United States

Transcranial magnetic stimulation (TMS) is a non-invasive technique used to regulate the synaptic activity of neurons in the brain, improving the functionality of connecting regions and bringing effective treatment to different neurological and psychiatric disorders. Treatment of many of these conditions requires application of external time-varying magnetic fields on a small cortical region to precisely alter connecting pathological sub-networks. The TMS induced field needs to be focused enough to avoid unwanted side effects caused by stimulation of the adjacent regions. Attempts at TMS in small animals[1] like rodents are highly constrained[2,3,4], since most of these studies use commercial equipment intended for humans, with power and coil geometries not intended for small animals. The present work shows the design and evaluation of customized arrays of two and four double-winding coils with a silicon steel core to restrict the stimulation to areas as small as 1 mm2, using finite element analysis with ANSYS Maxwell software. The coil is made with 50 turns of a wire with thickness = 1 mm, I.D. = 0.7 mm, O.D. = 4.5 mm and height = 25.4 mm. The cylindrical cores were designed with V-shape tip sharpening. The core material is silicon steel of 1.75 T of saturation flux density at 800 A/m and initial relative permeability of 500. The B-field was calculated 4.25 mm below the coil (vertical distance from the top of the scalp to the cortical layer 5/6 in adult rats) with currents of 1,000 A in short single (non-repetitive) pulses (≤ 4 msec) and showed values of up to 270 mT in 1 mm2. The very small area achieved supports the utility of the coil to perform in-vivo experimentation on rodents. Future works will seek to improve the duration of pulses for repetitive TMS (rTMS) with refrigeration and pulse conformation techniques and to validate the novel TMS device with in-vivo experiments in rat models. This study was partially funded by the Dept. of VA Biomedical Lab Research and Development 2I01BX001147-05A2 merit review award (M. Baron, PI).References: [1] J. Boonzaier, P. I. Petrov, W. M. Otte, N. Smirnov, S. F. W. Neggers, and R. M. Dijkhuizen, “Design and Evaluation of a Rodent Specific Transcranial Magnetic Stimulation Coil: An In Silico and In Vivo Validation Study,” Neuromodulation Technol. Neural Interface, p. ner.13025, Jul. 2019, doi: 10.1111/ner.13025. [2] J. Selvaraj, P. Rastogi, N. P. Gaunkar, R. L. Hadimani, and M. Mina, “Transcranial Magnetic Stimulation: Design of a Stimulator and a Focused Coil for the Application of Small Animals,” IEEE Trans. Magn., vol. 54, no. 11, Nov. 2018, doi: 10.1109/TMAG.2018.2846521. [3] M. T. Wilson, A. D. Tang, K. Iyer, H. McKee, J. Waas, and J. Rodger, “The challenges of producing effective small coils for transcranial magnetic stimulation of mice,” Biomed. Phys. Eng. Express, vol. 4, no. 3, Apr. 2018, doi: 10.1088/2057-1976/aab525. [4] I. P. de Sousa, C. R. H. Barbosa, and E. C. Monteiro, “Safe exposure distances for transcranial magnetic stimulation based on computer simulations,” PeerJ, vol. 2018, no. 6, 2018.

MMM 2020

Quadruple Silicon Steel Core Coil for Highly Focused Transcranial Magnetic Stimulation in Small Animals

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

Soft magnetic materials have been studied extensively in the recent years due to their applications in micro-transformers, micro-inductors, spin dependent memories etc. The unique features of these materials are the high frequency operability and high magnetic anisotropy. High uniaxial anisotropy is one of the most important properties for these materials. There are many methods to achieve high anisotropy field (Hk) which include sputtering with presence of magnetic field, exchange bias and oblique angle sputtering without the presence of the magnetic field, etc. There are multiple ways to increase the ferromagnetic resonance frequency which is proportional to coercivity Hk and magnetic saturation Ms. The ferromagnetic resonance depends on softness of the magnetic material to the applied field. With a highly soft magnetic material, one can operate the devices made out of these films at giga hertz regions without loss of efficiency. of the magnetic films is also highly desirable for many applications, such as power conversion and radio frequency (RF) devices operating at high frequencies. This work focuses on analyzing different growth conditions of thin films of CoZrTaB and the resulting magnetic and electrical properties of the films. Thin films are grown by oblique-angle sputtering method, where the sputtering gun forms an angle with respect to the sample substrate normal, ranging from 0 to 75 degrees. External magnetic field normally applied in order to form magnetic anisotropy is not used during film sputtering process. Using vibrating sample magnetometer, it was observed that films resulting from small oblique angles have no clear magnetic anisotropy developed; whereas in samples deposited at large angles close to 60 degree, there is clear magnetic anisotropy observed. Scanning electron microscopy imaging of the cross-section views of such film suggests the formation of tilted columns, which is likely to be the reason for magnetic anisotropy. Resistivity of the films was measured systematically and found to increase as the magnitude of oblique angle during sputtering increased.References: 1. M. Yamaguchi, K. H. Kim and S. Ikedaa, J. Magn. Magn. Mater. 304 (2), 208-213 (2006). 2. H. Wu, D. S. Gardner, W. Xu and H. B. Yu, IEEE Trans. Magn. 48 (11), 4123-4126 (2012). 3. H. Wu, D. S. Gardner, S. R. Zhao, H. Huang and H. B. Yu, J. Appl. Phys. 115 (17) (2014).

Magnetic Anisotropy and Electrical Property Of CoZrTaB Thin Films Deposited by Oblique Sputtering

Epitaxial films of Mn5Ge3/Ge<111> are interesting as a potential source of highly spin polarized electrons directly into Ge. Moreover, the high out-of-plane anisotropy of Mn5Ge3 opens up prospect for combining spintronics with data storage. The ferromagnetic Mn5Ge3 compound crystallizes in the hexagonal D88 structure; Mn atoms occupy two magnetically and structurally nonequivalent positions: 4d (MnI) and 6g (MnII). The Curie temperature of 296 K can be increased up to 445 K by doping with carbon [1]. Recent 55Mn NMR studies have shown that the magnetocrystalline anisotropy in Mn5Ge3 originates from the unquenched orbital moment of Mn in both crystallographic positions [2]. Furthermore, the 55Mn NMR study in Mn5Ge3C0.2/Ge(111) film has shown that carbon enters interstitially occupying the 2(b) octahedral voids and reduces the magnetic moment of the MnII atoms in the corners of a host octahedron [3]. To achieve further understanding of the role that carbon plays in this system, we carried out a systematic FMR and 55Mn NMR study on a series of epitaxial 30 nm thick Mn5Ge3Cx/Ge(111) films with the nominal carbon content x varying between 0 and 0.8. The FMR experiment shows that the uniaxial anisotropy constant Ku measured at 4.2 K systematically drops from 5,69x106 erg/cm3 to 8,06x105 erg/cm3 for the nominal concentration of x ≈ 0.6. The 55Mn NMR shows that in the concentration range up to x=0.5 the MnII atoms are found in two distinctly different magnetic states, identified as MnII (no carbon nearest neighbor) and MnII_C (one carbon nn). With increasing carbon concentration the NMR signal intensity is systematically transferred from MnII to MnII_C, and at x=0.5 no MnII NMR signal is observed anymore. On the other hand, no second satellite line is observed in the vicinity of the MnII signal in the entire concentration range, even though there are two available 2(b) positions around the MnII atoms. These two observations implicate that carbon does not enter statistically in the 2(b) voids, but shows a strong preference towards ordering, occupying every second 2(b) void along the hexagonal c-direction. This sets the limit for the uptake of the carbon atoms in the Mn5Ge3 lattice to x=0.5.References: [1] M. Gajdzik et al., J. Magn. Magn. Mater., Vol. 221 p. 248 (2000) [2] R. Kalvig et al., Phys. Rev. B, Vol. 97 p. 174428 (2018) [3] R. Kalvig et al., Phys. Rev. B, Vol. 101 p. 094401 (2020)

