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Keywords = Villari effect

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20 pages, 20556 KB  
Article
A Contactless Low-Carbon Steel Magnetostrictive Torquemeter: Numerical Analysis and Experimental Validation
by Carmine Stefano Clemente, Claudia Simonelli, Nicolò Gori, Antonino Musolino, Rocco Rizzo, Marco Raugi, Alessandra Torri and Luca Sani
Sensors 2024, 24(21), 6949; https://doi.org/10.3390/s24216949 - 29 Oct 2024
Viewed by 1753
Abstract
Torque measurement is a key task in several mechanical and structural engineering applications. Most commercial torquemeters require the shaft to be interrupted to place the sensors between the two portions of the shaft where a torque has to be measured. Contactless torquemeters based [...] Read more.
Torque measurement is a key task in several mechanical and structural engineering applications. Most commercial torquemeters require the shaft to be interrupted to place the sensors between the two portions of the shaft where a torque has to be measured. Contactless torquemeters based on the inverse magnetostrictive effect represent an effective alternative to conventional ones. Most known ferromagnetic materials have an inverse magnetostrictive behavior: applied stresses induce variations in their magnetic properties. This paper investigates the possibility of measuring torsional loads applied to a shaft made of ferromagnetic steel S235 through an inverse magnetostrictive torquemeter. It consists of an excitation coil that produces a time-varying electromagnetic field inside the shaft and an array of sensing coils suitably arranged around it, in which voltages are induced. First, the system is analyzed both in unloaded and loaded conditions by a Finite Element Method, investigating the influence of relative positions between the sensor and the shaft. Then, the numerical results are compared with the experimental measurements, confirming a linear characteristic of the sensor (sensitivity about 0.013 mV/Nm for the adopted experimental setup) and revealing the consistency of the model used. Since the system exploits the physical behavior of a large class of structural steel and does not require the introduction of special materials, this torquemeter may represent a reliable, economical, and easy-to-install device. Full article
(This article belongs to the Special Issue Magnetostrictive Transducers, Sensors, and Actuators)
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12 pages, 4580 KB  
Article
A Polyimide Composite-Based Electromagnetic Cantilever Structure for Smart Grid Current Sensing
by Zeynel Guler and Nathan Jackson
Micromachines 2024, 15(10), 1189; https://doi.org/10.3390/mi15101189 - 26 Sep 2024
Cited by 5 | Viewed by 4866
Abstract
Polyimides (PIs) have been extensively used in thin film and micro-electromechanical system (MEMS) processes based on their excellent thermal and mechanical stability and high glass transition temperature. This research explores the development of a novel multilayer and multifunctional polymer composite electro-piezomagnetic device that [...] Read more.
Polyimides (PIs) have been extensively used in thin film and micro-electromechanical system (MEMS) processes based on their excellent thermal and mechanical stability and high glass transition temperature. This research explores the development of a novel multilayer and multifunctional polymer composite electro-piezomagnetic device that can function as an energy harvester or sensor for current-carrying wires or magnetic field sensing. The devices consist of four layers of composite materials with a polyimide matrix. The composites have various nanoparticles to alter the functionality of each layer. Nanoparticles of Ag were used to increase the electrical conductivity of polyimide and act as electrodes; lead zirconate titanate was used to make the piezoelectric composite layer; and either neodymium iron boron (NdFeB) or Terfenol-D was used to make the magnetic and magnetostrictive composite layer, which was used as the proof mass. A novel all-polymer multifunctional polyimide composite cantilever was developed to operate at low frequencies. This paper compares the performance of the different magnetic masses, shapes, and concentrations, as well as the development of an all-magnetostrictive device to detect voltage or current changes when coupled to the magnetic field from a current-carrying wire. The PI/PZT cantilever with the PI/NdFeB proof mass demonstrated higher voltage output compared to the PI/Terfenol-D proof mass device. However, the magnetostrictive composite film could be operated without a piezoelectric film based on the Villari effect, which consisted of a single PI-Terfenol-D film. The paper illustrates the potential to develop an all-polymer composite MEMS device capable of acting as a magnetic field or current sensor. Full article
(This article belongs to the Section E:Engineering and Technology)
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15 pages, 3123 KB  
Article
Effect of Acoustic Oscillations on Non-Equilibrium State of Magnetic Domain Structure in Cubic Ni2MnGa Single Crystal
by Anxo Fernández González, Konstantin Sapozhnikov, Pavel Pal-Val and Sergey Kustov
Materials 2023, 16(7), 2547; https://doi.org/10.3390/ma16072547 - 23 Mar 2023
Viewed by 2094
Abstract
Magnetic hysteresis is a manifestation of non-equilibrium state of magnetic domain walls trapped in local energy minima. Using two types of experiments we show that, after application of a magnetic field to a ferromagnet, acoustic oscillations excited in the latter can “equilibrate” metastable [...] Read more.
