Third Chinese International Turbomachinery Conference

CITC, April 12, 2018; Chong Qing, China

Luis San Andres

Mast-Childs Chair Professor

Turbomachinery Laboratory

Mechanical Engineering Department

Texas A&M University

College Station, TX, USA

Lsanandres@tamu.edu

ADVANCED MODEL PREDICTIONS VS.

TEST DATA IN TILTING PAD BEARINGS

FOR COMPRESSORS

Funded by Turbomachinery Research Consortium

2

Behzad AbdollahiB.S. Aerospace Engineering from Sharif University of Technology (Iran).

Discovered a passion for turbomachinery and rotating equipment and

decided to further his education with an M.S. degree at Texas A&M

University - Turbomachinery Laboratory. Behzad is a Design Engineer at

Rotating Machinery Services (RMS – Bethlehem, PA) and works with

multiple turbomachinery equipment lines including axial compressors,

centrifugal compressors, steam turbines, and hot-gas expanders.

Luis San AndrésMast-Childs Chair Professor at Texas A&M University – Turbo Lab.

Performs research in lubrication and rotordynamics. Luis is a Fellow of

ASME and STLE, and a member of the Industrial Advisory Committees for the

Texas A&M Turbomachinery Symposia. Luis has published over 260 journal

and conference papers. Several papers are recognized as best in various

international conferences.

Authors

3

Introduction

Goal: To

accurately

predict bearing

performance

without costly &

time extensive

tests.

Abstract

Lecture introduces a novel model for the mixing

of flow and thermal energy at a lubricant feed port

in a tilting pad journal bearing.

Accurate estimation of the oil temperature and

the flow rate at a pad leading edge largely

determines the temperature rise along the pad

lubricated surface as well as the shear drag

power loss, and ultimately the bearing load

capacity.

An example of analysis predictions compared to

test data validates the model.

Designers have a new tool that allows the early

specification of flow rate as an input

parameter, not a consequence of analysis

nor a constraint during actual operation.

Tilting pad journal bearings (TPJBs)

• fluid film bearings with a number of

pivoted pads ( typically four or five).

Each pad can rotate freely about its pivot

and cannot support a moment.

• TPJBs support HP turbomachinery with

specific load to 300 psi (2 MPa).

• Small cross-coupled stiffnesses for

LOP and LBP configurations promote

rotor-bearing system stability.

4

Major concerns & desires

Pivot flexibility & wear

Pad flexibility & mechanical deformation

Subsynchronous vibration SSV Hash

Low flow rate & low power loss desired

Pressure field

Thermal effectsViscous shearing of lubricant causes

film temperature rise and power loss.

• High temperature in a pad

(Babbitt liner becomes soft ~121

°C).

• Lubricant loses its viscosity.

• Hot clearance ↓ and preload ↑to affect the minimum film thickness,

load capacity, & bearing force

coefficients.

x

y

Shaft rotation

speed, Ω

Static load, W

Bearing

housing

Pad

Pivot

Fluid film

Lubricant in the

groove

Lubricant in the

sump

Orifice

5

Aim: Use efficient lubricant delivery arrangements

to reduce power loss and temperature rise while

keeping a low supply flow.

6

The basics of TPJB analysis

7

Fluid film thickness in a pad

Ω

Y

XWY

WX

RB

RJ

θP

θθL

h

up

Fluid Film

Bearing Center OB

Pad Center OP

η

ξ

ξpiv

ηpiv

δp

Unloaded Pad

ΘP

Loaded PadPivot

Cp : Pad radial clearance

CB= Cp-rp Bearing assembled clearance

Rd= Rp+t : Pad radius and thickness

rp : Pad dimensional preload

dp : Pad tilt angle

xpiv, hpiv : Pivot radial and transverse

deflections

up: Pad upper surface deformation

cos sin

cos sin

k k

P p X Y

k k k k k

piv P p piv d p p

h C u e e

r R

x h d

• Laminar flow

• Includes temporal fluid inertiaeffects

• Average viscosity across film

8

3 3 2 2

2 2

1

12 12 2 12J

h P h P h h h h

R 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 filmY

X

Housing

Pad

Pivot

Fluid film

Journal

, Journal speed

W, static load

9

Thermal energy transport in thin film

T: film temperature h : film thickness

U,W: circ. & axial mean flow velocities

, , Cv : viscosity & density, specific heat

hB, hJ : heat convection coefficients

TB, TJ : bearing and journal temperatures

: journal speed

Uses 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 U

h

(Energy Disposed) = (Energy lost due to fluid shear)

Advected by fluid + conducted into pads= DISSIPATION

3D

version

used

• Heat flows from film into

shaft and is

• conducted into pads:

• + heat convection

boundary conditions on

all sides of a pad.

