多段圆弧曲线轮廓测点划分与拟合研究  

Research on Segmenting and Fitting Measured Points to Multi-Segment Circular Arcs

作　　者：姚松臣 赵凤霞[1] 赵晨[1] 张琳娜[1] YAO Song-chen;ZHAO Feng-xia;ZHAO Chen;ZHANG Lin-na(School of Mechanical and Power Engineering,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学机械与动力工程学院,郑州450001

出　　处：《组合机床与自动化加工技术》2023年第4期160-164,共5页Modular Machine Tool & Automatic Manufacturing Technique

基　　金：国家重点研发计划项目(2017YFF0206501-01)。

摘　　要：针对检测和拟合多段圆弧曲线中存在的测点划分不精确和整体拟合轮廓不平滑等问题,提出了一种B样条迭代平滑算法和一种基于曲率和最小二乘原理的分割拟合方法。首先,采用B样条迭代法对原始测点进行平滑处理,并生成相应的辅助点;其次,采用三点圆曲率分析法计算辅助点的曲率,然后对辅助测点曲率集进行均值匹配得到初始分割点;最后,通过构建分割临界区域,并采用带几何约束的最小二乘拟合法实现多段圆弧曲线轮廓测点的最优分割与平滑拟合。对某四圆弧凸轮进行仿真案例分析,在噪声水平s=0.01 mm,s=0.03 mm,s=0.05 mm下,最大相对拟合偏差分别为0.645%、2.237%、3.243%;实验结果表明,该方法能够准确找到圆弧段间的分割点,并保证整体拟合轮廓的光顺性。Aiming at the problems of inaccurate division of measured points and unsmooth of overall fitted profile in multi-segment circular arcs detection and fitting.A B-spline iterative smoothing method and a segmentation fitting method based on curvature and least-squares principle are proposed.Firstly,B-spline iterative method is used to smooth the original measured points and generate corresponding auxiliary points.After which three-point circular curvature analysis method is used to calculate the curvature of auxiliary points.Then,the initial segmentation points could be obtained by performing mean-matching on the curvature set of auxiliary points.Finally,the least-squares fitting method with geometric constraints is used to achieve the smooth fitting of multi-segment circular arcs,and the construction of segmentation critical region further supports the optimal segmentation of measured points.A simulation case study of a four-circular arc cam is performed,the maximum relative fitting deviations at noise level s=0.01 mm,s=0.03 mm,s=0.05 mm are 0.645%,2.237%,3.243%respectively;Experiment results show that the proposed approach can accurately find the segmentation points between circular arcs and guarantee the smoothness of the overall fitted profile.

关 键 词：多段圆弧曲线 B样条迭代 三点圆曲率分析 约束最小二乘拟合 

分 类 号：TH161[机械工程—机械制造及自动化] TG68[金属学及工艺—金属切削加工及机床]