Analysis of the Planar Magnetic Field of Linear Permanent Magnet Halbach Array



In this paper, the analytical solution to the planar magnetic field of a linear permanent magnet Halbach array is researched on. First, the magnetic field of a current surface is derived from the magnetic field produced by the molecular current of the permanent magnet. The magnetic fields of pieces of permanent magnet with vertical and diagonal magnetization direction are both solved by combining the magnetic field of current surfaces with different directions. Then the planar magnetic field of the entire linear permanent magnet Halbach array is obtained by calculating the vector addition of the magnetic field of all the permanent magnet cubes using Denavit-Hartenberg (D-H) transform technique, which yields the closed-form analytical expressions. The analytical algorithm proposed in this paper can be utilized to design and optimize the Halbach array, which in result can greatly simplify the calculation and expedite the progress. The effectiveness of the proposed method is evaluated by the finite element analysis software Maxwell.




Honghua Tan




X. Zhang et al., "Analysis of the Planar Magnetic Field of Linear Permanent Magnet Halbach Array", Applied Mechanics and Materials, Vols. 66-68, pp. 1336-1341, 2011


July 2011




[1] Miroslav Markovic and Yves Perriard. Optimization Design of a Segmented Halbach Permanent-Magnet Motor Using an Analytical Model[J]. IEEE Transactions On Magnetics. 2009, 45(7): 2955-2960.


[2] Z. Q. Zhu and D. Howe. Halbach Permanent Magnet Machines and Applications: a Review [J]. IEEE Proceedings.

[3] Jiefan, Cui, Lili Jiang Hemin Wang and Junzhu Wan. Research on Permanent Magnet Linear Synchronous Motor with Halbach Array[J]. Journal of Shenyang University of Technology. 2007, 29(4): 400-403.

[4] Haoming Zhang and Yukun Sun. Research of Halbach Array's Influence on Permanent Magnet Synchronous Motor's Performance [J]. Electric Machine and Control Application. 2007, 34(10): 5-7, 34.

[5] Yungang Li, Wensen Chang, Xiao Zhang and Hu Cheng. Structure Calculation of Permanent Magnet EDS Maglev Train and its Application[J]. Electric Drive for Locomotives, 2005(5): 29-32.

[6] D. B. Montgomery. Overview of the 2004 Magplane Design[C]. 18th International Conference on Magnetically Levitated Systems and Linear Drives. Shanghai, China: 106-113.

[7] Jiangbo Wang, Yaohua Li and Luguang Yan. Study on Applying the Linear Halbach Array to Eddy Current Brake System for Maglev[J]. Electric Driver. 2010, 40(5): 8-11.

[8] J. F. Hoburg. Modeling Maglev Passenger Compartment Static Magnetic Fields From Linear Halbach Permanent Magnet Arrays[J]. IEEE Transactions on Magnetics. 2004, 40(1): 59-64.


[9] Renyuan Tang. Modern Permanent Magnet Machines: Theory and Design[M]. China Machine Press, (2008).

[10] Cizhang Feng. Electromagnet Field[M]. People's Education Press. (1980).

[11] Yuanqing Zhou and Zaixing Zhang. Intelligent Robotics System[M]. Tsinghua University Press. (1989).

[12] Xiuhe Wang. Permanent Magnet Machines[M]. China Electric Power Press, (2007).