experimental analysis of the dynamic characteristics … · 1 experimental analysis of the dynamic...

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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

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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

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.

[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]

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4

Test rig layout

Shaker

Piezo. force sensor

Ball bearings

Foil thrustbearing

Shaft

Load cell

Runner

Springs

Aerodynamic bearing

The test rig

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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

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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)

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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

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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)

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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)






2nd order inter. poly.30 N static load

Standard deviation


Standard deviation


Standard deviation


Standard deviation


Standard deviation Static load

Dyn

amic

stiff

ness

of th

e fo

il st

ruct

ure

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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

)







30 N static loadStandard deviation





Equ

ival

ent v

isco

usda

mpi

ngof

the

foil

stru

ctur

e

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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

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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


The e.o.m. of the 3d.o.f. model:

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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

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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

)


Dyn

amic

stif

fnes

s (N

/m)


Dyn

amic

stif

fnes

s (N

/m)


Equ

ival

ent v

isco

us d

ampi

ng (

Ns/

m)


Equ

ival

ent v

isco

us d

ampi

ng (

Ns/

m)


Equ

ival

ent v

isco

us d

ampi

ng (

Ns/

m)


Standard deviationStandard deviation Standard deviation

Standard deviation

Standard deviation

Standard deviation

Equ

ival

ent v

isco

us d

ampi

ng (

Ns/

m)


Polynomial approximation of the equivalent viscous damping

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- 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

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- 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

experimental analysis of the dynamic characteristics … · 1 experimental analysis of the dynamic...

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