This study aims to investigate the influence of temperature on the linear and nonlinear rheological behavior of a MR fluid, MRF 132DG, using a rotational rheometer. The experiments were designed to obtain properties of the fluid under oscillatory shear strain in the amplitude and frequency sweep modes, while maintaining different constant temperatures (−5, 0, 20 and 50 °C). The data were used to evaluate the storage and loss moduli under different levels of magnetic flux density considering the linear as well as nonlinear viscoelastic regions. The critical strain amplitudes were further obtained. Results showed enhanced linear viscoelastic region with increasing magnetic field density. Moreover, the effects of temperature and magnetic field on the frequency dependency of the fluid properties are illustrated for small and large amplitudes of shear strains.

Static and dynamic properties of six magnetorheological elastomers (MRE) with iron particles volume fraction ranging from 12.5% to 40% were experimentally characterized under shear mode operation. The experiments were designed on the basis of standardized methods defined in ISO-1827 and ISO-4664. The static shear stress-shear strain data obtained under strains up to 30% were used to quantify absolute and relative MR effects of the MREs as functions of magnetic flux density in the 0 to 450 mT range. The MRE specimen with highest iron particles fraction and a softening agent revealed greatest MR effect. The dynamic characteristics of this MRE specimen were then evaluated under harmonic excitations in the 0.1–50 Hz frequency range with shear strain amplitude and magnetic flux density ranging from 2.5 to 20%, and 0 to 450 mT, respectively. The data were then utilized to evaluate elastic and loss shear moduli of the specimen.

Equivalent electromechanical circuit analysis models provide efficient tools for analysis of power flow across multiple physical domains. In this work, we use this tool to develop a model of the power flow through mechanical, magnetic and electrical domains for analysis of magnetostrictive material-based devices. The magnetostrictive unimorph system in this study consists of a magnetostrictive galfenol (Fe-Ga alloy) layer bonded to a non-magnetic flexible metal layer, a pickup coil wound around the bimetallic strip and an electrical load. Permanent magnets are used to set a magnetic bias field and to provide a tip mass load at the free end of the cantilevered unimorph. The electrical load is connected to the pickup coil, such that vibration in the magnetostrictive alloy layer caused by the vibrating structure generates electrical energy that is dissipated by the electrical load, thereby damping the vibrations in the structure. The pickup coil output voltage varies with fluctuation in the magnetic flux density due to vibration of the beam. The electrical load discussed in this paper includes an inductance and a resistor (work that also includes capacitance is on-going). An electromechanical circuit model of the electrically loaded magnetostrictive unimorph system is used to study system dynamics. For this purpose the circuit description is simplified by a transformation of the electrical and magnetic elements into the mechanical domain. The network model of this system and simulations of its dynamic behavior are presented.

This study will present a proof-of-concept non-contact strain sensor, utilizing a prototype magnetostrictive (Fe-Ga alloy, Galfenol) strip on a steel plate; coupled mechanical-magnetostrictive equations will be used to evaluate sensor performance prediction. In contrast with typical piezo-ceramic materials, Galfenol is ductile and has an excellent ability to withstand mechanical shock. Galfenol also changes its permeability in response to applied stress. This stress-based permeability change is not time dependent and can measure static loads. The variation of magnetic induction with stress depends strongly on bias magnetic field. Typically, the performance of Galfenol is measured in a compressional load region because it has higher response there. However, in this study, we are aiming to develop a sensor for tensile stress measurement. To achieve a compression load in the sensing element, a Galfenol strip is aligned perpendicular to a tension bar, so that tension in the bar creates compression in the strip, via the Poisson effect. The experimental setup in this study consists of a polycrystalline Galfenol strip bonded in the horizontal direction of a steel dog-bone shaped tension specimen. Two permanent magnets are attached at both ends of the Galfenol strip to provide a magnetic bias field through the strip. The magnetic flux through the Galfenol strip is measured with a non-contact Hall sensor during the tensile load test. The design reported here aims at low frequency applications, such as static and dynamic tension monitoring.

