The traditional eight-coefficient bearing model only considers the translational motion of the bearings and neglects the tilting motion and coupling effects between them. In this paper, the dynamic characteristics of the spiral-grooved opposed-hemisphere gas bearing considering five degrees-of-freedom are studied, and 50 dynamic coefficients including the translational, tilting, and coupling components are completely calculated. The Reynolds equations and their perturbed equations are solved by the finite element method to obtain the dynamic stiffness and damping coefficients. The effects of the tilting motion on the dynamic coefficients and response are analyzed, respectively. The results show that the coupling coefficients between the translational and tilting motions, which have been neglected in most previous studies, are significant at large eccentricity ratio. But these coupling coefficients have little effect on the dynamic response. On the other hand, the influences of the tilting motion on the synchronous response and natural frequency are remarkable and will decrease the stability of the rotor bearing system.

Issue Section:
Hydrodynamic Lubrication
Keywords:
Fluid film lubrication, Gas (air) bearings, Hydrodynamic lubrication
Topics:
Bearings, Damping, Gas bearings, Rotors, Stiffness, Degrees of freedom, Stability, Pressure

References

1.
Keating
,
W.
, and
Pan
,
C. H.
,
1968
, “
Design Studies of an Opposed-Hemisphere Gyro Spin-Axis Gas Bearing
,”
ASME J. Lubr. Technol.
,
90
(
4
), pp.
753
–
760
.
Google Scholar
Crossref
Search ADS
 
2.
Pan
,
C. H.
,
1998
, “
Compressible Narrow Groove Analysis—Part 2: Computation of Pressure Field in a Spherical Device Rotating in Either Direction
,”
ASME J. Tribol.
,
120
(
4
), pp.
765
–
771
.
Google Scholar
Crossref
Search ADS
 
3.
Lund
,
J.
,
1964
, “
Spring and Damping Coefficients for the Tilting-Pad Journal Bearing
,”
ASLE Trans.
,
7
(
4
), pp.
342
–
352
.
Google Scholar
Crossref
Search ADS
 
4.
Lund
,
J. W.
,
1968
, “
Calculation of Stiffness and Damping Properties of Gas Bearings
,”
ASME J. Tribol.
,
90
(
4
), pp.
793
–
803
.
5.
Lund
,
J.
,
1967
, “
A Theoretical Analysis of Whirl Instability and Pneumatic Hammer for a Rigid Rotor in Pressurized Gas Journal Bearings
,”
ASME J. Tribol.
,
89
(
2
), pp.
154
–
165
.
6.
Malik
,
M.
, and
Rodkiewicz
,
C. M.
,
1984
, “
The Dynamical Behaviour of Externally Pressurized Gas-Lubricated Unloaded Porous Journal Bearings
,”
Proc. Inst. Mech. Eng. Part C
,
198
(
1
), pp.
33
–
41
.
Google Scholar
Crossref
Search ADS
 
7.
Lund
,
J. W.
, and
Orcutt
,
F.
,
1967
, “
Calculations and Experiments on the Unbalance Response of a Flexible Rotor
,”
ASME J. Manuf. Sci. Eng.
,
89
(
4
), pp.
785
–
796
.
8.
Bonneau
,
D.
, and
Absi
,
J.
,
1994
, “
Analysis of Aerodynamic Journal Bearings With Small Number of Herringbone Grooves by Finite Element Method
,”
ASME J. Tribol.
,
116
(
4
), pp.
698
–
704
.
Google Scholar
Crossref
Search ADS
 
9.
Zirkelback
,
N.
, and
San Andres
,
L.
,
1998
, “
Finite Element Analysis of Herringbone Groove Journal Bearings: A Parametric Study
,”
ASME J. Tribol.
,
120
(
2
), pp.
234
–
240
.
Google Scholar
Crossref
Search ADS
 
10.
Chen
,
C. H.
,
Kang
,
Y.
,
Chang
,
Y. P.
,
Wang
,
Y. P.
, and
Lee
,
H. H.
,
2006
, “
Influence of Restrictor on Stability of the Rigid Rotor–Hybrid Bearing System
,”
J. Sound Vib.
,
297
(
3
), pp.
635
–
648
.
Google Scholar
Crossref
Search ADS
 
