The Two-Domain Model Utilizing the Effective Pinning Energy for Modeling the Strain-Dependent Magnetic Permeability in Anisotropic Grain-Oriented Electrical Steels.

This paper presents a newly proposed domain wall energy-based model of the 2D strain dependence of relative magnetic permeability in highly grain-oriented anisotropic electrical steels. The model was verified utilizing grain-oriented M120-27s electrical steel sheet samples with magnetic characteristics measured by an automated experimental setup with a magnetic yoke. The model's parameters, identified in the differential evolution-based optimization process, enable a better understanding of the interaction between stress-induced anisotropy and magnetocrystalline anisotropy in electrical steels. Moreover, the consequences of the simplified description of grain-oriented magnetocrystalline anisotropy are clearly visible, which opens up the possibility for further research to improve this description.

Model of a 3D Magnetic Permeability Tensor Considering Rotation and Saturation States in Materials with Axial Anisotropy.

The paper proposes a 3D extension of the linear tensor model of magnetic permeability for axially anisotropic materials. In the proposed model, all phases of a magnetization process are considered: linear magnetization, magnetization rotation, and magnetic saturation. The model of the magnetization rotation process is based on the analyses of both anisotropic energy and magnetostatic energy, which directly connect the proposed description with physical phenomena occurring during a magnetization process. The proposed model was validated on the base of previously presented experimental characteristics. The presented extension of the tensor description of magnetic permeability enables the modelling of inductive devices with cores made of anisotropic magnetic materials and the modelling of magnetic cores subjected to mechanical stresses. It is especially suitable for finite element modelling of the devices working in a magnetic saturation state, such as fluxgate sensors.

Inverse Transformation in Eddy Current Tomography with Continuous Optimization of Reference Defect Parameters.

This paper presents a methodology of inverse tomography transformation in eddy current tomography with the use of continuous optimization of reference defect parameters. Ferromagnetic steel samples with rectangular air inclusion defects of known dimensions were prepared and measured using an eddy current tomography setup. FEM-based (Finite Element Method based) forward tomography transformation was developed and utilized in inverse tomography transformation. The presented method of inverse tomography transformation is based on the continuous optimization of parameters that can describe the sample, such as the diameter and dimensions of the reference defect. The obtained results of inverse tomography transformation were in high accordance with the real parameters of the samples. Additionally, the presented method had acceptable repeatability. The obtained values of the sample parameters fit within the range of expanded uncertainty when compared to the real parameters of the sample.

A FEM-Based Optimization Method for Driving Frequency of Contactless Magnetoelastic Torque Sensors in Steel Shafts.

This paper presents a novel finite element method (FEM) of optimization for driving frequency in magneto-mechanical systems using contactless magnetoelastic torque sensors. The optimization technique is based on the generalization of the axial and shear stress dependence of the magnetic permeability tensor. This generalization creates a new possibility for the determination of the torque dependence of a permeability tensor based on measurements of the axial stress on the magnetization curve. Such a possibility of quantitative description of torque dependence of a magnetic permeability tensor has never before been presented. Results from the FEM-based modeling method were validated against a real magnetoelastic torque sensor. The sensitivity characteristics of the model and the real sensor show a maximum using a driving current of similar frequency. Consequently, the proposed method demonstrates the novel possibility of optimizing magnetoelastic sensors for automotive and industrial applications.

Elementary, Atomic-Level Friction Processes in Systems with Metallic Inclusions-Systematic Simulations for a Wide Range of Local Pressures.

In this work, simulations of friction at the atomic level were performed to evaluate the influence of inclusions coming from metallic nanoadditives in the friction pair. The simple 2D model was applied considering appropriate values of Lennard-Jones potential parameters for given sets of interacting atoms. The real sliding pairs were replaced by effective equivalents consisting of several atoms. The calculations were based on the pseudo-static approximation. The simplicity of the model enabled to repeat the fast calculations in a very wide range of local pressures and for several types of atomic tribopairs. The performed simulations demonstrated a strong dependence of the coefficient of friction (COF) on the atomic environment of the atoms constituting a tribopair. It was confirmed theoretically that the Mo-Fe pair is characterized by lower atomic COF than Fe-Fe, Cu-Fe, and Ag-Fe pairs. This points to the great applicational potential of metallic molybdenum coating applications in tribological systems. Moreover, it was demonstrated that, although Cu-Cu and Ag-Ag pairs are characterized by relatively high COF, they lower the friction as inclusions in Fe surfaces.

Generalization of the Model of Magnetoelastic Effect: 3D Mechanical Stress Dependence of Magnetic Permeability Tensor in Soft Magnetic Materials.

This paper presents a new solution enabling modeling of the mechanical stress tensor dependence of the 3D relative permeability tensor of isotropic material only on the basis of knowledge of the axial stress dependence characteristics. For the proposed model, the concept of principal stresses is utilized. In such a case, the sophisticated system of axial and shear stresses may be reduced to the set of axial stresses in a rotated coordination axes system. As a result, the proposed solution generalizes the explanation of the shape of magnetoelastic characteristics as well as radically extending possibility of the application of the finite elements methods (FEM) to describe sophisticated magnetoelastic systems.

