Dynamics of Spindle Assembly Metal-Cutting Machine Tool with Anisotropic Elastic Support

  • A. F. DenisenkoEmail author
  • M. V. Yakimov
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The article is devoted to the consideration of bending and translational-angular vibrations of spindles of metal-cutting machine tools. The features of the development of dynamic models associated with the significant difference in the values of the stiffnesses of the front and rear supports and the anisotropy of their radial rigidity are noted. The results of the investigation of the effect on the anisotropy of the radial stiffness of deviations from the roundness of the landing surfaces of the shaft and the shell of the bearings are presented. It has been shown experimentally that the stiffness of the front support of the spindle assembly of the lathe has an anisotropy. For the hodograph of stiffness in the form of ovality, analytical expressions are obtained for the natural frequencies of bending and translational-angular vibrations. It is shown that the presence of anisotropy of the stiffness of spindle supports leads to the appearance of a range of natural frequencies of the spindle which significantly complicates the implementation of diagnostic measures. The results of the estimation of the influence of the elastic characteristics of spindle supports on the assembly of the magnitude and range of the resulted stiffness coefficients and the frequency of the natural translational-angular vibrations are presented.


Spindle assembly Bending vibrations Translational-angular vibrations Natural frequencies Stiffness Hodograph of stiffness Anisotropy of the compliance Resulted stiffness coefficient 


  1. 1.
    Pisarev VI et al (2014) Maintenance and repair of metal-working machines with numerical control on the basis of an indisputable diagnostic of technical condition. Izv Samara Sci Cent Russ Acad Sci 16, 1(2):508–514Google Scholar
  2. 2.
    Marinescu I, Ispas C, Boboc D (2002) Handbook of machine tool analysis. In: Deckker M (ed). Marcel Dekker, Inc, New YorkGoogle Scholar
  3. 3.
    Gupta KN (1997) Vibration—a tool for machine diagnostics and condition monitoring. Sadhana 22(3):393–410CrossRefGoogle Scholar
  4. 4.
    Mannan MA, Stone BJ (1998) The use of vibration measurement for quality control of machine tool spindle. Int J Adv Manuf Technol 14:889–893CrossRefGoogle Scholar
  5. 5.
    Saravanan S, Yadava GS, Rao PV (2006) Condition monitoring studies on spindle bearing of a lathe. Int J Adv Manuf Technol 28:993–1005CrossRefGoogle Scholar
  6. 6.
    Mazid AM (2007) Evaluation of dynamic quality of lathe machines to categorise them for better productivity and accuracy reducing defects. In: Abstracts of 5th Australasian congress on applied mechanics, ACAM 2007, Brisbane, Australia, 10–12 Dec 2007Google Scholar
  7. 7.
    Orlikov ML (1989) Dynamics of machine tools. KievGoogle Scholar
  8. 8.
    Kelzon AS, Zhuravlev YuN, Yanvarev NV (1977) Calculation and design of rotary machines. Mechanical Engineering, LeningradGoogle Scholar
  9. 9.
    Dimentberg FM (1959) Bending vibrations of rotating shafts. Academy of Sciences of the USSR, MoscowGoogle Scholar
  10. 10.
    Filipovsky SV, Avramov KV (2009) Oscillations of rotors on nonlinear supports. Her Engine Build 3:127–132Google Scholar
  11. 11.
    Perepelkin NV, Mikhlin YuV (2010) Analysis of the forced vibration modes of a single-disk rotor on nonlinearly elastic supports. Mech Solid Body 40:221–232Google Scholar
  12. 12.
    Gorbenko AN (2006) On the influence of the nonlinearity of the rotor supports on the dynamics of the auto-balancing device. Autom Prod Process Mach Build Instrum Mak 40:63–69Google Scholar
  13. 13.
    Hong SW, Kang JO, Shin YC (2002) Dynamic analysis of rotor systems with angular contact ball bearings subject to axial and radial loads. Int J Korean Soc Precis Eng 3(2):61–71Google Scholar
  14. 14.
    Bae GH, Yoon YS, Hwang JH, Hong SW (2013) Effect of shaft alignment on the rotor-bearing system dynamics. In: Proceedings of the KSPE, pp 79–80Google Scholar
  15. 15.
    Lee D, Choi D (1997) A dynamic analysis of a flexible rotor in ball bearings with nonlinear stiffness characteristics. Int J Rotating Mach 3:73–80CrossRefGoogle Scholar
  16. 16.
    Hu W, Feng N, Haln E (2004) A comparison of techniques for identifying the configuration state of statically indeterminate rotor bearing systems. Tribol Int 37:149–157CrossRefGoogle Scholar
  17. 17.
    Tiwari R, Chakravarthy V (2006) Simultaneous identification of residual unbalances and bearing dynamic parameters from impulse responses of rotor-bearing systems. Mech Syst Signal Process 20:1590–1614CrossRefGoogle Scholar
  18. 18.
    Beyzelman RD, Tsypkin BV, Perel LYa (1975) Rolling bearings. Directory. Mechanical Engineering, MoscowGoogle Scholar
  19. 19.
    Wardle F (2015) Ultra precision bearings. Elsevier, CambridgeGoogle Scholar
  20. 20.
    Harris TA, Kotzalas MN (2007) Rolling bearing analysis. CRC Press, USAGoogle Scholar
  21. 21.
    Bourdon A, Rigal JF, Play D (1999) Static rolling bearing models in a C.A.D. environment for the study of complex mechanisms: part I: rolling bearing model. J Tribol 121:205–214. Scholar
  22. 22.
    Guay P, Frikha A (2015) Ball bearing stiffness. A new approach offering analytical expressions. In: Proceedings of ‘16th European space mechanisms and tribology symposium 2015’, Bilbao, Spain, 23–25 Sept 2015Google Scholar
  23. 23.
    Denisenko AF, Yakimov MV (2010) Anisotropy of the elastic properties of the rolling element support. In: Proceedings of international scientific and practical conference “fundamental problems and modern technologies in mechanical engineering”, Moscow, 1–3 June 2010Google Scholar
  24. 24.
    Denisenko AF, Yakimov MV (2012) Modeling of the rolling-element support for finite-element analysis of spindle knots of metal-cutting machines. Bull Samara State Tech Univ Ser Tech Sci 3(35):126–132Google Scholar
  25. 25.
    Guo Y, Parker R (2012) Stiffness matrix calculation of rolling clement bearings using a finite element/contact mechanics model. Mech Mach Theory 51:32–45CrossRefGoogle Scholar
  26. 26.
    Lazarus B, Perun G, Sławomir Bucki S (2008) Application of the finite-element method for determining the stiffness of rolling bearings. Transp Probl 3:33–40Google Scholar
  27. 27.
    Denisenko AF, Yakimov MV (2015) Experimental evaluation of the anisotropy of the stiffness of the front support of the spindle knot of the lathe. Eng Bull Don 1.
  28. 28.
    Jorgensen BR (1995) Dynamic analysis of spindle bearing system. Doctorate thesis, Purdue University, USAGoogle Scholar
  29. 29.
    Denisenko AF, Yakimov MV (2015) Determination of the own flexural frequencies of the spindle of a metal-cutting machine taking into account the anisotropic elasticity of supports. Bull Samara State Tech Univ Ser Tech Sci 1(45):159–166Google Scholar
  30. 30.
    Maslov GS (1968) Calculations of oscillations of shafts. Reference book. Mechanical Engineering, MoscowGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Samara State Technical UniversitySamaraRussia

Personalised recommendations