# Calibration of Collision Recovery Coefficient of Corn Seeds Based on High-Speed Photography and Sound Waveform Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

^{−1}.

## 3. Results and Discussion

#### 3.1. Determination of Intrinsic Parameters of Corn Seeds

#### 3.1.1. Density and Moisture Content of Corn Seeds

^{−3}, measured via the drainage method. The moisture content is measured according to the material moisture measurement method specified in the national standard GB/T3543.6. One hundred grams of corn seeds are randomly selected and dried in a constant temperature drying oven. The weight of the corn seeds after drying is measured, and the moisture content of the corn seeds is calculated by Formula (1):

#### 3.1.2. Determination of Poisson’s Ratio and Shear Modulus

^{8}Pa.

#### 3.1.3. Determination of Characteristic Dimensions of Corn Seeds

_{b3}and W

_{b2}of flat corn seeds is 0.553, and the ratio between W

_{Z3}and W

_{Z2}of quasi-conical corn seeds is 0.485. This study takes 0.5 as the standard value. The corn seed is flat when the ratio between the width of the bottom end of the corn seed and the width of the middle position is greater than or equal to 0.5. Otherwise, it is quasi-conical. According to the above conclusions, the corn seeds were classified again, and the proportion of each type of corn seed was counted. The proportion of flat, quasi-conical, and quasi-cylindrical corn seeds was 77.9%, 15.4%, and 6.7%, respectively. The modification results of characteristic dimensions of corn seeds are shown in Table 2.

#### 3.2. Determination of Static and Rolling Friction Coefficient of Corn Seeds

#### 3.2.1. Static Friction Coefficient

#### 3.2.2. Rolling Friction Coefficient

#### 3.3. Determination of Collision Recovery Coefficient of Corn Seeds

#### 3.3.1. Multi-Point Collision of Corn Seeds

#### 3.3.2. Test Principle of Collision Recovery Coefficient

#### 3.4. Validation Test

#### 3.4.1. Parameter Selection of Simulation Test

#### 3.4.2. Plane Collision Test

#### 3.4.3. Repose Angle Test

#### 3.5. Discussion

- (1)
- The multi-point collision of corn seeds will reduce the rebound height of corn seeds, but the rebound height of corn seeds is affected by various factors, such as the collision angle between corn seeds and the falling posture of corn seeds. Therefore, the rebound height of corn seeds cannot be used as the basis for judging the multi-point collision between corn seeds.
- (2)
- After the collision between corn seeds, the more turns the corn seeds spin in the air, the lower the height of the corn seeds rebound.
- (3)
- When using the lifting method to conduct the repose angle test of corn seeds, the high-speed camera is used to shoot the test process. At the beginning of the experiment, when the cylinder was lifted, the corn seeds were dispersed in all directions after losing the barrier of the cylinder. Because no other object was around to block the corn seeds, they directly collided with the bottom surface to a small degree (Figure 19a). As the experiment continued, the corn seeds piled up on the bottom surface, and the seeds inside the cylinder came into contact with the fallen seeds. When the cylinder is lifted, the corn seeds in the original cylinder will mainly slide and roll due to the obstruction of the seeds below (Figure 19b).

## 4. Conclusions

- (1)
- According to the shape of the surfaces of corn seeds, they can be divided into three categories: flat, quasi-conical, and quasi-cylindrical. The number of flat, quasi-conical, and quasi-cylindrical corn seeds accounted for 77.9%, 15.4%, and 6.7%, respectively.
- (2)
- The sound waveform’s peak value after the corn seeds’ single-point collision is positive and remains stable in a specific time interval. The peak value of the sound waveform after the multi-point collision of corn seeds is zero and maintains a stable value within a specific time interval.
- (3)
- Through physical tests, the corn–corn rolling friction coefficient and corn–PMMA rolling friction coefficient were 0.0784 and 0.0934, respectively. The corn–corn static friction coefficient and corn–PMMA static friction coefficient were 0.32 and 0.445, respectively. The corn–corn collision recovery and corn–PMMA collision recovery coefficients were 0.28 and 0.62, respectively.
- (4)
- The measurements are verified by plane collision and repose angle tests. The relative errors between the simulation test and physical test of the two verification methods are less than 5%, which proves that the technique combining high-speed photography and sound waveform is reliable.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Impact locations of corn seeds: (

**a**) impact the ventral part of the corn seed; (

**b**) impact the side of the corn seed; (

**c**) impact the top surface of the corn seed.

**Figure 4.**Characteristic dimensions definition diagram of corn seed: (

**a**) flat; (

**b**) quasi-conical; (

**c**) quasi-cylindrical.

**Figure 7.**Rolling friction coefficient measurement method: (

**a**) Principle diagram of rolling friction coefficient test; (

**b**) The motion tracking of quasi-cylindrical corn seeds: Under the influence of the outer surface, flat and quasi-conical corn seeds display infrequent rolling. In contrast, quasi-cylindrical corn seeds are more prone to rolling. Therefore, experiments were conducted using quasi-cylindrical corn seeds. The X coordinate and Y coordinate of the corn seed are the cosine value and the sine value of the scale value of the position of the corn seed.

**Figure 10.**Single-point collision of corn seeds: (

**a**) 1.232 s; (

**b**) 1.233 s; (

**c**) 1.234 s; (

**d**) 1.235 s; (

**e**) 1.380 s.

**Figure 11.**Multi-point collision of corn seeds: (

**a**) 1.379 s; (

**b**) 1.380 s; (

**c**) 1.381 s; (

**d**) 1.382 s; (

**e**) 1.432 s.

**Figure 12.**The sound waveform of the single-point collision: (

**a**) single-point collision; (

**b**) the rebound of corn seeds after the collision; (

**c**) sound waveforms generated by the collision between corn seeds.

**Figure 13.**The sound waveform of the multi-point collision: (

**a**) First collision; (

**b**) Second collision; (

**c**) The rebound of corn seeds after the second collision; (

**d**) Sound waveforms generated by collisions between corn seeds.

**Figure 16.**Simulation model of corn seeds: (

**a**) flat corn seeds; (

**b**) quasi-conical corn seeds; (

**c**) quasi-cylindrical corn seeds.

**Figure 17.**Plane collision test: (

**a**) physical test of flat corn seed; (

**b**) physical test of quasi-conical corn seed; (

**c**) physical test of quasi-cylindrical corn seed; (

**d**) simulation test of flat corn seed; (

**e**) simulation test of quasi-conical corn seed; (

**f**) simulation test of quasi-cylindrical corn seed.

**Figure 19.**Movement of corn seeds in repose angle test: (

**a**) Collision: The movement of corn seed in the red circle is shown on the left side of the picture; (

**b**) Slide: The movement of corn seed in the red circle is shown on the left side of the picture.

Shape | Characteristic Dimensions | Mean Value (mm) |
---|---|---|

Flat | W_{b1} | 8.21 |

W_{b2} | 7.77 | |

W_{b3} | 4.30 | |

H_{b0} | 12.77 | |

H_{b1} | 11.56 | |

H_{b2} | 11.50 | |

T_{b1} | 4.17 | |

T_{b2} | 4.29 | |

T_{b3} | 3.76 | |

Quasi-conical | W_{Z1} | 7.80 |

W_{Z2} | 7.21 | |

W_{Z3} | 3.50 | |

H_{Z} | 5.07 | |

T_{Z1} | 4.83 | |

T_{Z2} | 3.10 | |

T_{Z3} | 12.23 | |

Quasi-cylindrical | W_{Y1} | 7.05 |

W_{Y2} | 6.54 | |

H_{Y} | 4.08 | |

T_{Y1} | 3.62 | |

