Investigation of laser and process parameters for Selective Laser Erosion

Investigation of laser and process parameters for Selective Laser Erosion

Precision Engineering 34 (2010) 101–112 Contents lists available at ScienceDirect Precision Engineering journal homepage: www.elsevier.com/locate/pr...

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Precision Engineering 34 (2010) 101–112

Contents lists available at ScienceDirect

Precision Engineering journal homepage: www.elsevier.com/locate/precision

Investigation of laser and process parameters for Selective Laser Erosion E. Yasa ∗ , J.-P. Kruth Department of Mechanical Engineering, Catholic University of Leuven, Celestijnenlaan 300B, 3001 Heverlee, Belgium

a r t i c l e

i n f o

Article history: Received 21 August 2007 Received in revised form 29 October 2008 Accepted 6 April 2009 Available online 18 April 2009 Keywords: Laser erosion Parameter study

a b s t r a c t The process of Selective Laser Erosion (SLE) was investigated to study the effects of different process and laser parameters on the process outputs such as surface quality and erosion rate. The SLE process is a direct method to remove material in a layer-by-layer fashion due to high energy densities provided by the laser beam. In addition to its direct use as a subtractive manufacturing method, SLE may be used in combination with layer-additive techniques such as Selective Laser Melting (SLM). Such combination mainly makes sense when both processes can be performed with the same laser. However, one of the major problems involved in SLE process is the high number of the laser and process parameters (laser power, pulse frequency, scan speed, scan spacing, ambient atmosphere, etc.) and the complexity of the relations between them which has not yet been investigated completely. This paper presents an overview of the laser erosion process with nano-second Nd:YAG laser pulses and the results of several single-factor experiments that were carried out to determine the influence of the major parameters on the depth of erosion per layer and surface roughness. Additionally, the relations between the parameters are studied to investigate the interactions between them. The results from singlefactor experiments showed that some relations were highly governed by the power intensity of the laser beam and also that cross interactions between the parameters play an important role on the output characteristics. The paper explains how multiple parameters (spot size, pulse frequency, scan speed, scan spacing) can be combined to define two indirectly controlled geometrical parameters, namely the scan and pulse overlap factors. Those two parameters allow calculating the number of hits of the laser beam on a same location on the workpiece possible which is the first step in physical modeling the topography of the surface left behind. © 2009 Elsevier Inc. All rights reserved.

1. Introduction Lasers find wide applications in manufacturing industry due to their precise operation and flexibility. This holds for laser marking [1], engraving, laser milling [2,3], laser drilling [4–6], laser cutting [7,8], enhancement of surface morphology [9,10] or surface hardness, or for the generation of three-dimensional (3D) parts [11]. Yet, laser erosion is a comparatively new technology. It can be used in conjunction with rapid manufacturing (RM) and rapid prototyping (RP) and to machine parts in a wide range of materials including most metals, glass, ceramics and plastics. It is particularly suited for hard materials which cannot easily be machined by conventional manufacturing methods without sacrificing time and cost [12,13]. The Selective Laser Erosion (SLE) process is defined as the removal of material due to the heat provided by the incident laser beam in a layer-by-layer fashion. It is not only used as a self-standing process, but can also be employed to enhance other laser processes such as Selective Laser Melting [14].

∗ Corresponding author. Tel.: +32 16 322552; fax: +32 16 322987. E-mail address: [email protected] (E. Yasa). 0141-6359/$ – see front matter © 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2009.04.001

Laser erosion has some advantages over conventional material removal processes as it is a non-contact process; it has micromachining capability and is applicable to a wide range of materials. Being a non-contact process, there is no mechanical interaction and no tool wear during the process. The diameter of the laser beam can be reduced to as small as a dozen micrometers allowing very small internal radii and fine details to be produced giving SLE capability of micromachining [5,15]. Moreover, it is applicable to any material that absorbs light in a spectrum covering the wavelength of the laser source utilized on the machine. On the other hand, there are some short-comings of the process such as long processing times, heat-affected zones, process inefficiency and difficulty in machining vertical walls and the stair-effect, which is inherent to the layer-wise production. One of the major impediments in laser erosion is the high number of process and laser parameters. Moreover, their influences on the process and the interactions between them have not yet been completely studied and explored. The suitable processing strategies compromise between efficiency and precision [2]. Some studies are investigating the effect of some process parameters for laser marking applications. Qi et al. studies the effect of the pulse frequency on mark quality through single-factor

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experiments concluding that the mark depth, width and mark contrast depend on the interaction process of the laser beam and material, which is dramatically influenced by the pulse frequency [16]. Another study was performed by Tam et al. in order to optimize the process parameters in the stroke marking of plastic leadless chip carriers with a pulsed Nd:YAG laser [1]. They employed the Taguchi method of experimental design and used an L16 orthogonal array to study the effects of seven control factors and some of their interactions. Pham et al. studied the laser milling process of ceramic components reviewing the main parameters (lamp current, pulse duration, pulse frequency and scan speed) affecting the material removal characteristics of the process [3]. In the present study, the effects of several parameters such as the scanning strategy, scan speed, scan spacing pulse frequency, aperture opening (spot size) and laser current (in other words laser power) are explored using an Nd:YAG laser source with nanosecond pulse duration. Additionally, the relations between the input parameters are studied. Single-factor experimental strategy is utilized. 2. Laser erosion with nano-second pulses Laser heating of metal targets by laser pulses has been subjected to many experimental and theoretical studies [17–22]. In the pulsed-mode, the laser radiation is sent to the workpiece in an ordered sequence of pulses in order to allow the accumulated energy within one pulse period to be released in very short time intervals so that the formation of an extremely high peak power density is achieved. The actual process of material removal takes place within a pulse for pulsed laser machining. Several mechanisms exist for material removal in laser erosion [23,24]. A combination of theoretical and experimental studies conducted by Koerner et al., indicates that the material and the laser parameters determine whether the erosion process is mainly performed by evaporation or melt expulsion. As a third mechanism, spallation is observed in brittle materials, especially dielectric materials, in which the material removal is due to mechanical stresses inside the material and also due to the recoil of ablated material or an expanding plasma cloud [25]. The removal rate and the final geometry of the irradiated workpiece is a function of the material and the parameters used during the process. Laser radiation is characterized by high power density on a small spot area, monochromatic nature, good collimation and coherence and applicability to a wide variety of manufacturing processes [26]. When the laser radiation reaches the substrate material, the absorbed laser energy first melts the target surface and then heats it to the vaporization temperature. For the nanosecond

Fig. 1. Nanosecond and longer pulse laser ablation [2].

laser erosion, there is enough time for a thermal wave to propagate into the material and to create a relatively large layer of melted material. The molten material is partially ejected from the cavity by the vapour and plasma pressure but a part of it remains near the surface due to surface tension forces [2]. During the interaction, the main source of energy losses is the heat conduction into the solid target. Therefore, the thermal conductivity is a key material factor among others, such as laser absorption efficiency, melting energy and evaporation energy. This influences the dissipation of the absorbed energy into the bulk of the material, material removal efficiency and the dimensions of the heat-affected-zone (HAZ). The heat conduction is thus inevitable for nano-second laser ablation due to the long time available for the propagation of a thermal wave into the material as compared to femto- and pico-second laser ablation mechanisms. Hence a larger molten layer is created from which evaporation takes place within the nano-second laser pulse durations. In addition to a HAZ, secondary effects of nano-second laser erosion are a recast layer, micro-cracks, shock wave surface damage, plasma formation and debris of ejected material as shown in Fig. 1 [1,2].

Fig. 2. The Concept Laser M3 Linear machine (a) and Form Talysurf 3D measuring device (b).

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Fig. 4. The process window for SLE.

In the following sections, the results of the experiments are presented together with some physical explanations. 3.1. Process window for SLE Fig. 3. Some examples for eroded squares on AISI 1045 steel blocks under different test conditions.

