圆度误差评定的曲率法研究

An Evaluation Method for the Roundness Error Based on Curvature

提出了基于曲率的圆度误差评定方法。从曲率的定义出发,推导出了用最大内接圆或最小外接圆评定圆度误差时筛选点的条件:用最大内接圆评定时,筛选掉曲率半径最小的点;用最小外接圆评定时,筛选掉曲率半径最大的点。根据这一条件,可以得到满足圆度误差评定原则的3个特征点,从而确定圆度误差。筛选点时,用最小二乘圆把测量点分成内点集合和外点集合,最大内接圆从内点集合中筛选,最小外接圆从外点集合中筛选,这样就可大大减少了计算量。经过实例验证,表明该方法的正确性和可行性。

A novel method for evaluation of the roundness error based on curvature is presented. The condition for choosing points is derived from the definition of the curvature in evaluating the roundness error with maximum inscribed circle or minimum circumscribed circle. The points with the least radius of curvature are eliminated with maximum inscribed circle, whereas the points with the largest radius of curvature are eliminated with minimum circumscribed circle. According to the above condition three points satisfying with the criterion for evaluation of the roundness error are discovered, so the roundness error is determined, The points are divided into outer points and inter points according to the least square mean circle in order to reduce the amount of computation. The points are eliminated from internal points for maximum inscribed circle, but for minimum circumscribed the points are chosen from external points. The correctness and the feasibility of the method are proved through an example.