France



In recent years, magnetoelectric composite materials have received more attention in the field of energy and power conversion. Many kinds of research have been devoted to improving magnetoelectric composite materials for energy and power conversions, including transformers, energy harvesters, and ME gyrators [1]. However, numerous researches are mainly focused on how to maximize the power conversion efficiency. Studies have shown that the bias magnetic field has an important effect on many types of magnetoelectric composite materials. And the bias magnetic field also affects the energy conversion characteristics [2]. Generally, the power conversion efficiency of piezoelectric materials is defined as the ratio of output electrical power to input mechanical energy. Correspondingly, the energy conversion process of ME composites introduces the influence of magnetoelastic energy [3]. The efficiency of the entire energy conversion is affected by the process of converting magnetic field energy into mechanical energy and mechanical energy into electrical energy. Therefore, we have introduced nanocrystalline FeCuNbSiB as a functional layer in the magnetoelectric composite material to converge the space magnetic field energy with its extremely high magnetic permeability. The introduction of this functional layer reducing the bias magnetic field demand of the composite material and improving the energy conversion efficiency. Fig. 1 shows the effect of different layers of FeCuNbSiB on the magnetoelectric voltage coefficient of the Galfenol-PZT laminate structure. It can be observed that after the introduction of multilayer FeCuNbSiB, the optimal magnetic bias of the magnetoelectric composite material is reduced from 200 Oe to 110 Oe. This optimal bias reduction is due to the introduction of the high magnetic permeability layer has a certain convergence effect on the magnetic field. Fig. 2 shows the influence of the frequency of the alternating magnetic field on the magnetoelectric voltage coefficient after the FeCuNbSiB layer is introduced. The test of energy conversion efficiency shows that the power conversion efficiency of the magnetoelectric composite material is increased by 8.7% under the optimal load resistance and the optimal bias magnetic field. A series of results show that the introduction of high-permeability layers can significantly improve the magnetic deflection characteristics of the magnetoelectric composite material and increase its power conversion efficiency.

**References:**

[1] C. Q. Zhao, M. J. PourhosseiniAsl and S. Dong, Journal of Physics D: Applied Physics., Vol. 51, p.243001(2018).&lt;br/&gt;[2] Z. Xin, C.M. Leung and J. Li, IEEE Transactions on Industrial Electronics., Vol. 66, 2499-2505(2018).&lt;br/&gt;[3] Z. Xin, M. Gao and X. Tang, IEEE Sensors Journal., Vol. 20, p.752-759(2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/761d4cb67f6d6e7edcfc6f88a66ab72b.jpg)
Fig.1 Variation of magnetoelectric voltage coefficient with bias magnetic field introducing different layers of FeCuNbSiB

![](https://assets.underline.io/uploads/markdown_image/1/image/fb0cd5547f09c9534037de173f5a39e2.jpg)
Fig.2 The influence of alternating magnetic field frequency on magnetoelectric voltage coefficient under different bias magnetic fields after introducing 5 layers of FeCuNbSiB

INTERMAG 2021

 Enhanced power and energy conversion of magnetoelectric laminate heterostructures based on high-permeability FeCuNbSiB nanocrystalline

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In recent years, magnetoelectric composite materials have received more attention in the field of energy and power conversion. Many kinds of research have been devoted to improving magnetoelectric composite materials for energy and power conversions, including transformers, energy harvesters, and ME gyrators [1]. However, numerous researches are mainly focused on how to maximize the power conversion efficiency. Studies have shown that the bias magnetic field has an important effect on many types of magnetoelectric composite materials. And the bias magnetic field also affects the energy conversion characteristics [2]. Generally, the power conversion efficiency of piezoelectric materials is defined as the ratio of output electrical power to input mechanical energy. Correspondingly, the energy conversion process of ME composites introduces the influence of magnetoelastic energy [3]. The efficiency of the entire energy conversion is affected by the process of converting magnetic field energy into mechanical energy and mechanical energy into electrical energy. Therefore, we have introduced nanocrystalline FeCuNbSiB as a functional layer in the magnetoelectric composite material to converge the space magnetic field energy with its extremely high magnetic permeability. The introduction of this functional layer reducing the bias magnetic field demand of the composite material and improving the energy conversion efficiency. Fig. 1 shows the effect of different layers of FeCuNbSiB on the magnetoelectric voltage coefficient of the Galfenol-PZT laminate structure. It can be observed that after the introduction of multilayer FeCuNbSiB, the optimal magnetic bias of the magnetoelectric composite material is reduced from 200 Oe to 110 Oe. This optimal bias reduction is due to the introduction of the high magnetic permeability layer has a certain convergence effect on the magnetic field. Fig. 2 shows the influence of the frequency of the alternating magnetic field on the magnetoelectric voltage coefficient after the FeCuNbSiB layer is introduced. The test of energy conversion efficiency shows that the power conversion efficiency of the magnetoelectric composite material is increased by 8.7% under the optimal load resistance and the optimal bias magnetic field. A series of results show that the introduction of high-permeability layers can significantly improve the magnetic deflection characteristics of the magnetoelectric composite material and increase its power conversion efficiency.

