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.

In this paper, the best laser powder bed fusion (L-PBF) printing conditions for FeSi steels with two different Si content (3.0% and 6.5%) are defined. Results show very strict processing window parameters, following a lack of fusion porosity at low specific energy values and keyhole porosity in correspondence with high specific energy values. The obtained microstructure consists of grains with epitaxial growth starting from the grains already solidified in the underling layer. This allows the continuous growth of the columnar grains, directed parallel to the built direction of the component. The magnetic behaviour of FeSi6.5 samples, although the performances found do not still fully reach those of the best commercial electrical steels (used to manufacture magnetic cores of electrical machines and other similar magnetic components), appears to be quite promising. An improvement of the printing process to obtain thin sheets with increased Si content, less than 0.5 mm thick, with accurate geometry and robust structures, can result to an interesting technology for specific application where complex geometries and sophisticated shapes are required, avoiding mechanical machining processes for electrical steel with high silicon content.

In this paper, we propose a dynamic model of the electrical transformer suitable for the numerical prediction of the inrush currents due to the arbitrary initial excitation of a transformer after a switch-OFF. In particular, the proposed model can be helpful to control strategies to avoid a transient current overshoot, based on the prediction of the residual magnetic flux.

Rotational magnetizations of an Ni-Fe alloy are simulated using two different computer modeling approaches, physical and phenomenological. The first one is a model defined using a single hysteron operator based on the Stoner and Wohlfarth theory and the second one is a model based on a suitable system of neural networks. The models are identified and validated using experimental data, and, finally, an example of their application for a finite-element analysis is given.

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.