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

Abstract

This study aims to optimize and assess the quality of the sorting process into homogeneous size classes of dried and chopped medicinal plants, by obtaining multivariate regression functions of polytropic and polynomial forms. Assessment of sorting quality was carried out by calculating the average coefficient of separation. The influence of several important factors (material feed rate on the sieve, sieve dimensions, sieve inclination angle, sieve oscillation frequencies) on the sorting process was followed. Research was carried out on dried nettle herb (Urtica dioica) using a plant sorter with plane sieves, which allowed for modifying some constructive and functional parameters, making it possible to obtain optimal values. The results showed that the dry nettle herb chopped in bulk at 4 mm, with a moisture of 11.45%, was optimally sorted (index of average separation coefficient, 0.922) if the following parameters were met: drive mechanism speed n = 1000 rpm; sieve inclination angle α = 12.08°; material-specific flow q = 4 kg/dm·h; recommended sieve length L = 1.4 m. It was observed that at high rates, the average coefficient of separation decreased with the decrease in the sieve drive mechanism speed, and when the inclination angle of the sieve decreased, the average coefficient of separation increased. The maximum average deviation of the average separation coefficient was 5.5% for the polytropic function. The new advanced processing technologies of medicinal plants involve the short-term production of quality-finished products, thus supporting the processors of medicinal plants and the consumers of phytotherapeutic products with beneficial effects for health.

1. Introduction

Given the importance of medicinal plants for obtaining phytotherapeutic products beneficial to human health, as well as the diversity of medicinal species existing in the culture or spontaneous flora, many countries have created their own industry for manufacturing the machinery and equipment for processing medicinal plants. Thus, there is a wide variety of machines and equipment on the world market that respect the technical requirements and conditions from a constructive and functional point of view [1].

Currently, there are many studies on the quality of the seed sorting process of different plant crops, such as chickpea [2], rice [3], wheat and barley [4,5], buckwheat and wild radish [6], and rape [7,8]. Similar to the process of seed sorting, the sorting of green or dry medicinal plants was also studied, which, according to the sizes of the aerial vegetative parts, are used for obtaining teas, extracts, tinctures, and macerations.

The main factors influencing the sorting process on plane sieves are [9]: sieve loading with plant material, sieve size, mesh sizes, sieve inclination angle, amplitude and frequency of oscillations, friction coefficient, and moisture of medicinal plants. Depending on these factors, the efficiency and quality of the sorting process were studied on different mixtures of particles with different sizes, shapes, and compositions.

The separation of flax seeds on vibrating separators with parameter analysis (vibration amplitude A = 8–15 mm, screen inclination angle α = 9–12°, vibration direction angle ε = 30–45°, angular speed ω = 30–60 rad·s⁻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].

The authors of study [11] optimized the frequency and amplitude of vibrations according to the characteristics of the bulk material to be sorted (pea seeds, beans, sunflower).

The separation of raw coriander fruits using a sieve with a mesh size of 2 × 20 mm for the primary processing of the fruits was studied, for the production of more valuable essential oils. The operating modes used were: sieve vibration frequency of 400 vibrations·min⁻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].

The efficiency of separation on a vibrating separator depending on other working parameters, such as: size of sievemeshes, sieve length, angle of inclination, amplitude of the vibrations, and frequency of the vibrations, was studied in [13]. The maximum efficiency could reach over 80% when the following optimal intervals for the studied parameters were reached: size of the opening of the sieve mesh, 0.8–1.1 mm; sieve inclination, 25°; sieve length, 2–2.6 m; vibration amplitude, 3.5 mm; vibration frequency, 960 r·min⁻¹. According to the experimental results, the separation efficiency increased with the increase in the vibration amplitude and with the length of the sieve.

A previous study [14] showed the efficiency of the sorting process depending on the number of particle jumps on the sieve. The efficiency increases as the jumps of the material on the sieve increase. It was found that when the material remains for a long time on the sieve, the productivity decreases. The analysis of the experimental data regarding the number of throws showed that the number of jumps is influenced by two main parameters: the transport time of the material on the screen and the frequency of the vibrations of the action mechanism. An increase in the number of throws of the material (n) increases the time that the material remains on the screen surface, reduces the speed of the material passage, and, in general, reduces the productivity of the screen.

