Static Hysteresis Research Articles

The tensor magnetic phase theory for mesoscopic volume structures of soft magnetic materials – Quasi-static and dynamic vector polarization, apparent permeability and losses – Experimental identifications of GO steel at low induction levels

In this contribution, we propose to cope with the problem of soft magnetic materials heterogeneity and non-uniformity in terms of domains structure. This non-uniformity expresses itself with space variations of domains and walls geometry and characteristic properties from the bulk towards the surface. We investigate the possibility of describing and predicting these changes from a mesoscopic point of view. We begin with an introduction of typical subdivisions and define a tensor state variable [Λ2] to represent the diversity of magnetic structures with domains and walls. We then explain the material structuring thanks to an energy balance between the mesoscopic magnetic exchange, magneto-crystalline anisotropy, self-magnetostriction anisotropy, stress induced anisotropy and the dipolar demagnetizing energy. We write every contribution as a function of [V2] = [Λ2]−1. After minimizing the total energy, we derive a formulation compatible with classical numerical methods. [Λ2] is deduced thanks to a partial differential equation and surface boundary conditions. When a time varying field is applied to the material, damping effects occur either in the mass or at the surface. Eddy currents induced within domains lead to consider a volume dissipation energy. The surface magnetic field is also dampened by both the static hysteresis mainly due to defects and the dynamic hysteresis which stems from eddy currents around magnetic walls, added to the an-hysteretic field. The surface magnetic field, magnetic structure, and thus the polarization being known on the external surface, time variations of the volume magnetic structure can be calculated within the mass. Using the static or dynamic magnetic field coupling at the surface, the magnetic polarization can be rebuilt in the mass to calculate the apparent magnetic permeability. Finally, finding the geometry and frequency dependent vector magnetic behavior and iron losses becomes possible. The tensor magnetic phase theory is able to account for the sensitivity of the magnetic structure to the geometry, the macroscopic anisotropy partly influenced by the metallography, the residual or induced stress, some surface effects such as the texture, the rugosity or even any scribing patterns, at a mesoscopic scale. Two test cases for GO and NGO electrical steels are presented. Sensitivity analysis on the test case with GO steel are discussed. Results are then compared to static and dynamic measurements of GO SiFe sheet samples. This paper contributes to the investigations carried out on the geometry dependent magnetic behavior of soft magnetic materials.

Inter‐laminar fault analysis of magnetic cores with grain‐oriented electrical steels under harmonic distortion magnetisations

Inter-laminar faults (ILFs) have major impacts on the overall performance of the electrical machines and power transformers, among which extra power loss and hence lower efficiency could be highlighted. This paper presents an in depth analysis on energy loss and energy loss components of stacks of Grain-Oriented (GO) electrical steels subjected to different kinds of ILFs, under sinusoidal and non-sinusoidal inductions. Practical methods are developed to monitor quality of the magnetic cores, based on the measured static and dynamic hysteresis loops (SHL and DHL). The experimental results showed that, ILFs have a significant impact on the dynamic performance and dynamic energy loss of the cores, while their impact on the hysteresis loss is negligible. Furthermore, they become more destructive under non-sinusoidal inductions, and hence condition monitoring of the magnetic cores is more important for these applications.

Bulky Schiff-base ligand supported Co(ii) single-ion magnets with zero-field slow magnetic relaxation.

Two mononuclear Co(ii) complexes with tetrahedral coordination geometry have been constructed from different bulky Schiff-base ligands. Both complexes exhibit slow magnetic relaxation without a static field and their relaxation behaviors can be tuned by ligand substitution. Clear magnetic hysteresis loops were observed for both complexes at 2 K.

