A Tunable Nonlinear Magnetic Piezoelectric Energy Harvester

doi:10.12141/j.issn.1000-565X.220767

Abstract

Abstract:

To broaden the effective frequency band of piezoelectric energy harvesters, this paper designed a nonlinear magnetic piezoelectric energy harvester with adjustable frequency and fast switching between monostable and bi-stable mode. This harvester is composed by adding a pair of movable magnets on a piezoelectric cantilever beam with an end magnet. Firstly, the distributed parameter dynamics of the harvester was analyzed. The dynamics equation of the system was derived based on Euler-Bernoulli theory, and the expressions of kinetic energy, potential energy and electric energy of the system were analyzed according to Lagrange function. The magnetic force expression of the system was obtained according to the magnetic dipole model. The first-order reduced model of the system was obtained by Galerkin discrete method and Taylor expansion, and the analytical expression of the equations was derived via the harmonic balance method. Then, the monostable and bi-stable characteristics of the harvester were studied by simulation software, and the effects of magnet spacing, damping, load resistance and other parameters on the output voltage and output power of the system were analyzed and verified by the subsequent experiment. According to the experimental result, the nonlinear magnetic force brought by the movable magnet can significantly increase the output voltage and output power of the harvester; the resonant frequency of the energy harvester can be changed by adjusting the magnet spacing, which better widens the working frequency band; the energy harvesting system can rapidly switch between monostable mode and bi-stable mode by adjusting the magnet spacing, and use the monostable mode and and the bi-stable mode to harvest vibration energy in high-frequency environment and the low-frequency environment, respectively.

Key words: piezoelectric energy harvester, nonlinear magnetic force, tunable, broadband

CLC Number:

TN712⁺.5

DING Jiang, LU Mengen, ZENG Ziyang, et al.. A Tunable Nonlinear Magnetic Piezoelectric Energy Harvester[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(9): 30-43.

Figures/Tables 22

Fig.1

Fig.2

Fig.3

Table 1

Material and structural parameters of harvester"

参数	数值
悬臂梁和压电片长度L/mm	70
悬臂梁和压电片宽度w_b、w_p/mm	20
悬臂梁厚度h_b/mm	0.5
悬臂梁弹性模量Y_s/GPa	212
悬臂梁密度ρ_b/（kg·m^-3）	7 850
压电片厚度h_p/mm	0.3
压电片的弹性模量Y_p/GPa	67
压电片密度ρ_p/（kg·m^-3）	7 700
压电应力常数 $e 31$ /（C·m^-1）	-11.6
压电介电常数 $ε 33 σ$ /（nF·m^-1）	31.8
磁铁长度l/mm	20
磁铁宽度w_t/mm	5
磁铁厚度g/mm	5
磁铁密度ρ/（kg·m^-3）	7 500
磁化强度 M_A、 M_B、 M_C/（A·m^-1）	1.19×10⁶

