Optimal coil transducer geometry for an electromagnetic nonlinear vibration energy harvester

This paper investigates the optimisation of wire-coil transducers for a recently described strongly nonlinear electromagnetic (EM) vibration energy harvester, by coupling previously derived dynamics of the mechanical system with finite element analysis (FEA) to determine the harvester's EM response. The harvester is implemented in a permanent-magnet/ball-bearing arrangement, where vibrations in a host structure induce oscillations of the ball-bearing. The movement of the bearing changes the magnetic flux in a circular pancake wire-coil, inducing an electromotive force (EMF) in the coil and hence a voltage in the harvester circuit. A quintic-modified Duffing equation is applied to predict frequency-displacement relations for the nonlinear dynamics of the harvester. Faraday's Law of Induction is implemented with quasi-static FEA modelling of the magnetic field and linked to the dynamics of the system to develop a numeric model for voltage predictions. The issue of back-EMF and damping is also investigated. A fully integrated mechanical-electromagnetic model is shown to compare well to the quasi-static numerical model. The output characteristics of the prototype harvester are then compared with the numerical model. An optimal coil height of 2 mm is predicted, and demonstrated experimentally to produce 20.3 mW from a 12 Hz, 500 milli-g host vibration. Further investigation of coil inner radius and outer radius yields a predicted resistive load power transfer increase of 18% with the optimal coil geometry.