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In this paper the authors propose to consider the peculiarities of making mathematical models of rolling stock and its dynamic behavior when driving on irregular resilience railway line in the longitudinal direction. We present a qualitative and empirical analyzes of longitudinal resilience railway railway. In conclusion, given the conclusion, on the basis of its proposed further consideration of mathematical aspects of the above solutions of systems of differential equations of motion of the rolling stock on irregular resilience way.

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.

The article is devoted to the accounting problem of longitudinal non-equal-elasticity of railway track which led to forced vibrations for non-spring mass of rolling stock are interacting with multiplicative perturbation, that is increasing the amplitude of the bouncing wheel pair, or reducing it. This depends on the phase relationship between these influences .

In accordance with the long-term development program of JSC Russian Railways until 2025, it is planned to increase the level of economic connectivity of the territory of Russia by expanding the network of high-speed and high-speed transportation. This involves not only the construction of new high-speed highways, but also the modernization of the structures of individual components of rolling stock, as well as the introduction of energy and resource-saving technologies. The use of contact elements with an extended service life is one of the most economical and least costly ways to ensure reliable, economical and environmentally friendly transmission of electricity to rolling stock. An increase in the service life of the current collector element can be achieved, among other things, by reducing wear by the correct selection of contact pair elements, both from the point of view of their tribocompatibility and the ability to ensure high quality current collection. A methodology for conducting experimental studies of contact pairs of current collection devices has been developed and successfully tested at OSTU, which involves bench tests for each pair of contact materials “contact insert - contact wire” in order to determine their optimal combination to reduce wear and increase resource. Estimation of the amount of wear and prediction of the life of the elements of the contact pair is carried out including using mathematical models. However, the use of existing models for predicting wear under conditions of high-speed movement is not accurate enough due to the lack of consideration of the aerodynamic effects and the speed of the rolling stock on current collection processes. This article discusses the improvement of the mechanical component of the wear model of the elements of contact pairs of current collection devices in high-speed conditions. The graphs of the mechanical wear of the contact elements are obtained experimentally and as a result of calculation by a mathematical model. The analysis of the graphs allows us to conclude that it is possible to use an improved mathematical model for modeling the mechanical component of the wear process of the elements of contact pairs with a maximum error value of not more than 5 %.

The article devoted to results of the longitudinal multiplicative perturbation effect from railway track in relation to rolling stock.There is the technique for finding of difference type Raman resonances areas,which based on the theory of division in slow and fast components for motion of dynamic system.It proves a fact that the RMS-velocity for motion of the train is not a specific numerical value,but that is an area for which the width depends on the multiplicative factor driving

The article describes the general principles of the computational model of the traction power supply DC Railway to assess the potential energy recuperative braking, as well as ways of approbation the resulting model to determine its adequacy.

The article presents the main requirements for the development of traction motors commutation control digital device and the results of the development and testing of this device on the test bench. Justified the expediency of application of the input highpass filter when the power of the testing traction engine from the thyristor converter. Presented the technique of processing the diagnostic signal from bipolar brushes to filter out noise of different physical nature.

In general, improvement of methods for electrical calculations aimed at increasing the accuracy of the results. One of the ways to improve the methods of calculation is the account in the calculation of the various factors that affect the accuracy of calculation of the traction power system parameters. This article describes an approach aimed at improving the method of calculation in the electrical part to improve the accuracy by changing the algorithm for calculating and accounting for a number of additional factors.

The article shows the relevance of applying the method of mutual test load of asynchronous traction motors of railway rolling stock. On the basis of the recommendations of existing standards in testing of asynchronous motors is made up of a sequence of acceptance testing of asynchronous traction motors provided in the form of an algorithm. In line with the scheme proposed for testing procedures on the use of the basic equipment of the circuit. The analysis of the main types of tests, the comparison of the classical means for testing the functionality of the inverters eliminated the need for additional DC sources in determining the resistance of the stator windings, additional brake and step-down transformers during short circuit and experience to carry out simultaneous testing of two induction motors increased speed at the stand of mutual load.

