Six-dimensional B-spline fitting method for five-axis tool paths

Abstract

Piecewise linear segments (presented by a sequence of G01 G-Codes) are the widely adopted tool path format for five-axis computer numerical control (CNC) machining. Nevertheless, the G01 tool path has only G0 continuity, which may lead to feedrate and acceleration fluctuation, and produce machinery vibration and unexpected slowdowns during the process. Thus, tool path smoothing method such as B-spline fitting is developed to increase the continuity of the tool paths. This work proposes a six-dimensional B-spline fitting method with arc-length parameterization and quality evaluation/refinement for five-axis tool paths. First, establish the relationship of cutter contact (CC) error, and cutter location (CL) error and tool-axis error to ensure that the CC error of five-axis B-spline tool path can be accurately computed. Second, six-dimensional B-spline tool paths generated by three-axis B-spline fitting method in six-dimensional space are parameterized with arc-length, satisfying the stability condition of tool axis. Third, the chord errors of the fitted six-dimensional B-spline tool paths are computed using the Hausdorff distance. The chord error computation, smoothness assessment, and refinement algorithm are performed together to ensure the fitting quality. The simulation result demonstrates that the proposed six-dimensional fitting method is effective and suitable for five-axis blade machining, and the evaluation/refinement algorithm can ensure that the five-axis B-spline tool paths are shape-preserving strictly and satisfy the chord error constraint. The experimental results show that the proposed six-dimensional fitting method improves the machining quality and is suitable for industrial applications.