Enhancing the Quality and Sustainability of Laser Cutting Processes in Laser-Assisted Manufacturing Using a Box–Behnken Design

Abstract

This study aims to examine and optimize CO₂ laser cutting parameters—namely, laser power, cutting speed, and focal plane position—when applied to polypropylene material using an experimental methodology. This research aims to improve cutting quality, increase cutting speed, and reduce waste while adhering to sustainability objectives. To achieve these goals, a comprehensive experimental approach was employed, incorporating the Box–Behnken Design (BBD) based on the response surface methodology (RSM) to optimize the laser cutting process by evaluating the relationships between input parameters and output responses. Data were collected through a series of controlled experiments in which laser power (ranging from 30 to 60 W), cutting speed (ranging from 30 to 60 mm/s), and focal plane position (set at −3, 0, and +3 mm) were systematically varied. The responses, quantified regarding cut quality, include kerf width and the heat-affected zone (HAZ). Additionally, RSM was used to optimize the laser cutting process to improve kerf quality. The results indicated that cutting speed has an inverse effect on kerf width and HAZ, while laser power has a direct effect. Furthermore, the focal plane position was found to have the least impact on the output responses. The maximum kerf width and HAZ were observed at a minimum cutting speed of 30 mm/s and a maximum laser power of 60 W.

1. Introduction

Laser material processing (LMP) refers to a group of manufacturing techniques that utilize lasers for various processes such as laser milling [1], laser texturing [2], laser additive manufacturing [3,4], laser surface treatment [5], and laser cutting [6,7]. Laser cutting is widely used in the manufacturing industry for both metallic and non-metallic materials due to its superior precision, cut quality, and minimal waste compared to conventional cutting methods. A key advantage is its ability to shape, trim, and smooth components without requiring disassembly [8,9,10]. Despite the high quality typically associated with laser cutting, material failure may occasionally occur. This issue is primarily attributed to an insufficient understanding of the optimal input parameters that influence thermal damage, cutting quality, and the mechanical properties of the material. Carbon dioxide (CO₂) laser-cutting machines are widely utilized due to their versatility and cost-effectiveness, supporting various applications such as marking, cutting, and engraving of plastic materials. The quality of laser cutting is primarily influenced by parameters like laser power (P), cutting speed (S), laser focal plane position (FPP), and the use of assisted gas. Moreover, factors such as the heat-affected zone (HAZ), surface roughness, and kerf width significantly contribute to the overall cutting quality [11,12,13]. For optimal performance, these parameters must be carefully balanced.

Polypropylene is a highly favored polymer in the manufacturing industry, particularly in the automobile sector, due to its excellent chemical resistance, lightweight nature, and superior thermal and mechanical properties [14,15]. Der et al. [16] studied the laser cutting of polyethylene and polyvinyl chloride using a CO₂ laser machine. The results indicated that the optimal cutting performance for polypropylene was achieved at a laser power of 90 W and a cutting speed of 15 mm/s. Choudhury and Shirley [17] investigated the effects of gas pressure, cutting speed, and laser power on the heat-affected zone (HAZ) and surface roughness of PP, polycarbonate (PC), and polymethyl methacrylate (PMMA) sheets using a central composite design (CCD). Their results demonstrated that PMMA exhibited the smallest HAZ, followed by PC, with PP showing the largest HAZ. In a separate study, Deepa et al. [18] examined the impacts of laser power and cutting speed on the hardness, maximum flexural stress, and ultimate tensile strength (UTS) of PP sheets. They employed a Grey Relational Analysis (GRA) to optimize multiple process parameters. The impact of nanosecond laser parameters, including repetition rate, cutting speed, and repetition time, on the kerf width and HAZ of PP sheets was studied by Wu et al. [19]. The smallest kerf width of 21.26 μm and HAZ of 16.92 μm were achieved with a repetition rate of 100 kHz, a cutting speed of 250 mm/s, and repeat times of 4.