In a previous study [15], the separation efficiency was simulated on sieve length for different inclination angles and different amplitudes of the sieve. The results of the theoretical analysis revealed that at low amplitudes (0.5 mm and 2.55 mm) and at small inclination angles of the sieve (0° and 25°), the separation efficiency increases in the first part of the sieve, then it becomes insignificant toward the end of the sieve. At the amplitude of 4.49 mm and sieve inclination angle of 35°, the separation efficiency was proportional to the length of the sieve.

Study [16] presented the results of sieve oscillation regimes by adjusting the inclination angle of the electrovibrators at 80°, 73°, 63.5°, and 40°, with the progressive modification of the working capacity from 80 to 120 kg·h⁻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°.

Study [17] presented the efficiency of separating the sub-dimensional fractions, namely the ratio of the mass of particles smaller than sieve meshes to the mass of fine particles present in the feed rate. The research was performed on a sorter driven by two inertial motors, with the sieve tested having a length of 1500 mm and a width of 500 mm, the sieve meshes dimension being 0.63 mm, and the inclination angles being 15°, 20°, 25°, and 30°. Two types of dried material were used: one consisting of particles with sharp edges and another with spherical particles. The analysis of the results revealed the following: a separation efficiency higher than 0.95 was obtained for 15° and 20° sieve angles and 0.1–0.5 kg·s⁻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.

Improving the efficiency of the separation process can be achieved by using a sieve meshes cleaning mechanism equipped with cylindrical working bodies [18]. A statistical analysis of the diversity of the physical–mechanical characteristics [19] of the crops and their impact on the separation process was carried out in studies on cotton seeds [20] and buckwheat seeds [21]. The analysis of the mechanical properties of the species Fritillaria ussuriensis, the flowering plant of the lily family Liliaceae, originally from Korea, on the design of a sieve separation machine was studied in [22], and the influence of leaf content and size of plant particles on the extraction of compounds in teas was studied in [23]. Other studies presented the kinematic analysis of the sorting process of tea leaves on three types of separators [24] and on tobacco leaves [25].

A comparative analysis of the separation process on the site and the possibility of representation in the form of laws: normal distribution, Weibull, gamma, and beta, were carried out in [26,27], as well as applications with the Discrete Element Method for the simulation of the manufacturing process in the pharmaceutical industry [28,29,30,31].

This study had as the main objective the theoretical and experimental analysis of the sorting process of nettle, a medicinal plant that can be used in the preparation of various phytopharmaceutical products (including teas, macerates, tinctures, plant extracts, and essential oils). To fulfill the main objective, the following were accomplished:

• 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.

Based on the experimental results, some recommendations could be made for the separation of nettle on plane sieves.

2. Materials and Methods

2.1. Choice of the Medicinal Plant to Be Studied

This work is part of a larger study [1], in which the processing and phytotherapeutic intake of several common medicinal plants (which can be grown or can come from the spontaneous flora) in our area (Bucharest, Romania) were studied.

In this paper, we present the results of the tests carried out on nettle (Urtica dioica), a plant often used for phytotherapeutic purposes. The nettle was chosen on the one hand for the fact that it is often found in the spontaneous flora of Romania and grows in many places, not being sensitive to certain environmental conditions, such as climate, atmospheric, and soil properties; on the other hand, to study its optimal processing conditions when it is used for its phytotherapeutic properties.

The nettle provides a rich supply of nutrients (vitamins C, A, and K and contains calcium, magnesium, iron, silicon, and phosphorus) and bioactive substances (flavanols, gallic, tannic and formic acids, and carotids) necessary to supplement the diet to restore the normal functioning of the reno-urinary system.

Nettle is an herbaceous, perennial species, 20–50 (70) cm high, with ascending aerial stems, of the Lamium genus in the Lamiaceae (Labiatae) family, being spread from the hilly area to the alpine level. Nettle harvesting is performed before or during the flowering, from April to September [32].

The morpho-biological characteristics of nettle plant are as follows [32]:

-

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.

Nettle contains important bioactive substances: iridoids (lamiozide), saponins, tannins (12–14%), essential oil, flavonoids, mucilages, and polyphenol carboxylic acids (especially rosmarinic acid); biogenic amines: histamine, methylamine, and tyramine; vitamins C and K, carotenoids, and mineral salts, especially potassium [1,32].

