随着微机电系统技术不断发展，无线传感网络技术初步实现了煤矿井下旋转设备状态及周围环境的实时监测，这对智慧矿山建设具有积极推进作用。煤矿设备工作过程中旋转部件持续低频运转（旋转频率低于5 Hz，即转速低于300 r/min），致使放置监测传感器在线准确获取其状态信号比静止部件更加困难，实时监测面临更高的挑战性，集中体现在微电子器件的供电方式上。采用旋转能量俘获技术，将煤矿井下持续的低频旋转机械能转换成电能为无线传感器供电是一种极具有效的解决途径。本文基于磁力非线性研究，复合压电和电磁两种机电转换机制，设计出一种低频旋转式三稳态压电-电磁俘能器。俘能器结构紧凑且最大化提高了空间利用率，系统非线性的引入能够满足俘能器适应煤矿井下低频旋转环境。通过对系统动力学模型和响应特性的研究，揭示其非线性响应和不同机电转换机制之间协同影响机理，为低频旋转式俘能器优化设计及实现工业化应用奠定了理论和技术基础，具有重要的技术推动和研究意义。

为阐明低频旋转式三稳态压电-电磁俘能器系统工作机理，在旋转坐标系中建立系统分布式参数机电耦合动力学模型。考虑压电和电磁机电耦合作用及离心效应对系统模型的影响，提出一种改进型磁偶极子方法构建系统非线性磁力模型。针对磁铁与线圈不同的相对运动模式，根据法拉第电磁感应定律建立轴向式和径向式的电磁模型。根据Euler-Bernoulli梁理论和Rayleigh-Ritz法得到悬臂梁位移表达式，结合系统恢复力模型和重力模型，最后采用Lagrange方程和Kirchhof定律分别建立系统动力学方程和电学方程。为后续研究系统动力学响应提供理论分析基础。

基于系统离心力模型，揭示悬臂梁自身结构参数和旋转半径对系统刚度和固有频率影响规律。根据系统恢复力势能模型，研究磁铁轴向间距和径向间距对系统恢复力势能的影响机理。数值仿真结果表明：在正向配置旋转环境中，系统受离心硬化效应，阻碍悬臂梁形变；在反向配置旋转环境中，系统受离心软化效应，有利于悬臂梁扩大形变。随着转速的提高离心效应逐渐增强，此时悬臂梁长度越长、宽度越窄、厚度越薄有利于降低压电悬臂梁的刚度和固有频率；旋转半径长度越长，系统受离心力越强。磁铁间距是决定系统势垒高度的关键因素，存在一个最佳磁铁间距将系统构造为势垒最低、势阱最浅的三稳态系统，此时系统能够在较低激励水平下实现大幅响应。

选择低于5 HZ（300 r/min）的旋转速度模拟实际工况探究系统的动力学响应特性，利用四五阶Runge-Kutta算法对动力学模型进行数值求解。揭示离心硬化效应和离心软化效应对三稳态压电-电磁俘能器响应特性和输出电压的影响规律，分析对比三稳态系统与线性系统的输出响应。仿真分析表明：随着旋转速度的改变，系统表现出丰富的非线性行为，离心力对系统具有重要的影响。离心软化效应有利于系统在低频旋转环境中实现大幅阱间运动，能够提高俘能器响应输出及增强俘能器在煤矿井下低频环境的适应性。与线性系统相比，三稳态系统明显具备更加优异的输出性能。

为验证动力学模型预测精度和仿真结果的正确性，制备低频旋转式三稳态压电-电磁俘能器，搭建低频旋转测试平台。调整磁间距，测试不同间距下系统动力学响应特性；测试不同转速下系统压电单元和电磁单元的发电性能，并对各单元进行阻抗匹配测试，获得俘能器输出的最大平均功率。实验验证了系统机电耦合动力学模型的精确性和仿真分析的准确性，所设计的俘能器能够满足众多微功耗传感器供能。论文为低频旋转环境中俘能器的设计提供了强有力的理论支撑，对提升旋转式俘能器的输出性能提供了新的研究思路，并为俘能器煤矿井下应用提供有力基础。