Several studies have examined the cut quality of different polymers using CO₂ laser cutters [20,21,22]. Sabri et al. [23] evaluated the impacts of laser power, sheet thickness (t), and cutting speed on the kerf geometry dimensions of 3D-printed Polyethylene-Terephthalate-Glycol (PET-G) sheets. The effect of the laser cutting parameters on the top and bottom kerf width, the ratio of the top kerf to bottom kerf, and the HAZ were evaluated by using an analysis of variance (ANOVA). The results show that increases in the S and decreases in the P reduced the top and bottom kerf width and HAZ. Basar and Der et al. [24] used the integrating fuzzy analytic hierarchy process (AHP) and multi-criteria decision-making (MCDM) approaches to optimize focal length, laser power, and cutting speed, aiming to enhance cutting the kerf quality and surface roughness of polyethylene sheets. The results showed that the optimal parameters are a cutting speed of 12 mm/s, a power of 90 w, and a focal length of 8 mm. Aydın and Uğur [25] examined the effects of the focal plane, cutting speed, and laser power on the cutting kerf geometry dimensions and surface roughness PMMA sheets. The investigation employed an artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) to assess how cutting processing parameters influence the HAZ, kerf width at the cutting edge, and surface roughness. An experimental investigation explored the effect of two laser cutting parameters (cutting speed and laser power) on the cutting kerf quality of PLA sheets using a full factorial design [26]. Kechagiasa et al. [27] conducted a study that examined the influence of cutting speed, laser power, and stand-off distance (SoD) on the cutting kerf quality of PETG sheets by using the full factorial design method.

Based on a literature review, the main effects and interactions of cutting speed, laser power, and focal plane position on the cutting kerf quality of polypropylene sheets are less studied. Therefore, this research employs a scientific methodology—response surface methodology (RSM) and design of experiments (DOE)—to investigate the influence of laser cutting process parameters on the kerf width and heat-affected zone (HAZ) of PP sheets. The results are analyzed and interpreted using a statistical analysis of variance (ANOVA). Finally, the Box–Behnken Design (BBD), based on RSM, was utilized to optimize the laser cutting parameters using Design-Expert software (State-Ease, version 12).

2. Experimental Methodology

2.1. Box–Behnken Design

Response surface methodology (RSM) is a set of mathematical and statistical techniques employed to model and analyze problems where the desired outcome is influenced by multiple input factors [28]. The primary objective is to optimize the efficiency of the process or reaction. This methodology generates a regression equation (Equation (1)) that accurately characterizes the relationship between the input variables (χ) and the response variable (y). The equation is expressed as follows: y denotes the predicted response, χ signifies the independent variables, β represents the regression coefficients, β_ii denotes the quadratic coefficients, β_ij represents the interaction coefficients, and ε accounts for the observed error [29,30].

$$y={\beta }_0+{\displaystyle \sum _{i=1}^k{\beta }_i{x}_i+}{\displaystyle \sum _{i=1}^k{\beta }_{ii}{x}_i^2+}{\displaystyle \sum _i{\displaystyle \sum _j{\beta }_{ij}{x}_i{x}_j+\epsilon }}$$

(1)

This study focuses on determining the impact of input parameters and identifying the optimal values for the CO₂ laser cutting of polypropylene. An RSM with the Box–Behnken design (BBD) is used to systematically plan the experiments using Design Expert 12 software (State-Ease, version 12, Minneapolis, MN, USA). The BBD is an RSM used to optimize processes by evaluating the relationships between input parameters and output responses [31,32]. Figure 1 shows the cubic design space constructed by the design matrix derived from the BBD. The experiment was designed by identifying key input parameters; analyzing previous studies to determine the most influential factors; and selecting the laser power (at three levels: 30, 45, and 60 W), cutting speed (at three levels: 30, 45, and 60 mm/s), and focal plane position (at three levels: −3, 0, and +3 mm) as the input parameters.

Table 1. Laser cutting parameters and corresponding levels of each parameter.

Variables	Notation	Unit	−1	0	+1
Laser power	P	w	30	45	60
Cutting speed	S	mm/s	30	45	60
Focal plane position	FPP	mm	−3	0	3

presents the details of the independent parameters and the corresponding levels of each parameter. Based on the BBD, the experimental design and corresponding results are listed in

Table 2. Experimental design and results.

