Application and Verification of a Dynamic Vector-Hysteresis Model

Steentjes, Simon; Eggers, Daniel; Hameyer, Kay

doi:10.1109/tmag.2012.2199967

Cited by 6 publications

(6 citation statements)

References 5 publications

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“…The sum of two Langevin functions has been preferred over a single Langevin function (Steentjes et al, 2012;Rasilo et al, 2015;Steentjes et al, 2017). The addition of a second Langevin function increases the degrees of freedom, which is ideal in minimizing the fitting error after the knee region of a typical anhysteretic curve.…”

Section: Anhysteretic Magnetizationmentioning

confidence: 99%

A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model

Upadhaya

Rasilo²,

Perkkiö

et al. 2020

COMPEL

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Purpose Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops. Design/methodology/approach A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process. Findings The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops. Originality/value The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

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Section: Anhysteretic Magnetizationmentioning

confidence: 99%

A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model

Upadhaya

Rasilo²,

Perkkiö

et al. 2020

COMPEL

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“…We found that for m s = 1.23 · For numerical simulations we approximate the distribution by a mixture of N types of pseudoparticles with volume fractions ω l > 0, satisfying N l=1 ω l = 1. Each type is characterised by its own r = r l and, to account for partial reversibility of the material response [7], [12] we assign r = 0 to one of the pseudoparticle types.…”

Section: Model Of Magnetizationmentioning

confidence: 99%

“…2) we assume the magnetic field rotates, h = H m (t)(cos t, sin t), with the amplitude H m (t) = 110 min(t/6π, 1) growing with time until its maximal value 110 A/m is reached. This is a non-scalar situation and we compare the accurate numerical solution of (12), equivalent to the time discretized version of (8), to the explicit, at each time step, discretized vector play model based on the approximation (13). Although the solutions are different in the transient regime, the difference is small and disappears soon after the amplitude of the rotating magnetic field becomes constant.…”

Section: Energy Balance and Dry-friction Like Model Of Magnetizationmentioning

confidence: 99%

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On the Energy-Based Variational Model for Vector Magnetic Hysteresis

Prigozhin

Barrett

Zirka³

2016

IEEE Trans. Magn.

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We consider the quasi-static magnetic hysteresis model based on a dry-friction like representation of magnetization.The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the stored and dissipated energies at any moment in time, and hence not only on the completion of a closed hysteresis loop. We discuss the variational formulation of this model and derive an efficient numerical scheme, avoiding the usually employed approximation which can be inaccurate in the vectorial case. The parameters of this model for a nonoriented steel are identified using a set of first order reversal curves. Finally, the model is incorporated as a local constitutive relation into a 2D finite element simulation accounting for both the magnetic hysteresis and the eddy current.Index Terms-vector magnetic hysteresis, energy-based model, variational formulation, finite element simulation.Corresponding author: L. Prigozhin (email: leonid@math.bgu.ac.il).Both the Preisach and Jiles-Atherton models are scalar and, although there exist numerous vector modifications, these also lack a true physical justification. Furthermore, in a general situation, the use of these models to predict the evolving magnetization does not make computing the accompanying energy loss straightforward (see, e.g., [6]). In a seminal work [7], Bergqvist proposed a new quasi-static magnetic hysteresis model, phenomenological but having a consistent and genuine energy interpretation, intrinsically vectorial, and ensuring a direct calculation of the stored magnetic energy and the dissipated energy at any moment in time, and not only after the completion of a closed hysteresis loop as is usually the case. This model differs significantly from the previous

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“…It should be stressed that despite the considered approach precludes that hysteresis and eddy current effects are neglected, it may be useful as a building block for a vector hysteresis model. In some hysteresis models the thermodynamically reversible magnetisation curve, referred to as the anhysteretic, plays a crucial role [31][32][33][34][35][36]. This curve may be considered a 'spine' for the hysteresis loop; in fact it is common to assume the middle curve from the ascending and the descending loop branches as a reasonable approximation for the anhysteretic curve [31,34].…”

Section: Model Equationsmentioning

confidence: 99%

Anisotropic properties of non‐oriented steel sheets

Chwastek

2013

IET Electric Power Applications

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Even the so-called non-oriented steels used in electrical engineering reveal anisotropy of their magnetic properties. Anisotropy may have a substantial impact on the performance of magnetic circuits; therefore it is necessary to take this phenomenon into account already at the design stage. A simple formula useful for the description of magnetisation curves in two principal directions is proposed. The B(H) dependencies for other directions are determined using a model based on coenergy concept. The worst magnetic properties are obtained for the samples cut at approximately 60 degrees. The presented description may be useful for prediction of rotational loss in ferromagnetic sheets used as core material in electric machines.

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Application and Verification of a Dynamic Vector-Hysteresis Model

Cited by 6 publications

References 5 publications

A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model

A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model

On the Energy-Based Variational Model for Vector Magnetic Hysteresis

Anisotropic properties of non‐oriented steel sheets

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