轴承滚子凸度轮廓的最小二乘拟合与误差评定

为了实现对轴承滚子凸度轮廓误差的精确评定,依据圆弧修正型轴承滚子凸度素线轮廓的几何特征和形状误差的定义,基于最小二乘原理,研究了轴承凸度轮廓(两段圆弧和一段直线)的最小二乘拟合和误差评定方法。首先利用各测量点的曲率差值确定了圆弧段与直线段的相切参考点;其次分别选取两个参考点临近的测量点作为辅助相切参考点,并与对应的圆弧段测量点一起拟合出一系列的最小二乘圆弧并计算拟合误差;然后基于直线与两段圆弧相切的原则确定出一系列的直线方程并计算对应的直线度误差;通过比较判断最终确定出圆弧修正型轴承滚子凸度轮廓的最小二乘拟合及误差评定。实例结果表明:圆弧修正型凸度轮廓曲线的总误差0.020 9mm与文中设定标准凸度轮廓曲线引入的法向误差0.02mm相差4.5%。本方法可以有效的实现轴承凸度轮廓的拟合与误差评定,为平面多段曲线的最小二乘拟合提供了一种新的思路。

Least square fitting and error evaluation of the convex contour of bearing roller

In this investigation, we attempted to accurately evaluate the profile error of the bearing roller convexity, based on the definition of geometric characteristics and shape error of the arc corrected roller convexity line of bearing. This approach involves the least square principle, the method of total least squares fitting, and error evaluation of the convexity contour of the bearing roller. Firstly, the tangent reference points of the arc segment and the straight line are determined by the curvature difference of each measurement point. Secondly, the measurement points on both sides of the two reference points were selected as auxiliary tangent reference points, and a series of least squares arcs were fitted together with the corresponding circular arc measurement points, and the fitting errors were calculated. Then a series of linear equations were determined, and the corresponding straightness error was calculated using the tangent between the straight line and the two segment arcs. The least square fitting and error evaluation of the roller convexity contour of the circular arc modified roller is determined by comparison. The results of the investigated scenario indicate that the total error of the arc modified convex contour curve is 0.020 9, which is 4.5% less than the normal error of 0.02 that is introduced by the standard convex contour curve. This method can effectively evaluate the fitting and error of the convexity contour of the bearing roller and represents a new approach for least squares fitting of planar multi-section curves.