A mathematical model of a synchronous reluctance bearingless machine as a control object

Abstract

In this article, one type of bearingless electrical machine, a synchronous reluctance bearingless machine (SRBM), is considered. A simplified analytical description of the static characteristics of the SRBM nodule has been derived. A control law for the suspension current phase has been proposed. The validity of the derived equations was verified by numerical calculations by the finite element method. The radial electromagnetic forces of the module are described by linear dependences on the magnitude of the suspension currents and the displacement of the rotor in the corresponding radial direction. The dependence of the forces on the displacement in the perpendicular direction is simplified. The analytical model displays high accuracy of calculations in the operating ranges of the currents and displacements. The principal component of the SRBM torque is a square-law function of the drive current magnitude. The error of the torque prediction according to the analytical model was 1.8% with the rotor in the central position and no current in the suspension winding within the entire range of the current values at any torque angles. The graphs presented in the article show the impact of the suspension current and the rotor displacement on the torque. The control law proposed for the suspension current phase is a linear function of the rotation angle of the rotor, the radial displacement direction, and the torque angle of the synchronous machine drive. The proportionality ratio between the torque angle and the suspension current phase has been determined approximately. The error of calculation at different rotor displacements has been assessed and plotted.Keywords: synchronous reluctance bearingless machine, mathematical model of control object, direction and magnitude of radial force