10.1186/2251-7456-6-37

Conformal mapping: Schwarz-Christoffel method for flux-switching PM machines

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  • Esin Ilhan*1,
  • Emilia T Motoasca1,
  • Johan JH Paulides1,
  • Elena A Lomonova1,
  1. Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, 5612 AZ, NL
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Published in Issue 2012-09-18

How to Cite

Ilhan, E., Motoasca, E. T., Paulides, J. J., & Lomonova, E. A. (2012). Conformal mapping: Schwarz-Christoffel method for flux-switching PM machines. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-37
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Abstract

Abstract Purpose Flux-switching permanent magnet (FSPM) machines are double salient machines with a high energy density suitable for e-mobility. For a fast design process, machine specialists need easy-to-use motor models. For the FSPM model, analytical methods cost high efforts to create and to improve them. Numerical methods such as the finite element method (FEM) have been extensively studied in the literature with little emphasis given to their alternatives. Methods This research shows the implementation of the Schwarz-Christoffel (SC) mapping for the FSPM. With this numerical method, the double salient motor geometry is transformed into a simpler geometry to reduce the model complexity. For the electromagnetic analysis, SC mapping is implemented both as a stand-alone method and as an integrated method with the tooth contour method and the orthogonal field diagram method. Results Findings are presented in a comparative analysis for all created models including the finite element method. Results show a very good agreement among the presented models. Conclusions The results obtained in this paper show that SC mapping is a good alternative to the FEM. With the provided step-by-step explanation on how to implement SC mapping, the method can be expanded to other electrical machine classes.

Keywords

  • Conformal mapping,
  • Flux-switching machines,
  • Orthogonal field theory,
  • Schwarz-Christoffel mapping
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References

  1. Kim (2009) A study on the design of an inset-permanent-magnet-type flux-reversal machine 45(6) (pp. 2859-2862) https://doi.org/10.1109/TMAG.2009.2018776
  2. Owen et al. (2010) Hybrid-excited flux-switching permanent-magnet machines with iron flux bridges 46(6) (pp. 1726-1729) https://doi.org/10.1109/TMAG.2010.2040591
  3. Gysen et al. (2010) Modeling of flux switching permanent magnet machines with Fourier analysis 46(6) (pp. 1499-1502) https://doi.org/10.1109/TMAG.2009.2039921
  4. Huang et al. (2011) A novel flux-switching permanent-magnet linear generator for wave energy extraction application 47(5) (pp. 1034-1037) https://doi.org/10.1109/TMAG.2010.2093509
  5. Ilhan et al. (2010) Analytical hybrid model for flux switching permanent magnet machines 46(6) (pp. 1762-1765) https://doi.org/10.1109/TMAG.2010.2042579
  6. Ilhan et al. (2010) Tooth contour method implementation for the flux-switching pm machines (pp. 6-8)
  7. Qi et al. (2011) Blind direction-of-arrival estimation algorithm for conformal array antenna with respect to polarisation diversity 5(4) (pp. 433-442) https://doi.org/10.1049/iet-map.2010.0166
  8. Elnakib et al. (2010) Image-based detection of corpus callosum variability for more accurate discrimination between dyslexic and normal brains (pp. 14-17)
  9. Boughrara et al. (2010)
  10. Krop et al. (2008) Application of schwarz-christoffel mapping to permanent-magnet linear motor analysis 44(3) (pp. 352-359) https://doi.org/10.1109/TMAG.2007.914513
  11. Gysen et al. (2008) Analytical and numerical techniques for solving laplace and poisson equations in a tubular permanent magnet actuator: part II. Schwarz–Christoffel mapping 44(7) (pp. 1761-1767) https://doi.org/10.1109/TMAG.2008.923438
  12. Markovic et al. (2004) Analyzing an electromechanical actuator by Schwarz–Christoffel mapping 40(4) (pp. 1858-1863) https://doi.org/10.1109/TMAG.2004.828920
  13. Driscoll and Trefethen (2002) Cambridge University Press https://doi.org/10.1017/CBO9780511546808
  14. Driscoll T: Schwarz-Christoffel toolbox for MATLAB. . Accessed August 2012
  15. http://www.math.udel.edu/driscoll/software/SC/index.html