精密气浮运动平台动态误差建模与分析

Modeling and analysis of dynamic errors for ultra-precision motion stage

针对驱动合力偏离运动部件质心时,精密气浮运动平台运动部件会产生偏转振动,会带来运动和定位的动态误差,提出一种基于动力学分析的动态偏转误差评估方法.运用牛顿-欧拉法并引入欧拉四元数建立系统动力学方程,利用实验数据对静压气体轴承受力进行插值处理,有效解决了静压气体轴承受力非线性的问题,得到了更为精确的偏转误差曲线.以H形双边驱动XY运动平台为研究重点,分析其在不同受力情况下的偏转误差,结果表明:驱动不同步会引起运动平台较大幅度的偏转.该方法还可以推广到其他结构模型的运动平台.

As dynamic errors of movement and positioning are inevitably incurred in ultra-precision motion stages due to deflection vibration caused by non-colinearity of the direction of driving resultant force from the center of mass of the moving component,an approach to the evaluation of such kind of errors was proposed based on dynamic modeling analysis.The equations of motion of a typical precision motion stage were derived using Newton-Euler method and the expression in terms of Euler quaternion.The applied forces acted upon the hydrostatic air bearings involved in the stage were interpolated in terms of the experiment data,avoiding the assumption of linearization of the characteristics of hydrostatic air bearings,and as a consequence,more accurate dynamic error evaluation could be achieved.The H-shaped XY motion stage with twin linear drives was focused as case study,whose dynamic deflection errors were calculated and analyzed in various combinations of working conditions.The results show that the motion stage will vibrate substantially when the two drives are not synchronized in motion.The proposed approach can also be extended to stages with other topological configuration.