Scalar Hysteresis Research Articles

Frequency- and Temperature-Dependent Uncertainties in Hysteresis Measurements of a 3D-Printed FeSi wt6.5% Material.

Additive manufacturing of soft magnetic materials is a promising technology for creating topologically optimized electrical machines. High-performance electrical machines can be made from high-silicon-content FeSi alloys. Fe-6.5wt%Si material has exceptional magnetic properties; however, manufacturing this steel with the classical cold rolling methodology is not possible due to the brittleness of this material. Laser powder bed fusion technology (L-PBF) offers a solution to this problem. Finding the optimal printing parameters is a challenging task. Nevertheless, it is crucial to resolve the brittleness of the created materials so they can be used in commercial applications. The temperature dependence of magnetic hysteresis properties of Fe-6.5wt%Si materials is presented in this paper. The magnetic hysteresis properties were examined from 20 °C to 120 °C. The hysteresis measurements were made by a precision current generator-based hysteresis measurement tool, which uses fast Fourier transformation-based filtering techniques to increase the accuracy of the measurements. The details of the applied scalar hysteresis sensor and the measurement uncertainties were discussed first in the paper; then, three characteristic points of the static hysteresis curve of the ten L-PBF-manufactured identical toroidal cores were investigated and compared at different temperatures. These measurements show that, despite the volumetric ratio of the porosities being below 0.5%, the mean crack length in the samples is not significant for the examined samples. These small defects can cause a significant 5% decrement in some characteristic values of the examined hysteresis curve.

Robust Global Asymptotic Stabilization of Linear Cascaded Systems With Hysteretic Interconnection

We address the problem of setpoint regulation for cascaded minimum-phase linear systems interconnected through a scalar hysteresis, modeled as a Prandtl-Ishlinskii operator. Employing well-posed constrained differential inclusions to represent the hysteretic dynamics, we formulate the control problem in terms of stabilization of a compact set of equilibria depending on the hysteresis states. For our design, we firstly consider a proportional-integral controller for linear systems with hysteretic input, and provide model-free sufficient conditions based on high-gain arguments for closed-loop stability. Then, the controller is dynamically extended to obtain an inversion-free stabilizer of the overall cascade. For the presented schemes, we prove robust global asymptotic stability of a compact set that ensures setpoint regulation, regardless of the hysteresis states.

On hysteresis–reaction–diffusion systems: Singular fast-reaction limit derivation and nonlinear hysteresis feedback

This paper concerns a general class of PDE–ODE reaction–diffusion systems, which exhibits a singular fast-reaction limit towards a reaction–diffusion equation coupled to a scalar hysteresis operator. As applicational motivation, we present a PDE model for the growth of a population according to a given food supply, coupled to an ODE for the turnover of a food stock. Under realistic conditions the stock turnover is much faster than the population growth, yielding an intrinsic scaling parameter. We present two natural models of consume rate functions such that the dynamics for the food stock converges to a generalised play operator in the associated fast-reaction limit. We emphasise that the structural assumptions on the considered PDE–ODE models are quite general and that analogue systems might describe e.g. cell-biological buffer mechanisms, where proteins are stored and used at the same time. Finally, we present a new kind of hysteresis–diffusion-driven instability behaviour caused by the nonlinear coupling between a reaction–diffusion equation and a scalar generalised play operator. We discuss in detail how this coupling with a generalised play operator can lead to spatially inhomogeneous large-time behaviour or equilibration to a homogeneous state.

Tuned mass systems with the Bouc-Wen and a hybrid hysteresis

Tuned-mass-dampers are extensively used in physical systems in order to reduce the dynamic response of the primary structures. The damping in a tuned-mass-damper system plays a significant role. In many engineering systems, we see damping is hysteretic in nature. Tuned-mass systems with nonlinear hysteretic damping are mathematically challenging. In this paper, tuned mass systems with rate-independent hysteresis are studied. In particular, first we study tuned mass systems with the famous Bouc-Wen model, and then we study tuned mass systems with the Bouc-Wen model and a recently developed scalar hysteresis model in parallel. Numerical approaches are used to study the dynamic responses of the systems. The sine sweep responses show two resonance peaks. The sine sweep responses indicate the amplitude versus frequency of the systems. The numerical results obtained for two different hysteretic dampers are compared.

Anisotropic Congruency-Based Vector Hysteresis Model Applied to Non-Oriented Laminated Steels

A new approach is proposed to model the hysteretic behavior of magnetic materials in 2-D electromagnetic analyses. A scalar congruency-based hysteresis model is developed using the first-order reversal curves (FORCs) and verified by comparing the model results with quasi-static measurements. An anisotropic scalar model is obtained from two scalar hysteresis models using FORCs measured parallel and perpendicular to the material rolling direction. The established anisotropic scalar model is employed as the main building block to determine the vector hysteresis model based on the Mayergoyz vector hysteresis generalization. The obtained vector hysteresis model is coupled with a finite-element solver to analyze the three-limbed transformer core investigated in the TEAM problem number 32. The comparison between the simulation results and experimental data confirms the accuracy of the proposed model with an rms flux density error of less than 0.07 T.