There are various studies on the therapeutic use of nettle in Romania [33] and abroad [1,34,35].

Nettle, the medicinal plant chosen for this study, was identified and harvested from the spontaneous flora. Vegetable mixtures are non-homogeneous mixtures consisting of fragments of plant dried and chopped at different sizes.

The non-homogeneous mixture of nettle (was obtained by bulk chopping of the dried plant aerial parts. The chosen chopping size was 4 mm, according to the specifications of the Romanian Pharmacopoeia, because the fragments of these dimensions are of interest for obtaining plant extracts rich in bioactive substances, having a role in the treatment of human diseases [1]. The conditions under which the measurements were made were high atmospheric humidity, with the herb of the plants being bulk chopped with a medicinal plant chopping equipment (Timatic type), adjusted to the chosen size. Aspects with whole and chopped nettle are shown in Figure 1.

2.2. Granulometric Analysis of Plant Fragments

Separation by geometric dimensions is a commonly used method carried out by means of sieves. The working process of the sieve has two stages: the first stage consists in moving the mass of the plant fragments mixture distributed in a uniform layer and the second stage is the separation of the plant fragments through the sieve meshes due to the passage of fragments smaller than the dimensions of sieve meshes [27,36].

To determine the dimensional characteristics of chopped plant material, five samples were analyzed. Each sample of 120 g of plant material was weighed on a precision balance and separated in a Retsch-type sieve classifier, set to operate at 50 mm amplitude for 5 min. The Retsch classifier was used to establish the orifices dimensions for the sieves that were mounted on the industrial-type plant sorter developed at INMA Bucharest, which was later used during experiments. The results obtained on the classifier (share, p) were also used to calculate the average separation coefficient (C_e) of the plants sorter.

On each sieve, there was a quantity of plant material that represented all the fragments smaller than those of the upper sieve meshes and larger than the meshes of the sieve they passed through. Sieves were chosen so that the mesh dimensions were in geometric progression by the ratio $\sqrt{2}$ [37]. For 4 mm chopped nettle, sieves were disposed in increasing order of mesh size: 2.8–4.0–5.6–8.0 mm. Figure 2 shows the five sorts separated.

The physical and mechanical characteristics of the plant material subjected to the separation were: moisture 11.45%, particle average diameter 5.23 mm, density 47.2 kg/m³, specific mass 37.5 kg/m³, porosity 26%, and friction angle of fragments on the sieve 48.63°.

2.3. Plant Sorter Working Methodology

The plant sorter is used to separate plants not only into classes, having a high working capacity; the supply of material can be performed continuously, with the distribution being uniform on the surface of the vibrating sieve, which may have mesh dimensions from large to very small. The main technical characteristics of the sorter are shown in

Table 1. Main technical characteristics of the plant sorter.

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

.

The first experimental tests were focused on adjusting the sorter feed rate, with the sorter fed with plant material via an inclined belt conveyor (Figure 3a), which transported the material to the center of the sorter feed hopper (Figure 3b).

The sorting equipment had the sieve oscillation direction at 0° due to the position of the vertical suspension supports, where the inclination angle of the electric vibrating motors was 45°, the movement of the material on the sieve was made by detachment [38], and the amplitude of sieve oscillations was 5 mm.

2.4. Calculation of Average Separation Coefficient (Ce_med)—Experiment

In the case of the plant sorter used in the experimental research, the sieves were placed overlapped, in parallel (Figure 4).

The amount P (kg) of plant material reached the sieve with the largest meshes (1) in 30 s, corresponding to the specific flow q (kg/dm·h). Particles smaller than the sieve meshes (P₁) 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 (R₁ plus material), forming sort IV. It was considered that sort IV had the share p₄ (%) in the material entered on the sieve:

$$M_4=P·p_{4 }$$

(1)

The separation coefficient of the first sieve is defined as the ratio of the amount of material that passed through the sieve (P₁) and the amount of material that was supposed to pass through the sieve (P − M₄). The coefficient of separation for sieve 1 is calculated with Relation (2):

$$C{e}_1=\frac{P_1}{P-M_4}=\frac{\left(P-R_1\right)}{\left(P-M_4\right)}$$

(2)

Considering that R₁ > M₄, 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:

$$M_3^{\prime }=p_3·P-\frac{p_3\left(R_1-M_4\right) }{p_1+p_2+p_3}$$

(3)

$$M_2^{\prime }=p_2·P-\frac{p_3\left(R_1-M_4\right)}{p_1+p_2+p_3}$$

(4)

$$M_1^{\prime }=p_1·P-\frac{p_1\left(R_1-M_4\right) }{p_1+p_2+p_3}$$

(5)

where p₁—share of sort I in the initial material; p₂—share of sort II in the initial material; p₃—share of sort III in the initial material; p₄—share of sort IV in the initial material.

