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The resonance frequency shift characteristic of Terfenol-D rods for magnetostrictive actuators
Abstract
This paper focuses on the resonance frequency shift characteristic of Terfenol-D rods for magnetostrictive actuators. A 3D nonlinear dynamic model to describe the magneto-thermo-elastic coupling behavior of actuators is proposed based on a nonlinear constitutive model. The coupled interactions among stress- and magnetic-field-dependent variables for actuators are solved iteratively using the finite element method. The model simulations show a good correlation with the experimental data, which demonstrates that this model can capture the coupled resonance frequency shift features for magnetostrictive actuators well. Moreover, a comprehensive description for temperature, pre-stress and bias field dependences of resonance frequency is discussed in detail. These essential and important investigations will be of significant benefit to both theoretical research and the applications of magnetostrictive materials in smart or intelligent structures and systems.
... Piezoelectric transducers have traditionally been utilized to create the ultrasonic vibrations in RUM, however, giant magnetostrictive materials [3,4] are now being considered for this role. Giant magnetostrictive ultrasonic transducers (GMUT) have undergone extensive recent development, and possess numerous advantages over the piezoelectric materials, including a large magnetostrictive coefficient, high power capacity, fast response speed, and the ability to produce a large ultrasonic vibration amplitude output [5,6]. As such, the application of GMUT combined with giant magnetostrictive materials (such as Terfenol-D) as vibrators in RUM has become a popular field of research. ...
... To calculate , Terfenol-D must be analyzed. As noted in the literature [14,15], the strain composition of Terfenol-D is described as below: (6) where indicates elastic strain and represents magnetostrictive strain. Young′s modulus establishes the relationship between stress and strain as follows: (7) where is Young′s modulus of Terfenol-D. ...
Rotary ultrasonic machining (RUM) is widely used in the processing of brittle and hard materials, and giant magnetostrictive ultrasonic transducer (GMUT) with good vibration performance has gradually become a hot research topic of RUM. To establish a generalized amplitude prediction model of GMUT, an equivalent kinetics model of GMUT was firstly provided. Considering Terfenol-D and the external mechanical mechanism as the influence of interaction force, the prestress mechanism of Terfenol-D and the joint face of the horn are equivalent to two spring-damping systems in series, and the general GMUT vibration equation was established. Then the equivalent stiffness of the prestress mechanism was identified, and the mechanical quality factor of the vibration system was calculated by impedance analysis. The influence of the joint face of the horn and the prestress mechanism on the amplitude was studied by nonlinear least square fitting. Based on the magnetostriction and magnetization model, the odd power amplitude prediction model of mechanical quality factor, excitation current amplitude and excitation frequency was proposed. The experimental results shown that the proposed model can predict the output amplitude of GMUT with different mechanical quality factors under different excitation signals well. It provides a method for the system design and optimization of GMUT.
... It was subsequently shown that the temperature response of the magnetoelastic sensor could be made negative, positive, or zero by varying the DC biasing field [11,12]. Jin et al. proposed a 3D nonlinear dynamic model to describe the magneto-thermoelastic coupling behavior of actuators [13]. Woollett established the lumped-parameter equivalent circuit of transducers and an effective coupling factor was proposed to quickly reveal the relationship between the mechanical vibration and the electrical signals [14]. ...
... (25), according to which the resonance frequency decreases with increasing temperature. The frequency of the cross point of the mobility loop and real axis reduces according to Eqs. (13) and (20). This means that the impedance circle equation is appropriate for GMUTs at different temperatures, and can be used to reveal the effect of temperature on the resonance frequency and mechanical quality: ...
The effect of temperature on the performance of a giant magnetostrictive ultrasonic transducer (GMUT) was investigated by measuring variations in the resonance frequency and mechanical quality factor of the GMUT at different temperatures. The equivalent circuit model of the GMUT was presented and the total electrical impedance equation was obtained. Curves of the impedance circle were obtained at different temperatures to determine the resonance frequency and mechanical quality factor. To verify the impedance-based results and obtain precise values of the resonance frequency and effective frequency bandwidth, the amplitude-frequency response within the same temperature range was examined experimentally. These results were consistent with those of the impedance analysis, which demonstrates the validity of the equivalent circuit model. Moreover, the resonance frequency and effective bandwidth of the GMUT were found to decrease with increasing temperature, which means that the vibration amplitude is more sensitive to variation in the resonance frequency at high temperature owing, for example, to static or dynamic system loading, changes in the material properties, or drive-signal variability. Accordingly, the temperature in the GMUT should be precisely controlled to improve the stability of vibration.
... To obtain the constitutive relations in the form of polynomials, Jin [31] expressed the Gibbs free energy in a Taylor series expansion of stresses and magnetization at a reference point (σ ij , M k ) = (0, 0), and proposed the following general constitutive equations for nonlinear magnetostrictive materials. ...
... A similar approach with a distinct nonlinear strain function was later employed by Zhou et al. [256]. Jin et al. [257,258] further extended this temperature-dependent 1-D model for magnetostrictive thin films. ...
