气浮直线驱动平台定位误差影响因素研究

Influencing factors of positioning errors of the air bearing linear motor stage

为实现气浮直线驱动平台定位误差的精确补偿,对气浮直线驱动平台定位误差的影响因素进行了研究。试验测量了气浮直线驱动平台的定位误差,发现其测量结果中包含有随机误差、时变的热误差以及与位置相关的几何误差。对定位误差进行补偿的前提是根据不同误差的性质准确地将其分离,否则就会存在少补或过补的现象。本文利用统计学的方法求出随机误差的数学期望,对测量数据的均值进行修正,消除随机误差对测量值的影响。进一步对修正后的均值进行多项式拟合,将位置相关的几何误差和时变的热误差分离,并发现时变的热误差对超精密气浮直线驱动平台的定位误差影响很显著,需要进行在线实时补偿。提出使用NURBS曲线插值的方法,建立位置相关的几何误差的预测模型,从而实现对位置相关的几何误差进行精确的预测和离线误差补偿。

In order to realize accurate error compensation for the air bearing linear motor stage, the influencing factors of positioning errors of the stage were studied. The positioning errors was measured, and it was found that the testing results of the positioning errors contained the random error, the time varying error caused by thermal deformation and the positioning error associated with position. The premise of compensating the positioning errors was accurate separation according to the properties of the different errors. Otherwise, there will be less or over compensation phenomenon. This paper presented a new method to correct the mean value of the measured data on the basis of statistics ; thereby eliminate the influence of the random error of the measured values by mathematical expectation of random errors. Then the geometrical error associated with position and the time varying error caused by thermal deformation were separated by Polynomial fitting of the corrected mean value and it was found that the effect of the time varying error caused by thermal deformation in air bearing linear motor stage was very significant, the on-line timely compensation was needed. Finally, the forecasting model of the geometrical error associated was founded using the non-uniform rational B-splines（NURBS） curve interpolation, realizing the accurate forecasting and off-line error compensation for the positioning error associated with position.