临界曲率值分割曲线尖角的NURBS曲线插补

为兼顾插补含尖角NURBS曲线的精度与速度，提出尖角分割且速度修正插补算法。由插补弦高误差限、法向加速度及其导数约束，得满足插补精度及机床动力学性能的临界曲率；用大于临界曲率的局部极大曲率及临界曲率分割NURBS曲线为是否包含尖角的若干子段；用S曲线加减速算法规划各子段进给速度，并用段间速度及位移协调关系修正各段加速度及其导数，使各段加减速时间为整数倍插补周期。在相同约束条件下，分别用曲率单调无速度修正、尖角分割无速度修正及尖角分割有速度修正算法，规划一条含大曲率尖角NURBS曲线插补速度，并用一阶泰勒级数展开算法插补该曲线。对比结果表明尖角分割且有速度修正算法可稳定得到较高插补精度，因此该算法可用于含大曲率尖角NURBS曲线高速度高精度加工。

Interpolation for NURBS Curve with Corner on Curve Splitting According to its Critical Curvature

Considering feedrate and precision requirements for contouring NURBS curve characterizing large curvature corner, the interpolation algorithm by corner splitting with modifying means is proposed. Critical curvature of NURBS meeting both interpolation precision and dynamical properties of the CNC tools is defined according to chord height limit, centripetal acceleration and its derivative limits. In terms of the local maximal curvature greater than critical curvature and critical curvature of the NURBS curve, the whole NURBS curve is split into several sub-segments including sharp corner or not. For each sub-segments the feedrate are planned with S curve acc/dec, and then conforming to the compatibility relationship of feedrate and displacement between two adjacent ones, the acceleration and its derivative of each sub-segments are adjusted to ensure the integer multiple ac/dec duration to sampling time for each acc/dec phases. Under the same feed planning constraints. The feed for processing a piece of NURBS curve with large local curvature corner is planned on curvature monotonicity without modifying measure:Corner splitting without modifying method and corner splitting with modifying means. Then it is interpolated with first Taylor series expansion respectively. The comparison results indicate higher interpolation precision can be ensured by corner splitting with modifying means stably. So the proposed algorithm can be applied in high speed and high precision machining NURBS curve with large curvature corner.