**References:**

[1] C. Q. Zhao, M. J. PourhosseiniAsl and S. Dong, Journal of Physics D: Applied Physics., Vol. 51, p.243001(2018). [2] Z. Xin, C.M. Leung and J. Li, IEEE Transactions on Industrial Electronics., Vol. 66, 2499-2505(2018). [3] Z. Xin, M. Gao and X. Tang, IEEE Sensors Journal., Vol. 20, p.752-759(2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/761d4cb67f6d6e7edcfc6f88a66ab72b.jpg)
Fig.1 Variation of magnetoelectric voltage coefficient with bias magnetic field introducing different layers of FeCuNbSiB

![](https://assets.underline.io/uploads/markdown_image/1/image/fb0cd5547f09c9534037de173f5a39e2.jpg)
Fig.2 The influence of alternating magnetic field frequency on magnetoelectric voltage coefficient under different bias magnetic fields after introducing 5 layers of FeCuNbSiB

poster

A new type of rare-earth giant magnetostrictive transducer, working in ultrasonic frequencies, is designed by the structural dynamic model and the dynamic coupling model. Based on the vibration, wave and frequency equations, the structural dynamic model of the transducer is established. By using COMSOL Multiphysics software parametric design method, considering the influence of materials, shapes and dimensions on the output characteristics of the transducer, the optimum mechanical structure of the ultrasonic transducer is determined. The magnetic circuit structure is analyzed by the dynamic coupling model based on the Jiles-Atherton model, Maxwell’s equations and magneto-mechanical coupling effect. The prototype of the ultrasonic transducer is fabricated. The relationship between the output characteristics and the frequency is studied. The results demonstrate that the ultrasonic transducer can work in the range of 18-22 kHz, and exhibits higher magneto-mechanical conversion efficiency at the frequency of 19.5 kHz. I. Introduction The rare-earth giant magnetostrictive transducer has the advantages of high power, large amplitude and high response speed and it can be used in the fields of accurate actuation and ultrasonic machining [1]. At present, the transducers used in ultrasonic applications are mainly piezoelectric ceramic transducer [2]. Compared with piezoelectric materials, rare-earth giant magnetostrictive material, Terfenol-D (Tb0.7Dy0.3Fe2), has greater strain, smaller hysteresis, and lower saturation magnetic field. Wang designed a giant magnetostrictive transducer (GMT) with a resonant frequency of 2 kHz [3]. Karunanidhi designed a GMT. The resonant frequency was 3 kHz. The transducer with mechanical amplifier and permanent magnet biasing was designed and realized [4]. Sheykholeslami proposed an approach to design a GMT. The resonant frequency was 8.25 kHz. This approach can make the transducer have high mechanical quality factor [5]. Fang introduced a design and finite element analysis method of a GMT. The working frequency of the transducer is 15.2 kHz [6]. Karafi designed a new hybrid longitudinal–torsional GMT with a resonant frequency of 20.6 kHz. The output displacement of the transducer was 0.6 µm [7]. References [3]-[5] studied the design method and output characteristics at relatively lower frequency magnetostrictive transducers. Reference [7] designed the giant magnetostrictive ultrasonic transducers, but the output displacement is small. So, how to design and manufacture a rare-earth giant magnetostrictive transducer with large output displacement, working in ultrasonic frequencies, is still a crucial problem for the development of transducers. II. The magnetic circuit and mechanical structure design of the ultrasonic transducer The magnetic circuit design needs to improve the magnetic flux density of magnetostrictive rod and reduce losses of the magnetic circuit. Based on the Jiles-Atherton model, Maxwell’s equations and magneto-mechanical coupling effect, the magnetostrictive rod, magnetic yoke and magnetic circuit structure of the ultrasonic transducer are designed. It is found that the magnetic circuit structure of two Terfenol-D rods with coils in series connection is more suitable for the ultrasonic transducer. The radius of the Terfenol-D rod is 7.5 mm, and the length is 102 mm. To reduce the effect of dynamic losses, the Terfenol-D rod is machined into 2 mm slices and glued together by epoxy resin. The width of the magnetic yoke is 16 mm and the length is 60 mm. Based on the vibration, wave and frequency equations, the structural dynamic model of the ultrasonic transducer is established. By using COMSOL Multiphysics software parametric design method, considering the influence of materials, shapes and dimensions on the output characteristics of the ultrasonic transducer, the optimum mechanical structure of the ultrasonic transducer is determined. The whole mechanical structure of the transducer is analyzed, and the resonant frequency of the transducer is obtained. A detailed and complete design scheme is given and the main body of the ultrasonic transducer consists of two Terfenol-D rods, driving coils, disc spring, adjusting nut, vibrating horn, magnetic yoke and shell, as shown in Fig.1. III. Experimental results The prototype of the ultrasonic transducer was fabricated. The relationship between the output characteristics and the frequency is experimentally studied by using laser displacement sensor (LK-H008, KEYENCE). Output displacement amplitude versus frequency is shown in Fig.2. The amplitudes of exciting current are 1A and 2A. The frequencies are 16.5 kHz-22.5 kHz. The experimental results have obvious resonance peaks, and their changing tendencies are consistent. When f&lt;19.5 kHz, the amplitudes of vibration increase with increasing frequencies; When f=19.5 kHz, the output amplitude reaches the maximum value, the amplitude reaches 6.07 μm at 1A and 9.46 μm at 2A exciting current respectively; When f&gt;19.5 kHz, the amplitudes of vibration decrease with frequency increasing. It can be seen that the measured resonant frequency is 19.5 kHz, and the resonant frequency almost does not change at the different applied magnetic field.

