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Optodynamic study of multiple pulses micro drilling
Ultrasonics 44 (2006) e1191–e1194 www.elsevier.com/locate/ultras
Optodynamic study of multiple pulses micro drilling Rok Petkovsˇek *, Igor Panjan, Alesˇ Babnik, Janez Mozˇina Faculty of Mechanical Engineering, University of Ljubljana, Asˇkercˇeva 6, 1000 Ljubljana, Slovenia Available online 5 June 2006
Abstract This paper describes an analysis of pulsed lasers micro-drilling of different metals. Study focuses to an optodynamic phenomenon which appears as thermal effects induced by laser light pulses and leads to dynamic process manifested as ultrasonic shock waves propagating into the sample material. The shock waves are detected by a non-contact optical method by using arm compensated Michelson. Monitoring of the main parameters of the micro drilling such as material ablation rate and efficiency was realized by analysis of the optodynamic signals. The process is characterized by decreasing ablation rate that leads to the finite hole depth. The experimental part of study comprehends a comparison between various metals. In order to describe decreasing ablation rate a theoretical model based on the energy balance is proposed. It considers the energy/heat transfer from the laser beam to the material and predicts a decreasing drilling rate with an increasing number of successive laser pulses. According to the proposed model, the finite depth of the hole appears as a consequence of the increasing surface area through which the energy of the laser beam is conducted away to the material around the processed area. Decreasing ablation rate and the finite hole depth predicted by model were in good agreement with the experimental results. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Optodynamics; Laser; Ablation; Drilling
1. Introduction Multiple pulses micro drilling is a typical optodynamic process. It is well know that optical, laser-induced ablation are the source of the ultrasound shock wave that represents the dynamic process. In general two types of shock waves appear: one is propagated through the processed specimen and another through surrounding atmosphere [1–3]. This phenomenon can be used to study, monitor or control several types of pulsed-laser processes [4,5]. In this paper we describe an optodynamic method for investigating the laser multiple pulses micro-drilling process, which is characterized by a hole of finite depth. The analysis is based on measuring the time of flight of shock waves. The time of flight for shock waves propagating through the processed specimen was used to determine the micro hole depth. Since high sensitivity and broad dynamic range is required for
*
Corresponding author. E-mail address: [email protected] (R. Petkovsˇek).
0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.069
the measurement an arm-compensated Michelson interferometer is used. The decreasing drilling rate, determined by measurements, is explained with a theoretical approach based on the energy balance during the process. In general, during laser multiple pulses drilling the interaction of the laser light with the matter can be roughly divided into two processes: heating and material ablation. A complete theoretical description of these aspects and their mutual influence, including the solid, liquid, gaseous and plasma phases represents an extremely complex task, which up to now has not been possible. For relatively long laser pulses with a relatively low intensity, the theoretical study of material ablation is based on a mechanism of surface-evaporation-induced recoil pressure, which then ejects the molten material [6]. However, if the beam intensity is sufficiently high and the pulse time is short the material evaporates very quickly, and therefore significant melt movement cannot occur [7]. This means that pure evaporation dominates the ablation process.
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R. Petkovsˇek et al. / Ultrasonics 44 (2006) e1191–e1194
Instead of a detailed description of the ablation mechanism, which is explained elsewhere [8], we have focused on a model that can explain the decreasing ablation rate during the multiple pulses micro-drilling process. Since the finite hole depth cannot be theoretically explained using a one-dimensional model that considers only the heat transfer to the bottom of the hole, we have also taken into account heat transfer to the wall of the hole. Using a one-dimensional model some effects of the local surface of the hole on the ablation rates were neglected; however, these effects only have a particularly significant influence in the case of a small beam diameter and low intensities [9].
mine the leading edge of the sound signal and to compensate the interferometer, respectively. The Michelson interferometer was compensated using a carefully designed electronic circuit with proportional-integral-derivative (PID) control. This circuit held the interferometer in the range of its maximum sensitivity by compensating for any low-frequency disturbance. This relatively complex control was needed so as to make it possible to operate in an ordinary laboratory environment without any special requirements.
