Minimizing surface roughness and back wall dross for fiber laser micro-cutting on AISI 316 L tubes using response surface methodology

A response surface methodology (RSM) was performed to study the influence of spot overlapping and pulse energy on back wall dross and surface roughness for fiber laser cutting of AISI 316 L stainless steel minitubes. Three treatments were compared to expel molten material (argon gas, compressed air, and a control test). Our results indicated that back wall dross and dross height reduction is observed when argon gas or compressed air is used through tubes compared with the control test. Additionally, a higher value of spot overlap (87.49%) and a lower value of pulse energy (30.31 mJ) resulted as the optimal parameters to cut minitubes.


Introduction
Fiber laser micro-cutting has been widely used in the manufacturing of medical devices due to their higher precision in the fabrication of complex geometries compared to conventional technologies.Several studies are related to reducing dross adherence and surface roughness in the laser-cutting processing of minitubes [1][2][3][4].For example, according to Riveiro et al the gas velocity is related to removing molten material [5].A way to increase the gas's velocity is through the gas's pressure; however, it promotes some material to resolidify on the cut edge, causing striations.Additionally, some methods have been performed to improve the surface quality, expel molten materials produced from the fusion process, or reduce the solidified metal [6][7][8].Tessier et al proposed a coolant pumping system through the inner diameter of the tube to drag out the melted material during laser cutting [7].According to Darwish et al there is a relation between material viscosity and the gas type used to remove particles.For example, the oxidizing gas is commonly used in mild steel to remove dross located on the cut edge due to the formation of ferrous oxides.
In contrast, inert gasses are used for stainless steel, aluminum, and titanium due to the high viscosity of molten oxides [9].Additionally, surface topography on the cutting edge is caused by a combination of cutting parameters that causes periodic striations.These striations act as stress raises and can generate unpredictable geometric changes, eliminated with finishing operations [10].Therefore, postprocessing techniques such as electropolishing [11], mechanical polishing [12], and chemical etching [13], have been investigated to accomplish the required quality.The spot overlap (O f ), is associated with this periodic striation on the cut edge produced in pulsed mode and depends on cutting speed (v f ), pulse frequency (f), and spot diameter (d) [14].The influence of these parameters has different repercussions according to the manufactured material.Thawari et al [15], studied the effect of overlapping on quality attributes such as surface roughness, kerf width, and surface morphology in the Hastelloy-X sheet.Their results indicated that when the pulse overlap factor decreases, the kerf width decreases, and the surface roughness increases.
Additionally, Criales et al established that a pulse overlapping less than 85% was insufficient to retrieve a smoother surface in polydimethylsiloxane (PDMS) [14].The manufacture of laser micro-cutting of stainless steel samples implies several quality issues related to the applied pulse energy and spot overlap.These quality issues are dross, slag formation, heat-affected zones, and uniform topography.Table 1 presents the literature review on laser micro-cutting of thin stainless steel.For example, Texidor et al [2] studied the effect of several laser cutting parameters on cutting quality.Their results indicate that increasing peak pulse power and cutting speed increase kerf width, surface roughness, and dross deposition.Muhammad et al proposed passing water at a flow rate of 1567 mm3/s through the inner diameters of tubes [6].Their results indicated that wet cutting improved surface roughness and reduced back wall dross and kerf width.This study uses response surface methodology to reduce back wall dross and average surface roughness on stainless steel minitubes.The influence of passing two gases (argon gas and compressed air) through minitubes to drag molten particles is studied compared with a control test.

Materials and methods
2.1.Material AISI 316 L minitube with a diameter of 1.8 mm and a thickness of 0.11 mm was used for experimental trials.Table 2 presents the chemical composition of minitubes.

Experimental setup
A fiber laser machine (MedPro, PRECO, USA) was used for experimental work.The experimental setup is presented in figure 1.The minitube was mounted in a mechanical three-jaw chuck and adjusted with a tailstock to guarantee straightness in the cut zone.The laser source features are shown in our previous work [16].Laser optics include a focal lens of 50 mm and a 120 mm collimator, which result in a theoretical minimum spot size of 20.8 μm.The laser trajectory was programmed using G and M codes, and the laser cutting parameters were set in the database.