An extensive growth in the application of ferromagnetic materials require a firm theoretical understanding of the material behavior to accomplish accurate model prediction. The aim of this review article is to capture the evolutionary journey of the nonlinear magnetoelastic constitutive laws, spanning since the mid-twentieth century. This review discusses the prominent proposed constitutive models based either on physical or phenomenological considerations, by classifying them into two categories, the anhysteretic and the hysteretic, which further incorporates the effect of magnetic field, stress, temperature, and plastic deformation on the ferromagnetic material behavior. The respective advantages and limitations offered by the various classes of proposed approaches in the form of Jiles-Atherton model, Armstrong model, Zheng-Liu model, Preisach model, Stoner-Wohlfarth model, multiscale model, Play model, Plasticity based model, Continuum based model have been summarised. Finally, a holistic outlook is presented portraying the state of the art and avenues for improvement that future research might hold regarding the refinement of the available nonlinear magnetoelastic constitutive laws.
... A giant magnetostrictive transducer driven by a magnetic field using the giant magnetostrictive material Terfenol-D [13] is emerging as a promising new type of transducer for ultrasonic machining. Compared with the conventional piezoelectric transducer, the giant magnetostrictive transducer has higher load resistance, higher expansion coefficient, lower quality factors, and higher energy density [14,15]. However, the state-of-the-art giant magnetostrictive transducers have the drawbacks of poor heat dissipation, especially when at incomplete resonance state. ...
Rotary ultrasonic machining is regarded as a superior machining method for hard and brittle materials. It utilizes ultrasonic tool vibration to improve the material machinability, resulting in reduced cutting force and improved machining efficiency. The temperature stability and resonance quality of the ultrasonic system are critical for the reliable generation of ultrasonic vibration. This study presents a temperature-stable and complete-resonance separated rotary giant magnetostrictive ultrasonic (SRGU) system with novelly designed mechanical structures to improve energy transmission and heat dissipation. A theoretical analysis was performed to demonstrate the design principle of the SRGU system. By abolishing the contactless power system of fixed and rotary parts used in the conventional rotary ultrasonic system, and by using a unique incomplete shell, design methods of the mechanical structure, magnetic circuit, and excitation coil of the SRGU system were proposed. A prototype of the SRGU system was then fabricated and tested to verify the feasibility and efficacy of the proposed design methods. The experimental results demonstrated that the SRGU worked well with much-improved ultrasonic vibration stability and better complete resonance as compared to the conventional ultrasonic system. It was found to work with an ultrasonic amplitude of 10 μm for a continual 9 h with a temperature increase of only 3°C.
... Among GMM, bulk Tb 0.3 Dy 0.7 Fe 1.92 (Terfenol-D) presents a large room temperature strain at relatively low magnetic field (below 40 kA/m), good magneto-mechanical coupling factor, high energy density and fast response [1,2,3,4,5,6]. However, this behavior is highly nonlinear and very sensitive to mechanical loading [7,8,9,10,11,12,13]. With structural design in view, accurate models are needed to predict material properties under stress and to propose adapted design of Terfenol-D devices. ...
Giant magnetostrictive materials (GMM) can be integrated in actuator or sensor applications.The design of these systems is optimized based on a good knowledge of the material properties and conditions of use. Terfenol-D exhibits the greatest room temperature strain among commercially available GMM, however, its magneto-elastic behavior is very sensitive to pre-stress level. In this work, the design of an experimental setup dedicated to the characterization of GMM magneto-mechanical behavior under constant stress is described. A major difficulty is to master the mechanical boundary conditions while the sample is subjected to dynamic magnetic loading. The dynamic stress experienced by the sample is connected to the magnitude of the magnetostriction strain, the stiffness of the sample and the stiffness of the characterization setup. Results show that an appropriate setup is able to reduce the dynamic stress variations induced by magnetic excitation variations below 0.1 MPa, while this dynamic stress can reach up to 20 times the magnitude of the applied stress when the control system is not used. With the boundary conditions being controlled, magnetic and magnetostrictive behavior of Terfenol-D are characterized under various uniaxial compressive stress levels, from the stress-free conditions to 90 MPa. By comparing the results obtained under controlled and non-controlled stress conditions, it is shown that uncontrolled boundary conditions can be responsible for errors of several percent on the magnetic induction measurement. The measurement of strain is even more sensitive to the boundary conditions, with errors up to 40% and 30% on the longitudinal and transverse strains, respectively. This work highlights the utmost importance to control the boundary conditions in order to characterize the magneto-mechanical behavior of GMM.
... factor, high energy density and fast response [1][2][3][4][5][6]. However, this behavior is highly nonlinear and very sensitive to mechanical loading [7][8][9][10][11][12][13]. With structural design in view, accurate models are needed to predict material properties under stress and to propose adapted design of Terfenol-D devices. ...