Improved Direct Current Control for Grid-Connected Multilevel Inverters

This article presents a sensorless voltage detection method for direct current control in grid-connected multilevel inverters. The direct current control is based on scalar hysteresis controller (SHC). The SHC is a simplified, and parametric direct current controller with the ability to work with an arbitrary level count on multilevel inverters. In combination with the sensorless voltage detection method, it is able to improve the switching behavior, and minimize the current error compared to existing direct current controllers. The proposed control concept is validated with experimental measurements using a three-, and five-level diode clamped inverter under steady-state conditions, and various grid disturbances. In comparison to the standard SHC method, it is verified that the proposed concept shows an improved switching behavior, and a reduced error current.

Comparison and Combination of Techniques for Determining the Parameters of a Magnetic Hysteresis Model

The Jiles-Atherton scalar hysteresis model presents five parameters used to represent the material tested and used to calculate the magnetic losses. This article presents a comparative analysis of the performance of two methods of identifying these parameters. In the first method, the equations of Jiles-Atherton were assembled into a single non-linear ordinary differential equation as a function of the variables of interest. An algebraic system of five equations with five unknowns is obtained by evaluating the non-linear ordinary differential equation in five points belonging to the branch of the experimental hysteresis loop. The parameters are obtained by solving this system of equations using the method of Non-Linear Least Squares (NLLS). In the second method, the inverse model of Jiles-Atherton is used to calculate the magnetic field H from the experimental values of magnetic induction B. Using the method of genetic algorithms (MGA), the objective function given by the sum of the relative error of calculated magnetic field and experimental magnetic field along the hysteresis loop is minimized. To validate methods the experimental curves were compared with calculated ones. When applying the methods, it was verified that NLLS besides providing more accurate results, it is faster when compared to MGA. In the MGA the convergence of the calculated magnitudes to the experimental magnitudes improves when one of the chromosomes of the initial population is the solution obtained applying NLLS.

Losses Computation in Reciprocating Tubular Permanent Magnet Generator with SMC Core

Generally, the Permanent Magnet Tubular Generators (PMTG) are employed in the free-piston generator systems. In this paper, the PMTG with the core made of Soft Magnetic Composite (SMC) is employed, and then, the PMTG with the solid SMC core has cylindrical symmetry and also the outer diameter of the machine reduces in comparison to the ones with multipart laminated steel cores in which each part is radially placed along the air-gap and there is unexploited space between them. Here, a Finite Element Method (FEM) is developed in which the reciprocating motion of the translator is considered by moving mesh techniques and moreover, the Jiles-Atherton (JA) scalar hysteresis model is incorporated in the FE model to take into account the hysteresis losses. Then, the copper and core losses are computed and the equivalent circuit of the generator is derived. The calculated losses are compared with the ones obtained from the analytical methods.

Dynamic Magnetic Scalar Hysteresis Lump Model Based on Jiles–Atherton Quasi-Static Hysteresis Model Extended With Dynamic Fractional Derivative Contribution

Accurate and simple magnetic material law is necessary to correctly model the complete electromagnetic systems. In this article, a new formulation based on the scalar quasi-static hysteresis Jiles-Atherton model extended to dynamic behavior using fractional derivative dynamic contribution is proposed. The fractional contribution is solved using convolution which highly reduces the numerical issues. The order of the fractional derivation provides a new degree of freedom and allows to obtain correct simulation results on a very large frequency bandwidth. By using such a formulation, highly space and time consuming space discretization techniques (finite differences, finite elements) are avoided while keeping the global accurate simulation results.

A Scalar Hysteresis Model of Ferromagnetic Materials Based on the Elemental Operators

This paper introduces an elemental operator with biaxial anisotropy to simulate the scalar hysteresis phenomenon of the ferromagnetic materials. The equilibrium position of the magnetization for the elemental operator can be determined by energy minimization. To directly describe the magnetic properties of each operator, an improved analytical expression is deduced by the partial approximate substitutions. Moreover, this approach utilizes the concept of distribution function density in order to consider the interaction field and the coercive force of the elemental operators. To verify the presented model, the magnetic hysteresis of two different magnetic materials under alternating excitations is measured by the magnetic property measurement system and calculated by this elemental operator method, respectively. The comparisons suggest that this elemental operator is effective and can be a useful tool to simulate the scalar magnetic properties of ferromagnetic materials.

Magnetic Aging Effect Losses on Electrical Steels

The magnetic losses behavior on electrical steels related to the magnetic aging is analyzed in this paper. Experimental procedures involving thermal, metallurgical, and electromagnetic measurements were performed. The evolution of the losses is modeled using a scalar hysteresis model, and the aging prediction on electrical motor steels is proposed using the Arrhenius formula. The proposed study brings relevant information to be considered on designing electrical motors.

