数控系统切割中拐角NURBS插补处理算法

NURBS Interpolation Algorithm for Corner Cutting in CNC System

针对目前复杂零件的高速、高精加工需求,提出一种拐角处NURBS样条处理方法。算法可在满足轮廓加工精度的前提下,将拐角处的尖角用NURBS样条插补出来。该方法通过对基函数求一二阶导,计算曲线曲率,确定拐点位置,根据弓高误差计算拐点处能达到的最大速度。插补时,结合速度规划,根据一阶泰勒展开反算插补点,代入样条解析式求出插补坐标,完成拐角处NURBS轨迹插补。与原始轨迹相比,该算法在拐角处速度大于原始轨迹速度,由速度曲线可看出能更快完成切割任务。由插补结果来看,采用该方法后,轨迹在精度范围内,且能够保证原始轨迹形态。所以该方法在保证精度和速度连续的前提下,可有效提高切割速度,提高加工效率。

Aiming at the high speed and high precision machining requirements of complex parts, a corner NURBS spline processing method is proposed. The algorithm can interpolate the sharp corners with NURBS splines, which is satisfying the accuracy of contour machining. By calculating the first and second derivatives of the basis function, the curvature of the curve is calculated, the position of inflection point can be determined, then the maximum velocity can be reached at the inflection point is calculated according to the error of the bow height. During the interpolation process, the interpolation points are calculated in reverse according to the first-order Taylor expansion, and the interpolation coordinates can be obtained by substituting the analytical expression of splines to complete the NURBS interpolation of the corner. Compared with the original trajectory, the speed of the algorithm at the corner is greater than the original speed, and it can be seen from the velocity curve that the algorithm can complete the cutting task faster. According to the interpolation results, the trajectory is within the precision range and can guarantee the original trajectory shape. Therefore, this method can effectively improve the cutting speed and machining efficiency on the premise of ensuring the accuracy and speed continuity.