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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