# Optimization and Prediction of Mechanical Characteristics on Vacuum Sintered Ti-6Al-4V-SiCp Composites Using Taguchi’s Design of Experiments, Response Surface Methodology and Random Forest Regression

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{p}composites.

## 1. Introduction

## 2. Methodology

## 3. Design of Experiments

#### 3.1. Taguchi’s Design of Experiments

_{27}orthogonal array is employed to identify the optimal vacuum sintering process parameters. The levels and factors used for the vacuum sintering (TDOE) are shown in Table 5.

#### 3.2. Response Surface Methodology

#### 3.3. Random Forest Regression

_{27}TDOE for the hardness, porosity, and surface roughness of Ti-6Al-4V reinforced with 15 Wt. % SiC used as the input parameters were trained on the random forest model. Table 7 shows the algorithm used for random forest model in this paper.

- Step 1: The loading of the data sets.
- Step 2: The selection of the preprocessor.
- Step 3: Classifying the data sets for training and testing.
- Step 4: Training the model using the datasets.
- Step 5: Loading the test data set for a comparison.
- Step 6: Evaluating the prediction performance based on the accuracy and precision.

^{2}) as shown in the below equation [33].

_{ref}were reference values in the dataset, and Y

_{pred}were the predicted values of the models.

## 4. Results and Discussions

#### 4.1. Hardness

_{0.05,14,14}= 13.63), and hence the developed second order response function is quite adequate.

^{2}− 14.474B

^{2}+ 6.531C

^{2}− 0.053D

^{2}+ 1.016AB + 4.578AC − 0.633AD + 0.605BC + 2.033BD + 0.580CD

#### 4.2. Porosity

^{2}+ 0.0732B

^{2}+ 0.8017C

^{2}+ 0.1782D

^{2}+ 0.1597AB − 0.0465AC − 0.0677AD + 0.2167BC − 0.0118BD + 0.2807CD

_{0.05,14,14}= 10.00), and hence the developed second order response function is quite adequate.

#### 4.3. Surface Roughness

_{0.05,14,14}= 3.53), and hence the developed second order response function is quite adequate. The second order response surface representing the surface roughness (%) can be expressed as a function of the processing parameters such as the aging temperature (°C), aging time (h), heating rate (°C/min), and cooling rate (°C/min), as shown in Equation (7).

^{2}+ 0.03279D

^{2}− 0.17588AB − 0.14200AC + 0.14562AD + 0.02013BC − 0.13350BD + 0.09413CD

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Age temperature v/s hardness (BHN) at heating rate of 15 °C/min and cooling rate of 5 °C/min (constant).

**Figure 6.**Age Temperature v/s porosity (%). At heating rate of 25 °C/min and cooling rate of 5 °C/min (constant).

**Figure 8.**Porosity at different aging temperatures (

**a**) 1050 °C, (

**b**) 1150 °C, (

**c**) and 1250 °C ataging time (4 h), heating rate (25 °C/min), cooling rate (5 °C/min); constant.

**Figure 11.**Age temperature v/s surface roughness (µm). At heating rate of 25 °C/min and cooling rate of 1 °C/min (constant).

**Figure 13.**Surface roughness at different aging temperatures: (

**a**) 1050 °C, (

**b**) 1150 °C, (

**c**) 1250 °C; at aging time (4 h), heating rate (25 °C/min), and cooling rate (1 °C/min); constant.

Element | Al | V | Fe | O | C | N | Y | H | Ti |
---|---|---|---|---|---|---|---|---|---|

Wt (%) | 6.1 | 4 | 0.16 | 0.11 | 0.02 | 0.01 | 0.001 | 0.001 | Bal |

Element | C | Fe_{2}O_{3} | Si | Al_{2}O_{3} | CaO | SiO_{2} | P | S | SiC |
---|---|---|---|---|---|---|---|---|---|

Wt (%) | 1.17 | 0.66 | 1.43 | 0.25 | 0.14 | 0.8 | 0.32 | 0.04 | Bal |

Properties | Values (Units) |
---|---|

Density | 4.43 g/cm^{3} |

Melting point | 1604–1660 °C |

Beta transitional temperature | 980 °C |

Tensile strength, ultimate | 1170 Mpa |

Tensile strength, yield | 1100 Mpa |

Compressive strength | 1070 Mpa |

Modulus of elasticity | 114 Gpa |

Brinell hardness | 379 BHN |

Elongation at break | 10% |

Properties | Values (Units) |
---|---|

Density | 3.1 g/cm^{3} |

Melting point | 2730 °C |

Beta transitional temperature | 2000 °C |

Tensile strength, ultimate | 390 Mpa |

Compressive strength | 2000 Mpa |

Modulus of elasticity | 410 Gpa |

Vicker’shardness | 2720 Hv |

Elongation at break | 0% |

Control Factors | Levels | ||
---|---|---|---|

1 | 2 | 3 | |

Aging temperature (°C) | 1050 | 1150 | 1250 |

Aging time (h) | 2 | 3 | 4 |

Heating rate (°C/min) | 5 | 15 | 25 |

Cooling rate (°C/min) | 1 | 3 | 5 |

Control Factors | Levels | |
---|---|---|

1 | 3 | |

Aging temperature (°C) | 1050 | 1250 |

Aging time (h) | 2 | 4 |

Heating rate (°C/min) | 5 | 25 |

Cooling rate (°C/min) | 1 | 5 |

Algorithm: Random forest modeling. |

Input: Ti-6Al-4V- SiCp |

Output: Hardness, porosity, and surface roughness |

Source | DF | Seq SS | Adj SS | AdjMS | F | P | P% |
---|---|---|---|---|---|---|---|

