Optics & Laser Technology 43 (2011) 563–569

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Optics & Laser Technology

0030-39

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/optlastec

Investigating the effect of gravity on long pulsed laser drilling

Yuan Qin a, Gang Dai a, Bin Wang a, Xiao Wu Ni a,n, Juan Bi b, Xi He Zhang b

a Department of Applied Physics, Nanjing University of Science & Technology, Nanjing 210094, People’s Republic of Chinab School of Science, Changchun University of Science & Technology, Changchun 130022, People’s Republic of China

a r t i c l e i n f o

Article history:

Received 27 February 2010

Received in revised form

16 July 2010

Accepted 17 August 2010

Keywords:

Gravity action

Long pulsed laser

Hole shape

92/$ - see front matter & 2010 Elsevier Ltd. A

016/j.optlastec.2010.08.001

esponding author. Tel.: +86 02584315013.

ail address: jsnjnxw@gmail.com (X.W. Ni).

a b s t r a c t

With the aim of improving the efficiency of laser drilling, an upward drilling method is proposed. In the

experiment, a long pulsed laser beam was arranged to propagate upwards, in the opposite direction to

gravity, and was used to drill hole at the bottom of an aluminum slab. A semi-infinite axisymmetric

model of this system was also established. The analytical solution for the hole shape was derived by

assuming that material, once it melted, was removed from hole with the aid of gravity. The calculation

results agreed well with the experimental results. For further verification of the effects of gravity, the

removed molten material and the hole shape for the downward (along the gravity direction) and the

upward drilling cases were compared experimentally. In addition, the relationships between gravity,

the inertia force, the surface tension and the viscosity were discussed. The results show that more

molten material is expelled with the assistance of the gravity, and the laser energy is used more

efficiently to melt the aluminum slab in the upward drilling.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Pulsed lasers have been widely used for hole drilling inindustrial and manufacturing applications [1]. During the irradia-tion of the target material by the output from a high powerdensity laser with 10�8 s pulse width, vaporization is the mainmeans for mass removal which usually is accompanied by aplasma and shock wave. Since the depth of hole drilled by a singlepulse is in the order of microns, a number of laser pulses areneeded to obtain a deeper hole [2]. For millisecond pulse durationlaser drilling, the heat affect zone is larger due to the relativelylong laser-material interaction time. The region irradiated by laserbeam will be heated such that it melts or is vaporized. The vaporpressure expels the molten material from the hole. The sub-sequent laser pulse then irradiates the bottom of the hole directly.As a result, the hole can be millimeters deep [3].

To date, a series of theoretical researches have been carried outto study the evolution of the hole in laser drilling process. Kar andMazumder [4] obtained a two dimensional hole shape bysimulating the solid–liquid and liquid–vapor interfaces as curvesthat consisted of a straight line and a parabola. Xie and Kar [5]studied the melt depth of different metals under continuous-wavelaser irradiation analytically by assuming a temperature profilewhich satisfied the boundary condition. Based on the approach ofXie and Kar [5], Shen et al. [6] assumed that the temperaturevaried with depth exponentially and also obtained the melt depth.

ll rights reserved.

Based on the assumption that the material was ejected instantlywhen it was liquefied, Salonitis et al. [7] investigated theinfluences of pulse repetition rate and power density on the holedepth. Yilbas and Mansoor [8] calculated the shape of holesdrilled by short pulse lasers using the finite difference method.In these studies, the important mass removal means of vaporiza-tion and liquid ejection were ignored. For example, the materialwhose temperature had already been on the order of 104 K stillwas taken as liquid. Thereby, the calculated hole depth could notbe accurate. Chan and Mazumder [9] investigated the variationsof drilling rate, ejection rate and vaporization rate with laserpower density numerically. Solana et al. [10] indicated thatthere were two mechanisms for the liquid ejection, one was theexcess of recoil pressure over surface tension, and the other wasthe existence of radial pressure gradient in the vapor front.Ng et al. [11] studied the effect of assist gas O2 on the drillingvelocity. While the material removal process was considered inthese works, the hole was studied in one dimension as the mainpurpose was to investigate the maximum hole depth. Recently,Park and Na [12] studied the effect of scattering and multi-reflection on hole geometry. Based on the reported analyticalsolutions of temperature, vaporization rate, recoil pressure andejection rate, Samant et al. [13] simulated the process of laserdrilling of through hole in SiC. It can be concluded that thephysical mechanisms of laser drilling are complex and involvedwith thermology, hydromechanics and aerodynamics. Particu-larly, the solid–liquid and liquid–vapor interfaces are difficult totrack when material is vaporized or expelled. If material isremoved from hole once it melts, the solid–liquid interface will bethe hole’s outline. That is to say, the problem of ejection is solved,

Table 1Experimental parameters.

Laser energy Beam radius Pulse width Lens focal length Thickness of

Al slab

E¼18 J a0¼0.3 mm t¼3 ms 60 mm 10 mm

Y. Qin et al. / Optics & Laser Technology 43 (2011) 563–569564

and the vaporization process does not need to be considered aswell. The calculation of the hole shape will be simplified greatly.But, the key problem is what the applicable condition of thishypothesis is.

In this study, the hole shape was first obtained experimentallyby drilling a aluminum slab with long-pulsed laser propagating inan upward direction. According to the experiment, an axialsymmetric model was established. The temperature was derivedby solving the thermal conduction equation in the solid phase. Inthe melting stage, the action of the gravity was assumed to be theapplicable condition that was mentioned above, on the basis ofwhich the mathematical form of the hole shape was obtained bythe energy balance theory. Lastly, the removed molten materialand the hole shape were compared between the upward and thedownward laser drilling.

Fig. 2. The photograph of the hole surface.

2. Experiment and results

2.1. Experimental setup

Commonly, in laser drilling laser beam is incident on thetarget along the gravity direction and irradiates at the top surfaceof a sample, which is described as ‘‘downward drilling’’ in thispaper. With the aim of promoting the removal of molten material,laser beam is designed to travel in the opposite direction. Asshown in Fig. 1, a Nd:YAG laser beam is incident on a 451 total-reflection mirror and turns to propagate in the opposite directionto gravity. The beam is focused on the bottom surface of analuminum slab by a lens. To protect the lens from being damagedby ejected droplets, a glass slide is placed between the slab and thelens. The laser intensity distribution over the beam’s cross sectionis Gaussian. The glass slide is 75.6 mm long and 0.9 mm thick.Detailed experimental parameters are presented in Table 1.

A hole is drilled by a single millisecond duration laser pulse.After drilling, the hole diameter is measured with a microscope.The hole shape is obtained by cutting the aluminum slab alongthe hole diameter, and the cutting width is 0.5 mm.

2.2. Experimental results

Fig. 2 shows an image of the hole surface. As shown, the hole isnearly circular, and with a diameter of 0.936 mm. At the sametime, dross is observed to adhere on the edge of the hole. Fig. 3 is

Gravity

direction

Al slab

Focusing lens

Glass slide

Nd: YAG long pulsed laser

45° Reflecting mirror

hMelt

ejection

θ

Fig. 1. The schematic diagram of long pulsed laser drilling of an aluminum slab

upwardly.

Fig. 3. The photograph of the hole’s longitudinal section.

an image of the hole’s longitudinal section. The depth of theconical shaped hole is 3.001 mm.

3. The model of calculation

3.1. In the solid phase

In the experiment, the drilled hole is blind, and its depth is farless than the thickness of the aluminum slab. The properties of theslab are isotropic, and the distribution of the laser intensity isaxisymmetric in the cylindrical coordinates. Thus, a semi-infiniteaxial symmetric model can be established in the roz plane as

z

o

Laser beam

Aluminum Slab

r

Fig. 4. The semi-infinite axisymmetric model of laser-material interaction.

Y. Qin et al. / Optics & Laser Technology 43 (2011) 563–569 565

manifested in Fig. 4. The laser energy is assumed to be absorbedby the slab’s surface. The thermal conduction equation is [14]

rscs

ks

@Ts r,z,tð Þ

@t¼

1

r

@Ts r,z,tð Þ

@rþ@2Ts r,z,tð Þ

@r2þ@2Ts r,z,tð Þ

@z2ð1Þ

where Ts(r,z,t), ks, rs and cs are the temperature, thermalconductivity, density and specific heat in the solid phase,respectively. The boundary condition is

�ks@Ts

@z¼ AsIðrÞ, z¼ 0 ð2Þ

where As is the absorptivity, I(r) is the laser power density and canbe expressed as

IðrÞ ¼ I0exp �2r2

a20

!ð3Þ

where a0 is the beam radius. The initial temperature of the slab isassumed to be uniform and equal to the ambient temperature.As is known, during laser irradiation the radial and axialtemperature distributions are mainly determined by the laserintensity distribution and the heat conduction of material,respectively [6,14]. Accordingly, the temperature profile can bewritten as

Tsðr,z,tÞ ¼ TwðtÞexp �z

dsðtÞ

� �exp �

2r2

a20

!þT0 ð4Þ

where Tw(t), T0 and ds(t) are the temperature of the central point,initial temperature and thermal penetration depth, respectively.Then, the initial condition is

Tsðr,z,0Þ ¼ 0 ð5Þ

Substituting Eq. (4) into Eqs. (1) and (2), respectively, at thecentral point (r¼0, z¼0), Eqs. (1) and (2) become

1

as

dTwðtÞ

dt¼ TwðtÞ �

8

a20

!þTwðtÞ

1

ds2ðtÞ

ð6Þ

TwðtÞks

AsI0¼ dsðtÞ ð7Þ

where as is the thermal diffusivity and as¼ks/rscs. SubstitutingEq. (7) into Eq. (6) results in

1

as

dTwðtÞ

dt¼ TwðtÞ �

8

a20

!þ

A2s I2

0

ks2TwðtÞ

ð8Þ

By solving the differential equation for Tw(t), the temperatureof the central point is

TwðtÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2

0A2s I2

0

8ks2þC1 exp �

16as

a20

t

!vuut ð9Þ

Due to Eq. (9) satisfies the initial condition Eq. (5), we get

C1 ¼�a2

0A2s I2

0

8ks2

ð10Þ

Substituting Eq. (9) into Eq. (7), the thermal penetration depthds(t) is obtained

dsðtÞ ¼a0

2ffiffiffi2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�exp �

16as

a20

t

!vuut ð11Þ

What is more, Eq. (4) indicates that the temperature at thecentral point is the highest and will reach the melting tempera-ture Tm firstly. Thereby, the initial melting time is

tm ¼�a2

0

16asln 1�ðTm�T0Þ

2 8A2s

a20A2

s I20

!ð12Þ

3.2. In the melting stage

Generally, material will be removed only after it vaporizes inthe downward laser drilling. Meanwhile, molten material will beexpelled by vapor pressure, which also induces the liquidmechanism of mass removal. Chan and Mazumder [9] indicatedthat the liquid ejection was the main mass removal mechanismwhen the laser pulse width was 1 ms and the power was10–20 kW. A similar result was obtained by Semak andMatsunawa [15] when the laser power density was 4 MW/cm2.Hereby, the vaporized mass can be neglected. Moreover, thegravity is supposed to promote the removal of molten materialin the upward drilling. By considering these two aspects, in thecalculation liquid material is assumed to be removed from holeonce it melts. Subsequently the hole wall is irradiated directly bythe following laser beam and will be heated such that it melts.Based on the energy balance theory, the incident laser energy andthe energy consumed by melting should satisfy [16]

AsIðrÞðt�tmÞ ¼

Z Dðr,tÞ

0rsðcsðTm�Tsðr,z,tmÞÞþLmÞdz,tmotrt ð13Þ

where D(r,t) is the hole depth which varies with time and radius,and Lm is the latent heat. Substituting Eq. (4) and Eqs. (9)–(11)into Eq. (13) leads to

AsIðrÞðt�tmÞ ¼ rs csTmdsðtmÞexp�2r2

a20

!exp �

Dðr,tÞ

dsðtmÞ

� ��1

� �

þDðr,tÞðLmþcsðTm�T0ÞÞ

!ð14Þ

The hole depth D(r,t) is the only unknown quantity in Eq. (14),but it is still difficult to be expressed as a function. By definingD(r,t) as

Dðr,tÞ ¼ iDDðr,tÞ, i¼ 1,2, ::: ð15Þ

and substituting Eq. (15) into Eq. (14), keeping increasing i untilthe right term of Eq. (14) equals to the left, the depth can beobtained.

