A curvature optimal sharp corner smoothing algorithm for high-speed feed motion generation of NC systems along linear tool paths

Conventional tool paths for computer numerical-controlled (CNC) machine tools or NC positioning systems are mainly composed of linear motion segments, or the so-called G1 commands. This approach exhibits serious limitations in terms of achieving the desired part of geometry and productivity in high-speed machining. Velocity and acceleration discontinuities occur at the junction points of consecutive segments. In order to generate smooth and continuous feed motion, a geometric corner smoothing algorithm is proposed in this paper, which fits quintic B-splines to blend adjacent straight lines together. The proposed transition scheme ensures G(2) continuity transitions and optimal curvature geometry delivering fast cycle time without violating the axis acceleration limits. The cornering error is controlled analytically allowing the user to set the desired cornering tolerance. The feed profile along the corner-blended tool path is generated based on S-curve-type acceleration profile, and it is scheduled for minimum cycle time. At last, the corner-blended tool path is interpolated in real-time with minimum feed fluctuation for accurate and smooth feed motion. Proposed algorithms are implemented, and their effectiveness is tested on a CNC machine tool.