Marcelo J. Dapino

Structural magnetic strain model for magnetostrictive transducers

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.

Free energy model for hysteresis in magnetostrictive transducers

This article addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed for homogeneous materials with constant internal fields. In the second step, the effects of material nonhomogeneities and nonconstant effective fields are incorporated through the construction of appropriate stochastic distributions. Properties of the model are illustrated through comparison and prediction of data collected from a typical Terfenol-D transducer.

Overview of Magnetostrictive Sensor Technology

As sensors become integrated in more applications, interest in magnetostrictive sensor technology has blossomed. Magnetostrictive sensors take advantage of the efficient coupling between the elastic and magnetic states of a material to facilitate sensing a quantity of interest. Magnetic and magnetostrictive theory pertinent to magnetostrictive sensor technology is provided. Sensing configurations are based on the utilization of a magnetostrictive element in a passive, active, or combined mode. Magnetostrictive sensor configurations that measure motion, stress or force, torque, magnetic fields, target characteristics, and miscellaneous effects are discussed. The configurations are compared and contrasted in terms of application, sensitivity, and implementation issues. Comparisons are made to other common sensor configurations as appropriate. Experimental and modeling results are described when available and schematics of the configurations are presented.

A homogenized energy framework for ferromagnetic hysteresis

This paper focuses on the development of a homogenized energy model which quantifies certain facets of the direct magnetomechanical effect. In the first step of the development, Gibbs energy analysis at the lattice level is combined with Boltzmann principles to quantify the local average magnetization as a function of input fields and stresses. A macroscopic magnetization model, which incorporates the effects of polycrystallinity, material nonhomogeneities, stress-dependent interaction fields, and stress-dependent coercive behavior, is constructed through stochastic homogenization techniques based on the tenet that local coercive and interaction fields are manifestations of underlying distributions rather than constants. The resulting framework incorporates previous ferromagnetic hysteresis theory as a special case in the absence of applied stresses. Attributes of the framework are illustrated through comparison with previously published steel and iron data

A coupled structural-magnetic strain and stress model for magnetostrictive transducers

This paper addresses the modeling of strains and forces generated by magnetostrictive transducers in response to applied magnetic fields. The magnetostrictive effect is modeled by considering both the rotation of magnetic moments in response to the field and the elastic vibrations in the transducer. The former is modeled with the Jiles-Atherton model of ferromagnetic hysteresis in combination with a quartic magnetostriction law. The latter is modeled through force balancing which yields a PDE system with magnetostrictive inputs and boundary conditions given by the specific transducer design. The solution to this system provides both rod displacements and forces. The calculated forces are used to quantify the magnetomechanical effect in the transducer core, i.e., the stress-induced magnetization changes. This is done by considering a “law of approach” to the anhysteretic magnetization. The resulting model provides a representation of the bidirectional coupling between the magnetic and elastic states. It is demonstrated that the model accurately characterizes the magnetic hysteresis in the material, as well as the strains and forces output by the transducer under conditions typical of engineering applications.

Efficient magnetic hysteresis model for field and stress application in magnetostrictive Galfenol

We present a discrete energy-averaged model for the nonlinear and hysteretic relation of magnetization and strain to magnetic field and stress. Analytic expressions from energy minimization describe three-dimensional rotations of domains about easy crystal directions in regions where domain rotation is the dominant process and provide a means for direct calculation of magnetic anisotropy constants. The anhysteretic material behavior due to the combined effect of domain rotation and domain wall motion is described with an energy weighted average while the hysteretic material behavior is described with an evolution equation for the domain volume fractions. As a result of using a finite set of locally defined energy expressions rather than a single globally defined expression, the model is 100 times faster than previous energy weighting models and is accurate for materials with any magnetocrystalline anisotropy. The model is used to interpret magnetization and strain measurements of ⟨100⟩ oriented Fe79.1Ga20...

Experimental characterization of the sensor effect in ferromagnetic shape memory Ni–Mn–Ga

The characterization of a commercial Ni–Mn–Ga alloy for use as a deformation sensor is addressed. The experimental determination of flux density as a function of strain loading and unloading at various fixed magnetic fields gives the bias field needed for maximum recoverable flux density change. This bias field is shown to mark the transition from irreversible (quasiplastic) to reversible (pseudoelastic) stress-strain behavior. A reversible flux density change of 145mT is observed over a range of 5.8% strain and 4.4MPa stress at a bias field of 368kA∕m. The alloy investigated shows potential as a high-compliance, high-displacement deformation sensor.

A continuum thermodynamics model for the sensing effect in ferromagnetic shape memory Ni–Mn–Ga

A magnetomechanical model based on continuum thermodynamics is presented which describes the sensing effect in single-crystal ferromagnetic shape memory Ni–Mn–Ga. The model quantifies the stress and magnetization dependence on strain at different values of bias fields under isothermal conditions. A magnetic Gibbs energy is considered as the thermodynamic potential with Zeeman, magnetostatic, and anisotropy energy contributions. Constitutive equations for stress and magnetization are obtained in the isothermal case after restricting the process through the Clausius-Duhem inequality for the second law of thermodynamics. Mechanical dissipation and the microstructure of Ni–Mn–Ga are incorporated in the continuum model through the internal state variables volume fraction, domain fraction, and magnetization rotation angle. Closed-form solutions describing the evolution of the internal state variables are developed. The model requires only seven parameters identified from simple experiments: stress-strain curve ...

Statistical Analysis of Terfenol-D Material Properties:

This article focuses on the characterization of Terfenol-D material properties under magnetic bias, mechanical preloads, AC drive fields, frequencies of operation, and mechanical loads typical of many dynamic transducer applications. These are test conditions unlike those in most Terfenol-D characterization studies. The article also provides an explanation for prior experimental studies which suggest that significant variation in material properties are expected in Terfenol-D elements subjected to repeated tests under fixed operating conditions. Through a statistical framework for the design of experiments and data analysis, we conducted repeatability tests which demonstrate that such variations are likely to be due to imperfect control of the magnetic bias and mechanical preload from test to test, and not to intrinsic material behavior. Frequency response measurements from near DC to past the test transducers fundamental frequency were combined with classical electroacoustics theory to determine the functional dependence of magnetoelastic properties with respect to varying operating regimes. These properties include two elastic moduli, piezomagnetic coefficient, magnetomechanical coupling coefficient, and two magnetic permeabilities. Analysis of variance (ANOVA) calculations were employed to determine 95% prediction and confidence intervals for the overall material property trends and coefficients of variation associated with the repeatability tests.

An Active and Structural Strain Model for Magnetostrictive Transducers

We consider the modeling of strains generated by magnetostrictive materials in response to applied magnetic fields. The active or external component of the strain is due to the rotation of magnetic moments within the material to align with the applied field. This is characterized through consideration of the Jiles-Atherton mean field theory for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. The second component of the strain reflects the passive or internal dynamics of the rod as it vibrates. This is modeled through force balancing which yields a wave equation with magnetostrictive inputs. The validity of a combined transducer model is illustrated through comparison with experimental data.