NURBS双向插补中改进的误差圆整策略研究  

The Research on Improved Error Rounding Strategy in NURBS Bidirectional Intepolation

作　　者：张晨 张承瑞[1,2,3] 马威[1,2,3] 王公成 ZHANG Chen;ZHANG Cheng-rui;MA Wei;WANG Gong-cheng(School of Mechanical Engineering,Shandong Univ,Shandong Jinan 250061,China;Key Laboratory of High Efficiency and Clean Mechanical Manufacture,Shandong Univ,Shandong Jinan 250061,China;National Experiment Education Demonstration Center for Mechanical Engineering,Shandong Univ,Shandong Jinan 250061,China)

机构地区：[1]山东大学机械工程学院,山东济南250061 [2]山东大学高效洁净机械制造教育部重点实验室,山东济南250061 [3]山东大学机械工程国家级实验教学示范中心,山东济南250061

出　　处：《机械设计与制造》2021年第11期122-126,131,共6页Machinery Design & Manufacture

摘　　要：介绍了目前复杂曲线加工的现状,以及利用NURBS曲线进行复杂曲线加工的优势,同时提出了对NURBS曲线双向插补过程中正反向减加速阶段以及匀速阶段一种改进的误差圆整的算法。对NURBS曲线进行实时的双向插补时,在双向的加速度到达最大之前,插补数据正向输出,反向储存,经过这个阶段以后,需要对剩余的弧长进行正向速度规划和插补,包括S曲线加减速算法中的减加速阶段,匀速阶段,加减速阶段,经过前一阶段插补,三个阶段对应的时间T3、T4、T5已经计算获得,然而,无法保证T3、T4、T5的总和是插补周期T的整数倍,即存在圆整误差问题。传统的圆整误差算法满足了位移补偿要求,而将位移误差控制在可允许范围即1e-5mm之内,仅仅满足了插补速度平滑衔接的必要条件,还要考虑插补过程的加速度。因此,提出了一种NURBS双向插补中改进的误差圆整策略,并对其进行仿真。仿真结果表明该算法可以实现速度加速度满足了机床的约束且位移误差控制在了允许范围之内的同时,插补进入匀速阶段以后加速度可以过渡为零,并且大大提高了整个插补过程速度过渡的平滑性。The current status of complex curve processing and the advantages of using NURBS curves for complex curve processing are introduced.At the same time,an improved error rounding algorithm for forward and backward deceleration in the bidirection⁃al interpolation of NURBS curves is proposed.When performing real-time bidirectional interpolation on the NURBS curve,before the bidirectional acceleration reaches the maximum,the interpolation data is output in the forward direction and stored in the re⁃verse direction.After this stage,the remaining arc length needs to be planned and interpolated in the forward speed,including the acceleration-deceleration phase,constant speed phase,acceleration-deceleration phase in the S-curve acceleration/deceleration algorithm.After the previous phase interpolation,the time T3,T4,T5 corresponding to the three phases have been calculated.However,the sum of T3,T4 and T5 cannot be guaranteed to be an integral multiple of the interpolation period T,that is a round⁃ing error problem.The traditional rounding error algorithm satisfies the displacement compensation requirements,and the dis⁃placement error is controlled within the allowable range of 1e-5mm,which only satisfies the necessary conditions for the smooth connection of the interpolation speed,and the acceleration of the interpolation process must be considered.Therefore,an im⁃proved error rounding strategy in NURBS bidirectional interpolation is proposed and simulated.The simulation results show that the algorithm can realize the speed and the acceleration meets the constraints of the machine tool and the displacement error is controlled within the allowable range.After the interpolation enters the uniform speed stage,the acceleration can transition to ze⁃ro,and the smoothness of the velocity transition in the whole interpolation process is greatly improved.

关 键 词：NURBS曲线 误差圆整 双向插补 位移补偿 速度衔接 

分 类 号：TH16[机械工程—机械制造及自动化] TG502.12[金属学及工艺—金属切削加工及机床]