A two-stage electromagnetic coupling and structural optimisation for vibration energy harvesters

This paper demonstrates a two-stage optimisation for a single-degree-of-freedom (SDOF) electromagnetic vibration energy harvester under a harmonic base excitation vibration. In this paper, a designed cantilever beam was used to verify the optimisation methods. The dynamics of the beam was modelled using the Euler-Bernoulli beam theory. By deriving the exact expression of the power output under the optimum load resistance condition, the correct electromagnetic coupling coefficient was determined. The first optimisation stage involves maximising this coefficient by considering several coils and magnet parameters, allowing at this stage to define the electrical efficiency of the harvester which is described as the ratio of the harvester's power output to its power limit. The experimentally determined power output for this stage was 3.51 mW. The structural aspects of the harvester were then optimised by considering the addition and placement of proof masses and the structural dimensions of the harvester. This part represents the second optimisation and determines the power limit of the harvester. An experimental power output of 7.95 mW was achieved in this stage. All experimental results displayed a good agreement with the derived theoretical model, recording an error of less than 10.0%, hence validating the theoretical model. The first optimisation stage presented here can be applied to any linear electromagnetic SDOF harvester whereas the second optimisation stage can be easily modified to suit different structural considerations. Additionally, both stages can also be slightly modified to account for rotational systems.