This work presents a numerical simulation which studies the effect of elastomeric bushing on the dynamics of a deep-groove ball bearing. To achieve the objective, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model a cylindrical elastomeric bushing, which was then coupled with an existing dynamic bearing model (DBM). Constitutive relationship for the elastomer is based on the Arruda–Boyce model combined with a generalized Maxwell-element model to capture both hyperelastic and viscoelastic behaviors of the material. Comparisons between the bushing model developed for this investigation and the existing experimental elastomeric bushing study showed that the results are in good agreement. Parametric studies were conducted to show the effects of various elastomeric material properties on bushing behavior. It was also shown that a desired bushing support performance can be achieved by varying bushing geometry. Simulations using the combined EFEM bushing and DBM model demonstrated that the elastomeric bushing provides better compliance to bearing misalignment as compared to a commonly used rigid support model. As a result, less ball slip and spin are generated. Modeling with a bearing surface dent showed that vibrations due to surface abnormalities can be significantly reduced using elastomeric bushing support. It has also been shown that choosing a proper bushing is an efficient way to tuning bushing vibration frequencies.

References

References
1.
Hill
,
J. M.
,
1975
, “
Radical Deflections of Rubber Bush Mountings of Finite Lengths
,”
Int. J. Eng. Sci.
,
13
(
4
), pp.
407
422
.
2.
Horton
,
J. M.
, and
Tupholme
,
G. E.
,
2006
, “
Approximate Radial Stiffness of Rubber Bush Mountings
,”
Mater. Des.
,
27
(
3
), pp.
226
229
.
3.
Horton
,
J. M.
,
Gover
,
M. J. C.
, and
Tupholme
,
G. E.
,
2000
, “
Stiffness of Rubber Bush Mountings Subjected to Tilting Deflection
,”
Rubber Chem. Technol.
,
73
(
4
), pp.
619
633
.
4.
Berg
,
M.
,
1998
, “
A Non-Linear Rubber Spring Model for Rail Vehicle Dynamics Analysis
,”
Veh. Syst. Dyn.
,
30
(
3–4
), pp.
197
212
.
5.
Sjöberg
,
M. M.
, and
Kari
,
L.
,
2002
, “
Non-Linear Behavior of a Rubber Isolator System Using Fractional Derivatives
,”
Veh. Syst. Dyn.
,
37
(
3
), pp.
217
236
.
6.
Mooney
,
M.
,
1940
, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys.
,
11
(
9
), pp.
582
592
.
7.
Rivlin
,
R. S.
, and
Saunders
,
D. W.
,
1951
, “
Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber
,”
Philos. Trans. R. Soc., A
,
243
(
865
), pp.
251
288
.
8.
Yeoh
,
O. H.
,
1993
, “
Some Forms of the Strain Energy Function for Rubber
,”
Rubber Chem. Technol.
,
66
(
5
), pp.
754
771
.
9.
Ogden
,
R. W.
,
1972
, “
Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids
,”
Proc. R. Soc. London, Ser. A
,
326
(
1567
), pp.
565
584
.
10.
Wang
,
M. C.
, and
Guth
,
E.
,
1952
, “
Statistical Theory of Networks of Non-Gaussian Flexible Chains
,”
J. Chem. Phys.
,
20
(
7
), pp.
1144
1157
.
11.
Flory
,
P. J.
, and
Rehner
,
J.
, Jr.
,
1943
, “
Statistical Mechanics of Cross-Linked Polymer Networks—I: Rubberlike Elasticity
,”
J. Chem. Phys.
,
11
(
11
), pp.
512
520
.
12.
Treloar
,
L. R. G.
,
1946
, “
The Elasticity of a Network of Long-Chain Molecules—III
,”
Trans. Faraday Soc.
,
42
, pp.
83
94
.
13.
Treloar
,
L. R. G.
,
1975
,
The Physics of Rubber Elasticity
,
Oxford University Press
, Oxford, UK.
14.
Arruda
,
E. M.
, and
Boyce
,
M. C.
,
1993
, “
A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials
,”
J. Mech. Phys. Solids
,
41
(
2
), pp.
389
412
.
15.
Kuhn
,
W.
, and
Grun
,
F.
,
1942
, “
The Crystal Structure of Polyethylene
,”
Koll. Z.
,
101
(
3
), pp.
248
262
.
16.
Bergström
,
J. S.
, and
Boyce
,
M. C.
,
1998
, “
Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers
,”
J. Mech. Phys. Solids
,
46
(
5
), pp.
931
954
.
17.
Kaliske
,
M.
, and
Rothert
,
H.
,
1997
, “
Formulation and Implementation of Three-Dimensional Viscoelasticity at Small and Finite Strains
,”
Comput. Mech.
,
19
(
3
), pp.
228
239
.
18.
Kadlowec
,
J.
,
Wineman
,
A.
, and
Hulbert
,
G.
,
2003
, “
Elastomer Bushing Response: Experiments and Finite Element Modeling
,”
Acta Mech.
,
163
(
1–2
), pp.
25
38
.
19.
Olsson
,
A. K.
, and
Austrell
,
P. E.
,
2003
, “
Finite Element Analysis of a Rubber Bushing Considering Rate and Amplitude Dependent Effects
,”
3rd European Conference on Constitutive Models Rubber
, pp.
133
140
.
20.
Jones
,
A. B.
,
1960
, “
A General Theory for Elastically Constrained Ball and Radial Roller Bearings
,”
ASME J. Basic Eng., Ser. D
,
82
(
2
), pp.
309
320
.
21.
Harris
,
T. A.
,
1966
,
Rolling Bearing Analysis
,
Wiley
,
New York
.
22.
Gupta
,
P. K.
,
1984
,
Advanced Dynamics of Rolling Elements
,
Springer-Verlag
,
New York
.
23.
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
.
24.
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
.
25.
Saheta
,
V.
,
2001
, “
Dynamics of Rolling Element Bearings Using Discrete Element Method
,” M.S. thesis, Purdue University, West Lafayette, IN.
26.
Ghaisas
,
N.
,
Wassgren
,
C.
, and
Sadeghi
,
F.
,
2004
, “
Cage Instabilities in Cylindrical Roller Bearings
,”
ASME J. Tribol.
,
126
(
4
), pp.
681
689
.
27.
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
.
28.
Cao
,
L.
,
Brouwer
,
M. D.
,
Sadeghi
,
F.
, and
Stacke
,
L. E.
,
2016
, “
Effect of Housing Support on Bearing Dynamics
,”
ASME J. Tribol.
,
138
(
1
), p.
011105
.
29.
Brouwer
,
M. D.
,
Sadeghi
,
F.
,
Ashtekar
,
A.
,
Archer
,
J.
, and
Lancaster
,
C.
,
2015
, “
Combined Explicit Finite and Discrete Element Methods for Rotor Bearing Dynamic Modeling
,”
Tribol. Trans.
,
58
(
2
), pp.
300
315
.
30.
Ok
,
J. K.
,
Yoo
,
W. S.
, and
Sohn
,
J. H.
,
2007
, “
Experimental Study on the Bushing Characteristics Under Several Excitation Inputs for Bushing Modeling
,”
Int. J. Autom. Technol.
,
8
(
4
), pp.
455
465
.
31.
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
.
You do not currently have access to this content.