基于圆心约束最小二乘圆拟合的短圆弧测量

摘要

坐标测量中通常采用最小二乘法拟合几何元素.测量短圆弧时,由于特征点数少,受到的噪声干扰大,测量精度难以满足测量要求.本文针对短圆弧测量,分析了采用最小二乘法多点测圆时,圆弧中心角对圆心及半径测量误差的影响;考虑到短圆弧的功能特性和加工工艺往往将圆心作为固定值,在最小二乘圆拟合的基础上,提出了圆心约束最小二乘圆拟合方法.利用提出的方法测量了理论半径为10 mm,中心角为20°的短圆弧,测量误差＜0.01 mm.对比实验表明,利用圆心约束最小二乘圆拟合法测量短圆弧能有效提高拟合精度.提出的方法基于机器视觉检测系统,能对工件做在线非接触测量.与传统的短圆弧测量方法相比,具有精度高、速度快、测量范围广等优势.%The least-square method is usually adopted for fitting of geometric elements in a coordinate measurement.However,in the process of short arc measurement,it is difficult to offer a high precision due to the lack of feature points and the influence of noise jamming.Aimed at the measurement of short arc,this paper analyzes the influence of central angles on measurement errors of circle centre and radius by using the least-square method.Based on the fact that the circle center of the short arc is often set in a fixed position due to its functional property and processing technology,a centre constraint least-square circle fitting method is proposed in the study,It is proved that the measurement error is less than 0.01 mm by using the proposed method to measure a short arc with a central angle of 20° and a radius of 10 mm.A comparative experiment shows that the centre constraint least-square method can improve the accuracy of circle fitting efficiently in the short arc measurement.As the proposed method is based on machine vision system,it has advantages of high accuracy,fast speed,wide measuring ranges and on-line and non-contact measurement as compared with traditional measurement methods of short arc.