The magnetorheological Brake (MRB) is an electromechanical brake in which smart magnetorheological (MR) fluids have been utilized to generate the required braking torque. The purpose of this study is to design optimize a real-size MRB for automobile applications considering geometrical, material and magnetic circuit parameters. The mathematical equations governing the system’s braking torques are derived. The dynamic range of a disk-type MRB expressing the ratio of generated toque at on and off states has been formulated as a function of the rotational speed, geometrical and material properties, and applied electrical current. The magnetic circuit analysis of the proposed MRB is performed to find the relation between magnetic field intensity and the applied electrical current as a function of the MRB geometrical and material properties. Finally, a multidisciplinary design optimization problem has been formulated to identify the optimal brake geometrical parameters to maximize the dynamic range of the MRB under weight, size and magnetic flux density constraints. The optimization problem has been solved using combined Genetic Algorithm and Sequential Quadratic Programming techniques. The optimal design is then compared with those available in the literature.

This study presents mechanical energy dissipation with a proof-of-concept prototype magnetostrictive (Fe-Ga alloy, galfenol) based shunt circuit using passive electrical components. Magneto strictive material can harvest electricity out of the structural vibrations based on the Villari effect using permanent magnet and pickup coil configuration. The device in this study consists of a polycrystalline galfenol strip bonded to a brass cantilever beam. Two brass pieces, each containing a permanent magnet, are used to mass load at the end of the beam and to provide a magnetic bias field through the galfenol strip. The voltage induced in an induction coil closely wound around the cantilever beam captures the time rate of change of magnetic flux within the galfenol strip as the beam vibrates. To dissipate the electrical voltage output from the pickup coil and/or to change the phase of eddy current from the magnetic flux density fluctuation, a shunt circuit is attached. The effective mechanical impedance for the magnetostrictive shunt circuit is derived in a model. The effectiveness of a series L-R and L-C shunt circuit is demonstrated theoretically and experimentally. The non-linear model parameters, which include the mechanical-magnetic coupling factors, α and α T , and the permeability of galfenol, β , are extracted from experimental measurement. The shunted magnetostrictive damping model of both resistive and capacitance shunt cases compare well with the experimental results.

A globally convergent and fully coupled magnetomechanical model for 3D magnetostrictive systems is presented. In magnetostrictive actuators, magnetic field and stress inputs generate magnetic flux density and strain. We refer to models that follow this scheme as direct models (no relation to the direct magnetomechanical effect). In certain design and control situations, inverse models are necessary in which the magnetic field and stress are found from specified magnetic flux density and strains. This inversion typically involves an iterative procedure, which may be prone to convergence issues. An inverse model approach is proposed for arbitrary magnetostrictive materials. The inversion requirement is a continuous and second order differentiable direct model for any chosen magnetostrictive material. The approach is globally convergent, which makes it ideal for use in finite element frameworks. The premise of the proposed iterative system model is to constitute a recursive correction formula based on second order approximations of a novel scalar error function which allows to achieve a faster convergence rate. A continuation approach is then used to achieve global convergence for arbitrary input parameters. To illustrate, Galfenol is chosen as the magnetostrictive material, and analytical derivations of the Jacobian and Hessian matrices are presented. Finally, the computational efficiency of the proposed approach is shown to compare favorably against existing models.

Smart materials, such as thermal or magnetic shape memory alloys, provide interesting characteristics for new solid state actuators. However, their behavior is highly nonlinear and determined by strong hysteresis effects. This complex behavior must be adequately considered in simulation models which can be applied for efficient actuator design and optimization. We present a new phenomenological lumped element model for magnetic shape memory alloys (MSM). The model takes into account the two-dimensional hysteresis of the magnetic field induced strain as a function of both the compressive stress and the magnetic flux density. It is implemented in Modelica . The model bases on measured limiting hysteresis surfaces which are material specific. An extended Tellinen hysteresis modeling approach is used to calculate inner hysteresis trajectories in between the limiting surfaces. The developed model provides sufficient accuracy with low computational effort compared to finite element models. Thus, it is well suited for system design and optimization based on network models. This is demonstrated with exemplary models of MSM based actuators. System models and simulation results are shown and evaluated for different topologies.

