磁悬浮球形飞轮不平衡振动前馈抑制与实验
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摘要
针对磁悬浮球形飞轮转子存在的不平衡振动,建立磁轴承-球形转子动力学模型,提出了一种不平衡振动前馈抑制方法。依据达朗伯原理,将转子不平衡质量矩等效至转子两端配重面,得到了转子两端的轴承动反力。为维持球面磁极气隙的球壳形状,消除磁拉偏负力矩,将高速转子球心与定子球心始终重合。分析了转子质心偏离旋转轴引起的离心力,计算了转子质心偏离球心后,因电磁悬浮力始终指向转子球心而引起的偏转负力矩。仿真结果表明:转速为8 000 r/min,转子两配重面内不平衡质量矩处于对角位置且大小相等时,对转子施加前馈抑制,转子径向振幅从13.8μm减少至3.3μm,减少约76.1%,轴向振幅从21.6μm减少至5.6μm,减少约74.1%。实验结果与仿真结果一致,验证了转子不平衡振动模型的正确性和前馈抑制方法的有效性。
Aiming at the unbalance vibration of a magnetic bearing spherical flywheel rotor, an unbalance vibration feedforward restraint method was presented by establishing the dynamic model of its spherical rotor-magnetic bearing. Based on the D'Alembert's principle, the unbalance mass moments was equivalent to two counterweights on the end planes of rotor, and the dynamic reaction of the magnetic bearing was obtained. To keep the shell gap its spherical configuration between stator and rotor and relieve the negative magnetic deflection moment induced by non-uniform magnetic field, the sphere centers of the rotor was made always coinciding with that of the stator. The centrifugal force caused by the deviation between the rotor mass center and spin axis was analysed. Considerning the electromagnetic levitation force always pointing to the sphere center, the caused negative moment was also calculated when the rotor mass center deviates from the rotor sphere center. When the two unbalance mass moments with phase difference of π were identical, the feedforward restraint simulations were implemented at the speed of 8 000 r/min. The results show that the rotor's radial and axial amplitudes decrease from 13.8 μm and 21.6 μm to 3.3 μm and 5.6 μm, which are reduced by 76.1% and 74.1%, respectively. The tests results have a good agreement with those of the simulations, which indicates the dynamic model is correct and feedforward restraint method is effective.
Aiming at the unbalance vibration of a magnetic bearing spherical flywheel rotor, an unbalance vibration feedforward restraint method was presented by establishing the dynamic model of its spherical rotor-magnetic bearing. Based on the D'Alembert's principle, the unbalance mass moments was equivalent to two counterweights on the end planes of rotor, and the dynamic reaction of the magnetic bearing was obtained. To keep the shell gap its spherical configuration between stator and rotor and relieve the negative magnetic deflection moment induced by non-uniform magnetic field, the sphere centers of the rotor was made always coinciding with that of the stator. The centrifugal force caused by the deviation between the rotor mass center and spin axis was analysed. Considerning the electromagnetic levitation force always pointing to the sphere center, the caused negative moment was also calculated when the rotor mass center deviates from the rotor sphere center. When the two unbalance mass moments with phase difference of π were identical, the feedforward restraint simulations were implemented at the speed of 8 000 r/min. The results show that the rotor's radial and axial amplitudes decrease from 13.8 μm and 21.6 μm to 3.3 μm and 5.6 μm, which are reduced by 76.1% and 74.1%, respectively. The tests results have a good agreement with those of the simulations, which indicates the dynamic model is correct and feedforward restraint method is effective.
引文
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[14] 许国锋,蔡远文,任元,等.洛伦兹力磁轴承磁密均匀度设计与分析[J].北京航空航天大学学报,2016,42(1):1-9.XU Guofeng,CAI Yuanwen,REN Yuan,et al.Design and analysis for uniformity of magnetic flux density in Lorentz force-type magnetic bearing[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(1):1-9.
[15] XIANG Biao,TANG Jiqiang.Suspension and titling of vernier-gimballing magnetically suspended flywheel with Conical magnetic bearing and Lorentz magnetic bearing[J].Mechatronics,2015,28:46-54.
[16] FANG Jiancheng,XU Xiangbo,XIE Jinjin.Active vibration control of rotor imbalance in active magnetic bearing systems[J].Journal of Vibration and Control,2015,21(4):684-700.
[17] 缪存孝,徐向波,刘强.含转子不平衡的磁轴承建模与同频电流抑制[J].振动、测试与诊断,2014,34(6):1057-1064.MIAO Cunxiao,XU Xiangbo,LIU Qiang.Model development and synchronous current suppression in active magnetic bearing systems with rotor imbalance[J].Jouranl of Vibration,Measurement & Diagnosis,2014,34(6):1057-1064.
[18] JIANG Kejian,ZHU Changsheng,TANG Ming.A uniform control method for imbalance compensation and automation balancing in active magnetic bearing-rotor systems[J].Journal of Dynamic Systems Measurement & Control,2012,134(2):1-13.
[19] MARKUS H,GERALD K,MANFRED S.Redundant unbalance compensation of an active magnetic bearing system[J].Mechanical Systems and Signal Processing,2017,94:267-278.
[ 2 ] 王坤,赵阳,马文来,等.飞轮扰动作用下卫星结构响应能量预示方法[J].振动与冲击,2012,31(13):159-162.WANG Kun,ZHAO Yang,MA Wenlai.Vibration responses prediction of satellite structure caused by disturbances of flying wheels using energy method[J].Journal of Vibration and Shock,2012,31(13):159-162.
