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Combined analysis of stiffness and fatigue life of deep groove ball bearings under interference fits, preloads and tilting moments

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Abstract

The stiffness and fatigue life of deep groove ball bearings are greatly affected by interference fits, preloads and tilting moments. Up to now, most of current works failed to focus on the integrated analysis of stiffness and fatigue life, especially the off-diagonal stiffness items in the bearing stiffness matrix. This paper proposed an improved mathematical model of deep groove ball bearings with the consideration of interference fits and tilting moments. On this basis, the combined study on stiffness and fatigue life is conducted to determine the optimal match of interference fits, preloads and tilting moments. Moreover, the variations in off-diagonal stiffness items under different interference fits, preloads and tilting moments are also given. These results are beneficial for the assembly of deep groove ball bearings to obtain the best stiffness and fatigue life. Also, the sensitivity of off-diagonal stiffness items to interference fits, preloads and tilting moments is demonstrated, which greatly affects the dynamic characteristic of ball bearings.

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Abbreviations

A :

The distance between centers of inner and outer race groove curvature radii

A L :

A — 0.5*Pd

P d :

Radial clearance

D :

Ball diameter

d :

Diameter of bearing components

d m :

Bearing pitch diameter

E :

Elastic modulus

F :

Interaction force

f :

Coefficient of groove curvature

L :

Service life of bearings

M :

Moment acting on the bearing components

P 1 :

Pressure between inner ring hole and shaft

Q :

Contact load

u :

Ball-raceway contact ellipse major semi-axis

v :

Poisson’s ratio

α :

Contact angle

γ 0 :

D/d m

Δ:

Interference fit

ξ :

Second kind ellipse integral

ρ :

Material density

Ψ:

Angular position of balls

ψ :

Rotational angular of tilting moment

b :

Rolling balls

i :

Inner ring

o :

Outer ring

c :

Centrifugal direction or rated load

p :

Equivalent load

f :

Free non-contact state

g :

Gyroscopic effect

j :

The serial number of rolling balls

0:

Initial value

References

  1. E. P. Gargiulo, A simple way to estimate bearing stiffness, Machine. Design, 52(17) (1980) 107–110.

    Google Scholar 

  2. F. P. Wardle et al., Dynamic and static characteristics of a wide speed range machine tool spindle, Precision Engineering, 5(4) (1983) 175–183.

    Article  Google Scholar 

  3. T. C. Lim and R. Singh, Vibration transmission through rolling element bearings, part I: bearing stiffness formulation, Journal of Sound and Vibration, 139(2) (1990) 179–199.

    Article  Google Scholar 

  4. D. Noel et al., Complete analytical expression of the stiffness matrix of angular contact ball bearings, Journal of Tribology-Transactions of the ASME, 135(4) (2013) 1–8.

    Article  Google Scholar 

  5. Z. Yang et al., Influence of structural parameters and tolerance on stiffness of high-speed ball bearings, International Journal of Precision Engineering and Manufacturing, 17(11) (2016) 1493–1501.

    Article  Google Scholar 

  6. B. Fang et al., A comprehensive study on the speed-varying stiffness of ball bearing under different load conditions, Mechanism and Machine Theory, 136 (2019) 1–13.

    Article  Google Scholar 

  7. W. Wu et al., Investigation of non-uniform preload effect on stiffness behavior of angular contact ball bearings, Advances in Mechanical Engineering, 9 (3) (2017).

  8. J. Zhang et al., A general model for preload calculation and stiffness analysis for combined angular contact ball bearings, Journal of Sound and Vibration, 411 (2017) 435–449.

    Article  Google Scholar 

  9. S. Lin et al., Study of the stiffness matrix of preloaded duplex angular contact ball bearings, Journal of Tribology-Transactions of the ASME, 141 (2019) 032204.

    Article  Google Scholar 

  10. J. Liu et al., An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing, Mechanism and Machine Theory, 142 (2019) 103597.

    Article  Google Scholar 

  11. J. Bowen et al., Influence of misalignment on nonlinear dynamic characteristics for matched bearings-rotor system, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 228(K2) (2014) 172–181.

    Google Scholar 

  12. V. C. Tong et al., The effect of angular misalignment on the stiffness characteristics of tapered roller bearings, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science (2016) 1–16.

  13. K. Geng et al., Effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science (2019) 1–17.

  14. T. A. Harris, The effect of misalignment on the fatigue life of cylindrical roller bearings having crowned rolling members, Journal of Tribology-Transactions of the ASME, 91 (1969) 294–300.

    Google Scholar 

  15. L. Yang et al., Mechanical behavior of double-row tapered roller bearing under combined external loads and angular misalignment, International Journal of Mechanical Sciences, 142 (2018) 561–574.

    Article  Google Scholar 

  16. V. C. Tong et al., Fatigue life of tapered roller bearing subject to angular misalignment, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science, 230 (2015) 147–158.