Ordered occupancy of interstitial voids in Mn5Ge3 lattice by the carbon dopant

TiO2 crystallizes in three different structures such as anatase, brookite and rutile [1-3]. In addition, Magneli phase is a titanium sub oxide (TinO2n-1, 4 ≤ n ≤ 10) have been explored as a promising candidate because of their high electrical conductivity, chemical inertness and corrosion resistance [4]. Among the Magneli phase compounds, Ti4O7 is important for its high electrical conductivity. In general, Ti4O7 is synthesised by thermal reduction of TiO2 [5]. These Magneli phases can easily accommodate oxygen deficiency through anionic vacancies, which leads to the partial reduction of Ti4+ to Ti3+. This Ti3+ gives local ferromagnetism in the material through hopping of the single 3d electron [6]. In this work, ion irradiation is used as a unique tool for the material modification depending upon the projectile ion, energy and the nature of the target. Ion irradiation has been found to amorphize, recrystallise and induce crystalline to crystalline phase transition or defects in various materials. In our earlier studies, we have used 500 keV Ar2+ ions to irradiate on the TiO2 thin films grown on Si substrate by e-beam evaporation technique and subsequently annealed under O2 environment at 500 C [7-8]. However, we have observed phase transformation from anatase to brookite through amorphisation and room temperature ferromagnetism (RTFM) in the films attribute to oxygen vacancies [7-8]. Hence, in the present study we have explored the role of 500 keV Ar2+ ion irradiation on the structural and magnetic properties of TiO2 thin films annealed under Ar at 900 C. The annealed films show Ti4O7 phase which transform to anatase phase upon irradiation with fluence 1 × 1014 ions.cm-2 as observed from the glancing angle x-ray diffraction (GAXRD). Further, irradiation with fluence 5 × 1016 ions.cm-2 recrystallizes to Ti4O7 phase. Raman spectroscopic studies also support the changes in phase. AFM show small change of surface morphology upon ion irradiation with roughness, 0.060, 0.062, 0.079 nm and grain size, 28, 28, 29 nm for the pristine film, films irradiated with ion fluenece 1 × 1014 and 5 × 1016 ions.cm-2, respectively. The origin of RTFM is coined with the oxygen vacancies concentration in the films.References: [1] C. Rath, P. Mohanty, A.C. Pandey, N. C. Mishra, J. Phys, D: Appl. Phys 47 315001 (2009). [2] P. Mohanty, V. P. Singh, N. C. Mishra, S. Ojha, D. Kanjilal, C. Rath, J. Phys, D: Appl. Phys 47 315001 (2014). [3] B. Bharati, N. C. Mishra, A. S. K. Sinha, C. Rath, Materials Research Bulletin 123 110710 (2020). [4] P. Geng, J. Su, C. Miles, C. Comninellis, G. Chen, Electrochimica Acta 153 316–324. (2015) [5] G. Wang, Y. Liu, J. Ye, W. Qiu, Journal of Alloys and Compounds 704 18 (2017). [6] M. Parras, A. Varela, R. C. Gil, K. Boulahya, A Hernando, J. M. G. Calbet, J. Phys. Chem. Lett. 4 2171 (2013). [7] B. Bharati, N. C. Mishra, D. Kanjilal, C. Rath, Applied Surface Science 428 723 (2018). [8] B. Bharati, N. C. Mishra, C. Rath, Applied Surface Science 455 717 (2018).

