Analytical Solution of a Multi-Winding Coil Problem With an Air Core in Spherical Coordinates

Year 2024, , 255 - 261, 29.02.2024

Hüseyin Yıldız , Erol Uzal Hüseyin Çalık

https://doi.org/10.2339/politeknik.1052918

Abstract

In this study, electromagnetic fields and mutual inductance of two interacting coils were computed analytically, and the results were compared with numerical solutions and measurements. For the analytical solution, the fields were expressed in spherical coordinates in each coil’s frame. The total field due to two coils was calculated using superposition, resulting in infinite series involving associated Legendre functions. The numerical computations were carried out by finite element analysis capabilities of ANSYS Maxwell. At the end, the self-inductances and the mutual inductance coefficients between the coils (which depend on the angle between the coils) were computed. The results (analytical, finite element method, and the measurements) were compared, obtaining good agreement for various relative positions of the coils. 

Keywords

Magnetic field, Maxwell’s equations, mutual inductance, spherical coordinates

Hava Çekirdekli Çok Sargılı Bobbin Porbleminin Küresel Koordinatlarda Analitik Çözümü

Abstract

Bu çalışmada, bir biri ile etkileşen iki bobinin elektromanyetik alanı ve karşılıklı endüktans katsayısı analitik olarak hesaplanmış, sonuçlar sayısal çözümler ve ölçümlerle karşılaştırılmıştır. Analitik çözüm her bir bobinin etkisi küresel koordinatlarda genişletilerek hesaplandı. Her iki bobinden kaynaklanan toplam alanlar, süperpozisyon ilkesi gereği uyarlanmış legendre fonksiyonlarını içeren seri çözümler olarak elde edildi. Sayısal hesaplamalar ANSYS Maxwell programında sonlu elemanlar metodu kullanılarak elde edildi. Bobinlerin öz endüktans ve karşılıklı endüktans katsayıları (bobinler arasındaki açıya bağlı olarak) elde edildi. Sonuç olarak, elde edilen sonuçlar (analitik, sonlu elemanlar yöntemi ve ölçümler) kayaslanarak, bobinlerin çeşitli göreli konumları için analitik formüllerin geçerli oldukları gösterildi.

Keywords

Manyetik alan, karşılıklı endüktans, küresel koordinatlar

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