Hydrodynamic fluid film bearings and their effect on the ......4 Importance of fluid inertia in thin...

1

Notes 5 – Modern Lubrication

September 2010

Hydrodynamic fluid film bearings and their effect on

the stability of rotating machinery

http://rotorlab.tamu.edu/me626

Dr. Luis San AndresMast-Childs Professor

[email protected]

2

Lubricated Journal Bearings

AdvantagesDo not require external source of pressure.

Support heavy loads. The load support is a function of the lubricant viscosity, surface speed, surface area, film thickness and geometry of the bearing.

Long life (infinite in theory) without wear of surfaces.

Provide stiffness and damping coefficients of large magnitude.

DisadvantagesThermal effects affect performance if film thickness is too small or available flow rate is too low.

Potential to induce hydrodynamic instability, i.e. loss of effective damping for operation well above critical speed of rotor-bearing system

Radial and axial load support of rotating machinery – low friction and long life

Typically use MINERAL OIL as lubricant. Modern trend is to replace with working fluid (water)

3

Fundamentals of Thin Film Lubrication

Geometry of flow region in a thin fluid film bearing (h << Lx, Lz)

DB=2 RBDJ=2 RJ

Cylindrical bearing

•Film thickness << other dimensions•No curvature effects•Laminar flow, inertialess

TYP (c/L*) = 0.001

μρ cU*Re = SMALL Couette flow Reynolds #

( ) ( ) ( ) 0=∂

∂+

∂

∂+

∂∂

zv

yv

xv zyx

2

2

2

2

0;0yv

zP

yv

xP xx

∂∂

+∂∂

−=∂∂

+∂∂

−= μμ

Flow equations: continuity + momentum (x,y)

Quasi-static (pressure forces = viscous forces)

Figures 1 & 2

x

z

Lz

Lx

h(x,z,t)U

V

(U,V) surface velocities

Vx

Vy

Vz

h << Lx,Lz

y

x Lx

h(x,z,t)

U V

Vz

Vy

Vx

4

Importance of fluid inertia in thin film flows

Importance of fluid inertia effects on several fluid film bearing applications. (c/RJ )=0.001, RJ =38.1 mm (1.5 inch)

9,2969300.16313.30R134 refrigerant

8,4778480.17913.93Liquid nitrogen

7,9427940.19110.47Liquid oxygen

7,0527050.2161.075Liquid hydrogen

1,5881591.0064Water

711712.14120Light oil

515.130.01,682Thick oil

999.915.41.23Air

Re at 10,000 rpmRe at 1,000 rpmKinematic

viscosity (ν) centistoke

Absolute viscosity (µ) lbm.ft.s x 10-5

fluid

Fluid inertia is important for operation at high speeds and withprocess fluids. These are prevalent conditions in HP turbomachinery

Reynolds numbers

Table 1

5

Fluid inertia effects at inlet & edges

Fluid inertia (Bernoulli’s effect) causes sudden pressure drop (or raise) at sharp inlets (exits). Most important effect on annularpressure seals and hydrostatic bearings with process fluids

Pressure drop & rise at sudden changes in film thicknessFigure 3

ΔP ~ ½ ρU2

PP

U U

ΔP ~ ½ ρU2

PP

U U

6

Thin Film Lubrication: Reynolds Equation

Cylindrical journal bearing & coordinates

{ } { }⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

+⎭⎬⎫

⎩⎨⎧

Θ∂∂

Θ∂∂

=Θ∂∂Ω

+∂∂

zPh

zPh

Rhh

t μρ

μρρρ

12121

2

33

2

Pressure = ambient on sidesPressure > Pcavitation

θsinsincos eeech YX =Θ+Θ+=

Figure 4

X

Y

Θ

journal

e

Bearing center

Ω

cos sinX Yh C e eθ θ= + +

θ

Elliptical PDE in film region

Film thickness

eX = e cos(φ ); eY = e sin(φ )

Kinematics of journal motion:

X

Y

journal

e

Bearing center

φ

eY

eX

7

e

Vr

OJ

OB

eY

eX

φ

t

X

Y

Vt

r

Kinematics of journal motion

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ −=⎥

⎦

⎤⎢⎣

⎡φφφ

φφee

ee

Y

X

cossinsincos

Θ⎭⎬⎫

⎩⎨⎧ Ω

−+Θ⎭⎬⎫

⎩⎨⎧ Ω

+=⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

+⎭⎬⎫

⎩⎨⎧

Θ∂∂

Θ∂∂ sin

2cos

212121 33

2 XYYX eeeezPh

zPh

R μμ

Reynolds Eqn. in fixed coordinates (X,Y)

θφθμθμθ

sin2

cos1212

1 33

2 ⎭⎬⎫

⎩⎨⎧ Ω

−+=⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

+⎭⎬⎫

⎩⎨⎧

∂∂

∂∂ ee

zPh

zPh

R

Reynolds Eqn. in moving coordinates)

Set: incompressible fluid (oil)

For circular centered orbits:: radius (e) and 2/Ω=φHydrodynamic pressure P=0Loss of load capacity

eX = e cos(φ ); eY = e sin(φ )

θ

Θ

x=RΘ

Y

r

t

OB

OJ

e

Ω

h

y

Bearing

Journal

φ

A

Θ=θ+φ

8

Journal bearing reaction force

Fluid film force acting on journal surface

Dynamic forces = fn. of journal position and velocities, rotational speed (Ω), viscosity (μ) and geometry (L, D, c)

( ) dzdRtzPFF

L

t

r θθθ

θ

π

⋅⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡ ∫∫ sincos

,,

2

00

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡ −=⎥

⎦

⎤⎢⎣

⎡

t

r

Y

X

FF

FF

φφφφ

cossinsincos

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦⎤

⎢⎣⎡ Ω

−=Ω=2

,,, φααα eeFeeFF YX

θ P.cosθ

P.sinθ

P

r

θ

Θ

t

X

Y

P

journal

Ft

Fr

Force = integration of pressure field on journal surface

Figure 5

9

LONG journal bearing (limit geometry)

LONG BEARING MODEL

L/D >>> 1

Pressure does not vary axially. Not applicable for most practical cases, except sealed squeeze film dampers

{ } { }⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

=Θ∂∂Ω

+∂∂

zPh

zhh

t μ122

3

Figure 6

Ω

L

D journal

Axial pressure field

bearing

L/D >> 1

dP/dz → 0

10

SHORT journal bearing (limit geometry)

SHORT JOURNAL BEARING MODEL

L/D < 0.50

Applicable to actual rotating machinery

{ } { }hht

PhR Θ∂

∂Ω+

∂∂

=⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

2121 3

2 θμθ

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛−

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ Ω

−+=−

22

33 2

sin2

cos6),,( Lz

HC

eePtzP a

θφθμθ

Hydrodynamic pressure is proportional to viscosity (μ), speed (Ω), and most important to:

1/C3

Control of tolerances in machined clearance is critical for reliable performance

Figure 7

Ωjournal

L

D

Axial pressure field

bearingL/D << 1

dP/dθ → 0

11

STATIC LOAD PERFORMANCE

Force Balance for Static Load

Bearing reaction force = applied static load (% of rotor weight)

( ) ( ) 2/322

3

22

2

3

3

14;

1 ε

επμ

ε

εμ

−

⋅Ω+=

−

Ω−=

cLRF

cLRF tr

0 0.2 0.4 0.6 0.8 1100

1 .103

1 .104

1 .105

-FrFt

Static Forces for short length bearing

journal eccentricity (e/C)

Rad

ial a

nd T

ange

ntia

l for

ces [

N]

*

Radial and tangential forces for L/D=0.25 bearing. μ=0.019 Pa.s, L=0.05 m, c=0.1 mm, 3, 000 rpm,

Journal bearing can generate large reaction forces. Highly nonlinear functions of journal eccentricity

Ftangential

Fradial

Figures 8 & 9

X

Y

Wbearing

Rotor (journal)fluid

film

JournalRotation Ω

e

φ

Static load

X

Y

r

t

W-Fr

Ft

φ

12

DESIGN PARAMETER: STATIC LOAD PERFORMANCE

Given S, iterative solution to find operating journal eccentricity (ε = e/c) and attitude angle (φ):

Sommerfeld number N rotational speed (rev/s)W static load L, D=2R, c : clearance &μ viscosity

Attitude angle

2

⎟⎠⎞

⎜⎝⎛=

cR

WDLNS μ

( ) ( )( ){ }222

2222

1161

4 επεεεμπσ

−+

−=⎟

⎠⎞

⎜⎝⎛Ω

==cL

WRLDLS

( )ε

επφ

41

tang2−

=−=r

t

FF

Locus of journal center for short length bearing

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ey/c

ex/c

Journal locus

Clearance circle

load increases,low speed, lowviscosity

e/c

at t it udeangle

speed increases,load loads,high viscosity

clearancecircle

Wload

spindirection

Low load, high speed, large viscosity Low load, high speed, large viscosity

High load, low speed, small viscosity

Figure 12

13

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.01

0.1

1

10

journal eccentricity (e/c)

