# Structural Optimization of Combine Harvester Plate–Shell Undergoing Multi-Source Excitation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiment Object

^{3}, and Young’s modulus is 2.1 × ${10}^{11}$ MPa, and the Poisson’s ratio is 0.3. The structure shape is shown in Figure 3 and Figure 4.

#### 2.2. Experimenting Equipment

#### 2.3. Test Bench

#### 2.4. Optimization Method Based on the Surrogate Model

#### 2.5. Scheme Test Design

- (1)
- Effective space-filling ability. Latin Hypercube Design Number of Trials = Number of Levels Factors + 1. For example, a two-factor 9-level study requires 81 (=9 × 9) points for the full factor, while the Latin hypercube design only needs to study 9 points.
- (2)
- Fit the nonlinear response. Compared with the orthogonal experiment, the Latin hypercube design can study more combinations with the same number of points. For example, using 9 sample points for a two-factor experiment, an orthogonal experiment can only study 3 levels of each factor, so it can only fit a relationship of no more than second order; Latin hypercube design can study 9 levels of each factor, thus capable of fitting second-order or more nonlinear relationships.

#### 2.6. Approximate Model

#### 2.7. Optimization Algorithm

- (1)
- Gene coding

- (2)
- Fitness function

- (3)
- Genetic manipulation

- (3.1)
- Select operation

- (3.2)
- Crossover operation

- (3.3)
- Mutation operation

- Initialize the group;
- Calculate the fitness value of each individual in the group;
- Select individuals who will enter the next generation according to a certain rule determined by the individual fitness value;
- Carry out crossover operations according to probability;
- Perform mutation operation according to probability;
- If a certain stop condition is not met, go to step (2); otherwise, go to (7);
- Output the chromosome with the best fitness value in the population as the satisfactory or optimal solution of the problem.

## 3. Results and Discussion

#### 3.1. Parameters of Enhanced Reinforcement

#### 3.2. Hole Variation Parameters

#### 3.3. Change of Parameter of Edge-Stiffened Plate

#### 3.4. Results of Optimization

#### 3.5. Test Verification

## 4. Conclusions

- (1)
- In the multi-source excitation vibration environment, the structural factors that affect the forced vibration of the combine harvester plate and shell structure include the width, thickness, and position of the stiffened plate; the size of the hole, and the width of the edge stiffener. The closer the stiffened plate is to the excitation point, the better the restraint effect on vibration. By increasing the thickness of the stiffened plate, the multi-point excitation vibration response of the four-side clamped plate can be effectively controlled. By increasing the width of the stiffened plate, the vibration response of the multi-point excitation of the simply supported plate on four sides can be effectively controlled. The larger the hole in the plate, the larger its forced vibration response. By reducing the width of the stiffened plate, the response of the four-side clamped plate to the multi-point excitation forced vibration can be suppressed.
- (2)
- The effective optimization design of the combine harvester shell structure can be realized by using the Latin hypercube as the experimental design method, the Kriging model as the surrogate model, and the genetic algorithm as the optimization algorithm. Through the scheme of optimization, the width of the edge is optimized from 8 mm to 10 mm, the width of the stiffener is optimized from 25 mm to 7 mm, and the thickness of the foundation plate is optimized from 1.2 mm to 1.4 mm. The first-order natural frequency of the plate is improved, and the mass remains unchanged, avoiding the resonance range of the main excitation of the machine; at the same time, its dynamic response under the action of the multi-point harmonic force is also greatly reduced to 62.4%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Response diagram of stiffened plate with variable distance. (

**a**) Located at 100 mm. (

**b**) Located at 150 mm. (

**c**) Located at 200 mm.

**Figure 9.**Response diagram of stiffened plate with variable thickness. (

**a**) 2 mm thickness. (

**b**) 3 mm thickness. (

**c**) 4 mm thickness. (

**d**) 5 mm thickness.

**Figure 10.**Response diagram of variable width stiffened plate. (

**a**) 50 mm wide. (

**b**) 40 mm wide. (

**c**) 30 mm wide. (

**d**) 20 mm wide.

**Figure 11.**Response diagram of plate with variable hole position. (

**a**) Located at 50 mm. (

**b**) Located at 100 mm. (

**c**) Located at 150 mm.

**Figure 12.**Response diagram of variable aperture plate. (

**a**) 20 mm diameter. (

**b**) 40 mm diameter. (

**c**) 60 mm diameter.

**Figure 13.**Response diagram of plate with variable edge stiffener width. (

**a**) 50 mm wide. (

**b**) 40 mm wide. (

**c**) 30 mm wide. (

**d**) 0 mm wide.

**Figure 14.**Response diagram of plate with variable edge stiffening thickness. (

**a**) 2 mm thickness. (

**b**) 3 mm thickness. (

**c**) 4 mm thickness. (

**d**) 5 mm thickness.

Number | Equipment | Model | Manufacturer | Main Parameter |
---|---|---|---|---|