In summary, nano-second lasers typically provide much higher pulse energy and have traditionally provided faster machining compared to shorter pulse lasers, but they interact with material on a timescale characteristic of thermal damage. When the material is irradiated with shorter pulses (pico- or femto-second durations), the penetration depth and, therefore, the interaction volume is generally smaller, slowing down the material removal process. Since there are less secondary thermal effects, pico- and femto-second machining process results in better quality and cleaner surfaces at the expense of high processing times [23,27]. It can be derived that by going to shorter pulse lengths, the thermal damage is reduced and the machining efficiency deteriorates [6]. 3. Experimental set-up and results All laser erosion experiments are carried out on a Concept Laser M3 Linear machine [28], which is the sole machine in the market combining Selective Laser Erosion with an additive called Selective Laser Melting process (Fig. 2a). The machine employs an Nd:YAG laser with a wavelength of 1064 nm and a maximum laser output power in continuous mode of approximately 100 W. The laser has two possible beam diameters ˚1/e2 : 53 ␮m (small aperture) and 133 ␮m (big aperture) (˚99% respectively 80 and 200 ␮m). Surface profiles were measured without applying any filters by means of a roughness tester (Form Talysurf 120L) and roughness values were derived as well as the erosion depth values (Fig. 2b). In this study, the effects of several parameters on the erosion depth per layer and surface quality are explored on AISI 1045 steel blocks. The experiments consist of eroding squares with a dimension of 10 mm on the workpiece for a pre-specified number of layers with a scheme of changing the investigated parameter while keeping all others constant (Fig. 3). Although the single-factor experiments do not provide a complete picture of the phenomena involved due to the probable interactions between the factors, they give an idea of the influence of the process parameters on a particular target process output, facilitating process tuning and reducing the amount of trial and error tests involved in process adjustment. Single-factor experiments can also be used to determine if interactions exist and are important.

Before studying the effect of each parameter, more general tests are conducted to investigate the process window of the process. Some of the experiments gave very bad surfaces (black, very rough) whereas some were very difficult to recognize (very light color with almost no depth). Hence, the process window for SLE is derived as given in Fig. 4. Experiments are conducted at a scan spacing of 7 ␮m and a pulse frequency of 30 kHz with the small aperture (˚99% spot size of 80 ␮m). Many pairs of scan speed and laser power are tried to investigate at which points the laser energy is enough to remove material. In order to have a good surface quality, too much energy density should be avoided as well. As observed, high laser powers with low scan speeds result in too much energy and burned surfaces. In this case, the color of the left surface is almost black. High scan speeds in combination with low laser powers, on the other hand, result in inadequate energy and no erosion. The surface is only re-melted but no material could be removed. The region in between these two zones gives better results yielding a compromise in between good surface quality and high depth of erosion.

Fig. 5. The effect of scanning strategy on the roughness and depth of erosion.

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Fig. 6. Profiles of the surfaces exposed to different scan strategies (a) 3D height maps of the same surfaces (b).

In the following sections, the experimental results are given with an emphasis on each parameter investigated. 3.2. Scanning strategy The scanning strategy is the manner in which the laser beam scans the surface of the workpiece. Scan strategies (hatching) can differ in hatch angle, scan spacing, overlap factor and direction selection (unidirectional or bidirectional). Different scanning strategies were tested and measured to investigate the effect of applying multiple layers with different hatch angles as shown in Fig. 5. The first strategy is composed of a succession of two erosion layers (repeated six times) which have scan lines perpendicular to each other (0◦ and 90◦ ). In the second strategy, the hatch angles are selected as 45◦ and 135◦ , which is the same as the first strategy except that it is only rotated by 45◦ . The third scheme has only repetition of one layer (repeated 12 times) which consists of ‘ver-

tical’ scan lines (90◦ ). The fourth one is a combination (repeated six times) of one layer of ‘vertical’ hatch lines followed by diagonal hatch lines (90◦ and 135◦ ). The last one consists of four alternating layers (repeated three times), each with a different hatch angle (0–45–90–135◦ ). During the tests, the other test parameters are selected as follows: a scan speed of 480 mm/s, a scan spacing of 7 ␮m, a pulse frequency of 30 kHz, a current of 39 A (25 W) and the selection of the small aperture (˚99% spot size of 80 ␮m). The results and the direction of measurement are displayed in Fig. 5. As observed, the depth of erosion (d) is almost independent of the scanning strategy with a maximum variation in depth of about 4.5% which equals to 0.12 ␮m for the average depth value of 2.73 ␮m. This variation can be considered insignificant and due to experimental scatter (variations in oxygen content, temperature, etc.). However, the variations in roughness are pretty high and equal to 49% for average roughness Ra , and 33% for the total roughness Rt . As expected, the worst roughness values are exhibited by the third

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Fig. 7. The effect of scan speed on the depth of erosion for different test conditions.

