Results and Model Predictions - TRIBGROUP TAMUrotorlab.tamu.edu/tribgroup/14_TRC_slideshow/TE14 conference/GT201… · the HOT Gap between Experimental Results and Model Predictions

Tilting Pad Journal Bearings: On Bridgingthe HOT Gap between Experimental Results and Model Predictions

1

Luis San AndrésMast-Childs Professor, Fellow ASMETexas A&M University

Yujiao TaoRotordynamics EngineerSamsung Techwin

Yingkun LiGraduate Research Assistant Texas A&M University

Supported by the Turbomachinery Research Consortium

Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, June 16-20, 2014, Düsseldorf, Germany

Paper GT2014-25566

HOT Gap Bridging

between Experimental

Literature review – recent• Influence of pivot flexibility on

TPJBs force coefficients.

• Controversy on the frequency dependency of force coefficients K&C.

• Temporal fluid inertia effects neglected in conventional models.

• Knowledge of empirical parameters (hot bearing clearances, pivot stiffness, pad temperatures etc.)

• Accuracy of [K-C-M] curve-fitting procedure at frequency range with pivot flexibility

2

Experimental Work at TAMU

2009 Carter and Childs,ASME J. Eng. Gas Turbines Power

2009 Childs and Harris,ASME J. Eng. Gas Turbines Power

2010 Childs,IFToMM Korea

2011 Delgado et. al,ASME J. Eng. Gas Turbines Power

2012 Kulhanek and Childs, ASME J. Eng. Gas Turbines Power

TPJB recent model validations

2007 Dmochowski, ASME J. Eng. Gas Turbines Power

2012 Wilkes and Childs, Part I-III, ASME J. Eng. Gas Turbines Power

2013 San Andres and Tao, ASME J. Eng. Gas Turbines Power

A justification• Influence of pivot flexibility on

TPJBs force coefficients.

• Controversy on the frequency dependency of force coefficients K&C.

• Temporal fluid inertia effects neglected in conventional models.

• Knowledge of empirical parameters (hot bearing clearances, pivot stiffness, pad temperatures etc.)

• Accuracy of [K-C-M] curve-fitting procedure at frequency range with pivot flexibility

3

Experimental Work at TAMU

2009 Carter and Childs,ASME J. Eng. Gas Turbines Power

2009 Childs and Harris,ASME J. Eng. Gas Turbines Power

2010 Childs,IFToMM Korea

2011 Delgado et. al,ASME J. Eng. Gas Turbines Power

2012 Kulhanek and Childs, ASME J. Eng. Gas Turbines Power

TPJB recent model validations

2007 Dmochowski, ASME J. Eng. Gas Turbines Power

2012 Wilkes and Childs, Part I-III, ASME J. Eng. Gas Turbines Power

2013 San Andres and Tao, ASME J. Eng. Gas Turbines Power

NeedsEffects to consider for accurate prediction of tilting pad journal bearing performance

4

W, static load

Y

X

Housing

Pad

Pivot

Fluid film

Journal

, Journal speed

, Pad tilt angle

Pivot flexibility Hot bearing clearance Pad flexibility Flow turbulence Fluid inertia Feeding type (direct, LEG) Flooded vs. evacuated

Pivot flexibility reduces the force coefficients in heavily loaded TPJBs.

For LOP/LBP, preload (0~0.5)

5

cos sin

cos sinp X Y

piv p p piv d p p

h C e e

r R

Film thickness in a padCp : Pad radial clearance

CB = Cp-rp Bearing assembled clearance

Rd= Rp+t : Pad radius and thicknessrp : Pad dimensional preload

p : Pad tilt anglepivpiv Pivot radial and transverse

deflections

Unloaded Pad

Journal

P

X

Y

p

p

h

eRJ

WX

RB

piv

OB

RP

WY

OP

piv

P’

p

t

L

Bearing CenterPad CenterFluid film

Loaded Pad Film thickness:

• Laminar flow• Includes temporal fluid inertia

effects• Average viscosity across film

6

3 3 2 2

2 2

112 12 2 12J

h P h P h h h hR z z t t

On kth pad

h : fluid film thickness P : hydrodynamic pressure

μ : lubricant viscosity : journal speed

RJ : journal radius

Reynolds equation for thin film bearingY

X

Housing

Pad

Pivot

Fluid film

Journal

, Journal speed

W, static load

7

Thermal energy transport in thin filmT: film temperature

h : film thickness

U,W: circ. & axial flow velocities

Cv : viscosity & density, specific heat

hB, hJ : heat convection coefficients

TB, TJ : bearing and journal temperatures

: journal speed

Neglects temperature

variations across-film. Use bulk-flow

velocities and temperature

22 2212

12 2

v B B J JC U h T W h T h T T h T TR z

R RW Uh

CONVECTION + DIFFUSION= DISSIPATION(Energy Disposed) = (Energy Generated)

8

Journal & pads kinetics

0 0 0

0 0 01

padX

Y

kNX X

kkY Y

FW F

W F F

p piv

pad piv piv

piv piv

M MF FF F

M

Pad equations of motion about pivot P

sin cosd X p Y p dM R F F R F

Fluid film moment on pad

0

0

2

0

2

cos

sin

kt

kl

L kkpX k

Jk kLY p

FP R d dz

F

k=1,…Npad

Inertia matrix

Journal

X

Y

kth unloaded pad

WY

WX

X

Y

P’

kth loaded pad

PkF

piv

kFP

kpiv

piv

kF

kF

ee

kp

kXF

kYF

kpiv

kM

P

00

p

pad

I m l m lm l mm l m

M

Forces on journal and forces on a pad:

l,l , radial and transverse distances from pad mass center to pivot point

Nonlinear pivot deflection & stiffnessPivot deformation is typically nonlinear depending on the load (Fpiv), area of contact, hardness of the materials, surface conditions.

• Sphere on a sphere

Pivot and housing:Ep , Eh Elastic modulus p ,h Poisson’s ratiosDp , Dh Diameter of the curvature L Contact length

2 3 4

0 1 2 3 4piv piv piv piv pivF a a a a a piv

pivpiv

FK

• Sphere on a cylinder

•Cylinder on a cylinder

• Load-deflection function(empirical)

*Kirk, R.G., and Reedy, S.W., 1988, J. Vib. Acoust. Stress. Reliab. Des., 110(2), pp. 165-171.

• Ball in socket

• Rocker back

9

• Rocker back

10

Test rig

Test TPJB102mm (4 in.)

11

Parameter identificationFor small amplitude motions about the equilibrium position, bearing dynamic forces are modeled in linear form as

F = -Kz -Cz -Mz

F=Fx, FyT:lateral reaction forcez=x(t),y(t)T:journal center displacementK: bearing stiffness matrixC: bearing damping matrixM: bearing mass matrixZ: impedance

K, C, M coefficients extracted from dynamic load tests as curve fits to measured impedances Z

2Re( ) ( ), Im( )Z K M Z C

Carter, C. and Childs, D.W., 2009, ASME J. Eng. Gas Turbines Power Reliab. 131, pp. 012507.

Predictions for a five-pad TPJB

12

(Kulhanek and Childs*) Five pad, tilting pad bearing (LBP)

2012, ASME, J. Eng. Gas Turbines Power, 134, 052505

Number of pads, Npad 5Configuration LBPRotor diameter, D 101.6 mm (4 inch)Pad axial length, L 60.3 mm (2.3 inch)Pad arc angle, P 58o

Pivot offset 50%Pad preload, 0.27Nominal bearing clearance, CB 81 m (3.18 mil)Nominal pad clearance, CP 112 m (4.41 mil)Pad inertia, IP 2.49 kg.cm2 (0.85 lb.in2)Oil inlet temperature ~44 oC (111 oF)Lubricant type ISO VG32, DTE 797Oil supply viscosity, 0 0.0228 Pa.s

Pr

Specific load, W/LD 345 ~3,101 kPa (50 ~ 450 psi) Journal speed, 7 krpm-16 krpm

Cold conditions

13

Unknown pivot stiffness and hot clearance

* Tao, Y., 2012, Master Thesis, Texas A&M University, College Station, TX.

