RESEARCH ON DYNAMICS CHARACTERISTICS OF LINEAR-ARCH COMPOSED BEAM TRI-STABLE PIEZOELECTRIC ENERGY HARVESTER
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摘要: 利用振动能量俘获技术将设备工况振动能转化为电能, 为实现煤矿井下无线监测节点自供电提供了新的思路. 通过引入非线性磁力设计了一种线形−拱形组合梁式三稳态压电俘能器, 分析了磁铁水平间距、垂直间距和激励加速度对动力学特性的影响规律. 利用磁偶极子法建立磁力模型, 通过实验测量线形−拱形组合梁的恢复力, 并采用多项式拟合得到恢复力模型, 基于欧拉−伯努利梁理论和拉格朗日方程建立系统的动力学模型, 从时域角度仿真分析了磁铁水平间距、垂直间距和激励加速度对系统动力学特性的影响规律. 研制线形−拱形组合梁式三稳态压电俘能器样机并搭建实验平台进行实验研究, 通过采集组合梁末端响应速度数据, 验证了理论分析的正确性. 研究表明: 引入非线性磁场能够使系统势能呈现单势阱、双势阱或三势阱, 激励一定时, 调整磁铁水平间距和垂直间距能够使系统实现单稳态、双稳态或三稳态运动, 且在三稳态运动时响应位移较大, 增大激励水平有利于系统越过势垒实现大幅响应. 研究为线形−拱形组合梁式三稳态压电俘能器的设计提供了理论指导.Abstract: Vibration energy harvesting technology can convert the vibration energy of equipment working conditions into electrical energy, which provides a new idea for realizing self-powered wireless monitoring nodes in coal mines. In this paper, we design a linear-arch composed beam tri-stable piezoelectric energy harvester by introducing nonlinear magnetic force, and analyse the influence of the horizontal distance, vertical distance and excitation acceleration on dynamic characteristics. The nonlinear magnetic force model is established by the magnetic dipole method, the nonlinear restoring force of the linear-arch composed beam is measured experimentally, and the restoring force model is obtained by polynomial fitting. The dynamic model of the system is established based on Euler-Bernoulli beam theory and Lagrange’s equations. From the perspective of time domain, we analyse the influence of the horizontal distance, vertical distance of the magnets, and excitation acceleration on the dynamic characteristics of the system. A prototype of a linear-arch composed beam tri-stable piezoelectric energy harvester was fabricated, and an experimental platform was built for experimental research, by collecting the response speed data at the end of the composite beam after being excited, the speed-displacement data at the end of the composite beam was obtained, which verified the correctness of the theoretical simulation. The results show that the introduction of a nonlinear magnetic field can make the potential of the system have single potential well, double potential well or triple potential well. When we keep the excitation is constant, adjusting the horizontal and vertical spacing of the magnets can enable the system to achieve monostable, bi-stable or tri-stable motion, and the response displacement is relatively large during tri-stable motion. Increasing the excitation acceleration is beneficial for the system to across the barrier and achieve a large response. The research provides theoretical guidance for the design of linear-arch composed beam tri-stable piezoelectric energy harvester.
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图 4
${d_g}$ 对系统势能和磁力的影响Figure 4. The influence of
${d_g}$ on potential energy and magnetic force
图 5
$d$ 对系统势能和磁力的影响Figure 5. The influence of
$d$ on potential energy and magnetic force
6 不同水平间距
$d$ 下的系统相图和时间-位移图6. Phase portrait and time-displacement diagram of different magnetic distance
$d$ 
图 6 不同水平间距
$d$ 下的系统相图和时间-位移图(续)Figure 6. Phase portrait and time-displacement diagram of different magnetic distance
$d$ (continued)
7 不同垂直间距
${d_g}$ 下的系统相图和时间−位移图7. Phase portrait and time-displacement diagram of different magnetic distance
${d_g}$ 
图 7 不同垂直间距
${d_g}$ 下的系统相图和时间−位移图(续)Figure 7. Phase portrait and time-displacement diagram of different magnetic distance
${d_g}$ (continued)
图 10 不同激励加速度下的实验相图
Figure 10. Experimental phase diagrams under different excitation accelerations
表 1 三稳态压电俘能器结构和材料参数
Table 1. Structure and material parameters of TPEH
Parameter Value linear-arch beam $ {L_1} $/mm 20 $ {h_S} $/mm 0.2 $ b $/mm 8 $ r $/mm 10 density/ (kg·m−3) $ 8300 $ Young's modulus / (N·m−2) $1.28 \times {10^{11}}$ PVDF permittivity constant/ (F·m−1) $ 1.10 \times {10^{ - 10}} $ Young's modulus / (N·m−2) $ 3 \times {10^9} $ density / (kg·m−3) $ 1780 $ $ {h_P} $/mm 0.11 magnet structure size/mm $ 10 \times 10 \times 5 $ ${\mu _0}$/ (H·m−1) $4{\text{π}} \times {10^{ - 7} }$ 
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