多环盘组合结构的横向弯曲耦合振动建模与求解

Modeling and solving of transverse flexure coupled vibration for multi annular plate

超声谐振系统是旋转超声加工的核心设备,而多环盘结构是超声谐振系统中一种典型的负载结构,其横向弯曲耦合振动分析对于超声谐振系统设计具有重要意义。基于Mindlin厚板动力学理论,利用环盘的位移、转角、剪力和弯矩的连续条件和边界条件,建立了多环盘组合结构的横向弯曲耦合振动分析模型,推导了频率求解方程,并基于MATLAB设计了多环盘横向弯曲耦合振动频率的计算软件。通过理论模型求解、有限元模态分析和齿轮模态实验之间的对比分析,验证了该求解模型的准确性和程序的实用性,为旋转超声加工系统的设计提供了技术参考。

Ultrasonic resonant system is the core equipment of rotary ultrasonic machining（RUM）,and multi annular plate structure is a typical load structure of ultrasonic resonant system.The analysis of transverse flexure coupled vibration for this structure is of great significance for ultrasonic resonant system design.Based on Mindlin theory for thick plate,transverse flexure vibration analysis model of multi annular plate was established by the use of deflection,rotation angle,shear force,and bending moment of continuity and boundary conditions for annular plates.Frequency equation was derived,and calculating software for transverse flexure coupled vibration frequency of multi annular plate was designed by MATLAB.By the comparison among theoretical model,finite element model analysis and model experiment,the accuracy of the solving model and practicability of the calculating software were verified,which provided technical reference for RUM system design.