Laby in h seal design o space applica ions
Jose Pouza
a,*
, Da id Kos al
a
, La s-G¨
o an Wes e be g
b
, E ik Nybe g
c
, I an K upka
a
a
Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, B no, 61669, Czech Republic
b
Di ision o Fluid and Expe imen al Mechanics, Luleå Uni e si y o Technology, SE-971 87, Luleå, Sweden
c
Di ision o Machine Elemen s, Luleå Uni e si y o Technology, SE-971 87, Luleå, Sweden
ARTICLE INFO
Handling Edi o : P o . L.G. Hul man
Keywo ds:
Vacuum e apo a ion
Molecula low
Laby in h seals
Con amina ion
Liquid lub ican s
Space ibology
ABSTRACT
Laby in h seals, ex ensi ely used in space applica ions, se e o p e en he loss o liquid lub ican s and shield
sa elli e subsys ems om con amina ion. These seals a e essen ial o he eliable unc ioning o bea ings and o
p o ec ing sa elli e subsys ems om con amina ion. This s udy compa es analy ical p edic ions o lub ican loss
agains expe imen al measu emen s and compu e simula ions o op imize laby in h seal con igu a ions.
Analy ical models end o o e es ima e mass loss by 5–8 imes compa ed o expe imen al da a, indica ing limi ed
eliabili y o complex seal geome ies. Simula ions using MolFlow+and COMSOL Mul iphysics align closely
wi h expe imen al esul s, p o iding accu a e mass loss p edic ions. Key indings highligh ha laby in h leng h,
wid h, and su ace oughness a e c i ical ac o s in minimizing e apo a i e mass loss. No ably, s epped laby in h
seals wi h elie g oo es and op imized s ep posi ioning e ec i ely educe molecula beaming e ec s and
imp o e sealing pe o mance compa ed o s aigh geome ies. E ec i e sealing no only educes mission ailu es
bu also helps o minimize space deb is, he eby p omo ing sa e sa elli e missions.
Abb e ia ions and Symbols
bLaby in h gap wid h [mm] P
i
Inle p essu e [Pa]
d, d
1,2
Diame e o annula seal [mm] P
o
Ou le p essu e [Pa]
ESTL Eu opean Space T ibology
Labo a o y
QFlow a e [mba ⋅mm
3
/s]
ETR E apo a ion Tes Rig Q
m
Mass loss [g/s]
Kn Knudsen numbe [−] Ci cula a c adius [mm]
L, L
1,2,3
Laby in h pa h leng h [mm] Ra A e age oughness [
μ
m]
lRecess dep h [mm] Sa A i hme ic mean heigh
[
μ
m]
λMean ee pa h [mm] Sd De eloped in e acial a ea
a io [%]
MLub ican mola mass [g/mol] Sq Squa ed mean heigh [
μ
m]
N
0
, N Numbe o molecules (inle ,
ou le ) [−]
TAbsolu e empe a u e [K]
PFPE Pe luo opolye he TP T ansmission p obabili y
[−]
PFluid apo p essu e [ o ] A e age molecula
eloci y [m/s]
1. In oduc ion
Space echnology ope a es unde demanding condi ions, whe e
mechanical componen s o en lack edundancy due o weigh and size
limi a ions, hus posing a isk o sa elli e ailu e i mal unc ions occu
du ing a mission. T ibological ailu es, esul ing om inadequa e liquid
lub ica ion, such as lub ican c eep [1,2], he mo-ca aly ic deg ada ion
[3], and acuum e apo a ion [4–6], a e p ima y con ibu o s o mission
ailu es.
The e is a g owing po en ial o u ilizing g eases and base oils in
space applica ions, coupled wi h a need o ex end hei se ice li e [7].
Howe e , hei u ili y is limi ed by ex eme empe a u es and acuum
e apo a ion, which pose isks o b eakdown and con amina ion [5,8,9].
High empe a u es can induce molecula decomposi ion, while low
empe a u es lead o undesi able iscosi y inc eases [5]. Vacuum
e apo a ion occu s when he ambien acuum p essu e eaches he
subs ance apo p essu e [10–12], exace ba ing challenges by causing
con ac d ying and po en ial con amina ion [8,9], ul ima ely jeopa d-
izing subsys em pe o mance o leading o comple e ailu e. This
conce n is compounded by he inclusion o delica e op ical elemen s in
scien i ic missions [13].
In space applica ions, mechanisms con aining liquid lub ican s a e
pa ially enclosed [14], wi h lub ican s shielded om he open en i-
onmen using non-con ac laby in h seals. These seals inco po a e
na ow pa hways s a egically posi ioned be ween inne and ou e
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (J. Pouza ).
Con en s lis s a ailable a ScienceDi ec
Vacuum
jou nal homepage: www.else ie .com/loca e/ acuum
h ps://doi.o g/10.1016/j. acuum.2024.113882
Recei ed 12 Augus 2024; Recei ed in e ised o m 30 Oc obe 2024; Accep ed 24 No embe 2024
Vacuum 232 (2025) 113882
A ailable online 26 No embe 2024
0042-207X/© 2024 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license (
h p://c ea i ecommons.o g/licenses/by/4.0/ ).
o a ing pa s o mechanisms [12,14,15]. The hickness o he laby in h
gap is a c i ical pa ame e , balancing sa e mechanism ope a ion agains
low es ic ion. Cu en esea ch o e looks he indi idual e ec s o
laby in h geome y and su ace opog aphy op imiza ion on educing
liquid lub ican loss [12,16,17]. Fu he in es iga ion is needed o ully
unde s and and op imize hese c ucial componen s.
