Abstract
When the oil supply is not adequate to maintain the ideal lubrication, angular contact ball bearing will enter into the starved lubrication regime resulting in the potential performance degradation and consequently the severe failures. To study the effects of starved lubrication on the performance of angular contact ball bearing, this paper first proposes a multi-degree-of-freedom (DOF) tribo-dynamic model by introducing five-DOF inner ring, six-DOF balls, and six-DOF cage. The model considers the starved lubrication in the ball-raceway contact and the full multi-body interactions between the bearing components. With different ball-raceway starvation degrees being analyzed, the effects of starved lubrication on the bearing tribo-dynamic performance are first revealed. By comparison, it is found that the oil film thickness, the skidding performance, and the traction forces in the ball-raceway contact are significantly influenced by the starvation degrees. It is also found that the starvation-induced change of the ball-pocket contact force is dramatical under combined loads, and the maximum contact force under this load condition increases with the increasing starvation degrees.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a, b :
-
semimajor and semi-minor axises
- c :
-
damping coefficient
- C p :
-
pocket clearance
- d :
-
ball diameter
- d m :
-
pitch diameter
- D p :
-
pocket diameter
- f c :
-
asperity friction coefficient
- F a, F y, F z :
-
external loads
- F cj :
-
centrifugal force
- F cy, F cz :
-
oil film forces between cage and guiding surface
- F dj :
-
drag force
- F i/ox″j :
-
traction force in semimajor axis
- F i/oy″j :
-
traction force in semiminor axis
- F Rζj, F Rηj :
-
rolling components
- F Sξj, F Sηj :
-
sliding components
- G :
-
dimensionless material number
- G cage :
-
gravity of the cage
- h c :
-
central oil film thickness
- h ci/o,j :
-
oil film thickness
- I cx, I cy, I cz :
-
principal moments of inertia for cage
- I rx, I ry, I rz :
-
principal moments of inertia for inner ring and shaft
- J :
-
rotational inertia of ball
- k i/o,j :
-
load-deformation coefficient
- K c :
-
lubricant stiffness
- K n :
-
contact force-deformation coefficient
- L a—starved :
-
asperity load ratio in the starved case
- m :
-
mass of ball
- m c :
-
mass of the cage
- ṁ F :
-
mass flow rate in the fully flooded condition
- ṁ s :
-
mass flow rate in starved condition
- m inner :
-
mass of inner ring and shaft
- M cx :
-
friction moment between cage and guiding surface
- M gy′, M gz′ :
-
gyroscopic moments
- M i/oj :
-
traction moment
- M rx, M ry, M rz :
-
applied moments
- N :
-
number of balls
- p :
-
Hertz contact pressure
- p a :
-
asperity contact pressure
- p h :
-
hydrodynamic pressure
- p max :
-
maximum contact pressure
- Q cj :
-
normal force between ball and cage pocket
- Q i/oj :
-
contact force
- R ora :
-
radius of locus of outer raceway groove curvature centers
- R y :
-
equivalent contact radius in the rolling direction
- U :
-
dimensionless speed
- V :
-
dimensionless hardness number
- W :
-
dimensionless load
- X aj :
-
axial distance between ball center and outer raceway groove center
- X rj :
-
radial distance between ball center and outer raceway groove center
- Z cj :
-
distance between centers of pocket and ball
- αij, αoj :
-
contact angle between balls and raceways
- δ a,δ ry,δ rz :
-
axial and radial displacements of inner ring
- δ i/o,j :
-
deformation in the ball-raceway contact
- ∆U xi/o,j :
-
skidding velocity in semimajor axis
- ∆U yi/o,j :
-
skidding velocity in semiminor axis
- ∆X c, ∆ Y c, ∆Z c :
-
translational displacements of cage
- η :
-
oil viscosity
- θ pj :
-
transformation angle
- κ :
-
fellipticity parameter
- Λ :
-
limiting shear stress coefficient
- ρ :
-
lubricant density
- \({\bar \sigma}\) :
-
dimensionless surface roughness
- τ i/o :
-
shear stress
- φ c :
-
deflection angle
- φ j :
-
ball position angle
- \({\Phi _{{h_c}}},{\Phi _{{h_{\min}}}}\) :
-
ratio of starved to fully-flooded film thicknesses
- χ :
-
starvation degree
- ψ x,ψ y, ψ z :
-
angular displacements of cage
- ω c :
-
rotation speed of cage
References
Shi X J, Wang L Q. TEHL analysis of high-speed and heavy-load roller bearing with quasi-dynamic characteristics. Chinese J Aeronaut 28(4): 1296–1304 (2015)