• Convection to oil in back of pad

is important in sealed ends

bearings.

Temperature field in pads

0T

10

11

R

Upstream pad

Journal

Thermal mixing coefficient l (0< l <1) is empirical.

Downstream pad

QTE

TTE

Qsup

Tsup

QLE

TLE

Q Volumetric flow rates

T Lubricant temperatures

l ~0.6-0.95 for oil feeds with deep grooves and wide holes.

l ~ 0.5 for LEG feed arrangements and spray bars (w scrappers).

Hot oil Mixed oil

Cold oil

Thermal mixing at pad inlet

( )

LE sup TE

LE LE sup sup TE LE

Q Q Q

T Q Q T Q T

l

l

A fraction (l) of hot oil is

carried by shaft and mixes

with cold supply oil to fill in

the inlet (leading edge) of a

pad.

Conventional lubricant mixing in a feed groove

( )

sup LE TE

sup sup TE LE

LE

LE

Q Q Q

Q T Q TT

Q

l

l

• Required supply flow (Qsup) based only on upstream flow

(QTE) and downstream flow (QLE). (No oil churning considered)

• What if QLE < l QTE ? Qsup=0 ?

• During operation actual supply flow may differ from

predicted (during design)

• In practice, Qsup is controlled by available delivery system,

rarely varying with operating condition. 12

1967 Ettles, C. M., Proc.

IMechE: Part 3L

2D Navier-Stokes

equation, laminar flow

85% of the hot oil adheres to the shaft

and travels across the groove.

1983 Mitsu et al., ASME

J. Lubr. Technol.

Test the effect of oil

flow rate on fluid

mixing in a groove

Introduced an empirical coefficient for

the mixing of the lubricant flow with the

supply flow prior to reaching the pad inlet.

1986 Heshmat and

Pinkus, ASME J.

Tribol.

Observe flow,

measure temperature

Defined a thermal mixing quadratic

function based on empirical constants.

2012 He et al.,

Turbomachinery

Symposium

Investigation of the

directly lubricated

bearings

Used a model where the supply flow rate

is known assumes an evenly

distributed supply oil in the grooves.

2014 Uhkoetter et al.,

ASME Turbo Expo

3D CFD analysis and

test procedure for

verification

Guidelines on the numerical models and

characterized the mixing based on supply

flow Reynolds number.

2016 Rindi et al., ASME

J. Comp. Nonlin.

Dyn.

Calculate a pressure

at the groove

An orifice-like equation fails to properly

model the mixing phenomena)

2017 San Andrés et al.,

ASME Turbo Expo

Model TPJB starvation

condition with an

effective pad length

Using the conventional supply flow

distribution, a reduce in flow shortens the

effective pad circumferential length

IntroductionLiterature Review: Thermal Mixing in a Groove

1 2

34

2

SupQ

3

SupQ

4

SupQ

4

TEQ

1

LEQ

W1

SupQ 2

SupQ 3

SupQ 4

SupQ

Feed port or groovePlenum

1

SupQ

total

SupQ

Lubricant mixing in a feed port or groove

Supply flow rate

distributes

evenly as

Operation with increasing load:• Pressure rise in a pad → demands less supply flow

• Unloaded pads (low pressure) → demand excess lubricant

He, M., Cloud, C. H., Byrne, J. M., and Vazquez, J. A., 2012, 41st Turbomachinery Symposium

He, M., Allaire, P., Barrett, L., and Nicholas, J., 2005, Trib. Trans.

total

supi

sup

QQ

n

1 4 1( )LE TE supQ Q Q

14

Flow at pad leading edge & trailing edge = shear flow -/+

pressure flow

15

Small pressure gradient

(small load)