Fiber reinforced composites (FRP) for industrial applications face constantly increasing demands regarding efficiency, reliability and economy. Furthermore, it was shown that FRP’s with tailored reinforcements are superior to metallic or monolithic materials. However, a trustworthy description of load-specific failure behaviour and damage evolution of composite structures can hardly be given, because these processes are very complex and are still not entirely understood. Amongst other things, several research groups have shown that material damages like fiber fracture, delamination, matrix cracking or flaws can be discovered by analyzing the electrical properties of conducting composites, e.g. carbon fiber reinforced plastics (CFRP). Furthermore, it was shown that this method could be used for structural health monitoring or non-destructive testing (NDT) [8–12].Within this work, Magnetic Induction Tomography (MIT), which is a new imaging approach, is introduced into the topic of NDT of CFRP’s. This non-contacting imaging method gains the inner spatial distribution of conductivity of a specimen and depicts material inhomogeneity, like damages, in 2D or 3D images. Numerical and experimental investigations are presented and give a first impression of the performance of this technique. It is demonstrated that MIT is a promising approach for NDT and could be used for fabrication quality control of conductive FRP’s and could potentially be used as a health monitoring system using an integrated setup.

In this paper, numerical models are constructed to analyze the magneto-mechanical interaction in a laminate embedded with terfenol-D (TD) for sensing purposes. The first model is a linear 3D model constructed in multi-physics finite element software and examines mechanical and magnetic sensing parameters of a sensing layer embedded in a composite laminate with a delamination along the sensing layer. The structural plies in the model are defined with the anisotropic properties of T300/ carbon fiber reinforced polymer (CFRP) plies. The results of the first model show that there is a local change in stress and strain in the region of the delamination. However, by assuming the magnetic permeability is constant in the constitutive sensing equation, the sensing parameter (magnetic flux density) does not change as a function of stress but only magnetic field intensity. The second model is a 2D boundary element model constructed in FADD2D that analyzes the stress intensity factors generated by a crack in a beam of similar geometry and loading configuration. It is loaded mechanically through two endpoints on a beam and the crack is offset from the center of the beam. The results of the second model show no significant stress increase in the crack region due to the Poisson’s effect creating crack closure on the crack. These models are used to analyze the mechanical and magnetic mechanisms that allow Terfenol-D to be used as an embedded sensor in composites.

Magnetorheological elastomers (MREs) are a re-emerging class of smart materials whose novel behavior stems from their response to magnetic fields. Historically comprised of soft-magnetic carbonyl (spherical) iron particles embedded in highly compliant matrix materials, MRE research has focused on their apparent change in shear modulus (in excess of 60%) under a magnetic field. Recent work by the authors has departed from the experimental and theoretical focus on MREs made from soft-magnetic particles (S-MREs) to investigate MREs having hard-magnetic particle inclusions (H-MREs). While H-MRE materials do not perform well in dynamic shear stiffness applications when compared to the traditional S-MREs, H-MREs provide remotely powered, fully reversible actuation capabilities that S-MREs are unable to achieve. In addition, in the same dynamic shear stiffness applications these H-MREs provide a measure of active control of which S-MREs are also incapable. This work examines the role that particle magnetization, developed due to shape anisotropy, plays in the actuation response S-MREs in contrast to H-MREs. H-MRE response is predicated on the response of the hard-magnetic particles to the external magnetic field and to neighboring particles. Since hard-magnetic particles have an internal preferred magnetic orientation, they are able to generate torques at the particle level, T = M × B , where T is the torque density, M is the magnetization, and B is the local magnetic flux density. In contrast, soft-magnetic particles may develop an induced magnetization when exposed to an external field if the particles exhibit shape anisotropy. This induced magnetization is also capable of producing torque at the particle level, however, spherical particles like those historically used in MREs are geometrically isotropic and therefore do not develop induced magnetization either and consequently the widely studied MREs comprised of soft-magnetic spherical particles generate no torque at the particle level. Shape anisotropy further complicates the mechanical response by inducing Eshelby-type shape-dependent effects on the mechanical stresses developed local to the particle. These effects vary the local particle rotation, resulting from a given macroscopic loading, and in turn affect the local magnetic field by changing the particle’s magnetization axis with respect to the external field. The result is a material system whose elastomagnetic response depends on particle shape and orientation as well as on particle magnetization. In previous works the authors used barium hexaferrite (a hard magnetic material) and carbonyl iron powders to generate MRE materials having varying particle alignment and magnetization permutations. These materials were examined in cantilever bending modes to assess and differentiate their abilities as bending actuators. In this work, finite element studies mirroring the bending tests are performed to determine the role of particle/magnetization anisotropy on the behavior. Results show strong dependence on particle shape anisotropy.

