access icon openaccess Calculation of 3D transient Eddy current by the face-smoothed finite element–boundary element coupling method

This is an open access article published by the IET and CEPRI under the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/3.0/)
Received 08/10/2019, Accepted 21/02/2020, Revised 01/02/2020, Published 26/02/2020

To calculate the distribution of the magnetic field and eddy current density on the surface of an aluminium plate, a method that couples the face-smoothed finite element method (FS-FEM) to the boundary element method (BEM) is proposed in this study. This method combines the advantages of the FS-FEM and BEM, which can rapidly and accurately calculate the distributions of vertical magnetic field and eddy current field on the surface of an aluminium plate. The structural parameters and material properties of the coil and aluminium plate are considered. An accurate three-dimensional calculation model is established. Then, the vertical magnetic field and eddy current field distributions are calculated in this study. In the case of the same grid density, compared with the finite element–boundary element coupling algorithm, the simulation results show that the FS-FEM and the boundary element coupling method have obvious advantage in improving the calculation accuracy. The maximum relative error between the calculated results and measured results is only 4%. The proposed method in this study is available for reference to the transient open-domain eddy current field analysis.

Inspec keywords: boundary-elements methods; finite element analysis

Other keywords: face-smoothed finite element–boundary element coupling method; vertical magnetic field; aluminium plate; transient open-domain eddy current field analysis; face-smoothed finite element method; eddy current density; eddy current field distributions; boundary element method; finite element–boundary element coupling algorithm

Subjects: Finite element analysis; Numerical analysis; Numerical approximation and analysis; Finite element analysis

