Current (amps)

FIGURE 12 Force versus current for axial thrust bearing of multistage pump where kf =-\2blas = force constant or current stiffness kn =

-4k1i2bia negative stiffness or position stiffness

The position stiffness is the passive stiffness of the bearing with a bias field but with no control current. The position stiffness is always negative, indicating that if the rotor is displaced from center, it will be pulled further from its equilibrium position if no control current is applied. The force constant defines the relationship of the control force to current (lb/amp or N/amp) with the bearing centered. It is also negative, indicating that applying a control current pulls the rotor from its centered position. Many practitioners use positive values for the force constant and the position stiffness as a matter of convenience. In this case, the minus signs in Eq. 10 become plus signs.

The control current is determined by the measured displacement, y, and the characteristics of an adjustable sensor/compensator/amplifier transfer function:

Substituting Eq. 11 into Eq. 10 gives

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