Krzysztof Sokalski

Losses scaling in soft magnetic materials

Purpose – The paper presents an application of the scaling theory in a description of energy losses in soft magnetic materials in order to improve an agreement between measurements and theoretical models.Design/methodology/approach – The scaling theory allows the description of energy losses by a generalized homogenous function, which depends on scaling exponents α, β and amplitudes Γ(n). The values of the scaling exponents and amplitudes were estimated on the basis of measurement data of total energy losses.Findings – The main findings of the paper are: the linear relationships between the scaling exponents α and β, the data collapse of energy losses and the scaling laws for asymptotic exponents of energy losses derivatives.Research limitations/implications – The origin of the data collapse and the relationship between the scaling exponents will be the subject of further research with the aid of renormalization group methodPractical implications – The paper could be useful both for device designers and r...

Unified model of temperature dependence of core losses in soft magnetic materials exposed to non-sinusoidal flux waveforms and DC bias condition

Purpose – The purpose of this paper is to present modelling of power losses dependences on temperature in soft magnetic materials exposed to non-sinusoidal flux waveforms and DC bias condition. Design/methodology/approach – Scaling theory allows the power loss density to be derived in the form of a general homogeneous function, which depends on the peak-to-peak of the magnetic inductance ΔB, frequency f, DC bias HDC and temperature T. The form of this function has been generated through the Maclaurin expansion with respect to scaled frequency, which suit very much for the Bertotti decomposition. The parameters of the model consist of expansion coefficients, scaling exponents, parameters of DC bias mapping, parameters of temperature factor and tuning exponents. Values of these model parameters were estimated on the basis of measured data of total power density losses. Findings – The main finding of the paper is a unified methodology for the derivation of a mathematical model which satisfactorily describes ...

Scaling in Magnetic Materials

The chapter presents applications of the scaling in several problems of magnetic materials. Soft magnetic materials (SMMs) and soft magnetic composites (SMCs) are considered. Application of scaling in investigations of problems, such as power losses, losses separation, data collapse of the losses characteristics and modelling of the magnetic hysteresis, is presented. The symmetry group generated by scaling and gauge transformations enables us to introduce the classification of the hysteresis loops with respect to the equivalence classes. SMC materials require special treatment in the production process. Therefore, algorithms for optimization of the power losses are created. The algorithm for optimization processes is based on the scaling and the notion of the pseudo-equation of state. The scaling makes modelling and calculations easy; however, the data must obey the scaling. Checking procedure of statistical data to this respect is presented.