volume | PIER Journals

Abstract

The aim of this paper is to develop a hybrid modeling approach based on direct coupling between the finite element method (FEM) and the partial element equivalent circuits method (PEEC). Through this FEM-PEEC approach, we can efficiently compute the three-dimensional eddy current distribution created by a rectangular coil (exciting coil) in conductive and magnetic structures having heterogeneous dimensions. Magnetic field created by the rectangular coil is given by calculating quasi-static Green's function integrals. In goal to construct rectangular coil, the calculation is made for elementary parallelepipedic conductors oriented respectively in x and y directions. By this manner, three possible configurations are proposed and compared to show errors, especially in corners. By only meshing the active parts of the domain (without air region), we confirm through the issued results that the proposed methodology contributes to accelerate the execution time while maintaining the precision. The obtained results are validated with the numerical ones by 3D FEM (Flux 3D Software).

1. She, S., Y. Chen, Y. He, Z. Zhou, and X. Zou, "Optimal design of remote field eddy current testing probe for ferromagnetic pipeline inspection," J. Measurement, Vol. 168, No. 2, 108306, 2020.

2. Menana, H. and M. Feliachi, "Electromagnetic characterization of the CFRPs anisotropic conductivity: Modeling and measurements," EPJAP, Vol. 53, No. 2, 21101-21106, 2011.

3. Mohdeb, N., "Comparative study of circular flat spiral coils structure effect on magnetic resonance wireless power transfer performance," Progress In Electromagnetics Research M, Vol. 94, 119-129, 2020.
doi:10.2528/PIERM20051705

4. Wu, F., S. K. Moon, and H. Son, "Orientation measurement based on magnetic inductance by the extended distributed multi-pole model," Sensors, Vol. 14, 11504-11521, 2014.
doi:10.3390/s140711504

5. Gendron, M., B. Hazel, E. Boudreault, H. Champliaud, and X. Pham, "Coupled thermo-electromagnetic model of a new robotic high-frequency local induction heat treatment system for large steel components," Applied Thermal Engineering, Vol. 150, 372-385, 2019.
doi:10.1016/j.applthermaleng.2018.12.156

6. Boudreault, E., B. Hazel, J. Côté, and S. Godin, "A new robotic process for in situ heat treatment on large steel components," Proceedings of ASME Power Conference, V002T06A001, Boston, Massachusetts, USA, 2013.

7. Fu, X., B. Wang, X. Zhu, X. Tang, and H. Ji, "Numerical and experimental investigations on large-diameter gear rolling with local induction heating process," IJAMT, Vol. 91, No. 1-4, 1-11, 2017.

8. Kruzík, M. and A. Prohl, "Recent developments in the modeling, analysis, and numerics of ferromagnetism," SIAM Review, Vol. 48, No. 3, 439-483, 2006.
doi:10.1137/S0036144504446187

9. Albertz, D., S. Dappen, and G. Henneberger, "Calculation of the 3D nonlinear eddy current field in moving conductors and its application to braking systems," IEEE Trans. on Magnetics, Vol. 32, No. 3, 768-771, 1996.
doi:10.1109/20.497353

10. Aimé, J., B. Cogitore, G. Meunier, E. Clavel, and Y. Maréchal, "Numerical methods for eddy currents modeling of planar transformers," IEEE Trans. on Magnetics, Vol. 47, No. 5, 1014-1017, 2011.
doi:10.1109/TMAG.2010.2091398

11. Versaci, M., G. Angiulli, P. di Barba, and F. C. Morabito, "Joint use of eddy current imaging and fuzzy similarities to assess the integrity of steel plates," Open Physics, Vol. 18, No. 1, 230-240, 2020.
doi:10.1515/phys-2020-0159

12. Djemoui, S., H. Allag, M. Chebout, and H. Bouchekara, "Partial electrical equivalent circuits and finite difference methods coupling; application to eddy currents calculation for conductive and magnetic thin plates," Progress In Electromagnetics Research C, Vol. 114, 83-96, 2021.
doi:10.2528/PIERC21051602

13. Allag, H., J.-P. Yonnet, M. Fassenet, and M. E. H. Latreche, "3D analytical calculation of interactions between perpendicularly magnetized magnets - Application to any magnetization direction," Sensor Letters, Vol. 7, No. 3, 486-491, 2009.
doi:10.1166/sl.2009.1094

14. Albanese, R., G. Rubinacci, A. Tamburrino, S. Ventre, and F. Villone, "A fast 3D eddy current integral formulation," COMPEL, Vol. 20, No. 2, 317-331, 2001.
doi:10.1108/03321640110383221

15. Chebout, M., H. Azizi, and M. R. Mekideche, "A model assisted probability of detection approach for ecndt of hidden defect in aircraft structures," Progress In Electromagnetics Research Letters, Vol. 95, 1-8, 2021.
doi:10.2528/PIERL20092701

16. Simkin, J. and C. W. Trowbridge, "On the use of the total scalar potential in the numerical solution of field problem in electromagnetics," International Journal in the Numerical Methods in Engineering, Vol. 14, 423-440, 1979.

