Stress-dependent Hysteresis Research Articles

An improved stress-dependent magnetostriction model of silicon steel based on simplified multi-scale and Jiles–Atherton theory

Due to the magnetic domain movement and energy change under magnetic field and stress applied, the macroscopic magnetic properties and magnetostriction properties of non-oriented (NO) silicon steel are influenced. To present this effect of the magnetic domains’ motion mechanism, a stress-dependent magnetostriction must be modeled. This paper proposes an improved stress-dependent magnetostriction model (I-SDM model) for NO silicon steel based on a simplified multi-scale model. Firstly, the stress-dependent expression of the anhysteretic magnetization, obtained by assuming a six-domain structure and considering the volume fraction of magnetic domain energy, is introduced into the inverse Jiles–Atherton (JA) model. In this way, the stress-dependent hysteresis model is constructed. Then, coupling with the improved quadratic domain rotation model that considers pinning effects, the I-SDM model for NO silicon steel is built. Finally, with the parameters obtained from experimental results, the proposed model under varying stresses is simulated and compared with other models. It shows that the proposed model has the highest simulated accuracy for both λ-H loop and λ-B loop with stress applied.

Dynamic modeling for soft dielectric elastomer actuator considering different input frequencies and external loads

A dynamic model for the soft dielectric elastomer actuator (SDEA) is developed in this paper to describe its intricately nonlinear behaviors considering different input frequencies and external loads. Firstly, the characteristics of the SDEA are observed by several groups of experiments. A phenomenological model is proposed to describe the asymmetric hysteresis behavior of the SDEA, which consists of a Prandtl-Ishlinskii model with one-side play operator and a dead-zone model with one-side dead-zone operator. Meanwhile, a mathematical model is built to depict the creep behavior of the SDEA. The dynamic model including a module and a linear system is proposed to further handle the rate-dependent and the stress-dependent hysteresis behaviors of the SDEA, in which the module is the superposition of the asymmetric hysteresis model and the creep model. To ensure that the inverse solution of the module is existing, as well as the linear system is controllable and observable, the constraint conditions of parameter values of the dynamic model are constructed. Next, the parameter identification is divided into two steps, and the differential evolution algorithm is employed in each step. Finally, the generalization of the proposed dynamics model is demonstrated by comparing the model output with the experimental data.

Neural-Network-Based Iterative Learning Control for Hysteresis in a Magnetic Shape Memory Alloy Actuator

The typical characteristic of a magnetic shape memory alloy (MSMA)-based actuator is rate-dependent and stress-dependent hysteresis. In addition, the hysteresis in an MSMA-based actuator includes memory, multivalued mapping, and asymmetry properties, which seriously degrade the positioning accuracy. In this article, a feedforward neural network (FNN)-based nonlinear autoregressive moving average with exogenous inputs (NARMAX) model is employed to describe the hysteresis in an MSMA-based actuator. Through a Taylor expansion, it is revealed how the FNN constructs the nonlinear function of the NARMAX model. For the controller implementation, an FNN-based iterative learning control (ILC) strategy is proposed to achieve the desired tracking performance. The contributions of this study include exploring the update rule of the FNN-based ILC and analyzing the convergence properties of the proposed controller when the initial state of the system varies. To verify the effectiveness of the proposed method, experiments on an MSMA-based actuator were conducted. The results illustrate that the proposed modeling and control methods achieve an excellent performance and that the theoretical results are correct.

Stress sensitivity of tight reservoirs during pressure loading and unloading process

Abstract Laboratory experiments were conducted on laboratory-made tight cores to investigate the stress-dependent permeability hysteresis of tight reservoirs during pressure loading and unloading process. Based on experiment results, and Hertz contact deformation principle, considering arrangement and deformation of rock particles, a quantitative stress dependent permeability hysteresis theoretical model for tight reservoirs was established to provide quantitative analysis for permeability loss. The model was validated by comparing model calculated results and experimental results. The research results show that during the early pressure-loading period, structural deformation and primary deformation worked together, rock permeability reduced dramatically with increasing effective stress. When the effective stress reached a certain value, the structural deformation became stable while the primary deformation continued; the permeability variation tended to be smooth and steady. In the pressure unloading process, the primary deformation recovered with the decreasing effective stress, while the structural deformation could not. The permeability thus could not fully recover, and the stress-dependent hysteresis was obvious.