Large pressure gradient

(+ loaded) reduces net

flow rate

Shear and pressure

driven flows are in the

same direction

Leading edge

trailing edge

• Shear driven flow is proportional to film size: ↑demand • Film pressure gradient at leading edge induces flow in reverse

direction: ↓demand • Flow from upstream trailing edge provides large flow to fill in the

downstream pad leading edge film: ↓demand

Define a groove demand parameter (Ci)

to quantify the restriction or demand for

fresh flow in each groove1, ,1

|i

sheari i ni i

pressure TE

QC

Q Q

Flow at a pad leading and trailing edges

,

/2 3

,

/2 ,2 12

|

|

LE TE

LE TE

LE TE

shear pressure

L

s

sL

Q Q Q

R Lh h Pdz

R

Leading edge Trailing edge

Example : Flow fraction (𝜶𝒊) for each feed groove vs. shaft speed & spec. load

Total supply flow must meet total demand:1

n

total i

i

C C

A fraction of total supply flow allocated to each feed port:

1, ,

i total totalisup sup i sup i n

total

CQ Q Q

C

Flow distribution

17

• Equal supply flow distribution at

zero load (centered shaft).

• As load increases, pads 1 & 2

require of lesser flow, while pad 3

receives most of the lubricant

flow.

• Pad 4 receives a large flow from upstream pad (3) → low demand

of supply (fresh) flow.

4 pad bearing

LoadSpeed

Flow balance at a feed port or groove

Nicholas, J. C., Elliott, G., Shoup, T. P., and Martin, E., 2008, 37th Turbomachinery Symposium

Ha, H. C., Kim, H. J., and Kim, K. W., 1995, ASME J. Tribol.

Based on descriptions in:

ith pad(downstream)

TEQ

grQ

12 SLQ

LEQ

(i-1)th pad(upstream)

SupQ

18

1

1

if

i i i

TE sup LE

i i i i

SL TE sup LE

Q Q Q

Q Q Q Q

• Open ends bearing: Excess

of supply flow leaves a port

as a side leakage.

• Sealed ends bearing, +

lubricant is drawn from

churning flow in groove.

1

1

if i i i

TE sup LE

i i i i

gr LE TE sup

Q Q Q

Q Q Q Q

12 SLQ

Control volume analysis:

• Side leakage (QSL, TSL)

• Groove churning oil (Qgr, Tgr)

• The two flows above do not co-

exist!

• Heat fluxes across the adjacent

pad walls (ΦLE, ΦTE)

Thermal Mixing Model: Final Equation

From conservation of energy,

determine film temperature at

leading edge of downstream

pad 19

• With side leakage (QSL, TSL)

Evacuated bearing (with side leakage)

downstream pad leading edge

temperature:

1 1i i i i i TE LETE TE sup sup SL SL

pi

LE i

LE

Q T Q T Q Tc

TQ

20

Energy (upstream stream + supply

flow – side flow) + convection from

pad surfaces

• With churning flow (QSL, TSL)

Sealed ends bearing (with re-circulating oil)

downstream pad leading edge

temperature:

1 1i i i i i TE LETE TE sup sup gr gr

pi

LE i

LE

Q T Q T Q Tc

TQ

21

Energy (upstream stream +supply

flow + churning flow) + convection

from/to pads’ edges

PREDICTIONS VS. TEST DATA

Model Validation

22

23

2: four-pad TPJBCoghlan, D. M., and Childs, D. W., 2015, GT2015-42331.

Coghlan, D. M., 2014, M.S. Thesis, Texas A&M University.

24

Test-rig and bearing stator

ITEM No. PART No. QTY.

1 Bearing Stator 1

2 Stinger 2

3 Static Loader Yoke 1

4 Bearing End Cap 2

5 Load Cell 2

6 Accelerometer 2

7 Pressure Sensor 2

9 Thermocouple 3

10 Proximity Probe 4

Axial view

Side view

static load

2: a Four-Pad TPJB

Coghlan & Childs (2014) test a

four pad spherical seat TPJB with

various oil feed arrangements

and a constant (fixed) supply flow

rate.

25

» Flooded single-orifice (SO), labyrinth end seals

» Evacuated leading edge groove (LEG)

» Evacuated spray-bar (SB)

» Evacuated spray-bar blocker (SBB)

