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ROBUSTNESS OF MODELING OF OUT-OF-SERVICE GAS MECHANICAL FACE SEAL
Itzhak Green Georgia Institute of Technology
Atlanta, Georgia
ROBUSTNESS OF MODELING OF
OUT-OF-SERVICE GAS MECHANICAL
FACE SEAL
Itzhak GreenItzhak Green
Georgia Institute of Technology Georgia Institute of Technology
G. W. Woodruff School of Mechanical EngineeringG. W. Woodruff School of Mechanical Engineering
Atlanta, GA 30332Atlanta, GA 30332--04050405
NASA Seals Workshop Nov 14-15, 2006
___________________________________________
Gas lubricated mechanical face seal are ubiquitous in many high performance applications such as compressors
and gas turbines. The literature contains various analyses of seals having orderly face patterns (radial taper, waves, spiral grooves, etc.). These are useful for design purposes and for performance predictions. However, seals returning from service (or from testing) inevitably contain wear tracks and warped faces that depart from the aforementioned orderly patterns. Questions then arise as to the heat generated at the interface, leakage rates, axial displacement and tilts, minimum film thickness, contact forces, etc. This work describes an analysis of seals that may inherit any (i.e., random) face pattern. A comprehensive computer code is developed, based upon the Newton-Raphson method, which solves for the equilibrium of the axial force and tilting moments that are generated by asperity contact and fluid film effects. A contact mechanics model is incorporated along with a finite volume method that solves the compressible Reynolds equation. Results are presented for a production seal that has sustained a testing cycle.
NASA/CP—2007-214995/VOL1 289
https://ntrs.nasa.gov/search.jsp?R=20080003820 2020-04-09T05:10:48+00:00Z
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
2
Mo
de
lin
g C
ha
lle
ng
es
Mo
de
lin
g C
ha
lle
ng
es
Q.
Q.
Are
models
usefu
l, a
nd u
sefu
l fo
r w
hat?
Are
models
usefu
l, a
nd u
sefu
l fo
r w
hat?
A.
A.
Typic
ally u
sed f
or
desig
n, pre
dic
ting t
rends, etc
.Typic
ally u
sed f
or
desig
n, pre
dic
ting t
rends, etc
.
Q.
Q.
How
H
ow
��Com
ple
teCom
ple
te��
or
or ��R
obust
Robust ��
are
they?
are
they?
A.
A.
Lim
ited b
y a
ssum
ptions (
how
valid a
re t
hey?),
and c
apabilitie
s (
Lim
ited b
y a
ssum
ptions (
how
valid a
re t
hey?),
and c
apabilitie
s (
math
m
ath
m
odels
&
com
ple
xity, num
erical im
ple
menta
tion, and C
PU
tim
e)
models
&
com
ple
xity, num
erical im
ple
menta
tion, and C
PU
tim
e)
Q.
Q.
Can m
odels
be u
sed f
or
postm
ort
em
analy
sis
?Can m
odels
be u
sed f
or
postm
ort
em
analy
sis
?
Faces m
aybe f
lat
upon insta
llation
Faces m
aybe f
lat
upon insta
llation ��
hig
hly
unlikely
hig
hly
unlikely
that
they r
em
ain
as
that
they r
em
ain
as
such.
such.
Cra
cked f
aces/s
haft
s (
they h
appen, but
are
these m
odele
d?).
Cra
cked f
aces/s
haft
s (
they h
appen, but
are
these m
odele
d?).
W
orn
faces (
Worn
faces (�� w
ear
models
wear
models��
are
em
piric
al; f
irst
are
em
piric
al; f
irst --
law
& r
obust
law
& r
obust ��w
ear
models
wear
models��
are
yet
to b
e d
evelo
ped).
are
yet
to b
e d
evelo
ped).
Q.
Q.
How
robust
are
exis
ting m
odels
?H
ow
robust
are
exis
ting m
odels
?