scanning strategy where all scan lines have the same orientation. This can be explained by the fact that when the same hatch pattern is applied successively, the created peaks and valleys by the laser scan lines on the surface get more severe. The fifth scanning strategy, which is made of four alternating hatch layers, achieves the best Ra whereas the best Rt is obtained by the second one. This conclusion is confirmed by [9], where substantial reduction of the surface roughness was achieved by changing the scanning direction (hatch angle) from layer to layer. As a result of these tests, it can be concluded that alternating layers improves the surface roughness significantly, by about 50% for both average and total roughness values whereas it has no significant effect on the rate of erosion. In addition to comparisons of different scan strategies in terms of roughness and erosion depth, the average profiles of the surfaces along the measurement direction for a second set of tests are plotted in Fig. 6a. The test parameters were as follows; a scan speed of 480 mm/s, a laser power of 25 W, a pulse frequency of 30 kHz and an overlap factor of 80% (a scan spacing of 16 ␮m), small aperture, eight layers. The low surface quality of the scanning strategy consisting of only vertical scan lines (3) can also be observed from its average profile as given in Fig. 6a. In Fig. 6b, the 3D height maps of the same surfaces are also illustrated where the scan tracks can be easily recognized.

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Fig. 8. The effect of scan speed on the average roughness for different test conditions.

interactions between the test parameters, namely scan speed and scan spacing. The interaction between scan spacing and scan speed is expected to be significant since they together influence the overlapping factor between successive laser pulses and scan lines. Another important observation is that the first and second cases give very close results for both average roughness and depth of erosion. Hence the influence of the environment (N2 or regular air) on erosion depth and average roughness is insignificant for this material. 3.4. Scan spacing The scan spacing is the distance between two successive scan lines and is an important factor for the determination of overlapping between scan lines. For low values of scan spacing which correspond to high overlapping factor, the energy per unit area is high and results in higher amount of removed material. On the other hand, a scan spacing value which is greater than the effective laser spot diameter results in totally separate material removal tracks: some material in between tracks is not removed. This case is depicted in Fig. 9. For a good connection between successive scan tracks and low roughness values, high scan spacing values (low overlap values) should be avoided. The overlap factor is related to the scan spacing with the following equation:

3.3. Scan speed

scan spacing = (1 − overlap) × spot size (˚99% )

The scan speed is a very important key parameter on the depth per layer as well as on roughness. As the scan speed increases, the energy per unit area decreases, so does the depth per layer. On the contrary, the process time increases substantially when low scan speeds are selected. The scan speed also influences the overlapping between subsequent laser pulses; the lower the speed, the greater the overlap and the thicker the eroded layer due to multi-pulse radiation (explained more in Section 4). Experiments at different scan speeds are depicted in Figs. 7 and 8. The first case is a test performed with a scan spacing of 75 ␮m, a lamp current of 36 A and a frequency of 30 kHz with a big aperture under nitrogen (N2 ) environment with an oxygen (O2 ) content of less than 1%, whereas the second case is conducted at the same conditions except that it was carried out in regular air. The last case was also performed under regular air but with a scan spacing value of 25 ␮m. Figs. 7 and 8 show that depth of erosion and roughness are both inversely proportional to the scan speed. As the scan speed is increased, the surface quality improves but the depth of erosion per layer is decreased for all cases. The slopes of LSQ fitted lines for different scan spacing values differ. This refers to the possible

Fig. 9. Totally separate tracks due to incorrect selection of scan spacing value.

(1)

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Fig. 11. The effect of scan spacing on the average roughness.

Fig. 10. The effect of scan spacing on the depth of erosion.

The depth measured with different overlap values (10–95%) are presented in Fig. 10 for four different test conditions which are given in the table below the figure. The scanning was conducted in grid pattern (strategy number 1) applied four times (eight layers) with the selection of small aperture (˚99% —spot size of 80 ␮m). A lower scan spacing results in higher depth consistently with the expectations due to the increase of laser energy per unit area. At overlap

values lower than 50%, there is no material removal. The scanned surface is only molten and re-solidified leaving a very bad surface quality behind. Therefore, no value is specified in Fig. 10 for these two overlap values (10–30%). In Fig. 11, the variation of the average roughness is given with respect to scan spacing for the same conditions given in Fig. 10. An overlap factor of 10% or 30% results in very high average roughness. As the overlap factor is increased, the surface quality improves and reaches a minimum value. The relation between scan spacing and roughness changes after this critical overlap factor where the minimum Ra value for a specified set of conditions is achieved. As the overlap factor is further increased, the surface quality deteriorates. Generally, the critical overlap factor lies between 60% and 80%. The average profiles of the laser machined surfaces with different scan spacing values are illustrated in Fig. 12 where the numbers

Fig. 12. Average profiles of the scanned surfaces with different overlap factors.