A | 2 | 5.0606 | 5.0606 | 2.5303 | 124.7 | 0.000 | 0.0 |

B | 2 | 0.7590 | 0.7590 | 0.3795 | 18.72 | 0.003 | 0.15 |

C | 2 | 0.1894 | 0.1894 | 0.0947 | 4.67 | 0.060 | 3.15 |

D | 2 | 1.0789 | 1.0789 | 0.5399 | 26.63 | 0.001 | 0.05 |

A × D | 4 | 0.0191 | 0.0191 | 0.0047 | 0.24 | 0.908 | 47.8 |

B × D | 4 | 0.0161 | 0.0161 | 0.0154 | 0.76 | 0.586 | 0.31 |

C × D | 4 | 0.0165 | 0.0165 | 0.0041 | 0.20 | 0.927 | 48.54 |

Residual Error | 6 | 0.1216 | 0.1216 | 0.0202 | |||

Total | 26 | 7.3082 | 100 |

Source | DF | Seq SS | Adj SS | Adj MS | F | P |
---|---|---|---|---|---|---|

Regression | 14 | 10,841.1 | 10,841.12 | 774.37 | 13.63 | 0.000 |

Residual error | 14 | 795.5 | 795.53 | 56.82 | ||

Total | 29 | 11,636.7 |

Source | DF | Seq SS | Adj SS | Adj MS | F | P | P% |
---|---|---|---|---|---|---|---|

A | 2 | 8.4084 | 8.4084 | 4.2042 | 168.59 | 0.000 | 0.00 |

B | 2 | 6.2052 | 6.2052 | 3.1026 | 124.41 | 0.000 | 0.00 |

C | 2 | 0.7338 | 0.7338 | 0.3668 | 14.71 | 0.005 | 0.21 |

D | 2 | 2.0230 | 2.0230 | 1.0114 | 40.56 | 0.000 | 0.00 |

A × D | 4 | 0.0403 | 0.0403 | 0.0100 | 0.40 | 0.800 | 34.72 |

B × D | 4 | 0.0876 | 0.0876 | 0.0219 | 0.88 | 0.529 | 22.96 |

C × D | 4 | 0.0121 | 0.0121 | 0.0030 | 0.12 | 0.970 | 42.1 |

Residual error | 6 | 0.1496 | 0.1496 | 0.0249 | |||

Total | 26 | 17.660 |

Source | DF | Seq SS | Adj SS | Adj MS | F | P |
---|---|---|---|---|---|---|

Regression | 14 | 38.0486 | 38.0486 | 2.7178 | 10.00 | 0.000 |

Residual error | 14 | 3.8064 | 3.8064 | 0.2719 | ||

Total | 29 | 61.4427 |

Source | DF | Seq SS | Adj SS | Adj MS | F | P | P% |
---|---|---|---|---|---|---|---|

A | 2 | 1.8327 | 1.8327 | 0.9163 | 10.10 | 0.012 | 0.35 |

B | 2 | 7.4742 | 7.4742 | 3.7371 | 41.21 | 0.000 | 0.00 |

C | 2 | 0.4671 | 0.4671 | 0.2335 | 2.57 | 0.156 | 4.63 |

D | 2 | 0.3761 | 0.3761 | 0.1880 | 2.07 | 0.207 | 6.14 |

A × D | 4 | 0.0117 | 0.0117 | 0.0029 | 0.03 | 0.997 | 29.59 |

B × D | 4 | 0.0066 | 0.0066 | 0.0016 | 0.02 | 0.999 | 29.65 |

C × D | 4 | 0.0093 | 0.0093 | 0.0023 | 0.03 | 0.998 | 29.62 |

Residual error | 6 | 0.5442 | 0.5442 | 0.0906 | |||

Total | 26 | 10.7218 | 3.369 | 100 |

Source | DF | Seq SS | Adj SS | AdjMS | F | P |
---|---|---|---|---|---|---|

Regression | 14 | 10.8982 | 10.8982 | 0.7784 | 3.53 | 0.012 |

Residual error | 14 | 3.0889 | 3.0889 | 0.2206 | ||

Total | 29 | 23.9554 |

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**MDPI and ACS Style**

Hegde, A.L.; Shetty, R.; Chiniwar, D.S.; Naik, N.; Nayak, M.
Optimization and Prediction of Mechanical Characteristics on Vacuum Sintered Ti-6Al-4V-SiCp Composites Using Taguchi’s Design of Experiments, Response Surface Methodology and Random Forest Regression. *J. Compos. Sci.* **2022**, *6*, 339.
https://doi.org/10.3390/jcs6110339

**AMA Style**

Hegde AL, Shetty R, Chiniwar DS, Naik N, Nayak M.
Optimization and Prediction of Mechanical Characteristics on Vacuum Sintered Ti-6Al-4V-SiCp Composites Using Taguchi’s Design of Experiments, Response Surface Methodology and Random Forest Regression. *Journal of Composites Science*. 2022; 6(11):339.
https://doi.org/10.3390/jcs6110339

**Chicago/Turabian Style**

Hegde, Adithya Lokesh, Raviraj Shetty, Dundesh S Chiniwar, Nithesh Naik, and Madhukara Nayak.
2022. "Optimization and Prediction of Mechanical Characteristics on Vacuum Sintered Ti-6Al-4V-SiCp Composites Using Taguchi’s Design of Experiments, Response Surface Methodology and Random Forest Regression" *Journal of Composites Science* 6, no. 11: 339.
https://doi.org/10.3390/jcs6110339