# Collaborative Optimization of Density and Surface Roughness of 316L Stainless Steel in Selective Laser Melting

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Materials

#### 2.2. Experimental Equipment and Method

#### 2.3. Experimental Design

## 3. Results

#### 3.1. Main Effects of Processing Parameters

#### 3.2. Analysis of Variance

^{2}values of 96.65% and 96.54%, respectively. The corresponding prediction values R

^{2}are 80.26% and 79.77%, meaning that the models can effectively predict the RD and SR of parts.

## 4. Discussion

## 5. Conclusions

- For the main effects of single factor, the influences of different processing parameters on the RD and the SR of 316L stainless steel are similar. The effects of P and V on RD and SR of parts are highly significant, but that of S is weak.
- For interaction effects between two factors, there are some differences between the RD and the SR. All of the interaction influences containing P*V, P*S, V*S on the RD behave significantly, whereas for the SR only the V*S has a significant influence.
- Based on the RSM and the ANOVA, the mathematical relationship model between the RD/SR and processing parameters have been built, and can be used to effectively predict the processing parameters set or the target response.
- According to multi-objective optimization, an optimal processing parameters set with (P, V, S) values of (259.1 W, 900 mm/s, 86.7 μm) has been obtained. A resultant high RD of 98.7% and excellent SR of 8.04 μm can be achieved simultaneously using these values, which can further improve fatigue properties of SLMed 316L stainless steel products.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Surface morphologies of parts with different P values of (

**a**) 150 W, (

**b**) 225 W and (

**c**) 300 W, and different V values of (

**d**) 700 mm/s, (

**e**) 1000 mm/s and (

**f**) 1300 mm/s, and different S values of (

**g**) 60 μm, (

**h**) 90 μm and (

**i**) 120 μm.

**Figure 6.**Contour plots of (

**a**) SR and (

**b**) RD at hold values of P (259.1 W), V (900 mm/s), and S (86.7 μm), respectively.

Property | Value |
---|---|

Machine | FS271M |

Platform Dimension (L × W × H) | 275 mm × 275 mm × 320 mm |

Laser Type | Fiber laser |

Laser Diameter | 70~200 μm |

Maximum Laser Power | 500 W |

Maximum Scan Speed | 15.2 m/s |

Layer Thickness | 0.02~0.1 mm |

Volume Forming Rate | 20 cm^{3}/h |

**Table 2.**Different levels and coded values of processing parameters in the RSM (response surface method).

Input Factors (Coded Values) | The Levels of Input Factors | ||||
---|---|---|---|---|---|

−1.682 | −1 | 0 | 1 | 1.682 | |

Laser Power (W) | 150 | 180.4 | 225 | 269.6 | 300 |

Scanning Speed (mm/s) | 700 | 821.6 | 1000 | 1178.4 | 1300 |

Hatch Spacing (μm) | 60 | 72.2 | 80 | 107.8 | 120 |

**Table 3.**Experimental design matrix and measured results of selective laser melted (SLMed) 316L stainless steel parts.

Standard Sequence | The Processing Parameters | Measured Value | Calculated Value | Measured Value | ||
---|---|---|---|---|---|---|