NO	Input Variables						Output Variables
	Coded Values			Actual Values			Kerf with (µm)	HAZ (µm)
	P (W)	S (mm/s)	FPP (mm)	P (W)	S (mm/s)	FPP (mm)
#1	−1	−1	0	30	30	0	588.5	1335.3
#2	−1	0	1	30	45	+3	499.3	1287.8
#3	1	0	1	60	45	+3	651.8	1383.5
#4	0	0	0	45	45	0	604.3	1430.2
#5	0	−1	1	45	30	+3	535.3	1517.3
#6	0	−1	−1	45	30	−3	703.6	1522.3
#7	0	1	1	45	60	+3	485	1509.4
#8	0	0	0	45	45	0	595.7	1427.3
#9	0	1	−1	45	60	−3	466.9	1019.4
#10	1	0	−1	60	45	−3	607.9	1671.9
#11	−1	0	−1	30	45	−3	562.6	1264.8
#12	1	1	0	60	60	0	551.1	1313.7
#13	0	0	0	45	45	0	595.7	1385.6
#14	−1	1	0	30	60	0	414.4	827.3
#15	1	−1	0	60	30	0	585.6	1654.7

.

2.2. Experimental Work

This study used a polypropylene sheet with dimensions of 50 cm × 60 cm × 0.7 mm. Polypropylene, a widely utilized thermoplastic material in various industries, presents unique challenges and opportunities in laser cutting processes.

Table 3. Properties of the PP sheet used in this study [18].

Property	Unite	Value
Density	g/cm3	0.91
Melting point	°C	160
Modulus of Elasticity	GPa	0.9–1.1
Electrical Resistivity	Ω/cm	1016–1018
Thermal Coefficient	---	72–90

presents the properties of the PP sheet. The laser cutting experiments were performed using a continuous-wave (CW) CO₂ laser cutting machine operating at a wavelength of 1060 nm. The laser beam had a Gaussian profile with a spot size of 0.2 mm at the focal plane. A total of 15 distinct cuts were made, each corresponding to a unique combination of input parameters, as outlined in Table 2. All laser cutting experiments were conducted at a room temperature of 25 ± 1 °C. Figure 2 shows the schematic of the CO₂ laser cutting process used in this study.

After the laser cutting process, an optical microscope was employed to measure the kerf width and heat-affected zone (HAZ) to assess the cutting quality. Based on Figure 3, the kerf width and the heat-affected zone (HAZ) of the cutting kerf were measured using ImageJ software (version 1.54p).

3. Results and Discussion

The responses, including kerf width, depth of the cut, and HAZ, were analyzed by generating an ANOVA table. An ANOVA table presents the results of an ANOVA test, in which the probability connected to the F-statistic is known as the p-value.

3.1. Analysis of the Width of the Kerf

The kerf width in laser cutting refers to the width of the cut or groove created by the laser beam as it removes material during the cutting process. An analysis of variance (ANOVA) table (

Table 4. ANOVA results for kerf width.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	1.686 × 10−11	9	1.873 × 10−12	100.20	<0.0001
A—Laser power	3.347 × 10−12	1	3.347 × 10−12	179.06	<0.0001
B—Cutting speed	6.942 × 10−12	1	6.942 × 10−12	371.40	<0.0001
C—Focal plane position	4.234 × 10−13	1	4.234 × 10−13	22.65	0.0051
AB	2.053 × 10−12	1	2.053 × 10−12	109.83	0.0001
AC	4.575 × 10−13	1	4.575 × 10−13	24.48	0.0043
BC	1.029 × 10−12	1	1.029 × 10−12	55.05	0.0007
A2	1.935 × 10−13	1	1.935 × 10−13	10.35	0.0235
B2	2.502 × 10−12	1	2.502 × 10−12	133.87	<0.0001
C2	1.792 × 10−14	1	1.792 × 10−14	0.9589	0.3724
Residual	9.345 × 10−14	5	1.869 × 10−14
Lack of Fit	8.806 × 10−14	3	2.935 × 10−14	10.88	0.0853
Pure Error	5.395 × 10−15	2	2.697 × 10−15
Cor Total	1.695 × 10−11	14
R2 = 0.99			Adjusted R2 = 0.98