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Fig. 13. The 3D height maps of the surfaces in Fig. 12.

above the graphs represent the overlap factors. The parameters were fixed at following values during this set of experiments: 600 mm/s, 20 W, 45 kHz, small aperture, eight layers and with a selection of grid scanning strategy (strategy 1). The roughness improvement is clearly seen with an increasing overlap factor from very low factors to medium factors. The depth of erosion also increases substantially with decreasing scan spacing factor. The 3D height maps of the surfaces left behind are depicted in Fig. 13 where it is seen that the low overlap factors below 50% result in a bad connection between successive tracks and there is no erosion for those overlap factors. 3.5. Laser pump current (laser power) The pump current regulates the laser power and is one of the most important process parameters for SLE due to its direct effect on the removal rate and the layer. A lower limit for the laser power intensity ensures the evaporation of material necessary for SLE. If the laser power intensity is kept below a certain threshold, the workpiece material is only melted and not removed [29]. Tests were carried out with a pump current from 27 to 37 A. Different scan speeds during the tests are used as mentioned in Fig. 14, whereas the pulse frequency was set to 30 kHz with a scan spacing of 7 ␮m and a small aperture selection. Figs. 14 and 15 depict the results of those tests. The depth of erosion is expected to be highly dependent on the current since the average power of the laser beam increases linearly as a function of the lamp current as given in Fig. 14 where the effect of the scan speed is also illustrated. When the scan speed increases, the energy input per unit area to the workpiece becomes less and the depth per layer is thus reduced. The change of depth with varying pump current is therefore not an independent relation since the scan speed has a very significant influence. Fig. 15 shows the change of average roughness with different values of pump current and scan speed. The figure clearly indicates that as the current is increased, the surface quality deteriorates. The influence of the scan speed is in the reverse way; increasing the scan speed lowers the average roughness values, which is also consistent with the results of the experiments conducted for the effect of scan speed and scan spacing.

Fig. 14. The effect of current on the depth per layer for different scan speeds.

3.6. Pulse frequency The pulse frequency of a Q-switched Nd:YAG laser has a significant effect on the process. Experiments were done in a range of 20–50 kHz and the results are depicted in Figs. 16 and 17 for

Fig. 15. The effect of current on the average roughness for different scan speeds.

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Fig. 18. The variation of depth per layer for two different aperture openings. Fig. 16. The change of depth of erosion versus pulse frequency under different test conditions.

depth of erosion per layer and average roughness, respectively. The tests were conducted with a small aperture and a scan spacing of 7 ␮m. The tests are repeated for different laser powers and scan speeds. The relation between the frequency and the amount of material removed per layer is not the same for each selected set of testing conditions. For the first case (300 mm/s, 36 A corresponding to 21 W), the maximum depth of erosion is obtained at about 30–35 kHz and the relation can be best expressed with a quadratic polynomial. However, when the pump current, in other words the laser energy, is decreased, the relation of the pulse frequency with the depth of erosion approaches a linear trend. Furthermore, as the scan speed is raised to 480 mm/s from 300 mm/s, it is observed that the amount of material per layer expectedly decreases for the same level of laser power. It can be concluded that the relation between the frequency and depth of erosion highly depends on other testing conditions. This is due to the change in peak power and the average output power of the laser with change of the pulse frequency [10]. At low pulse frequency, the peak power is high enough to make materials evaporate during the process. Thus, the amount of material removed increases with the average output power of the laser, which can be defined as the energy transferred into the materials per unit time. At high frequency values, the peak power decreases by increasing pulse frequency. The decreasing peak power is no longer high enough to evaporate the materials completely. Therefore, the peak power determines the amount of the material removed in high

Fig. 17. The change of average roughness under different test conditions versus pulse frequency.

