In this investigation, a new approach was developed to study the influence of cage flexibility on the dynamics of inner and outer races and balls in a bearing. A 3D explicit finite element model (EFEM) of the cage was developed and combined with an existing discrete element dynamic bearing model (DBM) with six degrees of freedom. The EFEM was used to determine the cage dynamics, deformation, and resulting stresses in a ball bearing under various operating conditions. A novel algorithm was developed to determine the contact forces between the rigid balls and the flexible (deformable) cage. In this new flexible cage dynamic bearing model, the discrete and finite element models interact at each time step to determine the position, velocity, acceleration, and forces of all bearing components. The combined model was applied to investigate the influence of cage flexibility on ball-cage interactions and the resulting ball motion, cage whirl, and the effects of shaft misalignment. The model demonstrates that cage flexibility (deflection) has a significant influence on the ball-cage interaction. The results from this investigation demonstrate that the magnitude of ball-cage impacts and the ball sliding reduced in the presence of a flexible cage; however, as expected, the cage overall motion and angular velocity were largely unaffected by the cage flexibility. During high-speed operation, centrifugal forces contribute substantially to the total cage deformation and resulting stresses. When shaft misalignment is considered, stress cycles are experienced in the bridge and rail sections of the cage where fatigue failures have been observed in practice and in experimental studies.

References

References
1.
Walters
,
C. T.
, 1971, “
The Dynamics of Ball Bearings
,”
ASME J. Lubr. Technol.
,
93
(
2
), pp.
1
10
.
2.
Rumbarger
,
J. H.
, 1973, “
Gas Turbine Engine Mainshaft Roller Bearing—System Analysis
,”
ASME J. Lubr. Technol.
,
95
, pp.
401
416
.
3.
Gupta
,
P. K.
, 1984,
Advanced Dynamics of Rolling Elements
,
Springer-Verlag
,
New York
4.
Stacke
,
L.
,
Fritzson
,
D.
, and
Nordling
,
P.
, 1999, “
BEAST—A Rolling Bearing Simulation Tool
,”
Proc. Inst. Mech. Eng., Part K: J. Multibody Dyn.
,
213
(
2
), pp.
63
71
.
5.
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
539
.
6.
Pederson
,
B. M.
,
Sadeghi
,
F.
, and
Wassgren
,
C.
, 2006, “
The Effects of Cage Flexibility on Ball-To-Cage Pocket Contact Forces and Cage Instability in Deep Groove Ball Bearings
,” SAE Transmission and Driveline Symposium, Paper No. 2006-01-0358, pp.
43
54
.
7.
Weinzapfel
,
N.
, and
Sadeghi
,
F.
, 2009, “
A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations
,”
J. Tribol.
,
131
(
2
), p.
021102
.
8.
Houpert
,
L.
, 2010, “
CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations Part I: Basic Tribology Concepts
,”
Tribol. Trans.
,
53
(
1
), pp.
1
9
.
9.
Houpert
,
L.
, 2010, “
CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations Part II: Description of the Numerical Tool and Its Outputs
,”
Tribol. Trans.
,
53
(
1
), pp.
10
21
.
10.
Houpert
,
L.
, 2010, “
CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part III: Experimental Validation
,”
Tribol. Trans.
,
53
(
6
), pp.
848
859
.
11.
Sakaguchi
,
T.
, and
Kazuyoshi
,
H.
, 2009, “
Dynamic Analysis of Cage Stress in a Tapered Roller Bearing using Component-Mode-Synthesis Method
,”
J. Tribol.
,
131
,
011102
.
12.
Kingsbury
,
E.
, and
Walker
,
R.
, 1994, “
Motions of an Unstable Retainer in an Instrument Ball Bearing
,”
ASME J. Tribol.
,
116
, pp.
202
208
.
13.
Hinton
,
W.
, 1970, “
An Investigation Into the Causes of Ball Bearing Failures in Types P2 and P3 Engine-Driven Generators
,”
Wear
,
16
(
1–2
), pp.
3
42
.
14.
Crawford
,
T.
, 1970, “
The Experimental Determination of Ball Bearing Cage Stress
,”
Wear
,
16
(
1–2
), pp.
43
52
.
15.
Stacke
,
L.
, 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
.
16.
Gupta
,
P.
, 1991, “
Dynamic Loads and Cage Wear in High-Speed Rolling Bearings
,”
Wear
,
147
(
1
), pp.
119
134
.
17.
Gupta
,
P. K.
, 1975, “
Generalized Dynamic Simulation of Skid in Ball Bearings
,”
J. Aircr.
,
12
, pp.
260
265
.
18.
Hamrock
,
B.
,
Schmid
,
S.
, and
Jacobson
,
B.
, 2004,
Fundamentals of Fluid Film Lubrication
,
Marcel Dekker
,
New York
.
19.
Kragelskii
,
I. V.
, 1965,
Friction and Wear
,
Butterworths
,
London
.
20.
Gupta
,
P. K.
, 1974, “
Transient Ball Motion and Skid in Ball Bearings
,”
J. Lubr. Technol.
,
97
, pp.
261
269
.
21.
Ericson
,
C.
, 2005,
Real Time Collision Detection
,
Elseveir
,
New York
.
22.
Saheta
,
V.
, 2001, “
Dynamics of Rolling Element Bearings Using Discrete Element Method
,” M.S. thesis, Purdue University, West Lafayette, IN.
23.
Kannel
,
J. W.
, and
Bupara
,
S. S.
, 1978, “
A Simplified Model of Cage Motion in Angular Contact Ball Bearings Operating in the EHD Lubrication Regime
,”
ASME J. Lubr. Technol.
,
100
, pp.
395
403
.
You do not currently have access to this content.