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.