Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.     

Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment

A vibration-based bistable electromagnetic energy harvester coupled to a directly excited primary system is examined numerically. The primary goal of the study is to investigate the potential benefit of the bistable element for harvesting broadband and low-amplitude vibration energy. The considered system consists of a grounded, weakly damped, linear oscillator (LO) coupled to a light-weight, weakly damped oscillator by means of an element which provides both cubic nonlinear and negative linear stiffness components and electromechanical coupling elements. Single and repeated impulses with varying amplitude applied to the LO are the vibration energy sources considered. A thorough sensitivity analysis of the system's key parameters provides design insights for a bistable nonlinear energy harvesting (BNEH) device able to achieve robust harvesting efficiency. This is achieved through the exploitation of three BNEH main dynamical regimes; namely, periodic cross-well, aperiodic (chaotic) cross-well, and in-well oscillations.     

双稳态电磁式振动能量捕获器超谐波响应研究

超谐波响应是非线性振动系统在较大激励下表现的特性,在某种条件下双稳态振动能量捕获系统的超谐波响应可使系统产生优越的输出功率。本文将质量-非线性弹簧-阻尼系统与双稳态振动能量捕获器相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程。采用两项式谐波平衡法,获得了双稳态系统在简谐激励下产生大幅运动的基谐波和超谐波响应的解析解,借助数值仿真分析了质量比和调频比对双稳态振动能量捕获器产生大幅运动的影响规律,获得了双稳态系统的结构参数的最佳配置范围,且当外部激励频率处于低频段时,系统发电主要表现为超谐波发电,随着激励频率的增大,振动发电系统主要呈现基谐波发电。上述研究,为双稳态能量捕获装置的理论研究提供了参考。     

Modeling and analysis of magnetic spring enhanced lever-type electromagnetic energy harvesters

This study presents a novel enhanced monostable lever-type electromagnetic energy harvester (L-EEH). According to the positions of the coil and the lever pivot, four configurations are discussed to realize a better harvesting performance of the L-EEHs. On the basis of establishing the theoretical model of the L-EEH, the corresponding analytical solutions can be obtained by applying the harmonic balance method. The effects of the nonlinear coe-cient, the lever ratio, the mass ratio, and the circuit parameters on the energy harvesting performance of L-EEHs are analyzed and discussed. The numerical and experimental efforts are carried out to verify the theoretical model and the energy harvesting performance. The results demonstrate that the maximum output voltage can be achieved with an appropriate lever ratio. Furthermore, the L-EEH possesses a considerable energy harvesting performance under a smaller lever ratio compared with the other three configurations. The output power can also be improved by adjusting the tip mass of the lever. The proposed L-EEH has a considerable operating bandwidth and an output power, which can reach 146.6 mW under the excitation amplitude of 0.3g.     

基于人体运动的压电-电磁混合式振动能量采集研究

将人体运动产生的动能转化为可利用的电能为传感器供电一直是能量采研究中的一个热点。如何有效利用人体运动,增强环境适应能力以及提高能量采集性能仍是俘能研究中需要解决的关键问题。本文基于人体运动特性,设计了一种新型的混合式能量采集器,同时具有压电和电磁转化机制。压电俘能是基于压电梁变形产生电能,电磁发电机采用堆叠磁组构型来切割线圈产生电动势。首先建立了混合式能量采集器的动力学理论模型,用来描述输出电压特性,并与实验进行了对比验证。理论与实验研究均表明,混合式俘能器的输出电压在一定激励频率范围内出现两个波峰。通过调节压电梁长度,可以改变峰值大小以及两个峰值间的频段范围。人体运动实验表明,混合式俘能器中可以在短时间内提供较高的电压输出,比如当跑步速度为5km/h时,3s内就可以输出1.1V直流电压驱动传感器工作;跑步时长为30s时,传感器正常工作时常可以达到77s。本文设计的混合式俘能器不仅可以快速供电,还具有较强的续航能力,这为电池充电或传感器供电提供了潜在的应用价值。     

A piezoelectric energy harvester based on internal resonance

A vibration-based energy harvester is essentially a resonator working in a limited frequency range.To increase the working frequency range is a challenging problem.This paper reveals a novel possibility for enhancing energy harvesting via internal resonance.An internal resonance energy harvester is proposed.The excitation is successively assumed as the Gaussian white noise,the colored noise defined by a second-order filter,the narrow-band noise,and exponentially correlated noise.The corresponding averaged root-meansquare output voltages are computed.Numerical results demonstrate that the internal resonance increases the operating bandwidth and the output voltage.     

