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Influence of the kerf geometry on the flow field and the transfer of kinetic energy to the melt during laser fusion cutting as a function of cutting speed
Dieser Artikel geht auf die komplizierte Beziehung zwischen Schnittgeschwindigkeit, Schnittfugengeometrie und dem Strömungsfeld von Prozessgas beim Laserschmelzschneiden ein. Durch experimentelle Studien und CFD-Simulationen zeigen die Forschungen, wie unterschiedliche Schnittgeschwindigkeiten die Geometrie der Schnittfuge beeinflussen, was wiederum den Fluss von Prozessgas und die Übertragung von kinetischer Energie auf die Schmelze beeinflusst. Die Studie unterstreicht die Bedeutung eines optimalen Ausdehnungsverhältnisses, um eine Überdehnung des Prozessgases zu verhindern, die zu Gratbildung und Oxidation der Schnittkanten führen kann. Der Artikel stellt auch das Konzept des Dehnungsverhältnisses als Schlüsselgröße zur Beurteilung der Ausdehnung des Prozessgases in Schnittfugengeometrien vor und stellt damit ein praktisches Werkzeug zur Optimierung der Schneidparameter dar. Die Ergebnisse unterstreichen die Bedeutung des Verständnisses und der Kontrolle dieser Faktoren, um qualitativ hochwertige Schnitte in industriellen Laserschneidanwendungen zu erzielen.
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Abstract
We studied how cutting speed shapes kerf geometry in laser cutting of 2 mm S235 steel. We also examined its effect on the transfer of kinetic energy from the assist gas to the melt. Across a wide range of speeds, we measured the width of the cutting kerfs and described how the geometry changed with speed. Lower speeds produce more divergent kerfs, which correlates with burr formation and edge oxidation, while intermediate speeds keep the edges closer to parallel and reduce defects. We complemented the measurements with computational fluid dynamics (CFD) simulations based on geometries derived from measured cutting kerfs. The simulations resolve separation of the gas flow, fields of static pressure, and shear stresses. From experiments and simulations, we defined a dimensionless expansion ratio that describes gas expansion inside the kerf. The ratio provides a practical criterion for the performance of the gas flow and links geometry to the risk of defects. Small values are associated with flow that stays attached to the wall, and large values indicate geometry that promotes separation and defects. All findings apply within the considered parameters.
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1 Introduction
The geometry of the cutting kerf plays a major role in laser cutting as it determines the absorption of the laser radiation, the flow of the process gas and the melt flow within the cutting kerf [1, 2]. Each of these three process characteristics significantly influence the quality of the cut result [3‐5]. Achieving a desired process result involves meeting criteria such as a low surface roughness, low burr formation, and, in laser fusion cutting with nitrogen, the absence of oxidation of the cut edges [6].
Numerous studies have demonstrated that process parameters significantly affect cutting quality [7‐9]. In particular, the cutting speed has a substantial effect on the roughness of the cut edges, lower cutting speeds correlating with slower movement of the melt on the cutting front [7]. Additionally, low cutting speeds can lead to increased burr formation, indicating insufficient acceleration of the melt to overcome adhesion forces at the kerf exit [8, 9]. It is important to realize that during the performance of a commercial cutting program an industrial laser cutting machine will often automatically reduce its nominal programmed cutting speed when navigating fine detail and small radii.
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It is clear that sufficient transfer of kinetic energy from the process gas to the melt is essential for high-quality cuts. The importance of the flow field of the process gas during laser cutting has been demonstrated in several studies [2, 10‐14]. Given the correlation between cutting speed and cutting quality, it is important to understand how cutting speed influences the geometry of the kerf and, consequently, the flow field of the process gas within the kerf.
This paper aims to evaluate the influence of cutting speed on the transfer of kinetic energy from the process gas to the melt. Specifically, it examines how cutting speed affects the geometry of the cutting kerf and how these geometric changes affect the flow of the process gas and the resulting cutting quality. An experimental study, complemented by CFD simulations, was conducted to identify geometric changes over a range of cutting speeds, and their impact on the flow field of the process gas and cutting quality.
