Skip to main content
SpringerLink
Log in

An offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

The ability of drive unit limits the velocity, acceleration, and jerk of the axis, and the process and tool path geometry constrain the feedrate, acceleration, and jerk of the trajectory. It is of great difficulty and importance to schedule a suitable feedrate profile to achieve the higher machining efficiency and satisfy all the constraints. Due to the complexity of the feedrate scheduling algorithm, this paper presents an offline predictive feedrate scheduling method considering the constraints of trajectory system and drive system. The constraints in the drive system are transformed to the trajectory system appropriately, which reduces the difficulty of feedrate scheduling. The one-dimensional high-order time-optimal problem is solved by a numerical calculation method according to the bang-bang control method. The predictive method is applied to find the switching points of the jerk. Then a time-optimal feedrate profile under all the constraints is obtained. Both simulations and experiments are carried out to prove the effectiveness of the proposed offline predictive feedrate scheduling method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Beudaert X, Pechard P-Y, Tournier C (2011) 5-Axis tool path smoothing based on drive constraints. Int J Mach Tools Manuf 51(12):958–965. doi:10.1016/j.ijmachtools.2011.08.014

    Article  Google Scholar 

  2. Zhang LB, You YP, He J, Yang XF (2010) The transition algorithm based on parametric spline curve for high-speed machining of continuous short line segments. Int J Adv Manuf Technol 52(1–4):245–254. doi:10.1007/s00170-010-2718-z

    Google Scholar 

  3. Ernesto CA, Farouki RT (2011) High-speed cornering by CNC machines under prescribed bounds on axis accelerations and toolpath contour error. Int J Adv Manuf Technol 58(1–4):327–338. doi:10.1007/s00170-011-3394-3

    Google Scholar 

  4. Altintas Y, Erkorkmaz K, Zhu WH (2000) Sliding mode controller design for high speed feed drives. CIRP Ann Manuf Technol 49(1):265–270. doi:10.1016/s0007-8506(07)62943-6

    Article  Google Scholar 

  5. Pritschow G, Croon N (2013) Ball screw drives with enhanced bandwidth by modification of the axial bearing. CIRP Ann Manuf Technol 62(1):383–386. doi:10.1016/j.cirp.2013.03.086

    Article  Google Scholar 

  6. Varanasi KK, Nayfeh SA (2004) The dynamics of lead-screw drives: low-order modeling and experiments. J Dyn Syst Meas Control 126(2):388–396

    Article  Google Scholar 

  7. Bobrow JE, Dubowsky S, Gibson J (1985) Time-optimal control of robotic manipulators along specified paths. Int J Robot Res 4:3–17

    Article  Google Scholar 

  8. Shin K, McKay N (1985) Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans Autom Control 30:531–541

    Article  MATH  Google Scholar 

  9. Dong J, Stori JA (2006) A generalized time-optimal bidirectional scan algorithm for constrained feed-rate optimization. J Dyn Syst Meas Control 128(2):379. doi:10.1115/1.2194078

    Article  Google Scholar 

  10. Shin KG, McKay ND (1986) A dynamic programming approach to trajectory planning of robotic manipulators. IEEE Trans Autom Control 131(6):491–500

    Article  MATH  Google Scholar 

  11. Gourdeau R, Schwartz HM (1989) Optimal control of a robot manipulator using a weighted time-energy cost function. Decision and Control, 1989. Proceedings of the 28th IEEE Conference on. IEEE, 1628–1631

  12. Lai J-Y, Lin K-Y, Tseng S-J, Ueng W-D (2007) On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk. Int J Adv Manuf Technol 37(1–2):104–121. doi:10.1007/s00170-007-0954-7

    Google Scholar 

  13. Fan W, Gao X-S, Yan W, Yuan C-M (2012) Interpolation of parametric CNC machining path under confined jounce. Int J Adv Manuf Technol 62(5–8):719–739. doi:10.1007/s00170-011-3842-0

    Article  Google Scholar 

  14. Dong J, Ferreira PM, Stori JA (2007) Feed-rate optimization with jerk constraints for generating minimum-time trajectories. Int J Mach Tools Manuf 47(12–13):1941–1955. doi:10.1016/j.ijmachtools.2007.03.006

