截面最小二乘圆心位置的余弦回归提取法

截面最小二乘圆心在绝对坐标系内的位置是影响圆柱度形状误差大小的重要因素。合理确定其位置,是圆柱度形状误差重构的基础。从分离出的回转误差运动中有效地提取截面最小二乘圆心的偏心误差运动,目前还没有合适的方法。基于纯回转误差运动中一阶谐波分量仅影响重构出的圆柱体在绝对坐标系内的位置,不影响圆柱度误差的大小。提出了一种提取截面二乘圆心运动(圆柱度重构基准)的方法———余弦回归提取法,即采用分离出的回转误差运动中的一阶谐波分量来代替偏心误差运动。结果表明:该方法提取的最小二乘圆心在绝对坐标系内具有良好的复现性,从而有效地解决了圆柱度测量中重构基准难以确定的问题。

Cosine Regression Purifying Method to Determine Positions of Least Square Centers in Different Cross Sections

The position of the least square center for a cross section in the absolute coordinate system is an important factor that affects cylindrical form errors.To determine this position is the basis on which cylindrical form errors can be retraced.At present,there is no efficient way to retrace the eccentric error motion of the center from the separated revolved error motion.Since one-order harmonic component of pure rotation error motion only affects the position of reconstructed cylinder in the absolute coordinate systems and does not affect the value of cylindricity,a new method,named cosine regression purifying,to take the least square centers motion(i.e.cylindricity reconstruction datum) out of rotary error motion is presented.That is,the eccentric error motion is replaced by the one-order harmonic component of the rotation error motion.The test result indicates that the position of the least square centers purified by this method has good repeatability in the absolute coordinate systems.The reconstruction datum in the cylindricity measurement can be easily determined by means of this method.