E. Cardelli

A General Hysteresis Operator for the Modeling of Vector Fields

This paper deals with the modeling of vector fields that exhibit hysteresis. A general class of models of vector magnetizations with hysteresis that form a natural extension of the Classical Scalar Preisach Model is defined. Although the modeling was done for the 2-d case, the same theory can be extended to the 3-d case as well. After reviewing some general properties of conservative fields, the specific case of unit magnitude vector fields is discussed. The paper focuses on discussing the properties of a general vector hysteresis operator (hysteron). The mathematical approach followed here can be applied not only to the magnetic hysteresis, but also to any hysteresis process. Some examples of vector hysterons, deduced from the general definition, are presented and their properties analyzed.

A General Vector Hysteresis Operator: Extension to the 3-D Case

This paper deals with the mathematical definition of a general vector hysteresis operator in 3-D, as an extension of previous papers where the theory has been limited to the 2-D case. Although the paper is mainly focused on magnetic hysteresis, the definitions and the results reported can be applied to any general physical phenomenon that exhibits hysteresis. We show here the main general properties of the general hysteresis operator in 3-D.

Computation of the magnetic field in massive conductor systems

Some analytical expressions are reported for the calculation of the magnetic induction and the vector potential in iron-free media due to slab-shaped elements in which a current flows uniformly or linearly distributed in one direction. It is seen that no matter what current distribution functions and conductor geometries are considered, they can be approximated by a series of slabs in which the current distributions are represented by a sum of linear and constant distributions. The algorithms can also be used to calculate the magnetic field in more complicated geometries and to evaluate the self- and mutual-inductance coefficients in systems with massive conductors. >

Direct and inverse Preisach modeling of soft materials

A product-type Preisach model, called here the Modified Scalar Preisach Model (MSPM), is accounted for the modeling of the magnetic hysteresis in soft ferromagnetic materials. The hypothesis of stochastic independence of the switching field parameters leads to a formulation of the model that allows a relatively simple identification procedure, also from the viewpoint of the computational cost. The numerical efficiency of the procedure is shown in a series of proper applications.

A Benchmark Problem of Vector Magnetic Hysteresis for Numerical Models

In this paper, we present a benchmark problem for the validation of numerical models of vector magnetic hysteresis. The problem geometry and the measurement system are described. The materials considered are both oriented grain (OG) and not OG Si-Fe steels. A series of experimental data about magnetic field and magnetic induction loci under rotational magnetization are presented with the corresponding magnetic losses. The measured data can be useful as a reference for the numerical models testing, comparison, and development. In addition, we propose here a comparison of the experimental data with the numerical results computed using a vector hysteresis model based on the extension of the Preisach model in 2-D.

Surface field measurements in vector characterization of Si-Fe magnetic steel samples

In this work we discuss some procedures to increase the accuracy in the measurement of the magnetic field strength using Round Rotational Single Sheet Tester RRSST frames. The procedures are discussed jointly with the use of different magnetic field probes, such as flat coils and Hall sensors, and with a suitable shielding geometry. Experimental comparison between different methods and a discussion about the results is presented.

Numerical Modeling of Hysteresis in Si-Fe Steels

In this paper, we discuss the numerical modeling of hysteresis in magnetic steels with oriented and nonoriented grain. The modeling is fully 3-D, but it is applied here to typical 2-D magnetic problems. Starting from a vector generalization of the Preisach model, we introduce here the concept of an operative magnetic field, function of the state of magnetization of the material. This operative field is introduced to reproduce with more accuracy the peculiar behavior of Si-Fe steels approaching the saturation state. The properties of the model are discussed and some examples are reported.

Energy and Losses in Vector Thermal Aftereffect Model

This work deals with some energy properties of a vector thermal aftereffect model, recently presented. The model can compute magnetization and magnetic losses using an extension in 2-D of a Preisach-type approach. Some properties of the model are presented and discussed. An experimental validation is also included.

Magnetic field evaluation for thick annular conductors

The three-dimensional integration of the Biot-Savart law for conductors in annular sector shape, in which only a constant-density theta -directed current flows, is reported. The expressions obtained allow a quick and accurate evaluation of the components of the vector potential of the stationary magnetic field and of the magnetic induction due to this type of conductor, in iron-free media. The relations presented, together with similar expressions that are valid for other shapes of conductor and current distributions, can be useful for evaluating the magnetic fields in complex, linear, iron-free structures when the geometry can be well approximated with a series of current elements of elementary shape, for which the solution of Laplaces equation is known in closed form. >

Analytic expressions for magnetic field from finite curved conductors

Some analytical expressions for the calculation of the magnetic induction and the vector potential in iron-free media due to conductors in annular arc shape with regular cross section are reported. The algorithms derived, together with analogous algorithms reported previously for the calculation of the magnetic fields due to conductors in slab shape, can be used to calculate the magnetic fields in more complicated geometries and may be used to evaluate the self- and the mutual-inductance coefficients in systems with massive conductors.