2 The influence of the cutting speed on the Kerf geometry
An experimental cutting study was carried out to evaluate the influence of the cutting speed on the geometry of the cutting kerf. Samples were cut and their cross-sectional geometries were measured and evaluated. Except cutting speed, all process parameters were kept constant. The process parameters used to cut samples are shown in Table 1.
Table 1
Process parameters used to evaluate the influence of the cutting speed on the Kerf geometry
Parameter
Value
Material
S235
Material thickness
2 mm
Type of laser
Fiber laser (TruFiber 6000 S)
Wavelength
1,070 nm
Operating mode
Continuous-wave
Beam parameter product (BPP)
2 mm•mrad
Laser power
3 kW
Stand-off distance (SOD)
1.5 mm
Focal position
0 mm (top surface)
Focal diameter \(\:{d}_{f}\)
100 μm
Cutting gas
Nitrogen N2
Pressure of the cutting gas
2•106 Pa (20 bar)
Cutting speed
10, 25, 50, 75 and 100% vmax
i.e. 2.1, 5.25, 10.5, 15.75, and 21 m/min
As described in former work [15], the dimensions used to describe the cross-sectional geometries of the cutting kerfs are.
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the inlet width \(\:{w}_{i}\) (kerf width at the top surface of the sheet),
the constriction width \(\:{w}_{c}\) of the narrowest point within the kerf,
the outlet width \(\:{w}_{o}\) (kerf with at the bottom of the sheet) and.
the position of the constriction \(\:{z}_{c}\) (distance measured from the top surface of the sheet).
Figure 1 presents the cross sections for different cutting speeds, including the above listed measures. The samples were embedded in epoxy resin to prevent any deformation that might occur during grinding, to create a clean cross-section. An Olympus MVX10 microscope with an Olympus DP26 camera was used to image the cross section and measure the inlet width \(\:{w}_{i}\), the constriction width \(\:{w}_{c}\), the outlet width \(\:{w}_{o}\), and the position \(\:{z}_{c}\) of the constriction with the software “OLYMPUS Stream Essentials” characterizing the kerf geometry. The embedded samples and the respective measurements are shown in Fig. 1a-e for cutting speeds of 10%, 25%, 50%, 75% and 100% \(\:{v}_{max}\) (a-e). \(\:{v}_{max}\) (21 m/min) is defined as the maximum cutting speed that can be achieved without cutting interruptions with the process parameters used. Figure 1f summarizes the measured kerf widths as a function of cutting speed, including the respective measurement errors. The measurement uncertainty of the kerf dimensions was assessed following the principles of the Guide to the Expression of Uncertainty in Measurement (GUM). It accounts for contributions from the calibration of the microscope scale with a deviation of 1.5% and from the optical resolution of the system, which is approximately 0.4 μm. The resulting expanded uncertainty, determined with a coverage factor k = 2 corresponding to a confidence level of about 95%.
Fig. 1
The cross-section geometries of the cutting kerfs for the cutting speeds 10%, 25%, 50%, 75% and 100% of \(\:{v}_{max}\) at 21 m/min (a-e) and the measured kerf dimensions \(\:{w}_{i}\), \(\:{w}_{c}\), \(\:{w}_{o}\) and \(\:{z}_{c}\) (f)
The inlet width \(\:{\varvec{w}}_{\varvec{i}}\) is only moderately affected by the cutting speed and ranges between 158 μm at 75% \(\:{v}_{max}\) (d) and 185 μm at 10% \(\:{v}_{max}\) (a). At cutting speeds from 10% \(\:{v}_{max}\) to 75% \(\:{v}_{max}\), the entry area of the kerfs is initially converging, resulting in a constriction in the upper third of the cutting kerf (a-d).
