High-performance turbomachinery demands high shaft speeds, increased rotor flexibility, tighter clearances in the flow passages, advanced materials, and increased tolerance to imbalances. Operation at high speeds induces severe dynamic loading with large amplitude shaft motions at the bearing supports. Typical rotordynamic models rely on linearized force coefficients (stiffness K, damping C, and inertia M) to model the reaction forces from fluid film bearings and seal elements. These true linear force coefficients are derived from infinitesimally small amplitude motions about an equilibrium position. Often, however, a rotor–bearing system does not reach an equilibrium position and displaces with motions amounting to a sizable portion of the film clearance; the most notable example being a squeeze film damper (SFD). Clearly, linearized force coefficients cannot be used in situations exceeding its basic formulation. Conversely, the current speed of computing permits to evaluate fluid film element reaction forces in real time for ready numerical integration of the transient response of complex rotor–bearing systems. This approach albeit fast does not help to gauge the importance of individual effects on system response. Presently, an orbit analysis method estimates force coefficients from numerical simulations of specified journal motions and predicted fluid film reaction forces. For identical operating conditions in static eccentricity and whirl amplitude and frequency as those in measurements, the computational physics model calculates instantaneous damper reaction forces during one full period of motion and performs a Fourier analysis to characterize the fundamental components of the dynamic forces. The procedure is repeated over a range of frequencies to accumulate sets of forces and displacements building mechanical transfer functions from which force coefficients are identified. These coefficients thus represent best fits to the motion over a frequency range and dissipate the same mechanical energy as the nonlinear mechanical element. More accurate than the true linearized coefficients, force coefficients from the orbit analysis correlate best with SFD test data, in particular for large amplitude motions, statically off-centered. The comparisons also reveal the fallacy in representing nonlinear systems as simple K–C–M models impervious to the kinematics of motion.

References

References
1.
Zeidan
,
F.
,
San Andrés
,
L.
, and
Vance
,
J.
,
1996
, “
Design and Application of Squeeze Film Dampers in Rotating Machinery
,”
25th Turbomachinery Symposium
,
Texas A&M University
,
Houston, TX
, Sept. 16–19, pp.
169
188
.
2.
Vance
,
J.
,
1988
,
Rotordynamics of Turbomachinery
,
Wiley
,
New York
, pp.
234
246
.
3.
Tiwari
,
R.
,
Lees
,
A. W.
, and
Friswell
,
M. I.
,
2004
, “
Identification of Dynamic Bearing Parameters: A Review
,”
Shock Vib. Dig.
,
36
(
2
), pp.
99
124
.
4.
Choy
,
F. K.
,
Braun
,
M. J.
, and
Hu
,
Y.
,
1991
, “
Nonlinear Effects in a Plain Journal Bearing: Part 1—Analytical Study
,”
ASME J. Tribol.
,
113
(
3
), pp.
555
561
.
5.
El-Shafei
,
A.
, and
Eranki
,
R.
,
1994
, “
Dynamic Analysis of Squeeze Film Damper Supported Rotors Using Equivalent Linearization
,”
ASME J. Eng. Gas Turbines Power
,
116
(
3
), pp.
682
691
.
6.
Müller-Karger
,
C.
, and
Granados
,
A.
,
1997
, “
Derivation of Hydrodynamic Bearing Coefficients Using the Minimum Square Method
,”
ASME J. Tribol.
,
119
(
4
), pp.
802
807
.
7.
Czolczynski
,
K.
,
1999
,
Rotordynamics of Gas-Lubricated Journal Bearing Systems
,
Springer-Verlag
,
New York
, Chap. 2.4.
8.
Sawicki
,
J.
, and
Rao
,
T.
,
2001
, “
Nonlinear Prediction of Rotordynamic Coefficients for a Hydrodynamic Journal Bearing
,”
Tribol. Trans.
,
44
(
3
), pp.
367
374
.
9.
Sawicki
,
J.
, and
Rao
,
T.
,
2004
, “
Nonlinear Prediction of Rotordynamic Coefficients for a Hydrodynamic Journal Bearing
,”
Int. J. Rotating Mach.
,
10
(
6
), pp.
507
513
.
10.
Diaz
,
S.
, and
San Andrés
,
L.
,
2000
, “
Orbit-Based Identification of Damping Coefficients for a Rotor Mounted on Off-Centered Squeeze Film Dampers and Including Support Flexibility
,”
ASME
Paper No. 2000-GT-0394.
11.
San Andrés
,
L.
, and
De Santiago
,
O.
,
2004
, “
Forced Response of a Squeeze Film Damper and Identification of Force Coefficients From Large Orbital Motions
,”
ASME J. Tribol.
,
126
(
2
), pp.
292
300
.
12.
San Andrés
,
L.
,
2012
, “
Experimental Identification of Bearing Force Coefficients
,”
Modern Lubrication Theory
, Notes 14,
Texas A&M University Digital Libraries
, College Station, TX.
13.
San Andrés
,
L.
, and
Jeung
,
S.-H.
,
2015
, “
Experimental Performance of an Open Ends, Centrally Grooved, Squeeze Film Damper Operating With Large Amplitude Orbital Motions
,”
ASME J. Eng. Gas Turbines Power
,
137
(
3
), p.
032508
.
14.
Bradley
,
G.
,
2013
, “
Performance of a Short Open-End Squeeze Film Damper With Feed Holes: Experimental Analysis of Dynamic Force Coefficients
,” M.S. thesis, Texas A&M University, College Station, TX.
15.
San Andrés
,
L.
,
2012
, “
Extended Finite Element Analysis of Journal Bearing Dynamic Forced Performance to Include Fluid Inertia Force Coefficients
,”
ASME
Paper No. IMECE2012-87713.
16.
San Andrés
,
L.
, and
Delgado
,
A.
,
2012
, “
A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically
,”
ASME J. Eng. Gas Turbines Power
,
134
(
5
), p.
052509
.
17.
San Andrés
,
L.
,
2012
, “
Damping and Inertia Coefficients for Two Open Ends Squeeze Film Dampers With a Central Groove: Measurements and Predictions
,”
ASME J. Eng. Gas Turbines Power
,
134
(
10
), p.
102506
.
18.
San Andrés
,
L.
, and
Seshagiri
,
S.
,
2013
, “
Damping and Inertia Coefficients for Two End Sealed Squeeze Film Dampers With a Central Groove: Measurements and Predictions
,”
ASME J. Eng. Gas Turbines Power
,
135
(
12
), p.
112503
.
19.
San Andrés
,
L.
,
2014
, “
Force Coefficients for a Large Clearance Open Ends Squeeze Film Damper With a Central Groove: Experiments and Predictions
,”
Tribol. Int.
,
71
, pp.
17
25
.
20.
San Andrés
,
L.
,
Jeung
,
S.-H.
, and
Bradley
,
G.
,
2014
, “
Dynamic Forced Performance of Short Length Open-Ends Squeeze Film Damper With End Grooves
,”
IFToMM International Conference on Rotordynamics
, Sept. 22–25,
Milan, Italy
, pp.
855
866
.
21.
Jeung
,
S.-H.
,
2013
, “
Performance of an Open Ends Squeeze Film Damper Operating With Large Amplitude Orbital Motions: Experimental Analysis and Assessment of the Accuracy of the Linearized Force Coefficients Model
,” M.S. thesis, Texas A&M University, College Station, TX.
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