Shaft rotational speed Ω [RPM] 7000-16000

Shaft surface speed ΩR [m/s] 38-85

Specific Load W/(LD) [MPa] 0.7-2.9

Load orientation LBP

Number of pads 4

Shaft diameter [mm] 101.59

Pad thickness [mm] 190

Bearing axial length [mm] 61

Pad arc length 72°

Pivot offset 0.5

Preload 0.3

Pad clearance [μm] 134

Lubricant ISO VG46

Total supply flow (fixed) [LPM] 42 –38

Cp/R = 0.0013

L/D = 0.6

0°

1 2

34

θ xW

y

2: Bearing geometry and operating conditions

Flooded housing

26

Evacuated housing

N = 7000 RPMW/(LD) = 0.7 MPa

Novel ModelConventional

Model

Pad 𝑸𝑻𝑬𝒊−𝟏 𝑸𝑳𝑬

𝒊 𝜶𝒊 𝑸𝒔𝒖𝒑𝒊 𝑸𝑺𝑳

𝒊 𝑸𝒈𝒓𝒊 𝑸𝒔𝒖𝒑

𝒊

1 7 6.2 0.14 5.8 6.7 0 0.6

2 3.5 6.2 0.23 9.7 7 3.4

3 3.5 10.6 0.41 17.2 10.1 8.7

4 7.1 10.6 0.22 9.4 5.8 5.3

Total: 1 42 (L/min) 19 (L/min)

0

10

20

30

40

50

60

70

80

0 100 200 300

Angle (deg)

Supply

Temp.

2.9 MPa 0.7 MPa2.1 MPa

Test Data

Predictions

1 2

3 4

N=7000 RPMCgr = 0.6

Qtotal=42 L/min

2: Pad Surface Temperature vs. Speed & Load

• Conventional model

predicts flow = 19 LPM

< test delivered (42 LPM).

• Current model shows +

agreement with test data.

Pa

d S

urf

ac

e T

em

pe

ratu

re R

ise

(°C

)

0°

1 2

34

θ xW

y

27

Over-flooded → some oil

(side leakage) escapes

the bearing directly

without ever lubricating

pads.

N = 16000 RPMW/(LD) = 2.9 MPa

Novel ModelConventional

Model

Pad 𝑸𝑻𝑬𝒊−𝟏 𝑸𝑳𝑬

𝒊 𝜶𝒊 𝑸𝒔𝒖𝒑𝒊 𝑸𝑺𝑳

𝒊 𝑸𝒈𝒓𝒊 𝑸𝒔𝒖𝒑

𝒊

1 22.6 10.3 0.06 2.4 14.6 0 0

2 3.9 9.7 0.14 6 0.3 0 7.1

3 3.4 31.2 0.66 28 0.1 0 27.8

4 22.8 32.7 0.14 5.7 0 4.3 13.3

Total: 1 42 (L/min) 48 (L/min)

0

10

20

30

40

50

60

70

80

0 100 200 300

Angle (deg)

Supply Temp.

2.9 MPa 0.7 MPa2.1 MPa

Test Data

Predictions

Cgr = 0.6

Qtotal=42 L/min

N=16000 RPM

Pa

d S

urf

ac

e T

em

pe

ratu

re R

ise

(°C

)2: Pad Surface Temperature vs. Speed & Load

• Operation at 2.9 MPa requires

more flow (48 LPM) than 42

LPM delivered Likely oil

starvation in pad 4 (unloaded)

• Large side leakage (QSL) for pad

1 (15 LPM), in conventional

model Qsup=0.

0°

1 2

34

θ xW

y No recirculation flow

(Qgr=0) in an

evacuated housing.

2: Other Lubricant Delivery Types

0

10

20

30

40

50

60

70

80

0 100 200 300Angle (deg)

LEGSBB

Test Data

0°

1 2

34

θ xW

y

1 2 3 4

N=16000 RPM

Q=42 L/min

SO

Cgr=0.9

Cgr=0.5

Cgr=0.2Q=38 L/min

Pa

d S

urf

ac

e T

em

pe

ratu

re R

ise

(°C

)

Model predicts pad

temperature with less

than 10 °C difference

than test data.

29

SO(single orifice)

SB (spray bar)

SBB(spray bar blocker)

LEG(leading edge groove)

Coghlan, D. M., 2014, M.S. Thesis, Texas A&M University.

Oil feed type influences

film temperature due to

various factors.

2: Complex Stiffness & Parameter Identification

• Excitation frequency range : 10 Hz to 250 Hz

• Test complex stiffness H static stiffness K, damping C, &

virtual mass M coefficients

𝕽(𝑯) ℑ(𝑯)

0

50

100

150

200

250

300

350

400

450

500

10 50 90 130 170 210 250Frequency (Hz)

Im(Zyy)

Test Data

Im(Zxx) Im(Zyy) & Im(Zxx)

TEHD Prediction

0

50

100

150

200

250

300

350

400

450

500

10 50 90 130 170 210 250Frequency (Hz)

Re(Zyy)

Test Data

Re(Zxx) Re(Zyy) & Re(Zxx)

TEHD Prediction

(MN

/m)

(MN

/m)

2( ) ,and ( )H K M H C

N = 3000 RPM

W/(LD) = 2.5 MPa

2: Stiffness coefficients (MN/m)

• Kyy > Kxx

• Stiffness

Isotropy

(predictions)

• Average

difference for Kxx

~ 8% & for Kyy ~

17%

• Improved

predictions at

low load, high

speed.