Effects of stress dependent electrochemical reaction on voltage hysteresis of lithium ion batteries

Intercalation of lithium ions into the electrodes of lithium ion batteries is affected by the stress of active materials, leading to energy dissipation and stress dependent voltage hysteresis. A reaction-diffusion-stress coupling model is established to investigate the stress effects under galvanostatic and potentiostatic operations. It is found from simulations that the stress hysteresis contributes to the voltage hysteresis and leads to the energy dissipation. In addition, the stress induced voltage hysteresis is small in low rate galvanostatic operations but extraordinarily significant in high rate cases. In potentiostatic operations, the stresses and stress induced overpotentials increase to a peak value very soon after the operation commences and decays all the left time. Therefore, a combined charge-discharge operation is suggested, i.e., first the galvanostatic one and then the potentiostatic one. This combined operation can not only avoid the extreme stress during operations so as to prevent electrodes from failure but also reduce the voltage hysteresis and energy dissipation due to stress effects.

A modified residual stress dependent Jile-Atherton hysteresis model

Non-oriented electrical steel is widely used in the manufacturing of motor stators. The magnetic property will be influenced by the residual stress induced from manufacturing processes. The classical Jile-Atherton hysteresis model with constant parameters is widely used to describe the magnetization characteristic of ferromagnetic materials. In the model, the parameter a represents the domain density, k is the pinning factor reflecting the strength of the pinning effect, α is the domain coupling parameter affecting the slope of the mid-segment of the hysteresis loop and C is the coefficient of reversibility. However, all the four parameters are influenced by residual stress. Furthermore, the influence of magnetic peak induction on parameters can’t be ignored according to our work. The classical Jile-Atherton hysteresis model cannot reflect the influence of residual stress and magnetic peak induction. In this paper, a modified residual stress dependent Jile-Atherton hysteresis model was proposed, whose parameters are extended to functions related to residual stress and magnetic peak induction. A novel device was designed to carry out magnetic property testing experiments under large stress. The parameters were identified by a MATLAB program and the influence of residual stress and magnetic peak induction was analyzed. The accuracy of parameters was validated by experiments, which showed that the modified model worked well in describing the magnetization characteristic under different stresses and magnetic peak inductions. This could provide some guidance for the manufacturing processes of motor stators.

Modeling the Effect of Multiaxial Stress on Magnetic Hysteresis of Electrical Steel Sheets: A Comparison

The abilities of a simplified multiscale and a Helmholtz energy HE models models from the literature to predict the multiaxial stress dependent magnetic hysteresis behavior of electrical steel sheets are analyzed. The identification of the models is performed using only uniaxial magneto-mechanical measurements. Reasonable accuracy between the measurements and the modeled results is obtained. With this paper, the applicability of the HE-based model for predicting the multiaxial magneto-mechanical behavior of electrical steel sheets is verified for the first time. The differences between the studied models and possible modifications to increase the accuracy of them are discussed. Some brief guidelines for the applications are given.

Model for Stress-Dependent Hysteresis in Electrical Steel Sheets Including Orthotropic Anisotropy

An energy-based approach for anisotropic modeling of stress-dependent magnetization curves in electrical steel sheets is presented. The model is based on an orthotropic extension of an existing isotropic thermodynamic model and coupling to the Jiles-Atherton model of hysteresis. The model fits well to experimental results under uniaxial excitation, and it is numerically tested under rotational fields.

Hysteresis loop as the indicator of residual stress in drawn wires

The paper investigates the possibility of using the magnetic method for non-destructive determination of residual stress in drawn wires. The change in residual stress for different processing speeds is reflected in the shape of hysteresis loop. A simple model for stress-dependent hysteresis, based on the concept of the effective field, is proposed. The effective field includes an additional term related to stress, in accordance with previous Jiles’ and Sablik's results. The presented description may be useful for technologists seeking a simple tool for predicting residual stress.

