Analytical modeling and experimental verification of a multi-DOF spherical pendulum electromagnetic energy harvester

Low-frequency vibration energy harvesting is a promising technology for providing floating buoys and small marine robots with sustainable energy from ocean waves. A spherical vibration energy harvester with multiple degrees of freedom has the advantages of good multi-directional adaptability and compact structure. However, its magnetic field distribution in three-dimension space is much more complex due to the combined effect of a series of cylindrical permanent magnets mounted on the surface of a gimbaled pendulum. The traditional finite element method is too time-consuming to perform efficient parameter design and optimization. To solve this problem, this work develops an analytical electromagnetic model for the spherical vibration energy harvester based on Biot-Savart Law. This model can be used to predict spatial magnetic flux distribution and electromotive force for given magnet and coil parameters. The accuracy and computational cost of the analytical model is verified by the comparison with the finite element method. Furthermore, the optimization of electromagnetic parameters is implemented to achieve maximum energy conversion efficiency. Finally, an optimized prototype is fabricated and tested in both laboratory and real sea. The resonant frequency and energy conversion efficiency of the prototype reaches 1.0 Hz and 25.45 %, respectively. It is shown that the experimental results are in good accordance with the analytical results.