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The research object is a pneumatic spring of a modern rolling stock. Using a two - mass calculation scheme, the diagrams “force-deformation” of a pneumatic spring are designed at driving speed of 160-200 km/h and high-speed driving of 201-250 km/h. It is determined that when the diameter of the connecting pipeline is changed from 20 to 35 mm, the inclination angle of the diagram “force - deformation” of the pneumatic spring is changed at speed driving from 32 degrees up to 57 deg.; at high-speed driving from 30 deg. up to 48 deg. It is proposed to determine a pneumatic spring operation coefficient using the forms of the designed diagrams “force - deformation.” Studying the specified coefficient in the speed range from 160 to 250 km/h, and the connecting pipeline diameter from 20 to 35 mm showed that the values of the pneumatic spring operation coefficient vary from 0.089 to 0.24, and the dependencies are nonlinear. Using the pneumatic spring operation coefficient will make it possible to further evaluate the pneumatic spring suspension system operation depending on the operating conditions of the railway vehicle.

Investigation of damages of the subgrade slope in combination with its overwetting and rolling stock loading, which significantly affects safety traffic of the railway transport, has been carried out. The complex method of slope stability estimation of the subgrade is developed, which includes calculation of loads and vibration action of rolling stock on the main site of the subgrade, as well as the dynamic model of vibrations propagation in the body of the subgrade embankment and the model of plastic deformations accumulation. Dynamic and nonlinear plastic models are based on a finite-element model of the cross section of the subgrade. The plastic model takes into account the characteristics of soil strength of the subgrade, depending on the area of the vibration load impact. The developed method allows to carry out the estimation of external and internal factors impact on occurrence of subgrade destruction, which is of practical value for safety state estimation of the railway transport.

The problem of the interaction of rolling stock with the rail track has been analyzed in the present paper. It has been established that in the process of transport science development a number of methods for determining the causes of wheel pairs derailment are developed, which, in a varying degree, take into account the peculiarities of their interaction. The problem of choosing the most accurate method for estimating the causes of rolling stock derailment becomes more complicated because of the lack of sufficient experimental data that would allow us to verify the adequacy of the models. The indicators of stability of the wheel against derailment, which are used on the railways of Ukraine and Europe, have been examined. Their dependences on the speed of movement were derived. It has been established that the increase of the speed of motion leads to the increase of the interaction power of the rolling stock with the rail track, which may, under certain operational parameters, provoke its derailment. As a result of the calculations, it has been shown that the use of norms for car design and calculation used on Ukrainian railways can lead to an inadequate estimation of traffic safety parameters, since it does not take into account the unevenness of the railway track. It has been established that the requirements of BS EN 14363: 2005 European norms are stricter in comparison with the norms for calculation and evaluation of the bearing elements strength and dynamic qualities of motor-vehicle rolling stock used on Ukrainian railways. A comparison of the experimentally and theoretically calculated values of the stability margin coefficient against wheel derailment of the first wheel pair of the diesel train car was carried out.