Outlook of Preisach Modeling and Magnetic Non Destructive Testing

The Preisach formalism is used as a basis for a vector model of magnetic hysteresis in soft magnetic materials subject to tensile stress. The model uses as vector elementary hysteresis operator the Stoner-Wohlfarth mechanism of coherent rotation while the Preisach density is constructed as the weighed sum of probability density functions corresponding to the high and low induction regions. The model reproduces the basic phenomenology of stress-dependent hysteresis: the double peak in differential permeability modeled as the effect of internal demagnetizing fields emerging from residual stresses; the increase in coercivity due to increased pinning; the decrease in magnetic induction as the result of non-180o domain rotation. The role of the negative differential permeability near remanence and its derivative is discussed with respect to residual stresses and magnetic NDT.

Experimental characterization and modeling of stress-dependent hysteresis of a giant magnetostrictive actuator

The hysteresis nonlinearity of giant magnetostrictive actuator (GMA) is stress-dependent. In this paper, laboratory experiments were performed to characterize the stress-dependent hysteresis properties of a GMA under different compressive stresses ranging from −11.3 MPa to −24.3 MPa and harmonic current excitation with amplitudes from 0.6 A to 1.2 A. The experimental results showed that remarkable changes in peak-peak displacement responses, hysteresis loop width and hysteresis loss occurred with the increasing of compressive stress; no significant changes in coercive current were observed. Based on the analysis of experimental data and discussion of the influences of the weights of Modified Prandtl-Ishlinskii (MPI) on the characteristics of hysteresis loops, a stress-dependent Prandtl-Ishlinskii (SDPI) model was proposed by extending the MPI model to describe the effects of compressive stress, in which the weights of deadzone operators are extended as function of compressive stress. Good agreements were obtained between the model simulation results and the experimental data. Additional model validations were given by the performances of tracking control experiments with an inverse feedforward controller. The experimental results have clearly shown that the inverse SDPI is effective for compensating stress-dependent hysteresis including major and minor loops.

On Modeling and Tracking Control for a Smart Structure with Stress-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the stress-dependent hysteresis generated by varying mechanical loads. In this paper,a stress-dependent Preisach operator is proposed for describing the hysteresis nonlinearity under both varying input current and compressive stress featured by introducing the dependence of the density function on the compressive stress. Subsequently,the properties together with the parameter identification scheme based on a fuzzy tree method of the presented operator are investigated to formulate an inverse compensator. Then,a feedback control scheme combined with a feed-forward compensator is implemented to a magnetostrictive smart structure (MSS) for real-time precise trajectory tracking. Compared with the classical operator,the proposed operator and corresponding control scheme experimentally demonstrate a dramatically improved performance for mitigating the effects of stress-dependent hysteresis.

On Modeling and Tracking Control for a Smart Structure with Stress-dependent Hysteresis Nonlinearity

Abstract The performance of smart structures in trajectory tracking under sub-micron level is hindered by the stress-dependent hysteresis generated by varying mechanical loads. In this paper, a stress-dependent Preisach operator is proposed for describing the hysteresis nonlinearity under both varying input current and compressive stress featured by introducing the dependence of the density function on the compressive stress. Subsequently, the properties together with the parameter identification scheme based on a fuzzy tree method of the presented operator are investigated to formulate an inverse compensator. Then, a feedback control scheme combined with a feed-forward compensator is implemented to a magnetostrictive smart structure (MSS) for real-time precise trajectory tracking. Compared with the classical operator, the proposed operator and corresponding control scheme experimentally demonstrate a dramatically improved performance for mitigating the effects of stress-dependent hysteresis.

Magnetic measurement and vector modeling under applied mechanical stress

The scope of the work is the investigation of the properties of the magnetic characteristic under applied stress. The realization and the accuracy of a Preisach-type scalar magnetic hysteresis model are displayed with respect to the changing of the mechanical stress in the magnetic material. A stress dependent isotropic and anisotropic vector hysteresis model has been developed. The model represents the main properties of the tensile stress effects on the magnetic behavior.