Magnetic hysteresis is a manifestation of non-equilibrium state of magnetic domain walls trapped in local energy minima. Using two types of experiments we show that, after application of a magnetic field to a ferromagnet, acoustic oscillations excited in the latter can “equilibrate” metastable magnetic domain structure by triggering the motion of domain walls into more stable configurations. Single crystals of archetypal Ni2MnGa magnetic shape memory alloy in the cubic phase were used in the experiments. The magnetomechanical absorption of ultrasound versus strain amplitude was studied after step-like changes of a polarizing magnetic field. One-time hysteresis was observed in strain amplitude dependences of magnetomechanical internal friction after step-like variations of a polarizing field. We distinguish two ingredients of the strain amplitude hysteresis that are found in the ranges of linear and non-linear internal friction and show qualitatively different behavior for increasing and decreasing applied polarizing fields. The uncovered effect is interpreted in terms of three canonical magnetomechanical internal friction terms (microeddy, macroeddy and hysteretic) and attributed to “triggering” by acoustic oscillations of the irreversible motion of domain walls trapped in the metastable states. To confirm the suggested interpretation we determine the coercive field of magnetization hysteresis through the measurements of the reversible Villari effect. We show that the width of the hysteresis loops decreases when acoustic oscillations in the non-linear range of domain wall motion are excited in the crystal. The observed “equilibration” of the magnetic domain structure by acoustic oscillations is attributed to the periodic stress anisotropy field induced by oscillatory mechanical stress. Full article
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27 pages, 8952 KB  
Article
Design and Characteristic Analysis of Magnetostrictive Vibration Harvester with Double-Stage Rhombus Amplification Mechanism
by Huifang Liu, Hongkai Liu, Xinxin Zhao, An Li and Xingfu Yu
Machines 2022, 10(10), 848; https://doi.org/10.3390/machines10100848 - 23 Sep 2022
Cited by 16 | Viewed by 3841
Abstract
Vibration energy harvesting is a new alternative to lithium battery power for low-power devices, attempting to recover wasted or lost vibration energy to generate electricity. Magnetostrictive-based energy harvesting exploits the coupling properties of the Villari and Faraday electromagnetic induction effects to achieve mechanical–magnetic–electric [...] Read more.
Vibration energy harvesting is a new alternative to lithium battery power for low-power devices, attempting to recover wasted or lost vibration energy to generate electricity. Magnetostrictive-based energy harvesting exploits the coupling properties of the Villari and Faraday electromagnetic induction effects to achieve mechanical–magnetic–electric energy conversion. In order to better apply to the actual vibration environment, such as buses, and improve the ability to capture low-frequency vibration energy, a double-stage rhombus vibration energy harvesting device, based on Terfenol-D rods, was developed. By establishing an analytical model of the force amplification ratio of the harvesting device, the design is optimized using the Single-Objective Genetic Algorithm, and the safety and pre-magnetization layout methods are analyzed by Finite Element Analysis. The output characteristics of the prototype, including the output voltage frequency response under low-frequency regular excitation and random excitation, the effect of external resistance, and the vibration energy capture performance under random excitation, are investigated in detail through experiments. The results of the experiments showed that the peak output power of the fabricated prototype was 1.056 mW at 30 Hz operating frequency, the energy harvesting capability reached 41.4 μW/N, and the peak open circuit voltage and output power were 2.92 V and 266 mW, respectively, under random excitation. Practical application test results showed that the peak voltage generated was 1.06–1.51 V when the excitation level was 2.2–4.9 m/s2. The comparative study indicates that the output performance of the proposed double-stage rhombus magnetostrictive vibration energy harvesting system is a great improvement over the proposals of existing literature. Full article
(This article belongs to the Special Issue New Advances in Energy Harvesters)
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6 pages, 244 KB  
Article
Deriving the Hawking Temperature of (Massive) Global Monopole Spacetime via a Topological Formula
by Junlan Xian and Jingyi Zhang
Entropy 2022, 24(5), 634; https://doi.org/10.3390/e24050634 - 30 Apr 2022
Cited by 7 | Viewed by 2244
Abstract
In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking [...] Read more.
