Abstract: For evaluation geometry error problem with discrete sampling points,a evaluation method was proposed based on deviation vector of geometric features.The reference coordinate system was constructed according to the feature type of geometry errors.By using geometry tolerance definition,the actual deviation vectors of functional geometry was achieved,and the mathematical model of deviation area was constructed by combining with reference coordinate system.3D convex hull of discrete sampling points was set up with convex hull theory,an incremental algorithm in computational geometry theory.The evaluation mathematical model of geometry error was established by using constrained freedom and convex hull.The software modules were developed based on above model.The experiment result proved that the proposed algorithm could ensure the accuracy of datum plane and meet the engineering requirement compared with the least square method.

Key words: geometric error, fitting, computational geometry, deviation vector, coordinate measuring machining

摘要： 针对利用三坐标测量机离散采样点进行几何误差评定的问题,提出一种基于几何特征变动向量的几何误差评定方法。根据几何误差关联的几何特征类型建立基准坐标系;利用几何公差的定义完成功能几何实际变动向量的求解,并在此基础上与基准坐标系相结合构造功能几何变动区域的数学模型;利用计算几何中的凸包理论,建立功能几何关联离散采样点的三维凸包,并将凸包顶点与变动区域数学模型结合建立误差评定数学模型。基于上述模型和算法开发了几何误差评定软件模块,并进行了实例验证。实验结果表明：当采用同一组采样数据对几何误差进行评定时,与传统算法相比,所提算法更加符合几何公差的定义,能够保证误差评定的准确性,满足工程需求。

关键词: 几何误差, 拟合, 计算几何, 变动向量, 三坐标测量机