A dynamic model of a rotating shaft on two textured hydrodynamic journal bearings is presented. The hydrodynamic mean pressure is computed using multiscale periodic homogenization and is projected on a flexible shaft with internal damping. Harmonic balance method (HBM) is used to study the limit cycles of unbalance response of the coupled system discretized by finite element method (FEM). Stability is analyzed with Floquet multipliers computation. An example of an isotropic texturing pattern representing laser dimples on a lightweight rotor is analyzed. Vibration amplitude and stability zone are compared with plain bearing lubrication. It is shown in an example that full surface texturing leads to relatively higher vibration amplitude compared to plain bearings.

References

1.
Lund
,
J. W.
,
1974
, “
Modal Response of a Flexible Rotor in Fluid-Film Bearings
,”
ASME J. Manuf. Sci. Eng.
,
96
(
2
), pp.
525
533
.
2.
Myers
,
C. J.
,
1984
, “
Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings
,”
ASME J. Appl. Mech.
,
51
(
2
), pp.
244
250
.
3.
Vorst
,
E. L. B. V. D.
,
Fey
,
R. H. B.
,
Kraker
,
A. D.
, and
Campen
,
D. H. V.
,
1996
, “
Steady-State Behaviour of Flexible Rotordynamic Systems With Oil Journal Bearings
,”
Nonlinear Dyn.
,
11
(
3
), pp.
295
313
.
4.
Zheng
,
T.
, and
Hasebe
,
N.
,
1999
, “
Nonlinear Dynamic Behaviors of a Complex Rotor-Bearing System
,”
ASME J. Appl. Mech.
,
67
(
3
), pp.
485
495
.
5.
Muszynska
,
A.
,
2005
,
Rotordynamics
,
CRC Press
, Boca Raton, FL.
6.
Elrod
,
H. G.
,
1981
, “
A Cavitation Algorithm
,”
ASME J. Tribol.
,
103
(
3
), pp.
350
354
.
7.
Gropper
,
D.
,
Wang
,
L.
, and
Harvey
,
T. J.
,
2016
, “
Hydrodynamic Lubrication of Textured Surfaces: A Review of Modeling Techniques and Key Findings
,”
Tribol. Int.
,
94
, pp.
509
529
.
8.
Hamilton
,
D. B.
,
Walowit
,
J. A.
, and
Allen
,
C. M.
,
1966
, “
A Theory of Lubrication by Microirregularities
,”
ASME J. Basic Eng.
,
88
(
1
), pp.
177
185
.
9.
Patir
,
N.
, and
Cheng
,
H. S.
,
1978
, “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
ASME J. Tribol.
,
100
(
1
), pp.
12
17
.
10.
Elrod
,
H. G.
,
1979
, “
A General Theory for Laminar Lubrication With Reynolds Roughness
,”
ASME J. Tribol.
,
101
(
1
), pp.
8
14
.
11.
Bayada
,
G.
,
Martin
,
S.
, and
Vázquez
,
C.
,
2005
, “
An Average Flow Model of the Reynolds Roughness Including a Mass-Flow Preserving Cavitation Model
,”
ASME J. Tribol.
,
127
(
4
), pp.
793
802
.
12.
Almqvist
,
A.
,
Essel
,
E. K.
,
Persson
,
L. E.
, and
Wall
,
P.
,
2007
, “
Homogenization of the Unstationary Incompressible Reynolds Equation
,”
Tribol. Int.
,
40
(
9
), pp.
1344
1350
.
13.
Almqvist
,
A.
,
Fabricius
,
J.
, and
Wall
,
P.
,
2012
, “
Homogenization of a Reynolds Equation Describing Compressible Flow
,”
J. Math. Anal. Appl.
,
390
(
2
), pp.
456
471
.
14.
Arghir
,
M.
,
Roucou
,
N.
,
Helene
,
M.
, and
Frene
,
J.
,
2003
, “
Theoretical Analysis of the Incompressible Laminar Flow in a Macro-Roughness Cell
,”
ASME J. Tribol.
,
125
(
2
), pp.
309
318
.
15.
de Kraker
,
A.
,
van Ostayen
,
R. A. J.
, and
Rixen
,
D. J.
,
2010
, “
Development of a Texture Averaged Reynolds Equation
,”
Tribol. Int.
,
43
(
11
), pp.
2100
2109
.
16.
Tala-Ighil
,
N.
,
Fillon
,
M.
, and
Maspeyrot
,
P.