References

    1. 1)
      • 7. Matsuoka, F., Kameari, A.: ‘Calculation of three-dimensional eddy current by FEM–BEM coupling method’, IEEE Trans. Magn., 1988, 24, (1), pp. 182–185.
    2. 2)
      • 3. Nassiri, A., Kinsey, B., Chini, G.: ‘Shear instability of plastically deforming metals in high-velocity impact welding’, J. Mech. Phys. Solids, 2016, 95, (1), pp. 351–373.
    3. 3)
      • 27. Onuki, T., Wakao, T., Shimazaki, M.: ‘3D eddy current analysis by the hybrid FE-BE method using magnetic field intensity H’, IEEE Trans. Magn., 1992, 28, (5), pp. 2259–2261.
    4. 4)
      • 6. Badies, Z., Matsumoto, Y., Aoki, K., et al: ‘An effective 3D finite element scheme for computing electromagnetic fields distortions due to defects in eddy current nondestructive evaluation’, IEEE Trans. Magn., 1997, 32, (2), pp. 1012–1020.
    5. 5)
      • 10. Layth, Q., Razzak, M.: ‘Hybrid finite-element–boundary element analysis of a single-sided sheet rotor linear induction motor’, IEEE Trans. Energy Convers., 2014, 29, (1), pp. 188–195.
    6. 6)
      • 22. Liu, G.R., Nguyen, T.T., Lam, K.Y.: ‘An edge-based smoothed finite element method (ES-FEM) for static and dynamic problems of solid mechanics’, J. Sound Vib., 2009, 320, (2), pp. 1100–1130.
    7. 7)
      • 16. Kannadasan, R., Valsalal, P.: ‘Modelling and validation of metal oxide surge arrester for very fast transients’, High Volt., 2018, 3, (2), pp. 147–153.
    8. 8)
      • 4. Xing, L.L., Sheng, J.N.: ‘The ideal crack model of a conducting plate in eddy current non-destructive testing’, Proc. CSEE, 2002, 22, (2), pp. 41–46(in Chinese).
    9. 9)
      • 12. Lu, Y.M., Peyton, A., Yin, W.L.: ‘Acceleration of frequency sweeping in Eddy-current computation’, IEEE Trans. Magn., 2017, 53, (7), pp. 1–8.
    10. 10)
      • 25. Chen, L., Nguyen, H., Nguyen, T., et al: ‘Assessment of smoothed point interpolation methods for elastic mechanics’, Int. J. Numer. Methods Biomed. Eng., 2010, 26, (1), pp. 1635–1655.
    11. 11)
      • 19. He, Z.C., Li, G.R., Zhong, H.G., et al: ‘Analysis of an ungauged T, phi-phi formulation of the eddy current problem with currents and voltage excitations’, Esaim-Math. Model. Numer. Anal., 2017, 51, (6), pp. 2487–2509.
    12. 12)
      • 28. Fujiwara, K., Nakata, T.: ‘Results for benchmark problem 7 (asymmetrical conductor with a hole)’, COMPEL- Int. J. Comput. Math. Electr. Electron. Eng., 1990, 9, (3), pp. 137–154.
    13. 13)
      • 5. Fan, X.F., Chen, T., He, Y.T., et al: ‘An excitation coil layout method for improving the sensitivity of a rosette flexible eddy current array sensor’, Smart Mater. Struct., 2020, 29, (1), pp. 1–16.
    14. 14)
      • 24. Xie, D.X., Yao, Y.Y.: ‘Finite element analysis of three-dimensional eddy current field’ (Mech. Ind. Press,, China,, 2001, 2nd edn), pp. 9–16(in Chinese).
    15. 15)
      • 23. He, Z.C., Li, G.Y., Zhong, Z.H., et al: ‘An improved modal analysis for three-dimensional problems using face-based smoothed finite element method (FS-FEM)’, Acta Mech. Solida Sin., 2013, 26, (2), pp. 140–150.
    16. 16)
      • 21. Nguyen, T., Liu, G.R., Do, H.C., et al: ‘An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh’, Comput. Mech., 2009, 45, (1), pp. 23–44.
    17. 17)
      • 14. Lu, Y.M., Zhao, Q., Hu, P.P., et al: ‘Prediction of the asymptotical magnetic polarization tensors for cylindrical samples using the boundary element method’. Sensors Applications Symp. (SAS), Zadar, Croatia, April 2015, pp. 362–365.
    18. 18)
      • 11. Hollaus, K., Schoberl, J.: ‘Some 2D multiscale finite-element formulations for the eddy current problem in iron laminates’, IEEE Trans. Magn., 2018, 54, (4), pp. 1–15.
    19. 19)
      • 15. Li, Z.L., Du, B.X., Li, W.: ‘Evaluation of high-voltage AC cable grounding systems based on the real-time monitoring and theoretical calculation of grounding currents’, High Volt., 2018, 3, (1), pp. 38–43.
    20. 20)
      • 1. Li, X.X., Cao, Q.L., Lai, Z.P., et al: ‘Bulging behavior of metallic tubes during the electromagnetic forming process in the presence of a background magnetic field’, J. Mater. Process. Technol., 2020, 276, (1), pp. 1–16.
    21. 21)
      • 17. Liu, G.R., Nguyen, T.: ‘Smoothed finite element methods’ (CRC Press, Boca Raton, 2010).
    22. 22)
      • 9. Tong, Z.F., Xie, S.J., Li, X.D., et al: ‘Efficient numerical simulation of eddy current pulsed thermography NDT signals based on FEM–BEM method and energy equivalent principle’, Infrared Phys. Technol., 2019, 101, (1), pp. 138–145.
    23. 23)
      • 26. Zhao, W.C., Chen, L.L., Chen, H.B., et al: ‘Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM–BEM method’, Int. J. Numer. Methods Eng., 2019, 119, (5), pp. 404–431.
    24. 24)
      • 8. Ding, Y.M., Wang, H.: ‘FEM–BEM analysis of tyre-pavement noise on porous asphalt surfaces with different textures’, Int. J. Pavement Eng., 2019, 20, (9), pp. 1090–1097.
    25. 25)
      • 13. Zhou, W.B., Lu, Y.M., Chen, Z.Q., et al: ‘Three-dimensional electromagnetic mixing models for dual-phase steel microstructures’, Appl. Sci., 2018, 8, (1), p. 529.
    26. 26)
      • 20. Feng, S.Z., Cui, X.Y., Chen, F., et al: ‘An edge/face-based smoothed radial point interpolation method for static analysis of structures’, Eng. Anal. Bound. Elem., 2016, 68, (2), pp. 1–10.
    27. 27)
      • 2. Almind, M.R., Vendelbo, S.B., Hansen, M.F, et al: ‘Improving performance of induction-heated steam methane reforming’, Catal. Today, 2016, 342, (1), pp. 13–20.
    28. 28)
      • 18. Vomin, T., Chau, A., Nguyen, T., et al: ‘A node-based smoothed finite-element method for stability analysis of dual square tunnels in cohesive-frictional soils’, Scientia Iranica, 2018, 25, (3), pp. 1105–1121.
http://iet.metastore.ingenta.com/content/journals/10.1049/hve.2019.0279
Loading

Related content

content/journals/10.1049/hve.2019.0279
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading