This paper proposes a new virtual Halbach analytical method for improved Halbach permanent magnet (PM) slotless planar linear actuators, which have mixed neodymium iron baron (NdFeB) magnets and ferrite magnets to form a two-segment quasi-Halbach topology with different heights of main and auxiliary magnetic poles. The method has four steps, which are described in detail in the paper. One of the key steps is to visually regard the permanent magnet region magnetized only in the y direction as a Halbach array structure with a magnetization amplitude of 0 in the x direction that satisfies the Newman boundary condition. The investigation shows that the results of the new analytical method are in good agreement with the finite element method. Using this analytical method, the effect of improved Halbach permanent magnet slotless planar linear actuator with unequal height of the main and auxiliary magnetic poles on the magnetic field waveform is analyzed by means of a parametric research.
WangJ.HoweD. and JewellG.W., Fringing in tubular permanent-magnet machines: Part II. Cogging force and its minimization, IEEE Transactions on Magnetics39(2003) 3517–3522.
2.
ShenY. and ZhuZ.Q., Analysis of electromagnetic performance of Halbach PM brushless machines having mixed grade and unequal height of magnets, IEEE Transactions on Magnetics49(2013) 1461–1469.
3.
HuangH.JingL.QuR. and LiD., Analysis and application of discrete Halbach magnet array with unequal arc lengths and unequally changed magnetization directions, IEEE Transactions on Applied Superconductivity28(2018) 5201305.
4.
JiaoZ.WangT. and LiangY., Design of a tubular linear oscillating motor with novel compound Halbach magnet array, IEEE-ASME Transactions on Mechatronics22(2017) 498–508.
5.
XuY. and FengK., Analysis on toothless permanent magnet machine with Halbach array, in: 2006 CES/IEEE 5th International Power Electronics and Motion Control Conference, IPEMC, 2006, pp. 1–5.
6.
ZhuZ.Q. and HoweD., Halbach permanent magnet machines and applications: A review, IEE Proceedings Electric Power Applications148(2001) 299–308.
7.
HalbachK., Design of permanent multipole magnets with oriented rare earth cobalt material, Nuclear Instruments and Methods169(1980) 1–10.
8.
TiangT.L.IshakD.LimC.P. and KamarolM., A novel analytical method using virtual PM blocks to optimize magnet segmentations in surface-mounted PM synchronous machines, in: 2015 International Conference on Electrical Machines and Systems, ICEMS, 2015, pp. 1278–1283.
9.
DaiX.CaoJ.LongY.LiangQ.MoJ. and WangS., Analytical modeling of an eddy-current adjustable-speed coupling system with a three-segment Halbach magnet array, Electric Machines and Power Systems43(2015) 1891–1901.
10.
XiaC.GuoL. and WangH., Modeling and analyzing of magnetic field of segmented Halbach array permanent magnet machine considering gap between segments, IEEE Transactions on Magnetics50(2014) 1–9.
11.
AshabaniM. and MohamedA.R.I., Multiobjective shape optimization of segmented pole permanent-magnet synchronous machines with improved torque characteristics, IEEE Transactions on Magnetics47(2011) 795–804.
12.
IsfahaniA.H., Analytical framework for thrust enhancement in permanent-magnet (PM) linear synchronous motors with segmented PM poles, IEEE Transactions on Magnetics46(2010) 1116–1122.
13.
MarkovicM. and PerriardY., Optimization design of a segmented Halbach permanent-magnet motor using an analytical model, IEEE Transactions on Magnetics45(2009) 2955–2960.
14.
LeeM.G. and GweonD.G., Optimal design of a double-sided linear motor with a multi-segmented trapezoidal magnet array for a high precision positioning system, J. Magn. Magn. Mater.281(2004) 336–346.
15.
WangN.WangD.ChenK. and WuH., Research on analytical model and design formulas of permanent magnetic bearings based on Halbach array with arbitrary segmented magnetized angle, J. Magn. Magn. Mater.410(2016) 257–264.
16.