Liu Y Q, Wang W Z, Qing T, Zhang Y G, Liang H, Zhang S H. The effect of lubricant temperature on dynamic behavior in angular contact ball bearings. Mech Mach Theory 149: 103832 (2020)
Liu Y Q, Wang W Z, Liang H, Qing T, Wang Y L, Zhang S H. Nonlinear dynamic behavior of angular contact ball bearings under microgravity and gravity. Int J Mech Sci 183: 105782 (2020)
Wedeven L D, Evans D, Cameron A. Optical analysis of ball bearing starvation. Journal of Lubrication Technology 93: 349–361 (1971)
Poll G, Li X, Bader N, Guo F. Starved lubrication in rolling contacts—A review. Bearing World Journal 4: 69–81 (2019)
Porras-Vazquez A, Fillot N, Vergne P, Philippon D, Morales-Espejel G E. Influence of spin on film thickness in elastohydrodynamic starved point contacts. Tribol Int 156: 106825 (2021)
Xu M, Dai Q, Huang W, Wang X. Using magnetic fluids to improve the behavior of ball bearings under starved lubrication. Tribol Int 141: 105950 (2020)
Jacod B, Pubilier F, Cann P M E, Lubrecht A A. An analysis of track replenishment mechanisms in the starved regime. Tribology 36: 483–492 (1999)
Ali F, Křupka I, Hartl M. Analytical and experimental investigation on friction of non-conformal point contacts under starved lubrication. Meccanica 48: 545–553 (2012)
Ali F, Křupka I, Hartl M. An approximate approach to predict the degree of starvation in ball—disk machine based on the relative friction. Tribol T 56: 681–686 (2013)
Venner C H, van Zoelen M T, Lugt P M. Thin layer flow and film decay modeling for grease lubricated rolling bearings. Tribol Int 47: 175–187 (2012)
van Zoelen M T, Venner C H, Lugt P M. Prediction of film thickness decay in starved elasto-hydrodynamically lubricated contacts using a thin layer flow model. P I Mech Eng J-J Eng 223: 541–552 (2009)
van Zoelen M T, Venner C H, Lugt P M. The prediction of contact pressure-induced film thickness decay in starved lubricated rolling bearings. Tribol T 53(6): 831–841 (2010)
Chiu Y P. An analysis and prediction of lubricant film starvation in rolling contact systems. ASLE Transact 17: 22–35 (1974)
Wedeven L D. Traction and film thickness measurements under starved elastohydrodynamic conditions. J Lub Techn-T ASME 97(2): 321–329 (1975)
Svoboda P, Kostal D, Krupka I, Hartl M. Experimental study of starved EHL contacts based on thickness of oil layer in the contact inlet. Tribol Int 67: 140–145 (2013)
Damiens B, Lubrecht A A, Cann P M. Influence of cage clearance on bearing lubrication. Tribol T 47: 2–6 (2004)
Pasdari M, Gentle C R. Effect of lubricant starvation on the minimum load condition in a thrust-loaded ball bearing. ASLE Transact 30: 355–359 (1987)
Hargreaves R A, Higginson G R. Some effects of lubricant starvation in cylindrical roller bearings. Journal of Lubrication Technology 97: 66–71 (1976)
Pemberton J C, Cameron A. Optical study of the lubrication of a 65 mm cylindrical roller bearing. Ind Lubr Tribol 33: 84–94 (1981)
Cann P M E, Damiens B, Lubrecht A A. The transition between fully flooded and starved regimes in EHL. Tribol Int 37: 859–864 (2004)
Itoigawa F, Nakamura T, Matsubara T. Starvation in ball bearing lubricated by oil and air lubrication system. In Proceedings of the 24th Leeds-Lyon Symposium on Tribology, London, UK, 1998: 243–252.
Ghosh M K, Hamrock B J, Brewe D E. Starvation effects on the hydrodynamic lubrication of rigid nonconformal contacts in combined rolling and normal motion. ASLE Transact 30(1): 91–99 (1987)
Yang P, Wang J, Kaneta M. Thermal and non-Newtonian numerical analyses for starved EHL line contacts. J Tribol-T ASME 128: 282–290 (2006)
Faraon I C, Schipper D J. Stribeck curve for starved line contacts. J Tribol-T ASME 129: 181–187 (2007)
Kumar P, Khonsari M M. Effect of starvation on traction and film thickness in thermo-EHL line contacts with shear—Thinning lubricants. Tribol Lett 32: 171–177 (2008)
Lubrecht T, Mazuyer D, Cann P. Starved elastohydrodynamic lubrication theory: Application to emulsions and greases. Cr Acad Sci IV-Phys 2: 717–728 (2001)
Damiens B, Venner C H, Cann P M E, Lubrecht A A. Starved lubrication of elliptical EHD contacts. J Tribol-T ASME 126: 105 (2004)
McCool J I, Chiu Y P, Crecelius W J, Liu J Y, Rosenlieb J W. Influence of Elastohydrodynamic Lubrication on the Life and Operation of Turbine Engine Ball Bearings-Bearing Design Manual. SKF (Sweden): SKF Industries Inc., 1975.
