Calculation of frequency responses of electro-magnetic levitation magnets

As all EMS-vehicle magnets of the Transrapid family have heretofore been equipped with massive iron cores acting on massive armature rails eddy currents due to varying coil currents and air gaps must be taken into account if force (F) and current (J) have to be calculated correctly. A method is presented which allows their calculation for infinitely small harmonic voltage (dV) and gap variations (dG). In this case we have a linear problem to solve. We establish a two dimensional model of the magnet which contains the essential data of the magnet (air gap, pole width, amp.turns, average length of force lines) and which can be solved by simple fourier series expansion. In order to fit the results for frequency zero to experimental or theoretical force characteristics, we define the two relative permeabilities\mu_{r}= B/(H cdot \mu_{o})and\mu_{a} = dB/(dH \cdot \mu_{o})which are calculated by fitting F(J,G) and dF/dJ at the operating point. Although these frequency responses are only the basis for a parameter identification method for a given electro-mechanical structure of a magnet, we get good results for force variation and power consumption of the magnet if the amplitudes of voltage and gap variations are not too large.