The meshes of sieve 2 will pass the particles smaller than the mesh size (P₂), 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 (R₂). The coefficient of separation for sieve 2 is calculated with the following relation:

$$C{e}_2=\frac{P_2}{P_1-M_3^{\prime }}=\frac{\left(P-R_1-R_2\right)}{\left(P-R_1-M_3^{\prime }\right)}$$

(6)

Considering that R₂ > 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):

$$M_2^{″}=M_2^{\prime }-\frac{p_2\left(R_2-M_3^{\prime }\right)}{p_1+p_2}$$

(7)

$$M_1^{″}=M_1^{\prime }-\frac{p_1\left(R_2-M_3^{\prime }\right)}{p_1+p_2}$$

(8)

The separation coefficient of sieve 3 is calculated as:

$$C{e}_3=\frac{P_3}{P_2-M_2^{″}}=\frac{P_2-R_3}{P_2-M_2^{″}}=\frac{\left(P-R_1-R_2-R_3\right)}{\left(P-R_1-R_2-M_2^{″}\right)}$$

(9)

The average separation coefficient of the three sieves is calculated thus [1,39,40]:

$$C{e}_{med}=C{e}_1+C{e}_2+C{e}_3-C{e}_1·C{e}_2-C{e}_2·C{e}_3-C{e}_1·C{e}_3+C{e}_1·C{e}_2·C{e}_3$$

(10)

2.5. The Algorithm for Calculating Multivariate Function Coefficients for Average Separation Coefficient (Ce_med)—Mathematical Model

The polytropic regression function, with three independent variables, is [41]:

$$y=a_0·x_1^{a_1}·x_2^{a_2}·x_3^{a_3}$$

(11)

where x₁, x₂, and x₃ are independent variables and y is the dependent variable.

The coefficients (a₀, a₁, a₂, a₃, a₁₁, a₂₂, a₃₃, a₁₂, a₁₃, and a₂₃) are determined by the method of least squares. The sum of the squares of the measured values deviations is:

$$S={\displaystyle \sum }_{i=1}^n\left(y-a_0-{\displaystyle \sum }_{i=1}^3{a}_i{x}_i-{\displaystyle \sum }_{i=1}^3{a}_{ii}{x}_i^2-a_{12}{x}_1{x}_2-a_{13}{x}_1{x}_3-a_{23}{x}_2{x}_3\right)$$

(12)

To test the coefficients significance with the Fisher test, the sum of the squares of experimental errors is calculated:

$$S_e={\displaystyle \sum }_{i=n_{*+1}}^n\left(y_i-{\displaystyle \sum }_{i=n_{*+1}}^n\left.\frac{y_i}{n_0}\right)\right.$$

(13)

where n₀ 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_* + n₀.

The adequacy of the functions form was studied with the Fisher test. The ratio was calculated:

$$F=\frac{\left(S-S_e\right)·\left(n_0-1\right)}{S_e·\left(n-n_0-m_1\right)}<F·\left(1-\alpha ,n_{*}-m_1, n_0-1\right)$$

(14)

where m₁ is the number of function coefficients without a₀. If the condition is fulfilled, the form of the function is appropriate.

If F₀ ≥ F(1 − α, 1, n₀ − 1), F_j ≥ F (1 − α, 1, n₀ − 1), F_jj ≥ F(1 − α, 1, n₀ − 1), F_1j ≥ F (1 − α, 1, n₀ − 1), and F₂₃ ≥ F (1 − α, 1, n₀ − 1), coefficients a₀, a_j, a_jj, a_1i, and a₂₃ are significant. If the condition is not fulfilled, for one or more coefficients, they are equal to zero. Critical values F (P = 1 − α, k₁ = 1, k₂ = n₀ − 1) are given in [41] for the significance level α = 0.95.

