An Analytical 3-D Model for Calculating Eddy-Current Damping Force for a Magnetic Levitation System With Permanent Magnet

An analytical solution for obtaining steady-state eddy-current-based force on a levitated permanent magnet above a plate with linear conductivity in the field of an electromagnet having cylindrical symmetry is presented in this paper. In literature, the force due to eddy current in this levitation system have been used for high precision positioning of a levitated permanent magnet without providing an explicit analytical model. In this system, a change in the coil´s current and also the motion of the levitated permanent magnet in 3-D space generate eddy current in the plate. A novel explicit solution for obtaining damping forces due to these eddy currents is obtained as a function of geometric and material properties of the system. The analytical solution is derived by solving the quasi-static Maxwell equations using separation of variables method. Comparisons show that the analytical solution closely matches with the results of the finite element analysis.