附磁压电悬臂梁流致振动俘能特性分析

流致振动蕴含巨大的能量, 本文基于流致振动理论,设计了一种附加磁力激励的压电悬臂梁流致振动俘能器,并通过理论和实验研究其振动俘能特性.该俘能器由压电悬臂梁、圆柱绕流体和磁铁组成;首先基于Euler-Bernoulli梁理论,推导了流致振动附磁压电俘能器的能量函数,利用Hamilton原理建立了流致振动附磁压电俘能器的机电耦合方程;利用数值方法研究详细分析了流速、圆柱绕流体直径和长度、磁间距、磁极和外接电阻等系统参数对压电俘能器振动特性和输出电压的影响.分析结果表明, 该型压电俘能器的振动幅值在低流速条件下产生涡激振动,并产生最大的输出电压;磁力可以降低压电俘能器的共振频率并能够拓宽压电俘能器频带带宽,因此,附磁压电俘能器具有相比没有附磁的压电俘能器更适用于低速层流环境;实验结果与数值结果吻合较好,验证了附磁压电悬臂梁流致振动俘能器的理论分析的正确性.      

Structural and electrical dynamics of a grating-patterned triboelectric energy harvester with stick–slip oscillation and magnetic bistability

The majority of research work on triboelectric energy harvesting is on material science, manufacturing and electric circuit design. There is a lack of in-depth research into structural dynamics which is crucial for power generation in triboelectric energy harvesting. In this paper, a novel triboelectric energy harvester with a compact structure working in sliding mode is developed, which is in the form of a casing and an oscillator inside. Unlike most sliding-mode harvesters using single-unit films, the proposed harvester utilizes grating-patterned films which are much more efficient. A bistable mechanism consisting of two pairs of magnets is employed for broadening the frequency bandwidth. A theoretical model is established for the harvester, which couples the structural dynamics domain and electrical dynamics domain. This paper presents the first study about the nonlinear structural dynamics of a triboelectric energy harvester with grating-patterned films, which is also the first triboelectric energy harvester integrating grating-patterned films with a bistable magnetic system for power performance enhancement. Theoretical studies are carried out from the perspectives of both structural and electrical dynamics. Surface charge density and segment configuration of the films affect whether the electrostatic force influences the structural dynamics, which can be neglected under a low surface charge density. Differences in structural response and electrical output are found between a velocity-dependent model and Coulomb’s model for modelling the friction in the triboelectric energy harvesting system. The bistable mechanism can effectively improve the output voltage under low-frequency excitations. Additionally, the output voltage can also be obviously enhanced through increasing the number of the hollowed-out units of the grating-patterned films, which also results in a slight decrease in the optimal load resistance of the harvester. These findings enable innovative designs for triboelectric energy harvesters and provide fabrication guidelines in practical applications.

     

翼型颤振压电俘能器的输出特性研究

压电俘能器能够为自然界中低功率的微机电系统持续供能. 为了模拟机翼的沉浮?俯仰二自由度运动和有效俘获气动弹性振动能量, 本文提出一种新颖的翼型颤振压电俘能器. 基于非定常气动力模型, 推导翼型颤振压电俘能器流?固?电耦合场的数学模型. 建立有限元模型, 模拟机翼的沉浮?俯仰二自由度运动, 获得机翼附近的涡旋脱落和流场特性. 搭建风洞实验系统, 制作压电俘能器样机. 利用实验验证理论和仿真模型的正确性, 仿真分析压电俘能器结构参数对其气动弹性振动响应和俘获性能的影响. 结果表明: 理论分析、仿真模拟和实验研究获得的输出电压具有较好的一致性, 验证建立数学和仿真模型的正确性. 仿真分析获得机翼附近的压力场变化云图, 表明交替的压力差驱动机翼发生二自由度沉浮?俯仰运动. 当风速超过颤振起始速度时, 压电俘能器发生颤振, 并表现为极限环振荡. 当偏心距为0.3和风速为16 m/s时, 可获得最大输出电压为17.88 V和输出功率为1.278 mW. 功率密度为7.99 mW/cm3, 相比较于其他压电俘能器, 能实现优越的俘获性能. 研究结果对设计更高效的翼型颤振压电俘能器提供重要的指导意义.      

线绳驱动转速提升式低频俘能器的设计与研究

俘获周围环境中丰富的低频机械能对减少废旧电池数量、实现自维持传感器、降低传感器网络的使用和维护成本等具有重要意义, 但传统的振动型俘能器对低频机械能的俘获效果不佳. 为了有效收集周围环境中的低频机械能, 本文提出一种线绳驱动、具备转速提升功能的电磁式俘能器, 首先借助线绳驱动转轴结构将低频振动转换为双向旋转运动, 再通过刚度自动改变的拨片和磁齿轮将双向旋转运动转换为转速更高的单向旋转运动, 从而提高输出功率. 对所提出的俘能器建立了机电耦合动力学模型, 并通过样机制作和实验测试证实了理论模型的正确性. 实验研究表明, 在激励幅值40 mm和激励频率2 Hz的条件下, 通过本文设计制作的2.5倍转速提升功能的磁齿轮, 可将线绳驱动电磁式俘能器的最大输出功率增加至7.82 mW, 比对应的无磁齿轮提升转速的线绳驱动电磁式俘能器的最大输出功率(3.22 mW)高约143%. 在相同的激励条件下, 制作的俘能器的交流电能经过桥式整流器转换为直流后, 可在1.2 s内将220 μF储能电容器的电压从0 V提升至1.5 V. 在低频、不规则的振动激励下, 所制作的俘能器仍可提供0.35 mW的输出功率, 为设计高性能低频俘能器提供一条可行的解决方案.      

面内压电振动能量采集动力学设计与性能研究

压电振动能量采集将环境中普遍存在的机械能转换为电能,可以实现自供能传感、控制与驱动,具备灵活、节能环保、可持续的优势,具有广阔的应用前景。为了促进压电振动能量采集器件的集成与融合,提出面内压电振动能量采集,将压电振动能量采集器进行扁平化设计,使其在二维平面内采集振动能量,在保证较大功率输出下能够显著减小器件所需三维空间。为了提高输出功率与工作频宽,设计了具有双稳态与力放大机制的面内压电振动能量采集器。考虑弯张小变形,通过能量法建立了面内压电振动能量采集器的机电耦合动力学模型。分析了关键设计参数对面内压电振动能量采集器性能的影响。数值仿真了面内压电振动能量采集器在简谐激励下的俘能性能,结果表明,通过合理的设计,面内压电振动能量采集器可以低频、宽频弱激励下有效俘获能量。面内压电振动能量采集设计方法有利于推动便携式、可穿戴式自供能等方面的应用和产业化。     

基于非线性谐振电路的双稳态俘能器的俘能与动力学特性研究

双稳态俘能器可实现宽频和高效的俘能效果.目前的研究主要在双稳态结构中接入单一电阻电路进行俘能.本文将非线性RLC (电阻-电感-电容)谐振电路引入到三弹簧式双稳态结构中,构建两自由度非线性系统,以实现俘能特性的提升.设计永磁体与线圈的构型,获得了非线性机电耦合系数.推导并得到了两自由度非线性俘能器的控制方程.利用谐波平衡法推导得到了系统的电流与位移的频率响应关系.基于雅可比矩阵对解的稳定性进行了判别.将解析解与数值解进行了对比验证.结果表明,在双稳态俘能器中引入非线性二阶谐振电路不仅有利于低频俘能,还可进一步提升俘能响应,拓宽俘能带宽.相同的电路参数下,与线性电路相比非线性电路可通过电流的倍频现象实现结构更低频率的能量俘获.减小谐振电路与双稳态结构共振频率之比,增加基础激励幅值,减小静平衡点之间的距离均可提升俘能器的俘能效果.通过调控谐振电路与双稳态共振频率之比和基础激励幅值等参数,可实现系统单倍周期响应、多倍周期响应及混沌响应之间的切换.     

双稳态压电俘能器的簇发振荡与俘能效率分析

本文从理论上分析了双稳态压电俘能器在高频激励下的动力学行为和低频激励下的簇发振荡, 旨在为系统找到多条高能轨道从而提高俘能效率. 首先, 介绍了双稳态压电俘能器的结构以及一般模型. 与工程上研究俘能器的目的不同, 本文主要从动力学方面分析了俘能器的运动, 电压输出与效率, 包括高频激励下系统的低能阱内周期运动、阱间混沌运动等, 并说明了单个低频激励下双稳态压电俘能器会在阱间高能轨道上发生簇发振荡, 但在阱内低能轨道上只做周期运动. 同时, 结合振幅以及势阱深度等因素对簇发振荡的存在性和强度进行分析. 为了说明高能轨道与低能轨道对系统俘能效率的影响, 讨论了不同的等效阻尼、负载电阻下俘能器输出电压的变化, 找到了最优匹配. 最后, 对于多个低频外激励的情况, 从不同的轨道组合模式上得到了双高能簇发振荡模式输出的电压最大, 其次是单高能簇发振荡与单低能周期振荡的组合模式, 输出电压最低的是双低能周期振荡模式. 并与单个外激励进行对比, 表现了多个激励的良好性能.      

Energy harvesting in a nonlinear energy sink absorber using delayed resonators

Nonlinear Dynamics - This paper examines periodic and quasi-periodic (QP) vibration-based energy harvesting (EH) in a nonlinear energy sink (NES) absorber that is coupled to an electric circuit...     

带附加质量块的压电圆板能量采集器振动分析

基于圆板的压电能量采集技术在取代化学电池为低功耗电子器件提供能源方面具有巨大的潜能. 本文通过理论建模和数值仿真研究了考虑附加质量接触面积的压电圆板能量采集器的采集性能. 首先, 基于基尔霍夫薄板理论, 用广义哈密顿原理推导了带附加质量块的压电圆板能量采集器的机电耦合方程, 并用伽辽金法对方程近似离散, 通过离散方程得到电压、功率输出和最优负载阻抗的闭合解. 用有限元仿真对所提出的理论模型进行了验证, 结果表明该理论模型可以成功地预测压电圆板能量采集器输出电压和功率. 最后, 基于闭合解探讨了负载阻抗、附加质量块、压电圆板的内外半径等相关参数对压电圆板能量采集器固有频率、输出电压和功率的影响. 结果表明, 当质量块与复合板的接触半径足够小(本文中接触半径小于板半径的1/14)时, 质量块与复合圆板的接触面积可以忽略; 相较于无孔的压电片, 内径位于2.5 ~ 4 mm范围内的压电片可以提高能量采集器的采集性能; 附加质量、压电片外径和负载阻抗的合理选择既可以降低压电圆板的固有频率, 还可以提高其采集性能.      

On the design of an electromagnetic aeroelastic energy harvester from nonlinear flutter

A new energy harvester by coupling the electromagnetic induction and the pitch vibration of a rigid wing is built up in this paper. It is aimed: (1) to harvest energy from the pitch limit cycle oscillation (LCO) of the wing due to the preloaded free-play nonlinearity; (2) to introduce a theoretical analysis scheme based on the equivalent linearized method into the design of this harvester. With the equivalent linearized method, the domains of the single stable LCO and double stable LCOs are respectively obtained. Combining the analytical and numerical solutions, the single stable LCO along with the stable limit cycle amplitude greater than its corresponding unstable one is recognized as the better mode for harvesting, since the larger limit cycle domain is induced and the more energy are yielded. Based on such chosen mode, analyses of varying parameters are conducted with respect to the plunge stiffness, pitch stiffness, distance of elastic axis from center of gravity, distance of geometric center from elastic axis, load resistance and magnetic flux density. Meanwhile, three indicators are applied to reveal their effects on the harvesting performances: (1) the size of limit cycle domain, (2) the onset velocity of LCO, and (3) the energy output.     

