Advances in Manufacturing

, Volume 6, Issue 3, pp 308–318 | Cite as

Use of inverse stability solutions for identification of uncertainties in the dynamics of machining processes

  • Lutfi Taner TuncEmail author
  • Orkun Ozsahin


Research on dynamics and stability of machining operations has attracted considerable attention. Currently, most studies focus on the forward solution of dynamics and stability in which material properties and the frequency response function at the tool tip are known to predict stable cutting conditions. However, the forward solution may fail to perform accurately in cases wherein the aforementioned information is partially known or varies based on the process conditions, or could involve several uncertainties in the dynamics. Under these circumstances, inverse stability solutions are immensely useful to identify the amount of variation in the effective damping or stiffness acting on the machining system. In this paper, the inverse stability solutions and their use for such purposes are discussed through relevant examples and case studies. Specific areas include identification of process damping at low cutting speeds and variations in spindle dynamics at high rotational speeds.


Inverse stability Machining dynamics High speed milling Process damping Spindle dynamics 



The authors acknowledge the support of Turkish National Science Foundation (Grant No. 108M340).


  1. 1.
    Taylor FW (1907) On the art of cutting metals. American Society of Mechanical Engineers, New YorkGoogle Scholar
  2. 2.
    Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. Ann CIRP 44(1):357–362CrossRefGoogle Scholar
  3. 3.
    Insperger T, Stepan G (2002) Semi-discretization method for delayed systems. Int J Numer Methods Eng 55(5):503–518MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Tlusty J, Polacek M (1963) The stability of machine tools against self-excited vibrations in machining. Int Res Prod Eng 465–474Google Scholar
  5. 5.
    Das MK, Tobias SA (1967) The relation between the static and the dynamic cutting of metals. Int J Mach Tool Des Res 763:89Google Scholar
  6. 6.
    Koenigsberger F, Tlusty J (1967) Machine tool structures-Vol. I: stability against chatter. Pergamon Press, OxfordGoogle Scholar
  7. 7.
    Opitz H, Bernardi F (1970) Investigation and calculation of the chatter behavior of lathes and milling machines. Ann CIRP 18:335–343Google Scholar
  8. 8.
    Sridhar R, Hohn RE, Long GW (1968) A stability algorithm for the general milling process: contribution to machine tool chatter research 7. J Eng Ind 90(2):330–334CrossRefGoogle Scholar
  9. 9.
    Minis I, Yanushevsky T, Tembo R et al (1990) Analysis of linear and nonlinear chatter in milling. Ann CIRP 39:459–462CrossRefGoogle Scholar
  10. 10.
    Tlusty J (1978) Analysis of the state of research in cutting dynamics. Ann CIRP 27(2):583–589Google Scholar
  11. 11.
    Sisson TR, Kegg RL (1969) An explanation of low-speed chatter effects. ASME J Eng Ind 91:558–951CrossRefGoogle Scholar
  12. 12.
    Wu DW (1984) A new approach of formulating the transfer function for dynamic cutting processes. J Eng Ind 111:37–47CrossRefGoogle Scholar
  13. 13.
    Budak E, Tunc LT (2009) A new method for identification and modeling of process damping in machining. J Manuf Sci Eng 131(5):051019CrossRefGoogle Scholar
  14. 14.
    Rivin E (1999) Stiffness and damping in mechanical design. Marcel Dekker Inc., New YorkCrossRefGoogle Scholar
  15. 15.
    Stone BJ (1982) The state of the art in the measurement of the stiffness and damping of rolling element bearings. CIRP Ann Manuf Technol 31:529–538CrossRefGoogle Scholar
  16. 16.
    Harris TA (2001) Rolling bearing analysis, 4th edn. Wiley, New YorkGoogle Scholar
  17. 17.
