基于弧长参数的自由曲线实时误差估计算法

Real-time error estimation algorithm of free curve based on arc length parameters

针对复杂型面零件加工精度要求提高以及在自由曲线跟随任务中实时精确计算轮廓误差难度较大等问题,提出一种基于弧长参数的自由曲线实时误差估计算法。在MATLAB/Simulink中利用非均匀有理B样条(non-uniform rational B-spline, NURBS)插补对椭圆轨迹和双纽线轨迹进行规划,将基于弧长参数的自由曲线实时误差估计算法与切线法、圆近似法、平均速度法和三点圆法的轮廓误差估算精度与执行时间等性能评价指标进行对比分析。仿真试验结果表明,基于弧长参数的自由曲线实时误差估计算法较现有常用的轮廓误差估计算法具有更好的轮廓误差估算精度,并且适用于大曲率自由曲线的情况。利用该方法可以更进一步设计出先进的交叉耦合控制(cross-coupled control, CCC)运动控制方案。

Aiming at the problems that the machining accuracy of complex surface parts was required to be improved and it was difficult to accurately calculated the contour error in real time in the free curve tracking task,a real-time error estimation algorithm of free curve based on arc length parameters was proposed.In MATLAB/Simulink,non-uniform rational B-spline(NURBS)interpolation was used to plan the elliptical trajectory and the double twist trajectory.The real-time error estimation algorithm of free curve based on arc length parameters was compared with the contour error estimation accuracy and execution time of tangent line-based estimation,circular approximation,average velocity estimation and three points circular approximation.The simulation results showed that the real-time error estimation algorithm of free curve based on arc length parameters had better contour error estimation accuracy than the existing commonly used contour error estimation algorithm,and it was suitable for the case of large curvature free curve.The advanced cross-coupled control(CCC)scheme could be further designed by using this method.