Skip to main content
SpringerLink
Log in

Improved formulation for running torque in angular contact ball bearings

  • Regular Paper
  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

This paper presents an improved computational model for the angular contact ball bearing (ACBB) running torque. Considering the general loading condition, the friction torque formula of individual bearing balls was derived. Five friction components were considered: elastohydrodynamic lubrication (EHL) rolling resistance, elastic hysteresis friction, differential sliding loss, spinning friction, and lubricant viscous drag effect. The formulas for elastohydrodynamic lubrication rolling resistance and spinning friction, which contribute significantly to the ACBB running torque, were improved by investigating and re-formulating the contact related formulas. The friction coefficient between the ball and races was investigated in order to choose a suitable and reliable formula for the proposed model. The proposed model was verified through a comparison with formulas provided by a bearing manufacturer and with a set of experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kim, K.-S., Lee, D.-W., Lee, S.-M., Lee, S.-J., and Hwang, J.-H., “A Numerical Approach to Determine the Frictional Torque and Temperature of an Angular Contact Ball Bearing in a Spindle System,” Int. J. Precis. Eng. Manuf., Vol. 16, No. 1, pp. 135–142, 2015.

    Article  Google Scholar 

  2. Kim, M., Lee, S.-M., Lee, D.-W., Park, S., and Kim, S.-H., “Tribological Effects of a Rough Surface Bearing Using an Average Flow Analysis with a Contact Model of asperities,” Int. J. Precis. Eng. Manuf., Vol. 18, No. 1, pp. 99–107, 2017.

    Article  Google Scholar 

  3. Harris, T. A., “Rolling Bearing Analysis,” John Wiley and Sons, pp. 25–35, 2001.

    Google Scholar 

  4. Tong, V.-C. and Hong, S.-W., “The Effect of Angular Misalignment on the Running Torques of Tapered Roller Bearings,” Tribology International, Vol. 95, pp. 76–85, 2016.

    Article  Google Scholar 

  5. Hong, S.-W. and Tong, V.-C., “Rolling-Element Bearing Modeling: A Review,” Int. J. Precis. Eng. Manuf., Vol. 17, No. 12, pp. 1729–1749, 2016.

    Article  Google Scholar 

  6. Palmgren, A., “Ball and Roller Bearing Engineering,” Philadelphia: SKF Industries Inc., 1959.

    Google Scholar 

  7. Aihara, S., “A New Running Torque Formula for Tapered Roller Bearings under Axial Load,” Journal of Tribology, Vol. 109, No. 3, pp. 471–477, 1987.

    Article  Google Scholar 

  8. Townsend, D., Allen, C., and Zaretsky, E., “Study of Ball Bearing Torque under Elastohydrodynamic Lubrication,” Journal of Lubrication Technology, Vol. 96, No. 4, pp. 561–570, 1974.

    Article  Google Scholar 

  9. Witte, D. C., “Operating Torque of Tapered Roller Bearings,” ASLE Transactions, Vol. 16, No. 1, pp. 61–67, 1973.

    Article  Google Scholar 

  10. Zhou, R. S. and Hoeprich, M. R., “Torque of Tapered Roller Bearings,” Journal of Tribology, Vol. 113, No. 3, pp. 590–597, 1991.

    Article  Google Scholar 

  11. Houpert, L., “Ball Bearing and Tapered Roller Bearing Torque: Analytical, Numerical and Experimental Results,” Tribology Transactions, Vol. 45, No. 3, pp. 345–353, 2002.

    Article  Google Scholar 

  12. Bălan, M. R. D., Stamate, V. C., Houpert, L., and Olaru, D. N., “The Influence of the Lubricant Viscosity on the Rolling Friction Torque,” Tribology International, Vol. 72, pp. 1–12, 2014.

    Article  Google Scholar 

  13. SKF, “SKF General Catalogue, 6000/I EN,” http://www.boie.de/ftp/pub/skf/6000_I_EN.pdf (Accessed 27 NOV 2017)

  14. Cousseau, T., “Film Thickness and Friction in Grease Lubricated Contacts. Application to Rolling Bearing Torque Loss,” Ph.D. Thesis, Porto University, 2013.

    Google Scholar 

  15. Tong, V.-C. and Hong, S.-W., “Study on the Running Torque of Angular Contact Ball Bearings Subjected to Angular Misalignment,” Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2017. (DOI: 10.1177/1350650117732921)

    Google Scholar 

  16. Jorgensen, B. R. and Shin, Y. C., “Dynamics of Spindle-Bearing Systems at High Speeds Including Cutting Load Effects,” Transactions-American Society of Mechanical Engineers Journal of Manufacturing Science and Engineering, Vol. 120, No. 2, pp. 387–394, 1998.

    Google Scholar 

  17. Liebrecht, J., Si, X., Sauer, B., and Schwarze, H., “Investigation of Drag and Churning Losses on Tapered Roller Bearings,” Journal of Mechanical Engineering, Vol. 61, No. 6, pp. 399–408, 2015.

