基于公差带的二次连续贝塞尔曲线刀具轨迹平滑算法

G2 continuous Bezier trajectory generation algorithm based on specified tolerance band

为提高加工路径的光滑性和精度,在分析现有样条拟合方法不足的基础上,提出了一种基于公差带的G2连续Bézier刀具轨迹平滑算法。该算法根据双弓高误差限制,从由离散小线段构成的加工路径中识别出连续微小线段加工区域。对于连续微小线段加工区域,首先,对离散的指令点进行局部插值,将折线加工路径转化为G1连续的二次有理Bézier曲线;然后,调整相邻两条二次有理Bézier曲线的权值和连接点处的切线方向,使加工路径达到G2连续性;最后,通过建立公差带将不满足精度要求的二次有理Bézier曲线进行重构。实验结果表明:该算法实时性好,生成的加工轨迹满足G2连续性和精度要求,实现了在线轨迹平滑处理,有效提高了加工效率。

In order to improve the smoothness and precision of machining paths,a G2 continuous Bezier trajectory generation algorithm based on specified tolerance band was proposed.According to the double-chord error limit,the regions comprised of continuous small-line segments were recognized.For these continuous regions,first,small-line segments were locally interpolated into G1 quadratic rational Bezier curves.second,the G2 continuous trajectories were obtained by scaling the weights of every two adjacent curves and adjusting the tangent direction at the joint point.Finally,the undesired curves were detected and corresponding adjustments were conducted in the specofoed tolerance band.Experimental results reveal that the proposed algorithm is real-time well and can realize online trajectory smoothing.The synthetic trajectories satisfy the G2 continuity and contour error limit strictly,which can improve the machining efficiency greatly.