A nonlinear constitutive model for magnetostrictive materials

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.

Magnetostrictive and Kinematic Model Considering the Dynamic Hysteresis and Energy Loss for GMA

Due to the influence of magnetic hysteresis and energy loss inherent in giant magnetostrictive materials （GMM）, output displacement accuracy of giant magnetostrictive actuator （GMA） can not meet the precision and ultra precision machining. Using a GMM rod as the core driving element, a GMA which may be used in the field of precision and ultra precision drive engineering is designed through modular design method. Based on the Armstrong theory and elastic Gibbs free energy theory, a nonlinear magnetostriction model which considers magnetic hysteresis and energy loss characteristics is established. Moreover, the mechanical system differential equation model for GMA is established by utilizing D＇Alembert＇s principle. Experimental results show that the model can preferably predict magnetization property, magnetic potential orientation, energy loss for GMM. It is also able to describe magnetostrictive elongation and output displacement of GMA. Research results will provide a theoretical basis for solving the dynamic magnetic hysteresis, energy loss and working precision for GMA fundamentally.

GIANT MAGNETOSTRICTIVE ACTUATOR IN SERVO VALVE AND MICRO PIPE ROBOT

Performance of giant magnetostrictive material (GMM) is introduced. Principleof work, basic structure and key techniques of giant magnetostrictive actuator (GMA) are analyzed.Its dynamic models of magneto-mechanical coupling are established. The structure and principle ofthe pneumatic servo valve and the micro pipe robot with new homemade GMM are presented. Theexperiment is carried out under typical working conditions. The experiment results show that the GMMpneumatic servo valve has wide pressure control characteristics, good linearity, and fast responsespeed. The movement principles of the GMM robot system are reliably feasible and its maximal movingspeed is about 8 mm/s. It is preferable to the driving frequency of the robot within 100 approx 300Hz.

SOME PROBLEMS IN ELECTROSTRICTIVE AND MAGNETOSTRICTIVE MATERIALS

Some of the previous theories in the electrostrictive and magnetostrictive materials and their differences are discussed in this paper. A variational principle in the general thermodynamic sense is given and the governing equations can be derived from this principle. Illustrational examples are given.

Novel mechanism for boring non-cylinder piston pinhole based on giant magnetostrictive materials

To bear more loads for heavy truck pistons, the shape of heavy truck piston pinhole is often designed as noncylinder form. Current methods cannot meet the needs for precision machining on non-cylinder piston pinhole （NCPPH）. A novel mechanism based on giant magnetostrictive materials （GMM） is presented. New models are established for the servo mechanism, GMM, and magnetizing force of the control solenoid to characterize the relationship between the control current of the solenoid and the displacement of the giant magnetostrictive actuator （GMA）. Experiments show that the novel mechanism can meet the needs to perform fine machining on NCPPH effectively.

Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator

Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator(GMA).Therefore,in the present study we intend to investigate the influences of the system damping coefficient,system stiffness coefficient,disc spring cubic stiffness factor,and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA.In this regard,the nonlinear piezomagnetic equation,Jiles-Atherton hysteresis model,quadratic domain rotation model,and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA.Moreover,the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system.Then,the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed.Finally,the fourth-order Runge-Kutta method is used to obtain the time domain waveform,phase portrait and Poincarémapping diagrams of the system.Subsequently,the obtained three graphs are analyzed.The obtained results show that when the system output is stable,the variation range of each parameter can be determined.Moreover,the stability interval of system damping coefficient,system stiffness coefficient,and the coefficient of the cubic stiffness term of the disc spring are obtained.Furthermore,the stability interval of the exciting force and the excitation frequency are determined.

Development，Application，Markets，and Patent Situation of Magnetostrictive TERFENOL－D

The development of the giant magnetostrictive rare earth-iron materials is reported from their discovery in the early 1970's to their present use in transducer and sensor applications. Fifteen broad market areas, ranging from miniature devices in the medical industry to high powder sonar and seismic sources have been identified. A world-wide customer base in these high technology fields has been established and the superior properties of these materials are responsible for the rapid growth of the magnetostrictive transducer industries. The critical design criteria that lead to efficient devices are reported and the performance of several of these products is presented. The key patents associated with these giant magnetostrictive materials and devices using these materials are reviewed. The present and future of these technologies in reference to commercialization, market growth and the impact on the many transduction industries are discussed. (Author abstract) 9 Refs.

Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation

The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film （GMF）-shaped memory alloy （SMA） composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared based on an SMA plate, and combined into a GMF-SMA composite plate. The Van der Pol item is improved to explain the hysteretic phenomena of GMF and SMA, and the nonlinear dynamics model of a GMF-SMA composite cantilever plate subjected to in-plane stochastic excitation is developed. The stochastic stability of the system is analyzed, and the steady-state probability density function of the dynamic response of the system is obtained. The condition of stochastic Hopf bifurcation is discussed, the reliability function of the system is provided, and then the probability density of the first-passage time is given. Finally, the stochastic optimal control strategy is proposed by the stochastic dynamic programming method. Numerical simulation shows that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the system＇s reliability is improved through stochastic optimal control, and the first- passage time is delayed. A GMF-SMA composite plate combines the advantages of GMF and SMA, and can reduce vibration through passive control and active control effectively. The results are helpful for the engineering applications of GMF-SMA composite plates.

