INTERNAL CHARACTERIZATION AND HOLE FORMATION
MECHANISM IN THE LASER PERCUSSION DRILLING PROCESS
A izubie a, I, Lamikiz, A.*, Ma ínez, S., Uka , E., Tabe ne o, I.; Gi o , F.
Depa men o Mechanical Enginee ing, Uni e si y o he Basque Coun y
ETSII, c/Alameda de U quijo s/n, 48013 Bilbao, (Spain)
Tel.: +34-946014221, Fax: +34-946014215
Co esponding au ho
Ai zol Lamikiz
Depa men o Mechanical Enginee ing, Uni e si y o he Basque Coun y
ETSII-UPV, c/Alameda de U quijo s/n, 48013 Bilbao, Spain
Tel: +34-946014221, Fax: +34-946014215
E-mail: ai [email protected]
Figu es included in body ex o easie e iew
ABSTRACT
Lase pe cussion d illing is inc easing i s ele ance in many indus ial applica ions, being used
pa icula ly in he ai c a indus y in pe o ming he mic o-holes in nickel based alloys u bine
blades o cooling, o s ainless s eel medical componen s d illing, which equi e small holes size
and quali y. Lase pe cussion d illing p ocess p esen s ex emely high speed o high aspec
a io holes. Mo eo e , he quali y and accu acy o he holes can be excellen i he op imal
pa ame e s a e se .
The lase pe cussion d illing p ocess is usually pe o med wi h speci ic equipmen , including
lase s ha achie e high peak powe s o picoseconds du a ion. These sys ems a e usually
dedica ed exclusi ely o lase d illing ope a ion. I is also e y common o pe o m his p ocess
using he pa ame e s sugges ed by he manu ac u e o he equipmen and wi hou any
conside a ion abou he mechanism o o ma ion o he hole. On he o he hand, lase
pe cussion d illing is pe o med by a sequence o pulses on he pa su ace. Each pulse
emo es a ce ain amoun o ma e ial. The ene gy and du a ion o pulses se he amoun o
emo ed ma e ial by each one.
This wo k discusses he mechanisms o o ma ion o he holes in he lase pe cussion d illing
p ocess o an AISI 304 pla e, e alua ing he emo ed ma e ial olume in each lase pulse and
ob aining he e olu ion o he hole geome y o he comple e pulse sequence. In addi ion, his
expe imen al analysis has been apply also o he de elopmen o a nume ical model ha can
simula e he esul ing hole geome y o di e en pulse sequences.
Keywo ds: Lase pe cussion d illing, mic o-d illing, p ocess modelling.
This is he accep ed manusc ip o he a icle ha appea ed in inal o m in In e na ional Jou nal o Machine Tools and Manu ac u e
75 : 55-62 (2013), which has been published in inal o m a h ps://doi.o g/10.1016/j.ijmach ools.2013.08.004. © 2013 Else ie unde CC
BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
1. INTRODUCTION
Lase d illing p ocess has become an indus ial solu ion o massi e mic o o small hole d illing,
anging hole diame e s om 5 mic ons o 1 mm, high aspec a ios (up o 1:200) and a wide
ange o wo kpiece ma e ials. The main ad an age o his p ocess is he high p oduc i i y in
compa ison wi h mechanical d illing o USM, being able o each hund eds o holes pe second
in ce ain condi ions. This ope a ion is usually pe o med by applying a single pulse o a
sequence o ela i ely sho pulses ( ypically om 0.01-100ms) and peak powe s up o 50kW.
Howe e , lase pulses up o 100J can be achie ed and pulses om em oseconds o
milliseconds can be applied [1, 2]. The combina ion o he pulse peak powe and du a ion
signi ican ly in luences on he ma e ial emo al mechanism. Fo ul asho pulses (less han
100 s) and high ene gy densi y (mo e han 1016 W/cm2), ma e ial is emo ed by cold abla ion
mechanism, since he ma e ial in e ac s wi h he ene gy o he lase and he e is i ually no
mel ed ma e ial. On he o he hand, o longe pulses (mo e han 100µs) and lowe ene gy
densi y (less han 107 W/cm2), he ma e ial is emo ed by mel expulsion mechanism, combining
ma e ial apo iza ion and mel ing. The la e is he mos common case o con en ional lase
sou ces such as disc o ibe lase s [1].