[ 3 ] 刘超,刘刚,盖玉欢.基于磁力等效原理的刚性磁悬浮转子系统高精度在线动平衡[J].振动与冲击,2016,35(4):67-71.LIU Chao,LIU Gang,GE Yuhuan.Field balancing for a magnetically suspended rigid rotor based on magnetic forces equivalence principle[J].Journal of Vibration and Shock,2016,35(4):67-71.
[ 4 ] 王卫杰,任元,刘强,等.球面磁悬浮万向飞轮转子轮盘优化设计[J].航空学报,2016,37(9):2874-2883.WANG Weijie,REN Yuan,LIU Qiang,et al.Optimal design of rotary table for spherical rotor of magnetically suspending gambling flywheel[J].Acta Aeronautica et Astronautica Sinica,2016,37(9):2874-2883.
[ 5 ] 韩邦成,房建成,郭家富,等.不平衡质量对磁悬浮CMG转子运动特性的影响分析及实验[J].宇航学报,2008,29(2):585-589.HAN Bangcheng,FANG Jiancheng,GUO Jiafu,et al.Simulation analysis and test of the influence of imbalance mass on magnetically suspended rotor[J].Journal of Astronautics,2008,29(2):585-589.
[ 6 ] 宋腾,韩邦成,郑世强,等.基于最小位移的磁悬浮转子变极性LMS反馈不平衡补偿[J].振动与冲击,2015,34(7):24-32.SONG Teng,HAN Bangcheng,ZHENG Shiqiang,et al.Variable polarity LMS feedback based on displacement nulling to compensate unbalance of magnetic bearing[J].Journal of Vibration and Shock,2015,34(7):24-32.
[ 7 ] 刘强,房建成,韩邦成,等.磁悬浮反作用飞轮磁轴承动反力分析及实验[J].北京航空航天大学学报,2010,36(7):821-825.LIU Qiang,FANG Jiancheng,HAN Bangcheng,et al.Analysis and test of dynamic reaction of magnetic bearing reaction flywheel[J].Journal of Beijing University of Aeronautics and Astronautics,2010,36(7):821-825.
[ 8 ] 刘强,胡灯亮,吴波,等.磁悬浮飞轮不平衡振动前馈抑制方法与实验[J].航天控制,2017,35(1):71-76.LIU Qiang,HU Dengliang,WU Bo,et al.Unbalance vibration feedforward restraint and experiment for magnetic bearing flywheel[J].Aerospace Control ,2017,35(1):71-76.
[ 9 ] FANG Jiancheng,XU Xiangbo,TANG Jiqiang,et al.Adaptive complete suppression of imbalance vibration in AMB systems using gain phase modifier[J].Journal of Sound and Vibration,2013,332:6203-6215.
[10] XU Xiangbo,CHEN Shao,ZHANG Yanan,et al.Automatic balancing of AMB systems using plural notch filter and adaptive synchronous compensation[J].Journal of Sound and Vibration,2016,374:29-42.
[11] 辛朝军,蔡远文,任元,等.磁悬浮敏感陀螺动力学建模与关键误差源分析[J].北京航空航天大学报,2016,42(10):2048-2058.XIN Chaojun,CAI Yuanwen,REN Yuan,et al.Dynamic modeling and key error sources analysis of magnetically suspended sensitive gyroscopes[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(10):2048-2058.
[12] 刘强,胡灯亮,吴波,等.磁悬浮微框架球形飞轮及其转子优化设计研究[J].兵工学报,2017,38(11):2280-2288.LIU Qiang,HU Dengliang,WU Bo,et al.Vernier gimballing magnetically suspended spherical flywheel and its rotor optimization design[J].Acta Armamentarii,2017,38(11):2280-2288.
[13] 刘强,赵勇,曹建树,等.新型微框架磁悬浮飞轮用洛伦兹力磁轴承[J].宇航学报,2017,38(5):481-489.LIU Qiang,ZHAO Yong,CAO Jianshu,et al.Lorentz magnetic bearing for novel vernier gimbaling magnetically suspended flywheel[J].Jouranl of Astronautics,2017,38(5):481-489.
[14] 许国锋,蔡远文,任元,等.洛伦兹力磁轴承磁密均匀度设计与分析[J].北京航空航天大学学报,2016,42(1):1-9.XU Guofeng,CAI Yuanwen,REN Yuan,et al.Design and analysis for uniformity of magnetic flux density in Lorentz force-type magnetic bearing[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(1):1-9.
[15] XIANG Biao,TANG Jiqiang.Suspension and titling of vernier-gimballing magnetically suspended flywheel with Conical magnetic bearing and Lorentz magnetic bearing[J].Mechatronics,2015,28:46-54.
[16] FANG Jiancheng,XU Xiangbo,XIE Jinjin.Active vibration control of rotor imbalance in active magnetic bearing systems[J].Journal of Vibration and Control,2015,21(4):684-700.
[17] 缪存孝,徐向波,刘强.含转子不平衡的磁轴承建模与同频电流抑制[J].振动、测试与诊断,2014,34(6):1057-1064.MIAO Cunxiao,XU Xiangbo,LIU Qiang.Model development and synchronous current suppression in active magnetic bearing systems with rotor imbalance[J].Jouranl of Vibration,Measurement & Diagnosis,2014,34(6):1057-1064.
[18] JIANG Kejian,ZHU Changsheng,TANG Ming.A uniform control method for imbalance compensation and automation balancing in active magnetic bearing-rotor systems[J].Journal of Dynamic Systems Measurement & Control,2012,134(2):1-13.
[19] MARKUS H,GERALD K,MANFRED S.Redundant unbalance compensation of an active magnetic bearing system[J].Mechanical Systems and Signal Processing,2017,94:267-278.