KEYWORDS: 3D modeling, Magnetism, Transducers, Actuators, Systems modeling, Finite element methods, Data modeling, Chemical elements, Magnetostrictive materials, Electromagnetism
Galfenol is an alloy of iron and gallium which possesses a unique combination of structural strength and significant
magnetostriction. This alloy can be machined, welded and extruded into complex geometries opening
up avenues for a new class of load-bearing transducers with 3D functionality. This work addresses the development
of an advanced modeling tool to aid in the design of Galfenol transducers. The model describes the full
nonlinear coupling between the electrical, magnetic and mechanical domains in 3D Galfenol structures, yielding
complete system input-output relationships. Maxwell's equations for electromagnetics and Navier's equations for
mechanical systems are formulated in weak form. An energy-averaged constitutive model is employed to relate
magnetization and strain to magnetic field and stress in the Galfenol domain. The overall system is approximated
hierarchically; first, piecewise linearization is used to describe quasi-static responses and 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 input fields and stresses are described through
an implicit dynamic solution based on the trapezoidal rule. The model equations are solved on a commercial
finite element solver. A case study consisting of a Galfenol unimorph is presented which illustrates the model's
ability to describe transient dynamic responses.
A coupled axisymmetric finite element model is formulated to describe the dynamic performance of a hydraulically
amplified Terfenol-D mount actuator. The formulation is based on the weak form representations of Maxwell's
equations for electromagnetics and Navier's equation for mechanical systems. Terfenol-D constitutive behavior
is modeled using a fully coupled energy averaged model. Fluid pressure is computed from the volumetric
deformation of the fluid chamber and coupled back to the structure as tractions on the boundaries encompassing
the fluid. Seal friction is modeled using the Lugre friction model. The resulting model equations are coded into
COMSOL (a commercial finite element package) which is used for meshing and global assembly of matrices.
Results show that the model accurately describes the mechanical and electrical response of the actuator under
static and dynamic conditions. At higher frequencies there are some errors in the phase due to the anhysteretic
nature of the Terfenol-D constitutive law. A parametric study reveals that the performance of the actuator can
be significantly improved by stiffening the fluid chamber components and reducing seal friction.
A model is developed which describes the dynamic response of a Terfenol-D actuator with a hydraulic displacement
amplification mechanism for use in active engine mounts. The model includes three main components:
magnetic diffusion, Terfenol-D constitutive model, and mechanical actuator model. Eddy current losses are
modeled as a one-dimensional magnetic field diffusion problem in cylindrical coordinates. The Jiles-Atherton
model is used to describe the magnetization state of the Terfenol-D driver as a function of applied magnetic
fields. A quadratic, single-valued model for the magnetostriction dependence on magnetization is utilized which
provides an input to the mechanical model describing the system vibrations. Friction at the elastomeric seals is
modeled using the LuGre friction model for lubricated contacts. The actuator's dynamic response is quantified
in terms of the output displacement in the unloaded condition and force output in the loaded condition. The
model is shown to accurately quantify the dynamic behavior of the actuator over the frequency range considered,
from near dc to 500 Hz. An order analysis shows that the model also describes the higher harmonic content
present in the measured responses. A study on the variation of energy delivered by the actuator with the load
stiffness reveals that the actuator delivers the highest energy output near the stiffness match region.
A bidirectional magnetostrictive actuator with millimeter stroke and a blocked force of few tens of Newtons
has been developed based on a Terfenol-D driver and a simple hydraulic magnification stage. The actuator
is compared with an electrodynamic actuator used in active powertrain mounts in terms of electrical power
consumption, frequency bandwidth, and spectral content of the response. The measurements show that the
actuator has a flat free-displacement and blocked-force response up to 200 Hz, suggesting a significantly broader
frequency bandwidth than commercial electromagnetic actuators while drawing comparable amounts of power.
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