N Turns Per Pole

FIGURE 13 Control magnetic circuit for one axis of a homopolar magnetic bearing

The characteristics of the control transfer function Gcon(s) are determined in order to stabilize the rotor/bearing system.

homopolar bearing In the homopolar bearing, a bias flux is used for linearization just as in the heteropolar bearing; however, the bias flux and control flux follow different paths. Additionally, the bias flux can be generated by either a permanent magnet (most common) or an electromagnetic coil. The use of a permanent magnet for bias reduces power consumption and makes the bearing more linear at large position offsets.

a. Magnetic control circuit—The control circuit for one half of the homopolar bearing, shown in Figure 13, is across the top air gap, through the rotor, out the bottom air gap, and around the back iron.

When Eq. 1 is applied to this circuit, the result is similar to Eq. 2:

g lstat lrot

2Nic,

moA ßoßrtfatA momr,rotA

Again, if the iron permeability is high relative to the air gap, this can be reduced to the following:

Nlca-nnm

b. Magnetic bias circuit—The magnetic circuit equation for the bias circuit, shown in Figure 14, is

: BbiasA

moA moA

momr, magAm I

Where Br = residual induction of the magnet lm = axial length of the magnet m-tmag = relative permeability of the magnet (=1.0—1.05) Am = magnet cross-sectional area per quadrant With the magnet permeability assumed to be 1.0, this can be reduced to

Br lm l

FIGURE 14 Bias magnetic circuit for one quadrant of a homopolar magnetic bearing

c. Force calculation—The basic force equation for an air gap is given by Eq. 4. In the homopolar bearing, the pole face covers a broader arc of the rotor than in the heteropolar bearing; therefore, the air gap force must be integrated over the surface to obtain the desired vector force, Ftop. Both the front and back control stacks must also be included. The result is

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