带中心孔的复合超声变幅杆设计及性能分析

Design and analysis on compound ultrasonic horn with center hole

带中心孔的变幅杆可以实现旋转超声加工的中心供冷却液或气体,具有良好的冷却和排屑效果。针对单一形状变幅杆难以实现大振幅的超声振动,对带中心孔的复合超声变幅杆的设计原理和方法进行研究。根据任意截面杆的波动方程,得到带中心孔单一形状变幅杆的传输方程和传输矩阵,并通过对总体四端网络的传输方程和传输矩阵的运算,推导出带中心孔的圆锥过渡复合变幅杆的频率方程和放大倍数的一般公式。根据推导出的频率方程,设计出典型的复合变幅杆,并对所设计的变幅杆进行频率测试,测得的变幅杆频率与理论计算频率的误差在5%以内。研究带中心孔的圆锥过渡复合变幅杆各段长度及中心孔直径对变幅杆频率的影响规律,为复合变幅杆设计和调整提供了理论依据。

The inner cooling fluid or gas supply can be realized by ultrasonic horn with center hole which makes cooling and chip removal effective during rotary ultrasonic manufacturing. The method and theory of compound ultrasonic horn with center hole were investigated because it was difficult to realize ultrasonic vibration of large amplitude with single shape. The transfer equations and matrices of the horn with single shape and center hole were obtained based on wave equation. And then the frequency equation and the formula of magnification factor of the conical compound horn were deduced. A typical compound horn was designed according to the equation. The frequency of the horn was tested, and the errors between the tested one and the calculated one are within 5%. The influence of the length of each part with different cross-section shape and the diameter of the center hole on the frequency of the compound horn was researched, providing a theoretical basis for structural design and adjustment of the horn.