1 Introduction

The laser machining procedure has an extensive variety of applications in diverse production procedures because of its benefits of cost efficacy and high machining quality through a high production rate (Ref 1, 2). All engineering materials with complex shapes and close tolerances are machined by laser machining (Ref 3, 4). The first laser was built by Theodore H. Maiman in 1960. The laser focused on the workpiece generates a very high temperature because of which the workpiece is melted. A high-pressurized gas was used for ejecting melted material and generating kerf. A graphic of laser machining is shown in Fig. 1.

Fig. 1
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Kerf geometry

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The dimensional accuracy of the machined kerf depends upon kerf taper (Kt), kerf width (Kw) and kerf deviation (Kd). Kt and Kw were measured along the sheet thickness and machined length, respectively. The quality of machining could be improved by the optimal selection of process parameters. Kt and Kw remain the crucial performance characteristics of the laser machining process. Kt and Kw are mostly associated with dimensional accuracy and the high quality of the machined part.

SS304 (ASTM A240) sheet is a vital engineering material and is used in about 50% of stainless steel production and utilization. SS304 was selected as the workpiece material for the experimentation. In particular, SS304 is a nonmagnetic austenitic stainless steel. It is mainly composed of chromium (~ 18%) and nickel (~ 10%) with iron and additional elements. These elements affect ferrite austenite equilibrium. The microstructure depends on thermal parameters through phase transformation. The microstructure is changed due to the high heat generated during laser machining. SS304 offers advantages which include its better mechanical strength, oxidation resistance, corrosion resistance, chemical resistance and excellent visual appeal in architecture. It has developed as the preferred manufacturing material. SS304 sheets are applicable in various applications in the food industry, electronics, automobile headers, screws, machinery components, spacecraft and army devices. SS304 is hardened at some point of machining and subsequently turns into a tough material for conventional machining. But it is efficiently machined by laser machining (Ref 5,6,7).

2 Literature Review

A literature review was carried out to study significant process parameters and their effects on Kw and Kt and modeling and optimization methods. The laser machining process is categorized through various process parameters and their relations, which control the machining process effectivity. The effectivity of the process is measured in terms of productivity, quality and cost. These goals are achieved through the optimal selection of process parameters. In the industry, these process parameters are selected based on experience and a trial-and-error process. Such a way is time-consuming and does not give an optimal solution. Therefore, it is essential to accurately evaluate the relationship between process parameters and performance characteristics by mathematical modeling.

Elyas Haddadi et al. studied decreasing cutting speed and increasing laser power to cause an increase in kerf width (Ref 3). M. Moradi et al. found that the minimum taper obtained the lowest laser power and high frequency (Ref 4). Milos Madic et al. observed that the combination of low cutting speed and high gas pressure increases the energy supply to the workpiece surface and increases the kerf width considerably, and a decrease in the kerf width occurs with an increase in the cutting speed (Ref 8). Avanish Kumar Dubey et al. studied the consequences of process parameters on Kw, Kt and Kd. The appropriate selection of numerous process parameters could improve the machining quality of the cut (Ref 9). Arun Kumar Pandey et al. observed that pulse width was the utmost substantial parameter for Kw trailed by pulse frequency, gas pressure and cutting speed. A wider Kw was generated by an increase in pulse width. However, Kw was wider at a lower value of pulse frequency. Laser beam sheet metal interface time rises through an increase in pulse width to allow the transfer of absorbed heat to a bigger area, inflicting wider Kw. Then again, with the aid of reducing the pulse width and increasing peak power had a tendency to enter deeper with smaller heat conduction at edges because of the decreased beam and sheet metal interface time causing lower Kw. Higher pulse frequencies produce more pulse energy and result in deep penetration instead of melting more material from edges that generate reduced Kw. Kw increased up to a certain limit as pulse frequency increased and started reducing after that. Also, minimum Kw occurred at a lower pulse width (Ref 10). D. Kondayya et al. noticed that the Kw becomes narrower by raising the cutting speed and widens with a rise in pulse energy and pulse frequency. The outcome of varying pulse energy was comparatively greater than pulse frequency on Kw (Ref 11). K.K. Mandal et al. observed that an increase in frequency and laser beam power reduces Kw. Because of the increase in laser power, more heat was generated. The maximum amount of heat was accountable for producing a wider Kw by removing more material from the workpiece. Also, Kw widens with the increase in pulse frequency (Ref 12). Bekir Sami Yilbas et al. expressed and anticipated the Kw dimensions by the lump parameter evaluation model. The difference in Kw size rises with increasing cutting speed and laser power (Ref 13). Teeraphat Kongcharoen et al. noticed the outcome of process parameters on Kw in laser machining of mild steel plate. The results showed that an increase in the laser power increased Kw. The average Kw becomes narrower with the increase in cutting speed (Ref 14). Statistical and mathematical tools were accumulated in response surface methodology (RSM). RSM is intended for modeling, optimizing and evaluating the outcome of process parameters on performance characteristics. Process optimization was carried out with a smaller number of experiments and high accuracy of results (Ref 3, 15). S. C. Kulkarni et al. applied RSM for evaluating the outcome of process parameters and the adequacy of the model was tested by analysis of variance (ANOVA) (Ref 16). A.M. Sifullah et al. observed that laser power is the most influenced parameter with a 64.21% contribution to the kerf width of HAZ. The laser beam intensity increases with an increase in laser power resulting in a wider width of HAZ. While laser material interaction time decreases with an increase in cutting speed, this results in a narrowing of the width of HAZ. (Ref 17). A. D. Tura et al. used a hybrid approach of GA and RSM for optimization and analysis of laser machining parameters on SS304 (Ref 18). Mahmoud Moradi et al. found that as the cutting speed decreases and laser power increases, more heat input was supplied to the material resulting in more area of the material being heated and melted; therefore, the kerf width will become wider (Ref 19).

