工程科学学报，第40卷，第4期：492-499,2018年4月 Chinese Journal of Engineering,Vol.40,No.4:492-499,April 2018 DOI:10.13374/j.issn2095-9389.2018.04.013:http://journals.ustb.edu.cn 基于驻极体静电俘能器的优化设计与实验测试 路俊虎”，金磊”，高世桥”，高春晖”，吕庆山，刘海鹏⑧ 1)北京理工大学爆炸科学与技术国家重点实验室，北京1000812)中国兵器工业导航与控制技术研究所，北京100854 ☒通信作者，E-mail:lhp@bit.cdu.cm 摘要针对环境中的低频振动能量，建立了一种双端固支梁振动式驻极体静电俘能器理论模型.利用Matlab/Simulink数值 仿真对静电俘能器的各项关键参数进行了优化.分别研究了静电俘能器的输出功率、谐振频率、半功率带宽与驻极体表面电 位、空气间隙以及负载电阻的关系.在研究中，外部激励加速度幅值及驻极体尺寸保持恒定.数值分析结果如下：(1)存在一 个最佳表面电位使得静电俘能器的输出功率达到最大值，随着表面电位的增加，软弹簧效应逐渐增强使得俘能器谐振频率发 生偏移，半功率带宽逐渐增大。(2)当表面电位一定时，存在一个最佳初始空气间隙使得功率达到最大，随着间隙的增大，半功 率带宽随之减小.(3)当表面电位和空气间隙保持一定时，存在一个最佳负载使得功率达到最大，随着负载的减小，谐振频率 发生偏移.(4)当空气间隙一定时，存在一个最佳负载使得带宽达到最大，且表面电位越大，相同负载下的带宽越大.实验测 试了不同负载电阻下俘能器的输出特性：输出功率及半功率带宽都随着负载电阻的增大，先增大而后减小。当负载电阻为90 M时，对应的最大输出功率为0.188mW:当负载电阻为330M时，对应的半功率带宽达到最大值为4.7Hz. 关键词驻极体：表面电位；空气间隙：负载电阻：谐振频率；半功率带宽；实验测试 分类号TN712.4 Optimization design and experimental test of an electret-based electrostatic energy harvester LU Jun-hu",JIN Lei,GAO Shi-qiao,GAO Chun-hui,L0 Qing-shan2,LIU Hai-peng 1)State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology,Beijing 100081,China 2)Institute of Navigation and Control Technology of China Weaponry Industry,Beijing 100854,China Corresponding author,E-mail:Ihp@bit.edu.cn ABSTRACT A theoretical model of a vibrating electret electrostatic energy harvester for a double-ended fixed beam was established herein for a low-frequency vibration energy in the environment.The key parameters of the electrostatic energy harvester were optimized by a MATLAB/Simulink numerical analysis.The relationship between the output power,resonant frequency,and half-power bandwidth and the electret surface potential,air gap,and load resistance was also studied.The magnitude of the external excitation acceleration and the size of the electret remained constant.The numerical results are as follows:(1)the existence of an optimal surface potential makes the output power of the electrostatic energy harvester reach the maximum value.The soft spring effect gradually increases with the increase of the surface potential,making the resonant frequency of the energy harvester device shift.The bandwidth also gradually increases.(2)An optimal initial air gap maximizes the power when the surface potential is constant.The half-power bandwidth decrea- ses as the gap increases.(3)An optimal load maximizes the power when the surface potential and the air gap remains constant.The resonant frequency is offset as the load decreases.(4)An optimal load is used to maximize the half-power bandwidth when the air gap is constant.The larger the surface potential,the greater the half-power bandwidth under the same load.Experiments show that the out- put characteristics of the energy harvester under different load resistances have the following characteristics:with the increase of the 收稿日期：2017-06-12 基金项目：国家“863”计划基金资助项目(SS2013AA011104)工程科学学报，第 40 卷，第 4 期: 492--499，2018 年 4 月 Chinese Journal of Engineering，Vol． 40，No． 