In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking temperature of the global monopole spacetime can be obtained by the RVB method. We also discuss the Hawking temperature in massive gravity, and find that the effect of the mass term cannot be ignored in the calculation of the Hawking temperature; the corrected Hawking temperature in massive gravity can be derived by adding an integral constant, which can be determined by the standard definition. Full article
14 pages, 4497 KB  
Communication
Bendductor—Transformer Steel Magnetomechanical Force Sensor
by Przemysław Grenda, Monika Kutyła, Michał Nowicki and Tomasz Charubin
Sensors 2021, 21(24), 8250; https://doi.org/10.3390/s21248250 - 10 Dec 2021
Cited by 7 | Viewed by 3067
Abstract
In this paper, the design and investigation of an innovative force sensor, based on the Villari effect, is presented. The sensor was built from electrical steel, in a pressductor pattern, but working in bending load mode. The results of the experimental research allowed [...] Read more.
In this paper, the design and investigation of an innovative force sensor, based on the Villari effect, is presented. The sensor was built from electrical steel, in a pressductor pattern, but working in bending load mode. The results of the experimental research allowed for the evaluation of transducer’s performance, mitigation of measurement hysteresis, and optimization of its functional parameters. Several issues have been examined, among them the selection of supply and measured signals, the measured values’ impact on measurement hysteresis, harmonic analysis, and the selection of proper current waveforms and frequencies. The proposed sensor is robust, made from inexpensive materials, and has high sensitivity, as compared to other magnetoelastic sensors. It has much higher stress sensitivity than other magnetoelastic sensors due to deformation mode. Based on the tests, its measuring range can be defined as 0.5–5 N with a near-linear characteristic, SNR of 46 dB, and 0.11 N uncertainty. Full article
(This article belongs to the Special Issue Magnetostrictive Transducers, Sensors, and Actuators)
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13 pages, 3949 KB  
Article
Giant Stress-Impedance Effect in CoFeNiMoBSi Alloy in Variation of Applied Magnetic Field
by Piotr Gazda and Michał Nowicki
Materials 2021, 14(8), 1919; https://doi.org/10.3390/ma14081919 - 12 Apr 2021
Cited by 6 | Viewed by 2783
Abstract
The article presents the stress impedance investigation of CoFeNiMoBSi alloy in variation of the applied magnetic field. In order to carry out the study, a specialized stand was developed that allows for loading the sample with stresses and simultaneous action of the DC [...] Read more.
The article presents the stress impedance investigation of CoFeNiMoBSi alloy in variation of the applied magnetic field. In order to carry out the study, a specialized stand was developed that allows for loading the sample with stresses and simultaneous action of the DC (direct current) magnetizing field. The tests were carried out for as-cast and Joule annealed samples. The significant influence of the magnetizing field acting on the sample on the stress-impedance results was demonstrated and the dependence of the maximum impedance change in the stress-impedance effect was determined, depending on the field acting. The obtained results are important due to the potential use of the stress-impedance effect for the construction of stress sensors. Full article
(This article belongs to the Collection Magnetoelastic Materials)
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9 pages, 2408 KB  
Communication
Eddy Current Sensor System for Tilting Independent In-Process Measurement of Magnetic Anisotropy
by Frank Wendler, Rohan Munjal, Muhammad Waqas, Robert Laue, Sebastian Härtel, Birgit Awiszus and Olfa Kanoun
Sensors 2021, 21(8), 2652; https://doi.org/10.3390/s21082652 - 9 Apr 2021
Cited by 14 | Viewed by 4828
Abstract
Modern production equipment is based on the results of quality control as well as process parameters. The magnetic anisotropy of materials is closely connected to internal mechanical stress by the Villari effect, and also to hardening effects due to plastic deformations, and could [...] Read more.
