Comparison of different vector Preisach models for the simulation of ferromagnetic materials

Abstract

Purpose The numerical computation of magnetization processes in moving and rotating assemblies requires the usage of vector hysteresis models. A commonly used model is the so-called Mayergoyz vector Preisach model, which applies the scalar Preisach model into multiple angles of the halfspace. The usage of several scalar models, which are optionally weighted differently, enables the description of isotropic as well as anisotropic materials. The flexibility is achieved, however, at the cost of multiple scalar model evaluations. For solely isotropic materials, two vector Preisach models, based on an extra rotational operator, might offer a lightweight alternative in terms of evaluation cost. The study aims at comparing the three mentioned models with respect to computational efficiency and practical applicability. Design/methodology/approach The three mentioned vector Preisach models are compared with respect to their computational costs and their representation of magnetic polarization curves measured by a vector vibrating sample magnetometer. Findings The results prove the applicability of all three models to practical scenarios and show the higher efficiency of the vector models based on rotational operators in terms of computational time. Originality/value Although the two vector Preisach models, based on an extra rotational operator, have been proposed in 2012 and 2015, their practical application and inversion has not been tested yet. This paper not only shows the usability of these particular vector Preisach models but also proves the efficiency of a special stageless evaluation approach that was proposed in a former contribution.

Computation of rotational hysteresis losses by vector Preisach models based on rotational operators

“…In this context, ΔΦ 0 is a second model-specific parameter for SVPr that has to be retrieved from proper measurements. The actual definition of func(ΔΦ0,trueχ→α,βn−1,trueh→n) as well as further details regarding the functionality and the efficient implementation of SVPc and SVPr can be found in studies by Sutor et al (2012, 2015) and Nierla et al (2017, 2019) and is not repeated at this point. It shall be remarked, though, that ΔΦ will go to zero if the material is driven into saturation, i.e.…”

“…nÀ1 a;b ; h ! n as well as further details regarding the functionality and the efficient implementation of SVPc and SVPr can be found in studies by Sutor et al(2012Sutor et al( , 2015 and Nierla et al(2017Nierla et al( , 2019 and is not repeated at this point. It shall be remarked, though, that DU will go to zero if the material is driven into saturation, i.e.…”

“…where m anhyst accounts for the free-field contribution m 0 as well as additional anhysteretic parts that can be derived simultaneously with the weighting function }(a,b ) of the Preisach model (Sutor et al, 2015;Nierla et al, 2019).…”

“…M sat being the saturation magnetization and the discrete time step. For the following investigations, the discrete values of trueh→n as depicted in Figure 1 were prescribed and the corresponding normalized flux densities trueb→n got retrieved via where μ anhyst accounts for the free-field contribution μ 0 as well as additional anhysteretic parts that can be derived simultaneously with the weighting function ℘ ( α , β ) of the Preisach model (Sutor et al , 2015; Nierla et al , 2019).…”

“…The common concept of both the classical variant (SVPc) and the revised variant (SVPr) is the inclusion of an additional rotational operator to the standard scalar Preisach model. Both variants of this novel vector Preisach model have been shown to offer an accurate and computationally cheap alternative to the Mayergoyz vector model when combined with an efficient Everett-based evaluation scheme (Nierla et al, 2017(Nierla et al, , 2019. So far, however, these models have not been applied to the prediction of rotational hysteresis losses.…”