对数曲线轮廓度误差几何遍历搜索评定算法

摘要

结合平面曲线轮廓度误差评定的最小条件原则及对数曲线的几何特性,提出了基于几何遍历搜索的对数曲线轮廓度误差评定算法.首先,采用最小二乘法得到最小二乘对数曲线和最小二乘误差;其次,在最小二乘对数曲线上选取两个特征点作为参考点,并在并在参考点周围按一定规则布置一系列的辅助点;然后,以两个特征点周围的辅助点两两结合构造出一系列的辅助对数曲线,并计算所有测量点到辅助对数曲线的距离极差值;通过比较和判断,最终实现对数曲线轮廓度的最小区域评定.列出了该评定技术的详细原理和步骤,实例证明,与最小二乘法相比,该算法具有极高的评定精度,适用于一些误差精度要求较高的零件或设备的轮廓度误差评定.%According to the minimum condition principle of planar profile error evaluation and the geometric characteristics of logarithmic curve, an algorithm, which based on the geometric ergodicity search, for evaluating logarithmic curve profile error is proposed. Firstly, the least square logarithmic curve and the least square error can be obtained by the least square method. Then, two feature points in the least square logarithmic curve are chosen as the reference points, and around the reference points, a series of auxiliary points are arranged according to a certain rule. Next, based on two auxiliary points which are chosen from the auxiliary points around the two reference points, a series of auxiliary logarithmic curves can be constructed, and then, the range values between measurement points and each auxiliary logarithmic curve can be calculated. Through comparison and judgment, finally, the minimum zone evaluation of logarithmic curve profile can be realized. The principles and steps of the evaluation technology are described in detail. Example proves that the algorithm has a higher evaluation accuracy when compared with the least square method and can be applied to any profile error evaluation of parts or equipment which need higher accuracy.