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The article presents an improved mathematical model of the thermal state of the pantograph head for calculating the temperature distribution when interacting with different catenary with a double contact wire. The model takes into account the unevenness of the pantograph contact pressure on the wires along the suspension span and between them, allows using the databases of the car-laboratory for testing the contact network, calculating the thermal conditions of the skid on various sections of electrified Railways, including transients between them. The paper presents graphs of the zigzag distribution density of the contact wire of the Moscow - Saint Petersburg high-speed line, and defines the transient and steady state thermal states of the pantograph head when the pantograph interacts with them.

Resistive heating of the pantograph head due to the flow of traction current through the conductive elements of the upper node, has an uneven distribution along the frame structure and depends on the location of the contact wire on the insert. The aim of the work is to develop a mathematical model for calculating power losses in the pantograph panhead, allowing to estimate its value, taking into account the zigzag of the contact wire during the movement of electric rolling stock. The subject of the study is the pantograph panhead. The paper gives an example of calculating the frame skid of a pantograph equipped with carbon strips. Experimental studies of the current distribution over the shunts of the panhead depending on the position of the contact wire were carried out in February 2021 in the laboratory "Designs of contact networks, power lines and current collection devices" using a complex for testing current collection devices. The calculation of the heating power of the panhead is determined by the Joule-Lenz law. The results of the calculation showed that the maximum heating power is observed when the contact wire is in the middle of the panhead, while the places of the greatest losses located along its edges are above the places where the shunts are attached. The model makes it possible to obtain a functional dependence of the heating value along the panhead. The obtained results of the skid heating power distribution make it possible to supplement the complex model of the thermal state of the pantograph developed at the Omsk State Transport University with the participation of the authors of the article. The versatility of the developed model makes it possible to investigate various zigzags of the contact wire and evaluate the effect on the distribution of traction current along the panhead, depending on the location of the shunts and their number.