面向零件平面度误差估计的空间泛克里金插值建模  

Flatness Error Estimation based on Universal Kriging Interpolation Method

作　　者：费兰[1] 杜世昌[1] 

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《机械工程学报》2014年第15期127-135,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51275558;50905114);上海市青年科技启明星计划(13QA1402100);上海航天基金(12GFZ-JJ08-011)资助项目

摘　　要：机械加工零件表面平面度误差估计是零件质量控制的重要内容。三坐标测量机（Coordinate measuring machine．CMM）广泛应用于零件表面平面度误差测量，但是由于测量成本的限制，CMM获取的测量样本数量有限。因此需要采用空间插值方法，获取更准确的平面度误差估计。通过建立空间统计学的变异函数模型描述零件表面测量数据之间的空间相关性，并推导空间泛克里金插值方法预测零件表面未测量点的坐标高度值，最终将实际测量点和插值预测点通过最小二乘法建立平面度误差预测估计模型。实例研究的结果表明，球状变异函数模型较指数、高斯变异函数能够更有效地定量描述零件表面的空间相关性；同时，泛克里金插值方法提高平面度误差估计的准确程度，其估计精度优于传统方法5％～10％。The flatness error estimation under given machining conditions is an essential step in the assessment of product surface quality generated in machining processes. Coordinate measuring machine （CMM） is widely used to measure complicated surface flatness error. However, considering measurement cost, only a few measurement points are collected by CMM for a part surface. Therefore, spatial statistics method is adopted to achieve more interpolated points for more accurate form error estimation. The spatial correlation on part surface is characterized by appropriate variogram. By taking the spatial correlation into consideration, the universal Kriging （UK） method is derived to predict the height value of unmeasured points. Ultimately flatness error estimation model is established by the least square method. Through analyzing the case, it concludes that spherical variogram can effectively describe the spatial correlation on part surface and the Universal Kriging method could improve the accuracy of flatness error estimation 5%-10%over traditional method.

关 键 词：泛克里金方法 变异函数模型 平面度误差 空间相关性 

分 类 号：TG156[金属学及工艺—热处理]