Conferring to the literature, there has not been an inclusive study on the laser machining of the SS304 sheet. SS304 has wide applications in the industry. So, it seems important to study the laser machining of SS304, to produce high-quality and more accurate components. The objective of this work is to develop the model for optimizing and evaluating the numerous process parameter effects, for instance, the cutting speed, laser power, gas pressure and pulse frequency on the Kw and Kt for achieving precise laser machining. The central composite design (CCD) of the response surface methodology is utilized for the design of the experimental plan. A mathematical model based on response surface methodologies was used for the optimization of kerf width and kerf taper. The factor effects on kerf width and kerf taper are analyzed using a surface plot.

3 Experimental Setup

Experiment runs were conducted with a 2.5 Kw AMADA F0MTII3015 laser machine provided by Merasha Shapers Pvt. Ltd., Maharashtra, India. The machining was performed on a 5-mm-thick SS304 sheet. The chemical composition of SS304 is shown in Table 1.

Table 1 Chemical composition of SS304
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A photographic image of the experimental setup is displayed in Fig. 2.

Fig. 2
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Experimental setup

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The process parameters selected that affect the Kw and Kt were based totally on the literature review, machine specification and pilot experimentation. Through the above study, 4 parameters at 3 levels that mainly have an effect on the Kw and Kt have been decided. As for laser power, cutting speed, gas pressure and pulse frequency, they were taken into consideration as process parameters. In Table 2, laser machining process parameters along with machining levels were revealed.

Table 2 Process parameters
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The relationship among laser machining process parameters (cutting speed, laser power, gas pressure and pulse frequency) and the performance characteristics (Kw and Kt) was obtained from the RSM approach. Experimental effects, attained from the RSM experimental plan, have been used for evolving predictive models. The goal of this method was to simultaneously look for the optimum set of parameters so that this method is capable of appropriately modeling the laser machining process. Experiments are planned by applying the central composite design (CCD) of RSM. The interactive and higher-order effects are studied through the laser machining of SS304 by RSM. The ANOVA was used to test the adequacy of the established model. The laser machining parameters will be optimized for high machining accuracy and production. The effects of process parameters such as cutting speed, laser power, gas pressure and pulse frequency on Kw and Kt were evaluated and optimized. Straight cuts of 10 mm in length were machined as per the experimental run. The machining shape was designed with the aim of allowing the measurement of the kerf width in an easy and precise way. Kw is of two types: top and bottom Kw. Top and bottom Kw was measured along the machined length with a 10X magnification microscope at the top and bottom surfaces, respectively. The machined workpiece and the measurement setup are shown in Figs. 3 and 4, respectively.

