1 Luis San Andrés Mast-Childs Professor SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT...

1

Luis San Andrés Mast-Childs Professor

SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT

High Load SFD Test RigIdentification of SFD

force coefficients

May 2011

2

Static loader

Shaker assembly (Y direction)

Shaker assembly (X direction)

Static loader

Shaker in X direction

Shaker in Y direction

SFD test bearing

PW-SFD test rig (2010)

3

Test rig description

shaker Xshaker Y

Static loader

SFD

basesupport rods

Static loader

X

Y

shaker Xshaker Y

Static loader

SFD

basesupport rods

Static loader

X

Y

4

Flow path & main features

in

Oil out, Qb

BaseSupportrod

Bearing Cartridge

Journal (D) Oil out, Qt

Oil in, Qin

Central groove

L, 2L

L

L, 2L

End groove

End groove

Oil outOil collector

c

Oil out, Qb

BaseSupportrod

Bearing Cartridge


Oil in, Qin

Central groove

L, 2L

L

L, 2L

End groove

End groove


BaseSupportrod

Bearing Cartridge


Oil in, Qin

Central groove

L, 2L

L

L, 2L

End groove

End groove


c

Test rig main features

Journal diameter: 5.0”

Film clearance: (A) 5.55mil (B) 5.43mil

Film length: (A) 2x1”, (B) 2 x 0.5“

Centering stiffness: variable

ISO VG 2 oil

5

Test rig cross section – rods installation

12 x Φ 7/8

8

9

5.6

4.755

All dimensions in inches

4 x Φ 7/8

Test rig materials

Journals, journal base, pedestal, bearing cartridge, Main support

rods : AISI 1020 steel

Flexural rods: Alloy Steel per ASME

B18.3

Φ4.75

BC OD Φ7.50

Φ11.00

6

Sensor locations

Eddy current sensors and accelerometers

θ= 180o and 270o

Journal B

Top Land

Bottom Land

Central groove

Eddy current sensor (Proximity probe)

Side view: Sensors located in central groove

Top view

θ= 270o

θ= 180o

X Piezoelectric accelerometer

Y Piezoelectric accelerometer

θ= 90o

θ= 0oX eddy current sensor (X proximity probe)

Y eddy current sensor (Y proximity probe)

θ= 0o and 90o

Top Land

Bottom Land

Piezoelectric Accelerometer

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Pressure sensors

Side view: Sensors located at middle plane of film lands

Top view

θland = 210o

θland = 330o

θland = 210o and 330o

Journal B

Top Land

Bottom Land

Central groove

Bottom Land

and,Locations

Central groove

1.5 inch

0.5 inch

0.5 inch

Top Land

BC

PCB (pressure sensors)

PCB and Entran

PCB (Dynamic)

8

Pressure sensors

9

Test results for(c) SFD force coefficients – Comparison between short and long open ends dampers

10

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5 3

Static eccentricity e s [mil]

Dir

ec

t d

am

pin

g c

oe

ffic

ien

t [l

bf-

s/i

n]

Cxx 1/2 inchCyy 1/2 inchCxx 1 inchCyy 1 inch

Long and short SFDs (circular orbits)

compare SFD damping

CXX ~ CYY

Short (L=0.5 inch)

CXX ~ CYY

Long (L=1 inch)

Ratio of coefficients ~ (L/c3) 3

1

0.5

33

3 3

15.55 7.49

0.55.43

inch

inch

A

XX A

XX B

B

LC c

C Lc

11

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5 3

Static eccentricity e s [mil]

Ad

de

d M

as

s

co

eff

icie

nts

[lb

]

Mxx 1/2 inchMyy 1/2 inchMxx 1 inchMyy 1 inch

compare SFD inertia

MXX , MYY

Short (L=0.5 inch)

MXX , MYY

Long (L=1 inch)

Ratio of coefficients ~ (L/c)

1

0.5

15.55 1.96

0.55.43

inch

inch

A

XX A

BXX

B

LM c

LMc

Long and short SFDs (circular orbits)

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Film and groove dynamic pressures

Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA. Groove pressure PG = 0.72 bar

Frequency=250 Hz

0 1 2 3 410

5

0

5

10

top land (120 deg)bottom land (120 deg)

Pressures at film lands

time (-)

pres

sure

(ps

i) Lands

0 1 2 3 420

10

0

10

groove (165 deg)groove (285 deg)

Pressures at central groove

time (-)

pres

sure

(ps

i) GrooveTop Land

Bottom Land

Central groove

1 inch


1 inch

Top Land

Bottom Land

Central groove

1 inch


1 inch

L/D=0.2 x 2

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Film and groove peak-peak pressures

Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA. Groove pressure PG = 0.72 bar

