Contour error pre-compensation for five-axis high speed machining: offline gain adjustment approach

  • Tan-Quang Duong
  • Pedro Rodriguez-Ayerbe
  • Sylvain LavernheEmail author
  • Christophe Tournier
  • Didier Dumur


This paper presents an offline gain adjustment (OGA) approach to reduce contour error in five-axis high speed machining. The proposed contour error formulation is based on the estimation of tool contact points and the OGA is inspired from the idea of model predictive control (MPC). The control gains used in the position loop of servo drives are optimally adjusted offline to reduce the contour error for the considered trajectory. The obtained gain profiles are computed preserving axis kinematic limitations, stability criterion of servo drives, and the motor current constraints. The OGA is developed thanks to a validated machine simulator. The simulation results prove that the OGA reduces significantly the contour error in five-axis high speed machining.


Contour error CNC Offline gain adjustment Receding horizon Model predictive control 


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  1. 1.
    Altintas Y (2000) Manufacturing automation: metal cutting mechanics, machine tool calibrations and CNC design. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Hu P, Chen L, Tang K (2017) Efficiency-optimal iso-planar tool path generation for five-axis finishing machining of freeform surfaces. Comput Aided Des 83:33–50CrossRefGoogle Scholar
  3. 3.
    Huang J, Du X, Zhu LM (2018) Real-time local smoothing for five-axis linear tool-path considering smoothing error constraints. Int J Mach Tools Manuf 124:67–79CrossRefGoogle Scholar
  4. 4.
    Erkorkmaz K, Chen QGC, Zhao MY, Beudaert X, Gao XS (2017) Linear programming and windowing based feedrate optimization for spline toolpaths. CIRP Ann 66(1):393–396CrossRefGoogle Scholar
  5. 5.
    Altintas Y, Kersting P, Biermann D, Budak E, Denkena B, Lazoglu I (2014) Virtual process systems for part machining operations. CIRP Ann 63(2):585–605CrossRefGoogle Scholar
  6. 6.
    Altintas Y, Erkorkmaz K, Zhu WH (2000) Sliding mode controller design for high speed feed drives. CIRP Ann Manuf Technol 49(1):265–270CrossRefGoogle Scholar
  7. 7.
    Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part III: high speed tracking and contouring control of feed drives. Int J Mach Tools Manuf 41(11):1637–1658CrossRefGoogle Scholar
  8. 8.
    Dumur D, Susanu M, Aubourg M (2008) Complex form machining with axis drive predictive control. CIRP Ann Manuf Technol 57(1):399–402CrossRefGoogle Scholar
  9. 9.
    Tang L, Landers RG (2013) Multiaxis contour control - the state of the art. IEEE Trans Control Syst Technol 21(6):1997–2010CrossRefGoogle Scholar
  10. 10.
    Koren Y, Lo CC (1991) Variable-gain cross-coupling controller for contouring. CIRP Ann Manuf Technol 40(1):371–374CrossRefGoogle Scholar
  11. 11.
    Chiu GC, Tomizuka M (2011) Contouring control of machine tool feed drive systems: a task coordinate frame approach. IEEE Trans Control Syst Technol 9(1):130–139CrossRefGoogle Scholar
  12. 12.
    Altintas Y, Sencer B (2010) High speed contouring control strategy for five-axis machine tools. CIRP Ann Manuf Technol 59(1):417–420CrossRefGoogle Scholar
  13. 13.
    Yang J, Altintas Y (2015) A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools. Int J Mach Tools Manuf 88:9–23CrossRefGoogle Scholar
  14. 14.
    Cheng MY, Su KH (2009) Contouring accuracy improvement using a tangential contouring controller with a fuzzy logic-based feedrate regulator. Int J Adv Manuf Technol 41(1):75–85CrossRefGoogle Scholar
  15. 15.
    El Khalick MA, Uchiyama N (2011) Discrete-time model predictive contouring control for biaxial feed drive systems and experimental verification. Mechatronics 21(6):918–926CrossRefGoogle Scholar
