Abstract
A six degrees-of-freedom dynamic bearing model (DBM) was modified to include a novel cage pocket lubrication model. The motion of the cage was determined using the finite difference method to solve for the pressure generation and resultant forces inside of each cage pocket at each time-step of the dynamic model. The computational domain of the finite difference model was designed to reflect the specific cage pocket geometry of four common cage designs. Additionally, a bearing cage friction test rig was utilized to characterize the lubrication state inside of each cage. Experiments were performed that reveal the relationship between cage shape, ball speed, and relative ball—cage position. Specifically, information on the occurrence of kinematic starvation, the speed-dependent evacuation of oil from a cage pocket, was collected for use as an input condition to the dynamic bearing model. An inverse distance weighting scheme was utilized to predict starvation parameters for a general ball position inside of the cage pocket. Results from the dynamic simulation reveal new knowledge on the effect of cage geometry and lubrication on dynamic behavior. The inclusion of lubrication effects inside of the cage pocket reduces the median contact force between the balls and cage pocket and improves the stability of the predicted cage motion.
References
1.
FAG
, 2000
, “FAG Rolling Bearing Cages
,” Schweinfurt
, Germany
.2.
Tadic
, V.
, 1998
, “Engineering Polymers for Designer Cages
,” SKF Evol., p. 4
.3.
Damiens
, B.
, Lubrecht
, A. A.
, and Cann
, P. M.
, 2004
, “Influence of Cage Clearance on Bearing Lubrication
,” Tribol. Trans.
, 47
(1
), pp. 2
–6
. 4.
Ziaur Rahman
, M.
, Ohno
, N.
, and Tsutsumi
, H.
, 2003
, “Effect of Lubricating Oils on Cage Failure of Ball Bearings
,” Tribol. Trans.
, 46
(4
), pp. 499
–505
. 5.
Liang
, H.
, Zhang
, Y.
, and Wang
, W.
, 2021
, “Influence of the Cage on the Migration and Distribution of Lubricating Oil Inside a Ball Bearing
,” Friction
, 1
(1
), pp. 1
–11
. 6.
Munro
, G. J.
, Watters
, R. B.
, and Roberts
, E. W.
, 2007
, “The Impact of Cage Design on Ball Bearing Torque Behaviour
,” Eur. Sp. Agency (Special Publ. ESA SP, SP-653).7.
Barden
, 1998
, Barden Precision Cages for Spindle, Turbine, Miniature, and Instrument Ball Bearings
, Barden
, Danbury, CT
.8.
Gorycki
, Ł.
, 2015
, “Analysis of the Impact of the Cage Type on the Frictional Moment Ball Bearings
,” J. Mech. Eng. Autom.
, 5
(8
), pp. 450
–453
.9.
Brecher
, C.
, Hassis
, A.
, and Rossaint
, J.
, 2013
, “Cage Friction in High-Speed Spindle Bearings
,” Tribol. Trans.
, 57
(1
), pp. 77
–85
. 10.
Jones
, A. B.
, 1960
, “A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
,” ASME J. Basic Eng.
, 82
(2
), pp. 309
–320
. 11.
Jones
, A. B.
, 1959
, “Ball Motion and Sliding Friction in Ball Bearings
,” ASME J. Basic Eng.
, 81
(1
), pp. 1
–12
. 12.
Harris
, T. A.
, 1991
, Rolling Bearing Analysis
, John Wiley & Sons, Ltd.
, New York, NY
.13.
14.
Gupta
, P. K.
, 2020
, “Minimum Energy Hypothesis in Quasi-Static Equilibrium Solutions for Angular Contact Ball Bearings
,” Tribol. Trans.
, 63
(6
), pp. 1051
–1066
. 15.
Walters
, C. T.
, 1971
, “The Dynamics of Ball Bearings
,” ASME J. Lubr. Technol.
, 93
(1
), pp. 1
–10
. 16.
Gupta
, P. K.
, 1979
, “Dynamics of Rolling-Element Bearings Part I: Cylindrical Roller Bearing Results
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 293
–302
. 17.
Gupta
, P. K.
