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.

     

多稳态串联折纸结构的非线性动力学特性

折纸结构和折纸力学超材料由于其无穷的设计空间、出色的变形能力、超常规力学特性和广泛的应用前景,最近受到了学术界和工程界的 广泛关注.特别地,某些折纸结构单胞由于具有独特的双稳态特性而获得深入研究.注意到折纸结构和折纸超材料通常由多胞构成,但多胞 结构的多稳态特性及其诱发的动力学行为尚不清晰,相关的研究还较少.本文在双稳态Miura-ori堆叠结构单胞的基础上,研究由两个异构 双稳态单胞基于力平衡串联而成的结构.静力学分析指出,双胞串联结构具有4个定性不同的稳定构型,呈现出多稳态特征.动力学分析指 出,双胞串联结构在4个稳定构型处具有显著不同的固有频率特征. 逐渐增大激励幅值,双胞串联结构的多稳态特性诱发出类型丰富的复杂 非线性动力学响应,包括亚谐、超谐甚至混沌的阱内和阱间振动. 根据幅值特征,我们将稳态动力学响应分为九类,并开展了动力学响应的 吸引盆和吸引盆稳定性分析.结果表明,不同类型动力学响应的吸引盆稳定性(即出现概率)显著不同,且与激励幅值密切相关.本文得到的 多稳态双胞串联结构的静力学特性、动力学响应的分类,以及吸引盆稳定性相对于激励幅值的演化规律,对深入认识多稳态折纸结构的非 线性动力学特性,调控非线性动力学响应具有参考价值和指导意义.      

On the use of discontinuous nonlinear bistable dynamics to increase the responsiveness of energy harvesting devices

There is promise in the use of bistable devices to transduce ambient vibrations into electrical power. However, it is critical to sustain the relatively large amplitude snap-through motion, or interwell motion, to significantly improve the responsiveness of bistable devices as compared to linear resonance-based approaches. This work posits that relatively stiff structural elements can be placed in the vicinity of the equilibria of bistable devices such that the discontinuous change in dynamics will tend to eject an otherwise small amplitude motion into the large amplitude interwell orbit that is to be preferred for energy harvesting applications. The discontinuous nonlinear dynamic equations of motion are derived and a proxy system parametrically studied. These numerical studies demonstrate that discontinuous nonlinear bistable devices have a significantly broadened frequency range that elicits the large amplitude snap through behavior. It is also seen that interwell motion is achievable at significantly reduced excitation amplitudes through these discontinuous structural elements.     

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.     

压电与摩擦电复合型旋转能量采集动力学协同调控机制研究

低转速激励下能量采集性能差是目前制约旋转能量采集技术应用的瓶颈问题. 本文提出了动力学协同调控机制, 并用于调控系统的动力学行为, 可以使器件在低转速激励下有效工作, 提高了旋转能量采集系统的电学性能. 旋转刚度软化、非线性磁力、几何边界的协同调控既可以增加系统在低速下的振动位移以及压电材料的形变, 也可调控系统的最大位移, 使其振动可控并限制位移过大提高可靠性. 此外, 几何边界可以方便地集成摩擦纳米发电机, 实现压电与摩擦两种机电转换机制在振动和碰撞过程中协同发电, 有效利用空间和提高输出电能. 基于哈密顿原理建立了系统的机电耦合动力学模型并进行了实验验证. 实验结果表明系统能够在0~250 r/min的低转速范围内有效工作, 在转速为250 r/min时, 压电单元和摩擦纳米发电机的最大峰峰值电压分别为132 V和1128 V, 总平均功率为1426 μW. 本文提出的动力学协同调控机制为能量采集系统动力学和电学性能改进提供新的途径, 有益于促进自供能物联网技术的发展与应用.      