Fig. 3
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Machined workpiece

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Fig. 4
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Kerf width measurement setup

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Kerf taper is an important parameter determined by the top and bottom kerf width and workpiece thickness. Equation 1 is used for calculating the Kt

$${\text{Kerf}}\;{\text{taper }}({\text{K}}_{t}^{^\circ } ) = \frac{{\left( {{\text{Top}}\;{\text{kerf}}\;{\text{width}} - {\text{Bottom }}\;{\text{kerf}}\;{\text{width}}} \right) \times 180}}{{2\pi \times {\text{Thickness}}\;{\text{of}}\;{\text{workpiece}}}}$$
(1)

A central composite design of RSM was planned for an experimental run to study the relationship among the process parameters and performance characteristics revealed in Table 3. A total of 93 experiments with 3 replicates were performed.

Table 3 Experimental plan and observed Kw and Kt
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4 Results and Discussion

Process parameters and their effects were discussed in this section. A better sense of the relative impact of the one-of-a-kind parameter may be acquired with the aid of the decomposition of the variance, which is known as ANOVA. This is a statistical approach used to evaluate the contribution of process parameters to Kw and Kt. The adequacy of the model was tested by ANOVA, which also calculates the significance of coefficients. The ANOVA results were counted at a 95% of a significance level. The ANOVA results for Kw and Kt are enumerated in Tables 4 and 5, respectively. The higher F values of 99.4 and 88.89 of Kw and Kt, respectively, indicate that the generated model was found to be significant and adequate for Kw and Kt. Tables 4 and 5 also showed significant and nonsignificant parameters. The parameters having p values less than 0.05 considered significant. The probability value in the model represents the effect of different terms. Percentage contribution or F ratio represents the relative significance of a corresponding factor. A higher value of the F ratio indicates a more significant parameter.

Table 4 ANOVA results for kerf width
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Table 5 ANOVA results for kerf taper
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The Minitab 17 software was used to evaluate the Kw and Kt. For the Kw and Kt models, the ANOVA indicates that the cutting speed, laser power and gas pressure are having more significant effects on Kw and Kt. The interaction effect and square effect of process parameters are less significant than linear effects of process parameter. The RSM was applied to evaluate the relationship among different process parameters. The lower the better value is the optimum for Kw and Kt. The RSM methodology uses a scientific process to correlate the process parameters with the Kw and Kt and form a second-order polynomial equation. The generated model enumerates the relationships and evaluates the linear, square and interaction effects of process parameters on the performance characteristics. This model helps to study the behavior of processes. A model was developed for the response surface to analyze the influence of process parameters on the Kw and Kt. The Minitab 17 software is used to formulate the regression equation considering significant parameters only and compute the coefficients for Kw and Kt are shown in Eq 2 and 3, respectively. Insignificant model parameters can be eliminated through the step-wise regression method.

$$\begin{aligned} {\text{Kerf width }}\left( {K_{{\text{w}}} } \right) = & \;0.357 + 0.000221A - 0.000511\;B - 0.1882\;C \\ & \;\;\; + 0.000046\;D - 0.000073\;A*C + 0.000208\;B*C \\ \end{aligned}$$
(2)
$$\begin{aligned} {\text{Kerf taper }}K_{{\text{t}}} = & \; - 1.974 + 0.001879\;A - 0.000542\;B + 0.021\;C \\ & \;\; + 0.000603\;D + 0.000001\;B*B - 0.000001\;A*B \\ & \;\; - 0.000696\;A*C + 0.001146\;B*C{\mkern 1mu} - 0.000001\;B*D \\ \end{aligned}$$
(3)

where A, B, C and D are laser power, cutting speed, gas pressure and pulse frequency, respectively.

The ability of generated models (Eq 2 and 3) to represent machining processes is shown by ANOVA results. The ANOVA results showed the significance of linear terms A, B, C, D, square terms of A, B, C and D and the interaction terms AB, AC, AD, BC, BD, CD. For the kerf width model, the ANOVA indicates that the linear effects of all process parameters and the interaction effect between AC and BC are the significant model terms. While for the kerf taper model, the ANOVA indicates that the linear effect of all process parameters, the square effect of B and the interaction effect between AB, AC, BC and BD are the significant model terms. Cutting speed, laser power and gas pressure contributed 41.39, 31.71 and 16.71% to Kw and 31.23, 26.03 and 19.81% to Kt. The R2 and Adj. R2 values for Kw are achieved to be 94.28% and 93.81%, respectively, and for Kt 94.5 and 93.51%, respectively. These high values show a high correlation among the observed values and the predicted values. The deviation among R2 and predicted R2 value is smaller. The lack-of-fit value was not significant indicating a good-fitting model was preferred. The acceptable precision and adequacy index indicate a high accuracy level of the experimental data used in constructing a model. The normal probability plots for Kw and Kt shown in Figs. 5 and 6 indicate that the obtained model was practically acceptable. It showed that the residuals were close to straight line, indicating that good pattern and normal structure were found and the errors were normally distributed, supporting that the parameters considered in the established models were significant. Overall, the statistical study replicates that the experimental values and predicted values were well fitted for the preferred range of process parameters and the accuracy of the model was found adequate.