Modern production equipment is based on the results of quality control as well as process parameters. The magnetic anisotropy of materials is closely connected to internal mechanical stress by the Villari effect, and also to hardening effects due to plastic deformations, and could therefore provide an interesting basis for process control. Nevertheless, the analysis of anisotropic properties is extremely sensitive to sensor and workpiece misalignments, such as tilting. In this work, a novel eddy current sensor system is introduced, performing a non-contact measurement of the magnetic anisotropy of a workpiece and realizing a separation and correction of tilting effects. The measurement principle is demonstrated with the example of two samples with different magnetic anisotropy values induced by cold forming. Both samples are analyzed under different tilt angles between the sensor axis and the surface of the workpiece. In this work, digital signal processing is demonstrated on the acquired raw data in order to differentiate the effects of tilt and of anisotropy, with the use of preliminary results as an example of two prepared samples. Full article
(This article belongs to the Special Issue Fabrication and Machining Technologies for Sensors)
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15 pages, 4516 KB  
Article
Villari Effect at Low Strain in Magnetoactive Materials
by Graciela Riesgo, Laura Elbaile, Javier Carrizo, Rosario Díaz Crespo, María Ángeles García, Yadir Torres and José Ángel García
Materials 2020, 13(11), 2472; https://doi.org/10.3390/ma13112472 - 29 May 2020
Cited by 12 | Viewed by 4323
Abstract
Magnetic composites of soft magnetic FeGa particles embedded in a silicone matrix have been synthesized. The Villari effect has been studied depending on the size and concentration of the particles and on the magnetic state of the composite. The results indicate a decrease [...] Read more.
Magnetic composites of soft magnetic FeGa particles embedded in a silicone matrix have been synthesized. The Villari effect has been studied depending on the size and concentration of the particles and on the magnetic state of the composite. The results indicate a decrease in the Villari effect when the concentration of the magnetic particles increases. These results suggest a relationship between the Villari effect and the mechanical properties of the composites. The Young’s modulus of the composites has been obtained by microindentation and their values related to the intensity and slope of the Villari signals. The results are explained on the basis that the reduction in the cross section of the composite when submitted to stress is the main origin of the variation of the magnetic flux in the Villari effect in this kind of composite. It has also been obtained that the magnetic state of the composite plays an important role in the Villari signal. When the magnetization of the composite is greater, the magnetic flux across the composite is greater too and, so, the same reduction in the cross section originates a greater Villari signal. Full article
(This article belongs to the Special Issue Advances in Magnetic Measurements)
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25 pages, 11203 KB  
Article
Comprehensive Analysis of the Energy Harvesting Performance of a Fe-Ga Based Cantilever Harvester in Free Excitation and Base Excitation Mode
by Huifang Liu, Chen Cong, Qiang Zhao and Kai Ma
Sensors 2019, 19(15), 3412; https://doi.org/10.3390/s19153412 - 3 Aug 2019
Cited by 20 | Viewed by 4802
Abstract
Vibration energy harvesting attempts to generate electricity through recycling the discarded vibration energy that is usually lost or dissipated, and represents an alternative to traditional batteries and may even lead to reliable self-powered autonomous electronic devices. Energy harvesting based on magnetostrictive materials, which [...] Read more.