The article proposes an approach to improve the efficiency of using the automatic train guidance system based on instantaneous traction calculations using the actual movement parameters according to current measurements of on-board systems of electric locomotives. A critical analysis of scientific research on the improvement of auto-guidance systems for freight mainline electric locomotives based on modern technologies and machine learning algorithms, neural networks has been carried out. As a rule, all existing approaches to determining the optimal train driving modes are based on the application of traction calculation rules with the empirical setting of movement resistances and other factors without taking into account the real influence of the external environment. The results of comparison of traction calculations in the section of the West Siberian test site according to the current rules and in the KORTES program with the actual data of the on-board measurement systems of the 2ES6 series electric locomotive are presented. Based on the data deciphered from the recorders of motion parameters of electric locomotives of the 2ES6 series, the laws of control of the excitation current at rheostatic and running positions in the traction mode are investigated. The possibility of using the measured data of the on-board systems of electric locomotives to determine the parameters of the train, including the torque of the traction motors, the traction force of the electric locomotive sections, the actual total resistance to movement, inertial properties, etc., is substantiated. The calculation of these parameters for the traction mode is performed. The concept of equivalent mass is introduced and expressions are presented for determining the parameters of a train based on the equation of motion in the form of small increments of measured and calculated data. The obtained results of determining the parameters of the train based on instantaneous traction calculations and data of current measurements of the on-board systems of electric locomotives showed statistical stability and can be used in real time for automatic train guidance systems, providing an increase in the accuracy of determining control actions, taking into account the actual influence of the external environment and increasing the efficiency of using the automatic guidance system for freight trains. locomotives in general.

The main subject of this article is consideration of the possibility of applying in electric circuit of the diesel locomotive hybrid power sourse, thats consists of diesel internal combustion engine and traction energy storage (li-ion accumulator battery). The main target of this work is to describe the effectiveness of the applying Li-ion energy storage in traction and diesel internal combusion engine start modes. At the same time, the regular used lead-acit battery is excluded from the locomotive circuit and replaced by a traction accumulator battery. By using numerical simulation methods, the article considers the possibility of starting a diesel internal combustion engine with a traction li-ion accumulator battery and possibility of the increasing the torque of electric traction motors and technical characteristics of the locomotive when the li-ion traction accumutalor battery is turned on as an additional source of energy. The relevance of the results is to get data about increasing carrying mass of the train when using a hybvid energy source on a diesel locomotive. The results of the work demonstrate the effectiveness of the use of a traction battery it traction and engine start modes, while improving the performance of the locomotive. The conclusions of the work contain an analysis of the results of mathematical modeling of the use of a traction battery.

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.

The purpose of this article is to create mathematical models for a comprehensive assessment of the quality of repairs of collector-brush assembly drive motor vehicles, including an assessment of mechanical and switching components. The objectives of this study are to determine the linguistic variables based on the generated set of diagnostic features, including "beating of the working surface of the collector", "RMS heights collector lamellae", "amplitude of the first harmonic component of the profile of the collector", "the amplitude of the second harmonic component of the profile of the collector" "RMS heights collector slat excluding the first and second harmonic components", "minimum value of the second derivative of the profile of the collector function", "standard deviation of the second derivative of the profile of the reservoir function," "effective value of the higher harmonic components of the collector profile features" that have the greatest diagnostic value and determination of their membership functions, as well as the definition of the complex index of quality of repair and its components: complex index of quality of machining and integrated commutation quality index in the collector-brush unit of the traction motor. Solution of tasks performed using the mathematical apparatus of fuzzy logic through the use of statistical processing of the results of these pilot studies and the calculation of the diagnostic value of the measured and calculated parameters. As a result of the research formed the mathematical model of quality repair in the space of selected features using the apparatus of fuzzy logic for calculating the value of the proposed integrated indicators for arbitrary values of diagnostic parameters. The results may be used to control the quality of repairs of collector-brush assembly of traction motors of the rolling stock.

