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The article considers phenomenological and modelling approach to researching of interaction of a deformable wheel and a plane of support, their advantages and disadvantages are mentioned. In the context of phenomenological approach the five methods of locomotive tangent tractive force calculation were considered. There certainly must be pseudo-creeping to let locomotive tangent tractive force do work and change the kinetic energy of a train in the point of wheel and rail contact. Locomotive tractive force experts calculate the power as product of the locomotive tangent tractive force and the velocity of translational motion of a train, although in fact the velocity of the point of force application must be assumed. It is applied to a wheel pair, then the velocity of this point must be used to calculate the locomotive power. According to this fact the locomotive power is found several tens of times reduced.

Subject of researches is determination and the justification of mathematical characteristics of motion of a railway wheel adequately reflecting the gear of its interaction with a rail. The activity purpose is adaptation of fundamental positions of the cycloidal curves reflecting motion of a circle to motion of conditional points of topological circles of section of a shroud of a railway wheel, having a difficult structure. The activity methodology is constructed on study and systematisation of fundamental investigations in the field of geometry, mathematics and mechanics of idealised motion of a circle in which basis mathematical properties of cycloidal curves are put. The model of motion of a wheel of a railway mounted axle (with immovable wheels on an axis) in which basis are put kinematic and mechanical properties golonomnykh systems is fetched. Following general golonomnykh, fundamental mathematical properties of system, analytical relations and ratio of kinematic parametres of a forward speed of railway vehicles and speed of interaction of wheels with rails which allow to supplement methodology of thrust calculations at us and in other countries are installed. By the current moment time in domestic practice use tens various formulas which actuate a component of linear speed of motion, instead of speed of interaction of wheels with rails, taking into account their physical and geometric parametres. Linear (translational) speed of motion of a wheel not absolutely adequately reflects the gear of interaction of wheels of railway vehicles with rails. The fundamental theory of cycloidal curves gives the chance is proved to normalise analytically speed motion of railway vehicles of various types, to designers and founders it a priori to form constructional and technology - economic characteristics warranting reliability, life and overall performance of the equipment dolly parts, reducing risk of a traffic security of trains.

The article sets out the methodology of the study of a rigid mathematical model describing locomotive wheel and rail interaction, taking into account the hypothesis f. Carter. On the basis of the application of the theorem N.A. Tikhonova derived the differential equation for determining the rate of slippage of wheel pair on Rails. Determine the time dependence for the establishment of a process of kinematic slippage of wheel pair on Rails from the wheel speeds and locomotive, from inertial characteristics of trains and the wheel, as well as the coefficient of creep, annexed to the torque of wheel pair and the State of the surfaces of the Rails.

Based on the proposal for the formation of a railway track for operational deployment without ballast using a sub-rail base with a viscoelastic element forcedly filled with Newton's fluid and laid on an unprepared surface without ballast, an example of calculating the interaction of a wheel and a rail with this element based on the energy method is given. The possibility of using the design of the under-rail device for the operational laying of a railway track in difficult conditions on an unprepared surface without a track ballast layer is substantiated. The elastic dynamic impact of a wheel on a rail with initial speeds along a sub-rail base in the form of a box with shells laid on an unprepared surface is considered. The kinetic energy of a wheel hitting a rail laid on the proposed under-rail base passes not only into the potential energy of deformation, but also into the energy of wave and oscillatory processes. To improve the accuracy of solving the problem of dynamic impact, the transition of a part of the energy into the energy of local deformations in the contact area of the wheel with the rail is taken into account. Within a short period of time after touching the wheel at a certain speed, all elements of the rail acquire a certain strain rate. It is assumed that at the moment of contact with the wheel, the rail does not change its original shape, and the decrease in the speed of the wheel occurs due to local deformation of the materials of the contacting bodies; this period of impact will last until the velocities of the two bodies are equalized, after which the shape of the middle surface of the rail, modeled by a Bernoulli-Euler beam, will begin to change. Since the kinetic energy of the wheel is converted into the potential energy of bending, it is taken into account in the calculation to take into account the mass of the impacted body as the load of the wheel on the rail.

The article deals with the issue of the interaction of the track and rolling stock and the relationship of factors affecting the comfort of passengers. Examples of passenger comfort indicators are given and possible causes of deviations in the track geometry are considered. The results of experimental trips are analyzed and the data obtained by standard diagnostic tools are presented. Natural irregularities in the plan and profile were constructed in the analyzed areas where comfort indicators were exceeded. The data presented demonstrate the use of an additional indicator of the interaction of the track and rolling stock, which is advisable to take into account to identify deviations in the geometry of the track gauge when carrying out work on the current maintenance of the track, since there are irregularities or combinations of irregularities in the track that have an increased dynamic impact. It is worth noting that currently not all irregularities are registered, and accordingly such irregularities are not eliminated. Using the «passenger comfort» indicator calculated from the accelerations occurring in the elements of the rolling stock, it is possible to determine the places and deviations of the geometry of the track gauge that affect the dynamic characteristics of the rolling stock, causing increased comfort indicators.