To determine the coefficients of multivariate functions, the independent variables that influence the dependent variable and their variation range were chosen:

• 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).

Using computational programs developed in the programming language Turbo Pascal [1,41], the regression coefficients for the polytropic and polynomial form function were calculated.

3. Results

The amount of material separated on the Retsch-type classifier sieves, in the five samples, is shown in

Table 2. Distribution of nettle fragments chopped at 4 mm.

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

.

Although the size of chopped fragments was adjusted to 4 mm, a chopped material with uneven dimensions was obtained. It can be noticed that sort I with a fragment size smaller than 2.8 mm and the sorts with a fragment size larger than 5.6 mm (sorts IV and V) had a share of 8.22% and 9.46%, respectively. Sort II (fragments with dimensions between 2.9 and 4.0 mm) had the largest share, 69.15%.

Therefore, the shares (p%) of the sorts of nettle chopped at the size of 4 mm were:

• Sort 1 (l < 2.8 mm), p₁ = 8.22%;
• Sort 2 (l = 2.9–4.0 mm), p₂ = 69.15%;
• Sort 3 (l = 4.1–5.6 mm), p₃ = 13.18%;
• Sort 4 (l > 5.6 mm), p₄ = 9.46%.

From the analysis of the plant fragments distribution into sorts in terms of sieve meshes, that can be used alone or in groups of two or three sieves, depending on the sorting equipment, the following recommendations can be made: the nettle can be sorted on the sieves with mesh dimensions of 5.6 mm, 4.0 mm, and 2.8 mm.

Afterward, 37 experiments were performed on the plant sorter (

Table 3. Experimental raw data for chopped nettle separation.

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

) fitted with sieves as mentioned above on the material of nettle chopped at the size of 4 mm.

Table 4. Experimental program for average separation coefficient for nettle.

No.	Sample	Revolution Speed, n (rpm)	Sieve Angle, α (°)	Specific Flow, q (kg/dm·h)	Average Separation Coefficient Cemed
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

presents the raw values obtained for the sieved sorts recorded for 18 experiments randomly selected from the total number of experiments. The remaining 19 experiments were used for model validation.

The experimental testing program for the determination of multivariate functions to calculate the average separation coefficient for nettle is shown in Table 4, in which, from all initial raw data, only 18 samples were randomly chosen.

The polytropic function that allows for calculating the average separation (Ce_med) is:

$$C{e}_{med}=0.0000016·n^{2.7082166}·{\alpha }^{-2.0532161}·q^{-0.2362560}$$

(15)

where n—revolution speed (n = 900–1000 rpm); α—sieve inclination angle (α = 12.08–14.7°); q—sieve specific flow (q = 3.8–9.96 kg/dm·h).

The regression and testing coefficients obtained for the polytropic function are shown in

Table 5. Experimental program for polytropic function.

Regression Coefficients	Testing Coefficients	Coefficients’ Significance
a1 = 0.0000016	F1 = 3696.122765650 > 8.2560	Is significant
a2 = 2.7082166	F2 = 33.109848938 > 8.2560	Is significant
a3 = −2.0532161	F3 = 66.0598420435 > 8.2560	Is significant
a4 = −0.2362560	F4 = 21.306697235 > 8.2560	Is significant

. The coefficient of testing the adequacy of the function is F = 0.226 < F_t = 9.4, so the function form is adequate.

The deviation (A) of the average separation coefficient values calculated with Relation (16):

$$A=\frac{C{e}_{medexp}-C{e}_{medc}}{C{e}_{medexp}}·100 \left[\%\right]$$

(16)

where Ce_medc is the calculated average separation coefficient and Ce_medexp is the average separation coefficient obtained experimentally.

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 Cemedexp	Calculated with Equation (16) Cemedc	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

presents the deviations of the values calculated for the average separation coefficient with the polytropic function compared to the experimental ones.

It was observed that the deviation of the average separation coefficient values calculated with Relation (15) was a maximum of 5.5% for the polytropic function.

