Nonlinear Modeling and Characterization of the Villari Effect and Model-guided Development of Magnetostrictive Energy Harvesters and Dampers.

摘要

The Villari effect, through which mechanical energy is transferred to magnetic energy in magnetostrictive materials can be utilized in energy harvester and damper designs. Significant research has been conducted on two magnetostrictive materials, Terfenol-D (TbxDy1-xFe2.0, x ≈ 0.3) and Galfenol (Fe1-xGax, 0.15 ≤ x ≤ 0.3), due to their high magnetomechanical coupling. Both materials have strengths and weaknesses. Terfenol-D exhibits low eddy current loss, but it is brittle and difficult to machine. Terfenol-D also provides higher magnetostriction while requiring a large magnetic field. On the other hand, Galfenol is mechanically robust, and thus can be machined, welded, and formed into complex geometries. However, due to its severe eddy current effect, lamination is necessary in high frequency applications.;This work first characterized the Villari effect of Galfenol in terms of the piezo-magnetic constant d33* and hysteresis loss. The stress-flux density loops of oriented, polycrystalline Fe18.4Ga81.6 Galfenol were measured at quasi-static and dynamic regimes (up to 800 Hz). Advanced modeling tools are necessary for magnetostrictive device development. On the material level, this work proposed a dynamic, discrete energy-averaged (DEA) model incorporating time-dependent volume fractions into the static DEA framework. This dynamic DEA model took eddy current loss, mechanical loss, and pinning site loss into account and accurately simulated the measured Villari effect up to 600 Hz. On the system level, this work integrated a hysteresis static DEA model with a 3D finite element (FE) framework, and accurately modeled stress-flux density minor loops in a quasi-static state. Based on the assumption that the magnetostriction and magnetization are uniaxial, this work also proposed an efficient 2D FE framework describing nonlinear magnetostrictive responses via interpolation functions.;This enhanced knowledge of the Villari effect facilitates magnetostrictive vibration energy harvester designs. A Galfenol unimorph, bonding passive stainless steel on a Galfenol beam, was investigated. The performance of the proposed unimorph harvesters, subjected to impulsive and periodic excitations, was evaluated for different types of electrical loads. The maximum average output power density P¯ and the maximum energy conversion efficiency were 24.4 mW/cm3 and 5.9%, respectively. The fully coupled 2D FE model, incorporating magnetic, mechanical, and electrical dynamics, was validated using impulsive responses. A simplified and more efficient FE approach, which decoupled the electrical dynamics from the magnetostrictive coupling and utilized a two-step procedure to eliminate transient responses, was also presented, as was a comprehensive parametric study targeting coil size, magnet location, magnet strength, thickness ratio, and tip mass. The maximum P&barbelow;P¯ was improved by 15.2% via optimization. Energy harvester's bandwidth is another essential parameter that often needs to be optimized. This work conducted preliminary experiments on a nonlinear buckled unimorph beam, and achieved a 300% bandwidth improvement.;Besides its applications in energy harvesting, the Villari effect dissipates mechanical energy and thus can be implemented in dampers. This work conceptually proposed possible magnetostrictive dampers to attenuate noise in gearboxes. The loss factors eta of Terfenol-D and Galfenol damping units were first compared numerically in COMSOL Multiphysics. Based on the finite element results, the damping effect of Terfenol-D was then quantified experimentally. The maximum eta at 750 Hz was 0.2136 and 0.3679 for purely resistive and capacitive loads, respectively.