The constriction widths \(\:{\varvec{w}}_{\varvec{c}}\) at cutting speeds \(\:\le\:\) 75% \(\:{v}_{max}\) vary only slightly between \(\:{w}_{c}\) = 106 μm and \(\:{w}_{c}\) = 122 μm, but the position of the constriction gradually migrates upwards from \(\:{z}_{c}\) = 570 μm at 10% \(\:{v}_{max}\) to \(\:{z}_{c}\) = 210 μm at 75% \(\:{v}_{max}\) with increasing cutting speed. The constriction at \(\:{v}_{max}\) is located much further down the kerf, near the exit area (\(\:{z}_{c}\) = 1.692 mm), and is significantly smaller than the others with \(\:{w}_{c}\) = 59 μm (e).
The most significant changes can be observed in the outlet width \(\:{\varvec{w}}_{\varvec{o}}\). This has its maximum at the lowest cutting speed of 10% \(\:{v}_{max}\) with a width of \(\:{w}_{o}\) = 266 μm. This exit becomes smaller with increasing cutting speed and reaches its minimum of \(\:{w}_{o}\) = 100 μm at \(\:{v}_{max}\). It is clear from these results that the cutting speed has a significant effect on the shape of the cutting kerf. The fact that the outlet width \(\:{w}_{o}\) becomes smaller as the cutting speed increases means that the process gas expands significantly more in the cutting kerf at low cutting speeds within the parameters under consideration. As the following results demonstrate, this expansion has a direct effect on cutting quality.
3 Evaluation of the cutting quality
To determine the correlation between kerf geometry and cutting quality, a qualitative inspection of cut edges is combined by quantitative measurements of maximum burr height \(\:{h}_{b}\), the fraction of oxidized area \(\:{A}_{ox}\), and surface roughness \(\:{R}_{a}\) and \(\:{R}_{z}\).
\(\:{h}_{b}\) and \(\:{A}_{ox}\) were extracted with the same optical workflow as for the kerf widths in Sect. 2. \(\:{R}_{a}\) and \(\:{R}_{z}\) were measured with a Mahr MarSurf M400 at mid-thickness of the cut edge (z = 1 mm) in cutting direction. The cut edges for cutting speeds of 10%, 25%, 50%, 75% and 100% \(\:{v}_{max}\) are shown in Fig. 2a–e, and the corresponding roughness values are plotted in Fig. 2f.
Fig. 2
The cut edges for the cutting speeds 10%, 25%, 50%, 75% and 100% of \(\:{v}_{max}\) (21 m/min) and the associated cutting qualities
At 10% \(\:{v}_{max}\) in Fig. 2a the cut edge shows pronounced burr formation with \(\:{h}_{b}\) = 666 μm and oxidation with \(\:{A}_{ox}\) ≈ 10%. The roughness is \(\:{R}_{a}\) = 3.57 μm and \(\:{R}_{z}\) = 25.19 μm, as shown in Fig. 2f.
Between 25% and 75% \(\:{v}_{max}\) the edges show \(\:{h}_{b}\) ≤ 32 μm which corresponds to minimum burr formation, and with \(\:{A}_{ox}\) = 0% no oxidation was detected, as shown in Fig. 2b-d. For these cutting speeds the roughness ranges from \(\:{R}_{a}\) = 2.05 μm to 2.80 μm and \(\:{R}_{z}\) = 14.0 μm to 16.5 μm which are the lowest within the considered parameter range, as shown in Fig. 2f.
Figure 2e shows that at 100% \(\:{v}_{max}\) the burr height increases to \(\:{h}_{b}\) = 69 μm. A small amount of oxidation is present 0% < \(\:{A}_{ox}\) < 1%. Roughness increases to \(\:{R}_{a}\) = 3.50 μm and \(\:{R}_{z}\) = 22 μm, as shown in Fig. 2f. This deterioration at 100% \(\:{v}_{max}\) is probably due to an increase in the angle of inclination of the cutting front, and high mass flow rate [8, 10].