HogbergS.PedersenT.S.BendixenF.B.MijatovicN. and HolbollJ., Direct reuse of rare earth permanent magnets - wind turbine generator case study, in: 2016 XXII International Conference on Electrical Machines, ICEM, 2016, pp. 1625–1629.
17.
WuL. and ZhuZ.Q., Analytical modeling of surface-mounted PM machines accounting for magnet shaping and varied magnet property distribution, IEEE Transactions on Magnetics50(2014) 1–11.
18.
HongH. and YooJ., Shape design of the surface mounted permanent magnet in a synchronous machine, IEEE Transactions on Magnetics47(2011) 2109–2117.
19.
LaskarisK.I. and KladasA.G., Permanent-magnet shape optimization effects on synchronous motor performance, IEEE Transactions on Industrial Electronics58(2011) 3776–3783.
20.
TavanaN.R. and ShoulaieA., Analysis and design of magnetic pole shape in linear permanent-magnet machine, IEEE Transactions on Magnetics46(2010) 1000–1006.
21.
YongP.ZhuZ.Q. and FengZ.J., Cogging torque in cost-effective surface-mounted permanent-magnet machines, IEEE Transactions on Magnetics47(2011) 2269–2276.
22.
MeessenK.J.GysenB.PaulidesJ. and LomonovaE.A., Halbach permanent magnet shape selection for slotless tubular actuators, IEEE Transactions on Magnetics44(2008) 4305–4308.
23.
ZhangX.ZhangC.YuJ. and LiL., Analytical model of magnetic field of a permanent magnet synchronous motor with a trapezoidal Halbach permanent magnet array, IEEE Transactions on Magnetics99(2019) 1–5.
24.
DuanJ.SongX. and ZhangK., A novel 3-D analytical modeling method of trapezoidal shape permanent magnet Halbach array for multi-objective optimization, Journal of Electrical Engineering and Technology14(2019) 635–643.
25.
IsfahaniA.H.Vaez-ZadehS. and RahmanM.A., Performance improvement of permanent magnet machines by modular poles, IET Electric Power Applications3(2009) 343–351.
26.
IsfahaniA.H.Vaez-ZadehS. and RahmanM.A., Using modular poles for shape optimization of flux density distribution in permanent-magnet machines, IEEE Transactions on Magnetics44(2008) 2009–2015.
27.
NiY.LiuY. and WangQ., Magnetic field analysis and optimisation of permanent magnet machines with novel two-segment Halbach array, IET Electric Power Applications13(2019) 1355–1364.
28.
ZhuZ.Q.WuL.J. and XiaZ.P., An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent-magnet machines, IEEE Transactions on Magnetics46(2010) 1100–1115.
29.
JinP.YuanY. and LinH., General analytical method for magnetic field analysis of halbach magnet arrays based on magnetic scalar potential, Journal of Magnetics18(2013) 95–104.
30.
SunR.X.DengZ.G.GouY.F.LiY.J.ZhengJ.WangS.Y. and WangJ.S., Feasibility of low-cost magnetic rail designs by integrating ferrite magnets and NdFeB magnets for HTS Maglev systems, International Journal of Modern Physics B29(2015) 1542043.
31.
SunR.ZhengJ.ZhengB.QianN.LiJ. and DengZ., New magnetic rails with double-layer Halbach structure by employing NdFeB and ferrite magnets for HTS maglev, J. Magn. Magn. Mater.445(2018) 44–48.
32.
LiZ.WangD. and ZhengD., Analytical predictions and analysis of electromagnetic field and torque for eddy-current couplers with Quasi-Halbach magnet array, International Journal of Applied Electromagnetics and Mechanics57(2018) 347–366.
33.
JangG.KooM. and KimJ., Torque characteristic analysis and measurement of axial flux-type non-contact permanent magnet device with Halbach array based on 3D analytical method, AIP advances7(2017) 0566475.
34.
KooM.ChoiJ.ShinH. and KimJ., No-load analysis of PMLSM with Halbach array and pm overhang based on three-dimensional analytical method, IEEE Transactions on Applied Superconductivity26(2016) 0604905.
35.
MallekM.TangY. and LeeJ., An analytical subdomain model of torque dense Halbach array motors, Energies11(2018) 3254.
