SOME ADVANCES IN ENERGY HARVESTING TECHNOLOGY OF NONLINEAR TRIBOELECTRIC NANOGENERATOR
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摘要: 摩擦纳米发电技术是一种基于电负性不同的材料, 通过静电感应和摩擦起电的耦合作用实现材料间电荷转移, 从而将环境能量转化为电能的能量俘获技术. 因在物联网及其相关智慧产业以及新能源等领域的巨大应用潜力, 摩擦纳米发电俘能技术自被提出后便受到极大地关注并成为国内外的研究热点. 将非线性力学机制拓展至摩擦纳米发电俘能技术构造的非线性摩擦纳米发电机在低频环境激励下具有复杂的非线性动力学行为, 可以产生大幅值动力学响应, 进而高效地将低频环境能量转化为电能. 文章首先简要介绍了摩擦纳米发电俘能原理与非线性摩擦纳米发电机的基本工作原理, 然后从双稳态摩擦纳米发电俘能、多稳态摩擦纳米发电俘能和准零刚度摩擦纳米发电俘能等3个方面详细总结了非线性摩擦纳米发电俘能方法的研究工作. 此外, 从碰撞式摩擦纳米发电俘能、混合机制摩擦纳米发电俘能等两个方面详细阐述了非线性摩擦纳米发电俘能系统的性能提升策略. 最后, 通过总结非线性摩擦纳米发电俘能技术的研究进展, 分析了目前研究中的不足, 并对未来非线性摩擦纳米发电俘能技术的研究方向进行了展望.Abstract: Triboelectric nanogenerator (TENG) technology is a kind of energy harvesting technology based on materials with different electronegativity, which realizes charge transfer between materials through the coupling effect of electrostatic induction and triboelectric, so as to convert environmental energy into electric energy. Due to its huge application potential in the fields of the Internet of Things and its related smart industries and new energy, the TENG technology has received great attention and become a research hotspot at home and abroad since it was proposed. The nonlinear mechanical mechanism is extended to the TENG, which has complex nonlinear dynamic behavior under the excitation of low frequency environment and can generate large dynamic response, and then efficiently convert the low frequency environmental energy into electric energy. In this paper, the principle of energy harvesting by TENG (e.g., the sliding-mode TENG and the contact-separation mode TENG) and the basic working principle of nonlinear TENG are briefly introduced. Then, the research work of energy harvesting by nonlinear TENG is summarized in detail from three aspects: bistable TENG, multistable TENG and quasi-zero-stiffness TENG, etc., that are employed to harvest low-frequency ambient energy. Moreover, the fundamental principle of these nonlinear TENGs and the typical researches are reviewed as well. Meanwhile, it can be clearly seen that the frequency band of the energy harvesting of the nonlinear TENG is narrow, and the electrical output of the nonlinear TENG should be further improved. To address these issues, the researchers have proposed a lot of methods to improve the electrical performance of the nonlinear TENG. The performance improvement strategy of the nonlinear TENG is described in detail from two aspects, such as impact-mode TENG and hybrid TENG. Finally, this paper summarizes the research progress of nonlinear TENG, analyzes the shortcomings of current research, and prospects the future research direction of nonlinear TENG technology.
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引 言
近年来, 随着无线通讯技术的进步, 物联网信息技术得到了突飞猛进的发展, 其在智慧城市、智慧交通、智慧医疗和智慧物流等领域得到了广泛应用并受到了国内外学者的高度关注[1-3]. 物联网及其相关智慧产业的发展离不开庞大的传感器网络节点, 其将万物与互联网相连, 以进行信息交换, 从而实现对物品的智能化感知和管理[4]. 因此, 庞大的传感器网络节点是物联网技术广泛应用的关键所在, 如何稳定、持久且低成本地为数以万计的传感器网络节点供能, 是制约物联网技术进一步发展的瓶颈问题.
传统供能方式因成本较高以及后期维护困难等缺陷难以为物联网中庞大的传感器网络节点供能[5]. 因此, 发展新型供能方式为物联网传感器网络节点供能, 对推动物联网进一步发展具有重要意义. 物联网传感器网络节点周围环境中存在各种各样的可再生能量, 譬如风能[6-7]、波浪能[8-9]和振动能[10-11]等. 将这些环境可再生能量转化为电能为物联网传感器网络节点供能, 是解决物联网传感器网络节点供能问题的潜在方案之一[12-15].
到目前为止, 已经有诸多能量俘获技术相继被提出, 譬如: 电磁感应式俘能技术[16-18]、压电式俘能技术[19-21]、热释电式俘能技术[22-23]和静电感应式俘能技术[24-26]等. 摩擦纳米发电俘能技术是一种基于电负性不同的材料, 通过静电感应和摩擦起电的耦合作用实现材料间电荷转移, 从而将环境能量转化为电能的能量俘获技术. 王中林院士团队[27]于2012年设计了首个摩擦纳米发电机, 提出了摩擦纳米发电俘能方法, 见图1. 摩擦纳米发电俘能方法一经提出, 就以输出电压高、材料选择广、俘能装置易于制造和成本低等优点[28-30]迅速成为能量俘获领域的研究热点. 随着摩擦纳米发电俘能技术的发展, 研究人员发现摩擦纳米发电机的输出功率与材料本身的性质、介电质薄膜的相对滑动距离 (分离距离) 及滑动速度 (接触分离速度) 等密切相关[31-32]. 因此, 提高摩擦纳米发电机摩擦层材料本身的电学性质, 以及增强摩擦纳米发电机系统 (摩擦层) 运动响应是提升摩擦纳米发电机俘能效率的有效手段.
