# Modeling and Optimization Approaches of Laser-Based Powder-Bed Fusion Process for Ti-6Al-4V Alloy

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{5}or 3125 experiments are required for this method. The advantage of this approach is having the exact response for the effects of parameters and all of the combinations of their interactions [6]. However, conducting a full factorial DoE to determine L-PBF process parameters for novel materials is practically impossible. The reason is the high costs and time associated with manufacturing and characterizing these samples and modeling the correlations between the characterization and the process parameters. Therefore, fractional factorial DoE methods are required to evaluate the most significant process variables and to optimize the performance of the products.

_{25}orthogonal array. Manjunath et al. [9] employed a Taguchi L

_{9}orthogonal array design to optimize the DED process of colmonoy 52 SA, which is a hard nickel-chromium-boron alloy. They obtained the best interfacial bonding between the substrate and the deposition material by measuring the hardness variations in these regions. Yang et al. [10] pointed out the limitation of the Taguchi method in optimizing only a single performance characteristic at a time in the DED processing of Inconel 625. Donstov et al. [12] found the application of this method useful in improving the physical, mechanical, and tribological properties of FDM-manufactured metal-polymer composite samples in terms of uniformity of powder mixing as well as the structural uniformity of the produced samples. The Taguchi method has also been used for the L-PBF process optimization for various materials, including SS316 L [13,14], AlSi10 Mg [15,16], CoCrMo [17], Inconel [18], and Titanium alloys [17,19]. Joguet et al. [17] used this method to evaluate the effects of four L-PBF processing parameters, including laser spot size, hatch spacing, exposure time, and laser focal point distance, on porosity content of CoCrMo and Ti40 parts. Using the Taguchi approach, Kuo and Yang [20] obtained optimal laser power, scanning speed, hatch spacing, and layer thickness for fabricating plastic injection molds with higher hardness and better gas permeability. They reported the layer thickness as the most significant parameter affecting the response properties. Rathod and Karia [16] reported a similar conclusion for the significance of the layer thickness in determining the hardness and surface roughness. Sathish et al. [18] employed the Taguchi method to examine the influence of build orientation and heat treatment on the coefficient of friction in Inconel 718 samples fabricated by L-PBF. Jiang et al. [13] examined the effects of three factors—laser power, scanning speed, and hatch spacing—at three levels on three properties of L-PBF parts: top surface roughness, hardness, and density. They reported laser power as the most important parameter affecting all the examined properties. Calignano et al. [15] found that the scanning speed had the biggest impact on the surface roughness of the components fabricated by the L-PBF process. Although the reason for this difference in conclusions is unclear, it may be attributed to differences in the materials (stainless steel vs. aluminum alloys) or differences in the machines (EP250 vs. EOSINT M270) used for these experiments.

^{3}. El-Sayed et al. [25] used the RSM to propose the optimum process parameters, including laser power, scanning speed, and hatch spacing, for Ti-6Al-4V medical implant applications and concluded that higher energy densities resulted in lower surface roughness and lower porosity levels. Gajera et al. [26] used the Box-Behnken design of the RSM and established a relationship between the L-PBF process parameters and surface roughness values of CL50 WS steel parts to compare two optimization algorithms: a genetic algorithm and the Jaya algorithm. Bartolomeu et al. [27] manufactured Ti-6Al-4V samples by varying three processing parameters (i.e., laser power, scanning speed, and hatch spacing) at three levels in the L-PBF process and used the RSM to analyze the experimental results of shear stress, hardness, and density. They obtained a quadratic model for each of the output properties and presented a response surface for them. They achieved relatively good adequacy for their models with a coefficient of determination R

^{2}of 0.62–0.68. Please note that R

^{2}has values between 0–1 (higher values show higher accuracies) and increases when other higher-order terms are added to the model. Hence, an adjusted R

^{2}is recommended as a criterion for the model adequacy. The adjusted R

^{2}for their models ranged from 0.55–0.61. Krishnan et al. [28] used a full factorial DoE on three levels of three factors—laser power, scanning speed, and hatch spacing—to evaluate the most significant factor affecting the mechanical properties of L-PBF-manufactured AlSi10 Mg samples. They concluded that hatch spacing was the parameter with the most significant influence. Using the same approach, Pawlak et al. [29] fabricated AZ31 magnesium parts with relative densities higher than 99.5% using the L-PBF process. Sharma et al. [30] used the Taguchi method and RSM to investigate the influence of the laser power, scanning speed, and hatch spacing on density and surface roughness of PBF-fabricated AlSi10 Mg samples and reported the hatch spacing as the most significant factor in determining the output responses. Wang et al. [31] combined the two methods, i.e., Taguchi and RSM, to study the effect of the laser power, scanning speed, and hatch spacing, on the mechanical properties and microstructure of nickel-based superalloy samples fabricated by the PBF process. They applied linear, two-factor-interaction, and quadradic models to obtain response surfaces for the tensile strength of the manufactured samples and observed the quadratic modeling of this response yields to the lowest error value among all the tested models.

_{25}Taguchi orthogonal arrays are used for the DoE of L-PBF process parameters in five levels. Second, a fractional factorial DoE resulting in 1/125th of the full factorial experiments is used for the RSM and ANN optimizations of the processing parameters. Additionally, the correlations between the L-PBF process parameters and the target properties are modeled and extensively discussed. Finally, the sets of optimum processing parameters predicted by each method are determined and compared.

## 2. Materials and Methods

## 3. DoE for the L-PBF Process Parameters

#### 3.1. Taguchi Method

_{i}is the ith observed response value, n is the number of test results, and m is the target value of the response.

#### 3.2. Response Surface Method

^{k-p}design is a fractional factorial design in l

^{k−p}runs. As this study has five factors in five levels, a 5

^{5−3}design was chosen, which requires 5

^{2}or 25 runs, which is only 1/125th of the full factorial design observations (5

^{5}runs). To generate 25 runs for a 5

^{5−3}design, the 25 combinations of a 5

^{2}full factorial design were placed in the first two columns of the table. The cells of the three remaining columns were generated using the cells in the first two columns according to the following equations [58]:

_{i}is the ith column of the table. Mod 5 indicates that the modulus of the operation was 5, which was employed in the construction of five-level designs (under these conditions, any multiple of 5 equals zero). The fractional factorial design combinations of the factor levels for the number of experiments are shown in Table A2 in the appendix.

#### 3.3. Artificial Neural Network

## 4. Results and Discussions

#### 4.1. Taguchi Method

^{3}) considering all the combinations of the tested levels, i.e., the highest considered laser power and the lowest scanning speed and hatch spacing. Consequently, it can be concluded that the Taguchi method recommends the highest energy density level to obtain the smallest roughness values for the upskin and top surface roughness of L-PBF-manufactured parts. This is in contrast with the findings related to the optimum downskin roughness values where lower values of energy density (~55 J/mm

^{3}) correspond to the optimum downskin roughness values. A possible explanation for this observation may be offered by considering the gravitational force that smooths the melt lines on the top and upskin surfaces while coarsening the melt lines that are unsupported for downskin surfaces.

#### 4.2. Response Surface Method

^{2}values of these response equations were relatively high (Table 5), it can be concluded that modeling the upskin roughness parameters using a linear model can be less expensive without missing any significant quadratic effect of the main factors and their interactions.

