, Volume 7, Issue 6, pp 551–563 | Cite as

Modeling the frictional torque of a dry-lubricated tapered roller bearing considering the roller skewing

  • Chi Zhang
  • Le GuEmail author
  • Yuze Mao
  • Liqin Wang
Open Access
Research Article


In this paper, an equation for the calculation of the frictional torque of a dry-lubricated tapered roller bearing (TRB) is provided in which the effect of the roller skewing is emphasized. Calculations were performed to investigate the effect of the roller skewing on the torque of dry-lubricated TRB for two representative preload methods, that is, axial force preload and axial displacement preload. The results show that a proper roller skewing angle under axial force preload benefits the reduction of the TRB torque. However, the roller skewing angle should not exceed a certain critical value; otherwise, it will cause a steep rise in the TRB torque. Finally, the critical value of the roller skewing angle as a function of the friction coefficient and cage pocket clearance is presented. The developed torque model provides a tool for the internal design and torque optimization of dry-lubricated TRBs.


tapered roller bearing frictional torque roller skewing dry lubrication 



The authors are grateful for the support of the National Natural Science Foundation of China (Nos. 51675120 and U1637206).


  1. [1]
    Obara S, Suzuki M. Long-term operation of Si3N4 ball bearings at temperatures up to 650 °C in ultra-high vacuum. Tribol Trans40(1): 31–40 (1997)CrossRefGoogle Scholar
  2. [2]
    Nishimura M, Suzuki M. Solid-lubricated ball bearings for use in a vacuum-state-of-the-art. Tribol Int32(11): 637–647 (1999)CrossRefGoogle Scholar
  3. [3]
    Eiden M, Seiler R. Space mechanisms and tribology challenges of future space missions. Acta Astronaut55(11): 935–943 (2004)CrossRefGoogle Scholar
  4. [4]
    Lostado R, García R E, Martinez R F. Optimization of operating conditions for a double-row tapered roller bearing. Int J Mech Mater Des12(3): 353–373 (2016)CrossRefGoogle Scholar
  5. [5]
    Lostado R, Martinez R F, Mac Donald B J. Determination of the contact stresses in double-row tapered roller bearings using the finite element method, experimental analysis and analytical models. J Mech Sci Technol29(11): 4645–4656 (2015)CrossRefGoogle Scholar
  6. [6]
    Miyoshi K. Considerations in vacuum tribology (adhesion, friction, wear, and solid lubrication in vacuum). Tribol Int32(11): 605–616 (1999)CrossRefGoogle Scholar
  7. [7]
    Ohta H, Kanatsu M. Running torque of ball bearings with polymer lubricant (effect of the enclosure form of polymer lubricant). Tribol Trans48(4): 484–491 (2005)CrossRefGoogle Scholar
  8. [8]
    Marquart M, Wahl M, Emrich S, Zhang G, Sauer B, Kopnarski M, Wetzel B. Enhancing the lifetime of MoS2-lubricated ball bearings. Wear303(1–2): 169–177 (2013)CrossRefGoogle Scholar
  9. [9]
    Gonçalves D, Pinho S, Graça B, Campos A V, Seabra J H O. Friction torque in thrust ball bearings lubricated with polymer greases of different thickener content. Tribol Int96: 87–96 (2016)CrossRefGoogle Scholar
  10. [10]
    Yang Y, Danyluk S, Hoeprich M. Rolling element skew in tapered roller bearing. Tribol Trans43(3): 564–568 (2000)CrossRefGoogle Scholar
  11. [11]
    Yang Y Y, Danyluk S, Hoeprich M. On the measurement of skew of tapered roller bearings. Tribol Lett6(3–4): 221 (1999)CrossRefGoogle Scholar
  12. [12]
    Nelias D, Bercea I, Paleu V. Prediction of roller skewing in tapered roller bearings. Tribol Trans51(2): 128–139 (2008)CrossRefGoogle Scholar
  13. [13]
    Gupta P K. On the dynamics of a tapered roller bearing. J Tribol111(2): 278–287 (1989)CrossRefGoogle Scholar
  14. [14]
    Witte D C. Operating torque of tapered roller bearings. Tribol Trans16(1): 61–67 (1973)Google Scholar
  15. [15]
    Aihara S. A new running torque formula for tapered roller bearings under axial load. J Tribol109(3): 471–477 (1987)CrossRefGoogle Scholar
  16. [16]
    Zhou R S, Hoeprich M R. Torque of tapered roller bearings. J Tribol113(3): 590–597 (1991)CrossRefGoogle Scholar
  17. [17]
    Creju S, Bercea I, Mitu N. A dynamic analysis of tapered roller bearing under fully flooded conditions Part 1: Theoretical formulation. Wear188(1–2): 1–10 (1995)CrossRefGoogle Scholar
  18. [18]
    Tong V C, Hong S W. The effect of angular misalignment on the running torques of tapered roller bearings. Tribol Int95: 76–85 (2016)CrossRefGoogle Scholar
  19. [19]
    Palmgren A. Ball and Roller Bearing Engineering. 3rd ed. Philadelphia (USA): SKF Industries Inc., 1959.Google Scholar
  20. [20]
    Harris T A, Kotzalas M N, Yu W K. On the causes and effects of roller skewing in cylindrical roller bearings. Tribol Trans41(4): 572–578 (1998)CrossRefGoogle Scholar
  21. [21]
    Harris T A. Rolling Bearing Analysis. New York (USA): John Wiley & Sons, 2001: 275.Google Scholar
  22. [22]
    Karna C L. Performance characteristics at the rib roller end contact in tapered roller bearings. Tribol Trans17(1): 14–21 (1974)Google Scholar

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© The author(s) 2018

Open Access: The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Research Lab of Space & Aerospace TribologyHarbin Institute of TechnologyHarbinChina

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