基于有限元的二维超声椭圆振动台优化与分析

针对二维超声椭圆振动台振动轨迹误差较大的问题,结合数学理论,分析产生误差的主要原因。通过在SolidWorks中建立了振动台的几何模型,并利用有限元软件仿真了振动台的模态。以振动台的伸缩模态频率和弯曲模态频率为基础,采用区间消去法优化了二维振动台的尺寸参数,使得两种振动模态频率相近。并对所优化的模型进行谐响应分析,拟合了振动台表面的运动轨迹。最终通过优化得到振动台的设计尺寸,将振动台的两种模态频率差值控制在0.5Hz,由此减少了振动椭圆轨迹的误差。

Two-dimensional Ultrasonic Elliptical Vibrating Table Optimization and Analysis Based on FEM

Aiming at the vibration trajectory error of two-dimensional ultrasonic elliptical vibrating table,this paper combines mathematical theory to analyze the main causes of the error.The geometric model of the vibrating table is established in SolidWorks,and the modal of the vibrating table is simulated by finite element method.Based on the telescopic mode frequency and the bending mode frequency of the vibrating table,the interval parameters are used to optimize the size parameters of the two-dimensional vibrating table,so that the two vibrating modes have similar frequencies.The harmonic response analysis of the optimized model is performed,and the motion trajectory of the surface of the vibrating table is fitted.Finally,the design size of the vibrating table is obtained by optimization,and the difference between the two modal frequencies of the vibrating table is controlled at 0.5 Hz,thereby reducing the error of the vibrating elliptical trajectory.