermal 2D Alternating Direction Implicit (ADI) numerical method for temperature estimations in the train pantograph carbon strip, the aims being a better wear problems anticipation and the creation of a preventive maintenance. For that, an electrical model is coupled to the thermal one to take into account all Joule effects. The ADI strategy enables a significant computation time reduction against most classical resolution methods. Besides, the model involves two mathematical processes: the first one is an appropriate variable transform which induces a fixed surface heat production, while the second is based on locally refined meshes. Various numerical tests are presented and discussed in order to show the accuracy of the scheme. From a physical point of view, the results are much interesting. Further investigations, depending on the different parameters, should lead us to predict the strip critical thermal phases.

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The performance of the pantograph–catenary system is very significant in supplying reliable electrical power for the operation of trains. Many problems arise due to the increase in temperature inside the pantograph strip. More research works have been done to study the temperature extrema of the system but it is quite difficult to obtain the experimental values during a real-time train operation. Moreover, performing experimental tests needs a representative test bench of the system or a real train. This is challenging owing to the time and availability of materials and taking into account the number of physical phenomena to control and measure. To address this problem, the authors of this study present an electro-thermal modeling tool. The heat sources which characterize the system are analyzed to generate a heat equation formulation. This equation is solved with the finite differences numerical method in order to obtain the temperature distribution in the pantograph strip. In addition, some specifications such as computation time or required memory are taken into account. More precisely, mathematical and numerical optimizations are proposed to improve these specifications. The tool is validated by comparing the simulated results with the experimental tests obtained from a test bench located at POLIMI (Polytechnico Di Milano, Milan). Finally, thermal interpretations as well as relative gap analyses are done in different situations.