Ultra-low wide bandwidth vibrational energy harvesting using a statically balanced compliant mechanism

Abstract

Structure design of ultra-low wide bandwidth vibrational energy harvesters remains an open issue. In this research, a statically balanced compliant mechanism (SBCM) is proposed, dynamically modelled, and experimentally demonstrated to address this need. This SBCM is designed based on the concept of stiffness compensation between a linear component with positive-stiffness (two double parallelograms in parallel) and a nonlinear component with negative-stiffness (two sets of post-buckled fixed-guided compliant beams in parallel). A design guideline of the SBCM starting from using rapid-design stiffness compensation equation is provided for reasonably approximate and accurate results. Subsequently, a dynamic analytical model of the displacement response of the SBCM to harmonic base excitation has been derived based on the averaging method. The nonlinear force-displacement relationship of the system was obtained through nonlinear finite element analysis (FEA) simulations in this regard and a 5th order polynomial fit was chosen taking only odd terms into account. The accuracy of this analytical model is confirmed by numerical analysis. Next, a prototype of the SBCM was fabricated and its applicability to piezoelectric vibrational energy harvesters (PVEHs) was demonstrated by integrating piezoelectric capacitors made of PVDF films with compliant beams of the SBCM to generate electric outputs in response to the bending of the beams. Static balancing is achieved over a continuous displacement range of 2 mm around the origin. Bi-stability and mono-stability were observed with the same prototype by adjusting the length of the positive-stiffness beams. Under static-balancing condition, the SBCM is able to respond to a wide range of ultra-low frequencies with low accelerations, which has been established experimentally, analytically and numerically. In dynamic experiments, the steady-state relative displacement amplitude H is 2.9 mm under an excitation condition of 6 Hz and 0.1g (1g=9.8 m/s2), and it reaches a maximum of 9.4 mm under 12.75 Hz and 0.25 g. A 30%-Hmax frequency bandwidth is introduced to assess the nonlinear dynamic performance of the SBCM from a mechanical perspective. The maximum experimental 30%-Hmax bandwidth of the structure is 6.75 Hz (from 6 Hz to 12.75 Hz) at 0.25 g and the corresponding theoretical value is 8.73 Hz (from 3.34 Hz to 12.07 Hz). Under the same excitation condition, it is shown that the maximum relative displacement amplitude deceases as the jump-down frequency increases. In addition, super-harmonic and sub-harmonic oscillations are observed in the dynamic experiments. The SBCM can provide a practical structural solution for harvesting energy from a range of vibrational scenarios (e.g. ocean waves, human motions and bridge vibrations) with ultra-low wide bandwidth frequencies and weak accelerations. The concept of SBCM is suitable to be combined with various energy conversion principles and is not limited to piezoelectric sources alone. When miniaturized, the SBCM concept can be of particular interest to researchers active in energy harvesting for microelectromechanical systems (MEMS) technology.