This paper presents an analytical solution of the magnetic field in a coreless stator axial-flux permanent magnet (AFPM) machine, including axial, radial and circumferential components of the air-gap flux density. Based on the three-dimensional (3-D) analytical field solution, the paper also presents the analytical analysis of axial electromagnetic force of the rotor discs using Maxwell stress tensor method. The effect of some sizes on the axial electromagnetic force is analyzed. For the verification, 3-D finite element method (FEM) is accomplished to analyze the magnetic field and electromagnetic force. The solution and calculation are useful in design and optimization of coreless stator AFPM machines.
DaghighA., JavadiH. and TorkamanH., Design optimization of direct-coupled ironless axial flux permanent magnet synchronous wind generator with low cost and high annual energy yield, IEEE Trans. Magn.52(9) (2016), 1-11. doi: 10.1109/TMAG.2016.2560143.
2.
CvetkovskiG. and PetkovskaL., Multi-objective approach of design optimization of axial flux permanent magnet motor, International Journal of Applied Electromagnetics and Mechanics51(s1) (2016), s115-s123. doi: 10.3233/JAE-2006.
3.
StamenkovicI., MilivojevicN. and SchofieldN., Design, analysis and optimization of ironless stator permanent magnet machines, IEEE Trans. Power Elec.28(5) (2013), 2527-2538. doi: 10.1109/TPEL.2012.2216901.
4.
AydinM. and GulecM., A new coreless axial flux interior permanent magnet synchronous motor with sinusoidal rotor segments, IEEE Trans. Magn.52(7) (2016), 8105204. doi: 10.1109/TMAG.2016.2522950.
5.
LiuX.D., HuH., ZhaoJ. et al., Analytical solution of the magnetic field and EMF calculation in ironless BLDC motor, IEEE Trans. Magn.52(2) (2016), 8100510. doi: 10.1109/TMAG.2015.2481862.
6.
ChanT.F., LaiL.L. and XieS., Field computation for an axial flux permanent-magnet synchronous generator, IEEE Trans. Energy Convers.24(1) (2009), 1-11. doi: 10.1109/TEC.2008.2011830.
7.
TiegnaH., BellaraA. and AmaraY., Analytical modelling of the open-circuit magnetic fleld in axial flux permanent magnet machines with semi-closed slots, IEEE Trans. Magn.48(3) (2012), 1212-1226. doi: 10.1109/TMAG.2011.2171979.
8.
ChoiJ., LeeS., KoK. et al., Improved analytical model for electromagnetic analysis of axial flux machines with double-sided permanent magnet rotor and coreless stator windings, IEEE Trans. Magn.47(10) (2011), 2760-2763. doi: 10.1109/TMAG.2011.2151840.
9.
YazdanpanahR. and MirsalimM., Analytical study of axial-flux hybrid excitation eddy current brakes, International Journal of Applied Electromagnetics and Mechanics47(4) (2015), 885-896. doi: 10.3233/JAE-140019.
10.
VirticP., PišekP., MarciT. et al., Analytical analysis of magnetic fleld and back electromotive force calculation of an axial-flux permanent magnet synchronous generator with coreless stator, IEEE Trans. Magn.44(11) (2008), 4333-4336. doi: 10.1109/TMAG.2008.2001528.
11.
VirticP., VrazicM. and PapaG., Design of an axial flux permanent magnet synchronous machine using analytical method and evolutionary optimization, IEEE Trans. Energy Convers.31(1) (2016), 150-158. doi: 10.1109/TEC.2015.2477319.
12.
JennaneJ., FadliN., CharpentierJ.F. et al., Semi-analytical study of 3 kinds of axial flux PM actuator, International Journal of Applied Electromagnetics and Mechanics19(4) (2004), 299-302.
13.
DingX.F., LiuG.L., GuoH. et al., A 3-D magnetic equivalent circuit of an axial-flux MEMS micromotor, IEEE International Conference on Applied Superconductivity and Electromagnetic Devices, 2015. doi: 10.1109/ASEMD.2015.7453634.
14.
HuangY., GeB., DongJ. et al., 3-D analytical modeling of no-load magnetic field of ironless axial flux permanent magnet machine, IEEE Trans. Magn.48(11) (2012), 2929-2932. doi: 10.1109/TMAG.2012.2194699.
15.
YamazakiK. and KatoY., Iron loss analysis of interior permanent magnet synchronous motors by considering mechanical stress and deformation of stators and rotors, IEEE Trans. Magn.50(2) (2014), 7022504. doi: 10.1109/TMAG.2013.2282187.
16.
FeiW., LukP.C.K. and El-HasanT.S., Rotor integrity design for a high-speed model air-cored axial-flux permanent magnet generator, IEEE Trans. Industry Electronics58(9) (2011), 3848-3858. doi: 10.1109/TIE.2011.2106097.
17.
LiJ., LeeS.G. and ChoY.H., Structure analysis of axial flux permanent magnet synchronous machine for wind generators, International Journal of Applied Electromagnetics and Mechanics39(4) (2012), 1027-1033. doi: 10.3233/JAE-2012-1574.
18.
Di GerlandoA., FogliaG.M., IacchettiM.F. et al., Evaluation of manufacturing dissymmetry effects in axial flux permanent magnet machines: Analysis method based on field functions, IEEE Trans. Magn.48(6) (2012), 1995-2008. doi: 10.1109/TMAG.2011.2180919.
19.
ÖnerY. and Şenolİ., Analytical model of flux switching permanent magnet machine under armature reaction condition, International Journal of Applied Electromagnetics and Mechanics51(3) (2016), 297-306. doi: 10.3233/JAE-160020.
20.
de la BarriereO., HliouiS., Ben AhmedH. et al., 3-D formal resolution of Maxwell equations for the computation of the no-load flux in an axial flux permanent-magnet synchronous machine, IEEE Trans. Magn.48(1) (2012), 128-136. doi: 10.1109/TMAG.2011.2167347.
21.
Kreyszig E, Advanced engineering mathematics, in: New York: Wiley, 2011.
22.
ZhuZ.Q., HoweD., BolteE. et al., Instantaneous magnetic field distribution in brushless permanent magnet DC motors. I. Open-circuit field, IEEE Trans. Magn.29(1) (1993), 124-135. doi: 10.1109/20.195557.
23.
Al-SharifL., TaifourS. and KilaniM., Simulation and verification of the axial force of a linear permanent magnet synchronous actuator, International Journal of Applied Electromagnetics and Mechanics32(4) (2010), 249-265. doi: 10.3233/JAE-2010-1082.
24.
HongS.A., ChoiJ.Y., JangS.M. et al., Torque analysis and experimental testing of axial flux permanent magnet couplings using analytical field calculations based on two polar coordinate systems, IEEE Trans. Magn.50(11) (2014), 1-4. doi: 10.1109/TMAG.2014.2327954.
25.
JinP., LinH., FangS. et al., 3-D analytical linear force and rotary torque analysis of linear and rotary permanent magnet actuator, IEEE Trans. Magn.49(7) (2013), 3989-3992. doi: 10.1109/TMAG.2013.2238897.
26.
SunX.D., ShenY.C., ZhouZ. et al., Modeling and control of a bearingless permanent magnet synchronous motor, International Journal of Applied Electromagnetics and Mechanics Preprint (2016), 1-15. doi: 10.3233/JAE-160030.
27.
CaoY., YuL. and JiaH., Rotor mechanical stress and deformation analysis of coreless stator axial-flux permanent magnet machines, IEEE Magnetics Conference (Intermag), 2015. doi: 10.1109/INTMAG.2015.7156691.
