Introduction

Drilling is one of the oldest machining processes for creating various holes. With the development of materials and the demand for holes with high precision at a greater drilling rate, laser drilling is more practical than other traditional machining processes. It has a higher productivity rate for a wide variety of materials such as metals, wood, and polymers. It is also lower in cost compared to the CNC laser cutter [1,2,3,4,5,6,7]. Laser micromachining is also employed in biomedical activities, e.g., tissue engineering and biochips [8, 9].

The drilling procedure of the laser drilling technique is accomplished by converting optical power to thermal power. When the temperature of the element reaches a melting and/or vaporization point, the hole begins to form throughout different processes depending on the temperature of said element. Melting occurs without vaporization when the temperature falls below a certain threshold (typically around 500°C for PC). To complete the drilling operation, the melted object is ejected through the use of an assist gas jet. If laser radiation exceeds a certain threshold, its drilling debris is accomplished by evaporation [10,11,12,13,14].

Laser drilling involves several parameters, such as power, focal plane, exposure time (for CW laser) or pulse duration (for pulsed lasers), frequency, and wavelength. All parameters must be controlled to attain ideal hole features. The hole’s quality is essential for field applications [15]. Circularity, taper angle, barreling, and debris formation are all elements of a good product hole. The taper angle is, by definition, the angle formed by the drilled holes whose exit diameter is less than the entrance diameter. Hole circularity is measured by the difference in the diameter’s upper and lower limits just at the hole entry [16]. Feret’s diameter can also be used to describe circularity at the entry surface area of the workpiece hole [17]. The barreling determines the similarity of the hole’s sides. The recast layer placed on the workpiece surface from around the tunnel is referred to as spatter. Chen and Hu investigated the effects of power on the width of fabricated microchannels on a polycarbonate substrate. They discovered that as the power increases, the diameter of the hole expands [18].

Various laser types have been used throughout multiple industries for drilling, such as fiber laser, CO2 laser, semiconductor laser, excimer laser, and Nd: YAG laser [19]. CO2 is still the most productive and cost-effective drilling laser for polymers. Polymers are not electricity or heat conductors. The organic matter absorbs significant beam energy at 10.6-μm wavelength [20,21,22,23,24,25].

Polycarbonate has gained tremendous attention in the last decade due to its widespread application, replacing wood and steel. It possesses thermal properties that make it an effective heat insulator in sensors, and it is relatively inexpensive [23]. This material is suitable for laser micro-drilling since it has an 89% absorption rate for carbon dioxide radiant energy, lower thermal capacity, poor thermal conductivity, and lower temperature decay [18]. The surface can also be adapted for the fabrication of microelectronic thin-film circuit boards.

The purpose of this research is to practically and theoretically analyze the influence of continuous CO2 laser parameters on polycarbonate material by using the Design–Expert program. COMSOL Multiphysics software is also applied to simulate the temperature distribution of the PC sample during laser drilling. Due to the polycarbonate’s properties, the laser drilling process produces an opaque yellow color on the plane as well as burnt edges. Appropriate selection of laser drilling process parameters improves hole quality and eliminates burnt edges in this operation. This has not been observed in previous studies. The outcomes can optimize various microelectronic and microfluidic applications.

Methods

In this research, laser drilling was conducted on a polycarbonate (7 cm × 3 cm × 1 mm) using a CNC continuous CO2 laser with a 10.6-μm wavelength from the JK series. The Laser Cut 53 computer-aided design (CAD) program was applied to control the machine using manually defined instructions. The laser was directed at the polycarbonate plate using a lens with a focal length of 58 mm (see Fig. 1). The laser spot size on the sample was 300 μm. The material absorbs the laser beam’s energy, causing a surface temperature increase.

Fig. 1
figure 1

a The experimental setup of laser drilling. b PC sample. c Schematic diagram of the CO2 laser micromachining system

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Box–Behnken design (BBD)

Box–Behnken design (BBD) was chosen to investigate the influence of three input continuous CO2 laser drilling process variables—laser power, exposure time, and focal plane position (FPP)—on the hole geometry of a polycarbonate sheet of 1-mm thickness. Different process parameters were chosen in an experimental setting based on the ability of the laser source to change these parameters. A survey of laser drilling and cutting publications was accomplished before conducting the experiments. Table 1 displays the variation levels (−1, 0, 1) of the input parameters. The FPP was considered to be 0 when placed on the workpiece surface’s upper area. The lower and upper FPP surfaces were classified as negative and positive, respectively, as shown in Fig. 1. The properties of the materials are tabulated in Table 2. Tests were performed on the polycarbonate based on Design–Expert software, according to the experimental plan depicted in Table 3. Then, the entry diameter, depth, and HAZ were measured using a microscope at 50 × magnification for each run (each run required nine readings in addition to more than three repetitions of the middle value). Table 3 provides the mean values of the entry diameter, depth, and HAZ depending on BBD.