传统摩擦纳米发电机在低频激励下难以实现大幅动力学响应, 而大部分环境能量具有宽频和低频特征, 因此利用传统摩擦纳米发电机难以实现低频环境能量的高效俘获. 将非线性力学机制拓展至摩擦纳米发电, 构造的非线性摩擦纳米发电机, 在低频环境激励下具有复杂的非线性动力学行为, 可以产生大幅值动力学响应, 且能够高效地将低频环境能量转化为电能[33-35]. 目前, 国内外学者基于双稳态[36-38]、多稳态[39-41]和准梁刚度[42-44]等力学机制, 构造了诸多不同类型的非线性摩擦纳米发电机, 用来俘获低频环境能量. 部分研究成果已经在新能源领域、自供电传感器领域和健康监测等领域成功应用[45-47]. 然而, 非线性摩擦纳米发电机还存在诸如尺寸大、结构不够紧凑、可靠性不足等缺陷, 以及非线性力电耦合模型难以建立、低频俘能频带调控难等挑战, 限制了非线性摩擦纳米发电俘能技术的进一步发展.
本文首先拟从摩擦纳米发电俘能理论出发, 简要总结滑动式摩擦纳米发电机和接触-分离式摩擦纳米发电机的俘能原理. 然后, 从非线性力学机制入手, 系统阐述双稳态摩擦纳米发电、多稳态摩擦纳米发电和准零刚度摩擦纳米发电3种非线性摩擦纳米发电俘能方法, 详细介绍3种方法中摩擦纳米发电系统的基本原理、建模方法以及发展现状. 此外, 从非线性摩擦纳米发电俘能系统性能提升策略出发, 详细介绍碰撞式摩擦纳米发电俘能方法和多机制摩擦纳米发电俘能方法两种性能提升策略. 最后, 总结非线性摩擦纳米发电俘能方法的潜在应用.
1. 摩擦纳米发电俘能理论
摩擦纳米发电机是基于静电感应和摩擦起电效应收集环境能量的俘能装置. 从工作模式来看, 摩擦纳米发电机可以分为以下4种: 水平面内滑动模式[48-51]、垂直接触-分离模式[52-55]、单电极模式[56-59]和独立层模式[60-63]. 实际上, 工程中常用的模式为水平面内滑动模式与垂直接触-分离模式. 因此, 本章简要总结了滑动式与接触-分离式摩擦纳米发电机俘能原理.
1.1 滑动式摩擦纳米发电机俘能原理
按照摩擦层的类型分类, 滑动式摩擦纳米发电机可以分为介电质-介电质型滑动式摩擦纳米发电机和电极-介电质型滑动式摩擦纳米发电机. 具体而言, 介电质-介电质型滑动式摩擦纳米发电机主要由两片介电质薄膜与两片电极薄膜组成, 两片介电质薄膜构成摩擦层, 两片电极构成导电层, 如图2(a-I) 所示[31]. 电极-介电质型滑动式摩擦纳米发电机主要由一片介电质薄膜与两片电极薄膜组成, 介电质薄膜与其中一片电极薄膜构成摩擦层, 该电极薄膜与另一电极薄膜构成导电层, 如图2(a-II) 所示[31]. 图2(b) 给出了摩擦纳米发电机的等效电路模型, 其中, V表示摩擦纳米发电系统输出电压, R代表外电路中的负载电阻. 从图中可以清晰地看出, 滑动式摩擦纳米发电系统由一个等效电容C和一个开路电压源$ {V_{{{\mathrm{OC}}}}} $串联而成[64]. 基于此, 滑动式摩擦纳米发电机的电学控制方程为[65]
$$ V = - \frac{1}{C} Q + {V_{{{\mathrm{OC}}}}} $$ (1) 式中, C和$ {V_{{{\mathrm{OC}}}}} $分别代表滑动式摩擦纳米发电机的等效电容和开路电压, Q表示外电路中的电荷转移量, V表示滑动式摩擦纳米发电机的输出电压.
介电质-介电质型滑动式摩擦纳米发电机的电学控制方程为[31]
$$ V = - \frac{Q}{{w{\varepsilon _0}\left( {l - x} \right)}}\left( {\frac{{{d_1}}}{{{\varepsilon _{r1}}}} + \frac{{{d_2}}}{{{\varepsilon _{r2}}}}} \right) + \frac{{\sigma x}}{{{\varepsilon _0}\left( {l - x} \right)}}\left( {\frac{{{d_1}}}{{{\varepsilon _{r1}}}} + \frac{{{d_2}}}{{{\varepsilon _{r2}}}}} \right) $$ (2) 式中, l和w分别代表介电质薄膜的长和宽, $ {d_1} $和$ {d_2} $分别代表介电质1和介电质2的厚度, $ {\varepsilon _0} $表示真空介电常数, $ {\varepsilon _{r1}} $和$ {\varepsilon _{r2}} $分别表示介电质1和介电质2的相对介电常数, $ \sigma $代表摩擦膜的表面电荷密度, x代表介电质1和介电质2之间的相对滑动距离.
