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Rapid solution for analysis of nonlinear fluid film force and dynamic behavior of a tilting-pad journal bearing-rotor system with turbulent and thermal effects

  • Yingze Jin
  • Zhaoyang Shi
  • Xiaojing Zhang
  • Xiaoyang YuanEmail author
Open Access
Research Article


To analyze the nonlinear dynamics of a tilting-pad journal bearing (TPJB)-rotor system with high accuracy and speed, the database method (DM) is modified to rapidly determine the nonlinear fluid film force (NFFF) of a TPJB while considering turbulent and thermal effects. A high-accuracy, large-capacity NFFF database for a single pad is constructed by numerically solving the turbulent adiabatic hydrodynamic model for five equivalent state variables of the journal, which are discretized in the pad coordinates. The remaining variables are not discretized in the DM. A combined linear and parabolic interpolation polynomial based on the database is established to accurately calculate the NFFF of the tilting pads; thus, the NFFF of a four-pad TPJB is obtained in the bearing coordinates. The DM is applied to analyze and compare the nonlinear dynamic behavior of a water-lubricated TPJB-Jeffcott rotor system with and without turbulent and thermal effects. The present DM solution without these effects and the previous DM solution are shown to be consistent. The results demonstrate the importance of the flow regime and the negligibility of temperature increases in the nonlinear dynamics of a water-lubricated TPJB. This work contributes to the accurate and efficient analysis of the nonlinear dynamics of high-speed TPJBs and low-viscosity-fluid-lubricated TPJBs.


tilting-pad journal bearing nonlinear fluid film force rotor dynamics turbulent flow thermal effect 



This work was supported by the National Basic Research Program of China (Grant No. 2015CB057303) and the National Natural Science Foundation of China (Grant No. 51775412).