**References:**

[1] J. J. Scheidler and V. M. Asnani, Smart Materials and Structures, vol. 26, p. 035057 (2017) [2] X. Wei, Y. Yang and W. Yao, Sensors, vol. 17, p. 2253, (2017) [3] W. Wang and P. J. Thomas, Sensors and Actuators A: Physical, vol. 263. p. 113, (2017) [4] S. Karunanidhi and M. Singaperumal, Sensors and Actuators A: Physical, vol. 157, p. 185, (2010) [5] M. R. Sheykholeslami, Y. Hojjat and S. Cinquemani, Smart Structures & Systems, vol. 17, p. 313, (2016) [6] S. Fang, Q. Zhang and H. Zhao, Micromachines, vol. 9. p. 98, (2018) [7] M. R. Karafi, Y. Hojjat and F. Sassani, Smart Materials & Structures, vol. 22, p. 065013, (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f023af9851d401207c90b3e5c84b22a2.jpg)
Fig.1 (a) Structure of the ultrasonic transducer (b) Prototype of the ultrasonic transducer

![](https://assets.underline.io/uploads/markdown_image/1/image/01445a34938883b4dcd818b6e049f4f1.jpg)
Fig.2 Output displacement amplitude versus frequency at different exciting current

 The Design and Output Characteristics of Ultrasonic Transducer Based on Rare-earth Giant Magnetostrictive Material

Magneto-elastic beams in a cantilever configuration represents a quite common layout for a vibration energy harvester and its design is aimed to increase performances in terms of geometrical characteristic and power conversion [1-4]. Cantilever-like harvesters are employed when a quite constant vibration source is available, dealing to periodic steady state conditions. But the analysis of such a system is still a multiphysics problem, involving the mechanical deformation of the elastic body coupled with the electromagnetic problem through the magneto-elastic characteristics of the active material. In [1] and [4] the importance of cantilever’s geometry has been outlined, showing the importance of the neutral axis location for the output power optimization, also providing [4] a qualitative analysis describing the phenomenon. In the same contribution, the focus was on the design and development of the harvester through an experimental analysis of several layouts. The effort was so addressed on the identification of the converted electrical source supplying the output electrical circuit by the standard tools of circuit’s theory (Thevenin’s theorem), which was designed to optimize load resistance and efficiency for the whole device. The modeling of the harvester as a magneto-mechanical converter requires more effort, e.g. coupling the beam’s dynamics through the Euler-Bernoulli equation and the magneto-elastic characteristics of the beam. Despite interesting contributions exploiting 3-D FEM algorithms to describe the beam dynamics [3],[5],[6], in the present contribution attention is focused on the definition of a semi-coupled model where the mechanical behavior (in periodic steady state conditions) is taken into account through a model, described synthetically in Fig. 1b, and referred to the cantilever beam, described in Fig. 1a, supplied by a vertical sinusoidal acceleration on the left tip, in ACsinusoidal steady state, with amplitude a. The well-known solution (not provided for brevity) describes the behavior of the beam deformation w(z,t) which provides the moment bending and therefore the longitudinal stress and the strain along the cantilever, [7] and, through the assumed linear magneto-elastic coupling of the magnetostrictive alloy, the flux linkage and the emf at the coil terminals, the as shown in Fig. 2. The detailed derivation of eqns. requires some algebra and will be detailed in the paper. The emf measured at coil’s ends is related to the beam’s deformation dynamics and to the cantilever’s geometry. In particular, when the neutral axis is exactly in the middle of the magnetostrictive sheet (x1 = - x2) the total emf is zero. This result seems to fit with the experimental evidence of. In Fig. 2b where the output power on a 5.6Ω resistive load is plotted vs frequency, with a = 1g, 2g, 3g, 4g, for three different cantilever layouts. In the first one a magnetostrictive (Fe-Ga) lamination is “sandwiched” by two Al sheets (C2) and realizes a configuration with neutral axis at almost the middle of the active alloy. The second is conversely realized by an Al sheet “sandwiched” by two Fe-Ga laminations (C1), while in the last a single Al sheet is sticked to a Fe-Ga lamina (C3). In both C1 and C3 cases, the neutral axis lays outside the magnetostrictive laminas. All configurations share the same two bias magnets on the upper side of the cantilever. In linear assumptions, the RMS power in the plot is proportional to ε2 and according to the model shows a much lower converted power of C2 case with respect to other configurations. An accurate analysis on the influence of geometric and physical parameters of the cantilever by the proposed modeling will be discussed in the paper. Such plot confirms that a simplified magnetostrictive cantilever’s modeling could provide information on the parameters that impact the harvester design and represents a simple but effective generalization of [4]. Further, without significative effort, a natural introduction of a nonlinear magneto-elastic behavior could be plugged in.