(I)
First
Genera
tion (
cla
ssify,
(I)
First
Genera
tion (
cla
ssify, ��conta
cting,
conta
cting, ����non
non-- c
onta
cting,
conta
cting, ��
etc
.)etc
.)
(II)
Next
Genera
tion (
no c
lassific
ation n
eeded, in
clu
din
g m
ulti
(II)
Next
Genera
tion (
no c
lassific
ation n
eeded, in
clu
din
g m
ulti --eff
ects
)eff
ects
)
NASA/CP—2007-214995/VOL1 290
Flex
ibly
Mou
nted
Rot
or
Flex
ibly
Mou
nted
Rot
or
Face
Sea
l Tes
t R
igFa
ce S
eal T
est
Rig
sha
ft
roto
rstat
or
prox
imity
prob
e
lip s
eal
cont
actin
g se
al
carb
on r
ing
seal
ing
dam
roto
r ch
ambe
r
pres
suriz
ed a
irpr
essu
rized
wat
ersp
ind
le
Par
t IP
art I
IP
art I
II
coni
ng
spac
er
bolt
stat
or
hold
er
stat
or
NASA/CP—2007-214995/VOL1 291
FMR
Mec
hani
cal F
ace
Seal
Tes
t R
ig(P
hoto
grap
h)FM
R M
echa
nica
l Fac
e Se
al T
est
Rig
FMR
Mec
hani
cal F
ace
Seal
Tes
t R
ig(P
hoto
grap
h)(P
hoto
grap
h)
NASA/CP—2007-214995/VOL1 292
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
5
Pro
ng
I:
Re
al
Pro
ng
I:
Re
al --
Tim
e
Tim
e
Dia
gn
osti
cs
Dia
gn
osti
cs
Thre
e indic
ato
rs:
Thre
e indic
ato
rs:
��Tim
e d
om
ain
Tim
e d
om
ain
��pro
be s
ignals
pro
be s
ignals
��Fre
quency d
om
ain
Fre
quency d
om
ain
----
Pow
er
spectr
al
Pow
er
spectr
al
density f
unctions (
FFT)
density f
unctions (
FFT)
��Angula
r orb
it p
lots
Angula
r orb
it p
lots
��seal absolu
te a
nd/o
r seal absolu
te a
nd/o
r
rela
tive m
isalignm
ent,
re
lative m
isalignm
ent,
xxvs.
vs.
yy..
All c
alc
ula
tions a
re p
erf
orm
ed a
nd p
lott
ed
All c
alc
ula
tions a
re p
erf
orm
ed a
nd p
lott
ed
in
in r
ea
lre
al --
tim
e
tim
e (
usin
g a
PC w
ith a
(u
sin
g a
PC w
ith a
dSpace
dSpace
DAQ
board
).D
AQ
board
).
NASA/CP—2007-214995/VOL1 293
00.
050.
10.
150.
2-2
-1.8
-1.6
-1.4
-1.2-1
-0.8
-0.6
x 1
0-4
Tim
e (S
ec)
Amplitude (m)P
roxi
mity
Pro
be S
igna
ls
050
100
150
200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
x 1
0-6
Fre
quen
cy (
Hz)
PSD
Pow
er S
pect
ral D
ensi
ty (
Pro
be S
igna
ls)
-4-3
-2-1
01
23
4
x 10
-3
-4-3-2-101234x
10-3
radi
an
radian
Rot
or A
ngul
ar R
espo
nse
Orb
it
Non
con
tact
ing
Op
erat
ion
(in
Rea
l-T
ime)
Inte
rmit
ten
t Con
tact
ing
Op
erat
ion
(in
Rea
l-T
ime)
00.
050.
10.
150.