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。     

磁耦合式双稳态宽频压电俘能器的设计和俘能特性

为了同时提高振动能量俘获系统的效率和实用性, 俘能器主结构的振动特性与环境振动特性的匹配度显得尤为重要. 非线性系统复杂的动力学行为为设计高效的俘能器奠定了基础, 但结构一旦被设计、生成出来, 其工作频率往往是固定的, 无法根据环境中的振动而发生相应的改变. 本文利用可移动铰支座和非线性磁力设计了一种具有双稳态特性的宽频压电俘能器, 通过拓宽压电俘能器的工作频带, 来匹配环境中较宽的振动频率. 为了保证系统低频宽带的俘能效果, 详细分析了结构的长度比、磁间距、负载阻抗、外激励频率和幅值等对系统线性刚度、非线性刚度以及动力学行为的影响, 并进行了实验验证. 首先将系统简化为欧拉-伯努力梁, 利用拉格朗日方程建立系统的非线性动力学方程, 并利用谐波平衡法进行求解. 针对理论分析给出的不同外激励频率下的最优长度比, 搭建了实验平台进行验证. 理论和实验的结果表明: 非线性磁力的引入使系统呈现负刚度特性, 使俘能器能够在单稳态和双稳态之间的变换, 实现低频俘能效果; 通过调节可移动铰支座的位置, 改变系统的长细比, 能够实现从0到16 Hz的宽频俘能效果.      

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.     

附磁阶梯变厚度悬臂梁压电俘能器的理论建模及分析

论文建立了一种附磁阶梯变厚度压电悬臂梁的动力学模型并分析了系统的俘能特性。基于Euler-Bernoulli梁理论分段建立系统能量函数并引入非线性磁势能,利用Lagrange方程建立了系统机电耦合动力学方程;利用数值方法分析了磁间距对系统振动特性的影响,此外还研究了系统单稳态和双稳态响应,探讨了厚度比、长度比、磁间距和外激励幅值对系统动力学响应和俘能特性的影响。结果表明,磁间距是影响系统势能的主要因素,调节磁间距可使系统产生单稳态和双稳态响应,从而有效提高俘能器俘能特性;与传统等截面悬臂梁压电俘能器相比,通过优化结构参数,附磁阶梯变厚度悬臂梁压电俘能器能够发生明显的非线性振动现象,实现宽频带振动能量采集。     

Free Oscillations in Conservative and Dissipative Symmetric Cubic Two-Degree-of-Freedom Systems with Closed Natural Frequencies

Influence of damping on free oscillations of 2DOF nonlinear systems with symmetric characteristics and closed natural frequencies is studied. The behavior of such systems is found to be rather complicated and incorporates transitions from modulated coupled oscillations (with an energy exchange between two modes of the linearized system) to uncoupled oscillations, and inversely. It is shown that dynamics of dissipative systems under consideration can be explained by means of phase portraits analysis for correspondent conservative systems and their bifurcations at changing energy.     

利用摩擦纳米发电机的流体能量俘获研究新进展

环境中的流体 (包括气体和液体) 动能是十分丰富且重要的清洁能源之一, 流体能量可通过不同的能量俘获技术 (电磁发电技术、压电能量俘获技术) 被转化为电能并供人们使用. 自2012年王中林研究团队发明摩擦纳米发电机 (triboelectric nanogenerator, TENG) 以来, TENG已成为了最重要的能量, 俘获技术之一, 并应用于流体能量俘获研究中. 论文综述了当前用于流体能量俘获的摩擦纳米发电机 (fluidic energy harvesting TENG, FEH-TENG) 的研究现状. 介绍了 FEH-TENG 中摩擦电材料之间的电荷转移原理以及基本的工作模式. 在气流动能俘获方面, 流致振动 (如涡激振动、驰振、颤振和尾流驰振等)是一种有效的将流体动力转化为机械能的物理机制, 基于该机制, 总结了FEH-TENG在风能和流致振动能量俘获中的研究进展以及各类能量俘获结构. 液体动能俘获方面总结了 FEH-TENG 在波浪和雨滴能量俘获中的研究进展. 介绍了基于 FEH-TENG的混合能量俘获系统和摩擦电材料优化在提升FEH-TENG流体能量俘获效率方面的研究. 接着介绍了FEH-TENG在不同领域中的应用. 最后讨论了目前 FEH-TENG 在流体能量俘获中存在的问题并提出了一些展望. 论文工作有助于推动FEH-TENG在流体能量俘获领域的发展以及促进相关研究人员对该领域的认识.      

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.      

