Abstract
Ceramic bearings are widely used in industrial production. They can be used to maintain accurate operations over a long period of time. However, the bearing model that was so thoroughly investigated has not been adapted for ceramic bearings. To better calculate the characteristics of ceramic bearings, the existing model may be modified to account for the high stiffness of ceramics. In this paper, the vibration response is investigated and used to modify the analytical model of bearing-rotor dynamics. Under the influence of thermal deformation, the dynamic parameters of the bearing components, including stiffness, traction forces, and Hertz contact force, are analyzed first. On the basis of the modified dynamic model, the vibration response of the bearing-rotor system, time domain, Poincaré phase diagram, phase trajectory, and bifurcation diagram are simulated under various cage pocket hole diameters. The simulation results indicate that increasing the cavity diameter can appropriately improve the dynamics of the rotor system at high speeds. The established model is highly accurate, with an error of less than 8% when comparing the simulation and experimental results. The study’s relevance to bearing structural design has been confirmed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
The data are available from the corresponding author on reasonable request.
Abbreviations
- f 1 :
-
Structure and load correlation coefficient
- P 1 :
-
The calculated load of the friction torque
- η 0 :
-
Dynamic viscosity of lubricating oil
- R 1 :
-
Cage centering surface radius
- V 1 :
-
Sliding speed relative to the surface
- C 1 :
-
Cage guide gap
- L :
-
Cage centering surface width
- M 0 :
-
Friction torque generated by oil–gas lubrication
- d m :
-
The round diameter of the bearing joint
- ε :
-
Relative eccentricity of the cage center
- R P :
-
The effective radius curvature in the ξ direction
- R P :
-
Effective radius curvature in the η direction
- u Pηj :
-
The jth ball surface velocity in the η direction
- u Pξj :
-
The average of the jth ball surface velocity
- u SPξj :
-
The sliding velocity in the ξ direction
- u SPηj :
-
The sliding speed in the η direction
References
Arya U, Sadeghi F et al (2022) Experimental investigation of cage dynamics and ball-cage contact forces in an angular contact ball bearing. Proc Inst Mech Eng 236(12):2522–2534. https://doi.org/10.1177/13506501221077768
Bian W, Wang Z et al (2016) Thermo-mechanical analysis of angular contact ball bearing. J Mech Sci Technol 30:297–306. https://doi.org/10.1007/s12206-015-1233-4
Deng S, Zhu X et al (2022) Nonlinear dynamic mechanisms of angular contact ball bearings with waviness and cage whirl motion. Nonlinear Dyn 109:2547–2571. https://doi.org/10.1007/s11071-022-07604-2
Deng S, Zhao C et al (2023) Dynamic behaviors of angular contact ball bearings based on nonlinear dynamic model with flexible ring and cage motion whirl. Nonlinear Dyn 111:10879–10909. https://doi.org/10.1007/s11071-023-08412-y
Dong Y, Zhou Z et al (2017) Bearing preload optimization for machine tool spindle by the influencing multiple parameters on the bearing performance. Adv Mech Eng 9:1–9. https://doi.org/10.1177/1687814016689040
Ebrahimi R (2022) Chaos in coupled lateral-longitudinal vibration of electrostatically actuated microresonators. Chaos Solitons Fractals 156:111828. https://doi.org/10.1016/j.chaos.2022.111828
Ebrahimi R, Ghayour M et al (2017) Effects of some design parameters on bifurcation behavior of a magnetically supported coaxial rotor in auxiliary bearings. Eng Comput 34:2379–2395. https://doi.org/10.1108/EC-04-2017-0141
Gao S, Chatterton S et al (2021) Ball bearing skidding and over-skidding in large-scale angular contact ball bearings: nonlinear dynamic model with thermal effects and experimental results. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2020.107120
Kumar P et al (2021) Development of a novel approach for quantitative estimation of rotor unbalance and misalignment in a rotor system levitated by active magnetic bearings. Iran J Sci Technol Trans Mech Eng 45:769–786. https://doi.org/10.1007/s40997-020-00364-7
