prototype of registration report
TRANSCRIPT
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1. INTRODUCTION
The parallel sliding smooth surfaces generate unstable hydrodynamic film by couette velocity
variations with zero pressure distribution which can collapse when the external force is applied. One
of the better methods to produce stable hydrodynamic film between the parallel sliding surfaces is by
providing the determined surface textures. Deterministic micro textures are the surface features that
have specific pattern in terms of shape, size, and orientation. Depending on the size, shape, orientation
and distribution of the textures, the hydrodynamic lubrication characteristics of the surface can vary
significantly. Surface textures are of two types, namely, protrusions (bumps, posts and recesses
(holes which are shown in the !ig. ".
!igure". #egative and $ositive %sperities
2. LITERATURE REVIEW
&n the modern technology, there are several techni'ues to mae the surface textures including
chemical etching )"*, laser ablation )+*, &-% process )*, $hotolithography )/*. 0tsion )1* explained
the different techni'ues to mae the micro textures on the surfaces. The idea of an increased pressure
generated by micro2textures under conditions of hydrodynamic lubrication was originated in the late
"345s. 6ligerman et al., )4* numerically analyzed the effect of surface textures on circumferential gasseal by !07 modelling. &t has been observed that the textures have significant effect on the
hydrodynamic performance of gas seal. % lot of research wor has been done for the reduction of
friction on the reciprocating components and on mechanical seal )823*.
9rizmer et al., )"5* analytically finds the optimum area density of the dimples for maximum
load carrying capacity on the parallel thrust bearings by analyzing the full width textured and partial
width textured surfaces. 0tsion et al., )""* experimentally analyze the model explained by 9rizmer et
al., )"5* and the results showed good correlation with the theoretical results. Siripuram et al., )"+*
utilized numerical modelling techni'ues to explore the effect of basic asperity properties comprised of
shape, size, concavity and orientation on lubrication characteristics for a simple thrust slider
application. The authors examined different regular shapes, all distributed in s'uare array. They found
that friction coefficient is largely independent of asperity shape and orientation but very sensitive to
asperity area fraction (size and the leaage is dependent on asperity shape, concavity, orientation andsize. 7athematically, 9uscaglia et al., )"* analyzed the effect of surface texture on the static
characteristics of thrust bearing. The result shows that the load carrying capacity increases and friction
coefficient decreases by including textures. %rghir et al., )"/* utilized the numerical techni'ue to
explore the lift effect due to the pressure generation in the different macro2roughness textured cell.
The results indicate that by increasing the convective inertia, the macro2roughness patterns produces
higher lift force on the flat surface. :ahmani et al., )"1* solved the "D :eynolds e'uation with
sommerfeld boundary condition for partially textured thrust bearing to find the optimum geometry of
s'uare shaped micro2dimples. !rom the study it has been stated, for partially textured surfaces
increasing the number of dimples would not help in improving the load capacity or friction coefficient
in a pure hydrodynamic mode.
;upillard et al., )"4* numerically analyzed the inertia effect on textured parallel sliders in one
dimensional with #avier2Stoes e'uation and Stoes e'uation. The two types of models have beensolved by using finite volume method with software pacage ;!< "".5. The result shows depending
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!ig. + % model of textured surface
!ig. ;ross2section of the textured surface !ig. /
&ndividual cell of single texture
The film thicness hbetween the parallel surfaces of positive textures is
above the protrusion
elsewhere
gC hhC
=
The film thicness hbetween the parallel surfaces of negative textures is
above the recess
elsewhere
gC hh
C
+=
The #on2dimensional 'uantities used to non2dimensionalize the film thicness is
,h
hC
=
gh
HC
=
The non2dimensional form of the film thicness for positive textures is
" above theprotrusion
" elsewhere
Hh
=
The non2dimensional form of the film thicness for positive textures is
" above the recess
" elsewhere
Hh
+=
!.2 Theor$ Of ()%i* I+erti&
&nertia effects will be significant in super2laminar flow, and=or when there is a rapid change in
the cross2section )+5*. The #avier2Stoes e'uation with fluid inertia effect by neglecting the bodyforce is given as
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u u u u p uu v w
t x y z x y y
+ + + = +
5 p
y
=
w w w w p wu v w
t x y z z y y
+ + + = +
#avier2Stoes e'uation contains four unnowns, but there are only three e'uations. &n order to solve
this mathematically, another one e'uation is needed which is involving the velocity components. This
e'uation is provided by the principle of conservation of mass. The resulting e'uation is nown as the
e'uation of continuity.
