Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

References

References
1.
Kingsbury
,
E.
, and
Walker
,
R.
,
1994
, “
Motions of an Unstable Retainer in an Instrument Ball Bearing
,”
ASME J. Tribol.
,
116
(
2
), pp.
202
208
.
2.
Kannel
,
J. W.
, and
Bupara
,
S. S.
,
1978
, “
A Simplified Model of Cage Motion in Angular Contact Bearings Operating in the EHD Lubrication Regime
,”
ASME J. Lubr. Technol.
,
100
(
3
), pp.
395
403
.
3.
Gupta
,
P. K.
,
1979
, “
Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis
,”
ASME J. Lubr. Technol.
,
101
(
3
), pp.
293
302
.
4.
Gupta
,
P. K.
,
1979
, “
Dynamics of Rolling-Element Bearings—Part II: Cylindrical Roller Bearing Results
,”
ASME J. Lubr. Technol.
,
101
(
3
), pp.
305
311
.
5.
Gupta
,
P. K.
,
1979
, “
Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis
,”
ASME J. Lubr. Technol.
,
101
(
3
), pp.
312
318
.
6.
Gupta
,
P. K.
,
1979
, “
Dynamics of Rolling-Element Bearings—Part IV: Ball Bearing Results
,”
ASME J. Lubr. Technol.
,
101
(
3
), pp.
319
326
.
7.
Gupta
,
P. K.
,
1988
, “
Frictional Instabilities in Ball Bearings
,”
Tribol. Trans.
,
31
(
2
), pp.
258
268
.
8.
Gupta
,
P. K.
,
1990
, “
On the Frictional Instabilities in a Cylindrical Roller Bearing
,”
Tribol. Trans.
,
33
(
3
), pp.
395
401
.
9.
Gupta
,
P. K.
,
1991
, “
Modeling of Instabilities Induced by Cage Clearances in Cylindrical Roller Bearings
,”
Tribol. Trans.
,
34
(
1
), pp.
1
8
.
10.
Gupta
,
P. K.
,
1991
, “
Modeling of Instabilities Induced by Cage Clearances in Ball Bearings
,”
Tribol. Trans.
,
34
(
1
), pp.
93
99
.
11.
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
.
12.
Stacke
,
L.-E.
,
Fritzson
,
D.
, and
Nordling
,
P.
,
1999
, “
BEAST—A Rolling Bearing Simulation Tool
,”
Proc. Inst. Mech. Eng., Part K
,
213
(
2
), pp.
63
71
.
13.
Stacke
,
L.-E.
, and
Fritzson
,
D.
,
2001
, “
Dynamic Behaviour of Rolling Bearings: Simulations and Experiments
,”
Proc. Inst. Mech. Eng., Part J
,
215
(
6
), pp.
499
508
.
14.
Sakaguchi
,
T.
, and
Harada
,
K.
,
2006
, “
Dynamic Analysis of Cage Behavior in a Tapered Roller Bearing
,”
ASME J. Tribol.
,
128
(
3
), pp.
604
611
.
15.
Sakaguchi
,
T.
, and
Harada
,
K.
,
2009
, “
Dynamic Analysis of Cage Stress in Tapered Roller Bearings Using Component-Mode-Synthesis Method
,”
ASME J. Tribol.
,
131
(
1
), p.
011102
.
16.
Ghaisas
,
N.
,
Wassgren
,
C. R.
, and
Sadeghi
,
F.
,
2004
, “
Cage Instabilities in Cylindrical Roller Bearings
,”
ASME J. Tribol.
,
126
(
4
), pp.
681
689
.
17.
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
.
18.
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
.
19.
Brewe
,
D. E.
, and
Hamrock
,
B. J.
,
1977
, “
Simplified Solution for Elliptical-Contact Deformation Between Two Elastic Solids
,”
ASME J. Lubr. Technol.
,
99
(
4
), pp.
485
487
.
20.
Jacod
,
B.
,
Venner
,
C. H.
, and
Lugt
,
P. M.
,
2001
, “
A Generalized Traction Curve for EHL Contacts
,”
ASME J. Tribol.
,
123
(
2
), pp.
248
253
.
21.
Hamrock
,
B. J.
, and
Dowson
,
D.
,
1977
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts—Part III: Fully Flooded Results
,”
ASME J. Lubr. Technol.
,
99
(
2
), pp.
264
275
.
22.
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
,
224
(
8
), pp.
777
787
.
23.
Nogi
,
T.
,
2015
, “
Film Thickness and Rolling Resistance in Starved Elastohydrodynamic Lubrication of Point Contacts With Reflow
,”
ASME J. Tribol.
,
137
(
4
), p.
041502
.
24.
Kaneta
,
M.
,
Shigeta
,
T.
,
Hata
,
H.
, and
Yang
,
P.
,
2005
, “
Effects of Maximum Hertzian Pressure on the Maximum Traction Coefficient Under EHL Conditions
,”
Life Cycle Tribology: 31st Leeds-Lyon Tribology Symposium
,
D.
Dowson
,
M.
Priest
,
G.
Dalmaz
, and
A. A.
Lubrecht
, eds., Vol.
48
,
Elsevier
, Amsterdam, The Netherlands, pp.
231
237
.
25.
Harris
,
T. A.
,
2000
,
Rolling Bearing Analysis
,
4th ed.
,
Wiley
,
New York
.
26.
Abele
,
E.
,
Holland
,
L.
, and
Nehrbass
,
A.
,
2015
, “
Image Acquisition and Image Processing Algorithms for Movement Analysis of Bearing Cages
,”
ASME J. Tribol.
,
138
(
2
), p.
021105
.
27.
Yoshida
,
T.
,
Hirota
,
M.
, and
Yoshikawa
,
K.
,
2013
, “
Analysis of Cage Slip in Ball Bearings Considering Non-Newtonian Behavior and Temperature Rise of Lubricating Oil
,”
Tribol. Online
,
8
(
3
), pp.
210
218
.
28.
Nogi
,
T.
,
2015
, “
An Analysis of Starved EHL Point Contacts With Reflow
,”
Tribol. Online
,
10
(
1
), pp.
64
75
.
29.
Kimura
,
Y.
,
Endo
,
T.
, and
Dong
,
D.
,
2010
, “
EHL With Grease at Low Speeds
,”
Advanced Tribology—CIST2008 & ITS-IFToMM2008
,
J.
Luo
,
Y.
Meng
,
T.
Shao
, and
Q.
Zhao
, eds.,
Springer-Verlag, Berlin
, pp.
15
19
.
30.
Sakai
,
K.
,
Tokumo
,
Y.
,
Ayame
,
Y.
,
Shitara
,
Y.
,
Tanaka
,
H.
, and
Sugimura
,
J.
,
2016
, “
Effect of Formulation of Li Greases on Their Flow and Ball Bearing Torque
,”
Tribol. Online
,
11
(
2
), pp.
168
173
.
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