This s udy examines he pe o mance o laby in h seals in acuum
en i onmen s, aiming o unde s and and enhance hei e ec i eness. By
in eg a ing analy ical models, simula ion, and expe imen al alida ion,
he esea ch o e s comp ehensi e insigh s in o laby in h seal beha io
unde a ying condi ions. Addi ionally, he s udy explo es he impac o
su ace opog aphy on lub ican loss and add esses he molecula
beaming e ec in na ow passages [18,19]. These indings a e c ucial o
op imizing laby in h seal design o minimize lub ican loss and
con amina ion. By p e en ing ibological ailu es and con amina ion
associa ed wi h liquid lub ican e apo a ion, he likelihood o mission
ailu es is signi ican ly educed, hus dec easing economic and en i-
onmen al p oduc ion impac s and mi iga ing o bi al pollu ion—a
h ea o cu en and u u e space en u es [20].
2. Ma e ial and me hods
2.1. Expe imen al measu emen s
Expe imen al measu emen s a e conduc ed o ob ain eal-wo ld da a
ega ding he pe o mance o he laby in h seals. These empi ical esul s
se e as a c ucial benchma k o alida ing he accu acy o he analy ical
and simula ion ou comes and assessing he p ac ical applicabili y o he
modelled pa ame e s.
2.1.1. E apo a ion es ig
Fo he expe imen al measu emen o lub ican loss due o acuum
e apo a ion, he modi ied E apo a ion Tes Rig (ETR) equipmen [6] is
employed; see Fig. 1, de eloped speci ically o con inuous measu e-
men o mass loss esul ing om e apo a ion unde acuum condi ions.
The se up is based on a balance-scale mechanism, comp ising a pi o ed
scale beam wi h a laby in h seal pla o m on one side and coun e -
weigh s on he opposi e side. The sys em is equipped wi h sha p wedges,
allowing single-axis o a ion, and is balanced on a suppo beam wi hin
a acuum chambe . A capaci i e p oximi y senso , ixed o he chambe
lange, measu es he displacemen o he scale poin e du ing lub ican
e apo a ion. This displacemen is used o calcula e mass loss o e ime,
accoun ing o a ia ions in p essu e and empe a u e. The ETR ope a es
unde con olled acuum condi ions wi h ex e nally applied hea ing.
The expe imen al es ing begins a e empe a u e s abiliza ion, which is
achie ed by main aining cons an he mo- acuum condi ions o 24 h.
The con e sion a io be ween he p oximi y senso ’s displacemen
signal and mass loss is 10.0
μ
m pe 1.0 mg, wi h a weighing p ecision o
±0.04 mg unde he mo- acuum condi ions.
The laby in h seal pla o m is modula , acili a ing he es ing o
a ious laby in h seal geome ies. I consis s o a main pan a ached o
he ETR, housing he liquid lub ican ese oi , and accommoda ing
a ious laby in h con igu a ions (Fig. 2) o es ing unde high acuum
and ele a ed empe a u es. All componen s o he laby in h seal pla -
o m (main pan, laby in h seals) a e made o aluminum alloy 6061.
2.1.2. Tes sample
The E apo a ion es ig se up ensu es p ecise e alua ion o laby in h
seal pe o mance. The chosen geome ies o expe imen al es ing a e
selec ed o be compa able wi h he simula ion and analy ical models.
Th ee speci ic geome ies in Fig. 3 a e implemen ed du ing he expe i-
men al es ing, wi h dimensions speci ied in Table 1.
In addi ion o he o e all geome ies, he “LONG”laby in h seal was
p epa ed in wo a ia ions, each wi h di e en su ace oughness, o
allow u he e alua ion ( e e o Chap e 3.2). All laby in h seal sam-
ples we e es ed wi h he same oil o ensu e consis ency in assessing
hei e ec i eness.
In his s udy, a low-ou gassing oil, FOMBLIN Y LVAC 25/6 [35], was
selec ed o expe imen al es ing due o i s acuum compa ibili y; see
Table 2. The lub ican es sample is applied o he annulus ese oi o
he laby in h seal es ig pan (Fig. 2). The amoun o lub ican applied
mus be su icien o achie e an op imal ilm heigh co e ing he en i e
ese oi a ea o p e en local d ying. Howe e , excessi e lub ican may
lead o undesi ed c eep h ough he seal, po en ially comp omising he
expe imen al e alua ion. P io o expe imen a ion, a se ies o p e- es s
we e conduc ed o assess he he mal condi ions o he se up and e al-
ua e c eep in ensi y.
2.1.3. Expe imen al p ocedu e
Du ing he expe imen al measu emen s, only one speci ic laby in h
seal geome y can be e alua ed a a ime. Fi s , he sample oil is injec ed
in o he laby in h seal ese oi in an amoun speci ied in Table 2. The
chosen laby in h seal geome y (SHORT, LONG, o STEP) is hen
moun ed on o he ese oi using sc ews, ensu ing a secu e i o
main ain he laby in h gap condi ions h oughou he es . This laby-
in h assembly is subsequen ly a ached o he E apo a ion Tes Rig
(ETR), and expe imen al es ing unde acuum condi ions is ini ia ed.
To acili a e he acuum e apo a ion o he oil, expe imen s a e
conduc ed a ele a ed empe a u es. Inc eased empe a u es aise he
oil’s apo p essu e, p omo ing i s e apo a ion. As he oil e apo a es,
he ETR balance sys em compensa es o he mass loss by il ing. This il
is measu ed by a p oximi y senso , which ansla es he il da a in o
mass loss using calib a ed pa ame e s.
All subsequen expe imen s a e conduc ed unde consis en condi-
ions, including a hea ing empe a u e o 170 ◦C, a se poin empe a u e
o he laby in h seals o 90 ◦C (±5◦C), a se poin acuum p essu e o
2E-5 mba , and a du a ion inside he acuum chambe o 24 h. These
con olled pa ame e s ensu e he ep oducibili y o he esul s.