电极-介电质型滑动式摩擦纳米发电机的电学控制方程为[31]
$$ V = - \frac{Q}{{w{\varepsilon _0}\left( {l - x} \right)}}\frac{d}{{{\varepsilon _r}}} + \frac{{\sigma x}}{{{\varepsilon _0}\left( {l - x} \right)}}\frac{d}{{{\varepsilon _r}}} $$ (3) 式中, d代表介电质的厚度, $ {\varepsilon _r} $代表介电质的相对介电常数.
为了进一步了解滑动式摩擦纳米发电机的俘能原理, 图3给出了电极-介电质型滑动式摩擦纳米发电机的工作原理[65-66]. 在本例中, 介电质与电极2构成摩擦层. 当电极-介电质型滑动式摩擦纳米发电机处于工作状态时, 其电势分布云图与电荷转移示意图分别如图3(a) 和图3(b) 所示. 显然, 当介电质与电极2完全重合时, 由于其吸引电子的能力不同, 介电质带负电荷, 电极2带正电荷, 此时介电质与电极2之间的电势差为0, 如图3(a-I) 所示. 此时, 外电路中没有电荷转移, 如图3(b-I) 所示. 随着介电质相对于电极2向右滑动, 其间的电势差逐渐增大, 如图3(a-II) 所示. 正电荷从电极2 (高电势) 通过外电路转移至电极1 (低电势), 进而产生从电极2流向电极1的电流, 如图3(b-II) 所示. 一旦介电质与电极2之间的相对滑动距离达到最大时, 其间电势差达到最大, 电极2的正电荷将全部转移至电极1, 此刻外电路中没有电流产生, 如图3(a-III) 和图3(b-III) 所示. 随后, 介电质相对于电极2向左滑动, 其间电势差减小, 外电路中产生由电极1流向电极2的电流, 如图3(a-IV) 和图3(b-IV) 所示. 当滑动式摩擦纳米发电机处于工作状态时, 摩擦层之间将产生周期性滑动, 因此外电路中将产生交流电.
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图 3 电极-介电质型滑动式摩擦纳米发电机工作原理Figure 3. Operating principle of conductor-to-dielectric sliding-mode TENG1.2 接触-分离式摩擦纳米发电机俘能原理
根据摩擦层类别, 接触-分离式摩擦纳米发电机与滑动式摩擦纳米发电机相同, 可以分为介电质-介电质型接触-分离式摩擦纳米发电机和电极-介电质型接触-分离式摩擦纳米发电机, 分别如图4(a-I) 和4(a-II) 所示[32]. 接触-分离式摩擦纳米发电系统与滑动式摩擦纳米发电机相同, 等效电路模型由一个等效电容和一个开路电压源串联而成. 电极-介电质型接触-分离式摩擦纳米发电机的电学控制方程为[65]
$$ V = - \frac{Q}{{S{\varepsilon _0}}}\left( {\frac{d}{{{\varepsilon _r}}} + x} \right) + \frac{{\sigma x}}{{{\varepsilon _0}}} $$ (4) 式中, S代表摩擦层之间接触的面积.
介电质-介电质型接触-分离式摩擦纳米发电机的电学控制方程为[32]
$$ V = - \frac{Q}{{S{\varepsilon _0}}}\left( {\frac{{{d_1}}}{{{\varepsilon _{r1}}}} + \frac{{{d_2}}}{{{\varepsilon _{r2}}}} + x} \right) + \frac{{\sigma x}}{{{\varepsilon _0}}} $$ (5) 电极-介电质型接触-分离式摩擦纳米发电机工作状态下的电荷转移示意图与电势分布云图分别如图4(b) 和图4(c) 所示[65]. 由图4(b-I) 可知, 当介电质与电极2完全重合时, 外电路中没有电流产生. 这是因为介电质与电极2之间的电势差为0, 外电路中不发生电荷转移. 随着介电质与电极2分离, 其间产生电势差, 且随着分离距离增大, 电势差逐渐增大, 如图4(c) 所示. 因此, 随着介电质与电极2分离距离增大, 正电荷从电极2经过外电路转移到电极1, 电流方向与正电荷流动方向相同, 如图4(b-II) 所示. 当分离距离达到最大, 正电荷全部转移至电极1, 此时外电路中没有电流产生, 如图4(b-III) 所示. 随后, 介电质与电极2之间的分离距离减小, 其间电势差减小, 正电荷从电极1流向电极2, 外电路中产生与之相同流向的电流, 如图4(b-IV) 所示. 直到介电质与电极2再次完全重合, 正电荷全部转移至电极2. 因此, 当接触-分离式摩擦纳米发电机摩擦层周期性接触-分离时, 外电路中将产生交流电.
2. 非线性摩擦纳米发电俘能方法
传统线性摩擦纳米发电俘能方法难以高效俘获低频环境能量. 将非线性力学机制拓展至摩擦纳米发电, 发展非线性摩擦纳米发电俘能方法, 可以利用复杂的非线性动力学行为诱发高效的电学输出. 本章简要总结了具有低频环境能量高效俘获能力的典型非线性摩擦纳米发电俘能方法[67-70], 主要包括: 双稳态摩擦纳米发电俘能方法、多稳态摩擦纳米发电俘能方法和准零刚度摩擦纳米发电俘能方法.
