摘要
针对圆度误差的特点,提出一种基于几何优化的圆度误差评定算法。建立直角坐标采样、可同时实现圆度误差的最小区域法、最小外接圆法和最大内接圆法评定的评定模型。详细阐述利用几何优化算法求解圆度误差的过程和步骤,给出数学计算公式及计算机程序流程图。该算法不要求等间隔测量,不采用最优化及线性化方法,也无需满足小误差和小偏差假设,只需重复调用点与点之间的距离公式;其原理是以初始参考点为基准,布置一定边长的正六边形,依次以各顶点为理想圆心计算所有测点的半径值,通过比较、判断及重复设置六边形来获得相应评定方法(最小区域圆法、最小外接圆法和最大内接圆法)的圆度误差值。试验结果表明,该算法可以有效、正确地评定圆度误差。
According to the characteristics of roundness error,a new algorithm of evaluating roundness error based on geometry optimization is presented.The measured circle sampling points in rectangular spatial coordinates and the minimum zone circle （MZC）,the minimum circumscribed circle （MCC） and the maximum inscribed circle（MIC） errors can be evaluated simultaneously in the error evaluating method.The principle and step of using the algorithm to solve the roundness error is described in detail and the mathematical formula and program flowchart are given.The optimization method and linearization method and uniform sampling are not adopted in the algorithm.This algorithm need not satisfy assumed small error or small deviation and only calls the formula of distance between point to point repeatedly.The principle of the algorithm is that a hexagon is collocated on the basis of the initial reference point,the radius value of all the measured points are calculated by regarding each vertex of the hexagon as the ideal center,the roundness error value of corresponding evaluation method （MZC,MCC and MIC） are obtained through comparison,judgment and repeated arrangement of hexagon.The experimental results show that the roundness error can be evaluated effectively and exactly by using this algorithm.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2010年第12期8-12,共5页
Journal of Mechanical Engineering
基金
国家自然科学基金(50875076)
河南省教育厅自然科学研究计划(2008A460007)资助项目
关键词
误差评定
几何优化
圆度误差
最小区域
最小外接圆
最大内接圆
Error evaluation Geometry optimization Roundness error Minimum zone Minimum circumscribed circle Maximum inscribed circle
