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The article considers the dynamic processes of the oscillatory system «wagon - way», its mathematical model is formed and its features are established. The analysis of existing approaches to the consideration of the influence of dissipative forces on the stability of rolling stock is carried out, their shortcomings are revealed. When composing dynamic process equations, it is important to proceed from their exact expressions when considering kinetic and potential energy, i.e. to take into account the relationship between generalized coordinates, which will allow us to consider in detail the process of rolling stock oscillations. The zone of autoparametric resonance is found. It is established that dry friction forces do not interfere with parametric resonance. Dynamic equations are compiled taking into account the scattering forces arising in the contact points of the structural elements of the car. The influence of dry friction forces on the critical coefficient of parametric excitation is determined. The areas of dynamic instability of a car when moving along a railway track with different characteristics are determined. The features of the behavior of the system under the influence of dry friction forces are revealed. It is established that dry friction forces do not reduce the amplitude of bouncing and can lead to an increase in lateral pitching vibrations due to energy pumping.

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.

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.

The article deals with such important concept as the resonance to three cases: when rolling stock is described by a system of linear differential equations with constant coefficients, when the mathematical model of rolling stock represented a nonlinear system of differential equations, and when in the latter we take into account the multiplicative disturbance from railway, namely its non-equal-elasticity between sleepers. In this case, speak properly and correctly is not about a particular value of RMS-velocity, but on parametric instability areas.

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.

Explores the impact of truly existing longitudinal non-elastic railway track caused by the presence of sleepers and other factors on the vertical dynamic of vehicle. Formulas to determine the bounds of simple combinational and parametric resonances is obtained. Areas of dynamic instability of electric locomotive EP2K is builted.

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 .

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.

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

In article the new approach to calculation of power characteristics of quasiinvariant systems of suspension of mechanical objects different from other approaches by simplicity and logical clarity, however demanding the procedure of identification of the power characteristic of the compensator of external indignation of physical devices is offered.

A study of the influence of non-linear parameters spring of a freight car suspension (stiffness spring, length base of a bogie, roughnesses railway) on the amplitude and phase fluctuations bouncing body is completed. Defined own vibrational frequency jumps car body as a function of the parameters.