    Lee CW (1993) Vibration analysis of rotors. Kluwer, DordrechtCrossRefGoogle Scholar
  18. 18.
    Friswell MI, Penny JET, Garvey SD et al (2010) Dynamics of rotating machines. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  19. 19.
    Jiang JS, Zheng S (2010) A modeling approach for analysis and improvement of spindle-drawbar-bearing assembly dynamics. Int J Mach Tools Manuf 50(1):131–142CrossRefGoogle Scholar
  20. 20.
    Kruth JP, Liu AMM, Vanherck P et al (2002) A strategy for selection of optimal cutting parameter in high-speed milling to avoid chatter vibration. Int J Prod Eng Comput 4(5):35–42Google Scholar
  21. 21.
    Kilic ZM, Iglesias A, Munoa J et al (2010) Investigation of tool wear on the stability of milling process using an inverse method. In: CIRP 2nd international conference on process machine interactions, Vancouver, CanadaGoogle Scholar
  22. 22.
    Suzuki N, Kurata Y, Kato T et al (2012) Identification of transfer function by inverse analysis of self-excited chatter vibration in milling operations. Precis Eng 36(4):568–575CrossRefGoogle Scholar
  23. 23.
    Cao Y, Altintas Y (2004) A general method for the modeling of spindle-bearing systems. J Mech Des 126(6):557–566CrossRefGoogle Scholar
  24. 24.
    Altintas Y, Cao Y (2005) Virtual design and optimization of machine tool spindles. CIRP Ann Manuf Technol 54(1):379–382CrossRefGoogle Scholar
  25. 25.
    Lin CW, Tu JF, Kamman J (2003) An integrated thermo-mechanical-dynamic model to characterize motorized machine tool spindles during very high-speed rotation. Int J Mach Tools Manuf 43(10):1035–1050CrossRefGoogle Scholar
  26. 26.
    Tatar K, Gren P (2007) Measurement of milling tool vibrations during cutting using laser vibrometry. Int J Mach Tools Manuf 48:380–387CrossRefGoogle Scholar
  27. 27.
    Rantatalo M, Aidanpaa JO, Göransson B et al (2007) Milling machine spindle analysis using FEM and non-contact spindle excitation and response measurement. Int J Mach Tools Manuf 47:1034–1045CrossRefGoogle Scholar
  28. 28.
    Zaghbani I, Songmene V (2009) Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis. Int J Mach Tools Manuf 49:947–957CrossRefGoogle Scholar
  29. 29.
    Opitz H, Weck MC (1970) Determination of the transfer function by means of spectral density measurements and its application to dynamic investigation of machine tools under machining conditions. In: Proceedings of the 10th international MTDR conference, University of Manchester Institute of Science and Technology, ManchesterGoogle Scholar
  30. 30.
    Minis IE, Magrab EB, Pandelidis IO (1990) Improved methods for the prediction of chatter in turning Part 1: determination of structural response parameters. Trans ASME 112:12–20Google Scholar
  31. 31.
    Ozsahin O, Budak E, Ozguven HN (2011) Investigating dynamics of machine tool spindles under operational conditions. Adv Mater Res 223:610–621CrossRefGoogle Scholar
  32. 32.
    Bediz B, Kumar U, Schmitz TL et al (2012) Modeling and experimentation for three-dimensional dynamics of endmills. Int J Mach Tools Manuf 53(1):39–50CrossRefGoogle Scholar
  33. 33.
    Ozsahin O, Budak E, Ozguven HN (2015) In-process tool point FRF identification under operational conditions using inverse stability solution. Int J Mach Tools Manuf 89:64–73CrossRefGoogle Scholar
  34. 34.
    Tunç LT, Budak E (2013) Identification and modeling of process damping in milling. Trans ASME J Manuf Sci Eng 135(2):021001CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Integrated Manufacturing Technologies Research and Application Center, Faculty of Engineering and Natural SciencesSabanci UniversityTuzla, IstanbulTurkey
  2. 2.Department of Mechanical EngineeringMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations