Actuator gains for a toothless permanent-magnet self-bearing motor

Permanent-magnet self-bearing motors provide independent bearing and motori ng functionality in a single magnetic actuator. Typically, self-bearing mot or designs use toothed stators to provide minimum reluctance flux paths tha t create the magnetic bearing forces necessary to support the rotor. These toothed designs can have significant cogging torque, rendering them ineffec tive for smooth torque applications such as those found in aerospace. A too thless permanent-magnet self-bearing motor can provide smooth torque produc tion and adequate bearing force for low-gravity environments. Characterizat ion of the open-loop gains for this actuator is necessary for linear contro ller development. In this paper simple algebraic equations are derived for the motoring and bearing current gains, and an analytical method is present ed for computing the negative stiffness. The analytical method solves the D irichlet boundary value problem (BVP) in the eccentric annulus for the magn etomotive force (MMF) in the air gap subject to harmonic boundary condition s. A conformal transformation to bipolar coordinates is used, yielding a BV P that is solvable by separation of variables. Expressions for the flux den sity, Maxwell force on the rotor, and the negative stiffness in terms of th e MMF are presented. A sample problem is presented that illustrates the flu x distribution in the air gap and the operating principals of this actuator type.