Development of An Analytical Method for Design of Electromagnetic Energy Harvesters with Planar Magnetic Arrays

In this paper, an analytical method is proposed for the modeling of electromagnetic energy harvesters (EMEH) with planar arrays of permanent magnets. It is shown that the proposed method can accurately simulate the generation of electrical power in an EMEH from the vibration of a bridge subjected to traffic loading. The EMEH consists of two parallel planar arrays of 5 by 5 small cubic permanent magnets (PMs) that are firmly attached to a solid aluminum base plate, and a thick rectangular copper coil that is connected to the base plate through a set of four springs. The coil can move relative to the two magnetic arrays when the base plate is subjected to an external excitation caused by the vehicles passing over the bridge. The proposed analytical model is used to formulize the magnetic interaction between the magnetic arrays and the moving coil and the electromechanical coupling between both the electrical and mechanical domains of the EMEH. A finite element model is developed to verify the accuracy of the proposed analytical model to compute the magnetic force acting on the coil. The analytical model is then used to conduct a parametric study on the magnetic arrays to optimize the arrangement of the PM poles, thereby maximize the electrical power outputted from the EMEH. The results of parametric analysis using the proposed analytical method show that the EMEH, under the resonant condition, can deliver an average electrical power as large as 500 mW when the PM poles are arranged alternately along the direction of vibration for a peak base acceleration of 0.1 g. A proof-of-concept prototype of the EMEH is fabricated to test its performance for a given arrangement of PMs subjected to vibration in both the lab and field environments.