中文摘要：

针对目前NURBS曲线插补中加减速控制方法不足的问题,实现了加工过程中进给速度的平滑过渡,提出了一种新的NURBS曲线插补方法,包括速度规划和实时插补两个方面。速度规划采用了一种基于曲率自适应的简化计算的S型加减速方法,并结合“双向插补”的思想实时预测减速点,防止产生过大的弓高误差;实时插补则利用Muller插值和Newton迭代法计算了下一周期的插补参数,进而求出了下一时刻到达的空间坐标点。最后与已有插补方法进行了仿真分析比较。研究结果表明,该方法能保证加速度连续和加加速度有界,有效减少弓高误差和进给速度波动,提高机床运行的平稳性。

英文摘要：

Aiming at the deficiency of acceleration and deceleration control method in NURBS curve interpolation, and to realize the smooth transition of feedrate during the manufacturing process, a new method of NURBS interpolation was proposed, including feedrate planning and real time interpolation. In feedrate planning, a new simplified calculation method of s-shaped acceleration and deceleration based on curvature adaptive algorithm was adopted, and to prevent excessive chord error, the idea of bidirectional interpolation to predict the deceleration point in real time was also used. In real time interpolation, Muller interpolation method and Newton iterative method were utilized to calculate the interpolation parameter of the next period, and the space coordinates of the next period was given as well. Finally, the algorithm was compared with the existing interpolation methods for simulation analysis. The results indicate that this method can guarantee the continuity of acceleration and the boundedness of jerk, effectively reduce the chord error and feedrate fluctuation, and improve the stability of machine tool operation.