Calculation of Dynamic Hysteresis Loss of Power Transformer under Harmonic Background

The construction of smart grid uses a large number of power electronic equipment, which leads to the increase of harmonic content of transformer core winding, and brings some difficulties to the calculation of core loss. In order to study the influence of harmonics on core loss, a dynamic hysteresis loss model of transformer core under harmonics is established. On the basis of J-A static hysteresis model, the calculation methods of eddy current loss and abnormal loss under harmonic wave are deduced, and the calculation method of core loss under harmonic wave is established according to the principle of energy conservation. The core loss of three-phase transformer is simulated and verified by experiments under different harmonic frequency and harmonic voltage percentage. The results verify the validity of the model.

Study on Dynamic Hysteretic and Loss Properties of Silicon Steel Sheet Under Hybrid Harmonic and DC Bias Excitation

The dynamic and static hysteresis properties as well as loss properties of grain oriented (GO) silicon steel sheet are measured under the AC-DC hybrid excitation containing both DC bias and harmonic components. The influence of the DC-biasing magnetic field, harmonic orders and phase shift angles on the iron loss is analyzed in depth based on the experimental data under different excitations. A dynamic hysteresis model and the parameter identification method is presented to simulate the asymmetrical hysteresis curve with minor loops. According to the equivalence between loss separation and field separation, the static part of magnetic field intensity are calculated by an improved Preisach model, while the dynamic parts are obtained by fitting the classical loss as well as excess loss. The consistency between simulation and measurement verifies the effectiveness and accuracy of the proposed method.

An Improved Loss-Separation Method for Transformer Core Loss Calculation and Its Experimental Verification

The separation of core loss plays an important role in the transformer loss calculation. To obtain more accurate core loss, based on the comparison and analysis on two traditional loss separation methods, an improved loss separation method was proposed for the core loss calculation of the transformer in a wide magnetic flux density range. Firstly, through analysis the eddy current loss was obtained by direct calculation, while the hysteresis loss was obtained by performing the quasi-static magnetization process. And the coefficient corrections for the hysteresis loss and eddy current loss calculation were conducted by using the experimental data. The result comparison between the proposed method and traditional ones were made. Secondly, by setting up the Epstein frame platform, the total loss and static hysteresis loss of 14 types of industrial silicon steel were measured. In addition, the suggestive values and the corresponding value range of the loss coefficients of 14 kinds of industrial silicon steel were given. The results obtained by the proposed method were in good agreement with the measured data in the wide magnetic flux density range, while the suggestive values and the corresponding value range of 14 kinds of industrial silicon steel can provides an effective data support for the accurate core loss calculation.

Comparison of Preisach and Congruency-Based Static Hysteresis Models Applied to Non-Oriented Steels

Two hysteresis models are investigated for modeling static hysteresis phenomenon in nonoriented magnetic steels. First, the static Preisach model is studied, and two types of experimental data, i.e., first-order reversal curves (FORCs) and concentric hysteresis loops, are employed to identify the weight function. Due to negative values in the obtained experimental weight functions, the resulting Preisach models show nonphysical behavior. To eliminate this nonphysical behavior, an optimization procedure is applied to remove these negative values. The nonphysical behavior is resolved in the modified Preisach model; however, the model still has poor accuracy for asymmetric loops. Alternatively, a new congruency-based static hysteresis model is proposed. In this model, third- or higher-order reversal curves are approximated using measured FORCs and second-order reversal curves (SORCs) by means of a congruency regularity. According to this regularity, any third- or higher-order reversal curve is congruent to SORCs with the same reversal point. A 3-D piecewise interpolation function is employed to interpolate the measured major loop, FORCs, and SORCs. The proposed model results are compared with quasi-static measurements. The comparison reveals that the model is capable of approximating the magnetization curves for the measurements containing complex-shaped $B$ waveforms with a relative energy error of less than 4%.

The role of the substrate roughness in contact angle hysteresis and dynamic deviation

Static contact angle hysteresis and dynamic angle variation are two fundamental phenomena about the contact angle deviating from the equilibrium state. Various factors including solid roughness and disjoining pressure have been considered as the origins of the phenomena. This work made a reduction to absurdity by employing absolutely smooth solid surfaces in large-scale molecular dynamics simulations. The results showed that the equilibrium angles were well established on the absolutely smooth surface just as regular solid surfaces, while the hysteresis and the dynamic deviation vanished. In contrast, the solids made of atoms, even with atomic roughness, could bring significant static hysteresis and dynamic deviation. The convex nanobending, which was recently experimentally confirmed as a feature structure at advancing contact lines, was reproduced on atomic solids while vanished on the absolutely smooth one. The results indicated that the angle deviations could be unified to originate from the friction on solids, either static or dynamic, and that even the atomic roughness could be effective. As comparison, 3D observations were made using state-of-the-art helium ion microscopy for the first time revealing the ubiquitous nanoscopic distortion along the contact line on atomically smooth surfaces.

A correlation of metallic surface roughness with its hydrophobicity for dropwise condensation

Abstract The surface morphology alike lotus leaf has high contact angle and low contact angle hysteresis with respect to water droplet because of nanoscale roughness superimposed on micro order roughness in well-organized manner. The major application of superhydrophobic metallic substrate is in the condensing unit of energy and water harvesting devices. In this work, nanoscale roughness is superimposed on micro-order roughness of Aluminum substrate. The chemical texturing method is used to create micro-scale roughness onto Al surface. However, 0.6 keV Ar ions are irradiated for various time span to fabricate nano order roughness on chemically etched substrate. The roughness of samples is measured by Atomic Force Microscopy and static contact angles and their hysteresis are measured by lab customize Goniometer. It is found that the static contact angle and contact angle hysteresis increases after irradiation on chemical etched surfaces. Multi-scale roughness is observed on irradiated substrate. Results also shows that contact angle increases with increasing time of irradiation. However, maximum change in static contact angle is observed for samples irradiated for 45 s. Eventually, the static contact angle is correlated with its surface roughness. This correlation is vital for optimizing parameter affecting condensation rate in dropwise condensation. Finally, the moist air condensation experiments are conducted to know the condensation efficacy of the irradiated substrate. Also, it is found that the drop sliding frequency on vertical irradiated Al substrate is higher than the chemical etched Al substrate.

Hybrid hysteresis modeling and inverse model compensation of piezoelectric actuators

Piezoelectric actuators have shown great application potential in active vibration suppression and noise reduction. However, the nonlinear hysteresis effect in piezoelectric materials often compromises the control efficiency in practical application. This paper aims at presenting an innovative hybrid hysteresis model combining an original static operator and the frequency-dependent dynamic module. The static hysteresis operator is obtained through a system-level approach, using a butterfly-shape function which is inspired from the shape analysis of hysteresis loops. For the dynamic component, the classical Bouc–Wen model and the transfer function is introduced to predict the initial loop and frequency-dependent response, respectively. The comparison between the hybrid hysteresis model and experimental result performed on a unipolar piezoelectric actuator shows a good agreement with respect to the voltage range and the frequency bandwidth of interest. Meanwhile, it is able to track the transient initial loading loop and the major-minor loops switching phenomenon. Based on the identified hybrid hysteresis model, an inverse model compensation scheme is developed to linearize the relationship between the desired output and the practical output of the piezoelectric actuators. The mechanism of the inverse model compensator is theoretically investigated and experimentally verified. Therefore, it is a quite simple yet efficient compensation approach due to the accuracy and adaptability of the proposed hybrid hysteresis model.

The Microstructural Characterization, Physical and Dynamic Magnetic Properties of (Ni49Fe51)100−xCrx (x = 0,3,7) Thin Sheets

In this work, the effects of Cr on the microstructure, physical, and AC magnetic properties of the Ni49Fe51 alloy was studied. In this respect, three series of thin sheets of (Ni49Fe51)100−xCrx (x = 0, 3, and 7 at. pct) alloys with a final thickness of 120 µm were prepared by means of severe cold rolling and an 1150 °C annealing process at H2 atmosphere. Optical microscopy (OM), scanning electron microscopy (SEM), X-ray diffraction (XRD), (200) X-ray pole figure, and magnetic force microscopy (MFM) were employed to study microstructure, texture, and magnetic domain structure of the alloys. The magnetic characteristics of the samples were evaluated using BH-hysteresis loop tracer at a frequency range of 0.5 to 300 Hz. Based on the results obtained, it was shown that the mean magnetic domain width was increased from 1.006 to 1.398 μm for 0 Cr and 7 Cr samples, respectively. Furthermore, the magnitude of the static hysteresis loss increased and the excess and classical eddy current loss decreased for the Cr-added thin sheets.

Influence of Isothermal Heating on the Curie Temperature of FeCoB Bulk Amorphous Alloy

The article presents the results of research on the thermal treatment of amorphous alloys. As part of the work, an alloy with a chemical composition Fe63Co8Y8W1B20 was produced by rapid cooling. The method used to aspirate the liquid alloy into the copper mold was used. The produced material was subjected to annealing at 940K for 10 minutes. The alloy, after solidification and after heat treatment, was subjected to structure testing by means of X-ray diffraction. The soaking process led to the partial crystallization of the amorphous precursor. Using the Faraday magnetic balance, curves of the magnetic saturation polarization as a function of temperature were recorded, on the basis of their analysis, the Curie temperature of the produced materials was determined. Using the vibration magnetometer, the primary curves of magnetization and static magnetic hysteresis loops were measured. The alloy after the soaking process was characterized by higher Curie temperature and magnetically hard properties. The test results confirm the possibility of modifying the magnetic properties of high-temperature alloys through a suitably designed heat treatment.

Calculation Method of Magnetic Material Losses Under DC Bias Using Statistical Loss Theory and Energetic Hysteresis Model

The loss prediction of magnetic materials under dc bias is of great significance for the optimization of magnetic components, because the efficiency evaluation of magnetic components involves core loss computation under dc bias. Aiming to develop a calculation method for magnetic material losses under dc bias, a novel dynamic energetic hysteresis model combining the statistical theory of losses (STL) with a static energetic hysteresis model is proposed. Firstly, the effects of dc bias on the hysteresis, classical, and excess loss components are analyzed, respectively, using STL. Then, based on the equivalent field separation technique, the magnetic fields corresponding to classical and excess losses are derived using the analytical equations proposed by STL. Finally, a new dynamic energetic hysteresis model, which can take all the hysteresis, classical, and excess losses of magnetic materials under dc bias into account, is devised with the superposition principle. The simulation and experimental results confirmed the accuracy and efficiency of the proposed model.

Effect of stearic acid as a low cost and green material on the self-cleaning and anti-corrosion behavior of anodized titanium

A simple and highly effective route for preparation of superhydrophobic titanium (Ti) surface by single-step anodization in an organic electrolyte and subsequent stearic acid modification is suggested in this paper. Ti was anodized to produce micro-nano hierarchical morphology, which is extremely important for superhydrophobic surface. The anodized Ti was then treated with stearic acid to reduce surface energy. Surface morphology and structure of the anodized surfaces was characterized by field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). X-ray diffraction (XRD), X-ray energy dispersive spectrometry (EDS), and Fourier transform infrared (FT-IR) spectroscopy were utilized to specify chemical composition of superhydrophobic surfaces. The morphology of the surfaces was modified by adjusting anodizing parameters such as time (1, 2, 3, 4 and 5 h) and voltage (5, 20, 35 and 50 V). The results showed that static water contact angle and contact angle hysteresis on the best superhydrophobic Ti surface (with anodizing parameters of 3 h and 35 V) are 160.1° ± 0.5˚ and 7°, respectively. Furthermore, the superhydrophobic surface obtained has an acceptable self-cleaning and anticorrosion properties.