Hysteretic damping in an elastic body with frictional microcracks

Material stress strain curves often show dissipation via rate-independent hysteresis. Here we study an elastic plate with several randomly distributed and oriented frictional microcracks, loaded cyclically in plane stress. Computational solutions in ABAQUS show narrow hysteresis loops. Unlike the loops from Rowett׳s classic experiment (1914), or from simple hysteresis models such as the Bouc–Wen model (1967 and 1976), the present loops are pinched at the origin and partially resemble an ad hoc model proposed by Reid (1956). Such pinched loops have been revisited lately by others, but our results provide new justification for the same. We also propose a new simple scalar model that gives a better qualitative match with the numerically obtained hysteresis loops than any other model presently available. Our scalar hysteresis model may lead to better interpretations and modeling in, e.g., vibration response of structures with such internal frictional damping. Thus the contribution of this paper lies in adopting a dissipation model from micromechanics, idealizing the resulting dissipation loops, and presenting a new simple scalar equation that models such loops and can be easily incorporated into structural vibration damping models.

Identification of scalar Jiles-Atherton hysteresis model parameters with a new particle behaviour based metaheuristic algorithm

Identification of scalar Jiles-Atherton hysteresis model parameters with a new particle behaviour based metaheuristic algorithm

Weak differentiability of scalar hysteresis operators

Rate independent evolutions can be formulated as operators, calledhysteresis operators, between suitable function spaces. In thispaper, we present some results concerning the existence and theform of directional derivatives and of Hadamard derivatives ofsuch operators in the scalar case, that is, when the driving(input) function is a scalar function.

Improvement and Application of the Viscous-Type Frequency-Dependent Preisach Model

Iron parts of electrical machines are made of nonoriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of motors. The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed point method with stable scheme has been realized to take frequency-dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations. The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of T.E.A.M. Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure.

Differential Approach of Scalar Hysteresis Modeling Based on the Preisach Theory

This paper introduces a differential approach to model scalar hysteresis based on the Preisach theory. This model can generate hysteresis trajectories for both symmetrical and asymmetrical minor loops and keep the memory of a material in a proper manner. It can easily be inverted, it has a simple algorithm with suitable computational speed, and is not memory consuming. Also, the obtained results of the model are in very good agreement with measurements.

Non Linear Magnetic Hysteresis Modelling by Finite Volume Method for Jiles-Atherton Model Optimizing by a Genetic Algorithm

This paper describes a generalization methodology for nonlinear magnetic field calculation applied on two-dimensional (2-D) finite Volume geometry by incorporating a Jiles-Atherton scalar hysteresis model. The scheme is based upon the definition of modified governing equation derived from Maxwell’s equations considered the magnetization M. This paper shows how to extract optimal parameters for the Jiles-Atherton model of hysteresis by a real coded genetic algorithm approach. The parameters identification is performed by minimizing the mean squared error between experimental and simulated magnetic field curves. The calculated results are validated by experiences performed in an SST’s frame.

Ferromagnetic hysteresis modeling for sensor and actuator applications

This paper presents a hysteresis model for electromagnetic sensors and actuators, which are composed of ferromagnetic materials. The model is based on the Preisach operator, which is capable to fully describe major as well as minor hysteresis loops. To obtain the appropriate measured data for fitting the Preisach operator, we have developed an Epstein setup according to IEC 60404-2. This work also describes the use of the Lorentzian function as a possible candidate for the accurate approximation of the Preisach density function in the modeling of scalar hysteresis for nonoriented grain steels. In particular, we discuss here the identification procedure of the Preisach weighting functions from measured data.

Accurate minor loops calculation with a modified Jiles‐Atherton hysteresis model

PurposeAlthough the original Jiles‐Atherton (J‐A) hysteresis model is able to represent a wide range of major hysteresis loops, in particular those of soft magnetic materials, it can produces non‐physical minor loops with its classical equations. The purpose of this paper is to show a modification in the J‐A hysteresis model in order to improve the minor and inner loops representation. The proposed technique allows the J‐A model representing non‐centred minor loops with accuracy as well as improving the symmetric inner loops representation.Design/methodology/approachOnly the irreversible magnetization component is slightly modified keeping unchanged the other model equations and the model simplicity. The high‐variation rate of the irreversible magnetization, which causes the non‐physical behaviour of minor loops, is limited by introducing a new physical parameter linked to the losses. Contrarily to other modifications of the original model found in the literature, the previously knowledge of the magnetic field waveform is not needed in this case.FindingsThe modified hysteresis model is validated by comparison with experimental results. A good agreement is observed between calculations and measurements. The modified model retains the low‐computational effort and numerical simplicity of the original one.Originality/valueThis paper shows that a classical scalar hysteresis model can be suitably used to take into account the minor loops behaviour and be included in a finite element code. The methodology is useful for the design and analysis of electromagnetic devices under distorted flux patterns.

Outward pointing properties for vectorial hysteresis operators and some applications

In a number of papers, the concept of outward pointing hysteresis allowed the application of the method of invariant regions to derive uniform bounds for solutions to evolution equations involving scalar hysteresis operators and input perturbations.The aim of this note is to generalize the ‘pointing outward’ properties to vectorial hysteresis operators, and to show how these properties can be used to derive uniform estimates for differential equations involving vectorial hysteresis operators and input perturbations.