Low-frequency behavior of laminated electric steel sheet: Investigation of ferromagnetic hysteresis loops and incremental permeability

The frequency dependence of ferromagnetic hysteresis and the related core losses is still an open question. From scaling relations up to space discretized and simultaneous contributions resolutions, different levels of accuracy in the estimation of these losses can be reached. Below a given frequency known as the quasi-static threshold, it is well admitted that the hysteresis cycle remains unchanged. A precise evaluation of this threshold is fundamental to simulate and evaluate precisely the magnetization behaviors under higher frequencies. But this estimation is complex, especially through the unique observation of the hysteresis cycles and because of instrumentation limitations. In this manuscript, we propose an alternative and simple method to precisely refine this threshold's estimation. By using an alternative magnetic signature known as the magnetic incremental permeability butterfly loop ($\left(\underset{\_}{{\mu }_{\mathrm{IP}}}\right)\left(H\right)$), improvements are proposed in observing the very low-frequency magnetization behaviors and assessing the quasi-static threshold. This work constitutes a leap forward in understanding the magnetic low-frequency behaviors of laminated electric steel sheets.