Optimization of Parameters in Laser Powder Bed Fusion TA15 Titanium Alloy Using Taguchi Method

: In this work, laser powder bed fusion (LPBF) was explored to fabricate TA15 (Ti-6Al-2Zr-1Mo-1V) titanium alloy based on the experimental design obtained by using the Taguchi method. The impact of processing parameters (including laser power, scanning speed, and scanning interval) on the density and microhardness of the as-LPBFed TA15 titanium alloy was analyzed using the Taguchi method and analysis of variance (ANOVA). The interaction among parameters on the density of the as-LPBFed TA15 titanium alloy was indicated by a response surface graph (RSR). When the laser energy density was adjusted to 100 J/mm 3 , the highest relative density could reach 99.7%. The further increase in the energy input led to the reduction in relative density, due to the formation of tiny holes caused by the vaporization of material at a high absorption of heat. Furthermore, in order to better reveal the correlation between relative density and processing parameters, the regression analysis was carried out for relative density. The results showed that the experimental and predicted values obtained by the regression equation were nearly the same.


Materials
The gas-atomized TA15 titanium alloy powder used in this work was purchased from Avimetal Powder Metallurgy Technology Co., Ltd., China. The chemical composition of TA15 titanium alloy powder is listed in Table 1. The main alloying elements of TA15 titanium alloy are Al, V, Zr, Mo, and Ti, as indicated in Table 1. The morphology and size distribution of TA15 titanium alloy powder are presented in Figure 1. The powder

Materials
The gas-atomized TA15 titanium alloy powder used in this work was purchased from Avimetal Powder Metallurgy Technology Co., Ltd., China. The chemical composition of TA15 titanium alloy powder is listed in Table 1. The main alloying elements of TA15 titanium alloy are Al, V, Zr, Mo, and Ti, as indicated in Table 1. The morphology and size distribution of TA15 titanium alloy powder are presented in Figure 1. The powder particles were spherically shaped with an equivalent spherical diameter of 15-53 μm (D10 =21.46 μm, D50 =33.73 μm, and D90 =48.50 μm).

Sample Fabrications and Optimization of Parameters Using Taguchi Method
The LPBF experiments were carried out by a DiMetal-100 3D printing machine (Guangzhou Leijia Additive Technology Co., Ltd., Guangzhou, China) with an oxygen concentration below 100 ppm. High density is the premise for the sample to have excellent mechanical properties, and the density of the LPBF-fabricated TA15 titanium alloy was largely affected via process parameters, such as laser power, laser scanning speed, scanning interval, and powder-bed layer thickness.
In this investigation, the Taguchi method was utilized to optimize the parameters for the density of the LPBF-fabricated TA15 titanium alloy. Based on a previous study on the effect of laser energy density on the densification of titanium alloy [46] and the fact that the low power was expected to obtain a satisfactory surface quality, the regions of the process parameters were determined. The three controllable five-level process parameters are listed in Table 2. Considering the interaction among parameters, the experimental parameters combinations were determined by the orthogonal test method using the Taguchi method. An L25 orthogonal array was obtained as shown in Table 3 using MINITAB statistical software (MINITAB 16, Pennsylvania State University, Pennsylvania, USA). The 25 parametric combinations listed in Table 3 were then applied to fabricate 10 × 10 × 10 mm 3 cubes for the sake of parametric optimization. The experimental results are displayed in the form of S/N ratio, which could be separated from the three types of performance features: nominal-the-better, smaller-the-better, and larger-thebetter. In this study, the objective was to obtain maximum density in the LPBFfabricated TA15 titanium alloy. Thereafter, the larger-the-better feature was chosen. The larger-the-better S/N ratio can be obtained based on the following equation:

Sample Fabrications and Optimization of Parameters Using Taguchi Method
The LPBF experiments were carried out by a DiMetal-100 3D printing machine (Guangzhou Leijia Additive Technology Co., Ltd., Guangzhou, China) with an oxygen concentration below 100 ppm. High density is the premise for the sample to have excellent mechanical properties, and the density of the LPBF-fabricated TA15 titanium alloy was largely affected via process parameters, such as laser power, laser scanning speed, scanning interval, and powder-bed layer thickness.
In this investigation, the Taguchi method was utilized to optimize the parameters for the density of the LPBF-fabricated TA15 titanium alloy. Based on a previous study on the effect of laser energy density on the densification of titanium alloy [46] and the fact that the low power was expected to obtain a satisfactory surface quality, the regions of the process parameters were determined. The three controllable five-level process parameters are listed in Table 2. Considering the interaction among parameters, the experimental parameters combinations were determined by the orthogonal test method using the Taguchi method. An L 25 orthogonal array was obtained as shown in Table 3 using MINITAB statistical software (MINITAB 16, Pennsylvania State University, Pennsylvania, USA). The 25 parametric combinations listed in Table 3 were then applied to fabricate 10 × 10 × 10 mm 3 cubes for the sake of parametric optimization. The experimental results are displayed in the form of S/N ratio, which could be separated from the three types of performance features: nominal-the-better, smaller-the-better, and larger-the-better. In this study, the objective was to obtain maximum density in the LPBF-fabricated TA15 titanium alloy. Thereafter, the larger-the-better feature was chosen. The larger-the-better S/N ratio can be obtained based on the following equation: where y i refers to the value of density for the ith experiment, and n represents the total number of experiments. Finally, the percent contribution of each parameter and significant parameters for the density were obtained by the method of analysis of variance (ANOVA).

Characterizations
Inductively coupled plasma-atomic emission spectrometry (ICP-AES) was employed to determine the chemical component of TA15 titanium alloy powder. Scanning electron microscopy (Nova Nano SEM230) was performed for the morphology of TA15 titanium alloy powder. The size distribution of TA15 titanium alloy powder was counted by a laser particle size analyzer (Mastersizer 3000). The microstructure of the LPBF-fabricated TA15 titanium alloy samples was characterized by a scanning electron microscope (Nova Nano SEM230) using back-scattered mode (SEM-BSE).
The Archimedes principle was used to measure the relative density of LPBF-fabricated TA15 titanium alloy samples, and the results were indicated with a percentage of the TA15 titanium alloy density (4.45 g/cm 3 ) [47]. To decrease the randomness of the tests, five measurements were carried out for every sample, and the mean of the measurements was represented as the experimental value of the relative density. The vertical section (X-Y plane) of each sample was polished for Vickers microhardness tests and the tests were conducted by a digital microhardness instrument at a load of 100 g and a dwell time of 10 s. The results obtained for each set of samples were the average values of at least three measurements. the experimental results obtained by five parameter combinations under a certain level of laser power. It can be seen from Figure 2a that the relative density of the as-LPBFed TA15 titanium alloy was below 99% with an average value of 98.65% when the laser power was 150 W, but it was beyond 99% with the increase in laser power from 150 W to 170 W. The reason was that the low energy input corresponded to the low depth, width, and height of the molten pool, which was why some of the powders could not be fully melted in the LPBF process, resulting in the decrease in relative density, and the higher levels of laser power could melt more alloy powders in the molten pool to obtain higher relative density [48]. Subsequently, the laser power increased from 170 W to 180 W, further increasing the relative density. It is worth noticing that the relative density could reach up to 99.5% when the laser power was 180 W. However, the higher laser power of 190 W caused the decrease in relative density, which was owing to the excessive energy input to the elements by burning [41], resulting in a decreasing relative density of samples. Interestingly, as shown in Figure 2b, the samples of the lowest relative density indicated the highest microhardness, and the microhardness of these five levels of laser power from 150 W to 190 W represented a decreasing trend from 338.5 HV 0.1 to 319.8 HV 0.1 , from which it could be indicated that the mechanical properties of samples were not only determined by relative density but also by many factors. Meanwhile, the values of the relative density exhibited a significant change when the laser power increased from 150 W to 190 W, which indicated the significant contribution of laser power to the relative density of LPBF TA15 alloys. Figure 2 shows the effect of laser power on the density and microhardness of the as-LPBFed TA15 titanium alloy. Here, the value of each bar represents the average value of the experimental results obtained by five parameter combinations under a certain leve of laser power. It can be seen from Figure 2a that the relative density of the as-LPBFed TA15 titanium alloy was below 99% with an average value of 98.65% when the laser power was 150 W, but it was beyond 99% with the increase in laser power from 150 W to 170 W. The reason was that the low energy input corresponded to the low depth, width and height of the molten pool, which was why some of the powders could not be fully melted in the LPBF process, resulting in the decrease in relative density, and the higher levels of laser power could melt more alloy powders in the molten pool to obtain higher relative density [48]. Subsequently, the laser power increased from 170 W to 180 W, further increasing the relative density. It is worth noticing that the relative density could reach up to 99.5% when the laser power was 180 W. However, the higher laser power of 190 W caused the decrease in relative density, which was owing to the excessive energy input to the elements by burning [41], resulting in a decreasing relative density of samples. Interestingly, as shown in Figure 2b, the samples of the lowest relative density indicated the highest microhardness, and the microhardness of these five levels of laser power from 150 W to 190 W represented a decreasing trend from 338.5 HV0.1 to 319.8 HV0.1, from which it could be indicated that the mechanical properties of samples were not only determined by relative density but also by many factors. Meanwhile, the values of the relative density exhibited a significant change when the laser power increased from 150 W to 190 W, which indicated the significant contribution of laser power to the relative density of LPBF TA15 alloys.   Figure 3 shows the influence of scanning speed on the density and microhardness of the as-LPBFed TA15 titanium alloy. Here, the value of each bar represents the average value of experimental results obtained by five parameter combinations under a certain level of scanning speed. As the scanning speed increased from 800 mm/s to 1200 mm/s at an interval of 100 mm/s, the relative density of the as-LPBFed TA15 titanium alloy decreased from 99.44% to 98.85%, as shown in Figure 3a, which was due to the laser energy density decreasing as the scanning speed increased. Consequently, the generated molten pool caused by insufficient energy input could not fully catch the alloy powders, leading to the decrease in relative density [49]. Meanwhile, Figure 3b indicates the effect of scanning speed on the microhardness of the as-LPBFed TA15 titanium alloy, from which it could be seen that the trend of microhardness of the as-LPBFed TA15 titanium alloy was decreasing from 336.4 HV 0.1 to 329.4 HV 0.1 first upon the increase in scanning speed from 800 mm/s 900 mm/s. Then, the further increase in scanning speed from 900 mm/s to 1000 mm/s simultaneously improved the microhardness, and the microhardness reached 334.5 HV 0.1 when the scanning speed was 1000 mm/s. Then, the scanning speed increased from to the decrease in relative density [49]. Meanwhile, Figure 3b indicates the effect of scanning speed on the microhardness of the as-LPBFed TA15 titanium alloy, from which it could be seen that the trend of microhardness of the as-LPBFed TA15 titanium alloy was decreasing from 336.4 HV0.1 to 329.4 HV0.1 first upon the increase in scanning speed from 800 mm/s 900 mm/s. Then, the further increase in scanning speed from 900 mm/s to 1000 mm/s simultaneously improved the microhardness, and the microhardness reached 334.5 HV0.1 when the scanning speed was 1000 mm/s. Then, the scanning speed increased from 1000 mm/s to 1200 mm/s, giving rise to a steep descent in microhardness from 334.5 HV0.1 to 320.6 HV0.1.  Figure 4 shows the relationships between scanning interval and density and microhardness of the as-LPBFed TA15 titanium alloy. Here, the value of each bar represents the average value of experimental results obtained by five parameter combinations under a certain level of scanning interval. As the scanning interval increased from 0.06 mm to 0.10 mm with an interval of 0.01 mm, the density of the as-LPBFed TA15 titanium alloy decreased correspondingly from 99.41% to 98.72% with a smooth trend. The descent trend of density with increasing scanning interval was owing to the lower energy density per unit volume, leading to the decreasing energy adopted by the TA15 powders [41]. Meanwhile, the microhardness of the as-LPBFed TA15 titanium alloy also represented a reduction trend from 333.9 HV0.1 to 322.4 HV0.1 with the increase in scanning interval from 0.06 mm to 0.10 mm.  Figure 4 shows the relationships between scanning interval and density and microhardness of the as-LPBFed TA15 titanium alloy. Here, the value of each bar represents the average value of experimental results obtained by five parameter combinations under a certain level of scanning interval. As the scanning interval increased from 0.06 mm to 0.10 mm with an interval of 0.01 mm, the density of the as-LPBFed TA15 titanium alloy decreased correspondingly from 99.41% to 98.72% with a smooth trend. The descent trend of density with increasing scanning interval was owing to the lower energy density per unit volume, leading to the decreasing energy adopted by the TA15 powders [41]. Meanwhile, the microhardness of the as-LPBFed TA15 titanium alloy also represented a reduction trend from 333.9 HV 0.1 to 322.4 HV 0.1 with the increase in scanning interval from 0.06 mm to 0.10 mm.

Analysis of the Signal-to-Noise (S/N) Ratio
The output parameter (relative density) was utilized to measure the mean and signal-to-noise ratios of every input parameter for the best quality of the as-LPBFed TA15 titanium alloy specimens. The mean value and signal-to-noise ratio (S/N) were obtained to evaluate the effect of every process parameter on the as-LPBFed TA15 titanium alloy specimens. In this investigation, the larger the criterion, the better the model used to select the mean and S/N ratio to identify the response of the process parameters. Tables 4  and 5 show the response tables for relative density of the mean value and the signal-tonoise ratio, respectively. The larger the distinction between the S/N values, the more

Analysis of the Signal-to-Noise (S/N) Ratio
The output parameter (relative density) was utilized to measure the mean and signalto-noise ratios of every input parameter for the best quality of the as-LPBFed TA15 titanium alloy specimens. The mean value and signal-to-noise ratio (S/N) were obtained to evaluate the effect of every process parameter on the as-LPBFed TA15 titanium alloy specimens.
In this investigation, the larger the criterion, the better the model used to select the mean and S/N ratio to identify the response of the process parameters. Tables 4 and 5 show the response tables for relative density of the mean value and the signal-to-noise ratio, respectively. The larger the distinction between the S/N values, the more significant the process parameters were. Thus, it can be indicated that the laser power had the greatest effect on the relative density. In addition, the primary effect curves of the mean value and S/N ratio on the densities are shown in Figures 5 and 6. It can be seen that the highest relative density of the as-LPBFed TA15 titanium alloy specimens was obtained at the process parameters of laser power of 180 W, scanning speed of 800 mm/s, and scanning interval of 0.06 mm.

Analysis of Variance (ANOVA)
The percentage contribution of every parameter was calculated by ANOVA. ANO-VA facilitated the formal testing of the results of all the main factors and their relationships by assessing the mean squared deviation of the experimental error approximation at a defined confidence level. In this study, the percentage contribution of each process parameter to obtain the best molding quality of the specimen was performed by MINITAB software. The most significant process parameter obtained by calculating the percentage contribution was the laser power of 33.86%, followed by the scanning interval of 31.33% and finally the scanning speed of 25.35%. Table 6 indicates the results obtained by ANOVA of the densities. The results show that the laser power was the most significant process parameter affecting the relative density of the as-LPBFed TA15 titanium alloy.

Analysis of Variance (ANOVA)
The percentage contribution of every parameter was calculated by ANOVA. ANOVA facilitated the formal testing of the results of all the main factors and their relationships by assessing the mean squared deviation of the experimental error approximation at a defined confidence level. In this study, the percentage contribution of each process parameter to obtain the best molding quality of the specimen was performed by MINITAB software. The most significant process parameter obtained by calculating the percentage contribution was the laser power of 33.86%, followed by the scanning interval of 31.33% and finally the scanning speed of 25.35%. Table 6 indicates the results obtained by ANOVA of the densities. The results show that the laser power was the most significant process parameter affecting the relative density of the as-LPBFed TA15 titanium alloy.

Effect of Laser Energy Density on Relative Density of as-LPBFed TA15 Titanium Alloy
In this section, the interaction influences of scanning speed and laser power on the relative density of the alloy are discussed. Figure 7 shows the response surface graph and contour plot for the influence of laser power and scanning speed on the relative density obtained by using Design Expert software, from which it can be directly seen that the relative density of samples first increased obviously and then slightly reduced with the reduction in the scanning speed or the increase in the laser power. The effect of the scanning speed on relative density appeared more remarkable at lower laser powers, and so did laser power at high scanning speeds. As reported, volume energy density (E v ) is the critical element that determines the relative density, and it can be represented as follows: Crystals 2022, 12, 1385 9 of 13 Ev = P/vht (2) Here, P represents the laser power (W), v refers to the laser scanning speed (mm/s), h is the laser scanning interval (mm), and t is the layer thickness (mm), which remains at 0.03 mm throughout the investigation. Based on Equation (2), the Ev of each sample is listed in Table 3.  Figure 8 indicates the correlation between volume energy density and relative density of the TA15 alloy fabricated via LPBF processes. It can be found from Figure 8 that a lower relative density of 98.24% occurred at a lower energy density of 48.48 J/mm 3 , which was due to the low level of laser energy input not being able to make the powder surface melt completely, resulting in the lack of fusion, as shown in Figure 9a. Thus, a higher energy density could be utilized to realize higher values of relative density. When the laser energy density was adjusted to 100 J/mm 3 , the highest relative density Here, P represents the laser power (W), v refers to the laser scanning speed (mm/s), h is the laser scanning interval (mm), and t is the layer thickness (mm), which remains at 0.03 mm throughout the investigation. Based on Equation (2), the E v of each sample is listed in Table 3. Figure 8 indicates the correlation between volume energy density and relative density of the TA15 alloy fabricated via LPBF processes. It can be found from Figure 8 that a lower relative density of 98.24% occurred at a lower energy density of 48.48 J/mm 3 , which was due to the low level of laser energy input not being able to make the powder surface melt completely, resulting in the lack of fusion, as shown in Figure 9a. Thus, a higher energy density could be utilized to realize higher values of relative density. When the laser energy density was adjusted to 100 J/mm 3 , the highest relative density could reach 99.7%, as shown in Table 3. There are almost no defects such as pores, as indicated in (Figure 9b). Notably, the further increase in the energy input would lead slightly to the reduction in the relative density due to the vaporization of material caused by the high absorption of heat from melt pool turbulence or the interaction zone [36], which would result in the formation of tiny holes, as shown in Figure 9c.
Crystals 2022, 12, x FOR PEER REVIEW could reach 99.7%, as shown in Table 3. There are almost no defects such as pores dicated in (Figure 9b). Notably, the further increase in the energy input wou slightly to the reduction in the relative density due to the vaporization of m caused by the high absorption of heat from melt pool turbulence or the interactio [36], which would result in the formation of tiny holes, as shown in Figure 9c.

Confirmation Analysis
In order to better reveal the correlation between relative density and laser power, and scanning speed and scanning interval, the regression analysis was carried out for relative density. With the regression expression given according to the response parameter (relative density) and the three input process parameters (laser power (A), scanning speed (B), and scanning interval (C)) with the expression via a second-order polynomial, the equation is as follows [50]: Relative density = a0 + a1(A) + a2(B)+ a3(C) + a4(AB)+ a5(AC) + a6(BC) + a7(ABC) Table 7 shows the corresponding value of coefficients from a0 to a7 for the relative density. By replacing each value of these three process parameters and corresponding coefficients in the regression expression, the predicted value for relative density could be obtained. Recall above Table 3 that the values of prediction and experiment for relative density were clearly shown, and the values of prediction and experiment for relative density were compared. The result indicates that the difference between their values was not remarkable and their percentage of error was less than 0.5%. The confirmation analysis had been finished to identify that the values of prediction and experiment obtained by means of the regression equation were nearly the same. Directly, the high correlation

Confirmation Analysis
In order to better reveal the correlation between relative density and laser power, and scanning speed and scanning interval, the regression analysis was carried out for relative density. With the regression expression given according to the response parameter (relative density) and the three input process parameters (laser power (A), scanning speed (B), and scanning interval (C)) with the expression via a second-order polynomial, the equation is as follows [50]: Relative density = a 0 + a 1 (A) + a 2 (B) + a 3 (C) + a 4 (AB)+ a 5 (AC) + a 6 (BC) + a 7 (ABC) (3) Table 7 shows the corresponding value of coefficients from a 0 to a 7 for the relative density. By replacing each value of these three process parameters and corresponding coefficients in the regression expression, the predicted value for relative density could be obtained. Recall above Table 3 that the values of prediction and experiment for relative density were clearly shown, and the values of prediction and experiment for relative density were compared. The result indicates that the difference between their values was not remarkable and their percentage of error was less than 0.5%. The confirmation analysis had been finished to identify that the values of prediction and experiment obtained by means of the regression equation were nearly the same. Directly, the high correlation between experimental values and predicted values for relative density is directly shown in Figure 10.

Conclusions
(1) With the increase in laser power, the relative density first increased and then decreased. When the laser power was 180 W, the relative density could reach the peak value of 99.5%. However, the higher laser power of 190 W caused the decrease in relative density, which was owing to the excessive energy input to the elements by burning, resulting in the decrease in relative density. (2) As the scanning interval increased from 0.06 mm to 0.10 mm with an interval of 0.01 mm, the density of the as-LPBFed TA15 titanium alloy decreased correspondingly from 99.41% to 98.72% with a smooth trend. The descent trend of density with increasing scanning interval was owing to the lower energy density per unit volume, causing the decreased energy absorbed by the TA15 powders.

Conclusions
(1) With the increase in laser power, the relative density first increased and then decreased.
When the laser power was 180 W, the relative density could reach the peak value of 99.5%. However, the higher laser power of 190 W caused the decrease in relative density, which was owing to the excessive energy input to the elements by burning, resulting in the decrease in relative density. (2) As the scanning interval increased from 0.06 mm to 0.10 mm with an interval of 0.01 mm, the density of the as-LPBFed TA15 titanium alloy decreased correspondingly from 99.41% to 98.72% with a smooth trend. The descent trend of density with increasing scanning interval was owing to the lower energy density per unit volume, causing the decreased energy absorbed by the TA15 powders.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.