P (w) | V (mm/s) | S (μm) | Density (g/cm^{3}) | RD (%) | SR (μm) | |

1 | 180.4 | 821.6 | 72.2 | 7.845 | 98.31 | 11.57 |

2 | 269.6 | 821.6 | 72.2 | 7.870 | 98.62 | 10.38 |

3 | 180.4 | 1178.4 | 72.2 | 7.840 | 98.25 | 10.90 |

4 | 269.6 | 1178.4 | 72.2 | 7.871 | 98.63 | 10.35 |

5 | 180.4 | 821.6 | 107.8 | 7.869 | 98.61 | 10.25 |

6 | 269.6 | 821.6 | 107.8 | 7.863 | 98.53 | 8.47 |

7 | 180.4 | 1178.4 | 107.8 | 7.840 | 98.25 | 12.18 |

8 | 269.6 | 1178.4 | 107.8 | 7.851 | 98.38 | 10.73 |

9 | 150.0 | 1000.0 | 90.0 | 7.850 | 98.37 | 10.62 |

10 | 300.0 | 1000.0 | 90.0 | 7.877 | 98.71 | 8.35 |

11 | 225.0 | 700.0 | 90.0 | 7.879 | 98.73 | 8.11 |

12 | 225.0 | 1300.0 | 90.0 | 7.850 | 98.37 | 10.26 |

13 | 225.0 | 1000.0 | 60.0 | 7.855 | 98.43 | 11.73 |

14 | 225.0 | 1000.0 | 120.0 | 7.847 | 98.33 | 10.94 |

15 | 225.0 | 1000.0 | 90.0 | 7.872 | 98.65 | 8.73 |

16 | 225.0 | 1000.0 | 90.0 | 7.871 | 98.63 | 8.41 |

17 | 225.0 | 1000.0 | 90.0 | 7.870 | 98.62 | 8.06 |

18 | 225.0 | 1000.0 | 90.0 | 7.875 | 98.68 | 8.35 |

19 | 225.0 | 1000.0 | 90.0 | 7.877 | 98.71 | 8.04 |

20 | 225.0 | 1000.0 | 90.0 | 7.874 | 98.67 | 8.06 |

Source | DOF | Sum of Squares | Mean Square | The F-Value | P-Values | |||||
---|---|---|---|---|---|---|---|---|---|---|

RD | SR | RD | SR | RD | SR | RD | SR | |||

Model | 9 | 0.513907 | 37.2364 | 0.057101 | 4.1374 | 31.42 | 31.07 | 0.000 | 0.000 | |

Linear | 3 | 0.228636 | 9.9670 | 0.076212 | 3.3223 | 41.94 | 24.95 | 0.000 | 0.000 | |

P | 1 | 0.126006 | 5.6545 | 0.126006 | 5.6545 | 69.34 | 42.47 | 0.000 | 0.000 | |

V | 1 | 0.099457 | 3.6973 | 0.099457 | 3.6973 | 54.73 | 27.77 | 0.000 | 0.000 | |

S | 1 | 0.003173 | 0.6152 | 0.003173 | 0.6152 | 1.75 | 4.62 | 0.216 | 0.057 | |

Square | 3 | 0.197821 | 23.8852 | 0.06594 | 7.9617 | 36.28 | 59.80 | 0.000 | 0.000 | |

P^{2} | 1 | 0.034911 | 4.0903 | 0.034911 | 4.0903 | 19.21 | 30.72 | 0.001 | 0.000 | |

V^{2} | 1 | 0.030076 | 2.6237 | 0.030076 | 2.6237 | 16.55 | 19.71 | 0.002 | 0.001 | |

S^{2} | 1 | 0.161276 | 20.2991 | 0.161276 | 20.2991 | 88.74 | 152.45 | 0.000 | 0.000 | |

Two-Factor Interaction | 3 | 0.08745 | 3.3841 | 0.02915 | 1.1280 | 16.04 | 8.47 | 0.000 | 0.004 | |

P*V | 1 | 0.0098 | 0.1176 | 0.0098 | 0.1176 | 5.39 | 0.88 | 0.043 | 0.369 | |

P*S | 1 | 0.0512 | 0.2775 | 0.0512 | 0.2775 | 28.17 | 2.08 | 0.000 | 0.179 | |

V*S | 1 | 0.02645 | 2.9890 | 0.02645 | 2.9890 | 14.55 | 22.45 | 0.003 | 0.001 | |

Error | 10 | 0.018173 | 1.3315 | 0.001817 | 0.1331 | |||||

Lack of Fit | 5 | 0.012573 | 0.9529 | 0.002515 | 0.1906 | 2.25 | 2.52 | 0.198 | 0.167 | |

Pure Error | 5 | 0.0056 | 0.3785 | 0.00112 | 0.0757 | |||||

Total | 19 | 0.53208 | 38.5679 | |||||||

Summary of the Model | ||||||||||

Standard Deviation | Determination Factor R^{2} | R^{2} (Calibration) | R^{2} (Prediction) | |||||||

RD | SR | RD | SR | RD | SR | RD | SR | |||

0.0426299 | 0.364896 | 96.58% | 96.55% | 93.51% | 93.44% | 79.84% | 79.87% |

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**MDPI and ACS Style**

Deng, Y.; Mao, Z.; Yang, N.; Niu, X.; Lu, X.
Collaborative Optimization of Density and Surface Roughness of 316L Stainless Steel in Selective Laser Melting. *Materials* **2020**, *13*, 1601.
https://doi.org/10.3390/ma13071601

**AMA Style**

Deng Y, Mao Z, Yang N, Niu X, Lu X.
Collaborative Optimization of Density and Surface Roughness of 316L Stainless Steel in Selective Laser Melting. *Materials*. 2020; 13(7):1601.
https://doi.org/10.3390/ma13071601

**Chicago/Turabian Style**

Deng, Yong, Zhongfa Mao, Nan Yang, Xiaodong Niu, and Xiangdong Lu.
2020. "Collaborative Optimization of Density and Surface Roughness of 316L Stainless Steel in Selective Laser Melting" *Materials* 13, no. 7: 1601.
https://doi.org/10.3390/ma13071601