    Article  Google Scholar 

  15. Zhang K, Yuan C-M, Gao X-S (2012) 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. doi:10.1007/s00170-012-4450-3

    Google Scholar 

  16. Zhang K, Yuan C-M, Gao X-S, Li H (2012) A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk. Robot Comput Integr Manuf 28(4):472–483. doi:10.1016/j.rcim.2012.02.006

    Article  Google Scholar 

  17. Altintas Y, Erkorkmaz K (2003) Feedrate optimization for spline interpolation in high speed machine tools. CIRP Ann Manuf Technol 52(1):297–302. doi:10.1016/s0007-8506(07)60588-5

    Article  Google Scholar 

  18. Sencer B, Altintas Y, Croft E (2008) Feed optimization for five-axis CNC machine tools with drive constraints. Int J Mach Tools Manuf 48(7–8):733–745. doi:10.1016/j.ijmachtools.2008.01.002

    Article  Google Scholar 

  19. Zhang Q, Li S-R (2013) Efficient computation of smooth minimum time trajectory for CNC machining. Int J Adv Manuf Technol 68(1–4):683–692. doi:10.1007/s00170-013-4790-7

    Article  Google Scholar 

  20. Fan W, Gao X-S, Lee C-H, Zhang K, Zhang Q (2013) Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming. Int J Adv Manuf Technol 69(5–8):1373–1388. doi:10.1007/s00170-013-5083-x

    Article  Google Scholar 

  21. Erkorkmaz K, Heng M (2008) A heuristic feedrate optimization strategy for NURBS toolpaths. CIRP Ann Manuf Technol 57(1):407–410. doi:10.1016/j.cirp.2008.03.039

    Article  Google Scholar 

  22. Ridwan F, Xu X, Ho FCL (2012) Adaptive execution of an NC program with feed rate optimization. Int J Adv Manuf Technol 63(9–12):1117–1130. doi:10.1007/s00170-012-3959-9

    Article  Google Scholar 

  23. Heng M, Erkorkmaz K (2010) Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability. Int J Mach Tools Manuf 50(3):281–293. doi:10.1016/j.ijmachtools.2009.11.005

    Article  Google Scholar 

  24. Lee A-C, Lin M-T, Pan Y-R, Lin W-Y (2011) The feedrate scheduling of NURBS interpolator for CNC machine tools. Comput Aided Des 43(6):612–628. doi:10.1016/j.cad.2011.02.014

    Article  Google Scholar 

  25. Beudaert X, Lavernhe S, Tournier C (2012) Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path. Int J Mach Tools Manuf 57:73–82. doi:10.1016/j.ijmachtools.2012.02.005

    Article  Google Scholar 

  26. Sun Y, Bao Y, Kang K, Guo D (2013) An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining. Int J Adv Manuf Technol 68(9–12):1977–1987. doi:10.1007/s00170-013-4816-1

    Article  Google Scholar 

  27. Sun Y, Zhao Y, Bao Y, Guo D (2014) A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints. Int J Mach Tools Manuf 77:74–81. doi:10.1016/j.ijmachtools.2013.11.002

    Article  Google Scholar 

  28. Bryson AE, Ho YC (1975) Applied optimal control: optimization, estimation and control. Wiley, New York

    Google Scholar 

  29. Erkorkmaz K, Layegh SE, Lazoglu I, Erdim H (2013) Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics. CIRP Ann Manuf Technol 62(1):395–398. doi:10.1016/j.cirp.2013.03.084

    Article  Google Scholar 

  30. Guo J-X, Zhang K, Zhang Q, Gao X-S (2013) Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system. Comput Aided Des 45(12):1538–1546. doi:10.1016/j.cad.2013.07.002

    Article  Google Scholar 

  31. Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Science and Engineering, Jilin University, Changchun, 130025, People’s Republic of China

    Lei Lu, Lei Zhang, Shijun Ji, Yanjun Han & Ji Zhao

Authors
  1. Lei Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shijun Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanjun Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ji Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lei Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, L., Zhang, L., Ji, S. et al. An offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems. Int J Adv Manuf Technol 83, 2143–2157 (2016). https://doi.org/10.1007/s00170-015-8112-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-015-8112-0

Keywords

Search

Navigation