基于三轴测量机拓扑结构的单项几何误差模型

基于刚体模型和小角度假设，传统的几何误差模型采用传递矩阵建立几何误差与测量机空间误差的关系。但通过传递矩阵建立的几何误差模型难以清晰揭示各单项几何误差对空间误差的影响关系。为了更清楚地表达单项几何误差对空间误差的影响关系，基于三轴测量机拓扑结构建立了各单项几何误差模型，分析了测量机各项阿贝误差产生机制。利用所建立的单项几何误差模型分析各单项几何误差的影响权重，对自研测量机高权重几何误差进行辨识与补偿，结果表明，补偿后测量机测量直径150 mm平面与直径60 mm凹球面的PV值分别达到344.32 nm和161.74 nm，面形误差与波面干涉仪测量结果基本一致。单项几何误差模型有助于了解阿贝误差的产生机理；提出的几何误差权重计算方法有助于实现对测量机敏感误差的精确控制，指导高精度测量机结构设计与测量精度的提升。

Single Geometric Error Model of 3-axis Measurement Machine Based on Topological Structure

Based on the rigid body model and small angle assumption, the traditional geometric error model uses a homogeneous transfer matrix (HTM) to establish the volumetric error of a machine tool. Each geometric error will produce a corresponding volumetric error at the corresponding position, but the HTM ignores the influence mechanism of each geometric error on the volumetric error. In order to clearly express the influence mechanism and include more synthesis position variables, a single geometric error model based on the topological sturcture of machine was established. Special emphasis is placed on the relationship between the anglur error and Abbe error. The effect ratio is analysed using the single geometric error model, the large-ratio geometric error is measured and compensated. The results show that the accuracy of the measurement machine is improved by the compensating. The flat accuracy of φ150 mm is measured at 344.32 nm, and the concave accuracy of f60 mm is measured at 161.74 nm. The surface maps measured by the coordinate machine are similar to the surface maps measured by interferometer. The establishment process of the proposed error model was simple, which was helpful for understanding the influence mechanism of the angulr error on the Abbe error. The methods presented herin can be applied to design machine tools and improve the accuracy of measurement machine.