  16. 16.
    Yang S, Ghasemi AH, Lu X, Okwudire CE (2015) Precompensation of servo contour errors using a model predictive control framework. Int J Mach Tools Manuf 98:50–60CrossRefGoogle Scholar
  17. 17.
    Erkorkmaz K, Yeung CH, Altintas Y (2006) Virtual CNC system. Part II. High speed contouring application. Int J Mach Tools Manuf 46(10):1124–1138CrossRefGoogle Scholar
  18. 18.
    Khoshdarregi MR, Tappe S, Altintas Y (2014) Integrated five-axis trajectory shaping and contour error compensation for high-speed CNC machine tools. IEEE/ASME Trans Mechatron 19(6):1859–1871CrossRefGoogle Scholar
  19. 19.
    Zhang K, Yuen A, Altintas Y (2013) Pre-compensation of contour errors in five-axis CNC machine tools. Int J Mach Tools Manuf 74:1–11CrossRefGoogle Scholar
  20. 20.
    Jaen-Cuellar AY, Romero-troncoso R, de J, Morales-Velazquez L, Osornio-Rios RA (2013) PID-controller tuning optimization with genetic algorithms in servo systems. Int J Adv Robot Syst 10(324):1–14Google Scholar
  21. 21.
    Le Flohic J, Paccot F, Bouton N, Chanal H (2018) Model-based method for feed drive tuning applied to serial machine tool. The International Journal of Advanced Manufacturing Technology 95(1–4):735–745CrossRefGoogle Scholar
  22. 22.
    Susanu M, Dumur D (2006) Hierarchical predictive control within an open architecture virtual machine tool. CIRP Ann Manuf Technol 55(1):389–392CrossRefGoogle Scholar
  23. 23.
    Prévost D, Lavernhe S, Lartigue C, Dumur D (2011) Feed drive modelling for the simulation of tool path tracking in multi-axis high speed machining. Int J Mechatron Manuf Syst 4(3-4):266–284Google Scholar
  24. 24.
    Beudaert X, Lavernhe S, Tournier C (2014) Direct trajectory interpolation on the surface using an open CNC. Int J Adv Manuf Technol 75(1):535–546CrossRefGoogle Scholar
  25. 25.
    Duong TQ, Rodriguez-Ayerbe P, Lavernhe S, Tournier C, Dumur D (2016) Offline gain adjustment with constraints for contour error reduction in high speed milling. In: 2016 IEEE International Conference on Advanced Intelligent Mechatronics, pp 201–206Google Scholar
  26. 26.
    Duong TQ, Rodriguez-Ayerbe P, Lavernhe S, Tournier C, Dumur D (2016) Receding horizon based offline gain adjustment for contour error reduction in high speed milling. Procedia CIRP- 10th CIRP Conf Intell Comput Manuf Eng 62:227–232Google Scholar
  27. 27.
    Tournier C, Duc E (2005) Iso-scallop tool path generation in 5-axis milling. Int J Adv Manuf Technol 25(9):867–875CrossRefGoogle Scholar
  28. 28.
    Pritschow G (1996) On the influence of the velocity gain factor on the path deviation. CIRP Ann Manuf Technol 45(1):367–371CrossRefGoogle Scholar
  29. 29.
    Tung ED, Tomizuka M (1993) Feedforward tracking controller design based on the identification of low frequency dynamics. ASME J Dyn syst Measur Control 115(3):348–356CrossRefzbMATHGoogle Scholar
  30. 30.
    Younkin GW (2003) Industrial servo control systems: Fundamentals and applications. Marcel Dekker, Inc, New YorkGoogle Scholar
  31. 31.
    Camacho EF, Bordons Alba C (2013) Model predictive control. Springer Science & Business Media, BerlinGoogle Scholar
  32. 32.
    Maciejowski JM (2002) Predictive control with constraints. Pearson EducationGoogle Scholar
  33. 33.
    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 57:73–82CrossRefGoogle Scholar
  34. 34.
    Siemens (2005) Siemens configuration manual simodrive 611 / masterdrives MC, 1FT6 Synchronous Motors, Manual, pp 144–145Google Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.L2S, CentraleSupélec-CNRS-Univ. Paris-SudGif-sur-YvetteFrance
  2. 2.LURPA, ENS Paris-SaclayUniv. Paris-Sud, Université Paris-SaclayCachanFrance

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