4. Analytical results

Based on the derived solution, the drilled hole of theexperiment in Section 2 is simulated mathematically. The thermalparameters of aluminum are shown in Table 2. The DD(r,t) is setas 10�6 mm.

Table 2Properties of aluminum [6,21].

Symbol Definition Value

rs Density 2700 kg/m3

cs Specific heat 917 J/kg K

ks Thermal conductivity 238 W/m K

Tm Melting temperature 933 K

T0 Initial temperature 300 K

Lm Latent heat 3.88�105 J/kg

As Absorptivity 0.0588

s Surface tension 1 kg/s2

m Viscosity 2.7�10�3 Pa s

Fig. 5. Evolution of the hole shape, E¼18 J, a0¼0.3 mm, t¼3 ms.

Table 3Average removed mass of molten material in one hole.

Upward

drilling

h¼12 mm

Upward

drilling

h¼52 mm

Downward

drilling

h¼12 mm

Removed mass 0.99 mg 0.93 mg 0.43 mg

Trajectory angle y 0–721 0–361 0–721

Y. Qin et al. / Optics & Laser Technology 43 (2011) 563–569566

Fig. 5 depicts the evolution of hole shape during the long pulsedlaser upward drilling. The hole forms a bowl like shape at 0.1 ms dueto the temperature distribution in the solid phase. According toEq. (4), when the temperature at the point (r, 0) on the surface isequal to that of point (0, z) in the axis, the relationship betweenthe position of the two points is r2 ¼ za2

0=2dsðtÞ. Consequently, thetemperature contour is a parabolic curve, which affects the holeshape in the early stage of drilling. With the increasing of laserirradiation time, the size of the hole keeps expanding, and the depthincreases quickly. The hole shape becomes conical on account of thelaser intensity distribution. After drilling, the diameter of the hole is1.008 mm, and the depth is 2.895 mm. Compared with the experi-ment results in Section 2.2, the relative errors of the calculated resultsare 7.69% and 3.53%, respectively. The main reasons can be analyzed:(1) the energy loss due to the heat conduction is not considered in themelting stage; (2) the multi-reflection of laser beam in the hole is nottaken into account, which may cause the underestimate of the totalabsorbed laser energy [12]; (3) the thermal properties of aluminumare assumed to be independent of temperature.

Good agreement between the analytical and experimentalresults implies that the important assumption about the gravityaction is applicable in the long pulsed laser upward drilling.Meanwhile, melting will be the main mechanism if the moltenmaterial is expelled immediately. In contrast, vaporization is themore significant mechanism in the downward drilling case. Sincethe latent heat of vaporization is much greater than that ofmelting, it can be presumed that upward drilling is moreefficiency. For further analysis, the removal of molten materialand the hole shape of the two drilling cases are comparedexperimentally. The relationship between the gravity, the inertiaforce, the surface tension and the viscosity is discussed.

5. Comparison of molten material removal

For the downward drilling experiment, the 451 total-reflectedmirror is rotated 901 counterclockwise to cause the laser beam totransmit along the gravity direction and irradiate the top surfaceof the sample.

The removed droplets are collected by the glass slide which isweighed before and after drilling by an electronic balance with theprecision of 0.1 mg. Then, the mass of expelled molten material isobtained. The liquid will drop vertically if the gravity is the onlyforce driving the removal. As plotted in Fig. 1, by varying thedistance h from the slab to the glass slide and comparing the masschange of the molten material, the trajectory of droplet can beestimated. The upward drilling experiment consists of two groups.The distance h is 12 in group 1 and 52 mm in group 2 (the lensholder is 53 mm away from the slab). The droplets are collectedfrom 40 holes in each group. The glass slide will be broken if h is lessthan 12 mm. In the downward drilling experiment, the distance h is12 mm, and the droplets are collected from 30 holes.

5.1. The mass of removed molten material

After data processing, the average removed mass of one hole isshown in Table 3. Here, the trajectory angle y is the angle betweenthe trajectory of droplet and the normal line of the slab’s surface,and it can be obtained by the glass length and the distance h. FromTable 3, by comparing the two groups of the upward drillingexperiments, the average removed mass decreases with theincreasing of the distance h. That is to say, the trajectory angle yof some droplets is larger than 361, and both the vaporization andejection occur. In the downward drilling process, molten materialis squeezed by vapor pressure and is ejected. Even though no holewas plugged by recast, the average removed mass is less than halfof the mass in group 1. Hence, in upward drilling more materialmelts and is expelled from hole, and more of the laser energy willbe used to melt aluminum slab.

In addition, the recasts in the glass slides are different for thetwo drilling methods as presented in Fig. 6(a) and (b). In thedownward drilling, the recast is small. Molten material is ejectedand impinges on the glass slide with high velocity due to thevapor pressure, which forces the collected liquid material to movefrom the center to the side. In upward drilling, the liquid removalis not affected significantly by vapor pressure because the recastin the glass slide is uniform and ‘‘smooth’’. Moreover, larger sizesof recast are collected since more material melts and is expelledas described above. From Fig. 6(b), there are some small particlesin the glass slide, which proves the occurrence of vaporization.

5.2. The adherent dross

From previous reports, in gas assisted laser drilling [17] andcutting [18] it can be noticed that dross will cling on the laser exitsurface but not on the entrance surface. Here, the entrance surfaceis equivalent to the top surface in downward drilling. Researchersattributed the dross to the action of surface tension and the

Fig. 6. The photograph of the recast in the glass slide, (a) downward drilling,

(b) upward drilling, and h¼12 mm.

Y. Qin et al. / Optics & Laser Technology 43 (2011) 563–569 567

viscosity which makes it more difficult for the molten material tobe expelled by the gas jet.

In upward drilling, taper shaped dross often adheres onthe bottom surface of hole as depicted in Fig. 7, which is notobserved in the downward drilling. The direction of the actionof gravity is the only difference between the two drillingmethods, and probably is the reason for the formation of adherentdross. According to the experimental parameters, the ratio ofthe gravity to the surface tension can be estimated by theBond number [19]

Bo¼rsga2

0

s � 2� 10�3ð16Þ

where g and s are the gravity acceleration and the surfacetension, respectively. The value of Bond number shows that theinfluence of gravity is far less than is that of the surface tension.Now the problem is which force overcomes the surface tensionand expels the molten material.

Vapor pressure is known as the main force responsible for theremoval of molten material in laser drilling. When the vaporiza-tion starts, the vapor pressure rises and exceeds the surfacetension gradually. The molten material is driven to flow along theradial direction and turns to travel along the side wall of hole untilit is ejected [20]. The ratio of the inertia force, which is mainly dueto the vapor pressure, to the surface tension is expressed by theWeber number [21]

We¼rsa0v2

s� 0:81 ð17Þ

where v is the velocity of melt, and the average of which is 1 m/sapproximately in the experiment. The separation of the meltflow becomes unstable if the Weber number is less than 1 [22].It will be difficult for the molten material to be ejected, and thehole will be full of recast, which is not in accordance with theexperimental result shown in Fig. 3. The only interpretation isthat the velocity of the melt varies with time, as does the vaporpressure. Actually, the pressure decreases with the increasing ofthe hole depth [23], and it becomes difficult for the liquid to scalethe hole wall. In this stage, Solana et al. [10] believed that themain counteracting force is the liquid viscosity. Reynolds numberdescribes the ratio of the inertia force to the viscosity m [21],which is

Re¼rsa0v

m� 300 ð18Þ

Finally, the ratio of the gravity to the viscosity can beestimated

BoRe

We� 0:74 ð19Þ

The value demonstrates that gravity assists the vapor pressure toexpel the liquid in the upward drilling, although it does notovercome the viscosity absolutely. The competition betweenthe inertia force and the solidification induces that part ofliquid recasts in the hole wall before ejection [21]. Thereby, theassistance is small. Some molten material flows out and solidifieson the bottom surface. Subsequently, the taper shaped dross isformed.

