基于最小二乘圆拟合法的三轴转台垂直度误差测试

The verticality error test of three-axis turntable based on least square circle fitting method

为快速准确测量三轴转台的垂直度误差,采用电子水平仪测试方位轴与水平面间的垂直度误差以及采用自准直仪与平面反射镜测试三轴转台的方位轴与俯仰轴(俯仰轴与横滚轴)的垂直度误差。研究基于最小二乘圆拟合法进行误差分析与分离以及数据处理的方法:首先通过对最小二乘圆拟合法公式进行详细的推导,得出拟合圆曲线的理想圆心及半径的估计值;其次对实测数据进行误差分析与分离;最终不仅实现三轴转台的垂直度误差的测量计算,且可以快速获得各轴系倾角回转误差的测量计算。检测结果表明,测量结果直观可靠。这种经典的测试方法简单易行,该数据处理方式可以快速便捷地获取测量结果。

In order to quickly and accurately measure the perpendicularity error of the three-axis turntable,the perpendicularity error between the azimuth axis and the horizontal plane was tested with the electronic level instrument,and the perpendicularity error between the azimuth axis and the pitching axis(pitching axis and transverse roller axis)of the three-axis turntable was tested with the autocollimator and the plane mirror.The method of error analysis and separation and data processing based on the least square circle fitting method is studied.Firstly,by deducing the formula of the least square circle fitting method in detail,the estimated values of the ideal center and radius of the fitting circle curve are obtained.Secondly,error analysis and separation are carried out for the measured data.Finally,not only the measurement and calculation of the verticality error of the three-axis turntable,but also the measurement and calculation of the inclination rotation error of every shafting can be obtained quickly.The test results show that the measurement results are intuitive and reliable.This classical test method is simple and easy to perform,and the data processing method can obtain the measurement results quickly and conveniently.