NURBS Interpolator with Adaptive Smoothing Feedrate and Parameter Increment Compensation

doi:10.3901/JME.2022.05.178

Abstract

Abstract: In order to improve the smoothness of NURBS interpolation speed and solve the problem of the low accuracy of traditional interpolation parameter calculation methods, this paper proposes a NURBS interpolator with smooth feedrate scheduling and minimal feedrate fluctuation. The adaptive feedrate is obtained based on the constraints of chord error, normal acceleration and normal jerk.The curve is segmented according to the adaptive speed and the S-shaped acc/dec algorithm is used to smooth the speed curve. This paper improves the traditional S-shaped acc/dec planning method and makes a comprehensive planning for the adjacent sections meeting the merging conditions and adjusts the speed overrun area. Based on the second-order Runge-Kutta method, the initial increment value of the next interpolation point parameters is obtained and the backward difference method is used to simplify the calculation. The arc approximation method is used to obtain the compensation value of the parameter increment and finally the parameters of the next interpolation point are obtained. The performance of the proposed method is compared with that of the traditional method by simulation and experiment. The results show that the algorithm is effective.

Key words: NURBS interpolator, feedrate scheduling, S-shaped acc/dec, feedrate fluctuation, arc transition edge

CLC Number:

TG156

XU Bo, DING Yi, JI Wei. NURBS Interpolator with Adaptive Smoothing Feedrate and Parameter Increment Compensation[J]. Journal of Mechanical Engineering, 2022, 58(5): 178-189.

References

[1] YE P,ZHANG Y,XIAO J,et al.A novel feedrate planning and interpolating method for parametric toolpath in Frenet-Serret frame[J].The International Journal of Advanced Manufacturing Technology,2019,101:1915-1925.
[2] 刘献礼,周肖阳,李茂月,等.NURBS曲线S形加减速寻回实时插补算法[J].机械工程学报,2017,53(3):183-192.LIU Xianli,ZHOU Xiaoyang,LI Maoyue,et al.The real-time algorithm of NURBS curve retriever interpolation with S-type acceleration and deceleration control[J].Journal of Mechanical Engineering,2017,53(3):183-192.
[3] YEH S,HSU P.Adaptive feedrate interpolation for parametric curves with a confined chord error[J].Computer Aided Design,200234(3):229-237.
[4] XU Z,CHEN J,FENG Z.Performance evaluation of a real-time interpolation algorithm for NURBS curves[J].International Journal of Machine Tools and Manufacture,2001,41(9):1323-1345.
[5] DU D,LIU Y,YAMAZAKI K,et al.An accurate adaptive NURBS curve interpolator with real-time flexible acceleration/deceleration control[J].Robotics and Computer-Integrated Manufacturing,2010,26:273-281.
[6] JAHANPOUR J,ALIZADEH M.A novel acc-jerk-limited NURBS interpolation enhanced with an optimized S-shaped quintic feedrate scheduling scheme[J].International Journal of Advanced Manufacturing Technology,2015,77:1889-1905.
[7] DONG J,WANG T,LI B,et al.Smooth feedrate planning for continuous short line tool path with contour error constraint[J].International Journal of Machine Tools and Manufacture,2014,76,1-12.
[8] SUN Y,ZHAO Y,BAO Y,et al.A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints[J].International Journal of Machine Tools and Manufacture,2014,77,74-81.
[9] JIA Z,SONG D,MA J,et al.A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints[J].International Journal of Machine Tools and Manufacture,2017,116,1-17.
[10] SANG Y,YAO C,LV Y,HE G.An improved feedrate scheduling method for NURBS interpolation in five-axis machining[J].Precision Engineering,2020,64,70-90.
[11] WANG T,ZHANG Y,DONG J,et al.NURBSinterpolator with adaptive smooth feedrate scheduling and minimal feedrate fluctuation[J].International Journal of Precision Engineering and Manufacturing,2020,21:273-290.
[12] LIANG S,ZHAO W,XI X.Design of a real-time NURBSinterpolator with constant segment length for milling EDM[J].International Journal of Advanced Manufacturing Technology,2013,67:427-440.
[13] LIU H,LIU Q,ZHOU S,et al.A NURBS interpolation method with minimal feedrate fluctuation for CNCmachine tool[J].International Journal of Advanced Manufacturing Technology,2015,78(5-8):1241-1250.
[14] 李浩,吴文江,韩文业,等.基于自适应前瞻和预测校正的实时柔性加减速控制算法[J].中国机械工程,2019,30(6):690-699.LI Hao,WU Wenjiang,HAN Wenye,et al.Real-time flexible acceleration and deceleration control algorithm based on adaptive look-head and predictor-corrector method[J].China Mechanical Engineering,2019,30(6):690-699.
[15] WANG G,SHU Q,WANG J,et al.Research on adaptive non-uniform rational B-spline real-time interpolation technology based on acceleration constraints[J].International Journal of Advanced Manufacturing Technology,2016,91(5):1-12.
[16] NI H,ZHANG C,CHEN C,et al.A parametric interpolation method based on prediction and iterative compensation[J].International Journal of Advanced Robotic Systems,2019,16(1):1-10.
[17] CHEN M,ZHAO W,XI X.Augmented Taylor's expansion method for B-spline curve interpolation for CNC machine tools[J].International Journal of Machine Tools and Manufacture,2015,94:109-119.
[18] LIU M,HUANG Y,YIN L,et al.Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools[J].International Journal of Machine Tools and Manufacture,2014,87:1-15.
[19] ZHAO K,LI S,KANG Z.Smooth minimum time trajectory planning with minimal feed fluctuation[J].International Journal of Advanced Manufacturing Technology,2019,105:1099-1111.
[20] 吴香玉,王鹏.基于Runge-Kutta的NURBS曲线实时前瞻插补算法[J].华南理工大学学报,2017,45(10):121-128.WU Xiangyu,WANG Peng.A real-time look-ahead interpolation algorithm for NURBS curves based on Runge-Kutta[J].Journal of South China University of Technology,2017,45(10):121-128.
[21] XI X,CHEN H,LIU H,et al.Extended unit arc length increment interpolation for generalized NURBS curves in multi-axis EDM[J].Precision Engineering,2019,59:81-89.
[22] 陈琳,黄旭丰,刘梦,等.综合多约束条件优化连续轨迹前瞻算法[J].机械工程学报,2019,55(13):151-159.CHEN Lin,HUANG Xufeng,LIU Meng,et al.Optimized continuous trajectory look-ahead algorithmwith comprehensive multi-constraints[J].Journal of Mechanical Engineering,2019,55(13):151-159.
[23] 吴兹潛.黄金分割法最优性证明[J].中山大学学报,1979(2):3-19.WU Ziqian,Proof of optimality of golden section method[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,1979(2):3-19.
[24] 潘海鸿,杨微,陈琳,等.全程S曲线加减速控制的自适应分段NURBS曲线插补算法[J].中国机械工程,2010,21(2):68-73.PAN Haihong,YANG Wei,CHEN Lin,et al.Adaptive piecewise NURBS curve interpolation algorithm for entireness process S-curve ACC/DEC control[J].China Mechanical Engineering,2010,21(2),68-73.