A high-performance dual-mode energy harvesting with nonlinear pendulum and speed-amplified mechanisms for low-frequency applications

doi:10.1016/j.energy.2024.132553

Energy 能源

Volume 306, 15 October 2024, 132553
第 306 卷，2024 年 10 月 15 日，132553

https://doi.org/10.1016/j.energy.2024.132553 Get rights and content 获取权利和内容

Highlights 亮点

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A novel speed-amplified dual-mode energy harvesting is proposed.
提出了一种新颖的速度放大双模能量收集技术。
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The system incorporates nonlinear pendulum and speed-amplified mechanisms.
该系统包含非线性摆锤和速度放大机构。
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It achieves 3.79 W and 244 mW in rotation and vibration modes, respectively.
它在旋转和振动模式下的功率分别达到 3.79 W 和 244 mW。
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It supports daily appliances and wireless monitoring for railways and humans.
它支持铁路和人类的日常设备和无线监控。

Abstract 摘要

Vibrations induced by human motions and vehicle operations feature low-frequency, broadband, and time-varying. However, enhancing the power density of energy harvesting for various low-frequency applications presents a significant challenge. This paper proposes a high-performance dual-mode energy harvester (DM-EH) incorporating coupled nonlinear pendulum and speed-amplified mechanisms with gears for the simultaneous scavenging vibration and rotation energy. The pendulum serves as the energy capture unit for detecting vibration energy while ensuring the effective operation of the generation unit in rotational environments. The gears amplify the speed of the excitation and enable frequency up-conversion, thereby enhancing the energy conversion. Experimental results substantiate the DM-EH's ability to extract power from vehicle operations at speeds ranging from 60 to 540 rpm, as well as from human motions at frequencies of 0.7–1.5 Hz with 30° amplitudes. In rotation mode, the prototype achieves a maximum average direct current power of 3.79 W, while in vibration mode, it attains 244 mW. The prototype successfully powers portable electronics and supports battery-free triaxial acceleration and temperature multi-sensors during human motions and railway simulation tests. This prototype showcases immense potential as a sustainable power source for portable electronics and self-powered monitoring applications.
人体运动和车辆运行引起的振动具有低频、宽带和时变的特点。然而，在各种低频应用中提高能量收集的功率密度是一项重大挑战。本文提出了一种高性能双模式能量收集器（DM-EH），其中包含耦合非线性摆锤和带齿轮的速度放大机构，可同时收集振动和旋转能量。摆锤作为能量捕获装置，用于检测振动能量，同时确保发电装置在旋转环境中有效运行。齿轮可放大激振速度，实现频率上变，从而增强能量转换。实验结果证明，DM-EH 能够在 60 至 540 rpm 的速度范围内从车辆运行中提取能量，也能从频率为 0.7-1.5 Hz、振幅为 30° 的人体运动中提取能量。在旋转模式下，原型机实现了 3.79 W 的最大平均直流电功率，而在振动模式下，则达到了 244 mW。在人体运动和铁路模拟测试中，该原型成功地为便携式电子设备供电，并支持免电池三轴加速度和温度多传感器。该原型展示了作为便携式电子设备和自供电监测应用的可持续电源的巨大潜力。

Graphical abstract 图形摘要

Keywords 关键词

Dual-mode

Energy harvesting

Nonlinear pendulum

Speed-amplified

Low-frequency

双模式能量收集非线性摆速度放大低频

1. Introduction 1.导言

5G, artificial intelligence, and the Internet of Things have taken off at a brisk speed over the years, creating an intelligent network via tremendous sensors deployed in various scenarios [1,2]. However, the energy supply limits its wide application, especially in some difficult-to-reach locations, such as rotational machines, wilderness operations, and marine environments [3,4]. The batteries as power sources are not sustainable, pollute the environment, and are heavy for large-capacity. How to effectively harvest the redundant energy in the environment and convert it into electricity for electronic devices and sensors, avoid frequent battery replacement to achieve long-term device operation, has brought widespread attention from academe and industries [5,6].
这些年来，5G、人工智能和物联网迅猛发展，通过部署在各种场景中的大量传感器形成了一个智能网络[1,2]。然而，能源供应限制了其广泛应用，尤其是在一些难以到达的地方，如旋转机械、野外作业和海洋环境[3,4]。电池作为动力源不具有可持续性，会污染环境，而且重量大、容量小。如何有效收集环境中的冗余能量，并将其转化为电子设备和传感器所需的电能，避免频繁更换电池，实现设备的长期运行，已引起学术界和工业界的广泛关注 [5,6]。

The environment is replete with mechanical energy, thereby instigating the development of numerous transduction devices designed to convert mechanical vibrations into electrical energy [7,8]. These apparatuses exploit a variety of mechanisms, including electromagnetic [[9], [10], [11]], piezoelectric [[12], [13], [14]], and triboelectric [[15], [16], [17]] principles. Notably, ambient vibrations feature low-frequency, broadband, and time-varying, making efficient energy harvesting from such environmental sources exceedingly formidable [18,19]. The effectiveness of most vibration energy harvesters is heightened at higher excitation frequencies, given that the generated power is directly proportional to the cube of the vibration frequency [20]. Furthermore, a lower resonant frequency typically signifies a higher inertial mass or lower stiffness, consequently leading to the bulkiness of the harvesters [21]. To mitigate this challenge, innovative approaches such as frequency up-conversion techniques, including impact mechanism [[22], [23], [24]] and gear modulation [[25], [26], [27]] approach, have been proposed.
环境中充满了机械能，因此催生了许多旨在将机械振动转化为电能的传导装置[7,8]。这些装置利用了多种机制，包括电磁[[9], [10], [11]]、压电[[12], [13], [14]]和三电[[15], [16], [17]]原理。值得注意的是，环境振动具有低频、宽带和时变的特点，这使得从此类环境源高效采集能量变得极为困难[18,19]。由于产生的功率与振动频率的立方成正比，因此大多数振动能量收集器在较高的激励频率下会更加有效[20]。此外，较低的共振频率通常意味着较高的惯性质量或较低的刚度，从而导致能量收集器体积庞大 [21]。为缓解这一挑战，人们提出了一些创新方法，如频率上转换技术，包括撞击机制 [[22]、[23]、[24]] 和齿轮调制 [[25]、[26]、[27]] 方法。

The impact mechanism serves to transmute low-frequency excitation into high-frequency vibrations within the harvester through mechanical impacts or plucking [28], thereby accommodating low-frequency operational conditions and augmenting electromechanical conversion efficiency [29]. For example, the utilization of a ball [30] or a sliding mass [31] facilitates the conversion of human motion into high-frequency vibrations in a piezoelectric beam, culminating in an output voltage of 818 Hz when subjected to 5.8 Hz excitation [32]. The modulation of magnetic forces, designed to harmonize with the low-frequency lateral vibrations of a freight wagon, amplifies the resonant frequency of the power-generating beam, ultimately leading to a remarkable 150 % increase in electromechanical conversion efficiency [33]. Using a magnetic plucking mechanism converts omnidirectional and low-frequency vibration into high-frequency vibration of generating beam [34]. Furthermore, the implementation of a rotation-enhanced impact mechanism can boost output power by an astounding 682.8 % [35], primarily due to centrifugal forces that augment the impact's intensity [36]. The centrifugal force coupled with the nonlinearity surface impact mechanism improves the output power [37]. Nevertheless, it is imperative to acknowledge that, although the impact mechanism offers an efficient means to transfigure low-frequency motions into harvester's resonances, challenges concerning energy losses and mechanical wear persist and necessitate further enhancement. Additionally, it's worth noting that energy transfer occurs only once per cycle, imposing limitations on the prospects for elevating power density.
撞击机构的作用是通过机械撞击或拨动将低频激励转换为收割机内的高频振动[28]，从而适应低频操作条件并提高机电转换效率[29]。例如，利用球[30]或滑动块[31]可将人体运动转化为压电梁中的高频振动，在 5.8 赫兹的激励下可产生 818 赫兹的输出电压[32]。为了与货车的低频横向振动相协调，对磁力进行了调制，从而放大了发电梁的共振频率，最终使机电转换效率显著提高了 150%[33]。使用磁拨机构可将全向低频振动转换为发电梁的高频振动 [34]。此外，采用旋转增强型冲击机制可将输出功率提高惊人的 682.8 %[35]，这主要是由于离心力增强了冲击强度[36]。离心力加上非线性表面撞击机制提高了输出功率[37]。不过，必须承认的是，尽管冲击机制提供了将低频运动转化为收割机共振的有效方法，但有关能量损失和机械磨损的挑战依然存在，因此有必要进一步改进。此外，值得注意的是，能量传递在每个循环中只发生一次，这对提高功率密度的前景造成了限制。

In parallel with the impact mechanism, several gear modulation techniques, including rack-pinion [38,39], ball screw [40,41], and lead screw [42,43] configurations, have been explored for the conversion of low-frequency vibrations into accelerated rotation. The rack-pinion mechanism, for instance, transforms reciprocating vibrations experienced in suspension, railway settings, and human motions into the high-speed rotation of the generator [[44], [45], [46]]. Moreover, this mechanism enhances the relative motion between magnets and coils, thus improving the output performance of the harvester [[47], [48], [49]]. While the ball screw encounters rotational speed limitations due to internal ball wear within the nut, the lead screw may confront challenges associated with friction and substantial damping forces [50]. These mechanical structures are proficient at converting low-frequency and irregular reciprocating motions into unidirectional rotation. Nonetheless, their substantial physical dimension presents installation challenges and potential operational safety concerns for freight trains or humans.
与冲击机构并行的还有几种齿轮调制技术，包括齿条-小齿轮 [38,39]、滚珠丝杠 [40,41] 和导螺杆 [42,43]，用于将低频振动转换为加速旋转。例如，齿条-小齿轮机构可将悬挂、铁路设置和人体运动中的往复振动转化为发电机的高速旋转[[44], [45], [46]]。此外，这种机制还能增强磁铁和线圈之间的相对运动，从而提高收割机的输出性能[[47], [48], [49]]。滚珠螺杆会因螺母内部滚珠磨损而受到转速限制，而导螺杆则可能面临与摩擦和巨大阻尼力相关的挑战 [50]。这些机械结构擅长将低频和不规则的往复运动转换为单向旋转。然而，其巨大的物理尺寸给安装带来了挑战，并给货运列车或人类带来了潜在的运行安全问题。

Although the aforementioned harvesters could scavenge low-frequency energy through mechanical modulation, the energy loss and bulky size constrain the power density. Furthermore, for wearables such as smartwatches and wristbands, it is impractical to embed bulky energy harvesters as power sources. Besides, to the best of the authors' knowledge, there is rarely a report on the electromagnetic energy harvester that can harvest both the vibration and rotation energy for adapting to complex low-frequency environments. Therefore, this paper introduces a high-performance speed-amplified dual-mode energy harvesting (DM-EH) with a nonlinear pendulum mechanism, which not only harvests the vibration energy from human motions but also possesses the capability of scavenging the rotational energy from vehicle operations. The contributions of the DM-EH are as follows: (1) The pendulum serves a pivotal role in enabling the device's dual-mode operation. Specifically, it functions as the energy capture unit for detecting vibration energy while ensuring that the all-in-one generation unit operates effectively in rotational environments. (2) The prototype generates an average output power of 3.79 W and 244 mW with an optimal resistance load of 160 Ω, resulting in a power density of 182.58 mW cm⁻³ and 11.74 mW cm⁻³ at 540 rpm and a frequency of 1.5 Hz with an angle of 30°, respectively. (3) As the applications, the DM-EH exhibits the capability to power a range of daily electronic devices and commercial wireless sensors, including LED lights, smartwatches, smartphones, mobile power banks, acceleration sensors, and temperature sensors.
尽管上述能量收集器可以通过机械调制来收集低频能量，但能量损耗和笨重的体积限制了功率密度。此外，对于智能手表和腕带等可穿戴设备来说，嵌入笨重的能量收集器作为电源是不切实际的。此外，据作者所知，很少有关于电磁能量收集器能同时收集振动和旋转能量以适应复杂低频环境的报道。因此，本文介绍了一种具有非线性钟摆机构的高性能速度放大双模能量收集器（DM-EH），它不仅能收集人体运动的振动能量，还能收集车辆运行的旋转能量。DM-EH 的贡献如下：(1) 摆杆在该装置的双模式运行中发挥着关键作用。具体来说，它既是检测振动能量的能量捕获装置，又能确保一体化发电装置在旋转环境中有效运行。(2) 原型在最佳电阻负载为 160 Ω 的情况下，可产生 3.79 W 和 244 mW 的平均输出功率，在转速为 540 rpm、频率为 1.5 Hz、角度为 30° 时，功率密度分别为 182.58 mW cm ⁻³ 和 11.74 mW cm ⁻³ 。(3) 在应用方面，DM-EH 能够为一系列日常电子设备和商用无线传感器供电，包括 LED 灯、智能手表、智能手机、移动电源、加速度传感器和温度传感器。