( ) ( ) ( )5
u v w
t x y z
+ + + =
The #on2dimensional 'uantities used to non2dimensionalize the #avier2stoes and continuity
e'uations are+
X
pCp
UL= ,
X
xx
L= ,
yy
C= ,
Z
zz
L= ,
uu
U= , X
vLv
UC= ,
ww
U= , X
Z
Lk
L=
C
= , :e
UC
= , :e :e
X
C
L
=
The non2dimensional form of the #avier2Stoes e'uation including the fluid inertia effect is
+
+:e
u u u p uu v kw
x y z x y
+ + = +
+
+:e w w w p wu v kw k x y z z y + + = + ("
and the continuity e'uation is
( ) ( ) ( )5
u v wk
x y z
+ + =
!irst2order perturbation series in :e was used to determine the pressure generated in the
conformal contacting surfaces.
,ert%rb&tio+ -%&+titieA
5 ":ep p p= +
5 ":eu u u= +
5 ":ev v v= +
5 ":ew w w= +!irst2order perturbation method gives better results only at smaller values of the :educed2
:eynolds number. %ssume the flow is in the laminar region. Substitute the perturbation parameters in
the 0'. (" and separate the zeroth and first order terms of:e .
eroth or*er ter/ ( )5
:e A
+
5 5
+5
p u
x y
= +
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+
5 5
+5
p wk
z y
= +
( ) ( ) ( )5 5 5 5
u v wk
x y z
+ + =
(irt or*er ter/ ( )"
:e A
+
5 5 5 " "5 5 5 +
u u u p uu v kw
x y z x y
+ + = +
+
5 5 5 " "5 5 5 +
w w w p wu v kw k
x y z z y
+ + = +
( ) ( ) ( )" " "
5u v w
kx y z
+ + =
!rom the zeroth order term, :eynolds e'uation can be derived as follows
( ) + 5 5 4p p
h k h hx x z z x
+ =
!or the iso2viscous fluid, should be constant.
+ 5 5 4p p h
h k hx x z z x
+ = (+
!rom the first order term, the modified :eynolds e'uation can be derived for the solution of
perturb pressure
+ " "
5 5 5 5 5
5 5 5 5 5
"++
"++
y y yh h
x x
y y yh h
z z
p p hh k h K dydydy K dydy
x x z z x
hk K dydydy K dydy
z
+ =
+
(
Bhere,
5 5 55 5 5x
u u uK u v kw
x y z
= + +
5 5 5
5 5 5z
w w wK u v kw
x y z
= + +
The velocity components can be evaluated from the zeroth order terms
( )55"
+
p yu y y h
x h
= +
, ( )55
"
+
pw k y y h
z
=
( ) ( )5 5 55
" y
v u k w dyx z
= +
The boundary conditions and the periodicity condition in non2dimensional form is given as
5 5( , " 5, ( , 5 5p x z p x z= = = = (1
5 5( 5, ( ", p x z p x z= = = (4&n the present analysis, :eynolds cavitation condition is used. &t implies that, at the cavitation
boundary, the pressure gradient with respect to the direction normal to the boundary is zero. The 0's.
(+, (, and (/ is solved by finite difference method. % grid size of ( )< C ?"15 "15 "55 # # # and the convergence of 4"5 was chosen based on the accuracy, the graphs are shown in the next
chapter. The finite difference method leads to a set of algebraic e'uations which should be solved
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along with boundary condition 0'. (1 and periodicity condition 0'. (4. These e'uations are solved
with -auss2Siedel iterative method which is convenient for the evaluation of pressure distribution
with previously unnown cavitation region.