, 1979
, “Dynamics of Rolling-Element Bearings Part II: Cylindrical Roller Bearing Results
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 305
–311
. 18.
Gupta
, P. K.
, 1979
, “Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 312
–318
. 19.
Gupta
, P. K.
, 1979
, “Dynamics of Rolling-Element Bearings—Part IV: Ball Bearing Results
,” ASME J. Lubr. Technol.
, 101
(3
), pp. 319
–326
. 20.
Gupta
, P. K.
, 1984
, Advanced Dynamics of Rolling Elements
, Springer-Verlag
, New York, NY
.21.
Gupta
, P. K.
, 1991
, “Cage Unbalance and Wear in Ball Bearings
,” Wear
, 147
(1
), pp. 93
–104
. 22.
Li
, H.
, Li
, C.
, Li
, Y.
, Qi
, S.
, Liu
, Y.
, and Liu
, H.
, 2019
, “Influence of Pocket Wear on the Dynamic Characteristics of High-Speed Ball Bearing Cage
,” ASME 2019 International Mechanical Engineering Congress and Exposition
, Salt Lake City, UT
, Nov. 11–14
, pp. 1
–12
.23.
Li
, H.
, Liu
, H.
, Li
, H.
, Qi
, S.
, Liu
, Y.
, and Wang
, F.
, 2020
, “Effect of Cage-Pocket Wear on the Dynamic Characteristics of Ball Bearing
,” Ind. Lubr. Tribol.
, 72
(7
), pp. 905
–912
. 24.
Gupta
, P. K.
, 1988
, “On the Geometrical Imperfections in Ball Bearings
,” ASME J. Tribol.
, 110
(1
), pp. 19
–25
. 25.
Ashtekar
, A.
, Sadeghi
, F.
, and Stacke
, L. E.
, 2008
, “A New Approach to Modeling Surface Defects in Bearing Dynamics Simulations
,” ASME J. Tribol.
, 130
(4
), p. 041103
. 26.
Ashtekar
, A.
, Sadeghi
, F.
, and Stacke
, L. E.
, 2010
, “Surface Defects Effects on Bearing Dynamics
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 224
(1
), pp. 25
–35
. 27.
Gupta
, P. K.
, 2002
, Thermal Interactions in Rolling Bearing Dynamics, Clifton Park, NY, AFRL Report No. ADA409914.28.
Gao
, S.
, Chatterton
, S.
, Pennacchi
, P.
, Han
, Q.
, and Chu
, F.
, 2022
, “Skidding and Cage Whirling of Angular Contact Ball Bearings: Kinematic-Hertzian Contact-Thermal-Elasto-Hydrodynamic Model With Thermal Expansion and Experimental Validation
,” Mech. Syst. Signal Process.
, 166
(1
), p. 108427
. 29.
Pederson
, B. M.
, Sadeghi
, F.
, and Wassgren
, C.
, 2006
, “The Effects of Cage Flexibility on Ball-to-Cage Pocket Contact Forces and Cage Instability
,” J. Passeng. CAR Mech. Syst. J.
, 115
(1
), pp. 260
–271
.30.
Liu
, Y.
, Chen
, Z.
, Tang
, L.
, and Zhai
, W.
, 2021
, “Skidding Dynamic Performance of Rolling Bearing With Cage Flexibility Under Accelerating Conditions
,” Mech. Syst. Signal Process.
, 150
(1
), p. 107257
. 31.
Weinzapfel
, N.
, and Sadeghi
, F.
, 2009
, “A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations
,” ASME J. Tribol.
, 131
(2
), p. 021102
. 32.
Ashtekar
, A.
, and Sadeghi
, F.
, 2012
, “A New Approach for Including Cage Flexibility in Dynamic Bearing Models by Using Combined Explicit Finite and Discrete Element Methods
,” ASME J. Tribol.
, 134
(4
), p. 041502
. 33.
Gentle
, C. R.
, and Pasdari
, M.
, 1984
, “Measurement of Cage and Pocket Friction in a Ball Bearing for Use in a Simulation Program
,” ASLE Trans.