The paper's structural framework is delineated as follows: Section 2 elaborates on the design and working principle of the DM-EH. Section 3 presents modeling, dynamic analysis, and finite-element simulation of the prototype. Section 4 is devoted to the incorporation of experimental tests and the application of the harvester. The main findings are summarized in Section 5.
本文的结构框架如下：第 2 节阐述了 DM-EH 的设计和工作原理。第 3 节介绍原型的建模、动态分析和有限元模拟。第 4 节专门介绍收割机的实验测试和应用。第 5 节总结了主要研究结果。

2. Design and working principle
2.设计和工作原理

Fig. 1 provides an overview of the self-powered monitoring harvester designed for low-frequency environments, encompassing human motions, vehicle operations, and ocean waves. In recognition of the diverse nature of low-frequency motions, such as human limb vibration and the rotational movement of freight trains, this paper has engineered a high-performance speed-amplified dual-mode energy harvester (DM-EH) by integrating a pendulum mechanism into the frequency up-conversion technology.
图 1 是专为低频环境（包括人体运动、车辆运行和海浪）设计的自供电监测采集器的概览。考虑到低频运动（如人体肢体振动和货运列车的旋转运动）的多样性，本文通过将摆锤机构集成到频率上变频技术中，设计了一种高性能速度放大双模能量收集器（DM-EH）。

In Fig. 2a, a comprehensive structural overview of the DM-EH is provided through an exploded assembly diagram. The DM-EH is composed of three key components: a transmission unit, a generation unit, and a circuit. The transmission unit encompasses a sun gear, a planetary gear, and a substrate. The sun gear and planetary gear are positioned at the outer periphery of the substrate, with the sun gear's rotation located at the substrate's edge, while the planet gear's rotation is positioned in the central portion of the substrate, thus facilitating meshing between the sun gear and the planet gear. The generation unit incorporates a Halbach array magnet and a set of coils featuring permeability materials to augment the magnetic flux passing through the coils. The circuit includes an energy management module, encompassing a rectifier, voltage regulator, storage, and wireless sensing module.
图 2a 是 DM-EH 的全面结构示意图。DM-EH 由三个关键部件组成：传动装置、发电装置和电路。传动装置包括一个太阳齿轮、一个行星齿轮和一个基板。太阳齿轮和行星齿轮位于基板的外围，太阳齿轮的旋转位于基板的边缘，而行星齿轮的旋转位于基板的中央部分，从而促进了太阳齿轮和行星齿轮之间的啮合。发电装置包括一个哈尔巴赫阵列磁铁和一组线圈，线圈采用磁导率材料，以增强通过线圈的磁通量。电路包括一个能量管理模块，包括整流器、电压调节器、存储和无线传感模块。

Fig. 2b describes the working principle and energy flows of the DM-EH. When the structure is installed on the swing vibration part, the planetary gear revolves around the sun gear in response to excitations. Concurrently, the planetary gear impels the permanent magnet to generate high-speed rotation. The coil is connected to the permanent magnet via bearings, ensuring that the coil remains stationary for the planetary gear. This arrangement results in relative motion between the coil and the permanent magnet. On the other hand, when the device is installed within the rotational component, the sun gear rotates in synchronization with rotation excitation. Subject to the combined influences of gravity torque, magnetic torque, and friction torque, the planetary gear orbits around the sun gear until it attains a state of equilibrium. In this state, the sun gear drives the planetary gear to produce high-speed rotation along with the permanent magnets. Under the condition of swing and rotational vibrations, both the permanent magnet and the coil experience relative motion. Hence the generation unit serves three vital functions: (1) functions as a counterweight, efficiently converting low-frequency vibrations into high-speed rotation, thus enhancing electromechanical energy conversion performance; (2) the smooth operation of the transmission unit by transforming the rotation of the sun gear into high-speed rotation of the planetary gear under anchorless condition of planetary gear; (3) the primary function is to convert mechanical energy into the relative motion of magnets and coils. According to Faraday's law of electromagnetic induction, the coil generates induced current as shown in Fig. 2c. It is worth mentioning that a group of coils was selected as a representative to demonstrate the power generation progress due to the circular array configuration. Besides, to facilitate the comparison of the harvester states, the magnets remain stationary while the coils rotate during the simulation.
图 2b 描述了 DM-EH 的工作原理和能量流。当该结构安装在摆动振动部件上时，行星齿轮在激振力的作用下围绕太阳齿轮旋转。同时，行星齿轮推动永久磁铁产生高速旋转。线圈通过轴承与永磁体相连，确保线圈对行星齿轮保持静止。这种安排导致线圈和永久磁铁之间产生相对运动。另一方面，当设备安装在旋转部件内时，太阳齿轮会与旋转激励同步旋转。在重力力矩、磁力力矩和摩擦力矩的共同作用下，行星齿轮围绕太阳齿轮运行，直至达到平衡状态。在这种状态下，太阳齿轮驱动行星齿轮与永磁体一起产生高速旋转。在摆动和旋转振动的条件下，永磁体和线圈都会发生相对运动。因此，发电装置具有三个重要功能：(1) 作为配重，有效地将低频振动转换为高速旋转，从而提高机电能量转换性能；(2) 在行星齿轮无锚状态下，通过将太阳齿轮的旋转转换为行星齿轮的高速旋转，实现传动装置的平稳运行；(3) 主要功能是将机械能转换为磁体和线圈的相对运动。根据法拉第电磁感应定律，线圈会产生感应电流，如图 2c 所示。值得一提的是，我们选择了一组线圈作为代表，以展示圆形阵列配置所带来的发电进展。此外，为了便于比较收割机的状态，在模拟过程中，磁铁保持静止，而线圈则旋转。

This structural design offers the following advantages: (1) The generation unit facilitates the conversion of low-frequency vibrations to high-speed rotations, accommodating the low-frequency environments while meeting the high-frequency input requirements of the generation unit. (2) The prototype is capable of concurrently capturing both vibration and rotation motions, effectively harnessing multiple sources of excitation to improve the system's adaptability. (3) The generation unit serves as the inertial mass block of the pendulum, obviating the need for additional counterweights and simplifying the structural design.
这种结构设计具有以下优点：（1）发电装置有利于将低频振动转换为高速旋转，既能适应低频环境，又能满足发电装置的高频输入要求。(2) 原型能够同时捕捉振动和旋转运动，有效利用多种激励源，提高系统的适应性。(3) 发生单元作为摆锤的惯性质量块，无需额外配重，简化了结构设计。

3. Modeling and dynamic analysis of the DM-EH
3.DM-EH 的建模和动态分析

To further reveal the working principle and advantages of the DM-EH, an equivalent mechanical system model under human motion and vehicle operation is established to analyze its dynamic characteristics.
为了进一步揭示 DM-EH 的工作原理和优势，我们建立了人体运动和车辆运行下的等效机械系统模型，以分析其动态特性。

3.1. Theoretical modeling of the DM-EH under human motion
3.1.DM-EH 在人体运动下的理论建模

A pendulum is used to simulate the human arm motion. As shown in Fig. 3a, the DM-EH is fixed at the end of the pendulum. The detailed parameters of the DM-EH are given in Table 1. The coordinate O₀ signifies the inertial frame, depicting motion exclusively in the X-direction, while coordinate O₁ represents the reference frame fixed to the sun gear of the DM-EH, and O₂ designates the reference frame anchored to the base of the DM-EH. The coordinate O₁ in the fixed coordinate system can be described as(1)

\begin{array}{l} x_{1} = x_{0} + L \sin θ \\ y_{1} = - L \cos θ \end{array}

Table 1. Material properties and structural parameters of the proposed DM-EH.
表 1.拟议 DM-EH 的材料特性和结构参数。

Parameter 参数	Value 价值	Parameter 参数	Value 价值
Number of magnets 磁铁数量	24	Size of magnets (ring) 磁铁尺寸（环）	R15 × 14 × 10 mm R15 × 14 × 10 毫米
Material of magnets 磁铁材料	NdFeB-N35 钕铁硼-N35	Norm B 规范 B	1.5 T 1.5 T
Diameter of wire 电线直径	0.1 mm 0.1 毫米	Number of coil turns 线圈匝数	500
Internal resistance 内部电阻	160 Ω 160 Ω	Coil area 线圈面积	5 × 11 mm² 5 × 11 毫米 ²
The mass of the pendulum m 摆锤的质量 m	50.1 g 50.1 g	Moment of the pendulum I 摆锤力矩 I	23.22 g cm² 23.22 克厘米 ²
Length of the pendulum 摆锤长度l	15 mm 15 毫米	Mechanical damping c 机械阻尼 c	2e-4
The radius of the sun gear r 太阳齿轮的半径 r	13 mm 13 毫米	Transmission ratio n 传动比 n	5
Distance between O₀ and O₁ L O ₀ 和 O ₁ 之间的距离 L	50 cm 50 厘米	Costs of the prototype 原型的成本	10.25 USD 10.25 美元
Weight of the prototype 原型机的重量	78.4 g 78.4 g	Size of the prototype 原型的大小	20.79 cm³ 20.79 厘米 ³

The velocity of the coordinate O₁ is as follows(2)

\begin{array}{l} {\dot{x}}_{1} = v_{0} + L \dot{θ} \cos θ \\ {\dot{y}}_{1} = L \dot{θ} \sin θ \end{array}

坐标 O 的速度 ₁ 如下 (2)

\begin{array}{l} {\dot{x}}_{1} = v_{0} + L \dot{θ} \cos θ \\ {\dot{y}}_{1} = L \dot{θ} \sin θ \end{array}

The acceleration velocity(3)

\begin{array}{l} {\ddot{x}}_{1} = a_{0} + L α \cos θ - L ω^{2} \sin θ \\ {\ddot{y}}_{1} = L α \sin θ + L ω^{2} \cos θ \end{array}

加速度 (3)

\begin{array}{l} {\ddot{x}}_{1} = a_{0} + L α \cos θ - L ω^{2} \sin θ \\ {\ddot{y}}_{1} = L α \sin θ + L ω^{2} \cos θ \end{array}

The coordinate O₂ can be written as(4)

\begin{array}{l} x = x_{0} + L \sin θ + l \sin ϕ \\ y = - L \cos θ - L \cos ϕ \end{array}

坐标 O ₂ 可以写成 (4)

\begin{array}{l} x = x_{0} + L \sin θ + l \sin ϕ \\ y = - L \cos θ - L \cos ϕ \end{array}

The velocity of the coordinate O₂(5)

\begin{array}{l} \dot{x} = v_{0} + L ω \cos θ + l \dot{ϕ} \cos ϕ \\ \dot{y} = L ω \sin θ + l \dot{ϕ} \sin ϕ \end{array}

坐标 O ₂ (5)

\begin{array}{l} \dot{x} = v_{0} + L ω \cos θ + l \dot{ϕ} \cos ϕ \\ \dot{y} = L ω \sin θ + l \dot{ϕ} \sin ϕ \end{array}

