Longitudinal vibrations in electrodynamics suspension system

Abstract

A system of electrodynamics suspension (EDS) in which the primary source of the field (electromagnet) is moving in a straight line parallel to the surface of the track and his speed makes small oscillations around a mean value is considered. The approximation of an infinitely wide track is allowed, the primary source of the electromagnetic field acts as a so-called periodic source. This problem is a special case of the general problem of the rate of the transients in the EDS, caused by uneven movement. Named speed determines the amount of time constants that make sense, and in contrast to the simplest case of a one-dimensional linear oscillator system EDS characterizes not by a single time constant, but by infinite set of values. The method of calculation of levitation and braking forces acting in this oscillatory motion on carriage electromagnet is worked out and simple explicit formulas to calculate these forces are got. On the basis of the calculation of time constants the rate of the transients in the EDS, caused by uneven movement is assessed. The calculations of levitation and braking forces according to the developed technique are made. The results obtained allow to delimit the applicability of the so-called quasi-static approach which consists in that the irregularly moving of electromagnet replaced by concurrent, i.e., the same electromagnet, similarly disposed and uniformly moving with a speed coinciding with the instantaneous value of the actual longitudinal speed of the electromagnet. In the quasi-static approximation, fluctuations of levitation and braking forces are in phase with oscillations of speed and amplitude of the forces oscillations do not depends on the frequency of the speed oscillation. The calculations show that in reality there is phase shift between the forces oscillations and speed oscillations depending on the frequency. Amplitudes of levitation and braking forces oscillations also depend on the oscillation frequency, and for each speed value a resonance frequency exists at which they reach the maximum value.