Traditionally, a machine tool is regarded as a rigid-multi body system, and it is studied by integrated geometric error modeling. Considering a three axis-machine, this study introduced the ratio and effects of the geometric errors on the surface figure error. First, based on synchronous iteration location, a surface matching model was employed to assess the coordinate measurement result. Subsequently, considering all the geometric error functions having the same parameters, the effect ratio and the surface figure error of a single geometric error were obtained. Concurrently, based on the effect ratio and surface figure error results, the main geometric errors were obtained, such as EZX, EZY, EAX, and COY. Moreover, the proposed method and the main errors were experimentally verified. By compensating the main errors, the sphere accuracy was improved by 53.4% and the flat accuracy by 70.0%. Additionally, the method proposed in this paper could be utilized to detect the surface figure error.

传统上，机床被视为多体刚体系统，并通过集成几何误差建模对其进行研究。考虑到三轴机床，本研究介绍了几何误差对表面图形误差的比率和影响。首先，基于同步迭代定位，使用表面匹配模型评估坐标测量结果。随后，考虑所有具有相同参数的几何误差函数，获得单个几何误差的影响比和表面图形误差。同时，根据影响比和表面图形误差结果，获得了主要的几何误差，例如EZX，EZY，EAX和COY。此外，通过实验验证了所提出的方法和主要误差。通过补偿主要误差，球体精度提高了53.4％，平面精度提高了70.0％。另外，本文提出的方法可用于检测表面图形误差。