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Calculation of the Magnetic Field of the Permanent Magnet Using Multi-domain Differential Quadrature

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Intelligent Robotics and Applications (ICIRA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9244))

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Abstract

On the basis of the multi-domain differential quadrature, this paper formulates the equation of the magnetic field of the permanent magnet (PM), which is widely used in precision engineering. The multi-domain, including the PM domain and the air domain, is generated by dividing the whole computational domain of the PM. By applying the differential quadrature rule in each domain, the unknown magnetic vector potential can solved, and then the magnetic field distribution is obtained. Numerical results show that the magnetic field obtained by the multi-domain differential quadrature method is accurate and efficient, which is validated by the comparison with the finite difference method and the finite element method.

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References

  1. Meessen, K.J., Gysen, B.L.J., Paulides, J.J.H., Lomonova, E.A.: Halbach permanent magnet shape selection for slotless tubular actuators. IEEE Transactions on Magnetics 44(11 PART 2), 4305–4308 (2008)

    Article  Google Scholar 

  2. Jin, P., Yuan, Y., Jian, G., Lin, H., Fang, S., Yang, H.: Static characteristics of novel air-cored linear and rotary halbach permanent magnet actuator. IEEE Transactions on Magnetics 50(2) (2014). doi:10.1109/tmag.2013.2284277

  3. Park, M.G., Choi, J.Y., Shin, H.J., Jang, S.M.: Torque analysis and measurements of a permanent magnet type Eddy current brake with a Halbach magnet array based on analytical magnetic field calculations. J Appl Phys 115(17) (2014). doi:10.1063/1.4862523

  4. Bellman, R., Casti, J.: Differential quadrature and long-term integration. J. Math. Anal. Appl. 34(2), 235–238 (1971). doi:10.1016/0022-247x(71)90110-7

    Article  MathSciNet  MATH  Google Scholar 

  5. Shu, C.: Differential quadrature and its application in engineering. Springer (2000)

    Google Scholar 

  6. Bert, C.W., Malik, M.: Differential quadrature method in computational mechanics: A review. Applied Mechanics Reviews 49(1), 1–27 (1996)

    Article  Google Scholar 

  7. Jafari, A.A., Eftekhari, S.A.: A new mixed finite element-differential quadrature formulation for forced vibration of beams carrying moving loads. Journal of Applied Mechanics, Transactions ASME 78(1), 0110201–01102016 (2011)

    Article  Google Scholar 

  8. Karami, G., Malekzadeh, P.: Application of a new differential quadrature methodology for free vibration analysis of plates. International Journal for Numerical Methods in Engineering 56(6), 847–868 (2003)

    Article  MATH  Google Scholar 

  9. Xu, Q., Mazumder, P.: Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods. IEEE Transactions on Microwave Theory and Techniques 50(10), 2233–2246 (2002)

    Article  Google Scholar 

  10. Tang, M., Mao, J.: A differential quadrature method for the transient analysis of multiconductor transmission lines. In: 2008 International Conference on Microwave and Millimeter Wave Technology Proceedings, ICMMT 2008, pp. 1423–1426 (2008)

    Google Scholar 

  11. Tang, M., Mao, J.F., Li, X.C.: Analysis of interconnects with frequency-dependent parameters by differential quadrature method. IEEE Microwave and Wireless Components Letters 15(12), 877–879 (2005)

    Article  Google Scholar 

  12. Liu, J., Wang, X.W.: An assessment of the differential quadrature time integration scheme for nonlinear dynamic equations. Journal of Sound and Vibration 314(1–2), 246–253 (2008). doi:10.1016/j.jsv.2008.01.004

    Article  Google Scholar 

  13. Furlani, E.P.: Permanent Magnet and Electromechanical Devices, Materials, Analysis, and Applications Academic press series in electromagnetism. Academic Press (2001)

    Google Scholar 

  14. Halbach, K.: Design of permanent multipole magnets with oriented rare earth cobalt material. Nuclear Instruments and Methods 169(1), 1–10 (1980)

    Article  MathSciNet  Google Scholar 

  15. Lee, M.G., Gweon, D.G.: Optimal design of a double-sided linear motor with a multi-segmented trapezoidal magnet array for a high precision positioning system. Journal of Magnetism and Magnetic Materials 281(2–3), 336–346 (2004)

    Article  Google Scholar 

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Correspondence to Bo Zhang .

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Chen, Jw., Ma, Lt., Zhang, B., Ding, H. (2015). Calculation of the Magnetic Field of the Permanent Magnet Using Multi-domain Differential Quadrature. In: Liu, H., Kubota, N., Zhu, X., Dillmann, R., Zhou, D. (eds) Intelligent Robotics and Applications. ICIRA 2015. Lecture Notes in Computer Science(), vol 9244. Springer, Cham. https://doi.org/10.1007/978-3-319-22879-2_17

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  • DOI: https://doi.org/10.1007/978-3-319-22879-2_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22878-5

  • Online ISBN: 978-3-319-22879-2

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