This paper deals with the validation of the mathematical model for predicting the equivalent stiffness and damping of an active tilting-pad bearing. The active bearing design includes an injection nozzle in the pad and a hydraulic supply system featuring a servovalve, which enables to modify the pressurized oil flow into the bearing clearance. The servovalve is governed by a control signal, obtained in open- or closed-loop configuration. The mathematical model includes the dynamics related to journal, tilting pads, and associated hydraulic system. First, the model results are tested against experimental results from the literature for industrial grade passive tilting pad bearings. This initial validation is followed by a comparison with experimental identification results obtained from a test rig featuring the active bearing design. Good overall agreement is observed in both configurations. The results provide an overview about the feasibility of modifying the bearing impedance by means of the active lubrication system, both in open-loop (fixed control signal), or closed-loop, as a function of the journal position and proportional derivative (PD) controller gains.

References

References
1.
Lund
,
J.
,
1964
, “
Spring and Damping for the Tilting Pad Journal Bearings
,”
ASLE Trans.
,
7
(
4
), pp.
342
352
.10.1080/05698196408972064
2.
Klumpp
,
R.
,
1975
, “
A Contribution to the Theory of Tilting-Pad Bearings
,” Ph.D. thesis,
University of Karlsruhe
,
Karlsruhe, Germany
.
3.
Malcher
,
L.
,
1975
, “
The Stiffness and Damping Qualities of Slider Bearings for Turbomachines—Experimental Tests of MGF and Tilting Pad Bearings
,” Ph.D. thesis,
University of Karlsruhe
,
Karlsruhe, Germany
.
4.
Springer
,
H.
,
1980
, “
Dynamic Characteristics of Silding Bearings With Movable Segments
,”
VDI–Ber.
,
381
, pp.
177
184
.
5.
Santos
,
I. F.
,
1993
, “
Active Tilting Pad Bearings—Theory and Experiment
,”
VDI Fortschritt–Berichte of Reihe 11: Schwinsgungtechnik
,
VDI Verlag
, Dusseldorf.
6.
Dmochowski
,
W.
,
2007
, “
Dynamic Properties of Tilting-Pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects Due to Pivot Flexibility
,”
ASME J. Eng. Gas Turbines Power
,
129
(
3
), pp.
865
869
.10.1115/1.2436574
7.
Wilkes
,
J.
, and
Childs
,
D.
,
2012
, “
Tilting Pad Journal Bearings—A Discussion on Stability Calculation, Frequency Dependence and Pad and Pivot
,”
ASME J. Eng. Gas Turbines Power
,
134
(
12
), p.
122508
.10.1115/1.4007369
8.
San Andres
,
L.
, and
Tao
,
Y.
,
2013
, “
The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings
,”
ASME J. Eng. Gas Turbines Power
,
135
(
11
), p.
112505
.10.1115/1.4025070
9.
Allaire
,
P.
,
Parsell
,
J.
, and
Barrett
,
L.
,
1981
, “
A Pad Perturbation Method for the Dynamic Coefficients of Tilting-Pad Journal Bearings
,”
Wear
,
72
(
1
), pp.
29
44
.10.1016/0043-1648(81)90281-7
10.
Rouvas
,
C.
, and
Childs
,
D.
,
1993
, “
A Parameter Identification Method for the Rotordynamic Coefficients of a High Reynolds Number Hydrostatic Bearing
,”
ASME J. Vib. Acoust.
,
115
(
3
), pp.
264
270
.10.1115/1.2930343
11.
Dimond
,
T.
,
Younan
,
A.
, and
Allaire
,
P.
,
2010
, “
Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficients and Reduced Order Models Using Modal Analysis
,”
ASME J. Vib. Acoust.
,
132
(
5
), pp.
13
43
.10.1115/1.4001507
12.
Dimond
,
T.
,
Younan
,
A.
, and
Allaire
,
P.
,
2012
, “
The Effect of Tilting Pad Journal Bearing Dynamic Models on the Linear Stability Analysis of an 8-Stage Compressor
,”
ASME J. Eng. Gas Turbines Power
,
134
(
5
), p.
052503
.10.1115/1.4005208
13.
Ettles
,
C.
,
1980
, “
The Analysis and Performance of Pivoted Pad Journal Bearings Considering Thermal and Elastic Effects
,”
ASME J. Lubr. Technol.
,
102
(
2
), pp.
182
194
.10.1115/1.3251465
14.
Ettles
,
C.
,
1992
, “
The Analysis of Pivoted Pad Journal Bearing Assemblies Considering Thermoelastic Deformation and Heat Transfer Effects
,”
STLE Tribol. Trans.
,
35
(
1
), pp.
156
162
.10.1080/10402009208982103
15.
Brockwell
,
K.
, and
Dmochowski
,
W.
