Rotor dynamics of active magnetic bearing reaction whell

The paper presents the results of the calculation of dynamically unbalanced rotor vibration for an active magnetic bearing reaction wheel with angular momentum 1 N·m·s. Forces, required to keeping the rotor in contactless position, and the critical speeds in working angular velocity ranges are determined. Calculation is performed for various magnitudes of stiffness and damping coefficients of magnetic suspension and for various working angular velocity ranges. Required mass of rotor, axial and equatorial moments of inertia are determined by means of developed parametric 3D-model of rotor for every speed range. Maximum permissible eccentricity of the rotor, which describe the static imbalance, and maximum permissible angle between the geometrical axis of the rotor and its principal central axis of inertia, which characterize couple unbalance, are determined using the value of rotor mass and the desired residual unbalance in each correction plane. Calculation shows, that center of mass of spinning rotor perform mainly radial translations, generated due to the presence of static unbalance. The amplitude of the resulting oscillation of the rotor is 17 μm for a working angular velocity range 0-9000 RPM and 13 μm for the range 0-18000 RPM. The first critical speed of the rotor corresponds to the resonant frequency of its radial oscillations. In the range 0-18000 RPM there is an additional critical speed due to the fact that the equatorial moment of inertia of rotor exceeds the axial moment of inertia. There is the phenomenon of self-centering of the rotor in the overcritical regions. Results of rotor dynamic calculation make it possible to formulate the basic data for choosing a rotor speed range, air gaps in back-up bearings, gaps between rotor and stator of magnetic bearings, stiffness and damping coefficients of magnetic suspension.