General 2-d Transient Eddy Current Force Equations for a Magnetic Source Moving above a Conductive Plate

When a magnetic source is moved and/or oscillating above a conductive linear plate a traveling time varying magnetic field is created in the airgap. This field induces eddy currents in the plate that can simultaneously create normal and tangential forces. The transient fields and the forces created by the magnetic source are modeled using a novel 2-D analytic based A-φ method in which the presence of the source field is incorporated into the boundary conditions of the plate. The analytic based solution is obtained by using the spatial Fourier transform and temporal Laplace transform. The performance of the method is compared with a 2-D transient finite element model with a Halbach rotor source field. The derived transient force equations are written in a general form so that they can be applied to any magnetic source.