多项式加减速的NURBS插补策略研究  

Research on NURBS Interpolation Strategy for Polynomial Acceleration and Deceleration

作　　者：胡甜 唐清春[2] 王太子 潘文俊 张万顺 Hu Tian;Tang Qingchun;Wang Taizi;Pan Wenjun;Zhang Wanshun(School of Mechanical and Automotive Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China;College of Innovation and Entrepreneurship,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]广西科技大学机械与汽车工程学院,广西柳州545006 [2]广西科技大学创新创业学院,广西柳州545006

出　　处：《煤矿机械》2025年第2期81-85,共5页Coal Mine Machinery

基　　金：国家自然科学基金项目(52165054);广西壮族自治区自然科学基金项目(2020GXNSFAA159142)。

摘　　要：为了解决传统方法中的跃度变化引起机床系统产生冲击和振动等问题,提出了多项式加减速的NURBS插补优化方法。首先,采用辛普森积分方法计算出曲线长度,以弓高误差和最大加速度作为约束条件限制曲线各插补点的速度,并在曲率极大值处进行分段;其次,计算出分段曲线的参数值,对应于多项式加减速规划中的类型和时间;最后,在相同的插补周期下,以某S形试件为例,对该算法与传统的S形加减速算法进行MATLAB仿真对比。结果表明,该算法满足弓高误差、最大加速度等限制条件,规划后的速度和加速度曲线更柔和,跃度曲线连续且有规则变化,从而使得数控机床有良好的加减速柔性。In order to solve the problems such as the impact and vibration generated by the machine tool system due to the jerk variation in traditional methods,proposed an optimization method of NURBS interpolation with polynomial acceleration and deceleration.Firstly,the Simpson integration method was used to calculate the curve length.The chord error and the maximum acceleration were taken as the constraint conditions to limit the velocity of each interpolation point of the curve,and the curve was segmented at the maximum curvature value.Secondly,the parameter values of the segmented curves were calculated,corresponding to the types and times in the polynomial acceleration and deceleration planning.Finally,under the same interpolation period,taking a certain S-shaped specimen as an example,this algorithm was compared with the traditional S-shaped acceleration and deceleration algorithm through MATLAB simulation.The results show that this algorithm meets the constraint conditions such as chord error and maximum acceleration.The planned velocity and acceleration curves are smoother,and the jerk curve changes continuously and regularly,thereby enabling the CNC machine tool to have good acceleration and deceleration flexibility.

关 键 词：加减速控制 NURBS插补 S形试件 数控机床 

分 类 号：TG659[金属学及工艺—金属切削加工及机床]