volume | PIER Journals

2017-10-30

Harmonically Time Varying, Traveling Electromagnetic Fields Along a Laminate Approximated by a Homogeneous, Anisotropic Block with Infinite Length

Birger Marcusson,

Mr. Birger Marcusson

Engineering Sciences/Electricity

Uppsala University

Sweden

Homepage

Claes Urban Lundin

Dr. Claes Urban Lundin

Department of Engineering Sciences

Uppsala University

Sweden

Homepage

Progress In Electromagnetics Research B, Vol. 79, 65-81, 2017

doi:10.2528/PIERB17081706 | Google Scholar

Abstract

Analytical expressions that include arbitrarily directed fields on all laminate boundaries can be used for calculation of the fields inside the laminate when the boundary fields are known from, e.g., measurements. A linear laminate block could be used in non-destructive testing for comparisons between different laminates. This article contains derivation of Fourier series of harmonically time varying, traveling electromagnetic fields in homogeneous, anisotropic approximations of laminates. The component of the magnetic field strength in the stacking direction is used as a source term in twodimensional Poisson equations for the magnetic field strength in other directions. This approximation is here used in three dimensions under the precondition that the conductivity is much smaller in the laminate stacking direction than in the other directions. Sine interpolation and different choices of types of boundary conditions are discussed. Different alternative subdivisions of the Poisson boundary value problems are treated. Shorted derivations of simple analytical expressions are given for both traveling and standing waves in two dimensions. Results from Fourier series in the three-dimensional case are compared with results from finite element calculations.

Download Full Article (594) View Full Article volume

Citation

Copy Export

Birger Marcusson, and Claes Urban Lundin, "Harmonically Time Varying, Traveling Electromagnetic Fields Along a Laminate Approximated by a Homogeneous, Anisotropic Block with Infinite Length," Progress In Electromagnetics Research B, Vol. 79, 65-81, 2017.
doi:10.2528/PIERB17081706

References

1. Cheng, L., S. Sudo, Y. Gao, H. Dozono, and K. Muramatsu, "Homogenization technique of laminated core taking account of eddy currents under rotational flux without edge effect," IEEE Transactions on Magnetics, Vol. 49, No. 5, 1969-1972, May 2013.
doi:10.1109/TMAG.2013.2245876 Google Scholar

2. Reece, A. B. J. and T. W. Preston, Finite Element Methods in Electrical Power Engineering, Oxford University Press, 2000.

3. Lin, D., P. Zhou, Z. Badics, W. Fu, Q. Chen, and Z. Cendes, "A new nonlinear anisotropic model for soft magnetic materials," IEEE Transactions on Magnetics, Vol. 42, No. 4, 963-966, Apr. 2006.
doi:10.1109/TMAG.2006.871380 Google Scholar

4. Bermudez, A., D. Gomez, and P. Salgado, "Eddy-current losses in laminated cores and the computation of an equivalent conductivity," IEEE Transactions on Magnetics, Vol. 44, No. 12, 4730-4738, Dec. 2008.
doi:10.1109/TMAG.2008.2005118 Google Scholar

5. Lin, R., A. Haavisto, and A. Arkkio, "Axial flux and eddy-current loss in active region of a large-sized squirrel-cage induction motor," IEEE Transactions on Magnetics, Vol. 46, No. 11, 3933-3938, Nov. 2010.
doi:10.1109/TMAG.2010.2064782 Google Scholar

6. Marcusson, B. and U. Lundin, "Axial magnetic fields, axial force, and losses in the stator core and clamping structure of a synchronous generator with axially displaced stator," Electric Power Components and Systems, Vol. 45, No. 4, 410-419, 2017 [Online], Available: http://dx.doi.org/10.1080/15325008.2016.1266062.
doi:10.1080/15325008.2016.1266062 Google Scholar

7. Marcusson, B. and U. Lundin, "Harmonically time varying, traveling electromagnetic fields along a plate and a laminate with a rectangular cross section, isotropic materials and infinite length," Progress In Electromagnetics Research B, Vol. 77, 117-136, 2017.
doi:10.2528/PIERB17061909 Google Scholar

8. Brander, O., "Partiella Differentialekvationer-en kurs i fysikens matematiska metoder, del B,", Studentlitteratur, 1973. Google Scholar

9. Griffiths, D. J., Introduction to Electrodynamics, 3rd Ed., Pearson, Addison Wesley, 1999.

10. "Matweb website,", http://matweb.com/search/AdvancedSearch.aspx, accessed Feb. 16, 2017. Google Scholar

11. "Trigonometric interpolation,", [Online], Available: http://www.math.vt.edu/people/embree/math5466/lecture7.pdf. Google Scholar

12. "Trigonometric interpolation and the fft,", [Online], Available: http://math.gmu.edu/ tsauer/na/ch10.pdf. Google Scholar