Exact Analytical Method for Active Magnetic Bearings With Rotor Eccentricity

This article presents an exact analytical method for active magnetic bearings to obtain the magnetic field distribution with rotor eccentricity. Based on the subdomain method and the perturbation method, the active magnetic bearing is divided into two regions: the air gap and stator slots. Meanwhile, the zeroth-order and first-order equations in the polar coordinate are obtained and solved by the method of separation of variables, respectively. The magnetic field distribution is obtained by superimposing the first-order solution into the zeroth-order solution according to the perturbation method. The proposed analytical method has provided an effective way to study the magnetic bearing and other electromagnetic actuators. By using the Maxwell stress tensor theory, the unbalanced magnetic force is calculated to obtain the displacement stiffness and current stiffness. Finally, the consequences of magnetic field distribution and the unbalanced magnetic force are compared with those by the finite-element method. The result validates the correctness of the analytical method.