#### 4.3. Artificial Neural Network

#### 4.4. Comparison of the Predictions from the Taguchi Method, the Response Surface Method, and the Artificial Neural Network

## 5. Conclusions

- Both Taguchi and RSM approaches were successful in capturing the correlations between the L-PBF processing parameters and responses by using only 1/125th of the observations in full factorial experiments.
- The Taguchi results showed that the layer thickness was the most significant factor in determining all the three downskin roughness responses, in which the optimum layer thickness was the smallest value, i.e., 20 µM. Therefore, the layer thickness-related mechanisms, such as stair-stepping effect, were the dominant factors influencing the downskin roughness in the L-PBF process.
- The Taguchi method recommends the highest energy density level to obtain the smallest roughness values for the upskin and top surface roughness of L-PBF-manufactured parts, regardless of all the other properties.
- Similarly, the parameter combinations recommended by the RSM resulting in the smoothest up-facing surfaces in L-PBF-manufactured parts yields the highest energy densities.
- Using RSM results, we were able to assess whether two input parameters are independent in determining a response. The results showed that the interaction between the laser power and hatch spacing in predicting microhardness and relative density was the most significant among the two-way interactions between the other parameters. However, in the upskin roughness properties, the most significant interaction was between laser power and layer thickness.
- A multi-response optimization of all nine properties with the same weights is performed to obtain a single set of L-PBF processing parameters for optimizing all the response properties. The applied weight on each response can be altered based on their importance to the specific application of the L-PBF-manufactured component.
- Overall, the present analyses by both Taguchi and RSM methods showed that the layer thickness was the dominant factor controlling the downskin surface roughness parameters and was a significant factor influencing the top surface and upskin roughness parameters.
- The contribution of stripe width on most responses was negligible, which was attributed to its local importance near the boundaries of parts.
- The microhardness and relative density were both influenced by the energy density calculated based on the laser power, scanning speed, layer thickness, and hatch spacing. However, laser power played a more dominant role on the microhardness response than on the relative density response.
- The trained ANN model exhibited very good accuracy and performance in predicting the true response values based on the given input processing parameters.
- The comparison of the prediction errors corresponding to the ANN, the RSM, and the Taguchi method showed that all the three models exhibited reasonable predictive capabilities.
- Among the three models, the Taguchi method showed the least desirable performance in predicting each and all the response properties. We can conclude that nonlinearity exists in the behavior of the tested response properties of PBF-manufactured parts that the Taguchi method was not able to capture as accurately as the quadratic models.
- Although the RSM performed slightly better than the ANN in predicting microhardness values, the ANN showed much better performance in predicting the other properties. Therefore, it can be concluded that the ANN outperformed the predictive capabilities of the RSM and the Taguchi method.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Experiment No. | Processing Parameter Level | ||||
---|---|---|---|---|---|

A | B | C | D | E | |

1 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 1 | 1 | 1 | 1 |

3 | 0 | 2 | 2 | 2 | 2 |

4 | 0 | 3 | 3 | 3 | 3 |

5 | 0 | 4 | 4 | 4 | 4 |

6 | 1 | 0 | 1 | 2 | 3 |

7 | 1 | 1 | 2 | 3 | 4 |

8 | 1 | 2 | 3 | 4 | 0 |

9 | 1 | 3 | 4 | 0 | 1 |

10 | 1 | 4 | 0 | 1 | 2 |

11 | 2 | 0 | 2 | 4 | 1 |

12 | 2 | 1 | 3 | 0 | 2 |

13 | 2 | 2 | 4 | 1 | 3 |

14 | 2 | 3 | 0 | 2 | 4 |

15 | 2 | 4 | 1 | 3 | 0 |

16 | 3 | 0 | 3 | 1 | 4 |

17 | 3 | 1 | 4 | 2 | 0 |

18 | 3 | 2 | 0 | 3 | 1 |

19 | 3 | 3 | 1 | 4 | 2 |

20 | 3 | 4 | 2 | 0 | 3 |

21 | 4 | 0 | 4 | 3 | 2 |

22 | 4 | 1 | 0 | 4 | 3 |

23 | 4 | 2 | 1 | 0 | 4 |

24 | 4 | 3 | 2 | 1 | 0 |

25 | 4 | 4 | 3 | 2 | 1 |

Experiment No. | Processing Parameter Level | ||||
---|---|---|---|---|---|

A | B | C | D | E | |

1 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 1 | 1 | 2 | 3 |

3 | 0 | 2 | 2 | 4 | 1 |

4 | 0 | 3 | 3 | 1 | 4 |

5 | 0 | 4 | 4 | 3 | 2 |

6 | 1 | 0 | 1 | 1 | 1 |

7 | 1 | 1 | 2 | 3 | 4 |

8 | 1 | 2 | 3 | 0 | 2 |

9 | 1 | 3 | 4 | 2 | 0 |

10 | 1 | 4 | 0 | 4 | 3 |

11 | 2 | 0 | 2 | 2 | 2 |

12 | 2 | 1 | 3 | 4 | 0 |

13 | 2 | 2 | 4 | 1 | 3 |

14 | 2 | 3 | 0 | 3 | 1 |

15 | 2 | 4 | 1 | 0 | 4 |

16 | 3 | 0 | 3 | 3 | 3 |

17 | 3 | 1 | 4 | 0 | 1 |

18 | 3 | 2 | 0 | 2 | 4 |

19 | 3 | 3 | 1 | 4 | 2 |

20 | 3 | 4 | 2 | 1 | 0 |

21 | 4 | 0 | 4 | 4 | 4 |

22 | 4 | 1 | 0 | 1 | 2 |

23 | 4 | 2 | 1 | 3 | 0 |

24 | 4 | 3 | 2 | 0 | 3 |

25 | 4 | 4 | 3 | 2 | 1 |

Sample Code * | Relative Density (%) | Hardness (HV) | Roughness (µm) | ||||||
---|---|---|---|---|---|---|---|---|---|

Top Surface | Upskin Surface | Upskin Hor. Line | Upskin Ver. Line | Downskin Surface | Downskin Hor. Line | Downskin Ver. Line | |||

11111 | 99.893 | 364.91 | 4.86 | 16.63 | 9.14 | 9.85 | 20.52 | 12.18 | 12.99 |

12222 | 99.726 | 354.80 | 7.54 | 19.55 | 11.62 | 13.86 | 19.73 | 13.00 | 14.63 |

12234 | 99.712 | 362.83 | 8.85 | 21.97 | 11.79 | 14.65 | 20.85 | 12.07 | 15.31 |

13333 | 98.493 | 343.40 | 15.86 | 23.72 | 13.72 | 14.67 | 22.30 | 13.28 | 15.08 |

13352 | 98.824 | 346.91 | 28.42 | 27.79 | 13.30 | 16.27 | 24.70 | 14.79 | 15.61 |

14425 | 97.379 | 340.33 | 17.09 | 24.46 | 12.75 | 15.95 | 20.30 | 14.00 | 14.64 |

14444 | 99.053 | 343.74 | 27.52 | 30.08 | 15.03 | 17.09 | 26.73 | 13.27 | 15.07 |

15543 | 99.431 | 341.80 | 32.52 | 32.27 | 17.12 | 21.52 | 28.18 | 15.54 | 15.10 |

15555 | 98.685 | 339.18 | 38.84 | 38.19 | 16.83 | 21.44 | 32.74 | 17.36 | 18.02 |

