Determination of a stable lateral region of a floating disc – Mathematical analysis and FEM simulation

Abstract

A conducting disc above two series connected concentric coils carrying current in the opposite direction gets levitated by magnetic repulsion principle. The disc achieves stable floating position when the electromagnetic force developed on the disc is equal and opposite to the gravitational weight of the disc. However, when there is an external disturbance, the disc will throw off from the center laterally, due to the repulsive force, based on the direction of the disturbance. Several techniques exist in literature to determine the force on the disc coaxial with the coils based on Finite Element Methods (FEM). In this paper, an approach to solve the integrodifferential equations using Finite Difference Method (FDM) has proposed to calculate the lateral force on the disc when it moves away from the axis of the disc. By using the FDM, we can discretize the disc into several curvilinear elements, and a mathematical formulation has developed. The maximum lateral stable region that the disc can remain in its stable floating position has determined by using this lateral force. A mathematical program has developed in MATLAB to calculate the force on the disc. Also, a model has designed in COMSOL Multiphysics, to compare the results obtained.