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In article there are fluid flow mathematical models at the UV-sterilizer with concentric pipes installed in modernized water supply system of passenger car allowing to determine the velocity field of the rotational velocity component and assess the degree of attenuation depending on the chamber disinfection geometry, the inlet pressure in the water system, and fluid properties. There are exact solutions of the Navier-Stokes equations for a rotating fluid between fixed cylinder of infinite length and limited fictitious determined rotating lids provided Poiseuille axisymmetric flow. The decision explicitly contains the product of cylindrical Bessel functions and hyperbolic functions.

The article presents a method of calculation of the thermal state of the pantograph head. The density of the suspension zigzag distribution, taking into account a number of assumptions, has replaced the contact wire position function in the plan. Results of calculating the temperature of the pantograph head at different width of the zigzag of the typical suspension, including zero, are presented. The influence of sinusoidal and tangential contact suspensions on the temperature distribution of the pantograph head is estimated.

In the article there is the method of calculating the loss of water pressure in the water system of passenger cars, equipped with a cleaning system as a series of two filters installed and the flow of ultraviolet sterilizer screw design. There is the results of calculation of losses in the various water systems of cars with the maximum and minimum charging time and the water pressure in the water system station. The rational geometric parameters of the decontamination chamber flow ultraviolet sterilizer of the conditions to ensure complete filling of the tank car parking in the minimum time with minimum pressure of the water supply system of the station. The value of head loss does not exceed the nameplate values typical designs. The geometry of the sterilizer allows you to integrate the device into the car. Its design values are taken to develop the prototype of a UV sterilizer successfully tested. To be able to determine the loss of water pressure chamber decontamination sterilizer screw coil design is presented with a rectangular cross section, «wound» on the cylinder. Local loss of one turn calculated using the reference formula proposed by G.N. Abramovich.

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.

A mathematical model of thermal processes (dynamic) contact current collector with contact suspension (in motion), which allows to estimate the temperature distribution of heating the current collector during movement. The experimental evaluation of the proposed cooling device performance is given. The thermal model of the current collector in motion mode has been verified.

The article deals with the organizational features of the Federal law of the Russian Federation on "transportation security compliance requirements to ensure transport security objects (buildings, structures), not related to transport infrastructure objects and located on land adjacent to transport infrastructure objects in the security zones of land transport. Systematized the activities required for the implementation of such transport facilities. In the work used techniques of systems analysis, comparative method, methods of theoretical knowledge (formalisation), obshhelogicheskie methods and techniques of research (analysis, synthesis, classification, the analogy).

The article outlines modern approaches to determining the maximum permissible continuous current of current collectors when stopping and in motion. The features of techniques that reliably take into account operational factors when conducting tests in laboratory conditions are considered. A mathematical model is given for studying the distribution of current load in emergency mode of breaking a current-carrying shunt.

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.