%fter solving the e'uations, the pressure can be found as
5 ":ep p p= +
Once the pressure distribution is evaluated in the film region, the non2dimensional loadcarrying capacity, non2dimensional end flow and friction parameter are calculated from the
expressions" "
5 5
W pdxdz = "
5 "
5 5 5 5 5 5
:e"+ "+ +
y y yh h
z z
p pkh kh hQ K dydydy K dydy dx
z z
= + +
( XF
L CW
=
Bhere,
( )" "
5 "
5 5 5 5 5
" " " "!riction !orce :e
+ +
yh h
x x
p pF h h K d y K d ydy dxdz
x h x h
= + + + +
0. E((ECT O( SUARE S"A,E ,ROTRUSION ON ,ARALLEL SLIDIN CONTACTS
WIT" INCLUDIN T"E (LUID INERTIA
The numerical analysis was performed to determine the effect of various non2dimensional
parameters lie aspect ratio, texture height and :eynolds number on the steady2state hydrodynamic
performance characteristics of the parallel surface with single s'uare2shaped protrusion by including
the inertia effect. The limits of these parameters areA%spect ratio (%A 5." % 5.3 Texture height ratio (HA 5." 5.1h :educed :eynolds number ( :e A 5.+ :e "./ !irst, the mesh size and convergence parameter for pressure calculation are considered from the
following !ig. 1. The load carrying capacity variation is decreasing when the mesh size increases for
the convergence value of 4"5 .
15 "55 "15 +555."+
5."/
5."4
5.">
5.+
5.++
5.+/
5.+4
5.+>
7esh Size
#on2d
imensional,oadcarryingcapacity
;onvD"e2/
;onvD"e21
;onvD"e24
5 +5 /5 45 >5 "55 "+5 "/5 "45 ">5 +555.+8
5.+>
5.+3
5.
5."
5.+
#y mesh size
#on2d
imensionalloadcarryingcapacity
!ig. 1 7esh size and convergence of XN (ongitudinal, ZN (Transverse and YN(across the film.
andX ZN N
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!rom the figures, it has been concluded, for further calculation mesh size of "15 < "15
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5." 5."1 5.+ 5.+1 5. 5.1 5./ . . . .5
5.1
"
".1
+
+.1
Texture height ratio( H
5." 5."1 5.+ 5.+1 5. 5.1 5./5
5.51
5."
5."1
5.+
5.+1
5.
5.1
Texture height ratio( H
5." 5."1 5.+ 5.+1 5. 5.1 5./5
"5
+5
5
/5
15
45
Texture height ratio( H
!ig. 8 Gariation of #on2dimensional oad carrying capacity, 0nd flow and !riction parameter with
Texture height ratio.
!ig. 8, shows the hydrodynamic performance characteristics gives better result as the non2
dimensional texture height increases. !ig. > shows the variation of W and Q with the aspect ratio for
5./H= . The W and Q increases at lower aspect ratio but decreases at higher aspect ratios. %s thetexture size increases, the area of constant film thicness increases due to which the pressure
distribution gets uniform over the region and thus the W is reduced. %s the texture size increases
there is increase in obstruction to the flow due to which the Q is reduced. The ( XL C is @ust the
inversion of the W . The W is maximum for the aspect ratio of 5./, the Q is maximum for the aspect
ratio in between 5.+25. and the ( XL C is minimum for the aspect ratio in between 5.25./.
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5." 5.+ 5. 5./ 5.1 5.4 5.8 5.> 5.35.5/
5.54
5.5>
5."
5."+
5."/
5."4
5.">
5.+
5.++
i
i
ll
i
i
.
%spect ratio ( A
5." 5.+ 5. 5./ 5.1 5.4 5.85
5.5"
5.5+
5.5
5.5/
5.51
5.54
5.58
5.5>
5.53
5."
i
i
l
.
%spect ratio ( A
5." 5.+ 5. 5./ 5.1 5.41
"5
"1
+5
+1
5
1
/5
%spect ratio ( A
!ig.> Gariation of load carrying capacity, end flow and friction parameter with aspect ratio by varying
:eynolds number
The variation of hydrodynamic performance characteristics with the aspect ratio is shown in the !ig. 3
for :e 5./= .
5." 5.+ 5. 5./ 5.1 5.4 5.8 5.> 5.35
5.51
5."
