高档数控机床NURBS曲线Newton-Rapson迭代的插补算法  

Interpolation Algorithm Based on Newton-Rapson Iteration Methodof Machine Tool of High-grade Numerical Control of NURBSCurve

作　　者：张万军[1,2] 涂晶洁[3] 张育斌[1,3] 张景轩 张景怡 张景妍 

机构地区：[1]西安交通大学机械工程学院,陕西西安741049 [2]兰州工业化设备有限公司,甘肃兰州730050 [3]宁波大红鹰学院,浙江宁波315175

出　　处：《机床与液压》2017年第9期126-130,共5页Machine Tool & Hydraulics

基　　金："高档数控机床与基础制造装备"科技重大专项(2010ZX040001-181);国家自然科学基金资助项目(51165024)

摘　　要：为了解决NURBS曲线在Taylor一阶、二阶展开式求解曲线插补坐标点ui+1,存在计算量大、插补时间长等问题,提出一种Newton-Rapson迭代法的NURBS插补算法。该插补算法可以减少插补计算量和插补时间,提高插补精度,并提高曲线加工的效率。仿真实验结果表明,Newton-Rapson迭代法的NURBS插补算法计算过程简单、切实有效,具有可行性和实用性,满足数控系统实时、高速、高效率插补的要求,在其他数控插补的过程中具有很强的借鉴意义。In order to solve the NURBS curve interpolation problems of Taylor first, second-order expansion of coordinator point, such as large amount of calculation, interpolation time long and so on, a NURBS interpolation algorithm was proposed based on New-ton-Rapson iteration method. The method could be used to reduce the amount of calculation and interpolation time, improving the pre-cision of interpolation, and improve the efficiency of curve machining. Simulationexperimental results show that NURBS interpolation al-gorithm based on Newton-Rapson iteration method of the calculation process is simple, practical and effective. Itmee ts the real-time, high-speed, efficient numerical control （NC） system interpolation requirements, as well as hashigh reference significance in other NC interpolation.

关 键 词：NURBS曲线 插补算法 Taylor展开式 Newton-Rapson迭代法 实时插补 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TP391[自动化与计算机技术—控制科学与工程]