Table 1 Input parameter variation ranges in DOE
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Table 2 Polycarbonate properties used in the simulation [26,27,28,29,30,31]
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Table 3 Experimental results of the effect of laser power, exposure time, and FPP on the diameter, depth, and HAZ of drilled holes, as presented by Design–Expert software
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ANOVA was used to analyze the responses (output parameters) influenced by a number of factors (input parameters). Changes in the input variables were made in each experiment to determine the reason behind different response variables. The goal was to construct a mathematical model that represented a link between inputs and outputs (parameters and responses) with the fewest mistakes. Variable parameters differed depending on the input type.

A general quadratic equation was applied to predict the response for different levels of each factor, as given by [32]:

$$y={\beta}_{\textrm{o}}+\sum\nolimits_{i=1}^m{\beta}_{\textrm{i}}{x}_{\textrm{i}}+\sum\nolimits_{i=1}^m{\beta}_{\textrm{ii}}{x_{\textrm{i}}}^2+\sum\nolimits_i\sum\nolimits_j{\beta}_{ij}{x}_i{x}_j+\upvarepsilon$$
(1)

where m is the number of parameters, β is the constant, βi is the linear coefficient, βiiis the quadratic coefficient, βij is the interaction coefficient, and ɛ is the parameter’s error.

COMSOL Multiphysics 5.6 software

COMSOL software was employed for the simulation of CO2 laser interactions with the polycarbonate plate using the previously mentioned experimental parameters. 3D transparent polycarbonate material was created within the program, as shown in Fig. 2a. The series of holes was executed through the drilling simulation. The final shape is depicted in Fig. 2b. The CO2 laser was aimed at the sample’s top surface, and the holes were drilled perpendicular to the surface. Some laser characteristics (e.g., power, FPP, and exposure time) were modified in a systematic manner, whereas others remained constant, as presented in Table 1.

Fig. 2
figure 2

a 3D PC structure before irradiation, b laser beam drilling of several holes on a 3D PC sample, and c 2-dimensional mesh of a sample refined along with all laser spot sizes

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The technique for measuring each parameter’s effect was to change only one variable in each test while keeping the remaining values constant. This approach provides a better understanding of the holes’ evolution in each CO2 beam parameter increase throughout the modeling of the drilling process.

The surface materials were chosen from the COMSOL library. As a result, the elemental composition of PC is defined in the simulation program. Table 2 displays the most essential properties of the material for the modeling depending on the temperature in this work.

The distribution of the laser power varies within the laser beam’s spot. The highest is at the center and then diminishes towards the periphery [33]. For the zero focus position, the laser radiation was aimed at the top surface. The diameter of the CO2 laser was calculated from the following equation [34]:

$${d}_f=\frac{1}{\pi }\ \left(\ \frac{f_1\lambda }{d_0}\ \right)$$
(2)

where f1 represents the focal length of the focusing lens in mm, 𝝀 is the laser’s wavelength used, and d0 represents the laser beam’s diameter before adjusting the lens’ focus.

As for the defocused position laser drilling, the laser beam was set to strike a surface at the defocus distances of −2 and −4 mm. The defocus distances were chosen to keep the diameter of the beam spot below 500 μm at the hit surface. The larger spot size may result in a bigger hole diameter, more than the 500-μm range. The laser beam radius at the defocus distance can be calculated using Eq. 4 [35]:

$$w={w}_i{\left[\ 1+{\left({M}^2\frac{\lambda (z)}{\pi {w_i}^2}\right)}^2\right]}^{\frac{1}{2}}$$
(3)

where z is the depth from the focal plane; w is the beam radius at z; wi represents the original laser beam radius at the focus plane; M2 is the beam quality factor, which is equal to 1.5 (according to the laser manufacturer’s registration); and λ represents the laser beam’s wavelength.

Free triangle mesh was applied for all workpieces with size 0.1 mm. Such meshing does not require a long time to process. However, extra fine mesh was used for the beam spot size of size 0.002mm, which is regarded as the minimum element size, as shown in Fig. 2c. Fine meshing can result in more sophisticated peak temperature predictions.

This thermal model is proposed to compute the depth, HAZ, and diameter of the resulting sample after CO2 radiation. By applying heat transfer to the sample’s surface, materials with a temperature greater than their melting point are removed from the sample surface.

The simulation’s objective is to evaluate the parameters that will enable us to achieve an optimized hole diameter with the lowest cost. Simulations are also the best approach for predicting this process’ thermomechanical behavior.

