大尺寸矩形断面超声变幅杆固有频率的研究

A study to the resonant frequency of ultrasonic horns with large rectangular cross-section

超声变幅杆是功率超声技术中换能器振动系统的一个重要组成部分,本文利用表观弹性法研究了大尺寸矩形断面超声变幅杆的耦合振动,推出了常用的几种单一变幅杆(指数形,圆锥形,悬链线及阶梯形)的频率设计公式,为大尺寸矩形变幅杆的频率设计及计算提供了一种简单易行的方法,实验表明,利用本文公式设计的大尺寸矩形断面变幅杆,实测共振频率与理论计算频率基本一致,与一维振动理论的结果相比,利用耦合振动理论得出的变幅杆共振频率更加接近于测量值。

Ultrasonic horns are an important part in transducer vibrational systems, in this paper we studied the coupled vibration of the ultrasonic horns with large rectangular cross section on the basis of the apparent elasticity method, and derived out the resonant frequency equation of horns with single rectangular cross section (exponential, conical, catenoidal and stepped horns). Experiments show that measured frequencies of horns with large rectangular cross section agree well with calculated results. As compared with the results from the one-dimensional vibrational theory, the frequencies from the coupled vibrational theory in this paper are nearer to the measured results. The coupled vibrational theory will find wide applications in the analyses and calculations of large horns with rectangular cross-section and other large-dimensional ultrasonic hor-