Fig. 5
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Normal probability plot for Kw

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Fig. 6
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Normal probability plot for Kt

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Minitab 17 statistical software was used for the analysis using the main effects plot shown in Figs. 7 and 8 for Kw and Kt, respectively. Both Kw and Kt show a similar pattern for the main effects plot. The study depends on mathematical models and experimental results developed using RSM and ANOVA. The main effects plot shows increasing cutting speed results in decreasing Kw and Kt. Because of higher cutting speed, less the energy density provided to the workpiece results in less time used for the heat to melt edges and thus narrower the Kw and smaller Kt generated. As cutting speed increases, less power density provided to the metal sheet. During this small-time heat was diffused to sideways and a narrower kerf was produced. A higher laser power supplied considerable heat to the workpiece material and wider kerfs and larger Kt were produced. An increase in pulse frequency had a tendency to lower the interface time between workpiece and heat which results in less dispersion of heat. Therefore, Kw and Kt increase with an increase in pulse frequency. A higher gas pressure expels the melted material from the workpiece offering a cool cut and producing a narrower Kw.

Fig. 7
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Main effects plot for Kw

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Fig. 8
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Main effects plot for Kt

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The response surface plots of parameters for Kw are shown in Fig. 9. Process parameter values are maintained at the mid-level. In Fig. 9(a), cutting speed and pulse frequency values were kept constant at 800 mm/min and 1750 Hz. Kw increases with a decrease in cutting speed and an increase in laser power. However, the result of varying cutting speeds on Kw was more lead than laser power. At high cutting speed and low laser power, the machining process was more reliable and had consequences in low Kw. The effect of laser power and gas pressure is given in Fig. 9(b). It indicates Kw increased by an increase in laser power and a decrease in gas pressure. At high laser power and low gas pressure more heat is supplied to the sheet and molten metal is not removed quickly, so Kw increases. Figure 9(c) exhibits the significance of laser power and pulse frequency on Kw. It was increased with an increase in laser power and pulse frequency. Laser power was having more impact on Kw compared to pulse frequency. Figure 9(d) exhibits the intent of cutting speed and gas pressure on Kw. It was increased with a decrease in cutting speed and gas pressure. At higher cutting speeds and gas pressure, less time is offered for heat diffusion and melting hence lower Kw. Figure 9(e) shows the influence of cutting speed and pulse frequency on Kw. It was increased with a decrease in cutting speed and an increase in pulse frequency. At high cutting speed and low pulse frequency, the amount of heat supplied was limited, and thus, a lower Kw was produced. Figure 9(f) shows the impact of pulse frequency and gas pressure on Kw. It was increased with an increase in pulse frequency and gas pressure. At low levels of pulse frequency and high levels of gas pressure, the thermal energy incident on the sheet was to a small extent, resulting in lower Kw.

Fig. 9
figure 9

Surface plot for Kw: (a) laser power vs. cutting speed (b) gas pressure vs. laser power (c) pulse frequency vs. laser power (d) gas pressure vs. cutting speed (e) cutting speed vs. pulse frequency (f) gas pressure vs. pulse frequency

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The response surface plots of parameters for Kt are shown in Fig. 10. Process parameter values were maintained at the mid-level. Figure 10(a) evinces that an increase in laser power results in an increase in Kt and Kt increases with increase in cutting speed up to about mid-level and again increases with increase in cutting speed. It was slightly decreasing at mid values. The combined effect of laser power and gas pressure is shown in Fig. 10(b). Kt increases with a decrease in gas pressure and an increase in laser power. Figure 10(c) shows that melting and resolidification increase with higher values of pulse frequency and result in Kt increases. Figure 10(d) shows cutting speed was more significant than gas pressure. Higher gas pressure ejects melted material from the machined kerf, contributing to cool cutting and smaller Kt. As shown in Fig. 10(e), a lower cutting speed and lower pulse frequency can provide more energy to the workpiece, resulting in an increase in Kt. Figure 10(f) exhibits Kt increase with a decrease in gas pressure and an increase in pulse frequency. Gas pressure was the more significant parameter as compared to pulse frequency on Kt.

