Feedrate scheduling in computer numerical control (CNC) machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator. Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools. This study develops a general feedrate scheduling method for non-uniform rational B-splines (NURBS) tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion. The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths. The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes. The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method. To improve the computational efficiency, the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently. The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead. Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method.
The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-022-00413-1
Yang Li
,
Fu-Sheng Liang
,
Lei Lu
,
Cheng Fan
. Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining[J]. Advances in Manufacturing, 2023
, 11(1)
: 111
-129
.
DOI: 10.1007/s40436-022-00413-1
1. Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, New York
2. Yau HT, Kuo MJ (2001) NURBS machining and feed rate adjustment for high-speed cutting of complex sculptured surfaces. Int J Prod Res 39(1):21-41
3. Sun YW, Sun SX, Xu JT et al (2017) A unified method of generating tool path based on multiple vector fields for CNC machining of compound NURBS surfaces. Comput Aided Des 91:14-26
4. Jafarzadeh E, Movahhedy MR, Khodaygan S et al (2018) Prediction of machining chatter in milling based on dynamic FEM simulations of chip formation. Adv Manuf 6(3):334-344
5. Lyu H, Liu Y, Guo JY et al (2019) Tool-path generation for industrial robotic surface-based application. Adv Manuf 7(1):64-72
6. Liang FS, Kang CW, Fang FZ (2020) A review on tool orientation planning in multi-axis machining. Int J Prod Res 59(18):1-31
7. Liang FS, Kang CW, Fang FZ (2020) A smooth tool path planning method on NURBS surface based on the shortest boundary geodesic map. J Manuf Process 58:646-658
8. Lu L, Zhang J, Fuh JYH et al (2020) Time-optimal tool motion planning with tool-tip kinematic constraints for robotic machining of sculptured surfaces. Robot Comput Integr Manuf 65:101969. https://doi.org/10.1016/j.rcim.2020.101969
9. Chen JP, Gu L, He GJ (2020) A review on conventional and nonconventional machining of SiC particle-reinforced aluminium matrix composites. Adv Manuf 8(3):279-315
10. Sang YC, Yao CL, Lv YQ et al (2020) An improved feedrate scheduling method for NURBS interpolation in five-axis machining. Precis Eng 64:70-90
11. Zhao J, Xiang YC, Fan C (2021) A new method for polishing the inner wall of a circular tube with a soft abrasive rotating jet. Powder Technol 398:117068. https://doi.org/10.1016/j.powtec.2021.117068
12. Yang DCH, Kong T (1994) Parametric interpolator versus linear interpolator for precision cnc machining. Comput Aided Des 26(3):225-234
13. Yeh SS, Hsu PL (1999) The speed-controlled interpolator for machining parametric curves. Comput Aided Des 31(5):349-357
14. Yeh SS, Hsu PL (2002) Adaptive-feedrate interpolation for parametric curves with a confined chord error. Comput Aided Des 34(3):229-237
15. Farouki RT, Tsai YF, Wilson CS (2000) Physical constraints on feedrates and feed accelerations along curved tool paths. Comput Aided Geom D 17(4):337-359
16. Bobrow JE, Dubowsky S, Gibson JS (1985) Time-optimal control of robotic manipulators along specified paths. Int J Robot Res 4(3):3-17
17. Timar SD, Farouki RT, Smith TS et al (2005) Algorithms for time-optimal control of CNC machines along curved tool paths. Robot Comput Integr Manuf 21(1):37-53
18. Dong J, Stori JA (2006) A generalized time-optimal bidirectional scan algorithm for constrained feed-rate optimization. J Dyn Sys-T Asme 128(2):379-390
19. Sun YW, Wang J, Guo DM (2006) Guide curve based interpolation scheme of parametric curves for precision CNC machining. Int J Mach Tool Manu 46(3/4):235-242
20. Zhang K, Yuan CM, Gao XS (2013) Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration. Int J Adv Manuf Technol 66(9/12):1685-1697
21. Zhou JF, Sun YW, Guo DM (2014) Adaptive feedrate interpolation with multiconstraints for five-axis parametric toolpath. Int J Adv Manuf Technol 71(9/12):1873-1882
22. Barre PJ, Bearee R, Borne P et al (2005) Influence of a jerk controlled movement law on the vibratory behaviour of high-dynamics systems. J Intell Robot Syst 42(3):275-293
23. Bharathi A, Dong JY (2016) Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints. Int J Adv Manuf Technol 82(5/8):1029-1040
24. Erkorkmaz K, Altintas Y (2001) High speed CNC system design. part I:jerk limited trajectory generation and quintic spline interpolation. Int J Mach Tool Manu 41(9):1323-1345
25. Lin MT, Tsai MS, Yau HT (2007) Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm. Int J Mach Tool Manu 47(15):2246-2262
26. Tang L, Huang J, Zhu LM et al (2019) Path tracking of a cable-driven snake robot with a two-level motion planning method. IEEE-Asme T Mech 24(3):935-946
27. Jahanpour J, Alizadeh MR (2014) A novel acc-jerk-limited NURBS interpolation enhanced with an optimized S-shaped quintic feedrate scheduling scheme. Int J Adv Manuf Technol 77(9/12):1889-1905
28. Fang Y, Qi J, Hu J et al (2020) An approach for jerk-continuous trajectory generation of robotic manipulators with kinematical constraints. Mech Mach Theory 153:103957. https://doi.org/10.1016/j.mechmachtheory.2020.103957
29. Lee AC, Lin MT, Pan YR et al (2011) The feedrate scheduling of NURBS interpolator for CNC machine tools. Comput Aided Des 43(6):612-628
30. Huang J, Zhu LM (2016) Feedrate scheduling for interpolation of parametric tool path using the sine series representation of jerk profile. P I Mech Eng B-J Eng 231(13):2359-2371
31. Alintas Y, Erkormaz K (2003) Feedrate optimization for spline interpolation in high speed machine tools. CIRP Ann-Manuf Techn 52(1):297-302
32. Sencer B, Altintas Y, Croft E (2008) Feed optimization for five-axis CNC machine tools with drive constraints. Int J Mach Tool Manu 48(7/8):733-745
33. Liu H, Liu Q, Sun PP et al (2016) The optimal feedrate planning on five-axis parametric tool path with geometric and kinematic constraints for CNC machine tools. Int J Prod Res 55(13):3715-3731
34. Xie FB, Chen LF, Li ZY et al (2020) Path smoothing and feed rate planning for robotic curved layer additive manufacturing. Robot Comput Integr Manuf 65:101967. https://doi.org/10.1016/j.rcim.2020.101967
35. Erkorkmaz K, Heng M (2008) A heuristic feedrate optimization strategy for NURBS toolpaths. CIRP Ann-Manuf Techn 57(1):407-410
36. Sun YW, Zhao Y, Bao YR et al (2015) A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints. Int J Mach Tool Manu 97:86-97
37. Liang FS, Zhao J, Ji SJ (2017) An iterative feed rate scheduling method with confined high-order constraints in parametric interpolation. Int J Adv Manuf Technol 92(5/8):2001-2015
38. Li GX, Liu HT, Yue W et al (2021) Feedrate scheduling of a five-axis hybrid robot for milling considering drive constraints. Int J Adv Manuf Technol 112(11/12):3117-3136
39. Lu L, Zhang L, Ji S et al (2015) An offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems. Int J Adv Manuf Technol 83(9/12):2143-2157
