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### Numerical scalar hysteresis model and its precision

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The calculation of magnetic fields in the electromagnetic devices is an important part of the design process. The numerical approach in consideration to the measured material hysteresis is discussed in the paper. Some precision problems of the model are pointed out. The results of the calculation are compared with the measurement results made on the magnetization set up for the characterization of semi and hard magnetic materials. Streszczenie. Obliczanie pola magnetycznego w urządzeniach elektrycznych jest istotną częścia procesu projektowania. W artykule dyskutowane jest numeryczne podejście do zmierzonej histerezy. Pewne precyzyjne problemy zostały wypunktowane. Wyniki obliczeń porównane są z wynikami pomiarów wykonanych na zestawach magnetycznych charakterystycznych dla materiałów magnetycznych twardych i półtwardych. (Numeryczny model skalarny histerezy i jego dokładność) Keywords: Finite element methods, Magnetic fields, Measurement. Słowa kluczowe: metoda elementów skończonych, pole magnetyczne, pomiary Introduction The program for the 3D finite element magnetic field calculations includes the numerical scalar hysteresis model. The description of the magnetic material is based on the measured major hysteresis loop and as many as possible measured first order reversal curves (FORCs) for the increase and for the decrease of the excitation current. In each of the finite elements, the new magnetic induction B is calculated on the basis of the nonlinear finite element method calculation made with different magnetization curves in each finite element. The magnetic induction in each of the finite elements, calculated from the previous time step, the history of the magnetic density and the excitation current, are the basis for the evaluation of the new magnetization curve, which will be used for nonlinear calculation in the current time step. Some calculations must be repeated, if the result is on the wrong magnetization curve. S[...]

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