Experimental design
A response surface methodology was used to develop the experimental work.The surface response design of two factors with 14 runs and considering three replicates was used to evaluate average surface roughness (Ra) and back wall dross percentage (Dbw) responses.However, the average of such replicates was obtained and used for the analysis, thus having the original 14 runs.Three designs (i.e., without treatment, compressed air, argon gas) were run.The assisted gas used for all experiments was Nitrogen (P = 150 PSI), passed through a 0.5 mm diameter nozzle.Without treatment implied that only assisted gas (Nitrogen) passed through the nozzle as a regular cut.In contrast, compressed air and argon were passed through tubes for the other experiments.Table 3 presents the summarized cutting parameters for minitube and the flow rates used in experimental trials.Although figure 2(a) illustrates the laser cutting parameters and the spot overlap representation.Figure 2(b) shows the mechanism of molten material ejected using argon gas or air compressed as a gas supply.Sport overlap O f (%) was used for experimental design to evaluate the periodic striations at the cut edge.This parameter is related to cutting speed v f (mm/min), pulse frequency f (Hz), and spot diameter d (μm) (see equation (1)).
presents the pulse energy parameter associated with peak power (P peak ) and pulse width (t on ).
Although these equations reduce the number of variables, the laser variables are programmed individually in the machine.

Surface roughness and dross characterization
Surface roughness (R a ) was measured on the cut edge using a confocal microscope (Axio CSM 700, Carl Zeiss, Germany) by ISO 4288.Due to cut edge differences in surface roughness by the focal position, the cut edge was divided into two areas, and both surface roughness values were acquired by replicating.A stereomicroscope (Discovery V8, Carl Zeiss, Germany) was used to quantify back wall dross (D bw ).The methodology for determining back wall dross is explained in our previous work [18].This procedure consisted of measuring the area focused on the stereomicroscope.This total area was processed with Image J software.The dross images were transformed into binary particles.The dross percentage was quantified in the focused area, and image treatment was performed using Image J software.Back wall dross images were transformed into binary particles ranging between 16 and 100 μm.The dross back wall percentage (D bw ) is given by Where D p represents the dross particle area in binary, and A is the total image area.Additionally, dross height was quantified to study the slag adhered to the cut edge.Five dross particles were measured in the three replicates for experimental results (i.e., using the same set of samples at different treatments (passing argon gas,  compressed air, and control test)) and using a SEM microscope.The maximum height of these particles analyzed was reported.

Response surface methodology (RSM)
RSM is used for the analysis of this process.RSM allows statistical modeling of a response (often a performance measure or quality characteristic) using input variables or process parameters where its influence is evaluated [19].This technique is ideal for determining the significant parameters in a manufacturing process.A general model is expressed as: Where f is the true and unknown response form, and that depends on the controllable input variables.
x , x ,…,x , k and e (treated as a statistical error, assumed following a normal distribution with mean zero and constant variance).The coded model for second-order polynomial equation is expressed in equation (5) as follows: According to equation (5), Y is the response (R a or D bw ), x i and x j are process parameters.b 0 is a constant, and b , i b , ii and b ij are the linear, quadratic, and linear-by-linear interaction effects between the process parameters x i and x , j respectively.The model term of ε is the random error, which is approximately normally and independently disturbed with mean zero and constant variance.
RSM was performed to detect the significant parameters, and an optimization procedure using the desirability function for the optimal model based on input variables (i.e., spot overlapping and pulse energy) was used.For each response, a model equation was obtained to describe the responses (Back wall dross and Surface roughness).Table 4 shows the cutting parameters applied in the machine and the levels used in the response surface methodology (type Central Composite Design).The parameters pulse frequency, cutting speed, peak power, and pulse width correspond to the laser cutting parameters programmed in the machine.These cutting parameters were selected from preliminary experiments to avoid heat-affected zones.Additionally, a response optimizer from Minitab software was used, choosing a weight (from 0.1 to 10) to determine individual and composite desirability based on a target value.A desirability function has been used widely as a function that must be minimized.The value of the function is the range between 0 and 1 and is given by [20] ( ) Where T is the target value of the response (y i ), U is the acceptable upper limit of the response, and w represents the weight.In our study, the values set for the optimization process are presented in table 6.