Results and discussion

The results and discussion are divided into several parts, as follows.

Statistical analysis

The hole depth

Table 4 presents a variance analysis for the depth model. This table is the result of removing inefficient factors. The p-value illustrates how each factor affects the depth. The probability value is calculated under the assumption of “0”. If the p-value for each parameter is less than 0.05, this indicates that the parameter influences the depth, further proving the model’s relevance. The R2 values represent the quantity of data covered by the regression model. The quadratic regression equation for the depth is provided in Eq. 4. The final regression equation acquired also proved to be a good model for predicting and evaluating the impact of parameters. Figure 3 displays a three-dimensional graph with the highest depth obtained at −2 mm, zero distance from the sample surface, and with a power of 4 W. When the power was reduced to 3 W, the depth reduced at −2 FPP, while the entire hole remained at 0 FPP from the PC sheet surface. Due to the obvious Gaussian laser beam energy distribution, the energy input varied at different areas within the beam diameter. The highest energy density was at the center of the beam, while the lowest was at the outer end. Figure 4 displays the microscopic images of the depth with different FPPs at 0.15s and 4 W. With focus processing, the depth had a V-shaped cross-section. However, during the defocus process, it took on a U-shape.

Table 4 Variance analysis of the depth
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Fig. 3
figure 3

The hole depth curve for exposure time and power at FPP: a −4 mm, b −2 mm, and c 0 mm

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Fig. 4
figure 4

The shape of depth variation when irradiated with a laser exposure time of 0.15s and power of 4 W at different FPPs: a −4 and b 0, respectively

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$$\text{Depth}=+0.6+0.003\ast\text{P}-2.08\ast\text{t}+0.2\;\text{FPP}-1.5\ast\text{P}\ast\text{t}-0.025\ast\text{P}\ast\text{FPP}-0.55\ast\text{t}\ast\text{FPP}+0.05\ast\text{P}^2+25.9\ast\text{t}^2+0.009\ast\text{FPP}^{{}^2}$$
(4)

The entry hole diameter

The FPP parameter has the highest influence on the hole diameter, according to Table 5. Equation 5 further depicts a regression relationship for the diameter. Figures 5 and 6 show how laser power and exposure time have a direct relationship with the diameter. Increasing the contact time with the material leads to enlargements and deformations of the hole since the material was exposed to greater heat for a longer period of time. The hole diameter at focus remains lower than the hole diameter at defocus due to the decrease in laser beam spot diameter. The greatest result for the entry diameter was 618 μm at a focal plane distance of −4 from the sample surface. This is consistent with the findings of a recently published study [36].

Table 5 Analysis of the diameter
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Fig. 5
figure 5

The effect of laser power, exposure time, and FPP on the entry diameter

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Fig. 6
figure 6

The shape and diameter variation of the holes at the top surface when irradiated with laser powers of 2, 3, and 4 W at different exposure times (0.1, 0.15, and 0.2s) and different FPPs (−4 and 0mm)

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$$\textrm{Diameter}=+771.5-93.2\ast \textrm{P}-5242.6\ast \textrm{t}+71.9\ast \textrm{FPP}+590\ast \textrm{P}\ast \textrm{t}-10.6\ast \textrm{P}\ast \textrm{FPP}-10.6\ast \textrm{P}\ast \textrm{FPP}+40\ast \textrm{t}\ast \textrm{FPP}+4.1\ast {\textrm{P}}^{{}^2}+14342\ast {\textrm{t}}^{{}^2}+25.5\ast {\textrm{FPP}}^{{}^2}$$
(5)

The heat-affected zone of the hole

Various input factors have a similar influence on the HAZ, as shown in Table 6. Equation 6 describes the regression equation for HAZ. Figure 7 demonstrates the impact of various input parameters on HAZ. The results indicate that the laser power and time play a significant role on HAZ. As the power and time increase, the region of HAZ significantly increases due to receiving higher energy by the sample. Figure 8 shows how the size of HAZ expands as the laser FPP penetrates deeper through the material. The largest beam energy amount is towards the bottom of the piece at defocus, resulting in a greater heat-affected zone. Figure 9 presents the lowest HAZ which occurred at 0 FPP with 0.15s and 2 W, while the highest HAZ occurred at −4mm FPP.

