评定平面度误差的几何搜索逼近算法

Geometry searching approximation algorithm for flatness error evaluation

为了快速准确地评定机械零件的平面度误差,提出了基于几何搜索逼近的平面度误差最小区域评定算法。阐述了利用几何优化搜索算法求解平面度误差的过程和步骤,给出了数学计算公式。首先选择被测平面的3个边缘点为参考点构造辅助点、参考平面和辅助平面,然后以参考平面和辅助平面为假定理想平面,计算测量点至这些理想平面的距离极差;通过比较判断及改变参考点,构造新的辅助点、参考平面和辅助平面,最终实现平面度误差的最小区域评定。用提出的方法对一组测量数据进行了处理。结果表明,在终止搜索的条件为0.000 01mm时,几何搜索逼近评定算法的结果分别比凸包法、计算几何法、最小二乘法、遗传算法和进化策略计算的结果减小了17.1、7.3、18.03、6.13和0.3μm。得到的数据显示该算法不仅能准确地得到最小区域解,而且计算结果有良好的稳定性,适合在平面度误差测量仪器和三坐标测量机上使用。

To evaluate the flatness errors of mechanical parts accurately and rapidly,an algorithm using geometry searching approximation to evaluate the flatness error minimum zone was presented.The principle and steps of the algorithm to solve the flatness error was described in detail and the mathematical formulas were given.First,the three edge points of the measured plane were selected as reference points,and the auxiliary points,reference plane and auxiliary planes were constructed based on the reference points.Then,the distance differences of all measurement points to the supposed ideal planes were calculated by taking the reference plane and auxiliary planes as supposed ideal planes.The reference points,auxiliary points,reference plane and auxiliary planes were reconstructed by comparing the distance differences.Finally,by repeating this processes,the minimum zone evaluation for flatness error was implemented.The method was used to process a group of metrical data,and the results indicate that the flatness error value from this algorithm can be reduced by 17.1,7.3,18.03,6.13 and 0.3 μm respectively as compared with those from the convex hull method,computational geometric method,least square method,genetic algorithm and the evolutionary strategy when the criteria of stop searching is 0.000 01 mm,The results demonstrate that the algorithm can get not only the minimum zone solution accurately but also has good stability.It is suited for the evaluation of flatness error measuring instruments and Coordinate Measuring Machines（CMMs）.