磁力耦合道路能量收集设计与动力学分析

通过在交通环境布置无线传感器等小型机电系统, 实现交通状况监测、交通系统管控、交通设施健康状态监测等, 可以使交通系统更加安全、有序、高效地运行. 但是, 如何为这些广泛分布的小型机电系统供能？本文提出了一种磁力耦合道路能量收集设计, 用以收集车辆滚压能量并转换成电能. 通过磁力耦合进行无接触能量传递, 减小了装置受到的冲击并使得装置具有良好密封性, 从而提升装置的鲁棒性. 通过升频齿轮机构、棘轮机构将车辆滚压激励转换为高速单向旋转, 并且通过换向齿轮机构能够继续收集复位弹性势能, 提高了收集装置的输出功率. 基于磁力耦合道路能量收集系统的工作原理建立了机电耦合动力学模型. 数值仿真探究了减速带限位距离和复位弹簧刚度等关键设计参数对能量采集系统动力学和电学性能的影响. 能量采集系统在车速为50 km/h时最大输出电压为76.28 V, 最大功率为59.94 W. 磁力耦合道路能量收集装置可以成为未来智慧交通系统的重要组成部分, 俘获交通环境能量为交通环境中小型机电系统提供可持续的绿色无碳电力.      

The Response of a Parametrically Excited van der Pol Oscillator to a Time Delay State Feedback

We investigate the parametric resonance of a van der Pol oscillator under state feedback control with a time delay. Using the asymptotic perturbation method, we obtain two slow-flow equations on the amplitude and phase ofthe oscillator. Their fixed points correspond to a periodic motion forthe starting system and we show parametric excitation-response andfrequency-response curves. We analyze the effect of time delay andfeedback gains from the viewpoint of vibration control and use energyconsiderations to study the existence and characteristics of limit cycles of the slow-flow equations. A limit cycle corresponds to a two-periodmodulated motion for the van der Pol oscillator. Analytical results areverified with numerical simulations. In order to exclude the possibilityof quasi-periodic motion and to reduce the amplitude peak of theparametric resonance, we find the appropriate choices for the feedbackgains and the time delay.     

Nonlinear energy harvesting from vibratory disc-shaped piezoelectric laminates

Implementing resonators with geometrical nonlinearities in vibrational energy harvesting systems leads to considerable enhancement of their operational bandwidths. This advantage of nonlinear devices in comparison to their linear counterparts is much more obvious especially at small-scale where transition to nonlinear regime of vibration occurs at moderately small amplitudes of the base excitation. In this paper the nonlinear behavior of a disc-shaped piezoelectric laminated harvester considering midplane-stretching effect is investigated. Extended Hamilton's principle is exploited to extract electromechanically coupled governing partial differential equations of the system. The equations are firstly order-reduced and then analytically solved implementing perturbation method of multiple scales. A nonlinear finite element method(FEM) simulation of the system is performed additionally for the purpose of verification which shows agreement with the analytical solution to a large extent. The frequency response of the output power at primary resonance of the harvester is calculated to investigate the effect of nonlinearity on the system performance. Effect of various parameters including mechanical quality factor, external load impedance and base excitation amplitude on the behavior of the system are studied. Findings indicate that in the nonlinear regime both output power and operational bandwidth of the harvester will be enhanced by increasing the mechanical quality factor which can be considered as a significant advantage in comparison to linear harvesters in which these two factors vary in opposite ways as quality factor is changed.     

Dynamic interactions of an integrated vehicle–electromagnetic energy harvester–tire system subject to uneven road excitations

An investigation is undertaken of an integrated mechanical-electromagnetic coupling system consisting of a rigid vehicle with heave, roll, and pitch motions, four electro-magnetic energy harvesters and four tires subject to uneven road excitations in order to improve the passengers' riding comfort and harvest the lost engine energy due to uneven roads. Following the derived mathematical formulations and the proposed solution approaches, the numerical simulations of this interaction system subject to a continuous sinusoidal road excitation and a single ramp impact are completed. The simulation results are presented as the dynamic response curves in the forms of the frequency spectrum and the time history, which reveals the complex interaction characteristics of the system for vibration reductions and energy harvesting performance. It has addressed the coupling effects on the dynamic characteristics of the integrated system caused by:(1) the natural modes and frequencies of the vehicle;(2) the vehicle rolling and pitching motions;(3) different road exci-tations on four wheels;(4) the time delay of a road ramp to impact both the front and rear wheels, etc., which cannot be tackled by an often used quarter vehicle model. The guide-lines for engineering applications are given. The developed coupling model and the revealed concept provide a means with analysis idea to investigate the details of four energy harvester motions for electromagnetic suspension designs in order to replace the current passive vehicle isolators and to harvest the lost engine energy. Potential further research directions are suggested for readers to consider in the future.