Table 6 The analysis of HAZ
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Fig. 7
figure 7

The impact of various factors on HAZ

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Fig. 8
figure 8

The 3D surface of HAZ with different factors

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Fig. 9
figure 9

a The progression of the hole’s development at different times and powers with constant FPP (−4 mm). b The progression of the hole’s development at different times and powers with constant FPP (−2 mm). c The progression of the hole’s development at different times and powers with constant FPP (0)

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$$\textrm{HAZ}=+347.45-102.85\ast \textrm{P}-2182\ast \textrm{t}+20.475\ast \textrm{FPP}+395\textrm{P}\ast \textrm{t}+0.875\ast \textrm{P}\ast \textrm{FPP}-167\ast \textrm{t}\ast \textrm{FPP}+10.85\ {\textrm{P}}^{{}^2}+4140\ast {\textrm{t}}^{{}^2}+3.9\ast {\textrm{FPP}}^{{}^2}$$
(6)

Thermal analysis

Simulations of experiments were conducted depending on the Box–Behnken design (BBD). The CO2 laser heating of the material is affected by the laser power, exposure time, and FPP. To illustrate the material’s heating procedure while forming the hole, the COMSOL Multiphysics program was utilized to study the variations of thermal characteristics within the PC during machining, as well as various complexities of hole drilling. Several effective factors were examined during the laser drilling process. The laser’s power (2, 3, and 4 W), exposure time (0.1, 0.15, 0.2s), and different FPPs (−4, −2, and 0 mm) were applied in this research. These parameters were chosen according to the experimental test conditions of this research. The images were obtained from the cross-section region of the workpiece, as shown in Fig. 9. The temperature distribution of the material is shown after being subjected to a laser. The vaporized substance was displayed along the z-axis where the beam had penetrated the sample depth. The PC sheet vaporized at 500 °C. The dark red color area in the figure signifies the removed material when it reached a temperature greater than the vaporization point. The results further indicate the warm and cold sides close to the removed material. The warm edge represents HAZ and is shown as gradient temperature distribution colors. Similar outcomes were obtained from the experimental results, as shown in Fig. 10.

Fig. 10
figure 10

A comparison graph of an experimental and theoretical micro-drilling hole (depth, diameter, and HAZ) for different power, time, and FPP: a −4 mm, b −2 mm, and c 0 mm

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To illustrate, the numerical equation of the heat transfer model in this work is shown in Table 7 [33, 36].

Table 7 Numerical equation of the heat transfer model
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Numerical optimization

The numerical optimization technique was used to generate high-quality solutions for both constrained and unconstrained optimization problems because of its global search capabilities. Optimization uses probabilistic principles to minimize or maximize the objective function rather than deterministic ones, overcoming the constraints of traditional approaches [37, 38]. After attempting to acquire relatively similar results between the practical and theoretical tests, hole drilling optimization was accomplished using Design–Expert, in which several parameters and response constraints were analyzed (as shown in Table 8). This process resulted in several outputs (as shown in Fig. 11), which were later used in another piece of software (COMSOL); some results are depicted in Fig. 12. COMSOL was used to determine which output fitted the identical status or the ideal hole (full hole and suitable diameter with a small HAZ). After acquiring the best output from the simulation (which was the best output of Design–Expert), we changed to a real practical device (CO2 drilling device). Figure 13 presents the ideal hole (1-mm depth, 350-μm entry diameter, and 90-μm HAZ) with parameters 3.6 W power, 0.1 s time, and 0 FPP.

Table 8 Limitations of parameters and responses
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Fig. 11
figure 11

3D surface of predicted optimum hole results

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Fig. 12
figure 12

Prediction results suggested by Design–Expert via COMSOL with powers (3, 3.6, and 4W) and time (0.12, 0.1, and 0.1 s), respectively at 0 FPP, of PC

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Fig. 13
figure 13

Hole shape after optimization

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Conclusions

In this research, a 1-mm thickness polycarbonate sample was selected. The laser beam employed was on continuous mode. The input characteristics of the BBD included laser beam power, exposure time, and the laser’s FPP. The parameters (hole depth, entry diameter, and HAZ) were considered as output responses. Based on the results, the following conclusions were reached:

  • The hole diameter at the focus position was lower than the hole diameter at the defocus position due to a decrease in laser beam spot diameter.

  • The lowest HAZ that occurred at the focus position was at 0.15 s and 2 W laser drilling, providing a 0.8-mm depth with minimized diameter based on BBD.

  • The highest hole diameter was obtained at a distance of −4 from the PC sheet surface, with 4 W and at 0.15 s.

  • The cross-section changed from a V- to a U-shape when the focal position was altered from focus to defocus, respectively. However, this change was at the expense of hole deformation and an increase in hole diameter.

  • The ideal hole (full hole, with a diameter of 350 μm, and a small HAZ of 90 μm) was obtained at 3.6 W, 0.1 s, and 0 FPP.

    The similarity between the simulation results and the practical experiment under identical conditions was significantly close, indicating accurate modeling.