Multi-scale magnetic aging model: Precipitation kinetics and magnetic hysteresis coupling

Operating temperatures of electrical machines are known to cause various effects on magnetic performances and losses. On the one hand, reversible contributions may reduce iron losses through temporary lowering of conductivity, which in turn reduces eddy-current losses. On the other hand, when specific thermal conditions are met, the time–temperature combination may lead to irreversible changes of the magnetic material properties. This latter phenomenon, the so-called magnetic aging, need to be addressed to further improve energy efficiency, predict and reduce heat-dissipated iron losses. These service conditions indeed lead to changes in the microstructure of the electrical steels. Thus, iron losses suffer from these structural modifications as well as long exposure to constant operating temperatures; magnetic aging results from carbides precipitation and impacts the magnetization of these steels. The present paper hence explores a multi-scale approach, coupling the Johnson-Mehl-Avrami-Kolmogorov (JMAK) precipitation kinetics with a static Jiles-Atherton (J-A) model of magnetic hysteresis for a non-oriented soft ferromagnetic Fe-Si steel. Based on an experimental analysis for temperatures ranging from 160 °C to 200 °C, the applicability of the chosen approaches will be explored and a parameter-based modeling of magnetic aging will be proposed and proved to be in good agreement with measurement data.