的速度

The acceleration velocity of the coordinate O₂(6)

\begin{array}{l} \ddot{x} = a_{0} + L α \cos θ - L ω^{2} \sin θ + l \ddot{ϕ} \cos ϕ - l {\dot{ϕ}}^{2} \sin ϕ \\ \ddot{y} = L α \sin θ + L ω^{2} \cos θ + l \ddot{ϕ} \sin ϕ + L {\dot{ϕ}}^{2} \cos ϕ \end{array}

坐标 O 的加速度 ₂ (6)

\begin{array}{l} \ddot{x} = a_{0} + L α \cos θ - L ω^{2} \sin θ + l \ddot{ϕ} \cos ϕ - l {\dot{ϕ}}^{2} \sin ϕ \\ \ddot{y} = L α \sin θ + L ω^{2} \cos θ + l \ddot{ϕ} \sin ϕ + L {\dot{ϕ}}^{2} \cos ϕ \end{array}

The dynamic equation of the pendulum(7)

(I + m l^{2}) \ddot{ϕ} + F_{f} r + m g l \sin ϕ + F_{m} R = F l

摆的动态方程 (7)

(I + m l^{2}) \ddot{ϕ} + F_{f} r + m g l \sin ϕ + F_{m} R = F l

The electromagnetic damping force(8)

F_{m} = N P B I (t) L_{c} = \frac{N^{2} P^{2} B^{2} R^{2} L_{c}^{2} n \dot{ϕ}}{R_{c} + R_{e}}

I (t) = \frac{E (t)}{R_{c} + R_{e}} = N \frac{d Φ / d t}{R_{c} + R_{e}} = N \frac{d B S / d t}{R_{c} + R_{e}} = N P B \frac{R^{2} L_{c} n \dot{ϕ}}{R_{c} + R_{e}}

电磁阻尼力 (8)

F_{m} = N P B I (t) L_{c} = \frac{N^{2} P^{2} B^{2} R^{2} L_{c}^{2} n \dot{ϕ}}{R_{c} + R_{e}}

I (t) = \frac{E (t)}{R_{c} + R_{e}} = N \frac{d Φ / d t}{R_{c} + R_{e}} = N \frac{d B S / d t}{R_{c} + R_{e}} = N P B \frac{R^{2} L_{c} n \dot{ϕ}}{R_{c} + R_{e}}

The mechanical damping(9)

F_{f} = m c \dot{ϕ}

机械阻尼 (9)

F_{f} = m c \dot{ϕ}

The inertia driving force(10)

\begin{array}{l} F = m a = m \sqrt{{\ddot{x}}^{2} + {\ddot{y}}^{2}} = m (l \ddot{ϕ} + a_{0} \cos ϕ + L \ddot{ϕ} \cos θ \cos ϕ - L ω^{2} \sin θ \cos ϕ \\ + L \ddot{ϕ} \sin θ \sin ϕ + L ω^{2} \cos θ \sin ϕ) \end{array}

惯性驱动力 (10)

\begin{array}{l} F = m a = m \sqrt{{\ddot{x}}^{2} + {\ddot{y}}^{2}} = m (l \ddot{ϕ} + a_{0} \cos ϕ + L \ddot{ϕ} \cos θ \cos ϕ - L ω^{2} \sin θ \cos ϕ \\ + L \ddot{ϕ} \sin θ \sin ϕ + L ω^{2} \cos θ \sin ϕ) \end{array}

The dynamic equation of the pendulum(11)

\frac{I}{m l} \ddot{ϕ} + (\frac{c r}{l} + \frac{N^{2} P^{2} B^{2} R^{2} L_{c}^{2}}{R_{c} + R_{e}} n) \dot{ϕ} + g \sin ϕ = (a_{0} \cos ϕ + L α \cos θ \cos ϕ - L ω^{2} \sin θ \cos ϕ + L α \sin θ \sin ϕ + L ω^{2} \cos θ \sin ϕ)

摆的动态方程 (11)

\frac{I}{m l} \ddot{ϕ} + (\frac{c r}{l} + \frac{N^{2} P^{2} B^{2} R^{2} L_{c}^{2}}{R_{c} + R_{e}} n) \dot{ϕ} + g \sin ϕ = (a_{0} \cos ϕ + L α \cos θ \cos ϕ - L ω^{2} \sin θ \cos ϕ + L α \sin θ \sin ϕ + L ω^{2} \cos θ \sin ϕ)

To analyze the dynamic characteristics of the DM-EH, constant frequency excitation simulations were conducted within the frequency range of 0.7–1.5 Hz. Three arm swing angles (20°, 25°, and 30°) were selected as excitation levels to investigate the system's dynamic behavior. It is assumed that the arm swings at a constant speed, implying an angular acceleration α of 0. Fig. 3b and c illustrate the variation in DM-EH swing angle under different excitation levels with ODE 45 in Matlab 2019. It is worth noting that the pendulum exhibits nonlinear characteristics for its swing angle. Each point on the graph represents the amplitude of the swing at a specific frequency for each excitation cycle. The results show that with the increase of frequency and swing Angle, the swing Angle of the structure gradually increases, which means that the output voltage also increases.
为了分析 DM-EH 的动态特性，我们在 0.7-1.5 Hz 的频率范围内进行了恒频激励模拟。为研究系统的动态行为，选择了三个手臂摆动角度（20°、25° 和 30°）作为激励水平。图 3b 和 c 展示了 DM-EH 在不同激励水平下摆动角度的变化，并使用 Matlab 2019 中的 ODE 45 进行了分析。值得注意的是，摆锤的摆角呈现非线性特征。图中的每个点代表每个激励周期在特定频率下的摆幅。结果表明，随着频率和摆角的增加，结构的摆角逐渐增大，这意味着输出电压也随之增大。

3.2. Theoretical modeling of the DM-EH under vehicle operation
3.2.车辆运行时 DM-EH 的理论模型

The coordinates O₀ and O₁ coincide with each other under the rotation condition, as shown in Fig. 4a. The dynamic equation of a friction pendulum can be described as(12)

\frac{I}{m l} \ddot{ϕ} + g \sin ϕ = (\frac{c r}{l} + \frac{N^{2} P^{2} B^{2} R^{2} L_{c}^{2}}{R_{c} + R_{e}}) n (Ω - \dot{ϕ})

在旋转条件下，坐标 O ₀ 和 O ₁ 相互重合，如图 4a 所示。摩擦摆的动态方程可描述为 (12)

\frac{I}{m l} \ddot{ϕ} + g \sin ϕ = (\frac{c r}{l} + \frac{N^{2} P^{2} B^{2} R^{2} L_{c}^{2}}{R_{c} + R_{e}}) n (Ω - \dot{ϕ})

The pendulum's motion unfolds in two distinct stages: adhesion and detachment, representing the alternating interplay between static friction torque and dynamic friction torque (Fig. 4b), and the pendulum exhibits a piecewise nonlinearity. During the adhesion stage, the static friction torque and magnetic torque drive the friction pendulum and shaft to rotate synchronously. This continues until the accumulated torque reaches the point where it equals the sum of the maximum static friction torque and magnetic torque. In the detachment stage, the static friction torque converts into dynamic friction torque. However, as the dynamic friction torque is lower than the maximum static friction torque, the friction pendulum reverses its rotation under the influence of the applied torque(13)

(m_{c} c + \frac{N^{2} P^{2} B^{2} R^{3} L_{c}^{2}}{R_{c} + R_{e}}) i (Ω - \dot{ϕ}) = m_{c} g l

摆的运动分为两个不同的阶段：附着和脱离，代表了静摩擦力矩和动摩擦力矩的交替相互作用（图 4b），摆呈现出片状非线性。在附着阶段，静摩擦力矩和磁力矩驱动摩擦摆和轴同步旋转。这种情况一直持续到累积扭矩达到等于最大静摩擦扭矩和磁扭矩之和时为止。在脱离阶段，静摩擦扭矩转化为动摩擦扭矩。然而，由于动摩擦力矩低于最大静摩擦力矩，摩擦摆在外加力矩的影响下反向旋转 (13)

(m_{c} c + \frac{N^{2} P^{2} B^{2} R^{3} L_{c}^{2}}{R_{c} + R_{e}}) i (Ω - \dot{ϕ}) = m_{c} g l

。

Variations in the rotational speed of the rotor magnet induce distinct motion patterns in the friction pendulum. With increasing external speed, the motion amplitude of the friction pendulum gradually escalates until it attains π/2, marking the point referred to as the critical speed. The cumulative energy buildup eventually prompts the friction pendulum to rotate by π, resulting in the planetary gear to orbit around the solar gear. When the rotor magnet's speed exceeds the critical speed, the coil generates motion relative to the shaft end cover of the freights, leading to device malfunction. Consequently, this section undertakes a theoretical analysis of the critical speed. When the friction pendulum synchronously rotates to an angle of π/2 under the combined influence of static friction torque and magnetic torque, the gravitational moment reaches its peak(14)

m g l = (\frac{c r}{l} + \frac{{(N B L_{c} R)}^{2}}{m l R_{c}}) \dot{ϕ}

转子磁铁的转速变化会在摩擦摆中产生不同的运动模式。随着外部速度的增加，摩擦摆的运动幅度逐渐增大，直至达到 π/2，这一点被称为临界速度。累积的能量最终促使摩擦摆旋转 π，导致行星齿轮绕太阳齿轮运行。当转子磁铁的速度超过临界速度时，线圈会产生相对于齿轮轴端盖的运动，从而导致设备故障。因此，本节将对临界转速进行理论分析。当摩擦摆在静摩擦力矩和磁力矩的共同作用下同步旋转到 π/2 角时，重力力矩达到峰值。 (14)

m g l = (\frac{c r}{l} + \frac{{(N B L_{c} R)}^{2}}{m l R_{c}}) \dot{ϕ}

Fig. 4c illustrates the three-dimensional correlation of the critical mass, external excitation frequency, and resistance. As the excitation frequency rises, the external weight also increases. Simultaneously, the critical mass experiences a gradual reduction with the increase in resistance. This decrease in resistance leads to a decrease in circuit current, resulting in a diminished magnetic moment, which in turn weakens the external force responsible for upward pendulum movement.
图 4c 展示了临界质量、外部激励频率和阻力的三维相关性。随着激励频率的增加，外部重量也随之增加。同时，临界质量随着电阻的增加而逐渐减小。电阻的减小导致电路电流的减小，从而减弱了磁矩，进而减弱了摆锤向上运动的外力。

3.3. Finite-element of the generation unit
3.3.发电装置的有限元

To achieve a reasonable allocation of the magnets in DM-EH, magnetic flux density around the coils’ boundary with different magnetic pole pairs was simulated by COMSOL Multiphysics 6.0. Compared with conventional arrayed magnets, the Halbach arrayed magnets generate concentrated one-side magnetic flux, leading to the production of more power in coils (Fig. 5a).
为了实现 DM-EH 中磁体的合理分配，COMSOL Multiphysics 6.0 模拟了不同磁极对的线圈边界周围的磁通密度。与传统的阵列磁体相比，哈尔巴赫阵列磁体产生的单侧磁通量更集中，从而在线圈中产生更大的功率（图 5a）。

The increased pole pairs improve the value of the magnetic flux density, uniform the magnetic flux density, and add the waveform of magnetic flux density in one cycle as shown in Fig. 5b. Nevertheless, the trend of growth slows down when the magnetic pole pairs beyond 6. Besides, the increased magnetic pole pairs aggravate the difficulty of processing and installation of magnets. Therefore, the Halbach array with 6 magnetic pole pairs prototypes the DM-EH.
如图 5b 所示，磁极对的增加提高了磁通密度值，均匀了磁通密度，并在一个周期内增加了磁通密度的波形。然而，当磁极对超过 6 个时，增长趋势会放缓。此外，磁极对的增加也增加了磁体加工和安装的难度。因此，具有 6 个磁极对的哈尔巴赫阵列是 DM-EH 的原型。