The behaviour of Nitinol Wire Bundles for Structural Applications

Shape memory alloys (SMA) belong to a family of smart materials, which undergo diffusionless phase transformations when subjected to thermo-mechanical changes making them ideally suitable for utilization in several structural engineering applications. Within this class of materials, Ni-Ti (Nickel-Titanium) alloys are predominantly used due to their non-linear behaviour. Nitinol, one of the Ni-Ti alloys, possesses unique properties such as super-elasticity and shape- memory effect, which makes it suitable for damping vibrations transmitted to structures like buildings and bridges during high wind and seismic events. This paper presents selected results obtained from a series of tests conducted on Nitinol 55 wires and bundles made from wires having diameters of 0.25, 0.5, 0.55, and 1 mm. The tests conducted include microstructure analyses, static tensile tests, hysteresis tests, and cyclic dynamic tests performed on wire bundles of various diameters. It is demonstrated that wires having small diameters (0.25 and 0.5 mm) exhibit greater ultimate strength compared with the ones having a larger diameter (1 mm). The bundles produced from these wires displayed hysteretic behaviour under cyclic-dynamic testing conditions confirming their suitability in structural engineering applications.

Temperature-dependent hysteresis model for soft magnetic materials

PurposeTo understand the behavior of the magnetization processes in ferromagnetic materials in function of temperature, a temperature-dependent hysteresis model is necessary. This study aims to investigate how temperature can be accounted for in the energy-based hysteresis model, via an appropriate parameter identification and interpolation procedure.Design/methodology/approachThe hysteresis model used for simulating the material response is energy-consistent and relies on thermodynamic principles. The material parameters have been identified by unidirectional alternating measurements, and the model has been tested for both simple and complex excitation waveforms. Measurements and simulations have been performed on a soft ferrite toroidal sample characterized in a wide temperature range.FindingsThe analysis shows that the model is able to represent accurately arbitrary excitation waveforms in function of temperature. The identification method used to determine the model parameters has proven its robustness: starting from simple excitation waveforms, the complex ones can be simulated precisely.Research limitations/implicationsAs parameters vary depending on temperature, a new parameter variation law in function of temperature has been proposed.Practical implicationsA complete static hysteresis model able to take the temperature into account is now available. The identification is quite simple and requires very few measurements at different temperatures.Originality/valueThe results suggest that it is possible to predict magnetization curves within the measured range, starting from a reduced set of measured data.

Modeling and Discrete-Time Terminal Sliding Mode Control of a DEAP Actuator with Rate-Dependent Hysteresis Nonlinearity

Dielectric electro-active polymer (DEAP) materials, also called artificial muscle, are a kind of EAP smart materials with extraordinary strains up to 30% at a high driving voltage. However, the asymmetric rate-dependent hysteresis is a barrier for trajectory tracking control of DEAP actuators. To overcome the barrier, in this paper, a Hammerstein model is established for the asymmetric rate-dependent hysteresis of a DEAP actuator first, in which a modified Prandtl-Ishlinskii (MPI) model is used to represent the static hysteresis nonlinear part, and an autoregressive with exogenous inputs (ARX) model is used to represent the linear dynamic part. Applying Levenberg-Marquardt (LM) algorithm identifies the parameters of the Hammerstein model. Then, based on the MPI model, an inverse hysteresis compensator is obtained to compensate the hysteresis behavior. Finally, a compound controller consisting of the hysteresis compensator and a novel discrete-time terminal sliding mode controller (DTSMC) without state observer is proposed to achieve the high-precision trajectory tracking control. Stability analysis of the closed-loop system is verified by using Lyapunov stability theorem. Experimental results based on a DEAP actuator show that the proposed controller has better tracking control performance compared with a conventional discrete-time sliding mode controller (DSMC).

