The Vertical Dynamics of the Car, Taking into Account the Irregularity of the Track Gauge

The paper deals with the vertical dynamics of the car to ensure the safety of trains, the reliability of the cars and the track. It is accepted that the dynamic model of the car has five degrees of freedom. The complex oscillatory process is divided into separate components: vertical, transverse and longitudinal horizontal. It is taken into account that the springsuspended weight of the car can also make angular oscillations. The equations of motion of a mechanical system are composed using the second-kind Lagrange equations by first generating the expressions for potential and kinetic energy. Since one of the most important problems in the dynamics of rolling stock is the study of forced oscillations of railway vehicles caused by irregularities of rails, therefore, the formulas of Professor N.N. Kudryavtsev were used as a kinematic effect on bogies. In the model being developed, the two wheels of the car trolley will be considered as one, then the equivalent perturbation is the average value of the perturbations transmitted to each wheel, that is, the pitching of the bogies can be neglected. Isolated perturbations are determined using reasoning about the time of passage of the wheels over the track irregularity. The obtained differential equations are rather complicated for an analytical solution. Therefore, to find solutions, the MathCAD mathematical software package was used. It provides a set of built-in functions for the numerical solution of differential equations. The massinertial characteristics and geometrical dimensions of the gondola car of model 12-132 are taken as input data. The speed of movement of the car and the length of the irregularities varied in a fairly wide range. As a result of numerical modeling, graphs of linear and angular oscillations versus irregularity lengths were obtained. It was found that the amplitude of oscillations varies within certain limits from 0 to 0.007 (vertical oscillations) and from –10 to +10 rad. (for the speed of 20 m/s and the length of the irregularity of 25 m). Keywords—track gauge; vertical dynamics; safety of trains; dynamic model; oscillatory process