Numerical models are generated for magneto-mechanical analysis of Terfenol-D embedded in a carbon fiber laminate with delaminations. The modeling is broken down into three stages; each having studies to observe the affect of the controlling parameters on the magnetic signature. The first stage, which is presented in this paper, involves modeling the magnetostrictive layer and excitation coil. This stage contains three preliminary studies to observe the affect of the controlling parameters on the magnetic flux density. The modeling geometry and the magneto-mechanical properties of the magnetostrictive particle (MSP) layer, Terfenol-D, were also defined. Study I consisted of models with 1, 15, 30, and 100 subdomains in the Terfenol-D layer to simulate particulate actuation. The results revealed that subdomain refinement has a significant affect, altering the magnetic flux density by at least one order of magnitude. Furthermore, the study revealed that the magnitude of the magnetic flux density converged at 15, 30, and 100 divisions. Study II was conducted to investigate the affect of the alternating current frequency on the magnetic flux density magnitude. The frequency was varied from 100 Hz to 3000 Hz on all the models. The results from the frequency variation study revealed that flux density of the Terfenol-D modeled with the 15, 30, and 100 divisions was not significantly affected by the change in frequency from 100–3000 Hz. Study III uses Ampere’s Law and a magnetostriction equation for the magnetic flux density to analytically validate the numerical results from the flux density plot. The initial results reveal that the numerical results follow the correct trend, but the magnitudes are being validated. A preliminary model for the second stage, which consists of modeling the Terfenol-D layer embedded in a carbon fiber laminate, is shown. Experimental samples were also made to validate the numerical results in the future. These samples are made of unidirectional prepreg carbon fiber embedded with Terfnol-D. They have varying internal delaminations, ply orientations, and number of plies. The results presented in this work are preliminary, and will be used as a foundation for continuing this research.

The response time of magnetorheological (MR) fluids to an external magnetic field is a few milliseconds. However, the overall response time in MR devices under a magnetic field is a function of electromagnetic parameters, the capabilities of the driving electronics, as well as, the operation conditions. Therefore, the overall response time of a MR device depends on the internal device design parameters. In this work, the response times of MR fluid and MR fluid valves have been studied under various flow configurations. Two types of valving geometries; annular flow, and radial flow are considered in the MR fluid valve designs. The transient pressure response of MR fluid valves are evaluated by using a diaphragm pump with a constant volume flow rate. The performance of each MR valve is characterized using a voltage step input, as well as, a current step input while recording the activation electric voltage/current, magnetic flux density, and pressure drop as a function of time. The variation of the response time of the MR valves under constant volume flow rate is experimentally investigated. The system’s time constant is determined under induced pressure changes. In order to obtain the response time of the MR fluid a Maxwell model with a time constant is employed to describe the field induced pressure behavior of MR fluid under a steady flow. The results demonstrate that the pressure response times of the MR fluid and the MR valves depend on the designs of the electric parameters and the valve geometry. MR valves in annular flow geometry have a slow falling response time compared to their rising response time. MR valves in radial flow geometry result in faster pressure response times both in rising and falling states.