逆压电效应对双稳态压电俘能器的性能影响研究

为了研究逆压电效应对压电俘能效果的具体影响,本文首先分析了双稳态压电俘能器的分布参数型能量表达式,然后应用广义Hamilton变分原理推导了该俘能系统的动力学方程,最后采用谐波平衡法获得了动力响应解析解。通过对比不同激励频率下的数值仿真结果,讨论了逆压电效应对俘能系统动力响应的影响规律。结果表明,逆压电效应在不同工况下对俘能效果的影响并非单纯起抑制作用,在一定激励强度的高频激励下,逆压电效应对俘能效果的影响起增强作用;弱强度激励下的俘能效果则全程受到抑制作用。     

A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations

A minimal two degree of freedom model is used to clarify from an intuitive perspective the physical mechanisms underlying the mode-coupling instability of self-excited friction induced oscillations. It is shown that simultaneous out-of-phase oscillations of friction force and displacement tangential to the friction force may lead to energy transfer from the frictional system to vibrational energy. Also it is shown that the friction force acts like a cross-coupling force linking motion normal to the contact surface to motion parallel to it and that a necessary condition for the onset of instability is that these friction-induced cross-coupling forces balance the corresponding structural cross-coupling forces of the system. Finally the origin and the role of phase shifts between oscillations normal and parallel to the contact surface is clarified with respect to the mode-coupling instability. It may be expected that the intuitive picture gained will be of considerable help for practical design purposes.     

具有弹性放大器的双稳态压电俘能器建模及参数影响分析

利用广义Hamilton变分原理,建立了具有弹性放大器的双稳态压电俘能系统BPH+EM的动力学方程。考虑谐波激励,采用调和平衡法获得了BPH+EM系统的位移、输出电压和功率的解析解。利用求得的解析解,讨论了BPH+EM系统扩大能量俘获的频率范围和提高能量俘获效率的机理,研究了弹性放大器的刚度质量比对BPH+EM系统的动力性能影响规律。当弹性放大器的刚度质量比趋于无限大时,具有弹性放大器的双稳态压电俘能系统退化为双稳态压电俘能系统BPH。弹性放大器的刚度质量比趋于0但不等于0时,BPH+EM的俘能效率低于BPH。结果表明,在合适的刚度质量比范围内,BPH+EM的俘能效率显著优于BPH。研究结果为BPH+EM系统的优化设计提供了理论指导。     

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。     

Stochastic response and reliability of electromagnetic energy harvester with mechanical impact and Coulomb friction

Nonlinear Dynamics - Combining the complex factors of mechanical impact, Coulomb friction, harmonic excitation, and Gaussian white noise, an electromagnetic energy harvesting system is analytically...     

Empirical dry-friction modeling in a forced oscillator using chaos

The coefficient of friction is measured during relative oscillation between sliding surfaces. Measurements are made during regular oscillations in which the excitation has a modulated amplitude, and during chaotic oscillations in which the excitation amplitude is fixed. The friction force is measured for paper on paper, and titanium on titanium. A friction law is derived based on observations from the measurements. This friction law is applied to a simulation model of an experimental forced oscillator. The simulated and experimental oscillators have similar qualitative dynamical features in the phase space.     

Energy harvesting by two magnetopiezoelastic oscillators with mistuning

We examine an energy harvesting system of two magnetopiezoelastic oscillators coupled by electric circuit and driven by harmonic excitation. We focus on the effects of synchronization and escape from a single potential well. In the system with relative mistuning in the stiffness of the harvesting oscillators, we show the dependence of the voltage output for different excitation frequencies.     

盘-销摩擦系统摩擦接触力测试与特性分析

测量分析动态摩擦接触力是研究摩擦振动与噪声发生机理的关键.本文中建立了盘-销系统摩擦尖叫试验台架,成功再现了摩擦尖叫.采用三向力传感器对有无摩擦尖叫条件下的动态摩擦接触力进行了测量,并利用小波信号分解、概率密度函数、功率谱密度函数、时频分析等方法进行了分析和讨论.研究发现:在发生摩擦尖叫时,动态摩擦力和法向力发生高频波动,是系统噪声的激励源;无摩擦尖叫时的摩擦力和法向力的动态分量为典型的白噪声随机过程,呈非高斯分布;有摩擦尖叫时的摩擦力和法向力为窄带高频类谐波信号,摩擦力呈非高斯分布,而法向力近似为高斯分布;模态耦合是导致盘-销系统发生动态接触力高频波动以及摩擦尖叫的原因.