2-2
.5
-2.4
-2.3
-2.2
-2.1-2
-1.9
-1.8
-1.7
x 10
-4
Tim
e (S
ec)
Amplitude (m)
Pro
xim
ity P
robe
Sig
nals
050
100
150
200
250
0123456x
10-9
Fre
quen
cy (
Hz)
PSD
Pow
er S
pect
ral D
ensi
ty (
Pro
be S
igna
ls)
46
810
1214
x 10
-4
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
x 10
-3
radi
an
radian
Rot
or A
ngul
ar R
espo
nse
Orb
it
NASA/CP—2007-214995/VOL1 294
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
77
Pro
ng
II:
Se
al
Co
ntr
ol
Pro
ng
II:
Se
al
Co
ntr
ol ��
Co
nta
ct
Co
nta
ct
Re
du
cti
on
/E
lim
ina
tio
nR
ed
ucti
on
/E
lim
ina
tio
n��
Cle
ara
nce c
ontr
ol of
a m
echanic
al fa
ce s
eal is
achie
ved u
sin
g
Cle
ara
nce c
ontr
ol of
a m
echanic
al fa
ce s
eal is
achie
ved u
sin
g
cascade d
ual PI
contr
ollers
with a
nti
cascade d
ual PI
contr
ollers
with a
nti-- w
indup a
cting o
n t
he
win
dup a
cting o
n t
he
variance o
f pro
be s
ignals
.variance o
f pro
be s
ignals
.
��Syste
m identification:
experim
enta
lly (
phenom
enolo
gic
ally)
Syste
m identification:
experim
enta
lly (
phenom
enolo
gic
ally)
dete
rmin
ed s
eal m
odel
dete
rmin
ed s
eal m
odel --
theore
tical m
odel is
not
required.
theore
tical m
odel is
not
required.
��U
sin
g e
ddy c
urr
ent
pro
xim
ity p
robes t
o d
irectly m
easure
seal
Usin
g e
ddy c
urr
ent
pro
xim
ity p
robes t
o d
irectly m
easure
seal
cle
ara
nce a
nd t
ilts
as o
pposed t
o indirect
meth
ods (
such a
s
cle
ara
nce a
nd t
ilts
as o
pposed t
o indirect
meth
ods (
such a
s
usin
g t
herm
ocouple
s t
hat
measure
face t
em
pera
ture
).usin
g t
herm
ocouple
s t
hat
measure
face t
em
pera
ture
).
��The c
ontr
olled s
eal can f
ollow
seal cle
ara
nce s
et
The c
ontr
olled s
eal can f
ollow
seal cle
ara
nce s
et --
poin
t poin
t
changes w
ith m
inim
um
contr
ol eff
ort
, w
hile n
ot
bein
g
changes w
ith m
inim
um
contr
ol eff
ort
, w
hile n
ot
bein
g
aff
ecte
d b
y d
istu
rbances in s
haft
speed a
nd/o
r seale
d w
ate
r aff
ecte
d b
y d
istu
rbances in s
haft
speed a
nd/o
r seale
d w
ate
r
pre
ssure
.pre
ssure
.
NASA/CP—2007-214995/VOL1 295
Set
Poi
nt C
lear
ance
Con
trol
Set
Poi
nt C
lear
ance
Con
trol M
EC
HA
NIC
AL
FAC
E S
EA
LT
EST
RIG
PRO
XIM
ITY
PRO
BE
LO
W P
AS
SFI
LT
ER
CO
NT
RO
L A
LG
OR
ITH
M
(DS1
102
BO
AR
D,
A/D
, DSP
, D/A
)
PER
SO
NA
LC
OM
PU
TE
R
VO
LT
AG
ED
IVID
ER
EL
EC
TR
O-
PNE
UM
AT
ICT
RA
NSD
UC
ER
PRE
SSU
RIZ
ED
AIR
SU
PPL
Y
+
-
D
ESI
RE
DC
LE
AR
AN
CE
01
23
45
67
8
Tim
e (M
in.)
012345678
Clearance (m)
01020304050607080
Air pressure (kPa)
Des
ired
clea
ranc
eA
ctua
l cle
aran
ceA
ir pr
essu
re
20H
z15
Hz
0.20
7Mpa
0.20
7Mpa
20H
z0.
207M
pa0.
241M
pa
20H
z20
Hz
0.24
1Mpa
15H
z0.