Novel Giant Magnetoimpedance Magnetic Field Sensor.

The idea, design, and tests of the novel GMI sensor are presented, based on the compensation measurement principle, where the local 'zero-field' minimum of the double-peak characteristic was utilized as a sensitive null detector. The compensation field was applied in real-time with the help of microprocessor-based, two-step, quasi-Newtonian optimization. The process of material parameters optimization through Joule-annealing of chosen amorphous alloys is described. The presented results of the prototype test unit show linear output characteristic, low measurement uncertainty, and resistance against time and temperature drift.

Modelling the Characteristics of Ring-Shaped Magnetoelastic Force Sensor in Mohri's Configuration.

Magnetoelastic force sensors exhibit high sensitivity and robustness. One commonly used configuration of force sensor with a ring-shaped core was presented by Mohri at al. In this configuration force is applied in the direction of a diameter of the core. However, due to inhomogeneous distribution of stresses, model of such sensor has not been presented yet. This paper is filling the gap presenting a new method of modelling the magnetoelastic effect, which is especially suitable for the finite element method. The presented implementation of proposed model is in good agreement with experimental data and creates new possibilities of modelling other devices utilizing magnetoelastic effect.

Modeling the Influence of a Magnetomechanical Effect on the Permeability Tensor of a Tensductor Core.

This paper presents a new method of modeling the influence of mechanical stresses on a magnetic permeability tensor of soft magnetic materials. The proposed method utilizes the principal stresses concept to compensate the influence of shear stresses. As a result, the stress dependence of a magnetic permeability tensor may be assessed with only the knowledge about the influence of axial stresses on magnetic properties of isotropic material. The proposed method was used for a finite element method based model of a tensductor designed for measurements of tensile forces. Due to the fact that 2D stresses distribution occurs in a tensductor, simplification of both principal stresses and a magnetic permeability tensor rotation procedure was proposed. As a result, good agreement was reached between the results of modeling and the results of experimental tests. This result validates the possibility of utilization of the proposed modeling method for the design of magnetomechanical devices.

Strain Dependence of Hysteretic Giant Magnetoimpedance Effect in Co-Based Amorphous Ribbon.

The significant strain dependence of the hysteretic Giant Magnetoimpedance (GMI) effect in a Co67Fe3Cr3B12Si15 amorphous alloy in a low magnetizing field is presented. A simplistic test stand capable of continuous measurements of GMI characteristics under the influence of strain is detailed. Based on the results, a stress-impedance (SI) sensor is proposed, with a gauge factor similar to semiconductor strain gauges but more robust. An effective method of minimizing external magnetic field influence on the SI effect is given.

Experimental Verification of Isotropic and Anisotropic Anhysteretic Magnetization Models.

The anhysteretic magnetization curve is the key element of modeling magnetic hysteresis loops. Despite the fact that it is intensively exploited, known models of anhysteretic curve have not been verified experimentally. This paper presents the validation of four anhysteretic curve models considering four different materials, including isotropic, such as Mn-Zn soft ferrite, as well as anisotropic amorphous and nanocrystalline alloys. The presented results indicate that only the model that considers anisotropic energy is valid for a wide set of modern magnetic materials. The most suitable of the verified models is the anisotropic extension function-based model, which considers uniaxial anisotropy.

Unified First Order Inertial Element Based Model of Magnetostrictive Hysteresis and Lift-Off Phenomenon.

The present paper presents a new model of magnetostrictive hysteresis loop. A unified approach of both the hysteresis of λ(B) relation, as well as the lift-off phenomenon is proposed, which are explained together on the base of the response of the first order inertial element. Considering previously presented reports, the Maxwell-Boltzmann distribution based model of magnetostrictive characteristics with local maxima, enables modeling magnetostrictive loops. The model was validated on the results of measurements of magnetostrictive hysteresis loops of Mn0.70Zn0.24Fe2.06O4 ferrite for power applications. Good agreement was confirmed for major magnetostrictive loop, especially for smaller values of flux density. As a result, the proposed model may be used for modeling the magnetostrictive response of inductive components of electrical machines, power conversion devices or magnetostrictive actuators.

Influence of Torsion on Matteucci Effect Signal Parameters in Co-Based Bistable Amorphous Wire.

The Matteucci effect (ME) is one of the lesser-known magnetomechanical effects and is most prominent in bistable amorphous wires. It has some experimental applications-Matteucci effect-based magnetic field sensors are very easy to produce and have inherently linear, hybrid analog/digital output signal. The effect is still poorly understood, however, and although it relies on torsion of the wire to manifest, there is no available model, or much experimental data, which would quantitatively connect the ME with the sample twist. In this paper, experimental characteristics of ME signal parameters dependence on torsion in Co-based amorphous bistable wire are presented. The results hint at possible applications, such as rotation or critical current sensors, as well as the necessity of torsion control in the development of ME magnetic field sensors.