Frequency20-250 Hz

Top Land

Bottom Land

Central groove

1 inch


1 inch

Top Land

Bottom Land

Central groove

1 inch


1 inch

0 100 2000

10

20

30

40

Top land (120)Bottom land (120)Groove (165)

peak-peak pressures

Frequency (Hz)

P-P

pre

ssu

re (

psi

)

Bottom land

Top land

groove

Land length=1 inGroove width=0.5 in depth = 3/8 in (75 c)

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Test results for(d) SFD force coefficients – Comparison between open ends and sealed ends long dampers

I

A

B

II

BC

groove

journal Top land

Bottom land

A

B

15Open and sealed ends long SFD (circular orbits)

compare SFD damping

CXX ~ CYY

Open ends

CXX ~ CYY

Sealed ends

100

150

200

250

300

350

400

450

0.0 0.5 1.0 1.5 2.0 2.5

Da

mp

ing

co

eff

icie

nts

(lbf-

s/in

)

Eccentricity es (mil)

SFD (1 inch land lengths)

CSFD

open ends CXX

circular orbits

open ends CYY

Sealed ends CYY (B-B)Sealed ends CXX(B-B)

I

A

A

B

B

II

BC

groove

journalTop land

Bottom land

B-B sealed SFD

I

A

A

B

B

II

BC

groove

journalTop land

Bottom land

B-B sealed SFD

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0

10

20

30

40

50

60

70

80

90

100

0.0 0.5 1.0 1.5 2.0 2.5

Ad

ded

mas

s co

effi

cien

ts (l

b)

Eccentricity es (mil)

SFD (1 inch land lengths)

MSFD

open ends MXX

Open ends MYY

circular orbits

Sealed ends MXX(B-B)

Sealed ends MYY(B-B)

Test data for open and sealed ends (circular orbits)

compare SFD inertia

MXX , MYY

Open ends

MXX , MYY

Sealed ends

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Conclusions: Learning from tests and predictions

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Summary of learningOpen ends long damper shows ~ 7 times more damping than

short length damper. Inertia coefficients are two times larger.

SFD force coefficients are more a function of static eccentricity (max. 40%c) than amplitude of whirl (max 40%c) changing little with ellipticity of orbit (aspect ratios 1:1, 2:1 & 5:1)

Piston ring faces orientation affects leakage and force coefficients. Long Sealed SFD shows ~2.6 times more damping than open ends SFD

Code benchmarked for long and short SFDs (open and sealed ends).

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Proposed work (TRC)

Whirl Orbit Analysis for Identification of SFD force coefficients

Linear-Nonlinear Force Coefficients for Squeeze

Film Dampers

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Types of journal motionx= R

Y

X

e

h

R

e: amplitude of motion

whirl frequency

eXo

eYo

whirlingjournal

Film thickness

x= R

Y

X

2rX

rX, rY : amplitudes of motion

whirl frequency

eo

2rY

(a) small amplitude journal motions (b) large amplitude journal motions

K,C, M (force coefficients)RBS stability analysis

Applications:

FX, FY (reaction forces)RBS imbalance response& transient load effects

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SFD predictive codeOrbit

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

X/c

Y/c

2rX

2rY

Code & GUI: virtual tool for prediction of SFD forced response

(a) Linear force coefficients (K,C,M)(b) Instantaneous reaction forces

along orbital path (c) Automated orbit analysis for NL

parameter identification

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Purpose of whirl orbit analysis

for specified whirl orbit and over specifiedfrequency range: • predict SFD reaction forces vs. time,• conduct Fourier analysis, &• identify SFD linearized force coefficients

Orbit

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

X/c

Y/c

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SFD example

Journal Diameter 5.0 in

Total Length 1.0 in

Land Clearance 5.0 mil

NO Central Groove

Feed holes 3 (120deg)

Axial Length 0.5 in

Ambient Pressure 0.0 psig

Supply Pressure 10 psig

Cavitation Pressure -14.70 psig

Supply Temperature 77 oF

Viscosity at Tsupply 0.43 Reyns

Density 49 lb/ft3

L

Journal

Bearing

X

Y

D

Feed hole

ASection A-A

Open Ends SFD with feed holes

Pa, ambient pressure

Ps, supply pressureL

Journal

Bearing

X

Y

D

Feed hole

ASection A-A

Open Ends SFD with feed holes

Pa, ambient pressure

Ps, supply pressure

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whirl orbit induces forces

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

eX/c

e Y/c

SFD open ends L=1.0 inch - with holes - no central groove

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

-250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0

FXF

Y


lbf

SFD reaction force

Fundamental 1X Force

es/c=0.5c r/c=0.25c

Eccentric (Off-center)Elliptical orbit

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SFD 1X forces do not reproduce NL forces

SFD Forces: predicted and 1X

-250

-200

-150

-100

-50

0

50

100

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Bea

rin

g r

eact

ion

fo

rce

FX

FY

FX_1Fourier

FY_1Fourier

Fraction of Period


lbfes/c=0.5c r/c=0.25c

SFD reaction force

Fundamental 1X Force

Frequency 180 Hz

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

eX/c

e Y/c


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SFD reaction forces

The SFD instantaneous reaction force superimposes a

dynamic force to a static force, i.e., F=Fstatic+Fdyn.