Som

mer

feld

num

ber

*


Sommerfeld number

Sommerfeld # vs journal eccentricity

Low load, high speed, large viscosity


( )2

2

4⎟⎠⎞

⎜⎝⎛Ω

==cL

WRLDLS μπσ

Large eCentered journal

σ

Figure 10

N rotational speed (rev/s)W static load L, D=2R, c : clearance &μ viscosity

14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10102030405060708090


Atti

tude

angl

e

*


Sommerfeld number

Attitude angle # vs journal eccentricity

Low load, high speed, large viscosity


( )2

2

4⎟⎠⎞

⎜⎝⎛Ω

==cL

WRLDLS μπσ

Large eCentered journal

φ

Figure 11

N rotational speed (rev/s)W static load L, D=2R, c : clearance &μ viscosity

15

DYNAMICS OF ROTOR-BEARING SYSTEM

Symmetric - rigid rotor supported on short length journal bearings

Rigid rotor supported on journal bearings. (u) imbalance, (e) journal eccentricity

Equations of motion:

)cos(

)sin(2

2

tuMFYM

FtuMFXM

Y

oX

ΩΩ+=

+ΩΩ+=

Figure 13

X

Y

2Fo

disk

Clearance circle

Ωt

e

Static load

u

Disk

2M

journalbearing

Rigid

shaft

16

DYNAMICS OF ROTOR-BEARING SYSTEM

Consider small amplitude motions about static equilibrium position (SEP). SEP defined by applied static load.

Small amplitude journal motions about an equilibrium position

OOYXYoX eeeFFFOOOO

φ,or,,0, ⇒=−=

)(),( teeeteee YYYXXX OOΔ+=Δ+=Let:

YYFX

XFY

YFX

XFFF

YY

FXXFY

YFX

XFFF

YYYYYY

XXXXXX

O

O

Δ∂∂

+Δ∂∂

+Δ∂∂

+Δ∂∂

+=

Δ∂

∂+Δ

∂∂

+Δ∂

∂+Δ

∂∂

+=

Expansion of forces abut SEP

Figure 14

Wφo ΔX

ΔY

eXo

eY

eo

X

clearancecircle

YStatic load

Journal center

Ω

Wφo ΔX

ΔY

eXo

eY

eo

X

clearancecircle

YStatic load

Journal center

Ω

X

Y

r

t

W-Fr

Ft

φ

17

ROTORDYNAMIC FORCE COEFFICIENTS

Strictly valid for small amplitude motions. Derived

from SEPThe “physical representation” of stiffness and damping coefficients in lubricated bearings

;j

iij X

FK

∂∂

−=

j

iij X

FC

∂∂

−=

Stiffness:

Damping:

Inertia: ;j

iij X

FM

∂∂

−=

i,j = X,Y

Figure 15

Kxx, Cxx

journal

bearing

X

Y

Kxy, Cxy

Kyx, Cyx

Kyy Cyy

18

⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ

⎥⎦

⎤⎢⎣

⎡−

⎥⎥⎦

⎤

⎢⎢⎣

⎡=⎟⎟

⎠

⎞⎜⎜⎝

⎛

YX

CCCC

YX

KKKK

F

F

tFtF

YYYX

XYXX

YYYX

XYXX

Y

X

Y

X

O

O

)()(

ROTORDYNAMIC FORCE COEFFICIENTS

StiffnessMatrix:

DampingMatrix:

Static reaction force:

Inertia ~ 0 in journal bearings

Strictly valid for small amplitude motions. Derived from SEP

Linearized Equations of motion

⎟⎟⎠

⎞⎜⎜⎝

⎛ΩΩ

Ω=⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ

⎥⎦

⎤⎢⎣

⎡+⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ⎥⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛

ΔΔ

⎥⎦

⎤⎢⎣

⎡tt

uMYX

KKKK

YX

CCCC

YX

MOOM

YYYX

XYXX

YYYX

XYXX

sincos2

19

0.01 0.1 1 100.1

1

10

Sommerfeld #

Stiff

ness

y

0 0.2 0.4 0.6 0.8 10.1

1

10


Stiff

ness

Journal Bearing: STIFFNESS COEFFICIENTS

Care with non dimensional value interpretation

Eccentricity (e/c) Sommerfeld # (σ)

