Deformable force amplification frame promoting piezoelectric stack energy harvesting: Parametric model, experiments and energy analysis

Abstract

This article presents a nonlinear parametric model of force amplification ratio and an electromechanical model to couple the deformable frame with the piezoelectric stack in order to promote high-efficiency energy harvesting from human walking locomotion. Two improved frames (Frames I and II) are developed based on the modeling and simulation results. The experiments verified these modeling and simulation results that improved frames demonstrate a higher amplification ratio (8.4 for Frame II and 8.0 for Frame I), in comparison to the original frame (3.5). The experiments also verified these results that under the simulated walking excitation (100 N, ~1.4 Hz), the piezoelectric stack coupled with Frame II produces 4.1 mJ energy during each step, higher than the stand-alone stack (0.16 mJ) and the stack with the original frame (0.64 mJ). Note that the energy conversion efficiency of Frame II (9.1%) is even lower than that of Frame I (10.7%) and the stand-alone stack (25.8%). As such, this article concludes that the energy output of the piezoelectric stack depends largely on the frame deformations in terms of seven coupled frame parameters, instead of only one frame parameter (tilt angle), as commonly used in the referenced literature.

Strongly coupled piezoelectric energy harvesters: Finite element modelling and experimental validation

“…A piezoelectric stack energy harvester (PSEH) with a mechanical transformer was used to study in this work, which is a good example of strongly coupled PEH. Similar harvesters have been widely studied for low-frequency compressive force energy harvesting [31][32][33][34] due to the high electrical power output, which is a result of the force amplification mechanism and the high electromechanical coupling of piezoelectric stacks used [35].…”

“…To simplify the analysis, it is assumed that the hinges are free to flexure while the inclined beams do not change its length. In a quasi-static state, the following relationship can be obtained [33,36] 𝐹 𝑧 = 𝐹 𝑥 cot 𝛽 𝐷 𝑥 = 𝐷 𝑧 cot 𝛽 ( 11 ) where 𝐹 𝑥 and 𝐷 𝑥 are the input force and displacement; 𝐹 𝑧 and 𝐷 𝑧 are the force and displacement of the piezoelectric element.…”

“…Although Eqs. (11)(12) can be used for qualitative analysis, it must be noted that in reality, the relationship between the force/displacement amplification and the tilted angle is more complicated due to the elastic deformation of the inclined beams [33,34,36].…”

“…The elastic compliance along 𝑧-axis is particularly important because the piezoelectric stack vibrates along this direction. The elastic compliance of the piezoelectric stack 𝑠 33 𝐸 was estimated based on the stiffness (50 N/µm)) of the multilayer stack provided by the supplier, instead of using the material properties of PIC252. In the fabricated PSEH, the mechanical transformer was stretched to apply to static compressive stress on the piezoelectric element.…”

Design of a New Piezoelectric Energy Harvesting Handrail With Vibration and Force Excitations

“…Generally, piezoelectric stack exhibits a higher stiffness and can bear a larger compressive force. Thus, it is expected to produce more power output [14], [15]. Xu et al reported that the energy produced by a piezoelectric stack is proportional to the square of the exerted force [16].…”