Vibration energy harvesting attempts to generate electricity through recycling the discarded vibration energy that is usually lost or dissipated, and represents an alternative to traditional batteries and may even lead to reliable self-powered autonomous electronic devices. Energy harvesting based on magnetostrictive materials, which takes advantage of the coupling characteristics of the Villari effect and the Faraday electromagnetic induction effect, is a recent research field of great interest. Aiming to develop a new type of magnetostrictive energy harvester using Fe-Ga alloy, which is suitable for harvesting the vibration energy from base excitations and free excitations, a Fe-Ga based cantilever harvester was proposed. The energy harvesting performance of the harvester prototype, including its resonance characteristics, open-circuit output voltage-frequency response and amplitude characteristic under base excitation, influence of external resistance, energy harvesting performance under free excitation, the function of pre-magnetization and so on was studied systematically and carefully by experiments. In terms of the volume power density, the harvester prototype without pre-magnetized magnet when in series with the optimal resistor load displays a value of 2.653 mW/cm3. The average conversion efficiency without a pre-magnetic field is about 17.7% when it is in series with a 200 Ω resistance. The energy harvesting and converting capability can therefore be improved greatly once the Fe-Ga beam is highly pre-magnetized. The prototype successfully lit up multi-LEDs and digital display tubes, which validates the sustainable power generation capacity of the fabricated prototype. Full article
(This article belongs to the Section Physical Sensors)
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7 pages, 2697 KB  
Communication
Footstep Energy Harvesting with the Magnetostrictive Fiber Integrated Shoes
by Hiroki Kurita, Kenichi Katabira, Yu Yoshida and Fumio Narita
Materials 2019, 12(13), 2055; https://doi.org/10.3390/ma12132055 - 26 Jun 2019
Cited by 20 | Viewed by 4487
Abstract
Wearable energy harvesting devices attract attention as the devices provide electrical power without inhibiting user mobility and independence. While the piezoelectric materials integrated shoes have been considered as wearable energy harvesting devices for a long time, they can lose their energy harvesting performance [...] Read more.
Wearable energy harvesting devices attract attention as the devices provide electrical power without inhibiting user mobility and independence. While the piezoelectric materials integrated shoes have been considered as wearable energy harvesting devices for a long time, they can lose their energy harvesting performance after being used several times due to their brittleness. In this study, we focused on Fe–Co magnetostrictive materials and fabricated Fe–Co magnetostrictive fiber integrated shoes. We revealed that Fe–Co magnetostrictive fiber integrated shoes are capable of generating 1.2 µJ from 1000 steps of usual walking by the Villari (inverse magnetostrictive) effect. It seems that the output energy is dependent on user habit on ambulation, not on their weight. From both a mechanical and functional point of view, Fe–Co magnetostrictive fiber integrated shoes demonstrated stable energy harvesting performance after being used many times. It is likely that Fe–Co magnetostrictive fiber integrated shoes are available as sustainable and wearable energy harvesting devices. Full article
(This article belongs to the Special Issue Smart Materials and Devices for Energy Harvesting)
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21 pages, 4917 KB  
Review
Applications and Advances of Magnetoelastic Sensors in Biomedical Engineering: A Review
by Limin Ren, Kun Yu and Yisong Tan
Materials 2019, 12(7), 1135; https://doi.org/10.3390/ma12071135 - 7 Apr 2019
Cited by 59 | Viewed by 6535
Abstract
We present a comprehensive investigation into magnetoelastic sensors (MES) technology applied to biomedical engineering. This includes the working principles, detection methods, and application fields of MES technology. MES are made of amorphous metallic glass ribbons and are wireless and passive, meaning that it [...] Read more.
We present a comprehensive investigation into magnetoelastic sensors (MES) technology applied to biomedical engineering. This includes the working principles, detection methods, and application fields of MES technology. MES are made of amorphous metallic glass ribbons and are wireless and passive, meaning that it is convenient to monitor or measure the parameters related to biomedical engineering. MES are based on the inverse magnetoelastic (Villari) effect. When MES are subjected to mechanical stress, their magnetic susceptibility will change accordingly. And the susceptibility of MES is directly related to their magnetic permeability. The varying permeability can positively reflect the applied stress. The various detection methods that have been developed for different field applications include measurement of force, stress, and strain, monitoring of various chemical indexes, and consideration of different biomedical parameters such as the degradation rate and force conditions of artificial bone, as well as various physiological indexes including ammonia level, glucose concentration, bacteria growth, and blood coagulation. Full article
(This article belongs to the Collection Magnetoelastic Materials)
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11 pages, 2118 KB  
Article
Comparison of Stress-Impedance Effect in Amorphous Ribbons with Positive and Negative Magnetostriction
by Piotr Gazda, Michał Nowicki and Roman Szewczyk
Materials 2019, 12(2), 275; https://doi.org/10.3390/ma12020275 - 16 Jan 2019
Cited by 29 | Viewed by 4967
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Collection Magnetoelastic Materials)
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12 pages, 2646 KB  
Article
Low Field Magnetic and Thermal Hysteresis in Antiferromagnetic Dysprosium
by Iuliia Liubimova, Miguel Lluís Corró Moyà, Joan Torrens-Serra, Vicente Recarte, José Ignacio Pérez-Landazábal and Sergey Kustov
Metals 2017, 7(6), 215; https://doi.org/10.3390/met7060215 - 12 Jun 2017
Cited by 6 | Viewed by 9161
Abstract
Magnetic and thermal hysteresis (difference in magnetic properties on cooling and heating) have been studied in polycrystalline Dy (dysprosium) between 80 and 250 K using measurements of the reversible Villari effect and alternating current (AC) susceptibility. We argue that measurement of the reversible [...] Read more.