5."1
5.+
5.+1
5.
.
ll
.
%spect ratio ( A
5." 5.+ 5. 5./ 5.1 5.4 5.85
5.5"
5.5+
5.5
5.5/
5.51
5.54
5.58
5.5>
i
i
l
l .
%spect ratio ( A
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5." 5.+ 5. 5./ 5.1 5.4 5.8 5.> 5.35
+5
/5
45
>5
"55
"+5
"/5
"45
l
l .
%spect ratio ( A
!ig.3 Gariation of load carrying capacity, end flow and friction parameter with aspect ratio by varying
texture height ratio
!rom the above results, it can be concluded that the aspect ratio should be low and the non2
dimensional texture height should be high to get the better performance characteristics results.
3. E((ECT O( T"E DI((ERENT S"A,E O( ,OSITIVE TE4TURES ON ,ARALLEL
SLIDIN SUR(ACES
The numerical analysis is performed for the effect of different shapes of positive textures
namely, S'uare, ;ircular, Hexagonal, Dome, Triangular (apex perpendicular to flow and 0llipsoidal
(ma@or axis is parallel to flow on the tribological performance characteristics of the parallel sliding
contacts including the fluid inertia. To validate the numerical results, comparison is made with the :ef
)"+* by maing :e 5= because the analysis done in the :ef )"+* is without including the fluidinertia. !igure "5 shows the comparison of different shapes of textures with the :ef )"+*, a good
correlation is obtained. The variation is due to the mesh size.
0.0 0.2 0.4 0.6 0.8 1.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
---------
Triangular
Hexagonal
CircularSquare
PresentReerence !21"
#il$t
%ic&ness'$(
)s*ect Ratio0.0 0.2 0.4 0.6 0.8 1.0
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Reerence !21"
Present++++++++++
Triangular
Hexagonal
Circular
Square
Coeicientoriction'(
)s*ect ratio
!ig. "5 Galidation results of different shape of textures
The maximum aspect ratios of the different shapes of textures in an imaginary cell are shown in the
Table. ".
Table. ". 7aximum aspect ratios of different shapes
Sl. #o Init ;ell Description 7aximum %spect ratio
" S'uare 5.3
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+ ;ircular 5.8>
Hexagonal 5.41
/ Dome 5.8>
1 0llipsoidal 5.>
4 Triangular 5.+
The effect of different shape of textures on parallel sliding contacts with the variation of aspect ratio
for a certain value of :e 5./= and 5./H= is shown in the !ig. "". %s the aspect ratio increases,
the non2dimensional load carrying capacity ( W first increases and then decreases for the cases of allshapes of textures except triangular and dome. This is because as the aspect ratio increases, the more
area has the constant film thicness which uniforms the pressure distribution over the surface and thus
the W is reduced. %s the aspect ratio increases, the fluid gets more obstruction to the flow and thus
the Q is reduced.
5
5.51
5."
5."1
5.+
5." 5.+ 5. 5./ 5.1 5.4 5.81
"5
"1
+5
+1
5
%spect ratio ( A
!ig. "" 0ffect of different shapes on non2dimensional load carrying capacity, non2dimensional end
flow and friction parameter with the aspect ratio.
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The triangular shape of texture shows better non2dimensional load carrying capacity( W than the
other shapes. The hexagonal shape shows higher preferential end flow than the other shapes.
!or initial values of aspect ratio, the dome shape have lower non2dimensional load carrying capacity,
non2dimensional end flow and higher friction parameter but after the aspect ratio of 5. elliptical have
lower non2dimensional load carrying capacity, non2dimensional end flow and higher friction
parameter. !or an aspect ratio of 5.+A= and :e 5./= the effect of different shape of textures withthe variation of texture height ratio is shown in the !ig. "+. The non2dimensional load carrying
capacity, non2dimensional end flow increases and friction parameter decreases with the texture height
ratio. This is because as the texture height increases the film thicness decreases which develops
higher pressure and thus the non2dimensional load carrying capacity increases and friction parameter
is @ust inversely proportional to the non2dimensional load carrying capacity. The triangular shape
shows better load carrying capacity at higher texture height ratio and the hexagonal shape gives higher
preferential end flow than the other shapes. 0xcept dome and elliptical, remaining shapes has
negligible difference in the friction parameter. !orm this it can be concluded that the friction
parameter is independent for some shape of textures not for any shape.