Giant Magnetostrictive Material Loudspeaker System Acoustic Radiation Simulation

An infinite panel model of giant magnetostrictive material loudspeaker system （GMMLS） is proposed by making use of finite element method（FEM）. Bending wave eigenfunction is introduced to describe the acoustic radiation condition of the panel. Far-field response in different conditions is calculated by changing the mass surface density. Conclusion is obtained by analyzing the curves simulated, that panel which has larger mass surface density can hardly generate far-field acoustic radiation for lower frequency, while the panel has smaller mass surface density generates far-field acoustic radiation for lower frequency evenly and stronger.

Magnetostrictive Properties for Epoxy Bonded Tb_(1-x)Dy_xFe_2 Composites

The epoxy bonded Tb_(1- x )Dy_ x Fe_2 composites were prepared. The magnetostriction,dynamic magnetostrictive coefficient and magnetomechanical coupling coefficient of epoxy bonded Tb_(1- x )Dy_ x Fe_2 rod samples were measured by using multiple parameter magnetic measurement system. It is found that the magnetostriction,dynamic magnetostrictive coefficient and magnetomechanical coupling coefficient of epoxy bonded Tb_(0.3)Dy_(0.7)Fe_2 rod sample are higher than those reported. The reason for the high magnetostrictive properties of the sample was explained according to the theory of magnetization process. The result indicates that the epoxy bonded Tb_(0.3)Dy_(0.7)Fe_2 rod sample is of practical value.

Magnetic and magnetostrictive properties of amorphous TbFe/FeAl multilayer thin film

Exchange coupling multilayer thin films, which combined giant magnetostriction and soft magnetic properties, were of growing interest for applications. The TbFe/FeAl multilayer thin films were prepared by dc magnetron sputtering onto glass substrates. The microstructure, magnetic, and magnetostrictive properties of TbFe/FeAl multilayer thin film was investigated at different annealing temperatures. The results indicated that the soft magnetic and magnetostrictive properties for TbFe/FeAlmultilayer thin film compared with TbFe single layer film were obviously improved./n comparison with the intrinsic coercivity JHo of 59.2 kA/m for TbFe single layer film, the intrinsic coercivity jHc for TbFe/FeAl multilayer thin films rapidly dropped to 29.6 kA/m. After optimal annealing （350 ℃×60 min）, magnetic properties of Hs=96 kA/m and jHc=16 kA/m were obtained, and magnetostrictive coefficient could reach to 574×10^-6 under an external magnetic field of 400 kA·m^-1 for the TbFe/FeA1 multilayer thin film.

DYNAMIC FREE ENERGY HYSTERESIS MODEL IN MAGNETOSTRICTIVE ACTUATORS

A dynamic free energy hysteresis model in magnetostrictive actuators is presented. It is the free energy hysteresis model coupled to an ordinary different equation in an unusual way. According to its special structure, numerical implementation method of the dynamic model is provided. The resistor parameter in the dynamic model changes according to different frequency ranges. This makes numerical implementation results reasonable in the discussed operating frequency range. The validity of the dynamic free energy model is illustrated by comparison with experimental data.

Modeling and Control for Magnetostrictive Hysteresis

To deal with the rate-dependent hysteresis presented in a magnetostrictive actuator, a new method of modeling and control is proposed. The relationship between inputs and outputs of the actuator is approximately described by a dynamic differential equation with two rate-dependent coefficients, each expressed as a polynomial of frequency. For a given frequency, the coefficients will be able to be estimated by approximating the experimental data of the outputs of the magnetostrictive actuator. Based on this model, a quasi-PID controller is designed. In the space of the coefficients and frequency, the stable domain of closed loop system with hysteresis is analyzed. The numerical simulation and experiments have born witness to the feasibility of the proposed new method.

Magnetostrictive Flexible Thin Film Structure for Micro Devices

Polyimide (Kapton, Dupont Corp.) based magnetostrictive thin film structures were designed and fabricated for micro device applications. In particular the growth of films on flexible substrates was studied to allow a simple integration of the system in miniaturized magnetostrictive devices. The films were fabricated on different substrates to compare their different magnetic and structural properties. It showed much more magnetostriction and higher impact resistance results compared with traditional Si based film type actuators. In the fabrication process, amorphous TbDyFe films with thicknesses of 500 nm, 1 μm, 1.5 μm respectively, were deposited on the designed substrate by DC magnetron sputtering. During sputtering process the substrate holder was maintained at room temperature. After the sputter process, X-ray diffraction studies were also carried out to determine the film structure and thickness of the sputtered film. At last, magnetization from VSM (Vibrating Sample Magnetometer) and magnetostriction from optical cantilever method of each structure were measured to estimate the magneto-mechanical characteristics under the external magnetic field lower than 0.7 T for micro-system applications.

Study on preparation technique and properties of magnetostrictive epoxy bonded Tb_(1–x)Pr_x(Fe_(0.4)Co_(0.6))_(1.93) composites

The magnetic and magnetostrictive properties of epoxy bonded Tb1-xPrx（Fe0.4Co0.6）1.93 （0.85≤x≤1.00） composites, prepared with different epoxy proportions using cold compression-molding technique, were investigated. It is found that the optimal conditions were with a compaction pressure of 100 MPa and a mass ratio of resin to powder of 5：100. The Tb0.1Pr0.9（Fe0.4Co0.6）1.93 composite rod had a high magnetostriction of 770 ppm at an applied magnetic field of 960 kA/m, whereas the Pr（Fe0.4Co0.6）1.93 composite reached 500 ppm at 400 kA/m. The good magnetostrictive properties of Pr（Fe0.4Co0.6）1.93 composite at low-field （≤400 kA/m） could be explained by its low anisotropy. These results indicated that the epoxy bonded Tb1-xPrx（Fe0.4Co0.6）1.93 rod samples for high Pr content of x=0.9-1.0 were of practical value.

Experimental Investigation on Finishing Technology by Magnetostrictive Ultrasonic Vibration of Magnetic Liquid

Magnetic liquid can produce alternative internal pressure under the alternative high-frequency gradient magnetic field.Because it has higher bulk modulus,the internal pressure results in its volume change.Using piezoelectric transducers,the ultrasonic wave generated by the vibration of magnetic liquids can be detected,which shows that the magnetic liquids have the magnetostrictive effect and can generate the ultrasonic vibration under the alternative magnetic gradient field.Some nonmagnetic abrasives and rust-proofing agents can be mixed into the magnetic liquids,under the alternative magnetic field,the abrasives held by magnetic liquids grind the surface of the workpieces,and thus,the finishing for the surface with complex shape,mold cavity and inner wall of tiny tubes can be realized.

Vibration suppression of magnetostrictive laminated beams resting on viscoelastic foundation

The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam theory.Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam.Based on Navier’s approach,the solution of the dynamic system is obtained.The effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.

Modelling self-sensing of a magnetostrictive actuator based on a terfenol-D rod

A simplified quasi-static computational model for self-sensing applications of magnetostrictive actuators based on terfenol-D rods is presented. Paths and angle changes in the magnetic moments rotation of Tb0.3Dy0.7Fe2 alloy are studied as functions of compressive stress and magnetic field, and then used to determine the magnetization in its actuation. Then sensing of magnetic induction picked from a driving coil in an actuator is derived. The model is quick and efficient to solve moments rotation and its magnetization. Sensing results of compressive stress and magnetostriction calculated by the model are in good agreement with experiments and will be helpful in the design and control of self-sensing applications in actuators.

Research on Giant Magnetostrictive Actuator for Turning Vibration Control

Magnetostriction is a phenomenon in which a magneti c field is used to produce a change in size of some materials. This property has b een known in elements such as nickel, iron and cobalt. Because the rare-ear th alloy Terfenol-D can offer much larger strains than nickel, iron, cobalt, an d other smart materials such as piezoelectric materials, it is called giant magn etostrictive material. Making use of the giant magnetostrictive material, the gi ant magnetostrictive actuator has higher bandwidth and rapider response than oth er actuators. So it is widely used in active vibration control, especially in lo w frequency stage. In this paper, a turning vibration control system is develope d. The system has an actuator clamped in a flexor that is rigid in the feed and main cutting force directions, yet is flexible in the radial direction. The stru cture of the giant magnetostrictive actuator is developed after magnetic circuit and some structure parameter are calculated. According to the turning frequency , the transient and stable-state output of the giant magnetostrictive actuator is measured. The test result demonstrated that the actuator responses the input rapidly, and the actuator has perfect stable-state and transient output charact eristic. The characteristic includes the stable-state output linearity, repeata bility and transient delay between output displacement and input current.

Modeling and identification of magnetostrictive hysteresis with a modified rate-independent Prandtl-Ishlinskii model

This paper presents a modified rate-independent Prandtl-Ishlinskii （MRIPI） model based on the Fermi-Dirac distri- bution for the asymmetric hysteresis description of magnetostrictive actuators. Generally, the classical Prandtl-Ishlinskii （CPI） model can hardly describe the asymmetric hysteresis. To overcome this limitation, various complex operators have been developed to replace the classical operator. In this study, the proposed MRIPI model maintains the classical operator while a modified input function based on the Fermi-Dirac distribution is presented to replace the classical input function. With this method, the MRIPI model can describe the asymmetric hysteresis of magnetostrictive actuators in a relatively simple mathematic format and has fewer parameters to be identified. A velocity-based sine cosine algorithm （VSCA） is also proposed for the parameter identification of the MRIPI model. To verify the validity of the MRIPI model, experiments are performed and the results are compared with those of the existing modeling methods.