Nonlinear analysis of eddy current and hysteresis losses of 3-D stray field loss model (Problem 21)

The division of the total core losses in the electrical steel of the magnetic circuit into two components – losses dueto hysteresis and eddy currents – is a serious technical problem, the solution of which will effectively design and construct electrical machines with magnetic circuits having low magnetic losses. In this regard, an important parameter is the exponent α, with which the frequency of magnetization reversal is included in the total losses in steel. Theoretically, this indicator can take values from 1 to 2. Most authors take α equal to 1.3, which corresponds to the special case when the eddy current losses are three times higher than the hysteresis losses. In fact, for modern electrical steels, the opposite is true. To refine the index α, an attempt was made to separate the total core losses on the basis that the hysteresis component is proportional to the first degree of the magnetization reversal frequency, and the eddy current component is proportional to the second degree. In the article, the calculation formulas of these components are obtained, containing the values of the total losses measured in idling experiments at two different frequencies, and the ratio of these frequencies. It is shown that the rational frequency ratio is within 1.2. Presented the graphs and expressions to determine the exponent α depending on the measured no-load losses and the frequency of magnetization reversal.

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Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drz046 ◽

2019 ◽

Vol 40 (4) ◽

pp. 2802-2838 ◽

Cited By ~ 1

Author(s):

Giovanni Di Fratta ◽

Carl-Martin Pfeiler ◽

Dirk Praetorius ◽

Michele Ruggeri ◽

Bernhard Stiftner

Keyword(s):

Eddy Current ◽

Maxwell Equations ◽

Coupled System ◽

Second Order ◽

Stray Field ◽

Time Step ◽

Finite Element Scheme ◽

Second Order In Time ◽

Current Approximation ◽

Numer Math

Abstract Combining ideas from Alouges et al. (2014, A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation. Numer. Math., 128, 407–430) and Praetorius et al. (2018, Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl., 75, 1719–1738) we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau–Lifshitz–Gilbert (LLG) equation, which is unconditionally convergent, formally (almost) second-order in time, and requires the solution of only one linear system per time step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then we extend the scheme to the coupled system of the LLG equation with the eddy current approximation of Maxwell equations. Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires the solution of only two linear systems per time step.

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