  1. [1]
    Wang J K, Khonsari M M. Effects of oil inlet pressure and inlet position of axially grooved infinitely long journal bearings. Part I: Analytical solutions and static performance. Tribol Int 41(2): 119–131 (2008)CrossRefGoogle Scholar
  2. [2]
    Wang J K, Khonsari M M. Effects of oil inlet pressure and inlet position of axially grooved infinitely long journal bearings. Part II: Nonlinear instability analysis. Tribol Int 41(2): 132–140 (2008)CrossRefGoogle Scholar
  3. [3]
    Chang-Jian C W. Nonlinear analysis for gear pair system supported by long journal bearings under nonlinear suspension. Mech Mach Theory 45(4): 569–583 (2010)CrossRefzbMATHGoogle Scholar
  4. [4]
    Avramov K V, Borysiuk O V. Nonlinear dynamics of one disk asymmetrical rotor supported by two journal bearings. Nonlinear Dyn 67(2): 1201–1219 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Shi M L, Wang D Z, Zhang J G. Nonlinear dynamic analysis of a vertical rotor-bearing system. J Mech Sci Technol 27(1): 9–19 (2013)CrossRefGoogle Scholar
  6. [6]
    Dakel M, Baguet S, Dufour R. Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings. J Sound Vib 333(10): 2774–2799 (2014)CrossRefGoogle Scholar
  7. [7]
    Okabe E P, Cavalca K L. Rotordynamic analysis of systems with a non-linear model of tilting pad bearings including turbulence effects. Nonlinear Dyn 57(4): 481–495 (2009)CrossRefzbMATHGoogle Scholar
  8. [8]
    Zhang W, Xu X F. Modeling of nonlinear oil-film force acting on a journal with unsteady motion and nonlinear instability analysis under the model. Int J Nonlinear Sci Numer Simul 1(3): 179–186 (2000)CrossRefzbMATHGoogle Scholar
  9. [9]
    Zhao S X, Xu H, Meng G, Zhu J. Stability and response analysis of symmetrical single-disk flexible rotor-bearing system. Tribol Int 38(8): 749–756 (2005)CrossRefGoogle Scholar
  10. [10]
    Xia Z P, Qiao G, Zheng T H, Zhang W. Nonlinear modeling and dynamic analysis of the rotor-bearing system. Nonlinear Dyn 57(4): 559–577 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Bastani Y, de Queiroz M. A new analytic approximation for the hydrodynamic forces in finite-length journal bearings. J Tribol 132(1): 014502 (2010)CrossRefGoogle Scholar
  12. [12]
    Vignolo G G, Barilá D O, Quinzani L M. Approximate analytical solution to Reynolds equation for finite length journal bearings. Tribol Int 44(10): 1089–1099 (2011)CrossRefGoogle Scholar
  13. [13]
    Sfyris D, Chasalevris A. An exact analytical solution of the Reynolds equation for the finite journal bearing lubrication. Tribol Int 55(4): 46–58 (2012)CrossRefGoogle Scholar
  14. [14]
    Zhang Y F, Hei D, Liu C, Guo B J, Lu Y J, Müller N. An approximate solution of oil film forces of turbulent finite length journal bearing. Tribol Int 74(4): 110–120 (2014)CrossRefGoogle Scholar
  15. [15]
    Hei D, Lu Y J, Zhang Y F, Liu F X, Zhou C, Müller N. Nonlinear dynamic behaviors of rod fastening rotor-hydrodynamic journal bearing system. Arch Appl Mech 85(7): 855–875 (2015)CrossRefzbMATHGoogle Scholar
  16. [16]
    Abu-Mahfouz I, Adams M L. Numerical study of some nonlinear dynamics of a rotor supported on a three-pad tilting pad journal bearing (TPJB). J Vib Acoust Trans 127(3): 262–272 (2005)CrossRefGoogle Scholar
  17. [17]
    Wang Y L, Gao Y, Cui Y, Liu Z S. Establishment of approximate analytical model of oil film force for finite length tilting pad journal bearings. Int J Rotat Mach 2015: 531209 (2015)CrossRefGoogle Scholar
  18. [18]
    Chen Z B, Jiao Y H, Xia S B, Huang W H, Zhang Z M. An efficient calculation method of nonlinear fluid film forces in journal bearing. Tribol Trans 45(3): 324–329 (2002)CrossRefGoogle Scholar
  19. [19]
    Qin P, Shen Y, Zhu J, Xu H. Dynamic analysis of hydrodynamic bearing-rotor system based on neural network. Int J Eng Sci 43(5–6): 520–531 (2005)CrossRefGoogle Scholar
  20. [20]
    Jin Y Z, Shi Z Y, Hong H L, Zhang F, Yuan X Y. Axiomatic design method for supercritical rotor dynamics integrating nonlinear deep knowledge. Proced CIRP 53: 237–246 (2016)CrossRefGoogle Scholar
  21. [21]
    Ying J Y, Jiao Y H, Chen Z B. Nonlinear dynamics analysis of tilting pad journal bearing-rotor system. Shock Vib 18(1–2): 45–52 (2011)CrossRefGoogle Scholar
  22. [22]
    Lü Y J, Zhang Y F, Yu Y B. Yu L. Nonlinear dynamics of flexible rotor system supported on fixed-tilting pad combination journal bearing. J Central South Univ Technol Eng 18(3): 610–617 (2011)CrossRefGoogle Scholar
  23. [23]
    Hei D, Lu Y J, Zhang Y F, Lu Z Y, Gupta P, Müller N. Nonlinear dynamic behaviors of a rod fastening rotor supported by fixed-tilting pad journal bearings. Chaos Solitons Fractals 69: 129–150 (2014)CrossRefGoogle Scholar
  24. [24]
    Taylor C M. Turbulent lubrication theory applied to fluid film bearing design. Proc Inst Mech Eng Conf Proc 184(12): 40–47 (1969)Google Scholar
  25. [25]
    Constantinescu V N. Basic relationships in turbulent lubrication and their extension to include thermal effects. J Lubr Technol 95(2): 147–154 (1973)CrossRefGoogle Scholar

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Authors and Affiliations

  • Yingze Jin
    • 1
  • Zhaoyang Shi
    • 1
  • Xiaojing Zhang
    • 1
  • Xiaoyang Yuan
    • 1
    Email author
  1. 1.Key Laboratory of the Education Ministry for Modern Design and Rotor-Bearing SystemsXi’an Jiaotong UniversityXi’anChina

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