This paper proposes a 2D semi-analytical electromagnetic model to compute the magnetic field and eddy current generated by a variable current density along a conducting billet of induction heater. The developed model is based on the combination of the discretization method and the Biot-Savart theory. Firstly, the analytical solutions of the vector potential and the magnetic field are calculated in all elements discretized cylindrical geometry using the law of Biot-Savart. Then, the total field is determined by the contribution of the superposition of each element of the discretized geometry. The eddy currents are computed using the Ampere law, and it also allows us to determine the exact resulting heating power density, which is the heat source of the thermal problem. The results obtained are in agreement with those obtained using finite element method. Therefore, the developed magnetic model presents a fast and accurate tool for the design of induction heating devices.
2. Abdi, A., Y. Ouazir, and G. Barakat, Y. Amara, "Permanent magnet linear induction heating device: New topology enhancing performances," COMPEL --- The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 37, No. 5, 1755-1767, Oct. 2018.
3. Ho, S. L., J. Wang, and Y. H. Wang, "A novel crossed traveling wave induction heating system and nite element analysis of eddy current and temperature distributions," IEEE Transactions on Magnetics, Vol. 45, No. 10, 4777-4780, Oct. 2009.
4. Ouazir, Y., A. Abdi, and H. Bensaidane, "2D analytical solution of transverse flux induction heating of the aluminum plates," 2012 XXth International Conference on Electrical Machines, 2733-2738, Marseille, France, Sep. 2012.
5. Tavakoli, M. H., H. Karbaschi, and F. Samavat, "Computational modeling of induction heating process," Progress In Electromagnetics Research Letters, Vol. 11, 93-102, 2009.
6. Mach, F., P. Karban, I. Dolezel, P. Sima, and Z. Jelinek, "Model of induction heating of rotating non-magnetic billets and its experimental verification," IEEE Transactions on Magnetics, Vol. 50, No. 2, 309-312, Feb. 26, 2014.
7. Han, W., K. T. Chau, Z. Zhang, and C. Jiang, "Single-source multiple-coil homogeneous induction heating," IEEE Transactions on Magnetics, Vol. 53, No. 11, 1-6, Jun. 2017.
8. Moro, F. and L. Codecasa, "A 3-D hybrid cell method for induction heating problems," IEEE Transaction on Magnetics, Vol. 53, No. 6, 1-4, Jun. 2017.
9. Qin, Z., H. Talleb, and Z. Ren, "A proper generalized decomposition-based solver for nonlinear magnetothermal problems," IEEE Transactions on Magnetics, Vol. 52, No. 1, 1-11, Oct. 2016.
10. D'Angelo, L. A. M. and H. De Gersem, "Quasi-3D finite-element method for simulating cylindrical induction-heating devices," IEEE Transactions on Magnetics, Vol. 2, 134-141, Aug. 2017.
11. Paul, S., J. Wright, and J. Z. Bird, "3-D steady-state eddy current dampingand stiffness for a finite thickness conductive plate," IEEE Transactions on Magnetics, Vol. 50, No. 11, 6301404, Nov. 2014.
12. Boughrara, K., F. Dubas, and R. Ibtiouen, "2-D exact analytical method for steady-state heat transfer prediction in rotating electrical machines," IEEE Transactions on Magnetics, Vol. 54, No. 9, 1-19, Sept. 2018.
13. Jin, P., Y. Tian, Y. Lu, Y. Guo, G. Lei, and J. Zhu, "3-D analytical magnetic field analysis of the eddy current coupling with Halbach magnets," IEEE Transactions on Magnetics, Vol. 56, No. 1, 1-4, Jan. 2020.
14. Abdi, A., Y. Ouazir, G. Barakat, and Y. Amara, "Transient quasi-3D magneto-thermal analytical solution in pm induction heating device," COMPEL --- The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 39 , No. 5, 1131-1144, 2020.
15. Lubin, T. and A. Rezzoug, "3-D analytical model for axial-flux eddy-current couplings and brakes under steady-state conditions," IEEE Transactions on Magnetics, Vol. 51, No. 10, 1-12, Oct. 2015.
16. Diriye, A., Y. Amara, and G. Barakat, "Three-dimensional modeling of permanents magnets synchronous machines using a 3D reluctance network," 2018 XIII International Conference on Electrical Machines, 2304-2310, Alexandroupoli, Greece, Sep. 2018.
17. Jin, P., Y. Yuan, J. Minyi, F. Shuhua, L. Heyun, H. Yang, and S. L. Ho, "3-D analytical magnetic field analysis of axial ux permanent magnet machine," IEEE Transactions on Magnetics, Vol. 50, No. 11, 8103504, Nov. 2014.
18. Sahu, R., P. Pellerey, and K. Laskaris, "Eddy current loss model unifying the effects of reaction field and non-homogeneous 3-D magnetic field," IEEE Transactions on Magnetics, Vol. 56, No. 2, 1-4, Jan. 13, 2020.
19. Sun, X., S. Luo, L. Chen, R. Zhao, and Z. Yang, "Suspension force modeling and electromagnetic characteristics analysis of an interior bearingless permanent magnet synchronous motor," Progress In Electromagnetics Research B, Vol. 69, 31-45, 2016.
20. Verez, G., G. Barakat, and Y. Amara, "Influence of slots and rotor poles combinations on noise and vibrations of magnetic origins in `U'-core flux-switching permanent magnet machines," Progress In Electromagnetics Research B, Vol. 61, 149-168, 2014.