Modeling of Three-Dimensional Magnetostrictive Systems with Application to Galfenol and Terfenol-D Transducers

Magnetostrictive materials deform in response to applied magnetic fields and change their magnetic state when stressed. Because these processes are due to moment realignments, magnetostrictive materials are ideally suited for sensing and actuation mechanisms with a bandwidth of a few kHz. Significant research effort has been focused on two magnetostrictive alloys: Terfenol-D (an alloy of terbium, iron and dysprosium) and Galfenol (an iron gallium alloy), for their ability to produce giant magnetostrictive strains at moderate fields. Terfenol-D has higher energy density and magnetomechanical coupling factor than Galfenol but it is brittle and suffers from poor machinability. Galfenol on the other hand has excellent structural properties. It can be machined, welded, extruded into complex shapes for use in transducers with 3D functionality.;Advanced modeling tools are necessary for analyzing magnetostrictive transducers because these materials exhibit nonlinear coupling between the magnetic and mechanical domains. Also, system level electromagnetic coupling is present through Maxwell's equations. This work addresses the development of a unified modeling framework to serve as a design tool for 3D, dynamic magnetostrictive transducers. Maxwell's equations for electromagnetics and Navier's equations for mechanical systems are formulated in weak form and coupled using a generic constitutive law. The overall system is approximated hierarchically; first, piecewise linearization is used to describe quasistatic responses and perform magnetic bias calculations. A linear dynamic solution with piezomagnetic coefficients computed at the bias point describes the system dynamics for moderate inputs. Dynamic responses at large inputs are obtained through an implicit time integration algorithm. The framework simultaneously describes the effect of magneto-structural dynamics, flux leakages, eddy currents, and transducer geometry. Being a fully coupled formulation, it yields system level input-output relationships and is applicable to both actuators and sensors.;An anhysteretic 3D discrete energy-averaged constitutive law for Galfenol is incorporated into the framework to describe the dynamic performance of Galfenol transducers. A parameter identification algorithm is developed which takes as input the 1D material characterization curves and calculates the 3D constitutive model parameters. The algorithm is embedded within the finite element model such that the only inputs required are the constitutive parameters for passive materials (permeability, conductivity, Young's modulus etc.), the transducer geometry, and the 1D magnetostrictive material characterization curves. A case study on a Galfenol unimorph actuator illustrates the model's ability to accurately describe the dynamic mechanical and magnetic response of Galfenol transducers. A new energy-averaged model is formulated for Terfenol-D based on an implicit definition of domain volume fractions and a weighted anisotropy energy. The model is shown to simultaneously describe the strain-field and magnetization-stress behavior of Terfenol-D. The 3D finite element model is reduced to a 2D axisymmetric form to exploit the axisymmetric geometry of Terfenol-D transducers. The model describes the dynamic mechanical and electrical response of a hydraulically amplified Terfenol-D mount actuator. A parametric study on the actuator shows the applicability of the model to transducer design optimization.