,
1992
, “
Thermal Effects in the Tilting Pad Journal Bearing
,”
J. Phys. D: Appl. Phys
,
25
, pp.
384
392
.10.1088/0022-3727/25/3/008
16.
Fillon
,
M.
,
Bligoud
,
J. C.
, and
Frêne
,
J.
,
1990
, “
Influence of Bearing Element Displacements on Thermohydrodynamic Characteristics of Tilting-Pad Journal Bearings
,”
Japan International Tribology Conference
,
Nagoya
, pp.
635
640
.
17.
Fillon
,
M.
,
Bligoud
,
J. C.
, and
Frêne
,
J.
,
1992
, “
Experimental Study of Tilting-Pad Journal Bearings—Comparison With Theoretical Thermoelastohydrodynamic Results
,”
ASME J. Tribol.
,
114
, pp.
579
588
.10.1115/1.2920920
18.
Kim
,
J.
,
Palazzolo
,
A.
, and
Gadangi
,
R.
,
1994
, “
TEHD Analysis for Tilting Pad Journal Bearings Using Upwind Finite Element Method
,”
Tribol. Trans.
,
37
(
4
), pp.
771
783
.10.1080/10402009408983359
19.
Kim
,
J.
,
Palazzolo
,
A.
, and
Gadangi
,
R.
,
1995
, “
Dynamics Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility
,”
ASME J. Vib. Acoust.
,
117
(
1
), pp.
123
135
.10.1115/1.2873856
20.
Wygant
,
K. D.
,
Flack
,
R. D.
, and
Barrett
,
L.
,
1999
, “
Influence of Pad Pivot Friction on Tilting-Pad Journal Bearing Measurements—Part I: Steady Operating Position
,”
Tribol. Trans.
,
42
(
1
), pp.
210
215
.10.1080/10402009908982210
21.
Wygant
,
K. D.
,
Flack
,
R. D.
, and
Barrett
,
L.
,
1999
, “
Influence of Pad Pivot Friction on Tilting-Pad Journal Bearing Measurements—Part II: Dynamic Coefficients
,”
Tribol. Trans.
,
42
(
1
), pp.
250
256
.10.1080/10402009908982215
22.
Kim
,
S.
, and
Kim
,
K.
,
2008
, “
Influence of Pad Pivot Friction on Tilting Pad Journal Bearing
,”
Tribol. Int.
,
41
, pp.
694
703
.10.1016/j.triboint.2007.12.003
23.
Dimond
,
T.
,
Sheth
,
P.
,
Allaire
,
P.
, and
He
,
M.
,
2009
, “
Identification Methods and Test Results for Tilting Pad and Fixed Geometry Journal Bearing Dynamic Coefficients—A Review
,”
Shock Vib.
,
16
, pp.
13
43
.10.1155/2009/708363
24.
Tiwari
,
R.
,
Lees
,
W.
, and
Friswell
,
M.
,
2004
, “
Identification of Dynamic Bearing Parameters: A Review
,”
Shock Vib. Dig.
,
36
(
2
), pp.
99
124
.10.1177/0583102404040173
25.
Glienicke
,
J.
,
1966
, “
Experimental Investigation of Stiffness and Damping of Turbine Bearings and Their Application to Instability Predictions
,”
Proc. ImechE
,
181
(
2
), pp.
116
129
.
26.
Brockwell
,
K.
,
Kleinbub
,
D.
, and
Dmochowski
,
W.
,
1989
, “
Measurement and Calculation of the Dynamic Operating Characteristics of the Five Shoe Tilting-Pad Journal Bearing
,”
STLE Tribol. Trans.
,
33
(
4
), pp.
481
492
.10.1080/10402009008981979
27.
Ha
,
H.
, and
Yang
,
S.
,
1999
, “
Excitation Frequency Effects on the Stiffness and Damping Coefficients of a Five Pad Tilting Pad Journal Bearing
,”
ASME J. Tribol.
,
121
(
3
), pp.
517
522
.10.1115/1.2834098
28.
Childs
,
D.
, and
Carter
,
C.
,
2011
, “
Rotordynamics Characteristics of a Five Pad, Rocker-Pivot, Tilting Pad Bearing in a Load-on-Pad Configuration; Comparisons to Predictions and Load-Between-Pad Results
,”
ASME J. Eng. Gas Turbines Power
,
133
(
8
), p.
082503
.10.1115/1.4000893
29.
Kulhanek
,
C.
, and
Childs
,
D.
,
2012
, “
Measured Static and Rotordynamic Coefficients Results for a Rocker-Pivot, Tilting-Pad Bearing With 50% and 60% Offsets
,”
ASME J. Eng. Gas Turbines Power
,
134
(
5
), p.
052505
.10.1115/1.4004723
30.
