基于曲率约束和位移补偿的NURBS曲线柔性高精插补方法  

NURBS Curve Interpolation Method with Flexibility and High Accuracy Based on Curvature Constraint and Displacement Compensation

作　　者：高翔宇 刘晓健 裘乐淼[1] 张树有[1] Gao Xiangyu;Liu Xiaojian;Qiu Lemiao;Zhang Shuyou(Department of Mechanical Engineering,Zhejiang University,Hangzhou 310027)

机构地区：[1]浙江大学机械工程学院,杭州310027

出　　处：《计算机辅助设计与图形学学报》2018年第12期2213-2223,共11页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(51375437);浙江省自然科学基金(LY18E05001);浙江省公益技术研究项目(2015C31079);浙江大学流体动力与机电系统国家重点实验室青年基金

摘　　要：针对NURBS曲线插补过程中曲率极大值点附近进给速度容易超限和分段插补末端位移损失的问题,提出一种基于曲率约束和位移补偿的NURBS曲线柔性高精插补方法.首先根据NURBS曲线曲率极大值对曲线进行分段并计算每段弧长,结合曲线曲率变化和机床动力学性能得到进给速度约束;然后以加加速度渐变的柔性加减速方法进行速度控制,根据曲线分段长度和曲率采取对应的速度规划策略;在实时插补中,根据实际位移计算各插补周期的平均速度并对末端位移损失进行补偿,将连续的速度曲线离散为各周期的阶跃速度变化;最后以改进的牛顿迭代方法计算插补参数,输出插补点坐标.仿真实验结果表明,该方法可以有效地提高插补精度,降低速度波动.Feedrate near the maximum curvature points of a NURBS curve can easily exceeds limits.Furthermore,when the interpolation reaches the terminal of a NURBS segment,it may cause a displacement error.Aiming at these problems,this paper presents a NURBS curve interpolation method with flexibility and high accuracy based on curvature constraint and displacement compensation.Firstly,the NURBS curve is divided into several segments according to the maximum curvature points and the length of each segment is estimated.The limits of feedrate are acquired according to NURBS curvature and machine kinematic constraints.Then the jerk-varied flexible acceleration and deceleration is applied to control feedrate.Feedrate is scheduled according to the length of the NURBS segment and NURBS curvature.In the stage of real-time interpolation,the average velocity and displacement compensation is proposed to turn the continuous feedrate curve into discrete feedrate on every interpolation period.Finally,an improved Newton iterative method is applied to generate the position of interpolation point.Experiment is conducted to prove the proposed method can improve the interpolation accuracy and reduce feedrate fluctuation efficiently.

关 键 词：NURBS插补 柔性加减速 速度离散 牛顿迭代 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]