, 28
(4
), pp. 536
–541
. 34.
Molina
, M. A.
, and Gohar
, R.
, 1978
, “Hydrodynamic Lubrication of Ball-Bearing Cage Pockets
,” J. Mech. Eng. Sci.
, 20
(1
), pp. 11
–20
. 35.
Molina
, M. A.
, and Gohar
, R.
, 1979
, “Hydrodynamic Design of Ballbearing Cage Pockets
,” Tribol. Int.
, 12
(1
), pp. 15
–20
. 36.
Ma
, F.
, Jiang
, F.
, and An
, Q.
, 2014
, “Simulation of Hydrodynamic Lubrication Between Cage Pockets and Rollers in Cylindrical Roller Bearings
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 229
(14
), pp. 2551
–2560
. 37.
Russell
, T.
, and Sadeghi
, F.
, 2022
, “The Effects of Lubricant Starvation on Ball Bearing Cage Pocket Friction
,” Tribol. Int.
, 173
(1
), p. 107630
. 38.
Houpert
, L.
, 2009
, “CAGEDYN : A Contribution to Roller Bearing Dynamic Calculations Part I : Basic Tribology Concepts
,” Tribol. Trans.
, 53
(1
), pp. 1
–9
. 39.
Houpert
, L.
, 2010
, “CAGEDYN : A Contribution to Roller Bearing Dynamic Calculations. Part III : Experimental Validation CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations. Part III: Experimental Validation
,” Tribol. Trans.
, 53
(6
), pp. 848
–859
. 40.
Takabi
, J.
, and Khonsari
, M. M.
, 2014
, “On the Influence of Traction Coefficient on the Cage Angular Velocity in Roller Bearings
,” Tribol. Trans.
, 57
(5
), pp. 793
–805
. 41.
Selvaraj
, A.
, and Marappan
, R.
, 2011
, “Experimental Analysis of Factors Influencing the Cage Slip in Cylindrical Roller Bearing
,” Int. J. Adv. Manuf. Technol.
, 53
(5–8
), pp. 635
–644
. 42.
Schwarz
, S.
, Grillenberger
, H.
, Tremmel
, S.
, and Wartzack
, S.
, 2021
, “Investigations on the Rolling Bearing Cage Dynamics With Regard to Different Operating Conditions and Cage Properties
,” IOP Conf. Ser. Mater. Sci. Eng.
, 1097
(1
), p. 012009
. 43.
Yuan
, D.
, Wang
, R.
, Chen
, S.
, and Chen
, X.
, 2022
, “Experimental Research on Cage Motion With Different Pocket Shapes in Angular Contact Ball Bearing
,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
, 236
(7
), pp. 1325
–1335
. 44.
Arya
, U.
, Sadeghi
, F.
, Conley
, B.
, Russell
, T.
, Peterson
, W.
, and Meinel
, A.
, 2022
, “Experimental Investigation of Cage Dynamics and Ball–Cage Contact Forces in an Angular Contact Ball Bearing
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 236
(12
), pp. 2522
–2534
.45.
Abele
, E.
, and Holland
, L.
, 2017
, “Image-Based Movement Analysis of Bearing Cages of Cylindrical Hybrid Roller Bearings
,” ASME J. Tribol.
, 139
(6
), p. 061101
. 46.
Chen
, H.
, Wang
, W.
, Liang
, H.
, and Ge
, X.
, 2022
, “Observation of the Oil Flow in a Ball Bearing With a Novel Experiment Method and Simulation
,” Tribol. Int.
, 174
(1
), p. 107731
. 47.
Wen
, B.
, Li
, Y.
, Wang
, M.
, and Yang
, Y.
, 2023
, “Measurement for Lubricant Distribution in an Angular Contact Ball Bearing and Its Influence Investigation
,” Lubricants
, 11
(2
), p. 63
. 48.
Chen
, H.
, Liang
, H.
, Wang
, W.
, and Zhang
, S.
, 2023
, “Investigation on the Oil Transfer Behaviors and the Air–Oil Interfacial Flow Patterns in a Ball Bearing Under Different Capillary Conditions
,” Friction
, 11
(2
), pp. 228
–245
. 49.