Development and characterization of a MnCu-based high damping alloy plate

From the viewpoint of engineering application, the Mn-Cu based alloy plates are prepared to characterize both the mechanical properties as well as the damping capacity by employing the tensile test and dynamic mechanical analysis (DMA), respectively. The microstructure of MnCu alloy were determined by optical microscopy, while the tensile fracture morphology was observed by using a scanning electron microscopy. It is verified that the mechanical properties are similar to that of A3 steel while the vibration noise across the MnCu alloy plate cut about 5-15dB off during all the experiment frequency range from 20 to 300 Hz when the alloy backing plates are applied under a turbine electric generator. The internal friction characteristic of the alloy is disclosed to be dynamic hysteresis closely related to the vibration frequency, as well as to be static hysteresis that depending on strain amplitudes. With whatever vibration frequencies or strain amplitudes, the damping capacity (tan δ) of the alloy plate still shows satisfactory engineering application value higher than 0.02 at ambient temperature range around room temperature.

Deformation, speed, and stability of droplet motion in closed electrowetting-based digital microfluidics

Electrowetting-based microdrop manipulation has received considerable attention owing to its wide applications in numerous scientific areas based on the digital microfluidics (DMF) technology. However, the techniques for highly precise droplet handling in such microscopic systems are still unclear. In this work, the deformation, speed, and stability of droplet transporting in closed electrowetting-based DMF systems are comprehensively investigated with both theoretical and numerical analyses. First, a theoretical model is derived which governs the droplet motion and includes the influences of the key electrowetting system parameters. After that, a finite volume formulation with a two-step projection method is used for solving the microfluidic flow on a fixed numerical domain. The liquid-gas interface of the droplet is tracked by a coupled level-set and volume-of-fluid method, and the surface tension at the interface is computed by the continuum surface force scheme. A parametric study has been carried out to examine the effects of the static contact angles (θs,ON and θs,OFF), hysteresis effect (Δθ), channel height (H), and electrode size (LE) on droplet shape, speed, and deformation during transport, which unanimously shows that droplet length, neck width, and transport stability are directly related to a dimensionless parameter κ* that only comprises θs,ON, θs,OFF, H, LE, and the hysteresis angle Δθ. Based on the results, the scaling laws for estimating droplet shape and stability of the transport process have been developed, which can be used for promoting the accuracy and efficiency of droplet manipulation in a large variety of droplet-based DMF applications.

Ill-conditioned dynamic hysteresis compensation for a low-frequency magnetostrictive vibration shaker

We report an adaptive feedforward controller to address the ill-conditioned dynamic hysteresis on a custom-developed magnetostrictive vibration shaker. The vibration shaker works within low-frequency bandwidth. Magnetostrictive-induced hysteresis is a main issue that affects excitation waveform replication. Generally, the shape of dynamic hysteresis loop depends on the amplitude and frequency of input current. Many studies, e.g., Prandtl–Ishlinskii (PI)-based feedforward control approach, are conducted to address nonlinear dynamics in the hysteresis. Particularly, the dynamic hysteresis loop characterizes non-positive gradient (i.e., ill condition) when the frequency of input current is increasing. Under the ill condition, traditional PI-based feedforward control is ineffective. In this paper, we investigate this phenomenon according to a few experiments. Then, a novel static hysteresis and dynamics hybrid compensator is presented to deal with the ill-conditioned dynamic hysteresis issue. The dynamic compensator is a finite-impulse-response-based model whose coefficients are updated by the modified filtered-x normalized least mean square (MFxNLMS) algorithm. The static hysteresis compensator is constructed with the polynomial-modified PI (PMPI) model. The parameters of PMPI model are acquired by particle swarm optimization. Two simulations are conducted to show (1) the convergence of the MFxNLMS algorithm; (2) the efficacy of proposed model to describe the ill-conditioned dynamic hysteresis. Furthermore, the experimental device is constructed and a couple of experiments are implemented. The experimental results show that, with the proposed controller, the magnetostrictive vibration shaker can replicate both narrowband and wideband waveforms accurately. Moreover, it is robust to load variation.