多约束条件的NURBS曲线自适应前瞻插补算法  

Adaptive Look-ahead Interpolation Algorithm for NURBS Curves with Multiple Constraints

作　　者：盖荣丽[1] 马淑雅 GAI Rongli;MA Shuya(School of Information Engineering, Dalian University, Dalian 116021, China)

机构地区：[1]大连大学信息工程学院,辽宁大连116021

出　　处：《郑州大学学报（理学版）》2022年第3期59-65,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(61602074);科技重大专项资助项目(2019ZX04014001)。

摘　　要：针对数控系统加工过程中的刀具抖动和机床震荡等问题,提出多约束条件的NURBS曲线自适应前瞻插补算法。在预处理阶段,根据曲率变化对NURBS曲线进行分段,速度规划采用改进正弦三角函数加减速算法,获取连续和平滑的加加速度曲线;综合NURBS曲线弓高误差、最大法向加速度和加加速度以及机床动力学等多约束条件对进给速度进行自适应调节。在实时插补中,采用二阶泰勒展开式计算插补参数,实时计算进给速度。仿真结果表明,多约束条件能全面且自适应地处理曲率极值点等特殊位置的进给速度,曲线插补输出的弓高误差小于设定的最大值,满足高速高精的加工要求。Aiming to solve the problems of tool jitters and machine vibration in the machining of the CNC system,an adaptive look-ahead interpolation algorithm for NURBS curve with multiple constraints was proposed.In the preprocessing stage,the NURBS curve was segmented according to the curvature change.The speed planning adopted improved sinusoidal trigonometric acceleration and deceleration algorithm to obtain continuous and smooth jerk curve.Comprehensive NURBS curve chord error,maximum normal acceleration and jerk,machine tool dynamics,and other constraints were adaptively adjusted the feed rate.In real-time interpolation,the second-order Taylor expansion was used to calculate the interpolation parameters,and the feed rate was calculated in real time.The simulation results indicated that the multiple constraints could handle the feed rate of special positions such as the curvature extreme point comprehensively and adaptively.The output of chord error by the curve interpolation was less than the setting maximum value,which met the requirements of high-speed and high-precision machining.

关 键 词：NURBS曲线 速度规划 多约束条件 自适应前瞻 插补算法 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]