Electromechanical network models are used in this paper to analyze a prototype micro-gyro sensor that employs the
magnetostrictive alloy GalFeNOL for transduction of Coriolis induced forces into an electrical output at a given angular
velocity. The sensor is designed as a tuning fork structure which reacts with vibration of the prongs in tangential
direction due to an excited vibration in radial direction. A GalFeNOL patch attached to the axial-radial-surface changes
its permeability depending on the bending. When it is surrounded by a solenoid coil and a magnet creates a bias
magnetic field in the sensor patch, then this field fluctuates with the prong vibration. The induced voltage in the sensor
coil is used as sensor output. A sinusoidal angular velocity being effective on the tuning fork structure causes an
amplitude modulation of the excitation frequency which is the carrier frequency.
A circuit representation of the electromechanical system is derived where the prongs are modeled as dynamic bending
beams. The network model enables an understanding and explanation of the behavior of this system involving different
physical domains, as well as fast analytical and numerical calculations, e.g. with pSpice. Experiments confirm the
predicted sidebands of the sinusoidal rotation.
This work investigates the equivalence of thermodynamic potentials utilizing stress-induced anisotropy energy
and potentials using elastic, magnetoelastic, and mechanical work energies. The former is often used to model
changes in magnetization and strain due to magnetic field and stress in magnetostrictive materials. The enthalpy
of a ferromagnetic body with cubic symmetry is written with magnetization and strain as the internal
states and the equilibrium strains are calculated by minimizing the enthalpy. Evaluating the enthalpy using
the equilibrium strains, functions of the magnetization orientation, results in an enthalpy expression devoid
of strain. By inspecting this expression, the magnetoelastic, elastic, and mechanical work energies are identified to be equivalent to the stress-induced anisotropy plus magnetostriction-induced fourth order anisotropy.
It is shown that as long as the value of fourth order crystalline anisotropy constant K1 includes the value of
magnetostriction-induced fourth order anisotropy constant ΔK1, energy formulations involving magnetoelastic,
elastic, and mechanical work energies are equivalent to those involving stress-induced anisotropy energy. Further,
since the stress-induced anisotropy is only given for a uniaxial applied stress, an expression is developed for a
general 3D stress.
This paper presents a magneto-elastic model developed by coupling a finite element elastic and magnetic
formulations with an energy based probabilistic magnetostrictive model. Unidirectional coupled model is
presented first for both sensor and actuator applications and then a fully coupled bidirectional model is developed.
The unidirectional sensor model was validated against experimental results for a 1.58 mm diameter and 32.74 mm
long Galfenol cantilever beam. The model was further used to investigate the response of Galfenol nanowire array
that will be used in a nanowire acoustic sensor. Model predictions suggest that differences in the phase of bending
motion of nanowires in an array will not produce a significant effect on the magnetic response of the array. It also
predicts that the response of a single nanowire can be measured by a magnetic sensor with active measurement
area much larger than the nanowire dimensions.