Skip to main content
SpringerLink
Log in

A feedrate optimization method for CNC machining based on chord error revaluation and contour error reduction

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

Abstract

Interpolation of parametric curves is one of the most effective methods in high-performance computer numerical control (CNC) machining. Its precision highly depends on chord errors from feedrate scheduling and contour errors from real-time machining. In order to improve machining precision, a novel feedrate optimization method is proposed in this paper. The osculating circle (OC) method can effectively estimate the chord errors, but its precision degrades if the trajectory curvature changes dramatically. Therefore, an iterative algorithm based on OC method is developed to reevaluate the chord errors, which can upgrade the estimation precision and further improve the feedrate constraints. To reduce the contour error, feature zones on the trajectory are firstly selected according to the kinestates and a specified zone length. In each feature zone, the projection of tracking error onto the zone chord-line is calculated as a new vector, based on which an indirect contour error compensation method is proposed through refining the feedrate profile. To ensure that the contour error can be reduced, the compensation performance is pre-estimated before implementation. Finally, simulation results in different scenarios are presented to validate the high precision of the proposed 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Piegl L, Tiller W (1997) The NURBS book. Springer, Berlin

    Book  Google Scholar 

  2. Tulsyan S, Altintas Y (2015) Local toolpath smoothing for five-axis machine tools. Int J Mach Tools Manuf 96:15–26

    Article  Google Scholar 

  3. Ye PQ, Zhang Y, Xiao JX, Zhao MY, Zhang H (2019) A novel feedrate planning and interpolating method for parametric toolpath in Frenet-Serret frame. Int J Adv Manuf Technol 101(5-8):1915–1925

    Article  Google Scholar 

  4. Jahanpour J, Alizadeh MR (2015) 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

    Article  Google Scholar 

  5. Chanda L, Cripps RJ (2018) Characterising the effects of shape on tool path motion. Int J Mach Tools Manuf 132:17–35

    Article  Google Scholar 

  6. Tajima S, Sencer B (2017) Global tool-path smoothing for CNC machine tools with uninterrupted acceleration. Int J Mach Tools Manuf 121:81–95

    Article  Google Scholar 

  7. Wang GX, Shu QL, Wang J, Li L (2017) Research on adaptive non-uniform rational B-spline real-time interpolation technology based on acceleration constraints. Int J Adv Manuf Technol 91(5-8):2089–2100

    Article  Google Scholar 

  8. Liu H, Liu Q, Yuan SM (2017) Adaptive feedrate planning on parametric tool path with geometric and kinematic constraints for CNC machining. Int J Adv Manuf Technol 90(5-8):1889–1896

    Article  Google Scholar 

  9. Yeung CH, Altintas Y, Erkorkmaz K (2006) Virtual CNC system. Part I. System architecture. Int J Mach Tools Manuf 46:1107–1123

    Article  Google Scholar 

  10. Faux ID, Pratt MJ (1979) Computational geometry for design and manufacture. Ellis Horwood Ltd, New York

    MATH  Google Scholar 

  11. Yeh SS, Hsu PL (2002) Adaptive-feedrate interpolation for parametric curves with a confined chord error. Comput Aided Des 34:229–237

    Article  Google Scholar 

  12. Tajima S, Sencer B (2016) Kinematic corner smoothing for high speed machine tools. Int J Mach Tools Manuf 108:27–43

    Article  Google Scholar 

  13. Fan W, Ji JW, Wu PY, Wu DZ, Chen H (2020) Modeling and simulation of trajectory smoothing and feedrate scheduling for vibration-damping CNC machining. Simul Model Pract Th 99: 102028

  14. Yong T, Narayanaswami R (2003) A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining. Comput Aided Des 35:1249–1259

    Article  Google Scholar 

  15. Li JG, Liu Y, Li YN, Zhong GG (2019) S-model speed planning of NURBS curve based on uniaxial performance limitation. IEEE ACCESS 7:60837–60849

    Article  Google Scholar 

  16. Fan W, Gao XS, Yan W, Yuan CM (2012) Interpolation of parametric CNC machining path under confined jounce. Int J Adv Manuf Technol 62(5-8):719–739

    Article  Google Scholar 

  17. Huang J, Zhu LM (2017) Feedrate scheduling for interpolation of parametric tool path using the sine series representation of jerk profile. Proc IMechE Part B: J Engineering Manufacture 231(13):2359–2371

    Article  Google Scholar 

  18. Jin YA, He Y, Fu JZ, Lin ZW, Gan WF (2014) A fine-interpolation-based parametric interpolation method with a novel real-time look-ahead algorithm. Comput Aided Des 55:37–48

    Article  Google Scholar 

  19. Ni HP, Yuan JP, Ji S, Zhang CR, Hu TL (2018) Feedrate scheduling of NURBS interpolation based on a novel jerk-continuous ACC/DEC algorithm. IEEE Access 6:66403–66417