The comparison between the cross sections in Fig. 1 and the corresponding cut edges in Fig. 2 indicates a correlation between the geometry of the cutting kerf and the cutting quality. Industrial laser cutting requires high quality, high process speeds, and high reliability. The requirement for high reliability means that pre-programmed cutting speeds are always considerably lower than \(\:{v}_{max}\) for any material-laser combination. Another consideration which limits the speed is that of the quality of the cut edge. From Fig. 2 it is clear that a cutting speed between 50% and 75% \(\:{v}_{max}\) would give a high-quality cut edge, characterized by almost vertical striations, no burr and no oxidation. Above 75% \(\:{v}_{max}\) the striations on the cut edge show evidence of the elongation of the cutting front in the direction of cutting. This leads to inefficient material removal, an increase in cut edge roughness and, eventually, to the collapse of the cutting process. For these reasons the top pre-set cutting speeds for any industrial machine are always set considerably below \(\:{v}_{max}\) for the material involved. However, Fig. 2a makes it clear that there is also a lower limit on cutting speed if a high-quality cut is required.
It has been previously noted [10] that a pronounced divergence of the cutting kerf can lead to a separation of the gas flow between the process gas and the melt within the kerf. This separation diminishes the effectiveness of the melt removal by the process gas and is associated with an overexpansion of the gas flow within the kerf. The following sections describe the results of a theoretical examination of the effects of the kerf cross section on the flow field of the process gas within the kerf.
4 Evaluation of the gas flow in different Kerf geometries
The experimental results presented in the previous sections demonstrated that the cutting speed has a strong influence on the kerf geometry and on the cutting quality. In particular, low cutting speeds resulted in highly divergent kerfs and poor edge quality, suggesting that the expansion of the process gas inside the kerf plays a major role in melt ejection. To better understand the underlying mechanisms and to isolate the geometric influence from other process parameters, CFD simulations were carried out on kerf geometries derived from experimentally measured cross sections. The following section therefore investigates how variations in kerf geometry affect the gas flow, pressure distribution, and shear stresses within the kerf. This provides a quantitative explanation of the experimental trends and supports the definition of a dimensionless expansion ratio that links geometry to cutting performance.
To conduct the CFD simulations under realistic conditions, a typical high quality industrial cut sample was created. The parameters used to cut the sample were chosen such that the process resulted in minimum burr formation and minimum oxidation of the cut edges. The geometry of the cutting kerf of this sample is considered the reference geometry in the following.
To evaluate the influence of kerf geometry constrictions (\(\:{w}_{c}<\text{m}\text{i}\text{n}({w}_{i},{w}_{o})\)), and bulges (\(\:{w}_{c}\:>\:\text{m}\text{a}\text{x}({w}_{i},{w}_{o})),\) on the process result, the constriction width \(\:{w}_{c}\) of the modelled geometry was varied in the simulations while the inlet width \(\:{w}_{i}\), the outlet width \(\:{w}_{o}\), and the constriction position \(\:{z}_{c}\) were kept constant. These varied geometries used in the CFD simulations are referred to as derived geometries in the following.
4.1 Cutting and modelling of the reference geometry
To model the reference geometry of the cutting kerf, multiple samples were cut with a laser using the same process parameters. The process parameters are shown in Table 2. The cutting speed of 12 m/min is equivalent to approximately 75% of \(\:{v}_{max}\) for this laser-material combination (as would be typical in an industrial application).
Table 2
Process parameters used to cut the samples to determine the reference geometry
Parameter
Value
Material
S235
Material thickness
2 mm
Type of laser
Disc Laser (TruDisk 3001)
Wavelength
1,030 nm
Operating mode
Continuous-wave
Beam parameter product (BPP)
4 mm•mrad
Laser power
3 kW
Stand-off-Distance (SOD)
1 mm
Focal position
0 mm (on top surface)
Focal diameter df
170 μm
Cutting gas
Nitrogen N2
Pressure of the cutting gas
1.4•106 Pa (14 bar)
Cutting speed
12 m/min
The experimental setup is illustrated in Fig. 3. The apex line of the cutting front is marked in green and the transition line between the cutting front and the cut edges is marked in blue.
Fig. 3
Sketch of the experimental setup. The apex line of the cutting front and the transition line between the cutting front and the cut edges are marked in green and blue
The geometry of the cutting front was determined by means of frozen cuts, as described in [16, 17]. The samples were ground in the YZ-plane down to a distance of a few hundred micrometers from the frozen cutting front. This allowed for a topographical measurement of the apex line of the front, which is shown by the green line in Fig. 3, using a laser scanning microscope VK-X210 from Keyence. Due to temporal fluctuations in the shape of the cutting front [1, 18, 19], the measurement was averaged from five samples. Finally, the kerf geometry was three dimensionally reproduced using CAD. It is useful to note that the almost straight and vertically inclined cutting front used in this CAD model differs significantly from the geometry at cutting speeds above 75% of \(\:{v}_{max}\) [15]. However, the current investigation is concerned with gas flow effects at speeds below 75% \(\:{v}_{max}\). As mentioned above, these lower speeds are occasionally imposed upon industrial machines as a result of mechanical or software constraints when cutting fine detail such as small radii.
Figure 4a shows the sample reference geometry. The derived CAD model is shown in Fig. 4b. Figure 4c shows the measured contour of the apex line of the cutting front. Figure 4d shows the derived CAD model in longitudinal section at the cutting front. The domain for the CFD simulations is shown in Fig. 4e and f.
Fig. 4
(a) Reference sample showing \(\:{w}_{i}\), \(\:{w}_{c}\) and \(\:{w}_{o}\). (b) The derived CAD model in cross-section. (c) The measured cutting front. (d) The derived CAD model in longitudinal section, close to the cutting front. (e) Resulting computational domain. (f) Magnification of the cutting kerf in the computational domain
The reference geometry was used to generate five computer modelled geometries which varied only by having different values of\(\:\:{w}_{c}\). The cross sections of these geometries are shown in Fig. 5 (\(\:{w}_{c}\) = 25, 50, 100, 150 [reference], 250 and 350 μm). These modelled geometries are, of course, great simplifications of the actual kerf geometries shown in Fig. 1, as the dimensions \(\:{w}_{i},{w}_{o}\) and \(\:{z}_{c}\) all remain unchanged, and they all share the same longitudinal geometry. However, as the following discussion shows, useful information about gas flow within the kerf can be produced simply by changing \(\:{w}_{c}\) in isolation.
Fig. 5
The Kerf geometries in cross-section for the considered constriction widths \(\:{w}_{c}\) = 25, 50, 100, 150 (reference), 250 and 350 μm (a-f)
The gas flow within the extracted kerf geometries was simulated in SolidWorks Flow Simulation 2022 under steady, compressible conditions with nitrogen modeled as an ideal gas. Turbulent flow was modeled using the standard k–ε turbulence model. The inlet total pressure was set to 1.4•106 Pa and the outlet static pressure to 105 Pa. All solid walls were assumed adiabatic and smooth, except for the kerf surfaces, where \(\:Rz\) = 20 μm was applied. The computational domain was discretized using a Cartesian mesh of approximately 10 million cells. The wall temperature at the cutting front was estimated to be about 2500 K and to decrease to ambient temperature within 1 mm along the x-direction, according to [13].
4.4 Flow speed and pressure distribution in the cutting Kerfs
Fig. 6 shows the gas flow speeds \(\:u\) and the distributions of the static pressures \(\:{p}_{s}\) of the kerf models with \(\:{w}_{c}\) = 25, 50, 100, 150, 250 and 350 μm (a - l) in the YZ-plane.
Fig. 6
Illustration of the gas flow speeds \(\:u\) and static pressures \(\:{p}_{s}\) in the kerf computed by the CFD simulations for the constriction widths \(\:{w}_{c}\) = 25 μm (a, g), \(\:{w}_{c}\) = 50 μm (b, h), \(\:{w}_{c}\)= 100 μm (c, i), \(\:{w}_{c}\) = 150 μm (d, j), \(\:{w}_{c}\) = 250 μm (e, k) and \(\:{w}_{c}\) = 350 μm (f, l)
As the constriction width \(\:{w}_{c}\) increases, the flow speed in the upper ∼ 0.5 mm of the kerf increases. The flow speed is approximately \(\:u\) = 100 m/s at \(\:{w}_{c}\) = 25 μm (a) and \(\:u\) = 300 m/s at \(\:{w}_{c}\) = 350 μm (f). This significant increase in the flow speed is due to the reduction in the hindrance to flow as the constriction width \(\:{w}_{c}\) increases.