需要注意的是, 非线性摩擦纳米发电机在工作状态下, 摩擦膜之间存在静电力. 然而, 根据文献[66]可知, 静电力对非线性摩擦纳米发电机的力学响应和电学性能的影响可以忽略不计. 因此, 本文所提及的非线性摩擦纳米发电机动力学控制方程中并没有体现力电耦合项 (静电力).
2.1 双稳态摩擦纳米发电俘能方法
将负刚度机构拓展至摩擦纳米发电, 构造具有双稳态力学机制的摩擦纳米发电俘能系统, 即可得到双稳态摩擦纳米发电机. 通常, 双稳态摩擦纳米发电机由双稳态结构与摩擦纳米发电俘能模块构成. 双稳态结构由负刚度机构构成, 摩擦纳米发电俘能模块由介电质薄膜和电极薄膜构成. 从能量角度分析, 双稳态摩擦纳米发电俘能系统具有两个稳定平衡点与一个不稳定平衡点, 当系统动能足以驱动其跨越不稳定平衡点时, 系统将在两个稳定平衡点之间作大幅值高速度阱间振荡, 此时双稳态摩擦纳米发电机可以高效地将低频环境能量转化为电能. 基于此原理, 国内外学者设计了各种各样的双稳态摩擦纳米发电机, 其可以高效俘获低频环境能量[71-73].
基于双翅目昆虫飞行机制, Luo等[74]提出了一款双稳态摩擦纳米发电机, 如图5(a-I) 所示. 该双稳态摩擦纳米发电机可以模拟双翅目昆虫飞行过程中翅膀的运动形态. 其中, 当刚性梁长度较短时, 系统只有一个稳定平衡点, 是一个单稳态系统. 一旦刚性梁长度增大, 系统具有两个稳定平衡点, 此时系统表现出双稳性. 基于拉格朗日方程, 可以得到仿双翅目双稳态摩擦纳米发电机的动力学控制方程
$$ {\boldsymbol{M}}\ddot {\boldsymbol{X}} + {\boldsymbol{\xi}} \dot {\boldsymbol{X}} + {\boldsymbol{F}} = {\boldsymbol{M}}\ddot {\boldsymbol{z}} $$ (6) 式中, M和$ {\boldsymbol{\xi}} $分别表示质量和阻尼矩阵, F为系统所受力的矩阵形式, X代表集中质量的相对位移, $\ddot {\boldsymbol{z}}$是系统所受基础激励. 经过理论分析与实验研究, 可以发现仿双翅目双稳态摩擦纳米发电机在低频区域具有复杂的动力学行为, 当其运动形式为大幅值阱间运动时, 可以高效地将低频振动能量转化为电能.
受拉弓时动能势能转化原理启发, Tan等[75]设计了悬臂梁-摆臂式负刚度机构, 进而提出了仿弓形双稳态摩擦纳米发电机, 其基本构型如图5(a-II) 所示. 弓形双稳态摩擦纳米发电系统包含两个稳定平衡点和一个不稳定平衡点, 具有典型的双阱特征. 稳定平衡点和不稳定平衡点之前的势能差被称为势能壁垒, 当系统的动能足以克服势能壁垒时, 弓形双稳态摩擦纳米发电机的运动状态为大幅值阱间运动, 此时可以产生高幅值输出电压, 如图5(a-II)所示. 当系统难以跨越不稳定平衡点时, 运动状态表现为小幅值阱内运动, 此时输出电压幅值较小. 这表明当双稳态摩擦纳米发电机的运动形式为阱间运动时, 可以实现高效的低频振动能量俘获.
上述双稳态摩擦纳米发电机主要通过机械式负刚度机构实现双稳态力学机制, 然而机械式双稳态结构在实际工作环境下具有装配误差大以及稳定性差的缺陷. 针对这些问题, 研究人员将磁致式负刚度机构引入摩擦纳米发电系统, 提出了多种磁致式双稳态摩擦纳米发电机[76-77]. 研究结果表明, 磁致式双稳态摩擦纳米发电机不仅可以实现低频环境能量的高效俘获, 还可以有效降低装配误差, 并提高系统稳定性. 利用磁致式负刚度机构, Zhao等[76]设计了一款磁致式双稳态摩擦纳米发电机, 如图5(b) 所示. 图5(b-I) 给出了该摩擦纳米发电机的简化模型, 理论和实验结果均表明, 该磁致式双稳态摩擦纳米发电机可以在低频区域高效地将振动能量转化为电能, 且其俘能带宽约为传统摩擦纳米发电机 (不考虑双稳态力学机制) 的两倍.
旋转运动能量作为一种常见的环境能量, 广泛分布于旋转式机械装置周围. Zhao等[77]提出了一款具有动态协同调节机制的圆盘形磁致式双稳态摩擦纳米发电机, 如图5(c) 所示. 经过实验测试, 发现该摩擦纳米发电机在动态调节机制的引导下可以高效地将旋转能量转化为电能. 此外, Zhao等[78]基于磁致式负刚度机构提出了另一种新型双稳态摩擦纳米发电机, 同样可以实现旋转运动能量的高效俘获. 将该摩擦纳米发电机安装至汽车轮胎上, 进行实际道路测试, 结果表明, 该摩擦纳米发电机能够为转子供电并实现其状态监测.