The dynamic components of the SFD reaction forces are modeled in a linearized form as

dyn SFD SFD SFDF K z C z + M z

where z is a vector of dynamic displacements and

(K, C, M)SFD are matrices of stiffness, viscous damping and inertia force coefficients

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Analysis (I)The dynamic or time varying part of the SFD reaction force is periodic with fundamental period T=2/.

Using Fourier series decomposition,

2 31 ....i t i t i te e e dyn II IIIF F F F

To first order effects (fundamental frequency)

1i te dynF F 2

1 i SFD SFD SFD 1 1F K M C z H z

2 i SFD SFD SFDH K M Cwhere

is the matrix of damper impedances

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Analysis (II)

The code predicts the SFD time varying reaction forces for the orbital path and delivers the fundamental Fourier components of motion and forces, i.e. z and F. Forward and backward whirl orbits ensure linear independence of the two SFD reaction forces.

Solution of the system of algebraic equations:

leads to the determination of the impedances:

HXX, HXY,HYX, HYY

1 2 1 2F F H z z

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Analysis (III)

The analysis stacks impedances for a set of frequencies (k=1,2,….N) from which, by linear curve fits, one determines :

)Re(2 HMK SFDSFD

)Im(HCSFD

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SFD Real Impedances vs. frequency

-1.00E+04

-5.00E+03

0.00E+00

5.00E+03

1.00E+04

1.50E+04

2.00E+04

2.50E+04

0 50 100 150 200 250Imp

edan

ces

(rea

l par

t)

Hxx

Hyy

Hxy

Hyx


lbf/in

Whirl frequency (Hz)

Re(H)

HYY fits well model K-M2

HXX will give M<0

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

eX/c

e Y/c


Frequency range 20-200 Hz

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SFD Ima Impedances vs. frequency

-2.00E+04

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

0 50 100 150 200 250Imp

edan

ces

(imag

par

t)

Hxx

Hyy

Hxy

Hyx


lbf/in

Whirl frequency (Hz)

Ima(H)

HYY fits OK model C

HXX gives average C

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

eX/c

e Y/c



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SFD NL-Linear force coefficients

Linear force model

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

eX/c

e Y/c


Mxx Myy Mxy Myx

lbm lbm lbm lbm

-5.0 2.0 0.2 0.2

Cxx Cyy Cxy Cyx

lbf-s/in lbf-s/in lbf-s/in lbf-s/in

68.5 37.7 -0.6 -0.6

Kxx Kyy Kxy Kyx

lbf/in lbf/in lbf/in lbf/in

2.12E+03 -2.11E+02 -6.35E+01 -6.13E+01

-250

-200

-150

-100

-50

0

50

100

-100 -80 -60 -40 -20 0 20 40 60 80

FourieranalysisLinearizedforcesNonlinearforces

FY vs FX


SFD NL force response

DISSIPATED ENERGY IN A PERIOD or MOTION

lbf-in -0.637Non-linear (from time transient response)

-0.590Linear from ALL force coefficients

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Proposed tasks (2011-12)

X

Y

X

Y

X

Y

elliptical orbitscircular orbits

centered journal off-centered journal

1. Test ACTUAL short length open ends damper with dynamic loads (20-300 Hz) inducing off-centered elliptical orbital motions with amplitude ratios (5:1) to reach 0.8c.

2. Identify SFD force coefficients from test impedances, and correlate coefficients with linear force coefficients and experimental coefficients for smallest whirl amplitude (0.05c).

3. Perform numerical experiments, similar to the physical tests, to extract linearized SFD force coefficients from the nonlinear forces. Quantify goodness of linear-nonlinear representation from an equivalence in mechanical energy dissipation.

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Budget (2011-12)

X

Y

X

Y

X

Y

elliptical orbitscircular orbits

centered journal off-centered journal

Support for graduate student (20 h/week) x $ 1,800 x 12 months $ 21,600

Fringe benefits (0.6%) and medical insurance ($191/month) $ 2,419

Travel to (US) technical conference $ 1,200

Tuition three semesters ($3,802 x 3) $ 10,138

Supplies for test rig $ 1,500

Total Cost: $ 37,108

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1 Luis San Andrés Mast-Childs Professor SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT...

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Transcript of 1 Luis San Andrés Mast-Childs Professor SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT...