Modeling and compensation of volumetric errors for five-axis machine tools

• Error motion twists are introduced to model geometric errors.
• Volumetric error model is developed by using screw theory.
• 20 Geometric errors of rotary axes are identified and decoupled simultaneously.
• Compensation strategy for 41 volumetric errors is proposed and verified in detail.

This article proposes a method to measure, model and compensate both geometrically dependent and independent volumetric errors of five-axis, serial CNC machine tools. The forward and inverse kinematics of the machine tool are modeled using the screw theory, and the 41 errors of all 5 axes are represented by error motion twists. The component errors of translational drives have been measured with a laser interferometer, and the errors of two rotary drives have been identified with ballbar measurements. The complete volumetric error model of a five-axis machine has been modeled in the machine's coordinate system and proven experimentally. The volumetric errors are mapped to the part coordinates along the tool path, and compensated using the kinematic model of the machine. The compensation strategy has been demonstrated on a five-axis machine tool controlled by an industrial CNC with a limited freedom, as well as by a Virtual CNC which allows the incorporation of compensating all 41 errors.