**References:**

[1] T. Ueno, S. Yamada, Performance of energy harvester using iron–gallium alloy in free vibration, IEEE Trans. Magn. 47 (10) (2011) 2407–2409. [2] J.-H. Yoo, A.B. Flatau, A bending-mode Galfenol electric power harvester, J. Intell. Mater. Syst. Struct. 23 (6) (2012) 647–654. [3] Z. Deng, M.J. Dapino, Modeling and design of Galfenol unimorph energy harvesters, Smart Mater. Struct. 24 (12) (2015) 125019. [4] V. Apicella, C. S. Clemente, D. Davino, D. Leone, C. Visone, Magneto-mechanical optimization and analysis of a magnetostrictive cantilever beam for energy harvesting, J. of Magnetism and Magnetic Materials, 475, (2019), 401-407. [5] Mojtaba Ghodsi, Hamidreza Ziaiefar, Morteza Mohammadzaheri, Amur Al-Yahmedi, Modeling and characterization of permendur cantilever beam for energy harvesting, Energy, 176 (2019), 561-569. [6] M. Borowiec, A. Syta, G. Litak, Energy Harvesting Optimizing with a Magnetostrictive Cantilever Beam System, International Journal of Structural Stability and Dynamics Vol. 19, No. 05, 1941002 (2019). [7] S. H. Crandall, Mechanics of Solids, McGraw-Hill, Third Edition.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7cfc0d5eff81b7d787608d9a833e4c02.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/6787b6aca4d66b15409c7c97beb82ee6.png)

 Effects of geometrical and physical parameters on a cantilever beam energy harvester in periodic steady state conditions.

As a single solid element, the magnetoelectric (ME) gyrator has verified Tellegen's conjecture about the gyrator. In recent years, a number of attempts have been made to reduce losses in the energy conversion process. It is well known that the properties of spinel ferrites are dependent on such as composition, cation substitutions. A small contents of rare earth doping can modify the magnetic and magnetostrictive properties by replacing the tetrahedral (A) or octahedral (B) sites, which is beneficent to ME coupling1. It has been reported that Dy elements possess high magnetocrystalline anisotropy due to the strong anisotropy of the 4f electron clound, thus inducing strong magnetostriction2. However, due to the high loss in the energy conversion process of the pure spinel ferrite ME gyrator, it is necessary to improve the ability of energy capture by means of the change of magnetic properties caused by Dy3+ doping. Therefore, the research on the improvement of gyration properties caused by high magnetostriction induced by Dy3+ doped ferrite has been initiated. Here, a variety of ME gyrators composed of nickel zinc ferrite and piezoelectric ceramic under various Dy3+ concentration were fabricated with coil around it and systematically characterized of magnetic properties,dynamic piezomagnetic coefficient, resonance ME response, V/I-I/V conversion ratio and power conversion efficiency, and each stage involved in the magneto-mechanical-electric energy conversion process under influences of Dy3+ concentration was clarified. Fig.1 shows the V/I conversion ratio spectra of the ME gyrators with frequency, applied flied and Dy3+ concentration, respectively. It can be clearly seen that under the resonant frequency and optimal bias, the maximum V/I of 1610 V/A occurring at sample with x=0.04 while the minimum of 998 V/A occurring at the one with x=0. Compared with pure spinel ferrite, the conversion effect of the ME gyrators is improved by 161% by Dy3+ doping. The experimental results attributed to the strong ME coupling is caused by the high magnetocrystalline anisotropy of Dy3+. Therefore, it can be concluded that Dy3+ doping reduces the loss in the energy conversion process of ME gyrator and promotes the improvement of gyration properties. Consequently, the high gyration properties of ME gyrator has important potential application for miniaturized V/I converters for power electronics.

**References:**

1 A. Anwar, S. Zulfiqar, and M. A. Yousuf, Journal of Materials Research and Technology-Jmr&T. Vol. 9, p.5313-5325 (2020) 2 T. Y. Jin, W. Wu, and C. B. Jiang, Scripta Materialia. Vol. 74, p.100-103 (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/606efb870463e67f36a0cefd9acfefa5.jpg)
Fig.1 V/I conversion of the ME gyrators with different Dy3+ concentrations under optimal bias in the frequency range of 54kHz-66kHz. The insets are the V/I as a function of the Dy3+ concentration and Applied Flied respectively.

 Improvement of gyration effects by dysprosium doping in spinel ferrite/piezoelectric magnetoeletric gyrators

In recent years, energy harvester around power lines have received widely attention due to the convenient power supply for monitoring devices around power lines such as vibration and conductor temperature sensors, fault diagnosis and prediction devices, intelligent sensor monitoring devices etc. Generally, energy harvested from near power lines includes solar energy, wind energy, sound energy, vibration and magnetic field, and so on. In terms of reliability and stability, energy harvesting using magnetic fields has been reported as optimum mode to provide energy to monitoring devices around power lines. Compared to solar and wind energy sources, magnetic field energy is almost unaffected by the environment or weather conditions. Traditional magnetic energy harvesters are the best represented by electromagnetic induction energy harvesters. While featuring low cost and wide applicability, these electromagnetic induction energy harvesters are generally limited by large volume, heavy weight and low output power density[1]. The recent development of magnetoelectric (ME) materials enables novel electromagnetic devices. The ME energy harvester are composed of ME composites that show many excellent advantages, such as low cost, small volume perfect and high output power density[2]. These advantages offer the potential of ME energy harvesters to be a new generation of magnetic energy harvesters. Over the past decade, considerable reports have been published using ME materials to realize magnetic energy harvest. Previous investigations have focused on ME laminates whose piezoelectric/magnetostrictive layers are some simple configurations of disk, square, or rectangular shapes. However, for harvesting the magnetic energy around power lines, these geometries cannot make full use of the magnetic energy. In this case, the ME sample best geometry is the toroidal configuration. It is thus desirable to develop ME energy harvester with toroidal configuration, along with high output power density. This paper is on a high power density, dual-output ME energy harvester. It consisted of strictly concentric ferrites/piezoelectric rings with toroidal solenoid wound around that was operated in C-C mode. The electrode lead of the piezoelectric ring is port 1 and the coil lead is port 2 forming dual port. The ferrite in the collector senses the alternating magnetic field and transforms it into circumferential dynamic strain, which is transferred to the piezoelectric ring and finally output in the form of voltage from port 1. At the same time, according to the principle of electromagnetic induction, due to the existence of closed loop alternating magnetic field, the coil will produce induced electromotive force and output in the form of voltage from part 2. This dual-output ME energy harvester can ample harvest of the magnetic field energy produced by power lines and offer unique possibilities for possible use of ME energy harvester.

