An integrated method for compensating and correcting nonlinear error in five-axis machining utilizing cutter contacting point data

Abstract

In current five-axis computer numerical control (CNC) machining, the use of minute linear path segments as an approximation for the ideal cutter contacting (CC) point trajectory is still prevalent. However, introducing rotation axes leads to a deviation of the actual CC point trajectory from the ideal, resulting in nonlinear errors. An integrated method is proposed in this paper for compensating and correcting both the contour error, associated with the approximation of the part surface by the ideal CC point trajectory and the nonlinear error of the CC point trajectory based on the information in the CC point data. By analyzing the spatial relationship between the tool posture and the CC point path during the five-axis linear interpolation process, two adjacent machining tool positions containing CC point data information are selected as the starting and ending points of the five-axis linear interpolation machining. The ideal tool center point and the actual CC point are calculated during the interpolation process, as well as the distance and the unit vector in the perpendicular direction between the actual CC point and the ideal CC point trajectory segment. In the comprehensive error compensation and correction phase, the obtained unit vectors are used as direction vectors for error compensation, and the tool center point during interpolation is first compensated and corrected. This ensures the actual CC point and the contour curve are on the same plane. The compensation direction for contour error is calculated using the start/end tool axis vectors and the ideal CC point trajectory vectors. The size of the contour error approximating the contour curve is calculated through the chord error. A second compensation and correction are applied to the tool center point for interpolation, ultimately achieving comprehensive compensation and correction of nonlinear errors. The data calculations were conducted in the MATLAB environment using actual machining data. After compensation and correction, the contour error was reduced by 76%, the nonlinear error of the CC point trajectory decreased to below 0.88 μm, and the comprehensive nonlinear error of the CC point trajectory was reduced from 19 to 1.5 μm, a reduction of 93%. This demonstrates significant practical value in enhancing the accuracy of five-axis CNC machining. Through actual machining verification, after using the method described in this paper, the average surface roughness decreased from 1.133 to 0.220 μm, and the maximum surface roughness decreased from 6.667 to 1.240 μm. This significantly demonstrates that the compensation and correction method proposed in this paper can significantly improve the surface quality of machined parts.