# Contributions to the Optimization of the Medicinal Plant Sorting Process into Size Classes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}, coefficient of kinematic limits k = 2–5) was studied to determine the separation efficiency. The maximum efficiency obtained was 0.87 with the identification of the following optimal parameters: A = 10 mm, ε = 30°, k = 2–3, α = 9°, sieve capacity Q = 0.72 kg·s

^{−1}·m

^{−2}. The increase was less obvious in the case of the increase in value of ω, α, k, and ε [10].

^{−1}, sieve vibration amplitude of 8 mm, sieve tilt angle of 8˚, and thickness of material layer on the sieve of 5 mm. The innovative technology developed and the main flow of the production line of raw coriander in two fractions, whole and split fruits, showed an efficiency of up to 91.8% [12].

^{−1}. According to the experimental results, the separation efficiency increased with the increase in the vibration amplitude and with the length of the sieve.

^{−1}dried medicinal plants in order to identify the optimal sorting regime. It was concluded that to achieve a high efficiency of the separation process if a feed rate of less than 80–90 kg·h

^{−1}is used, the optimal inclination angle of the electrovibrators should be 80°, while for a feed rate of more than 110 kg·h

^{−1}, the maximum efficiency should be at an inclination angle of 40°.

^{−1}flow rates and for a 30° sieve angle and 0.8 kg·s

^{−1}flow rate; an efficiency of the separation process of less than 0.8 was obtained for a sieve angle of 25° and sieve flow rate of 0.3 kg·s

^{−1}.

- Identifying the dimensional characteristics of dried and chopped nettle fragments, in order to determine the mesh sizes of the sieve for obtaining the dimensional sorts.
- Variation in several parameters of the plane sieve for plants, in order to optimize the sorting process.
- Evaluation of the quality of the sorting process by calculating the average separation coefficient.
- Determination of multivariable regression functions of the polytropic form, in order to assess the constructive, functional, and qualitative indices of the sieving equipment.

## 2. Materials and Methods

#### 2.1. Choice of the Medicinal Plant to Be Studied

- -
- Underground part: horizontal elongated rhizomes, from which underground stolons start;
- -
- Aerial stem: develops on the stolons, has 4 obvious edges and is hairy, generally unbranched, empty inside;
- -
- Leaves: arranged opposed, triangular-ovate lamina being 4–7 cm long and half wide, serrated edge with large teeth, hairs on both sides; lower leaves have a long petiole while upper ones have a short petiole;
- -
- Flowers: disposed in cymes at the base of the leaves, with 3–6 white, large flowers, corolla of up to 2 cm, with the upper lip having the form of a helmet, and the lower one the form of a spoon;
- -
- Fruits: nucleus with three edges, brown, grouped 4 in the persistent calyx.

#### 2.2. Granulometric Analysis of Plant Fragments

_{e}) of the plants sorter.

^{3}, specific mass 37.5 kg/m

^{3}, porosity 26%, and friction angle of fragments on the sieve 48.63°.

#### 2.3. Plant Sorter Working Methodology

#### 2.4. Calculation of Average Separation Coefficient (Ce_{med})—Experiment

_{1}) reached sieve (2), and the larger ones as well as the smaller particles that failed to pass through the sieve were collected at the end of the sieve (R

_{1}plus material), forming sort IV. It was considered that sort IV had the share p

_{4}(%) in the material entered on the sieve:

_{1}) and the amount of material that was supposed to pass through the sieve (P − M

_{4}). The coefficient of separation for sieve 1 is calculated with Relation (2):

_{1}> M

_{4}, the difference is extracted from the other sorts in proportion to their share in the initial material entered on the sieve. The mass of the other sorts is:

_{1}—share of sort I in the initial material; p

_{2}—share of sort II in the initial material; p

_{3}—share of sort III in the initial material; p

_{4}—share of sort IV in the initial material.

_{2}), and the particles that are larger than the sieve meshes will reach the end of the sieve, as well as the particles of sorts II and I (R

_{2}). The coefficient of separation for sieve 2 is calculated with the following relation:

_{2}> M′

_{3}, the difference comes from sorts I and II in proportion to their share. The mass of these sorts is calculated with Relations (7) and (8):

#### 2.5. The Algorithm for Calculating Multivariate Function Coefficients for Average Separation Coefficient (Ce_{med})—Mathematical Model

_{1}, x

_{2}, and x

_{3}are independent variables and y is the dependent variable.

