# Measurement Method of Collision Restitution Coefficient between Corn Seed and Soil Based on the Collision Dynamics Theory of Mass Point and Fixed Surface

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis of CRC

## 3. Measurement Method of CRC between Corn Seed and Soil

#### 3.1. Analysis of Collision Process when Taking Corn Seed as Mass Point

_{i}is the mass of the ith soil particle; ${\overline{u}}_{i}$ is the velocity of the center of mass at the end of collision of the ith soil particle; ${\overline{v}}_{i}$ is the velocity of the center of mass of the ith soil particle at the beginning of collision, and the soil is stationary at the beginning of the collision, ${\overline{v}}_{i}$ = 0; ${\overline{S}}_{i}{}^{\left(e\right)}$ is the external impact impulse on the ith soil particle; ${\overline{S}}_{i}{}^{\left(i\right)}$ is the internal impact impulse on the ith soil particle.

_{1}is the impulse absorbed by soil particles; S

_{2}is the impulse of corn seed collision and separation stage; N is the quality of corn seed; V is the maximum velocity before the corn seed contacts the soil; U is the maximum velocity of corn seed separated from the soil.

#### 3.2. Analysis of Collision Process when Taking Soil Particles as Mass Point

_{1}is kinetic energy change value in compression stage; ΔE

_{2}is kinetic energy change value in the recovery stage, J; m

_{1}is the mass of the mass point, g; m

_{2}is the mass of the fixed surface, g; v

_{10}is the velocity before particle collision, m/s; v

_{20}is the velocity of the fixed surface before the collision, m/s; v

_{1t}is the velocity of the particle after the collision, m/s; v

_{2t}is the velocity of fixed surface after the collision, m/s; v

_{11}is the velocity of mass point when separation, m/s; v

_{22}is the velocity of fixed surface when separation, m/s.

_{20}, v

_{2t}, v

_{22}both are 0 and m

_{2}is much larger than m

_{1}. Accordingly:

_{1t}and the approaching velocity v

_{10}of the mass point.

#### 3.3. Measurement Method

- (1)
- The experiment was conducted in a relatively closed environment to avoid the influence of the airflow field in the experiment space on the measurement results.
- (2)
- To obtain the CRC between corn seed and soil, improve the contrast and ensure the shooting effect, a simple CRC experiment bench was built with a white background plate.
- (3)
- The white background plate was vertically placed on the desktop to obtain the actual distance of soil particle movement. The vertical distance between the high-speed camera and the soil particle movement plane in all experiments should be kept consistent.
- (4)
- Drawn a straight line parallel to the desktop on the white background plate to facilitate the experiment and subsequent high-speed camera data analysis.The main experiment equipment was the revealer 5f01 high-speed camera produced by Hefei Fuhuang Junda high tech Information Technology Co., Ltd. (Hefei, China), with a shooting frame rate of 1000 fps and an exposure time of 998 μs, using high-speed video target tracking measurement software to process image data.

- (1)
- Fix the corn seed on the tabletop of the experiment bench, and the side is close to the background plate so that the surface is relatively smooth and flat, and the large plane with uniform distribution of horny endosperm is upward as the fixing surface.
- (2)
- Open the high-speed camera control software to make the high-speed camera ready for shooting. Adjust the focus, exposure rate, white balance and other parameters of the high-speed camera according to the images collected by the control software. Make the white background plate and corn seed in the center of the video acquisition area, and ensure the best definition of the picture. Adjust the position of the lighting device to ensure that shadows do not cover the movement range of soil particles.
- (3)
- To avoid the influence of sweat and grease secreted by fingers on the properties of soil particles, during the experiment, the soil particles were clamped with tweezers, and the tweezers were loosened at the straight positions of different heights to make them fall naturally and collide with corn seed. In the cause of capturing the complete falling process, trigger the high-speed camera shooting command before releasing the tweezers.

