# Numerical modelling of magnetic materials for computer aided design of electromagnetic devices

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In design and simulation of electromagnetic devices, it is essential to model the properties of
magnetic materials, such as the relation between magnetic flux density B and magnetic field H
or B-H curve and electromagnetic power losses or core losses with various kinds of magnetic
field excitations, in order to assess the performance correctly.
The major part of the work is concerned with the modelling of hysteresis loops with alternating
magnetic field, and core losses with alternating and/or rotating magnetic fields. Various novel
models are developed.
A critical comparison between various available models of magnetic hysteresis shows that the
Preisach theory appears to be suitable for practical engineering applications. A new normal
Preisach model is obtained with the help of a graphical representation of the theory. The new
model features simple formulation and easy parameter identification. The input data is the
limiting hysteresis loop. It can provide correct results for a medium or large magnetic field, but
fails when the hysteresis loop to be predicted is close to the origin of the B-H plane owing to
some intrinsic defects of the model. These defects are eliminated in a new generalised model,
which contains a reversible magnetisation component and a magnetisation feed back. The input
data required by the generalised model are the limiting hysteresis loop and the normal
magnetisation curve. These can be obtained from either manufacturers' data sheets or from
simple measurements. Better accuracy is achieved by the generalised model.
New dynamic discrete circuit models with hysteresis, eddy current, and anomalous losses
included are developed to simulate the performance of magnetic cores in devices with nonsinusoidal
alternating flux. At low frequencies, a simple equivalent circuit model consisting of a
constant equivalent resistor for eddy current loss, a nonlinear equivalent resistor for anomalous
loss, and a non-ideal inductor for modelling the hysteresis loop and hysteresis loss is used. This
model is generalised into a ladder network model for simulation at high frequency by
subdividing the cross section of the core into a few assumed eddy current paths. All
parameters of these models can be identified from data sheets provided by manufacturers.
For rotational core loss measurement, a single sheet square specimen tester is developed. The
precision of two dimensional field strength measurement at the surface of the specimen is
improved by a novel sandwich H sensing coil arrangement. The relationship between the core
loss due to the rotational component of magnetic field and the total core loss is clarified using a
new equation and the arguments are supported by the experimental results.
Rotational core losses in grain oriented and non-oriented silicon steel sheets were measured
using the testers at the University of Technology, Sydney and the Physikalisch-Technische
Bundesanstalt, Braunschweig, Germany. These measurements provided much useful
information for both understanding of the loss mechanisms and modelling of the losses.
Similar to the case of alternating core losses, rotational core loss can also be separated into
rotational hysteresis, eddy current, and anomalous losses. The rotational hysteresis loss is fitted
by a novel model based on a strong analogy between the retarding torque due to the rotational
hysteresis loss and the electromagnetic torque in a single phase induction machine. With a
circular flux density, the rotational eddy current loss is twice as much as the alternating eddy
current loss. The rotational anomalous loss can be modelled using the same formula as for
alternating anomalous loss, but the coefficient of rotational anomalous loss is generally a
function of flux density, and eventually reduces to zero when the material is saturated and all
domain walls disappear.
Total core losses with an elliptical flux density are predicted from the pure rotational and
alternating core losses by a new formulation derived from the total core loss formula used in
rotational core loss measurement. The new model is applicable to hysteresis as well as total
core losses. Comparisons with experimental data show that this new model is more accurate
than a linear interpolation between alternating and pure rotational core losses.
Core losses in an AC permanent magnet motor are modelled. The magnetic flux density
distribution is calculated by a finite element code. Fourier series analysis is used for an
arbitrary two dimensional rotating flux density. The total core loss is finally calculated by
summing up all the contributions from different elliptically rotating harmonics of flux density in
each finite element. The discrepancy between calculated and measured results is about 13%.

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