Results and discussions
Due to the physical mechanism of metal melting when the tube is laser cut, there is an intrinsic mark caused by spot overlapping.Additionally, fusion cutting causes melt drops which are accumulated on the back wall of the tube called dross.The desirability function of the optimized model using the RSM approach was used to evaluate the effect of cutting parameters clustered in spot overlap and pulse energy on surface roughness and back wall dross.
Figure 3(a)-(c) presents the resulting surface plots for the average back wall dross using different treatments.Equations that predict back wall dross response are shown below each plot, and their terminology is based on table 4. Surface response methodology offers some advantages compared to classical experimental methods due to its viability to obtain a large amount of information from a small number of experiments and its feasibility to observe the interaction effect of the independent parameters on the response [15].
Our results show that without passing gas through the tube (control test), results in back wall dross range between 1.7% and 7% with an average of 4.2%.Compressed air through the tube results in a back wall dross range between 0.8% and 2.2% with an average of 1.4%, and using argon gas through the tube results in a back wall dross range between 0.4% and 1.8% with an average of 0.8%.Therefore, the back wall dross is minimized when gases pass through tubes, as seen in figure 4. Figure 4 shows the comparison between the three treatments (argon gas (Ar) , compressed air (Ca) and without treatment or control test (Wt)) to compare their changes in means.From this figure we interpret that the most categorical variable that influence the back wall dross response in Argon gas.
According to Thawari et al spot overlap plays a crucial role in pulsed Nd:YAG laser cutting of nickel-base superalloys [15].Their results reveal that kerf width decreases when the spot overlap is reduced while the surface roughness is affected.
Also, Thawari et al demonstrated a range between 50% and 100% of spot overlap and 2.88 J of pulse energy to obtain minimum surface roughness values (4 μm < R a < 6 μm) in 1 mm thick Hastelloy X-sheet.Although average surface roughness values are higher than those obtained in these results, this is presumably due to the different working parameters and materials experimented with.Table 5 presents the ANOVA results for average surface roughness and back wall dross; significant p-values were highlighted.Although some equations in figure 3 do not present pulse energy terms, these equations are valid for all the pulse energy ranges shown in table 4.These are experimental models which predict the back wall dross.
Figures 5-7 present the optimization results of surface roughness and back wall dross for without treatment (figure 4), compressed air gas treatment (figure 5), and argon gas treatment (figure 6) for the reduced model.These results are based on table 6.Table 6 presents both responses' minimum values (Target) and upper values.Therefore, the optimization charts are related to minimizing surface roughness and back wall dross.In terms of validation of the reduced model for pairs of Ra and D bw for all three treatments independently, using a significance level of 0.05, the fit is assumed adequate, and residuals follow a normal distribution and are homoskedastic and independent.According to our results, similar parameters must be maintained in all treatments, which means that passing gas through tubes does not influence the surface roughness; however, it influences back wall dross.Therefore, the overlap must be maintained at the highest level (87.49%) for all results and pulse energy at their lowest value (30.31mJ) for control tests and Argon gas, and with a slightly higher value (30.38 mJ) for compressed air.When experimental tests without treatment (figure 4) and passing compressed air gas (figure 5) are compared, the individual and composite desirability are lower for compressed air gas.However, when argon gas is compared with samples without any treatment, the desirability is higher in pieces manufactured when argon gas is passed.The objective is to maximize the composite desirability with respect to the factors.We found that passing argon gas is the better technique to pass through tubes; however, economically, it can be non-sustainable.Therefore, compressed air is an excellent option for processing minitubes.
The experimental work did not include the optimal predicted result for pulse energy because 30.3 mJ is an axial point from the surface response design, which was not included in the experimental design.Therefore, to study the error of experimental trials with predicted models, the spot overlap factor selected was 87.5%, and the pulse energy was 31.3 mJ.Table 7 presents the response optimizer tool's average experimental and predicted values.The composite desirability for these cutting parameters without treatment, passing compressed air, and argon gas were 0.961, 0.964, and 1.0.Although values are not higher than optimal results, relative error stays below 16%, obtained with a control test to cut material.Figure 8 presents the dross height measured in 15 particles by treatment with the optimal experimental parameters (Spot overlap 87.5% and pulse energy = 31.3mJ). Figure 9 presents (a, b), the control test experiment, (c ,d) passing argon gas, and (e, f) passing compressed air.Figures 9(b), (d), (f) corresponds to a zoom-in view from figures 9(a), (c) (e), respectively.In SEM images, it is possible to see cut striation caused by laser and differences between dross adhered on the cut edge (red oval).There is a considerable difference in the dross height comparing figure 9(b) versus when a gas is  passing through the tube (figures 9(d) and (f)).According to our results, there is a significant difference between treatments in the dross height formation, which is explained by the drag forces moving the melted particles along the tube.According to Ullah et al the differences in the surface roughness on the cut edge are caused by the solidification of the abundant molten metal at the lower edge of the cut [21].To consider this phenomenon, surface roughness was measured in the different zones on the cut edge.According to Singh et al there is a considerable reduction in normalized dross height (from 0.231 to 0.053 μm) and dross area (from 2.27 to 0.62 μm 2 ) when laser is tilted [22].In our results, average dross height without treatment, compressed air, and using argon gas resulted in 122.4,48.8, and 39.5 μm.Therefore, the use of gas inside tubes is an effective method to reduce particle adhesion and dross height.This phenomenon is not observed for argon gas results, and the dross height is considerably reduced compared with the control test.The significant differences between gas treatments can be explained by their density values (i.e., air density = 1.22 kg m −3 v −1 s −1 .argon gas density = 1.78 kg m −3 ).Furthermore, according to our SEM images, compressed air pushed away the molten particles; however, this molten material is located as small and elongated particles internally in the tube.Although this material is placed along the tube's surface, it is considerably smaller than the dross deposited on the cut edge.