Estimated pivot stiffness: 641 MN/m

1 1 1

piv m fK K K

Kpiv, pivot stiffness Km, experimental static stiffness Kf, predicted film stiffness (rigid pivot)

Leading edge groove (LEG)Pivot type: Rocker-back

Estimated hot bearing clearance= bB c avgC T

CB, cold bearing clearanceαcb, thermal expansion coefficient ∆Tavg, average temperature change

Bearing hot clearance reduces by up to 21%

to 64 m. Preload increases to 0.32

Murphy (2014) reports:~700 MN/m Bearing hot clearance change may vary 10% ~ 30%.

Journal eccentricity vs. static load

14

Rotor speed =7 krpm

Predictions and test data agree at low loads.At high loads, pivot stiffness is too low.

Max. 450 psi

-eY

eX

*Kulhanek, C.D., and Childs, D.W., 2012, ASME, J. Eng. Gas Turbines Power, 134, 052505

Symbols: test dataLines: prediction

CB=64 m

CB=81 m

Temperature vs. static load

15

Rotor speed =7 krpm, 16 krpmUnit load W/LD = 3,101 kPa (450 psi)

Predicted film temperatures show reasonable agreement with recorded pad temperatures.*Kulhanek, C.D., and Childs, D.W., 2012, ASME, J. Eng. Gas Turbines Power, 134, 052505

16 krpm

7 krpm

Prediction: film averageTest data: pad sub-surface

Pad 1 Pad 2Pad 3 Pad 4 Pad 5


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Real part

Predictions for Re(Z) correlate well with test data, in particular at low frequencies (ω < Ω=1X).

Re(ZXX)

Re(ZYY)

Re(Z)K-M2

Impedances Specific load = 1,723 kPa (250 psi)

Rotor speed =7 krpm

1X


Rotor speed =16 krpm

1XRe(ZYY)

Re(ZXX)


17

At 7 krpm, predicted Im(ZYY) agrees with test data & Im(ZXX) is over predicted. At 16 krpm, correlation is best.

Im(ZXX)

Im(ZYY)


Rotor speed =7 krpm

1X


1X

Im(ZYY)

Im(ZXX)

Imaginary part Im(Z)C



18

Stiffnesses increase with load, shaft speed has little effect.

KXX

KYY

Stiffness coefficients

Rotor speed =7 krpm

KYY

KXX




Very good agreement between predictions and tests. Best at 16 krpm.

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CYY grows with load at lowest shaft speed. Predicted CYYis lower than test data. Largest disagreement at peak load (3,103 kPa=450 psi).

CXX

CYY

Damping coefficients

Rotor speed =7 krpm Rotor speed =16 krpm

CYYCXX



20

At 16 krpm, virtual masses are small & negative. At 7 krpm, predicted larger (negative) magnitude shows a dynamic stiffness hardening effect. Prediction depends on frequency range for [K-C-M] model.

MXXMYY

Virtual mass coefficients

Rotor speed =7 krpm Rotor speed =16 krpm

MYYMXX

*Kulhanek, C.D., and Child, D.W., 2012, ASME, J. Eng. Gas Turbines Power, 134, 052505


Quantify the effect of pivot stiffness on the performance of the TPJB tested by Kulhanek and Childs (2012).Select three pivots (flexible to rigid):

kpiv= 2.4

kpiv= 5.9

kpiv= ∞max

piv Ppiv

K Ck

W

Kpiv, dimensional pivot stiffnessCp, cold pad clearanceWmax, maximum static load

21

dimensionless

kKulhanek=3.8

OBJECTIVE: Update standard charts of performance from Nicholas [1979] & Someya [1989]for TPJBs with rigid pivots.L/D~0.6

Effect of Pivot Stiffness on journal eccentricity

Journal center displacement exceeds bearing clearance for large loads and a bearing with flexible pivots.