Recently, an experimental setup dedicated to the characterization of GMM magneto-mechanical behavior under constant stress has been designed. This setup is able to reduce the dynamic stress variations induced by magnetic excitation variations below 0.1 MPa. The present work focuses on the effect of loading boundary conditions on the measurement of material properties of Terfenol-D under stress levels from 0 to 90 MPa. Comparison of measurement results obtained under controlled and uncontrolled stress conditions show that uncontrolled boundary conditions can be responsible for errors of several percent on the measurement of the maximum and remnant magnetic induction. The measurement of strain is even more sensitive to the boundary conditions, with errors up to 40% and 30% on the longitudinal and transverse strain, respectively. In addition, evolutions in the measurement of susceptibility and (longitudinal and transverse) piezomagnetic properties reach +30%, +125% and +300% respectively. This work highlights the utmost importance to precisely control the boundary conditions for an accurate characterization of GMM properties under mechanical loading.
... Among GMM, bulk Tb 0.3 Dy 0.7 Fe 1.92 (Terfenol-D) presents a large room temperature strain at relatively low magnetic field (below 40 kA m −1 ), good magneto-mechanical coupling factor, high energy density and fast response [1][2][3][4][5][6]. However, this behavior is highly nonlinear and very sensitive to mechanical loading [7][8][9][10][11][12][13]. With structural design in view, accurate models are needed to predict material properties under stress and to propose adapted design of Terfenol-D devices. ...
Le développement d’outils de caractérisation du comportement magnéto-élastique de matériaux à magnétostriction géante (GMM) permet d’optimiser la conception d’actionneurs ou de capteurs dans lesquels ces matériaux sont souvent intégrés. Parmi eux, le Terfenol-D et le Galfenol possèdent chacun un comportement magnéto-élastique très sensible au niveau de précontrainte statique. Ce travail illustre l’influence du
contrôle des conditions aux limites sur l’évaluation du comportement du Terfenol-D. La comparaison des comportements obtenus en condition de traverse bloquée et de
contrainte contrôlée illustre la sensibilité des mesures de comportement magnéto-élastique des GMM aux conditions aux limites et montre l’importante nécessité du contrôle de ces conditions.
... Much attention has been given to the effects of temperature on the properties of GMMs (i.e., Terfenol-D) and the performance of magnetostrictive transducers [6][7]. Jin et al. investigated the resonance frequency shift characteristics of Terfenol-D rods for magnetostrictive actuators [8]. The dynamic model and experimental dates both show that the variations in the resonance frequency with temperature depends on the bias fie1d. ...
In this paper, a high-power rotary ultrasonic machining system was proposed using a novel magnetostrictive material with giant magnetostriction (over 1000 ppm), high energy density, and fast response speed, namely Giant magnetostriction ultrasonic processing system (GMUPS). By applying the equivalent circuit of the GMUPS, the electromechanical conversion efficiency model was presented, and the effects of temperature rise on the electromechanical conversion efficiency and optimal compensation parameter were studied. The impedance of the GMUPS using various compensation capacitances were measured to determine the optimal compensation capacitances under three kinds of steady temperatures, and the variations in vibration amplitude output of the GMUPS were tested using a specific excitation voltage to validate the results of impedance analysis. These results show that the vibration amplitude was maximized by using optimal compensation, and the optimal compensation capacitance was consistent at whole temperatures. In addition, the relation between electromechanical conversion efficiency and temperature was established by measuring the impedance circles of the GMUPS with optimal compensation under various temperatures. As demonstrated by comparison with the results of vibration test, the electromechanical conversion efficiency of the GMUPS was found to decrease with increasing temperature, while the power output by the power supply increases using a specific excitation voltage. As a result, the vibration-amplitude-current sensitivity firstly increases and then decreases rapidly with temperature rise. It is of great practical value for controlling and adjusting the vibration amplitude for the GMUPS.
... 13 Through considering the temperature effect to GMM's performance, the GMM's nonlinear constitutive model coupling with magnetism, elasticity, and heat is also established. 14,15 Hence, this model can describe the GMM's inherent nonlinear feature coupling with magnetism, elasticity, and heat more comprehensively and accurately. Yet, because of ignoring the power loss in GMM magnetizing a) ...
A novel Giant Magnetostrictive Actuator (GMA) experimental system with Fiber Bragg Grating (FBG) sensing technique and its modeling method based on data driven principle are proposed. The FBG sensors are adopted to gather the multi-physics fields' status data of GMA considering the strong nonlinearity of the Giant Magnetostrictive Material and GMA micro-actuated structure. The feedback features are obtained from the raw dynamic status data, which are preprocessed by data fill and abnormal value detection algorithms. Correspondingly the Least Squares Support Vector Machine method is utilized to realize GMA online nonlinear modeling with data driven principle. The model performance and its relative algorithms are experimentally evaluated. The model can regularly run in the frequency range from 10 to 1000 Hz and temperature range from 20 to 100 °C with the minimum prediction error stable in the range from -1.2% to 1.1%.
... Compared with conventional friction brakes, it has many desirable characteristics, such as a simple structure, a smooth and reliable working process, a rapid and reversible response, as well as easy control. As a consequence, MR brakes have many prospective applications in various fields and equipment, such as the automobile industry, the construction industry, exercise equipment and computer numerical control machine tools [6][7][8][9]. ...
