Abstract: A kind of adaptive measuring method for free-form surfaces was put forward based on double parameter directions of CMM. At first, a measurable area was generated by boundary points of the surfaces. Then, a few uniform initial scan lines and uniform initial measuring points of each line topology were automatically generated by the measurable area. A B-spline curves were generated by fitting the initial points that automatically measured by the CMM in the U parameter direction and the locations of next point were adaptively predicted by the end curve curvatures. A B-spline surface was fitted by the initial scan lines point cloud, then the next line positions were adaptively determined by the border maximum curvatures of the surfaces in the V parameter direction, and the scanning lines of U parameter direction were measured adaptively, until measurements were completed. Distribution density of the measuring points was determined by the curvature variation characteristics of the measured surfaces. The larger the curvature of the surfaces, the greater the distribution density of the measuring points and the smaller the curvatures of the surfaces, the smaller the distribution density of the measuring points, which guarantees the important feature points not leaking and avoid the data redundancy. The results of measurement experiments for theoretical curves and surfaces show that the measurement precision may reach μm level. The feasibility of the method was verified by an example of a part measurements.

Key words: free-form surface, coordinate measuring machine（CMM）, double parameter direction, adaptive measurement, fully automation

摘要： 提出一种基于三坐标测量机的双参数向自适应测量自由曲面方法。CMM手动测量被测曲面边界点后，连接点生成可测区域，由可测区域自动拓扑生成几条均布初始扫描线以及每条扫描线的均匀初始点，对于U向的各条扫描线，CMM在自动测完初始点后，不断拟合已测点为B样条曲线，由曲线末端曲率自适应预测下一测点并指导CMM自动测量。测完初始扫描线后拟合已测点云为B样条曲面，由曲面V向边界最大曲率自适应确定下一扫描线位置，并进行该条扫描线U向自适应测量，重复这一过程直至曲面测量完毕。测点可随被测曲面自身曲率变化特性而疏密分布，曲率变化大的重要特征区域分布密集，曲率变化小的非重要区域分布稀疏，既保证了重要特征点不会遗漏又避免了数据冗余。理论曲线曲面自适应测量实验结果表明该方法测量精度可达微米级，实例零件应用验证了该方法的可行性。

关键词: 自由曲面, 三坐标测量机, 双参数向, 自适应测量, 全自动