Determination of the Location and Magnetic Moment of Ferromagnetic Objects Based on the Analysis of Magnetovision Measurements.

This article is concerned with the localization of ferromagnetic objects on the basis of magnetovision measurement analysis. In the presented case, the concept of localization is understood as the indication of the x, y, and z coordinates of the magnetic moment of the sought object. Magnetovision measurement provides a much simpler, two-dimensional localization of magnetic anomalies compared to existing active and passive mobile devices, largely based on operator knowledge and experience. In addition, the analysis of the obtained magnetovision measurement, by fusing data with a mathematical model, enables a quantitative assessment of the position of an object in space and the determination of the value and spatial orientation of its magnetic moment vector. The detection and localization method was verified using the certified magnetic moment standard. An additional novelty is the inclusion of the influence of the constant gradient of the external field in the model, which corresponds to disturbing the measurement by the influence of large, but distant, objects. The proposed three-dimensional magnetovision measurement method and its analysis enable the determination of the x, y, and z coordinates; the angular position; and the magnetic moment values of unknown magnetic dipoles in real conditions (effects of disturbances generated by other distant objects and background noise), thus precisely detecting and locating the ferromagnetic object.

Comparison of Stress-Impedance Effect in Amorphous Ribbons with Positive and Negative Magnetostriction.

The SI (stress-impedance) effect in amorphous ribbons with varying magnetostriction was investigated. Iron- and cobalt-based ribbons with different magnetostriction coefficients were put under tensile stress in a dead weight tester and the impedance change was investigated in function of applied stresses. Significant differences of characteristics are presented. Stress-impedance analog of Villari reversal point was observed. The reversal point showed driving current frequency dependence, in which this point manifests for different stress values. Based on the obtained SI characteristics and magnetoelastic hysteresis, the most appropriate stress-sensing material was selected for development of precise small forces sensor.

Magnetostrictive Properties of Mn0.70Zn0.24Fe2.06O4 Ferrite.

This paper presents the results of measurements of magnetostrictive properties of Mn0.70Zn0.24Fe2.06O4 ferrite for power applications. Frame-shaped samples were used for measurements to guarantee a uniform magnetizing field and magnetostrictive strain distribution. Magnetostrictive hysteresis loops were measured by semiconductor strain gauges. The results indicate that the magnetostrictive characteristic of Mn0.70Zn0.24Fe2.06O4 ferrite is non-monotonic and magnetostriction changes have opposite signs for higher values of the magnetizing field.

Modeling the Hysteresis Loop of Ultra-High Permeability Amorphous Alloy for Space Applications.

This paper presents investigation results regarding the Jiles-Atherton-based hysteresis loop modeling of ultra-high permeability amorphous alloy MELTA® MM-5Co. The measurement stand is capable of accurately measuring minor and major hysteresis loops for such a material together with exemplary measurement results. The main source of the measurement error is highlighted, which includes the Earth's field influence. The results of hysteresis loop modeling with the original Jiles-Atherton model and with two of its modifications are given. In all cases, the parameters of the Jiles-Atherton model were identified in two-step identification on the basis of a differential evolution optimization algorithm. The results indicate that both the original and modified Jiles-Atherton models are suitable for modeling the ultra-soft amorphous alloy. However, the hysteresis model's parameters vary significantly.

Model of the Magnetostrictive Hysteresis Loop with Local Maximum.

This paper presents a model of the magnetostrictive hysteresis loop with local maximum. The model is based on the differential equations describing magnetostriction due to the domain wall movement as well as domain magnetization rotation. The transition between these mechanisms of magnetization is quantified by the Maxwell⁻Boltzmann distribution. Moreover, the lift-off phenomenon in the magnetostrictive hysteresis loop is considered. The proposed model was validated on the results of measurements of magnetostrictive hysteresis loops of Mn0.70Zn0.24Fe2.06O4 ferrite for power application and 13CrMo4-5 construction steel. The results of modeling confirm that the proposed model corresponds well with experimental results. Good agreement was confirmed by determination coefficient R², which exceeded 0.995 and 0.985 for Mn0.70Zn0.24Fe2.06O4 ferrite for power application and 13CrMo4-5 construction steel, respectively.

The Additional Error of Inertial Sensors Induced by Hypersonic Flight Conditions.

The emergence of hypersonic technology pose a new challenge for inertial navigation sensors, widely used in aerospace industry. The main problems are: extremely high temperatures, vibration of the fuselage, penetrating acoustic radiation and shock N-waves. The nature of the additional errors of the gyroscopic inertial sensor with hydrostatic suspension components under operating conditions generated by forced precession of the movable part of the suspension due to diffraction phenomena in acoustic fields is explained. The cause of the disturbing moments in the form of the Coriolis inertia forces during the transition of the suspension surface into the category of impedance is revealed. The boundaries of occurrence of the features on the resonance wave match are described. The values of the "false" angular velocity as a result of the elastic-stress state of suspension in the acoustic fields are determined.

A Mathematical Model of the Thermo-Anemometric Flowmeter.

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.