An analysis o he ecen esea ch wo k abou lase d illing e eal ha he e is high in e es on
he p ocess and he mechanism o hole o ma ion. The main aim o hese wo ks is o imp o e
he lase d illing p ocess, conside ing he di e en lase d illing p ocess ypes. Lase d illing
p esen s h ee di e en a ian s. Fi s , he lase epanning p ocess, which consis s in
ansla ing he lase beam in ci cula pa hs o cu he pe ime e o he hole [3, 4]. I is a lase
cu ing p ocess, a he han a lase d illing p ocess. Secondly, he lase single pulse lase
d illing p ocess is a e y as p ocess, in which all he ma e ial is emo ed in a single pulse [1]. I
is mainly used in low- hickness pa s o holes wi h less han 1:10 aspec a ios. Finally, he
lase pe cussion d illing is based on emo ing ma e ial by a sequence o pulses. Each pulse
emo es a ce ain olume o ma e ial so ha he en i e sequence o pulses can achie e deep
hole sizes wi h diame e s anging be ween 25 and 500 mic ons.
The lase pe cussion d illing is widely used in he indus y and di e en esea ch wo ks, ocused
on he e alua ion o he p ocess can be ound. Thus, Dubey [5, 6] e iew some wo ks abou
p ocess analysis, ocused on a be e unde s anding o he physical phenomena in ol ed in he
d illing p ocess and hole o ma ion mechanism. Simila ly, esea ch conduc ed a ound he lase
pe cussion d illing can be sepa a ed in o wo g oups. On one side, he expe imen al s udies ha
e alua e he in luence o p ocess pa ame e s and analyses he geome y o he esul ing holes,
while on he o he side a e hose whe e he goal is o model he p ocess.
Beginning wi h he expe imen al s udies, he analysis o he in luence o p ocess pa ame e s on
he inal geome y o he holes shows he mos ele an pa ame e s a e he peak powe and
pulse du a ion, being he mos uni o m esul s as peak powe is highe and he pulse is sho e
[2, 7, 8]. One o he main p oblems in pe cussion lase d illing is he low epea abili y o he
p ocess, an aspec ha has been analyzed om he poin o iew o he inal geome y o he
holes [2, 9], and measu ing he bu gene a ed a ound he hole because o he mel ejec ion.
Low e alua e also his p oblem, concluding ha spa e o ma ion is he main cause o he poo
epea abili y o he p ocess [10]. In all hese wo ks, he measu ed alues we e he inle and
ou le diame e s as well as he ape o he holes. The measu emen o hese pa ame e s was
pe o med by di e en me hods (mic oscopy, measu emen based on a i icial ision, e c.) and
he ape alue was commonly ob ained by he a io o he diame e s di e ence and he pa
hickness. Mo eo e , hese wo ks ag ee ha wo mechanisms o hole o ma ion coexis s: mel ed
ma e ial expulsion by gas p essu e and apo iza ion o ma e ial. Al hough he emo al o mel ed
ma e ial is mo e e icien , since he e is no need o p o ide he la en hea , his mechanism
esul in lowe quali y holes. The e o e, he pa ame e s o lase pe cussion d illing should se he
apo iza ion mechanism as he dominan one, in o de o ob ain high quali y holes, wi h less
HAZ and ecas laye . Fo example, Seze e al [11], s udied he in luence o he lase beam incidence
angle ela i e o he wo kpiece in o de o minimize he HAZ and he ecas laye o Nickel based alloys
o he mal ba ie coa ings.
Rega ding o he cha ac e iza ion o he in e nal geome y o he hole and he emo ed ma e ial
olume in each pulse, he e a e ela i e ew e e ences and mo e limi ed da a. Thus, Low [12]
p esen s a s udy on he quali y o a ays o e y close lase d illed holes. As one o he
p esen ed esul s, some sec ions showing he in e nal shape o he holes a e p esen ed.
Meanwhile, Li [13] also has some sec ions o he ob ained holes, bu his wo k also p esen s he
inal shape o he hole and does no analyze he o ma ion mechanism o he hole. Dö ing [14]
discusses he o ma ion o a mic o-d illing by measu ing di e en sec ions o he holes d illed
wi h an ul asho pulsed lase wi h a beam size o 30 mic ons. The s udy was ocused on he
analysis o plasma expansion o each pulse, concluding ha he expansion can cause ab asion
o he hole sidewalls and he shape o he hole can be modi ied by his e ec .
On he o he hand, modeling o lase d illing p ocess has been conside ed by di e en au ho s
who ha e used di e en app oaches o sol e i . The e olu ion o he nume ic models, om he
i s one-dimensional models, has been owa d mo e complex and ealis ic models including 3D
models conside ing non-linea e ec s such as phase ans o ma ion, a iable ma e ial
p ope ies, e c. [15], [16]. O he ele an app oaches, ca ied ou by Mish a and Yada a, include
he es ima ion o he d ill p o ile conside ing empe a u e-dependen he mal p ope ies, op ical
p ope ies and phase change phenomena o he shee ma e ials. These wo ks p esen di e en
app oaches such as FEM modeling [17], [18] and he use o ANN models [19]. 2D axisymme ic
models ha e been also de eloped, conside ing in his case he e ec o he e lec ions o he
lase beam wi h he walls o he hole du ing pe cussion d illing p ocess [20, 21]. In any case,
hese models include assump ions ha help educe he numbe o a iables o conside and
educe he calcula ion ime. The mos common simpli ying assump ions a e no conside ing he
e ec o he plasma and i s possible gene a ion, he assump ion o he absence o mel ed
ma e ial displacemen due o he mal g adien s and he assump ion ha he mel phase ins an ly
solidi ies a e he lase pulse, main aining he same geome y o he hole.
In mos o he analyzed wo ks, an empi ical s udy o nume ical p oblem is sol ed, bu sepa a ely
and decoupled. Fu he mo e, mos o he wo ks ocus on he inal esul s o he d illing p ocess,
such as inle and ou le diame e s o he holes, wi hou analyzing he shape o he hole o he
mechanism o he p ocess. Thus, his pape analyzes he geome y o he holes made by a ibe
lase wi h a maximum powe o 1 kW on a 1mm hick shee o AISI 304 s ainless s eel.
2. EXPERIMENTAL PROCEDURE
The es s ha e been ca ied ou using a ibe lase Ro in-Sina FL010 wi h a 1 kW maximum
powe . The lase has been guided using a 100µm ibe and posi ioned by a Hu yscan 25
scanne head, ocusing he beam on o he pa uppe su ace. The ocal poin has been
main ained cons an o all he es s so, igo ously, he densi y ene gy o he beam is no uni o m
as he hole becomes deepe . An ai nozzle has also been ins alled o he comple e e acua ion
o he ma e ial. The nozzle guides a 5 ba p essu e ai s eam and has been se a a dis ance o
4 mm om he uppe su ace o he shee and o ms an angle o 20° measu ed om he su ace
no mal. Finally, bo h he scanne and he ai nozzle we e ixed o a con en ional 3 axis CNC
machine cen e . The e o e, he comple e p og amming o he expe imen s has been ca ied ou
using con en ional CNC p og amming. Figu e 1 shows he expe imen al se -up o he d illing
p ocess.
Figu e 1. Expe imen al lase sys em scheme
Z Axis
X Axis
Y Axis
Nozzle
AISI 304 shee
Ai
100 µm
ib e
Scanne
Lase
Fib e
coupling
The d illing es s ha e been ca ied ou in a AISI 304 s ainless s eel 1mm hickness shee , and
he dis ance be ween d ills has been se o 2 mm, ensu ing ha each es do no a ec he
su ounding ones. The composi ion o AISI 304 is basically 66%-74% o I on, 0.08% maximum
o Ca bon, 18%-20% Ch omium and 8%-10.5% Nickel, p esen ing o he elemen s as
Manganese o Silicon. The AISI 304 is an aus eni ic C -Ni s ainless s eel ha p esen s high
co osion esis ance, high duc ili y and excellen o mabili y p ope ies. This s ainless s eel is
mainly used in ood and chemical indus y. The es s o his wo k ha e been ca ied ou on cold
o med shee s wi hou any coa ing and ea men .
The es s pa ame e s ha e been se o ob ain ene gy densi y alues be ween 107 and 108
W/cm2. Resul s o ela ed wo ks, shows ha apo iza ion mechanism s a s o be he dominan
one o his ange o ene gy densi y. Thus, each lase pulse has been se a a powe o 800 W
and a du a ion o 0.3 ms, esul ing in a se ies o pulses o an ene gy densi y o 1.02·107 W/cm2
and sho enough o ensu e ha he apo iza ion mechanism is dominan . In o de o e alua e
he in luence o each pulse in he o ma ion o hole, 10 di e en es s ha e been pe o med wi h
he same pa ame e s, changing only he numbe o pulses applied o each hole. Thus, he i s
es consis s o a single pulse on he shee su ace, whe eas in he las es a ain o 10 pulses
ha e been applied o he es pa . To ensu e ha he es esul s a e obus and elimina e
possible dispe sion, all he es s ha e been epea ed 5 imes unde he same condi ions. Each
se ies was done in a line and each hole was sepa a ed 2 mm o a oid he possible in luence o
he su ounding holes. The esul s a e i e lines o 10 holes each, which we e measu ed by
mic oscope. Table 1 shows he pa ame e s o he pe o med es s and Figu e 2 show he
scheme o he es s.
Table 1. Expe imen al es s pa ame e s o lase d illing p ocess
Tes un
Powe
[W]
[Hz]
pulse
[ms]
Num.
pulses
1
800
500
0.3
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
Figu e 2. a) De ail o he es s pe o med on he shee . b) Sec ion o he holes o one o he
ounds. c) Measu emen o he inle and ou le diame e o one o he holes.
c)
1
Numbe o pulses
2
3
4
5
6
7
8
9
10
Sec ion AA
a)
b)
Inle diame e
Ou le diame e
A
A
D illing es s
1s
ound
2nd
ound
3 d
ound
2 mm
Once he es s ha e been pe o med, wo ypes o analysis ha e been ca ied ou . Fi s , he inle
and ou le diame e s we e measu ed in o de o cha ac e ize he holes. Mo eo e , hese
measu emen s ha e been used also o analyze he dispe sion o he esul s. Second, an
analysis o he en i e sec ion o he holes was made in o de o s udy i s o ma ion. Thus, his
analysis has calcula ed he amoun o emo ed ma e ial o each pulse.
3. TEST RESULTS AND DISCUSSION
3.1 Hole diame e cha ac e iza ion
The measu emen s o he hole diame e s we e pe o med by mic oscopy. The equipmen used
was a Leica DCM3D con ocal mic oscope, wi h an unce ain y o 0,1 mic ons. Measu emen
includes bo h, he inle and ou le diame e s. In o de o a oid dispe sion, he diame e s o he
i e ounds we e measu ed and he mean alue was ob ained o each es . The esul s o he
measu emen s, p esen e y low dispe sion, and same ange o alues o diame e s we e
ob ained o all he ounds. In ac , he i s 8 es s esul in blind holes in all cases, while 9 h and
10 h es s o he i e ounds esul in h ough-holes. Table 2 p esen he inle diame e s o he
i s es (co esponding o he single pulse es ) o he i e epe i ions. As i can be obse ed,
he a ia ion o he diame e is below 2.5 % o all ounds. Simila alues ha e been ob ained o
he es o he es s. Figu e 3 show he inle diame e s o he i s 5 es s, co esponding o he
es s om a single pulse o a se ies o i e pulses pe hole.
Table 2. Measu emen s o he inle diame e o he one pulse es o he 5 ounds.
Round
No.
Dx (µm)
Dy (µm)
Dm (µm)
Va ia ion
1
138.5
143.3
140.9
2.19%
2
137.2
138.5
137.8
0.01%
3
132.8
139.8
136.3
-1.09%
4
139.3
139.8
139.6
1.25%
5
133.7
135.5
134.6
-2.34%
Mean alue (µm)
137.8
Figu e 3. Inle diame e s o a) Single pulse es . b) 2 pulse es . c) 3 pulse es .
d) 4 pulse es . e) 5 pulse es .
The mean diame e s o each g oup o holes ha e been ob ained. The esul s shows ha he
inle diame e anges 150 mic ons, while he ou le diame e a ound 115 mic ons. Resul s
p esen dispe sion below 5% in all cases and he lase d illing p ocess canno ge h ough he
shee un il 9 pulses pe hole a e used. The mean diame e s o all es s a e shown on Figu e 4,
whe e inle and ou le diame e s a e plo ed. I can be obse ed ha he inle diame e is la ge
han he ou le diame e because o he ape -shape o he holes. This is a ypical e ec o he
lase d illing p ocess due o he ma e ial emo al mechanism.
a)
b)
c)
d)
e)
Dy
Dx
𝐷𝑚 =𝐷𝑥+𝐷𝑦
2
x
y
0,1 mm
0,1 mm
0,1 mm
0,1 mm
0,1 mm
x
y
x
y
x
y
x
y
Figu e 4. Mean alues o inle and ou le diame e s o all he d illing es s.
3.2 Hole in e nal shape cha ac e iza ion
The in e nal sec ions o he holes ha e been e alua ed wi h he ollowing p ocedu e. Fi s , a
WEDM cu has been pe o med 0.3 mm close o he cen e o he holes. Then, he cu pa has
been polished wi h a 400 g i pape size un il he i s measu ing. Once he sec ions ha e been
measu ed, he es pa has been polished again wi h a smoo he ab asi e (1200 g i size). The
educ ion o he sample hickness o each polishing ope a ion has been measu ed wi h a
mic ome e . The e o e, he p ocedu e allows he measu ing and loca ing o di e en longi udinal
sec ions o he holes. Figu e 5 shows he scheme o he measu ing p ocedu e o each ound.
Figu e 5. Le ) P ocedu e o he measu ing o he in e nal shape o he holes.
Righ ) Resul o he measu emen s o a 9 pulse es .
The measu emen s o he di e en sec ions ha e been used o e alua e he o ma ion o he
holes pulse by pulse, e alua ing he olume o emo ed ma e ial o each pulse. In o de o
calcula e he olume o each es , he di e en mic oscopic pho og aphs o each sec ion ha e
been impo ed on a 3D CAD so wa e, and he 3D in e nal shape o he d ills ha e been
econs uc ed. Figu e 6 shows he econs uc ion o he es numbe 9 as an example o he
me hodology o ob aining he 3D p o ile o each es .
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10
Diame e (µm)
Numbe o pulses
Inle Diame e Ou le Diame e
Num.
