A novel acc-jerk-limited NURBS interpolation enhanced with an optimized S-shaped quintic feedrate scheduling scheme

This paper presents a new adaptive acc-jerk-limited nonuniform rational B-spline (NURBS) interpolation method based on an optimized S-shaped C2 quintic feedrate planning scheme. At first, the modified quintic feedrate profile for each sharp corner during the acceleration/deceleration (acc/dec) stage is constructed. To this end, two feedrate slope correction coefficients (FSCC) are introduced for zero end point acceleration and jerk conception in acc/dec stage of each sharp corner. Also, a new algorithm is recommended to compute the acc/dec stage traverse time with respect to the deceleration starting time in this paper. Then, the modified quintic feedrate scheduling scheme equipped with the FSCC is improved for the tool path containing several sharp corners. The FSCC and the deceleration starting times corresponding to all sharp corners are evaluated using an optimization method such that the total machining time to be minimized. In this paper, the pattern search algorithm equipped with the nonlinear constraint function including the acceleration and jerk limitations Matlab code is used for obtaining the optimized parameters to accomplish the acc-jerk-limited feedrate scheduling scheme along the tool path. The proposed interpolation method is performed for several case studies and compared with the previously published methods to evaluate the effectiveness of the designed adaptive acc-jerk-limited feedrate scheduling scheme. The simulation results demonstrate that the proposed interpolation algorithm is capable for providing a smooth feedrate transition for all stages of motion along the tool path and yields satisfactory performances such as total machining time and the interpolation steps.

[1]  Wenwu Cao,et al.  Applied Numerical Methods Using MATLAB®: Yang/Applied Numerical MATLAB , 2005 .

[2]  Le Xie,et al.  Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining , 2008 .

[3]  Mi-Ching Tsai,et al.  Real-time variable feed rate NURBS curve interpolator for CNC machining , 2004 .

[4]  Y. Altintas,et al.  Quintic Spline Interpolation With Minimal Feed Fluctuation , 2005 .

[5]  Jianzhong Fu,et al.  A new adaptive interpolation scheme of NURBS based on axis dynamics , 2011 .

[6]  Ming-Yang Cheng,et al.  Contouring accuracy improvement using cross-coupled control and position error compensator , 2008 .

[7]  Dongbiao Zhao,et al.  Research and Implementation of NURBS Real-Time and Look-Ahead Interpolation Algorithm , 2009, 2009 International Conference on Measuring Technology and Mechatronics Automation.

[8]  Min-Yang Yang,et al.  A study on a generalized parametric interpolator with real-time jerk-limited acceleration , 2004, Comput. Aided Des..

[9]  Youping Chen,et al.  An accurate NURBS curve interpolation algorithm with short spline interpolation capacity , 2012 .

[10]  Ranga Narayanaswami,et al.  A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining , 2003, Comput. Aided Des..

[11]  X. Zhiming,et al.  Performance Evaluation of a Real-Time Interpolation Algorithm for NURBS Curves , 2002 .

[12]  Rida T. Farouki,et al.  Performance analysis of CNC interpolators for time-dependent feedrates along PH curves , 2001, Comput. Aided Geom. Des..

[13]  Yun-Fei Zhou,et al.  A universal velocity profile generation approach for high-speed machining of small line segments with look-ahead , 2007 .

[14]  Wŏn-yŏng Yang,et al.  Applied Numerical Methods Using MATLAB , 2005 .

[15]  Seung-Han Yang,et al.  Design of jerk bounded feedrate with ripple effect for adaptive nurbs interpolator , 2008 .

[16]  Rida T. Farouki,et al.  Exact Taylor series coefficients for variable-feedrate CNC curve interpolators , 2001, Comput. Aided Des..

[17]  Meng-Shiun Tsai,et al.  Development of integrated acceleration/deceleration look-ahead interpolation technique for multi-blocks NURBS curves , 2011 .

[18]  Daniel C. H. Yang,et al.  Parametric interpolator versus linear interpolator for precision CNC machining , 1994, Comput. Aided Des..

[19]  Behnam Moetakef Imani,et al.  Real-time P-H curve CNC interpolators for high speed cornering , 2008 .

[20]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[21]  Haibo Liu,et al.  Curvature-Based Real-Time NURBS Surface Interpolator with Look-Ahead ACC/DEC Control , 2012, Math. Comput. Sci..