The experimental results show that the gravity assists thevapor pressure to expel the liquid, as the result of which more ofthe available laser energy is used to melt material in the upwarddrilling. It can be further speculated that the shape or size of theupwardly drilled hole will be different from that of the down-wardly drilled one. To prove the speculation, the hole shape isobtained and analyzed in below.

6. Comparison of the hole shape

According to the experiment in Section 2, the diameter of thehole surface is less than 1 mm. It is difficult to obtain a completehole’s longitudinal section as the cutting width is already 0.5 mm.Here, the aluminum slab is cut into several pieces before laserdrilling. Two pieces are fixed together and the laser beam isfocused on the joint line with the width of 0.10070.010 mm.The hole shape will be obtained easily by separating the twopieces after laser drilling.

Fig. 7. The photograph of the adherent dross.

Fig. 8. The photograph of the hole’s longitudinal section, (a) downward drilling,

(b) upward drilling.

Y. Qin et al. / Optics & Laser Technology 43 (2011) 563–569568

Fig. 8(a) and (b) present images of the holes’ longitudinalsection. The depth of the downwardly drilled hole is 3.824 mm,and its maximum diameter is 0.407 mm. In the upward drilling,

the corresponding depth of the hole is 3.513 mm and it diameteris 0.581 mm. In the drilling process, aluminum vaporizes, and thevapor diffuses to the joint layer which is full of air. The vaporpressure decreases and becomes not large enough to expel moltenmaterial from the laser entrance surface. Consequently, recastsare observed inside and around the two holes. That is thedrawback of the joint drilling method.

As depicted in Fig. 8(a), the hole drilled downwardly is long andthin. The ratio of the depth to the maximum diameter of thelongitudinal section is 9. By contrast, the upwardly drilled hole isshort and wide with the ratio of 6 as plotted in Fig. 8(b). Thedifference is analyzed in two aspects. In the aspect of depth, theupwardly drilled hole is 0.9 times shallower than the downwardlydrilled hole. Molten material at the bottom of the hole is squeezed tothe side wall along the radial direction by vapor pressure. In bothcases, the laser beam irradiates directly at the hole bottom, whichleads to the similar depth. In the aspect of diameter, the moltenmaterial accumulates on the side wall and will not be ejected untilthe vapor pressure is large enough in the downward drilling. Duringthis period, the temperature of the molten material will to possiblyreach the vaporization temperature, due to the heat conduction andlaser irradiation, the process of which consumes a lot of laser energy.In the upward drilling, with the assistance of the gravity, moremolten material is expelled. Laser energy is mainly used to meltmaterial. This opinion is also proved by the phenomenon that morerecasts are observed around the longitudinal section of the upwardlydrilled hole. Thus, the maximum diameter of hole in the upwarddrilling case is 1.4 times larger than that of the downward drillingcase. Combining these two aspects, it can be found that largerdamage range will be caused in the upward drilling. Meanwhile, thedifference of size is not great, which demonstrates that the gravityplays an assistant role in the long pulsed laser drilling.

7. Conclusion

The hole in an aluminum slab drilled by the long pulsed laserpropagated upwardly was obtained experimentally. The correspond-ing analytical solution for the hole shape was derived by assumingthat material was removed once it melted with the assistance ofgravity. The calculation results agree well with the experimental

Y. Qin et al. / Optics & Laser Technology 43 (2011) 563–569 569

results. The hole shape is determined by temperature distribution inthe early stage of laser drilling, later it is determined by the laserintensity distribution over beam’s cross section. The removedmolten material and the hole shape in the cases of downward andupward drilling were compared. The results indicate that, in upwarddrilling, the removed mass is more than two times that in thedownward drilling case, and the damage range is larger than that ofthe downward drilling case. In conclusion, the removal of moltenmaterial is promoted with the assistance of the gravity in theupward drilling. More laser energy is used to melt material. Theupward laser drilling method is efficient, and the obtained resultscould provide theoretical and experimental reference for laserdrilling.

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