不同激励下宽频磁浮俘能器俘能试验

振动能量俘获是获取可再生的清洁能源一种有效途径，具有广阔的应用前景，有利于社会的可持续性发展。目前，随机功率谱激励下的高功率密度和宽频能量回收仍然是研究的难点。该研究设计了一种可有效利用宽频振动能量的高功率密度磁浮式俘能器，采用COMSOL Multiphysics软件计算悬浮磁体非线性回复力与位移的关系式，根据磁浮振动系统的控制方程和基尔霍夫定律建立俘能器的数学模型，详细研究了模型参数变化对俘能器性能的影响。随后进行正弦扫频和驻频试验以验证俘能器的发电能力。同时，从俘能器的效率、效能和体积优质3个指标对俘能性能进行评价；并结合实际应用，设计俘能器稳压电路。根据丘陵山区农业机械工作的随机路谱特性，建立随机激励的数学模型，根据响应幅值的概率密度函数的FPK方程表达式，得到了平稳概率密度函数的解。结果表明：在激励频率从9.77到31.75 Hz变化时，俘能器最大输出电压在5.92和21.52 V之间；最大输出功率在10 Hz时达81.93 mW，从5到50Hz，输出功率范围为5.76到81.93 mW；俘能器的效率、效能和体积优质分别为2.85%，9.85%和39.74%；俘能器电压输出的功率谱密度有5个峰值点，对应频率分别为9.804、29.41、36.76、36.76、51.47和71.08 Hz，进一步验证了该研究提出的磁浮式俘能器具有宽频发电性能，并可满足丘陵山区农机设备监测传感器的供电需求。

Energy-harvesting experiment of a broadband magnetic-floating energy harvester under diverse vibration excitations

Abstract: Vibration energy harvesting systems can convert the vibrational energy into the useful electric power, thereby offer a promising source of renewable energy for sustainable development of a society. However, there remains a great challenge on high power density and broadband energy collection under random power spectrum. In this study, a high power-density and broadband magnetic-floating energy harvester (MFEH) was presented for diverse vibration excitations. A COMSOL Multiphysics software was used to calculate the relationship between magnetic restoring force and displacement during the vibration. A mathematical model was established to explore the effects of different parameters on the performance of energy harvester, according to the governing equations of magnetic-floating vibration system and Kirchoff''s law. The simulation results show that the maximum output voltage varied slightly from 16 V to 22 V, as the mass of levitated magnet increased, indicating that the variation in mass can pose some influence on the maximum output voltage. Nevertheless, the resonant frequency decreased, when the mass of levitated magnet increased. The excitation acceleration has a significant influence on the maximum output voltage, whereas, there was a relatively small increase in the resonant frequency. Specifically, the spacing, d0, has a significant impact on the curve shape of output voltage. There was only a unique solution for the governing equation, when the values of d0 were 53 mm and 52 mm, respectively, where the curves of output voltage were stable. But the solution for the governing equation was not unique, when the d0 was less than 52 mm. Consequently, the curve included the stable and unstable solutions, indicating that the jump phenomenon occurred in this case. Analogous to the parameter spacing d0, the damping ratio also strongly determined the curve shape. When the damping ratio was less than 0.21, the curve also included the stable and unstable solution in presence of the jump phenomenon. Diverse excitation conditions, such as the sinusoidal sweeping and fixed frequency vibration, were selected to verify the capacity of power generation. Subsequently, the performance of energy harvester was evaluated by the indexes of efficiency, effectiveness, and the volume figure of merit. A regulated power supply circuit was also designed, combined with the practical application. A mathematical model of random excitation was established, according to the spectrum characteristics for a random road, when an agricultural machine working on hilly and mountainous areas. The solution of stationary probability density was obtained using the Fokker-Planck-Kolmogorov (FFK) equation expression for the response amplitude of probability density function. Experimental results showed the maximum output voltage ranged from 5.917 V to 21.52 V, as the excitation frequency varied from 9.772 Hz to 31.75 Hz under diverse amplitude. The maximum power reached 81.93 mW at 10 Hz. From 5 Hz to 50 Hz, the deliverable power varied from 2.166 mW to 81.93 mW. The efficiency, effectiveness, and the volume figure of merit for the designed energy harvester were 2.85%, 9.85% and 39.74%, respectively. Five peaks can be obtained for the power spectral density of output generating voltage in energy harvester, where the frequencies were 9.804, 29.41, 36.76, 36.76, 51.47 Hz, and 71.08 Hz, indicating a broadband power response. The proposed device can be applied for powering the most sensors of agricultural machinery and equipment in hilly and mountainous areas.