4: 492--499，April 2018 DOI: 10． 13374 /j． issn2095--9389． 2018． 04． 013; http: / /journals． ustb． edu． cn 基于驻极体静电俘能器的优化设计与实验测试 路俊虎1) ，金 磊1) ，高世桥1) ，高春晖1) ，吕庆山2) ，刘海鹏1)  1) 北京理工大学爆炸科学与技术国家重点实验室，北京 100081 2) 中国兵器工业导航与控制技术研究所，北京 100854 通信作者，E-mail: lhp@ bit． edu． cn 摘 要 针对环境中的低频振动能量，建立了一种双端固支梁振动式驻极体静电俘能器理论模型． 利用 Matlab/ Simulink 数值 仿真对静电俘能器的各项关键参数进行了优化． 分别研究了静电俘能器的输出功率、谐振频率、半功率带宽与驻极体表面电 位、空气间隙以及负载电阻的关系． 在研究中，外部激励加速度幅值及驻极体尺寸保持恒定． 数值分析结果如下: ( 1) 存在一 个最佳表面电位使得静电俘能器的输出功率达到最大值，随着表面电位的增加，软弹簧效应逐渐增强使得俘能器谐振频率发 生偏移，半功率带宽逐渐增大． ( 2) 当表面电位一定时，存在一个最佳初始空气间隙使得功率达到最大，随着间隙的增大，半功 率带宽随之减小． ( 3) 当表面电位和空气间隙保持一定时，存在一个最佳负载使得功率达到最大，随着负载的减小，谐振频率 发生偏移． ( 4) 当空气间隙一定时，存在一个最佳负载使得带宽达到最大，且表面电位越大，相同负载下的带宽越大． 实验测 试了不同负载电阻下俘能器的输出特性: 输出功率及半功率带宽都随着负载电阻的增大，先增大而后减小． 当负载电阻为 90 MΩ 时，对应的最大输出功率为 0. 188 mW; 当负载电阻为 330 MΩ 时，对应的半功率带宽达到最大值为 4. 7 Hz． 关键词 驻极体; 表面电位; 空气间隙; 负载电阻; 谐振频率; 半功率带宽; 实验测试 分类号 TN712. 4 收稿日期: 2017--06--12 基金项目: 国家“863”计划基金资助项目( SS2013AA011104) Optimization design and experimental test of an electret-based electrostatic energy harvester LU Jun-hu1) ，JIN Lei1) ，GAO Shi-qiao1) ，GAO Chun-hui1) ，L Qing-shan2) ，LIU Hai-peng1)  1) State Key Laboratory of Explosion Science and Technology，Beijing Institute of Technology，Beijing 100081，China 2) Institute of Navigation and Control Technology of China Weaponry Industry，Beijing 100854，China Corresponding author，E-mail: lhp@ bit． edu． cn ABSTＲACT A theoretical model of a vibrating electret electrostatic energy harvester for a double-ended fixed beam was established herein for a low-frequency vibration energy in the environment． The key parameters of the electrostatic energy harvester were optimized by a MATLAB/ Simulink numerical analysis． The relationship between the output power，resonant frequency，and half-power bandwidth and the electret surface potential，air gap，and load resistance was also studied． The magnitude of the external excitation acceleration and the size of the electret remained constant． The numerical results are as follows: ( 1) the existence of an optimal surface potential makes the output power of the electrostatic energy harvester reach the maximum value． The soft spring effect gradually increases with the increase of the surface potential，making the resonant frequency of the energy harvester device shift． The bandwidth also gradually increases． ( 2) An optimal initial air gap maximizes the power when the surface potential is constant． The half-power bandwidth decrea￾ses as the gap increases． ( 3) An optimal load maximizes the power when the surface potential and the air gap remains constant． The resonant frequency is offset as the load decreases． ( 4) An optimal load is used to maximize the half-power bandwidth when the air gap is constant． The larger the surface potential，the greater the half-power bandwidth under the same load． Experiments show that the out￾put characteristics of the energy harvester under different load resistances have the following characteristics: with the increase of the