Akademik Veri Yönetim Sistemi
JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY, sa.1, ss.65-75, 2024 (SCI-Expanded)
In this study, analytical formulas were obtained for the electric field (E) and magnetic field (B) vectors formed by the coils inside a spherical magnetic core. Figure A shows the analytical and FEA (Finite Element Analysis) results of the vector potential (A). The results are very close to each other. So, it is understood that the analytical results are usable.Purpose:Traditional machines are slowly being replaced by more complicated and efficient mechanisms such as devices with spherical geometry that can move in more than one axis. Therefore, calculation of the parameters of spherical electromagnetic systems by analytical or semi-analytical methods has become one of the important research topics in recent years. The aim of this study is to calculate the magnetic field distribution in the magnetic core and in the air and obtain analytical formulas for the inductance coefficients.Theory and Methods:Maxwell's equations were solved analytically for a single turn coil placed inside a magnetic sphere. Analytical expressions for magnetic vector potential, electric and magnetic fields, A, E and B were obtained. Analytical formulas for multi-turn coils were derived by utilizing the single-turn coil solution (Green's function) and the superposition principle. The end result is the mutual inductance coefficient between the two coils. FEA analyses were also performed and compared with the analytical solution.Results:It was observed that the analytical results differ from the FEA results around the coil's position. This is due to the inherent singularity of the single-turn coil solution and the fact that the FEA method cannot handle these types of singularities. The multi-turn coil solution smooths-out the singularity as is common for such superposition solutions. The results for multi-turn coil show agreement between analytical and FEA solutions (Figure A).Conclusion:Analytical solution takes negligible time compared to FEA solution and gives accurate results. Therefore, it is very useful for geometric optimization.