Magnetic and thermal hysteresis (difference in magnetic properties on cooling and heating) have been studied in polycrystalline Dy (dysprosium) between 80 and 250 K using measurements of the reversible Villari effect and alternating current (AC) susceptibility. We argue that measurement of the reversible Villari effect in the antiferromagnetic phase is a more sensitive method to detect magnetic hysteresis than the registration of conventional B(H) loops. We found that the Villari point, recently reported in the antiferromagnetic phase of Dy at 166 K, controls the essential features of magnetic hysteresis and AC susceptibility on heating from the ferromagnetic state: (i) thermal hysteresis in AC susceptibility and in the reversible Villari effect disappears abruptly at the temperature of the Villari point; (ii) the imaginary part of AC susceptibility is strongly frequency dependent, but only up to the temperature of the Villari point; (iii) the imaginary part of the susceptibility drops sharply also at the Villari point. We attribute these effects observed at the Villari point to the disappearance of the residual ferromagnetic phase. The strong influence of the Villari point on several magnetic properties allows this temperature to be ranked almost as important as the Curie and Néel temperatures in Dy and likely also for other rare earth elements and their alloys. Full article
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14 pages, 2290 KB  
Article
Research on the Lift-off Effect of Receiving Longitudinal Mode Guided Waves in Pipes Based on the Villari Effect
by Jiang Xu, Yong Sun and Jinhai Zhou
Sensors 2016, 16(9), 1529; https://doi.org/10.3390/s16091529 - 20 Sep 2016
Cited by 11 | Viewed by 7517
Abstract
The magnetostrictive guided wave technology as a non-contact measurement can generate and receive guided waves with a large lift-off distance up to tens of millimeters. However, the lift-off distance of the receiving coil would affect the coupling efficiency from the elastic energy to [...] Read more.
The magnetostrictive guided wave technology as a non-contact measurement can generate and receive guided waves with a large lift-off distance up to tens of millimeters. However, the lift-off distance of the receiving coil would affect the coupling efficiency from the elastic energy to the electromagnetic energy. In the existing magnetomechanical models, the change of the magnetic field in the air gap was ignored since the permeability of the rod is much greater than that of air. The lift-off distance of the receiving coil will not affect the receiving signals based on these models. However, the experimental phenomenon is in contradiction with these models. To solve the contradiction, the lift-off effect of receiving the longitudinal mode guided waves in pipes is investigated based on the Villari effect. A finite element model of receiving longitudinal guided waves in pipes is obtained based on the Villari effect, which takes into account the magnetic field in the pipe wall and the air zone at the same time. The relation between the amplitude of the induced signals and the radius (lift-off distance) of the receiving coil is obtained, which is verified by experiment. The coupling efficiency of the receiver is a monotonic decline with the lift-off distance increasing. The decay rate of the low frequency wave is slower than the high frequency wave. Additionally, the results show that the rate of change of the magnetic flux in the air zone and in the pipe wall is the same order of magnitude, but opposite. However, the experimental results show that the error of the model in the large lift-off distance is obvious due to the diffusion of the magnetic field in the air, especially for the high frequency guided waves. Full article
(This article belongs to the Special Issue Non-Contact Sensing)
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