The extremely severe heating of magnetorheological (MR) brakes restricts their application in high-power situations. This study aims to develop a novel MR brake with a high-torque capacity. To achieve this goal, a water cooling method is adopted to assist in heat dissipation. In the study, a structural model design of the high-torque MR brake is first developed according to the transmission properties of the MR fluid between the rotating plates. Then, the operating principle of the MR brake is illustrated, which is followed by a detailed design of the water channel. Moreover, theoretical analysis, including the transmitted torque, magnetic field and thermal analysis, is performed as well. After this, an experimental prototype of the proposed MR brake is fabricated and assembled. Then the torque transmission and heat dissipation of the prototype are experimentally investigated to evaluate the torque transmission properties and water cooling efficiency. Results indicate that the proposed MR brake is capable of producing a highly controllable brake torque, and the water cooling method can effectively assist in heat dissipation from the MR brake.
Ultrasonic metal welding (USMW) technology receives widespread attention because of its advantages of environmental protection, high efficiency, high welding strength, and low joint resistance. This paper systematically discusses the research progress of the ultrasonic generator, transducer, booster and horn. Furthermore, the latest research achievements of USMW in improving joint performance, the numerical simulation of accurate welding process and the mechanism of interface bonding are summarized. In addition, future directions of USMW are outlined, aiming to provide references for the research of USMW.
A vibrating screen is widely used in raw coal screening, but intensive resonance in the startup and shutdown stages shortens the service life of the vibrating screen and generates vibration damage to surrounding buildings. Therefore, we designed a novel vibration isolator based on a magnetorheological damper, aiming to improve the vibration isolation performance of the vibrating screen. The rheological mechanical model of damping force was analyzed based on the Bingham model, and a magnetic circuit was designed according to electromagnetic theory. Then, an experiment was designed to evaluate the vibration isolation performance of the vibration isolator. The results show that the novel vibration isolator, compared with the metal spring ones, reduces the maximum resonance amplitude by 64 % in the resonance region. In addition, the time of passing through the resonance region in startup and shutdown stages is also reduced by 50 % and 60 %, respectively. This study can provide a new method to improve the vibration isolation performance of vibrating screens.
In this chapter, the bending behavior of magnetostrictive beams is investigated. A nonlinear constitutive model is used to relate the magnetomechanical properties of the beam material. The beam is subjected to a linear prestress through a mechanical bending moment as well as a uniform longitudinal magnetic field. A semi-analytical algorithm is proposed for obtaining the magnetization, stress profile, and deflection of simply supported and cantilever beams. Comparing the results with those of experimental works, it is shown that the one-dimensional nonlinear model which was previously used to model the magnetostrictive rods and thin films can also accurately model the beams. It is shown that in a constant mechanical bending moment, the beam deflection first increases in the region of low fields and then decreases smoothly as the magnetic field increases. The nonlinear magnetization and stress profiles through the thickness of the beam are obtained for various values of bending moment as complementary results.
Highly flexible, conductive, and two-way reversible shape memory polyurethane nanocomposites were prepared with the in situ synthesized method, containing different graphene nanosheet contents ranging from 1.0 to 8.0 wt%. The dispersion of the nanocomposites in the polymer was monitored by scanning electron microscopy and thermal properties, mechanical properties, electrical properties, shape memory properties were comparatively investigated. The results showed that the nanocomposite was more stable when the content of graphene is 2 wt% in the crosslinked network structure. In comparison to pristine polyurethane, the graphene crosslinked polyurethane composite exhibited better thermostability, breaking stress, and exceptional elongation-at-break. The resulting composite exhibited 93 % shape fixity, 95 % shape recovery of 2.0 % loading, and fast electroactive shape recovery rate. Moreover, the polymers also showed good reversible two-way shape memory behaviors, thus it could be a promising material for the fabrication of graphene-based actuating devices.
Purpose
– The finite element method (FEM) for 3D models needs heavy computational cost. The computational cost for FE analysis of moving objects, e.g. Vibration energy harvester, must be reduced to exploit the simulation of the dynamic system in its design. The paper aims to discuss these issues.
Design/methodology/approach
– To reduce the computational time of FEM, the model order reduction (MOR) based on proper orthogonal decomposition has been proposed. For the moving systems, MOR is modified.
Findings
– It is shown that proposed MOR makes it possible to drastically reduce the coupling analysis of the energy harvester in which the equations of motion, magnetostatics, and circuit are repeatedly solved.
Originality/value
– To reduce the computational time of FEM, block-MOR is presented, in which the whole domain is subdivided into N-blocks. As a result computational cost for MOR can be reduced.
Purpose
– This study aims to reveal the temperature rise characteristic of magnetorheological (MR) fluid in a multi-disc MR clutch under slip condition, including the temperature distribution regularity and the impact factors.