_{0}, a

_{1}, a

_{2}, a

_{3}, a

_{11}, a

_{22}, a

_{33}, a

_{12}, a

_{13}, and a

_{23}) are determined by the method of least squares. The sum of the squares of the measured values deviations is:

_{0}is the number of identical experiments of the independent variables required to determine the experimental error; n

_{*}is the number of experiments performed for different values of the independent variables, necessary for determining the coefficients; the total number of experiments is: n = n

_{*}+ n

_{0}.

_{1}is the number of function coefficients without a

_{0}. If the condition is fulfilled, the form of the function is appropriate.

_{0}≥ F(1 − α, 1, n

_{0}− 1), F

_{j}≥ F (1 − α, 1, n

_{0}− 1), F

_{jj}≥ F(1 − α, 1, n

_{0}− 1), F

_{1j}≥ F (1 − α, 1, n

_{0}− 1), and F

_{23}≥ F (1 − α, 1, n

_{0}− 1), coefficients a

_{0}, a

_{j}, a

_{jj}, a

_{1i}, and a

_{23}are significant. If the condition is not fulfilled, for one or more coefficients, they are equal to zero. Critical values F (P = 1 − α, k

_{1}= 1, k

_{2}= n

_{0}− 1) are given in [41] for the significance level α = 0.95.

- Speed of sieve drive mechanism (n = 1000 rpm, n = 950 rpm; n = 900 rpm);
- Sieve inclination angle (α = 12.08°, α = 13.33°, α = 14.7°);
- Specific flow of sieve loading with plant material (q = 4–10 kg/dm·h).

## 3. Results

- Sort 1 (l < 2.8 mm), p
_{1}= 8.22%; - Sort 2 (l = 2.9–4.0 mm), p
_{2}= 69.15%; - Sort 3 (l = 4.1–5.6 mm), p
_{3}= 13.18%; - Sort 4 (l > 5.6 mm), p
_{4}= 9.46%.

_{med}) is:

_{t}= 9.4, so the function form is adequate.

_{medc}is the calculated average separation coefficient and Ce

_{medexp}is the average separation coefficient obtained experimentally.

- -
- For α = 12.08°:

- -
- For α = 13.33°:

- -
- For α = 14.7°:

_{med}> 0.8) for the angle of inclination of the sieve of α = 12.08°, of medium quality (Ce

_{med}> 0.65) for α = 13.33°, and of lower quality for the inclination of the sieve of α = 14.7°.

_{med}= 0.753, for n = 1000 rpm and q = 4 kg/dm·h, and the minimum value was obtained, Ce

_{med}= 0.456, for n = 900 rpm and q = 10 kg/dm·h.

_{med}= 0.616, for n = 1000 rpm and the minimum value, Ce

_{me}

_{d}= 0.37, for n = 900 rpm.

_{med}= 0.373, was obtained for: α = 14.7°, n = 900 rpm, and q = 10 kg/dm·h, and the maximum value of the average separation coefficient, Ce

_{med}= 0.922, was obtained for: α = 12.08°, n = 1000 rpm, and q = 4 kg/dm·h.

_{med}= 0.922 for α = 12.08°, Ce

_{med}= 0.753 for α = 13.33°, and Ce

_{med}= 0.616 for α = 14.7°. At higher specific flows, the average separation coefficient decreased.

## 4. Discussion

^{3}, specific mass 37.5 kg/m

^{3}, porosity 26%, friction angle of fragments on the sieve 48.63°) and the sieve (rectangular shape with a length of 1495 mm and a width of 600 mm, made of wire with square meshes). The sizes of sieve meshes used in sets of 3 per sieve block were 2.8–4.0–5.6–8.0 mm, and the sieve feed flow rate was 4 kg/dm

^{2}. The equipment had the following optimized settings: sieve oscillation direction, 0°; angle of inclination of electrovibrating motors, 40°; vibration amplitude, A = 5 mm; kinematic coefficient, k = 5.

_{med}curves was decreasing at all three angles of inclination of the sieves. The values of the average separation coefficient decreased in the case of the three revolutions as the feed flow rate, q, increased. The values of the Pearson correlation coefficient (R

^{2}= 0.9512–0.9993) showed a good distribution of the average separation coefficient calculated for different feed rates and tilt angles of the different sieves. The efficiency of the separation of agricultural products by varying various working parameters was studied by many authors [1,12,13,14,18,26,39].

_{med}values were higher at values of n = 1000 rpm, then it decreased as α and q increased. The lowest Ce

_{med}values were recorded at low values of n = 900 rpm and at high flow rates, q = 10 kg/dm·h, and high angles, α = 14.70°.

