Unbalance Vibration Control And Stability Analysis Of Magnetically Suspended Spherical Flywheel

Magnetically suspended spherical flywheel(MSSFW)has the functions of attitude control and attitude measurement as a new attitude control mechanism for spacecraft.It is an ideal choice for spacecraft to achieve high precision and high stability attitude control.The radial and axial translation and the radial deflection of the MSSFW rotor are carried out by pure magnetic resistance bearings and the Lorentz-force type magnetic bearings respectively.Which not only reduces the power consumption of the flywheel system,but also improves the accuracy of the rotor deflection control.At the same time,the disturbing moment caused by the air gap deformation is eliminated by spherical rotor structure when the rotor deflected.In this paper,the main research contents of the MSSFW are as follows:(1)In order to estimate the rotor dynamic model of the MSSFW,the working principle and mechanical structure of the MSSFW are introduced.According to the actual mechanical structure of the MSSFW,the coordinate system is defined,thus the size and position relationship of the key components of the MSSFW is simplified,and the rotor bearing system of the MSSFW is established.At the same time,the dynamic model is matrixes and formulated,and the position and angle relations of the key components in the rotor magnetic bearing system of the MSSFW are formulated in the form of transformation matrix.Finally,the dynamic equation corresponding to the dynamic model of the bearing rotor system is obtained.(2)Aiming at the mathematical modeling of translational magnetic bearings and deflection magnetic bearings for the MSSFW,the structure and principle of pure magnetic resistance bearings for rotor translationcontrol are analyzed firstly.The model of translational magnetic bearings is established by deriving the displacement stiffness and current stiffness of bearings.Secondly,the structure and principle of Lorentz-force type magnetic bearings for rotor deflection control are analyzed.By comparing the magnetic density uniformity of different permanent magnets,the trapezoidal permanent magnet scheme is determined,and its simulation analysis and equivalent magnetic circuit construction are carried out.The flux reluctance of magnetic bearings is quantified mathematically,and the deflection magnetic bearings model is completed.(3)To compensate the unbalanced vibration of the MSSFW,a feedforward compensation control method for the MSSFW is proposed.According to D'Alembert's principle,the unbalance mass moments is equivalent to two counterweight planes of rotor,and the dynamic reaction of magnetic bearing is obtained.To keep gap spherical shell between stator and rotor and relieve negative magnetic deflection moment induced by non-uniform magnetic field,magnetic poles sphere centers of stator overlap that of rotor.The centrifugal force caused by deviation between rotor mass center and spin axis is got.Concerning electromagnetic levitation force always point to sphere center,another negative moment is calculated when rotor mass center deviates from rotor sphere center.The simulation system model of the MSSFW is built and the simulation program is compiled.Based on this,the feedforward suppression links under different loading sequence are simulated,and the optimal suppression sequence is determined.The simulation and experimental study of unbalanced vibration are completed.(4)The stability of magnetic suspension spherical flywheel system is analyzed and studied.The mechanical errors in the system caused by the processing and assembling of the MSSFW are analyzed,including the non-spherical errors caused by the low grinding accuracy of the rotor when the rotor rotates at high speed,and the installation errors caused by the non-coincidence of the rotor centroid,the mass centroid and the displacement sensor detection center.The error of matrix and control channel in the control system of the MSSFW is analyzed,including the control error caused by the matrix conversion between the measuredvalue of sensor and the actual displacement value of rotor,and the control error caused by the coupling in the control channel of the MSSFW deflection by Lorentz force-type magnetic bearing.Through the research of the causes and error mechanism of the above error,the control error of the MSSFW is analyzed and the stability analysis of the flywheel system is completed.