Table 1

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

References 22

1	SI H Y， DONG J L， CHEN L，et al ．Study of the ambient vibration energy harvesting based on piezoelectric effect［J］．International Journal of Nanoscience，2015，14（1/2）：1460017/1-7.
2	孟广伟，李霄琳，周立明，等．基于MEMsFEM的功能梯度压电板力电耦合分析［J］．华南理工大学学报（自然科学版），2016，44（10）：81-86.
	MENG Guang-wei， LI Xiao-lin， ZHOU Li-ming，et al ．Electromechanical coupling analysis of functionally graded piezoelectric plate based on MEMsFEM［J］．Journal of South China University of Technology（Natural Science Edition），2016，44（10）：81-86.
3	ZOU H X， LI M， ZHAO L C，et al ．A magnetically coupled bistable piezoelectric harvester for underwater energy harvesting［J］．Energy，2021，217：119429/1-8.
4	黄怀纬，贺万里，曹亚军．基于多尺度法的预载压电梁俘能特性［J］．华南理工大学学报（自然科学版），2022，50（5）：118-126.
	HUANG Huaiwei， HE Wanli， CAO Yajun ．Energy harvesting characteristics of preloaded piezoelectric beams based on multi-scale approach［J］．Journal of South China University of Technology（Natural Science Edition），2022，50（5）：118-126.
5	SHAHRUZ S M ．Design of mechanical band-pass filters with large frequency bands for energy scavenging［J］．Mechatronics，2006，16（9）：523-531.
6	RAMLAN R， BRENNAN M J， MACE B R，et al.Potential benefits of a non-linear stiffness in an energy harvesting device［J］.Nonlinear Dynamics，2010，59（4）：545-558.
7	CHALLA V R， PRASAD M G， SHI Y，et al ．A vibration energy harvesting device with bidirectional resonance frequency tunability［J］．Smart Materials and Structures，2008，17（1）：15035/1-10.
8	STANTON S C， MCGEHEE C C， MANN B P ．Reversible hysteresis for broadband magnetopiezoelastic energy harvesting［J］．Applied Physics Letters，2009，95（17）：174103/1-3.
9	YANG W， TOWFIGHIAN S ．A parametric resonator with low threshold excitation for vibration energy harvesting［J］．Journal of Sound and Vibration，2019，446：129-143.
10	MANSOUR M O， ARAFA M H， MEGAHED M S ．Resonator with magnetically adjustable natural frequency for vibration energy harvesting［J］．Sensors and Actuators A Physical，2010，163（1）：297-303.
11	FERRARI M， BAÙ M， GUIZZETTI M，et al ．A single-magnet nonlinear piezoelectric converter for enhanced energy harvesting from random vibrations［J］．Sensors and Actuators A-Physical，2011，172（1）：287-292.
12	WANG G Q， WU H Q， LIAO S J，et al ．A modified magnetic force model and experimental validation of a tri-stable piezoelectric energy harvester ［J］．Journal of International Material Systems and Structures，2020，31（7）：967-979.
13	WU H， SOH C K， TANG L H，et al ．Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester［J］．Journal of Intelligent Material Systems and Structures，2014，25（14）：1875-1889.
14	FIROOZY P， KHADEM S E， POURKIAEE S M ．Broadband energy harvesting using nonlinear vibrations of a magnetopiezoelastic cantilever beam［J］．International Journal of Engineering Science，2017，111：113-133.
15	唐炜，王小璞，曹景军．非线性磁式压电振动能量采集系统建模与分析［J］．物理学报，2014，63（24）：76-89.
	TANG Wei， WANG Xiaopu， CAO Jingjun ．Modeling and analysis of piezoelectric vibration energy harvesting system using permanent magnetics［J］．Acta Physica Sinica，2014，63（24）：76-89.
16	吴义鹏，季宏丽，裘进浩，等．共振频率可调式非线性压振动能量收集器［J］．振动与冲击，2017，36（5）：12-16.
	WU Yipeng， JI Hongli， QIU Jinhao，et al ．A nonlinear piezoelectric vibration energy harvesting device with tunable resonance frequencies［J］．Journal of Vibration and Shock，2017，36（5）：12-16.
17	杜小振，张龙波，于红．磁力调频压电电磁复合发电设计与实验［J］．光学精密工程，2016，24（11）：2753-2760.
	DU Xiaozhen， ZHANG Longbo， YU Hong ．Design and experiment of piezoelectric electromagnetic hybrid broadband generator with magnetic force tuning［J］．Optical and Precision Engineering，2016，24（11）：2753-2760.
18	DAI H L， WANG Y K， WANG L ．Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory［J］．International Journal of Engineering Science，2015，94：103-112.
19	FAROKHI H， GHAYESH M H， HUSSAIN S ．Large-amplitude dynamical behaviour of microcantilevers［J］．International Journal of Engineering Science，2016，106：29-41.
20	FRISWELL M I， ALI S F， BILGEN O，et al ．Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass［J］．Journal of Intelligent Material Systems and Structures，2012，23（13）：1505-1521.
21	ERTURK A， INMAN D J ．An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations［J］．Smart Materials and Structures，2009，18（2）：025009-1-18.
22	ERTURK A， INMAN D J ．Broadband piezoelectric power generation on high-energy orbits of the bistable duffing oscillator with electromechanical coupling［J］．Journal of Sound and Vibration，2011，330（10）：2339-2353.

[1]	YE Weilin, TU Zihan, XIAO Xupeng, et al. On Multi-Parameter Influence of TDLAS Detection System Based on LabVIEW [J]. Journal of South China University of Technology (Natural Science Edition), 2021, 49(6): 141-148.
[2]	YAO Ruohe HE Xiaomeng . Broadband Low Noise Amplifier Architecture Based on Coupling and Negative Feedback [J]. Journal of South China University of Technology (Natural Science Edition), 2019, 47(2): 16-23.
[3]	YE Jun LIANG Wei-peng XIONG Jian. Fluorescence Properties of Tunable Luminescence Color CMC-Tb /Eu Nano Complexes Synthesized via Microwave-Assisted Heating [J]. Journal of South China University of Technology(Natural Science Edition), 2017, 45(9): 110-117.
[4]	XU Ken CAI Min HE Xiao-yong. Multi-Stage Operational Amplifier for Broadband Δ-Σ ADC [J]. Journal of South China University of Technology (Natural Science Edition), 2017, 45(1): 42-47.
[5]	Li Hong-tao Wei Xiao-Dong Hu Bin-Jie Zhang Hong-lin Zeng Wei-sen. Dual-Band Orthogonal Power Divider with Variable Power Division Ratio Applied to ETC System [J]. Journal of South China University of Technology (Natural Science Edition), 2015, 43(3): 72-77.
[6]	Chu Qing-xin Yang Lin Lin Feng. Dual-Band Broadband Coupler with SIR Branches [J]. Journal of South China University of Technology (Natural Science Edition), 2010, 38(5): 51-54,70.