NURBS曲线插补弓高误差的双向Hausdorff距离评估方法  

A Two-way Hausdorff Distance Evaluation Method of Chord Error using NURBS Curve Interpolation

作　　者：鲁毛毛 刘宝泉 徐梦杰 方建平 LU Maomao;LIU Baoquan;XU Mengjie;FANG Jianping(School of Electrical and Control Engineering,Shaanxi University of Science&Technology,Xi′an 710021,China;Xi′an Toll Microelectronics Co.,Ltd.,Xi′an 710000,China)

机构地区：[1]陕西科技大学电气与控制工程学院,西安710021 [2]西安拓尔微电子有限责任公司,西安710000

出　　处：《机械科学与技术》2022年第2期253-262,共10页Mechanical Science and Technology for Aerospace Engineering

基　　金：陕西省2020年重点研发计划项目(2020GY-042)。

摘　　要：数控系统中采用插补方法进行复杂曲线加工会引入弓高误差。利用密切圆(Osculating circle,OC)近似法和单向Hausdorff距离近似法可以获取弓高误差并对其进行后续补偿,但弓高误差求解与补偿精度较低。基于弓高误差的双向Hausdorff距离定义,提出了一种弓高误差的迭代评估算法。该算法能在不考虑曲线复杂度的情况下提升弓高误差的求解精度,并获取满足误差限制要求的最大插补步长,从而进一步生成精确的进给速度限制,防止加工精度及效率因引入其它误差而下降。最后利用该算法对‘∞’形和花瓣形NURBS曲线进行仿真,仿真结果验证了算法的性能及其有效性。In numerical control system,interpolation is often used to realize complex curve machining,which will introduce some chord errors.The commonly used Osculating Circle(OC)method and single-direction Hausdorff distance method can obtain estimated chord errors,then make subsequent compensations,but they both introduce other errors in the estimation process.For this problem,based on the both-direction Hausdorff distance definition of the chord error,an iterative evaluation algorithm is proposed in this paper.This algorithm can improve the estimation precision of chord error without considering the flexibility of curves,and obtain the maximum interpolation step length that satisfies the error limitation,thereby further generating the accurate feed rate constraints to prevent the reduction of both machining accuracy and efficiency due to the introduction of other errors.Finally,it is simulated by‘∞’-shaped and petal-shaped NURBS curves,the simulation results verify the performance and the effectiveness of the proposed algorithm.

关 键 词：插补法 OC近似法 弓高误差 双向Hausdorff距离 NURBS曲线 

分 类 号：TG65[金属学及工艺—金属切削加工及机床]