High speedLow loadLarge viscosity


Low speedLarge loadLow viscosity

kαβ = Kαβ (c/Fo)

kxxkxx

kyykyy

kxy kxy

-kyx-kyx

Figure 16 & 17

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

Bearing stiffnesses versus eccentricity and design number (σ)

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

20

0.01 0.1 1 101

10

100

CxxCyyCxyCyx

S#

Dam

ping

*

0 0.2 0.4 0.6 0.8 11

10

100


Dam

ping

Journal Bearing: DAMPING COEFFICIENTS

Care with non dimensional value interpretation




cαβ = Cαβ (cΩ/Fο)

cxx cxx

cyycyycxy

cxy

=cyx

=cyx

Figure 16 & 17

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

Bearing damping versus eccentricity and design number (σ)


2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

21

Journal Bearing: OPERATION at CENTERED CONDITION


eo→ 0, φo = 90 deg

Significance of cross-coupled effect in journal bearing

Pure cross-coupling effect

Kxy = Cxx Ω/2

2;

24 3

3

3

3 πμπμc

LRcCCcc

LRkKK YYXXYXXY ===Ω

=Ω

==−=

Kxx = Kyy =0 no direct stiffness

Ω

F

Non-rotating structure

F

Rotating structure

F F

22

STABILITY OF ROTOR-BEARING SYSTEM

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ

⎥⎦

⎤⎢⎣

⎡+⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ

Δ⎥⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛

ΔΔ

⎥⎦

⎤⎢⎣

⎡00

YX

KKKK

YX

CCCC

YX

MOOM

YYYX

XYXX

YYYX

XYXX

If rotor-bearing system is to become unstable, this will occur at athreshold speed of rotation (Ωs) with rotor performing (undamped) orbital motions at a whirl frequency (ωs)

1;; −===== jeBeByeAeAx jtjjtj ss τωωτωω

X

Y

2Fo

disk

Clearance circl

Ωt

e

Static load

u

Disk

2M

journal bearing

Rigid

shaft

23

STABILITY OF ROTOR-BEARING SYSTEM

= whirl frequency (ωs)/threshold speed instability (Ωs)

o

S

YYXX

YXXYXYYXXXYYYYXXeqss F

MCcc

kckcckckkp

222 ω

ω =+

−−+==

( )( ) 22

⎟⎟⎠

⎞⎜⎜⎝

⎛Ω

=−

⋅−−−=

s

s

YXXYYYXX

YXXYYYeqXXeqs cccc

kkkkkk ωω

Equivalent support stiffness

Whirl frequency ratio

The WFR is independent of the rotor characteristics (rotor mass and flexibility)

eqo

eqs KCF

kM =⎟⎠⎞

⎜⎝⎛=2ω n

eqs M

Kωω ==

whirl frequency equals the natural frequency of rigid rotor supported on journal bearings

X

Y

2Fo

disk

Clearance circl

Ωt

e

Static load

u

Disk

2M

journal bearing

Rigid shaft

24

0.01 0.1 1 1000.10.20.30.40.50.60.70.80.9

1

S#

whi

rl fr

eque

ncy

ratio

.5

* *

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.10.20.30.40.50.60.70.80.9

1

e/c

whi

rl fr

eque

ncy

ratio

.5

*

WHIRL FREQUENCY RATIO




Rotor becomes unstable at speed = twice system natural frequency

0as50.0 →== εΩω

XX

XY

s

s

ckWhirl

frequency ratio

0;;;0 ==−==== YXXYYXXYYYXXYYXX cckkcckk

( ) XXXYXYXXXXeq ckcckk += =0

At centered condition

0.50

Figure 18

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ


25

0.01 0.1 1 100123456789

10

S#*0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

123456789

10

e/c*

Threshold speed of instability




unstable

stable

unstable

stable

Figure 19

Fully stable for operation with ε > 0.75, all bearings (L/D). Threshold speed decreases as eccentricity (e/c) 0

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

Threshold speed of instability versus eccentricity and design number (σ)


Ps = M Ωs2 c/Fo

26

0.01 0.1 1 100123456789

10

S#*

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10123456789

10

e/c*

CRITICAL MASS




Critical mass equals maximum mass rotor is able to support stably if current operating speed = threshold speed of instability.

Critical mass decreases for centered condition. Unlimited for large (e/c)

unstable unstable

stable stable

Figure 20

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

Critical mass versus eccentricity and design number (σ)


27

0.01 0.1 1 100

2

4

6

rigidT/c=0.1T/c=1T/c=10

Threshold speed (ps) for flexible rotor

Modified Sommerfeld number

Thre

shol

d sp

eed

(ps)

EFFECTS OF ROTOR FLEXIBILITY

Static sag

Sommerfeld # (σ)

High speedSmall loadHigh viscosity


Rotor flexibility decreases system natural frequency, thus lowering threshold speed of instability. WFR still = 0.50

unstable

More flexibilitystable

⎟⎠⎞

⎜⎝⎛+

=

CTk

pp

eq

ssf

1

22

roto KFT =

Figure 21

2

4⎟⎠⎞

⎜⎝⎛Ω

=cL

WRLμσ

bearing2MKRot

28

PHYSICS of WHIRL MOTION

At centered condition: No radial support, tangential force must be < 0 to oppose whirl motion

Figure 22

⎟⎟⎠

⎞⎜⎜⎝

⎛Δ

Δ⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛Δ

Δ⎥⎦

⎤⎢⎣

⎡−=⎟⎟

⎠

⎞⎜⎜⎝

⎛φφ 00 e

eCCCC

ee

KKKK

FF

tttr

trrr

tttr

rtrr

dt

r

2;

2

0

3

3 πμC

LRCCCCKKK

CCKK

rrtttrrt

trrtttrr

===Ω

=−==

====

Forces in rotating coordinate system

Bearing force coefficients at (e/c)=0

Resultant forces

eKCFF rttttr ddΔ−−== )(;0 ω

whirl orbit

X

Y

Ft= -(Cttω + Ktr) Δe

Rotor spin Ω

Fr= -(Crtω + Krr) Δe

Δe

29


Figure 22 Force diagram for circular centered whirl motions

Loss of damping for speeds above ωs

0)1( <=− eqrttt CKCω

whirl orbit, ω

X

Y

Ft= -(Cttω + Ktr) Δe

Rotor spin Ω

Fr= -(Crtω + Krr) Δe

Δe

30


Figure 23 Forces driving and retarding rotor whirl motion

Cross-coupled force is a FOLLOWER force0)1( <=− eqrttt CKC

ω

whirl orbit, ω

X

Y

Cross-coupled force = Krt Δe

Damping force =

- Ctt ω Δe

Rotor spin, Ω

31

( ) ωωπ eqorbitrttt CAreaKCeE 2)(2 2 −=−Δ−=


Figure 24 Follower force from cross-coupled stiffnesses

Work from bearing forces. E<0 is dissipative; E>0 adds energy to whirl motion

FX=-KXY ΔY

X

Y

whirl orbit, ω

FY=-KYX ΔX

KXY > 0, KYX < 0 ΔX<0, ΔY>0

32


Figure 24 Influence of bearing asymmetry on whirl orbits

Bearing asymmetry creates strong stiffness asymmetry – a remedy to reduce potential for hydrodynamic instability

Energy from cross-coupled forces = Area (Kxy-Kyx)

X

Y

X

Y

33

EXPERIMENTAL EVIDENCE of INSTABILITY

Figures 25 & 26

Amplitudes of rotor motion versus shaft speed. Experimental evidence of rotordynamic instability

Waterfall of recorded rotor motion

demonstrating subsynchronous whirl

34


WFR ~ 0.47 X

Transition from oil whirl to oil whip (sub sync freq. locks at system natural frequency)

35


Automotive Turbocharger

FRBFRB

FRBFRB

WFR ~ 0.50 X

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

Frequency [Hz]

Am

plitu

de [-

]

Compressor End - Y

61X

12.5 krpm

65 krpm

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

Frequency [Hz]

Am

plitu

de [-

]

Compressor End - Y

61X

12.5 krpm

65 krpm

TC supported on floating ring bearings

36


Automotive Turbocharger

Multiple sub-synchronous motions

0 1000 2000 3000 4000 5000 60000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45TEST-Vertical displacement

Frequency [Hz]

Am

plitu

de [-

]

Ymax 0.306=

29.76 krpm

243.8 krpm

127.7 krpm

1X

TC supported on semi-floating ring bearings

37


Metal Mesh Gas Foil Bearing

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

10

15

20

25

30

35

40Waterfall -Horizontal

Frequency [Hz]

Am

plitu

de

.