241M
pa0.
207M
pa15
Hz
15H
z0.
207M
pa
shaf
t spe
ed
seal
ed w
ater
pre
ssur
e
NASA/CP—2007-214995/VOL1 296
Unc
ontr
olle
d/C
ontr
olle
d Se
alU
ncon
trol
led/
Con
trol
led
Seal
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Tim
e (s
ec.)
0.00
16
0.00
17
0.00
18
0.00
19
0.00
20
0.00
21
0.00
22
0.00
23
0.00
24
0.00
25
Rotor misalignment, r, (rad)
stat
or m
isal
ignm
ent =
2 m
rad
cont
rol o
n(1
st ti
me)
cont
rol o
n(2
nd ti
me)
cont
rol o
ff(1
st ti
me)
cont
rol o
ff(2
ndtim
e)co
ntro
l off
(3rd
tim
e)
cont
rol o
n(3
rd ti
me)
Con
trol
led
Sea
l:�
Rot
or b
ette
r tr
acks
st
ator
mis
alig
nm
ent
�V
irtu
al e
lim
inat
ion
of
hig
her
har
mon
ic
osci
llat
ion
s�
Clo
ser
to c
ircu
lar
orbi
ts,
i.e.,
non
con
tact
ing
oper
atio
n
0.0
01
60
.00
17
0.0
01
80
.00
19
0.0
02
00
.00
21
0.0
02
2
(
rad
)
0.0
00
3
0.0
00
4
0.0
00
5
0.0
00
6
0.0
00
7
0.0
00
8
(rad)
co
ntr
ol
off
, 1
st
tim
ec
on
tro
l o
n,
1s
t ti
me
co
ntr
ol
off
, 2
nd
tim
ec
on
tro
l o
n,
2n
d t
ime
co
ntr
ol
off
, 3
rd t
ime
co
ntr
ol
on
, 3
rd t
ime
co
ntr
ol
off
co
ntr
ol
on
NASA/CP—2007-214995/VOL1 297
Pro
ng I
II:
Pro
ng I
II: C
rack
Det
ecti
on in
C
rack
Det
ecti
on in
Se
al/R
otor
Dri
ving
Sha
ft (
Seal
Se
al/R
otor
Dri
ving
Sha
ft (
Seal
A
bsen
t)A
bsen
t)
NASA/CP—2007-214995/VOL1 298
Mod
elin
gM
odel
ing
C
rack
ed R
otor
s
Cra
ck M
odel
ing
C
rack
In
dic
ator
s
M
eth
ods
of D
etec
tion
A
nal
ytic
al W
ork
-P
art I
(G
reen
an
d C
asey
, 200
5)
E
xper
imen
tal W
ork-
Par
t II
X
Y
NASA/CP—2007-214995/VOL1 299
Supe
rcri
tica
l 2X
Com
pone
ntSu
perc
riti
cal 2
X C
ompo
nent
Th
eory Exp
er.