Santos
,
I. F.
,
1996
, “
Theoretical and Experimental Identification on the Stiffness and Damping Coefficients of Active-Tilting Pad Journal Bearings
,”
Identification in Engineering Systems
,
M.
Friswell
, and
J.
Mottershead
, eds.,
The Cromwell Press Ltd.
,
Swansea, Great Britain
, pp.
325
334
.
31.
Santos
,
I. F.
,
1994
, “
Design and Evaluation of Two Types of Active Tilting Pad Journal Bearings
,”
The Active Control of Vibration
,
C. R.
Burrows
, and
P. S.
Keogh
, eds.,
Mechanical Engineering Publications Limited
,
London
, pp.
79
87
.
32.
Santos
,
I. F.
, and
Scalabrin
,
A.
,
2003
, “
Control System Design for Active Lubrication With Theoretical and Experimental Examples
,”
ASME J. Eng. Gas Turbines Power
,
125
(
1
), pp.
75
80
.10.1115/1.1451757
33.
Nicoletti
,
R.
, and
Santos
,
I.
,
2005
, “
Frequency Response Analysis of an Actively Lubricated Rotor/Tilting-Pad Bearing System
,”
ASME J. Eng. Gas Turbines Power
,
127
(
3
), pp.
638
645
.10.1115/1.1850940
34.
Varela
,
A. C.
, and
Santos
,
I. F.
,
2012
, “
Performance Improvement of Tilting-Pad Journal Bearings by Means of Controllable Lubrication
,”
Mech. Ind.
,
13
(
1
), pp.
17
32
.10.1051/meca/2012004
35.
Varela
,
A. C.
,
Fillon
,
M.
, and
Santos
,
I. F.
,
2012
, “
On the Simplifications for the Thermal Modeling of Tilting-Pad Journal Bearings Under Thermoelastohydrodynamic Regime
,”
ASME
Paper No. GT2012-68329.10.1115/GT2012-68329
36.
Varela
,
A. C.
, and
Santos
,
I. F.
,
2014
, “
Tilting-Pad Journal Bearings With Active Lubrication Applied as Calibrated Shakers: Theory and Experiment
,”
ASME J. Vib. Acoust.
,
136
(
6
), p.
061010
.10.1115/1.4028452
37.
Cerda
,
A.
,
Bjerregaard Nielsen
,
B.
, and
Santos
,
I. F.
,
2013
, “
Steady State Characteristics of a Tilting Pad Journal Bearing With Controllable Lubrication: Comparison Between Theoretical and Experimental Results
,”
Tribol. Int.
,
58
(
1
), pp.
85
97
.10.1016/j.triboint.2012.10.004
38.
Santos
,
I. F.
, and
Russo
,
F.
,
1998
, “
Tilting-Pad Journal Bearings With Electronic Radial Oil Injection
,”
ASME J. Tribol.
,
120
(
3
), pp.
583
594
.10.1115/1.2834591
39.
Haugaard
,
A. M.
, and
Santos
,
I. F.
,
2010
, “
Stability of Multi Orifice Active Tilting-Pad Journal Bearings
,”
Tribol. Int.
,
43
(
9
), pp.
1742
1750
.10.1016/j.triboint.2010.04.013
40.
Carter
,
C.
,
2007
, “
Measured and Predicted Rotordynamic Coefficients and Static Performance of a Rocker-Pivot Tilt Pad Bearing in Load-on-Pad and Load-Between-Pad Configurations
,” Master thesis,
Texas A&M University
,
College Station, TX
.
41.
Kulhanek
,
C.
,
2010
, “
Dynamic and Static Characteristics of a Rocker-Pivot, Tilting-Pad Bearing With 50% and 60% Offset
,” Master thesis,
Texas A&M University
,
College Station, TX
.
42.
Kirk
,
R.
, and
Reedy
,
S.
,
1988
, “
Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs
,”
ASME J. Vib., Acoust., Stress Reliab. Des.
,
110
(
2
), pp.
165
171
.10.1115/1.3269494
43.
Haugaard
,
A. M.
,
2010
, “
On Controllable Elastohydrodynamic Fluid Film Bearings
,” Ph.D. thesis,
Technical University of Denmark
,
Lyngby, Denmark
.
44.
Cerda
,
A.
,
2013
, “
Mechatronics Applied to Fluid Film Bearings: Towards More Efficient Machinery
,” Ph.D. thesis,
Technical University of Denmark
,
Lyngby, Denmark
.
45.
Cerda
,
A.
, and
Santos
,
I. F.
,
2012
, “
Stability Analysis of an Industrial Gas Compressor Supported by Tilting-Pad Journal Bearings Under Different Lubrication Regimes
,”
ASME J. Eng. Gas Turbines Power
,
134
(
2
), p.
022504
.10.1115/1.4004214
You do not currently have access to this content.