=0pr

=0.5pr Dash

Solid

kpiv=2.4

kpiv= ∞

kpiv=5.9

2

P

μNLD RSW C

Load increases

=0pr

=0.5pr

22

Effect of Pivot Stiffness on Friction Coefficient

=0pr

=0.5pr

friction coefficient not affected by pivot.f(rigid pivot)≈f(kpiv=5.9) ≈f(kpiv=2.4)

Preload rpdecreases

Load between pad

f=Torque/(W R)

2

P

μNLD RSW C

Load increases

23

Effect of Pivot Stiffness on TPJB Stiffness coefficients

Stiffness coefficients of bearing with large preload (rp=0.5) are more sensitive to pivot flexibility.

kpiv= ∞kpiv=5.9

kpiv=2.4

KYY Solid

2

P

μNLD RSW C

Load increases

PK Ck

W KXX Dash

24

Effect of Pivot Stiffness on TPJB Damping Coefficients

=0 & 0.5 pr

CXX Dash

CYY Solid

Pivot flexibility has a more pronounced effect in reducing damping than the bearing stiffnesses.

kpiv=5.9

kpiv= ∞

PC Cc

W

2

P

μNLD RSW C

Load increases

kpiv=2.4

25

Effect of Pivot Stiffness on TPJB Virtual Mass Coefficients

=0 & 0.5 pr

MXX Dash

MYY Solid

Virtual masses become negative as pivot stiffness decreases. Pivot flexibility leads to a hardening of the bearing dynamic stiffness.

kpiv= ∞

2PM C

mW

2

P

μNLD RSW C

Load increases

kpiv=5.9

kpiv=2.4

26

√ Temporal Fluid Inertia

√ Pad Mass Moment of Inertia

√ Pad Mass

kpiv= 3.8 Kpiv=641 MN/m

kpiv= ∞ Rigid pivot

Quantify the effect of pad inertia and fluid inertia on the impedances of test TPJB - Kulhanek and Childs (2012).

OBJECTIVE: Update predictions of impedances vs. frequency to assess importance of pivot flexibility.

27

28

Real part

Poor predictions when neglecting pivot flexibility.

Re(ZYY)

Re(ZXX)

Re(Z)K-M2

Impedances

Rotor speed =7 krpm

1X


1X

Re(ZXX)

Re(ZYY)

Test dataNeglect all three effectsInclude all three effectsInclude fluid inertia

kpiv= ∞

Specific load = 3,103 kPa (450 psi)

29

Re(ZYY)Re(ZXX)


Rotor speed =7 krpm

1X


1X

Re(ZXX) Re(ZYY)



Poor predictions neglecting pivot flexibility.

kpiv= ∞

30

Real part

At 7 krpm, fluid inertia reduces K at high frequency.

Re(ZYY)

Re(ZXX)

Re(Z)K-M2

Impedances

Rotor speed =7 krpm

1X


Re(ZXX)

Re(ZYY)


1X

Specific load = 3,103 kPa (450 psi)

kpiv= 3.8

31

No major impact of pad mass and its moment of inertia on damping.

Re(ZYY)

Re(ZXX)


Rotor speed =7 krpm

1X


1X

Re(ZXX)

Re(ZYY)



kpiv= 3.8

Conclusions

3232

• Good correlation between test data in:and predictions when applying a-priori knowledge of pivot stiffness and bearing & pad hot clearances.

• Selection of an adequate frequency range is crucial when determining the bearing force coefficients extracted from a [K-C-M] curve-fitting procedure.

• Pad mass and pad mass moment of inertia have no major impact onTPJB impedances. Fluid inertia reduces the dynamic stiffness at a low shaft speed (7 krpm).