4. Performance investigation
4.绩效调查

4.1. Fabrication of the DM-EH
4.1.DM-EH 的制造

The DM-EMH consists of a generation unit, a transmission unit, and a circuit. Generation unit: a base connected to the three-phase coil through a sleeve, featuring an inner diameter of 3 mm, an outer diameter of 9.7 mm, and a height of 5 mm. The rotor contains a ring magnet with dimensions of R15 × 14 × 10 mm, comprising 6 pairs of Halbach array magnets. These magnets are embedded in the rotor and attached to the planetary gear using a shaft and MR63ZZ bearings. It is worth noting that magnetism materials encapsulate the coils to enhance the magnetic flux passing through them. Transmission unit: a 0.5 mold 50-tooth sun gear, in conjunction with an MR63ZZ bearing, was affixed to the base through an R3 × 10 mm lug boss. The sun gear diameter, center hole, and tooth thickness are 26 mm, 6 mm, and 5 mm, respectively. The sun gear engaged with a 0.5 mold 10-tooth planetary gear. Circuit: a three-phase rectifier is constructed using six A7 diodes, while zener diodes ensure a stable DC voltage within the capacitances.
DM-EMH 由发电单元、传输单元和电路组成。发电单元：底座通过套筒与三相线圈相连，内径 3 毫米，外径 9.7 毫米，高 5 毫米。转子包含一个尺寸为 R15 × 14 × 10 毫米的环形磁铁，由 6 对哈尔巴赫阵列磁铁组成。这些磁铁嵌入转子中，并通过轴和 MR63ZZ 轴承连接到行星齿轮上。值得注意的是，磁性材料封装了线圈，以增强通过线圈的磁通量。传动装置：0.5 模 50 齿太阳齿轮与 MR63ZZ 轴承通过 R3 × 10 毫米凸耳固定在基座上。太阳齿轮的直径、中心孔和齿厚分别为 26 毫米、6 毫米和 5 毫米。太阳齿轮与一个 0.5 模 10 齿行星齿轮啮合。电路：使用六个 A7 二极管构成三相整流器，齐纳二极管确保电容内的直流电压稳定。

4.2. Characterization and measurements
4.2.特征描述和测量

Ensuring exceptional electrical output from the harvester is paramount, particularly for portable power and battery-free wireless sensor applications. Therefore, the energy harvesting performance of the DM-EH in rotation mode was investigated, as depicted in Fig. 6a–c. The prototyped DM-EH was driven by a speed-controlled servo motor (model: HZXT-008, Wuxi Houde Automation Meter CO., LTD.), and the corresponding output voltage at various speeds was recorded and captured using an oscilloscope (model: DSOX1204G, Keysight). Employing Origin 2018 processes experimental data and generates visual images. Fig. 6b demonstrates the alternating current (AC) generated by the DM-EH ranging from 60 to 540 rpm, effectively covering the typical speed of 80 km h⁻¹ for freight trains in China [51,52]. Notably, the peak voltage reached 3.12 V at 60 rpm, gradually increasing with the growth of rotation speed, and eventually arriving at a peak of 25.14 V at 540 rpm. The direct current (DC) performance was further examined for most wireless sensors requiring DC voltage (Fig. 6c and d). It's evident that with increasing speed, the corresponding RMS voltage improved, as the induced voltage is highly dependent on the relative speed between the magnets and coils. Notably, the experiments involved testing 10 groups of DC voltage measurements, each conducted for 60 s at a constant speed, to ensure the validity of the experimental data. The DC voltage is a directly measured parameter, and the root mean square (RMS) values of this voltage output over 10 min were calculated.
确保采集器输出卓越的电能至关重要，尤其是在便携式电源和无电池无线传感器应用中。因此，我们研究了 DM-EH 在旋转模式下的能量收集性能，如图 6a-c 所示。原型 DM-EH 由一个速度可控的伺服电机（型号：HZXT-008，无锡厚德自动化仪表有限公司）驱动，并使用示波器（型号：DSOX1204G，Keysight）记录和捕捉不同速度下的相应输出电压。采用 Origin 2018 处理实验数据并生成可视图像。图 6b 展示了 DM-EH 在 60 至 540 rpm 范围内产生的交流电，有效覆盖了中国货运列车 80 km h ⁻¹ 的典型速度 [51,52]。值得注意的是，峰值电压在 60 rpm 时达到 3.12 V，随着转速的增加而逐渐升高，最终在 540 rpm 时达到 25.14 V 的峰值。对于大多数需要直流电压的无线传感器，直流电性能得到了进一步检验（图 6c 和 d）。很明显，随着转速的提高，相应的有效值电压也在提高，因为感应电压与磁铁和线圈之间的相对速度有很大关系。值得注意的是，实验涉及 10 组直流电压测量，每组在恒定速度下进行 60 秒，以确保实验数据的有效性。直流电压是一个直接测量的参数，在 10 分钟内该电压输出的均方根值被计算出来。

To assess the output power capability, the prototype was connected to a resistance box, where the resistance ranged from 10 to 500 Ω with steps of 10 Ω in the range of 10–300 Ω and 100 Ω in the range of 300–500 Ω, respectively. The output voltage and power versus resistance at typical frequencies revealed that the prototype achieved maximum power when the external resistance closely matched the coils' internal resistance (160 Ω). The maximum average power reached 59 mW - 3.79 W with optimal resistance at 60–540 rpm, resulting in the highest power density reaching 182.58 mW cm⁻³.
为评估输出功率能力，将原型机连接到电阻箱上，电阻箱的电阻范围为 10 Ω 至 500 Ω，在 10 Ω 至 300 Ω 的范围内以 10 Ω 为步长，在 300 Ω 至 500 Ω 的范围内以 100 Ω 为步长。典型频率下的输出电压和功率与电阻的关系表明，当外部电阻与线圈内阻（160 Ω）非常接近时，原型达到了最大功率。在 60-540 rpm 的最佳电阻条件下，最大平均功率达到 59 mW - 3.79 W，最高功率密度达到 182.58 mW cm ⁻³ 。

To analyze the arm swing angle during various body movements, gait analysis was conducted using an optical 3D motion capture system (Model: NOKOV Mars 4H), as depicted in Fig. 7a. This system accurately captured real-time 3D coordinates of each marker node on the human body during motion, facilitating subsequent 3D reconstruction and model analysis. The arm angle data under DM-EH on and off conditions during slow walking, fast walking, jogging, and rushing scenarios are presented in Fig. 7b. The results indicate that the arm swing angle has little change with the DM-EH compared to the DM-EH off conditions. To determine the swing frequency of the human arm during daily movements, the swing characteristics of the human arm at speeds ranging from 2 to 10 km h⁻¹ were characterized. Fourier transform analysis revealed the arm swing frequency ranges from 0.7 Hz to 1.5 Hz, as demonstrated in Fig. 7c.
如图 7a 所示，为了分析各种身体运动时的手臂摆动角度，我们使用光学三维运动捕捉系统（型号：NOKOV Mars 4H）进行了步态分析。该系统能准确捕捉运动过程中人体各标记节点的实时三维坐标，便于后续的三维重建和模型分析。图 7b 展示了 DM-EH 在慢走、快走、慢跑和奔跑时开启和关闭条件下的手臂角度数据。结果表明，与 DM-EH 关闭条件相比，DM-EH 的手臂摆动角度变化不大。为了确定人体手臂在日常运动中的摆动频率，对人体手臂在 2 至 10 km h ⁻¹ 速度下的摆动特性进行了表征。傅立叶变换分析显示，手臂摆动频率范围为 0.7 赫兹至 1.5 赫兹，如图 7c 所示。

To investigate the performance of the DM-EH at swing conditions, an experiment platform simulates the human motion as shown in Fig. 8a. A speed-controlled servo motor drove the crank linkage, and the corresponding output voltage at different frequencies and signals were recorded and saved by an oscilloscope (model: DSOX1204G, Keysight). It is worth noting that the speed of the motor and the length of the rocker tune the swing frequency and angle of the rod. Since the amplitude and frequency at 1.6 km h⁻¹ walking speed are approximately 20° and 0.7 Hz, the 4 km h⁻¹ fast walking corresponding to 25° and 0.9 Hz, and the 10 km h⁻¹ running speed matching to 30° and 1.5 Hz, the rotor frequency range was set 0.7–1.5 Hz to simulate the vibration of arms. Fig. 8b shows the performance of the DM-EH at the frequency range from 0.7 to 1.5 Hz for amplitudes of 20, 25, and 30°. It can be found that the increased amplitude or frequency promotes the output voltage due to the excitation acceleration highly depending on the frequency and amplitude. The RMS DC voltage is 2.13–6.25 V at the frequency from 0.7 to 1.5 Hz with 30° amplitudes. The maximum RMS DC power output achieves 244 mW, which is better than that of most counterparts as shown in Fig. 8c and d.
为了研究 DM-EH 在摆动条件下的性能，实验平台模拟了人体运动，如图 8a 所示。转速可控的伺服电机驱动曲柄连杆机构，相应的不同频率输出电压和信号被示波器（型号：DSOX1204G，Keysight）记录并保存。值得注意的是，电机的转速和摇杆的长度可调节连杆的摆动频率和角度。由于 1.6 km h ⁻¹ 步行速度下的振幅和频率约为 20° 和 0.7 Hz，4 km h ⁻¹ 快速步行对应 25° 和 0.9 Hz，10 km h ⁻¹ 跑步速度对应 30° 和 1.5 Hz，因此将转子频率范围设定为 0.7-1.5 Hz，以模拟手臂的振动。图 8b 显示了 DM-EH 在振幅为 20、25 和 30°、频率范围为 0.7 至 1.5 Hz 时的性能。可以发现，振幅或频率的增加会促进输出电压，因为激励加速度高度取决于频率和振幅。在频率为 0.7 至 1.5 Hz、振幅为 30° 时，直流电压有效值为 2.13 至 6.25 V。如图 8c 和 d 所示，最大有效值直流输出功率达到 244 mW，优于大多数同类产品。

4.3. Performance comparison
4.3.性能比较

A performance comparison between the proposed energy harvester and the recently reported low-frequency energy harvesters was conducted, validating the operational capabilities of the DM-EH, as depicted in Fig. 9a and b and summarized in Table 2. The average output power per unit volume/mass and the operational frequency serve as the key metrics for assessing the energy harvester's performance. Normalized power density, defined as the output power divided by the harvester's volume/mass and the square of the frequency, provides a reliable metric for evaluating energy harvesting performance.
如图 9a 和 b 所示，拟议的能量收集器与最近报道的低频能量收集器进行了性能比较，验证了 DM-EH 的运行能力，总结见表 2。单位体积/质量的平均输出功率和工作频率是评估能量收集器性能的关键指标。归一化功率密度的定义是输出功率除以能量收集器的体积/质量和频率的平方，它是评估能量收集性能的可靠指标。

Table 2. Comparison of DM-EH with recently reported low-frequency harvesters.
表 2.DM-EH 与最近报道的低频收割机的比较。