不同于旋转运动能量, 扭转振动能量存在于轴系以及人体关节处且具有低频特征. 利用两块相斥的磁块实现负刚度, Zhao等[79]提出了一款圆盘形双稳态摩擦纳米发电机, 如图5(d-I) 所示. 研究结果表明, 该摩擦纳米发电机可以高效地将低频扭转振动能量转化为电能. Tan等[80]基于柔性机构设计理论设计了S形柔性梁, 进而构造了一款紧凑型柔性双稳态摩擦纳米发电机, 如图5(d-II) 所示. 实验结果表明, 该摩擦纳米发电机不仅可以高效俘获低频扭转振动能量, 还能够将人体运动能量转化为电能, 并驱动低功率传感器.
综上所述, 双稳态摩擦纳米发电机在低频激励下具有复杂的动力学行为, 当系统可以跨越不稳定平衡点时, 其在两个稳定平衡点之间作大幅值阱间振荡. 此时, 双稳态摩擦纳米发电机可以高效地将低频环境能量转化为电能.
2.2 多稳态摩擦纳米发电俘能方法
为了进一步提高低频环境能量的俘获效率, 研究人员将双稳态力学机制拓展至多稳态力学机制, 提出了多稳态摩擦纳米发电俘能方法. 与双稳态系统相比, 多稳态系统的稳定平衡点大于两个, 呈现多势能阱特性. 在同一工况下, 多稳态系统的势能壁垒低于双稳态系统. 因此, 多稳态系统比双稳态系统更容易克服势能壁垒, 跨越不稳定平衡点, 实现大幅值阱间运动, 进而高效地将低频环境能量转化为电能. 一般情况下, 多稳态系统分为: 三稳态系统[81-83]、四稳态系统[84-86]以及五稳态系统[87-89]等.
基于磁致式负刚度力学机制, Fu等[66]提出了悬臂梁式三稳态摩擦纳米发电机, 如图6(a-I) 所示. 为了研究悬臂梁式三稳态摩擦纳米发电机的动力学特性, 基于哈密顿原理, 结合拉格朗日方程推导了该摩擦纳米发电机的动力学控制方程
$$ \ddot q + 2\xi \omega \dot q + {\omega ^2}q + {F_{{\mathrm{m}}}} = \alpha \ddot g + {F_{{\mathrm{f}}}}\phi \left( {{L_{{\mathrm{b}}}}} \right) $$ (7) 式中, $ \xi $代表系统阻尼比, $ \omega $表示悬臂梁第一阶固有频率, $ \ddot g $表示基础激励, $ {F_{{\mathrm{m}}}} $和$ {F_{{\mathrm{f}}}} $分别表示悬臂梁端部磁块所受磁力和摩擦层薄膜之间的摩擦力, $ \phi \left( {{L_{{\mathrm{b}}}}} \right) $表示悬臂梁末端的模态变形. 图6(a-II) 给出了悬臂梁式三稳态摩擦纳米发电机的势能云图, 从图中可以明显看出, 该摩擦纳米发电机具有三稳态力学机制. 理论分析结果表明, 相较于双稳态摩擦纳米发电系统, 三稳态摩擦纳米发电系统的势能壁垒更低, 更容易实现大幅值阱间运动, 从而可以高效地将低频振动能量转化为电能.
受仿生类4肢结构与双翅目飞行机制启发 (图6(b-I)), Yang等[90]提出了一种仿生多稳态摩擦纳米发电机, 如图6(b-II) 所示. 由静力学分析结果可知, 该摩擦纳米发电机具有四稳态力学机制. 当该摩擦纳米发电机运动状态为大幅值阱间运动时, 其具有高效的电学输出性能. Wang等[91]利用磁致式负刚度机构, 设计了一款磁致式多稳态摩擦纳米发电机, 如图6(c-I) 所示. 从图6(c-II) 可以看出, 该摩擦纳米发电机在不同的系统参数下分别呈现出双稳态、三稳态和多稳态力学特性. 由系统势能云图6(c-III) 可知, 随着俘能系统从双稳态系统变为三稳态系统以及多稳态系统, 势能壁垒将逐渐降低. 研究结果表明, 该磁致式多稳态摩擦纳米发电机可以在低频激励下产生大幅值动力学响应, 高效地将低频振动能量转化为电能.
利用磁悬浮机制, Yang等[92]设计了一款磁悬浮式三稳态摩擦纳米发电机, 如图6(d-I) 所示. 研究结果表明, 与传统摩擦纳米发电机相比, 该摩擦纳米发电机在低频结构振动激励下可以产生大幅值动力学响应, 具有更优异的电学输出性能. Yang等[93]提出了一种弹簧式多稳态摩擦纳米发电机, 如图6(d-II) 所示. 该多稳态摩擦纳米发电机在低频振动激励下具有复杂的动力学行为, 可以高效地将低频振动能量转化为电能.
相比于双稳态摩擦纳米发电机, 多稳态摩擦纳米发电机具有更低的势能壁垒, 相同工况下多稳态摩擦纳米发电机更容易在低频区域产生大幅值动力学响应. 因此, 多稳态摩擦纳米发电机可以高效地将低频振动能量转化为电能, 实现高效的电学输出性能.
