两端固支式双晶片压电梁建模及发电特性分析

Modelling of Bimorph Piezoelectric Cantilevered Beam Fixed at Both Ends and Analysis of Energy Generation Characteristic

压电梁能将机械振动转换为电能,有效解决了轨道车辆走行部件安全监测传感器的供电问题。为获取其发电特性,根据小弯曲变形理论建立压电梁的弯矩方程,按照一维压电片应力和电位移方程建立压电梁机电转换数学模型。采用Nelder⁃Mead单纯形算法实现结构参数优化并分析了压电梁材料、结构参数和振动频率对发电效能的影响规律,通过仿真及实验验证了理论模型的正确性。结果表明:双晶片梁的发电效能随弹性模量比增加而减小;低弹性模量的金属基底构成的压电梁,输出能量较高且共振频率低;压电梁存在最佳厚度比使其发电效能最大,铍铜的最佳厚度比为0.213,锰白铜为0.261。实测值与理论值相比,输出有效电压最大偏差为0.13 V,相对偏差小于2.8%;输出功率最大偏差为0.024 mW,相对偏差小于2.9%。

The piezoelectric beam can convert vibration-energy into electrical-energy,which solves the sensor power challenges for the running parts of rail vehicles.In order to explore energy generation characteristics of the piezoelectric beam,the bending moment equation of the piezoelectric beam is established according to the small bending deformation theory,and the electromechanical conversion model is obtained with the one-dimensional piezoelectric stress.By using the Nelder-Mead simplex algorithm,optimization parameters of bimorph piezoelec⁃tric beam are given.And the influence of materials,structural parameters and frequency on conversion efficiency is analyzed.The theoretical model is verified correctly by simulation and experiment.The results show that the energy generation efficiency of the beam decreases with the increase of the elastic modulus ratio;the beams with low elastic modulus metal have high power-peaks and low resonant-frequencies.the beams get max-power at the optimal thickness ratio,the beryllium copper is 0.213,and manganese copper is 0.261.Compared with the mea⁃sured value,the deviation of the output voltage is less than 0.13 V,the relative deviation is less than 2.8%,the deviation of the output power is less than 0.024 mW and the relative deviation is less than 2.9%.