Mono-stable and bi-stable magnetic spring based vibration energy harvesting systems subject to harmonic excitation: Dynamic modeling and experimental verification

Abstract

Abstract This work develops a comparative study using theoretical models and experimental evaluation of the dynamic behavior of a magnetic spring based vibration energy harvester that can be switched from a mono-stable to a bi-stable configuration. The design uses coupled magnetic interactions to achieve bi-stability. A mono-stable configuration consists of an oscillating magnet that is levitated between two stationary top and bottom magnets. A cluster of peripheral solid magnets is fixed around the harvester casing and results in a bi-stable configuration. Traditionally, magnetic forces in magnetic spring based harvesters are represented using empirical polynomial fits that are integrated into the equation of motion. In this work, first principle physics based analytical models describing the interaction between magnets are developed and integrated into the equation of motion. Results suggest that, for the bi-stable configuration, introduced analytical model provides more accurate results compared to those obtained using polynomial functions. Results show that a variety of load-deflection characteristics can be obtained by changing geometric ratios of the peripheral magnets in the bi-stable configuration. During dynamic operation, the bi-stable configuration exhibits interwell, chaotic, and intrawell motion at different acceleration levels. Thinner peripheral magnets are favorable for the bi-stable design, especially at lower acceleration levels. Thinner peripheral magnets yield lower energy barriers, improved frequency responses, and exhibit approximately zero stiffness near equilibrium position. Furthermore, the use of thinner peripheral magnets causes the harvester to move towards monostability.