2. Experimental
The aim of the proposed theoretical model is to explain the decreasing drilling rate during the micro-drilling process, as was observed experimentally. In general, the multiple pulses laser-drilling process consists of two mutually dependent processes: material heating and material ablation. In the proposed theoretical model we assumed that due to relatively high laser pulse intensity (108 W/cm2) the heating stage occurred instantly [9,12], and thus we considered only the material-removal stage. According to the model the input energy of the laser beam is absorbed predominately at the bottom of the hole and in the plasma that appears as a consequence of the high-intensity laserbeam–material interaction. The energy is then conducted away in two different ways, as follows (Fig. 2): first, the part of the energy absorbed in the material and the energy due to the interaction between plasma, vapour and melt with the hole wall and bottom is ‘‘lost’’ by conduction into the surrounding area of the specimen; second, the rest of the energy is carried away by the plasma, vapour and melt that leave the hole. The last one directly contributes to the increase of the hole depth. The equation for the energy balance can be written as
The experimental setup (Fig. 1) was constructed in order to study and control the micro-drilling process by using optodynamic analysis. A Nd-YAG laser was used as the ablation source for the micro-drilling. The pulse length was 200 ns, and the maximum energy per pulse was 9 mJ. For the specimens we used polished aluminium, steel and copper plate with different thicknesses. The principle of the measuring system is based on a measurement of the time of flight for the shock wave spreading into the processed material. The shock wave spreading into the processed material was measured on the specimen side, which is on the opposite side to where the drilling was performed. In this case an arm-compensated Michelson interferometer was used [10,11]. This represents the main part of the measuring system. It was designed to detect the leading edge of the sound waves in order to determine the time of flight and, consequently, the hole depth. In order to detect the relatively weak leading edge of the signal, and filter it from the unwanted signal and noise, several measures were taken. The high- and low-frequency parts of the signal were separated at the same time as a current-to-voltage conversion was used to keep the noise as low as possible. The highand low-frequency parts of the signal were used to deter-
Fig. 1. Experimental setup.
3. Theoretical model
EL ¼ EQW þ EQB þ EV ;
ð1Þ
Fig. 2. Schematic description of the energy balance in the case of percussion drilling, as proposed by the theoretical model.
R. Petkovsˇek et al. / Ultrasonics 44 (2006) e1191–e1194
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where EL is the energy of the laser pulse, EQW and EQB represent the energy transfer from the laser beam and the vapour and molten material by conduction through the hole bottom and the wall, respectively. EV is the energy of the ablated material (vapour, plasma and molten material). Considering the sequence of N pulses and using onedimensional heat transfer the above equation can be transformed into the following relation: Z tL Z tP Z tL dhN 2 dt; ð2Þ P L dt ¼ jQ ðprhN þ pr Þdt þ qqpr2 dt 0 0 0 where r is the hole radius, hN is the hole depth after the N-th pulse, q is the mass density of processed material, q is the specific heat needed to ablate the material. tL and tP in are the laser-pulse duration and the decay time of the vapour inside the hole, respectively. jQ is the heat flux density that appears as a consequence of heat conduction through the wall and the bottom of the hole. In a onedimensional model it can be approximated by kðT W T 0 Þ pffiffiffiffiffiffiffi ; ð3Þ 2 atP pffiffiffiffiffiffiffi where the 2 atP represents the characteristic length of the heat conduction, which means that the majority of the temperature change lies within this depth for a given time tP. As was already mentioned, a high beam intensity and short pulses induce pure evaporation, which dominates the ablation process. Therefore, q can be roughly estimated by the specific heat needed to evaporate the material. It is important to note that the energy lost by heat conduction through the hole wall does not occur only when the laser beam is applied. The energy is also conducted away after the laser pulse is terminated, because the hot vapour still exist in the hole and interact with the wall and therefore decrease the effectiveness of the drilling process. This means that in addition to the pure laser-pulse characteristic, the decay time of the vapour inside the hole also have a significant influence on the hole-depth increment. From Eq. (2) it follows that the energy lost by conduction through the hole boundary is proportional to the hole depth hN. Therefore, for an increasing number of consecutive pulses, and at constant laser-pulse energy, the drilling rate, represented by the last term in Eq. (2), decreases. jQ ¼
4. Results The hole depth during the drilling process was measured by detecting the shock wave’s time of flight, which appears as a typical optodynamic phenomenon. A typical displacement as a consequence of the sound wave spreading into the processed material is shown in Fig. 3. The time zero in the graph corresponds to the start of the laser pulse. The depth of the hole hN, after N-th pulse is applied, can be obtained from time-of-flight measurement using the simple relation: hN ¼ d cL tFN ;
Fig. 3. Displacement due to shock wave propagating into processed material for 1st, 25th and 50th laser pulse and corresponding time of flights: tF1, tF25 and tF50. It is obtained from compensated Michelson interferometer.