[22]  Moshe Shpitalni,et al.  Realtime curve interpolators , 1994, Comput. Aided Des..

[23]  Tae Jo Ko,et al.  NURBS interpolator for constant material removal rate in open NC machine tools , 2004 .

[24]  Jianfeng Zhou,et al.  Adaptive feedrate interpolation with multiconstraints for five-axis parametric toolpath , 2014 .

[25]  Meng-Shiun Tsai,et al.  Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery , 2008, Comput. Aided Des..

[26]  Xiaoqi Tang,et al.  A NURBS interpolation algorithm with continuous feedrate , 2012 .

[27]  M. Mori,et al.  Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics , 2005 .

[29]  Dongming Guo,et al.  Variable feedrate interpolation of NURBS Toolpath with geometric and kinematical constraints for five-axis CNC machining , 2013, J. Syst. Sci. Complex..

[30]  Syh-Shiuh Yeh,et al.  The speed-controlled interpolator for machining parametric curves , 1999, Comput. Aided Des..

[31]  Tae Jo Ko,et al.  Precision NURBS interpolator based on recursive characteristics of NURBS , 2013 .

[32]  Ming Chen,et al.  Design of a real-time adaptive NURBS interpolator with axis acceleration limit , 2010 .

[33]  Meng-Shiun Tsai,et al.  Real-time NURBS interpolation using FPGA for high speed motion control , 2006, Comput. Aided Des..

[34]  Yongbo Li,et al.  Real-time NURBS curve interpolator based on section , 2011 .

[35]  Syh-Shiuh Yeh,et al.  Adaptive-feedrate interpolation for parametric curves with a confined chord error , 2002, Comput. Aided Des..

[36]  M. Cheng,et al.  Contour error reduction for free-form contour following tasks of biaxial motion control systems , 2009 .

[37]  Min-Yang Yang,et al.  Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method , 2005 .

[38]  W. T. Lei,et al.  Fast real-time NURBS path interpolation for CNC machine tools , 2007 .

[39]  Fu-Chung Wang,et al.  Open Architecture Controllers for Machine Tools, Part 2: A Real Time Quintic Spline Interpolator , 1998 .

[40]  Alessandro Bardine,et al.  A real-time configurable NURBS interpolator with bounded acceleration, jerk and chord error , 2012, Comput. Aided Des..

[41]  Robert Michael Lewis,et al.  Pattern Search Algorithms for Bound Constrained Minimization , 1999, SIAM J. Optim..

[42]  M. Tsai,et al.  High-speed contouring control with NURBS-based C2 PH spline curves , 2010 .

[43]  Yoram Koren,et al.  CNC INTERPOLATORS: ALGORITHMS AND ANALYSIS , 1993 .

[44]  Kazuo Yamazaki,et al.  An accurate adaptive NURBS curve interpolator with real-time flexible acceleration/deceleration control , 2010 .

[45]  An-Chen Lee,et al.  The feedrate scheduling of NURBS interpolator for CNC machine tools , 2011, Comput. Aided Des..

[46]  PooGyeon Park,et al.  Parametric interpolation using sampled data , 2006, Comput. Aided Des..

[47]  Xiaoting Zhang,et al.  An iterative feedrate optimization method for real-time NURBS interpolator , 2012 .

[48]  Xiao-Shan Gao,et al.  Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration , 2013 .

[49]  J. Jahanpour,et al.  The improved NURBS-based C2 PH spline curve contour following task with PDFF controller , 2014 .

[50]  Xin Wang,et al.  An adaptive parametric interpolator for trajectory planning , 2010, Advances in Engineering Software.

[51]  Mi-Ching Tsai,et al.  A real-time predictor-corrector interpolator for CNC machining , 2003 .

[52]  Les A. Piegl,et al.  On NURBS: A Survey , 2004 .

[53]  Dong Xu,et al.  An optimization of NURBS interpolation algorithm , 2012, IEEE 10th International Conference on Industrial Informatics.

[54]  Zhenyuan Jia,et al.  Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties , 2008 .

[55]  Daoshan Du,et al.  An accurate adaptive parametric curve interpolator for NURBS curve interpolation , 2007 .

[56]  Leszek Rutkowski,et al.  Novel Online Speed Profile Generation for Industrial Machine Tool Based on Flexible Neuro-Fuzzy Approximation , 2012, IEEE Transactions on Industrial Electronics.

[57]  Jiing-Yih Lai,et al.  On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk , 2008 .