2.2. Analy ical model
In ou expe imen s, e apo a ed lub ican molecules a el in he
molecula low egime, cha ac e ized by ex emely low gas densi ies and
long mean ee pa hs be ween molecules, as desc ibed by he Knudsen
numbe [21,22].
Kn =λ
L,(1)
Fig. 1. E apo a ion es ig (ETR) wi h laby in h seal pla o m.
J. Pouza e al. Vacuum 232 (2025) 113882
2
whe e λis he mean ee pa h o he gas molecules, and Lis a cha ac-
e is ic leng h o he sys em, such as he chambe diame e o leng h [16,
23]. Lowe Knudsen numbe s (Kn <0.01) indica e iscous o con inuum
low, whe e in e molecula collisions domina e. As he Knudsen numbe
inc eases abo e 0.5, in e molecula collisions become a e, and su ace
in e ac ions p e ail [16,23,24]. Unde he acuum condi ions used
du ing hese expe imen s, wi h p essu es a ound 2E−5 mba , and
empe a u es a ound 81 ◦C he Knudsen numbe (Kn) anges om
app oxima ely 11 o 13. This ange places he sys em i mly in he ee
molecula low egime (Kn >0.5), whe e molecula mo emen is la gely
in luenced by in e ac ions wi h he chambe su aces a he han colli-
sions be ween molecules [16,23,24]. Wi hin he laby in h, he mole-
cules empo a ily adhe e o su aces be o e dispe sing, losing hei
p e ious di ec ion and eloci y wi h each in e ac ion [23].
E alua ing e apo a ion a es o liquid lub ican s in space equi es
analy ical and expe imen al me hods [12,15,25], wi h analy ical models
se ing as i al ools o p edic ing lub ican loss due o acuum e ap-
o a ion [15,26–28]. To calcula e he low a e o leakage h ough lab-
y in h seals analy ically, he laby in h o iginal geome y con igu a ion
mus unde go a con e sion o a linea ized s a e, whe ein i s diame e ,
gap wid h and leng h dimensions a e equi alen ly ep esen ed [15].
This linea ized laby in h ep esen a ion acili a es he calcula ion o he
low a e using a combina ion o p essu e g adien , molecule ans-
mission p obabili y h ough he laby in h, and a e age molecula e-
loci y acco ding o
Q=(Pi−Po)
π
db
(4+1,5
b).(2)
Based on a de ailed analysis o expe imen al da a om ESTL, a
e inemen o Eq. (2)has been p oposed [12] o o e he mos accu a e
co ela ion wi h eal-wo ld es s cu en ly a ailable, se ing as an
exp ession o he low o molecules. Impo an ly, his e inemen
main ains consis ency wi h he p e ious app oach ega ding he p ocess
o simpli ying analy ical compu a ions [15], such ha he o e all
me hodology emains cohe en and p ac ical o implemen a ion in
ele an applica ions
Qm=0,0436 •
P
π
db(M
T)0,5
1+0,375 •L
b
.(3)
The ESTL model p esen ed in Eq. (3)se es as he mos eliable
analy ical ins umen s o p edic ing he quan i y o lub ican molecules
leaking h ough he laby in h seal. Howe e , hese analy ical models
exhibi inhe en limi a ions [12,15,27] mainly due o hei simpli ied
geome ical ep esen a ions and possibly due o lub ican he mal his-
o y and inaccu a e apo p essu e de e mina ion [17,29,30]. Compa -
ison wi h expe imen ally measu ed esul s indica es o e es ima ion o
he analy ical e apo a ion a es p edic ion by an o de o magni ude
[11,12]. Manu ac u e s ypically de e mine apo p essu e using he
Knudsen e usion me hod, which lacks s anda diza ion and po en ially
yields inaccu acies [11,31]. P oposed co ec ion ac o s aim o align
analy ical p edic ions wi h eal-wo ld scena ios, elying on expe i-
men al da a [11,29].
Despi e widesp ead adop ion, analy ical models equen ly all sho
in accu a ely p edic ing e apo a ed molecule low a es [6,12].
Add essing hese dispa i ies may in ol e employing nume ical simula-
ion ools, such as Mon e Ca lo andom sampling unc ions [30,32,33].
Mon e Ca lo simula ion s ands as a obus compu a ional echnique
c ucial o acqui ing nume ical app oxima ions o molecula low
beha io wi hin complex sys ems o p ocesses [19,34].
Fo p edic ing he mass o lub ican e apo a ion h ough speci ic
laby in h seal geome ies, he ESTL model p esen ed in Eq. (3)is ypi-
cally u ilized, despi e i s demons a ed lack o accu acy. This analy ical
model will be employed o compa e he p edic ed e apo a ion a es wi h
simula ion and expe imen al measu emen s. This compa a i e app oach
aims o highligh he disc epancies be ween he analy ical p edic ions
and he mo e p ecise da a ob ained om simula ions and expe imen al
es s, he eby acili a ing imp o emen s in he p edic i e accu acy o
lub ican e apo a ion a es o space applica ions.
2.3. Modeling and simula ion
This phase ocuses on de eloping ma hema ical models o accu a ely
simula e molecula low wi hin laby in h seal geome ies. The inpu
Fig. 2. Laby in h seal pla o m se up and assembly b eakdown.
J. Pouza e al. Vacuum 232 (2025) 113882
3
da a o he simula ions and analy ical models a e de i ed om
bounda y condi ions measu ed du ing he expe imen al phase. These
include he empe a u e o he laby in h seal, he acuum chambe
p essu e, and he pa ame e s o he e apo a ed oil; see Table 2. Since he
p essu e inside he laby in h seal ese oi (a he laby in h seal inle )
canno be measu ed di ec ly, i is assumed o be equal o he oil apo
p essu e in he simula ion models.
