Geometric Error Modeling for CNC Machine Tools Using Differential Transformation

In this paper, a geometric error modeling method for five-axis CNC machine tools based on differential transformation method is proposed. Firstly, the machine geometry error model is established based on the coordinate system differential variation matrix. Secondly, based on the forward kinematic chain sequence of the machine tool, the differential change matrix of each motion axis is established, and the influence of the geometric error of the motion axis on the tool accuracy is calculated by combining the differential motion vector corresponding to the geometric error of each motion axis. The sum of the differential matrices in the tool coordinates is obtained by adding. Thirdly, the machine tool position error is obtained by converting the tool comprehensive error to the table coordinate system through the machine forward kinematics model. Finally, the spatial comprehensive error model of the rotating shaft of the five-axis CNC machine tool is obtained, which provides a theoretical basis for machine tool design and compensation.