复合盘压电超声换能器的径向振动频率方程-机械工程学报.pdf

第 44 卷第 9 期 机 械 工 程 学 报 Vol.44 No.9 2008 年 9 月 CHINESE JOURNAL OF MECHANICAL ENGINEERING Sep. 2008 DOI ：10.3901/JME.2008.09.065 复合盘压电超声换能器的径向振动频率方程* 1 2 刘世清 林书玉 (1 ．浙江师范大学数理与信息工程学院 金华 321004 ； 2 ．陕西师范大学应用声学研究所 西安 710062) 摘要：提出并研究一种复合盘压电超声换能器的径向振动特性。依据机电类比原理，建立复合系统的径向振动等效电路，并 推导出其径向振动频率方程。数值计算表明，当换能器半径比一定时，对给定材料换能器径向共振频率与压电晶片直径的积 为常数。此外，径向复合换能器不满足传统的“半波长”级联规律，必须进行整体设计。作为算例，给出常用材料钢、铝和 钛与 PZT-4 复合压电超声换能器的径向共振频率常数与其半径比的拟合关系曲线。试验加工两个径向复合压电超声换能器， 并测定其共振基频。结果表明，换能器谐振频率误差小于 3%，能够满足工程应用需要。 关键词：盘型超声换能器 径向振动系统 频率常数 等效电路 频率方程 中图分类号：O426 1 Radial Vibration Frequency Equation of Composite Disc Piezoelectric Ultrasonic Transducer LIU Shiqing1 LIN Shuyu2 (1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004; 2. Applied Acoustics Institute, Shaanxi Normal University, Xi’an 710062) Abstract ：The radial vibration characteristic of a new kind of radial composite piezoelectric ultrasonic transducer is studied. Based on the electromechanical analogy principle, the equivalent circuit is set up and the frequency equation of the transducer is derived. Numerical computation indicates that the product of radial resonance frequency and diameter of piezoelectric ceramic slice of the transducer is constant if the radius ratio and the material of transducer are specified. Furthermore, the radial composite transducer cannot meet the conventional half-wave length cascade law, so an overall design is necessary. In addition, the relationships between the resonance frequency constant an