Evolution of Structural and Magnetic Properties of Ar2+ Ion Irradiated TiO2 Thin Films Annealed under Argon Atmosphere

The rare earth nitride (REN) series is a promising candidate for spintronics applications. It is the only epitaxy-compatible series of intrinsic ferromagnetic semiconductors, with members possessing complementary and contrasting magnetic properties.1 It is established that REN properties display high sensitivity to native defects, mainly the nitrogen vacancies (VN). VN form at the level of a few percent or less during thin film growth even in the most nearly stoichiometric films. The vacancies act as dopants and introduce n-type conductivity. The literature reports on more VN-induced effects in the REN such as the enhanced Curie temperature in GdN (from 50K to 70K) due to the formation of magnetic polarons at VN sites, and superconductivity below 4K in heavily VN-doped ferromagnetic semiconducting SmN thin films 2,3 Here, we show that the rate of N2 flow during growth and thin film properties are intimately linked, suggesting that the growth stoichiometry is key for understanding the structural, transport, and magnetic properties of the REN. X-ray diffraction, magnetic, Hall-effect, and transport measurements are carried out on a series of polycrystalline REN (GdN, SmN, and DyN) thin films. We show remarkable changes to the properties of the films: SmN film resistivity can be controlled over six orders of magnitude by less than one order of magnitude change of the N2/RE growth ratio. Hall-effect measurements correlate this increase in resistivity to a drop in the VN concentration. We also observe the signature of a secondary structural phase of GdN associated with N-deficient regions that develops as the N2 pressure decreases during the growth and has a smaller lattice parameter than stoichiometric GdN. We also observe an enhanced TC (up to 90 K) for the films grown with the lowest N2/Gd ratio.References: 1F. Natali et al, Prog. Mater. Sci. 58, 1316 (2013). 2F. Natali, et al, Phys. Rev. B 87, 035202 (2013). 3E. M. Anton et al, Phys. Rev. B 94, 024106 (2016).

Effect of the N2/RE Ratio During Growth on the Properties of Rare Earth Nitrides

Patients with schizophrenia often receive rTMS treatment, in which the dorsolateral prefrontal cortex or the primary auditory cortex and the Temporo-Parietal Junction are stimulated in order to treat negative symptoms and cognitive deficits or auditory hallucinations, respectively [1], [2]. Finite element (FE) simulations of TMS on heterogeneous head models have been conducted to mimic what might be happening electromagnetically within the brain, a comparison between clinical resting motor threshold (RMT) data and simulation data has not been published [3]. In this study, we used individualized finite element models derived from patients’ MRIs to investigate the correlation between RMT and brain anatomy. We first developed anatomically accurate head and brain models of 20 schizophrenia patient MRIs using SimNIBS pipeline. We then utilized FE analysis software to compute induced electric fields using patient’s clinical parameters during their investigational procedure as shown in Fig. 1. In this way, the simulations were based on real patient data and completely customized to each subject. The electric field induced in the brain was recorded and compared with variables such as cortex-coil distance (CCD), age, and RMT as shown in Fig 2 (a) and (b) respectively. Our results show that there is little to no correlation between the measured CCD at M1 and the clinically-reported RMT or the maximum electric field recorded in the brain after TMS was simulated using Sim4Life. Thus, we hypothesize that the lack of clear correlation between the CCD at M1 and the measured RMT suggests that there are many other variables which may be influencing an individual’s RMT, beyond the CCD. We hope the results of this study highlight key considerations that may be useful to future researchers designing methodology for studying RMT in TMS FE simulations. This project was partially funded by NSF (#1357565) and Wellcome Trust / DBT India Alliance Early Career Fellowship to U. M. Mehta (IA/E/12/1/500755)References: [1] E. Poulet, J. Brunelin, B. Bediou, R. Bation, L. Forgeard, and J. Dalery, “Slow Transcranial Magnetic Stimulation Can Rapidly Schizophrenia,” Soc. Biol. Psychiatry, pp. 95–98, 2005, doi: 10.1016/j.biopsych.2004.10.007. [2] H. He, J. Lu, L. Yang, J. Zheng, F. Gao, Y. Zhai, J. Feng, Y. Fan, and X. Ma, “Repetitive transcranial magnetic stimulation for treating the symptoms of schizophrenia: A PRISMA compliant meta-analysis,” Clin. Neurophysiol., vol. 128, no. 5, pp. 716–724, 2017, doi: 10.1016/j.clinph.2017.02.007. [3] E. G. Lee, P. Rastogi, R. L. Hadimani, D. C. Jiles, and J. A. Camprodon, “Impact of non-brain anatomy and coil orientation on inter- and intra-subject variability in TMS at midline,” Clin. Neurophysiol., vol. 0, no. 0, doi: 10.1016/J.CLINPH.2018.04.749.

