基于四阶龙格—库塔算法的NURBS曲线插补
2019-08-02
作者：刘高领，朱海星，刘振忠
单位：天津市先进机电系统设计与智能控制重点实验室；机电工程国家级实验教学示范中心（天津理工大学）
摘要：为了提高数控机床的精密加工能力，提出了基于四阶龙格—库塔算法的NURBS曲线插补方法。该方法通过使用四阶龙格—库塔算法求解NURBS曲线节点矢量，得到更高精度的NURBS曲线节点矢量增量，并采用后向差分法代替微分求导的复杂计算过程，提高NURBS曲线插补的稳定性，通过弓高和最大加速度约束插补步长的方法对NURBS曲线插补步长进行限制，减小插补误差对该插补算法的影响。NURBS曲线插补算法过程运用MATLAB软件进行仿真及数据分析处理，验证了该NURBS曲线插补方法的合理性和可行性。
关键词：四阶龙格—库塔；NURBS曲线；插补算法；数控机床
中图分类号：TG659；TH162；TP391.9文献标志码：ADOI：10.3969/j.issn.1000-7008.2019.08.015
NURBS Curve Interpolation Based on Fourthorder RungeKutta Algorithm
Liu Gaoling，Zhu Haixing，Liu Zhenzhong
Abstract:In order to improve the precision processing ability of NC machine tools，a NURBS curve interpolation method based on fourthorder RungeKutta algorithm is proposed in this paper.In this method，the fourthorder RungeKutta algorithm is used to solve the node vector of NURBS curve，and the node vector increment of NURBS curve with higher accuracy is obtained.The backward difference method is used instead of the complex calculation process of differential derivation to improve the stability of NURBS curve interpolation.The interpolation step of NURBS curve is limited by the method of bow height and maximum acceleration constraints to reduce the influence of interpolation error on the interpolation algorithm.The NURBS curve interpolation algorithm process is simulated and analyzed by using MATLAB software，which is verified the rationality and feasibility of the NURBS curve interpolation method.
Keywords:fourth order RungeKutta；NURBS curve；interpolation algorithm；CNC machine tool