In addition, in Fig. 6a - f can be observed that a separation of the gas flow occurs at the top edges of the kerf. The larger the constriction width \(\:{w}_{c}\), the smaller the separation becomes.
In Fig. 6g-i can be seen that the static pressure \(\:{p}_{s}\) in the lower ∼ 1 mm of the kerf decreases with decreasing constriction width \(\:{w}_{c}\) due to the increasing expansion of the process gas within the kerf. At \(\:{w}_{c}\) = 25, 50 and 100 μm, the pressure in the lower section of the cutting kerf drops below the ambient pressure of 105 Pa. Such a pressure drop generates a shock wave in the gas flow [20]. At \(\:{w}_{c}\) = 25 μm and 50 μm, the shock wave occurs within the cutting kerf, as shown in Fig. 6 g and h, causing a separation of the gas flow from the cut edges at the outlet of the kerf, which is illustrated in Fig. 6a and b).
Because a separation of the gas flow can significantly influence the flow of the process gas, e.g. through reverse flow [20], this aspect is considered here in more detail. For this purpose, the flow speed of the process gas \(\:u\) in the lower 0.5 mm of the cutting kerf for the constriction widths \(\:{w}_{c}\) = 25 μm, 50 μm and 100 μm is shown in Fig. 7. In addition to the magnitude of the flow speed, the vectors of the flow direction are also indicated.
Fig. 7
Illustration of the flow speeds in the kerf computed by the CFD simulations for the constriction widths \(\:{w}_{c}\) = 25 μm (a), \(\:{w}_{c}\) = 50 μm (b) and \(\:{w}_{c}\) = 100 μm (c)
Close to the bottom of the cut edges for \(\:{w}_{c}\) = 25 μm, there is a pronounced gas flow in the positive z direction (i.e. upwards, into the kerf). This upwards gas flow has computed speeds of up to 130 m/s. A similar upwards flow can be seen at \(\:{w}_{c}\) = 50 μm, however, this is less pronounced than at \(\:{w}_{c}\) = 25 μm and significantly slower, with a maximum speed of approx. 100 m/s. At \(\:{w}_{c}\) = 100 μm there is no gas flow in the positive z direction, which is due to the fact that there is no separation of the gas flow.
Whenever the separation of the gas flow takes place, this leads to ambient air being sucked into the bottom of the kerf and can promote oxidation (see Fig. 2a). In addition, shear stresses in the vertically upwards direction are to be expected, which impedes efficient melt expulsion [21].
4.5 Shear stresses on the cutting front
Shear stresses in the cutting kerf are dependent upon the interaction between the process gas and the melt [10, 13]. The shear stresses represent the parameter that defines the transfer of kinetic energy from the process gas to the melt, which is essential for efficient melt ejection [10, 13]. The component of the shear stress \(\:{\tau\:}_{w,z}\) that acts in the negative z direction towards the outlet (bottom) of the cutting kerf is responsible for the expulsion of the melt from the cutting kerf [10, 13]. The negative x axis component \(\:{\tau\:}_{w,x}\) of the shear stress, horizontally directed back along the cut edges can contribute to the formation of burr and increase roughness [10, 15].
Due to their different influences on the results of the process, these components of the shear stress are considered separately within this study and were evaluated at two distinct positions: along the apex line of the cutting front, and on the transition line between the cutting front and the cut edges, highlighted in green and blue respectively in Fig. 3.
The calculated shear stresses on the apex line of the cutting front are shown in Fig. 8. The z position of the constriction \(\:{z}_{c}\) is marked with a black dashed line. The downward shear stresses \(\:-{\tau\:}_{w,z}\) in the outlet direction (negative z direction) are shown in Fig. 8a and the shear stresses \(\:{-\tau\:}_{w,x}\) in the negative x direction are shown in Fig. 8b. As already noted, the position of the shear stresses under consideration is along the apex line of the cutting front and the coordinate system and its origin are shown in Fig. 8c.
