AN ACCURATE MODELLING METHOD OF MAGNETIC FORCE IN MULTI-STABLE ENERGY HARVESTING SYSTEM
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摘要: 混沌和分岔使得多稳态俘能系统的非线性动力学响应对系统结构参数非常敏感, 导致了系统的非线性特性正向设计比较困难. 为了定量地表征非线性恢复力与结构参数的关系, 提出了一种多稳态俘能系统的准确磁力建模方法. 推导了多稳态俘能系统端部磁铁和外部磁铁的相对距离和转角位置, 并采用磁荷理论建立了多稳态系统的非线性磁力模型. 通过搭建实验平台测量了不同结构参数条件下多稳态系统的非线性磁力, 并对比了本方法与传统方法和实验测量的结果. 结果表明: 本方法的磁力计算结果与实验测量值吻合较好, 双稳态系统和三稳态系统的磁力峰值误差分别仅为4.3%和6.49%, 验证了本方法计算多稳态系统非线性磁力的有效性. 此外, 基于本方法探究了多稳态系统结构参数对系统势阱的影响机理, 获取了多稳态系统的稳态临界位置, 研究了双稳态和三稳态系统在不同结构参数下的响应电压规律. 参数优化结果表明, 双稳态系统在竖直距离为34 mm时, 均方电压最大为10.22 V; 三稳态系统在竖直距离为28 mm且水平距离为8 mm时, 均方电压最大为12.7 V. 该研究提出的模型以期为多稳态系统的输出性能优化设计提供借鉴.Abstract: Chaos and bifurcation make the nonlinear dynamic response sensitive to structural parameters for multi-stable energy harvesting system, so that it is difficult to design the nonlinear characteristics directly from structural parameters. In order to acquire the relationship between the nonlinear restoring force and the structural parameters quantitatively, an accurate modelling method of magnetic force for multi-stable energy harvesting system is proposed. The relative distance and the rotational angle between the end magnet and the external magnet are calculated to determine the relative spatial position between magnets, and the magnetic charge theory is adopted to deduce the model of the nonlinear magnetic force in multi-stable energy harvesting system. Then, the experimental platform is carried out to measure the nonlinear magnetic force under different structural parameters for multi-stable energy harvesting system. The comparative analysis shows that the magnetic force calculated by the proposed method is in a better agreement with the experimental result than other methods. The effectiveness of the proposed method for magnetic force prediction is verified by the peak values errors of 4.3% and 6.49% for bi-stable energy harvesting system and tri-stable energy harvesting system respectively. In addition, the influence mechanism of structural parameters on potential wells is investigated to obtain the steady states critical positions of multi-stable energy harvesting system based on the proposed method, and also the influence of different structural parameters on voltage response is analysed for bi-stable and tri-stable energy harvesting systems. After parameters optimization, the maximal RMS voltage response for bi-stable system is 10.22 V in case of the vertical distance 34 mm, while for tri-stable system the maximal RMS voltage response is 12.7 V in case of the vertical distance 28 mm and horizontal distance 8 mm. This research is expected to provide the guidance for the output performance optimization of multi-stable energy harvesting system.
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图 6 竖直距离h对双稳态系统势阱的影响
Figure 6. Influence of vertical distance h on bi-stable potential well
图 7 竖直距离h对双稳态系统响应电压的影响
Figure 7. Influence of vertical distance h on bi-stable voltage response
图 8 竖直距离h对双稳态系统频带影响
Figure 8. Influence of vertical distance h on bandwidth of bi-stable system
图 9 不同竖直距离h的双稳态系统相轨迹图
Figure 9. Phase trajectory of bi-stable system under different vertical distance h
图 11 竖直距离h对三稳态系统势阱的影响
Figure 11. Influence of vertical distance h on tri-stable potential well
图 12 竖直距离h对三稳态系统响应电压的影响
Figure 12. Influence of vertical distance h on tri-stable voltage response
图 13 竖直距离h对三稳态系统频带影响
Figure 13. Influence of vertical distance h on bandwidth of tri-stable system
图 14 不同竖直距离h的三稳态系统相轨迹图
Figure 14. Phase trajectory of tri-stable system under different vertical distance h
图 15 水平距离d对三稳态系统势阱的影响
Figure 15. Influence of horizontal distance d on tri-stable potential well
图 16 水平距离d对三稳态系统响应电压的影响
Figure 16. Influence of horizontal distance d on tri-stable voltage response
图 17 水平距离d对三稳态系统频带影响
Figure 17. Influence of horizontal distance d on bandwidth of tri-stable system
图 18 不同水平距离d的三稳态系统相轨迹图
Figure 18. Phase trajectory of tri-stable system under different horizontal distance d
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[1] Yi Z, Yang B, Zhang W, et al. Batteryless tire pressure real-time monitoring system driven by an ultralow frequency piezoelectric rotational energy harvester. IEEE Transactions on Industrial Electronics, 2020, 68(4): 3192-3201 [2] Qian J, Kim DS, Lee DW. On-vehicle triboelectric nanogenerator enabled self-powered sensor for tire pressure monitoring. Nano Energy, 2018, 49: 126-136 doi: 10.1016/j.nanoen.2018.04.022 [3] Wang Y, Yang Z, Li P, et al. Energy harvesting for jet engine monitoring. Nano Energy, 2020, 75: 104853 doi: 10.1016/j.nanoen.2020.104853 [4] Wu Y, Zhang H, Zuo L. Thermoelectric energy harvesting for the gas turbine sensing and monitoring system. Energy Conversion and Management, 2018, 157: 215-223 doi: 10.1016/j.enconman.2017.12.009 [5] Zhang Z, Du K, Chen X, et al. An air-cushion triboelectric nanogenerator integrated with stretchable electrode for human-motion energy harvesting and monitoring. Nano Energy, 2018, 53: 108-115 doi: 10.1016/j.nanoen.2018.08.011 [6] Park JH, Wu C, Sung S, et al. Ingenious use of natural triboelectrification on the human body for versatile applications in walking energy harvesting and body action monitoring. Nano Energy, 2019, 57: 872-878 doi: 10.1016/j.nanoen.2019.01.001 [7] Ji B, Chen Z, Chen S, et al. Joint optimization for ambient backscatter communication system with energy harvesting for IoT. Mechanical Systems and Signal Processing, 2020, 135: 106412 doi: 10.1016/j.ymssp.2019.106412 [8] Fan K, Tan Q, Zhang Y, et al. A monostable piezoelectric energy harvester for broadband low-level excitations. Applied Physics Letters, 2018, 112(12): 123901 doi: 10.1063/1.5022599 [9] 杨涛. 多稳态能量收集系统的非线性动力学行为及应用研究. [博士论文]. 哈尔滨: 哈尔滨工业大学, 2019Yang Tao. Study on nonlinear dynamics behavior and application of multi-stable energy harvesting systems. [PhD Thesis]. Harbin: Harbin Institute of Technology, 2019 (in Chinese)) [10] Zhou Z, Qin W, Zhu P, et al. Harvesting more energy from variable-speed wind by a multi-stable configuration with vortex-induced vibration and galloping. Energy, 2021, 237: 121551 doi: 10.1016/j.energy.2021.121551 [11] 李海涛, 丁虎, 陈立群等. 三稳态能量收集系统的同宿分岔及混沌动力学分析. 应用数学和力学, 2020, 41(12): 1311-1322 (Li Haitao, Ding Hu, Chen Liqun, et al. Homoclinic bifurcations and chaos thresholds of tristable piezoelectric vibration energy harvesting systems. Applied Mathematics and Mechanics, 2020, 41(12): 1311-1322 (in Chinese) [12] Wang J, Geng L, Zhou S, et al. Design, modeling and experiments of broadband tristable galloping piezoelectric energy harvester. Acta Mechanica Sinica, 2020, 36(3): 592-605 doi: 10.1007/s10409-020-00928-5 [13] Sun S, Leng Y, Su X, et al. Performance of a novel dual-magnet tri-stable piezoelectric energy harvester subjected to random excitation. Energy Conversion and Management, 2021, 239: 114246 doi: 10.1016/j.enconman.2021.114246 [14] Erturk A, Hoffmann J, Inman DJ. A piezomagnetoelastic structure for broadband vibration energy harvesting. Applied Physics Letters, 2009, 94(25): 254102 doi: 10.1063/1.3159815 [15] Moon FC, Holmes PJ. A magnetoelastic strange attractor. Journal of Sound and Vibration, 1979, 65(2): 275-296 doi: 10.1016/0022-460X(79)90520-0 [16] Zhou S, Cao J, Inman DJ, et al. Broadband tristable energy harvester: modeling and experiment verification. Applied Energy, 2014, 133: 33-39 doi: 10.1016/j.apenergy.2014.07.077 [17] Zhou S, Cao J, Erturk A, et al. Enhanced broadband piezoelectric energy harvesting using rotatable magnets. Applied Physics Letters, 2013, 102(17): 173901 doi: 10.1063/1.4803445 [18] Huang D, Zhou S, Litak G. Theoretical analysis of multi-stable energy harvesters with high-order stiffness terms. Communications in Nonlinear Science and Numerical Simulation, 2019, 69: 270-286 doi: 10.1016/j.cnsns.2018.09.025 [19] Cao J, Zhou S, Wang W, et al. Influence of potential well depth on nonlinear tristable energy harvesting. Applied Physics Letters, 2015, 106(17): 173903 doi: 10.1063/1.4919532 [20] Upadrashta D, Yang Y. Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction. Smart Materials and Structures, 2015, 24(4): 045042 doi: 10.1088/0964-1726/24/4/045042 [21] Ferrari M, Ferrari V, Guizzetti M, et al. Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters. Sensors and Actuators A:Physical, 2010, 162(2): 425-431 doi: 10.1016/j.sna.2010.05.022 [22] 周生喜, 曹军义, Erturk Alper等. 压电磁耦合振动能量俘获系统的非线性模型研究. 西安交通大学学报, 2014, 48(1): 106-111Zhou Shengxi, Cao Junyi, Erturk Alper, et al. Nonlinear model for piezoelectric energy harvester with magnetic coupling, Journal of Xi’an Jiaotong University, 2014, 48(1): 106-111 (in Chinese) [23] Abdelmoula H, Zimmerman S, Abdelkefi A. Accurate modeling, comparative analysis, and performance enhancement of broadband piezoelectric energy harvesters with single and dual magnetic forces. International Journal of Non-Linear Mechanics, 2017, 95: 355-363 doi: 10.1016/j.ijnonlinmec.2017.07.008 [24] Yung KW, Landecker PB, Villani DD. An analytic solution for the force between two magnetic dipoles. Magnetic and Electrical Separation, 1970, 9: 079537 [25] Li H, Qin W, Lan C, et al. Dynamics and coherence resonance of tri-stable energy harvesting system. Smart Materials and Structures, 2015, 25(1): 015001 [26] Zhao LC, Zou HX, Yan G, et al. A water-proof magnetically coupled piezoelectric-electromagnetic hybrid wind energy harvester. Applied Energy, 2019, 239: 735-746 doi: 10.1016/j.apenergy.2019.02.006 [27] 谭江平, 王光庆, 鞠洋等. 多稳态压电振动能量采集器的非线性动力学特性及其实验研究. 振动工程学报, 2021, 34(4): 765-774 (Tan Jiangping, Wang Guangqing, Ju Yang, et al. Nonlinear dynamic characteristics and experimental validation of a multi-stable piezoelectric vibration energy harvester. Journal of Vibration Engineering, 2021, 34(4): 765-774 (in Chinese) [28] Zou HX, Li M, Zhao LC, et al. A magnetically coupled bistable piezoelectric harvester for underwater energy harvesting. Energy, 2021, 217: 119429 doi: 10.1016/j.energy.2020.119429 [29] Wang G, Wu H, Liao WH, et al. A modified magnetic force model and experimental validation of a tri-stable piezoelectric energy harvester. Journal of Intelligent Material Systems and Structures, 2020, 31(7): 967-979 doi: 10.1177/1045389X20905975 [30] Wang G, Zhao Z, Liao WH, et al. Characteristics of a tri-stable piezoelectric vibration energy harvester by considering geometric nonlinearity and gravitation effects. Mechanical Systems and Signal Processing, 2020, 138: 106571 doi: 10.1016/j.ymssp.2019.106571 [31] Agashe JS, Arnold DP. A study of scaling and geometry effects on the forces between cuboidal and cylindrical magnets using analytical force solutions. Journal of Physics D:Applied Physics, 2008, 41(10): 105001 doi: 10.1088/0022-3727/41/10/105001 [32] Leng Y, Tan D, Liu J, et al. Magnetic force analysis and performance of a tri-stable piezoelectric energy harvester under random excitation. Journal of Sound and Vibration, 2017, 406: 146-160 doi: 10.1016/j.jsv.2017.06.020 [33] Stanton SC, McGehee CC, Mann BP. Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator. Physica D:Nonlinear Phenomena, 2010, 239(10): 640-653 doi: 10.1016/j.physd.2010.01.019 [34] Erturk A. Assumed-modes modeling of piezoelectric energy harvesters: Euler–Bernoulli, Rayleigh, and Timoshenko models with axial deformations. Computers & Structures, 2012, 106: 214-227 [35] Charpentier JF, Lemarquand G. Optimal design of cylindrical air-gap synchronous permanent magnet couplings. IEEE Transactions on Magnetics, 1999, 35(2): 1037-1046 doi: 10.1109/20.748851 [36] Friswell MI, Ali SF, Bilgen O, et al. Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass. Journal of Intelligent Material Systems and Structures, 2012, 23(13): 1505-1521 doi: 10.1177/1045389X12455722 -
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