基于Mindlin理论的功率超声纵弯谐振变幅器设计理论与实验研究  

Design and experiment of ultrasonic longitudinal-flexural resonance transducer based on Mindlin theory

作　　者：付俊帆 秦慧斌[1] 吕明 FU Junfan;QIN Huibin;Lü Ming(Shanxi Key Laboratory of Advanced Manufacturing Technology,North University of China,Taiyuan 030051,China;Shanxi Key Laboratory of Precision Machining,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[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

出　　处：《振动与冲击》2018年第7期259-266,共8页Journal of Vibration and Shock

基　　金：精密加工山西省重点实验室开放基金(201601);先进制造技术山西省重点实验室开放基金(XJZZ201603);中北大学研究生科技基金(20161311)

摘　　要：多种材料的阶梯环盘负载与变幅杆共同组成了功率超声纵弯谐振变幅器,在超声加工、超声处理等领域有着广泛应用。为了快速准确地对纵弯谐振变幅器进行设计,提出了一种基于Mindlin理论的变幅器设计方法。基于Mindlin理论求出了中厚环盘单元的位移、转角、弯矩和剪力的解析表达式。通过振动单元间的连续条件和边界条件,建立了纵弯谐振变幅器的振动模型与频率方程。基于该振动模型,利用MATLAB/GUI开发了纵弯谐振变幅器尺寸设计软件。通过理论计算设计了纵弯谐振变幅器,并进行了有限元模态分析、阻抗分析试验和超声谐振试验。仿真与试验的结果证明,基于Mindlin理论的纵弯谐振变幅器设计方法所设计的纵弯谐振变幅器的谐振频率与设计频率相符合,具有较好的设计精度,可为变幅器设计提供参考。An ultrasonic longitudinal-flexural resonance transducer is consisted of a horn and a stepped annular plate with multi materials,and applied on ultrasonic machining and ultrasonic treatment.In order to design longitudinal-flexural resonance transducer rapidly and accurately,a design method for transducers was proposed based on Mindlin theory.Formulae for displacement,rotation angle,bending moment,and shear force of moderately thick annular plates were obtained.Base on continuous and boundary conditions among vibrating elements,vibration model and equations of longitudinal-flexural resonance transducer were established,and a design software for the transducer is developed with MATLAB/GUI.Two longitudinal-flexural resonance transducers were designed theoretically.Finite element analysis,impedance experiment and ultrasonic resonance experiment of the transducers were carried out.It was proved that resonance frequency of transducers designed by this design method was in good agreement with design frequency.The design method was proved to be accurate and effective.

关 键 词：Mindlin理论 纵弯谐振 超声变幅器 阶梯环盘 

分 类 号：TH113.1[机械工程—机械设计及理论]