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超声变幅杆是功率超声振动系统的重要组成部分,它的主要功能是把机械振动位移放大并把能量集中在较小的辐射面上,变幅杆的放大系数是超声振动系统中的重要参数。用微元法建立圆锥形超声变幅杆纵向振动的波动方程,用分离变量法和连续振动体的边界条件求解超越波动方程,得到圆锥形超声变幅杆放大系数与变幅杆的大小端直径之比、长度以及外激频率3个变量之间的数学表达式。为研究变幅杆的放大系数与变幅杆的大小端直径之比、长度以及外激频率的关系,依次把3个变量中的2个变量设为常量,对另外一个变量进行抽样,计算变幅杆的放大系数。通过Matlab对超声变幅杆放大系数的样本计算数据进行曲线拟合,定性分析了圆锥形超声变幅杆放大系数随变幅杆大小端直径之比、长度、外激振动频率变化的关系。
Ultrasonic horn is an important part of the power ultrasonic vibration system. Its main function is to amplify the mechanical vibration displacement and concentrate the energy on the smaller radiation surface. The amplification factor of the horn is an important parameter in the ultrasonic vibration system . The wave equation of the longitudinal vibration of a cone-shaped ultrasonic horn was established by using the micro-element method. By using the separation variable method and the boundary conditions of the continuous vibrating body, the transcendental wave equation was solved and the enlargement coefficient of the cone-shaped horn and the size of the horn Ratio, length, and the frequency of the external shock three variables between mathematical expressions. In order to study the relationship between the amplification factor of the horn and the size of the horn, the length and the frequency of the external horn, two of the three variables are set as constants and the other is sampled to calculate Amplification factor. Through the curve fitting of the sample calculation data of ultrasonic horn amplifying coefficient by Matlab, the relationship between the amplifying coefficient of cone-shaped ultrasonic horn and the ratio of the end-to-end diameter of horn, length and external shock frequency was analyzed qualitatively.