Fig. 10
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Surface plot for Kt: (a) laser power vs. cutting speed (b) gas pressure vs. laser power (c) pulse frequency vs. laser power (d) gas pressure vs. cutting speed (e) cutting speed vs. pulse frequency (f) gas pressure vs. pulse frequency

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Optimal plot of Kw and Kt is shown in Figs. 11 and 12, respectively. Figure 11 indicates that minimum Kw found at laser power of 1800 W, cutting speed of 1000 mm/min, gas pressure of 1.30 bar and a pulse frequency of 1500 Hz and minimum Figure 12 indicates that Kt found at laser power of 1800 W, cutting speed of 826.26 mm/min, gas pressure of 1.30 bar and a pulse frequency of 1500 Hz.

Fig. 11
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Optimality plot of Kw

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Fig. 12
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Optimality plot of Kt

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An increase in laser power leads to higher Kw and Kt resulting in the reduction of machined kerf quality. At higher laser power, if gas pressure is not increased, more molten material is ejected toward the top of the interaction zone and melts additional material, resulting in a large kerf. Higher gas pressure easily ejected molten material from the machined kerf. At higher cutting speeds, less energy is provided to the workpiece material, less time is available for melting and heat diffusion and hence produces lower Kw. But Kt first decreases with an increase in cutting speed up to mid-level and then increases with increase in cutting speed. At a lower pulse frequency, the machining process is steadier and results in low Kw and Kt. Pulse frequency is directly proportional to pulse energy. Due to the low pulse frequency, more time is available to cooling down the material. At high pulse frequencies, the intense melting and vaporization produce a wider Kw and higher Kt. Also, resolidification and dross formation will increase with an increase in pulse frequency. Main effects plot shows that process parameters became more significant from middle to higher levels.

5 Conclusion

This work optimized and evaluated the effects of the process parameters during laser machining of a 5-mm sheet of SS304 by using the CCD of RSM and ANOVA. The following outcomes can be concluded from this work:

  • The central composite design of RSM was used to design an experiment and a regression model evaluating the relationship between Kw, Kt, and process parameters were developed. The developed model was tested by ANOVA and found adequate. The experimental values and predicted values were well fitted with an R2 value of 94.69% and 94.50% for Kw and Kt, respectively.

  • A high cutting speed and gas pressure and low laser power and pulse frequency result in a decrease in Kw and Kt. A low laser power generates less heat, a high cutting speed results in a concentration of heat for less time, high gas pressure would eject the molten metal from the kerf and contribute to a cool cut, and a low pulse frequency avoids excessive melting and resolidification resulting in lower Kw and Kt. An increase in laser power and pulse frequency and a decrease in cutting speed and gas pressure increase the kerf width. Also, increase in laser power and pulse frequency and a decrease in gas pressure increase the kerf taper. But kerf taper first decreases with an increase in cutting speed up to mid-level and then increases with increases in cutting speed.

  • The cutting speed, laser power and gas pressure had a contribution of 41.39, 31.71 and 16.71% on the Kw and 31.23, 26.03 and 19.81% on the Kt. The cutting speed was observed to be the most influenced process parameter in this machining range.

  • RSM was used to identify optimal parameters in the laser machining of SS304. The optimal machining conditions of Kw found at laser power of 1800 W, cutting speed of 1000 mm/min, gas pressure of 1.30 bar and a pulse frequency of 1500 Hz and of Kt at laser power of 1800 W, cutting speed of 802 mm/min, gas pressure of 1.30 bar and a pulse frequency of 1500 Hz.

  • This work showed that the proposed optimization method is effective in optimizing the process and analyzing the effects of process parameters on performance characteristics. This method is applicable for development in the laser machining industry by improving machining quality through suitable selection of process parameters. This method can provide an essential basis for manufacturers using laser machining technology.