11.
Chen
,
S. K.
,
Chou
,
H. C.
, and
Kang
,
Y.
,
2012
, “
Stability Analysis of Hydrodynamic Bearing With Herringbone Grooved Sleeve
,”
Tribol. Int.
,
55
, pp.
15
–
28
.
Google Scholar
Crossref
Search ADS
 
12.
Nishio
,
U.
,
Somaya
,
K.
, and
Yoshimoto
,
S.
,
2011
, “
Numerical Calculation and Experimental Verification of Static and Dynamic Characteristics of Aerostatic Thrust Bearings With Small Feedholes
,”
Tribol. Int.
,
44
(
12
), pp.
1790
–
1795
.
Google Scholar
Crossref
Search ADS
 
13.
Zhang
,
X.-Q.
,
Wang
,
X.-L.
,
Liu
,
R.
, and
Zhang
,
Y.-Y.
,
2013
, “
Modeling and Analysis of Micro Hybrid Gas Spiral-Grooved Thrust Bearing for Microengine
,”
ASME J. Eng. Gas Turbines Power
,
135
(
12
), p.
122508
.
Google Scholar
Crossref
Search ADS
 
14.
Das
,
S.
,
Guha
,
S.
, and
Chattopadhyay
,
A.
,
2001
, “
On the Conical Whirl Instability of Hydrodynamic Journal Bearings Lubricated With Micropolar Fluids
,”
Proc. Inst. Mech. Eng. Part J
,
215
(
5
), pp.
431
–
439
.
Google Scholar
Crossref
Search ADS
 
15.
Zachariadis
,
D. C.
,
2006
, “
Unbalance Response of Rotors Supported on Hydrodynamic Bearings Placed Close to Nodal Points of Excited Vibration Modes
,”
ASME J. Eng. Gas Turbines Power
,
128
(
3
), pp.
661
–
669
.
Google Scholar
Crossref
Search ADS
 
16.
Jang
,
G. H.
, and
Kim
,
Y. J.
,
1999
, “
Calculation of Dynamic Coefficients in a Hydrodynamic Bearing Considering Five Degrees of Freedom for a General Rotor-Bearing System
,”
ASME J. Tribol.
,
121
(
3
), pp.
499
–
505
.
Google Scholar
Crossref
Search ADS
 
17.
Kim
,
M.
,
Jang
,
G.
, and
Kim
,
H.
,
2010
, “
Stability Analysis of a Disk-Spindle System Supported by Coupled Journal and Thrust Bearings Considering Five Degrees of Freedom
,”
Tribol. Int.
,
43
(
8
), pp.
1479
–
1490
.
Google Scholar
Crossref
Search ADS
 
18.
Murata
,
S.
,
Miyake
,
Y.
, and
Kawabata
,
N.
,
1980
, “
Exact Two-Dimensional Theory of Spherical Spiral Groove Bearings
,”
ASME J. Tribol.
,
102
(
4
), pp.
430
–
438
.
19.
Choi
,
W. C.
,
Shin
,
Y. H.
, and
Choi
,
J. H.
,
2001
, “
Numerical Analysis of Stiffness of Self-Acting Air Bearings of Various Curvatures
,”
JSME Int. J. Ser. C Mech. Syst. Mach. Elem. Manuf.
,
44
(
2
), pp.
470
–
475
.
Google Scholar
Crossref
Search ADS
 
20.
Choi
,
W. C.
,
Shin
,
Y. H.
, and
Choi
,
C. W.
,
2001
, “
Effect of an Out-of-Sphericity Error on the Radial Stiffness of an Air Dynamic Bearing
,”
JSME Int. J. Series C Mech. Syst. Mach. Elem. Manuf.
,
44
(
2
), pp.
421
–
426
.
Google Scholar
Crossref
Search ADS
 
21.
Adiletta
,
G.
,
Guido
,
A. R.
, and
Rossi
,
C.
,
1997
, “
Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings—Part I: Theoretical Analysis
,”
Nonlinear Dyn.
,
14
(
1
), pp.
57
–
87
.
Google Scholar
Crossref
Search ADS
 
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