Exp
erim
enta
l Orb
its
at
vari
ous
crac
k d
epth
s
NASA/CP—2007-214995/VOL1 300
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
13
Ro
bu
st
Mo
de
lin
g
Ro
bu
st
Mo
de
lin
g
Ob
jecti
ve
sO
bje
cti
ve
s
Robust
modeling s
hould
addre
ss t
hese issues:
Robust
modeling s
hould
addre
ss t
hese issues:
--D
ynam
ics (
hig
h s
peeds, la
rge m
asses
Dynam
ics (
hig
h s
peeds, la
rge m
asses --
> inert
ia e
ffects
)>
inert
ia e
ffects
)
----sta
bility,
transie
nts
response, ste
ady
sta
bility,
transie
nts
response, ste
ady-- s
tate
:sta
te:
mis
alignm
ents
, secondary
seals
and a
nti
mis
alignm
ents
, secondary
seals
and a
nti--
rota
tion p
ins (
Gre
en (
1985, 2006))
rota
tion p
ins (
Gre
en (
1985, 2006))
----couple
d r
oto
rdynam
ics? (
syste
ms a
ppro
ach)
couple
d r
oto
rdynam
ics? (
syste
ms a
ppro
ach)
--Asperity
Conta
ct
Asperity
Conta
ct
----m
echanic
al (
mechanic
al ( ��
dry
dry��)
fric
tion in s
lidin
g)
fric
tion in s
lidin
g
----m
echanic
al lo
ad s
upport
and d
efo
rmation (
EP)
mechanic
al lo
ad s
upport
and d
efo
rmation (
EP)
--M
echanic
al D
efo
rmations (
Pre
ssure
)M
echanic
al D
efo
rmations (
Pre
ssure
)
--Therm
al D
efo
rmations (
vis
cous a
nd d
ry f
riction, TEI)
Therm
al D
efo
rmations (
vis
cous a
nd d
ry f
riction, TEI)
--W
ear
Wear
--Face p
att
ern
s (
lift
Face p
att
ern
s (
lift
-- off
seals
, ty
pic
ally f
or
com
pre
ssib
le s
eals
)off
seals
, ty
pic
ally f
or
com
pre
ssib
le s
eals
)
NASA/CP—2007-214995/VOL1 301
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
14
To
de
ve
lop
a (
nu
me
ric
al)
pro
ce
du
re
T
o d
eve
lop
a (
nu
me
ric
al)
pro
ce
du
re
wh
ere
th
e s
olu
tio
n i
nclu
de
s m
ult
iw
he
re
th
e s
olu
tio
n i
nclu
de
s m
ult
i --
co
up
led
ph
en
om
en
a (
e.g
., t
he
co
up
led
ph
en
om
en
a (
e.g
., t
he
Re
yn
old
s a
nd
en
erg
y
Re
yn
old
s a
nd
en
erg
y E
qs
Eq
s.,
th
e E
OM
, .,
th
e E
OM
,
co
nta
ct
me
ch
an
ics,
we
ar m
od
els
).
co
nta
ct
me
ch
an
ics,
we
ar m
od
els
).
Th
e s
olu
tio
n m
ust
be
T
he
so
luti
on
mu
st
be
sim
ultaneous
sim
ultaneous
in
in
all
th
e d
eg
re
es o
f fr
ee
do
m.
all
th
e d
eg
re
es o
f fr
ee
do
m.
Obj
ecti
ves
(con
t.)
NASA/CP—2007-214995/VOL1 302
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
15
Fla
t/co
ne
d f
ace
Fla
t/co
ne
d f
ace
In
ward
/Outw
ard
Flo
wIn
ward
/Outw
ard
Flo
w
NASA/CP—2007-214995/VOL1 303
/
ref
t/
NASA/CP—2007-214995/VOL1 304
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
17
Ou
tO
ut--o
fo
f --S
ervic
e f
ace
sS
ervic
e f
ace
s**
--w
ea
r?
we
ar?
--th
erm
al/
me
ch
an
ica
l w
arp
ing
?th
erm
al/
me
ch
an
ica
l w
arp
ing
?
