parameter identification (hybrid brush seal) 8 example 2 hbs...a 2nd example of system parameter...
TRANSCRIPT
A 2nd example of system
parameter identification
(Hybrid Brush Seal)
Luis San Andrés (lecturer)
Thanks to Adolfo Delgado, José Baker & the
support from Siemens Power Generation
MEEN 459 - April 2008 2019
Structural parameters
Kshaft= 243 lbf/in (42.5 kN/m)
Ms+d= 9.8 lb (4.45 kg)
z: 0.01 % (damping ratio)
Installation:
6.550” diameter brush seal
Max. air Pressure: 60 psig
Shaker (20 lb max)
Test Rig: Rotordynamic Configuration
1020
30 4050
6070
80 90 100
cm
Supply pressure
inlet
Eddy current
sensosrs
Pressure
Vessel
Flexible
coupling
Quill shaft
Rotor StingerElectromagnetic
Shaker
DC Motor
Supporting
springs
Roller
bearing
assembly
Eddy current
sensor
Spring
Ball bearing
Shaft
Disk
High pressure air
Flow
Flow Flexible
coupling to
motor
Hybrid brush
sealDetail view of brush seal test rig
Experimental Facility
GT2008-50532
Brush Seals
Reduce secondary leakage in turbomachinery
Replace labyrinth seals in HP TM (hot side of steam & gas turbines)
Wear and thermal distortions are a reliability problem
Hybrid Brush Seals
Novel improvement over BS. Reduce more leakage and do not
introduce wear or thermal distortion. Allow bi-directional rotation
High Pressure Side Low Pressure Side
Bristle Bed
Pad or shoe
Spring-Lever
Mechanism
Back Plate
*: Close-up courtesy of Advanced Technologies Group, Inc.
Spring Lever
Mechanism
* Close-up courtesy of Advanced
Technologies Group, Inc.Courtesy of Advanced Turbomachinery Group®
Fext x
L Meq
Keq
Ceq
Ks
ss
z
Ls Lf
Fext
x Lf =244 mm
Lf =221 mm
L= 248 mm
Dynamic Load Tests (no shaft rotation)
eq eq eq extM x K x C x F
Equivalent Test System
Fext x
L Meq
Keq
Ceq
Ks
ss
z
Ls Lf
Fext
x Lf =244 mm
Lf =221 mm
L= 248 mm
Harmonic force
& displacements
Impedance Function
Work External
Viscous Dissipation
tixex ti
ext eFF
eqeqeq CiMKx
FZ )( 2
extFW x dt
xFxKE eqeqdis 42
2xCE eqdis
Parameter Identification (no shaft rotation)
ASME DETC2005-84159
DRY
FRICTION &
STRUCTURAL
DAMPING
Frequency [Hz]
Re(
F/X
) [N
/m]
Frequency [Hz]
Re(
F/X
) [N
/m]
Frequency [Hz]
Re(
F/X
) [N
/m]
Frequency [Hz]
Re
(F
/X)
[kN
/m]
0 20 40 60 80 100 120
-400
-300
-200
-100
0
100
200
300
400
Keq – Meqω2
Pr=1.7Pr=1.7
Frequency [Hz]
Re(
F/X
) [N
/m]
Pr=1.7Pr=1.7
Frequency [Hz]
Re(
F/X
) [N
/m]
Pr=3.0Pr=3.0
Frequency [Hz]
Re(
F/X
) [N
/m]
Pr=3.0Pr=3.0
Frequency [Hz]
Re(
F/X
) [N
/m]
Pr=2.4
Pr=2.4
Frequency [Hz]
Re(
F/X
) [N
/m]
Pr=2.4
Pr=2.4
Frequency [Hz]
Re(
F/X
) [N
/m]
Model Test Data
Pr = 1.7
Pr = 2.4
Pr = 3.0
Pr = 1.7
Pr = 2.4
Pr = 3.0
HBS Dynamic Stiffness vs. Frequency
(no shaft rotation)
ModelTESTs
Load = 63 N, frequency: 20-100Hz
Model reproduces
real part of the
impedance under
the given supply
pressure
conditions.
Frequency [Hz]
Re (
F/x
) [k
N/m
]
2eqeq MK
Pressure ratio (Pr = Ps/Pd) = Discharge/Supply
Load = 63 N, frequency 20-110Hz
0 20 40 60 80 100 120
100
1000
10000
Frequency, [Hz]
Lo
g (
Ceq),
[N
-s/m
]
0 20 40 60 80 1000
2000
4000
6000
8000
Pr = 1.7 0 20 40 60 80 1000
2000
4000
6000
8000
Pr = 2.40 20 40 60 80 1000
2000
4000
6000
8000
Pr = 3.0
Test Data Test Data
ΔP +
Equivalent damping
increases slightly with
pressure differential.
