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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.

Possibilities of expansion of settle of typical elementary links of mechanical oscillation systems are considered. As examples of links for transformation of movement the screw and level mechanisms are offered. Introduction of new links is equivalent of elementary links with transfer function of differential of second order. The method for definition of parameters of dynamical absorbtions of oscillation are offered.

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.

The article describes three variants of the mathematical model of the sensitivity function of the magnetoinduction sensor for assessing the influence of various sensor parameters in the electromechanical system «wheel - rail - magnetoinduction sensor» for diagnosing the technical condition of the rolling surface of the rolling wheels of rolling stock in the process of its movement over the sensor. An example of an algorithm for identifying defects located on the surface of the wheel rolling circle is described. The proposed multi-vector mathematical model allows simulating various defects on the rolling surface of the wheel, developing and testing new algorithms for processing the output signal of the sensor on the basis of modern hardware and software. The implemented defect identification algorithm is based on the property of the centrally symmetric form of the sensitivity function of the magnetoinduction sensor and the allocation of a useful signal corresponding to a certain type of defect, based on the application of a mutual correlation function and the assessment of its maximum and minimum values in comparison with the specified thresholds and confidence intervals. The main requirement for the implementation of the model is the uniform movement of the train above the sensor along a straight section of the rail track. This article discusses only one of the possible digital signal processing algorithms, but the proposed model allows us to compare the efficiency of other possible algorithms identification of defects in the rolling surface of wheelsets. The developed model confirms the prospects of using magnetic induction sensors for identification of not only visible, but also hidden defects on the rolling surface of the wheel in the process of movement of the train.

To improve the accuracy of the diagnosis of the technical condition of rolling stock, it is necessary to develop new algorithms for the digital processing of signals coming from sensors at the time of the passage of the axes of wheeled pairs of wagon carts during the uniform movement of the train on the straight section of the railway track. The use of modern mathematical application software packages to model digital-based data processing algorithms reduces the cost and time of developing automated systems to diagnose the technical condition of the rolling stock of railways. To assess the accuracy of the fixation by the magneto-induction sensor of the moment of passage of wheel pairs axly, an asthigmatic model is proposed, allowing to investigate not only the energy properties of the sensor, but also the shape of the output signal, taking into account the real dimensions of its magnetic core. The developed model allows you to classify the pore. The developed model allows to classify the order of astigmatism model magnetoinduction sensor based on a set of discrete virtual sensors

The article presents the results of research of a point magneto-induction sensor based on a mathematical model, which allows you to increase the reliability of automated systems for diagnosing technical condition rolling stock in the course of train movement by improvement the accuracy of the initial information, that is, the moments of fixation passing of wheelset axles over magneto-induction sensors. At the first stage of developing a stigmatic mathematical model the analytical dependence of the value of the magnetic flux in the magnetic core and the output EMF value on resistance of the air gap between the sensor and the wheel crest. At the second stage of development of the mathematical model found time dependence of the magnetic resistance of the air gap between the core of the magneto-induction sensor and the comb wheels of a railway car moving along a straight track at a constant speed. On the basis of application the developed stigmatic model allows evaluating the energy parameters of magneto-induction sensors depending on the properties of modern magnetic materials. The simulation results showed that the MMF value is constant the magnet determines the main parameters of magneto-induction sensors, so the use of modern magnets based on rare earth they allow to eliminate the traditional disadvantage of outdated types of magneto-induction sensors, that is, to reduce their size and weight. The application of the proposed stigmatic model expands the scope of possible solutions to extreme problems for selection and justification parameters of magneto-induction sensors, helps to improve the accuracy of systems for diagnosing the technical condition of the car fleet and traffic safety on railway transport.