Abstract:

The study of ultrasonic variable amplitude rods is an important part of ultrasonic vibration system. The cosine half?period cylindrical composite horn was designed to realize the smooth transition between the cosine section and the cylindrical section. By theoretical calculation, its frequency equation and amplification coefficient equation were derived. The results show that the frequency equation of the new cosine cylindrical composite variable amplitude rod is simpler than that of the cylindrical conical composite variable amplitude rod and the stepped variable amplitude rod; the amplification coefficient equation of the new cosine cylindrical composite variable amplitude rod is similar to that of the stepped variable amplitude rod, which is more concise than that of the cylindrical conical composite variable amplitude rod. Using ABAQUS finite element analysis software, modal analysis of the designed cosine cylindrical composite variable amplitude rod was carried out to determine its inherent frequency and vibration type; harmonic response analysis was conducted to check the feasibility of the theoretical design. The results of the modal analysis and harmonic response analysis show that the performance of the ultrasonic composite variable amplitude rod is optimal when the length of the cosine section is 55 and 60 mm. The research results provide a reference for the design and application of ultrasonic composite amplitude rod.

Key words: Cosine, Variable amplitude rod, ABAQUS, Modal analysis, Harmonic response analysis

摘要：

超声变幅杆是超声振动系统中的一个重要部件。设计了余弦半周期圆柱形复合变幅杆，实现了余弦段与圆柱段的平滑过渡。通过理论计算，推导了其频率方程和放大系数公式。结果表明，新型余弦圆柱形复合变幅杆的频率方程比圆柱圆锥形复合变幅杆和阶梯形变幅杆更为简单；新型余弦半周期圆柱形复合变幅杆的放大系数公式与阶梯形变幅杆相似，比圆柱圆锥形复合变幅杆更为简捷。利用ABAQUS有限元分析软件，对所设计的余弦半周期圆柱形复合变幅杆进行了模态分析，确定了其固有频率和振型；进行谐响应分析，检查了理论设计的可行性。模态分析和谐响应分析结果表明，当余弦段长度为55、60 mm时，超声复合变幅杆性能最优。研究结果为超声复合变幅杆的设计与应用提供了参考。

关键词: 余弦形, 变幅杆, ABAQUS, 模态分析, 谐响应分析