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Optimum arrangement of PMs in surface-mounted PM machines: cogging torque and flux density harmonics

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Abstract

In surface-mounted PM machines, the cogging torque and the low-order harmonics of the air gap magnetic flux density are the main sources of the torque pulsation. These variables are strongly influenced by the distribution of the PMs on the surface of the rotor as well as the PMs’ magnetization. In the presented work, the impact of the arrangement of the PMs and the PMs’ magnetization pattern is studied. The PMs are arranged by some techniques such as PM arc optimization, PM shifting, PM segmentation and applying mixed material PMs. In addition, the parallel and radial magnetizations are investigated. For this purpose, the air gap flux density and cogging torque in the slotted SPM machines are predicted analytically. Using the analytical model and applying a direct search algorithm, the optimum arrangement for each technique is found. Moreover, to perform a multi-objective optimization, a weighted normalization method is applied. Finally, the proposed model and the obtained results are validated by finite element analysis.

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Abbreviations

R r :

Rotor radius (m)

R o :

Stator external radius (m)

R PM :

Permanent magnet region radius (m)

R s :

Stator bore radius (m)

h PM :

Height of permanent magnet (m)

h slot :

Height of stator slot (m)

b o :

Slot opening distance (m)

γ s :

Slot pitch angle

γ so :

Slot opening angle (rad)

g :

Air gap length

υ i+ /υ i− :

Angle of right/left side of the ith slot opening (rad)

τ p :

Pole pitch angle (rad)

α :

The ratio of the PM arc to the pole pitch

p :

Machine pole pairs

T cog :

Cogging torque (N m)

μ 0 :

Free space permeability

θ r :

Rotor angular position (rad)

l stk :

Machine stack length (m)

B rem :

Permanent magnet remnant flux density (T)

r/φ :

Radial/angular values in the cylindrical coordinate

ar/aφ :

The unitary, normal vectors in the radial/circumferential direction

B :

Magnetic flux density (Wb/m2)

J :

Real current density (A/m2)

H :

Magnetic field intensity (A/m)

J m :

Volume EMC density (A/m2)

J ms :

Surface EMC density (A/m)

M :

Magnetization vector (A/m)

References

  1. Hwang SM, Eom JB, Hwang GB et al (2000) Cogging torque and acoustic noise reduction in permanent magnet motors by teeth paring. IEEE Trans Magn 36(5):3144–3146

    Article  Google Scholar 

  2. Zhu ZQ, Howe D (2000) Influence of design parameters on cogging torque in permanent magnet machines. IEEE Trans Energy Convers 15(4):407–412

    Article  Google Scholar 

  3. Wu L, Zhu ZQ (2014) Analytical modeling of surface-mounted PM machines accounting for magnet shaping and varied magnet property. IEEE Trans Magn 50(7):8101511

    Article  Google Scholar 

  4. Boroujeni ST, Zamani V (2016) Influence of magnet shaping on cogging torque of surface-mounted PM machines. Int J Numer Model 29(5):859–872

    Article  Google Scholar 

  5. Chen N, Ho SL, Fu WN (2010) Optimization of permanent magnet surface shapes of electric motors for minimization of cogging torque using FEM. IEEE Trans Magn 46(10):2478–2481

    Article  Google Scholar 

  6. Pang Y, Zhu ZQ, Feng ZJ (2011) Cogging torque in cost-effective surface-mounted permanent-magnet machines. IEEE Trans Magn 47(9):2269–2276

    Article  Google Scholar 

  7. Ruangsinchaiwanich S, Zhu ZQ, Howe D (2005) Influence of magnet shape on cogging torque and back-EMF waveform in permanent magnet machines. In: Proceedings of 8th international conference on electrical machines and systems, pp 284–289

  8. Yang Y, Wang X, Zhang R, Ding T, Tang R (2006) The optimization of pole arc coefficient to reduce cogging torque in surface-mounted permanent magnet motors. IEEE Trans Magn 42(4):1135–1138

    Article  Google Scholar 

  9. Bianchi N, Bolognani S (2002) Design techniques for reducing the cogging torque in surface-mounted PM motors. IEEE Trans Magn 38(5):1259–1265

    Google Scholar 

  10. Islam MS, Sebastian T (2004) Issues in reducing the cogging torque on mass produced permanent magnet brushless Dc motor. IEEE Trans Ind Appl 40(3):813–820

    Article  Google Scholar 

  11. Lateb R, Takorabet N, Meibody Tabar F (2006) Effect of magnet segmentation on the cogging torque in surface-mounted permanent- magnet motors. IEEE Trans Magn 42(3):442–445

    Article  Google Scholar 

  12. Ashabani M, Abdel-Rady MY (2011) Multi-objective shape optimization of segmented pole permanent-magnet synchronous machines with improved torque characteristics. IEEE Trans Magn 47(4):795–804

    Article  Google Scholar 

  13. Shen Y, Zhu ZQ (2013) Analysis of electromagnetic performance of Halbach PM brushless machines having mixed grade and unequal height of magnets. IEEE Trans Magn 49(4):1461–1469

    Article  Google Scholar 

  14. Chaithongsuk S, Takorabet N, Meibody Tabar F (2009) On the use of pulse width modulation method for the elimination of flux density harmonics in the air-gap of surface PM Motors. IEEE Trans Magn 45(3):1736–1739

    Article  Google Scholar 

  15. Boroujeni ST, Zamani V (2015) A novel analytical model for no-load, slotted, surface-mounted PM machines: air gap flux density and cogging torque. IEEE Trans Magn 51(4):8104008

    Google Scholar 

  16. Boroujeni ST, Jalali P, Bianchi N (2015) Analytical modeling of no-load eccentric slotted surface mounted PM machines: cogging torque and radial force. IEEE Trans Magn 30(2):754–760

    Google Scholar 

  17. Varahram A, Mohassel JR, Mafinezhad K (2004) Optimization of array factor in linear arrays using modified genetic algorithm. Int J Eng Trans B 74(6):367–380

    Google Scholar 

  18. Ebadi F, Mardaneh M, Rahideh A, Bianchi N (2019) Analytical energy-based approaches for cogging torque calculation in surface-mounted PM motors. IEEE Trans Magn 55(5):2906107

    Article  Google Scholar 

  19. Zarko D, Ban D, Lipo TA (2006) Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance. IEEE Trans Magn 42(7):1–8

    Article  Google Scholar 

  20. Wu LJ, Zhu ZQ, Staton DA, Popescu M, Hawkins D (2012) Comparison of analytical models of cogging torque in surface-mounted PM machines. IEEE Trans Ind Electron 59(6):2414–2425

    Article  Google Scholar 

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Acknowledgements

This research is carried out under the Grant Number 96GRD1M930 of the Shahrekord University.

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Authors and Affiliations

  1. Engineering Department, Shahrekord University, Shahrekord, Iran

    Vahid Zamani Faradonbeh & Samad Taghipour Boroujeni

  2. Université de Lorraine – GREEN, Nancy, France

    Noureddine Takorabet

Authors
  1. Vahid Zamani Faradonbeh
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  2. Samad Taghipour Boroujeni
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  3. Noureddine Takorabet
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Correspondence to Samad Taghipour Boroujeni.

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Zamani Faradonbeh, V., Taghipour Boroujeni, S. & Takorabet, N. Optimum arrangement of PMs in surface-mounted PM machines: cogging torque and flux density harmonics. Electr Eng 102, 1117–1127 (2020). https://doi.org/10.1007/s00202-020-00925-8

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  • DOI: https://doi.org/10.1007/s00202-020-00925-8

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