TY - JOUR

T1 - Convergence analysis of the fixed-point method with the hybrid analytical modeling for 2-D nonlinear magnetostatic problems

AU - Ceylan, Doga

AU - Friedrich, Léo A.J.

AU - Boynov, Konstantin O.

AU - Lomonova, Elena A.

PY - 2021/2

Y1 - 2021/2

N2 - This paper presents the convergence analysis of the fixed-point method (FPM) to model the nonlinear magnetic characteristics of a 2-D magnetostatic problem. In this study, FPM is used as the iterative nonlinear solver of the hybrid analytical modeling (HAM) technique for the accurate computation of the magnetic field distribution. The benchmark consists of a stator with excitation windings, an airgap, and a slotless mover. The relative errors between two successive iterations are calculated using different error estimators: the attraction force on the mover, the Fourier coefficients defined in the airgap, the magnetic flux density, and the magnetic scalar potential distributions. The effect of the number of mesh elements and harmonics on the accuracy and computational cost of the model is investigated for different levels of magnetic saturation. It is observed that the maximum rate of change in the relative difference of attraction force during the iterations is found to be 0.52 under the magnetic saturation. In addition, the absolute error of the attraction force between the developed hybrid model with FPM and the finite element method (FEM) is achieved to be 0.18%, while HAM has approximately three times less number of degrees-of-freedom compared to FEM.

AB - This paper presents the convergence analysis of the fixed-point method (FPM) to model the nonlinear magnetic characteristics of a 2-D magnetostatic problem. In this study, FPM is used as the iterative nonlinear solver of the hybrid analytical modeling (HAM) technique for the accurate computation of the magnetic field distribution. The benchmark consists of a stator with excitation windings, an airgap, and a slotless mover. The relative errors between two successive iterations are calculated using different error estimators: the attraction force on the mover, the Fourier coefficients defined in the airgap, the magnetic flux density, and the magnetic scalar potential distributions. The effect of the number of mesh elements and harmonics on the accuracy and computational cost of the model is investigated for different levels of magnetic saturation. It is observed that the maximum rate of change in the relative difference of attraction force during the iterations is found to be 0.52 under the magnetic saturation. In addition, the absolute error of the attraction force between the developed hybrid model with FPM and the finite element method (FEM) is achieved to be 0.18%, while HAM has approximately three times less number of degrees-of-freedom compared to FEM.

KW - Convergence analysis

KW - fixed-point method (FPM)

KW - hybrid analytical modeling (HAM)

KW - nonlinear magnetic characteristics

UR - http://www.scopus.com/inward/record.url?scp=85099773560&partnerID=8YFLogxK

U2 - 10.1109/TMAG.2020.3024539

DO - 10.1109/TMAG.2020.3024539

M3 - Article

VL - 57

JO - IEEE Transactions on Magnetics

JF - IEEE Transactions on Magnetics

SN - 0018-9464

IS - 2

M1 - 9201167

ER -