frequency values. The depth of erosion declines as the frequency increases. Fig. 17 illustrates the change of average roughness with respect to frequency. As frequency increases, the general trend for the roughness is a decreasing one. However, the amount of reduction is not independent of power and scan speed. For the low scan speed (300 mm/s) and high laser power (21 W), the lowest average roughness is achieved with the highest frequency value used in the experiments. This result is also valid at high scan speed (480 mm/s). For the low power (12 W) and low scan speed (300 mm/s), the influence of frequency on the average roughness is rather limited and not very significant. 3.7. Spot size The power intensity of the laser is highly dependent on the spot size. On the Concept Laser M3 Linear machine, there are only two available aperture settings yielding a spot size of ˚1/e2 : 53 ␮m (small aperture) and 133 ␮m (big aperture) (˚99% respectively 80 and 200 ␮m). Four sets of experiments are carried out both for small and big apertures with different scan speeds and laser powers at fixed pulse frequency (30 kHz) and scan spacing (5 ␮m). The test conditions as well as the results are given in Figs. 18 and 19. The results show that the big aperture always results in higher values in both depth of erosion and average roughness. The amount of the change from small to big spot size is not fixed and depends strongly on other parameters.

Fig. 19. The change of average roughness for two different spot sizes.

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Fig. 20. The illustration of scan spacing, spot size and overlap.

In order to machine fine details and/or thin walls, the smaller spot size would be more suitable. However, when processing time is the most important parameter to be minimized, the big spot size is selected which shortens the processing time significantly. 4. Combining parameters for topography modelling

Fig. 21. Overlap behavior at a spot diameter of 70 ␮m.

The laser power intensity is highly dependent on the pulse overlap and the overlap between successive scan lines. Thus, the material removal rate during laser beam scanning is proportional to the number of passes of high-energy laser beam over the same spot on the workpiece. The more the number of passes, the more energy is inserted on that spot and the more material is removed due to multi-pulsation. In order to have a complete physical model of the erosion process, the overlap factors between successive laser pulses and scan lines should be investigated to be able to calculate the number of passes on each spot. If the overlap factors were written as a function of other parameters, the number of laser and process parameters that need to be investigated for their effects on the process outputs could be reduced. Fig. 20 illustrates the relation between scan spacing, spot size and pulse overlap. The scan spacing together with the spot size defines the overlap between the successive scan lines whereas the pulse overlap is dependent on the selection of scan speed, frequency and spot size. The percentage overlap between successive scan lines (scan overlap) can be calculated according to Eq. (1) whereas the percentage overlap of individual laser pulses (pulse overlap) equal to:



Up = 1 −

v f ·d



× 100

(2)

where v is the scan speed (mm/s), f the pulse frequency (kHz) and d is the spot size (˚99% ) (␮m) [26]. Thus, an increasing scan speed, decreasing frequency and decreasing spot size reduce the pulse

overlap whereas increasing scan spacing results in a lower scan overlap. Eq. (2) is illustrated in Fig. 21. The mathematical formulation of overlapping factors gives an advantage for understanding the real physics behind the process. Using these equations, the number of pulses that target the same location on the workpiece can be calculated and the scanning of the surface can be simulated off-line before the process starts. A 3D measurement of a scanned track is given in Fig. 22. The picture left gives a top view (2D) of a scan track. The two white lines are delimiting the area that is depicted in perspective view (3D) on the picture right. Obviously such picture could only be obtained (i.e. measured) after the process is completed. However, it would be very useful to get such picture before the process starts in order to be able to predict the resulting surface. A manual MATLAB code was written in order to simulate any given test conditions. Some examples are depicted in Figs. 23 and 24. Due to different scales in x and y axes, laser beam spots appear as ellipses whereas they are plotted as circles having the diameter of 70 ␮m. In Fig. 23, the effects of the scan speed and pulse frequency are shown. The selection of the scan spacing is not necessary for pulse overlap as seen in the equation for pulse overlap (Eq. (2)). Increasing the scan speed decreases the pulse overlap whereas increasing the pulse frequency results in higher overlaps. Fig. 24 depicts the pulse and scan overlaps together in the same simulation. Fig. 24a shows a case where the scan spacing is equal to the spot size of the laser beam whereas the scan spacing is half of the spot size in Fig. 24b. The last case depicts a scan spacing of less than the half of the spot size.

Fig. 22. The 3D measurement results of one test case (32 A, 20 kHz, 450 mm/s, small aperture).

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Fig. 25. MATLAB code’s working principle.

Fig. 23. The effect of scan speed and pulse frequency on pulse overlap: (a) Up = 60 ␮m, (b) Up = 35 ␮m and (c) Up < 0.

