基于轨迹参数法的轴系倾角回转误差测试与分析

Measurement and Analysis of Axis Rotation Error Based on the Track Parameters Method

为了满足非完整周旋转轴系倾角回转误差测试分析需求,在数学建模轨迹分析基础上研究了一种新的轴系倾角回转误差测试分析方法。首先,采用四元数方法对测试中平面镜和准直仪安装误差数学建模,证明了两者安装误差引起待测轴转动过程中准直仪靶面光十字丝轨迹为椭圆,当误差为小量时轨迹退化为圆心不在原点的圆。然后,基于最小二乘原理建立了轨迹圆参数圆心和半径拟合方法,在测试数据中去除平面镜和准直仪安装误差的影响。最后,分别开展了仿真分析与实验测试对方法的有效性和可靠性进行了验证。结果表明:轨迹参数法在非完整周旋转轴系倾角回转误差测试中具有独特优势,可以作为传统傅里叶级数法有益补充,且该方法无需精调平面镜,在一定程度上提高了测试分析效率。

In order to meet the test and analysis requirements of axis rotation error for the axis that cannot rotate complete circle,a new method is researched on the basis of the mathematical modeling track analysis.At first,the measurement error model caused by the pose errors of plane mirror and collimator for axis rotation error test is derived by using the quaternion method.The pose errors of plane mirror and collimator will cause an ellipse track on the collimator screen,while the ellipse will degenerate into a standard circle when the errors are small.Then,the fitting method of track parameters,including the center and radius,is established based on the least square principle to remove the influences of the pose errors on the test results.Finally,the effectiveness of the method proposed in this paper is verified by simulations and experiments.The experimental results indicate that the track parameters method has obvious advantages in the axis rotation error test for the axes that cannot rotate a complete circle and it can be used as a powerful supplement to the traditional Fourier series method.Besides the method needs not to fine adjust the plane mirror and collimator in the test,increasing the test and analysis efficiency.