Magneto-rheological (MR) fluids have been successfully introduced to prosthetic devices. One such a device is a biomechanical prosthetic knee joint that uses a MR fluid to actively control its rotary stiffness while an amputee walks. The knee is a synergy of artificial intelligence, advanced sensors and MR actuator technology. The MR fluid has response time in the order of milliseconds, making it possible to vary the knee’s stiffness in real-time, depending on sensors data. The focus of this paper is on the design of the magnetic circuit of the actuator and on the geometry of the fluid chamber. The paper describes the function of the MR rotary actuator and shows how design optimization techniques can aid in the development of the actuator. The design is optimized, with respect to three important design objectives. These objectives are: the maximum obtainable field-induced braking torque, the minimum obtainable rotary damping in the absence of a magnetic field, and the weight of the actuator. Multi-objective design optimization techniques are presented and applied to the prosthetic knee actuator design problem. Trade-offs between design objectives are investigated giving valuable information on the development of the actuator. Maximizing the field-induced braking torque is important for the knee to be capable of supporting heavy amputees. Minimizing the off-state stiffness is important for fast movements of the knee, in load-free movements. Furthermore, minimizing the weight of the actuator is important for allowing heavy components like batteries to be installed. It is realized that these design objectives can not be addressed separately and to some extend, the design goals are contradictory. Mathematical models are presented that describe the design objectives as a function of selected design parameters. Determining the field-induced braking torque requires a magnetic finite element analysis, to evaluate the magnetic flux density in the MR fluid, and the shear-yield stress curve of the MR fluid. Evaluating the off-state stiffness requires the off-state viscosity of the MR fluid, along with friction in bearings and oil seals. The models are based on rheological measurements of the MR fluid employed in the knee. Evaluating the weight of the actuator requires the geometry of the actuator and the density of its materials. The optimization is restricted by practical manufacturing design constraints. Mapping the dependency between the maximum torque, the minimum damping, and the weight of the MR actuator gives valuable insight into the design of the prosthetic knee actuator.

Regaining biomechanical function, comfort and quality of life is a prime consideration when designing prosthetic limbs. Recently, microprocessor-controlled prosthetic knees, which rely on magneto-rheological (MR) technology, have become available and have the potential to meet these needs. One of these promising products is a prosthetic knee manufactured by the company Ossur Inc. The knee is a synergy of artificial intelligence, advanced sensors and MR actuator technology. A critical factor in the success of the prosthetic knee is the composition of the MR fluid. In the prosthetic actuator, the fluid is used in shear mode in a micron-sized fluid gap. The characteristics of the MR fluid, such as, the off-state viscosity, the field-induced shear yield stress, the post-yield viscosity, and the particle sedimentation rate, determine the properties of the prosthetic knee. This paper describes a novel perfluorinated polyether (PFPE)-based MR fluid with properties that are tailored for the requirements of the prosthetic knee actuator. Rheological measurements of monodisperse and bidisperse PFPE-based fluid mixtures are presented. The monodisperse fluid consists of micron-sized carbonyl iron particles and the bidisperse mixture contains micron- and nano-sized particles. A few different concentrations of nano particles are investigated; first by holding the total solid concentration constant, and then by increasing the total solid concentration, to exceed that of the MR fluid containing only micron-sized particles. An MR fluid composition is sought that has a suitable balance between field-induced strength, off-state viscosity and sedimentation rate, for the proposed application. This balance is determined by desired qualities of the prosthetic knee and relate directly to the MR fluid. The field-induced shear stress of MR fluid samples is measured as a function of the magnetic flux density along with the off-state viscosity as a function of the shear-rate. The shear stress and off-state viscosity at high-shear rates are of particular interest, since the working shear rate in the prosthetic knee is high, due to the micron-sized gap between the blades in the fluid chamber of the actuator. Mathematical models are presented that describe how the MR fluid properties relate to the behavior of the prosthetic knee. The paper shows how a tailored design of an MR fluid can further the success of the MR prosthetic knee.