21222 | 99.732 | 357.64 | 5.26 | 18.96 | 7.74 | 12.66 | 23.64 | 15.26 | 13.14 |

21234 | 99.650 | 367.69 | 6.52 | 19.48 | 11.35 | 11.74 | 22.57 | 14.45 | 16.37 |

22345 | 99.258 | 361.82 | 11.23 | 24.02 | 11.15 | 14.51 | 24.29 | 14.14 | 14.68 |

23413 | 99.734 | 360.61 | 10.26 | 18.69 | 10.67 | 12.52 | 16.63 | 11.00 | 11.58 |

23451 | 98.493 | 343.4 | 23.30 | 30.04 | 13.63 | 16.58 | 27.03 | 15.02 | 14.56 |

24512 | 99.277 | 349.54 | 16.51 | 21.21 | 12.13 | 13.44 | 18.29 | 11.02 | 10.65 |

24531 | 97.399 | 352.40 | 20.98 | 26.77 | 13.65 | 14.84 | 24.70 | 14.99 | 16.37 |

25123 | 99.712 | 362.52 | 10.93 | 21.47 | 11.49 | 12.27 | 20.32 | 12.48 | 12.77 |

25154 | 99.383 | 361.53 | 12.83 | 26.63 | 14.11 | 15.21 | 25.48 | 16.45 | 15.91 |

31333 | 99.571 | 363.98 | 6.81 | 19.67 | 8.22 | 11.03 | 24.48 | 14.52 | 14.85 |

31352 | 99.503 | 365.48 | 9.81 | 23.61 | 10.04 | 12.70 | 28.47 | 13.81 | 15.31 |

32413 | 99.650 | 361.67 | 7.42 | 20.87 | 10.94 | 11.21 | 21.58 | 12.15 | 13.66 |

32451 | 99.573 | 362.20 | 13.39 | 25.31 | 11.62 | 15.71 | 27.59 | 15.37 | 16.12 |

33524 | 99.602 | 360.59 | 13.72 | 22.69 | 11.75 | 13.16 | 21.55 | 12.85 | 13.07 |

34135 | 99.646 | 364.18 | 6.79 | 22.11 | 11.86 | 13.48 | 22.60 | 14.97 | 15.11 |

34142 | 99.358 | 368.30 | 7.74 | 26.43 | 12.17 | 13.87 | 27.13 | 16.52 | 16.63 |

35215 | 99.789 | 364.02 | 11.74 | 25.00 | 12.59 | 17.80 | 19.41 | 12.19 | 11.94 |

35241 | 99.470 | 363.05 | 14.38 | 23.99 | 11.86 | 13.64 | 24.81 | 13.07 | 14.98 |

41425 | 99.684 | 366.77 | 7.96 | 19.36 | 9.68 | 11.12 | 22.39 | 13.23 | 14.40 |

41444 | 99.702 | 370.83 | 9.95 | 22.43 | 11.55 | 12.32 | 29.14 | 18.46 | 16.36 |

42512 | 99.735 | 365.98 | 8.54 | 23.54 | 11.36 | 14.14 | 24.15 | 14.66 | 13.68 |

42531 | 99.669 | 363.44 | 12.17 | 24.94 | 12.78 | 14.27 | 27.09 | 14.50 | 15.44 |

43135 | 99.801 | 370.56 | 15.24 | 19.02 | 10.35 | 10.46 | 24.93 | 14.97 | 15.63 |

43142 | 99.714 | 366.28 | 6.78 | 21.74 | 10.55 | 11.41 | 29.16 | 15.82 | 17.98 |

44253 | 99.286 | 363.92 | 13.00 | 25.16 | 11.50 | 13.91 | 28.96 | 15.70 | 16.69 |

45314 | 99.632 | 359.07 | 13.11 | 19.37 | 11.53 | 13.16 | 17.79 | 10.90 | 11.07 |

45321 | 99.516 | 361.75 | 13.55 | 23.36 | 11.83 | 14.93 | 23.58 | 13.75 | 13.48 |

51543 | 99.283 | 364.92 | 12.16 | 22.96 | 11.73 | 11.37 | 26.21 | 13.40 | 14.84 |

51555 | 99.570 | 372.44 | 12.78 | 25.81 | 10.37 | 13.27 | 31.39 | 17.78 | 15.67 |

52123 | 99.787 | 354.08 | 4.49 | 17.81 | 8.18 | 10.49 | 26.96 | 15.38 | 14.29 |

52154 | 99.681 | 358.51 | 5.83 | 17.92 | 6.97 | 11.25 | 29.87 | 13.65 | 17.58 |

53215 | 99.830 | 359.80 | 5.69 | 18.29 | 10.64 | 11.05 | 20.04 | 12.10 | 12.96 |

53241 | 99.615 | 360.61 | 7.69 | 25.32 | 11.88 | 13.62 | 39.59 | 20.22 | 20.96 |

54314 | 99.338 | 365.06 | 8.89 | 22.76 | 12.13 | 13.51 | 24.00 | 14.23 | 16.04 |

54321 | 99.600 | 361.15 | 9.55 | 22.83 | 11.81 | 13.81 | 23.74 | 14.02 | 13.58 |

55432 | 99.551 | 363.42 | 18.46 | 23.81 | 12.41 | 14.63 | 23.76 | 14.61 | 14.91 |

Weight | Bias | |||
---|---|---|---|---|

−0.817226931 | 1.2743454058 | −0.4373294332 | −0.2543893758 | 0.0672884998 |

−0.1742719803 | 0.0407326757 | −0.9436160018 | −0.076517916 | 0.7709497912 |

0.4618549711 | 0.1455196574 | −0.2580787273 | −0.8655356556 | −0.1703290546 |

0.4420987284 | 0.9007528946 | 1.051149895 | 0.7140146312 | 0.5015783122 |

0.9768443561 | −0.4022851406 | −0.6007116257 | −0.078794974 | 0.9597908008 |

0.3804623429 | −0.8645048849 | 0.279432945 | −0.4744703392 | 0.5012114738 |

Weight | Bias | |||||
---|---|---|---|---|---|---|

0.69163044 | −0.29082017 | −0.68915516 | 0.01657495 | 0.53058497 | 0.62056222 | −0.29844372 |

−0.4943906 | 0.56887031 | −0.02349223 | −0.7047001 | −1.19140218 | 0.17356839 | −0.17197129 |

−0.1946129 | −0.09454516 | 0.01747523 | −1.2967566 | 0.12582357 | 0.47763527 | −0.12213046 |

0.22637272 | 0.11649799 | −0.09655429 | 0.84722914 | −0.74640528 | 0.25596798 | −0.30446552 |

−0.2527528 | 0.746188496 | 0.899036494 | 0.83378385 | 0.256524716 | −0.0999083 | −0.0819088467 |

Weight | Bias | ||||
---|---|---|---|---|---|

−0.0951860163 | −0.5847561682 | 0.2450872866 | −0.5658932656 | −0.0712814703 | 0.280699756 |

0.8474751074 | −1.3345236156 | 0.6504012392 | −0.3931396363 | 0.0672525452 | −0.47777086 |

−0.9487583799 | −0.3165275189 | −0.8272228144 | −0.5577874479 | −1.0364007486 | −0.26500424 |

**Figure A1.**Response surface plots of each two-parameter combination for (

**a**) downskin horizontal line roughness, (

**b**) top surface roughness, (

**c**) upskin surface roughness, (

**d**) downskin surface roughness, and (

**e**) upskin horizontal line roughness. Constant parameters kept at: A (laser power) = 280 w, B (scan speed) = 1200 mm/s, C (hatch spacing) = 140 µM, and D (layer thickness) = 30 µM. Each surface shows the variations of the response (vertical axis) versus variations of two process parameters (horizontal axes) at a time, while the other two parameters are kept constant at their default values mentioned in the figure legend. For simplicity, and to increase the figure readability, the parameter values are normalized as 0 represents the value of the first level and 1 represents the value of the highest level.