- (1)
- Coordinate system is set at the starting point of soil particle falling;
- (2)
- Calibrate the size in the drawing, measure the scale in the drawing, and calculate the corresponding ratio between the actual size and the picture size: L
_{Actual}:L_{Figure}= k:1 is used for conversion of experiment data. If the camera position changes during the experiment, it needs to be recalibrated; - (3)
- After the calibration is completed, the soil particle is set as the tracking target, and the target tracking module is used to obtain the movement trajectory of the soil particles, the separation velocity v
_{1t}of the soil particles after the collision, and the approaching velocity v_{10}of the soil particles before the collision. The CRC is obtained from Equation (10).

## 4. Experiment Verification

#### 4.1. Measurement of CRC

^{3}, the shape was complete, and the surface was flat. To reduce the influence of corn seed’ uneven surface on CRC measurement results, the large surface with a uniform and flat distribution of horny endosperm was used as the fixed surface. During the experiment, the soil was first treated with a sieve. After natural air drying, the soil particles were taken as the mass points. The soil bulk density was 1346 kg/m

^{3,}and the particle size range was 2–3 mm. It should be noted that according to the mass point fixed surface collision kinetics theory, the CRC is independent of the weight of the mass point. However, in the actual measurement, multiple particles were bonded together due to the little cohesion between soil particles in the natural state. Soil particles with large size were formed by the bonding of several small particles with little cohesion between them. In actual measurements, dispersion occurred after collision, which was inconsistent with the particle-fixed surface collision dynamics theory. Soil particles with small size, whose motion process was affected by air resistance close to its own gravity, greatly influence the motion state, and could not be used to measure the CRC. Therefore, the diameter of soil particles should not be too large or too small.

_{10}and separation velocity v

_{1t}were analyzed. Since the surface of corn seed is not an ideal plane, the direction of soil particles and corn will have a divergent shift after the collision, resulting in the measured separation velocity being smaller than the ideal state. In this paper, the maximum SAVR in the normal direction of the contact was taken as the CRC. Sorted out the experiment data, measured the collision approaching velocity and separation velocity of soil particles, calculated the SAVR, and took the maximum value as the corn seed soil CRC = 0.607.

#### 4.2. Verification of Measurement Results

#### 4.2.1. Seed Impact Soil DESE

_{0}and separation velocity V

_{t}were saved and the SAVR ${\xi}_{1}$ was calculated automatically, the calculation equation is shown in Equation (11). Each group of experiments was repeated five times to obtain the mean value.

#### 4.2.2. Soil Bin Experiment

_{0}and separation velocity v

_{t}of the corn seed when the contact positions are a, b, c, d, and calculated the SAVR ${\xi}_{2}$, the calculation equation is shown in Equation (12).

#### 4.2.3. Comparison and Analysis of Experiment Results

- (1)
- Comparative Analysis of the Movement State of Corn Seed

_{0}, and collides with the soil. The movement state changes, causing a sudden change in velocity. After the corn seed moves to the lowest point, it starts to rebound, the elastic deformation between particles recovers, and the elastic strain energy is converted into the potential energy of particles. The velocity of corn seed begins to increase and reaches the maximum value v

_{t}when it separated from soil particles, that is, the collision separation velocity is v

_{t}.

- (2)
- Comparative Analysis of SAVR ξ

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Comparison of movement status. (

**a**–

**c**) represent three groups of comparative tests, in each group of tests the falling height and contact position of corn seeds in the DESE and the SBE are the same, to compare the movement state of seeds in the DESE and the SBE.

Number | Falling Height (mm) | Characteristic Velocity (mm/s) |
---|---|---|

1 | 400 | 2857.1 |

2 | 500 | 3130.5 |

3 | 600 | 3429.3 |

4 | 700 | 3704.1 |

Parameter | Corn | Soil | ||||||
---|---|---|---|---|---|---|---|---|

Particle Density ρ/(kg/m ^{3}) | Particle Radius r/mm | Poisson’s Ratio v | Shear Modulus G/(MPa) | Particle Density ρ/(kg/m ^{3}) | Particle Radius r/mm | Poisson’s Ratio v | Shear Modulus G/(MPa) | |

value | 1197 | 2.4~2.5 | 0.40 | 1.37 $\times $ 10^{6} | 1346 | 0.5 | 0.40 | 1 $\times $ 10^{6} |