Hamrock B J, Dowson D. Isothermal elastohydrodynamic lubrication of point contacts Part IV—Starvation results. Journal of Lubrication Technology 99: 15–23 (1977)
Olaru D N, Gafitanu M D. Starvation in ball bearings. Wear 170: 219–234 (1993)
Nijenbanning G, Venner C H, Moes H. Film thickness in elastohydrodynamically lubricated elliptic contacts. Wear 176: 217–229 (1994)
Chevalier F, Lubrecht A A, Cann P M E, Colin F, Dalmaz G. Film thickness in starved EHL point contacts. J Tribol-T ASME 120(1): 126–133 (1998)
Masjedi M, Khonsari M M. A study on the effect of starvation in mixed elastohydrodynamic lubrication. Tribol Int 85: 26–36 (2015)
Zhao C J, Yu X K, Huang Q X, Ge S D, Gao X. Analysis on the load characteristics and coefficient of friction of angular contact ball bearing at high speed. Tribol Int 87: 50–56 (2015)
Wen C W, Meng X H, Lyu B G, Gu J M, Xiao L. Influence of angular misalignment on the tribological performance of high-speed micro ball bearings considering full multibody interactions. P I Mech Eng J-J Eng 235(6): 1168–1189 (2021)
Wen C W, Meng X H, Fang C C, Gu J M, Xiao L, Jiang S. 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 (2021)
Zhang X, Xu H, Chang W, Xi H, Xing Y, Pei S Y, Wang F C. Torque variations of ball bearings based on dynamic model with geometrical imperfections and operating conditions. Tribol Int 133: 193–205 (2019)
Gupta P K. Advanced Dynamics of Rolling Elements. New York (USA): Pringer-Verlag Press, 1984.
Liu Z, Meng X H, Wen C W, Yu S R, Zhou Z. On the oil-gas-solid mixed bearing between compression ring and cylinder liner under starved lubrication and high boundary pressures. Tribol Int 140: 105869 (2019)
Masjedi M, Khonsari M M. On the effect of surface roughness in point-contact EHL: Formulas for film thickness and asperity load. Tribol Int 82: 228–244 (2015)
Wang Y L, Wang W Z, Zhang S G, Zhao Z Q. Investigation of skidding in angular contact ball bearings under high speed. Tribol Int 92: 404–417 (2015)
Masjedi M, Khonsari M M. An engineering approach for rapid evaluation of traction coefficient and wear in mixed EHL. Tribol Int 92: 184–190 (2015)
Wang Y L, Wang W Z, Zhang S G, Zhao Z Q. Effects of raceway surface roughness in an angular contact ball bearing. Mech Mach Theory 121: 198–212 (2018)
Servais C, Bozet J L. New computational method of the ball/race contacts transverse loads of high speed ball bearings without race control hypothesis. Tribol Int 113: 206–215 (2017)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 52130502 and 51875344) and the Research Project of State Key Laboratory of Mechanical System and Vibration (Grant No. MSVZD202107).
Author information
Authors and Affiliations
Corresponding author
Additional information
Chengwei WEN. He received his bachelor degree in mechanical engineering and automation in 2015 from Wuhan University of Technology. Then he got his Ph.D. degree in the School of Mechanical Engineering at Shanghai Jiaotong University. His research interests include computational fluid dynamics (CFD) simulation, rolling bearing analysis, and wireless measurement.
Xianghui MENG. He received his bachelor degree and master degree in 1995 and 1999 from Xi’an Jiaotong University, and Ph.D. degree in 2006 from Shanghai Jiaotong University. He was invited to visit the Massachusetts Institute of Technology (MIT) during 2011–2012. His current position is a professor and doctorial supervisor at School of Mechanical Engineering, Shanghai Jiaotong University. His research areas cover the tribology of internal combustion engines, low friction design, and wear mechanism. He has presided many research projects and has published more than 60 papers on international engineering journals.
Lin XIAO. She received her master degree in mechanical engineering in 2016 from Shanghai University, China. She works at Shanghai Tian An Bearing Co., Ltd. and Shanghai Prime Machinery Co., Ltd. Bearing Technical Center as a senior engineer. Her current research focuses on the design and application of rolling bearings.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Wen, C., Meng, X., Gu, J. et al. Starved lubrication analysis of angular contact ball bearing based on a multi-degree-of-freedom tribo-dynamic model. Friction 11, 1395–1418 (2023). https://doi.org/10.1007/s40544-022-0661-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40544-022-0661-2