Mode 模式	Reference 参考资料	Operating conditions (excitation and resistance) 工作条件（激励和电阻）	Power (mW) 功率（毫瓦）	Power density (mW cm⁻³ Hz⁻²) 功率密度 (mW cm ⁻³ Hz ⁻² )	Power density (mW g⁻¹ Hz⁻²) 功率密度（毫瓦 g ⁻¹ Hz ⁻² )
Human 人类	2023 (7)	2.4Hz, 12 mm, 400Ω 2.4赫兹、12毫米、400Ω	4.3 (AC)	∼8.55e-3	∼9.33e-3
	2024 (26)	7 km h⁻¹, 288Ω	73.01(AC)	/	∼4.5e-2
	2023 (27)	7 km h⁻¹, 80Ω	2034 (DC) 2034 年（特区）	∼11.72	/
	2023 (38)	10 km h⁻¹, 100MΩ/20Ω	2000 (AC)	/	/
	2024 (45)	4Hz, 20°	930 (DC)	∼0.31	∼0.32
	2021 (48)	1Hz, 25°, 60Ω 1赫兹，25°，60Ω	1.46 (AC)	∼0.45	∼0.07
	2023 (49)	5Hz, 1g, 14MΩ/13kΩ/400Ω 5赫兹，1克，14MΩ/13kΩ/400Ω	124 (AC)	∼0.53	/
	This work 这项工作	1.5Hz, 30°, 160Ω 1.5赫兹，30°，160Ω	244 (DC)	4.78	1.38
Vehicle 车辆	2024 (4)	220 rpm, 50Ω 220 转/分，50Ω	210 (DC)	∼1.25e-2	∼5.66e-3
	2022 (9)	2050 rpm, 100 kΩ 2050 转/分，100 kΩ	7910 (AC)	∼9.57e-2	∼7.21119e-2
	2024 (14)	19.9Hz, 0.5g, 470 kΩ 19.9赫兹，0.5克，470千欧	78.87 (AC)	∼2.04e-2	/
	2022 (22)	180 rpm, 5 m s⁻², 24.6Ω	13.13 (AC)	∼0.13	∼0.11
	2024 (23)	14.1Hz, 0.6g, e3.6Ω 14.1赫兹，0.6克，e3.6Ω	307.8 (AC)	∼4.73e-3	∼3.3e-2
	2023 (41)	80 rpm, 798Ω 80 转/分，798Ω	965 (AC)	∼0.43	/
	2024 (46)	1260 rpm, 164Ω 1260 转/分，164Ω	712 (DC)	∼7.65e-2	∼1.87e-2
	This work 这项工作	540 rpm, 160Ω 540 转/分，160Ω	3794 (DC)	0.85	0.25

The DM-EH demonstrates superior performance, particularly in terms of the power density under vehicle operations. The incorporation of the pendulum mechanism and frequency up-conversion technology not only enhances energy harvesting efficiency but also broadens the operational bandwidth at low frequencies. However, due to its relatively small volume (Fig. 9c and d), its normalized power density does not achieve the optimal value compared to that reported in Reference 27 for low-frequency human motions. Additionally, to enhance wearability, the volume and mass of DM-EH should be further reduced. Furthermore, the output stability and mechanical durability, which are essential prerequisites for commercial viability, were rigorously assessed by recording the output voltage before and after 30 days at 120 rpm, as presented in Fig. 9e. The prototype's output stability, mechanical robustness, and system safety align seamlessly with the design requirements for wireless monitoring.
DM-EH 性能卓越，尤其是在车辆运行时的功率密度方面。钟摆机构和频率上变频技术的采用不仅提高了能量收集效率，还拓宽了低频工作带宽。不过，由于其体积相对较小（图 9c 和 d），其归一化功率密度与参考文献 27 中报告的低频人体运动功率密度相比，并没有达到最佳值。此外，为了提高可穿戴性，应进一步减小 DM-EH 的体积和质量。此外，输出稳定性和机械耐久性是实现商业可行性的重要先决条件，我们通过记录 120 转/分 30 天前后的输出电压进行了严格评估，如图 9e 所示。原型的输出稳定性、机械耐用性和系统安全性完全符合无线监控的设计要求。

4.4. Practical applications
4.4.实际应用

Considering that the daily appliances and commercial wireless sensors require DC power, a three-phase rectifier was paralleled with a 560 μF capacitor (model: 1210) and zener diodes (model: MCC349B) to ensure that the 220 μF 10V capacitor stores a stable DC voltage, as shown in Fig. 11. Fig. 10a illustrates the charging curves of the DM-EH for commercial capacitors with capacitances of 100, 220, and 470 μF, as well as supercapacitors with 0.22 and 1.5 F at 120 rpm. Notably, the DM-EMH efficiently charges capacitors exceeding 5 V within 5 s. Remarkably, the charging speeds are nearly identical for capacitors with capacitances of 100, 220, and 470 μF, highlighting its outstanding charging capability. Furthermore, the DM-EH was capable of charging supercapacitors in a shorter time. As displayed in Fig. 10b and c and Video S1, the harvester effectively powered an LED light while simultaneously providing power to a cellphone (model: Huawei P10, Huawei Technologies Co., Ltd) and a smartwatch (Honor Band 4, Hornor) at 120 rpm.
考虑到日常电器和商用无线传感器需要直流电源，如图 11 所示，三相整流器与 560 μF 电容器（型号：1210）和齐纳二极管（型号：MCC349B）并联，以确保 220 μF 10V 电容器存储稳定的直流电压。图 10a 展示了 DM-EH 在 120 rpm 转速下对电容值为 100、220 和 470 μF 的商用电容器以及电容值为 0.22 和 1.5 F 的超级电容器的充电曲线。值得注意的是，DM-EMH 能在 5 秒内为超过 5 V 的电容器有效充电。值得注意的是，电容为 100、220 和 470 μF 的电容器的充电速度几乎相同，这突出表明了其出色的充电能力。此外，DM-EH 还能在更短的时间内为超级电容器充电。如图 10b 和 c 以及视频 S1 所示，该收割机在 120 rpm 的转速下有效地为 LED 灯供电，同时还为手机（型号：华为 P10，华为技术有限公司）和智能手表（Honor Band 4，Hornor）供电。

The DM-EH, when integrated with a wireless sensor, could effectively provide feedback on the vehicle's operating conditions. Acknowledging the significance of temperature and vibration information within vehicles, a commercial wireless temperature sensor and an acceleration sensor were integrated with the DM-EH. Fig. 11 and Video S2 demonstrated that the prototype successfully drove both the acceleration (model: ICM-42688-P, TDK) and temperature (model: ET80B, Chip source) sensors, enabling them to transmit signals while operating at 150 rpm.
DM-EH 与无线传感器集成后，可以有效地反馈车辆的运行状况。考虑到车内温度和振动信息的重要性，我们将商用无线温度传感器和加速度传感器与 DM-EH 集成在一起。图 11 和视频 S2 显示，原型机成功驱动了加速度传感器（型号：ICM-42688-P，TDK）和温度传感器（型号：ET80B，Chip source），使它们能够在 150 rpm 的转速下传输信号。

The viability of the DM-EH as a practical sustainable energy for converting mechanical energy for human motions has been evaluated for its capacity to maintain wearable devices and commercial wireless sensors described in Fig. 12. The prototype drove acceleration wireless sensor (model: ICM-42688-P, TDK) to offer motion signal under 7 km h⁻¹ corresponding vibration frequency of arms 1.2 Hz (Video S3).
DM-EH 作为一种用于转换人体运动机械能的实用可持续能源，其维护可穿戴设备和图 12 所述商用无线传感器的能力已得到评估。原型驱动加速度无线传感器（型号：ICM-42688-P，TDK）在 7 km h ⁻¹ 下提供运动信号，相应的振动频率为 1.2 Hz（视频 S3）。

It is worth noting that the DM-EH could charge electronic devices such as the smartwatch (model: Honor Band 4, Honor) and the cellphone (model: Huawei P10, Huawei Technologies Co., Ltd) for positioning and health monitoring, and charge the mobile power bank (model: L2, 5200mAh, Solove) help meet higher power needs for wilderness operations (Video S4). Smartwatch and cellphone have increased their battery power from 0 % to 60 % and 30 % within an hour under a speed of 4 km h⁻¹ and 8 km h⁻¹, respectively. Besides, the prototype could power LED lights to improve visibility and increase exercise safety during the night. The vertical vibrations contribute to increasing the swing amplitude and enhancing the relative motion between the coils and magnets of the generation unit, thereby improving the output performance of the DM-EH under vibration conditions.
值得注意的是，DM-EH 可为智能手表（型号：Honor Band 4，Honor）和手机（型号：华为 P10，华为技术有限公司）等电子设备充电，用于定位和健康监测，还可为移动电源（型号：L2，5200mAh，Solove）充电，帮助满足野外作业的更高电量需求（视频 S4）。智能手表和手机在 4 公里/小时 ⁻¹ 和 8 公里/小时 ⁻¹ 的速度下，电池电量在一小时内分别从 0% 增加到 60% 和 30%。此外，原型车还可以为 LED 灯供电，以提高能见度和夜间运动的安全性。垂直振动有助于增加摆动幅度，加强发电装置的线圈和磁铁之间的相对运动，从而提高 DM-EH 在振动条件下的输出性能。

The DM-EH effectively captures the rotational motion of the wheelset with a 1/2-scale freight wagon. A control box adjusts the speed of triple-phase asynchronous motors, which drive the roller rig via a gearbox. The roller rigs stimulate the rotation of wheelsets in a 1/2-scale freight wagon. The rotational speed of the 1/2-scale wheelset was controlled at approximately 110 rpm and 80 rpm during the railway simulation tests for battery-free temperature and acceleration sensors, respectively. The stable DC voltage of the DM-EH reached 3.13V and 4.55 V at 110 rpm and 80 rpm, respectively. Since there are no cables in the freight wagons, the DM-EH holds significant value in harnessing rotational energy for self-powered monitoring of wheelset bearing temperature (Video S5) and acceleration (Video S6) in railway environments as presented in Fig. 13. The whole volume and weight of the prototype are 20.79 cm³ and 78.4 g, respectively. When considering the volume and weight of freight vehicles, the impact of the prototype on the vehicles is negligible. In addition, considering that the counterweight may flip π, leading to synchronous rotation between the coils and magnets and a sharp drop in output voltage for emergency braking or abnormal vibrations, the DM-EH served as an early warning sensor to assess motion state and improve the reliability of vehicles.
DM-EH 可有效捕捉 1/2 比例货运车轮组的旋转运动。控制箱可调节三相异步电动机的速度，而三相异步电动机则通过变速箱驱动滚轮装置。滚轮装置可刺激 1/2 比例货运车的轮组旋转。在无电池温度传感器和加速度传感器的铁路模拟测试中，1/2 比例车轮组的转速分别控制在大约 110 rpm 和 80 rpm。在 110 rpm 和 80 rpm 时，DM-EH 的稳定直流电压分别达到 3.13 V 和 4.55 V。由于货车上没有电缆，DM-EH 在铁路环境中利用旋转能量自供电监测轮对轴承温度（视频 S5）和加速度（视频 S6）方面具有重要价值，如图 13 所示。原型机的整体体积和重量分别为 20.79 厘米 ³ 和 78.4 克。考虑到货运车辆的体积和重量，原型机对车辆的影响可以忽略不计。此外，考虑到配重可能翻转 π，导致线圈和磁铁同步旋转，以及紧急制动或异常振动时输出电压急剧下降，DM-EH 可作为评估运动状态的预警传感器，提高车辆的可靠性。

5. Conclusion 5.结论

A high-performance dual-mode energy harvester (DM-EH) is proposed to scavenge low-frequency vibrations generated by human motions and vehicle operations. The generation unit, serving as a pendulum, efficiently converts irregular vibrations into rotation energy while ensuring effective operation for anchorless installation in rotational environments. The transmission unit plays a pivotal role in converting low-frequency vibrations into high-frequency ones, enabling it to accommodate low-frequency environments and satisfy the high-frequency input requirements of the generation unit. Dynamic experimental results substantiate the DM-EH's performance when subjected to low-frequency vibration sources.
本文提出了一种高性能双模式能量收集器（DM-EH），用于收集人体运动和车辆运行产生的低频振动。作为摆锤的发电单元可有效地将不规则振动转换为旋转能量，同时确保在旋转环境中进行无锚安装时的有效运行。传动装置在将低频振动转换为高频振动方面起着关键作用，使其既能适应低频环境，又能满足发电装置的高频输入要求。动态实验结果证明了 DM-EH 在承受低频振动源时的性能。

