Position-dependent stability analysis of turning with tool and workpiece compliance

  • Andreas Otto
  • Firas A. Khasawneh
  • Günter Radons


A universal frequency domain approach for studying the dynamics of metal cutting with a flexible workpiece and a compliant tool is derived. The method is used for the identification of the position-dependent stability lobes in turning. It enables a fast, accurate, and systematic stability analysis of turning processes in the parameter space, which is not restricted to simple dynamic models with only a specific number of modes in one spatial direction. In particular, a combination of experimental data for the tool tip dynamics with analytical or numerical data for the workpiece dynamics is possible, which is demonstrated by a concrete example. The effect of the mode interaction between tool and workpiece modes via the cutting process is illustrated. Counterintuitively, the possibility of a process destabilization for an increased workpiece stiffness was observed, which can be explained by the mode interaction. The presented methods and results can be efficiently used for optimizing machine tool development and process planning.


Chatter Vibration Stability Turning Boring Beam theory 


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  1. 1.
    Zhao MX, Balachandran B (2001) Dynamics and stability of milling process. Int J Solids Struct 38(10–13):2233– 2248CrossRefzbMATHGoogle Scholar
  2. 2.
    Khasawneh FA, Mann B, Insperger T, Stépán G (2009) Increased stability of low-speed turning through a distributed force and continuous delay model. J Comput Nonlin Dyn 4(4):041,003CrossRefGoogle Scholar
  3. 3.
    Butcher E, Bobrenkov O, Bueler E, Nindujarla P (2009) Analysis of milling stability by the Chebyshev collocation method: Algorithm and optimal stable immersion levels. J Comp Nonlin Dyn 4(3):031,003CrossRefGoogle Scholar
  4. 4.
    Otto A, Radons G (2013) Application of spindle speed variation for chatter suppression in turning. CIRP J Manuf Sci Technol 6(2):102–109CrossRefGoogle Scholar
  5. 5.
    Yu SD, Shah V (2009) Theoretical and experimental studies of chatter in turning for uniform and stepped workpieces. J Vibr Acoustics 130(6):061,005CrossRefGoogle Scholar
  6. 6.
    Gang L (2009) Study on deformation of titanium thin-walled part in milling process. J Mater Proc Technol 209(6):2788– 2793CrossRefGoogle Scholar
  7. 7.
    Han X, Ouyang H, Wang M, Hassan N, Mao Y (2012) Self-excited vibration of workpieces in a turning process. Proc Inst Mech Eng C J Mech Eng Sci 226(8):1958–1970CrossRefGoogle Scholar
  8. 8.
    Song Q, Ai X, Tang W (2011) Prediction of simultaneous dynamic stability limit of time-variable parameters system in thin-walled workpiece high-speed milling processes. Int J Adv Manuf Technol 55(9–12):883–889CrossRefGoogle Scholar
  9. 9.
    Urbikain G, de Lacalle LL, Campa F, Fernandez A, Elias A (2012) Stability prediction in straight turning of a flexible workpiece by collocation method. Int J Mach Tools Manuf 54–55:73–81CrossRefGoogle Scholar
  10. 10.
    Eksioglu C, Kilic Z, Altintas Y (2012) Discrete-time prediction of chatter stability, cutting forces, and surface location errors in flexible milling systems. J Manuf Sci Engin 134(6):061,006CrossRefGoogle Scholar
  11. 11.
    Thevenot V, Arnaud L, Dessein G, Cazenave-Larroche G (2006) Integration of dynamic behaviour variations in the stability lobes method: 3d lobes construction and application to thin-walled structure milling. Int J Adv Manuf Technol 27(7–8):638–644CrossRefGoogle Scholar
  12. 12.
    Bravo U, Altuzarra O, de Lacalle LL, Sanchez J, Campa F (2005) Stability limits of milling considering the flexibility of the workpiece and the machine. Int J Mach Tools Manuf 45(15):1669–1680CrossRefGoogle Scholar
  13. 13.
    Chen C, Tsao Y (2006) A stability analysis of turning a tailstock supported flexible work-piece. Int J Mach Tools Manuf 46(1):18–25CrossRefGoogle Scholar
  14. 14.
    Vela-Martinez L, Jauregui-Correa J, Rubio-Cerda E, Herrera-Ruiz G, Lozano-Guzman A (2008) Analysis of compliance between the cutting tool and the workpiece on the stability of a turning process. Int J Mach Tools and Manuf 48(9):1054–1062CrossRefGoogle Scholar
  15. 15.
    Sekar M, Srinivas J, Kotaiah K, Yang S (2009) Stability analysis of turning process with tailstock-supported workpiece. Int J Adv Manuf Technol 43(9–10):862–871CrossRefGoogle Scholar
  16. 16.
    Chen D, Lin B, Han Z, Zhang Y (2013) Study on the optimization of cutting parameters in turning thin-walled circular cylindrical shell based upon cutting stability. Int J Adv Manuf Technol 69(1–4):891–899CrossRefGoogle Scholar
  17. 17.
    Altintas Y (2000) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. Cambridge University Press, New YorkGoogle Scholar
  18. 18.
    Otto A, Radons G (2015) Stability analysis of machine-tool vibrations in the frequency domain. Proc 12th IFAC TDS Workshop, Ann ArborGoogle Scholar
  19. 19.
    Pakdemirli M, Boyaci H (2002) Effect of non-ideal boundary conditions on the vibrations of continuous systems. J Sound Vibr 249(4):815–823MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zatarain M, Bediaga I, Muñoa J, Insperger T (2010) Analysis of directional factors in milling: importance of multi-frequency calculation and of the inclusion of the effect of the helix angle. Int J Adv Manuf Techn 47:535–542CrossRefGoogle Scholar
  21. 21.
    Adhikari S (2006) Damping modelling using generalized proportional damping. J Sound Vibr 293(1–2):156–170CrossRefGoogle Scholar
  22. 22.
    Budak E, Ozlu E (2007) Analytical modeling of chatter stability in turning and boring operations: A multi-dimensional approach. CIRP Annals 56:401–404CrossRefGoogle Scholar
  23. 23.
    Otto A, Rauh S, Kolouch M, Radons G (2014) Extension of tlusty’s law for the identification of chatter stability lobes in multi-dimensional cutting processes. Int J Mach Tools Manuf 82–83:50–58CrossRefGoogle Scholar
  24. 24.
    Danek O, Polacek M, Spacek J, Tlusty J (1962) Selbsterregte Schwingungen an Werkzeugmaschinen. VEB Technik, BerlinGoogle Scholar
  25. 25.
    Al-Regib E, Ni J, Lee SH (2003) Programming spindle speed variation for machine tool chatter suppression. Int J Mach Tools Manuf 43(12):1229–1240CrossRefGoogle Scholar
  26. 26.
    Tyler C, Schmitz T (2013) Analytical process damping stability prediction. J Manuf Proc 15(1):69–76CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Andreas Otto
    • 1
  • Firas A. Khasawneh
    • 2
  • Günter Radons
    • 1
  1. 1.Institute of PhysicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Mechanical EngineeringSUNY Polytechnic InstituteUticaUSA

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