Electric power installation of a special self-propelled rolling stock used in the power supply divisions is considered in the paper; the expediency of its use for the analysis of the main energy indices, in particular, the evaluation of the efficiency of electro-hydro-mechanical units at separate and joint operation, is shown. To assess the energy efficiency, an integrated efficiency factor has been proposed that allows to account the energy parameters of electrical installations operating in various modes. Recommendations have been given to increase the power factor of electrical installations.

The article considers the current situation regarding the organization of control over the use of traction and energy resources of JSC «Russian Railways». The main provisions of the proposed method are stated. The influence factors on the specific electric power consumption of electric locomotives of series 2ES6 and VL10, as well as the evaluation of the quality of the constructed models of multiple nonlinear regression were estimated. New scientifically grounded technological solutions and developments are proposed that allow to reduce the specific consumption and unproductive losses of electric energy within the boundaries of the railway accounting areas.

The article presents the main results of experimental studies within the boundaries of the Fadino - Novoseletsk, Novoseletsk - Strela interstitial zones of the Entrance - Irtysh section. As a result of the research identified problems that currently hinder the online monitoring of operational parameters of the electric rolling stock (EPS) and power supply devices: a lack of data on the work of the traction substations, the presence of EPS without registration motion parameters (RAPS), the lack of process data collection with RAP, the lack of a single source and process for obtaining data, insufficient memory storage device of cartridge, lack of data latch on the locomotive in General, lack a set of fixed parameters, non-constant sampling of parameter fixing, insufficiently detailed final documentation, imperfect software for exporting data from cartridges and lack of binding to global time. Shown the possibility of joining data from different automated systems of JSC "RZD" and measuring systems OSTU, which will allow us to estimate the losses in the traction network, the expense on own needs of electric rolling stock , the electric power consumption for traction and return of electric energy to contact network, as well as move forward with implementation of predictive control operation modes of the electric rolling stock and power infrastructure and Railways in a changing environment in the transportation process, to ensure the best conditions for the realization of tractive effort, regenerative braking, set train schedules, including in case of critical restrictions on the part of the power supply system, preventing train traffic from stopping.

The article describes the design of a universal measuring pantograph, designed to obtain during the test trips sets of accurate and adequate information on the quality of current collection due to the possibility of modeling parameters and characteristics of advanced domestic and foreign current collectors, mounted on a modern electric rolling stock. Presented the results of his testing at the West-Siberian railway.

The article describes the types of irrational electric power losses for train traction and sets the annual planning levels of their improvement. Represented the basic methods of irrational electric power losses determination which are currently used in JSC "Russian Railways". Shown an example of the irrational losses determining algorithm in case of making up for train delay and given its description. Formulated technical results of the proposed method for determining the irrational electric power losses .

The article sets the task of determining the level of dynamic loading in the «trolley-leash-traction motor» subsystem to reduce the dynamic impact in the «locomotive-path» system. The model of vertical vibrations of traction rolling stock, obtained on the basis of the Lagrange equation of the second kind, in the form of a system of fourteen differential equations allows us to estimate the loading of locomotive units in operation, integrated using the MathCAD application package. The approximation of random disturbances using the spectral density of the path irregularity of Professor A. I. Belyaev is chosen as the spectral density of random disturbances. A more detailed design scheme of the crew has been compiled and in order to simplify the calculation within the engineering error, a single-mass discrete model of the path is used. Entering symmetric coordinates allows us to obtain from the original system of differential equations a simplified system with characteristic equations with simple roots, therefore, the natural oscillation frequencies of the bouncing of the body, trolley and wheelset will be determined with minimal error. The transfer function is determined by Kramer's formulas. With the help of a computer, the values are calculated and graphs of the amplitude-frequency characteristics of vertical movements, maximum accelerations of the body, trolley, traction motor and wheelset of the electric locomotive in question are constructed. A comparative analysis of the calculation results and empirical data is carried out. Based on a comparative analysis, it can be argued that the considered mathematical model of vibrations of the electric locomotive 2ES6 «Sinara» is adequate and allows determining the dynamic loading of the locomotive for the entire range of operating speeds. The task of changing the existing design of the suspension system of the traction electric motor of the electric locomotive in question and the mathematical analysis of the vibrations of its nodes in further research is set.