Fig. 24. The effect of scan speed on the scan overlap: (a) Up = 60 ␮m, scan spacing = 70 ␮m, (b) Up = 35 ␮m, scan spacing = 35 ␮m and (c) Up < 0, scan spacing = 20 ␮m.

In the simulation, the number of hits at every grid point is calculated by representing a pre-specified sample area as a set of points located at very small distances from each other as shown in Fig. 25. In the simulations, the grid distance is taken as 0.3 ␮m for a good resolution and accuracy. Then, the number of hits on each grid point in this area is calculated until the scanning process is completed by checking if the point lies in the moving laser beam spot. The result is a contour plot showing the number of hits on each region in the pre-specified area. An example is given in Fig. 26. The maximum number of hits occurs in the inner regions and in this example it is equal to 29 which means that those areas are hit 29 times in total. Assuming a constant erosion depth per pulse, we can model the shape of the eroded surface in 3D. This gives us the opportunity to analyze the influence of various process parameters on outputs such as the surface roughness and depth of erosion per layer. As seen in Fig. 26, the generated shape is rather complicated. The surface profile left behind is definitely a function of this topography which is further influenced by the interaction between the laser beam and material in terms of the laser power and material properties. On the other hand, the model only takes the number of hits on one point into account but not the Gaussian intensity profile of the laser beam or the melt flow. However, for low pulse overlap factors, the surfaces can be simulated. The simulation for one

Fig. 26. The contours showing the number of hits.

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Fig. 27. Comparison of simulation and experimental results for a single scanned line, case 1.

Fig. 28. Comparison of simulation and experimental results for a single scanned line, case 2.

Fig. 29. Comparison of simulation and experimental results for a scanned area.

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scan line which is eroded by a scan speed of 600 mm/s, pulse frequency of 5 kHz, small aperture (˚99% 80 ␮m), laser power of 25 W, is shown in Fig. 27. The first plot shows the MATLAB simulation result whereas the second one is 3D height map of the line that is derived by 3D measurements. The last plot illustrates the average profile along the scanning direction. A travel period of 1.5 mm is shown in the plots where 13 spots are visible both in simulation and experimental results. A second example for single line scanning is given in Fig. 28. The good agreement between the experimental and simulation results is also present for this case which was also shown in Fig. 22 as a sample test case. Another example is given for multiple scan tracks in Fig. 29 where the two plots on the left illustrate the experimental results derived by 3D measurements whereas the last column represents the simulation results. The simulation and experimental results are in good agreement to accurately calculate the distances between the peaks or valleys but it is still difficult to predict the complete surface without taking other aspects such as Gaussian beam intensity, material–laser interaction, and melt flow into consideration. Using the overlap factors, the need to study many process and laser parameters (spot size, scan speed, pulse frequency, scan spacing) is lessened since they are combined in one single parameter. Therefore, the factors that affect the output parameters can be summarized as scan overlap, pulse overlap and laser power for one single layer. This absolutely helps to decrease the size of experiments, either in single-factor studies or in design of experiments. 5. Conclusions This paper has presented an overall view of the Selective Laser Erosion process for pulsed laser mode with nano-second durations. The results of single-factor experiments are analyzed in order to investigate the influence of several parameters on the process. The studied parameters, such as scan strategy, scan speed, scan spacing, pulse frequency, laser pump current (laser power) and spot size, generally exhibit a behavior that is not consistent for all testing conditions although the general trends are the same. This is due to the fact that the relations highly depend on the selection of the other parameters, which suggests that cross interactions between the parameters play an important role on the responses (depth of erosion and roughness) of the process. Experimental design was employed in previous studies of the authors to investigate the main factor effects and their interactions and the results were reported in [30]. However, single-factor experiments are adequate to give a general idea about the change of output factors (depth of erosion and average roughness) with respect to process and laser parameters. Additionally, they are very necessary for the identification of factor ranges in the experimental design. The paper also discussed how to combine some parameters through mathematical formulation of two overlap factors: scan and pulse overlap factors. Thus, the number of parameters to be investigated is reduced both for single-factor experiments and the design of experiments. The calculation of the number of hits of the laser on the same location is a first step in physical modeling the topography of the surface left behind. A manually written MATLAB code can be employed to calculate the depth of erosion per one layer and the roughness, after the relation between the output parameters and laser power is explored. Acknowledgements The authors would like to thank TUBITAK (The Scientific and Technological Research Council of Turkey) for its financial support given to Evren Yasa under the name of “Ph.D. support program

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