Analytical modeling and design optimization of piezoelectric bimorph energy harvester.

摘要

As wireless sensor networks continue to grow in size and scope, the limited life span of batteries produces an increasingly challenging economic problem, in terms of not only the capital cost of replacing so many batteries, but also the labor costs incurred in performing battery replacement, particularly with sensor nodes in remote or limited-access locations. This growing problem has motivated the development of new technologies for harvesting energy from the ambient environment. Piezoelectric energy harvesters (PEH) are under consideration as a means for converting mechanical energy, specifically vibration energy, to electrical energy, with the goal of realizing completely self-powered sensor systems. There are three primary goals with regards to this study. The first goal is to develop an analytical model for the resonant frequency of a piezoelectric cantilever bimorph (PCB) energy harvester, aiming to study the geometric effects of both the piezoelectric bimorph and the proof mass on the resonant frequency of a PEH. The analytical model is developed using the Rayleigh-Ritz method and Lagrange's equation of motion and is validated by finite element analysis (FEA) and laboratory experiments. It is shown that this analytical model is better at predicting resonant frequencies than a model currently available in the literature. The second goal is the development of an enhanced analytical model for the voltage and power output of the PCB. The modified analytical model is realized using the conservation of energy method and Euler-Bernoulli beam theory. It is compared with a general equivalent spring-mass-damper model and an equivalent electrical circuit model, and validated by the laboratory prototype experiments. The results show that the modified model provides improved prediction of PCB voltage and power output. Simultaneously, finite element analysis on piezoelectric structures using the commercially available software package ANSYSRTM Multiphysics is also carried out to study the dynamic response of the PCB in terms of both tip displacements and the electrical potentials of the top and bottom electrodes. It is shown that the simulations are quite close to the experimental results, in terms of both peak frequencies and peak amplitudes. The third goal is the design optimization of the PCB energy harvester in order to maximize the power harvesting from the ambient vibration. Three design optimization approaches are carried out, including multi-parameter optimization of the single PCB generator using a genetic algorithm (GA), a band-pass generator design with a group of the PCB generators based on the system transfer function, and the new design features of the PCB generator for consideration of the improvements of the strain energy and the lifetime. The results of the optimized designs are validated through FEA, and the discrepancies between the theoretical derivation and FEA are also analyzed. Other optimal design considerations are also discussed.