A five-axis tool path is often composed of a linear path that has a tangential discontinuity so that the tangential velocity will be abrupt or be equal to zero at the corner of the adjacent segments. Therefore, it greatly affects the machining efficiency and quality. Thus, a corner smoothing transition algorithm based on double cubic NURBS, which is curvature-continuous and satisfies the given accuracy constraint, is proposed to smooth the local corner at the adjacent five-axis linear path. On the basis of the smoothing transition model, the parametric synchronization between the smoothed double NURBS trajectories and the remaining two linear segments are respectively constructed to realize the smoothing variation along the tool tip translational trajectory and tool axis rotational trajectory. The simulation and examples show that the proposed transition algorithm can satisfy the error constraints, reduce the feedrate fluctuation, and improve the machining quality. Keywords: five-axis machining, corner transition, double NURBS curves, tool path Highlights • A corner smoothing transition algorithm based on double cubic NURBS is proposed to smooth the five-axis linear tool path. • The proposed algorithm is curvature-continuous and satisfies the given accuracy constraint. • The approximation error has an analytical relationship with the transition length of the smoothed curve. • The synchronization method can guarantee tool-tip translation and tool axis rotation with continuous and smooth variation. • The proposed method has been validated with simulations and experimental results.
Aiming at the problem of acceleration and jerk fluctuation caused by the discontinuity at the corner of the tool path in the continuous short-line machining process, a real-time corner smoothing and interpolation algorithm for realizing the continuous motion of the tool axis jerk is proposed. In the corner smoothing process, the C3 continuity of tool path is realized by constructing a symmetrical PH transition curve satisfying the maximum approximation error constraint between adjacent short lines. In the interpolation process, based on the flexible acceleration and deceleration control method, the feed rate, chord error, acceleration, and jerk constraints are considered. For the smooth C3 continuous path, the acceleration and deceleration profile with jerk-continuous is used for velocity planning and interpolation, and the continuous motion of the tool axis jerk is realized. In this paper, the proposed method is compared and analyzed with the C2 continuous algorithm and the traditional point-to-point interpolation algorithm through simulation and experiment for the same tool path. The results show that the jerk fluctuation of the proposed algorithm is reduced by 60.36% on average compared with the C2 continuous algorithm, and the processing time is reduced by 19.5% compared with the point-to-point interpolation algorithm. It proves that the proposed algorithm can effectively reduce the vibration of the machine tool and improve the processing efficiency.
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