Magnetic Force of Radial Magnetic Bearing Considering Eddy Currents Effect

The magnetic force of a radial magnetic bearing including the eddy current effects due to the rotation of shaft and the variation of the dynamic control current is investigated in this paper. With assumptions of moderate eddy currents developed in the rotor and stator, an approximate general form of the magnetic force is derived. The results show that the eddy current due to rotation of the rotor affects the magnitude of the static force and amplitude of the dynamic force while that induced by the dynamic control current will reduce the amplitude of the dynamic force and cause phase lag. Moreover, eddy current due to rotation results in equal decrease in the magnitude or amplitude of the static and dynamic forces. The current stiffness then derived with the dynamical force shows that the varieties of the stiffness with speed has a similar trend to that of the static one. A case study was investigated by FEM and the results agree well with the analysis. Furthermore, since the flux saturation in the eddy current regions is moderate, the nonlinear model considering flux saturation gives nearly the same results as the linear one. The result is applicable to not only solid rotor and stator but also to laminated structures.