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Effect of cortex-coil distance on resting motor threshold in Schizophrenia patients during transcranial magnetic stimulation INVITED

Abstract – Cutting is a necessary manufacturing technique when using silicon steel to produce electrical devices. Different cutting methods have different effects on the internal structure and magnetic properties of electrical steel sheets[1]. Laser cutting will produce thermal stress during processing, while mechanical cutting will produce plastic deformation near the cutting edge, which both lead to deterioration in the magnetic properties of the material. Therefore, studying the effect of different cutting techniques on magnetic properties is of great significance to accurately simulate and predict the iron losses of electrical equipment. The existing research methods cut the same sample into the different number of strips along the rolling direction, and these methods conclude that the cutting has a certain influence on the magnetic properties of the electrical steel sheet. But they cannot systematically compare the differences in magnetic properties and degraded range of the three cutting methods[2]. In this paper, the influence of cutting methods, such as wire cutting, laser cutting, and shear cutting on the local magnetic properties of the silicon steel sheet is studied and analyzed. The magnetic properties measurement system is shown in Fig. 1. A mobile B-H composite sensor is designed to sense the distribution of local magnetic properties near the cutting edges. The results show that different cutting methods have different effects on the spatial distribution of magnetic flux and the corresponding B-H curves. With the increase of the distance from the cutting edge, the degree of magnetic degradation decreases gradually. Two mathematical models used to simulate the cutting edge effect by the finite element simulation can also better describe the magnetization curve of the electrical steel sheet damage trend, thus providing a model basis for the application of electrical equipment under actual working conditions.References: [1] G. Loisos, A. J,Moses,Journal of Materials Processing Tech., vol. 161, p. 151-155(2005) [2] A. Saleem, N. Alatawneh, R. R. Chromik and D. A. Lowther, IEEE Transactions on Magnetics., vol. 52, no. 5, p. 1-4(2016)

Magnetic Properties Measurement and Simulation of Electrical Steel Sheet under Cutting Influence

Some recent nondestructive testing methods have been developed to detect very small variations in the magnetic field surrounding a massive ferromagnetic structure, such as a tank or pipe [1]. In particular, the detection of sinking in buried pipelines becomes possible [2]. The sinking is characterized by local plastic deformation and the creation of long range residual stresses. These two elements are known to have a considerable influence on the magnetic behavior [3,4,5]. One of the keys to detection is the substantial modification of the remanent magnetization of the material. The study material is a two-phase ferrito-pearlitic steel. Strips are subjected to an incremental tensile plastic deformation interspersed with elastic unloading. The magnetic behavior is carried out along the tensile direction at different levels of applied stress after deformation. The figure below shows the typical evolution of the remanent magnetization. The figure highlights: (i) that the remanent magnetization increases with the applied stress to a maximum value then decreases; (ii) that the plastic strain at zero stress considerably reduces the remanent magnetization in a highly non-linear manner; (iii) that the behavior of the deformed material seems to be able to be obtained by a simple translation in the stress space of the behavior at the undeformed state. These results join some former results [6] and the interpretation of the effect of plastic deformations by Hubert & Lazreg [7]. Following this work, a magneto-elastic two-phase modeling of the magnetization is proposed. Plasticity is introduced as an internal stress state inherent with the plastic deformation of the two-phase material (so-called kinematic hardening). The associated mechanical state being multiaxial, an equivalent uniaxial state can be calculated, requiring the use of a new material coefficient making it possible to consider the effect of the pearlitic phase on the average behavior of the medium. It is shown that the translation in the stress space predicted by the model is consistent with the experimental values.References: [1] international patent CA2998095A1 [2] E. A. Fnaiech, M.Munschy, S. Corbineau, M. Marzin, P. Rohart, S. Takillah, “Large stand-off magnetometry (LSM) for buried pipeline inspection: Influence of dent depth on residual magnetic signal “, Pipeline Technology Conference, Berlin (2020) [3] R.M. Bozorth, Ferromagnetism, Wiley-IEEE press, (1993) [4] J.M. Makar, B.K. Tanner, J. Magn. Magn. Mater. 184, p.193 (1998) [5] O. Hubert, M. Clavel, I. Guillot, E. Hug, Jal Phys. IV, 9, p.207 (1999) [6] V.E. Iordache, E. Hug, N. Buiron, Mater. Sci. Eng. A 359, p.62 (2003) [7] O. Hubert, S. Lazreg, Journal of Magnetism and Magnetic Materials, 424 2, p.421 (2017)

