基于C^(3)连续PH曲线的短线段拐角实时光顺算法

Real-time smoothing algorithm for short-line corners based on C^(3) continuous PH curve

为了实现连续短线段加工过程中机床各轴运动的跃度连续,基于PH曲线弧长可解析计算的特点,提出了C^(3)连续实时光顺算法。通过在相邻短线段间构造满足最大近似误差约束的对称PH曲线,实现了直线段与PH曲线衔接点处C^(3)连续的平滑转接。同时采用五次多项式的柔性加减速曲线对光顺后的刀具路径进行速度规划与插补,保证了机床各轴运动的跃度连续。针对相同的刀具路径,通过仿真实验对两种拐角光顺算法进行对比分析,结果表明,所提算法相对于C^(2)连续光顺算法的跃度波动平均下降了44.3%,加工时间减少了4.6%,降低了机床的振动,提高了加工质量和效率,具有更平滑的跃度曲线。

To realize the jerk continuous of each axis movement in the process of continuous short line segments machining,based on the analytic calculation of PH curve arc length,the C^(3) continuous real-time smoothing algorithm was proposed.By constructing a symmetrical PH curve satisfying the maximum approximation error constraint between adjacent short line segments,the smooth transition of C^(3) at the junction point between straight line segment and PH curve was realized.At the same time,the flexible acceleration and deceleration curve of quintic polynomial was used to plan and interpolate the speed of the smoothed tool path,so as to ensure the continuous of the motion of each axis of the machine tool.For the same tool path,two corner smoothing algorithms were compared and analyzed through simulation experiments.The results showed that the jerk fluctuation of the proposed algorithm decreased by 44.3%on average compared with the C^(2) continuous smoothing algorithm,and the processing time decreased by 4.6%,which could reduce the vibration of machine tool and improve the machining quality and efficiency,had smoother jerk curve.