Transcript Document

TRC May 2008
Upgrade XLTRC2 Computational Model
for Hydrodynamic Journal Bearings –
Thermal Effects
Thermohydrodynamic Analysis
of Hydrodynamic Fluid Film
Bearings
Luis San Andres
Mast-Childs Professor
1
TRC Project 32513/1519 T4
XLPresDm® - FEPressDamJB
Equation for
flow in film
lands
Flow
conditions
Bearing
Types
Reynolds Equation. Finite Element
solution
Laminar flow, isoviscous & isothermal
Multiple lobe with preload (elliptical, lemon
type, offset pads, etc); pressure dam bearing
XLPresDm®
2
CODE & GUI proposed additions & enhancements
1. NO thermal effects (mechanical
energy dissipation and transport by
lubricant)
2. NO changes in clearance due to thermal
and mechanical deformation effects.
3. Outdated I/O operations with Fortran
code NOT efficient.
4. No informed “guess” for starting
calculations.
Known Issues with XLPresDm®
3
Geometry for bearing pad with preload
Nomenclature
c: pad clearance
cm: assembled clearance
e : journal eccentricity

Pad center
rp=c-cm : preload,
Bearing center
rp =0, cylindrical pad
rp =c, journal and pad
contact
rp

l
e
Pad with
preload
Film thickness:
Y
journal
p
h  c  eX cos  eY sin   rp cos(  p )
t
X
4
Thin Film Lubrication: Reynolds Equation
Nomenclature
P : film pressure
h : film thickness
 : viscosity, fn (T)
 : journal speed
 h3 P
  h
h

P  

 12 (T )
 2 
t


Film thickness:
c : pad clearance
rp : pad preload
eX, eY: journal eccentricity
viscosity:
h  c  eX cos  eY sin   rp cos(  p )
  S e
V T TS 
Boundary conditions:
Pad leading edge, =l.
trailing edge, t.
Pad sides, z= +/- ½ L,
Film pressure P>
P = PS (supply pressure)
P = Pa = 0 (ambient pressure)
P=Pa (ambient)
Major
assumption:
Viscosity is average
across film
thickness
Laminar flow
Pcav (oil cavitation pressure)
Reynolds Equation for laminar thin film flows
5
Finite Element solution of Reynolds Equation
n pe
P0e    i P0ei
i 1
Flow
domain
n pe
k
j 1
e
ij
P0ej   q ie  f i e
e
e
 h 
k   
 i , x  j , x   i , z  j , z  dx dz


12  
e 
R
e
e
fi 
h

i . x dx dz

2 e
3
e
ij
Nodal pressures
z
e
q Flow rate
x=R
Finite element model for pressure field
in fluid film bearing
FEM for solution of Pressure field
Assemble system of
equations, impose
boundary conditions
and solve 6
Thin Film Lubrication: Thermal Energy Transport
Nomenclature
h
h
h
T: film temperature
1
1
1
U   Udy ; W   Wdy ; T   Tdy
h : film thickness
h0
h0
h0
U,W: circ. & axial flow velocities
, r, Cp : viscosity & density, specific heat
hB, hJ : heat convection coefficients
TB, TJ : bearing and journal temperatures
 : journal speed
Major
assumption:
Integrate energy
transport equation
across film. Neglect
temperature
variations. Use bulkflow velocities and
temperature.
Laminar flow
 


r Cp 
 U h T    W h T   hB T  TB   hJ T  TJ 
z
 R 

2
2 2

12 
R 
R   CONVECTION + DIFFUSION= DISSIPATION
2

 U 
 W 


h 
12
2   (Energy Disposed) = (Energy Generated)

7
Thermal Energy Transport in thin film flows
Thin Film Lubrication: Thermal Energy Transport
T=T
TN
West face
P
ap TP  aw TW  ae TE  an TN  S P  QJB
East face
½L
Source of energy
Sink of energy
Numerical solution uses
Upwind scheme.
a’s are a function of flow rates:
z
Pressure
Finite
element
rhU)e|e+1
rhU)w|e
z
L/2

Fe 
0
Pressure
node
x=R
TW
0
 r hU  dz , F w 
e
L/2

 r hU  dz ,
w
0
e
TP
TE
F    r hW  z  L / 2 dx  F e  F w
n
w
8
Algebraic equation for transport of film temperature
Heat Convection Models
Ti
Ts
Heat flow:
Q = h A (TS – Ti)
A: wetted area for heat transfer
h: heat convection coefficient, a function of Nusselt #,
oil conductivity and hydraulic diameter (=clearance).
1
koil
; Nu  f  Re, Pr  Nusselt # =depends on flow conditions (Prandtl # and
Reynolds #)
DH
 Cp  
r Rc
Pr  
;
Re


k


oil
Reynolds/Colburn Analogy), Nu=3 Pr0.33
2
Kays and Crawford - constant wall temperature, Nu =7.54
3
Kays and Crawford - constant wall heat flux, Nu =8.22
4
Haussen - thermally developing constant wall temperature, Nu >3.657
5
Shah -
6
Stephan - Simultaneous developing, constant wall temp, Nu >3.66
7
9
Stephan - Simultaneous developing constant wall heat flux, Nu > 4.364
h  Nu
thermally developing constant wall heat flux, Nu > 4.364
Thermal mixing at pad inlet
Nomenclature
F : flow
T : temperature
l : thermal mixing coefficient
= 0.80
(TYP)
Finlet = Fsupply + l Fup
Flow balance
Finlet Tinlet = Fsupply Tsupply + l Fup Tup
Energy balance
R
Fup
Tup
Upstream pad
Finlet
Tinlet
Fsupply
Tsupply
Thermal mixing at pad trailing edge
Downstream pad
10
Status of computational code
Fortran code : complete – L. San Andres full development
graduate student worked for 4 months (no progress)
GUI (Excel interface) – To be done – NO student available
(UGS quit after 1 month) integration with XLTRC2
expected by end of summer 08.
Examples for calibration:
(pressure and temperature fields)
oil 360 deg journal bearing
Dowson et al. (1966)
Ferron, Frene, Boncompain (1983)
Costa, Fillon (2000 2003)
oil two pad arc journal bearing
Costa, Fillon (2000 2003)
Brito, Fillon (2006, 2007)
Pressure dam bearing
Childs et al (2007, 2008)
Load capacity & force
coefficients
11
Example 1 : Ferron bearing (1983)
Journal diameter
Bearing Length
Radial clearance
Groove width
groove arc length
Lubricant
Density
Specific Heat
Thermal conductivity
Viscosity at 40 C
Visc-temp coefficient
Inlet oil temperature
Inlet oil pressure
Load range
Speed range
Prandtl No
Load No
Diffusivity
Sommerfeld #
D
L
c
100
80
0.152
18

Cp



860
2000
0.13
0.0277
0.034
40
0.7
1kN-10 kN
1-4 kRPM
426
mm
mm
mm
mm
deg
kg/m3
J/kg-C
W/m-C
Pa.s
1/C
C
bar
Ferron,J., Frene, J., and R.
Boncompain, 1983, “A Study
of the Thermohydrodynamic
Performance of a Plain
Journal Bearing Comparison
Between Theory and
Experiments”, ASME
Journal of Tribology, Vol.
105, pp. 422-428,
Load
23.98
7.55814E-08 m2/s
S 
 N LDR
W
2
 
C 
12
Ferron et al. bearing (1983)
Load
Test data
Film temperature
temperature
Temperature (deg C)
50
48
46
44
42
40
0
*
60
90 120 150 180 210 240 270 300 330 360
angle (deg)
pressurepressure
Midplane
2
Pressure (MPa)
30
1.5
1
0.5
0
0
30
*
60
90 120 150 180 210 240 270 300 330 360
angle (deg)
p
*
Pressure and temperature fields – 4 kRPM, 6 kN
13
Ferron et al. bearing (1983)
Load
0.9
2000
3000
4000
Test data
eccentricity ratio
0.8
RPM
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
Sommerfeld #
0.6
S
0.7
 N LD R
S
0.8
0.9
2
 L


W N
C D  R 
W
2
 
C 
14
Eccentricity ratio (e/c) vs Sommerfeld #
Ferron et al. bearing (1983)
Load
Test data
45
40
2000
3000
4000
RPM
Peak pressure
35
30
25
20
15
10
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
eccentricity ratio
15
Peak film pressure vs. eccentricity ratio (e/c)
Ferron et al. bearing (1983)
Load
14
deg C
Test data
Peak temperature rise
12
10
8
6
4
2
Tsupply=40 C
2000
3000 RPM
4000
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
eccentricity ratio
16
Peak film temperature vs. eccentricity ratio (e/c)
Example 2: two axial groove bearing
Journal diameter
Bearing Length
Radial clearance
preload
Feed groove width
Pad arc length
Lubricant
Density
Specific Heat
Thermal conductivity
Viscosity at 40 C
Visc-temp coefficient
Inlet oil temperature
Inlet oil pressure
Load range
Speed range
Prandtl No
D
L
c
rp
100
80
0.085
0
70
162
r
870
2000
0.13
0.0293
0.032
35,40,50
0.7,1.4, 2.1
1kN-10 kN
1-4 kRPM
451
Cp
k


mm
mm
mm
mm
mm
deg
kg/m3
J/kg-C
W/m-C
Pa.s
1/C
C
bar
Brito,F.P., Miranda, A.S., Bouter, J.,
and Fillon, M., Frene, J., and R.
Boncompain, 2007, “Experimental
investigation on the influence of
Supply temperature and Supply
Pressure on the Performance of a
Two-Axial Groove Hydrodynamic
Journal Bearing”, ASME Journal of
Tribology, Vol. 129, pp. 98-105,
Load
17
Brito et al. bearing (2007)
Load
Film temperature
Midplane pressure
Journal locus
Test data
3
3.5
Predictions
70
70
temperature (C)
2
2
1.5
1
1
0.5
temperature (C)
2.5
0
65
65
Pressure (MPa)
e/c=0.43
f  56 deg
1.35 kW
3.0 LPM
28 bar max
Pressure (MPa)
3
60
55
50
0
0 45 90 135 180 225 270 315 360
45 90 135 180 225 270 315 360
*
angle (deg)
angle (deg)
40
55
50
45
45
0
60
0
40
0 45 90 135 180 225 270 315 360
45 90 135 180 225 270 315 360
angle (deg)
angle (deg)
Pressure and temperature fields – 4 kRPM, 10 kN
*
18
Example 3 – Pressure dam bearing
Journal diameter
D
117.1
Bearing Length
L
76.2
Radial clearance
c
0.142
pad arc
170
Dam arc length
D
130
LD
width (0.75 L)
57.1
depth
0.4
LR
Reilef groove width
19.05
depth
0.1
Lubricant
ISO VG 32
Density
r
860
Specific Heat
Cp
2000
Thermal conductivity
k
0.13
Viscosity at 45 C

0.028
Visc-temp coefficient

0.034
Inlet oil temperature
40-55 ?
Inlet oil pressure
N/A
Load range
0.1-12
Speed range
4,6,8,10,12
mm
mm
mm
deg
deg
mm
mm
mm
mm
Al-Jughaiman, and Childs, D., 2007,
“Static and Dynamic Characteristics
for a Pressure-Dam Bearing”, ASME
Paper GT2007-25577
W
Y
X
kg/m3
J/kg-C
W/m-C
Pa.s
1/C
C
bar
e
kN
krpm
Missing details on bearing geometry, lubricant and feed conditions. Even with test
data at hand, not able to reproduce test results in paper. VERY PECULIAR
19
THERMAL EFFECTS
Status of computational code
Fortran code : complete
GUI (Excel interface) – in progress
Delivery at end of Summer 08:
a) Complete Excel GUI(s) and interface with XLTRC2
b) Enhance code to include prediction of fluid inertia
(mass) coefficients
c) MAY Include changes in operating clearance due to
thermal effects and shaft rotation
Upgrade to XLPresDm®
20
Example 3 – Pressure dam bearing
12
Power Loss (kW)
10
8
6
4
4000 rpm
6000 rpm
8000 rpm
10000 rpm
12000 rpm
2
0
0
250
500
750
1000
1250
1500
Unit Load (kPa)
GT2007-25577
Power loss
21
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing with relief track
145 psi
1.0
eccentricity ratio (e/c)
0.9
0.8
0.7
0.6
0.5
0.4
4 krpm (pred)
10 krpm (pred)
4 krpm (test data)
10 krpm (test data)
12 krpm (pred)
test data 12 krpm
W
Y
0.3
X
0.2
e
0.1
0.0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Journal eccentricity vs specific pressure
22
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
90
Attitude angle (deg)
W
80
Y
X
70
e
60
50
40
30
4 krpm (pred)
10 krpm (pred)
4 krpm (test)
10 krpm (test)
20
10
145 psi
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Attitude angle vs specific pressure
23
Example 3 – Pressure dam bearing
W
TAMU Pressure Dam Bearing
Y
X
Stiffness [MN/m]
1200
e
KYY
1000
800
600
400
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
200
0
0
200
400
600
800
1000
1200
1400
145 psi
Unit Load (W/LD) [kPa]
Direct stiffness KYY vs specific pressure
24
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
W
145 psi
Y
250
KXX
200
Stiffness [MN/m]
X
e
150
100
4 krpm (pred)
10 krpm (pred)
4 krpm (test)
10 krpm (test)
50
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Direct stiffness KXX vs specific pressure
25
Example 3 – Pressure dam bearing
W
TAMU Pressure Dam Bearing with relief track
Y
145 psi
X
180
KXY
160
Stiffness [MN/m]
e
140
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
120
100
80
60
40
20
0
-20
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Cross stiffness KXY vs specific pressure
26
Example 3 – Pressure dam bearing
W
TAMU Pressure Dam Bearing
Note: prediction changed sign
600
X
145 psi
KYX
500
Stiffness [MN/m]
Y
e
400
300
200
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
100
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Cross stiffness KYX vs specific pressure
27
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
W
Y
2000
CYY
1800
Damping [kN.s/m]
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
1600
1400
X
e
1200
1000
800
600
400
200
145 psi
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Direct DAMPING CYY vs specific pressure
28
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
W
300
X
CXX
250
Damping [kN.s/m]
Y
145 psi
e
200
150
100
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
50
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Direct DAMPING CXX vs specific pressure
29
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
600
CXY
Damping [kN.s/m]
500
W
Y
X
e
400
300
200
100
145 psi
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Cross DAMPING CXY vs specific pressure
30
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
Note: prediction changed sign
W
Y
Damping [kN.s/m]
700
4 krpm (pred)
10 krpm (pred)
test 4 krpm
test 10 krpm
CYX
600
500
X
e
400
300
200
100
145 psi
0
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Cross DAMPING CYX vs specific pressure
31
Example 3 – Pressure dam bearing
TAMU Pressure Dam Bearing
W
Y
0.50
WFR
Whirl frequency ratio
0.45
X
4 krpm (pred)
10 krpm (pred)
0.40
e
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
200
400
600
800
1000
1200
1400
Unit Load (W/LD) [kPa]
Whirl frequency ratio WFR vs specific pressure
32
Continuation Proposal
Budget from TRC for 2008/2009:
Support for programmer (GUI)
Total Cost:
$ 25,000
$ 25,000
a) Complete Excel GUI(s) and interface with XLTRC2
b) Enhance code to include prediction of fluid inertia
(mass coefficients)
c) Include changes in operating clearance due to thermal
effects and shaft rotation
BUDGET for Upgrade to XLPresDm®
33
Thin Film Lubrication: Thermal Energy Transport
Major assumption:
In oil lubricated bearings, temperature does not vary across axial length,
T=T.
TN
Fn
L/2
Tn
x
Fw
Te
Fe
TW
TP
TE
z
Tw
0
Midplane (symmetry line)
x=R
Fs =0 (W=0)
Integrate energy
transport equation along
axial length to obtain
Fe – Fw + Fn =0
34
Energy transport equation (temperature invariant along axial direction)
Thin Film Lubrication: Thermal Energy Transport
.
In oil lubricated bearings, T=T
L/2
e
L/2
 e L/2

e
w
r CP T   hU  dz  T w   hU  dx  Tn   H W  z  L / 2 dx     S  Qs  dz dx
0
w
 0
 0
Thermal energy advected by fluid flow = Mechanical Power – Energy conducted
to B &J
2
12   2  2 R 2 
R  
S
 U 
W 
 Mechanical energy dissipation

h 
12
2

 
Qs  hB T  TB   hJ T  TJ 
h2  P
W 
;
12   z
h2  P  R
U 

12   x
2
Heat flow into bearing and journal
Axial and circumferential (bulk-flow)
velocities
Thermal energy transport equation
35
TRC 2008
Questions ????
36
Ferron et al. bearing (1983)
Load
Test data
Ferron et al. bearing (1983),
0.9
eccentricity ratio (e/c)
0.8
0.7
0.6
0.5
0.4
0.3
2 krpm
0.2
3 krpm
kRPM
0.1
4 krpm
0.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Load (kN)
37
Journal eccentricity (e/c) vs. applied static load
TRC 2008
38
Perturbation analysis of flow equations
Consider small amplitude journal and pad motions about static
equilibrium position (SEP)
An applied external static load (Wo)
determines the rotor equilibrium position
fo
(eX, eY)o with steady pressure field Po
and film thickness ho
Fo
eY
eY
Y
clearance
circle
e
eo
eX
t
eX
ef
r
Let the journal whirl with frequency 
and small amplitude motions (eX,
eY) about the equilibrium position.
Hence
e X  e Xo  e X e it ,
eY  eYo  eY e it ,
39
Small amplitude journal motions about an equilibrium position
Force coefficients
Bearing dynamic reaction forces:
 FX 
 K XX
F   K
Z Y 
 YX
Y
Y
X
K XY   X  C XX
  

K YY  B  Y   CYX
C XY   X 
 

CYY  B  Y 
X
Displacements (X,Y)
Measure of stability:
Whirl frequency ratio
WFR = Kxy/(Cxx
Stiffness
coefficients
Damping
coefficients
Typically:
No fluid inertia accounted for
Force coefficients independent of excitation
frequency for incompressible fluid.
Functions of speed & load
40
Bearing force coefficients
Dynamic reacion forces:
 FX 
 K XX
F   K
 Y
 YX
K XY 
K YY  S
 X  C XX
  
 Y   CYX
Stiffness
coefficients
C XY 
CYY  S
 X  M XX
   
 Y   M YX
Damping
coefficients
M XY 
M YY  S
 X 
  
Y 
Inertia
coefficients
Y
Y
Z
X
X
41
Idealization of thermal energy transport
Casing (or ambient)
TBouter
Bearing
Thermal Energy
conducted to
bearing
TB
Exit flow
carrying
thermal
energy
Film
T
Mechanical power (P ) by
film shearing
~ Torque x 
Thermal Energy
conducted to /
from journal

Journal
TJ
L
42