Effect of plastic straining on the remanent magnetization of ferrite-pearlitic steel: experimental and modeling aspects

Magnetic flux leakage (MFL) is a widely used non-destructive method for the detection of defects and abnormalities in magnetic structures such as oil and gas steel tubes for health and condition monitoring [1]. MFL involves the application of a magnetizing field in close proximity to the inspected magnetic medium and measuring the resulting leakage magnetic fields from defects, which are key for the detection and characterization of defects. To understand the correlation between the measured fields and physical defects dimensions, leakage fields are conventionally modeled for simple defect shapes (such as rectangles [2] or cylinders [3,4]) using magnetic charge sheets representing the inner surfaces of the defect. This approach assumes uniform magnetic charges through the defect and ignores nonlinear saturation effects in the corners which makes characterization and sizing of defects from measured field distributions difficult and inaccurate. Frequency domain analysis of leakage fields in MFL provide an alternative and less explored method for characterization of defects. The spectrum of the leakage magnetic fields in MFL was recently derived for rectangular defects based on magnetic charge sheets [5,6]. This approach revealed spectral features that potentially enable more accurate sizing of defects from measured MFL signals compared to direct analysis of spatial field distributions. In this work the Fourier transforms of the leakage magnetic fields from rectangular and tilted two-dimensional defects are analytically derived using scalar magnetic potential theory and superposition [7,8]. This approach does not assume uniform magnetic charges through the defect surfaces. The scalar magnetic potential approach yielded closer agreement to more detailed finite-element calculations and published measurements, and used to assess the sensitivity and feasibility of the spectral sizing method for different defect geometries.References: [1] D. E. Bray and R. K. Stanley, Nondestructive Evaluation, Part IV: Magnetic Flux Leakage Techniques in Nondestructive Evaluation, Florida: CRC Press (1997). [2] N. Zatsepin and V. Shcherbinin, Defektoskopiya 5, 50 (1966). [3] C. Mandache and L. Clapham, J. Phys. D: Appl. Phys. 36, 2427 (2003). [4] S. M. Dutta, F. H. Ghorbel, and R. K. Stanley, IEEE Trans. Magn. 45, 1959 (2009). [5] Li E, Kang Y, Tang J, Wu J, and Yan X, IEEE Trans. Magn. 54, 1 (2018). [6] M. M. Aziz, R. Abdulla, and M. Al-Dujaili, IEEE Mag. Lett. 10, 2102404 (2019). [7] M. M. Aziz, A. Edress, and C. D. Wright, IEEE Trans. Magn. 52, 3300712 (2016). [8] D. A. Lindholm, IEEE Trans. Magn. 12, 710 (1976). 