## 5. Conclusions

_{med}> 0.8) for sieve inclination angle α = 12.08°, medium quality (Ce

_{med}> 0.65) for α = 13.33°, and low quality (Ce

_{med}< 0.65) for sieve inclination angle α = 14.7°.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Industrial-type sieve sorter developed at INMA Bucharest. (

**a**) Plant conveyor; (

**b**) Plant sorter.

**Figure 4.**Scheme of sieves disposal on the industrial plant sorter [1].

**Figure 5.**Variation in the separation coefficient for nettle depending on the specific flow for the three angles of sieve inclination.

**Figure 6.**Variation in separation coefficient for nettle according to the specific flow for n = 1000 rpm.

Characteristic | Unit of Measurement | Values |
---|---|---|

Drive | - | 2 electric vibrating motors |

Electric motors power | kW | 0.15 |

Overall dimensions:- ✓
- length
- ✓
- width
- ✓
- height
| m | 2.330 1.150 1.530 |

Number of sieve frames | pieces | 3 |

Dimensions of changeable sieve frames meshes (9 pcs.) | mm | 1.15; 2.8; 3.15; 4.0; 5.6; 6.3; 8.0; 10.0; 13.2 |

Dimensions of sieve frames- ✓
- length
- ✓
- width
- ✓
- height
| m | 1.495 0.600 0.040 |

Maximum revolution speed Amplitudes of sieve oscillations | rpm mm | 1000 1–10 |

Sieve inclination in three fixed positions, α | ° | 12.08; 13.33; 14.7 |

Mass | kg | 260 |

No. | Fraction Limits (mm) | Sort | Sample (g) | Average (g) | Share p (%) | ||||
---|---|---|---|---|---|---|---|---|---|

P1 | P2 | P3 | P4 | P5 | |||||

1 | <2.8 | I | 9.49 | 9.68 | 9.88 | 10.07 | 10.26 | 9.88 | 8.22 |

2 | 2.9–4.0 | II | 83.17 | 83.37 | 82.59 | 82.78 | 82.98 | 82.98 | 69.15 |

3 | 4.1–5.6 | III | 15.81 | 15.49 | 15.98 | 16.14 | 15.65 | 15.81 | 13.18 |

4 | 5.7–8.0 | IV | 8.23 | 7.88 | 8.02 | 7.87 | 8.12 | 8.02 | 6.70 |

5 | >8.1 | V | 3.47 | 3.45 | 3.12 | 3.09 | 3.4 | 3.31 | 2.76 |

Sample mass (g) | 120 | 120 | 120 | 120 | 120 | 120 | 100 |

Sample | Revolution Speed, n (rpm) | Sieve Angle α (°) | Sort 1 P3 (kg) | Sort 2 R3 (kg) | Sort 3 R2 (kg) | Sort 4 R1 (kg) | Mass of Sorts P (kg) |
---|---|---|---|---|---|---|---|

