In many applications, such as four-point contact slewing bearings or main shaft angular contact ball bearings, the rings and housings are so thin that the assumption of rigid rings does not hold anymore. In this paper, several methods are proposed to account for the flexibility of rings in a quasi-static ball bearing numerical model. The modeling approach consists of coupling a semianalytical approach and a finite element (FE) model to describe the deformation of the rings and housings. The manner in which this weak coupling is made differs depending on how the structural deformation of the ring and housing assemblies is injected into the set of nonlinear geometrical and equilibrium equations in order to solve them. These methods enable us to account for ring ovalization, ring twist, and raceway opening (including change of conformity) since a tulip deformation mode of the ring groove is observed for high contact angles. Either the torus fitting technique or mean displacement computation are used to determine these geometrical parameters. A comparison between the different approaches allows us to study, in particular, the impact of raceway conformity change. The loads used in this investigation are chosen in order that the maximum contact pressure (the Hertz pressure) at the ball-raceway interface remains below 2000 MPa, without any contact ellipse truncation. For the ball bearing example considered here, relative differences of up to 30% on the axial displacement, 10% on the maximum contact pressure, and 10% on the contact angle are observed by comparing rigid and deformable rings for a typical loading representative of the one encountered in operation. Despite the local change of conformity, which becomes significant at high contact angles and for thin ball bearing flanges, it is shown that this hardly affects the internal load distribution. The paper ends with a discussion on how the ring and housing flexibility may affect the loading envelope when the truncation of the contact ellipse is an issue.

References

References
1.
Young
,
W.
, and
Budynas
,
R.
,
2002
,
Roark's Formulas for Stress and Strain
,
McGraw-Hill
,
New York
.
2.
Harris
,
T. A.
,
2001
,
Rolling Bearing Analysis
,
4th ed.
,
Wiley
New York
.
3.
Cavallaro
,
G.
,
Nelias
,
D.
, and
Bon
,
F.
,
2005
, “
Analysis of High-Speed Intershaft Cylindrical Roller Bearing With Flexible Rings
,”
Tribol. Trans.
,
48
(
2
), pp.
154
164
.10.1080/05698190590923851
4.
Yao
,
T.
,
Chi
,
Y.
, and
Huang
,
Y.
,
2012
, “
Research on Flexibility of Bearing Rings for Multibody Contact Dynamics of Rolling Bearings
,”
Procedia Eng.
,
31
, pp.
586
594
.10.1016/j.proeng.2012.01.1071
5.
Leblanc
,
A.
,
Nelias
,
D.
, and
Defaye
,
C.
,
2009
. “
Nonlinear Dynamic Analysis of Cylindrical Roller Bearing With Flexible Rings
,”
J. Sound Vib.
,
325
(
1–2
), pp.
145
160
.10.1016/j.jsv.2009.03.013
6.
Daidié
,
A.
,
Chaib
,
Z.
, and
Ghosn
,
A.
,
2008
, “
3D Simplified Finite Elements Analysis of Load and Contact Angle in a Slewing Ball Bearing
,”
ASME J. Mech. Des.
,
130
, p.
082601
.
7.
Smolnicki
,
T.
, and
Rusiński
,
E.
,
2006
, “
Superelement-Based Modeling of Load Distribution in Large-Size Slewing Bearings
,”
ASME J. Mech. Des.
,
129
(
10
), pp.
459
463
.10.1115/1.2437784
8.
Bourdon
,
A.
,
Rigal
,
J. F.
, and
Play
,
D.
,
1999
. “
Static Rolling Bearing Models in a C.A.D. Environment for the Study of Complex Mechanisms—Part 1: Rolling Bearing Model
,”
ASME J. Tribol.
,
121
, pp.
205
214
.10.1115/1.2833923
9.
Bourdon
,
A.
,
Rigal
,
J. F.
, and
Play
,
D.
,
1999
, “
Static Rolling Bearing Models in a C.A.D. Environment for the Study of Complex Mechanisms—Part 2: Complete Assembly Model
,”
ASME J. Tribol.
,
121
, pp.
215
223
.10.1115/1.2833924
10.
Chen
,
G.
, and
Wen
,
J.
,
2012
, “
Load Performance of Large-Scale Rolling Bearings With Supporting Structure in Wind Turbines
,”
ASME J. Tribol.
,
134
(
4
), p.
041105
.10.1115/1.4007349
11.
Olave
,
M.
,
Sagartzazu
,
X.
,
Damian
,
J.
, and
Serna
,
A.
,
2010
, “
Design of Four Contact-Point Slewing Bearing With a New Load Distribution Procedure to Account for Structural Stiffness
,”
ASME J. Mech. Des.
,
132
(
2
), p.
021006
.10.1115/1.4000834
12.
Leblanc
,
A.
, and
Nelias
,
D.
,
2007
, “
Ball Motion and Sliding Friction in a Four-Contact-Point Ball Bearing
,”
ASME J. Tribol.
,
129
(
4
), pp.
801
808
.10.1115/1.2768079
13.
Leblanc
,
A.
, and
Nelias
,
D.
,
2008
, “
Analysis of Ball Bearings With 2, 3 or 4 Contact Points
,”
Tribol. Trans.
,
51
(
3
), pp.
372
380
.10.1080/10402000801888887
14.
Jones
,
A. B.
,
1959
, “
Ball Motion and Sliding Friction in Ball Bearings
,”
ASME J. Basic Eng.
,
81
(
1
), pp.
1
12
.
15.
Hamrock
,
B. J.
, and
Anderson
,
W. J.
,
1973
, “
Analysis of an Arched Outer-Race Ball Bearing Considering Centrifugal Forces
,”
ASME J. Lubr. Technol.
,
95
(
3
), pp.
265
271
.10.1115/1.3451796
16.
Hamrock
,
B.
,
1975
, “
Ball Motion and Sliding Friction in an Arched Outer Race Ball Bearing
,”
ASME J. Lubr. Technol.
,
97
(
2
), pp.
202
210
.10.1115/1.3452555
17.
Nelias
,
D.
,
Sainsot
,
P.
, and
Flamand
,
L.
,
1994
, “
Power Loss of Gearbox Ball Bearing Under Axial and Radial Loads
,”
Tribol. Trans.
,
37
(
1
), pp.
83
90
.10.1080/10402009408983269
18.
Nelias
,
D.
and
Yoshioka
,
T.
,
1998
, “
Location of an Acoustic Emission Source in a Radially Loaded Deep Groove Ball-Bearing
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
212
(
J1
), pp.
33
45
.10.1243/1350650981541877
19.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, England
.
20.
Lukács
,
G.
,
Martin
,
R.
, and
Marshall
,
D.
,
1998
, “
Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation
,”
ECCV’98, Proceedings of the 5th European Conference on Computer Vision
,
Springer-Verlag, Berlin
, Vol.
1
, pp.
671
686
.
21.
Shakarji
,
C. M.
,
1998
, “
Least-Squares Fitting Algorithms of the NIST Algorithm Testing System
,”
J. Res. Natl. Inst. Stand. Technol.
,
103
(
6
), pp.
633
641
.10.6028/jres.103.043
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