Magnetic shape memory alloys (MSMAs) are relatively new materials that exhibit a magnetic shape memory effect as a result of the rearrangement of martensitic variants under the influence of magnetic fields. Due to the MSMAs newness there is limited understanding of their magneto-mechanical behavior. This work presents experimental and modeling results of MSMAs for cases in which the material is loaded and unloaded in uniaxial compression in the presence of a constant magnetic field. The experiments are performed with the magnetic field applied perpendicular and at an angle to the mechanical loading axis. During the loading and unloading process, the evolution of the magnetic flux density is monitored to assess the potential of these materials for power harvesting applications. The modeling is based on the thermodynamic approach proposed by Kiefer and Lagoudas [1]. This model was modified and calibrated to reproduce material response under biaxial constant magnetic field and variable uni-axial compressive stress. Comparing the experimental and simulated results, one can recognize that further work is needed to improve the model.

The bidirectionally coupled magnetoelastic model (BCMEM) developed by [1] has been modified to include electric currents in its magnetic finite element formulation. This enables the model to capture the magnetoelastic behavior of magnetostrictive materials subjected to elastic stresses and magnetic fields applied not only by permanent magnets but also by current carrying coils used often in actuator applications. This model was implemented by combining COMSOL Multiphysics 3.4 (Finite Element Modeling software) with an energy-based non-linear magnetomechanical constitutive model. The coupling variables are magnetostriction and magnetic permeability that are dependent on both magnetic (magnetic flux density) and mechanical (stress) properties. In this research, the BCMEM was used to simulate actuator load lines for a magnetostrictive Fe 84 Ga 16 alloy, which were then compared to experimental data [2]. Also, the ability of the model to capture the presence of the ΔE effect in Galfenol was demonstrated using the BCMEM. Finally, the use of the BCMEM to as a tool for transducer design optimization is demonstrated by using the model to visualize the influence of different magnetic circuit designs on transducer performance.

The recent discovery of Iron-Gallium alloy (Galfenol) as a “large” magnetostrictive material (as high as 400 ppm) offers a particularly promising transducer material that combines largely desirable mechanical attributes with superior magnetic properties [1]. The high permeability of this material makes it easy to magnetize, however it also causes a relatively low cutoff frequency in dynamic applications, above which eddy currents form and introduce significant power losses. To reduce the eddy current losses, magnetostrictive drivers used in dynamic applications are commonly laminated. A second transducer design consideration is the introduction of an initial alignment of domains inside of the material to maximize the magnetostriction performance. It is common to achieve this by imposing an external compressive prestress to align magnetic moments perpendicular to the direction of actuation. An alternative to the application of an external prestress is to build-in a uniaxial magnetic anisotropy through stress annealing [2]. Stress annealing is a high temperature process with simultaneous application of an external load and subsequent cooling under load in which the magnetic moment alignment developed at temperature is retained upon removal from the stress annealing fixture. The external load needed to build in a useful uniaxial magnetic anisotropy in Galfenol is greater than the buckling load for Galfenol laminae sized for use in high frequency dynamic applications. In this study, prior work on stress annealing of solid rods of single and polycrystalline samples of Galfenol is successfully extended to thin laminae of Galfenol by introducing fixtures to avoid buckling of the laminae under compression during the heat treatment process. Values of the uniaxial anisotropy, cubic anisotropy, saturation magnetic induction, and saturation magnetostriction were obtained from measurements of the magnetization and magnetostriction of stress-annealed Galfenol strip as a function of compressive and tensile stress. These values were derived from fitting magnetization and magnetostriction curves to the energy expression formula [3]. Data are presented that demonstrate the magnetic uniaxial anisotropy developed by stress annealing of laminated Galfenol rods. An annealing temperature of 500 °C and a compressive stress of 200 MPa produced a uniaxial anisotropy of 11.3 kJ/m 3 in this study.