Prediction of hysteresis losses by an advanced vector hysteresis stop model with threshold surfaces

Abstract

Purpose The ordinary vector hysteresis stop model with constant threshold values is not able to prohibit the hysteretic property after the saturation correctly. This paper aims to develop an improved vector hysteresis stop model with threshold surfaces. This advanced anisotropic vector hysteresis stop model can represent the magnetic saturation properties and the hysteresis losses under alternating and rotating magnetizations. Design/methodology/approach By integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model, the anisotropy of the permeability of an electrical steel sheet can be represented. Instead of the commonly used constant threshold value for plastic elements of the hysteresis model, threshold surfaces are applied to the stop hysterons. The threshold surfaces can be derived directly from measured alternating major loops of the material sample. By saturated polarization, the constructed threshold surfaces are vanishing. In this way, the reversible magnetic flux density is in the same direction of the applied magnetic flux density. Thus, the saturation properties are satisfied. Findings Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows that the clockwise (CW) and counter-CW (CCW) rotational hysteresis losses decrease by saturated flux density. At this state, instead of the domain wall motion, the magnetization rotation is dominant in the material. As a result, the hysteresis losses, which are related to the domain wall motion, are vanished near the saturation. In one stop operator, the plastic element represents the hysteresis part of the model. Integrating threshold surface into the plastic element, the hysteresis part can be modified to zero near the saturation to represent the saturation properties. Originality/value The results of this work demonstrate that the presented vector hysteresis stop model allows simulation of anisotropic hysteresis effects, alternating and rotating hysteresis losses. The parameters of the hysteresis model are determined by comparing the measured and modeled minor loops in different alternating magnetization directions. With the identified parameters, the proposed model is excited with rotated excitations in CW and CCW directions. The rotated hysteresis losses, derived from the model, are then compared with those experimentally measured. The modified vector stop model can significantly improve the accuracy of representing hysteresis saturations and losses.

Analysis of the convergence of Newton method by finite element simulation with vector hysteresis stop model

“…R temp,n describes the threshold values in x and y directions of the n th stop operator. More details about the construction of the threshold surface are presented in the previous work (Xiao et al, 2022). The parameter B re t describes the reversible part of the magnetic flux density of time step t. The formal definition of a stop operator in equation (1) implies that the system can be divided into an elastic state and a plastic dissipated state.…”

“…R temp,n describes the threshold values in x and y directions of the n th stop operator. More details about the construction of the threshold surface are presented in the previous work (Xiao et al , 2022). The parameter bold-italicBret describes the reversible part of the magnetic flux density of time step t .…”