where d is the thickness of the test specimen, cL is the speed of the longitudinal mode of sound and tFN is the time of flight for the N-th pulse. According to the proposed model the energy lost as a result of heat conduction, and therefore the hole-depth increment, depends on the decay time of the vapour inside the hole. The decay time of vapour depends on the hole depth and effective speed veff of the vapour living the hole: tP ¼ tP ðhN Þ
hN ; veff
ð4Þ
By integrating Eq. (2) using (3) and (4), and rearranging the obtained results, the following relation for the depth increment can be obtained: pffiffiffiffiffiffi EL 2hN kðT W T 0 Þ DhN ¼ h 1 þ ð5Þ pffiffiffiffiffiffiffiffiffi : N 2qq veff a qP qpr2 r Or the hole depth is: X hN h¼ N
Maximum hole depth can be estimated (limit case when DhN = 0) from Eq. (5) by considering that the r h (typical r = 0.05 mm): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 veff EL ð6Þ h¼ kcP q 2prðT W T 0 Þ A comparison of the experimental data and the theoretical prediction based on our model for three different metals (aluminium, steel and copper) are depicted in Fig. 4. The radius r of the hole was obtained from experimental data and the temperature of the hole boundary was set to the melting point. The effective speed veff is set to be same for all metals and is obtained from the (6) using a fitting procedure, where theoretically predicted maximum depth of the hole for different metals are fitted to the data obtained
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tion. Furthermore, it is important to take into account that the heat is conducted away not only because of laser-light absorption, but also due to the interaction between the hole surface and the vapour existing inside the hole. Consequently, with an increasing depth of hole the energy that is available for the ablation is decreased and so the drilling rate is decreased too. By measuring the radius of the drilled hole the decreasing ablation rate and the finite hole depth predicted by model were in good agreement with the experimental results. References
Fig. 4. Hole-depth dependency of successive laser pulses for three different metals (aluminium, steel and copper). The circles, triangles, squares and the straight lines correspond to the data from the measurements and theoretical model, respectively.
