Cubic Extrapolation of Steel Magnetization Curves for Highly Saturated Electric Machines

Accurate electromagnetic analysis of modern automotive electrical machinery requires polarization curves that are valid at very high fields. However, due to hardware and cost limitations, test data are typically available for only moderate field levels. In this letter, an approach is outlined given a known high field reference curve to determine the lowest field testing level required to reasonably extrapolate the measured data using several methods. Furthermore, a cubic extrapolation method is proposed, which is shown to have the lowest testing requirements. A training set of steels is first used to establish empirical values for the percentage magnetization required as associated with each method, from which reasonably accurate extrapolations to high fields can be obtained. These empirical values are further validated on an alternate set of steels, for which the extrapolation is performed and verified against reference curves.