Abstract: 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.

Key words: geometric error, Abbe error, coordinate measurement machine, error sensitive, measurement accuracy