**References:**

[1] J. Ryu, J. Kang, and Y. Zhou, Energy & Environmental Science. Vol. 7, P.2402-2408 (2015) [2] D. Zhao, N. Han, Energy Convers Manage. Vol. 178, p.311–21 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c899e3e5797e3392284061b4210fbcbe.jpg)
Fig.1. Schematic diagram of the presented dual-output magnetoelectric energy harvester

 A dual-output magnetoelectric energy harvester in ferrite/piezoelectric toroidal magnetoelectric composites

Magnetostrictive materials possess the potential to be used in wide variety applications such as sensing, straintronic, spintronic devices etc due to the coupling between the strain and the magnetization. In this context, FeGa which has a very high magnetostrictive constant, high tensile strength and low coercivity proves to be an efficient material for current research. Commercial producibility of FeGa is cheaper and easier compared to the rare earth alloy families since it does not include any rare earth elements. Fe100-xGax with x = 19% has the highest magnetostriction constant with a value of around 3/2 × λ100= 400 ppm [1]. A thin film with this composition is attributed to the formation of next-nearest-neighbours (NNN) Ga-Ga pairs along [100] directions which leads to the formation of ordered D03 lattice structure [2]. In our report, we characterized the magnetic properties of Fe70Ga30 deposited on Si/SiO2 substrate (rigid material) and Kapton substrate (flexible material) by measuring room-temperature hysteresis loops by AGFM and MFM characterisation as a function of magnetic field. The magnetic hysteresis behaviour is quite different for Fe70Ga30 sputtered Si/SiO2 and Kapton as shown in Fig. 1(a, b). The coercive field obtained for Fe70Ga30/Kapton is approximately 20 times higher than that of Fe70Ga30/SiO2/Si. This can be referred to the interface induced strain which results in higher anisotropy for Fe70Ga30/Kapton. MFM results reveal linear stripe domains for the both Fe70Ga30/SiO2/Si and Fe70Ga30/Kapton shown in Fig. 1(c, d). The periodicity of domains is higher for the samples on Kapton due to high anisotropy. The substrate induced effect largely changes the properties of FeGa. We further try to measure the properties of Fe81Ga19 deposited on both Si/SiO2 and Kapton for comparison. The dependence of strain percentage with magnetic anisotropy will be studied for Fe81Ga19/Kapton.

**References:**

[1] A. E. Clark et al. Journal of Applied Physics 93, 8621 (2003). [2] H. Yangkun et al. Adv. Funct. Mater. 28 (20) 1800858 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fe11bced4390bcf46677e66807dd5c28.jpg)
Fig. 1 Hysteresis loops and MFM domain patterns of Fe70Ga30/SiO2/Si (a, c) and Fe70Ga30/Kapton (b, d), respectively.

 Magnetic Properties of FeGa on Rigid and Flexible Substrates

Under high-frequency excitation, the large magnetic energy losses of magnetostrictive materials have limited the output characteristic of the magnetostrictive transducer [1]. Many magnetostrictive transducers are usually operated under DC bias to eliminate the frequency doubling effect and optimize the output performance. Based on the Steinmetz losses model, Ref. [2] proposed an improved total iron losses model considering DC bias, however, the separated losses compositions were not explored. Ref. [3] established a separated core losses model with the DC pre-magnetization, however, the model is more suitable for rectangular excitation and it was not about the giant magnetostrictive materials. Ref. [4] measured the magnetic energy losses on Terfenol-D material at different frequency f and peak flux magnetic density Bm, variable coefficients separated losses model without biased magnetic field had been shown. However, the effect of DC bias on magnetic energy losses of Terfenol-D cannot be ignored due to the max losses deviation will reach 27.6％when f=10 kHz and Bm＝0.06T by losses measuring. Therefore, it is not suitable to use the losses model of an unbiased magnetic field to predict the operation condition with a bias magnetic field. On this basis, an improved magnetic energy losses separation model on giant magnetostrictive materials considering DC bias excitation at high-frequency is emphatically studied here. In this paper, according to the actual operation conditions, a kind of high-frequency losses testing system for magnetostrictive materials under DC bias is built. The dynamic hysteresis loops of Terfenol-D samples at different magnetic frequencies and exciting magnetic densities are studied experimentally under the condition of variable DC bias excitation. The total magnetic energy losses are obtained from these dynamic hysteresis loops aimed to provide the data basis for the establishment of a high-frequency magnetic energy losses model. The three-variables magnetic energy loss matrix is established by these measured data. Based on the Bertotti losses separation theory, the high-frequency losses calculating model of magnetostrictive materials considering variable DC bias excitation is established by using the algorithm of Levebverg-Marquard and the method of matrix transformation. In this model, according to the multivariate parametric regression, the losses coefficients are modified by introducing DC bias-related terms. The comparison of computed and experimental data of losses at different operating conditions are compared and analyzed. By comparing the experimental data, it is proved that the computed results in this proposed model are in good agreement with the experimental results. Based on the built dynamic magnetic characteristic testing system, the dynamic hysteresis loops of Terfenol-D samples at different f (1 kHz~20 kHz), Bm (0.01 T~0.06 T), and Hdc (0 A/m~5000 A/m) can be measured. And the trend of hysteresis loops varying with different DC bias excitation can be shown in Fig.1. It can be seen that the dynamic hysteresis loops will be seriously distorted and asymmetric when the different DC bias applied. This phenomenon is caused by the increase of the magnetization working point and the change of the relative permeability of the material. And the losses can be computed based on the measured hysteresis loops. Using the proposed variable coefficients losses model, the losses could be separated into magnetic hysteresis, eddy-current, and anomalous losses. In fig.2, the bar graphs of the losses changing with DC bias frequency are obtained. The magnetic energy losses decrease with the DC bias. When the f=15 kHz and Bm=0.05T, the measured losses change from 513.74 W/kg to 409.022 W/kg with the DC bias changing from 0 to 5000 A/m. Based measured losses matrix and the method of multivariate parametric regression, an improved losses separation model is proposed to calculate the losses components when the Terfenol-D samples under DC bias excitation. The computed losses in this proposed model have high accuracy over the measured results (average percentage error&lt;5.6%). It shows that the suitable DC bias can decrease the losses for the magnetostrictive materials. This research could provide significant theoretical guidance and experimental data support for the giant magnetostrictive device structure optimization and thermal analysis at high-frequency excitation.