    Article  Google Scholar 

  18. Brecher, C., Hassis, A., and Rossaint, J., “Cage Friction in High-Speed Spindle Bearings,” Tribology Transactions, Vol. 57, No. 1, pp. 77–85, 2014.

    Article  Google Scholar 

  19. Aramaki, H., Shoda, Y., Morishita, Y., and Sawamoto, T., “The Performance of Ball Bearings with Silicon Nitride Ceramic Balls in High Speed Spindles for Machine Tools,” Journal of Tribology, Vol. 110, No. 4, pp. 693–698, 1988.

    Article  Google Scholar 

  20. Kanatsu, M., and Ohta, H., “Running Torque of Ball Bearings with Polymer Lubricant (Running Torque Formulas of Deep Groove Ball Bearings under Axial Loads),” Journal of Tribology, Vol. 130, No. 4, Paper No. 041507, 2008.

    Google Scholar 

  21. Jones, A., “A General Theory for Elastically Constrained Ball and Radial Roller Bearings under Arbitrary Load and Speed Conditions,” Journal of Basic Engineering, Vol. 82, No. 2, pp. 309–320, 1960.

    Article  Google Scholar 

  22. Wang, Y., Lin, F., Jiang, H., and Yuan, W., “Investigation on Frictional Characteristic of Deep-Groove Ball Bearings Subjected to Radial Loads,” Advances in Mechanical Engineering, Vol. 7, No. 7, 2015. (DOI: 10.1177/1687814015586111)

    Google Scholar 

  23. Stolarski, T., “Tribology in Machine Design,” Butterworth-Heinemann, 1990.

    Google Scholar 

  24. Marchesse, Y., Changenet, C., and Ville, F., “Numerical Investigations on Drag Coefficient of Balls in Rolling Element Bearing,” Tribology Transactions, Vol. 57, No. 5, pp. 778–785, 2014.

    Article  Google Scholar 

  25. Paleu, V., Cretu, S., Dragan, B., and Balan, R., “Test Rig for Friction Torque Measurement in Rolling Bearings,” The Annals of “Dunarea de Jos” University of Galati, Fascicle VIII, Tribology, pp. 86–93, 2004.

    Google Scholar 

  26. Sakaguchi, T. and Harada, K., “Dynamic Analysis of Cage Behavior in a Tapered Roller Bearing,” Journal of Tribology, Vol. 128, No. 3, pp. 604–611, 2006.

    Article  Google Scholar 

  27. Hamrock, B. J. and Dowson, D., “Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III—Fully Flooded Results,” Journal of Lubrication Technology, Vol. 99, No. 2, pp. 264–275, 1977.

    Article  Google Scholar 

  28. Zhu, D. and Hu, Y.-Z., “A Computer Program Package for the Prediction of EHL and Mixed Lubrication Characteristics, Friction, Subsurface Stresses and Flash Temperatures Based on Measured 3-D Surface Roughness,” Tribology Transactions, Vol. 44, No. 3, pp. 383–390, 2001.

    Article  Google Scholar 

  29. SKF. “SKF Angular Contact Ball Bearings-Your Key to Longer Service Life,” http://www.dexis-iberica.com/ficheros/2.pdf (Accessed 27 NOV 2017)

  30. Tong, V.-C. and Hong, S.-W., “Characteristics of Tapered Roller Bearing with Geometric Error,” Int. J. Precis. Eng. Manuf., Vol. 16, No. 13, pp. 2709–2716, 2015.

    Article  Google Scholar 

  31. Yang, Z., Li, B., and Yu, T., “Influence of Structural Parameters and Tolerance on Stiffness of High-Speed Ball Bearings,” Int. J. Precis. Eng. Manuf., Vol. 17, No. 11, pp. 1493–1501, 2016.

    Article  Google Scholar 

  32. Lee, C.-M., Woo, W.-S., and Kim, D.-H., “The Latest Preload Technology of Machine Tool Spindles: A Review,” Int. J. Precis. Eng. Manuf., Vol. 18, No. 11, pp. 1669–1679, 2017.

    Article  Google Scholar 

  33. Park, Y.-J., Kim, J.-G., Lee, G.-H., Kim, Y.-J., and Oh, J.-Y, “Effects of Bearing Characteristics on Load Distribution and Sharing of Pitch Reducer for Wind Turbine,” Int. J. Precis. Eng. Manuf.-Green Tech., Vol. 3, No. 1, pp. 55–65, 2016.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical System Engineering, Kumoh National Institute of Technology, 61, Daehak-ro, Gumi-si, Gyeongsangbuk-do, 39177, Republic of Korea

    Van-Canh Tong & Seong-Wook Hong

Authors
  1. Van-Canh Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seong-Wook Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seong-Wook Hong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tong, VC., Hong, SW. Improved formulation for running torque in angular contact ball bearings. Int. J. Precis. Eng. Manuf. 19, 47–56 (2018). https://doi.org/10.1007/s12541-018-0006-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-018-0006-2

Keywords

Search

Navigation