二维精密工作台离散点测量结果误差分离的新方法研究

A New Error Separation Method for Measurement Results of Discrete Points of 2D Precision Stage

针对测量结果中包含的误差，提出一种能够分离精密工作台系统误差的方法。首先利用辅助测量栅格板和二维精密工作台的不同位置进行测量，然后根据栅格板上标记点的测量数据和标称值建立误差分离的数学模型，最终实现对测量结果的误差分离。通过仿真验证了算法的有效性。仿真结果表明：当不存在测量噪声时，能够实现误差的完全分离；当存在测量噪声时，计算值与给定值标准差的相对误差在X轴和Y轴上分别为1．95％和1．52％。对于不同幅度的噪声，工作台系统误差计算值稳定。该算法对噪声不敏感，表现出很好的鲁棒性，可用于测量结果和仪器性能的评价。

To separate the system error of precision stage, a new method for separation was put forward. Firstly different positions of auxiliary measuring grid plate and 2D-stage were measured. Then according to the measurement data of mark points on the grid plate and their corresponding nominal values, a mathematical model for error separation was established, which could separate errors from the measured results. The effectiveness of the algorithm was verified through simulation. Simulation results showed that when there was no measurement noise, the algorithm could realize complete error separation, while in the case of the presence of measurement noise, the relative error of standard deviation of calculated values and the given values were 1.95% and 1.52% in X-axis and Y-axis respectively. For noises with different amplitudes, the calculated values of system errors were stable. The algorithm is not sensitive to noise and can be very useful in evaluation of measurement results and instrument performances.