Design/methodology/approach
– Three-dimensional transient heat conduction equation for the MR fluid in the working gap was derived based on the heat transfer theory. Then, numerical simulation was conducted to analyze the temperature field of MR fluid. Furthermore, an experimental study was performed to explore the temperature distribution of the MR fluid in radial and circumferential directions, as well as the effects of disc groove, slip power and gap size on temperature rise characteristic of the MR fluid.
Findings
– The results show that temperature appears to be largest in the center of the working gap and the temperature difference increases with the slip time. However, the temperature field in a circumferential direction is basically the same, but it presents slightly lower in the groove area. The temperature of the MR fluid increases linearly with the slip time and the rise rate increases with the slip power. Moreover, the temperature rise value decreases with the increase of gap size.
Originality/value
– In this paper, the temperature gradients, both in radial and circumferential directions, are experimentally measured going beyond the estimation by computer simulations. In addition, the factors that influence the temperature rise characteristic of MR fluid were fully analyzed. The results could provide a reliable basis for the development of cooling technology for high-power MR devices.
Magnetostrictive amorphous ribbons are widely used in electronic article surveillance as well as for magnetoelastic sensors. Both applications utilize the fact that the ribbons' resonant frequency can be read out remotely by applying external magnetic AC fields. This paper proposes a magnetomechanical model to simulate the dynamics of such ribbons. The goal was to only use general material properties as input parameters, which are usually denoted in the data sheet of amorphous metals. Thus, only the magnetization curve at zero stress has to be gained via measurement. The magnetization under stress is calculated thereof. The equation of motion for a longitudinally oscillating ribbon is derived and coupled to Maxwell's equations for magnetostatics. The fully coupled initial value problem is solved simultaneously by a finite difference approach. The model is validated by comparing calculated and measured resonant frequencies of various amorphous ribbons, which turned out to be in good agreement. When slightly adapting single material properties from the data sheet, the match is almost perfect. The model is then used to calculate the local magnetic and mechanical properties inside static and vibrating ribbons. These local distributions can be directly linked to the field dependence of the resonant frequency and its higher harmonics.
A micromechanical analysis is offered for the prediction of the effective behavior and internal field distribution of multiphase magnetostrictive composites. The analysis is based on the homogenization technique for periodic composites. The nonlinear coupled constitutive relations of the monolithic magnetostrictive have been recently established at room and elevated temperatures and verified by comparisons with experimental results. Due to the nonlinearity of these constitutive equations, the micromechanical method is based on an incremental procedure which provides the instantaneous magneto-thermo-elastic concentrations tensors that relate the local field to the externally applied loading. In addition, the analysis provides the instantaneous effective tangent tensors as well as the macroscopic constitutive equations which govern the current global behavior of the magnetostrictive composite. The present analysis provides an efficient tool for analyzing magnetostrictive composites with continuous and arbitrary inclusion phases. Results present a parametric study of the effect of applied pre-stresses, elevated temperatures and magnetostrictive phase geometry and volume fraction on a magnetostrictive/epoxy composite response that is subjected to external magnetic field. The distributions of the induced magnetostrictions in the constituents are shown in various circumstances.
A new multidisk magnetorheological fluid actuator was proposed using the shear stress of magnetorheological fluid between rotating disks. The transmission torque was calculated based on the Bingham model, and the magnetic circuit was designed in accordance with electromagnetic theory. Then, a magnetostatic simulation was conducted to validate the designed magnetic circuit. Furthermore, an experimental study was performed to investigate the performance of the prototype. The results show that the transmission torque increases approximately linearly with the input current within the saturation range of magnetorheological fluid. Both the input current and the gap thickness have little influence on the dynamic response property of the proposed magnetorheological fluid actuator. Moreover, the temperature of magnetorheological fluid increases linearly with the time in the slip and loaded states, and the greater the slip power is, the faster the temperature rises. Furthermore, the temperature rise of magnetorheological fluid will result in the reductions of the torque transmission ability and the dynamic response speed. On the whole, the proposed multidisk magnetorheological fluid actuator has a higher torque capacity and a slightly slower dynamic response in comparison with the present magnetorheological devices. It is promising for applications in many high torque occasions.
A theory based on equivalent circuit was proposed to demonstrate that magnetodielectric (MDE) effect and electric-induced magnetic permeability (EIMP) exist in the magnetoelectric composite. Both MDE and EIMP are sensitive to the amplitude of inspiring signal. They were researched in a simple Pb(Zr,Ti)O3/Terfenol-D laminate composite experimentally. A large MDE coefficient over 85% was found near the resonance frequency under a low magnetic field of 40 Oe. The EIMP was also observed in the composite. They are mainly originated from the magnetoelectric coupling between the piezoelectric and magnetostrictive components. These results are significant in the device applications of modulating dielectric constant and magnetic permeability at room temperature.
This paper analyzes a prototype microgyrosensor that employs the magnetostrictive alloy Galfenol for transduction of Coriolis-induced forces into an electrical output for quantifying a given angular velocity. The magnetic induction distribution in the Galfenol sensor patch depends on its bending shape and magnetoelastic properties and is investigated using a finite element model. Fluctuations in magnetic induction caused by a sinusoidal rotation of the sensor produce an amplitude modulated voltage in a surrounding coil which is simulated and measured.