____
____
____
____
____
____
____
____
____
____
____
____
* G
reen
an
d A
rtil
es(2
006)
, man
usc
rip
t in
pre
par
atio
n
NASA/CP—2007-214995/VOL1 305
seco
ndar
y se
al
sprin
g
shaf
t
hous
ing
stat
or
roto
r
Fac
e p
atte
rn (
wav
es,
gro
ove
s, w
ear)
Sche
mat
ic o
f N
onco
ntac
ting
Mec
hani
cal F
ace
Seal
wit
h Fl
exib
ly M
ount
ed S
tato
r
NASA/CP—2007-214995/VOL1 306
Fin
ite
Ele
men
t D
iscr
etiz
atio
n(F
EM
)
Ù
W
TÖ
ph
3
p
6µu
ph
W
T1
2µ
(p
h)
t
dÙ
0
Dis
cret
ize
dom
ain
into
sm
all f
init
e el
emen
ts:
e
r i
e
14
8
32
5
r o
e
e
n
n
4
3 21
69
6
7
e
e
5
7
89
n e
e
x
y
Pola
r co
ordi
nate
dis
cret
izat
ion
Car
tesi
an c
oord
inat
e di
scre
tizat
ion
x
y
U
r
p(î
,ç)
9
i1
Ni(î
,ç)
pi
p
(î,ç
)
î
9 i1
Ni,î
(î,ç
)p
i
p
(î,ç
)
ç
9
i1
Ni,ç
(î,ç
)p
i
Mul
tiply
ing
RE
by
a w
eigh
t fac
tor
WT
and
inte
grat
ion
by p
arts
giv
es th
e w
eak
form
:
NASA/CP—2007-214995/VOL1 307
Fin
ite
Vol
ume
Dis
cret
izat
ion
(FV
M)
Ã
Öp
h3
p
6µu
ph
n
dÃ
Ù
12µ
p
h
t
12µ
h
p
t
dÙ
App
ly G
reen�s
theo
rem
to R
E -
repr
esen
ts m
ass
cons
erva
tion
ove
r th
e do
mai
n
Dis
cret
ize
the
dom
ain
into
sm
all f
inite
vol
umes
:
CW
E
SN
Gro
ove
Lan
d
Fini
te V
olum
e G
roov
e/R
idge
Bou
ndar
yn
1-
n
e
s
1-
s
r
r
v
v
r
CW
E
SN
x
y
y
y
U
Fini
te V
olum
e
v
x
v
Pol
ar c
oord
inat
e fi
nite
vol
ume
disc
reti
zatio
nC
arte
sian
coo
rdin
ate
fini
te v
olum
e di
scre
tizat
ion
s
e
n
w
x
NASA/CP—2007-214995/VOL1 308
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
21
In
co
mp
re
ssib
le F
low
In
co
mp
re
ssib
le F
low
Issu
es:
-Fl
ow f
acto
rs (
Pat
ir&
Cha
ng)
-C
avit
atio
n (E
lrod
, JFO
)
-St
arva
tion
(?)
(ca
n be
an
issu
e in
lo
w p
ress
ure
sea
ls)
NASA/CP—2007-214995/VOL1 309
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
22
Co
mp
re
ssib
le F
low
C
om
pre
ssib
le F
low
��
He
rrin
gb
on
e w
avy s
ea
l (w
/o
H
errin
gb
on
e w
avy s
ea
l (w
/o
an
d w
/ f
ace
de
f.)
an
d w
/ f
ace
de
f.)
NASA/CP—2007-214995/VOL1 310
EP
Con
tact
Loa
d Su
ppor
tE
P C
onta
ct L
oad
Supp
ort
(Jac
kson
& G
reen
, 200
5)(J
acks
on &
Gre
en, 2
005)
**
01.
9t
3
/2*
*FP
**
t
55
**
*3
/2*
*12
94
11
exp
()
1ex
p4
25G
Fy
HP
CS
�Sta
tistically t
his
form
ula
tion d
iffe
rs f
rom
the F
EM
data
for
all f
ive m
ate
rials
by a
n a
vera
ge e
rror
of
0.9
4%
and a
maxim
um
of
3.5
%.
�Found t
o b
e v
alid n
ot
only
for
ste
els
, but
als
o f
or
cupper,
alu
min
um
, and
oth
er
meta
llic
mate
rials
(Q
uic
ksall,
Jackson a
nd G
reen, 2004).
NASA/CP—2007-214995/VOL1 311
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
24
Ro
ug
h S
urfa
ce
s
Ro
ug
h S
urfa
ce
s -
---
Sta
tisti
ca
l S
tati
sti
ca
l
Mo
de
lM
od
el
G
reen
woo
d an
d W
illia
mso
n (1
966)
fo
rmul
ated
the
stat
istic
al
mod
el u
sing
Her
tz c
onta
ct.