2.3 准零刚度摩擦纳米发电俘能方法
为了进一步提高低频甚至超低频区域振动能量的俘获效率, 研究人员将准零刚度力学机制[94-96]拓展至摩擦纳米发电, 提出准零刚度摩擦纳米发电俘能方法, 设计了多种准零刚度摩擦纳米发电机[97-98]. 通常, 准零刚度机构由一个垂直弹簧和两个水平弹簧构成[99]. 准零刚度系统的刚度远低于传统线性系统, 如图7(a-I) 所示. 相比于传统线性系统, 准零刚度系统在低频区域具有大幅值动力学响应, 如图7(a-II) 所示[97]. 因此, 通过引入准零刚度机构发展准零刚度摩擦纳米发电俘能方法是提高摩擦纳米发电机低频、超低频区域能量俘获性能的有效途径.
针对超低频振动能量难以俘获的问题, Wang等[98]将准零刚度机制拓展至摩擦纳米发电, 提出了一款准零刚度摩擦纳米发电机, 其基本构型如图7(b-I)所示. 该准零刚度摩擦纳米发电机的运动方程为
$$ M\ddot y + c\dot y + F = - MA\sin \left( {\omega t} \right) $$ (8) 式中, M代表准零刚度摩擦纳米发电机的集中质量, c表示准零刚度摩擦纳米发电机的系统阻尼, F代表准零刚度系统回复力, A代表基础激励幅值, $ \omega $代表激励频率.
图7(b-II) 给出了该准零刚度摩擦纳米发电机的位移-势能曲线. 由图可知, 不同的系统刚度比下, 该摩擦纳米发电机呈现出不同的力学特性, 当刚度比大于0.77时, 该摩擦纳米发电机呈现出准零刚度特性, 此时系统在超低频区域可以产生大幅值动力学响应, 从而高效地将超低频振动能量转化为电能.
为了进一步深入研究准零刚度摩擦纳米发电机力电耦合系统非线性动力学行为与电学输出之间的相互作用关系, Wang等[97]提出了双极准零刚度摩擦纳米发电机, 如图7(c-I) 所示, 其中负刚度机构由准零刚度弹簧构成. 图7(c-II) 给出了双极准零刚度摩擦纳米发电机的刚度特性, 由图可知, 该摩擦纳米发电机具有准零刚度特性. 当该摩擦纳米发电机处于准零刚度区间时, 其可以产生大幅值动力学响应, 进而产生较高的电学输出. 基于双翅目昆虫飞行机制, Yang等[90]设计了一款仿生型准零刚度摩擦纳米发电机, 如图7(d-I) 所示. 从系统刚度曲线可以看出, 该仿生型准零刚度摩擦纳米发电机具有平坦且较宽的准零刚度区间. 当仿生型准零刚度摩擦纳米发电机在此区间内时, 其可以高效地俘获低频振动能量.
综上所述, 准零刚度摩擦纳米发电机具有高静刚度、低动刚度的准零刚度特性, 当准零刚度摩擦纳米发电系统处于准零刚度区间时, 可以高效地俘获低频甚至超低频振动能量.
3. 非线性摩擦纳米发电俘能系统性能提升策略
到目前为止, 国内外学者已经提出了各种各样的非线性摩擦纳米发电俘能系统, 可以有效俘获低频环境能量. 然而, 传统的非线性摩擦纳米发电俘能系统在低频区域的俘能频带较窄, 俘能效率有待提升. 基于此, 本章总结了两种非线性摩擦纳米发电俘能系统性能提升策略, 分别为碰撞式摩擦纳米发电俘能方法与混合机制摩擦纳米发电俘能方法.
3.1 碰撞式摩擦纳米发电俘能方法
传统滑动式双稳态摩擦纳米发电机的俘能频带集中在狭窄的阱间运动频带, 严重限制了其低频俘能性能. 针对这一问题, Tan等[65]将碰撞模式引入滑动式摩擦纳米发电机中, 提出了滑动-碰撞一体式双稳态摩擦纳米发电机, 如图8(a-I) 所示. 滑动-碰撞一体式双稳态摩擦纳米发电机的动力学控制方程为
$$ M\ddot z + {F_1} + {F_2} - {F_3} = {M_1}\ddot u + {F_{\text{f}}} $$ (9) 式中, M代表系统的等效质量, $ {F_1} $, $ {F_2} $和$ {F_3} $分别代表不同分量的合力, $ {M_1}\ddot u $代表基础激励, $ {F_{\text{f}}} $代表摩擦力. 当系统发生碰撞事件时, 用$ {t^ - } $和$ {t^ + } $分别表示碰撞前的时刻和碰撞后的时刻, 有
$$ \dot z\left( {{t^ + }} \right) = - r\dot z\left( {{t^ - }} \right) $$ (10) 式中, $ \dot z\left( {{t^ - }} \right) $和$ \dot z\left( {{t^ + }} \right) $分别代表滑块碰撞前后的相对速度, r代表恢复系数.
图8(a-II) 给出了滑动-碰撞一体式双稳态摩擦纳米发电机和滑动式双稳态摩擦纳米发电机在不同运动模式下的输出功率. 由图可知, 当俘能系统运动模式为阱内运动时, 滑动-碰撞一体式双稳态摩擦纳米发电机的输出功率相较于滑动式双稳态摩擦纳米发电机最高提升了114% (激励频率为6 Hz). 因此, 通过引入碰撞模式, 可以有效提升双稳态摩擦纳米发电机的低频俘能效率, 并拓宽低频俘能频宽.