Th ough hese simula ions, c i ical pa ame e s in luencing seal pe -
o mance a e iden i ied and comp ehensi ely desc ibed. This se es as
he ounda ion o unde s anding he dependence be ween a ious
laby in h geome y ac o s and hei impac on seal e ec i eness in
p e en ing molecula low. To simula e space condi ions and molecula
low egimes wi hin laby in h seal geome ies, wo ep esen a i e so -
wa e ools a e u ilized.
2.3.1. MolFlow+
MolFlow +[36] is employed o molecula low simula ion and
e alua ion o laby in h seal geome y pa ame e s. I is p ima ily used o
p essu e dis ibu ion calcula ions wi hin complex geome ies unde
ul a-high acuum condi ions [36,37]. The so wa e employs Mon e
Ca lo simula ion echniques o accu a ely model pa icle beha io in
a e ied gas en i onmen s, making i pa icula ly sui able o analyzing
molecula low.
2.3.2. COMSOL mul iphysics
Fo he pu pose o compa ing simula ion esul s, COMSOL Mul i-
physics .6.2 so wa e [38] was in eg a ed in o he esea ch me hodol-
ogy. The so wa e accommoda es a ious s udy ypes, encompassing
s a iona y and ime-dependen ( ansien ) s udies, as well as linea and
nonlinea s udies. In his esea ch, wo dis inc modules a e employed:
a) Molecula Flow Module: Simula ing kine ic gas lows, his module
o e s specialized physics in e aces ideal o acuum sys ems simu-
la ion. I is designed o add ess kine ic gas lows wi h Knudsen
numbe s g ea e han 0.1, encompassing bo h he ansi ional and
ee molecula low in e aces. In ou expe imen s, he Knudsen
numbe s exceeded 11, making his module highly app op ia e o
ou applica ion. This me hod compu es low by in eg a ing luxes
om all isible su aces, wi h dependencies con ined o su ace
a iables.
b) Pa icle acing module: This module p o ides a e sa ile ool o
acking pa icles h ough a ious geome ies unde di e en o ces.
The ma hema ical pa icle acing in e ace allows o lexible
o mula ion o pa icle mo ion using Lag angian o Hamil onian
app oaches, ideal o ee molecula low simula ions. Special a i-
ables o e insigh s in o pa icle popula ions and s a is ical da a,
aiding in analysis. This module compu es quan i ies like pa icle
coun and ansmission p obabili y, acili a ing he isualiza ion and
analysis o pa icle ajec o ies.
Fig. 3. Laby in h seal geome ies and hei expe imen al se up (SHORT,
LONG, STEP).
Table 1
Laby in h seal geome y dimensions.
Laby in h Wid h Diame e Leng h
[mm]
SHORT b =0.5 d =86.5 L =1.5
LONG b =0.5 d =86.5 L =10
STEP b =0.5 d
1
=86.5 L
1
=8.25
d
2
=92.5 L
2
=3.00
L
3
=1.75
Table 2
Oil es sample p ope ies [35].
Lub ican name FOMBLIN Y LVAC 25/6
Lub ican ype PFPE
Vapo p essu e (mba ) 6e-8 (25 ◦C)
6e-5 (100 ◦C)
Kinema ic iscosi y (cS ) 276 (20 ◦C)
Viscosi y index 113
Molecula weigh (g/mol) 3300
Densi y (g/cm
3
) 1.90
Applied oil sample:
mass (g) 1.8–2
olume (ml) 0.95–1.05
J. Pouza e al. Vacuum 232 (2025) 113882
4
3. Resul s
The esul s encompass analy ical, expe imen al, and simula ion ap-
p oaches, which a e compa ed and collec i ely e alua ed. The main
e alua ion subjec is a se o h ee laby in h seals (Table 1), ea u ing
p ecisely manu ac u ed and measu ed geome ies u ilized in bo h
analy ical and simula ion models. Fo expe imen al es ing, he modi-
ied ETR measu ing de ice [6] is employed, along wi h he laby in h seal
assembly, o con inuously measu e lub ican mass loss esul ing om
acuum e apo a ion. Subsequen esea ch ex ends o e alua ing he
o e all geome y’s impac on he laby in h seal’s e ec i eness, as well
as explo ing he in luence o su ace oughness and molecula beaming
e ec s occu ing in na ow co ido s wi hin he molecula low egime.
3.1. Laby in h compa ison
The expe imen al sec ion ini ially compa es h ee laby in h geome-
ies (Fig. 3) h ough mul iple independen measu emen s. The
measu ed esul s ob ained om he ETR a e depic ed as displacemen
signals, which a e hen con e ed in o lub ican mass loss using cali-
b a ion a ios. As a esul , he measu emen ou comes po ay a
con inuous signal o lub ican mass loss o e a speci ied ime pe iod o
all h ee ypes o laby in h seal geome ies; Fig. 4. To u he alida e he
measu ed mass loss, he expe imen al se up is weighed bo h be o e and
a e he expe imen . The esul s clea ly indica e ha mo e complex
geome ies exhibi supe io sealing capabili ies, aligning closely wi h
he expec ed beha io acco ding o he esea ch [12,14,27].
The empe a u e and p essu e o expe imen al measu emen s we e
eco ded and subsequen ly inco po a ed in o he analy ical and simu-
la ion models o achie e close co ela ion. The analy ical app oach
u ilized he ESTL model (Eq. (3)), while bo h he MolFlow+and COM-
SOL Mul iphysics so wa e we e employed o simula ion. A compa ison
o he esul s ob ained om all h ee app oaches is shown in Fig. 5 and
e eals ha he analy ical app oach yields signi ican ly g ea e mass
loss, po en ially due o simpli ica ions inhe en in he analy ical model.