This paper addresses the modeling of strains generated by
magnetostrictive transducers in response to applied magnetic fields. The
measured strains depend on both the rotation of moments within the
material in response to the field and the elastic properties of the
material. The magnetic behavior is characterized by considering the
Jiles-Atherton mean field theory for ferromagnetic hysteresis in
combination with a quadratic moment rotation model for magnetostriction.
Elastic properties must be incorporated to account for the dynamics of
the material as it vibrates. This is modeled by force balancing, which
yields a wave equation with magnetostrictive inputs. The validity of the
resulting transducer model is illustrated by comparison with
experimental data
ELECTROMAGNETISM: MAGNETIC PHENOMENA ON THE MACROSCOPIC SCALE Magnetic Fields Magnetic Field Magnetic Induction Magnetic Field Calculations References Further Reading Exercises Magnetization and Magnetic Moment Magnetic Moment Magnetic Poles and Amperian Bound Currents Magnetization Magnetic Circuits and the Demagnetizing Field Penetration of Alternating Magnetic Fields into Materials References Further Reading Exercises Magnetic Measurements Induction Methods Force Methods Methods Depending on Changes in Material Properties Superconducting Quantum Interference Devices References Further Reading Exercises Magnetic Materials Classification of Magnetic Materials Magnetic Properties of Ferromagnets Different Types of Ferromagnetic Materials for Applications Paramagnetism and Diamagnetism References Further Reading Exercises MAGNETISM IN MATERIALS: MAGNETIC PHENOMENA ON THE MICROSCOPIC SCALE Magnetic Properties Hysteresis and Related Properties Barkhausen Effect and Related Phenomena Magnetostriction Magnetoresistance References Further Reading Exercises Magnetic Domains Development of Domain Theory Energy Considerations and Domain Patterns References Further Reading Exercises Domain Walls Properties of Domain Boundaries Domain-Wall Motion References Further Reading Exercises Domain Processes Reversible and Irreversible Domain Processes Determination of Magnetization Curves from Pinning Models Theory of Ferromagnetic Hysteresis Dynamics of Domain Magnetization Processes References Further Reading Exercises Magnetic Order and Critical Phenomena Theories of Paramagnetism and Diamagnetism Theories of Ordered Magnetism Magnetic Structure References Further Reading Exercises Electronic Magnetic Moments Classical Model of Magnetic Moments of Electrons Quantum Mechanical Model of Magnetic Moments of Electrons Magnetic Properties of Free Atoms References Further Reading Exercises Quantum Theory of Magnetism Electron-Electron Interactions Localized Electron Theory Itinerant Electron Theory References Further Reading Exercises MAGNETICS: TECHNOLOGICAL APPLICATIONS Soft Magnetic Materials Properties and Applications of Soft Magnets Materials for AC Applications Materials for DC Applications Materials for Magnetic Shielding References Further Reading Materials Conferences Hard Magnetic Materials Properties and Applications of Hard Magnets Permanent Magnet Materials References Further Reading Materials Conferences Magnetic Recording History of Magnetic Recording Magnetic Recording Media Recording Heads and the Recording Process Modeling the Magnetic Recording Process References Further Reading Magnetic Evaluation of Materials Methods for Evaluation of Materials Properties Methods for Detection of Flaws and Other Inhomogeneities Magnetic Imaging Methods Sensitivity to Microstructure and Material Treatment References Further Reading Solutions to Exercises
Flapper–nozzle type Electro Hydraulic Servo Valve (EHSV) operated by conventional torque motor actuators has been used in wide range of industrial applications. As their bandwidths are limited, they are not suitable for high-speed applications. The work presented in this paper deals with the mechatronic approach for the design of a magnetostrictive actuator with flexure amplifier and a magnetically biased magnetostrictive actuator for application in high frequency flapper–nozzle servo valve. A magnetostrictive actuator has been designed, built and integrated into an existing flapper–nozzle servo valve by replacing the torque motor. Incorporating the dynamics of the magnetostrictive actuator, the dynamics of the valve was simulated. Necessary parameters for the actuator have been arrived by finite element model. No load flow characteristics are analyzed and compared with experimental values. Step response has been compared with conventional valve. The results show that the valve has satisfactory static and dynamic characteristics for applications in high-speed actuation systems.
The variation of the magnetoelastic resonance frequency as a function of the temperature is investigated for sensing purposes in two samples with different properties. It is observed that maximum sensitivity is reached when biasing the sample close to the anisotropy field. A compensation field is also found at which the resonance frequency is insensitive to temperature changes. It is demonstrated that the observed behavior is determined mainly by the temperature dependence of the anisotropy constants of the samples. The results suggest the viability of remote temperature monitoring even trough opaque barriers.
