Building a mathematical model of the oscillations in subway cars equipped with electromechanical shock absorbers

A mathematical model has been built of the subway car on two double-axle bogies with an axial characteristic of 20–20, whose spring suspension’s central link is equipped with springs and electromechanical dampers. A special feature of the model is its integration of such components as 17 differential equations of the second order, which describe the operation of the mechanical part «carriage-rail track», as well as 8 differential equations of the first order that describe the operation of 4 electromechanical shock absorbers. The model is complemented with three polynomials of orders 32 and 63 describing the state of the magnetic field of electromechanical shock absorbers and their electromagnetic force, as well as 4 algebraic coupling equations. The mathematical model of the «carriage-rail track» system equipped with electromechanical shock absorbers takes into consideration the following components: – the longitudinal and transverse oscillations by wheelsets of the car bogies and body; – the parameters of a rail track; – the electromagnetic features of electric shock absorbers; – the excitation arising from a track irregularity; – the path parameters, as well as the properties of other elements in a spring suspension. This paper reports a study into the operation of a subway car’s spring suspension that travels over a track with a sinusoidal irregularity. The study has established that the electromechanical processes in electric shock absorbers can be divided into three parts. The oscillation free mechanical components, free components, and the forced electromagnetic components. The duration of action, the amplitudes, and nature of the oscillations’ components have been determined. The oscillation amplitude varies considerably with the increased speed: from 0.01 A and 2 V at 40 km/h up to 0.9 A and 115 V at 100 km/h. The oscillations are harmonious. The frequency of oscillations corresponds to the frequency of the track irregularity. The electric power of the electric shock absorber increases from 0.018 W at 40 km/h to 98 W at 100 km/