,
2011
, “
Effect of Textured Area on the Performances of a Hydrodynamic Journal Bearing
,”
Tribol. Int.
,
44
(
3
), pp.
211
219
.
17.
Brizmer
,
V.
, and
Kligerman
,
Y.
,
2012
, “
A Laser Surface Textured Journal Bearing
,”
ASME J. Tribol.
,
134
(
3
), p.
031702
.
18.
Ramesh
,
J.
, and
Majumdar
,
B. C.
,
1995
, “
Stability of Rough Journal Bearings Using Nonlinear Transient Method
,”
ASME J. Tribol.
,
117
(
4
), pp.
691
695
.
19.
Turaga
,
R.
,
Sekhar
,
A. S.
, and
Majumdar
,
B. C.
,
2000
, “
Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Hydrodynamic Journal Bearings With Rough Surfaces
,”
Tribol. Trans.
,
43
(
3
), pp.
447
452
.
20.
Lin
,
J.-R.
,
2007
, “
Application of the Hopf Bifurcation Theory to Limit Cycle Prediction of Short Journal Bearings With Isotropic Roughness Effects
,”
Proc. Inst. Mech. Eng., Part J
,
221
(
8
), pp.
869
879
.
21.
Lin
,
J.-R.
,
2012
, “
The Surface Roughness Effects of Transverse Patterns on the Hopf Bifurcation Behaviors of Short Journal Bearings
,”
Ind. Lubr. Tribol.
,
64
(
5
), pp.
265
270
.
22.
Lin
,
J.-R.
,
2014
, “
The Influences of Longitudinal Surface Roughness on Sub-Critical and Super-Critical Limit Cycles of Short Journal Bearings
,”
Appl. Math. Modell.
,
38
(
1
), pp.
392
402
.
23.
Cameron
,
T. M.
, and
Griffin
,
J. H.
,
1989
, “
An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems
,”
ASME J. Appl. Mech.
,
56
(
1
), pp.
149
154
.
24.
Sarrouy
,
E.
, and
Thouverez
,
F.
,
2010
, “
Global Search of Non-Linear Systems Periodic Solutions: A Rotordynamics Application
,”
Mech. Syst. Signal Process.
,
24
(
6
), pp.
1799
1813
.
25.
Nayfeh
,
A. H.
,
1995
,
Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods
(Wiley Series in Nonlinear Science),
Wiley
,
New York
.
26.
Giacopini
,
M.
,
Fowell
,
M. T.
,
Dini
,
D.
, and
Strozzi
,
A.
,
2010
, “
A Mass-Conserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation
,”
ASME J. Tribol.
,
132
(
4
), p.
041702
.
27.
Woloszynski
,
T.
,
Podsiadlo
,
P.
, and
Stachowiak
,
G. W.
,
2015
, “
Efficient Solution to the Cavitation Problem in Hydrodynamic Lubrication
,”
Tribol. Lett.
,
58
(
1
), pp.
1
11
.
28.
Zorzi
,
E. S.
, and
Nelson
,
H. D.
,
1977
, “
Finite Element Simulation of Rotor-Bearing Systems With Internal Damping
,”
ASME J. Eng. Power
,
99
(
1
), pp.
71
76
.
29.
Nacivet
,
S.
,
Pierre
,
C.
,
Thouverez
,
F.
, and
Jezequel
,
L.
,
2003
, “
A Dynamic Lagrangian Frequency–Time Method for the Vibration of Dry-Friction-Damped Systems
,”
J. Sound Vib.
,
265
(
1
), pp.
201
219
.
30.
Peletan
,
L.
,
Baguet
,
S.
,
Torkhani
,
M.
, and
Jacquet-Richardet
,
G.
,
2013
, “
A Comparison of Stability Computational Methods for Periodic Solution of Nonlinear Problems With Application to Rotordynamics
,”
Nonlinear Dyn.
,
72
(
3
), pp.
671
682
.
31.
Xie
,
L.
,
Baguet
,
S.
,
Prabel
,
B.
, and
Dufour
,
R.
,
2016
, “
Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics
,”
ASME J. Vib. Acoust.
,
138
(
2
), p.
021007
.
32.
Zhou
,
B.
,
Thouverez
,
F.
, and
Lenoir
,
D.
,
2014
, “
Essentially Nonlinear Piezoelectric Shunt Circuits Applied to Mistuned Bladed Disks
,”
J. Sound Vib.
,
333
(
9
), pp.
2520
2542
.
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