from the measurement. From the Fig. 4 one can find good agreement between the experimentally obtained data and theoretical model. Therefore by using Eq. (6) a maximum hole depth can be predicted for metal samples with known physical properties and known laser pulses parameters. 5. Conclusion The non-contact optodynamic method described in this paper for an investigation of the laser-percussion microdrilling process proved to be very successful for studying the micro-drilling process. The decreasing drilling rate that leads to the finite hole depth was obtained from experimental data. A theoretical calculation based on a one-dimensional model and the energy balance characterized by the finite hole depth was carried out. The model relies on the fact that the heat flux conducted into the processed specimen is ‘‘lost’’ and therefore useless for the material abla-
[1] J.B. Spicer, A.D.W. Mckie, J.W. Wagner, Quantitative theory for laser ultrasonic-waves in a thin plate, Appl. Phys. Lett. 57 (1990) 1882. [2] T.W. Murray, J.W. Wagner, Laser generation of acoustic waves in the ablative regime, J. Appl. Phys. 85 (1999) 2031. [3] J. Diaci, Response function of the laser-beam deflection probe for detection of spherical acoustic-waves, Rev. Sci. Instrum. 63 (1992) 5306–5310. [4] S. Strgar, J. Mozˇina, An optodynamic determination of the depth of laser-drilled holes by the simultaneous detection of ultrasonic waves in the air and in the workpiece, Ultrasonics 40 (2002) 791. [5] J. Diaci, J. Mozˇina, Ultrasonic international 1989, Conference Proceedings (1989) 724. [6] M. Von Allmen, Laser drilling velocity in metal, J. Appl. Phys. 47 (1976) 5460–5463. [7] V. Semak, X. Chen, K. Mundra, J. Zhao, Numerical simulation of hole profile in high beam intensity laser drilling, Proc. of Laser Material Processing Conf. (1997) 81–90. [8] P. Solana, P. Kapadsia, J.M. Dowden, P.J. Marsden, An analitical model for the laser drilling of metals with absorption within the vapor, J. Phys. D: Appl. Phys. 32 (1999) 942–952. [9] A. Ruf, P. Berger, F. Dausinger, H. Huegel, Analytical investigation on geometrical influences on laser drilling, J. Phys. D: Appl. Phys. 34 (2001) 2918–2925. [10] T.W. Murray, J.B. Deaton, J.W. Wagner, Experimental evaluation of enhanced generation of ultrasonic waves using an array of laser sources, Ultrasonics 34 (1996) 69–77. [11] R. Petkovsek, M. Grisa, J. Mozina, Optodynamic characterization of the shock waves after laser-induced breakdown in water, Optics Express 13 (2005) 4107–4112. [12] G. Chryssolouris, Laser MachiningTheory and Practice, SpringerVerlag, New York, 1991.
Optodynamic study of multiple pulses micro drilling Rok Petkovsˇek *, Igor Panjan, Alesˇ Babnik, Janez Mozˇina Faculty of Mechanical Engineering, University of Ljubljana, Asˇkercˇeva 6, 1000 Ljubljana, Slovenia Available online 5 June 2006
Abstract This paper describes an analysis of pulsed lasers micro-drilling of different metals. Study focuses to an optodynamic phenomenon which appears as thermal effects induced by laser light pulses and leads to dynamic process manifested as ultrasonic shock waves propagating into the sample material. The shock waves are detected by a non-contact optical method by using arm compensated Michelson. Monitoring of the main parameters of the micro drilling such as material ablation rate and efficiency was realized by analysis of the optodynamic signals. The process is characterized by decreasing ablation rate that leads to the finite hole depth. The experimental part of study comprehends a comparison between various metals. In order to describe decreasing ablation rate a theoretical model based on the energy balance is proposed. It considers the energy/heat transfer from the laser beam to the material and predicts a decreasing drilling rate with an increasing number of successive laser pulses. According to the proposed model, the finite depth of the hole appears as a consequence of the increasing surface area through which the energy of the laser beam is conducted away to the material around the processed area. Decreasing ablation rate and the finite hole depth predicted by model were in good agreement with the experimental results. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Optodynamics; Laser; Ablation; Drilling
1. Introduction Multiple pulses micro drilling is a typical optodynamic process. It is well know that optical, laser-induced ablation are the source of the ultrasound shock wave that represents the dynamic process. In general two types of shock waves appear: one is propagated through the processed specimen and another through surrounding atmosphere [1–3]. This phenomenon can be used to study, monitor or control several types of pulsed-laser processes [4,5]. In this paper we describe an optodynamic method for investigating the laser multiple pulses micro-drilling process, which is characterized by a hole of finite depth. The analysis is based on measuring the time of flight of shock waves. The time of flight for shock waves propagating through the processed specimen was used to determine the micro hole depth. Since high sensitivity and broad dynamic range is required for
*
Corresponding author. E-mail address: [email protected] (R. Petkovsˇek).
0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.069
the measurement an arm-compensated Michelson interferometer is used. The decreasing drilling rate, determined by measurements, is explained with a theoretical approach based on the energy balance during the process. In general, during laser multiple pulses drilling the interaction of the laser light with the matter can be roughly divided into two processes: heating and material ablation. A complete theoretical description of these aspects and their mutual influence, including the solid, liquid, gaseous and plasma phases represents an extremely complex task, which up to now has not been possible. For relatively long laser pulses with a relatively low intensity, the theoretical study of material ablation is based on a mechanism of surface-evaporation-induced recoil pressure, which then ejects the molten material [6]. However, if the beam intensity is sufficiently high and the pulse time is short the material evaporates very quickly, and therefore significant melt movement cannot occur [7]. This means that pure evaporation dominates the ablation process.
e1192
R. Petkovsˇek et al. / Ultrasonics 44 (2006) e1191–e1194
Instead of a detailed description of the ablation mechanism, which is explained elsewhere [8], we have focused on a model that can explain the decreasing ablation rate during the multiple pulses micro-drilling process. Since the finite hole depth cannot be theoretically explained using a one-dimensional model that considers only the heat transfer to the bottom of the hole, we have also taken into account heat transfer to the wall of the hole. Using a one-dimensional model some effects of the local surface of the hole on the ablation rates were neglected; however, these effects only have a particularly significant influence in the case of a small beam diameter and low intensities [9].
mine the leading edge of the sound signal and to compensate the interferometer, respectively. The Michelson interferometer was compensated using a carefully designed electronic circuit with proportional-integral-derivative (PID) control. This circuit held the interferometer in the range of its maximum sensitivity by compensating for any low-frequency disturbance. This relatively complex control was needed so as to make it possible to operate in an ordinary laboratory environment without any special requirements.
2. Experimental
The aim of the proposed theoretical model is to explain the decreasing drilling rate during the micro-drilling process, as was observed experimentally. In general, the multiple pulses laser-drilling process consists of two mutually dependent processes: material heating and material ablation. In the proposed theoretical model we assumed that due to relatively high laser pulse intensity (108 W/cm2) the heating stage occurred instantly [9,12], and thus we considered only the material-removal stage. According to the model the input energy of the laser beam is absorbed predominately at the bottom of the hole and in the plasma that appears as a consequence of the high-intensity laserbeam–material interaction. The energy is then conducted away in two different ways, as follows (Fig. 2): first, the part of the energy absorbed in the material and the energy due to the interaction between plasma, vapour and melt with the hole wall and bottom is ‘‘lost’’ by conduction into the surrounding area of the specimen; second, the rest of the energy is carried away by the plasma, vapour and melt that leave the hole. The last one directly contributes to the increase of the hole depth. The equation for the energy balance can be written as
The experimental setup (Fig. 1) was constructed in order to study and control the micro-drilling process by using optodynamic analysis. A Nd-YAG laser was used as the ablation source for the micro-drilling. The pulse length was 200 ns, and the maximum energy per pulse was 9 mJ. For the specimens we used polished aluminium, steel and copper plate with different thicknesses. The principle of the measuring system is based on a measurement of the time of flight for the shock wave spreading into the processed material. The shock wave spreading into the processed material was measured on the specimen side, which is on the opposite side to where the drilling was performed. In this case an arm-compensated Michelson interferometer was used [10,11]. This represents the main part of the measuring system. It was designed to detect the leading edge of the sound waves in order to determine the time of flight and, consequently, the hole depth. In order to detect the relatively weak leading edge of the signal, and filter it from the unwanted signal and noise, several measures were taken. The high- and low-frequency parts of the signal were separated at the same time as a current-to-voltage conversion was used to keep the noise as low as possible. The highand low-frequency parts of the signal were used to deter-
Fig. 1. Experimental setup.