**References:**

[1] Rudd, Jonathan, Myers, et al. Experimental fabrication and nondestructive testing of carbon fiber beams for delaminations using embedded Terfenol-D particles. Journal of intelligent material systems and structures,29(4):600-609 (2018). [2] W. Chen, X. Huang, S. Cao, et al. Predicting Iron Losses in Soft Magnetic Materials Under DC Bias Conditions Based on Steinmetz Premagnetization Graph. IEEE Transactions on Magnetics, 52, (7):1-4 (2016) [3] Y. Zhou and Q. Chen, Predicting core losses under the DC bias based on the separation model, IEEE Journal of Emerging and Selected Topics in Power Electronics 5, 833 (2017). [4] W. M. Huang, X. Q. Wu, and P. P. Guo, Variable Coefficient Magnetic Energy Losses Calculation Model for Giant Magnetostrictive Materials, IEEE Transactions on Magnetics, Aug.2020. DOI: 10.1109/TMAG.2020.3013393, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e716e9343e523cfb8b7a2e376dc67e90.jpg)
Fig.1.Measured dynamic hysteresis loops at different DC bias excitation)

![](https://assets.underline.io/uploads/markdown_image/1/image/f3b3a5fe58667b168d8946a6c05f0e6c.jpg)
Fig.2 Calculated loss components and measured values with different DC bias (f=15 kHz, Bm=0.05T)

 High-frequency Losses Calculating Model for Magnetostrictive Materials Considering Variable DC Bias

The giant magnetostrictive material TbDyFe alloy is considered to be an ideal material for making the core drive components of high-power, high-frequency magnetostrictive transducers. It has the characteristics of fast output response and large output displacement. Under high-frequency excitation conditions, the accurate calculation of TbDyFe alloy magnetic energy loss is a major and difficult point, and it is also an important step in the design of high-power magnetostrictive devices. Reference [1] improves the traditional loss separation formula based on high-frequency loss test data of TbDyFe alloy. Reference [2] analyzed the dynamic magnetic characteristic parameters of the TbDyFe alloy laminations, and conducted an in-depth study on the loss mechanism in the high frequency range. The above studies all assume that the temperature of the sample remains unchanged, but in actual work, the magnetostrictive transducer will produce serious hysteresis loss, eddy current loss and coil copper loss under high-frequency excitation, which will change the temperature distribute of the device. Considering the temperature-sensitive characteristics of TbDyFe alloy [3], the novelty of this article is mainly to study the change trend of the magnetic properties and loss characteristics of TbDyFe alloy at different temperatures. On the basis of the existing research, a temperature-controllable high-frequency magnetic characteristic test platform is built with AMH-1M-S dynamic magnetic characteristic tester and temperature box, so as to obtain the dynamic magnetic characteristic curve and loss of TbDyFe alloy at different temperatures. When the magnetic density amplitude and frequency are constant, the dynamic hysteresis loop of the sample at different temperatures is shown in Figure 1. As the temperature increases, the dynamic hysteresis loop narrows laterally, the required magnetic field strength decreases, and the coercive force gradually decreases. When the magnetic density amplitude is constant, the magnetic loss of the sample at different temperatures at different frequencies is shown in Figure 2. In the classic Bertotti loss separation model, the loss is a binary function of the magnetization frequency f and the magnetic density amplitude Bm. The formula assumes that under a fixed magnetization condition, no matter what the temperature of the sample is, the calculation results of the loss model will not change, which is obviously inconsistent with the experimental results. At the same time, because the TbDyFe alloy is significantly affected by the eddy current skin effect and dynamic hysteresis under high frequency conditions, the loss coefficient is no longer constant. Hence, the traditional calculation method is no longer accurate and must be improved. In order to solve the above problems, a high-frequency loss calculation model of magnetostrictive materials under variable temperature conditions is proposed. The model corrects the loss coefficient by introducing temperature-related terms. In addition, considering the effects of high-frequency hysteresis characteristics and skin effect, a loss-added magnetic flux density term and loss-added frequency term are introduced. The hysteresis, eddy current and residual loss coefficients kh, ke and ka are all regarded as ternary functions of ΔT, f, Bm. Combining the experimental test data, analyze the influence weights of the three free variables of temperature, frequency and magnetic density amplitude on the loss coefficient through curve fitting, and obtain the changes of hysteresis loss, eddy current loss and residual loss with ΔT, f, Bm. Thus an improved loss calculation model that can effectively consider the temperature effect is established. The results show that the calculation method can accurately calculate the high-frequency magnetic energy loss of magnetostrictive materials under variable temperature conditions. The average error between the calculated value and the measured value is 2.29%.