T
he in
tegr
als
are
eval
uate
d us
ing
Gau
ss-
Lege
ndre
qua
drat
ure.
Ja
ckso
n &
Gre
en (
2005
)
d
R
yz
s
hm
ean
of a
sper
ity h
eigh
t
mea
n of
sur
face
hei
ght
NASA/CP—2007-214995/VOL1 312
{ÿp}
{
R}
Sÿp
R
Kin
etic
equ
atio
ns (
incl
udin
g ti
me-
depe
nden
t the
rmal
eff
ects
):
+
Lub
rica
tion
equ
atio
ns:
or
=F
EM
:[A
(t,ö
)]{ÿ ö
}
{R(t
,ö)}
FV
M:
{ÿ ö
}
{R(t
,ö)}
Cou
pled
set
of
firs
t-or
der
OD
Es:
1) S
yste
mat
ic c
oupl
ing
of k
inet
ican
d lu
bric
atio
n eq
uati
ons
2) S
imul
tane
ous
solu
tion
usi
ngnu
mer
ical
OD
E s
olve
r
Subs
yste
m C
oupl
ing
2
2
/
/ /2
/
//
/
sZfZ
cls
sxfx
ss s
s
syfy
ss
ref
ref
rre
f
FF
Fm
ZZ
ZM
MI
tM
MI
hh
NASA/CP—2007-214995/VOL1 313
Lan
d
Gro
ove
r
r i
r o
p i
g
Sec
tion
B-B
Lan
dG
roov
e
op B
jr
Y
X
Sea
ling
Dam
wl
wg
Dir
ectio
n of
Mat
ing
Fac
e R
otat
ion
Sta
tor
Rot
or
Y Y
X
Y
X
0C
Sta
tor
Rot
or
X
sx
sy
rx
ry
r
h
s
r
sz
rz
Z r
t
Gro
oves
unde
rnea
th
B
Spir
al G
roov
e �
Loa
d Su
ppor
t in
Com
pres
sibl
e F
low
3 de
gree
s of
fre
edom
:
Acc
ordi
ng to
line
ariz
edga
s fi
lm p
rope
rtie
s,th
e ax
ial m
ode
is d
ecou
pled
fro
m th
e ti
lt m
odes
:
k f,Z0
0
0k m
X,ã X
k mX
,ãY
0k m
Y,ã
Xk m
Y,ã
Y
k f,Zk f,ã
Xk f,ã Y
k mX
,Zk m
X,ã
Xk m
X,ã
Y
k mY,Z
k mY,ã
Xk m
Y,ã
Y
ãsã
Xe X
ã
Ye Y
Tilt
s ar
e sm
all,
so tr
eate
d as
vec
tor
tilts
:
NASA/CP—2007-214995/VOL1 314
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
27
Sp
ira
l G
ro
ove
(e
xa
mp
le)
Sp
ira
l G
ro
ove
(e
xa
mp
le)
NASA/CP—2007-214995/VOL1 315
Axi
al F
orce
Fre
quen
cy R
espo
nses
for
Mec
hani
cal F
ace
Seal
102
103
104
105
·
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
G f, Z
=
125
6.6
rad/
s
= 1
675.
5 ra
d/s
=
209
4.4
rad/
s
= 2
513.
3 ra
d/s
=
293
2.2
rad/
s
Sto
rage
Mod
ulus
- R
eal P
art
Loss
Mod
ulus
- Im
agin
ary
Par
t
NASA/CP—2007-214995/VOL1 316
Dir
ect
Mom
ent
Fre
quen
cy R
espo
nses
for
Mec
hani
cal F
ace
Seal
102
103
104
105
·
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
G mX, X , G mY, Y
=
125
6.6
rad/
s
= 1
675.
5 ra
d/s
=
209
4.4
rad/
s
= 2
513.