As micro electromechanical systems continue to develop, wireless sensor network technology has initially realized real-time monitoring of the status of rotating equipment and surrounding environment in underground coal mines, which plays a positive role in promoting the construction of smart mines. In the working process of coal mining equipment, the continuous low-frequency rotation of rotating parts (rotation frequency less than 5 Hz, speed lower than 300 r/min) makes it more difficult to accurately obtain the status signal of the rotating components for online monitoring than stationary parts, resulting in higher challenges for real-time monitoring, especially in the power supply of microelectronic devices. Using rotational energy harvesting technology to convert the continuous low-frequency rotational mechanical energy in underground coal mines into electrical energy to power wireless sensors is an effective solution. Based on nonlinear magnetic studies, a composite piezoelectric-electromagnetic dual electromechanical conversion mechanism is designed to produce a low-frequency rotation-based tri-stable piezoelectric-electromagnetic energy harvester. The harvester has a compact structure and maximizes spatial utilization, and the introduction of system nonlinearity enables the harvester to adapt to the low-frequency rotating environment in underground coal mines. Through the study of the system's dynamic model and response characteristics, the nonlinear response and collaborative impact mechanism between different electromechanical conversion mechanisms are revealed, laying the theoretical and technical foundation for the optimized design and industrial application of the low-frequency rotation-based energy harvester, which has significant technological and research significance.

To clarify the working mechanism of the low-frequency rotation-based three-stable-state piezoelectric-electromagnetic energy harvester system, a distributed parameter electromechanical coupling dynamic model of the system is established in a rotating coordinate system. The influence of piezoelectric and electromagnetic electromechanical coupling effects and centrifugal effects on the system model are considered, and an improved magnetic dipole method is proposed to construct a nonlinear magnetic force model for the system. Considering different relative motion patterns between the magnet and the coil, axial and radial electromagnetic models are established based on Faraday's electromagnetic induction law. By applying Euler-Bernoulli beam theory and Rayleigh-Ritz method, the deflection expression of a cantilever beam is obtained, combined with the system's restoring force model and gravity model, and finally, the Lagrange equations and Kirchhoff's laws are used to establish the system's dynamic equations and electrical equations. This provides a theoretical basis for the subsequent study of the system's dynamic response.

Based on the centrifugal force model of the system, the influence of the structural parameters and the rotating radius of the cantilever beam on the system's stiffness and natural frequency is revealed. By analyzing the system's potential energy model of the restoring force, the research investigates the mechanism of how the axial and radial distances of the magnets affect the system's restoring force potential energy. Numerical simulation results indicate that in a forward-configuration rotating environment, the system experiences centrifugal stiffening effects, hindering the deformation of the cantilever beam; conversely, in a reverse-configuration rotating environment, the system undergoes centrifugal softening effects, facilitating the expansion of the cantilever beam deformation. As the rotational speed increases, the centrifugal effects gradually strengthen. In this scenario, longer beam lengths, narrower widths, and thinner thicknesses are advantageous for reducing the stiffness and natural frequency of the piezoelectric cantilever beam. Moreover, longer rotating radii result in stronger centrifugal forces acting on the system. The magnet spacing is a critical factor determining the system's potential barrier height. There exists an optimal magnet spacing that configures the system as a three-stable-state system with the lowest potential barrier and shallowest potential well. At this point, the system can achieve significant responses at lower excitation levels.

At rotational speeds below 5 Hz (300 r/min), simulating actual operating conditions to explore the dynamic response characteristics of the system, the dynamics model is numerically solved using the fourth or fifth-order Runge-Kutta algorithm. The investigation reveals the effects of centrifugal stiffening and softening on the response characteristics and output voltage of the three-stable-state piezoelectric-electromagnetic energy harvester. A comparison is made between the output responses of the three-stable-state system and a linear system, analyzing their differences.Simulation analysis demonstrates that as the rotational speed changes, the system exhibits rich nonlinear behavior, with centrifugal forces playing a significant role in influencing the system. The centrifugal softening effect is beneficial for enabling the system to undergo significant inter-well motion in low-frequency rotating environments, thereby enhancing the energy harvester's response output and its adaptability to low-frequency conditions in underground coal mines. Compared to linear systems, the three-stable-state system shows significantly improved output performance.

To verify the accuracy of the dynamic model predictions and simulation results, a low-frequency rotating three-stable-state piezoelectric-electromagnetic energy harvester was prepared, and a low-frequency rotating test platform was set up. The magnet spacing was adjusted to test the system's dynamic response characteristics at different spacings. The power generation performance of the piezoelectric and electromagnetic units of the system at different speeds was tested, and impedance matching tests were conducted on each unit to obtain the maximum average power output of the energy harvester. The experiments validated the accuracy of the system's electromechanical coupled dynamic model and the precision of the simulation analysis. The designed energy harvester can meet the energy supply needs of various low-power consumption sensors. The paper provides strong theoretical support for the design of energy harvesters in low-frequency rotating environments, offers new research perspectives to enhance the output performance of rotating energy harvesters, and lays a solid foundation for the application of energy harvesters in underground coal mines.

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