Stress-Dependent Hysteresis Modeling and Tracking Control of Giant Magnetostrictive Actuator for Periodic Reference Input

The tracking control accuracy of giant magnetostrictive actuator (GMA) is limited due to its inherent hysteresis nonlinearity. Hysteresis characteristic of GMA is stress-dependent. This paper proposes a stress-dependent Prandtl-Ishlinskii (SDPI) hysteresis model for GMA by extending the modified Prandtl-Ishlinskii (MPI) model to account for the hysteresis of GMA at varying compressive stress. It is shown experimentally that the weights of play operators is non-sensitive to the compressive stress applied in longitudinal direction of GMA and the relationships between weights of deadzone operators and compressive stress could be modeled by quadratic functions. Then the inverse of SDPI model is established and implemented in open-loop feedforward controller for real-time tracking control for periodic reference input. Comparisons are made between feedforward controller with stress-dependent hysteresis model and stress-independent model. Experimental results show that tracking performance is noticeably improved by using SDPI model.

Measurement of the differential susceptibility of soft magnetic ribbons under applied tensile and compressive stress

This paper presents a method which allows the determination of the magnetisation curve of thin ribbons and its stress dependence for both tensile and compressive stress. In the case of the latter, the sample is agglutinated between two polymer sheets to prevent buckling. This sandwich is then mounted in a mechanical set-up, where the stress is applied by means of a spiral spring and a worm drive. The sample is ac magnetized and the flux is measured inductively yielding the stress dependent hysteresis curve as a basis for the determination of the differential susceptibility.

A Stress-Dependent Hysteresis Model for PZT

AbstractThis paper addresses the development of an energy-based characterization framework which quantifies stress-induced dipole switching in ferroelectric materials. Helmholtz and Gibbs energy relations that accommodate 90° and 180° dipole orientations as equilibrium states are constructed at the lattice level. For regimes in which thermal relaxation mech- anisms are negligible, minimization of the Gibbs relations provides local polarization and strain relations. Alternatively, behavior such as creep or thermal relaxation can be incorpo- rated by balancing Gibbs and relative thermal energies through Boltzmann principles. In the nal step of the development, stochastic homogenization techniques based on the assump- tion that parameters such as coercive and induced elds are manifestations of underlying distributions are employed to construct macroscopic models suitable for nonhomogeneous polycrystalline compounds. Attributes and limitations of the model are illustrated through comparison with experimental PLZT data.

Hysteresis modeling of tunneling magnetoresistance strain sensor elements

Utilizing the inverse magnetostriction effect, magnetic tunneling junction (MTJ) elements have been demonstrated to also be useful as highly sensitive stress or strain transducers. The prediction of the stress dependent hysteresis of the tunneling magnetoresistance R is done by the energetic model (EM), minimizing the total magnetization work which consists of the Zeeman energy density, of magnetocrystalline and stress anisotropy of the magnetization rotation processes, and of reversible and irreversible contributions of domain wall displacements. Furthermore, the law of approach to saturation and the initial susceptibility relate the parameters of the EM to the effective anisotropy energy which has to be overcome for a magnetization reversal. The calculated R(H) curves are in good aggreement with the measurements, allowing several predictions of the MTJ parameters as magnetostriction constant, stress (strain) sensitivity and hysteresis, and misalignment of the easy axis.

Effects of tensile stress on magnetic Barkhausen emissions in amorphous FeSiB alloy

Magnetic hysteresis and Barkhausen emissions have been measured for amorphous Fe 82B 10Si 8 samples with positive magnetostriction of λ s = 27 × 10 −6 under tensile stress of up to 35 MPa. The root mean square voltage of the Barkhausen signal and the number of events per cycle increased monotonically with the applied stress. The results are explained in terms of a theory which includes a stress-dependent hysteresis model and a stochastic process model for the Barkhausen emissions.