Pulses
Di (µm)
Mean alue
Do (µm)
Mean alue
1
137.8
-
2
144.2
-
3
149.9
-
4
150.1
-
5
147.7
-
6
149.1
-
7
150.9
-
8
145.8
-
9
148.3
113.3
10
145.4
119.3
1s WEDM cu ing
Polished sec ions
1s Sec ion
2nd Sec ion
3 d Sec ion
4 h Sec ion
5 h Sec ion
6 h Sec ion
Resul s o es No. 9
Figu e 6. a) Sequence o images o each sec ion. b) D ill p o ile econs uc ion o each sec ion.
c) D ill p o iles o all sec ions. d) Recons uc ion o he 3D shape o he d ill.
Mo e han 100 nodes a e aken o he econs uc ion o he splines o each sec ion. The e o e,
he unce ain y o he econs uc ion can be simila o he mic oscope (0,1 mic ons). Fo he
comple e hole econs uc ion, 11 sec ions a e aken o each hole, esul ing in a sec ion e e y
13-14 mic ons. The exac posi ion o he sec ion has been measu ed a e he polishing o he
hole. Thus, he unce ain y be ween di e en sec ions is highe , because o he la ge
disc e iza ion s eps. This unce ain y can be only measu ed on he inle diame e o he holes
and compa ing expe imen al esul s wi h econs uc ed hole geome ies. The e o s ound in
ha compa ison anges 1 µm.
Once he 3D geome y o he d ills is ob ained, he olume o emo ed ma e ial in each es can
be e alua ed. Figu e 7 show he e olu ion o he emo ed ma e ial pe pulse and he
accumula ed olume o he sequence o 10 pulses. The emo ed ma e ial olume o each
pulse has been designa ed as V, while he accumula ed emo ed olume o ma e ial o he
sequence o he pulses has been designa ed as V. The measu emen show ha he d illing a e
dec eases as he hole o ma ion goes deepe in o he pa . The maximum emo ed olume o
ma e ial is ob ained in he i s pulse, whe e a hole ini ia ion is achie ed. The measu emen
show ha he d illing a e dec eases as he hole o ma ion goes deepe in o he pa , due o he
di icul y o ma e ial e acua ion and lase de ocusing e ec because o he hickness o he pa .
Figu e 7 show also ha he olume o emo ed ma e ial pe pulse becomes ela i ely cons an
a e he 2nd pulse. The e is a a ia ion o hese a e in he 5 h pulse, due o a ull apo iza ion o
he ma e ial, and in e nal ma e ial esolidi ied a e 4 h pulse has been comple ely emo ed,
inc easing he d illing a e.
Figu e 7. E olu ion o he olume o emo ed ma e ial pe pulse.
0.00
2.00
4.00
6.00
8.00
10.00
12.00
0246810
V [mm3x10-3]
Numbe o pulses
V [mm3x10-3] DV[mm3x10-3]
a)
b)
c)
d)
V [mm3x10-3]
V [mm3x10-3]
4. NUMERIC MODELLING OF THE LASER PERCUSSION DRILLING
PROCESS
Wi h he aim o unde s anding he p ocess mechanisms and y o explain he expe imen al
esul s, a nume ical model has been de eloped. This nume ical model can p edic and explain
he expe imen al esul s wi h a easonable accu acy. The main goal is o p edic he inal
geome y o he holes and se he lase pe cussion d illing pa ame e s wi hou es ing.
The nume ical model has been de eloped as a ool o sol e he p oblem in an app oxima e way
wi h he minimum numbe o pa ame e s and compu a ion ime. The e o e, i does no ake in o
accoun he he mo- luid-dynamic phenomena o mol en ma e ial in o he holes bu i conside s
he he mal p oblem and ha he ma e ial is emo ed by apo iza ion. This aspec has been
e i ied expe imen ally. The model p esen s also some assump ions o simpli y he model
de elopmen and calcula ion o he emo ed ma e ial:
• The pa ma e ial is conside ed con inuous, homogeneous and iso opic.
• As i has been men ioned, he mechanism o ma e ial emo al is apo iza ion.
• The e a e no conside a ions abou luid-dynamic phenomena.
• The he mal model conside s he con ec ion and adia ion ene gy wi hin an o e all loss
coe icien "A".