    Article  Google Scholar 

  17. B. Warda et al., Fatigue life prediction of the radial roller bearing with the correction of roller generators, International Journal of Mechanical Sciences, 89 (2014) 299–310.

    Article  Google Scholar 

  18. J. Zheng et al., Fatigue life analysis of double-row tapered roller bearing in a modern wind turbine under oscillating external load and speed, Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science (2020) 1–15.

  19. Y. Zhang et al., Fatigue life analysis of ball bearings and a shaft system considering the combined bearing preload and angular misalignment, Applied Sciences, 10(8) (2020) 2750.

    Article  Google Scholar 

  20. Y. Zhang et al., The effect of the uncertain initial angular misalignment on fatigue life of spindle-bearing system, Forsch. Ingenieurwes, 85(7) (2021) 1–18.

    MathSciNet  Google Scholar 

  21. G. Zeng et al., Life extension analysis of high speed ball bearing based on multi-parameter coupling, Journal of Mechanical Science and Technology, 35(4) (2021) 1569–1581.

    Article  Google Scholar 

  22. J. Zhang et al., Effect of preload on ball-raceway contact state and fatigue life of angular contact ball bearing, Tribology International, 114 (2017) 365–372.

    Article  Google Scholar 

  23. X. Shi et al., Relative fatigue life prediction of high-speed and heavy-load ball bearing based on surface texture, Tribology International, 101 (2016) 364–374.

    Article  Google Scholar 

  24. V. C. Tong et al., Analysis of the stiffness and fatigue life of double-row angular contact ball bearings, Journal of the Korean Society for Precision Engineering, 34(11) (2017) 813–821.

    Article  Google Scholar 

  25. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, Third Ed., McGraw-Hill, New York (1970).

    MATH  Google Scholar 

  26. J. Zhang et al., A comparative study and stiffness analysis of angular contact ball bearings under different preload mechanisms, Mechanism and Machine Theory, 115 (2017) 1–17.

    Article  Google Scholar 

  27. D. Changan et al., Raceway control assumption and the determination of rolling element attitude angle, Proceedings of the Symposium of Mechanical Engineering, New York (2000) 158–163.

  28. G. Lundberg et al., Dynamic capacity of rolling bearings, Journal of Applied Mechanics-Transactions of the ASME, 7(3) (1947) 1–52.

    Google Scholar 

  29. J. Okamoto, Design and Calculation of Ball Bearings, China Machine Press, Beijing (2003).

    Google Scholar 

  30. L. Hao et al., Accurate prediction method of initial value of high-speed ball bearing model and gyroscopic torque analysis, Journal of Mechanical Science and Technology, 34(9) (2020) 3745–3755.

    Article  MathSciNet  Google Scholar 

  31. B. Fang et al., Research on the influence of clearance variation on the stiffness fluctuation of ball bearing under different operating conditions, Journal of Mechanical Design, 143(2) (2020) 1–34.

    Google Scholar 

  32. G. Yi et al., Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model, Mechanism and Machine Theory, 51(5) (2012) 32–45.

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the Important Science and Technology Innovation Program of Hubei province (No. 2019AAA001) and National Key Research and Development Program of China (2019YFB2004304) for the support given to this research.

Author information

Authors and Affiliations

  1. Research Center of Cultural and Tourism Industries, Wuhan Business University, Wuhan, 430056, China

    Yi Jiang

  2. Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China

    Tianyu Zhu & Song Deng

  3. Luoyang Bearing Research Institute Co., Ltd., Luoyang, 471000, China

    Song Deng

Authors
  1. Yi Jiang
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  2. Tianyu Zhu
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  3. Song Deng
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Corresponding author

Correspondence to Song Deng.

Additional information

Yi Jiang received her Ph.D. degree in Management of Small and Medium-sized Enterprises from Huazhong Agricultural University, China, in 2022. She is currently a Lecturer at the Rsearch Center of Cultural and Tourism Industries of Wuhan Business University, China. Her research areas include structure design and dynamic behavior of high-speed bearing.

Tianyu Zhu is currently a graduate student majoring in Mechanical Engineering at Automotive Components of Wuhan University of Technology, China. His research areas include structure design and dynamic behavior of high-speed bearing.

Song Deng received his Ph.D. degree in Vehicle Engineering from Wuhan University of Technology, China, in 2014. He is currently an Associate Professor at Automotive Components of Wuhan University of Technology, China. His research areas include structure design and dynamic behavior of high-speed bearing.

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Jiang, Y., Zhu, T. & Deng, S. Combined analysis of stiffness and fatigue life of deep groove ball bearings under interference fits, preloads and tilting moments. J Mech Sci Technol 37, 539–553 (2023). https://doi.org/10.1007/s12206-023-0101-x

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  • DOI: https://doi.org/10.1007/s12206-023-0101-x

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