基于双Hamming的NURBS曲线插补算法  

NURBS Curve Interpolation Algorithm Based on Double Hamming

作　　者：潘盛湖 吕彭杰 徐尚飞 彭伦文 PAN Shenghu;LYU Pengjie;XU Shangfei;PENG Lunwen(Oil and Gas Equipment Technology Sharing and Service Platform of Sichuan Province,Chengdu 610500,China)

机构地区：[1]石油天然气装备技术四川省科技资源共享服务平台,成都610500

出　　处：《组合机床与自动化加工技术》2024年第8期70-74,共5页Modular Machine Tool & Automatic Manufacturing Technique

基　　金：四川省自然科学基金项目(2022NSFSC2002)。

摘　　要：针对传统非均匀有理B样条(NURBS)曲线插补中,由于理想插补步长和实际插补步长误差较大引起速度波动的问题,提出一种基于双Hamming的NURBS曲线插补算法。推导差分和导数定义分别变换Hamming方法,得到插补参数的预估、校正公式,再判断校正公式所得插补参数值是否满足速度波动率要求,满足则可继续进行插补,否则利用密勒-牛顿迭代公式对插补参数值进行迭代校正。使用四阶Runge-Kutta方法对初始两插补参数进行求解,并推导插补数值方法关于插补周期的稳定性约束条件。最后对该算法进行仿真,仿真结果表明该算法相较于二阶Taylor、四阶R-K和Adams隐显预估校正算法,平均速度波动率减少30.54%~65.57%,迭代次数减少1.23%~13.12%,证明了该算法在保证较小迭代次数的同时减少了进给速度波动率。Aiming at the problem of speed fluctuation caused by the large error between the ideal interpolation step size and the actual interpolation step size in the traditional non-uniform rational B-spline(NURBS)curve interpolation,a NURBS curve interpolation algorithm based on double Hamming is proposed.The differential and derivative definitions are derived to transform the Hamming method respectively,and the prediction and correction formulas of the interpolation parameters are obtained.Then,it is judged whether the interpolation parameter values obtained by the correction formula meet the speed fluctuation rate requirements,and the interpolation can be continued.Otherwise,the Miller-Newton formula is used to iteratively correct the interpolation parameter values.In order to ensure the calculation accuracy and avoid solving high-order derivatives.The fourth-order Runge-Kutta method is used to solve the initial two interpolation parameters,and the stability constraints of the interpolation numerical method with respect to the interpolation period are derived.Finally,the algorithm is simulated.The simulation results show that compared with the second-order Taylor,fourth-order R-K and Adams implicit-explicit predictor-corrector algorithms,the average speed fluctuation rate is reduced by 30.54%~65.57%,and the number of iterations is reduced by 1.23%~13.12%.It is proved that the algorithm reduces the feed speed fluctuation rate while ensuring a small number of iterations.

关 键 词：NURBS曲线插补 双Hamming法 速度波动率 稳定性 

分 类 号：TH165[机械工程—机械制造及自动化] TG659[金属学及工艺—金属切削加工及机床]