Suryarghya Chakrabarti

A dynamic model for a displacement amplified magnetostrictive driver for active mounts

A magnetostrictive actuator with a hydraulic displacement amplification mechanism is designed to be used as a driver in active engine mounts. The dynamic response of the actuator is quantified in terms of the output displacement and the magnetostriction. Eddy current losses are modeled as a one-dimensional magnetic diffusion problem in cylindrical coordinates. The Jiles-Atherton model is used to describe the magnetization state of the material as a function of applied magnetic fields. Magnetostriction, which is modeled as a single-valued function of magnetization, provides an input to the mechanical model describing the system vibrations. Friction at the elastomeric seals is modeled using the LuGre (Lund-Grenoble) friction model for lubricated contacts. Results show that the model accurately describes the dynamic behavior of the actuator up to 500 Hz. An order analysis of the data and calculated responses shows that the model describes the fundamental and higher-order spectral components generated by the device.

Nonlinear finite element model for 3D Galfenol systems

This work addresses the development of an advanced modeling tool which describes the full nonlinear coupling in three-dimensional (3D) Galfenol transducers to provide system level input–output relationships. Maxwells equations for electromagnetics and Naviers equations for mechanical systems are formulated in weak form. The constitutive behavior of Galfenol is described through a nonlinear discrete energy-averaged model. 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 a given magnetic bias describes the system dynamics for moderate inputs. Dynamic responses at large input fields and stresses are quantified through an implicit dynamic solution based on the trapezoidal rule. The model simultaneously incorporates the effects of eddy currents, flux leakage, structural dynamics and nonlinear material behavior. A case study on a Galfenol unimorph actuator validates the model in quasistatic and dynamic conditions.

Fully coupled discrete energy-averaged model for Terfenol-D

A fully coupled 3D energy-avaraged model is presented which describes the magnetomechanical behavior of Terfenol-D. Conventional energy averaging with eight easy axis orientations yields an unphysical kink in the magnetization response and fails to describe the gradual approach to saturation present in Terfenol-D magnetostriction. Superposition of an empirically weighted global anisotropy energy onto an anisotropy energy locally defined around each easy axis eliminates the unphysical kink in the response, while an implicit definition of the domain volume fraction describes the gradual approach to saturation. Anhysteretic bulk material response is described through a weighted sum of individual domains; the weights (or domain volume fractions) are calculated using Boltzmann-type energy averaging. A hysteretic extension is built from an evolution equation for the domain volume fractions. Although solution of the implicit equation for the anhysteretic domain volume fractions requires iteration, the model take...

Modeling of 3D Magnetostrictive Systems with Application to Galfenol and Terfenol-D Transducers

This work presents a unified approach to model three dimensional magnetostrictive transducers. Generalized procedures are developed for incorporating nonlinear coupled constitutive behavior of magnetostrictive materials into an electro-magneto-mechanical finite element modeling framework. The finite element model is based on weak forms of Maxwells equations for electromagnetics and Naviers equations for mechanical systems. An implicit time integration scheme is implemented to obtain nonlinear dynamic system responses. The model is implemented into a finite element (FE) solver and applied to two case studies, a Galfenol unimorph actuator and a magnetohydraulic Terfenol-D actuator for active engine mounts. Model results are compared with experiments, and parametric analyses are conducted which provide guidelines for optimization of actuator design.

Hydraulically Amplified Terfenol-D Actuator for Adaptive Powertrain Mounts

A magnetostrictive actuator with a stroke of 61 mm and a blocked force of 625 N has been developed based on a Terfenol-D driver and a hydraulic stroke amplification mechanism. A mechanical model for this magneto-hydraulic actuator (MHA) is formulated by combining linear piezomagnetic relations for Terfenol-D and a lumped parameter mechanical system model describing the system vibrations. Friction at the fluid seals is described by the LuGre model. The model accurately describes the frequency-domain behavior of the actuator in mechanically-blocked and mechanically-free conditions. The MHA is benchmarked against a commercial electromagnetic driver used in active powertrain mounts in terms of mechanical performance (blocked force and unloaded displacement) and electrical power consumption. Measurements show that the MHA achieves more than twice the frequency bandwidth of the commercial device in the free displacement response, along with comparable static displacements. The commercial device produces higher blocked forces in the frequency range of 10 Hz to 120 Hz beyond which the generated forces are comparable up to 400 Hz. Spectral analysis reveals significant second order components in the commercial actuator displacement response which are absent in the MHA. Further, the MHA achieves superior performance than the commercial actuator operated at maximum current (6 A) with power consumption identical to that of the commercial actuator operated at minimum current (4 A). [DOI: 10.1115/1.4004669]

Design and modeling of a hydraulically amplified magnetostrictive actuator for automotive engine mounts

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.

