连续时间周期化的NURBS曲线插补及其速度规划  

Continuous to Periodic Time NURBS Curve Interpolation and Its Speed Planning

作　　者：何改云[1] 陶浩 王太勇[1] 董甲甲 张永宾[1] He Gaiyun;Tao Hao;Wang Taiyong;Dong Jiajia;Zhang Yongbin(School of Mechanical Engineering,Tiaxljin University,Tianjin 300350,China)

机构地区：[1]天津大学机械工程学院,天津300350

出　　处：《天津大学学报（自然科学与工程技术版）》2018年第8期844-853,共10页Journal of Tianjin University：Science and Technology

基　　金：国家自然科学基金资助项目(51605328)~~

摘　　要：根据机床动力学性能,提前预测NURBS曲线插补时的速度极小值点,以这些点为基准将曲线分段,同时估算每条子曲线的长度.利用捷度阶跃式7段S型加减速规律对每条子曲线进行连续时间域下的速度规划,以插补总时间周期化为原则对连续时间域下的加减速各阶段运行时间做周期化离散处理.为了减小子曲线间衔接速度的波动,提出连续时间域运行时间重新规划的方法.为了减小NURBS曲线实时插补时的速度波动率,提出利用反向二次插补法进行实时插补计算,该方法不需要迭代计算且计算精度较高.仿真实验结果表明,连续时间域重新规划和周期化离散处理方法能够实现捷度满足机床性能要求的S型加减速速度规划,且实时插补阶段的速度波动率能够达到10-6级.According to the dynamic performance of the machine tool, the minimum speed points in a NURBS curve could be defined before real-time interpolation process. Based on these points the NURBS curve was segmented into sub-curves, whose length was estimated simultaneously. Then the 7-stage S-type ACC/DEC principle was applied to each sub-curve of speed planning in the continuous time domain. After that, the total interpolation time was perio- dized to output discrete speed values in every interpolation circle. In order to minimize the speed jump in conjuncture between two sub-curves, an approach of ACC/DEC time rescheduling was proposed here. To reduce the speed fluc- tuation caused by NURBS interpolating parameter calculation, the inverse quadratic interpolation （IQI）method, which needs no iteration and has high calculation precision, was implemented instead of the normal way of 2-order Taylor expansion. Simulation results show that the ACC/DEC time rescheduling and periodic discretization methods meet the dynamic performance of the machine tool, and the speed fluctuation reaches 10-6 level.

关 键 词：NURBS曲线插补 S型加减速 周期化离散 反向二次插补法 

分 类 号：TH166[机械工程—机械制造及自动化]