Page 69 - 《应用声学》2021年第4期

第 40 卷 第 4 期 Vol. 40, No. 4
2021 年 7 月 Journal of Applied Acoustics July, 2021

⋄ 研究报告 ⋄

旋转超声磨削平行砂轮复合变幅器设计与试验 ∗

周瑞峰 1 秦慧斌 1† 冯 毅 1 庞学慧 1 吕 明 2

(1 中北大学先进制造技术山西省重点实验室 太原 030051)
(2 太原理工大学精密加工山西省重点实验室 太原 030024)
摘要：为了获得大负载平行砂轮复合变幅器的设计方法，将复合变幅器简化为复合变幅杆与多阶环盘组成。
利用 Mindlin 中厚板理论，求解了各振动环盘的位移、转角、弯矩和剪力解析表达式，通过复合变幅杆各振动单
元间的力、位移的边界条件和连续条件，以及复合变幅杆和环盘两者结构间力与位移的耦合条件，建立了复合
变幅器的数学模型和频率方程。针对频率方程进行编程求解，设计了平行砂轮复合变幅器。通过有限元仿真
分析、实物阻抗特性试验、谐振试验验证。试验结果表明：平行砂轮复合变幅器的实际谐振频率、节圆位置与理
论设计的误差小于 5%，验证了其理论设计方法的正确性。为研制大负载平行砂轮复合变幅器提供了一种有效
的设计方法。
关键词：平行砂轮；复合变幅器；Mindlin 理论；频率方程；谐振试验
中图法分类号: TH113.1 文献标识码: A 文章编号: 1000-310X(2021)04-0553-09
DOI: 10.11684/j.issn.1000-310X.2021.04.009

Design and experimental research on composite amplitude transformer of

rotating ultrasonic grinding parallel grinding wheel

ZHOU Ruifeng 1 QIN Huibin 1 FENG Yi 1 PANG Xuehui 1 LYU Ming 2

(1 Shanxi Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China)
(2 Shanxi Key Laboratory of Precision Machining, Taiyuan University of Technology, Taiyuan 030024, China)
Abstract: In order to obtain the design method of the composite amplitude transformer of the large
load parallel grinding wheel, the structure of the composite amplitude transformer was simplified as a
combination of a composite horn and a stepped annular plate. Based on Mindlin theory, the analytical
expressions of displacement, rotation angle, bending moment and shear force between the vibration rings of
various orders were derived. Through the boundary and continuous conditions of force and displacement
between the vibration elements of the composite horn, and the coupling conditions of force and displacement
between the composite horn and annular plate, the mathematical model and frequency equation of the
composite amplitude transformer were established. The frequency equation programming was used to
solve the problem, and the composite amplitude transformer with parallel grinding wheel was designed.
It was verified by finite element simulation analysis, physical impedance characteristic test and resonance
test. The experimental results show that the error between the experimental resonant frequency, node
circle position and theoretical design of the parallel grinding wheel composite amplitude transformer is less
than 5%. The correctness of the theoretical design method is verified. The research provides an effective
design method for the development of the large load parallel grinding wheel composite amplitude transformer.

2020-10-13 收稿; 2021-01-08 定稿
山西省高校科技成果转化培育项目 (2020CG033), 山西省研究生教育创新项目 (2020SY351), 国家留学基金委资助项目 (201908140056)
∗
作者简介: 周瑞峰 (1995– ), 男, 山西忻州人, 硕士研究生, 研究方向: 功率超声加工理论与技术。
† 通信作者 E-mail: qhbsss@163.com