Parameter Optimization Algorithm of a Discrete Energy-Averaged Model for Galfenol Alloys

An optimization algorithm is proposed to determine the parameters of a discrete energy-averaged (DEA) model for Galfenol alloys. A new numerical approximation approach for partial derivative expressions is developed, which improves computational speed of the DEA model by 61% relative to existing partial derivative expressions. Initial estimation of model parameters and a two-step optimization procedure, including anhysteresis and hysteresis steps, are performed to improve accuracy and efficiency of the algorithm. Initial estimation of certain material properties such as saturation magnetization, saturation magnetostriction, Young’s modulus, and anisotropy energies can improve the convergence and enhance efficiency by 41% compared to the case where these parameters are not estimated. The two-step optimization improves efficiency by 28% while preserving accuracy compared to one-step optimization. Proposed algorithm is employed to find the material properties of Galfenol samples with different compositions and heat treatments. The trends obtained from these optimizations can guide future Galfenol modeling studies. INTRODUCTION Magnetostrictive materials deform when exposed to magnetic fields and undergo change in magnetization when stressed. Magnetostrictive iron-gallium alloys, also known as Galfenol, possess a unique combination of mechanical robustness and 1Currently affiliated with GE Global Research Center, Niskayuna, New York 12309 moderate magnetostriction. Galfenol can withstand bending, tensile, and torsional loads and can be machined, welded, or extruded into complex geometries. Thus it opens up avenues for three-dimensional (3D) functional, structural, and versatile magnetostrictive devices including energy harvesters [1, 2, 3, 4], sensors [5, 6, 7, 8, 9], actuators [10, 11, 12, 13, 14], and mechanical dampers [15, 16, 17]. Implementing constitutive models of magnetostrictive materials in device-level modeling can be challenging. Finite element modeling has been implemented to that effect, both in 2D [18, 19, 20] and in 3D [21, 22, 23] frameworks. Lumped parameter approximations have also been implemented, including single degree of freedom [2, 24], and multiple degrees of freedom [25, 26, 27]. The constitutive models should have two essential characteristics: efficiency that allows for high computational speed and accuracy that describes the fully-coupled and nonlinear magnetostrictive behavior. Earlier works modeled magnetostrictive behavior using measurement-fitted polynomial [28, 29, 30] that can be easily differentiated and implemented. However, this procedure requires a different set of coefficients once the preload or bias magnetic field conditions change. The measurement-fitted polynomial only works for 1D cases, since the computational effort increases exponentially with respect to the dimension of spline functions. Fully-coupled 3D modeling frameworks for magnetostrictive materials have been developed in previous studies following an energy-based approach, which was first introduced by Armstrong [31]. In this approach, the bulk behavior is defined as a weighted sum of the local response of each magnetic domain, 1 Copyright c

3D dynamic finite element model for magnetostrictive galfenol-based devices

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. Maxwells equations for electromagnetics and Naviers 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 models ability to describe transient dynamic responses.

Coupled axisymmetric finite element model of a magneto-hydraulic actuator for active engine mounts

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 Maxwells equations for electromagnetics and Naviers 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.

Modeling of a Displacement Amplified Magnetostrictive Actuator for Active Mounts

A hydraulically-amplified Terfenol-D actuator is developed to be used as a driver in active engine mounts. A measure of the actuator’s performance is obtained through electromechanical tests in mechanically-blocked and mechanically-free conditions. A nonlinear model for the actuator is presented. The Jiles-Atherton model is coupled with Maxwell’s equations in order to quantify the radial dependence of magnetization and associated dynamic losses. Magnetostriction, which is modeled as a single-valued function of magnetization, 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. Results show that the model is able to accurately describe the dynamic behavior of the actuator up to 400 Hz. An order analysis on the data and modeled responses show that the model is capable of describing the higher harmonic content of the device with sufficient accuracy for control design.© 2009 ASME