Identification of the scalar Preisach model with a single branch of descending hysteresis loop and numerical interpolation for the electrical steel sheet lamination with soft magnetic properties

The developed scalar Preisach model predicts the hysteresis behavior of the soft magnetic, electrical steel sheet. The experimental hysteresis loops of the electrical steel lamination prepare the Everett function required to predict the hysteresis behavior of the electrical steel lamination. We obtain the Everett function in two ways, from the series of minor loops and a single descending branch of a hysteresis loop. The Everett function has a closed algebraic form in the method using the minor loops. A genetic algorithm carries out the subsequent fitting based on the closed algebraic equation and optimization; however, the calculated flux values have highly deviated from the measured values. In another way, the Everett function consists of numerically driven Fs and B factorable functions. The values extracted from a limiting hysteresis loop determine the function Fs and B. The predicted values are correct, and the proposed method for determining the Everett function is only valid for soft magnetic materials representing symmetric and non-exchange-bias hysteresis behavior. While the method has application limitations to general magnetic hysteresis, it demonstrates the validity of using a function derived from experimentally measured hysteresis loops rather than a closed-algebraic equation to determine the Everett function. With the Everett surface the Preisach distribution function (PDF) is numerically derived and represents the difference in domain structure between two specimens.