基于Halbach阵列的永磁轴承能有效地增强永磁轴承的承载能力，具有广阔的应用前景。但目前关于Halbach阵列的永磁轴承的理论模型研究并不完善，缺少任意角度连续磁化的Halbach阵列永磁轴承的解析模型和设计方法，限制了其应用。研究针对Halbach阵列的永磁轴承，利用标量磁位的模型建立了永磁体阵列的磁场分布模型，在此基础上基于虚位移法建立了永磁轴承的承载力模型和支承刚度模型，并对永磁轴承的最大承载力和支承刚度特性展开了研究，给出了永磁轴承设计过程中的参考因素。最后利用有限元分析软件对所建立的理论模型和提出的结论进行了验证，取得了较好的效果。
王念先
,
王东雄
,
陈奎生
,
吴华春
. 基于Halbach阵列的永磁轴承承载力解析模型及设计方法[J]. 机械工程学报, 2016
, 52(3)
: 128
-135
.
DOI: 10.3901/JME.2016.03.128
The bearing capacity of permanent magnetic bearings can be improved efficiently by Halbach array and the Halbach PMBs can be used wildly. However, the research on theoretical model of Halbach PMBs has not been developed, and the absence of the analytical model and design method of Halbach PMBs with arbitrary magnetized angle has limits the application of Halbach PMBs. In this research, the magnetic flux model of the Halbach PMBs has been built by using magnetic scalar potential model, and then the bearing capacity model and the bearing stiffness model of the Halbach PMBs have been built based on the virtual displacement method. Also, the maximum bearing force and the bearing stiffness of the Halbach PMBs are been studied, and the reference factor for the design of permanent magnetic bearings is given. Finally, the theoretical model and the conclusions of the proposed model are verified by the finite element analysis software.
[1] 胡业发，周祖德，江征风. 磁力轴承的基础理论与应用[M]. 北京：机械工业出版社，2006.HU Yefa，ZHOU Zude，JIANG Zhengfeng. Basic theory and application of magnetic bearings[M] . Beijing：China Machine Press，2006.
[2] LE Yun，FANG Jiancheng，SUN Jinji. Design of a Halbach array permanent magnet damping system for high speed compressor with large thrust load[J]. IEEE Transactions on Magnetics，2015，51(1)：8300109.
[3] SUN Jinji，REN Yuan，FANG Jiancheng. Passive axial magnetic bearing with Halbach magnetized array in magnetically suspended control moment gyro application[J]. J. Magn. Magn. Mater.，2011，323(15)： 2103-2107.
[4] CHOI Y，GWEON D. A high-precision dual-servo stage using Halbach linear active magnetic bearings[J]. IEEE/ASME Transactions on Mechatronics，2011， 16(5)：925-931.
[5] WANG Nianxian，HU Yefa，ZHANG Jinguang，et al. Research on forces and dynamics of maglev wind turbine generator[J]. Journal of Magnetics，2013，18(4)：443-453.
[6] 梁欢，马宏忠，王庆燕，等. 基于Halbach 阵列的水轮发电机组永磁悬浮承重装置[J]. 电力建设，2014，35(10)：7-12.LIANG Huan，MA Hongzhong，WANG Qingyan，et al. Permanent magnetic-levitation weight support system of hydroelectric generating set based on Halbach array[J]. Electric Power Construction，2014，35(10)：7-12.
[7] RAVAUD R，LEMARQUAND G. Halbach structures for permanent magnets bearings[J]. Progress in Electromagnetics Research M，2010，14：263-277.
[8] YONNET J. Rare earth iron permanent magnets[M]. Oxford：Oxford University Press，1996.
[9] YONNET J，HEMMERLIN S，RULLIERE E，et al. Analytical calculation of permanent magnet couplings [J]. IEEE Transactions on Magnetics，1993，29(6)：2932-2934.
[10] 田录林，李言，田琦，等. 径向磁化的多环嵌套永磁轴承轴向磁力解析模型[J]. 计算力学学报，2010(2)： 379-384.TIAN Lulin，LI Yan，TIAN Qi，et al. Axial magnetic force analytical model for radial magnetization multi-annular nesting permanent magnetic bearings[J]. Chinese Journal of Computational Mechanics，2010(2)：379-384.
[11] 田录林，李言，田琦，等. 轴向磁化的双环永磁轴承轴向磁力研究[J] .中国电机工程学报，2007，27(36)：41-45.TIAN Lulin，LI Yan，TIAN Qi，et al. Research on the axial magnetic force of axially magnetized Bi-annular-shaped permanent magnetic bearings[J]. Proceedings of the CSEE，2007，27(36)：41-45.
[12] BACHOVCHIN K，HOBURG J，POST R. Stable levitation of a passive magnetic bearing [J]. IEEE Transactions on Magnetics，2013，49(1)：609-617.
[13] RAVAUD R，LEMARQUAND G，LEMARQUAND V. Force and stiffness of passive magnetic bearings using permanent magnets. Part 1：Axial magnetization[J]. IEEE Transactions on Magnetics，2009，45(7)：2996-3002.
[14] RAVAUD R，LEMARQUAND G，LEMARQUAND V. Force and stiffness of passive magnetic bearings using permanent magnets. Part 2：Radial magnetization[J]. IEEE Transactions on Magnetics，2009，45(9)：3334-3342.
[15] 孙立军，张涛，赵兵.永磁磁轴承数学模型的研究[J].机械工程学报，2005，41(4)：69-74.SUN Lijun，ZHANG Tao，ZHAO Bing. Study of mathematic model of permanent magnetic bearings[J]. Chinese Journal of Mechanical Engineering，2005，41(4)：69-74.
[16] BRAD P，NELSON G，JAMES F. Design formulas for permanent magnet bearings[J]. Transactions of the ASME，2003，125：734-738.
[17] 陈君辉，杨逢瑜，杨龙，等. 一种Halbach 阵列永磁轴承的磁力模型研究[J]. 哈尔滨理工大学学报，2006，16(5)：72-75.CHEN Junhui，YANG Fengyu，YANG Long，et al. Research on a magnetic force model for halbach array permanent magnet bearings[J]. Journal of Harbin University of Science and Technology，2006，16(5)： 72-75.
[18] XU Feipeng，LI Tiecai，LIU Yajing. A study on passive magnetic bearing with Halbach magnetized array[C]//International Conference on Electrical Machines and Systems，2008，417-420.
[19] XIA Z，ZHU Z，HOWE D. Analytical magnetic field analysis of Halbach magnetized permanent-magnet machines[J]. IEEE Transactions on Magnetics，2004，40(4)：1864-1872.
[20] DANIEL J，MARK J，GERALD T. An overview of magnetic bearing technology for gas turbine engines [R] . NASA/TM—2004-213177，2004.
[21] JEROEN L，JOHANNES J，JOHN C，et al. Three-dimensional analytical calculation of the torque between permanent magnets in magnetic bearings[J]. IEEE Transactions on Magnetics，2010，46(6)：1748-1751.
[22] HAN Bangcheng，ZHENG Shiqiang，HU Xiaofei. Dynamic factor models of a thrust magnetic bearing with permanent magnet bias and subsidiary air gap [J]. IEEE Transactions on Magnetics，2013，49(3)：1221-1230.