17. Le-Duc, T., G. Meunier, O. Chadebec, and J.-M. Guichon, "A new integral formulation for eddy current computation in thin conductive shells," IEEE Trans. on Magnetics, Vol. 48, No. 2, 427-430, 2012.
doi:10.1109/TMAG.2011.2173920

18. Chadebec, O., J. L. Coulomb, and F. Janet, "A review of magnetostatic moment method," IEEE Tran. on Magnetics, Vol. 42, No. 4, 515-520, 2006.
doi:10.1109/TMAG.2006.870929

19. Kruzík, M. and A. Prohl, "Recent developments in the modeling, analysis, and numerics of ferromagnetism," SIAM Review, Vol. 48, No. 3, 439-483, 2006.
doi:10.1137/S0036144504446187

20. Albertz, D., S. Dappen, and G. Henneberger, "Calculation of the 3D nonlinear eddy current field in moving conductors and its application to braking systems," IEEE Trans. on Magnetics, Vol. 32, No. 3, 768-771, 1996.
doi:10.1109/20.497353

21. Zarko, D., S. Stipetic, M. Martinovic, M. Kovacic, T. Jercic, and Z. Hanic, "Reduction of computational efforts in finite element based permanent magnet traction motor optimization," IEEE Transactions on Industrial Electronics, Vol. 65, No. 2, 1799-1807, 2018.
doi:10.1109/TIE.2017.2736485

22. Aomar, L., H. Allag, M. Feliachi, and J. P. Yonnet, "3-D integral approach for calculating mutual interactions between polygon-shaped massive coils," IEEE Trans. on Magnetics, Vol. 53, No. 11, 1-5, 2017.
doi:10.1109/TMAG.2017.2706022

23. Allag, H. and J.-P. Yonnet, "3-D analytical calculation of the torque and force exerted between two cuboidal magnets," IEEE Trans. on Magnetics, Vol. 45, No. 10, 3969-3972, 2009.
doi:10.1109/TMAG.2009.2025047

24. Allag, H., J.-P. Yonnet, and M. E. H. Latreche, "Analytical calculation of the torque exerted between two perpendicularly magnetized magnets," Journal of Applied Physics, Vol. 109, No. 7, 07E701, 2011.
doi:10.1063/1.3535148

25. Babic, S. and C. Akyel, "New formulas for mutual inductance and axial magnetic force between magnetically coupled coils: Thick circular coil of the rectangular cross-section-thin disk coil (Pancake)," IEEE Trans. on Magnetics, Vol. 49, No. 2, 860-868, 2013.
doi:10.1109/TMAG.2012.2212909

26. Ekman, J., G. Antonini, A. Orlandi, and A. E. Ruehli, "Stability of PEEC models with respect to partial element accuracy," Symposium on EMC, Vol. 1, 271-276, Santa Clara, California, USA, 2004.

27. Ruehli, A. E., "Inductance calculations in a complex integrated circuit environment," IBM Journal of Research and Development, Vol. 16, No. 5, 470-481, 1972.
doi:10.1147/rd.165.0470

28. Antonini, G., D. Deschrijver, and T. Dhaene, "Broadband macromodels for retarded partial element equivalent circuit (rPEEC) method," IEEE Trans. EMC, Vol. 49, 35-48, 2007.

29. Babic, S. and C. Akyel, "New formulas for mutual inductance and axial magnetic force between magnetically coupled coils: Thick circular coil of the rectangular cross-section-thin disk coil (Pancake)," IEEE Trans. on Magnetics, Vol. 49, No. 2, 860-868, 2013.
doi:10.1109/TMAG.2012.2212909

30. Ekman, J., G. Antonini, A. Orlandi, and A. E. Ruehli, "Stability of PEEC models with respect to partial element accuracy," Symposium on EMC, Vol. 1, 271-276, Santa Clara, California, USA, 2004.

31. Ruehli, A. E., G. Antonini, and L. Jiang, Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques, Wiley & Sons, Inc., 2017.
doi:10.1002/9781119078388

32. Kwon, O. M., M. V. K. Chari, S. J. Salon, and K. Sivasubramaniam, "Development of integral equation solution for 3-D eddy current distribution in a conducting body," IEEE Tran. on Magnetics, Vol. 39, No. 5, 2612-2614, 2003.
doi:10.1109/TMAG.2003.816497

33. Kriezis, E. E., T. D. Tsiboukis, S. M. Panas, and J. A. Tegopoulos, "Eddy currents: Theory and applications," Proceeding of the IEEE, Vol. 80, No. 10, 1559-1589, 1992.
doi:10.1109/5.168666

Dr. Lyes Aomar

Dr. Hicham Allag