Aamer
, S.
, Sadeghi
, F.
, Russell
, T.
, Peterson
, W.
, Meinel
, A.
, and Grillenberger
, H.
, 2022
, “Lubrication, Flow Visualization, and Multiphase CFD Modeling of Ball Bearing Cage
,” Tribol. Trans.
, 65
(6
), pp. 1088
–1098
.50.
Saheta
, V.
, 2001
, “Dynamics of Rolling Element Bearings Using the Discrete Element Method
,” MS thesis
, Purdue University
, West Lafayette, IN
.51.
Houpert
, L.
, 1986
, “Piezoviscous-Rigid Rolling and Sliding Traction Forces, Application: The Rolling Element-Cage Pocket Contact
,” ASME J. Tribol.
, 109
(2
), pp. 363
–370
. 52.
Hamrock
, B.
, Schmid
, S.
, and Jacobson
, B.
, 2004
, Fundamentals of Fluid Film Lubrication
, CRC Press
, New York
.53.
Biboulet
, N.
, and Houpert
, L.
, 2010
, “Hydrodynamic Force and Moment in Pure Rolling Lubricated Contacts. Part 2: Point Contacts
,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
, 224
(8
), pp. 777
–787
. 54.
Biboulet
, N.
, and Houpert
, L.
, 2010
, “Hydrodynamic Force and Moment in Pure Rolling Lubricated Contacts. Part 1: Line Contacts
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 224
(8
), pp. 765
–775
. 55.
Talbot
, D.
, Kahraman
, A.
, and Seetharaman
, S.
, 2014
, “A Helical Gear Pair Pocketing Power Loss Model
,” ASME J. Tribol.
, 136
(2
), p. 021105
. 56.
Chaari
, F.
, Romdhane
, M. B.
, Baccar
, W.
, Fakhfakh
, T.
, and Haddar
, M.
, 2012
, “Windage Power Loss in Spur Gear Sets
,” WSEAS Trans. Appl. Theor. Mech.
, 7
(2
), pp. 159
–168
.57.
Liebrecht
, J.
, Si
, X.
, Sauer
, B.
, and Schwarze
, H.
, 2015
, “Investigation of Drag and Churning Losses on Tapered Roller Bearings
,” J. Mech. Eng.
, 61
(6
), pp. 399
–408
. 58.
Peterson
, W.
, Russell
, T.
, Sadeghi
, F.
, and Berhan
, M. T.
, 2021
, “Experimental and Analytical Investigation of Fluid Drag Losses in Rolling Element Bearings
,” Tribol. Int.
, 161
(1
), pp. 1
–12
. 59.
Shafiee
, A.
, Russell
, T.
, Sadeghi
, F.
, and Wilmer
, M. G.
, 2022
, “Analytical Investigation of Roller Skew and Tilt in a Spherical Roller Bearing
,” ASME J. Tribol.
, 144
(7
), p. 071201
. 60.
Schnell
, T. J.
, Sadeghi
, F.
, and Trope
, E. J.
, 1996
, “Performance Characteristics of Perfluoroalkylpolyether Synthetic Lubricants
,” Tribol. Trans.
, 39
(4
), pp. 849
–854
. 61.
Russell
, T.
, Sadeghi
, F.
, Peterson
, W.
, Aamer
, S.
, and Arya
, U.
, 2021
, “A Novel Test Rig for the Investigation of Ball Bearing Cage Friction
,” Tribol. Trans.
, 64
(5
), pp. 943
–955
. 62.
Peterson
, W.
, Sadeghi
, F.
, Meinel
, A.
, and Grillenberger
, H.
, 2023
, “Investigation of Roller Bearing Cage Pocket Lubrication and Friction
,” ASME J. Tribol.
, 145
(5
), p. 054302
. 63.
Boesiger
, E. A.
, Donley
, A. D.
, and Loewenthal
, S.
, 1992
, “An Analytical and Experimental Investigation of Ball Bearing Retainer Instabilities
,” ASME J. Tribol.
, 114
(3
), pp. 530
–538
. 64.