## References

- Qiu, C.; Al Kindi, M.; Aladawi, A.S.; Al Hatmi, I. A Comprehensive Study on Microstructure and Tensile Behaviour of a Selectively Laser Melted Stainless Steel. Sci. Rep.
**2018**, 8, 1–16. [Google Scholar] [CrossRef] - Charles, A.; Elkaseer, A.; Thijs, L.; Hagenmeyer, V.; Scholz, S.G. Effect of Process Parameters on the Generated Surface Roughness of Down-Facing Surfaces in Selective Laser Melting. Appl. Sci.
**2019**, 9, 1256. [Google Scholar] [CrossRef] [Green Version] - Perevoshchikova, N.; Rigaud, J.; Sha, Y.; Heilmaier, M.; Finnin, B.; Labelle, E.; Wu, X. Optimisation of Selective Laser Melting Parameters for the Ni-Based Superalloy IN-738 LC Using Doehlert’s Design. Rapid Prototyp. J.
**2017**, 23, 881–892. [Google Scholar] [CrossRef] [Green Version] - Fox, J.C.; Moylan, S.P.; Lane, B. Effect of Process Parameters on the Surface Roughness of Overhanging Structures in Laser Powder Bed Fusion Additive Manufacturing. Procedia CIRP
**2016**, 45, 131–134. [Google Scholar] [CrossRef] [Green Version] - Chen, Z. Understanding of the Modeling Method in Additive Manufacturing. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 711. [Google Scholar] [CrossRef] - Fisher, R.A. Design of Experiments. BMJ
**1936**, 1, 554. [Google Scholar] [CrossRef] - Nath, R.; Murugesan, K. Optimization of Double Diffusive Mixed Convection in a Bfs Channel Filled With Alumina Nanoparticle Using Taguchi Method and Utility Concept. Sci. Rep.
**2019**, 9, 1–19. [Google Scholar] [CrossRef] - Liu, Y.; Liu, C.; Liu, W.; Ma, Y.; Tang, S.; Liang, C.; Cai, Q.; Zhang, C. Optimization of Parameters in Laser Powder Deposition AlSi10Mg Alloy Using Taguchi Method. Opt. Laser Technol.
**2019**, 111, 470–480. [Google Scholar] [CrossRef] - Manjunath, B.; Vinod, A.; Abhinav, K.; Verma, S.; Sankar, M.R. Optimisation of Process Parameters for Deposition of Colmonoy Using Directed Energy Deposition Process. Mater. Today Proc.
**2020**, 26, 1108–1112. [Google Scholar] [CrossRef] - Yang, B.; Lai, Y.; Yue, X.; Wang, D.; Zhao, Y. Parametric Optimization of Laser Additive Manufacturing of Inconel 625 Using Taguchi Method and Grey Relational Analysis. Scanning
**2020**, 2020, 1–10. [Google Scholar] [CrossRef] - Cherkia, H.; Kar, S.; Singh, S.S.; Satpathy, A. Fused Deposition Modelling and Parametric Optimization of ABS-M30. In Advances in Materials and Manufacturing Engineering; Springer: Singapore, 2020; pp. 1–15. [Google Scholar]
- Dontsov, Y.V.; Panin, S.; Buslovich, D.G.; Berto, F. Taguchi Optimization of Parameters for Feedstock Fabrication and FDM Manufacturing of Eear-Resistant UHMWPE-Based Composites. Materials
**2020**, 13, 2718. [Google Scholar] [CrossRef] - Jiang, H.-Z.; Li, Z.-Y.; Feng, T.; Wu, P.-Y.; Chen, Q.-S.; Feng, Y.-L.; Li, S.-W.; Gao, H.; Xu, H.-J. Factor Analysis of Selective Laser Melting Process Parameters With Normalised Quantities and Taguchi Method. Opt. Laser Technol.
**2019**, 119, 105592. [Google Scholar] [CrossRef] - Campanelli, S.; Casalino, G.; Contuzzi, N.; Ludovico, A. Taguchi Optimization of the Surface Finish Obtained by Laser Ablation on Selective Laser Molten Steel Parts. Procedia CIRP
**2013**, 12, 462–467. [Google Scholar] [CrossRef] - Calignano, F.; Manfredi, D.; Ambrosio, E.P.; Iuliano, L.; Fino, P. Influence of Process Parameters on Surface Roughness of Aluminum Parts Produced by DMLS. Int. J. Adv. Manuf. Technol.
**2013**, 67, 2743–2751. [Google Scholar] [CrossRef] [Green Version] - Rathod, M.K.R.; Karia, M.M.C. Experimental Study for Effects of Process Parameters of Selective Laser Sintering for alsi10mg. Int. J. Technol. Res. Eng.
**2020**, 7, 6957–6960. [Google Scholar] - Joguet, D.; Costil, S.; Liao, H.; Danlos, Y. Porosity Content Control of CoCrMo and Titanium Parts by Taguchi Method Applied to Selective Laser Melting Process Parameter. Rapid Prototyp. J.
**2016**, 22, 20–30. [Google Scholar] [CrossRef] - Sathish, S.; Anandakrishnan, V.; Dillibabu, V.; Muthukannan, D.; Balamuralikrishnan, N. Optimization of Coefficient of Friction for Direct Metal Laser Sintered Inconel 718. Adv. Manuf. Technol.
**2019**, 371–379. [Google Scholar] [CrossRef] - Dong, G.; Marleau-Finley, J.; Zhao, Y.F. Investigation of Electrochemical Post-Processing Procedure for Ti-6AL-4V Lattice Structure Manufactured by Direct Metal Laser Sintering (DMLS). Int. J. Adv. Manuf. Technol.
**2019**, 104, 3401–3417. [Google Scholar] [CrossRef] - Kuo, C.-C.; Yang, X.-Y. Optimization of Direct Metal Printing Process Parameters for Plastic Injection Mold With Both Gas Permeability and Mechanical Properties Using Design of Experiments Approach. Int. J. Adv. Manuf. Technol.
**2020**, 109, 1219–1235. [Google Scholar] [CrossRef] - Gunst, R.F.; Mason, R.L. Fractional Factorial Design. Wiley Interdiscip. Rev. Comput. Stat.
**2009**, 1, 234–244. [Google Scholar] [CrossRef] - Dada, M.; Popoola, P.; Mathe, N.; Pityana, S.; Adeosun, S. Parametric Optimization of Laser Deposited High Entropy Alloys Using Response Surface Methodology (RSM). Int. J. Adv. Manuf. Technol.
**2020**, 109, 2719–2732. [Google Scholar] [CrossRef] - Pant, P.; Chatterjee, D.; Nandi, T.; Samanta, S.K.; Lohar, A.K.; Changdar, A. Statistical Modelling and Optimization of Clad Characteristics in Laser Metal Deposition of Austenitic Stainless Steel. J. Braz. Soc. Mech. Sci. Eng.
**2019**, 41, 283. [Google Scholar] [CrossRef] - Read, N.; Wang, W.; Essa, K.; Attallah, M.M. Selective Laser Melting of ALSi10Mg Alloy: Process Optimisation and Mechanical Properties Development. Mater. Des.
**2015**, 65, 417–424. [Google Scholar] [CrossRef] [Green Version] - El-Sayed, M.A.; Ghazy, M.; Youssef, Y.; Essa, K. Optimization of SLM Process Parameters for Ti6Al4V Medical Implants. Rapid Prototyp. J.
**2019**, 25, 433–447. [Google Scholar] [CrossRef] [Green Version] - Gajera, H.M.; Darji, V.; Dave, K. Application of Fuzzy Integrated JAYA Algorithm for the Optimization of Surface Roughness of DMLS Made Specimen: Comparison with GA. In Advances in Intelligent Systems and Computing; Springer Science and Business Media LLC: Amsterdam, The Netherlands, 2019; Volume 949, pp. 137–152. [Google Scholar]
- Bartolomeu, F.; Faria, S.; Carvalho, O.; Pinto, E.; Alves, N.; Silva, F.S.; Miranda, G. Predictive Models for Physical and Mechanical Properties of Ti6Al4V Produced by Selective Laser Melting. Mater. Sci. Eng. A
**2016**, 663, 181–192. [Google Scholar] [CrossRef] - Krishnan, M.; Atzeni, E.; Canali, R.; Calignano, F.; Manfredi, D.G.; Ambrosio, E.P.; Iuliano, L. On the Effect of Process Parameters on Properties of AlSi10Mg Parts Produced by DMLS. Rapid Prototyp. J.
**2014**, 20, 449–458. [Google Scholar] [CrossRef] - Pawlak, A.; Rosienkiewicz, M.; Chlebus, E. Design of Experiments Approach in AZ31 Powder Selective Laser Melting Process Optimization. Arch. Civ. Mech. Eng.
**2017**, 17, 9–18. [Google Scholar] [CrossRef] - Marmarelis, M.G.; Ghanem, R.G. Data-Driven Stochastic Optimization on Manifolds for Additive Manufacturing. Comput. Mater. Sci.
**2020**, 181, 109750. [Google Scholar] [CrossRef] - Wang, G.; Huang, L.; Liu, Z.; Qin, Z.; He, W.; Liu, F.; Chen, C.; Nie, Y. Process Optimization and Mechanical Properties of Oxide Dispersion Strengthened Nickel-Based Superalloy by Selective Laser Melting. Mater. Des.
**2020**, 188, 108418. [Google Scholar] [CrossRef] - Okaro, I.A.; Jayasinghe, S.; Sutcliffe, C.; Black, K.; Paoletti, P.; Green, P.L. Automatic Fault Detection for Laser Powder-Bed Fusion Using Semi-Supervised Machine Learning. Addit. Manuf.
**2019**, 27, 42–53. [Google Scholar] [CrossRef] - Nguyen, D.S.; Park, H.-S.; Lee, C.-M. Optimization of Selective Laser Melting Process Parameters for Ti-6Al-4V Alloy Manufacturing Using Deep Learning. J. Manuf. Process.
**2020**, 55, 230–235. [Google Scholar] [CrossRef] - Qi, X.; Chen, G.; Li, Y.; Cheng, X.; Li, C. Applying Neural-Network-Based Machine Learning to Additive Manufacturing: Current Applications, Challenges, and Future Perspectives. Engineering
**2019**, 5, 721–729. [Google Scholar] [CrossRef] - Sood, A.K.; Ohdar, R.K.; Mahapatra, S.S. Experimental Investigation and Empirical Modelling of FDM Process for Compressive Strength Improvement. J. Adv. Res.
**2012**, 3, 81–90. [Google Scholar] [CrossRef] [Green Version] - Rumelhart, D.E.; Hinton, G.E.; Williams, R.J. Learning Representations by Back-Propagating Errors. Nature
**1986**, 323, 533–536. [Google Scholar] [CrossRef] - Zhang, Y.; Hong, G.S.; Ye, D.; Zhu, K.; Fuh, J. Extraction and Evaluation of Melt Pool, Plume and Spatter Information for Powder-Bed Fusion AM Process Monitoring. Mater. Des.
**2018**, 156, 458–469. [Google Scholar] [CrossRef] - Paul, A.; Mozaffar, M.; Yang, Z.; Liao, W.-K.; Choudhary, A.; Cao, J.; Agrawal, A. A Real-Time Iterative Machine Learning Approach for Temperature Profile Prediction in Additive Manufacturing Processes. In Proceedings of the 2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA), Washington, DC, USA, 5–8 October 2019; pp. 541–550. [Google Scholar]
- Caggiano, A.; Zhang, J.; Alfieri, V.; Caiazzo, F.; Gao, R.X.; Teti, R. Machine Learning-Based Image Processing for on-Line Defect Recognition in Additive Manufacturing. CIRP Ann.
**2019**, 68, 451–454. [Google Scholar] [CrossRef] - Shevchik, S.A.; Kenel, C.; Leinenbach, C.; Wasmer, K. Acoustic Emission for in Situ Quality Monitoring in Additive Manufacturing Using Spectral Convolutional Neural Networks. Addit. Manuf.
**2018**, 21, 598–604. [Google Scholar] [CrossRef] - Ali, T.K.; Balasubramanian, E. Study on Compressive Strength Characteristics of Selective Inhibition Sintered UHMWPE Specimens Based on ANN and RSM Approach. CIRP J. Manuf. Sci. Technol.
**2020**. [Google Scholar] [CrossRef] - Li, M.; Han, Y.; Zhou, M.; Chen, P.; Gao, H.; Zhang, Y.; Zhou, H. Experimental Investigating and Numerical Simulations of the Thermal Behavior and Process Optimization for Selective Laser Sintering of PA6. J. Manuf. Process.
**2020**, 56, 271–279. [Google Scholar] [CrossRef] - Guo, Y.; Lu, W.F.; Fuh, J. Semi-Supervised Deep Learning Based Framework for Assessing Manufacturability of Cellular Structures in Direct Metal Laser Sintering Process. J. Intell. Manuf.
**2020**, 1–13. [Google Scholar] [CrossRef] - Zhang, M.; Sun, C.-N.; Zhang, X.; Goh, P.C.; Wei, J.; Hardacre, D.; Li, H. High Cycle Fatigue Life Prediction of Laser Additive Manufactured Stainless Steel: A Machine Learning Approach. Int. J. Fatigue
**2019**, 128, 105194. [Google Scholar] [CrossRef] - Li, L.; Anand, S. Hatch Pattern Based Inherent Strain Prediction Using Neural Networks for Powder Bed Fusion Additive Manufacturing. J. Manuf. Process.
**2020**, 56, 1344–1352. [Google Scholar] [CrossRef] - Yan, J. 3D Printing Optimization Algorithm Based on Back-Propagation Neural Network. J. Eng. Des. Technol.
**2020**, 18, 1223–1230. [Google Scholar] [CrossRef] - Marrey, M.; Malekipour, E.; El-Mounayri, H.; Faierson, E.J. A Framework for Optimizing Process Parameters in Powder Bed Fusion (PBF) Process Using Artificial Neural Network (ANN). Procedia Manuf.
**2019**, 34, 505–515. [Google Scholar] [CrossRef] - Tran, H.-C.; Lo, Y.-L. Systematic Approach for Determining Optimal Processing Parameters to Produce Parts With High Density in Selective Laser Melting Process. Int. J. Adv. Manuf. Technol.
**2019**, 105, 4443–4460. [Google Scholar] [CrossRef] - Lo, Y.-L.; Liu, B.-Y.; Tran, H.-C. Optimized Hatch Space Selection in Double-Scanning Track Selective Laser Melting Process. Int. J. Adv. Manuf. Technol.
**2019**, 105, 2989–3006. [Google Scholar] [CrossRef] - Rahimi, M.H.; Shayganmanesh, M.; Noorossana, R.; Pazhuheian, F. Modelling and Optimization of Laser Engraving Qualitative Characteristics of Al-SiC Composite Using Response Surface Methodology and Artificial Neural Networks. Opt. Laser Technol.
**2019**, 112, 65–76. [Google Scholar] [CrossRef] - Mehrpouya, M.; Gisario, A.; Rahimzadeh, A.; Nematollahi, M.; Baghbaderani, K.S.; Elahinia, M. A Prediction Model for Finding the Optimal Laser Parameters in Additive Manufacturing of NiTi Shape Memory Alloy. Int. J. Adv. Manuf. Technol.
**2019**, 105, 4691–4699. [Google Scholar] [CrossRef] - Khorasani, A.M.; Gibson, I.; Ghasemi, A.; Ghaderi, A. Modelling of Laser Powder Bed Fusion Process and Analysing the Effective Parameters on Surface Characteristics of Ti-6Al-4V. Int. J. Mech. Sci.
**2020**, 168, 105299. [Google Scholar] [CrossRef] - Akhil, V.; Raghav, G.; Arunachalam, N.; Srinivasu, D.S. Image Data-Based Surface Texture Characterization and Prediction Using Machine Learning Approaches for Additive Manufacturing. J. Comput. Inf. Sci. Eng.
**2020**, 20, 1–39. [Google Scholar] [CrossRef] - Hiren, M.; Gajera, M.E.; Dave, K.G.; Jani, V.P. Experimental Investigation and Analysis of Dimensional Accuracy of Laser-Based Powder Bed Fusion Made Specimen by Application of Response Surface Methodology. Prog. Addit. Manuf.
**2019**, 4, 371–382. [Google Scholar] [CrossRef] - Fotovvati, B.; Etesami, S.A.; Asadi, E. Process-Property-Geometry Correlations for Additively-Manufactured Ti–6Al–4V Sheets. Mater. Sci. Eng. A
**2019**, 760, 431–447. [Google Scholar] [CrossRef] - Fotovvati, B.; Asadi, E. Size Effects on Geometrical Accuracy for Additive Manufacturing of Ti-6Al-4V ELI Parts. Int. J. Adv. Manuf. Technol.
**2019**, 104, 2951–2959. [Google Scholar] [CrossRef] - ASTM B311-17. Standard Test Method for Density of Powder Metallurgy (PM) Materials Containing Less Than Two Percent Porosity; ASTM International: West Conshohocken, PA, USA, 2017; Available online: www.astm.org (accessed on 26 October 2020).
- Wu, C.-F.; Hamada, M. Experiments: Planning, Analysis, and Optimization; Wiley: Hoboken, NJ, USA, 2009; ISBN 9780471699460. [Google Scholar]
- Beale, H.D.; Demuth, H.B.; Hagan, M.T. Neural Network Design; Pws: Boston, MA, USA, 1996. [Google Scholar]
- Wasserstein, R.L.; Lazar, N.A. The ASA Statement on p-Values: Context, Process, and Purpose. Am. Stat.
**2016**, 70, 129–133. [Google Scholar] [CrossRef] [Green Version] - Debroy, T.; Wei, H.; Zuback, J.; Mukherjee, T.; Elmer, J.; Milewski, J.; Beese, A.; Wilson-Heid, A.; De, A.; Zhang, W. Additive Manufacturing of Metallic Components–Process, Structure and Properties. Prog. Mater. Sci.
**2018**, 92, 112–224. [Google Scholar] [CrossRef] - Sun, J.; Yang, Y.; Wang, D. Parametric Optimization of Selective Laser Melting for Forming Ti6Al4V Samples by Taguchi Method. Opt. Laser Technol.
**2013**, 49, 118–124. [Google Scholar] [CrossRef] - Fotovvati, B.; Wayne, S.F.; Lewis, G.; Asadi, E. A Review on Melt-Pool Characteristics in Laser Welding of Metals. Adv. Mater. Sci. Eng.
**2018**, 2018, 1–18. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**a**) The dimensions of two examples of manufactured samples using various L-PBF parameters and (

**b**) illustration of the geometry and surfaces of the samples used in this study.

**Figure 2.**The ANN architecture used in this research with six and five nodes in two hidden layers. Four input parameters enter the network and after processing, three response properties are predicted as the output values.

**Figure 3.**Main effects plot for S/N ratios versus each process parameter, i.e., A-E that are shown at five levels each, for different output responses, including (

**a**) microhardness, (

**b**) relative density, (

**c**) top surface roughness, (

**d**) upskin surface roughness, (

**e**) downskin surface roughness, (

**f**) upskin horizontal line roughness, (

**g**) upskin vertical line roughness, (

**h**) downskin horizontal line roughness, and (

**i**) downskin vertical line roughness. The values of the input parameters at each level are mentioned on the horizontal axes at the bottom of the figure.

**Figure 4.**Response surface plots of each two-parameter combination for (

**a**) relative density, (

**b**) downskin vertical line roughness, (

**c**) microhardness, and (

**d**) upskin vertical line roughness. Constant parameters kept at: A (laser power) = 280 w, B (scan speed) = 1200 mm/s, C (hatch spacing) = 140 µM, and D (layer thickness) = 30 µM. Each surface shows the variations of the response (vertical axis) versus variations of two process parameters (horizontal axes) at a time, while the other two parameters are kept constant at their default values mentioned in the figure legend. For simplicity, and to increase the figure readability, the parameter values are normalized as 0 represents the value of the first level and 1 represents the value of the highest level. Identical figures for other response parameters are shown in Figure A1 at the appendix.

**Figure 5.**Comparison between the actual and ANN predicted results of training (

**a**,

**c**,

**e**) and test data (

**b**,

**d**,

**f**) for microhardness (

**a**,

**b**), relative density (

**c**,

**d**), and top surface roughness (

**e**,

**f**). A batch of 25 samples was used for training (left figures) and another batch of 20 samples was used for testing of the network performance (right figures). The higher conformity of the solid and dashed lines means the higher accuracy of the network prediction.

Process Parameter | Symbol | Level 0 | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|---|---|

Laser power (W) | A | 170 | 210 | 250 | 290 | 330 |

Scan speed (mm/s) | B | 900 | 1050 | 1200 | 1350 | 1500 |

Hatch spacing (µM) | C | 100 | 120 | 140 | 160 | 180 |

Layer thickness (µM) | D | 20 | 30 | 40 | 50 | 60 |

Stripe width (mm) | E | 3 | 4 | 5 | 6 | 7 |

Response | The Best Combination of L-PBF Parameters * | Energy Density (J/mm^{3}) | Significance Ranking | ||||
---|---|---|---|---|---|---|---|

Microhardness | A4 290 | B1 900 | C1 100 | D2 30 | E2 4 | 107.4 | A > B > C > D > E |

Relative density | A4 290 | B1 900 | C1 100 | D2 30 | E2 4 | 107.4 | D > C > A > B > E |

Top surface roughness | A5 330 | B1 900 | C1 100 | D1 20 | E5 7 | 183.3 | C > B > D > A > E |

Upskin surface roughness | A5 330 | B1 900 | C1 100 | D1 20 | E4 6 | 183.3 | D > C > B > A > E |

Downskin surface roughness | A2 210 | B5 1500 | C2 120 | D1 20 | E4 6 | 58.3 | D > A > C > E > B |

Upskin H. line roughness | A5 330 | B1 900 | C1 100 | D1 20 | E4 6 | 183.3 | C > A > B > D > E |

Upskin V. line roughness | A5 330 | B1 900 | C1 100 | D1 20 | E3 5 | 183.3 | B > D > C > A > E |

Downskin H. line roughness | A2 210 | B1 900 | C3 140 | D1 20 | E4 6 | 83.3 | D > E > A > C > B |

Downskin V. line roughness | A2 210 | B4 1350 | C3 140 | D1 20 | E1 3 | 55.6 | D > A > C > B > E |

**Table 3.**p-values and contribution percent of the process parameters in different responses based on ANOVA linear regression results.

Parameter | Microhardness | Relative Density | Top Surface Roughness | |||

p-Value | Contribution (%) | p-Value | Contribution (%) | p-Value | Contribution (%) | |

A (laser power) | 0.071 | 45.3 | 0.103 | 22.6 | 0.004 | 19.0 |

B (scan speed) | 0.185 | 23.3 | 0.197 | 14.1 | 0.002 | 27.7 |

C (hatch spacing) | 0.334 | 13.9 | 0.098 | 23.5 | 0.001 | 33.6 |

D (layer thickness) | 0.542 | 7.9 | 0.075 | 28.0 | 0.004 | 17.6 |

E (stripe width) | 0.984 | 0.7 | 0.464 | 6.2 | 0.282 | 1.3 |

Error | − | 8.8 | − | 5.6 | − | 0.7 |

Parameter | Upskin Surface | Upskin Horizontal Line | Upskin Vertical Line | |||

p-Value | Contribution (%) | p-Value | Contribution (%) | p-Value | Contribution (%) | |

A (laser power) | 0.304 | 11.4 | 0.192 | 22.6 | 0.035 | 20.4 |

B (scan speed) | 0.196 | 16.6 | 0.15 | 27.3 | 0.02 | 28.2 |

C (hatch spacing) | 0.114 | 24.8 | 0.131 | 30.0 | 0.034 | 20.8 |

D (layer thickness) | 0.065 | 35.9 | 0.5 | 8.8 | 0.029 | 22.8 |

E (stripe width) | 0.624 | 4.7 | 0.878 | 2.5 | 0.258 | 5.2 |

Error | − | 6.6 | − | 8.8 | − | 2.6 |

Parameter | Downskin Surface | Downskin Horizontal Line | Downskin Vertical Line | |||

p-Value | Contribution (%) | p-Value | Contribution (%) | p-Value | Contribution (%) | |

A (laser power) | 0.646 | 5.6 | 0.956 | 2.9 | 0.694 | 7.6 |

B (scan speed) | 0.996 | 0.3 | 0.99 | 1.2 | 0.879 | 3.6 |

C (hatch spacing) | 0.772 | 3.7 | 0.972 | 2.2 | 0.705 | 7.3 |

D (layer thickness) | 0.024 | 81.2 | 0.141 | 64.7 | 0.071 | 66.9 |

E (stripe width) | 0.974 | 0.9 | 0.769 | 9.0 | 0.966 | 1.6 |

Error | − | 8.3 | − | 20.0 | − | 13.0 |

Parameter | Micro-Hardness | Rel. Density | Top Surface | Upskin Surface | Upskin Hor. Line | Upskin Ver. Line | Downskin Surface | Downskin Hor. Line | Downskin Ver. Line |
---|---|---|---|---|---|---|---|---|---|

Constant | 364.05 | 100.31 | 4.72 | 16.44 | 8.572 | 10.55 | 19.32 | 11.66 | 12.15 |

A | 16.1 | 1.45 | −15.78 | −1.25 | −3.16 | −1.74 | 3.59 | 3.89 | −2.13 |

B | 7.1 | −0.23 | −9.3 | 6.98 | 5.91 | 0.43 | −5.4 | 0.31 | 5.82 |

C | −35.3 | −2.13 | 0.35 | 0.07 | −1.06 | 3.87 | 5.73 | 2.83 | 2.20 |

D | 7.2 | −0.26 | 13.31 | 6.11 | 2.78 | 1.67 | 2.55 | 2.80 | 4.88 |

A2 | −26.74 | −2.007 | 14.67 | 2.61 | 2.70 | 2.31 | 7.44 | 1.79 | 3.97 |

B2 | −6.7 | −0.77 | 11.42 | 1.21 | −0.74 | 5.15 | 2.12 | 0.72 | −5.43 |

C2 | 12.3 | 0.50 | 20.1 | 2.43 | 1.94 | −0.29 | −1.75 | 3.77 | −3.43 |

D2 | −2.65 | 0.417 | 7.31 | 2.62 | 0.31 | 3.58 | −0.49 | −3.19 | −3.97 |

AB | 5.4 | 1.21 | 18.8 | −3.27 | −1.60 | −0.49 | −3.85 | −7.38 | −2.49 |

AC | 34.3 | 1.89 | −21.6 | 1.03 | 1.48 | −3.03 | −8.07 | 1.02 | 1.35 |

AD | 3.79 | −0.277 | −10.62 | −3.90 | −2.22 | −3.28 | 4.07 | 1.45 | 1.48 |

BD | −11.2 | −0.50 | −11.94 | −2.95 | −0.89 | −3.85 | 6.71 | 4.74 | 2.90 |

**Table 5.**p-values and contribution % associated with different coefficients obtained from ANOVA of response surface regression for different responses.

DownskinVer. Line | Cont. % | - | 13.5 | 0.9 | 0.9 | 27.7 | 5.9 | 6.8 | 1.6 | 3.8 | 0.8 | 0.3 | 0.9 | 1.9 | Fitting coefficients | 70.7 | 41.4 | ||||||||||

p-Value | 0.070 | 0.052 | 0.578 | 0.584 | 0.009 | 0.180 | 0.152 | 0.466 | 0.274 | 0.599 | 0.758 | 0.586 | 0.428 | ||||||||||||||

DownskinHor. Line | Cont. % | - | 32.1 | 0.2 | 0.5 | 19.4 | 1.1 | 0.1 | 1.8 | 2.3 | 6.9 | 0.2 | 0.8 | 4.8 | 76.9 | 53.8 | |||||||||||

p-Value | 0.024 | 0.004 | 0.776 | 0.650 | 0.016 | 0.517 | 0.836 | 0.406 | 0.358 | 0.122 | 0.808 | 0.578 | 0.189 | ||||||||||||||

DownskinSurface | Cont. % | - | 31.2 | 1.6 | 0.0 | 29.6 | 3.8 | 0.2 | 0.1 | 0.0 | 0.4 | 1.9 | 1.3 | 1.9 | 77.8 | 55.6 | |||||||||||

p-Value | 0.020 | 0.003 | 0.417 | 0.980 | 0.004 | 0.223 | 0.778 | 0.857 | 0.946 | 0.695 | 0.381 | 0.472 | 0.379 | ||||||||||||||

UpskinVer. Line | Cont. % | - | 19.5 | 23.0 | 9.4 | 5.9 | 1.4 | 4.5 | 0.0 | 2.3 | 0.0 | 1.1 | 3.3 | 2.5 | 81.5 | 63.0 | |||||||||||

p-Value | 0.008 | 0.012 | 0.008 | 0.065 | 0.131 | 0.440 | 0.186 | 0.952 | 0.337 | 0.919 | 0.506 | 0.253 | 0.314 | ||||||||||||||

UpskinHor. Line | Cont. % | - | 10.1 | 47.6 | 9.0 | 7.7 | 3.1 | 0.1 | 0.6 | 0.0 | 0.4 | 0.4 | 2.3 | 0.2 | 87.8 | 75.5 | |||||||||||

p-Value | 0.001 | 0.025 | 0.000 | 0.032 | 0.045 | 0.180 | 0.765 | 0.544 | 0.899 | 0.619 | 0.620 | 0.241 | 0.719 | ||||||||||||||

UpskinSurface | Cont. % | - | 3.7 | 26.5 | 10.4 | 30.5 | 1.0 | 0.1 | 0.3 | 0.6 | 0.5 | 0.1 | 2.4 | 0.8 | 85.4 | 70.8 | |||||||||||

p-Value | 0.002 | 0.192 | 0.003 | 0.039 | 0.002 | 0.494 | 0.801 | 0.695 | 0.579 | 0.603 | 0.859 | 0.287 | 0.541 | ||||||||||||||

TopSurface | Cont. % | - | 14.5 | 6.0 | 19.9 | 17.9 | 5.7 | 2.1 | 4.0 | 0.9 | 3.4 | 5.3 | 3.3 | 2.4 | 86.7 | 73.4 | |||||||||||

p-Value | 0.001 | 0.004 | 0.045 | 0.002 | 0.002 | 0.049 | 0.206 | 0.092 | 0.398 | 0.116 | 0.057 | 0.120 | 0.186 | ||||||||||||||

RelativeDensity | Cont. % | - | 19.9 | 15.1 | 8.5 | 1.5 | 16.3 | 0.8 | 0.3 | 0.5 | 2.1 | 3.2 | 0.4 | 0.8 | 71.7 | 37.7 | |||||||||||

p-Value | 0.123 | 0.029 | 0.051 | 0.127 | 0.501 | 0.044 | 0.615 | 0.772 | 0.685 | 0.426 | 0.329 | 0.726 | 0.630 | ||||||||||||||

Micro-Hardness | Cont. % | - | 30.6 | 1.3 | 7.7 | 0.1 | 19.8 | 0.8 | 1.6 | 0.1 | 0.3 | 13.9 | 0.4 | 2.2 | 87.0 | 73.9 | |||||||||||

p-Value | 0.001 | 0.001 | 0.405 | 0.059 | 0.781 | 0.006 | 0.521 | 0.366 | 0.794 | 0.692 | 0.016 | 0.626 | 0.290 | ||||||||||||||

Source | Model | A | B | C | D | A^{2} | B^{2} | C^{2} | D^{2} | AB | AC | AD | BD | R^{2} (%) | R^{2}_{adj} (%) |

Response | Parameters Combination | Optimized Response | Energy Density | SE Fit | 90% CI | |||
---|---|---|---|---|---|---|---|---|

A | B | C | D | |||||

Microhardness | 330 | 1024 | 180 | 54 | 372.5 | 33.2 | 3.72 | (365.88, 379.15) |

Relative Density | 170 | 900 | 180 | 20 | 99.99 | 52.5 | 1.69 | (97.07, 103.17) |

Top surface Roughness | 250 | 900 | 138 | 20 | 0.1 | 100.6 | 3.77 | (−6.59, 6.83) |

Upskin Surface Roughness | 208 | 900 | 100 | 20 | 16.29 | 115.6 | 1.49 | (13.65, 18.94) |

Upskin Horizontal Line Roughness | 262 | 900 | 104 | 20 | 7.64 | 140.0 | 0.893 | (6.051, 9.233) |

Upskin Vertical Line Roughness | 230 | 900 | 100 | 20 | 10.23 | 127.8 | 1.20 | (8.08, 12.37) |

Downskin Surface Roughness | 173 | 1500 | 180 | 20 | 16.08 | 32.0 | 4.07 | (7.71, 24.45) |

Downskin Horizontal Line Roughness | 170 | 900 | 180 | 20 | 10.32 | 52.5 | 4.38 | (2.51, 18.13) |

Downskin Vertical Line Roughness | 236 | 1500 | 180 | 20 | 10.64 | 43.7 | 1.56 | (6.84, 14.43) |

**Table 7.**Multi-parameter multi-response optimization results achieved using the following parameters combination: laser power = 239.5 W, scan speed = 1500 mm/s, hatch spacing = 100 µM, and layer thickness = 20 µM.

Micro-Hardness (HV) | Rel. Density (%) | Top Surface (µm) | Upskin Surface (µm) | Upskin Hor. Line (µm) | Upskin Ver. Line (µm) | Downskin Surface (µm) | Downskin Hor. Line (µm) | Downskin Ver. Line (µm) |
---|---|---|---|---|---|---|---|---|

362.9 | 99.89 | 7.76 | 18.18 | 10.44 | 11.22 | 17.57 | 10.95 | 10.75 |

**Table 8.**Comparison of fractional prediction error (%) in prediction performance of the Taguchi method, RSM, and the ANN using the testing data presented in this research.

Method | Mean Fractional Error of Prediction in Percentage (95% CI) | |||
---|---|---|---|---|

Microhardness | Relative Density | Top Surface Roughness | All | |

Taguchi | 1.68 (1.15, 2.21) | 0.41 (0.19, 0.62) | 32.59 (15.54, 49.65) | 11.56 (4.8, 18.32) |

RSM | 1.06 (0.68, 1.44) | 0.30 (0.20, 0.39) | 30.16 (16.73, 43.59) | 10.51 (4.85, 16.16) |

ANN | 1.16 (0.78, 1.54) | 0.23 (0.13, 0.32) | 10.80 (4.80, 16.80) | 4.06 (1.75, 6.38) |

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Fotovvati, B.; Balasubramanian, M.; Asadi, E.
Modeling and Optimization Approaches of Laser-Based Powder-Bed Fusion Process for Ti-6Al-4V Alloy. *Coatings* **2020**, *10*, 1104.
https://doi.org/10.3390/coatings10111104

**AMA Style**

Fotovvati B, Balasubramanian M, Asadi E.
Modeling and Optimization Approaches of Laser-Based Powder-Bed Fusion Process for Ti-6Al-4V Alloy. *Coatings*. 2020; 10(11):1104.
https://doi.org/10.3390/coatings10111104

**Chicago/Turabian Style**

Fotovvati, Behzad, Madhusudhanan Balasubramanian, and Ebrahim Asadi.
2020. "Modeling and Optimization Approaches of Laser-Based Powder-Bed Fusion Process for Ti-6Al-4V Alloy" *Coatings* 10, no. 11: 1104.
https://doi.org/10.3390/coatings10111104