An analytical local tool path smoothing method with curvature control

In traditional multi-axis machining, the linear tool path generated by computer-aided manufacturing systems is still in a broad tool path format, resulting in discontinuities at the corners, which slow down tool motion, and also trigger tool vibration, reducing machining accuracy and surface quality. In order to ensure the C³ continuity of the tool during the multi-axis machining process, this paper proposes an analytical B-spline local smoothing method with curvature control. The tool position trajectory and tool orientation are both smoothed by a 5th spline curve with 9 control points. Optimal control points are determined for position and orientation splines to achieve C³ continuity at the junctions between the spline and linear segment while preserving the predefined geometric tolerance limits and minimizing the maximum curvature of the inserted B-spline curve. The smoothed tool path is expected to have less curvature fluctuation, which can significantly improve both the kinematic performance of the machine tool and the machining efficiency. Both computer simulations and physical printing experiments are carried out to demonstrate the improvements of our proposed method in motion smoothness and tracking accuracy in multi-axis machining tasks.