为了研究引入碰撞模式后摩擦纳米发电机的非线性动力学行为与电学性能, Zhao等[100]设计了一款胶囊型摩擦纳米发电机, 如图8(b-I) 所示. 当胶囊型摩擦纳米发电机发生碰撞行为时, 系统将产生复杂的非线性动力学行为. 相比于不发生碰撞事件的摩擦纳米发电机, 发生碰撞事件时的摩擦纳米发电机的输出功率有明显提高, 如图8(b-II) 所示. 结果表明, 引入碰撞机制可以诱导摩擦纳米发电机产生复杂的非线性动力学行为, 进而有效提升非线性摩擦纳米发电机的电学输出性能.
针对传统非线性摩擦纳米发电机低频俘能频带较窄的问题, Qi等[101]提出了一种新型非线性摩擦纳米发电机, 如图8(c-I) 所示. 当该摩擦纳米发电机处于工作状态时, 上碰撞板和下碰撞板处均会发生碰撞. 理论分析与实验结果均表明, 通过引入碰撞模式, 增加上下碰撞板, 可以有效拓宽非线性摩擦纳米发电机的低频俘能频宽. Ibrahim等[102]设计了一款二自由度碰撞式摩擦纳米发电机, 其理论模型如图8(c-II) 所示. 经过理论分析与实验研究, 发现二自由度碰撞式摩擦纳米发电机在低频振动激励下可以产生复杂的非线性动力学行为, 进而有效拓宽其俘能频宽. 针对低频风能难以俘获以及俘能频带较窄的问题, 通过引入碰撞机制, Zhao等[103]提出了一款悬臂梁式摩擦纳米发电机, 如图8(d) 所示. 研究结果表明, 当该摩擦纳米发电机处于工作状态时, 其中碰撞行为对该摩擦纳米发电机的电学性能有显著影响, 不仅能够明显提高该摩擦纳米发电机的输出功率, 还可以有效拓宽其俘能频宽. 因此, 开发碰撞式非线性摩擦纳米发电机可以有效提升非线性摩擦纳米发电机的电学性能.
3.2 混合机制摩擦纳米发电俘能方法
为了进一步提升非线性摩擦纳米发电机的俘能效率, 显著拓宽非线性摩擦纳米发电机的俘能频带, 国内外学者结合不同的俘能机制 (电磁感应式俘能机制、摩擦纳米发电俘能机制等), 提出了混合机制摩擦纳米发电俘能方法, 开发了各种混合机制摩擦纳米发电机[104-107].
通过引入电磁感应式俘能机制, Zhao等[108]提出了一种电磁-摩擦电混合式纳米发电机, 如图9(a-I) 所示. 图9(a-II) 给出了该电磁-摩擦电混合式纳米发电机的工作原理. 图9(a-III) 中, 蓝色曲线和红色曲线分别代表摩擦电俘能系统与电磁俘能系统的输出电压. 通过对比可知, 电磁俘能系统的电学输出略低于摩擦电俘能系统. 因此, 通过引入电磁俘能机制, 可以有效提升非线性摩擦纳米发电系统的电学性能.
为了提高非线性摩擦纳米发电机的低频振动能量俘获效率, 通过结合电磁俘能机制与摩擦电俘能机制, 陈延辉等[104]提出了一种非谐振式电磁-摩擦电混合式纳米发电机, 如图9(b-I) 所示. 研究结果表明, 引入电磁俘能机制, 可以极大提升该非线性摩擦纳米发电机的电学输出性能. 此外, 任静等[109]设计了一款新型电磁-摩擦电混合式纳米发电机, 如图9(b-II) 所示, 可有效俘获人体低频运动能量. 实验结果表明, 将电磁俘能机制引入摩擦纳米发电机构造的电磁-摩擦电混合式纳米发电机, 不仅能够显著提高人体低频运动能量的俘获效率, 增强发电机的电学输出性能, 还可以有效拓宽其俘能频宽.
针对引入电磁俘能机制后构造的滑动式电磁-摩擦电混合式纳米发电机, 杨亚等[110]详细地阐述了其工作原理, 如图9(b-III) 所示. 研究结果表明, 与传统非线性摩擦纳米发电机相比, 电磁-摩擦电混合式纳米发电机具有更大的输出功率, 更高的机电转换效率. 此外, 电磁-摩擦电混合式纳米发电机在自驱动传感器、可穿戴设备的供电和物联网等方面具有重要的应用前景. Han等[111]设计了一款双面绒毛式电磁-摩擦电混合式纳米发电机, 如图9(c) 所示. 该纳米发电机通过结合电磁俘能机制与摩擦电俘能机制, 显著提高了发电机空间利用率, 并极大提升了发电机超低频波浪能俘获效率. 实验结果表明, 该电磁-摩擦电混合式纳米发电机能够高效俘获超低频波浪能, 并为微小型电子设备和蓝牙系统供能, 可助力海洋环境状态实时监测. 总体而言, 通过引入电磁等俘能机制, 发展混合机制摩擦纳米发电俘能方法, 可有效提升非线性摩擦纳米发电机的电学性能.