5
5.1
"
".1
5." 5."1 5.+ 5.+1 5. 5.1 5./ 5./15
+5
/5
45
>5
Texture height ratio( H
!ig. "+ 0ffect of different shapes on the non2dimensional load carrying capacity, non2dimensional end
flow and friction parameter with the texture height ratio.
0ffect of the shape of textures on the performance parameters with the fluid inertia i.e., by varying
reduced :eynolds number is shown in the !ig. " for a certain value of
5.+A= and
5./H=. The
figure clearly shows that the fluid inertia has significant effect on the performance parameters of
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different shapes. The non2dimensional load carrying capacity, non2dimensional end flow increases
and friction parameter decreases with the variation of reduced :eynolds number. The effect of fluid
inertia in dome shape is very small when compared with the other textures. The triangular shows
higher non2dimensional load carrying capacity and lower friction parameter whereas hexagonal shows
higher preferential non2dimensional end flow.
5.51
5."
5."1
5.+
5.+1
5 5.+ 5./ 5.4 5.> "4
>
"5
"+
"/
"4
:educed:eynolds number (:e
!ig. " 0ffect of different shapes on non2dimensional load carrying capacity, non2dimensional end
flow and friction parameter with reduced :eynolds number.
!rom the !igs. "", "+ and ", it can be concluded that the friction parameter is independent of some
shape of the texture but not for any shape. The triangular shape gives better non2dimensional load
carrying capacity and friction parameter when compared with the other shape of textures. !rom the
sealing point of view, the hexagonal shape gives better performance parameters than the other shapes.
5. E((ECT O( SUARE6S"A,ED 7ULTI6TE4TURES IN TRANSVERSE6DIRECTION ON
,ARALLEL SLIDIN SUR(ACES
The effect of the number of textures in the transverse2direction is analyzed for the
hydrodynamic performance on the s'uare2shaped texture parallel sliding surface. The effect of
number of textures on the hydrodynamic performance for a reduced :eynolds number and aspect ratio
of 5./ and 5.+ respectively is shown in !ig. "/.
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" + / 1 45
5."
5.+
5.
5./
5.1
5.4
5.8
5.>
5.3
" + / 1 45
5.5+
5.5/
5.54
5.5>
5."
5."+
5."/
5."4
" + / 1 45
"5
+5
5
/5
15
45
85
>5
!ig. "/ ;omparison of number of textures with load carrying capacity, end flow and frictionparameter for different texture height.
!ig. "5 shows that as the number of textures increases in the z2direction, the W and Q
decreases and ( XL C increases. The reduction of Q is favourable interms of leaage point of
view. !or a particular Hand A values of 5.+ and 5./ respectively, the steady2state performance
characteristics are shown in the !ig. "1.
" + / 1 45.54
5.5>
5."
5."+
5."/
5."4
5.">
" + / 1 45.5+>
5.5
5.5+
5.5/
5.54
5.5>
5.5/
5.5/+
5.5//
5.5/4
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" + / 1 44
8
>
3
"5
""
"+
"
"/
"1
!ig. "1 ;omparison of number of textures with load carrying capacity, end flow and friction
parameter for different :eynolds number.
The Q is reduced further with inertia effect incomparison with the Q without inertia when thenumber of textures increases more than five (See !ig. "1. !rom the above results, it is observed that
the number of textures should be less in the z2direction.
8. E4,ERI7ENTAL STUD# O( ,OSITIVE 7ICRO6TE4TURES ON T"RUST ,AD
9EARIN
0xperimental setup used for conducting the experiment is shown in the !ig. "4
!ig. "4 0xperimental set2up
". Thrust pad +. 7onitor . $roximity probe /. D%F card 1. oading arm
4. ;ontroller 8. Strain measuring system (S;%D 155 >. Tachometer
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The test specimens were made by using %luminium foil of 1Jm thicness. Different orientations of
texture are shown in Table. +
Table +. Different shape and orientation of textures
Orientation S'uare (%rea"55mm+ Triangle (%rea"55mm+
5 degree
5 degree
45 degree
35 degree
The results are obtained by varying speed for different load conditions, the !ig. "8 shows thevariations of film thicness with the speed. !rom the figure, it is observed that, for the case of low
load, the film thicness is decreasing as the speed increases.
