Manyetik nüve içerisinde çok sarımlı bobin probleminin küresel koordinatlarda analitik çözümü ve FEA sonuçları ile karşılaştırılması

Teknolojinin gelişimi ile birlikte hareket ve kontrol mekanizmaları çok eksende hareket edebilen, daha hızlı ve hassas hareket sağlanabilecek cihazlara ihtiyaç duymaktadır. Bu nedenle; küresel koordinat sisteminde elektromanyetik sistemlerin parametrelerinin analitik veya yarı analitik yöntemlerle hesaplanması son yıllarda önemli araştırma konularından biri haline gelmiştir. Bu çalışmada manyetik bir nüve içerisine sarılmış çok sarımlı bobin yapısı incelenmiştir. Öncelikle tek sarımlı bobin yaklaşımından yararlanarak çok sarımlı bobinler için B, E ve A ifadeleri analitik olarak hesaplanmıştır. Aynı geometriler, sonlu elemanlar analizi (FEA) kullanılarak ANSYS Maxwell programında dairesel simetri kabulü ile hesaplanmıştır. Son olarak, biri r1 yarıçapına sahip manyetik nüve içerisinde olan, eş merkezli iki bobin geometrisi belirlenmiştir. Bu geometriler için öz indüktans (Lii) ve karşılıklı indüktans (Mij) katsayıları küresel koordinatlarda γ açısına bağlı olarak incelenmiştir. ANSYS Maxwell programı üzerinde bobin geometrilerinin 3 boyutlu modeli oluşturularak benzetim çalışmaları yapılmıştır. FEA ve analitik sonuçlar kıyaslanarak geçerliliği gösterilmiştir.

Anahtar Kelimeler:

Küresel koordinatlar, Maxwell denklemleri, Sonlu elemanlar analizi (FEA), Karşılıklı indüktans

Analytical solution of multi-winding coil problem in magnetic core in spherical coordinates and comparison with FEA results

With the development of technology, motion and control mechanisms need devices that can move in multiple axes and provide faster and more precise movement. So, the calculation of the parameters of electromagnetic systems in the spherical coordinate system by analytical or semi-analytical methods has become one of the important research topics. In this study, the structure of the multi-winding coil which is in the magnetic core was investigated. First of all, the expressions B, E and A for multi-winding coils were calculated analytically by using the single-winding coil approach. The same geometries were calculated using finite element analysis (FEA) in the ANSYS Maxwell program with circular symmetry assumption. Finally, two concentric coil geometries, one of which is inside the magnetic core with radius r1, are determined. The coefficients of self-inductance (Lii) and mutual inductance (Mij) were investigated in spherical coordinates depending on the γ angle. Simulation studies were carried out by creating a 3D model of coil geometries on the ANSYS Maxwell program. FEA and analytical results were compared and validated.

Keywords:

Spherical coordinates Magnetic fields, Maxwell’s equations, Finite element analysis‎ (FEA), mutual inductance,

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