Modeling of a bearingless motor using distributed magnetic circuit

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Bearingless motors are the rotational electric machine which utilize a common magnetic structure for rotation and magnetic suspension. Since the bearing function is combined with the motor, the shaft length can be shortened resulting in higher critical speeds. Relationship between suspension force and current of bearingless motor is clearly derived by prior research. However, relationship between displacement of rotor and suspension force is not precisely defined. In this paper, we present model of bearingless motor describing the radial force variation due to the movement of the rotor. Using a distributed magnetic circuit and maxwell stress tensor, we derived a mathematical expression for the radial force. For a slotless bearingless motor, we are able to find an analytical model presented in the form of stiffness. For a slotted motor, we can compute the stiffness by semi-analytical analysis. This model is validated by a finite-element-analysis.