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It is shown that dynamic systems, «rolling stock - way» due to the unevenness of the path on length should be described by ordinary differential equations with variable coefficients, the method of analyzing differential equations with constant, variable and random coefficients describing the movement of electric locomotive nodes when they move along an uneven path. In the transition to a new paradigm, we can talk about areas of dynamic instability, which in the case of simple parametric resonances develop near critical frequencies, but this is not one specific point, but a zone that expands with increasing coefficients of parametric excitation. In addition, the presence of friction in the system does not guarantee the limitation of resonant amplitudes. The effect of parametric arousal factors on the width of the dynamic instability zone has been established. There are many other features in the behavior of differential equations with variable coefficients, so it is impossible to replace the action of unevenness with some equivalent geometric irregularity, since at this moment there is no exact solution to the problem with which to compare the results of approximate mathematical models.

This article describes different ways of mass-burned fraction curve calculation, shows the Pugachev’s combustion rate equation structure, method of this equation factors selection and simulating versus experimental data matching.

He method of researching the dynamic properties of the railway crew in the action on it harmonic parametric perturbation, caused by the changing rigidity of the base of the rail, is set out. For such differential equations there are no regular methods of solving them, moreover, their exact solutions are not known at present, so they are used by approaching methods. A two-degree mechanical system with a harmonic parametric perturbation described by a system of ordinary homogeneous differential equations is considered. One of the hard-bone parameters is a function of time and varies from 2000 to 3000 N/m. To calculate the boundaries of dynamic instability (parametric resonance) a method of generalized Hill definers is used, which does not require the introduction of small parameters. The area of interaction of parametrically excited and forced vibrations has been determined.

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 assesses the influencing factors for electric power consumption for the needs of the electric locomotives of the 2ES6 series, statistical models for normalizing the electric power consumption for own power have been generated, and their quality has been assessed.

Considered forced oscillations of four-axle vehicle with dual spring suspension. It is obtained that the movement system with six degrees of freedom with sufficient accuracy can be represented by a system with two degrees of freedom. Therefore, the vehicle body has two degrees of freedom: lateral skidding and wobbling, Bouncing and galloping trucks will be neglected. The total number of degrees of freedom of the model equal to two. The method, which leads to a closed solution of the forced oscillation. Defined. That tends and to (n = 1, 2,…), the amplitude of the oscillations will be unlimited. Therefore, the parameters k1, k2 and T must be selected on the basis of required values of amplitudes. As a result of research compiled by the differential equation of motion of the system and obtained analytical solution for the case of external piecewise constant driving force.

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 subject of the study is the fuel utilization system of a diesel power plant as a diesel locomo-tive or other vehicle main lead, which is a complex technical system consisting of actual diesel in-ternal combustion engine, fuel lines and low pressure fuel processing and high pressure line includ-ing various elements of liquid fuels consumption dosing and control. The aim of our study was to analyze the system functioning, to determine the dynamic proper-ties and the nature of changes in the internal parameters of the system as a whole. To achieve the goal the system analysis methods were used. The processes of complex technical system operation were interpreted by means of the continuous linear stationary deterministic model of the list of others. For this particular model the body of mathematics developed on the basis of linear differential equations with constant coefficients is the most complete one. The chosen mathematical model was presented by us in the first stage in the form of a finite graph as a subgraph of obtained earlier generalized model which had both methodological and theoretical foundation. In accordance with the methodology of the systematic approach the graph model of the diesel power plant fuel utilization system operation was described in relation to major significant factors affecting the system parameters transformation dynamics. Given the complexity of the of fuel ignition and combustion mechanism located in the diesel engine cylinder, the use of the techniques of the modern automated control theory is adopted for numerical processes simulation with the system described in terms of the said theory. The criteria of efficiency, mechanical loads and thermal loads levels were chosen as the fuel utilization system internal state variables. Taking into account the Pareto principle the most important efficiency criterion components were chosen for the analysis; and the system of differential equations of the efficiency dynamics in the form of three balance equations was created. The factual description of the included equations allowed us to derive preliminary qualitative conclusions about the dynamic properties of the internal criteria: controllability, observability and stability of the fuel utilization system. The differential equations system parameters linearizing procedure and the introduction of small deviations allowed us to obtain the dynamic mathematical model of the fuel and air transfor-mation in the diesel engine heat cylinder. As the result of transformations we have obtained the equations presented in the form of the matrices, which allowed us to conclude that the process of the fuel and air transformation in the cylinder is controllable, the system is asymptotically stable, and the process is stochastic with the presence of perturbing parameters influenced by the engine's variable modes of operation. The further research areas have been suggested, and the practical results have been predicted: the creation of optimal (in terms of efficiency) control system with the technical solution in the form of the optimal controller (in relation to fuel consumption).

The article presents the results of modeling the force fields in the elements of the wheel-motor unit of the electric locomotive 2ES10. The mathematical model is obtained on the basis of the Lagrange equations of the ΙΙ kind. A design scheme for the study of the dynamic behavior of the wheel-motor unit is presented. Expressions for the deflection of the elastic elements of the traction motor suspension, elastic and dissipative forces are given. A method for determining the vector force field at the articulation site of the bracket and thrust suspension TEM is proposed.

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.

At present, the “Afrosiyob” high-speed passenger train runs on the Tashkent - Samarkand, Samarkand - Karshi, Samarkand - Bukhara sections. In the near future, it is planned to launch freight trains on sections of the Bukhara-Misken route. On high-speed double - track sections Tashkent - Samarkand, Samarkand-Navаi, the movement of freight trains is combined with passenger trains. Which, in turn, negatively affects the throughput of stations and hauls. In connection with this, the actual issue is the movement of freight trains on these sections. Additional research is needed to increase the capacity of sections where freight and high-speed passenger trains run. The article considers options for the aerodynamic interaction of freight and high - speed passenger trains moving in one or the opposite direction. At the same time, the idea of the safe organization of freight trains during the movement of high-speed passenger trains was put forward. As a result of this study, the possibilities of carrying cargo trains in one direction or in the opposite direction are determined by ensuring the safety of movement on two-way parcels in which high-speed “Afrosiyob” high - speed electric trains travel. This makes it possible to develop recommendations for more effective use of the ability of parcels to conduct trains. When calculating the aerodynamic interaction, scientific ideas put forward by scientists from Europe, the USA, Russia and other countries were analyzed. Methods for solving the Navier - Stokes equations using existing programming models are described.

This article presents an algorithm and a method for calculating power flow of an open electric network with a voltage of 6-35 kV, taking into account the temperature dependence of active resistances. Calculation of the electric and thermal conditions of the electric network is carried out with a joint solution of the equations. The determination of stresses in the nodes is carried out using the inverse matrix of the nodal and intrinsic conductivities. The inverse matrix of nodal and intrinsic conductivities is determined based on the well-known direct Jordan-Gauss method. The equation of the heat balance of the wire used to calculate the actual temperature is solved numerically. Convective heat transfer is recorded only for forced convection, because wires of overhead power lines with a voltage of 6 kV and higher are located on various types of poles, at a height of at least 10 m. This fact allows us to abandon the use of formulas for natural convection and use expressions only for forced convection. Accounting for solar radiation in the presented algorithm is possible on the basis of two methods: simplified and considered in the standard of PJSC FGC UES, which allows you to take into account the actual location of the wire relative to the north. Using the test circuit as an example, the steady-state mode was calculated taking into account the temperature dependence of the active resistances. The results of a numerical experiment are presented, confirming the operability of the developed algorithm. The refinement in determining active power losses with and without taking into account the heating factor for the considered circuit is about 13%. Verification of the algorithm that implements the method of calculating the steady state (SS) of an open electrical network of a medium voltage class taking into account the temperature dependence of active resistances showed that in technically acceptable modes the developed algorithm has good accuracy in comparison with the RastrWin3 software package.

An approach to the evaluation the actual energy savings achieved when implementing service contracts energy, based on the development of mathematical models of power consumption, taking into account the impact of production and climatic factors. An example of the calculation of the ac-tual efficiency of introduction of energy-saving devices at the Sverdlovsk railway is presented

The algorithm of constructing the confidence interval of the model estimating the reliability of liner-tamping-straightening machines. The basis for assessing the reliability of transport-technological process initiated the concept of reliability, as the probability of reaching a liner-tamping-straightening machines ultimate goal in the manufacture of track work. One of the main factors reliability of track machines is the utilization of their time and availability to work. The guidelines are outdated factor data used during the working time that must be updated, as the machines are constantly being improved. According to the results of field testing of the liner-tamping-straightening machines was established database of values of the coefficients of availability and utilization over time. The data base values were recorded, the last two stages of verification: logical and mathematical. In the article the example of constructing a confidence interval values of the coefficient of use of time depending on the complex index of reliability: availability. To create the model formed the sample values from the database. After sampling in accordance with GOST R 8.736-2011 State system for ensuring the uniformity of measurements. The direct measurement repeated. Methods of processing the results of measurements were tested for their adherence to the law of normal distribution using the goodness of fit Pearson. Then built a model of the utilization of time depending on the availability liner-tamping-straightening machines (regression equation) and the confidence interval of the model. The proposed model works liner-tamping-straightening machines allow us to predict the main complex organizational and technological performance of a specific machine at the design stage of technological processes of track work. This method is versatile and can be used to assess the technical reliability of any machine systems, complete sets and individual cars.

In transit shortly stacking forest freights on specialized platforms-hlystovozakh consignors have problems with development of technical documentation on placement and fastening of these freights as in normative documents there are no data on the allowed bending moments in frames of such platforms. In work as authors the method of calculation for distribution of lump of forest products on stacks on a platform-hlystovoze which can be used when transporting other stacking freights is offered and reasonable.

The most important task of the Russian Federation's energy strategy is the efficient use of energy resources. Rail transport is a one of the major consumers of diesel fuel and electricity, where the major energy consumption is used for traction. Traction energy consumption depends on a number of operational factors, including the characteristics of high-speed trains. The article is devoted to the designation of ways to assess the impact of changes in the coefficient of the precinct speed of freight trains on the change in specific energy consumption of locomotives. It is concluded that the calculation influence coefficient use indicators of locomotives, including the coefficient of the precinct speed must be performed for each of the structural units and analyzed the calendar period. Proposed by the authors for this formula is included in the methods of analysis and forecasting of energy resources consumption for traction trains introduced on the Russian train system in 2015.

The article presents a nonlinear mathematical model of heating a two-layer body with allowance of the finite velocity of heat propagation and the temperature dependence of the properties of materials. A numerical solution of the nonlinear hyperbolic heat conduction problem is obtained for the case when the absorption of the radiation energy is modeled by a volumetric heat source. The implementation of the grid method using a three-layer implicit difference scheme in solving a nonlinear heat conduction problem in a two-layer body with allowance for the relaxation of the heat flux and the conjugation conditions in the case of ideal contact at the interface junction is considered. The described algorithm for calculating the temperature field for high-intensity heating of a coated body, taking into account the dependence of the thermophysical characteristics of materials from temperature, is based on the implementation of the sweep method with iterative correction of the coefficients. Programs are developed and the results of calculating the temperature fields are presented using nonlinear hyperbolic heat conduction equations and the corresponding linear ones taking into account the average integrated thermal and optical characteristics of the materials. Based on a comparison of the results obtained the necessity of taking into account the temperature dependence of the properties of materials during the study of processes of high-intensity heating of bodies.The developed mathematical model on the basis of a system of nonlinear hyperbolic equations can be used to create technological processes using methods for processing the surface of multilayer bodies by laser radiation.

The article is devoted to numerical methods for solving nonlinear heat conduction problems with considering for the relaxation of heat flow. A mathematical model is developed on the basis of a non-linear heat equation of the hyperbolic type for calculating the temperature field in an infinitely extended (unlimited) plate. The implementation of the grid method using a three-layer implicit difference scheme for solving the nonlinear hyperbolic heat conduction problem is presented for the case when the absorption of radiation energy is modeled by a volumetric heat source. A numerical solution of the nonlinear heat conduction problem in an unbounded plate is obtained taking into account the relaxation of the heat flow on the basis of the finite difference technique using the sweep method and iterative refinement of the coefficients. A calculation algorithm with a graphical representation of the results of calculating the temperature field in an unbounded plate under the influence of concentrated energy flows is described. A comparison of the results of calculations of temperature fields in mathematical modeling on the basis of the nonlinear hyperbolic heat equation and the corresponding linear model using the mean integral values of thermophysical and optical characteristics is presented. The significant differences obtained between the temperature fields corresponding to the nonlinear and linear problems justify the need to take into account the temperature dependence of the thermophysical characteristics and the absorptivity in the study of high-intensity processes of heating the bodies. The developed nonlinear mathematical model of body heating with allowance for the finite speed of heat distribution and the temperature dependence of the material properties, can be used to select the modes for processing mode bodies with high-intensity energy flows.

The use of new self-supporting insulated wires and high-temperature wires in the operation of power lines allows increasing the capacity of lines and, as a rule, reducing operational costs. An optimal utilization of the power line load capacity depends on the precise determination of the permissible current loads. The values of permissible currents and steady-state temperature are the main parameters of the line operating mode, affecting the strength and sag of the conductor. The temperature of the wire depends on weather conditions and current load. There are methods for determining the temperature and permissible currents for widely used traditional wires such as AC. They are partially outlined in the EIS (Electrical Installation Standard) and the standard of PJSC FGC UES (Federal Grid Company of Unified Energy System) of 2013. However, there is lack of studies in new types of wires. The paper considers the effect of weather conditions and load on the temperature and real-power losses in insulated and high-temperature wire, and solar radiation is under special consideration. For comparison, we present the results of calculations on traditional AC wires. The research shows that solar radiation, being taken into account, provides an increase of real-power losses of about 2 % with the given values of load and weather conditions. Calculations of permissible current values according to the developed technique for classical AC wires reveal a high coincidence with the values from PJSC FGC UES standard. The relative error is within two percent, and the proposed method is more generalized. It allows simultaneous analysis of both uninsulated and insulated wires. Due to the widespread use of self-supporting insulated wires, power industry experts can use the developed software in the design and operation of modern power lines to optimize capacity.

The article presents theoretical studies of the interaction of the compacting machine with the soil of the road bed of the railway embankment. The results of the studies make it possible to establish the parameters of the sealant, which ensure an efficient flow of the compaction process of the ground environment. It is established that the rigidity of the working body of the roller must vary over a wide range. Experimental studies of a new sample of the working body confirmed the possibility of adjusting the rigidity in the required range for the effective use of vibrating rollers in the construction of railroad soil embankments.