1 | Exciting force hammer | LC02 | PCB | Gain: 0.255 mV/pC range: 5000 N |

2 | Force sensor | 3A102 | PCB | Sensitivity: 4.512 pC/N |

3 | Piezoelectric acceleration sensor | 1A312E | PCB | Range: ±500 g |

4 | Signal acquisition instrument | DH5902 | DongHua Test | Number of channels: 36 |

Influencing Factors | Initial Value/mm | Least Value/mm | Crest Value/mm |
---|---|---|---|

Width of Edge | 8 | 2 | 12 |

Width of Stiffener | 25 | 5 | 30 |

Thickness of foundation plate | 1.2 | 0.8 | 2 |

Name | P3—Width of Edge (mm) | P4—Width of Stiffener (mm) | P20—Surface Body Thickness (mm) | P12—Geometry Mass (kg) | P11—Total Deformation 2 Reported Frequency (Hz) | P19—Total Deformation Maximum (mm) |
---|---|---|---|---|---|---|

1 | 4.95 | 25.37 | 1.10 | 8.16 | 76.20 | 1.63 |

2 | 7.35 | 14.12 | 0.85 | 6.01 | 59.24 | 5.54 |

… | … | … | … | … | … | … |

99 | 8.85 | 9.12 | 1.44 | 8.92 | 96.35 | 0.95 |

100 | 7.25 | 19.37 | 1.37 | 9.24 | 93.30 | 0.15 |

Parameter | Candidate Point 1 | Candidate Point 2 | Candidate Point 3 |
---|---|---|---|

Width of Edge/mm | 10.837 | 10.436 | 10.215 |

Width of Stiffener/mm | 7.0781 | 12.124 | 7.0952 |

Thickness of foundation plate/mm | 1.4139 | 1.3558 | 1.4117 |

total mass/kg | 8.6894 | 8.7348 | 8.657 |

First natural frequency/Hz | 94.164 | 91.981 | 93.818 |

Dynamic response/mm | 0.30028 | 0.23176 | 0.4407 |

Parameter | Initial Value | Optimized Value | Correction Amount |
---|---|---|---|

Width of Edge/mm | 8 | 10 | +25% |

Width of Stiffener/mm | 25 | 7 | −72% |

Thickness of foundation plate/mm | 1.2 | 1.4 | +16.7 |

total mass/kg | 8.7596 | 8.657 | −1.2% |

First natural frequency/Hz | 85.591 | 93.818 | +9.6% |

Dynamic response/mm | 1.1735 | 0.4407 | −62.4% |

Modal Order | Fundamental Frequency of Original Board | Fundamental Frequency of Optimized Plate | Correction |
---|---|---|---|

1 | 88.08 | 100.95 | +14.6% |

2 | 114.48 | 140.29 | +22.5% |

3 | 140.21 | 157.62 | +12.4% |

4 | 163.54 | 178.03 | +8.9% |

5 | 171.52 | 201.27 | +17.3% |

6 | 210.88 | 213.61 | +1.3% |

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**MDPI and ACS Style**

Gu, X.; Zhang, B.; Tang, Z.; Zhang, H.; Wang, H.
Structural Optimization of Combine Harvester Plate–Shell Undergoing Multi-Source Excitation. *Appl. Sci.* **2022**, *12*, 5930.
https://doi.org/10.3390/app12125930

**AMA Style**

Gu X, Zhang B, Tang Z, Zhang H, Wang H.
Structural Optimization of Combine Harvester Plate–Shell Undergoing Multi-Source Excitation. *Applied Sciences*. 2022; 12(12):5930.
https://doi.org/10.3390/app12125930

**Chicago/Turabian Style**

Gu, Xinyang, Ben Zhang, Zhong Tang, Hao Zhang, and Haoyang Wang.
2022. "Structural Optimization of Combine Harvester Plate–Shell Undergoing Multi-Source Excitation" *Applied Sciences* 12, no. 12: 5930.
https://doi.org/10.3390/app12125930