**References:**

[1] W. M. Huang, C.Y. Gao, et al. Experimental and Calculating Analysis of High Frequency Magnetic Energy Losses for Terfenol-D Magnetostrictive Material. IEEE Trans. Magn, 99 (2018): 1-4. [2] W. M. Huang, X.Q. Wu, et al. Analysis of high frequency dynamic magnetic characteristics and loss characteristics of TbDyFe alloy[J]. Chinese Journal of Scientific Instrument, 2020, 41(01): 215-222. [3] Jin K , Kou Y , et al. A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys[J]. Journal of Magnetism & Magnetic Materials, 2012, 324(12):1954-1961.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0329a17f3fa659f6ad808c5272f42a5f.jpg)
Fig.1. Dynamic hysteresis loop at different temperatures 
(f=10kHz, Bm =0.06T)

![](https://assets.underline.io/uploads/markdown_image/1/image/c6ac98b1f9107a7725f4cae4a60d7fa2.jpg)
Fig.2. Variation of loss with frequency at different temperatures（Bm=0.05T）

 High Frequency Characteristic Test and Loss Calculation of TbDyFe Alloy under Variable Temperature

We report on an investigation of the effect of different types of magnetic particles on the effective magneto-induced strain behavior of magnetorheological elastomers (MREs). MREs are composites consisting of magnetically permeable particles dispersed in a nonmagnetic polymeric matrix [1]. Under the action of an externally applied magnetic field, a large deformation change occurs in these materials [2]. Such deformation changes the mechanical properties of these materials. This is often attributed to the magnetic interaction among the magnetic filler particles [3]. In this study, we determined the effect of different types of magnetic filler particles on the effective magneto-induced strain of these materials. Four types of magnetic particles including nickel steel mumetal, nickel steel permalloy nongrain oriented (NGO), soft iron (without losses), and cobalt iron 2V permendur were selected from the computational software COMSOL Multiphysics magnetic materials library. With the assumption of constant shape and size for the selected particles, microscale modeling using a finite element analysis (FEA) based on continuum field theory was used in the study of the macroscopic behavior of the MREs. Without the simplifying assumption of magnetic dipoles, the magnetic and mechanical behavior was resolved by considering the polymer matrix and magnetic fillers as continua of distinct material properties. A suitable computational homogenization scheme [4] was used to relate the microscopic behavior to the composite's effective macroscopic properties. Here, both linear and nonlinear magnetic constitutive relationships were considered. The simulations were performed for isotropic microstructures with a constant particle-volume fraction (φ= ~20%) and varying magnetic fillers. From the analysis, only a small change is observed in the effective magneto-induced strain (ε) parallel (ε11) and transverse (ε22) to the direction of the applied magnetic field for the different magnetic particles, particularly in the effective smaller magnetic flux density (B &lt; 0.3T) region as shown in Figs. 1 (a) and (b). As seen from Figs. 1 (a) and (b) at higher B &gt; 0.3T, a reversal in the magneto-induced deformation which for the nonlinear magnetization significant differences in magneto-induced strain for the different magnetic particles is observed. This can be attributed to saturation magnetization effects in this region.

**References:**

[1] W. M. Kiarie, E. J. Barron, A. P. S. Baghel, I. C. Nlebedim, M. D. Bartlett and D. C. Jiles, IEEE Transactions on Magnetics, doi: 10.1109/TMAG.2020.3024878. [2] D. Borin, G. Stepanov, and P. Storozhenko, Polymers (Basel)., vol. 12, no. 10, pp. 1–25, 2020. [3] M. R. Jolly, J. D. Carlson, and B. C. Muñoz, Smart Mater. Struct., vol. 5, no. 5, pp. 607–614, 1996. [4] C. Spieler, M. Kästner, J. Goldmann, J. Brummund, and V. Ulbricht, Acta Mech., vol. 224, no. 11, pp. 2453–2469, 2013.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/58f70e303d7eeee4c3a0b5287fb86e30.jpg)
Effective magneto-induced strain behavior for isotropic MRE with particle-volume fraction (φ= ~20%) and varying magnetic particles assuming a) linear

![](https://assets.underline.io/uploads/markdown_image/1/image/df87d706739aeee53b1223da21ec1021.jpg)
b) nonlinear magnetization.