Results typical of a
system with dry-friction
& material damping
energy dissipation
HBS Equivalent Viscous Damping vs.
Frequency (no shaft rotation)
x
FKC
eqeq
eq
4
Frequency [Hz]
Lo
g(C
eq)
[N-s
/m]
Viscous Model
Pressure ratio (Pr = Ps/Pd) = Discharge/Supply
Identification of Rotordynamic Force Coefficients
iy
ixx
yyyx
xyxx
yyyx
xyxx
yyyx
xyxx
F
FF
y
x
CC
CC
y
x
KK
KK
y
x
MM
MM
0
Eddy current
sensors
Y
X
Ω
Electromagnetic
Shaker Load Cell
Stinger
Disk
HBS
Imbalance forces (1X=W)
Excitation force
(frequency )
Kxx, Cxx
Kxy, Cxy
Kyx, Cyx
Kyy, Cyy
X
Y
Kxx, Cxx
Kxy, Cxy
Kyx, Cyx
Kyy, Cyy
X
Y
Identification of Rotordynamic Force Coefficients
0 0
0 0 0
xx xy ixxx xx x
xy xx iyxx xx
K K FM Cx x x F
K K FM Cy y y
For periodic force excitation:
Kxx, Cxx
Kxy, Cxy
Kyx, Cyx
Kyy, Cyy
X
Y
Kxx, Cxx
Kxy, Cxy
Kyx, Cyx
Kyy, Cyy
X
Y
tixex
tiyey i t
x xF F e .
xxyxx FyZxZ
0 yZxZ yyyx
EOMS reduce to:
yxiCMKZ ,
2 ,
With impedances:
For centered operation
(axi-symmetry) Zxx = Zyy Zxy = -Zyx
Measured Mode Shapes (one end fixed)
-1
-0.5
0
0.5
1
1.5
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Axial Location [m.]
No
rmali
zed
Dis
pla
cem
en
t
Measured (Nat. Freq. 20 Hz) Prediction (Nat. Freq. ~21 Hz)
Hybrid Brush Seal Rotor/Shaft AssemblyFirst Fixed-Free Mode Shape Plot (one end fixed)
Hybrid Brush Seal Rotor Assembly
Measured Mode Shapes (one end fixed)
-1
-0.5
0
0.5
1
1.5
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Axial Location [m.]
No
rmali
zed
Dis
pla
cem
en
t
Measured (Nat. Freq. 20 Hz) Prediction (Nat. Freq. ~21 Hz)
Hybrid Brush Seal Rotor/Shaft Assembly
Measured Mode Shapes (one end fixed)
-1
-0.5
0
0.5
1
1.5
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Axial Location [m.]
No
rmali
zed
Dis
pla
cem
en
t
Measured - (Nat. Freq. 144 Hz) Prediction - (Nat. Freq. 151.5 Hz)
Hybrid Brush Seal Rotor/Shaft Assembly
Second Fixed-Free Mode Shape Plot (one end fixed) Hybrid Brush Seal Rotor Assembly
Measured Mode Shapes (one end fixed)
-1
-0.5
0
0.5
1
1.5
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Axial Location [m.]
No
rmali
zed
Dis
pla
cem
en
t
Measured - (Nat. Freq. 144 Hz) Prediction - (Nat. Freq. 151.5 Hz)
Hybrid Brush Seal Rotor/Shaft Assembly
Rotor mode shapes
Only first mode excited
in rotor speed range (0-
1200 rpm)
FIRST MODE
SECOND MODE
Effect of rotor speed on rotor-HBS natural frequency
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
0.1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Axial Location, [m]
Sh
aft
Ra
diu
s, [
m]
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
0.1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Axial Location, [m]
Sh
aft
Ra
diu
s, [
m]
Hybrid Brush Seal location
Axial Location, [m]
Roller bearing support
Disk
Shaft
Location of external force
Location of displacement measurements
Sh
aft
Rad
ius
, [m
]
Gyroscopic effects
negligible for test
rotor speeds
(600 and 1,200 rpm
[20 Hz])
Rotor
Speed [RPM]
1st Backward Nat.
Frequency, [Hz]
1st Forward Nat.
Frequency, [Hz]
2nd Forward Nat.
Frequency, [Hz]
3rd Forward Nat.