The DM-EH demonstrated its operational capability over a broad range, encompassing vehicle rotations from 60 to 540 rpm and human motions ranging from 0.7 to 1.5 Hz with 30° amplitudes. It achieved a peak direct current RMS power output of 3.79 W and 244 mW with an optimal resistance of 160 Ω at 540 rpm for vehicle operations and 1.5 Hz with 30° amplitudes for human motions, resulting in power densities of 182.58 and 11.74 mW cm⁻³, respectively. These performance levels surpass those of traditional low-frequency harvesters. Regarding applications, the prototype successfully powered daily electrical appliances (such as LED, smartwatches, cellphones, and mobile power banks), rapidly recharged capacitance and supercapacitor, and drove temperature and acceleration sensors during vehicle operations and human motions. These results represent a substantial step toward the potential deployment of self-powered wireless condition monitoring systems for both human motions and vehicle operations.
DM-EH 演示了其在广泛范围内的运行能力，包括 60 至 540 rpm 的车辆旋转和 0.7 至 1.5 Hz、30° 振幅的人体运动。在车辆运行 540 rpm 和人体运动 1.5 Hz、振幅 30° 时，它的直流 RMS 功率输出峰值分别为 3.79 W 和 244 mW，最佳电阻为 160 Ω，功率密度分别为 182.58 和 11.74 mW cm ⁻³ 。这些性能水平超过了传统的低频采集器。在应用方面，原型成功地为日常电器（如 LED、智能手表、手机和移动电源）供电，为电容和超级电容器快速充电，并在车辆运行和人体运动期间驱动温度和加速度传感器。这些成果标志着向潜在部署用于人类运动和车辆运行的自供电无线状态监测系统迈出了实质性的一步。

CRediT authorship contribution statement
CRediT 作者贡献声明

Zhixia Wang: Writing – original draft, Visualization, Validation, Methodology, Funding acquisition, Data curation, Conceptualization. Siwei Kang: Validation, Investigation. Hongzhi Du: Validation, Conceptualization. Pengju Feng: Validation, Data curation. Wei Wang: Writing – review & editing, Supervision, Funding acquisition.
王志霞写作-原稿、可视化、验证、方法学、资金获取、数据整理、概念化。Siwei Kang：验证、调查。杜宏志验证、概念化。冯鹏举：验证、数据整理。王伟写作--审阅和编辑、监督、获取资金。

Declaration of competing interest
利益冲突声明

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者声明，他们没有任何可能会影响本文所报告工作的已知经济利益或个人关系。

Acknowledgments 致谢

The work was supported by the National Natural Science Foundation of China (Grant Nos. 12302022, 12172248, 12132010, 12021002), the Tianjin Research Program of Application Foundation and Advanced Technology (Grant No. 22JCQNJC00780), and Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province (Grant No. QCCK2024-0019).
这项工作得到了国家自然科学基金（批准号：12302022、12172248、12132010、12021002）、天津市应用基础与先进技术研究计划（批准号：22JCQNJC00780）和四川省车辆测控与安全重点实验室（批准号：QCCK2024-0019）的支持。

Appendix A. Supplementary data
附录 A.补充数据

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References

[1]
X. Zhao, H. Askari, J. Chen
Nanogenerators for smart cities in the era of 5G and Internet of Things
Joule, 5 (2021), pp. 1391-1431
View PDF View article View in Scopus Google Scholar
[2]
D. Hao, Y. Gong, J. Wu, Q. Shen, Z. Zhang, J. Zhi, et al.
A self-sensing and self-powered wearable system based on multi-source human motion energy harvesting
Small (2024), Article 2311036
View in Scopus Google Scholar
[3]
L. Zhao, H. Zou, K. Wei, S. Zhou, G. Meng, W. Zhang
Mechanical intelligent energy harvesting: from methodology to applications
Adv Energy Mater, 13 (2023)
Google Scholar
[4]
Y. Zhang, X. Wu, Y. Lei, J. Cao, W.-H. Liao
Self-powered wireless condition monitoring for rotating machinery
IEEE Internet Things, 11 (2) (2024), pp. 3095-3107
Crossref View in Scopus Google Scholar
[5]
W. Xu, H. Zheng, Y. Liu, X. Zhou, C. Zhang, L. Song, et al.
A droplet-based electricity generator with high instantaneous power density
Nature, 578 (7795) (2020), pp. 392-396
Crossref View in Scopus Google Scholar
[6]
H. Fu, J. Jiang, S. Hu, J. Rao, S. Theodossiades
Multi-stable ultra-low frequency energy harvester using a nonlinear pendulum and piezoelectric transduction for self-powered sensing
Mech Syst Signal Pr, 189 (2023), Article 110034
View PDF View article View in Scopus Google Scholar
[7]
R. Li, K. Fan, X. Ma, T. Wen, Q. Liu, X. Gao, et al.
A rotational energy harvester with a semi-flexible one-way clutch for capturing low-frequency vibration energy
Energy, 281 (2023), Article 128266
View PDF View article View in Scopus Google Scholar
[8]
H. Li, T. Zheng, W. Qin, R. Tian, H. Ding, L. Chen
Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations
Appl Math Mech-Engl, 45 (3) (2024), pp. 461-478
Crossref View in Scopus Google Scholar
[9]
M. Yao, X. Wang, Q. Wu, Y. Niu, S. Wang
Dynamic analysis and design of power management circuit of the nonlinear electromagnetic energy harvesting device for the automobile suspension
Mech Syst Signal Pr, 170 (2022), Article 108831
View PDF View article View in Scopus Google Scholar
[10]
M.R. Rashki, K. Hejazi, V. Tamimi, M. Zeinoddini, P. Bagherpour, M.M.A. Harandi
Electromagnetic energy harvesting from 2DOF-VIV of circular oscillators: impacts of soft marine fouling
Energy, 282 (2023), Article 128964
View PDF View article View in Scopus Google Scholar
[11]
W. Wang, B. Li, J. Wang, B. Fang, Z. Li, S. Liu, et al.
Harnessing energy from hand-shaking vibration for electronics through a magnetic rolling pendulum bistable energy harvester
Energy Convers Manag, 310 (2024), Article 118466
View PDF View article View in Scopus Google Scholar
[12]
D.G. Lee, J. Shin, H.S. Kim, S. Hur, S. Sun, J.S. Jang, et al.
Autonomous resonance-tuning mechanism for environmental adaptive energy harvesting
Adv Sci, 10 (2023), Article 2205179
View in Scopus Google Scholar
[13]
W. Fan, C. Zhang, Y. Liu, S. Wang, K. Dong, Y. Li, et al.
An ultra-thin piezoelectric nanogenerator with breathable, superhydrophobic, and antibacterial properties for human motion monitoring
Nano Res, 16 (9) (2023), pp. 11612-11620
Crossref View in Scopus Google Scholar
[14]
M. Gong, Y. Gao, W. Wang, H. Long, X. Mao, Y. Long, et al.
Asymmetry stagger array structure ultra-wideband vibration harvester integrating magnetically coupled nonlinear effects
Appl Energy, 356 (2024), Article 122366
Google Scholar
[15]
L. Zhou, D. Liu, J. Wang, Z. Wang
Triboelectric nanogenerators: fundamental physics and potential applications
Friction, 8 (2020), pp. 481-506
Crossref View in Scopus Google Scholar
[16]
G. Pace, A.E.D. Castillo, A. Lamperti, S. Lauciello, F. Bonaccorso
2D materials-based electrochemical triboelectric nanogenerators
Adv Mater, 35 (23) (2023), Article 202211037
Google Scholar
[17]
P. Lu, X. Liao, X. Guo, C. Cai, Y. Liu, M. Chi, et al.
Gel-based triboelectric nanogenerators for flexible sensing: principles, properties, and applications
Nano-Micro Lett, 16 (1) (2024), p. 206
View in Scopus Google Scholar
[18]
C. Wang, C. Wang, Y. Ji, G. Li, G. Wen, Y. Ni, et al.
Boosting output performance of tri-hybrid vibration-based generator via quin-stable nonlinearity and speed amplification
Mech Syst Signal Pr, 204 (2024), Article 110809
Google Scholar
[19]
X. Su, J. Xu, X. Chen, S. Sun, D.-G. Lee, B. Zhu, et al.
A piezoelectric-electromagnetic hybrid energy harvester with frequency-up conversion mechanism towards low-frequency-low-intensity applications
Nano Energy, 124 (2024), Article 109447
View PDF View article View in Scopus Google Scholar
[20]
Z. Yang, S. Zhou, J. Zu, D.J. Inman
High-performance piezoelectric energy harvesters and their applications
Joule, 2 (2018), pp. 642-697
View PDF View article View in Scopus Google Scholar
[21]
X. Rui, Z. Zeng, Y. Li, Y. Zhang, Z. Yang, X. Huang, et al.
Modeling and analysis of a rotational piezoelectric energy harvester with limiters
J Mech Sci Technol, 33 (2019), pp. 5169-5176
Crossref View in Scopus Google Scholar
[22]
G. Miao, S. Fang, S. Wang, S. Zhou
A low-frequency rotational electromagnetic energy harvester using a magnetic plucking mechanism
Appl Energy, 305 (2022), Article 117838
View PDF View article View in Scopus Google Scholar
[23]
L. Zhao, G. Hu, S. Zhou, Y. Peng, S. Xie, Z. Li
Magnetic coupling and amplitude truncation based bistable energy harvester
Int J Mech Sci, 273 (2024), Article 109228
View PDF View article View in Scopus Google Scholar
[24]
M.M. Ahmad, N.M. Khan, F.U. Khan
Review of frequency up-conversion vibration energy harvesters using impact and plucking mechanism
Int J Energ Res, 45 (2021), pp. 15609-15645
Crossref View in Scopus Google Scholar
[25]
W. Salman, X. Zhang, H. Li, X. Wu, N. Li, A. Azam, et al.
A novel energy regenerative shock absorber for in-wheel motors in electric vehicles
Mech Syst Signal Pr, 181 (2022), Article 109488
View PDF View article View in Scopus Google Scholar
[26]
D. Hao, Y. Li, J. Wu, L. Zeng, Z. Zhang, H. Chen, et al.
A self-powered and self-sensing knee negative energy harvester
iScience, 27 (2024), Article 109105
View PDF View article View in Scopus Google Scholar
[27]
J. Hou, S. Qian, X. Hou, J. Zhang, H. Wu, Y. Guo, et al.
A high-performance mini-generator with average power of 2 W for human motion energy harvesting and wearable electronics applications
Energy Convers Manag, 277 (2023), Article 116612
View PDF View article View in Scopus Google Scholar
[28]
H. Zou, L. Zhao, Q. Gao, L. Zuo, F. Liu, T. Tan, et al.
Mechanical modulations for enhancing energy harvesting: principles, methods and applications
Appl Energy, 255 (2019), Article 113871
View PDF View article View in Scopus Google Scholar
[29]
X. Xiahou, S. Wu, Li H. GuoX, C. Chen, M. Xu
Strategies for enhancing low-frequency performances of triboelectric, electrochemical, piezoelectric, and dielectric elastomer energy harvesting: recent progress and challenges
Sci Bull, 68 (15) (2023), pp. 1687-1714
View PDF View article View in Scopus Google Scholar
[30]
Y. Gu, W. Liu, C. Zhao, P. Wang
A goblet-like non-linear electromagnetic generator for planar multi-directional vibration energy harvesting
Appl Energy, 266 (2020), Article 114846
View PDF View article View in Scopus Google Scholar
[31]
C. Wang, S. Lai, J. Wang, J. Feng, Y. Ni
An ultra-low-frequency, broadband and multi-stable tri-hybrid energy harvester for enabling the next-generation sustainable power
Appl Energy, 291 (2021), Article 116825
View PDF View article View in Scopus Google Scholar
[32]
M.A. Halim, J.Y. Park
Modeling and experiment of a handy motion driven, frequency up-converting electromagnetic energy harvester using transverse impact by spherical ball
Sensor Actuat A-Phys, 229 (2015), pp. 50-58
View PDF View article View in Scopus Google Scholar
[33]
Z. Wang, W. Wang, L. Tang, R. Tian, C. Wang, Q. Zhang, et al.
A piezoelectric energy harvester for freight train condition monitoring system with the hybrid nonlinear mechanism
Mech Syst Signal Pr, 180 (2022), Article 109403
View PDF View article View in Scopus Google Scholar
[34]
Z. Wang, Y. Chen, R. Jiang, Y. Du, S. Shi, S. Zhang, et al.
Broadband omnidirectional piezoelectric-electromagnetic hybrid energy harvester for self-charged environmental and biometric sensing from human motion
Nano Energy, 113 (2023), Article 108526
View PDF View article View in Scopus Google Scholar
[35]
S. Fang, S. Wang, S. Zhou, Z. Yang, W. Liao
Exploiting the advantages of the centrifugal softening effect in rotational impact energy harvesting
Appl Phys Lett, 116 (2020), Article 63903
Google Scholar
[36]
Y. Wang, Z. Yang, P. Li, D. Cao, W. Huang, D.J. Inman
Energy harvesting for jet engine monitoring
Nano Energy, 75 (2020), Article 104853
View PDF View article View in Scopus Google Scholar
[37]
L. Zhao, H. Zou, Y. Zhao, Z. Wu, F. Liu, K. Wei, et al.
Hybrid energy harvesting for self-powered rotor condition monitoring using maximal utilization strategy in structural space and operation process
Appl Energy, 314 (2022), Article 118983
View PDF View article View in Scopus Google Scholar
[38]
H. Zou, M. Li, L. Zhao, X. Liao, Q. Gao, G. Yan, et al.
Cooperative compliant traction mechanism for human-friendly biomechanical energy harvesting
Energy Convers Manag, 258 (2022), Article 115523
View PDF View article View in Scopus Google Scholar
[39]
C. Fan, H. Li, Z. Zhang, Y. Pan, X. Wu, A. Ahmed
An H-shaped coupler energy harvester for application in heavy railways
Energy, 270 (2023), Article 126854
View PDF View article View in Scopus Google Scholar
[40]
X. Wu, T. Zhang, J. Liu, T. Zhang, W. Kong, Y. Pan, et al.
A vibration energy harvesting system for self-powered applications in heavy railways
Sustain Energy Techn, 53 (2022), Article 102373
View PDF View article View in Scopus Google Scholar
[41]
S. Huo, P. Wang, H. Long, Z. Ren, Q. Yi, J. Dai, et al.
Dual-mode electromagnetic energy harvester by Halbach arrays
Energy Convers Manag, 286 (2023), Article 117038
View PDF View article View in Scopus Google Scholar
[42]
H. Wang, W. Wu, L. Cui, Y. Wu, L. Zhu, E. Koutroulis, et al.
A new wave energy converter for marine data buoy
IEEE T Ind Electron, 70 (2023), pp. 2076-2084
Crossref View in Scopus Google Scholar
[43]
T. Jintanawan, G. Phanomchoeng, S. Suwankawin, W. Thamwiphat, V. Khunkiat, W. Watanasiri
Design of a more efficient rotating-EM energy floor with lead-screw and clutch mechanism
Energies, 15 (2022), p. 6539
Crossref View in Scopus Google Scholar
[44]
T. Zhang, H. Cao, Z. Zhang, W. Kong, L. Kong, J. Liu, et al.
A variable damping vibration energy harvester based on half-wave flywheeling effect for freight railways
Mech Syst Signal Pr, 200 (2023), Article 110611
View PDF View article View in Scopus Google Scholar
[45]
L. Ren, Y. Zhou, X. Zhang, H. Zhang, Y. Tan
Active self-powered human motion assist system
Smart Mater Struct, 33 (2024), Article 055003
Crossref View in Scopus Google Scholar
[46]
Z. Wang, H. Du, W. Wang, Q. Zhang, F. Gu, A. Ball, et al.
A high performance contra-rotating energy harvester and its wireless sensing application toward green and maintain free vehicle monitoring
Appl Energy, 356 (2024), Article 122370
View PDF View article View in Scopus Google Scholar
[47]
D. Hao, L. Kong, Z. Zhang, W. Kong, A.M. Tairab, X. Luo, et al.
An electromagnetic energy harvester with a half-wave rectification mechanism for military personnel
Sustain Energy Techn, 57 (2023), Article 103184
View PDF View article View in Scopus Google Scholar
[48]
M. Cai, W. Liao
High-power density inertial energy harvester without additional proof mass for wearables
IEEE Internet Things, 8 (2021), pp. 297-308
Crossref View in Scopus Google Scholar
[49]
C. Wang, Y. Ji, S. Lai, Y. Liu, Y. Hao, G. Li, et al.
A speed-amplified tri-stable piezoelectric-electromagnetic-triboelectric hybrid energy harvester for low-frequency applications
Nano Energy, 114 (2023), Article 108630
View PDF View article View in Scopus Google Scholar
[50]
Z. Liu, X. Wang, E. Al Shami, N.J. Baker, X. Ji
A study of a speed amplified linear generator for low-frequency wave energy conversion
Mech Syst Signal Pr, 149 (2021), Article 107226
View PDF View article View in Scopus Google Scholar
[51]
China Railway Transport Department
Introduction to railway
China Railway Publishing House (2022)
Google Scholar
[52]
M. Gao, J. Cong, J. Xiao, Q. He, S. Li, Y. Wang, et al.
Dynamic modeling and experimental investigation of self-powered sensor nodes for freight rail transport
Appl Energy, 257 (2020), Article 113969
View PDF View article View in Scopus Google Scholar