Fig. 8
The shear stresses in the outlet direction, \(\:{-\tau\:}_{w,z}\), and negative x direction, \(\:{-\tau\:}_{w,x}\), for different constriction widths \(\:{w}_{c}\) on the apex line of the cutting front
Figure 8a shows an increase of the vertical shear stresses \(\:-{\tau\:}_{w,z}\) in the upper ∼ 0.5 mm of the cutting kerf (1) with increasing constriction width \(\:{w}_{c}\). This increase is due to the higher acceleration of the process gas in the kerf allowed by a larger constriction width, as described in the context of Fig. 6a - f. The higher speed of the process gas results in higher shear stresses in outlet direction [20].
The intersection of the curves at \(\:z\) = 0.1 mm above \(\:{z}_{c}\) (2) is due to the compression of the process gas in this area, as shown in Fig. 6 g - l. This leads to an increase in the normal forces acting on the cut edges and subsequently increases the shear stresses [20]. In the lower ∼ 0.2 mm of the kerf, it is noticeable that for constriction diameters \(\:{w}_{c}\) = 25 μm and \(\:{w}_{c}\) = 50 μm there is a sudden decrease in shear stresses to \(\:{\tau\:}_{w,z}\) = 0 N/mm² and = 500 N/mm² respectively (3). This is because of narrow constriction widths, which cause the separation of the gas flow, and its associated reversal of the gas flow discussed above.
The shear stresses in the negative x direction \(\:-{\tau\:}_{w,x}\) in the upper ∼ 0.5 mm of the kerf have similar characteristics to the shear stresses in the vertical direction \(\:-{\tau\:}_{w,z}\) in this area (4). A larger constriction width \(\:{w}_{c}\) generates a larger shear stress \(\:{-\tau\:}_{w,x}\). At \(\:{w}_{c}\) = 25 μm and \(\:{w}_{c}\) = 50 μm, shear stresses \(\:{\tau\:}_{w,z}\) in positive z direction occur at \(\:z\) = 1.8 mm to \(\:z\) = 2 mm. This could lead to adhesion of the melt and therefore burr formation, as demonstrated in Fig. 2a.
4.6 Shear stresses on the transition line between the cutting front and the cut edges
The shear stresses computed by the CFD simulations for the considered constriction widths \(\:{w}_{c}\) at the transition line between the cutting front and the cut edge are shown in in Fig. 9.
Fig. 9
Representation of the shear stresses in the outlet direction \(\:{-\tau\:}_{w,z}\) and negative x direction \(\:{-\tau\:}_{w,x}\) for different constriction widths \(\:{w}_{c}\) on the transition line between cutting front and the cut edges
The shear stresses \(\:{-\tau\:}_{w,z}\) in the outlet direction (negative z direction) are shown in Fig. 9a and the shear stresses \(\:-{\tau\:}_{w,x}\) in the negative x direction are shown in Fig. 9b. The position of the shear stresses is highlighted by the blue line in Fig. 9c and the coordinate system and its origin are also shown in Fig. 9c.
Shear stresses in inlet direction occur at the upper ∼ 0.2 mm of the kerf (1), which is due to the separation of the gas flow that occurs at the sharp inlet edge of the cutting kerf, shown in Fig. 6a - f. At the z position of the constriction \(\:{z}_{c}\), the highest \(\:-{\tau\:}_{w,z}\) occur for the lowest \(\:{w}_{c}\). This is due to the compression of the process gas in the narrower constrictions, as shown in Fig. 6 g – l. At the lower ∼ 0.2 mm of the kerfs with constriction widths of \(\:{w}_{c}\) = 25 μm and \(\:{w}_{c}\) = 50 μm, the shear stresses in the outlet direction \(\:-{\tau\:}_{w,z}\) suddenly decrease to approximately \(\:{-\tau\:}_{w,z}\) = −1,000 N/mm² and \(\:{-\tau\:}_{w,z}\) = 0 N/mm² respectively (3), which can be attributed to overexpansion of the process gas, shown in Fig. 6 g h. The curve of \(\:{w}_{c}\) = 350 μm shows an increase to \(\:{-\tau\:}_{w,z}\)= 3,000 N/mm² (4). This is due to under-expansion of the process gas leading to a flow around the trailing edge and thus high shear stresses.