Frequency, [Hz]
0 30.5 30.5 146 1351
600 29.7 31.4 154 1351
1200 28.8 32.2 163 1351
Axial Location, z [m]
Shaft
Rad
ius [
m]
T=32 Hz
40 40 120 200 280 360 4400
250
500
750
1000
Frequency [Hz]
X -
Dis
pla
ce
me
nt [u
m]
40 40 120 200 280 360 4400
250
500
750
1000
Frequency [Hz]
Y -
Dis
pla
ce
me
nt [u
m]
32 Hz Due to excitation
Synchronous with speed (1X)
32 Hz
Due to excitation
22 N
22 N
Synchronous with speed (1X)
CROSS-Coupling Effects under rotation
For load along X
direction,
rotor principal (X)
motions
>>>cross (Y) motions
3X motions
always small
Load=22 N, 600 rpm
Frequency [Hz]
X-d
ispla
cem
ent
[
m]
Y-d
ispla
cem
ent
[
m]
Frequency [Hz]
0 20 40 60 80400
300
200
100
0
100
200
300
400
Frequency, [Hz]
Re
(Zxx1
), [
kN/m
]
0 20 40 60 80400
300
200
100
0
100
200
300
400
Frequency, [Hz]
Re
(Zxx1
), [
kN/m
]
0 20 40 60 80400
300
200
100
0
100
200
300
400
Frequency, [Hz]
Re
(Zxx1
), [
kN/m
]
0 20 40 60 80400
300
200
100
0
100
200
300
400
Frequency, [Hz]
Re
(Zxx1
), [
kN/m
]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
Test Data
600 rpm, Pr = 1.7
1200 rpm, Pr = 1.7
600 rpm, Pr = 2.4
1200 rpm, Pr = 2.4
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
0 20 40 60 80 1001 10
6
5 105
0
5 105
Test DataModel
Frequency [Hz]
Re
(Zxx1
) [N
/m]
Model
Kxx - Mxx2
Test dynamic stiffness vs. frequency
Load = 22 N, frequency 25-80Hz
)( 22 yx
xFZ x
xx
Model
reproduces the
measured real
part of
impedance.
Little effect of
pressurization
2
xx xxK M
Model
Frequency [Hz]
Re (
Zxx)
[kN
/m]
Pressure ratio (Pr = Ps/Pd) = Discharge/Supply
0 20 40 60 800
50
100
150
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Test Data [Img(F/X)]
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Test Data [Img(F/X)]
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Test Data [Img(F/X)]
Frequency [Hz]
Im(F
/X),
[kN
/m]
0 20 40 60 800
50
100
150
Test Data [Img(F/X)]
Frequency [Hz]
Im(F
/X),
[kN
/m]
FFk DC1
d
k
4 F
1 1.1 Ktip DC1
d
k
2
600 rpm, Pr = 1.7
1200 rpm, Pr = 1.7
600 rpm, Pr = 2.4
1200 rpm, Pr = 2.4
Test Data
Frequency, [Hz]
Im (
Zxx1
), [kN
/m]
Test quadrature stiffness vs. frequency
Load = 22 N, frequency 25-80Hz
Damping is
NOT viscous
Viscous Model
TESTs
Frequency [Hz]
Ima (
Zxx)
[kN
/m]
x
yZZ yyyx Pressure ratio (Pr = Ps/Pd) = Discharge/Supply
Equivalent Viscous Damping (Cxx~Ceq) vs. Frequency
Damping decreases
with frequency, with
little effect of supply
pressure. Minimum
value at test system
natural frequency
(~32 Hz)
Pr=1.7
600 rpm
Pr=2.4
1200 rpm
HBS predicted & test direct stiffness vs. frequency
Frequency 25-100 Hz Predicted HBS stiffness
(Ksxx) drops slightly in
range from 20- 100 Hz.
