Phillip G. Evans

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 Implementation of a Hybrid Nonlinear Control Design for Magnetostrictive Actuators

Abstract : A hybrid nonlinear optimal control design is experimentally implemented on a ferromagnetic Terfenol-D actuator to illustrate enhanced tracking control at relatively high speed. The control design employs a homogenized energy model to quantify rate-dependent nonlinear and hysteretic ferromagnetic switching behavior. The homogenized energy model is incorporated into a finite-dimensional nonlinear optimal control design to directly compensate for the nonlinear and hysteretic ferromagnetic constitutive behavior of the Terfenol-D actuator. Additionally, robustness to operating uncertainties is addressed by incorporating proportional-integral (PI) perturbation feedback around the optimal open loop response. Experimental results illustrate significant improvements in tracking control in comparison to PI control. Accurate displacement tracking is achieved for sinusoidal reference displacements at frequencies up to 1 kHz using the hybrid nonlinear control design whereas tracking errors become significant for the PI controller for frequencies equal to or greater than 500 Hz.

State-Space Constitutive Model for Magnetization and Magnetostriction of Galfenol Alloys

We present a thermodynamic model that quantifies the magnetization and magnetostriction of annealed or unannealed Galfenol alloys subjected to magnetic fields and mechanical stresses. The model requires a small number of parameters directly related to physical properties of the data, thus providing a useful tool for material characterization and design. Furthermore, the model is formulated in state-space form, which simplifies computations for design and control of Galfenol devices.

Dynamic Model for 3-D Magnetostrictive Transducers

A comprehensive analytical framework is developed for the study of magnetostrictive transducers with arbitrary geometries operated in dynamic regimes. Weak form equations are derived from Maxwells equations and linear momentum without restricting the form of the constitutive behavior of the magnetostrictive material. For validation, the framework is implemented for a unimorph beam actuator which has both active and passive media.

Efficient model for field-induced magnetization and magnetostriction of Galfenol

A fully coupled, nonlinear model is presented that characterizes the three-dimensional (3D) strain and magnetization response to magnetic field at constant stress in cubic magnetostrictive materials. A multiscale thermodynamic approach is taken which accounts for nonlinear anisotropy, material texture, and hysteresis effects. The model is validated with measurements of textured polycrystalline Galfenol. The model provides an efficient framework for characterization, design, and control of Galfenol (Fe–Ga) devices with 3D functionality subjected to combined magnetic field and stress loading.

Optimization and Dynamic Modeling of Galfenol Unimorphs

Design and modeling of a bi-laminate, Galfenol-driven composite beam is presented in which the elasticity of the adhesive layer is considered. The optimal thickness ratio necessary to maximize the tip deflection is found by minimization of the internal energy of the beam. Model simulations show that use of a substrate material with high modulus leads to larger tip deflections. Stainless steel was therefore utilized as substrate in the experiments. In order to reduce eddy currents, a laminated silicon steel frame was employed to magnetize the beam. A dynamic model is proposed by coupling the structural dynamics of the beam and adhesive layer with the magnetostriction generated by the Galfenol layer. The latter is described with a linear piezomagnetic law with uniform magnetic field distribution along the length of the beam. Galerkin discretization combined with Newmark numerical integration are employed to approximate the dynamic response of the beam. The model is shown to describe both the transient and steady-state response of the composite beam tip displacement under harmonic excitation between 10 and 320 Hz. The RMS error between model and data range between 1.44% at 10 Hz and 6.34% at 320 Hz, when the same set of model parameters (optimized at quasistatic frequency) is utilized.

Recursive Memory-based Hysteresis Modeling for Solid-state Smart Actuators

This article presents a new modeling approach for the memory-dependent hysteresis phenomenon in a broad class of smart structures and systems. We propose a recursive formulation to relate the minor hysteresis trajectories to their surrounding loops. More specifically, each internal (minor) trajectory targets its previous turning point and converges to its neighboring loop with a tunable exponential rate. By applying the ‘curve alignment’ and the ‘wiping out’ properties at the turning points, we present a new strategy within the context of a memory-based hysteresis modeling framework. A Galfenol-driven micropositioning actuator and a piezoelectrically driven nanopositioning stage are used to experimentally validate the model. Galfenol exhibits large butterfly-type nonlinearity with a small hysteresis effect, while the piezoelectric actuator exhibits wide hysteresis loops. The model is able to precisely predict the major and minor hysteresis loops in both the Galfenol and piezoelectric actuators, and is expected to be effectively and conveniently applicable to general systems exhibiting memory-dependent hysteresis.

Experimental Implementation of a Nonlinear Control Method for Magnetostrictive Transducers

In this paper, we discuss the development and experimental implementation of a nonlinear control design for magnetostrictive transducers operating in hysteretic regimes. The hysteresis and constitutive nonlinearities are characterized using a homogenized energy framework based on energy relations at the lattice level employed in combination with stochastic homogenization techniques that incorporate material and field nonhomogeneities. Using this framework, we employ nonlinear optimal control theory to construct open loop inputs for tracking. We subsequently employ Pi-based perturbation feedback to ensure robustness with respect to model uncertainty and sensor noise. Experimental implementation results at frequencies up to 1000 Hz demonstrate the feasibility of the method for high speed tracking while operating in highly nonlinear operating regimes.

Stress-dependent susceptibility of Galfenol and application to force sensing

A sensing principle, operating regime, and composition range are identified for force sensing with Galfenol alloys. Magnetization measurements of Fe79.1Ga20.9 and Fe81.6Ga18.4 are performed under applied magnetic field at constant stress. Stress-dependent, linear regions with negligible hysteresis are observed in the Fe79.1Ga20.9 sample over a large range of fields and stresses, for which an analytic model for unbiased loops is formulated. Similar regions are observed in the Fe81.6Ga18.4 sample, with a more limited stress and field range. The small signal operating regime (small in field, not in stress) centered about zero magnetic field is particularly advantageous because in this regime there is no observable hysteresis, since the magnetization process occurs by domain rotation only. The measurements and model show that in this region the susceptibility of Fe79.1Ga20.9 is more sensitive to stress (owing to a significantly lower fourth-order anisotropy constant) with only a small reduction in the saturat...

Fully-coupled magnetoelastic model for Galfenol alloys incorporating eddy current losses and thermal relaxation

A general framework is developed to model the nonlinear magnetization and strain response of cubic magnetostrictive materials to 3-D dynamic magnetic fields and 3-D stresses. Dynamic eddy current losses and inertial stresses are modeled by coupling Maxwells equations to Newtons second law through a nonlinear constitutive model. The constitutive model is derived from continuum thermodynamics and incorporates rate-dependent thermal effects. The framework is implemented in 1-D to describe a Tonpilz transducer in both dynamic actuation and sensing modes. The model is shown to qualitatively describe the effect of increase in magnetic hysteresis with increasing frequency, the shearing of the magnetization loops with increasing stress, and the decrease in the magnetostriction with increasing load stiffness.