Cited by (0)

View Abstract

[1] [1]
X. Zhao, H. Askari, J. Chen
Nanogenerators for smart cities in the era of 5G and Internet of Things
Joule, 5 (2021), pp. 1391-1431
View PDF View article View in Scopus Google Scholar

[2] [2]
D. Hao, Y. Gong, J. Wu, Q. Shen, Z. Zhang, J. Zhi, et al.
A self-sensing and self-powered wearable system based on multi-source human motion energy harvesting
Small (2024), Article 2311036
View in Scopus Google Scholar

[3] [3]
L. Zhao, H. Zou, K. Wei, S. Zhou, G. Meng, W. Zhang
Mechanical intelligent energy harvesting: from methodology to applications
Adv Energy Mater, 13 (2023)
Google Scholar

[4] [4]
Y. Zhang, X. Wu, Y. Lei, J. Cao, W.-H. Liao
Self-powered wireless condition monitoring for rotating machinery
IEEE Internet Things, 11 (2) (2024), pp. 3095-3107
Crossref View in Scopus Google Scholar

[5] [5]
W. Xu, H. Zheng, Y. Liu, X. Zhou, C. Zhang, L. Song, et al.
A droplet-based electricity generator with high instantaneous power density
Nature, 578 (7795) (2020), pp. 392-396
Crossref View in Scopus Google Scholar

[6] [6]
H. Fu, J. Jiang, S. Hu, J. Rao, S. Theodossiades
Multi-stable ultra-low frequency energy harvester using a nonlinear pendulum and piezoelectric transduction for self-powered sensing
Mech Syst Signal Pr, 189 (2023), Article 110034
View PDF View article View in Scopus Google Scholar

[7] [7]
R. Li, K. Fan, X. Ma, T. Wen, Q. Liu, X. Gao, et al.
A rotational energy harvester with a semi-flexible one-way clutch for capturing low-frequency vibration energy
Energy, 281 (2023), Article 128266
View PDF View article View in Scopus Google Scholar

[8] [8]
H. Li, T. Zheng, W. Qin, R. Tian, H. Ding, L. Chen
Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations
Appl Math Mech-Engl, 45 (3) (2024), pp. 461-478
Crossref View in Scopus Google Scholar

[9] [9]
M. Yao, X. Wang, Q. Wu, Y. Niu, S. Wang
Dynamic analysis and design of power management circuit of the nonlinear electromagnetic energy harvesting device for the automobile suspension
Mech Syst Signal Pr, 170 (2022), Article 108831
View PDF View article View in Scopus Google Scholar

[10] [10]
M.R. Rashki, K. Hejazi, V. Tamimi, M. Zeinoddini, P. Bagherpour, M.M.A. Harandi
Electromagnetic energy harvesting from 2DOF-VIV of circular oscillators: impacts of soft marine fouling
Energy, 282 (2023), Article 128964
View PDF View article View in Scopus Google Scholar

[11] [11]
W. Wang, B. Li, J. Wang, B. Fang, Z. Li, S. Liu, et al.
Harnessing energy from hand-shaking vibration for electronics through a magnetic rolling pendulum bistable energy harvester
Energy Convers Manag, 310 (2024), Article 118466
View PDF View article View in Scopus Google Scholar

[12] [12]
D.G. Lee, J. Shin, H.S. Kim, S. Hur, S. Sun, J.S. Jang, et al.
Autonomous resonance-tuning mechanism for environmental adaptive energy harvesting
Adv Sci, 10 (2023), Article 2205179
View in Scopus Google Scholar

[13] [13]
W. Fan, C. Zhang, Y. Liu, S. Wang, K. Dong, Y. Li, et al.
An ultra-thin piezoelectric nanogenerator with breathable, superhydrophobic, and antibacterial properties for human motion monitoring
Nano Res, 16 (9) (2023), pp. 11612-11620
Crossref View in Scopus Google Scholar

[14] [14]
M. Gong, Y. Gao, W. Wang, H. Long, X. Mao, Y. Long, et al.
Asymmetry stagger array structure ultra-wideband vibration harvester integrating magnetically coupled nonlinear effects
Appl Energy, 356 (2024), Article 122366
Google Scholar

[15] [15]
L. Zhou, D. Liu, J. Wang, Z. Wang
Triboelectric nanogenerators: fundamental physics and potential applications
Friction, 8 (2020), pp. 481-506
Crossref View in Scopus Google Scholar

[16] [16]
G. Pace, A.E.D. Castillo, A. Lamperti, S. Lauciello, F. Bonaccorso
2D materials-based electrochemical triboelectric nanogenerators
Adv Mater, 35 (23) (2023), Article 202211037
Google Scholar

[17] [17]
P. Lu, X. Liao, X. Guo, C. Cai, Y. Liu, M. Chi, et al.
Gel-based triboelectric nanogenerators for flexible sensing: principles, properties, and applications
Nano-Micro Lett, 16 (1) (2024), p. 206
View in Scopus Google Scholar

[18] [18]
C. Wang, C. Wang, Y. Ji, G. Li, G. Wen, Y. Ni, et al.
Boosting output performance of tri-hybrid vibration-based generator via quin-stable nonlinearity and speed amplification
Mech Syst Signal Pr, 204 (2024), Article 110809
Google Scholar

[19] [19]
X. Su, J. Xu, X. Chen, S. Sun, D.-G. Lee, B. Zhu, et al.
A piezoelectric-electromagnetic hybrid energy harvester with frequency-up conversion mechanism towards low-frequency-low-intensity applications
Nano Energy, 124 (2024), Article 109447
View PDF View article View in Scopus Google Scholar

[20] [20]
Z. Yang, S. Zhou, J. Zu, D.J. Inman
High-performance piezoelectric energy harvesters and their applications
Joule, 2 (2018), pp. 642-697
View PDF View article View in Scopus Google Scholar

[21] [21]
X. Rui, Z. Zeng, Y. Li, Y. Zhang, Z. Yang, X. Huang, et al.
Modeling and analysis of a rotational piezoelectric energy harvester with limiters
J Mech Sci Technol, 33 (2019), pp. 5169-5176
Crossref View in Scopus Google Scholar

[22] [22]
G. Miao, S. Fang, S. Wang, S. Zhou
A low-frequency rotational electromagnetic energy harvester using a magnetic plucking mechanism
Appl Energy, 305 (2022), Article 117838
View PDF View article View in Scopus Google Scholar

[23] [23]
L. Zhao, G. Hu, S. Zhou, Y. Peng, S. Xie, Z. Li
Magnetic coupling and amplitude truncation based bistable energy harvester
Int J Mech Sci, 273 (2024), Article 109228
View PDF View article View in Scopus Google Scholar

