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1
EXPERIMENTAL ANALYSIS OF THE DYNAMIC CHARACTERISTICS OF A FOIL
THRUST BEARING
Franck BALDUCCHIHutchinson, UK
Mihai ARGHIRInstitut PPRIME, CNRS UPR3346, Université de Poitiers, France
Romain GAUTHIERSNECMA, Space Propulsion Division, France
2
Content
I. The aerodynamic Foil Thrust Bearing - Literature
II. The test rig1. Layout and explanations
2. Dynamic analysis of the test rig
III. Dynamic analysis of the foil thrust bearing1. Foil structure only
2. Validation
3. Foil structure and air film
IV. Summary and conclusion
3
.
[1] Dykas, B., Bruckner, R., DellaCorte, C. , Emonds, B., Prahl, J., 2009 "Design, Fabrication, and Performance of Foil Gas Thrust Bearings for Microturbomachinery Applications," Journal of Engineering for Gas Turbines and Power, vol. 131, no. 1
Experimental analysis of start-up characteristics[2] Balducchi, F. Arghir, M., Gauthier, R., Renard, E., 2013, "Experimental Analysis of the Start-up Torque of a Mildly Loaded Foil Thrust Bearing," Journal of Tribology, vol. 135, 031703, doi: 10.1115/1.4024211.
Experimental analysis of dynamic characteristics[3] Ku, C. P. R., Heshmat, H., 1992 "Compliant Foil Bearing Structural Stiffness Analysis-Part 1: Theoretical Model Including Strip and Variable Bump Foil Geometry," ASME Journal of Tribology, no. 114, pp. 394-400. [4] Ku, C. P. R., Heshmat, H., 1994 "Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Theoretical Considerations," STLE Tribology Transactions, vol. 3, no. 37, pp. 525-533. [5] Ku, C. P. R., Heshmat, H., 1994 "Structural Stiffness and Coulomb Damping in Compliant Foil Journal Bearings: Parametric Studies," STLE Tribology Transactions, vol. 3, no. 37, pp. 455-462.[6] Ku, C. P. R., 1994 "Dynamic Structural Properties of Compliant Foil Thrust Bearings- Comparison Between Experimental and Theoretical Results," ASME Journal of Tribology, no. 116, pp. 70-75. [7] Ku, C. P. R. , Heshmat, H., 1993 "Compliant Foil Bearing Structural Stiffness Analysis-Part 2: Experimental Investigation," ASME Journal of Tribology, no. 115, pp. 364-369. [8] Kim, K.-S. 2007 "An Experimental Study on the Performance of Air Foil Thrust Bearing for Application to Turbomachinery," Doctoral Thesis, Korea Advanced Institute of Science and Technology. [9] Lee, Y. -B., Kim, T. Y., Kim, C. H., Kim, T. H., 2011 "Thrust Bump Air Foil Bearings with Variable Axial Load: Theoretical Predictions and Experiments," Tribology Transactions, no. 54, pp. 902-910.
The aerodynamic Foil Thrust Bearing
The Foil Thrust Bearing used in the analysis [1]
3
4
Test rig layout
Shaker
Piezo. force sensor
Ball bearings
Foil thrustbearing
Shaft
Load cell
Runner
Springs
Aerodynamic bearing
The test rig
5
Aerostatic bearing
Bearings
Static loading spring
Runner
Load cell
Runner (rotating)
Shaft (non rotating)
Weight relief spring
Upper shaft
Lower shaft
Thrust bearingholding bell
Test rig schematic and explanations
The test rig schematic
6
The 2 DOF dynamic model of the upper shaft
Identified stiffness of the static force transducer
Dynamic analysis of the test rig
1 1 + 1 + 1 − 2 = 2 2 + 2 − 1 = 0 11 + 1 + 1 − 2 = 22 + 2 − 1 = 0
= 2222 − 1
= − 112 + 12 − 1
(1)
(2)
7
Dynamic model of the test rig
m1
m2
kr
kc
x1
x2
F
m3x3
kb
krl
cb
m1
m2
kr
kc
x1
x2
F
kb cb
A1
A2
A1
A2
Accelerometres
The test configuration for the foil structure only (Spinner replaced by a bolted plate)
The test configuration for the foil structure and the air film
m1
m2
kr
kc
x1
x2
F
kb cb
A1
A2
Accelerometres
8
The e.o.m. of the 2d.o.f. model
11 + + 1 − 2 = 22 + 2 − 1 + 2 + 2 = 0 11 + + 1 − 2 = 22 + 2 − 1 + 2 = 0 −121 + + 1 − 2 = −122 + 2 + 1 + 2 = 0
= 22 − 2 − 122
The impedance of the foil structure
The test configuration for the foil structure only (Spinner replaced by a bolted plate)
9
Charge statique
Dyn
amic
stif
fnes
s (N
/m)
Dyn
amic
stif
fnes
s (N
/m)
Dyn
amic
stif
fnes
s (N
/m)
Dyn
amic
stif
fnes
s (N
/m)
Dyn
amic
stif
fnes
s (N
/m)
Dyn
amic
stif
fnes
s (N