 Effective Magneto-deformation Behavior of Soft Magnetically Susceptible Elastomer Composites

We report on an investigation of the temperature-dependent magnetic properties of magnetorheological elastomers (MREs). These are a class of composites that consist of magnetically permeable particles dispersed in a nonmagnetic polymeric matrix [1,2]. When subjected to an external magnetic field, a large deformation occurs altering the mechanical properties of these materials. Due to their magnetoelastic coupling response, these materials are finding increasing interest among the scientific community. The performance of these polymer-based composites depends on many factors [3,4], which temperature is one of the biggest influencing factors requiring further investigations. In this work, the magnetic properties of isotropic polyurethane-based MRE with varying iron (Fe) particle loading fractions (40, 50, 60 and 70% by weight) were investigated under different temperatures. From the analysis, the magnetization response of these materials is observed to almost overlap for all the measured temperature values as shown in Fig. 1a. Although, zooming in the saturation magnetization is observed to decrease with an increase in temperature (See Fig.1a). Figure 1b shows the saturation magnetization for varying temperature and particle loading fractions. Generally, ~ 3% decrement in the saturation magnetization is obtained for each of the loading fraction between the lowest (300K) and the highest (400K) measured temperature. Hence, as it can be seen the magnetization response of these materials is only slightly sensitive to temperature changes. This can be attributed to the measured temperature being below the curie temperature (Tc) of Fe. Further, the magnetization response is observed to increase with the increase in the particle loading fraction (See Fig. 1b).

**References:**

[1] Bastola A K and Hossain M 2020 Compos. Part B 108348 [2] W. M. Kiarie, E. J. Barron, A. P. S. Baghel and D. C. Jiles, IEEE Transactions on Magnetics, doi: 10.1109/TMAG.2020.3024878. [3] Kallio M 2005 The elastic and damping properties of magnetorheological elastomers [4] Jin Q, Xu Y G, Di Y and Fan H 2015 Mater. Sci. Forum 809–810 757–63

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ee903258cb47e8d2fbdd758b17ec7ce8.jpg)
a) Magnetization curve for 50wt. % iron in polyurethane for different temperatures

![](https://assets.underline.io/uploads/markdown_image/1/image/3e066829e8670862563f45fb8430d653.jpg)
b) Saturation magnetization for varying temperature and particle loading fraction

 Temperature-dependent Magnetic Properties of Magnetorheological Elastomers

Composite materials, in the form of laminated and polymer matrix composites, are being increasingly used in manned and unmanned vessels and aircraft structures mainly due to their high strength and high stiffness to weight ratios. Composite structures are susceptible to degradation due to prolonged use, exposure to severe service environments, fatigue, sand abrasion as well as operator abuse, and neglect. This degradation increases the risk of operation and the cost of maintenance. Over the last two decades, progress has been made in structural state awareness using various sensing techniques such as acoustic emission, eddy current, and ultrasonic pitch hatch to diagnose damage and predict remaining life of the composite. Despite this progress, reliable detection and quantification of composite damage, particularly in the early stage, has remained a major challenge. Structural damage may be considered as a process that compromises the integrity of a structure. Delamination and cracking, two of the most common safety concerns of airframe structures, propagate rather slowly in the early stage but grow at a much faster rate in the later stage. Since early stage damage is not detectable using current technologies, it may be possible that by the time this damage is detected, the remaining life of a structure or its capacity has been severely degraded. The objective of this study is to show the feasibility of early stage damage detection utilizing embedding magnetic particles (Terfenol-D powder, a magnetostrictive material) into the composite structure, which is affected by the compressive stress surrounding them. Magnetostrictive materials exhibit dimensional changes in response to external magnetic fields. The inverse is also true; magnetization changes due to applied external stresses. When a composite material is cured, the particles are brought into compression due to shrinking of the resin, which provides a localized magnetic response. In this study, Terfenol-D (Tb0.3Dy0.7Fe1.92) was embedded between layers of a composite structure. A laminated panel, 8 inches by 8 inches, was fabricated from thirteen 0.01 inch thick unidirectional plies of a pre-impregnated AS4/3501-6 carbon/epoxy material system. The panel was pressed in an aluminum mold and cured in autoclave at 175 oC under vacuum pressure for about 3.5 hours. The Rectangular panels were cut to a nominal size of 8 inch by 1-inch tensile specimens. A pair of tapered fiber glass tabs was attached at both ends of the rectangular specimens in accordance with the ASTM standard D-3039/D3479. Figure 1(a) shows the test specimen and a disk cut out of the specimen for built-in anisotropy measurement using a VSM (Vibrating Sample Magnetometer). The specimen was then subjected to a quasi-static load up to 70% of the UTS (ultimate tensile strength/ultimate tensile stress to failure). Figure 1(b) shows the magnetization measurement within the VSM system and shows the reference measurement angle for the built-in anisotropy. Figure 2 shows the magnetization results for the different measurement angles, showing the built-in anisotropy before (2a) and after (2b) the load cycle. Following unidirectional loading, the sample clearly shows a change in built-in anisotropy. The slope of the hysteresis loop is now dependent upon angle, demonstrating a possible way to detect early stage damage using magnetostrictive particles embedded in a composite structure. Additionally, it appears to also provide information on the major load direction.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ec7579761fac7b3092e06a41e62c5e2b.jpg)
Figure 1. (a) Tensile test specimen and a disk cut for magnetic characterization out of the Terfenol-D powder embedded composite panel. (b) Schematic of the magnetization measurement angle with respect to the tensile specimen loading direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/f66edcf048cee46500e581eb85ca91bf.jpg)
Figure 2. Magnetic hysteresis loop measurement of the Terfenol-D embedded composite panel measured (a) before loading, and (b) after loading to 70% of UTS (Ultimate Tensile Strength).

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