Conclusions
This study was focused on assessing the influence of process parameters on average surface roughness (R a ), back wall dross (D bw ), and dross height (D h ) during fiber laser micro-cutting of miniature tubes, with potential applications in medical implants such as coronary stents.Our results can be summarized as follows: • Surface response plots show that back wall dross is reduced when compressed air and argon gas are used as treatments compared with control tests.
• The optimization results identified a higher value of spot overlap (87.49%) and reduced pulse energy (30.31 mJ) to minimize surface roughness and back wall dross responses.
• Dross height was statistically significant between the treatments used to expel molten material.Dross height was significantly reduced by passing argon gas compared to without treatment.• Although the back wall dross was reduced when compressed air was passed through tube, the dross was extended in the inner part of the tube.This phenomenon was not observed with the argon gas treatment, where inner tubes were cleaner with compressed air.

Figure 2 .
Figure 2. (a) Laser cutting parameters, (b) Mechanism of molten material ejected using argon gas or air compressed as gas supply.

Figure 3 .
Figure 3. Average surface roughness (a) without treatment (b) passing air compressed (c) passing argon gas and back wall dross (d) without treatment (e) passing air compressed (f) passing argon gas.

Figure 5 .
Figure 5. Optimization results for samples without treatment.

Figure 6 .
Figure 6.Optimization results for samples passing compressed air through minitubes.

Figure 7 .
Figure 7. Optimization results for samples passing argon gas through minitubes.

Table 1 .
Literature review of fiber laser cutting of thin stainless steel (thickness lower than 500 μm).

Table 3 .
Cutting parameters for surface response.

Table 4 .
Applied laser cutting parameters for RSM.

Table 5 .
ANOVA results for 1.8 mm tube and 110 μm wall thickness.

Table 6 .
Parameter of response optimization.

Table 7 .
Optimization results of laser micro-cutting process with different treatments.