Compensation of Destabilizing Rotor Position Dependency in Asymmetric Radial Magnetic Bearings

Due to the nature of magnetic forces, the forces of a magnetic bearing depend not only on the coil currents but also on the position of the rotor with respect to the stator of the bearing. For conventional radial magnetic bearings with even number of poles, the destabilizing position dependency is modeled as a negative stiffness by linearizing the quadratic force-current relationship with respect to a constant bias current and zero displacements. Then, it is possible to apply a linear feedback control to stabilize it. Asymmetric bearings with odd number of poles have nonlinear and cross-coupled force-current relationships. In this paper, we use magnetic circuit theory to derive the force-current relationships of asymmetric bearings with odd number of poles. Through a linearization process, a new method of compensating the position dependency is proposed. A test rig consisting of a prototype compressor equipped with 9-pole radial bearings is constructed. Test results verify that the compensation is critical to achieve stable levitation. Only with the proposed compensation, the output sensitivities of the bearings satisfy the standard.