[24] [24]
M.M. Ahmad, N.M. Khan, F.U. Khan
Review of frequency up-conversion vibration energy harvesters using impact and plucking mechanism
Int J Energ Res, 45 (2021), pp. 15609-15645
Crossref View in Scopus Google Scholar

[25] [25]
W. Salman, X. Zhang, H. Li, X. Wu, N. Li, A. Azam, et al.
A novel energy regenerative shock absorber for in-wheel motors in electric vehicles
Mech Syst Signal Pr, 181 (2022), Article 109488
View PDF View article View in Scopus Google Scholar

[26] [26]
D. Hao, Y. Li, J. Wu, L. Zeng, Z. Zhang, H. Chen, et al.
A self-powered and self-sensing knee negative energy harvester
iScience, 27 (2024), Article 109105
View PDF View article View in Scopus Google Scholar

[27] [27]
J. Hou, S. Qian, X. Hou, J. Zhang, H. Wu, Y. Guo, et al.
A high-performance mini-generator with average power of 2 W for human motion energy harvesting and wearable electronics applications
Energy Convers Manag, 277 (2023), Article 116612
View PDF View article View in Scopus Google Scholar

[28] [28]
H. Zou, L. Zhao, Q. Gao, L. Zuo, F. Liu, T. Tan, et al.
Mechanical modulations for enhancing energy harvesting: principles, methods and applications
Appl Energy, 255 (2019), Article 113871
View PDF View article View in Scopus Google Scholar

[29] [29]
X. Xiahou, S. Wu, Li H. GuoX, C. Chen, M. Xu
Strategies for enhancing low-frequency performances of triboelectric, electrochemical, piezoelectric, and dielectric elastomer energy harvesting: recent progress and challenges
Sci Bull, 68 (15) (2023), pp. 1687-1714
View PDF View article View in Scopus Google Scholar

[30] [30]
Y. Gu, W. Liu, C. Zhao, P. Wang
A goblet-like non-linear electromagnetic generator for planar multi-directional vibration energy harvesting
Appl Energy, 266 (2020), Article 114846
View PDF View article View in Scopus Google Scholar

[31] [31]
C. Wang, S. Lai, J. Wang, J. Feng, Y. Ni
An ultra-low-frequency, broadband and multi-stable tri-hybrid energy harvester for enabling the next-generation sustainable power
Appl Energy, 291 (2021), Article 116825
View PDF View article View in Scopus Google Scholar

[32] [32]
M.A. Halim, J.Y. Park
Modeling and experiment of a handy motion driven, frequency up-converting electromagnetic energy harvester using transverse impact by spherical ball
Sensor Actuat A-Phys, 229 (2015), pp. 50-58
View PDF View article View in Scopus Google Scholar

[33] [33]
Z. Wang, W. Wang, L. Tang, R. Tian, C. Wang, Q. Zhang, et al.
A piezoelectric energy harvester for freight train condition monitoring system with the hybrid nonlinear mechanism
Mech Syst Signal Pr, 180 (2022), Article 109403
View PDF View article View in Scopus Google Scholar

[34] [34]
Z. Wang, Y. Chen, R. Jiang, Y. Du, S. Shi, S. Zhang, et al.
Broadband omnidirectional piezoelectric-electromagnetic hybrid energy harvester for self-charged environmental and biometric sensing from human motion
Nano Energy, 113 (2023), Article 108526
View PDF View article View in Scopus Google Scholar

[35] [35]
S. Fang, S. Wang, S. Zhou, Z. Yang, W. Liao
Exploiting the advantages of the centrifugal softening effect in rotational impact energy harvesting
Appl Phys Lett, 116 (2020), Article 63903
Google Scholar

[36] [36]
Y. Wang, Z. Yang, P. Li, D. Cao, W. Huang, D.J. Inman
Energy harvesting for jet engine monitoring
Nano Energy, 75 (2020), Article 104853
View PDF View article View in Scopus Google Scholar

[37] [37]
L. Zhao, H. Zou, Y. Zhao, Z. Wu, F. Liu, K. Wei, et al.
Hybrid energy harvesting for self-powered rotor condition monitoring using maximal utilization strategy in structural space and operation process
Appl Energy, 314 (2022), Article 118983
View PDF View article View in Scopus Google Scholar

[38] [38]
H. Zou, M. Li, L. Zhao, X. Liao, Q. Gao, G. Yan, et al.
Cooperative compliant traction mechanism for human-friendly biomechanical energy harvesting
Energy Convers Manag, 258 (2022), Article 115523
View PDF View article View in Scopus Google Scholar

[39] [39]
C. Fan, H. Li, Z. Zhang, Y. Pan, X. Wu, A. Ahmed
An H-shaped coupler energy harvester for application in heavy railways
Energy, 270 (2023), Article 126854
View PDF View article View in Scopus Google Scholar

[40] [40]
X. Wu, T. Zhang, J. Liu, T. Zhang, W. Kong, Y. Pan, et al.
A vibration energy harvesting system for self-powered applications in heavy railways
Sustain Energy Techn, 53 (2022), Article 102373
View PDF View article View in Scopus Google Scholar

[41] [41]
S. Huo, P. Wang, H. Long, Z. Ren, Q. Yi, J. Dai, et al.
Dual-mode electromagnetic energy harvester by Halbach arrays
Energy Convers Manag, 286 (2023), Article 117038
View PDF View article View in Scopus Google Scholar

[42] [42]
H. Wang, W. Wu, L. Cui, Y. Wu, L. Zhu, E. Koutroulis, et al.
A new wave energy converter for marine data buoy
IEEE T Ind Electron, 70 (2023), pp. 2076-2084
Crossref View in Scopus Google Scholar

[43] [43]
T. Jintanawan, G. Phanomchoeng, S. Suwankawin, W. Thamwiphat, V. Khunkiat, W. Watanasiri
Design of a more efficient rotating-EM energy floor with lead-screw and clutch mechanism
Energies, 15 (2022), p. 6539
Crossref View in Scopus Google Scholar

[44] [44]
T. Zhang, H. Cao, Z. Zhang, W. Kong, L. Kong, J. Liu, et al.
A variable damping vibration energy harvester based on half-wave flywheeling effect for freight railways
Mech Syst Signal Pr, 200 (2023), Article 110611
View PDF View article View in Scopus Google Scholar

[45] [45]
L. Ren, Y. Zhou, X. Zhang, H. Zhang, Y. Tan
Active self-powered human motion assist system
Smart Mater Struct, 33 (2024), Article 055003
Crossref View in Scopus Google Scholar

[46] [46]
Z. Wang, H. Du, W. Wang, Q. Zhang, F. Gu, A. Ball, et al.
A high performance contra-rotating energy harvester and its wireless sensing application toward green and maintain free vehicle monitoring
Appl Energy, 356 (2024), Article 122370
View PDF View article View in Scopus Google Scholar

[47] [47]
D. Hao, L. Kong, Z. Zhang, W. Kong, A.M. Tairab, X. Luo, et al.
An electromagnetic energy harvester with a half-wave rectification mechanism for military personnel
Sustain Energy Techn, 57 (2023), Article 103184
View PDF View article View in Scopus Google Scholar

[48] [48]
M. Cai, W. Liao
High-power density inertial energy harvester without additional proof mass for wearables
IEEE Internet Things, 8 (2021), pp. 297-308
Crossref View in Scopus Google Scholar

[49] [49]
C. Wang, Y. Ji, S. Lai, Y. Liu, Y. Hao, G. Li, et al.
A speed-amplified tri-stable piezoelectric-electromagnetic-triboelectric hybrid energy harvester for low-frequency applications
Nano Energy, 114 (2023), Article 108630
View PDF View article View in Scopus Google Scholar

[50] [50]
Z. Liu, X. Wang, E. Al Shami, N.J. Baker, X. Ji
A study of a speed amplified linear generator for low-frequency wave energy conversion
Mech Syst Signal Pr, 149 (2021), Article 107226
View PDF View article View in Scopus Google Scholar

[51] [51]
China Railway Transport Department
Introduction to railway
China Railway Publishing House (2022)
Google Scholar

[52] [52]
M. Gao, J. Cong, J. Xiao, Q. He, S. Li, Y. Wang, et al.
Dynamic modeling and experimental investigation of self-powered sensor nodes for freight rail transport
Appl Energy, 257 (2020), Article 113969
View PDF View article View in Scopus Google Scholar

Outline 概要

Figures (14) 数字 (14)

Tables (2)

Extras (6)

Energy 能源

Highlights 亮点

Abstract 摘要

Graphical abstract 图形摘要

Keywords 关键词

1. Introduction 1.导言

2. Design and working principle
2.设计和工作原理

3. Modeling and dynamic analysis of the DM-EH
3.DM-EH 的建模和动态分析

3.1. Theoretical modeling of the DM-EH under human motion
3.1.DM-EH 在人体运动下的理论建模

3.2. Theoretical modeling of the DM-EH under vehicle operation
3.2.车辆运行时 DM-EH 的理论模型

3.3. Finite-element of the generation unit
3.3.发电装置的有限元

4. Performance investigation
4.绩效调查

4.1. Fabrication of the DM-EH
4.1.DM-EH 的制造

4.2. Characterization and measurements
4.2.特征描述和测量

4.3. Performance comparison
4.3.性能比较

4.4. Practical applications
4.4.实际应用

5. Conclusion 5.结论

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益冲突声明

Acknowledgments 致谢

Appendix A. Supplementary data
附录 A.补充数据

Data availability

References

Cited by (0)

Energy 能源

A high-performance dual-mode energy harvesting with nonlinear pendulum and speed-amplified mechanisms for low-frequency applications用于低频应用的高性能双模式能量收集装置，带非线性摆和速度放大机构

Highlights 亮点

Abstract 摘要

Graphical abstract 图形摘要

Keywords 关键词

1. Introduction 1.导言

2. Design and working principle2.设计和工作原理

3. Modeling and dynamic analysis of the DM-EH3.DM-EH 的建模和动态分析

3.1. Theoretical modeling of the DM-EH under human motion3.1.DM-EH 在人体运动下的理论建模

3.2. Theoretical modeling of the DM-EH under vehicle operation3.2.车辆运行时 DM-EH 的理论模型

3.3. Finite-element of the generation unit3.3.发电装置的有限元

4. Performance investigation4.绩效调查

4.1. Fabrication of the DM-EH4.1.DM-EH 的制造

4.2. Characterization and measurements4.2.特征描述和测量

4.3. Performance comparison4.3.性能比较

4.4. Practical applications4.4.实际应用

5. Conclusion 5.结论

CRediT authorship contribution statementCRediT 作者贡献声明

Declaration of competing interest利益冲突声明

Acknowledgments 致谢

Appendix A. Supplementary data附录 A.补充数据

Data availability

References

A high-performance dual-mode energy harvesting with nonlinear pendulum and speed-amplified mechanisms for low-frequency applications
用于低频应用的高性能双模式能量收集装置，带非线性摆和速度放大机构

2. Design and working principle
2.设计和工作原理

3. Modeling and dynamic analysis of the DM-EH
3.DM-EH 的建模和动态分析

3.1. Theoretical modeling of the DM-EH under human motion
3.1.DM-EH 在人体运动下的理论建模

3.2. Theoretical modeling of the DM-EH under vehicle operation
3.2.车辆运行时 DM-EH 的理论模型

3.3. Finite-element of the generation unit
3.3.发电装置的有限元

4. Performance investigation
4.绩效调查

4.1. Fabrication of the DM-EH
4.1.DM-EH 的制造

4.2. Characterization and measurements
4.2.特征描述和测量

4.3. Performance comparison
4.3.性能比较

4.4. Practical applications
4.4.实际应用

CRediT authorship contribution statement
CRediT 作者贡献声明

Declaration of competing interest
利益冲突声明

Appendix A. Supplementary data
附录 A.补充数据