3. Theoretical model
EL ¼ EQW þ EQB þ EV ;
ð1Þ
Fig. 2. Schematic description of the energy balance in the case of percussion drilling, as proposed by the theoretical model.
R. Petkovsˇek et al. / Ultrasonics 44 (2006) e1191–e1194
e1193
where EL is the energy of the laser pulse, EQW and EQB represent the energy transfer from the laser beam and the vapour and molten material by conduction through the hole bottom and the wall, respectively. EV is the energy of the ablated material (vapour, plasma and molten material). Considering the sequence of N pulses and using onedimensional heat transfer the above equation can be transformed into the following relation: Z tL Z tP Z tL dhN 2 dt; ð2Þ P L dt ¼ jQ ðprhN þ pr Þdt þ qqpr2 dt 0 0 0 where r is the hole radius, hN is the hole depth after the N-th pulse, q is the mass density of processed material, q is the specific heat needed to ablate the material. tL and tP in are the laser-pulse duration and the decay time of the vapour inside the hole, respectively. jQ is the heat flux density that appears as a consequence of heat conduction through the wall and the bottom of the hole. In a onedimensional model it can be approximated by kðT W T 0 Þ pffiffiffiffiffiffiffi ; ð3Þ 2 atP pffiffiffiffiffiffiffi where the 2 atP represents the characteristic length of the heat conduction, which means that the majority of the temperature change lies within this depth for a given time tP. As was already mentioned, a high beam intensity and short pulses induce pure evaporation, which dominates the ablation process. Therefore, q can be roughly estimated by the specific heat needed to evaporate the material. It is important to note that the energy lost by heat conduction through the hole wall does not occur only when the laser beam is applied. The energy is also conducted away after the laser pulse is terminated, because the hot vapour still exist in the hole and interact with the wall and therefore decrease the effectiveness of the drilling process. This means that in addition to the pure laser-pulse characteristic, the decay time of the vapour inside the hole also have a significant influence on the hole-depth increment. From Eq. (2) it follows that the energy lost by conduction through the hole boundary is proportional to the hole depth hN. Therefore, for an increasing number of consecutive pulses, and at constant laser-pulse energy, the drilling rate, represented by the last term in Eq. (2), decreases. jQ ¼
4. Results The hole depth during the drilling process was measured by detecting the shock wave’s time of flight, which appears as a typical optodynamic phenomenon. A typical displacement as a consequence of the sound wave spreading into the processed material is shown in Fig. 3. The time zero in the graph corresponds to the start of the laser pulse. The depth of the hole hN, after N-th pulse is applied, can be obtained from time-of-flight measurement using the simple relation: hN ¼ d cL tFN ;
Fig. 3. Displacement due to shock wave propagating into processed material for 1st, 25th and 50th laser pulse and corresponding time of flights: tF1, tF25 and tF50. It is obtained from compensated Michelson interferometer.
