Linear Tool Path-Smoothing Method in High-Speed Machining Based on Error Feasible Area and Curvature Optimization

Abstract

Linear tool path is widely used in high-speed NC machining. However, the geometrical discontinuity of the corner between the linear tool paths will lead to fluctuations in speed, acceleration and jerk, which can excite machinery vibration and reduce the machining efficiency and surface quality. To solve these problems, a novel corner smoothing method based on error feasible area and curvature optimization is proposed in this paper. Compared with most traditional corner smoothing methods using higher-order curves with all control points lying in the straight segment and inside of the tool path, the proposed method constructs B-spline transition curves with smaller curvatures to smooth the corners by reasonably distributing the curve control points inside and outside the straight line segment of the tool path (i.e., error feasible area). Furthermore, the corner transition curve is optimized by the minimum curve curvature extreme to improve the smoothness of the corner transition curve and reduce fluctuation in the kinematic profiles while respecting the G3 continuity (i.e., curvature-smooth), transition length limits and the uniqueness of curvature extremum. Finally, the simulation results show that the proposed method can reduce the curvature value and improve the smoothness of the curve and the minimum transitional velocity of the corner, which means that it can enhance machining efficiency and weaken machining vibration. The feasibility and effectiveness of the method are also verified.