Con e sely, he simula ion app oach closely aligns wi h expe imen ally
acqui ed esul s. When compa ing mass loss and ela i e leak a e, using
he expe imen al esul s as a e e ence (see Table 3), he analy ical
model o e es ima es he leak a e 5–8 imes, while simula ions de ia e
by only 29 % a mos . These indings indica e ha simula ion models
o e a be e i o complex geome ies, hough hey may be less ac-
cu a e o sho e laby in h gaps.
Expanding upon he p e ious indings, a design o expe imen
analysis was unde aken o comp ehensi ely explo e he p incipal
in luencing pa ame e s o laby in h seals. To acili a e a meaning ul
compa ison o laby in h pa ame e s, he e alua ion o ansmission
p obabili y (TP) is employed, indica ing he a io o molecules
a e sing om he inle o he ou le [23,39].
TP =N
N0
,(4)
whe e Nis he numbe o molecules a he ou le , and N0is he numbe
o molecules a he inle . This p obabili y, essen ial o conduc ance
calcula ions, o e s a con enien me ic o compa ing laby in h geom-
e y pa ame e s. No ably, he p ima y in luencing pa ame e s encom-
pass he wid h o he laby in h gap and he leng h o he co ido , as
depic ed in Fig. 6. These esul s align wi h he assump ions de i ed om
p e ious esea ch.
Acco ding o he esul s shown in Fig. 4, he laby in h seal wi h a
s epped geome y is he mos e ec i e sealing solu ion, la gely due o i s
ex ended co ido leng h, iden i ied as he p ima y in luencing pa am-
e e in Fig. 6. The longe co ido inc eases he p obabili y o molecula
in e ac ions wi h he seal su aces be o e molecules each he ou le .
Addi ionally, he s epped s uc u e in oduces mul iple su aces a
a ious angles, which inc eases he likelihood o molecules e lec ing o
hese su aces a he han passing di ec ly h ough he seal. This
e lec i e beha io dis up s he di ec low o molecules, signi ican ly
educing ansmission p obabili y and enhancing o e all sealing pe -
o mance. The combina ion o an elonga ed pa h and mul iple e lec ion
poin s wi hin he s epped geome y c ea es a mo e e icien ba ie o
molecula low compa ed o simple seal designs.
3.2. Su ace oughness
In addi ion o conside ing he o e all geome y o he laby in h seal,
su ace opog aphy mus also be aken in o accoun , as i can signi i-
can ly impac conduc ance esul s. Cu en knowledge lacks e idence o
su ace oughness e alua ion in laby in h seals o space applica ions.
The e o e, a se ies o expe imen al es s we e conduc ed o unde sco e
he impo ance o he su ace oughness pa ame e . Two LONG geom-
e y laby in h seals p oduced using a u ning machining p ocess and
wi h di e en su ace inishes - one un ea ed (ROUGH) and he o he
polished (SMOOTH) - we e compa ed (Table 4). The inne and ou e
su ace oughness o he laby in h seal was assessed using a Con ou GT-
X 3D op ical p o ilome e (Fig. 7), and he da a was subsequen ly
inco po a ed in o he COMSOL Mul iphysics simula ion en i onmen o
molecula low analysis, conside ing eal su ace opog aphy.
The analy ical model does no include a su ace ex u e pa ame e ;
he e o e, i will no be compa ed u he wi h o he app oaches. The
compa ison be ween expe imen al measu emen s and simula ions
Fig. 4. Expe imen al measu emen s compa ison o mass loss o a ious laby-
in h seal geome ies.
Fig. 5. Compa ison o analy ical, expe imen al and simula ion app oaches o
e apo a ion mass loss.
J. Pouza e al. Vacuum 232 (2025) 113882
5
e eals a signi ican in luence o su ace oughness on he mass loss o
e apo a ed lub ican molecules; see Fig. 8. The in ensi y o mass loss
a ies by 14.4 % in expe imen al measu emen s and 14.6 % in simula-
ions o he di e en su ace oughness. The esul s p esen ed ha e
been uni ied o ensu e compa abili y ac oss he same seal geome ies,
wi h one being subjec ed o a polishing p ocess.
Based on he expe imen al measu emen s, he sealing e iciency o
he SMOOTH laby in h seal dec eased by 14.4 % due o i s lowe su ace
oughness, esul ing in an o e all lub ican loss ha was 0.55 mg/h
highe compa ed o he ROUGH laby in h seal, which ea u ed a highe
su ace oughness. The inc eased oughness in he ROUGH seal likely
enhanced he in e ac ion be ween he seal su aces and he e apo a ing
lub ican molecules, con ibu ing o be e sealing pe o mance. Su -
aces wi h highe a ea oughness exhibi imp o ed sealing e ec i eness
which can be in e p e ed in wo ways:
1) Inc eased su ace oughness esul s in app oxima ely a 1.7 % la ge
a ea o molecula adhesion ( e e o he Sd pa ame e in Table 4).
2) Highe su ace oughness in oduces geome ically complex pas-
sages, impeding molecule p opaga ion.
3.3. Molecula beaming e ec
One o he ac o s ha has no been conside ed in he op imiza ion o
laby in h seal geome y design is he phenomenon o molecula beam-
ing e ec , which occu s in long and na ow ubes. When he impinge-
men a e o he ube ace s in he no mal di ec ion is highe han o
he pa allel ace s, he angula dis ibu ion o molecula eloci ies is no
longe cosine-like, esul ing in mo e molecules a eling along he lab-
y in h co ido pa h [19,40]. This beaming e ec is always p esen and
should be aken in o accoun in he op imiza ion o laby in h geome y
as i may in luence he o e all mass loss o lub ican molecules.
