Increase of the electromechanical coupling of piezoelectric vibration harvesters through lateral bars

Abstract

To enhance the performance of vibration energy harvesters, it is essential to maximise the electromechanical coupling coefficient k${}^2$ of piezoelectric devices. This enables sufficient harvested power and tuning capability of the resonant frequency through electrical methods. While much literature treats the optimisation of piezoelectric cantilevers, the optimisation range is usually limited by the transverse coupling coefficient k31${}^2$ of the material. This work introduces an innovative solution to extend the optimisation range and increase the coupling coefficient of piezoelectric cantilevers. This is achieved by minimising lateral strain in the beam using lateral bars to maximise the equivalent material coupling coefficient. The theoretical basis of this innovation is demonstrated through the exploitation of the constitutive equations of piezoelectric materials. The interest of the addition of lateral bars to increase the coupling coefficient is demonstrated and studied with simulations based on the finite elements method. Finally, a proof of concept is realised using a aluminum cantilever prototype integrating a lead-free KNaNbO3 (KNN) piezoelectric material. It is tested under vibration at 0.1 m/s${}^2$ with variable resistive loads. The results show that the coupling coefficient increases by 30% and the relative frequency bandwidth by 32% with resistive tuning of the resonant frequency, by fixing eight steel bars to the cantilever. The designed prototype is a highly performant leadfree vibration energy harvester. It produces a maximum power of 49.9 $μ$W at resonance, and its normalised power density is equal to 16.5 mW/G${}^2$/cm${}^3$. Its relative frequency bandwidth is equal to 3.1%.