4. 非线性摩擦纳米发电机的潜在应用
随着化石能源的日渐减少, 人类生活环境中存在的大量可再生能源, 譬如风能、水能、波浪能和振动能等, 逐渐进入人们的视野. 利用非线性摩擦纳米发电机从环境中俘获可再生能源, 将其转化为电能是解决化石能源日益减少的有效途径之一. 迄今为止, 国内外学者已经开发了不同的非线性摩擦纳米发电俘能系统, 用于俘获自然环境中存在的风能、波浪能和振动能等, 如图10(a) 所示[112-114]. 相关研究结果表明, 非线性摩擦纳米发电机可以在环境激励下产出复杂的非线性动力学行为, 高效地将低频环境能量转化为电能. 因此, 利用非线性摩擦纳米发电俘能方法俘获环境可再生能源, 发展新能源技术是非线性摩擦纳米发电俘能方法的潜在应用之一.
众所周知, 物联网的发展离不开数以万计的微型传感器, 传统供能方式难以为数量众多, 规模庞大的传感器网络节点供能. 非线性摩擦纳米发电机可以高效地将环境能量转化为电能, 因此, 国内外学者利用非线性摩擦纳米发电机俘获物联网传感器网络节点周围的环境能量, 开发了多种自供电传感器, 在电子皮肤[118]、低功率传感器[119]、可穿戴电子设备[120]和物联网[121]等领域得到了广泛的应用, 如图10(b) 所示[108,115-116]. 因此, 利用非线性摩擦纳米发电俘能方法开发自供电传感器, 以助力物联网及其相关领域的进一步发展也是非线性摩擦纳米发电俘能方法的潜在应用之一.
随着工程领域的发展和人类社会的进步, 信号监测技术在工程实际中以及人们生活中的应用越来越广泛, 譬如机械结构健康监测、土木结构健康监测和人体健康监测等. 信号监测技术的发展离不开微型无线传感器, 利用非线性摩擦纳米发电机俘获机械结构振动能量、土木工程结构振动能量和人体运动能量等, 来为这些微型无线传感器供能, 进而实现信号监测以及健康监测, 已经成为当前的研究热点之一[117,122-125], 如图10(c) 所示. 因此, 利用非线性摩擦纳米发电俘能方法助力结构健康监测同样是非线性摩擦纳米发电俘能方法的潜在应用之一.
5. 总结与展望
摩擦纳米发电机的提出有望解决物联网传感器网络节点供能难的问题, 进一步促进物联网及其相关智慧产业的发展. 然而, 由于物联网传感器网络节点周围的环境能量具有低频和宽频特征, 传统摩擦纳米发电机难以俘获低频环境能量为传感器网络节点供能. 非线性摩擦纳米发电机在低频环境激励下具有复杂的非线性动力学行为, 可以产生大幅值动力学响应, 并能够高效地将低频环境能量转化为电能. 本文首先简要介绍了摩擦纳米发电俘能理论与非线性摩擦纳米发电机的基本工作原理. 然后详细总结了3种用于俘获低频环境能量的典型非线性摩擦纳米发电俘能方法, 厘清了非线性摩擦纳米发电机的非线性动力学行为与电学输出之间的相互作用机制. 此外, 详细总结了两种非线性摩擦纳米发电俘能系统性能提升策略. 最后, 从可再生新能源、自供电传感器以及健康监测技术等3个方面分析了非线性摩擦纳米发电俘能方法的潜在应用.
非线性摩擦纳米发电机是近年来新能源领域的研究热点之一, 目前已经在结构设计、材料制备、数学模型建立以及实践应用等方面取得了丰硕的研究成果. 但是, 非线性摩擦纳米发电机在工程实际中还存在诸如尺寸大、结构不够紧凑、可靠性低和非线性力电耦合模型难以建立与求解, 低频俘能频带较窄等多方面的不足. 因此, 非线性摩擦纳米发电机的发展还面临如下挑战.
(1) 紧凑型非线性摩擦纳米发电机的创新设计. 传统非线性摩擦纳米发电机多由机械结构组成, 结构复杂、尺寸较大、自重较重且系统不紧凑. 因此, 基于柔性结构设计方法, 结合优化设计方法, 创新设计小尺寸、紧凑型非线性摩擦纳米发电机是非线性摩擦纳米发电俘能方法进一步发展的关键.
(2) 非线性摩擦纳米发电机的力电耦合模型建立与分析方法. 非线性摩擦纳米发电机是复杂的力电耦合系统, 其中包含诸如摩擦及碰撞等复杂的非线性因素. 因此, 基于哈密顿原理, 结合摩擦纳米发电俘能理论, 考虑摩擦力与静电力对力电耦合系统的影响, 建立非线性力电耦合模型, 并求解非线性力电耦合方程, 是完善非线性摩擦纳米发电俘能方法理论部分的核心问题.
(3) 非线性摩擦纳米发电机的低频俘能频带调控方法. 环境能量具有低频和宽频的特征, 传统非线性摩擦纳米发电机的低频俘能频带较窄, 且目前非线性摩擦纳米发电机的低频俘能频带调控方法较少. 因此, 如何拓宽非线性摩擦纳米发电机低频俘能频带, 且对低频俘能频带实现自主调控是非线性摩擦纳米发电机在实际应用中的另一关键性问题.
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图 3 电极-介电质型滑动式摩擦纳米发电机工作原理
Figure 3. Operating principle of conductor-to-dielectric sliding-mode TENG
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