Magnetic Field Spectra and Sizing of Defects in Magnetic Flux Leakage Inspection

The noise produced by power transformers and electrical machines is harmful and its reduction is the hot subject in continuous research. Such systems are likely to be in resonance and become more vociferous, and the resonance may be mechanical or magnetic forces. The interaction between deformation due to magnetostriction and mechanical resonance of a structure made up of laminated steel sheets is investigated in this paper. The resonance phenomena are generally studied and analyzed by considering that frequency and spatial distribution of electromagnetic forces coincide with natural frequency and modes shapes of the corresponding structure. It is observed that magnetostriction may induce a resonance without the need to combine these two conditions. Two closed sheets structures of frame shape and ring shape consisting of cold-rolled grain-oriented (GO) and non-grain oriented (NO) electrical steels are used to confirm this assumption. Finite element (FE) calculations and measurements are made and compared with vibration displacements. Results of mechanical resonance induced by the magnetostrictive strain from ferromagnetic materials are shown, as well as the corresponding vibration spectrums. CONTENT: This paper presents a complete study on magnetostriction induced resonance from mechanical study to resonance detection. In Section II, the studied structure is described. In Section III, a comparison between Maxwell stresses and magnetostrictive strains is introduced and results of simulation are discussed. In Section IV, a complete study of mechanical properties of structure is presented and comparison between experimental and modeling results is described. In Section V, the summary of mechanical resonance due to magnetostriction is detailed. CONCLUSION: This paper has demonstrated that magnetostriction deformation can be implicated in mechanical resonance of a laminated structure and should be considered at the design stage for cold-rolled GO and NO electrical materials or any magnetostrictive materials grade.References: [1] K. Fonteyn, A. Belahcen, R. Kouhia, et al, “FEM for directly coupled magneto-mechanical phenomena in electrical machines,” IEEE Trans. Magn., vol. 46, no. 8, pp. 2923-2926, Aug. 2010. [2] U. Aydin, et al., “Magneto-mechanical modeling of electrical steel sheets,” J. Magn. Magn. Mater., vol. 439, pp. 82-90, Oct. 2017. [3] M. Liu, et al., “Reduction of power transformer core noise generation due to magnetostriction-induced deformations using fully coupled finite element modeling optimization procedures,” IEEE Trans. Magn., vol. 53, no. 8, Aug. 2017, Art. no. 8400511. [4] S. Somkun, A. J. Moses, and P. I. Anderson, “Mechanical resonance in nonoriented electrical steels induced by magnetostriction under PWM voltage excitation,” IEEE Trans. Magn., vol. 44, no. 11, pp. 4062-4065, Nov. 2008.

Study of Mechanical Resonance Induced by Magnetostriction in Closed Structures Based on Fe-Si

In the eddy current testing (ECT), a coil carrying alternating current is used to induce eddy current in the test object and/or collect signals. The resistance and reactance of the coil change with frequency because of skin and proximity effects in the winding. There is also stray capacitance between the wires. The coil resonates at a particular frequency. For conventional ECT, the coil normally operates far below its self-resonant frequency, the capacitance is negligible; the resistance and reactance are considered to be frequency-invariant. An ECT coil is practically modelled by a serially connected resistance and reactance without taking into account the eddy current effect in the coil itself. In last decades, the range of ECT application is expanded, together with widening of operating frequency. Probes working at extremely high and low frequencies have been developed. On the other hand, the conventional ECT coil is explored anew in ‘unconventional’ frequency range. Nevertheless, in-depth understanding of a coil’s frequency characteristic is essential. As the first trial, we studied a simple air-cored coil’s frequency characteristics and apply it to exam conductivity change. The signals were attained from sweep frequency eddy current testing [1], analyzed based on lumped element circuit model, together with simplified analytical and numerical analysis. Fig. 1 shows the impedances of the coil itself, the coil on test pieces of conductivity AISC 100.98%, 57.71% and 19.70%, respectively. Different resonant frequency and impedance-at-resonant correspond to different conductivity. For signals taken far below the resonant frequency, the local minimum of normalized resistance [1] (enclosed by ellipse in Fig. 2) also indicates conductivity change. All the indicators appear at frequencies that the effect of the test piece’s thickness is cut to minimum. Acknowledgement: This work was partially supported by JSPS KAKENHI Grant Number JP20k05000.References: Weiying Cheng, Thickness Measurement of Metal Plates Using Swept-Frequency Eddy Current Testing and Impedance Normalization, IEEE Sensors Journal, July 15, 2017, Vol.17, No.14, pp.4558-4569, DOI: 10.1109/JSEN.2017.2710356

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