3 ra
d/s
=
293
2.2
rad/
s
Sto
rage
Mod
ulus
- R
eal P
art
Loss
Mod
ulus
- Im
agin
ary
Par
t
NASA/CP—2007-214995/VOL1 317
Cro
ss-C
oupl
ed M
omen
t F
requ
ency
Res
pons
es f
or M
echa
nica
l Fac
e Se
al
102
103
104
105
·
-0.0
8
-0.0
6
-0.0
4
-0.0
2
0.00
0.02
0.04
G mY, X , - G mX, Y
=
125
6.6
rad/
s
= 1
675.
5 ra
d/s
=
209
4.4
rad/
s
= 2
513.
3 ra
d/s
=
293
2.2
rad/
s
Sto
rage
Mod
ulus
- R
eal P
art
Loss
Mod
ulus
- Im
agin
ary
Par
t
NASA/CP—2007-214995/VOL1 318
m.
Z̈
k f,Z,g
Z
k sZZ
d
sZÿ Z
I tã̈
X
k mX
,ãX,gã
Xã
rco
s(Ù
t)
k sãã
X
dsãÿã
X
k mX
,ãY,gã
Yã
rsi
n(Ù
t)
MX
i
I tã̈
Y
k mY
,ãX,gã X
ã
rco
s(Ù
t)
k mY
,ãY,gã
Yã
rsi
n(Ù
t)
k sãã
Y
dsãÿã
Y
shaf
t
roto
r
stat
or
ã rã
m
MX
i=
ãm·k
sã
Stat
ic s
tato
r m
isal
ignm
ent p
rovi
des
cons
tant
mom
ent a
bout
Xax
is
Z
Y X
Rot
or r
unou
tan
d st
atic
sta
tor
mis
alig
nmen
t
Equ
atio
ns o
f m
otio
n w
ith p
seud
o sp
ring
s re
pres
enti
ng th
e ga
s fi
lm s
tiff
ness
(Axi
al m
ode
deco
uple
d fr
om th
e ti
lt m
odes
:
NASA/CP—2007-214995/VOL1 319
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
rel · ro /C0
Dire
ct N
umer
ical
Sim
ulat
ion
ãre
l
ãr m
ax
0.1
35C
ompa
riso
n of
Sol
utio
ns f
or T
rans
mis
sibi
lity
Cor
resp
onde
nce
Prin
cipl
e:
ãre
l
ãr m
ax
0.1
44
Dir
ect N
umer
ical
Sim
ulat
ion:
r o=6.
0 m
m
r j=5.
16 m
mr i=
4.80
mm
C0=
6.0 ì
m
Ù=
2094
.4 r
ad/s
µ=
1.8
(10)
-5N·s
/m2
Pi=
1.0
(10)
5Pa
Po=
2.0
(10)
5Pa
m* =
1.0
kgI t* =
1.8
(10)
-3kg·m
2N
g=12
á=
160
deg
â=
0.5
ä=
12 (
10)-6
mk sZ
=5.
0 (1
0)5
N/m
d sZ=
300.
0 N·s
/mk sã
=90
0.0
N·m
/rad
d sã=
0.54
N·m·s
/rad
ã r=
0.2
mra
dã m
= 0
.5 m
rad
NASA/CP—2007-214995/VOL1 320
Tra
nsi
ent
op
erat
ion
co
nd
itio
ns
wh
ere
Vis
a d
esir
edst
ead
y-st
ate
valu
e
{}
{,
,}
ri
oV
por
p
1
3
1
12
22
33
2
00,
0
1t t
ft
tt
fV
tt
fV
tt
t
tt
fV
tt
tt
t
t 1
V
t 2t 3
NASA/CP—2007-214995/VOL1 321
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
gate
ch.e
du
gre
en@
gate
ch.e
du
34
NASA/CP—2007-214995/VOL1 322
NASA S
eals
Work
shop
NASA S
eals
Work
shop
Novem
ber
14
Novem
ber
14-- 1
5, 2006
15, 2006
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Dr.
Itz
hak G
reen, G
A T
ech, M
echanic
al
Engin
eering, Atlanta
GA 3
0332
Engin
eering, Atlanta
GA 3
0332
gre
en@
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