Non-linear model and optimization method for a single-axis linear-motion energy harvester for footstep excitation

Abstract

We propose and develop an electrical and mechanical system model of a single-axis linear-motion kinetic energy harvester for impulsive excitation that allows its generated load power to be numerically optimised as a function of design parameters. The device consists of an assembly of one or more spaced magnets suspended by a magnetic spring and passing through one or more coils when motion is experienced along the axis. The design parameters that can be optimised include the number of coils, the coil height, coil spacing, the number of magnets, the magnet spacing and the physical size. We use the proposed model to design optimal energy harvesters for the case of impulse-like motion like that experienced when attached to the leg of a human. We generate several optimised designs, ranked in terms of their predicted load power output. The three best designs are subsequently constructed and subjected to controlled practical evaluation while attached to the leg of a human subject. The results show that the ranking of the measured output power corresponds to the ranking predicted by the optimisation, and that the numerical model correctly Predicts the relative differences in generated power for complex motion. It is also found that all three designs far outperform a baseline design. The best energy harvesters generated an average power of 3.01mW into a 40$\Omega$ test load when driven by footsteps whose measured peak impact was approximately 2.2g. With respect to the device dimensions, this corresponds to a power density of 179.380$\mu\text{W/cm}^3$.