) was generated using Expert 12 software to determine the significant and insignificant parameters affecting kerf width statistically. According to Table 4, the p-values of the main laser cutting parameters—laser power (P), cutting speed (S), and focal plane position (FPP)—along with their interaction terms and the quadratic terms of P (A²) and S (B²), are all less than 0.05. This indicates that these parameters have a significant effect on kerf width. The F-values for P, S, and FPP are 371.40, 179.06, and 22.65, respectively, suggesting that cutting speed has the most significant effect on kerf width, followed by laser power and focal plane position. The final regression equation for the kerf width model is presented in Equation (2) (in terms of actual factors).

$$\begin{array}{cc}{\left(Kerf width\right)}^{-1.98}& \\ & =+\left(5.33999\times {10}^{-6}\right)+\left(8.58352\times {10}^{-9}\times P\right)-\left(8.58352\times {10}^{-9}\times S\right)\\ & +\left(9.22082\times {10}^{-7}\times FPP\right)-\left(3.1840\times P\times S\right)- \left(7.51538\times {10}^{-9}\times P\times FPP\right)\\ & - \left(1.12712\times {10}^{-8}\times S\times FPP\right)+ \left(1.01751\times {10}^{-9}\times P^2\right)+\left(3.65871\times {10}^{-9}\times S^2\right)\\ & +\left(7.74143\times {10}^{-9}\times {FPP}^2\right)\end{array}$$

(2)

Kerf width is a critical parameter for evaluating the performance of the laser cutting process, as it directly affects the quality of the cut. The main effect plot of kerf width (Figure 4) illustrates that the cut width increases with rising laser power and decreasing cutting speed. It has been observed that kerf width is inversely proportional to cutting speed and directly proportional to laser power. An increase in laser power raises the temperature in the cutting zone, generating more molten metal and resulting in a wider kerf, especially at lower cutting speeds. These findings are consistent with the research conducted by Ming [33] and Yilbas [34], who reported that an increase in laser power (P) and a decrease in cutting speed (S) resulted in a wider kerf width. Ultimately, it is evident that within the range of the focal plane position examined in this study, FPP has a negligible effect on the kerf width. In contrast, laser speed and power exhibit a more significant influence.

The surface plot is a three-dimensional graphical representation used to evaluate the response of the kerf width concerning cutting speed, laser power, and focal plane position. In this plot, kerf width is depicted along the z-axis, while cutting speed, laser power, and focal plane position are represented on the x- and y-axes. Figure 5 provides a detailed visualization of how these parameters influence the kerf width. Figure 5a,b show that FPP only slightly affects kerf width, unlike the significant impact of laser power and cutting speed on kerf width. Kerf width can be decreased by minimizing laser power and maximizing cutting speed. According to Figure 5a, the lowest kerf width is observed at 60 mm/s cutting speed and 30 w power.

3.2. Analysis of Heat-Affected Zone (HAZ)

Table 5. ANOVA results for HAZ.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	2.297 × 1017	3	7.658 × 1016	7.34	0.0057
A—Laser power	1.200 × 1017	1	1.200 × 1017	11.50	0.0060
B—Cutting speed	1.091 × 1017	1	1.091 × 1017	10.46	0.0080
C—Focal plane position	6.900 × 1014	1	6.900 × 1014	0.0661	0.8018
Residual	1.148 × 1017	11	1.043 × 1016
Lack of Fit	1.139 × 1017	9	1.266 × 1016	29.91	0.0328
Pure Error	8.463 × 1014	2	4.232 × 1014
Cor Total	3.445 × 1017	14
R2 = 0.66			Adjusted R2 = 0.57

presents the ANOVA table for the heat-affected zone (HAZ), generated using response surface methodology (RSM). The ANOVA results show that cutting speed (S, represented by term B) and laser power (P, represented by term A) are significant factors influencing the HAZ in the CO₂ laser cutting of polypropylene. The regression equation derived from the primary data analysis is shown in Equation (3).

$$\begin{array}{cc}{(heat affected zone)}^{2.74}& \\ & =+\left(3.98037\times {10}^8\right)+\left(8.16353\times {10}^6\times P\right)-\left(7.78498\times {10}^6\times S\right)\\ & +\left(3.09578\times {10}^6\times FPP\right)\end{array}$$

(3)

Figure 6 presents the main effect plot for HAZ, illustrating the impact of laser power, cutting speed, and focal plane position. HAZ increases with decreasing laser power and increasing cutting speed, and increasing the laser power results in a higher energy input, which raises the temperature of the material over a broader region. This extended heat exposure causes the thermal gradient to spread farther from the cut, enlarging the HAZ [35,36]. Simultaneously, decreasing the cutting speed means the laser remains in contact with a given point on the material for longer. This prolonged interaction allows more heat to diffuse into the surrounding areas, further expanding the HAZ [17,36]. The results illustrated in Figure 6 indicate that variations in the FPP exert a negligible influence on the heat-affected zone HAZ.

