Mathematical Modeling of Transient Processes in Magnetic Suspension of Maglev Trains

Abstract

On the basis of a generalized interdisciplinary method that consists of a modification of Hamilton–Ostrogradski principle by expanding the Lagrange function with two components that address the functions of dissipation energy and the energy of external conservative forces, a mathematical model is presented of an electromechanical system that consists of the force section of a magneto-levitation non-contact maglev suspension in a prototype traction vehicle. The assumption that magnetic potential hole, generated naturally by means of cryogenic equipment, is present in the levitation suspension, serving to develop the model system. Contrary to other types of magnetic cushion train suspensions, for instance, maglev–Shanghai or Japan–maglev, this suspension does not need a complicated control system, and levitation is possible starting from zero train velocity. As high-temperature superconductivity can be generated, the analysis of levitation systems, including the effect of magnetic potential holes, has become topical. On the basis of the model of a prototype maglev train, dynamic processes are analyzed in the levitation system, including the effect of the magnetic potential hole. A system of ordinary differential equations of the dynamic state is presented in the normal Cauchy form, which allows for their direct integration by both explicit and implicit numerical methods. Here, the results of the computer simulations are shown as figures, which are analyzed.