Revisiting the dry friction-like magnetic vector hysteresis model

Physically correct simulations of magnetic devices require precise and energy-consistent hysteresis models. Electrical steel sheets of, e.g., power transformers or rotating machines represent one crucial element in such a simulation since the hysteresis is revealed uni- and multi-axial, and the steel sheets may have anisotropy. A dedicated vector hysteresis model based on dry friction-like pinning is revisited and derived in terms of thermodynamic state equations in a theoretical manner. The model is then linked to an incremental energy minimization procedure used in elasto-plasticity theory. A numerically efficient two-dimensional solution scheme of the hysteresis model is extended to the three-dimensional case. Rotational losses are also in the scope of this paper since the model cannot describe this loss type by nature. Therefore, numerical adaptations are discussed to account for vanishing rotational losses in saturation.