夹角型超声变幅杆的矩阵解析法

On matrix analytical method of angled ultrasonic longitudinal solid horn

对新型的夹角型超声变幅杆的设计方法进行研究,借鉴传输矩阵法的思想利用一维振动理论推导了均匀杆两端界面各矢量间关系的特性矩阵,结合变幅杆连接处位移、力、转角和力矩的连续条件得到了夹角型超声变幅杆谐振频率的矩阵解析法.计算了不同尺寸变幅杆的谐振频率,计算结果与实验测试结果相一致.

The engineering method of the new type angled ultrasonic longitudinal solid horn has been investigated in this paper.At first,the characteristic matrix of the relationship between the vectors on the input and output ends of the straight rod has been calculated.Then,the coupling relationship of the displacements,forces,bending moments and angles of rotation at the junction of the input and output rods has been obtained. At last,the matrix analytical method,which has been used to calculate the resonant frequency,has been presented based on the characteristic matrix and coupling relationship.The resonant frequencies of the angled solid horns with different geometrical dimensions have been calculated and basically agree with the values by experiment.This method,featuring clear physical concept and convenient calculation,can serve as reference for the design of the angled ultrasonic longitudinal solid horn.