Gao
, S.
, Han
, Q.
, Zhou
, N.
, Pennacchi
, P.
, and Chu
, F.
, 2022
, “Stability and Skidding Behavior of Spacecraft Porous Oil-Containing Polyimide Cages Based on High-Speed Photography Technology
,” Tribol. Int.
, 165
(1
), p. 107294
. 65.
Zhenhuan
, Y.
, and Liqin
, W.
, 2015
, “Effect of External Loads on Cage Stability of High-Speed Ball Bearings
,” Proc. IMechE Part J J. Eng. Tribol.
, 229
(11
), pp. 1300
–1318
. 66.
Gao
, S.
, Han
, Q.
, Zhou
, N.
, Pennacchi
, P.
, Chatterton
, S.
, Qing
, T.
, Zhang
, J.
, and Chu
, F.
, 2022
, “Experimental and Theoretical Approaches for Determining Cage Motion Dynamic Characteristics of Angular Contact Ball Bearings Considering Whirling and Overall Skidding Behaviors
,” Mech. Syst. Signal Process.
, 168
(1
), p. 108704
. 67.
Stacke
, L. E.
, and Fritzson
, D.
, 2001
, “Dynamic Behaviour of Rolling Bearings: Simulations and Experiments
,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
, 215
(6
), pp. 499
–508
. 68.
Li
, Q.
, Chen
, X.
, Zhang
, T.
, Chen
, S.
, and Gu
, J.
, 2019
, “Experimental Research on Cage Dynamic Characteristics of Angular Contact Ball Bearing
,” Mech. Ind.
, 20
(2
), pp. 204
–215
.69.
Schwarz
, S.
, Grillenberger
, H.
, Tremmel
, S.
, and Wartzack
, S.
, 2021
, “Prediction of Rolling Bearing Cage Dynamics Using Dynamics Simulations and Machine Learning Algorithms
,” Tribol. Trans.
, 65
(2
), pp. 1
–23
.70.
Tu
, W.
, Luo
, Y.
, and Yu
, W.
, 2019
, “Dynamic Interactions Between the Rolling Element and the Cage in Rolling Bearing Under Rotational Speed Fluctuation Conditions
,” ASME J. Tribol.
, 141
(9
), pp. 091101
. 71.
Wen
, B.
, Ren
, H.
, Zhang
, H.
, and Han
, Q.
, 2017
, “Experimental Investigation of Cage Motions in an Angular Contact Ball Bearing
,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
, 231
(8
), pp. 1041
–1055
. 72.
Gupta
, P. K.
, 1991
, “Modeling of Instabilities Induced by Cage Clearances in Ball Bearings
,” Tribol. Trans.
, 34
(1
), pp. 93
–99
. 73.
Liu
, X.
, Deng
, S.
, and Teng
, H.
, 2011
, “Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings
,” Trans. Tianjin Univ.
, 17
(1
), pp. 20
–27
. 74.
Sathyan
, K.
, Gopinath
, K.
, Lee
, S. H.
, Hsu
, H. Y.
, Khobar
, A.
, and Arabia
, S.
, 2012
, “Bearing Retainer Designs and Retainer Instability Failures in Spacecraft Moving Mechanical Systems
,” Tribol. Trans.
, 55
(4
), pp. 503
–511
. 75.
Wen
, B.
, Wang
, M.
, Zhou
, X.
, Ren
, H.
, and Han
, Q.
, 2018
, “Multi-Harmonic Motions of Bearing Cage Affected by Rotor Unbalance
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 232
(15
), pp. 2610
–2625
. 76.
Han
, Q.
, Wen
, B.
, Wang
, M.
, and Deng
, S.
, 2017
, “Investigation of Cage Motions Affected by Its Unbalance in a Ball Bearing
,” Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn.
, 232
(2
), pp. 169
–182
.77.
Sakaguchi
, T.
, and Harada
, K.
, 2006
, “Dynamic Analysis of Cage Behavior in a Tapered Roller Bearing
,” ASME J. Tribol.
, 128
(3
), pp. 604
–611
. Copyright © 2023 by ASME
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