Triboelectric energy harvesting from the vibro-impact of three cantilevered beams

Abstract

Abstract A new system that harvests vibration energy through triboelectric and electrostatic effects from the vibro-impact of three parallel cantilevered beams is theoretically studied and experimentally validated. Two modelling methods of the mechanical vibration, which differ in the consideration of the eccentricity of the tip mass, are presented and compared with the experimental results for validation. An experimentally identified and numerically fitted relationship between the just-before-impact velocity and the coefficient of restitution is used to model the impact. The electrical model of the triboelectric energy harvester is then established. The ordinary differential equation (ODE) modelling the electrical output of the triboelectric energy harvester is found to be stiff. Two schemes, which are based on the TR (the trapezoidal rule) and TR-BDF2 (the composite of the trapezoidal rule and the second order backward differentiation formula) methods, are proposed to solve the non-smooth mechanical system and the stiff electrical system. The experimental investigations of the effects of electrostatic force and air damping between cantilever tips suggest that their effects are negligible. This enables the mechanical and electrical systems to be modelled as uncoupled. Good agreement between numerical and experimental results is found, especially for vibration responses. The modelling method, not involving the eccentricity of the tip mass, offers better agreement with experiments. A new numerical scheme combining the TR and TR-BDF2 methods is found to be superior because it is the only method that can solve the electrical system and produce stable results around the impacts. Larger amplitude vibration associated with smaller tip mass ratios does not guarantee higher electricity generation while larger mass ratios perform better at higher frequencies and have a wider effective bandwidth over which their electricity generation performance is superior. Both the responses of vibration and electrical output increases linearly with the excitation level while the relationship between the tribo-charge surface density and the excitation amplitude is found to be quadratic.