To mi iga e he molecula beaming e ec , i is ecommended o
employ mo e in ica e geome ies ha edi ec he low o molecules,
p e en ing hem om a eling in a s aigh line. An e ec i e geome y
in ol es a s epped con igu a ion, al e ing he di ec ion o molecula
low by 90◦. Ca e ul conside a ion should be gi en o he placemen o
he s ep wi hin he laby in h o minimize he impac o he molecula
beaming e ec . To achie e his, a simula ion o he o iginal s epped
laby in h seal, used in he expe imen al measu emen s, was pe o med
using COMSOL Mul iphysics so wa e. Adjus men s we e made o he
s ep posi ion along he en i e leng h o he laby in h by pe o ming a
pa ame ic sweep ac oss he 10 mm wid h o he laby in h in 0.5 mm
inc emen s. The esul s in Table 5 indica e he a o able placemen o
he s ep in he middle o he laby in h seal (Fig. 9), e ec i ely educing
he g owing in luence o he molecula beaming e ec .
Gi en he exis ence o he molecula beaming e ec and he necessi y
o a s epped geome y in laby in h seals o e ec i ely diminish i s
impac , u he esea ch in o he geome y o he s ep co ne has been
conduc ed. In he co ne whe e he molecula beam s ikes he su ace
and dispe ses he molecules, he co ne geome y is essen ial o dis-
up ing he sp ead o molecules h ough he laby in h seal.
Con en ionally, he classical geome y o a manu ac u ed laby in h
seal lacks co ne op imiza ion, and he co ne is ounded due o he
manu ac u ing p ocess. Consequen ly, his geome ical shape inc eases
he likelihood o molecules p opaga ing u he , necessi a ing i s elim-
ina ion. To add ess his issue, a se ies o local geome ical shapes o he
co ne we e simula ed using COMSOL Mul iphysics (Fig. 10), and hei
impac in e ms o mass loss educ ion was assessed; see Table 6. Based
on hese indings, i is ecommended o inco po a e co ne shaping in o
he manu ac u ing p ocess, such as implemen ing co ne elie g oo es.
These geome ic modi ica ions, designed o be p oduced using con en-
ional machining p ocesses, con ibu e o a sligh educ ion in mass loss
while po en ially yielding signi ican lub ican sa ings o e he sa el-
li e’s li e ime.
4. Discussion
The s udy aims o explo e he undamen al aspec s o laby in h seals
used in space mechanisms, ocusing on unde s anding he beha io o
liquid lub ican molecules ha e apo a e in acuum condi ions. To
unde s and how lub ican molecules leak h ough hese seals, we use
h ee me hods: expe imen al es ing, analy ical analysis, and compu e
simula ion.
Table 3
Mass low e alua ion o speci ic laby in hs using di e se app oaches.
App oach SHORT LONG STEP
[mg/h] ela i e leak a e [mg/h] ela i e leak a e [mg/h] ela i e leak a e
Expe imen 4.350 1 3.41 1 2.73 1
Analy ical 32.81 7,54 19.27 5,65 16.69 6,11
Simula ion MolFlow+5.39 1,24 3.24 0,95 2.33 0,85
COMSOL 5.63 1,29 3.58 1,05 2.72 1,00
Fig. 6. Iden i ica ion o key laby in h geome y pa ame e s impac ing ans-
mission p obabili y (TP).
Table 4
Su ace oughness analysis o inne and ou e componen s o laby in h seals.
Su ace oughness ROUGH SMOOTH
Inne Ou e Inne Ou e
Ra [
μ
m]
a
3.88 1.30 0.13 0.56
Sa [
μ
m] 3.70 1.30 0.14 0.56
Sq [
μ
m] 4.34 1.60 0.16 0.67
Sd [
μ
m] 1.99 % 5.56 % 0.01 % 4.14 %
a
A e age Ra pa ame e in he di ec ion o highligh ed mid-planes shown in
Fig. 7.
J. Pouza e al. Vacuum 232 (2025) 113882
6
Expe imen al es ing is c ucial o compa ing he ou comes o he
analy ical and simula ion app oaches. The main inaccu acies a ise om
he expe imen al measu emen s, so each measu emen mus unde go a
calib a ion p ocedu e be o e he ac ual es . Calib a ion ocuses p i-
ma ily on empe a u e dis ibu ion measu emen , he con e sion a io
be ween p oximi y senso dis ance change and ac ual weigh loss, and
achie able acuum condi ions. The con e sion a io calib a ion o he
e apo a ion es ig is pe o med be o e each laby in h seal modi ica-
ion. The de ailed p ocess o his calib a ion is desc ibed in p e ious
esea ch [6].
Fig. 7. Su ace oughness analysis o inne and ou e componen s o laby in h seal LONG geome ies using a 3D op ical p o ilome e .
Fig. 8. Expe imen al and simula ion in es iga ion o su ace oughness impac
on laby in h seal pe o mance.
Table 5
Laby in h co ne geome ies and hei impac on e apo a ed lub ican loss.
S ep posi ion (see Fig. 9) Mass loss [mg/h] Loss a e
a
10 % 0.665 +5.19 %
25 % 0.643 +1.62 %
50 % 0.633 –
75 % 0.640 +1.24 %
90 % 0.662 +4.71 %
a
Rela i e o he e e ence s ep posi ion a he midpoin (50 %) o he laby in h
seal.
Fig. 9. Mass loss a ia ion in laby in h STEP geome y in luenced by molecula
beaming e ec on s ep posi ion.