Especially in the region below the constriction at \(\:-z\) ≥ 0.67 mm, the shear stresses in the negative x direction \(\:{-\tau\:}_{w,x}\) vary strongly with varying constriction widths \(\:{w}_{c}\) (5). It can be seen that the smaller \(\:{w}_{c}\), the smaller \(\:{-\tau\:}_{w,x}\). The shear stresses in the x direction \(\:{\tau\:}_{w,x}\) are up to − 2,000 Pa and thus of the same order of magnitude as the shear stresses in the outlet direction \(\:-{\tau\:}_{w,z}\). In this case, a pronounced redistribution or separation of the melt flow from the cutting front can be expected for narrow constrictions. The suction of ambient air into the kerf can also be assumed from the shear stresses in the positive z direction (6).
The simulations show that highly divergent cutting kerfs can lead to a reduction in the transfer of kinetic energy from the process gas to the melt. A strong divergence can lead to a separation of the gas flow in the outlet region of the cutting kerf, so that no kinetic energy is transferred in the outlet direction to the melt in this region. This can result in adhesion of melt and burr formation.
5 Analytical key figure of the expansion of the process gas in cutting kerfs
The geometry of the kerf and the flow field of the process gas within depend on a multitude of process parameters. To avoid time consuming and complex numerical modelling and to provide a simple estimation how much the process gas may expand in a cutting kerf, the.
key figure is introduced. This is calculated for the investigations presented in this paper. For the calculation of the expansion ratio, two types of kerf geometries are distinguished. If the constriction width \(\:{w}_{c}\) is larger than the inlet width \(\:{w}_{i}\) (\(\:{w}_{c}\:\ge\:{\:w}_{i}\)) the expansion ratio is calculated from the outlet width \(\:{w}_{o}\) and the inlet width \(\:{w}_{i}\). If the constriction width \(\:{w}_{c}\) is smaller than the inlet width \(\:{w}_{i}\) (\(\:{w}_{c}<{w}_{i}\)), the expansion ratio is calculated from the outlet width \(\:{w}_{o}\) and the constriction width \(\:{w}_{c}\).
As shown in Figs. 1 and 2, the experimental study yielded good cutting quality when the expansion ratio was less than 4.7. Furthermore, Fig. 6 indicates that in the simulation study, no separation of the gas flow occurred when the expansion ratio was less than 5.8.
The deviation between these values is approximately 20% and can be attributed to slightly different process parameters used for the simulation and the experimental study and to deviations of the simulation model from reality.
Consequently, it is imperative to maintain an expansion ratio below 4.5 to ensure acceptable cutting quality for the experimental parameters used in this study. By maintaining an expansion ratio below 4.5, separation of the flow of the process gas within the kerf can be avoided, significantly enhancing the quality at low cutting speeds.
6 Conclusions
This paper presents an experimental and simulation analysis of the influence of the cutting speed during laser cutting on the geometry of the cutting kerf and the resulting flow field of the process gas in the kerf. For the first time the geometric characteristics of a cutting kerf have been systematically varied on the geometric basic of an experimentally determined cutting front. The following conclusions were drawn within the parameters under consideration:
Low cutting speeds lead to a significant increase of the outlet width \(\:{w}_{o}\). This can lead to overexpansion of the process gas in the cutting kerf. The resulting separation of the gas flow leads to burr formation and oxidation of the cut edges,
The expansion ratio was introduced as a key Fig. with which to evaluate the expansion of the process gas in kerf geometries,
In this case, to avoid overexpansion, the kerf geometry must not exceed an expansion ratio of 4.5.
Acknowledgements
This work was supported by the Landesministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg (Ministry of Science, Research and the Arts of the State of Baden-Wurttemberg) within the Nachhaltigkeitsförderung (sustainability support) of the projects of the Exzellenzinitiative II.
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Competing interests
The authors declare no competing interests.
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Influence of the kerf geometry on the flow field and the transfer of kinetic energy to the melt during laser fusion cutting as a function of cutting speed
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