Physical interpretation of eddy current losses in ferromagnetic materials. I. Theoretical considerations

Abstract

The basic physical mechanism responsible for the general behavior of eddy current losses versus magnetizing frequency fm is recognized in the competition between the external field and local internal fields, due to magnetostatic, coercive, and eddy current effects. The concept of magnetic object, corresponding to a group of neighboring walls evolving in a highly correlated fashion, is introduced in order to take into proper account the role of short-range internal correlation fields. With a random spatial distribution of magnetic objects, the dynamic loss is essentially a function of the number ñ of magnetic objects which are simultaneously active at each value of fm. It is shown that the dynamic balance between applied field and local eddy current counterfields leads, with increasing fm, to a progressive increase of ñ governed by the simple linear law ñ=ñ0+Hexc/V0, where Hexc represents the part of the applied field in excess of the hysteresis and classical contributions. Under these conditions, a general law of losses is derived, which turns out to be in excellent agreement with several experimental results concerning different iron-based ferromagnetic alloys. On the basis of the general validity of the obtained loss equation, a bidimensional map of dynamic losses is defined and constructed, in which the parameters ñ0 and V0 are used as orthogonal coordinates of representative points characterizing the loss behavior of different materials. This map provides the proper basis for a general classification of dynamic losses, which might also be useful from the applicative point of view.

Effect of Mechanical Stress on Excess Loss of Electrical Steel Sheets

“…The fundamental premise for the statistical loss theory is the movement of magnetic objects (MOs) which depict a number of magnetic domain walls transitioning in a highly correlated manner [10]. Based on the microscopic and macroscopic levels of magnetization process in these MOs, the applied magnetic field H that induces a uniform induction, is segregated into hysteresis H hy , classical eddy current H ed and excess fields H ex .…”

“…In [9], [10], and [12] a linear correlation between n and H ex , was obtained from measurements for non-oriented electrical sheets and grain oriented sheets with respect to the rolling direction. Thus, the number of simultaneously active MOs can also be expressed as…”

“…From the statistical loss theory [10], the time averaged approximation of the number of simultaneously active MOs (i.e. n) for the sinusoidal induction in a cross section S of the lamination is given by…”

Magnetic Materials

“…This analysis is being extended on the basis of statistical theories of loss [111][112][113]. Such theories also attempt to describe the situation in the NO materials, which is more difficult because the complicated microstructure implies more complex domain structures.…”

Iron Losses in Electromagnetic Devices: Nonlinear Adaptive MEC & Dynamic Hysteresis Model

“…A second models category brings together the formalisms based on the magnetic loss separation assumption which owes its popularity to Bertotti [6][7][8] who separates the iron losses into three contributions: hysteresis losses, classical eddy current loss and excess losses. The latter having been established first for sinusoidal waveforms, it has been improved in [9] for non-sinusoidal and rotational magnetic flux density waveforms.…”