Terfenol-D rods, as a kind of giant magnetostrictive materials, are often used as active elements of device for anti-vibration application due to its superior material properties. Their magneto-mechanical responses exhibited in many experiments are nonlinear and coupled. In order to have a good understanding on their coupling characters for accurate control, the numerical simulation on dynamic behavior of a Terfenol-D rod is conducted based on a nonlinear and coupling constitutive model proposed in this paper. The results show that the constitutive model can effectively describe some intrinsic coupling phenomena observed by experiments involving the maximum magnetostrictive strain of a Terfenol-D rod changing with pre-stresses and the corresponding dynamic responses show that the frequency and the amplification of the Terfenol-D rod change with magnetic bias field and pre-stresses, which are also consistent with experimental data and cannot be captured by previous constitutive model.
In this paper magnetostrictive rods are analyzed coupling a magnetoelastic model of Terfenol-D rods based on Preisach theory with a finite element electromagnetic field solution, accounting for dynamic effects within the rod. The computed results, compared with experiments, evidence the influence of eddy currents and magnetization dynamic on the magnetostrictive rod behavior.
We quantify the dependence of strain on dynamic magnetic field in magnetostrictive transducers. Dynamic eddy current losses are modeled as a one-dimensional (1D) magnetic diffusion problem in cylindrical coordinates. The constitutive magnetostrictive response to an average diffused magnetic field is quantified with the Jiles–Atherton model. The transducer is represented as a lumped-parameter, single-degree-of-freedom resonator with force input dictated by the magnetostriction. This equivalent force is expressed as a summation of Fourier series terms. The total dynamic strain output is obtained by superposition of strain solutions due to each harmonic of the force input.
This paper describes a bidirectionally coupled magnetoelastic model, BCMEM. BCMEM is a 3D nonlinear finite element-based model comprising magnetic and elastic boundary value problems (BVPs) that are bidirectionally coupled through stress and field dependent coupling variables—magnetostriction and magnetization. The coupling variables are calculated using an energy-based magnetomechanical model. The BVPs are solved iteratively using the finite element method with values of coupling variables updated every iteration to account for the bidirectional coupling. Such an approach is effective in incorporating the apparent variation in modulus of elasticity (the ΔE effect) and permeability with changing stress and magnetic field, as well as modeling their effects on stress and field distributions. Thus, BCMEM allows the prediction of both nonlinear sensing and actuating behaviors of magnetostrictive materials. Moreover, the use of the finite element method provides the model with the ability to incorporate demagnetizing fields due to shape anisotropy and hence the capability to predict the response of magnetostrictive materials in complex 3D structures. The model predictions of magnetic flux density and bending strain for an aluminum–Galfenol unimorph cantilever structure showed good correlation when compared against experimental results obtained from both magnetically unbiased and biased single-crystal Galfenol (Fe84Ga16) active layers.
A general nonlinear constitutive model is proposed for magnetostrictive materials, based on the important physical fact that a nonlinear part of the elastic strain produced by a pre-stress is related to the magnetic domain rotation or movement and is responsible for the change of the maximum magnetostrictive strain with the pre-stress. To avoid the complicity of determining the tensor function describing the nonlinear elastic strain part, this paper proposes a simplified model by means of linearizing the nonlinear function. For the convenience of engineering applications, the expressions of the 3-D (bulk), 2-D (film) and 1-D (rod) models are, respectively, given for an isotropic material and their applicable ranges are also discussed. By comparison with the experimental data of a Terfenol-D rod, it is found that the proposed model can accurately predict the magnetostrictive strain curves in low, moderate and high magnetic field regions for various compressive pre-stress levels. The numerical simulation further illustrates that, for either magnetostrictive rods or thin films, the proposed model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves, while none of the known models can capture all of them. Therefore, the proposed model enjoys higher precision and wider applicability than the previous models, especially in the region of the high field.
The RFe 2 alloys (R=Tb,Dy,Sm) offer opportunities for achieving very high magnetostrictions at temperatures far above room temperature. Saturation strains greater than 1000 ppm have been measured at temperatures as high as 200°C. In addition to saturation strain measurements, we have measured magnetostriction of Tb .27 DY .73 Fe 2 under compressive stress from -30°C to 80°C, a temperature range encountered in many magnetomechanical transducers. From these data optimum magnetic and mechanical biases can be determined. These measurements give an insight into the magnetization process in three distinct regions: (1) high cubic [100] easy anisotropy, (2) low anisotropy and (3) high cubic [111] easy anisotropy.
The influence of internal stress on the magnetic anisotropy and the magnetostriction was investigated in sputter‐deposited amorphous (Tb 0.27 Dy 0.73 ) 0.42 Fe 0.58 films. Films with tensile stress show in‐plane anisotropy and giant magnetostriction of λ ‖ =400×10<sup>-6</sup> at 1 T measured in a field parallel to the film plane at room temperature. The magnetostriction rises rapidly to λ ‖ =200×10<sup>-6</sup> at 0.05 T and the coercivity is less than 0.01 T. On the other hand films with compressive stress show perpendicular anisotropy and still higher magnetostriction of λ ‖ =540×10<sup>-6</sup> at 1 T; however, this is by far a slower increase of magnetostriction at small fields. This different behavior is explained by considering the nature of magnetization processes, i.e., domain‐wall motion and spin rotation.