• Pivot stiffness

50

100

150

200

250

300

350

0.7 1.8 2.9

Kyy

Test Data

TEHD

Prediction

Kxx

N=7000 RPM50

100

150

200

250

300

350

0.7 1.8 2.9

Kyy

Test Data

TEHD

Prediction

Kxx

N=10000 RPM

50

100

150

200

250

300

350

0.7 1.8 2.9

Kyy

Test Data

TEHD

Prediction

Kxx

N=13000 RPM50

100

150

200

250

300

350

0.7 1.8 2.9

Kyy

Test Data

TEHD

Prediction

Kxx

N=16000 RPM

Specific Load W/(LD) (MPa)Specific Load W/(LD) (MPa)

(MN/m)

2: Damping Coefficients (kNs/m)

0

50

100

150

200

0.7 1.8 2.9

Cyy

Test Data

TEHD

Prediction

Cxx

N=7000 RPM0

50

100

150

200

0.7 1.8 2.9

Cyy

Test Data

TEHD

Prediction

Cxx

N=10000 RPM

0

50

100

150

200

0.7 1.8 2.9

Cyy

Test Data

TEHD

Prediction

Cxx

N=13000 RPM0

50

100

150

200

0.7 1.8 2.9

Cyy

Test Data

TEHD

Prediction

Cxx

N=16000 RPMDir

ec

t D

am

pin

g (

kN

·s/m

)

Specific Load W/(LD) (MPa)Specific Load W/(LD) (MPa)

• Similar trends

but

• different, Cxx ~

25% & Cyy ~ 40%

• Pivot stiffness

2: Virtual Mass Coefficients (kg)

-50

-40

-30

-20

-10

0

0.7 1.8 2.9

Test Data TEHD

Prediction

MyyMxx

N=7000 RPM-50

-40

-30

-20

-10

0

0.7 1.8 2.9

Test Data

TEHD

Prediction

MyyMxx

N=10000 RPM

-50

-40

-30

-20

-10

0

0.7 1.8 2.9

Test Data

TEHD

Prediction

MyyMxx

N=13000 RPM-50

-40

-30

-20

-10

0

0.7 1.8 2.9

Test DataTEHD

Prediction

MyyMxx

N=16000 RPM

Specific Load W/(LD) (MPa)Specific Load W/(LD) (MPa)

• Negative virtual mass → stiffening

effect.

• Similar order of

magnitude.

• Mass estimation

has a significant

uncertainty.

(kg)

CONCLUSION

34

The mixing for thermal energy

35

TEQ

grQ

LEQ

SupQ

SEALED ENDS

TEQ

12 SLQ

LEQ

SupQ

12 SLQ

EVACUATED ENDS

Recommended thermal mixing efficiency parameter (Cgr)

36

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Single OrificeSpray Bar

Spray Bar BlockerLeading Edge Groove

Evacuated (w/o end seals)Flooded (w/ end seals)

• More efficient oil feed type → lowers oil temperature → high Cgr

• Evacuated housing (with direct lubrication method: LEG, SB, SBB) reduces hot oil carry over → side oil leakage

carries most of thermal energy from hot upstream oil.→ Cgr 1 (TLE TTE : exit temperature of upstream pad).

• Flooded bearing → upstream oil mostly recirculates in a

groove → Cgr 0 (Tgr TTE).

Conclusion• For accurate temperature prediction with a conventional

thermal mixing model, the predicted flow rate must be

same as actual supplied flow.

• Unlike with hot oil carry over factor (l), the novel mixing

efficiency parameter (Cgr) does not need tailoring to each

operating condition.

• In one example, the novel thermal mixing model improves temperature

prediction by up to 17 °C (37 °C at reduced supply flow).

• Side leakage flow and groove recirculating flow (flooded port) have

significant influence on the lubricant film temperature.

• Comparisons to test data show novel model delivers more

accurate predictions. Model has ability to specify flow delivered.

37

Questions?

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

Thanks!