Tests show nearly constant
Ksxx
Pressure (Pr = Ps/Pd) has
negligible effect on seal
direct stiffness, Ksxx
60
70
80
90
100
110
120
130
140
0 20 40 60 80 100 120
Frequency [Hz]
Stiffness C
oeffic
ients
[kN
/m]
60
70
80
90
100
110
120
130
140
0 20 40 60 80 100 120
Frequency [Hz]
Stiffness C
oeffic
ients
[kN
/m]
600 rpm
1,200 rpm
60
70
80
90
100
110
120
130
140
0 20 40 60 80 100 120
Frequency [Hz]
Stiffness C
oeffic
ients
[kN
/m]
Ksxx = Ksyy, Pr = 1.0
Ksxx = Ksyy, Pr = 1.7
Ksxx = Ksyy, Pr = 2.4
Ksxx = Ksyy, Pr = 1.0
Ksxx = Ksyy, Pr = 1.7
Ksxx = Ksyy, Pr = 2.4
HBS Equivalent Stiffness, Ks HBS Equivalent Stiffness, Ks
HBS Measured Stiffness, Ks
60
70
80
90
100
110
120
130
140
0 20 40 60 80 100 120
Frequency [Hz]
Stiffness C
oeffic
ients
[kN
/m]
Ksxx = Ksyy, Pr = 1.0
Ksxx = Ksyy, Pr = 1.7
Ksxx = Ksyy, Pr = 2.4
Ksxx = Ksyy, Pr = 1.0
Ksxx = Ksyy, Pr = 1.7
Ksxx = Ksyy, Pr = 2.4
HBS Equivalent Stiffness, Ks HBS Equivalent Stiffness, Ks
HBS Measured Stiffness, Ks
Code: XLTPGASBEAR
Frequency [Hz]
Stiffness C
oeffic
ients
[kN
/m]
ASME GT2004-53614
0 20 40 60 804 10
4
2 104
0
2 104
4 104
Zxy=-Zyx (Test Data)Zxy=-Zyx (Model)
Frequency [Hz]
Re
(Zxy)
[N/m
]
0 20 40 60 804 10
4
2 104
0
2 104
4 104
Zxy=-Zyx (Test Data)Zxy=-Zyx (Model)
Frequency [Hz]
Re
(Zxy)
[N/m
]
0 20 40 60 80
4 104
2 104
0
2 104
4 104
Zxy=-Zyx (Test Data)Zxy=-Zyx (Model)
Zxy=Zyx (Test Data)Zxy=Zyx (Model)
Frequency [Hz]
Re
(F/X
) [N
/m]
0 20 40 60 804 10
4
2 104
0
2 104
4 104
Zxy=-Zyx (Test Data)Zxy=-Zyx (Model)
Zxy=Zyx (Test Data)Zxy=Zyx (Model)
Frequency [Hz]
Re
(F/X
) [N
/m]
0 20 40 60 804 10
4
2 104
0
2 104
4 104
Zxy=-Zyx (Test Data)Zxy=-Zyx (Model)
Zxy=Zyx (Test Data)Zxy=Zyx (Model)
Frequency [Hz]
Re
(F/X
) [N
/m]
0 20 40 60 804 10
4
2 104
0
2 104
4 104
Zxy=-Zyx (Test Data)Zxy=-Zyx (Model)
Zxy=Zyx (Test Data)Zxy=Zyx (Model)
Frequency [Hz]
Re
(F/X
) [N
/m]
Model
Test Data
1200 rpm
600 rpm
Pr = 2.4, Zxy =- Zyx
HBS predicted & test cross stiffness vs. frequency
Frequency 25-100 Hz
HBS cross stiffness
(Ksxy) << direct
stiffness (Ksxx)
Pressure (Pr = Ps/Pd) has
negligible effect on seal
cross stiffness, Ksxy
Frequency [Hz]
Stiffness C
oeffic
ient
[N/m
]
yx xx
yZ Z
x
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
]
1200 rpm
Increasing loss factor (
HBS predicted & test damping vs. frequency
Frequency 25-100 Hz
HBS direct damping (Csxx) decreases with excitation frequency. Loss factor
coefficient () models well seal structural (hysteresis) damping
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
] Cxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, CeqCxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, Ceq
1200 rpm
Increasing loss factor (
Pr = 2.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
] Cxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, CeqCxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, Ceq
1200 rpm
Increasing loss factor (
Pr = 1.7
1,200 rpm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Da
mp
ing
Co
eff
icie
nts
[kN
-s/m
]0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Da
mp
ing
Co
eff
icie
nts
[kN
-s/m
]
1200 rpm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
]
1200 rpm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
]
1200 rpm
Increasing loss factor (
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
] Cxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, CeqCxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, Ceq
1200 rpm
Increasing loss factor (
Pr = 1.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Da
mp
ing
Co
eff
icie
nts
[kN
-s/m
] Cxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, CeqCxx = Cyy, = 0.25Cxx = Cyy, = 0.55Equivalent Viscous Damping, Ceq
1200 rpm
Increasing loss factor (
Pr = 2.4
600 rpm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Da
mp
ing
Co
eff
icie
nts
[kN
-s/m
]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Da
mp
ing
Co
eff
icie
nts
[kN
-s/m
]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
Frequency [Hz]
Dam
pin
g C
oeffic
ients
[kN
-s/m
]
Increasing loss factor () Increasing loss factor ()
Pressure ratio (Pr = Ps/Pd) = Discharge/Supply
Conclusions
• A structural loss factor (γ) and a dry friction
coefficient() effectively characterize the energy
dissipation mechanism of a Hybrid Brush Seal (HBS).
• HBS Direct stiffness (Ksxx = Ksyy) decreases minimally
with rotor increasing rotor speed for Pr = 1.7 and 2.4 HBS Cross-coupled stiffness (Ksxy = -Ksyx) is much smaller than the direct
stiffnesss.
• HBS Direct viscous damping coefficients decrease as a
function of increasing excitation frequency.