Non-public railway tracks and junction stations of mainline railway transport are the most important links of the «railway - clients» system. At these points, car traffic is generated and extinguished, as well as information and documents are exchanged. When organizing interaction, it is necessary to take into account the interests of not only the carrier and the owner (user) of the non-public track, but also the owners of rolling stock. The most effective solution is to develop an automated interaction management system. The purpose of the work is to determine the factors that lead to idle of cars while waiting for technological operations to be performed with them. This will allow you to find control solutions aimed at eliminating (reducing) the negative impact on the operation of the “railway - clients” system. To achieve this, an algorithm has been developed for the presence of a car on non-public railway tracks, and factors that have a negative impact on the idle of cars on non-public tracks have been identified. The proposed algorithm is the basis for developing a mathematical model for calculating the time spent by a car on non-public tracks. The presence of cars on non-public tracks is presented as a control object for the subsequent development of an automated control system for the interaction of junction stations and non-public tracks. It will have a comprehensive approach to calculating the costs and risks of all participants in the «railway - clients» system.

Currently, much attention is paid to the creation of terminal «dry port» for maintenance of traffic node. «Dry port» is one of the possible ways to increase capacity of the transport node. The capacity of transport node depends on the following interrelated elements: infrastructure solutions, technological, technical, organizational, and exogenous. Insufficiency of technical equipment, low level of production culture, informational inconsistency - lead to excessive downtime of vehicles at berths and terminal and warehouse facilities of the port. Technical devices, shunting locomotives, lifting and transport equipment cannot cope with the increasing flow of transportation of containers and cargo, leading to paralysis of the movement of freight flows. The result is the accumulation of cars at the entrances to the transportation hub the formation of «abandoned» trains. The lack of logistics management principles of traffic promotion in the organization of multimodal transport required a modern approach to organization of effective work of the transport node. In this work the effective interaction between various types of transport in the transport node is represented in the form of a set-theoretic model. Considered the elements that contribute to the throughput of dry ports and sea port. The efficiency of technological processes systems of interaction of railway and marine transport in the node depends on the following conditions: the actual time of wagons in transportation must comply with regulatory process time; organization supply wagons in accordance with the processing capabilities of the cargo platforms; ensuring the maximum amount of overload of goods on the «direct option». To implement these conditions it is necessary to organize the interaction of different modes of transport in the transport node together with the terminal «dry port» in the system «terminal - station - port», in which the capacity of the railway component of the transport node is treated comprehensively along with the «dry port». Further technical and technological development of transport nodes is organization of cargo handling outside the port terminal «dry port».

Today the most part of world commodity and cash flows is concentrated in the Pacific Rim. The strategy of development for the Far East is based on increase in export to Asia-Pacific countries and also growth of volume of foreign investments. In September, 2018 in Vladivostok at the IV East economic forum the VaninoTransUgol company will submit the construction project in seaport Vanino of transport transshipment facility with transshipment capacities to 40 million tons. In 2017 the volume of transfer of freights in Vanino port was 7,2 million tons, the seaport continues to increase the refinery capacities, but the insufficient capacity of infrastructure of railway transport is the limiting element of development of the transport hub. Construction of the new terminal for transfer of coal will demand corresponding development of railway infrastructure of the Vanino transport hub. In the conditions of increase in volumes of transfer of freights, it is necessary to resolve an issue of the extreme number of cars which can be processed in "the railway station-seaport" system. The author has developed the program of imitating modeling which allows to determine the capacity of a railway component of the transport hub at the existing hardware and in the conditions of increase in loading of "the station-the port" system. In this work results of imitating modeling of work of the Vanino transport hub at increase in unloading of coal by 40% up to 280 cars a day are presented. The working park of the Vanino station has made 305 cars and continued to increase, ways of the station have been filled with cars waiting for operations. Two groups of possible ways of increase in capacity of the transport hub - infrastructure and technology solutions are presented. In the conditions of limitation of territorial development, construction of additional railway infrastructure becomes impossible therefore it is possible to increase the capacity of the transport hub due to change of specialization of moorings of port. It will allow to reduce the number of the cars which are on the ways of the station waiting for unloading and to accelerate processing of the rolling stock. After re-equipment of moorings of port, the working park of the Vanino station has made 230 cars and the capacity reserve for reception of an additional traffic volume has appeared. By means of this program of imitating modeling it is necessary to analyse work of key transport hubs of the Far East for definition of the maximum traffic volume at which transport hubs will steadily function, in the optimum mode.