# Design Optimization of Alloy Wheels Based on a Dynamic Cornering Fatigue Test Using Finite Element Analysis and Multi-Additional Sampling of Efficient Global Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Multi-Objective Efficient Global Optimization

#### 2.1. Multi-Additional Sampling

#### 2.2. Kriging Method

#### 2.3. Genetic Algorithm

## 3. Dynamic Cornering Fatigue Analysis

## 4. Materials and Methods

#### 4.1. Design of Experiment

#### 4.2. Finite Element Simulation

#### 4.3. Surrogate Model and Data Improvement

#### Surrogate Model

#### 4.4. Data Improvement

## 5. Results and Discussion

## 6. Mechanical Validation of Finite Element Simulation

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Type of alloy wheel in general industry and components. (

**a**) Disc type, (

**b**) spoke type, (

**c**) fin type, (

**d**) mesh type, and (

**e**) rim and disc type.

**Figure 14.**(

**a**) Distribution of initial sampling and additional sampling (

**b**) Pareto front of design variables related to the weight and principal stress.

**Figure 15.**(

**a**) The contour plot of the principal stress according to the design parameters (

**b**) The contour plot of weight according to the design parameters.

**Figure 17.**The comparison result of the strain between the mechanical test and FE analysis; (

**a**) strain position one, (

**b**) strain position two, (

**c**) strain position three, and (

**d**) strain position four.

Si | Fe | Mg | Ti | Sr |
---|---|---|---|---|

6.5–7.5% | <0.15% | 0.27–0.29% | 0.1–0.15% | 0.005–0.0155% |

Property | Yield Strength | Ultimate Strength | Elongation | Modulus of Elasticity |
---|---|---|---|---|

(MPa) | (MPa) | (%) | (GPa) | |

220 | 265 | 3 | 70 |

Iteration | No. | Width: w | Thickness: t | Principle | Weight |
---|---|---|---|---|---|

Sampling | (mm) | (mm) | Stress (MPa) | (kg) | |

31 | 62.59079 | 13.0003 | 212.3612 | 4.41644 | |

1 | 32 | 61.11105 | 14.43483 | 167.0227 | 4.47476 |

33 | 61.34294 | 13.85585 | 176.4588 | 4.45779 | |

34 | 61.99754 | 13.00002 | 199.0943 | 4.42878 | |

2 | 35 | 60.91956 | 14.99054 | 160.1323 | 4.49212 |

36 | 60.63268 | 16.63042 | 152.9984 | 4.52772 | |

37 | 61.23932 | 14.14289 | 173.8995 | 4.46194 | |

3 | 38 | 60.59958 | 17.19233 | 151.2951 | 4.54639 |

39 | 61.52394 | 13.653 | 182.1939 | 4.44935 | |

40 | 62.9134 | 13.0004 | 222.6176 | 4.4083 | |

4 | 41 | 61.60852 | 15.8109 | 163.6573 | 4.49525 |

42 | 61.00742 | 14.72151 | 163.2752 | 4.48355 | |

43 | 62.27858 | 13.0000 | 189.2561 | 4.4413 | |

5 | 44 | 61.78113 | 13.12851 | 191.8577 | 4.43697 |

45 | 62.83157 | 13.02221 | 217.3689 | 4.41237 | |

46 | 62.2888 | 13.00558 | 207.6239 | 4.42054 | |

6 | 47 | 60.82259 | 15.51454 | 157.7641 | 4.50077 |

48 | 61.20637 | 14.21846 | 169.126 | 4.47055 | |

49 | 60.64988 | 16.47167 | 152.9984 | 4.52772 | |

7 | 50 | 62.16986 | 13.00006 | 203.1897 | 4.42465 |

51 | 60.57336 | 17.99858 | 150.0935 | 4.56472 |

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**MDPI and ACS Style**

Ariyarit, A.; Rooppakhun, S.; Puangchaum, W.; Phiboon, T.
Design Optimization of Alloy Wheels Based on a Dynamic Cornering Fatigue Test Using Finite Element Analysis and Multi-Additional Sampling of Efficient Global Optimization. *Symmetry* **2023**, *15*, 2169.
https://doi.org/10.3390/sym15122169

**AMA Style**

Ariyarit A, Rooppakhun S, Puangchaum W, Phiboon T.
Design Optimization of Alloy Wheels Based on a Dynamic Cornering Fatigue Test Using Finite Element Analysis and Multi-Additional Sampling of Efficient Global Optimization. *Symmetry*. 2023; 15(12):2169.
https://doi.org/10.3390/sym15122169

**Chicago/Turabian Style**

Ariyarit, Atthaphon, Supakit Rooppakhun, Worawat Puangchaum, and Tharathep Phiboon.
2023. "Design Optimization of Alloy Wheels Based on a Dynamic Cornering Fatigue Test Using Finite Element Analysis and Multi-Additional Sampling of Efficient Global Optimization" *Symmetry* 15, no. 12: 2169.
https://doi.org/10.3390/sym15122169