/m)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
2nd order inter. poly.30 N static load
Standard deviation
2nd order inter. poly.60 N static load
Standard deviation
2nd order inter. poly.90 N static load
Standard deviation
2nd order inter. poly.120 N static load
Standard deviation
2nd order inter. poly.150 N static load
Standard deviation Static load
Dyn
amic
stiff
ness
of th
e fo
il st
ruct
ure
10
Static load
Dam
ping
(N
s/m
)D
ampi
ng (
Ns/
m)
Dam
ping
(N
s/m
)
Dam
ping
(N
s/m
)D
ampi
ng (
Ns/
m)
Dam
ping
(N
s/m
)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
Excitation frequency (Hz)
30 N static loadStandard deviation
60 N static loadStandard deviation
90 N static loadStandard deviation
120 N static loadStandard deviation
150 N static loadStandard deviation
Equ
ival
ent v
isco
usda
mpi
ngof
the
foil
stru
ctur
e
11
From both e.o.m. of the 2d.o.f. model:
Remark: only the 2nd e.o.m. was used inZb identification
Validation of the impedance of the foil structure
−121 + + 1 − 2 = −122 + 2 + 1 + 2 = 0
1 = 22 2 − − δ
2 = −2δ
δ = −12 + + −22 + + − 2
Mode Exp (Hz) Th(Hz) Rel. error (%)
ω1, anti-resonance m1 480 520 7.70
ω1, anti-resonance m1 710 685 -3.65
12
Similar experimental values reported in the foil journal bearing literature:
[10] San Andrès, L., Camero, J., Muller, S., Chirathadam, T., Ryu, K., 2010 "Measurements of Drag Torque, Lift-Off Speed and Structural Parameters in 1st Generation Floating Gas Foil Bearings," in Proc. 8th IFToMM Int. Conf. On Rotordynamics, Seoul, Korea, Sept 12-15.
The loss factor η=cω⁄k of the foil structure
Loss
fact
or
Excitation frequency (Hz)
The e.o.m. of the 3d.o.f. model:
13
The impedance of the foil thrust bearing with air film
m1
m2
kr
kc
x1
x2
F
m3x3
kb
krl
cb
A1
A2 1 1 + 1 + 1 − 2 = 2 2 + 2 − 1 + 2 − 3 + 2 − 3 = 03 3 + 3 − 2 + 3 − 2 + " 3 = 0
= − 2223 + 2 − 1223
The test configuration for the foil structure and the air film
14
Operating conditions: Static load: 30N, 60N and 90N Rotation speed: 0 and 35 krpm
Evolution of stiffness and equivalent viscous damping with the
rotation speedD
ynam
ic s
tiffn
ess
(N/m
)
Excitation frequency (Hz)
Dyn
amic
stif
fnes
s (N
/m)
Excitation frequency (Hz)
Dyn
amic
stif
fnes
s (N
/m)
Excitation frequency (Hz)
Equ
ival
ent v
isco
us d
ampi
ng (
Ns/
m)
Excitation frequency (Hz)
Equ
ival
ent v
isco
us d
ampi
ng (
Ns/
m)
Excitation frequency (Hz)
Equ
ival
ent v
isco
us d
ampi
ng (
Ns/
m)
Excitation frequency (Hz)
Standard deviationStandard deviation Standard deviation
Standard deviation
Standard deviation
Standard deviation
Equ
ival
ent v
isco
us d
ampi
ng (
Ns/
m)
Excitation frequency (Hz)
Polynomial approximation of the equivalent viscous damping
15
- Structure only (without air film) : Equivalent viscous damping increases with the static load
- Conclusion on the impact of the different parameters cannot be drawn, due to the high standard
deviations observed in the last slide
16
- The characteristics of the bump foil structure (Ω=0) were measured for W=30 N and 150 N while the FTB with air film was tested at Ω=35 krpm for W=30 N, 60 N and 90 N.
The measured dynamic stiffness showed low standard deviations.
The equivalent damping was measured with larger standard deviations especially for tests with rotation speed i.e. when the air film was present.
The stiffness of the bump foil structure and of the FTB (i.e. with air film) increases with the excitation frequency and with the static load.
The equivalent viscous damping decreases with the excitation frequency and increases with the static load.
The loss factor of the bump foil structure shows almost constant values for excitation frequencies larger than 300 Hz; the measured values are close to the ones given in the foil journal bearings literature.
For 35 krpm rotation speed, the stiffness and the equivalent viscous damping of the FTB are lower than for the bump foil structure alone thus showing the influence of the air film; this tendency increases with increasing load.
Summary and conclusions
Thanks for your attention