搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于磁化电流法的双稳压电悬臂梁磁力精确分析

张雨阳 冷永刚 谭丹 刘进军 范胜波

引用本文:
Citation:

基于磁化电流法的双稳压电悬臂梁磁力精确分析

张雨阳, 冷永刚, 谭丹, 刘进军, 范胜波

Accurate analysis of magnetic force of bi-stable cantilever vibration energy harvesting system with the theory of magnetizing current

Zhang Yu-Yang, Leng Yong-Gang, Tan Dan, Liu Jin-Jun, Fan Sheng-Bo
PDF
导出引用
  • 双稳压电悬臂梁结构常常用于振动能量采集系统,其中的非线性磁力与系统势函数和动力学方程的建立紧密相关,非线性磁力的正确分析和精确计算对系统振动响应和能量采集效果的准确预测至关重要.本文采用形状函数分析方法,通过悬臂梁弯曲斜率的整体积分计算,得到了悬臂梁末端的运动轨迹及其末端磁铁精确的位置与姿态,并由此根据磁化电流理论建立了双稳压电悬臂梁能量采集系统的磁力计算模型,给出了末端磁铁受到的水平轴向磁力和竖直纵向磁力及其合磁力的变化规律.数值模拟发现,随着末端磁铁竖直纵向位移逐渐增大,磁铁受到的水平轴向磁力和竖直纵向磁力都会依次由排斥力转变为吸引力,从而导致磁力合力的方向会随磁铁位移发生跨越两个象限的大幅度变化.实验验证表明,磁力计算结果与实验测量结果符合良好,其精确度优于现有文献方法的精度,因此本文的方法可以准确预测双稳压电悬臂梁振动过程的磁力变化规律.
    In the study of piezoelectric cantilever energy harvesting system, a bi-stable nonlinear cantilever with magnets added to the structure has a wider frequency band response and a higher energy output efficiency. Hence, the calculation accuracy of the magnetic force on which the potential function and dynamics of the system depend is essential to predicting the output response and energy harvesting effect. In this work, we use a shape function to describe the relation between the deflections of an arbitrary point and the free-end point on the beam, and then calculate the trace and deflection angle of the beam's free-end by integrating the entire slope of the cantilever beam. The magnetic force is consequently derived from the magnets' real-time relative positions and postures by using the magnetizing current method. With comprehensively considering the axial magnetic force and the lateral magnetic force, the simulation results demonstrate that when the displacement of the magnet at the end of the beam is large enough, the directions of axial and lateral magnetic force change from repulsive to attractive, which leads to a large veer of the resultant magnetic force across two quadrants. So, it means that a smaller interval between magnets may not cause a larger deflection of the beam, and the magnetic force existing as attractive force could diminish the well space of potential function (that is, the distance between two equilibrium positions of the system). The experimental data in this work are nicely consistent with the simulation results. And in this work, we also make a comparison of the simulation results with those from our method and existing method, showing that the accuracy of the proposed method is much higher than that from the existing calculation method, especially in the scenario where the magnet at the end of the beam is far from the horizontal axis.
      通信作者: 冷永刚, leng_yg@tju.edu.cn
    • 基金项目: 国家自然科学基金(批准号:51675370)和天津市应用基础与前沿技术研究计划(批准号:15JCZDJC32200)资助的课题.
      Corresponding author: Leng Yong-Gang, leng_yg@tju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51675370) and Tianjin Research Program of Application Foundation and Advanced Technology, China (Grant No. 15JCZDJC32200).
    [1]

    Roundy S J 2003 Ph. D. Dissertation (Berkeley: University of California, Berkeley)

    [2]

    Sun J, Li Y G, Liu J Q, Yang C S, He D N (in Chinese) [孙健, 李以贵, 刘景全, 杨春生, 何丹农 2009 微纳电子技术 46 673]

    [3]

    Gao Y J, Leng Y G, Fan S B, Lai Z H 2014 Smart Mater. Struct. 23 095003

    [4]

    Wang Q, Luo Y, Gu J Z (in Chinese) [王强, 骆英, 顾建祖 2008 电子元件与材料 27 47]

    [5]

    Cottone F, Vocca H, Gammaitoni L 2009 Phys. Rev. Lett. 102 080601

    [6]

    And B, Baglio S, Trigona C, Dumas N, Latorre L, Nouet P 2010 J. Micromech. Microeng. 20 125020

    [7]

    Stanton S C, McGehee C C, Mann B P 2010 Physica D 239 640

    [8]

    Fan K Q, Xu C H, Wang W D, Fang Y 2014 Chin. Phys. B 23 084501

    [9]

    Yung K W, Landecker P B, Villani D D 1998 Magn. Electric. Separat. 9 39

    [10]

    Neubauer M, Twiefel J, Westermann H, Wallaschek J 2012 Small-Scale Energy Harvesting (Rijeka: InTech) p303

    [11]

    Tang L H, Yang Y W 2012 Appl. Phys. Lett. 101 094102

    [12]

    Akoun G, Yonnet J P 1984 IEEE Trans. Magn. 20 1962

    [13]

    Tan D, Leng Y G, Fan S B, Gao Y J 2015 Acta Phys. Sin. 64 060502 (in Chinese) [谭丹, 冷永刚, 范胜波, 高毓璣 2015 64 060502]

    [14]

    Lin J T, Lee B, Alphenaar B 2010 Smart Mater. Struct. 19 126

    [15]

    Chen Z S, Yang Y M 2011 Acta Phys. Sin. 60 074301(in Chinese) [陈仲生, 杨拥民 2011 60 074301]

    [16]

    Ferrari M, Ba M, Guizzetti M, Ferrari V 2011 Sens. Actuators A 172 287

    [17]

    Zhou S, Cao J, Erturk A, J Lin Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505

    [18]

    Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505

    [19]

    Esmailzadeh E, Nakhaie-Jazar G 1998 Int. J. Non-Linear Mech. 33 567

    [20]

    Ali S F, Padhi R 2009 P. I. Mech. Eng. I-J. Sys. Contr. Eng. 223 657

    [21]

    Nayfeh A H, Pai P F 2007 Linear and Nonlinear Structural Mechanics (Hoboken:Wiley) pp65-110

    [22]

    Agashe J S, Arnold D P 2008 J. Phys. D:Appl. Phys. 41 1586

    [23]

    Bobbio S, Delfino F, Girdinio P, Molfino P 2000 IEEE Trans. Magn. 36 663

    [24]

    Furlani E P, Reznik S, Kroll A 1995 IEEE Trans. Magn. 31 844

  • [1]

    Roundy S J 2003 Ph. D. Dissertation (Berkeley: University of California, Berkeley)

    [2]

    Sun J, Li Y G, Liu J Q, Yang C S, He D N (in Chinese) [孙健, 李以贵, 刘景全, 杨春生, 何丹农 2009 微纳电子技术 46 673]

    [3]

    Gao Y J, Leng Y G, Fan S B, Lai Z H 2014 Smart Mater. Struct. 23 095003

    [4]

    Wang Q, Luo Y, Gu J Z (in Chinese) [王强, 骆英, 顾建祖 2008 电子元件与材料 27 47]

    [5]

    Cottone F, Vocca H, Gammaitoni L 2009 Phys. Rev. Lett. 102 080601

    [6]

    And B, Baglio S, Trigona C, Dumas N, Latorre L, Nouet P 2010 J. Micromech. Microeng. 20 125020

    [7]

    Stanton S C, McGehee C C, Mann B P 2010 Physica D 239 640

    [8]

    Fan K Q, Xu C H, Wang W D, Fang Y 2014 Chin. Phys. B 23 084501

    [9]

    Yung K W, Landecker P B, Villani D D 1998 Magn. Electric. Separat. 9 39

    [10]

    Neubauer M, Twiefel J, Westermann H, Wallaschek J 2012 Small-Scale Energy Harvesting (Rijeka: InTech) p303

    [11]

    Tang L H, Yang Y W 2012 Appl. Phys. Lett. 101 094102

    [12]

    Akoun G, Yonnet J P 1984 IEEE Trans. Magn. 20 1962

    [13]

    Tan D, Leng Y G, Fan S B, Gao Y J 2015 Acta Phys. Sin. 64 060502 (in Chinese) [谭丹, 冷永刚, 范胜波, 高毓璣 2015 64 060502]

    [14]

    Lin J T, Lee B, Alphenaar B 2010 Smart Mater. Struct. 19 126

    [15]

    Chen Z S, Yang Y M 2011 Acta Phys. Sin. 60 074301(in Chinese) [陈仲生, 杨拥民 2011 60 074301]

    [16]

    Ferrari M, Ba M, Guizzetti M, Ferrari V 2011 Sens. Actuators A 172 287

    [17]

    Zhou S, Cao J, Erturk A, J Lin Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505

    [18]

    Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505

    [19]

    Esmailzadeh E, Nakhaie-Jazar G 1998 Int. J. Non-Linear Mech. 33 567

    [20]

    Ali S F, Padhi R 2009 P. I. Mech. Eng. I-J. Sys. Contr. Eng. 223 657

    [21]

    Nayfeh A H, Pai P F 2007 Linear and Nonlinear Structural Mechanics (Hoboken:Wiley) pp65-110

    [22]

    Agashe J S, Arnold D P 2008 J. Phys. D:Appl. Phys. 41 1586

    [23]

    Bobbio S, Delfino F, Girdinio P, Molfino P 2000 IEEE Trans. Magn. 36 663

    [24]

    Furlani E P, Reznik S, Kroll A 1995 IEEE Trans. Magn. 31 844

  • [1] 孙帅令, 冷永刚, 张雨阳, 苏徐昆, 范胜波. 双磁铁多稳态悬臂梁磁力及势能函数分析.  , 2020, 69(14): 140502. doi: 10.7498/aps.69.20191981
    [2] 杨建华, 马强, 吴呈锦, 刘后广. 分数阶双稳系统中的非周期振动共振.  , 2018, 67(5): 054501. doi: 10.7498/aps.67.20172046
    [3] 秦立振, 张振宇, 张坤, 丁建桥, 段智勇, 苏宇锋. 抗磁悬浮振动能量采集器动力学响应的仿真分析.  , 2018, 67(1): 018501. doi: 10.7498/aps.67.20171551
    [4] 吴娟娟, 冷永刚, 乔海, 刘进军, 张雨阳. 窄带随机激励双稳压电悬臂梁响应机制与能量采集研究.  , 2018, 67(21): 210502. doi: 10.7498/aps.67.20180072
    [5] 代显智, 刘小亚, 陈蕾. 一种采用双换能器和摆式结构的宽频振动能量采集器.  , 2016, 65(13): 130701. doi: 10.7498/aps.65.130701
    [6] 杜超凡, 章定国. 基于无网格点插值法的旋转悬臂梁的动力学分析.  , 2015, 64(3): 034501. doi: 10.7498/aps.64.034501
    [7] 武丽明, 张晓青. 交联聚丙烯压电驻极体的压电性能及振动能量采集研究.  , 2015, 64(17): 177701. doi: 10.7498/aps.64.177701
    [8] 谭丹, 冷永刚, 范胜波, 高毓璣. 外加磁场压电悬臂梁能量采集系统的磁化电流法磁力研究.  , 2015, 64(6): 060502. doi: 10.7498/aps.64.060502
    [9] 范纪华, 章定国. 旋转柔性悬臂梁动力学的Bezier插值离散方法研究.  , 2014, 63(15): 154501. doi: 10.7498/aps.63.154501
    [10] 李海涛, 秦卫阳, 周志勇, 蓝春波. 带有分数阶阻尼的压电能量采集系统相干共振.  , 2014, 63(22): 220504. doi: 10.7498/aps.63.220504
    [11] 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.  , 2014, 63(24): 240504. doi: 10.7498/aps.63.240504
    [12] 高毓璣, 冷永刚, 范胜波, 赖志慧. 弹性支撑双稳压电悬臂梁振动响应及能量采集研究.  , 2014, 63(9): 090501. doi: 10.7498/aps.63.090501
    [13] 方建士, 章定国. 旋转内接悬臂梁的刚柔耦合动力学特性分析.  , 2013, 62(4): 044501. doi: 10.7498/aps.62.044501
    [14] 林敏, 黄咏梅. 双稳系统随机共振的能量输入机理.  , 2012, 61(22): 220205. doi: 10.7498/aps.61.220205
    [15] 陈仲生, 杨拥民. 悬臂梁压电振子宽带低频振动能量俘获的随机共振机理研究.  , 2011, 60(7): 074301. doi: 10.7498/aps.60.074301
    [16] 代显智, 文玉梅, 李平, 杨进, 江小芳. 采用磁电换能器的振动能量采集器.  , 2010, 59(3): 2137-2146. doi: 10.7498/aps.59.2137
    [17] 董浩, 任敏, 张磊, 邓宁, 陈培毅. 电流驱动磁化翻转中的热效应.  , 2009, 58(10): 7176-7182. doi: 10.7498/aps.58.7176
    [18] 于晓梅, 张大成, 王丛舜, 李婷, 阮勇. U形阵列式微机械悬臂梁的研究.  , 2004, 53(1): 31-36. doi: 10.7498/aps.53.31
    [19] 刘长清, 金柱京, 李美栓, 呼和吉夫, 吴维?. 悬臂梁弯曲法研究氮化钛薄膜临界开裂行为与损毁机理.  , 1992, 41(7): 1137-1142. doi: 10.7498/aps.41.1137
    [20] 胡海昌. 各向异性的悬臂梁负担均布载荷的弯曲问题.  , 1956, 12(4): 339-349. doi: 10.7498/aps.12.339
计量
  • 文章访问数:  6824
  • PDF下载量:  143
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-03-22
  • 修回日期:  2017-08-21
  • 刊出日期:  2017-11-05

/

返回文章
返回
Baidu
map