The aim of this article is results representing of work focused to automation of electrical machines armature coils diagnostics process based on wave response method. Technical decisions used in development of mobile device for insulation diagnostics via wave response method described. Techniques of generalized diagnostics coefficient calculation described. Article presents test results of NB436V and NB-431P auxiliary machines installed VL-10 electromotive.

In article the issues of electric power imbalance in train traction research are considered, including the method providing an estimation of the contribution of imbalance components to its total value with the possibility of their separation between the participants of the transportation process: the electrification and power supply service, the automatics and telemechanics service, the directorates of locomotive traction and motorized rolling stock. Described method allows in more detail to analyze the factors that affected the change in the components of imbalance and further develop organizational and technical measures to reduce it.

The problems of optimization of organization of maintenance and repair of locomotives. The article presents new approaches for calculating the norms of spare parts and materials. Models of vehicle systems consisting of a fleet of operated locomotives are given, taking into account all conditions.

The article deals with the issue of improving the energy efficiency of DC and AC electric locomotives operated at the enterprises of JSC “Russian Railways». The main goals and objectives of the development program and energy strategy of JSC «Russian Railways» are analyzed and briefly considered. In accordance with these tasks, the relevance of scientific research in the field of improving the energy efficiency of electric locomotives is substantiated. The current data on traction rolling stock, on modern traction resource management systems and on Russian and foreign scientific research in the field of energy efficiency are analyzed. As a result of the analysis, it was found that most of the studies are aimed at studying the influence of key operational factors on energy efficiency indicators, so, in this case, on the specific power consumption for train traction. However, the reverse question has been poorly studied - the selection of the train mass and the technical speed on the basis of a preliminary assessment of the specific power consumption for train traction by analyzing the statistical data of trips on a certain section of the railway. The purpose of this study is to assess the possibility and develop a method for determining the optimal values of the key parameters of the operation of electric freight locomotives in order to achieve maximum operational efficiency in relation to them according to the criterion of energy efficiency. Two models were created in the program «Complex of calculations of traction power supply» (CORTES) - for DC and AC electric locomotives, describing the dependence of the energy efficiency indicator (specific power consumption for train traction) on operational indicators, such as the train mass and the technical speed. The initial data for further modeling were obtained by modeling trips on a conditional site.

This paper deals with the determination of the coordinates of the rolling stock for the railway station. Proposed and justified the use of mathematical tools of conformal mappings.

The article presents an analysis of the failures of the mechanical components of the mainline electric locomotives 2ES6 «Sinara» in operation at the landfill of the West Siberian Railway, the causes and consequences of failures of the most vulnerable nodes are determined. The analysis of failures of the mechanical components showed that a significant share of them falls on the components of the wheel-motor unit of the locomotive. The analysis of the design features of the crew part is carried out. The main structural difference of suspension is the absence of leaf springs in the axle box stage, which were widely used on electric locomotives of previous generations. In the body stage, helical springs (Flexicoil) are used instead of the cradle suspension. The connection of the traction motor with the trolley frame is a pendulum. The suspension of the traction motor to the trolley frame is carried out through a leash. When considering the vibrations of railway carriages, it is customary to represent the locomotive and the track as a single mechanical system. The task of forming a mathematical model of the «electric locomotive - path» system is set and a mathematical model of vertical vibrations of an electric locomotive is formed taking into account the dynamics of wheel-motor blocks based on the Lagrange equation of the second kind in the form of a matrix equation, which allows us to assess the loading of mechanical components in operation. The mathematical model represents a system of differential equations in which six equations determine the fluctuations of the bouncing and galloping of the body and trolleys, four - the galloping of wheel-motor blocks, four - the bouncing of wheel pairs together with the reduced mass of the track. The obtained mathematical model makes it possible to determine the level of dynamic loading of the components of the mechanical part of the electric locomotive 2ES6 «Sinara» by integrating the matrix equation using the MathCAD application package.