• Stiffness and damping coefficients of LBP TPJBs (rp=0.5) with a heavy load (small Sommerfeld #) are more sensitive to pivot flexibility than a lightly loaded bearing with zero preload.

Other predictions for LOP not shown for brevity.

Paper GT2014-25566

Kulhanek & Childs, D, 2012, J. Eng. Gas Turbines

33

Acknowledgments

Thanks to the

Turbomachinery Research Consortium and

students of Prof. Childs.

Questions (?)

Learn more at http://rotorlab.tamu.edu

Paper GT2014-25566

Small amplitudes perturbation analysis

• Consider small journal motion displacements with frequency () about the equilibrium position:

34

0

0

( )( )

XX X i t

Y YY

ee t ee

e t ee

• The journal motions induce changes in the kth pad rotation and pivot displacements with frequency ():

0

0

0

( )( )( )

pp pi t

piv piv piv

piv pivpiv

tt et

• Journal and pad motions induce changes in the film thickness and pressure fields.

k=1,…NpadWo X

Y

eXo

eY

eo

X

clearancecircle

YStatic load

Journal center

Wo X

Y

eXo

eY

eo

X

clearancecircle

YStatic load

Journal center

35

Reduced force coefficients

Use same whirl frequency to reduce to 4 impedances (ZR X, Y)

X

Y

R TRZ A Z A

25 force impedances for kth pad

/2

/2

l P

l

L

L

Z P h Rd dz

X, Y,

12R JP s pad P PJ

Z Z Z Z M Z Z

cos sinsin cos

p p

p p

A

K+iC =

transformation matrix

36

R

Upstream pad

Journal

Pad inlet thermal mixing coefficientThermal mixing coefficient (0< <1) is empirical.

in s hF F F

in in s s h hF T FT F T

Downstream pad

FhTh

FsTs

FinTin

Fs , Fh , Fin Volumetric flow ratesTs , Th , Tin Fluid flow temperatures

~0.6-0.95 for conventional lubricant feed arrangements with deep grooves and wide holes.

small (~0.5) for TPJBs with LEG feed arrangements and spray bars (and scrappers).

Hot oil Mixing oil

Cold oil

Effect of Pivot Stiffness on Journal eccentricity

LBP & LOP

kpiv=2.4

kpiv=5.9

kpiv= ∞

LBP Dash

LOP Solid

2

P

μNLD RSW C

Load increases

Load configuration has negligible effect on journal eccentricity.

Effect of Pivot Stiffness on Journal EccentricityFriction Coefficient

LBP & LOPLBP Dash

LOP Solid

2

P

μNLD RSW C

Load increases

Friction coefficient does not vary with load configurations and pivot flexibility.f(rigid pivot)≈f(kpiv=5.9) ≈f(kpiv=2.4)

Effect of Pivot Stiffness on TPJB Stiffness coefficients

LBP & LOP

kpiv=2.4

kpiv=5.9

kpiv= ∞

Kxx Dash

Kyy Solid

2

P

μNLD RSW C

Load increases

A bearing with rigid pivot has more orthotropic stiffness at low Sommerfeld number.

Effect of Pivot Stiffness on TPJB Damping coefficients

LBP & LOP

kpiv= ∞Cxx Dash

Cyy Solid

2

P

μNLD RSW C

Load increases

kpiv=2.4

kpiv=5.9

Load configuration has no major impact on dampings. Pivot flexibility reduces damping at small Sommerfeld number.

Effect of Pivot Stiffness on TPJB Virtual mass coefficients

LBP & LOP

kpiv=2.4

kpiv=5.9

kpiv= ∞

LBP Dash

LOP Solid

2

P

μNLD RSW C

Load increasesVirtual masses between the LOP and LBP bearings are most notable for low S (<0.5).

Documents

Results and Model Predictions - TRIBGROUP TAMUrotorlab.tamu.edu/tribgroup/14_TRC_slideshow/TE14 conference/GT201… · the HOT Gap between Experimental Results and Model Predictions