J. Pouza e al. Vacuum 232 (2025) 113882
7
Tempe a u e is he mos c i ical pa ame e in luencing he e apo-
a ion p ocess, as i di ec ly a ec s he subs ance’s apo p essu e [12,
41]. Du ing he expe imen s, i is no possible o measu e he exac
empe a u e o he oil sample inside he laby in h seal es ig. To
add ess his, we pe o m a he mal calib a ion p ocedu e be o e expe -
imen al es ing, whe e e e ence empe a u es a e measu ed a speci ic
loca ions (see. Fig. 1) and a he main pan o he laby in h seal pla o m
(see Fig. 11). The measu ed empe a u e di e ence o app oxima ely
20 ◦C be ween he laby in h seal and he suppo beam holding he
e apo a ion es ig is p ima ily due o he di e ing mechanisms o hea
ans e a ec ing each componen . The suppo beam is di ec ly con-
nec ed o he hea ed acuum chambe , which allows o e icien hea
conduc ion. In con as , he laby in h seal expe iences hea ing p e-
dominan ly h ough adia ion. The p esence o e y limi ed conduc i e
pa hs makes adia i e hea ans e he dominan mechanism, which is
less e icien compa ed o conduc ion. I was expe imen ally e i ied in a
dedica ed es wi h addi ional he mocouples ha he lub ican su ace
empe a u e is equal o he ese oi empe a u e and he laby in h seal
gap su ace, due o con ec ion e ec s.
Despi e ini ial he mal calib a ion, he oil su ace empe a u e e-
mains es ima ed, as he mocouples canno be placed in he pan du ing
e apo a ion es s wi hou comp omising weighing p ecision. The es ig
o he laby in h seals and he oil a e main ained a a empe a u e o
92.0 (±0.3) ◦C, which is dependen on he geome y. Once he subs ance
s a s o e apo a e a speci ic empe a u es and p essu es, i cools down
as a esul o he e apo a ion p ocess. The empe a u e subsequen ly
s abilizes a a new alue depending on he e apo a ion a e o he
cooling liquid and he ex e nal hea ing. This de i ed empe a u e in-
oduces he p ima y inaccu acy in bo h he analy ical and simula ion
app oaches. None heless, du ing he expe imen s wi h a ious laby in h
seals, he he mal condi ions emained consis en , wi h a maximum
de ia ion o only 1 ◦C; see Fig. 12.
The apo p essu e o he liquid lub ican is es ima ed using he
Clausius-Clapey on app oxima ion [17,42], making i en i ely depen-
den on he known apo p essu es p o ided by he manu ac u e .
Howe e , he Knudsen e usion me hod used by manu ac u e s o apo
p essu e de e mina ion lacks s anda diza ion. Consequen ly, he apo
p essu e alues in he oil da ashee migh be inaccu a ely de e mined,
leading o disc epancies in expe imen al and o he esul s [11,31]. To
add ess his issue, i is ad isable o es he oil’s apo p essu e using he
Knudsen e usion me hod p io o he expe imen al measu emen s.
Howe e , in ou expe imen s, apo p essu es we e sou ced om he
da ashee , which could po en ially in luence he esul s ob ained
h ough analy ical and simula ion app oaches. Al hough he exac de-
ia ion in apo p essu e measu emen is unknown, he simula ion e-
sul s align well wi h he expe imen al da a.
The p essu e o he acuum chambe is measu ed ou side he laby-
in h seal es ig as i can’ be di ec ly measu ed inside he laby in h
seal. The e o e, he exac p essu e in he lub ican ese oi a he inle
o he laby in h seal is assumed o be equal o he apo p essu e o he
liquid lub ican . The p essu e inside he acuum chambe was moni-
o ed du ing he expe imen s and emained cons an a 2E-5 (±1E-6)
mba . A he se oil empe a u es, he oil’s apo p essu e is es ima ed o
be 3.3E-5 (±7E-7) mba , sligh ly highe han he chambe ’s acuum
p essu e. While his di e ence is small, he p ima y indica o o he
e apo a ion p ocess is he measu ed change in dis ance, which ollows a
mos ly linea end and only occu s once oil e apo a ion begins.
O he signi ican dis up i e ac o s in he expe imen al
Fig. 10. Local geome ies in he co ne o laby in h seals wi h s ep-
ped geome y.
Table 6
Laby in h co ne geome ies and hei impac on e apo a ed lub ican loss.
Co ne geome y Cha ac e is ic pa ame e Loss educ ion
Classical – –
Ci cula a c =b 3.8 %
Relie g oo e ype G
a
3.9 %
Dead end l =2b 4.3 %
a
ISO 18388:2016.
Fig. 11. The mal calib a ion analysis o laby in h seal es ig expe imen s.
Fig. 12. Tempe a u es o suppo beam du ing he expe imen s o a ious
laby in h seals.
J. Pouza e al. Vacuum 232 (2025) 113882
8
measu emen s s em om he design o he laby in h seal es ig. Un-
wan ed mo emen o he lub ican in he es ig may occu du ing
sample handling due o he absence o a po ous ese oi . Addi ionally,
empe a u e and p essu e a ia ions o e ime du ing he expe imen
can lead o lub ican c eep. The oil may c eep along he su ace, h ough
he laby in h seal gap, and e en h ough he igh ening con ac su aces.
This could lead o inc eased weigh loss due o he g ea e oil su ace
a ea, hus inc easing e apo a ion in ensi y. Du ing he calib a ion and
expe imen al es ing, lub ican c eep was add essed h ough isual in-
spec ions be o e and a e he expe imen s; howe e , i was no obse ed
a all. In ac ual space applica ions, laby in h seals inco po a e an i-c eep
ba ie su ace coa ings wi h low su ace ension [43] o p e en lub i-
can c eep h ough he seal. Howe e , hese ilms we e no used du ing
he expe imen s because isual inspec ions did no de ec any c eep.
