# Optimization of the Sowing Unit of a Piezoelectrical Sensor Chamber with the Use of Grain Motion Modeling by Means of the Discrete Element Method. Case Study: Rape Seed

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model of Grain Motion in the System of a Piezoelectric Sensor

- Motion in the seed delivery tube,
- Motion after leaving the seed delivery tube until hitting against the seed drill surface,
- Impact with the sensor surface, with partial energy loss,
- Grain motion after collision with velocity v
_{k}, different (smaller due to impact) from its velocity before a collision with the sensor.

_{C}with normal component N (connected with the impact pressure and damping) and tangential component T resulting from grain sliding friction (Figure 3). The equation of grain translational motion is expressed by:

_{o}—particle overlap (Equation (10)), E

_{1}, E

_{2}—Young moduli of two bodies at contact, ${\upsilon}_{1},{\upsilon}_{2}$—Poisson coefficient of bodies at contact, R—radius of grain curvature at the contact point, d—length between the grain gravity center and the contact surface.

_{nH}—damping coefficient of normal forces in Hertz theory, m*—effective mass (relative), ${v}_{n}^{rel}$—relative velocity of normal component.

_{n}according to equation:

_{n}is determined based on the value of the restitution coefficient ε. The restitution coefficient and damping coefficient are connected by the following dependency:

_{τ}—tangential component of relative displacement, s

_{τ,}

_{max}—maximum relative displacement.

_{t}—tangential coefficient of damping, ${v}_{t}^{rel}$—tangential component of relative velocity.

_{w}is determined from equation [35]:

_{r}—coefficient of rolling friction, $\overrightarrow{\omega}$—vector of angular velocity, $\left|\overrightarrow{r}\right|$—rolling radius.

#### 2.2. Experimental Tests

- seed dosing unit (rotational plate with 23 holes) powered by an electric motor with the use of a belt transmission with adjustable speed,
- Chronos 1.4. video camera
- screen with a scale in the form of graph paper,
- vertical-telescopic seed delivery tube (tube for seed drill S107, PMR Meprozet, Miedzyrzecz Podlaski, Poland,
- two led lamps with stabilizing systems, 400 W each,
- laboratory table.

_{0}in axis X. The measurement distance in the Y axis was assumed to be 0 for a grain after collision. In the experimental tests, 4 different tilt angles of the grain transport tube were analyzed: 0°, 5°, 10°, 15°, presented in Figure 5, diversifying in this way the angle of grain falling on the sensor, in order to assess the impact of the tube tilt angle on the efficiency of the piezoelectric sensor and the number of its indication errors. Additionally, two different configurations of the exit hole end with internal diameter 15 mm were used: straight end (yellow), and diagonal end (red), cut at an angle of 45° (Figure 6). Measurements of coordinates were performed for 20 grains in each configuration.

#### 2.3. Simulation Tests with the Use of the Finite Element Method

**Figure 7.**Axes of the coordinate system during determination of the grain point of collision with the sensor and the distance after the impact for the vertical tube (tilt 0°).

#### 2.4. Analysis of Results

_{i}—values of the i-th measurement, n—number of measurements.

_{0}—measured value.

## 3. Results and Discussion

_{0}(Table 3), though not all values were statistically significant which could have been caused by a small sample size (four values of tilt angle). An analysis of correlation showed that for the straight exit hole the coordinate of the grain collision with the sensor in axis X and grain flight length were positively correlated with the tilt angle, whereas the collision point coordinate in axis Y was negatively correlated (Table 3). In the case of a diagonal opening, coordinates of the collision point in axis X and Y were negatively correlated, whereas the flight length was correlated positively with the tilt angle (Table 3). Similar correlations between the variables were obtained for the straight exit hole from a simulation analysis in RockyDEM (Table 4). For the diagonal exit end, the results of a correlation analysis in DEM simulation differed from those obtained from the experiment. Contrary to experimental tests, there were negative correlations (though statistically insignificant), between the collision point coordinates on axis Y and the grain flight length after the impact (Table 4).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Scheme of a piezoelectric sensor chamber, d—grain exit hole diameter, h—distance between the highest point of the sensor mounting place, H—height of the chamber with sensor, l—length of piezoelectric sensor, c—length between the most protruding point of the sensor and the casing wall, α—tilt angle with the horizontal, a—width of the chamber with sensor, k-seed.

**Figure 3.**Scheme of forces affecting grains upon impact with the sensor surface, N–normal force, T–tangential force, G–gravitation force, α–tilt angle of sensor surface, x–the distance the grain collides with the sensor, l–the sensor length.

**Figure 4.**Scheme of a laboratory station for tests of the piezoelectric sensor PZT (ceramic): 1. Casing of sensor enabling adjustment of the seed delivery tube tilt angle, 2. Seed dispenser- in the form of a plate with holes, 3. Telescope seed delivery tube (length 65 cm), 4. Fast video camera, 5. Dedicated lighting 2 psc. LED lamp with a stabilization system).

**Figure 5.**Scheme of the transport tube tilt (seed delivery tube) and its end at angles: 0°, 5°, 10°, 15°: 1—sensor housing, 2—piezoelectric sensor, 3—exit hole.

**Figure 6.**Tested configurations of the exit hole: (

**a**) straight system, (

**b**) diagonal system: 1—sensor housing, 2—piezoelectric sensor, 3—exit hole.

**Figure 8.**Geometry of simulation using the discrete element method: (

**a**) straight system, (

**b**) diagonal system.

**Figure 9.**Grain collision point measured in axis X for different tilt angles—experimental and simulation results.

**Figure 10.**Grain collision point measured in Y axis for different tilt angles—experimental and simulation results.

**Figure 11.**Final position of grain X

_{0}after collision for different tilt angles during experimental and simulation tests.

**Figure 12.**Relative error of piezoelectric sensor indication depending on its tilt angle in experimental tests.

**Figure 13.**Relative error of piezoelectric sensor indication depending on its tilt angle in simulation tests.

Model | |
---|---|

Diameter [mm] | 2.2 |

Mass of one thousand seeds [g] | 3.5 |

Density [kg/m^{3}] | 631 |

Young’s modulus [MPa] | 700 |

Poisson coefficient | 0.3 |

Mass flow [kg/h] | 10 |

Parameter | Particle-Particle | Particle-Surface |
---|---|---|

Restitution coefficient | 0.5 | 0.6 |

Tangential friction coefficient | 0.6 | 0.8 |

Dynamic friction coefficient | 0.2 | 0.2 |

**Table 3.**Analysis results of correlation between tilt angle of the exit hole and the grain collision point coordinates and sensor indication error in experimental tests.

Type of Exit Hole | Factor | X | Y | X_{0} | Relative Error |
---|---|---|---|---|---|

Straight exit hole | Pearson Corr. | 0.755 | −0.786 | 0.752 | 0.867 |

p-value | 0.245 | 0.214 | 0.248 | 0.133 | |

Diagonal exit hole | Pearson Corr. | −0.701 | −0.958 * | 0.933 * | 0.058 |

p-value | 0.299 | 0.042 | 0.067 | 0.942 |

**Table 4.**Analysis results of correlation between tilt angle of the exit hole and coordinates of the grain collision point and the sensor indication error in simulation tests.

Type of Exit Hole | Factor | X | Y | X_{0} | Relative Error |
---|---|---|---|---|---|

Straigth exit hole | Pearson Corr. | 0.905 * | −0.873 | 0.685 | 1.000 * |

p-value | 0.095 | 0.127 | 0.315 | - | |

Diagonal exit hole | Pearson Corr. | −0.183 | −0.667 | −0.894 | 0.944 * |

p-value | 0.817 | 0.333 | 0.106 | 0.056 |

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**MDPI and ACS Style**

Gierz, Ł.; Kruszelnicka, W.; Robakowska, M.; Przybył, K.; Koszela, K.; Marciniak, A.; Zwiachel, T.
Optimization of the Sowing Unit of a Piezoelectrical Sensor Chamber with the Use of Grain Motion Modeling by Means of the Discrete Element Method. Case Study: Rape Seed. *Appl. Sci.* **2022**, *12*, 1594.
https://doi.org/10.3390/app12031594

**AMA Style**

Gierz Ł, Kruszelnicka W, Robakowska M, Przybył K, Koszela K, Marciniak A, Zwiachel T.
Optimization of the Sowing Unit of a Piezoelectrical Sensor Chamber with the Use of Grain Motion Modeling by Means of the Discrete Element Method. Case Study: Rape Seed. *Applied Sciences*. 2022; 12(3):1594.
https://doi.org/10.3390/app12031594

**Chicago/Turabian Style**

Gierz, Łukasz, Weronika Kruszelnicka, Mariola Robakowska, Krzysztof Przybył, Krzysztof Koszela, Anna Marciniak, and Tomasz Zwiachel.
2022. "Optimization of the Sowing Unit of a Piezoelectrical Sensor Chamber with the Use of Grain Motion Modeling by Means of the Discrete Element Method. Case Study: Rape Seed" *Applied Sciences* 12, no. 3: 1594.
https://doi.org/10.3390/app12031594