• The physical p ope ies o he ma e ial only depend on empe a u e.
The nume ic model is based on a con en ional he mal model, de eloped and pa icula ized
speci ically o lase ma e ial p ocessing. The comple e desc ip ion o he base model is in [22].
The model is based on he gene al hea ans e equa ion (Eq. 1).
(1)
Whe e a is he he mal di usi i y [m2/seg], so ha a=λ/ρCp, θ is he empe a u e in [K], q he
sou ce in [W/m3], ρ is he densi y [Kg/m3], cp is he speci ic hea [J/KgK], ime in [s] and A he
global looses ac o .
The bounda y condi ions necessa y o he di e en ial equa ion sol ing a e on one hand, he
ini ial empe a u e condi ion same as oom empe a u e (Eq.2) and on he o he hand, he
bounda y condi ion o hea low in each elemen (Eq.3).
oom
== )0(
(2)
( )
zyxqq ssss ,,,=
(3)
This he mal model does no ake in o accoun he phase ans o ma ion om solid-liquid and
liquid- apou . The e o e, in o de o inco po a e his phenomena and conside he la en hea o
he phase ans o ma ions, a a iable speci ic hea is conside ed o he ma e ial. Thus, i he
empe a u e o a node is in he phase change ange, an ex a hea will be needed o inc ease
he empe a u e o he ma e ial. Figu e 8 shows he speci ic hea a ia ion conside ed o AISI
304 ma e ial and he alues o some empe a u es. This Figu e also shows he esul o he
nume ic model applica ion o a pe cussion d illing ope a ion.
( )
c
qA
a
p
=
−
1
2
Figu e 8. The mal p ope ies o he AISI304 and a iable speci ic hea o nume ic model.
The model has been alida ed by compa ison o wo di e en alues. Fi s , he inle diame e o
he hole on he op o he su ace and, second, he olume o emo ed ma e ial in each es .
The alues, showed in Table 3, show a easonable good ag eemen , conside ing ha he model
neglec any luid-dynamic phenomena o mol en ma e ial in o he holes. E o s, bo h in olume
o in diame e a e always below 10% and he model p edic s he hole o ma ion o di e en
pulse sequences. Figu e 9 show he sec ion o bo h, eal and simula ed es s o di e en
numbe o pulses. As i can be obse ed, he esul s shows ha he model can p edic he
geome y o he holes, including he ape shape o he d ills and he numbe o pulses needed
o ge a h ough hole.
Table 3. Model alida ion: Es ima ed and measu ed inle diame e [µm] and emo ed ma e ial
olume [mm3x10-3].
Num.
Pulses
V eal
[mm3x10-3]
Vmodel
[mm3x10-3]
E o [%]
D eal
[µm]
Dmodel
[µm]
E o [%]
1
5.50
5.95
8.13
137.83
141.15
2.41
2
6.33
5.93
-6.35
144.23
158.23
9.71
3
7.37
6.94
-5.82
149.85
158.23
5.59
4
7.87
7.19
-8.63
150.08
158.23
5.43
5
9.69
10.39
7.15
147.71
158.23
7.12
6
10.16
11.10
9.23
149.09
158.23
6.13
7
10.54
11.70
11.05
150.93
158.23
4.84
8
11.23
12.87
14.56
145.79
158.23
8.53
9
11.61
11.91
2.57
148.34
158.23
6.67
10
11.85
11.63
-1.85
145.43
158.23
8.80
Cp
Cp0
TS=1400ºC
Ma e ial
apo iza ion
Ma e ial mel ing
T
TL=1455ºC
TV=2470ºC
The mal P ope ies o AISI304
Cp(20ºC)=500 J/kg·K
Cp(327ºC)=557 J/kg·K
Cp(527ºC)=582 J/kg·K
𝐶𝑝=500+0.1575(𝜃−20)[J
kg·K]
LF=247 J/g
LV=7,600 J/g
