一种拟合三维复杂螺旋刀具轨迹NURBS插值逼近方法

NURBS Interpolation Approximation Method for 3D Complex Helical Tool Path Fitting

目的 提出一种基于非均匀有理B样条拟合的空间螺旋刀具路径整体插值逼近方法,解决曲面弧度急变产生的刀具路径插值拟合误差较大的问题。方法 通过解析几何特征,找出拟合误差较大的型值点,在合适位置插入适量的虚拟数据点,计算插入数据点后的曲线拟合误差,并与误差期望值进行比较,若不满足期望误差值则继续插入虚拟数据点。结果 拟合得到的空间曲线逐渐逼近原始型值点,拟合误差符合工况要求,计算量较小。结论 笔者所提方法以较少计算量拟合曲线,能准确表达刀具路径的参数,适用于曲率急变的空间曲线或曲面拟合的刀具轨迹规划工作。

This paper proposed a method for the global spiral tool path interpolation based on non-uniform rational B-spline fitting,which can solve the problem of fitting error caused by the sharp change of the tool path.By analyzing geometric features,type value points with larger fitting errors were found out,and then the appropriate amount of virtual data points were inserted at the appropriate positions.The fitting error was calculated after inserting data points and compared with the excepted value of the error.If the expected error value is not achieved,the above work of inserting data points and calculating error will continue.The space curve obtained by fitting approximates the original value points gradually,and the fitting error meets the requirements of the working conditions with less computation.The method proposed by the author can accurately express the parameters of the tool path with less computation,which is suitable for the path planning of space curve or space surface fitting with sharp curvature change.