Universal geometric error modeling of the CNC machine tools based on the screw theory

The methods to improve the precision of the CNC (Computerized Numerical Control) machine tools can be classified into two categories: error prevention and error compensation. Error prevention is to improve the precision via high accuracy in manufacturing and assembly. Error compensation is to analyze the source errors that affect on the machining error, to establish the error model and to reach the ideal position and orientation by modifying the trajectory in real time. Error modeling is the key to compensation, so the error modeling method is of great significance. Many researchers have focused on this topic, and proposed many methods, but we can hardly describe the 6-dimensional configuration error of the machine tools. In this paper, the universal geometric error model of CNC machine tools is obtained utilizing screw theory. The 6-dimensional error vector is expressed with a twist, and the error vector transforms between different frames with the adjoint transformation matrix. This model can describe the overall position and orientation errors of the tool relative to the workpiece entirely. It provides the mathematic model for compensation, and also provides a guideline in the manufacture, assembly and precision synthesis of the machine tools.