Figure 7a shows the variation in the HAZ based on the combined impact of S (30 to 60 mm/s) and P (30 to 60 W), while Figure 7b shows the variation in HAZ based on the combined impact of FPP (30 to 60 mm) and P (30 to 60 W). The surface plot reveals that the HAZ reaches its minimum at the highest cutting speed (60 mm/s) and maximum laser power (60 W). Conversely, the maximum HAZ occurs at the lowest cutting speed (30 mm/s) and maximum laser power (60 W).

4. Optimization

In general, various methods and algorithms can be used for numerical optimization [37,38,39], with response surface methodology (RSM) being one of the most widely used techniques for optimization [40]. The main objective of this study is to achieve precise and smooth cutting of polypropylene materials using a CO₂ laser cutting machine. To accomplish this, the goal is to minimize the heat-affected zone (HAZ) and kerf width. These objectives serve as the foundation for the optimization process, with detailed information provided in

Table 6. Optimization criteria.

Parameter/Response			Goal	Lower	Upper	Importance
Parameter		Laser power	In range	30	60	-
		Cutting speed	In range	30	60	-
		Focal plane position	In range	−3	+3	-
Response	Criteria Set 1	Kerf width	Minimize	414.388	703.597	3
		Heat-Affected Zone	Minimize	827.338	1671.94	3
	Criteria Set 2	Kerf width	Minimize	414.388	703.597	2
		Heat-Affected Zone	Minimize	827.338	1671.94	5
	Criteria Set 3	Kerf width	Minimize	414.388	703.597	5
		Heat-Affected Zone	Minimize	827.338	1671.94	2

. Table 6 sets specific goals for each response, with minimum values defined. The targets for optimization are based on these goals. To achieve better quality cuts, each response is assigned equal weight and importance, with a weightage of 1 for each response. The optimal solution is the set of values for the decision variables that yields the best possible outcome according to the objective function while satisfying all constraints. The solution, in terms of actual values, generated using Design Expert 12 software for the response surface design, is presented in

Table 7. Optimization result.

Solution	Laser Power	Cutting Speed	Focal Plane Position	Kerf Width	HAZ	Desirability
1	30.000	60.000	−3.000	415.721	1001.314	0.935
2	30.000	60.000	−2.999	415.720	1001.294	0.912
3	30.000	60.000	−3.000	415.721	1001.293	0.958

. Figure 8 shows the desirability graph representing the impact of laser cutting and laser power on output responses, predicting the actual responses for kerf width and heat-affected zone (HAZ) at the desired levels of input parameters. The solution obtained from Design Expert 12 software for optimal cutting quality suggests the following values: laser power at 30 watts, cutting speed at 60 mm/s, and focal plane at −3 mm. With this combination, the heat-affected zone (HAZ) will be 1001.314 µm, and the cut width will be 415.721 µm. The desirability of the solution is 0.935.

5. Conclusions

This study investigates the CO₂ laser cutting technology for polypropylene materials and aims to optimize input parameters using response surface methodology (RSM) to enhance cut quality, cutting speed, and overall performance. The key findings include the following:

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The experiments conducted using the response surface methodology (RSM) show that cutting speed and laser power have a significant influence on both kerf width and HAZ. In contrast, within the range of focal plane position (FPP) examined in this study, FPP exhibits a negligible effect on kerf width and HAZ.

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The findings show that a decrease in cutting speed and an increase in laser power increase both kerf width and HAZ.

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The lowest kerf width (414.388 µm) and HAZ (827.338 µm) are observed at a cutting speed of 60 mm/s and a laser power of 30 W.

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The results indicated that the optimal parameter settings for achieving the minimum kerf width and HAZ are a cutting speed of 60 mm/s, a laser power of 30 W, and a focal plane position of −3 mm.