Frequency [Hz]

Dis

plac

emen

t [um

]

1 X

Whirl and bifurcation at high rotor speeds

Rot

or c

oast

ing

dow

n

Max. Rotor speed = 69 krpm

38

CLOSURE

Cutting axial grooves in the bearing to supply oil flow into the lubricated surfaces generates some of these geometries.

Other bearing types have various patterns of variable clearance (preload and offset) to create a pad film thickness that has strongly converging wedge, thus generating a direct stiffness for operation even at the journal centered position.

In tilting pad bearings, each pad is able to pivot, enabling its own equilibrium position. This feature results in a strongly converging film region for each loaded pad and the near absence of cross-coupled stiffness coefficients.

Commercial rotating machinery implements bearing configurations aiming to reduce and even eliminate the potential of hydrodynamic instability (sub synchronous whirl)

39

OTHER BEARING GEOMETRIES

Used primarily on high speed turbochargers for PV and CV engines

1. Subject to oil whirl (two whirl frequencies from inner and outer films (50% shaft speed, 50% [shaft + ring] speeds)

1. Relatively easy to make2. Low Cost

Floating Ring

Round bearings are nearly always “crushed” to make elliptical or multi-lobe

1. Subject to oil whirl1. Easy to make2. Low Cost

Axial Groove

Bearing used only on rather old machines

1. Poor vibration resistance2. Oil supply not easily contained

1. Easy to make2. Low Cost3. Low horsepower loss

Partial Arc

Round bearings are nearly always “crushed” to make elliptical bearings

1. Most prone to oil whirl1. Easy to make2. Low Cost

Plain Journal

Comments Disadvantages Advantages Bearing Type

Table 2 Fixed Pad Non-Pre Loaded Journal Bearings

40


Currently used by some manufacturers as a standard bearing design

1. Expensive to make properly2. Subject to whirl at high speeds

1. Good suppression of whirl2. Overall good performance3. Moderate cost

Three and Four Lobe

High horizontal stiffness and low vertical stiffness -may become popular - used outside U.S.

1. Fair suppression of whirl at moderate speeds2. Load direction must be known

1. Excellent suppression of whirl at high speeds2. Low Cost3. Easy to make

Offset Half (With Horizontal Split)

Probably most widely used bearing at low or moderate rotor speeds

1. Subject to oil whirl at high speeds2. Load direction must be known

1. Easy to make2. Low Cost3. Good damping at critical speeds

EllipticalComments Disadvantages Advantages Bearing Type

Fixed Pad Pre-Loaded Journal Bearings Table 2

41


Fixed Pad Pre-Loaded & Hydrostatic Bearings Table 2

Generally high stiffness properties used for high precision rotors

1. Poor damping at critical speeds2. Requires careful design3. Requires high pressure lubricant supply

1. Good suppression of oil whirl2. Wide range of design parameters3. Moderate cost

Hydrostatic

Used as standard design by some manufacturers

1. Complex bearing requiring detailed analysis2. May not suppress whirl due to non bearing causes

1. Dams are relatively easy to place in existing bearings2. Good suppression of whirl3. Relatively low cost 4. Good overall performance

Multi-Dam Axial Groove or Multiple-Lobe

Very popular in the petrochemical industry. Easy to convert elliptical over to pressure dam

1. Goes unstable with little warning2. Dam may be subject to wear or build up over time3. Load direction must be known

1. Good suppression of whirl2. Low cost3. Good damping at critical speeds4. Easy to make

Pressure Dam (Single Dam)

CommentsDisadvantagesAdvantagesBearing Type

42


Tilting Pad Bearings & Foil BearingsTable 3

Used mainly for low load support on high speed machinery (APU units).

1. High cost.2. Dynamic performance not well known for heavily loaded machinery.3. Prone to subsynchronous whirl

1.Tolerance to misalignment.2.Oil-free

Foil bearing

Widely used bearing to stabilize machines with subsynchronous non-bearing related excitations

1. High Cost2. Requires careful design3. Poor damping at critical speeds4. Hard to determine actual clearances5. Load direction must be known

1. Will not cause whirl (no cross coupling)

Tilting Pad journal bearing

Flexure pivot, tilting pad bearing

CommentsDisadvantagesAdvantagesBearing Type

Bump foils

Top foil

Spot weld

Journal

Bearing sleeve

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