Dynamic Hysteresis Model Research Articles

Dynamic Hysteresis Model of GO Silicon Steel Considering Skin Effect and Saturation Effect

Dynamic Hysteresis Model of GO Silicon Steel Considering Skin Effect and Saturation Effect

Modeling and identification of hysteresis of marine damper considering shock environment based on evolutionary sparrow search algorithm

The mechanical properties of marine dampers are usually highly nonlinear in order to adapt to dynamic and shock environments. The dampers are subjected to dynamic and shock tests and the hysteresis curves are found to be rate-dependent and asymmetric. To be able to describe the dynamic hysteresis and shock hysteresis, a rate-dependent generalized Prandtl-Ishlinskii (RDGPI) model is proposed based on the generalized Prandtl-Ishlinskii (GPI) model, which is a hybrid of the GPI model and the radial basis function (RBF) neural network. Due to the large number of parameters in the model, thus aiming to improve the effect of parameter identification, an evolutionary sparrow search algorithm mixed with sparrow search algorithm and differential evolutionary algorithm is proposed. Compared with other algorithms, sparrow search algorithm is verified to have ideal optimization effect and convergence speed, and it is not easy to fall into the local optimum. Finally, the RDGPI model is experimentally verified, and the results show that the prediction error of the RDGPI model for dynamic hysteresis is within 0.06 kN, and the prediction error for shock hysteresis is within 0.8 kN, which is capable of describing the rate-dependent characteristics of the damper hysteresis. And it has a very good generalization ability, which makes it very suitable to be used in the modeling of the mechanical characteristics of the marine damper.

Iron Loss and Temperature Rise Analysis of a Transformer Core Considering Vector Magnetic Hysteresis Characteristics under Direct Current Bias.

Direct current (DC) bias induced by the DC transmission and geomagnetically induced current is a critical factor in the abnormal operation of electrical equipment and is widely used in the field of power transmission and distribution system state evaluation. As the main affected component, the vector magnetization state of a transformer core under DC bias has rarely been studied, resulting in inaccurate transformer operation state estimations. In this paper, a dynamic vector hysteresis model that considers the impact of rotating and DC-biased fields is introduced into the numerical analysis to simulate the distribution of magnetic properties, iron loss and temperature of the transformer core model and a physical 110 kV single-phase autotransformer core. The maximum values of B, H and iron loss exist at the corners and T-joint of the core under rotating and DC-biased fields. The corresponding maximum value of the temperature increase is found in the main core limb area. The temperature rise of the 110 kV transformer core under various DC-biased conditions is measured and compared with the FEM (Finite Element Method) results of the proposed model and the model solely based on the magnetization curve B||H. The calculation error of the temperature rise obtained by the improved model is approximately 3.76-15.73% and is much less than the model solely based on magnetization curve B||H (approximately 50.71-66.92%).

A nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator

Compared with traditional actuators, the giant magnetostrictive actuator has the merits of fast response, high accuracy, and high reliability and has been widely applied. However, its performance is affected by the electromagnetic loss and the temperature, prestress, and magnetic coupling effect. In order to accurately analyze its performance, it is necessary to establish a nonlinear dynamic model including the electromagnetic loss and the magnetic–prestress–thermal coupling effect. First, based on the field separation approach, the magnetic fields generated by the eddy current loss and the anomalous loss are obtained and added to the Jiles–Atherton model. Second, the magnetostrictive model is given with the magnetic–prestress–thermal coupling effect. Finally, assuming the transmission of the giant magnetostrictive actuator as a mass–spring–damper system, a nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator is developed. Based on this model, the output displacement curves of the giant magnetostrictive actuators under different driving currents and frequencies are given. The comparison with the experimental results shows that this model agrees well with the experiment.

A Calculation Method for Static Hysteresis Loop and its Applications

Background: Due to experimental equipment limitations, it is usually difficult to measure the quasi-static hysteresis loop at extremely low frequencies, which inevitably introduces errors in the static hysteresis model. Objective: This study aims to propose a method for calculating the static hysteresis loops of grainoriented silicon steel sheets so as to improve the accuracy of the static and dynamic hysteresis model. Methods: The parameters n0 and V0 in the magnetic field strength expression of the excess loss are determined by the measured losses within the range of 0-100Hz. Subsequently, the dynamic components in the quasi-static hysteresis loops are eliminated. Furthermore, a dynamic hysteresis model is established based on the loss and field separation theory, which incorporates the inverse Preisach model. Results: The dynamic hysteresis loops of the grain-oriented silicon steel sheets are measured in the range of 8-250Hz and compared with the results of both the improved model and the original model. Conclusion: Experimental results demonstrate the effectiveness and accuracy of the improved model. The proposed method for calculating static hysteresis loops has universal applicability and is meaningful for accurate simulation and prediction of magnetic properties in soft magnetic materials.

An improved dynamic magnetic hysteresis model in soft magnetic composites

In this paper, an improved static Jiles-Atherton (J-A) hysteresis model is proposed to simulate the hysteresis properties of soft magnetic composites (SMC) by introducing an excitation factor to control the rotational component of magnetic domains in the effective magnetic field based on the internal demagnetization effect and magnetization mechanism. On the other hand, Since SMC is usually applied in the mid-frequency band, an improved dynamic hysteresis model is necessary to be proposed. The analytical expression for calculating the intraparticle eddy current loss is proposed based on the microstructural parameters of the SMC. And the microstructural parameters are determined by discrete element method DEM. For the intraparticle eddy current loss, the squared term of the mean particle size in the expression is further clarified. Eventually, this improved dynamic J-A hysteresis model was derived through the theory of magnetic field separation. The results show that SMC hysteresis loops with magnetic flux densities up to 1.5 T and frequencies up to 1 kHz can be evaluated by the proposed model.

Modeling and simulation of magnetostrictive actuators based on ΔE effect Preisach model

Based on the classical Preisach model, combined with the magneto-mechanical coupling effect of Giant magnetostrictive materials (GMM), this paper introduces the Everett function to optimize the classical Preisach hysteresis model and improve its accuracy. By importing dynamic parameters, the dynamic Preisach hysteresis model is established. Combined with the constitutive model of GMM, a dynamic Preisach hysteretic nonlinear magnetostrictive actuator model based on the ΔE effect is established. Then, the finite element simulation is carried out by Comsol software and compared with the theoretical model simulation. The results show that the error between the magnetostrictive strain of the established hysteresis model and the finite element simulation results is less than 100 ppm, which verifies the accuracy of the proposed model. Finally, the curves of magnetic field intensity, magnetic induction intensity, magnetization, magnetostrictive strain and ΔE effect of GMA are obtained by using this model.

Hysteretic magnetic field analysis with Second-Order homogenization

A dynamic hysteresis model represented by the Cauer circuit was combined with the finite element analysis to efficiently compute magnetic field in micro-structured iron-cores. A finite element eddy-current analysis with higher order homogenization method is reformulated to implement the Cauer circuit representation. Three types of hysteretic Cauer circuits for the 2nd-order homogenization were examined. The analysis of wounded core under sinusoidal excitation showed that the 2nd order homogenization scheme with finite difference approximation improved the accuracy of representation of iron loss and current-flux loops. The 2nd-order scheme also improved the accuracy of homogenized representation under pulse-width-modulation excitation. The computation time was greatly reduced by the homogenization schemes.

Dynamic Hysteresis Model and Loss Prediction of GO Silicon Steel Under DC-Biased High-Frequency Excitation

Dynamic Hysteresis Model and Loss Prediction of GO Silicon Steel Under DC-Biased High-Frequency Excitation

A dynamic hysteresis model of heat and mass transfer for hygrothermal bio-based materials

The hygrothermal behaviour of porous building materials is significantly determined by the moisture and heat transfer phenomena. However, most of existing models used to predict this phenomenon neglect moisture hysteresis effect and dynamic capillarity effect, limiting their accuracy in assessing the efficiency and sustainability of bio-based building materials. To bridge this gap, the model presented in this paper considers both dynamic and hysteresis effects. The Finite Element Method (FEM) is adopted for the discrete approximation of the partial differential equations governing heat and moisture transfer. The model is validated with respect to experiment performed on bio-based material subjected to thermo-hygrical boundaries conditions. Results show unequivocally that dynamic capillarity effect and moisture hysteresis effect should be considered simultaneously to quantify hygrothermal behaviour of porous building materials. This critical insight underscores the significance of this research, offering a comprehensive model for evaluating the efficiency and sustainability of these materials by addressing the often-neglected aspects of moisture behaviour, i.e., dynamic and hysteresis effects. This model is marked by its precision and thorough consideration of essential factors, making it an indispensable contribution to the field and advances the understanding of the hygrothermal behaviour of bio-based building materials in real conditions. It would help in designing optimized building envelop.

A nonlinear dynamic hysteresis model with magnetic-thermal-stress-fluid coupling effect for hydraulically amplified magnetostrictive actuator

The hydraulic amplified magnetostrictive actuator (HAMA) has the advantages of large output displacement and fast response speed, but it is affected by coupling effects of electromagnetism, temperature, prestress, fluid, and other factors. In order to accurately analyze its performance, it is necessary to establish a nonlinear dynamic model including the coupling effect of eddy current loss, hysteresis, prestress, temperature, and fluid. First, a nonlinear magnetostrictive model including the magnetic-thermal-stress coupling effect is developed from the perspective of free energy. Based on the conservation of magnetization energy, the influence term of the eddy current is added to the anhysteretic magnetization and a nonlinear dynamic magnetization model including the effect of eddy current is developed. Based on the fluid transmission theory and HAMA’s equivalent dynamic model, a dynamic model of HAMA was established. Finally, a nonlinear dynamic hysteresis model with the magneto-thermal-stress-fluid coupling effect of HAMA is developed, and the performance of HAMA was studied by simulation and experiments. The results show that the output displacement is from −58.2 to 58.2 µm when the control current changes from −2 to 2 A, and the simulation results have a better agreement with the experiment result when the frequency is less than 200 Hz.

A dynamic hysteresis prediction model of grain-oriented silicon steel sheet under AC-DC hybrid magnetization

Firstly, a new method for parameter identification of inverted Preisach model is proposed to simulate static DC-biasing hysteresis behavior of the grain-oriented (GO) silicon steel sheet by using the measured quasi-static concentric hysteresis loops under DC-biasing magnetization. Then, the dynamic magnetic field intensity related to excess loss is improved by considering the nonlinear relationship between the statistical parameter V0 and the AC peaked magnetic flux density, DC magnetic field intensity as well as frequency. Finally, a dynamic hysteresis model in form of field separation is presented to predict asymmetric hysteresis curves under multi-harmonic and DC-biasing hybrid magnetization. The simulated hysteresis curves as well as losses under different AC-DC hybrid magnetizations are compared with the measured ones, which verifies the accuracy and effectiveness of the proposed method.

Dynamic rate-dependent hysteresis modeling and trajectory prediction of voice coil motors based on TF-NARX neural network

Dynamic rate-dependent hysteresis modeling and trajectory prediction of voice coil motors based on TF-NARX neural network

Development of a new dynamic hysteresis model for magnetorheological dampers with annular-radial gaps considering fluid inertia and compressibility

Modeling the inherent non-linear dynamic hysteresis behavior of magnetorheological (MR) fluid dampers is a fundamental necessity for their practical implementation. Quasi-static models, have been developed under very low frequency and small amplitude excitation conditions, are only beneficial in the early stages of MR dampers design and are sufficient for manufacturing requirements. These models, however, have failed to predict the non-linear hysteresis behavior of MR dampers (i.e., force-displacement and force-velocity characteristics) under low to moderate ranges of frequency and displacement amplitudes. The main contribution of the present work is to formulate a novel physic-based dynamic model to predict the non-linear behavior of MR dampers featuring an annular-radial bypass valve under different applied currents, and low to moderate input excitations. The proposed model incorporates unsteady fluid behavior and the fluid compressibility effect on the hysteretic response without relying on experimental data to evaluate the model parameters. To derive the model, the velocity profile and the pressure drop have been derived by solving the fluid momentum equation via the Laplace transform technique and Cauchy residue theory. The continuity equation has been employed for considering the compressibility contribution to hysteretic response based on the variation of bulk moduli. The predicted results for the force-displacement and force-velocity behavior of the MR damper were subsequently compared with the experimental results. Results suggest the effectiveness of the proposed model for predicting the dynamic hysteresis characteristics of the annular-radial MR fluid dampers under the relatively sufficient variation of mechanical and magnetic loading conditions considered.

Review of Hysteresis Models for Magnetic Materials

There are several models for magnetic hysteresis. Their key purposes are to model magnetization curves with a history dependence to achieve hysteresis cycles without a frequency dependence. There are different approaches to handling history dependence. The two main categories are Duhem-type models and Preisach-type models. Duhem models handle it via a simple directional dependence on the flux rate, without a proper memory. While the Preisach type model handles it via memory of the point where the direction of the flux rate is changed. The most common Duhem model is the phenomenological Jiles–Atherton model, with examples of other models including the Coleman–Hodgdon model and the Tellinen model. Examples of Preisach type models are the classical Preisach model and the Prandtl–Ishlinskii model, although there are also many other models with adoptions of a similar history dependence. Hysteresis is by definition rate-independent, and thereby not dependent on the speed of the alternating flux density. An additional rate dependence is still important and often included in many dynamic hysteresis models. The Chua model is common for modeling non-linear dynamic magnetization curves; however, it does not define classical hysteresis. Other similar adoptions also exist that combine hysteresis modeling with eddy current modeling, similar to how frequency dependence is included in core loss modeling. Most models are made for scalar values of alternating fields, but there are also several models with vector generalizations that also consider three-dimensional directions.

Underwater dynamic hysteresis modeling and feedforward control of flexible caudal fin actuated by macro fiber composites

Underwater bionic robotics and vehicles that use flexible structures as power sources have attracted considerable attention. Thus, the underwater dynamic behaviors of the flexible structure of a variable cross-section actuated by smart actuators must be further investigated. In this study, underwater dynamic hysteresis modeling and feedforward compensation of a flexible caudal fin driven by macro fiber composites (MFC) at different frequencies were investigated. The MFC-actuated flexible caudal fin is considered a Euler–Bernoulli beam. A revised hydrodynamic function governed by the thickness of the viscous layer and the gap-to-width ratio of the cross-section was developed. Then, a characteristic-frequency-dependent extended transform function model is proposed for the hydrodynamic response of a non-uniform beam. An asymmetric hysteresis model is presented to characterize the rate-independent hysteresis behavior of the MFC actuators. Further, the underwater dynamic equation of the MFC-actuated caudal fin with hysteresis is obtained by connecting the two established models in series. Experiments demonstrate the dynamic behavior between the underwater responses of the caudal fin and the input voltages have an ellipse-like shape and vary in shape and size with oscillating frequency. The ellipse-like dynamic hysteresis loop first grows, reaching its maximum at the resonant frequency, and then decreases, because of the frequency-dependent dynamic behavior. Meanwhile, a phase shift of approximately 90°between the input voltage and underwater dynamic response was observed at the resonant state. Furthermore, the experimental results demonstrate that the proposed model can describe the nonlinear underwater dynamic hysteresis behavior of the proposed caudal fin at different frequencies. The trajectory tracking performances are remarkably improved over a broad frequency range with the proposed compensator. Consequently, the effectiveness of the proposed dynamic model and compensation method was demonstrated. These results are helpful for robotic fish or autonomous underwater vehicles propelled by oscillating foils actuated by smart actuators, including MFC.

A study of dynamic hysteresis model for a magnetorheological damper

1. Ahmed K., Yan P., Li S., 2021, Duhem model-based hysteresis identification in piezo-actuated nano-stage using modified particle swarm optimization, Micromachines, 12, 3, 315. CrossRef Google Scholar

A Novel Modeling Technique via Coupled Magnetic Equivalent Circuit With Vector Hysteresis Characteristics of Laminated Steels

This paper proposes a method to include the anisotropic hysteresis characteristics of soft-magnetic laminated steels in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the nonlinearity of the anisotropic magnetic hysteresis, including the dynamic classical eddy-current and excess fields. The developed MEC model is coupled with both the single-valued <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H$</tex-math></inline-formula> curve (SVC) in magnetostatic and the dynamic vector hysteresis model (VHM) in transient analysis. Results with a single elementary MEC element show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between the magnetic flux densities calculated by the VHM and SVC at 50 and 200 Hz excitation frequencies. Moreover, the proposed modeling technique is verified experimentally using the laminated transformer core of TEAM problem 32. The induced voltage calculated by the MEC model with the VHM demonstrates a good agreement with the measurements, while the MEC model with the SVC calculates inaccurate voltage waveforms. Lastly, the total iron loss dissipated in the transformer's iron core is investigated to verify the proposed technique under different excitation levels and frequencies up to 500 Hz. It is observed that the proposed MEC model with the vector hysteresis characteristics of laminated steels is able to calculate the iron loss accurately, while the conventional single-valued curve method fails to estimate the iron loss.

Dynamic Hysteresis Model of Metal-net Rubber Combination Damper Based on Power Series and Ellipse Equation

Dynamic Hysteresis Model of Metal-net Rubber Combination Damper Based on Power Series and Ellipse Equation

A hybrid dynamic hysteresis model based on the Preisach model and stacked auto-encoder

With the increase in power electronic equipment in power system, the excitation of ferromagnetic materials often involves a large number of harmonics. Therefore, it is necessary to construct an accurate dynamic hysteresis model to adapt to this complicated operating state of electrical equipment. In this paper, a Hybrid Dynamic Hysteresis Model (HDHM), which can effectively characterize the harmonic excitation of materials is studied based on the Preisach model and Stacked Auto-Encoder (SAE) model. The static part of this model takes the form of the inverse Preisach model. And the Multiple Dynamic Hysteresis Model Set (MDHMS) is constructed by multiple dynamic models of eddy currents and excess characteristics of the ferromagnetic materials. The dynamic part of the HDHM takes the form of the model structure combining the Stacked Auto-encoder and the MDHMS. The calculation results of the hysteresis loop and ferromagnetic loss in the harmonic condition of silicon steel sheet proves the validity of this model. Moreover, compared with the conventional dynamic hysteresis model, the HDHM has better accuracy and generalization ability.