Lei C, Li F et al (2020) An integrated model to characterize comprehensive stiffness of angular contact ball bearings. Math Probl Eng 4951828:1–12. https://doi.org/10.1155/2020/4951828
Li Te, Kolar P et al (2020a) Research development of preload technology on angular contact ball bearing of high speed spindle: a review. Int J Precis Eng Manuf 21:1163–1185. https://doi.org/10.1007/s12541-019-00289-5
Li J, Lei C et al (2020b) Modeling and analysis of the composite stiffness for angular contact ball bearings. Shock Vib 8832750:1–22. https://doi.org/10.1155/2020/8832750
Liu P, Wang L et al (2023) Influence of assembly clearance on vibration characteristics of angular contact ball bearings in the thermal environment. Tribol Int 181:108317. https://doi.org/10.1016/j.triboint.2023.108317
Shi H, Bai X et al (2019) Effect of thermal-related fit clearance between outer ring and pedestal on the vibration of full ceramic ball bearing. Shock Vib 8357807:1–15. https://doi.org/10.1155/2019/8357807
Upadhyay N, Metsebo J et al (2018) An improved theoretical model of unbalanced shaft-bearing system for accurate performance prediction of ball bearing due to localized defects. Iran J Sci Technol Trans Mech Eng 42:293–309. https://doi.org/10.1007/s40997-017-0098-9
Wang H, Guan X et al (2019) Characteristics analysis of rotor-rolling bearing coupled system with fit looseness fault and its verification. J Mech Sci Technol 33:29–40. https://doi.org/10.1007/s12206-018-1204-7
Wang Z, Zhang Ke, Wang Z (2021) Research on vibration of ceramic motorized spindle influenced by interference and thermal displacement. J Mech Sci Technol 35:2325–2335. https://doi.org/10.1007/s12206-021-0505-4
Wang Z, Wang Z, Bai X et al (2022) Effect of interference fit on dynamic characteristics of spindle rotor system. J Braz Soc Mech Sci Eng 44(316):1–11. https://doi.org/10.1007/s40430-022-03545-4
Wen B, Ren H et al (2017) Experimental investigation of cage motions in an angular contact ball bearing. Proc Inst Mech Eng Part J J Eng Tribol 231(8):1041–1055. https://doi.org/10.1177/1350650116689457
Wen C, Meng X et al (2021) Dynamic behaviors of angular contact ball bearing with a localized surface defect considering the influence of cage and oil lubrication. Mech Mach Theory 162:104352. https://doi.org/10.1016/j.mechmachtheory.2021.104352
Yan H, Yuhou Wu et al (2020a) Research on sound field characteristics of full-ceramic angular contact ball bearing. J Braz Soc Mech Sci Eng 42(311):1–16. https://doi.org/10.1007/s40430-020-02295-5
Yan H, Yuhou Wu et al (2020b) Acoustic model of ceramic angular contact ball bearing based on multi-sound source method. Nonlinear Dyn 99:1155–1177. https://doi.org/10.1007/s11071-019-05343-5
Zhan Z, Fang B et al (2023) A novel approach to the thermal-deformation coupling calculation of the high-speed spindle-bearing system. Int J Mech Mater Des 19:391–406. https://doi.org/10.1007/s10999-022-09634-5
Zhang Ke, Wang Z et al (2020) Effect of preload on the dynamic characteristics of ceramic bearings based on a dynamic thermal coupling model. Adv Mech Eng 12(1):1–18. https://doi.org/10.1177/1687814020903851
Zhao Y, Ma Z et al (2023) Skidding and spinning investigation for dry-lubricated angular contact ball bearing under combined loads. Friction 11:1987–2007. https://doi.org/10.1007/s40544-022-0703-9
Zheng D, Chen W et al (2021) An enhanced estimation on heat generation of angular contact ball bearings with vibration effect. Int J Therm Sci 159:106610. https://doi.org/10.1016/j.ijthermalsci.2020.106610
Acknowledgements
This work was supported by the National Natural Science Foundation of China [Grant numbers: 52205117, 62173238], Exchange project of the Fourth China-Ukraine Intergovernmental Meeting [Grant numbers: 35], Doctor Research Project of Liaoning Provincial Science and Technology Department (Grant No. 2022-BS-193).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wang, Z., Wang, Q., Zhou, P. et al. Dynamic Analysis of the Bearing-Rotor System with the Variation of Cage’s Pocket Hole Diameter. Iran J Sci Technol Trans Mech Eng (2024). https://doi.org/10.1007/s40997-024-00764-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40997-024-00764-z