1 | 1000 | 12.08 | 0.00001 | 0.06750 | 0.10400 | 0.07749 | 0.249 |

2 | 1000 | 12.08 | 0.00003 | 0.12858 | 0.10187 | 0.11900 | 0.349 |

3 | 1000 | 12.08 | 0.00035 | 0.25500 | 0.09400 | 0.13900 | 0.488 |

4 | 1000 | 12.08 | 0.00050 | 0.09700 | 0.15000 | 0.25048 | 0.498 |

5 | 1000 | 13.33 | 0.00023 | 0.12400 | 0.06700 | 0.05900 | 0.250 |

6 | 1000 | 13.33 | 0.00027 | 0.16200 | 0.09300 | 0.09200 | 0.347 |

7 | 1000 | 13.33 | 0.00040 | 0.04500 | 0.08000 | 0.22262 | 0.348 |

8 | 1000 | 13.33 | 0.00048 | 0.22700 | 0.09600 | 0.11100 | 0.434 |

9 | 1000 | 14.7 | 0.00015 | 0.12800 | 0.05900 | 0.06000 | 0.247 |

10 | 1000 | 14.7 | 0.00002 | 0.02500 | 0.04300 | 0.18098 | 0.249 |

11 | 1000 | 14.7 | 0.00024 | 0.18400 | 0.09000 | 0.10100 | 0.375 |

12 | 1000 | 14.7 | 0.00026 | 0.21800 | 0.12400 | 0.11800 | 0.460 |

13 | 1000 | 14.7 | 0.00000 | 0.02700 | 0.05000 | 0.38200 | 0.459 |

14 | 950 | 12.08 | 0.00035 | 0.20200 | 0.08400 | 0.08900 | 0.375 |

15 | 950 | 12.08 | 0.00009 | 0.05800 | 0.10000 | 0.21589 | 0.374 |

16 | 950 | 12.08 | 0.00033 | 0.22600 | 0.09100 | 0.14600 | 0.463 |

17 | 950 | 13.33 | 0.00020 | 0.13100 | 0.03500 | 0.06200 | 0.228 |

18 | 950 | 13.33 | 0.00022 | 0.02580 | 0.05000 | 0.15193 | 0.228 |

19 | 950 | 13.33 | 0.00037 | 0.16200 | 0.05200 | 0.09700 | 0.311 |

20 | 950 | 13.33 | 0.00020 | 0.03000 | 0.05700 | 0.22380 | 0.311 |

21 | 950 | 13.33 | 0.00020 | 0.03500 | 0.07300 | 0.20280 | 0.311 |

22 | 950 | 13.33 | 0.00001 | 0.02800 | 0.04800 | 0.23499 | 0.311 |

23 | 950 | 13.33 | 0.00010 | 0.03000 | 0.05300 | 0.22790 | 0.311 |

24 | 950 | 13.33 | 0.00047 | 0.20300 | 0.12400 | 0.15900 | 0.486 |

25 | 950 | 13.33 | 0.00025 | 0.02900 | 0.06400 | 0.39279 | 0.486 |

26 | 950 | 14.7 | 0.00019 | 0.19600 | 0.07700 | 0.07100 | 0.344 |

27 | 950 | 14.7 | 0.00000 | 0.01650 | 0.03400 | 0.29450 | 0.345 |

28 | 950 | 14.7 | 0.00031 | 0.23300 | 0.11800 | 0.14700 | 0.498 |

29 | 900 | 12.08 | 0.00035 | 0.03000 | 0.06000 | 0.13664 | 0.227 |

30 | 900 | 12.08 | 0.00034 | 0.17500 | 0.08700 | 0.05900 | 0.321 |

31 | 900 | 13.33 | 0.00048 | 0.02800 | 0.10000 | 0.28952 | 0.418 |

32 | 900 | 13.33 | 0.00018 | 0.16500 | 0.07600 | 0.09500 | 0.336 |

33 | 900 | 13.33 | 0.00015 | 0.01550 | 0.04000 | 0.28035 | 0.336 |

34 | 900 | 13.33 | 0.00030 | 0.19100 | 0.08700 | 0.11300 | 0.391 |

35 | 900 | 14.7 | 0.00005 | 0.00750 | 0.01800 | 0.16441 | 0.190 |

36 | 900 | 14.7 | 0.00027 | 0.05680 | 0.07600 | 0.26500 | 0.398 |

37 | 900 | 14.7 | 0.00010 | 0.00800 | 0.03010 | 0.35980 | 0.398 |

No. | Sample | Revolution Speed, n (rpm) | Sieve Angle, α (°) | Specific Flow, q (kg/dm·h) | Average Separation Coefficient Ce _{me}_{d} |
---|---|---|---|---|---|

1 | 29 | 900 | 12.08 | 4.54 | 0.70 |

2 | 1 | 1000 | 12.08 | 4.98 | 0.87 |

3 | 35 | 900 | 14.7 | 3.8 | 0.48 |

4 | 10 | 1000 | 14.7 | 4.98 | 0.6 |

5 | 31 | 900 | 12.08 | 8.36 | 0.59 |

6 | 4 | 1000 | 12.08 | 9.96 | 0.77 |

7 | 37 | 900 | 14.7 | 7.96 | 0.4 |

8 | 13 | 1000 | 14.7 | 9.18 | 0.52 |

9 | 33 | 900 | 13.33 | 6.72 | 0.51 |

10 | 7 | 1000 | 13.33 | 6.96 | 0.68 |

11 | 27 | 950 | 14.7 | 6.9 | 0.48 |

12 | 15 | 950 | 12.08 | 7.48 | 0.71 |

13 | 25 | 950 | 13.33 | 9.72 | 0.54 |

14 | 18 | 950 | 13.33 | 4.56 | 0.65 |

15 | 20 | 950 | 13.33 | 6.22 | 0.61 |

16 | 21 | 950 | 13.33 | 6.22 | 0.64 |

17 | 22 | 950 | 13.33 | 6.22 | 0.59 |

18 | 23 | 950 | 13.33 | 6.22 | 0.60 |

Regression Coefficients | Testing Coefficients | Coefficients’ Significance |
---|---|---|

a_{1} = 0.0000016 | F_{1} = 3696.122765650 > 8.2560 | Is significant |

a_{2} = 2.7082166 | F_{2} = 33.109848938 > 8.2560 | Is significant |

a_{3} = −2.0532161 | F_{3} = 66.0598420435 > 8.2560 | Is significant |

a_{4} = −0.2362560 | F_{4} = 21.306697235 > 8.2560 | Is significant |

**Table 6.**Deviations of calculated values compared to the experimentally determined ones (for validation) for average separation coefficient for nettle.

No. | Sample | Average Separation Coefficient | Deviation, A (%) | |
---|---|---|---|---|

Experimental Ce _{medexp} | Calculated with Equation (16) Ce _{medc} | with Equation (16) | ||

1 | 2 | 0.854 | 0.865 | −0.549 |

2 | 3 | 0.762 | 0.748 | 1.532 |

3 | 5 | 0.679 | 0.668 | 1.830 |

4 | 6 | 0.612 | 0.596 | 2.268 |

5 | 8 | 0.524 | 0.514 | 1.24 |

6 | 9 | 0.622 | 0.598 | 1.967 |

7 | 11 | 0.544 | 0.538 | 0.412 |

8 | 12 | 0.494 | 0.478 | 2.409 |

9 | 14 | 0.697 | 0.679 | 3.028 |

10 | 16 | 0.587 | 0.483 | 1.814 |

11 | 17 | 0.516 | 0.508 | 0.361 |

12 | 19 | 0.492 | 0.476 | 2.777 |

13 | 24 | 0.409 | 0.401 | 2.159 |

14 | 26 | 0.645 | 0.664 | −2.906 |

15 | 28 | 0.587 | 0.602 | −2.488 |

16 | 30 | 0.565 | 0.546 | 3.439 |

17 | 32 | 0.421 | 0.401 | 4.826 |

18 | 34 | 0.7 | 0.668 | 4.627 |

19 | 36 | 0.647 | 0.612 | 5.479 |

Specific Flow, q (kg/dm·h) | α = 12.08° | α = 13.33° | α = 14.7° | ||||||
---|---|---|---|---|---|---|---|---|---|

Revolution Speed, n (rpm) | Revolution Speed, n (rpm) | Revolution Speed, n (rpm) | |||||||

900 | 950 | 1000 | 900 | 950 | 1000 | 900 | 950 | 1000 | |

4 | 0.693 | 0.803 | 0.922 | 0.566 | 0.656 | 0.753 | 0.463 | 0.536 | 0.616 |

5 | 0.658 | 0.761 | 0.875 | 0.537 | 0.622 | 0.715 | 0.439 | 0.509 | 0.585 |

6 | 0.630 | 0.729 | 0.838 | 0.515 | 0.596 | 0.685 | 0.421 | 0.487 | 0.560 |

7 | 0.607 | 0.703 | 0.808 | 0.496 | 0.574 | 0.66 | 0.406 | 0.470 | 0.540 |

8 | 0.589 | 0.681 | 0.783 | 0.481 | 0.557 | 0.64 | 0.393 | 0.455 | 0.523 |

9 | 0.572 | 0.663 | 0.761 | 0.468 | 0.541 | 0.622 | 0.383 | 0.443 | 0.509 |

10 | 0.558 | 0.646 | 0.743 | 0.456 | 0.528 | 0.607 | 0.373 | 0.432 | 0.496 |

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## Share and Cite

**MDPI and ACS Style**

Pruteanu, M.A.; Ungureanu, N.; Vlăduț, V.; Matache, M.-G.; Niţu, M.
Contributions to the Optimization of the Medicinal Plant Sorting Process into Size Classes. *Agriculture* **2023**, *13*, 645.
https://doi.org/10.3390/agriculture13030645

**AMA Style**

Pruteanu MA, Ungureanu N, Vlăduț V, Matache M-G, Niţu M.
Contributions to the Optimization of the Medicinal Plant Sorting Process into Size Classes. *Agriculture*. 2023; 13(3):645.
https://doi.org/10.3390/agriculture13030645

**Chicago/Turabian Style**

Pruteanu, Mirabela Augustina, Nicoleta Ungureanu, Valentin Vlăduț, Mihai-Gabriel Matache, and Mihaela Niţu.
2023. "Contributions to the Optimization of the Medicinal Plant Sorting Process into Size Classes" *Agriculture* 13, no. 3: 645.
https://doi.org/10.3390/agriculture13030645