where d is the thickness of the test specimen, cL is the speed of the longitudinal mode of sound and tFN is the time of flight for the N-th pulse. According to the proposed model the energy lost as a result of heat conduction, and therefore the hole-depth increment, depends on the decay time of the vapour inside the hole. The decay time of vapour depends on the hole depth and effective speed veff of the vapour living the hole: tP ¼ tP ðhN Þ
hN ; veff
ð4Þ
By integrating Eq. (2) using (3) and (4), and rearranging the obtained results, the following relation for the depth increment can be obtained: pffiffiffiffiffiffi EL 2hN kðT W T 0 Þ DhN ¼ h 1 þ ð5Þ pffiffiffiffiffiffiffiffiffi : N 2qq veff a qP qpr2 r Or the hole depth is: X hN h¼ N
Maximum hole depth can be estimated (limit case when DhN = 0) from Eq. (5) by considering that the r h (typical r = 0.05 mm): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 veff EL ð6Þ h¼ kcP q 2prðT W T 0 Þ A comparison of the experimental data and the theoretical prediction based on our model for three different metals (aluminium, steel and copper) are depicted in Fig. 4. The radius r of the hole was obtained from experimental data and the temperature of the hole boundary was set to the melting point. The effective speed veff is set to be same for all metals and is obtained from the (6) using a fitting procedure, where theoretically predicted maximum depth of the hole for different metals are fitted to the data obtained
e1194
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tion. Furthermore, it is important to take into account that the heat is conducted away not only because of laser-light absorption, but also due to the interaction between the hole surface and the vapour existing inside the hole. Consequently, with an increasing depth of hole the energy that is available for the ablation is decreased and so the drilling rate is decreased too. By measuring the radius of the drilled hole the decreasing ablation rate and the finite hole depth predicted by model were in good agreement with the experimental results. References
Fig. 4. Hole-depth dependency of successive laser pulses for three different metals (aluminium, steel and copper). The circles, triangles, squares and the straight lines correspond to the data from the measurements and theoretical model, respectively.
from the measurement. From the Fig. 4 one can find good agreement between the experimentally obtained data and theoretical model. Therefore by using Eq. (6) a maximum hole depth can be predicted for metal samples with known physical properties and known laser pulses parameters. 5. Conclusion The non-contact optodynamic method described in this paper for an investigation of the laser-percussion microdrilling process proved to be very successful for studying the micro-drilling process. The decreasing drilling rate that leads to the finite hole depth was obtained from experimental data. A theoretical calculation based on a one-dimensional model and the energy balance characterized by the finite hole depth was carried out. The model relies on the fact that the heat flux conducted into the processed specimen is ‘‘lost’’ and therefore useless for the material abla-
[1] J.B. Spicer, A.D.W. Mckie, J.W. Wagner, Quantitative theory for laser ultrasonic-waves in a thin plate, Appl. Phys. Lett. 57 (1990) 1882. [2] T.W. Murray, J.W. Wagner, Laser generation of acoustic waves in the ablative regime, J. Appl. Phys. 85 (1999) 2031. [3] J. Diaci, Response function of the laser-beam deflection probe for detection of spherical acoustic-waves, Rev. Sci. Instrum. 63 (1992) 5306–5310. [4] S. Strgar, J. Mozˇina, An optodynamic determination of the depth of laser-drilled holes by the simultaneous detection of ultrasonic waves in the air and in the workpiece, Ultrasonics 40 (2002) 791. [5] J. Diaci, J. Mozˇina, Ultrasonic international 1989, Conference Proceedings (1989) 724. [6] M. Von Allmen, Laser drilling velocity in metal, J. Appl. Phys. 47 (1976) 5460–5463. [7] V. Semak, X. Chen, K. Mundra, J. Zhao, Numerical simulation of hole profile in high beam intensity laser drilling, Proc. of Laser Material Processing Conf. (1997) 81–90. [8] P. Solana, P. Kapadsia, J.M. Dowden, P.J. Marsden, An analitical model for the laser drilling of metals with absorption within the vapor, J. Phys. D: Appl. Phys. 32 (1999) 942–952. [9] A. Ruf, P. Berger, F. Dausinger, H. Huegel, Analytical investigation on geometrical influences on laser drilling, J. Phys. D: Appl. Phys. 34 (2001) 2918–2925. [10] T.W. Murray, J.B. Deaton, J.W. Wagner, Experimental evaluation of enhanced generation of ultrasonic waves using an array of laser sources, Ultrasonics 34 (1996) 69–77. [11] R. Petkovsek, M. Grisa, J. Mozina, Optodynamic characterization of the shock waves after laser-induced breakdown in water, Optics Express 13 (2005) 4107–4112. [12] G. Chryssolouris, Laser MachiningTheory and Practice, SpringerVerlag, New York, 1991.