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:. CONCLUDIN RE7AR;S
&n the present wor, the numerical techni'ue is used to explore the effect of fluid inertia on the
different shaped protrusions of the parallel sliding contacts. !rom the results, it has been concluded
that
". There is a significant change in the non2dimensional load carrying capacity ( W , non2dimensional end flow (Q and friction parameter ( ( XL C when the fluid inertia effect is
considered.
+. The performance characteristics are very sensitive with the :eynolds number.
. The aspect ratio should be low to get the better hydrodynamic performance characteristics.
The W is maximum for the aspect ratio of 5./, the Q is maximum for the aspect ratio in
between 5.+25. and the CF is minimum for the aspect ratio in between 5.25./.
/. The number of textures in the transverse2direction should be less to get the high W and low
CF .
1. %s the number of textures increases in transverse2direction the Q decreases, which is
favorable from the application point of view to prevent the leaage.
4. The friction parameter is independent of some shape of the texture but not for any shapes.
8. The triangular shape of texture shows better performance than the other shape of textures.
>. !or sealing point of view, the hexagonal texture shows better result than the other shape of
textures.
The main limitation of the present wor is this method is applicable for smaller values of non2
dimensional :educed :eynolds number because the first order perturbation method is mainly
preferable for small perturbs.
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1=. NO7ENCLATURE
C maximum clearance between the surfaces
XL length of the imaginary cell inx2direction
ZL length of the imaginary cell iny2direction
, ,x y zN N N mesh size in x, y and z directions respectively:e :eynolds number
U maximum velocity inx2zplane
h film thicness of the lubricant
gh height of the protrusion
k ratio of the imaginary cell lengths ( X ZL L
l length of the s'uare protrusionp pressure of the lubricant film
u, v, w velocity components in thex,yandz directions respectively
5 5 5, ,u v w non2dimensional steady state velocity components
" " ", ,u v w non2dimensional first order perturb velocity components
A aspect ratio ( area of textured surface area of imaginary cell
F non2dimensional friction force
H texture height ratio (texture height=maximum clearance between the surfaces
Q non2dimensional end flow
:e :educed :eynolds number
( R C non2dimensional friction parameter
W non2dimensional load carrying capacity
h non2dimensional film thicness
H texture height ratio
p non2dimensional pressure of lubricant film
5p steady2state non2dimensional pressure
"p non2dimensional first order perturb pressure
, ,x y z non2dimensional co2ordinates (y non2dimension is across the film dynamic viscosity of the lubricant density of the lubricant
non2dimensional density of the lubricant
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7icroasperity2ubricated !ace SealsM, %S70 K.ubr. Technol., pp.8+4N8".
)+* 0tsion &., Halperin -., and :y -. >(+555, L&mproving Tribological $erformance of 7echanical
;omponents by aser Surface TexturingM, Kournal of the 9alan Tribological %ssociation, 5> +, pp.
8+N88.
)* 9ecer 0. B., 0hrfeld B., Hagmann $., 7aner % and 7unchmeyer D., ("3>4, L!abrication of
7icrostructures Bith 0xtreme Structural Heights by Synchrotron :adiation ithography,
-alvanoforming and $lastic 7oulding(&-%$rocessM, 7icroelectron 0ng., 0, pp.1N14.
)/* 7adou 7., ("338, L!undamentals of 7icrofabricationM,;:; $ress ;.
)1* 0tsion &., ?+551, LState of the art in laser surface texturingM, Transactions of %S70 Kournal ofTribology, 128, pp. +/>2+1.
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)4* 6ligerman and ?., 0tsion &., (+55", L%nalysis of the hydrodynamic effects in a surface textured
circumferential gas sealM, Tribology Transactions, 00, , pp. /8+2/8>.
)8* :y -., 6ligerman ?., and 0tsion &., (+55+, L0xperimental investigations of laser surface
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