Small-signal modeling and optimal operating condition of magnetostrictive energy harvester

open5sìMagnetostrictive energy harvesting has drawn attention in recent years for its high energy conversion efficiency and environmental durability. Magnetostrictive harvesters are mainly composed of giant magnetostrictive material, a magnetic circuit, and an electric circuit, which involves complex mechanical-electromagnetic coupled problems. Therefore, in many studies, the analysis of such device was implemented by finite element method. However, numerical calculation generally requires a great deal of time and does not provide adequate physical understanding of the effect of the design parameters on the harvester characteristics. In many previous studies, magnetostrictive harvesters have been operated under a small-signal vibration imposed over a constant prestress and magnetic bias. In such operating conditions, linearized small-signal models can be used to derive important analytical expressions for the harvester characteristics and their dependency on the design parameters. This paper presents the linearized modeling of a magnetostrictive energy harvester using linearized constitutive equations. The energy loss due to eddy currents is also considered for high-frequency application. The influence of parameter variation on the output power is investigated from the algebraically obtained output power, and the existence of an optimal value in resistance and capacitance of the electric circuit is discussed. These optimal design parameters are also presented in form of an algebraic solution. The obtained output power is finally proven to fit with experimental results when an appropriate permeability and magnetostrictive constant are given.openMizukawa, Yoshito; Ahmed, Umair; Zucca, Mauro; Blažević, David; Rasilo, PaavoMizukawa, Yoshito; Ahmed, Umair; Zucca, Mauro; Blažević, David; Rasilo, Paav

Validation of thermodynamic magneto-mechanical finite-element model on cantilever-beam type magnetostrictive energy harvester

This paper presents the validation of a thermodynamic magneto-mechanical model to analyze a galfenol based cantilever beam type energy harvesting device. As compared to some earlier modeling approaches that were tested only on specific harvester geometries, the thermodynamic model has already been validated on rod-type harvesters and is now shown to be suitable for analyzing also beam-type devices. Moreover, the paper discusses the influence of magnetostriction upon resonant frequency. The thermodynamic model is implemented in a 3D finite element solver using COMSOL Multiphysics software. This allows optimizing the device design by tuning the geometric parameters and magnetic bias under available operating conditions (amplitude and frequency of vibrations) easily and efficiently. A unimorph cantilever beam type prototype harvester device consisting of a galfenol beam bonded to an aluminum substrate is constructed for validating the model. Simulated and measured results are compared at base excitation amplitudes of 0.5 to 2 g under varying vibration frequencies. The results show that the maximum induced voltage is obtained at the resonant frequency which decreases slightly with an increase in the vibration amplitude. Furthermore, it is shown that the resonant frequency decreases from 201 Hz to 187 Hz at 1 g base acceleration when the magnetic bias is removed. The comparison of measured and simulated results show that the model can accurately predict the resonant frequency with a relative error of less than 2%, validating the modeling approach. The model can also reasonably determine the open circuit voltage with some discrepancies at large vibration amplitudes.publishedVersionPeer reviewe

Modeling and efficiency maximization of magnetostrictive energy harvester under free vibration

Vibration energy harvesting is becoming increasingly attractive in line with the development of wireless sensor technologies. Magnetostrictive materials inherently exhibit high mechanical strength and are thus suitable for various applications and mass manufacturing of energy harvesting devices. Many studies have been conducted to increase the output power of harvesters, and some utilized analytical methods. However, the optimization methods often take into account only the resonant frequency of the system under forced vibration. These models can produce correct predictions only when steady-state harmonic excitation inputs are considered. In this study, we propose the modeling and optimization method for a cantilever-type magnetostrictive harvester under free vibration. The cantilever has a double-beam structure composed of two parallel Fe-Ga beams with pickup coils. In the modeling, the shape function of the cantilever-type magnetostrictive energy harvester was derived based on the continuity of the internal force and magnetic flux. Hamilton’s principle for an electromagnetic-mechanically coupled system was derived from the virtual work principle. The equation of motion, magnetic circuit equation, and electric circuit equation of the system were respectively derived from the corresponding Euler–Lagrange equations. The harvestable energy of the magnetostrictive energy harvester was calculated by using the symmetric property of eigenvalues. In the efficiency maximization of the harvestable energy, we found that the optimal solution differs depending on the type of given energy. The optimal parameters to maximize the energy efficiency to potential energy and kinetic energy are respectively derived in the form of algebraic solutions. Experimental validation was conducted by measuring the energy harvesting efficiency at different loads.publishedVersionPeer reviewe

Small-Signal Modeling and Optimal Operating Condition of Magnetostrictive Energy Harvester

Magnetostrictive energy harvesting has drawn attention in recent years for its high energy conversion efficiency and environmental durability. Magnetostrictive harvesters are mainly composed of giant magnetostrictive material, a magnetic circuit, and an electric circuit, which involves complex mechanical-electromagnetic coupled problems. Therefore, in many studies, the analysis of such device was implemented by finite element method. However, numerical calculation generally requires a great deal of time and does not provide adequate physical understanding of the effect of the design parameters on the harvester characteristics. In many previous studies, magnetostrictive harvesters have been operated under a small-signal vibration imposed over a constant prestress and magnetic bias. In such operating conditions, linearized small-signal models can be used to derive important analytical expressions for the harvester characteristics and their dependency on the design parameters. This paper presents the linearized modeling of a magnetostrictive energy harvester using linearized constitutive equations. The energy loss due to eddy currents is also considered for high-frequency application. The influence of parameter variation on the output power is investigated from the algebraically obtained output power, and the existence of an optimal value in resistance and capacitance of the electric circuit is discussed. These optimal design parameters are also presented in form of an algebraic solution. The obtained output power is finally proven to fit with experimental results when an appropriate permeability and magnetostrictive constant are given.acceptedVersionPeer reviewe