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不倒翁式电磁俘能器的非线性动力学特性研究

潘侠圭 余宁 严博

潘侠圭, 余宁, 严博. 不倒翁式电磁俘能器的非线性动力学特性研究. 力学学报, 2023, 55(10): 2336-2346 doi: 10.6052/0459-1879-23-332
引用本文: 潘侠圭, 余宁, 严博. 不倒翁式电磁俘能器的非线性动力学特性研究. 力学学报, 2023, 55(10): 2336-2346 doi: 10.6052/0459-1879-23-332
Pan Xiagui, Yu Ning, Yan Bo. Nonlinear dynamics characteristics of tumbler-inspired electromagnetic energy harvesters. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2336-2346 doi: 10.6052/0459-1879-23-332
Citation: Pan Xiagui, Yu Ning, Yan Bo. Nonlinear dynamics characteristics of tumbler-inspired electromagnetic energy harvesters. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2336-2346 doi: 10.6052/0459-1879-23-332

不倒翁式电磁俘能器的非线性动力学特性研究

doi: 10.6052/0459-1879-23-332
基金项目: 国家自然科学基金(52175125)和浙江理工大学基本科研业务费(23242094-Y)资助项目
详细信息
    通讯作者:

    严博, 教授, 主要研究方向为高端装备动力学与控制. E-mail: yanbo@zstu.edu.cn

  • 中图分类号: O322

NONLINEAR DYNAMICS CHARACTERISTICS OF TUMBLER-INSPIRED ELECTROMAGNETIC ENERGY HARVESTERS

  • 摘要: 海洋波浪能作为一种可再生能源, 将其俘获并转化为电能为无线传感器持续供电, 可以推动海洋环境监测的数字化改造升级. 然而, 海浪能的低频与随机性等特征导致其俘获难度大. 不倒翁结构具有不同于传统结构的超低频振动特性, 并且其对低频激励敏感的特点, 可以吸收周围振动能量. 为此, 文章通过引入不倒翁机制与Halbach磁铁阵列, 构建了磁非线性力, 设计一种不倒翁式电磁俘能器, 以实现提高低频波浪能的俘获效果. 首先, 基于拉格朗日方程建立不倒翁式电磁俘能器的理论模型, 并用谐波平衡法推导了不倒翁摆角与输出电压的频率响应关系. 将解析解与数值解进行对比验证. 其次, 探究了激励频率与幅值等参数对系统动力学行为的影响规律. 最后, 研制了不倒翁式电磁俘能器原理样机, 搭建俘能试验平台并进行试验, 验证了理论模型的正确性. 研究表明: 引入磁非线性力使得系统呈现刚度硬化特征, 有利于提升低频俘能效率. 不倒翁式电磁俘能器随激励频率与幅值的变化, 呈现周期、准周期及混沌运动等复杂动力学行为. 低频与大激励条件更容易造成俘能器系统的混沌运动, 有利于提高俘能效果. 本研究为不倒翁式电磁俘能器的设计及在低频波浪能高效俘获的应用提供了理论支持.

     

  • 图  1  不倒翁式电磁俘能器的设计示意图

    Figure  1.  Schematic diagram of the tumbler-inspired electromagnetic energy harvester

    图  2  不倒翁式电磁俘能器的理论模型

    Figure  2.  Theoretical model of the tumbler-inspired electromagnetic energy harvester

    图  3  不倒翁式电磁俘能器摆角与感应电压解析解与数值解对比

    Figure  3.  Comparison between theoretical solution and numerical solution of the swing angle and the voltage of the tumbler-inspired electromagnetic energy harvester

    图  4  摆角响应和电压随激励频率的分岔图

    Figure  4.  Bifurcation diagram of the swing angle and voltage with respect to the excitation frequency

    图  5  激励频率在2.5 Hz时俘能器的摆角和电压响应、相轨迹与庞加莱截面和傅里叶频谱

    Figure  5.  Time-domain histories, phase orbit, Poincare map and Fourier spectrum of the swing angle and voltage for the excitation frequency is 2.5 Hz

    图  6  激励频率在4 Hz时俘能器摆角和电压响应、相轨迹与庞加莱截面和傅里叶频谱

    Figure  6.  Time-domain histories, phase orbit, Poincare map and Fourier spectrum of the swing angle and voltage for the excitation frequency is 4 Hz

    图  7  激励频率在10 Hz时俘能器摆角和电压响应、相轨迹与庞加莱截面和傅里叶频谱

    Figure  7.  Time-domain histories, phase orbit, Poincare map and Fourier spectrum of the swing angle and voltage for the excitation frequency is 10 Hz

    图  8  摆角响应和电压随激励幅值的分岔图

    Figure  8.  Bifurcation diagrams of the swing angle and voltage with respect to the excitation amplitude

    图  9  激励幅值在A = 0.35g时俘能器的摆角和电压响应、相轨迹与庞加莱截面和傅里叶频谱

    Figure  9.  Time-domain histories, phase orbit, Poincare map and Fourier spectrum of the swing angle and voltage for the excitation amplitude is 0.35g

    图  10  激励幅值在A = 0.5g时俘能器的摆角和电压响应、相轨迹与庞加莱截面和傅里叶频谱

    Figure  10.  Time-domain histories, phase orbit, Poincare map and Fourier spectrum of the swing angle and voltage for the excitation amplitude is 0.5g

    图  11  激励幅值在A = 0.8g时俘能器摆角和电压响应、相轨迹与庞加莱截面、傅里叶频谱

    Figure  11.  Time-domain histories, phase orbit, Poincare map and Fourier spectrum of the swing angle and voltage for the excitation amplitude is 0.8g

    图  12  试验平台照片

    Figure  12.  Photograph of the experimental platform

    图  13  俘能器的平均功率

    Figure  13.  Average power of the harvester

    图  14  不同激励频率时实验电压响应与傅里叶频谱

    Figure  14.  Experimental time-domain history and Fourier spectrum of voltage under different excitation frequencies

    表  1  非线性磁力的刚度系数

    Table  1.   Stiffness coefficients of nonlinear magnetic force

    Parameterk1k2k3
    Value−0.5181−11.5839.05
    下载: 导出CSV

    表  2  俘能器的几何和材料参数

    Table  2.   Geometric and material properties of the harvester

    CategoriesParametersValues
    tumbler structurer/mm30
    e/mm1.9
    m/kg0.4
    Jc/(kg·mm2)269.54
    H/mm26
    magnetic structure(a1,b1,c1)/mm20,10,10
    (a2,b2,c2)/mm10,30,10
    (xOA,yOA)/mm−75, −85
    $\beta $/(°)40
    Br1/T1.25
    Br2/T1.25
    othersc0.002
    L/mH8.26
    Ra/$\Omega $20
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-07-26
  • 录用日期:  2023-08-22
  • 网络出版日期:  2023-08-23

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