A mathematical theory of hysteresis in ferromagnetic materials is presented based on existing ideas of domain wall motion and domain rotation. Hysteresis is shown to occur as a result of impedances to changes of magnetization such as when domain walls are pinned, while the mutual interactions of the magnetic moments are shown to be of secondary importance in this respect. An equation for the anhysteretic or ideal magnetization curve is derived based on a mean field approximation and this is shown to be dependent on the mutual interactions of the moments but independent of impedances such as pinning. The introduction of a term which measures the impedance to changes in magnetization leads to a simple differential equation of state for a ferromagnet which exhibits all the features of hysteresis. Some modifications of the simple model are necessary in order to bring the solution closer to the real situation. Results are presented which show all the features of hysteresis such as initial magnetization curve, major hysteresis loops, and minor hysteresis loops in excellent agreement with experimental results.
Large ‘‘jumps’’ in the magnetostriction have been observed in twinned single crystals of Tb 0.3 Dy 0.7 Fe 1.9 (Terfenol‐D) for magnetic fields parallel to the crystalline [112¯] direction. The interpretation of these large magnetostriction discontinuities is based upon a model of twinned dendritic Terfenol‐D in which the magnetization of one twin jumps between two [111] directions while the magnetization of the remaining twin undergoes a continuous rotation of the magnetization. The field dependence of the magnetization and magnetostriction of cubic single crystals with λ 1 1 1 ≫λ 1 0 0 was calculated using an expression which included the anisotropy constants K 1 and K 2 and compressive loads along [112¯]. With K 1 =-0.6 J/m<sup>3</sup> and K 2 =-2.0 J/m<sup>3</sup> (values appropriate for Terfenol‐D near room temperature), magnetization ‘‘jumping’’ is predicted. For the twinned crystal, the jump in the magnetostriction was calculated to be greater than 1000 ppm. Because of this large magnetostriction, it is possible to configure a device to perform a substantial amount of work by the application of only a triggering magnetic field centered about an optimum bias field.
To overcome some deficiencies in previous constitutive models of giant magnetostrictive materials, a nonlinear and coupled model is suggested to describe the constitutive relations for a Terfenol-D rod subjected to an axial pre-stress and then located in an axial magnetic field. The numerical simulation by the model proposed in this paper shows predicted magnetostrictive strain curves for various compressive pre-stresses in good agreement with the experimental data not only in the region of low and moderate magnetic field but also in the region of high field. In comparison with the previous models, the proposed model can more effectively describe the effect of the pre-stress on the maximum magnetostrictive strain. Moreover, the effect of the stress and the magnetic field on the Young’s modulus of the materials, i.e., the Δ E effect, can also be predicted. In the proposed model, there are only five material parameters. They are the saturation magnetization M<sub>s</sub> , the saturation magnetostrictive strain λ<sub>s</sub> , the intrinsic (or saturation) Young’s modulus E<sub>s</sub> and the initial Young’s modulus E<sub>0</sub> as well as the linear magnetic susceptibility χ<sub>m</sub> . Since these parameters are easily measured in experiments, the proposed model is convenient to be used in engineering applications.
The magnetostrictive strain-applied field curve typical of giant magnetostrictive materials is nonlinear and it is affected notably by prestress and temperature. A constitutive model to describe these properties is suggested in this paper. The model considered here is built on the Gibbs free energy function G(σ<sub>ij</sub>,M<sub>k</sub>,T) . Thermodynamic relations are used to obtain the constitutive expressions. Results based on the model show that the nonlinear property of magnetostrictive strain, the magnetization, and Young’s modulus under different prestress and temperature are in excellent agreement with experimental data. Moreover, the proposed model is convenient to be used in engineering applications since the parameters referred to the model can all be easily determined by experiments.
A mechanical resonator made of a freestanding magnetostrictive strip as a mass sensor is used as the sensor platform for the development of biosensors. It is found that these sensors have a Q value in air (∼1000) and water (>100) . The mass sensitivity of the sensor is strongly dependent on the location of the mass load. For the mass load at node(s), a close to zero sensitivity is obtained. However, for the mass load at the points with the maximum oscillation amplitude, the highest sensitivity is obtained. This highest sensitivity is about twice the sensitivity of the sensor for the mass load uniformly distributed over the sensor surface. Due to the wireless nature and freestanding configuration, both even and odd harmonic modes of resonators can be measured. By using odd and even modes, the “blind point” issues with the sensors based on mechanical resonators can be overcome.
The paper proposes a two-stage model able to describe the dynamic behavior of a commercial magnetostrictive actuator in the frequency range of interest for fast actuation purposes. The first stage is a static model of hysteresis, while the second one is a linear dynamic model. The model structure allows to define well-assessed identification procedures for both stages. In particular, the identification of the dynamic stage is realized by the compensation of the transducer's hysteresis, through the employment of a pseudo-compensator. Experimental validation of the model is also reported and further applications to other magnetostrictive actuators is addressed.