    Article  Google Scholar 

  20. Koren Y (1980) Cross-coupled biaxial computer control for manufacturing systems. Journal of Dynamic Systems Measurement and Control 102:265–272

    Article  Google Scholar 

  21. Yeh SS, Hsu PL (2000) A new approach to biaxial cross-coupled control. In: Proceedings of the 2000 IEEE International Conference on Control Applications, pp 168–173

  22. Yeh SS, Hsu PL (2002) Estimation of the contouring error vector for the cross-coupled control design. IEEE/ASME Trans Mechatron 7(1):44–51

    Article  Google Scholar 

  23. Zhang DL, Yang JX, Chen YH, Chen YP (2015) A two-layered cross coupling control scheme for a three-dimensional motion control system. Int J Mach Tools Manuf 98:12–20

    Article  Google Scholar 

  24. Liu WR, Ren F, Sun YW, Jiang SL (2018) Contour error pre-compensation for three-axis machine tools by using cross-coupled dynamic friction control. Int J Adv Manuf Technol 98(1-4):551–563

    Article  Google Scholar 

  25. Lam D, Manzie C, Good MC (2013) Model predictive contouring control for biaxial systems. IEEE Trans Control Syst Technol 21(2):552–559

    Article  Google Scholar 

  26. Ngo PD, Shin YC (2013) Milling contour error control using multilevel fuzzy controller. Int J Adv Manuf Technol 66(9-12):1641–1655

    Article  Google Scholar 

  27. Mao WL, Shiu DY (2020) Precision trajectory tracking on XY motion stage using robust interval type-2 fuzzy PI sliding mode control method. Int J Precis Eng Man 21(5):797–818

    Article  Google Scholar 

  28. Dong JC, Wang TY, Li B, Ding YY (2014) Smooth feedrate planning for continuous short line tool path with contour error constraint. Int J Mach Tools Manuf 76:1–12

    Article  Google Scholar 

  29. Chen MS, Sun YW (2018) A moving knot sequence-based feedrate scheduling method of parametric interpolator for CNC machining with contour error and drive constraints. Int J Adv Manuf Technol 98(1-4):487–504

    Article  Google Scholar 

  30. Jia ZY, Song DN, Ma JW, Hu GQ, Su WW (2017) A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints. Int J Mach Tools Manuf 116:1–17

    Article  Google Scholar 

  31. Wang J, Sui Z, Tian YT, Wang XL, Fang L (2015) A speed optimization algorithm based on the contour error model of lag synchronization for CNC cam grinding. Int J Adv Manuf Technol 80 (5-8):1421–1432

    Article  Google Scholar 

  32. Du X, Huang J, Zhu LM, Ding H (2019) Third-order chord error estimation for freeform contour in computer-aided manufacturing and computer numerical control systems. Proc IMechE Part B: J Engineering Manufacture 233(3):863–874

    Article  Google Scholar 

  33. Lin FM, Shen LY, Yuan CM, Mi ZP (2018) Certified space curve fitting and trajectory planning for CNC machining with cubic B-splines. Comput Aided Des 106:13–29

    Article  Google Scholar 

  34. Min K, Lee CH, Yan CY, Fan W, Hu PC (2020) Six-dimensional B-spline fitting method for five-axis tool paths. Int J Adv Manuf Technol 107(5-6):2041–2054

    Article  Google Scholar 

  35. Min K, Sun YY, Lee CH, Hu PC, He SS (2019) An improved B-spline fitting method with arc-length parameterization, G2-continuous blending, and quality refinement. Int J Adv Manuf Technol 20(11):1939–1955

    Google Scholar 

  36. Zhong WB, Luo XC, Chang WL, Ding F, Cai YK (2018) A real-time interpolator for parametric curves. Int J Mach Tools Manuf 125:133–145

    Article  Google Scholar 

  37. Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I jerk limited trajectory generation and quintic spline interpolation. Int J Mach Tools Manuf 41(9):1323–1345

    Article  Google Scholar 

  38. Lai JY, Lin KY, Tseng SJ, Ueng WD (2008) 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical & Control Engineering, Shaanxi University of Science & Technology, Xi’an, China

    Baoquan Liu, Mengjie Xu & Yong Shi

  2. TOLL Microelectronics Co., Ltd, Xi’an, China

    Jianping Fang

Authors
  1. Baoquan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mengjie Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianping Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yong Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mengjie Xu.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, B., Xu, M., Fang, J. et al. A feedrate optimization method for CNC machining based on chord error revaluation and contour error reduction. Int J Adv Manuf Technol 111, 3437–3452 (2020). https://doi.org/10.1007/s00170-020-06288-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-020-06288-5

Keywords

Search

Navigation