An energy‐based vector hysteresis model for ferromagnetic materials

Abstract

Purpose -Proposes a new quasi-static vector hysteresis model based on an energy approach, where dissipation is represented by a friction-like force. Design/methodology/approach -The start point is the local energy balance of the ferromagnetic material. Dissipation is represented by a friction-like force, which derives from a non-differentiable convex functional. Several elementary hysteresis cells can be combined, in order to increase the number of free parameters in the model, and therefore improve the accuracy. Findings -A friction-like force is a good way to represent magnetic dissipation at the macroscopic level. The proposed method is easy to implement and non-differentiability amounts in this case to a simple "if" statement.Research limitations/implications -The next steps are the extension to dynamic hysteresis and the in-depth analysis of the identification process, which is only sketched in this paper. Practical implications -This vector model, which is based on a reasonable phenomenological description of local magnetic dissipation, enables the numerical analysis of rotational hysteresis losses on a sound theoretical basis. Originality/value -It proposes a simple, general purpose macroscopic model of hysteresis that is intrinsically a vector one, and not the vectorization of a scalar model.

Magnetic material modeling for the optimization of the electrical machine design

“…Therefore, the distribution of the magnetic field in the laminated sheet vs time is calculated by the approximating nonlinear algebraic equations that is the numerical approximation of equation (8) for the point at the surface between the magnetic material and the air. In the equation (9) (10) and (11) above the index m refers to the space position (see Fig. 8) and the index n refers to the time step.…”

“…In general the magnetic hysteresis is a complex phenomena that needs several sophisticated models for different cases and applications [3][4][5][6][7][8][9]. Recently some vector models have been proposed and discussed for the electrical steels representation [10][11][12], one of them is the Vector Hysteron Model (VHM) [13] which is a natural extension of the Preisach theory to the vector case. In this work we present the VHM formulation in order to model experimental hysteresis loops, scalar and rotational, for both NOG (Not oriented grain) and OG (Oriented grain) steels.…”

Application and Verification of a Dynamic Vector-Hysteresis Model

“…Both models lack a true physical background and suffer in general from poor accuracy in the interesting ranges of flux density and frequency for electrical machine design, i.e., outside the measurement ranges used for the parameter identification. Many of the currently used hysteresis models are fundamentally scalar models and are solely vectorized to 2-D or 3-D quite artificially [3], [4]. An alternative approach treats the problem directly at the microscopic level and uses multi-scale techniques [5] to trace the microscopic information over to the macroscopic level.…”

“…However, considering their very high computational cost, they are impracticable in modeling engineering applications. The purpose of this paper is to introduce an energy-based modeling of magnetic materials [3], [4], [6] in order to characterize the nonlinear behavior of magnetic materials as well as the associated energy losses for any instant of time. This enables to go beyond the limitations of currently used models.…”

Comparison of macroscopic descriptions of magnetization curves

“…[47][48][49]. Figure 4 depicts a saturating hysteresis loop and some first order reversal curves (FORCs) simulated with the GRUCAD model.…”