Chen Shao-En, Gunawan Hadi, Wu Chia-Che
Department of Mechanical Engineering, National Chung Hsing University, Taichung 40227, Taiwan.
Innovation and Development Center of Sustainable Agriculture (IDCSA), National Chung Hsing University, Taichung 40227, Taiwan.
Sensors (Basel). 2022 Mar 14;22(6):2237. doi: 10.3390/s22062237.
In this paper, an analytical solution for a clamped-edge bimorph disk-type piezoelectric transformer with Kirchhoff thin plate theory is proposed. The electromechanical equations for transient motions are first derived, and coupled expressions for mechanical response and voltage output are obtained. For the case of excitation around the first resonant frequency, the resulting equations are further simplified. There are analytical solutions for a mechanical response, voltage, current, and power outputs. According to the analytical model, the output voltage is affected by the inner radius of the input and output electrodes, the radius of the piezoelectric transformer (PT), and the thickness ratio between the lead zirconate titanate (PZT) layer and the substrate. When the inner radius of the input electrode approaches zero (electrode becomes circular shape), it achieves maximum output voltage at the first resonance frequency excitation. On the contrary, when the inner radius of the output electrode approaches zero, the output voltage reaches its minimum value. Voltage ratios remain constant as the disk radius changes, and the first resonance frequency is inversely proportional to the square of the disk radius. The voltage ratio is fixed even with the miniaturization of the PT.
本文提出了一种基于基尔霍夫薄板理论的夹支边双压电晶片圆盘型压电变压器的解析解。首先推导了瞬态运动的机电方程，并得到了机械响应和电压输出的耦合表达式。对于在第一共振频率附近激励的情况，所得方程进一步简化。存在机械响应、电压、电流和功率输出的解析解。根据解析模型，输出电压受输入和输出电极的内半径、压电变压器（PT）的半径以及锆钛酸铅（PZT）层与衬底之间的厚度比影响。当输入电极的内半径接近零时（电极变为圆形），在第一共振频率激励下可实现最大输出电压。相反，当输出电极的内半径接近零时，输出电压达到最小值。随着圆盘半径变化，电压比保持恒定，且第一共振频率与圆盘半径的平方成反比。即使PT小型化，电压比也保持不变。
