Mathematical Modeling of a Two Degree of Freedom Vibration Energy Harvester for Low Speed Rotary Structure Application

This paper presents mathematical modeling of a two degree of freedom energy harvester which converts slow mechanical rotation into piezoelectric vibration using gravity force and magnetic repelling force, for large-scale machinery monitoring such as wind turbine blades. The harvester consists of a disk with an unbalanced mass, a piezoelectric cantilevered beam, and two magnets attached to both the beam and the disk. Three coupled equations that describe the motion of the disk, vibration of the beam, and the harvester voltage output are derived using the energy method. Then ODE45 in MATLAB software is used to solve the equations. The result shows that the energy harvester’s performance varied by blade rotational speed. At low blade speed (less than 15 rpm), the harvester generates power by regularized magnetic excitation per blade revolution. The power output of the harvester increases by increasing the blade speed. At high blade speed, however, the disk behavior and the power generation mechanism changes due to the increased centrifugal force. The results show that the model can predict the power peak as a function of blade speed, and the proposed harvester can generate a considerable amount of power for self-sustainable sensing and structural health monitoring.