NURBS曲线敏感点速度平滑插补算法研究

摘要

NURBS插补相对于传统直线和圆弧插补具有极大优势,但其存在敏感点区域插补速度波动剧烈而引起超出机床加工运动能力范围的问题.为了提高NURBS曲线插补运动学性能,改善其加速度和加加速度轨迹突变问题,提出一种NURBS曲线几何特性的敏感点区域速度平滑的插补算法.其通过搜索G1或G2不连续的断点和具有大曲率的关键点,在这些敏感点处分别利用FIR级联滤波器进行S型加速度的平滑速度规划,而后采用断点处速度近似调整的方法,来对其运动学特性进一步改善.仿真和实验结果表明,该算法在敏感点处平滑速度规划和运动学性能良好.%Compared with conventional linear and circular interpolation,non-uniform rational B-spline (NURBS) interpolation has a greater advantage.However,it has the intense interpolation feedrate fluctuation problem that causes the excessive machining motion capability of a machine tool.In order to improve the kinematic performance of the NURBS interpolation and modify the saltation of acceleration and the jerk of motion,this paper proposes a smooth feedrate scheduling interpolation algorithm for the sensitive points of the NURBS curves based on their geometric characteristics.Through searching for the breakpoints,which are G1 or G2 discontinuity,and the critical points that have great curvature,the feedrate profile for these points are smoothed with the S-shaped acceleration by using the finite impulse response (FIR) cascade filter.Furthermore,this paper proposes an approximation method for fixing the feedrate of breakpoints to make their acceleration and jerk satisfy the desired requirements.Thus,this method can enhance the performance of NURBS interpolation.The simulation and experimental results verify that the algorithm proposed in the paper can smooth the feedrate and has a satisfactory kinematic performance in the sensitive points.