Parameter | Corn-Corn | Soil-Soil | Soil-Corn | ||||||
---|---|---|---|---|---|---|---|---|---|

Coefficient of Static Friction μs _{1} | Coefficient of Rolling Friction μr _{1} | CRC e _{1} | Coefficient of Static Friction μs _{2} | Coefficient of Rolling Friction μr _{2} | CRC e _{2} | Coefficient of Static Friction μs _{3} | Coefficient of Rolling Friction μr _{3} | CRC e _{3} | |

value | 0.431 | 0.0782 | 0.182 | 0.2 | 0.4 | 0.3 | 0.22 | 0.727 | 0.607 |

Level | Touch Soil Position | Falling Height/(mm) |
---|---|---|

1 | a | 400 |

2 | b | 500 |

3 | c | 600 |

4 | d | 700 |

Falling Height/cm | Touch Soil Position | The SBE ξ_{2} | The DESE ξ_{1} | Relative Error/% |
---|---|---|---|---|

40 | a | 0.169 ± 0.00676 | 0.07 ± 0.00245 | 58.6 |

b | 0.172 ± 0.00516 | 0.168 ± 0.009408 | 2.3 | |

c | 0.27 ± 0.0189 | 0.294 ± 0.014994 | 8.9 | |

d | 0.15 ± 0.009 | 0.137 ± 0.007124 | 8.7 | |

50 | a | 0.226 ± 0.0113 | 0.049 ± 0.002744 | 78.3 |

b | 0.153 ± 0.006579 | 0.16 ± 0.004 | 4.6 | |

c | 0.253 ± 0.013156 | 0.261 ± 0.003915 | 3.2 | |

d | 0.137 ± 0.007535 | 0.123 ± 0.004305 | 6.1 | |

60 | a | 0.146 ± 0.00949 | 0.054 ± 0.001836 | 63 |

b | 0.142 ± 0.0071 | 0.145 ± 0.004495 | 2.1 | |

c | 0.208 ± 0.00728 | 0.206 ± 0.00206 | 2.9 | |

d | 0.116 ± 0.0029 | 0.121 ± 0.00605 | 4.3 | |

70 | a | 0.183 ± 0.008235 | 0.06 ± 0.0021 | 67.2 |

b | 0.135 ± 0.007425 | 0.145 ± 0.003625 | 7.4 | |

c | 0.175 ± 0.0042 | 0.182 ± 0.005642 | 4 | |

d | 0.134 ± 0.005762 | 0.125 ± 0.0065 | 6.7 |

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**MDPI and ACS Style**

Gao, Z.; Lu, C.; Li, H.; He, J.; Wang, Q.; Huang, S.; Li, Y.; Zhan, H.
Measurement Method of Collision Restitution Coefficient between Corn Seed and Soil Based on the Collision Dynamics Theory of Mass Point and Fixed Surface. *Agriculture* **2022**, *12*, 1611.
https://doi.org/10.3390/agriculture12101611

**AMA Style**

Gao Z, Lu C, Li H, He J, Wang Q, Huang S, Li Y, Zhan H.
Measurement Method of Collision Restitution Coefficient between Corn Seed and Soil Based on the Collision Dynamics Theory of Mass Point and Fixed Surface. *Agriculture*. 2022; 12(10):1611.
https://doi.org/10.3390/agriculture12101611

**Chicago/Turabian Style**

Gao, Zhen, Caiyun Lu, Hongwen Li, Jin He, Qingjie Wang, Shenghai Huang, Yunxiang Li, and Huimin Zhan.
2022. "Measurement Method of Collision Restitution Coefficient between Corn Seed and Soil Based on the Collision Dynamics Theory of Mass Point and Fixed Surface" *Agriculture* 12, no. 10: 1611.
https://doi.org/10.3390/agriculture12101611