Modeling and efficiency maximization of magnetostrictive energy harvester under free vibration

Abstract

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.