Addi ionally, using ba ie ilms could ha e dis o ed he esul s, espe-
cially when measu ing he e ec o laby in h seal su ace oughness.
The inaccu acies o he analy ical e apo a ion model o laby in h
seals s em om se e al simpli ica ions. The model simpli ies he com-
plex geome y o he laby in h seal, he eby o e looking he beha io o
molecules in he molecula low egime and he eme gence o he mo-
lecula beaming e ec . Ano he simpli ica ion in ol es app oxima ing
he laby in h ansmission p obabili y, which should ideally be calcu-
la ed di e en ly o each ype o geome y. These simpli ica ions cause
he analy ical model o be less accu a e in p edic ing lub ican loss
du ing he acuum e apo a ion p ocess, wi h accu acy a ying based on
he seal’s geome y; see Fig. 5.
Disc epancies be ween simula ion models and expe imen al mea-
su emen s may a ise mainly om he eal oil empe a u e and
assump ion o a uni o m empe a u e dis ibu ion ac oss he seal. O he
limi a ions o he simula ion model s em om su ace oughness gen-
e a ion, mesh inesse, p essu e dis ibu ion, and he nume ical model
used. Despi e hese challenges, he solid simula ion model emains he
closes o expe imen al measu emen s. The e o e, i is ecommended o
simula e each laby in h seal assembly wi h an op imized simula ion
model and calib a ed ini ial condi ions o accu a ely p edic lub ican
mass loss o e ime.
5. Conclusion
The acuum e apo a ion in ensi y o space oils h ough laby in h
seals was in es iga ed using expe imen al, analy ical, and simula ion
app oaches. The s udy unde sco es he need o e ine analy ical models,
as hey end o o e es ima e mass loss by 5–8 imes compa ed o
expe imen al esul s. I also demons a es a s ong co ela ion be ween
simula ion esul s and expe imen al da a. The simula ion ools
MolFlow+and COMSOL Mul iphysics a e ecommended o accu a ely
p edic ing oil e apo a i e mass loss.
Key indings ega ding he in luence o laby in h seal geome y on
molecula low include:
•S epped laby in h seal con igu a ions p o ide enhanced sealing
pe o mance. A compa ison o wo laby in h seals—one ea u ing a
s aigh , long co ido and he o he a s epped con ig-
u a ion— e eals ha he s epped seal, which is 30 % longe , should
heo e ically p o ide a 16 % imp o emen in sealing e ec i eness
due o i s inc eased leng h. Howe e , he s epped design ac ually
achie ed a 20 % imp o emen , indica ing addi ional bene i s om
he s epped geome y i sel .
•Molecula beaming e ec s wi hin laby in h seals con ibu e o oil
mass loss. This e ec can be signi ican ly educed by using a s epped
con igu a ion wi h he s ep posi ioned a he midpoin o he seal,
which bes dis ibu es he molecula beaming e ec . Con e sely,
placing he s ep nea he inle o ou le can nega i ely impac sealing
pe o mance by inc easing he mass loss a e by up o 5 %.
•Su ace oughness impac s molecula ansmission p obabili y. A
compa ison be ween wo seals, wi h a e age su ace oughness
alues o Ra 2.6 and Ra 0.3, shows ha he seal wi h g ea e
oughness achie es a 14.4 % imp o emen in sealing pe o mance
o e he smoo he seal.
•Local geome ical adjus men s, such as adding elie g oo es, can
enhance sealing e iciency. Depending on he speci ic modi ica ion,
sealing e ec i eness can imp o e by up o 4 %.
CRediT au ho ship con ibu ion s a emen
Jose Pouza : W i ing –o iginal d a , Visualiza ion, Valida ion,
So wa e, P ojec adminis a ion, Me hodology, In es iga ion, Funding
acquisi ion, Fo mal analysis, Da a cu a ion, Concep ualiza ion. Da id
Kos al: W i ing – e iew &edi ing, Supe ision, Me hodology,
Concep ualiza ion. La s-G¨
o an Wes e be g: W i ing – e iew &edi -
ing, Supe ision, Concep ualiza ion. E ik Nybe g: W i ing – e iew &
edi ing, Me hodology, Concep ualiza ion. I an K upka: Supe ision,
Resou ces, Funding acquisi ion.
Decla a ion o compe ing in e es
The au ho s decla e he ollowing inancial in e es s/pe sonal e-
la ionships which may be conside ed as po en ial compe ing in e es s:
Jose Pouza epo s inancial suppo was p o ided by Eu opean Space
Agency. I an K upka epo s inancial suppo was p o ided by Eu o-
pean Union. I he e a e o he au ho s, hey decla e ha hey ha e no
known compe ing inancial in e es s o pe sonal ela ionships ha could
ha e appea ed o in luence he wo k epo ed in his pape .
Acknowledgmen
This esea ch was suppo ed by he ac i i y “E ec o local
geome ical changes and pola iza ion o laby in h seal su aces on he
e apo a ion a e o liquid lub ican s in space applica ions”, unded as a
Disco e y elemen con ac 4000139889 by he Eu opean Space
Agency; and by he p ojec “Mechanical Enginee ing o Biological and
Bio-inspi ed Sys ems”, unded as p ojec No. CZ.02.01.01/00/22_008/
0004634 by P og amme Johannes Amos Comenius, call Excellen
Resea ch.
Da a a ailabili y
The da a suppo ing he indings o his s udy a e openly a ailable on
[Zenodo.o g] a [h ps://doi.o g/10.5281/zenodo.12190559], e e -
ence numbe [12190559].
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J. Pouza e al. Vacuum 232 (2025) 113882
9