T_{Y2} | 10.28 |

Shape | Characteristic Dimensions | Mean Value (mm) |
---|---|---|

Flat | W_{b1} | 8.14 |

W_{b2} | 7.83 | |

W_{b3} | 4.37 | |

H_{b0} | 12.71 | |

H_{b1} | 11.57 | |

H_{b2} | 11.45 | |

T_{b1} | 4.14 | |

T_{b2} | 4.29 | |

T_{b3} | 3.78 | |

Quasi-conical | W_{Z1} | 7.76 |

W_{Z2} | 7.20 | |

W_{Z3} | 3.32 | |

H_{Z} | 5.02 | |

T_{Z1} | 4.80 | |

T_{Z2} | 3.04 | |

T_{Z3} | 12.18 | |

Quasi-cylindrical | W_{Y1} | 7.05 |

W_{Y2} | 6.54 | |

H_{Y} | 4.08 | |

T_{Y1} | 3.62 | |

T_{Y2} | 10.28 |

Angle (°) | $\mathbf{cot}{\mathit{\theta}}_{1}$ | ${\mathit{C}}_{\mathit{f}1}$ |
---|---|---|

20 | 2.747 | 0.273 |

22 | 2.475 | 0.251 |

25 | 2.145 | 0.257 |

27 | 1.963 | 0.181 |

30 | 1.732 | 0.241 |

32 | 1.600 | 0.165 |

35 | 1.428 | 0.151 |

37 | 1.327 | 0.131 |

40 | 1.192 | 0.135 |

42 | 1.111 | 0.137 |

Angle (°) | $\mathbf{cot}{\mathit{\theta}}_{2}$ | ${\mathit{C}}_{\mathit{f}2}$ |
---|---|---|

20 | 2.747 | 0.681 |

22 | 2.475 | 0.647 |

25 | 2.145 | 0.622 |

27 | 1.963 | 0.645 |

30 | 1.732 | 0.633 |

32 | 1.600 | 0.629 |

35 | 1.428 | 0.612 |

37 | 1.327 | 0.593 |

40 | 1.192 | 0.553 |

42 | 1.111 | 0.5 |

Parameters | Value |
---|---|

Density of corn seed/(kg·m^{−3}) | 1197 |

Poisson’s ratio of corn seed | 0.4 |

Shear modulus of corn seed/Pa | 1.36 × 10^{8} |

Normal Stiffness of corn seed/(N·m^{−3}) | 3.54 × 10^{9} |

Shear stiffness of corn seed/(N·m^{−3}) | 2.53 × 10^{9} |

Critical normal stress of corn seed/Pa | 1.1 × 10^{7} |

Critical shear stress of corn seed/Pa | 4.1 × 10^{6} |

Bonded disk radius/mm | 1 |

Density of PMMA/(kg·m^{−3}) | 1200 |

Poisson’s ratio of PMMA | 0.35 |

Shear modulus of PMMA/Pa | 1.30 × 10^{9} |

Corn–corn rolling friction coefficient | 0.0784 |

Corn–PMMA rolling friction coefficient | 0.0934 |

Corn–corn collision recovery coefficient | 0.28 |

Corn–PMMA collision recovery coefficient | 0.62 |

Corn–corn static friction coefficient | 0.32 |

Corn–PMMA static friction coefficient | 0.445 |

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## Share and Cite

**MDPI and ACS Style**

Li, X.; Zhang, W.; Xu, S.; Ma, F.; Du, Z.; Ma, Y.; Liu, J.
Calibration of Collision Recovery Coefficient of Corn Seeds Based on High-Speed Photography and Sound Waveform Analysis. *Agriculture* **2023**, *13*, 1677.
https://doi.org/10.3390/agriculture13091677

**AMA Style**

Li X, Zhang W, Xu S, Ma F, Du Z, Ma Y, Liu J.
Calibration of Collision Recovery Coefficient of Corn Seeds Based on High-Speed Photography and Sound Waveform Analysis. *Agriculture*. 2023; 13(9):1677.
https://doi.org/10.3390/agriculture13091677

**Chicago/Turabian Style**

Li, Xinping, Wantong Zhang, Shendi Xu, Fuli Ma, Zhe Du, Yidong Ma, and Jing Liu.
2023. "Calibration of Collision Recovery Coefficient of Corn Seeds Based on High-Speed Photography and Sound Waveform Analysis" *Agriculture* 13, no. 9: 1677.
https://doi.org/10.3390/agriculture13091677