Vertical dynamics of the Maglev vehicle Transrapid

The Maglev vehicle Transrapid is levitated by magnetic forces which pull the vehicles levitation frames toward the guideway from below. The magnets possess poles with alternating fluxes which are part of the synchronous long stator linear motor. Although the Transrapid glides along its guideway without mechanical contact, this alternation as well as the loading and unloading of the guideway girders excite vibrations of the ground. In order to calculate the time behavior of the vibrational emissions, a simulation of the transfer of a Transrapid vehicle over several guideway girders is proposed. The equations of motion for the vehicle and the girders are calculated separately by the MBS software NEWEUL and assembled and numerically integrated in MATLAB/SIMULINK. The control law for the magnet forces is simplified by the characteristics of linear spring-damper elements. The controlled magnet forces travel along the guideway continuously and include the dynamic component due to the alternating fluxes and the geometry of the poles and stator. Results of a complete vehicle moving along a guideway consisting of several girders can be obtained within a few minutes of computation time. Therefore, the mechanism of excitations can be analyzed by numerical time integration in the full state space. The results are validated by measurements of the forces in the joints of the guideway girders. The vibrational emission along the Transrapid guideway differs from the vibrations of contact-afflicted vehicles as no impacts and fewer stochastic effects occur.