Nonlinear Model for Magnetostrictive Vibration Energy Harvester Considering Dynamic Forces

A magnetostrictive vibration energy harvester (MVEH) has obvious advantages in output stability, strain capacity, and electromechanical coupling. For MVEH, multiple bidirectional coupling of mechanical–magnetic–electrical and nonlinear characteristics occur in the process of energy conversion. So, the models based on the linear piezomagnetic equation will have large prediction errors in the output characteristic analysis. In this study, the magnetostrictive material, Galfenol alloy, is used as the core component of harvester, and the magnetic properties of material are tested under different magnetic excitations and compressive stresses. Using the Gibbs free energy as theoretical underpinning, the nonlinear constitutive model of the Galfenol material is constructed. The inverse hyperbolic sine function is introduced to characterize the saturation effect and nonlinearity of materials. The unknown parameters in the model are identified by a nonlinear least square method according to the magnetic properties test data. Then, for MVEH, considering the influence of dynamic vibration force, magnetic flux leakage, and bias magnetic field, a mechanical–magnetic–electrical nonlinear three-port equivalent circuit for harvester is constructed. In the circuit, the nonlinear controlled voltage source is used to express the coupling relationship between each port. Finally, a prototype harvester made of two Galfenol rods that can withstand large vibration forces is designed, and the change trends of the output voltage of the harvester are studied under dynamic vibration force and different load resistances. The results calculated by the proposed model are highly consistent with the experimental ones, which shows the validity of the nonlinear equivalent circuit model for MVEHs.