曲率单调分割NURBS 曲线及双侧优化进给速度 - 计算机辅助设计与.PDF

第29 卷 第2 期 计算机辅助设计与图形学学报 Vol. 29 No.2 2017 年2 月 Journal of Computer-Aided Design Computer Graphics Feb. 2017 曲率单调分割NURBS 曲线及双侧优化进给速度 1) 2) 3) 季国顺 , 俞武嘉 , 陈子辰 1) (杭州电子科技大学机械工程学院 杭州 310018) 2) (杭州电子科技大学自动化学院 杭州 310018) 3) (浙江大学制造工程及自动化研究所 杭州 310027) (jgsh888@163.com) : 针对常用速度规划方法忽视速度与 NURBS 曲线参数点之间贴合程度影响轮廓插补精度的问题, 提出按曲 率单调性分割NURBS 曲线及其规划进给速度的算法. 首先分析了NURBS 曲率单调性; 其次按照临界曲率点、临界 曲率值点及曲率单调性转折点分割 NURBS 曲线, 并求取各分段弧长; 最后结合机床动力学性能, 从曲率临界点出发, 用S 曲线分别向前、后2 个方向朝曲率临界值点、曲率转折点优化进给速度. 与常用规划算法进行对比的结果表明, 该 算法可以通过加工时间的较小延长, 极大地提高轮廓插补精度. ：NURBS 曲线; 曲率单调性; 曲率临界值; 双侧优化 ：TP391.4; TP273 Bilateral Optimization Feedrate on Splitting NURBS Curve with its Curvature Monotonicity Ji Guoshun1), Yu Wujia2), and Chen Zichen3) 1) (School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018) 2) (School of Automation, Hangzhou Dianzi University, Hangzhou 310018) 3) (Institute of Manufacturing Engineering and Automation, Zhejiang University, Hangzhou 310027) Abstract: Accuracy degree of mapping relation between curve parameter and feedrate affecting interpolation precision is neglected with conventional planning feedrate method generally. Aiming at this problem, a method of splitting the NURBS curve following its curvature monotonicity and thereby planning feedrate algorithm is pro- posed. First set the critical value of curvature; second analyze the curvature monotonicity of NURBS curve, and then split the NURBS curve into several sub-segments according its critical value of curvature, critical and transi- tion points of curvature, and calculate arc length of each