If sieve inclination angle is considered constant, then the following polytropic calculation relations of the average separation coefficient are obtained:

-

For α = 12.08°:

$$C{e}_{med}=9.603\times {10}^{-9}·n^{2.7082166}·q^{-0.2362568}$$

(17)

-

For α = 13.33°:

$$C{e}_{med}=7.845\times {10}^{-9}·n^{2.7082166}·q^{-0.2362568}$$

(18)

-

For α = 14.7°:

$$C{e}_{med}=6.417\times {10}^{-9}·n^{2.7082166}·q^{-0.2362568}$$

(19)

For the specific flow q = 4–10 kg/dm·h and revolution speed n = 900–1000 rpm, the average separation coefficient was calculated with the relations above. The data are presented in

Table 7. Average separation coefficient calculated for nettle for different flow rates.

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

.

Figure 5 shows the variation in the average separation coefficient for nettle according to the specific flow of the plant material for sieve inclination angles of 12.08°, 13.33°, and 14.7° at different speeds of the drive mechanism.

Sorts of chopped nettle at a size of 4 mm were separated on flat sieves in percentages that increase with the increase in the average extraction coefficient. It can be seen from Figure 5 that at high flow rates, the average extraction coefficient decreased as the speed of the sieve actuation mechanism decreased, and when the angle of inclination of the sieve decreased, the extraction coefficient increased.

It was found that the nettle separation was of superior quality (Ce_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°.

In the case of sieve inclination at 12.08°, the average coefficient of separation had the maximum values for the drive mechanism speed of 1000 rpm at minimum flow. The average separation coefficient decreased with the increase in feed rate and lowering of the speed.

At the sieve inclination angle of 13.33°, for the average coefficient of separation, the maximum value was obtained, Ce_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.

For the inclination angle of 14.7°, the average separation coefficient recorded the maximum value, Ce_med = 0.616, for n = 1000 rpm and the minimum value, Ce_med = 0.37, for n = 900 rpm.

For nettle, the minimum value of the average separation coefficient, Ce_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.

Figure 6 shows the variation in separation coefficient for nettle according to the specific flow for n = 1000 rpm and for different inclination angles of sieves.

For the speed of the drive mechanism n = 1000 rpm (k = 5.59) and constant specific flow q = 4 kg/dm·h, the average separation coefficient for nettle was Ce_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.

Figure 6 shows that the nettle separation was of superior quality for n = 1000 rpm, of medium quality for n = 950 rpm, and of low quality for n = 900 rpm.

The regression functions allow the calculation of the average extraction coefficient for dry nettle chopped to 4 mm, with a deviation from the experimentally determined values of a maximum of 5.5%.

The dimensional uniformity of the sorts obtained from fragments of plant material is very important in the preparation of different categories of plant products (macerations, tinctures, teas). In practice, machines for sorting non-homogeneous mixtures in bulk with different fractions, with the programming of work parameters, which effectively process medicinal plants, are frequently used.

The results presented in the paper are important because they show the processing of experimental data and the obtaining of multivariable regression functions of polynomial form that allow the calculation of the average extraction coefficient for medicinal plants, for the following parameters: the angle of inclination of the sieve (α = 12.08–14.7°), the speed of the sieve drive mechanism (n = 900–1000 rpm), and the specific flow rate on the sieve surface (q = 4–10 kg/dm·h). Following the theoretical and experimental studies, a series of recommendations are made for specialists in the field of design and processing of medicinal plants.

4. Discussion

At present, in the technological process of medicinal plant processing, it is necessary to increase the working capacity and the quality in the processes of sorting chopped medicinal plants, this being achieved by the use of efficient, complex, high-productivity machines and equipment, which can work individually or within medicinal plant processing lines.

In the case of machines and equipment for sorting medicinal plants, it has always been sought to make improvements and modernizations of a constructive and functional order that meet technical requirements and conditions, in order to carry out the working process in good conditions.

Based on numerous studies [1,17,39,40], it is known that the efficiency of the separation process is directly influenced by many factors [9] that depend on: material (particle shape and dimensions, particle weight, moisture, density, coefficient of friction between particles), sieve (sizes and shape of sieve meshes, shape of sieve, the material from which the sieve is made, the angle of inclination of the sieves, the feeding flow of the sieve, the dispersion of the material on the sieve), and equipment (the type of mechanism of actuation, the frequency and amplitude of oscillations, the speed impressed on the particles on the sieve) [10,42].

The experiments performed showed that the factors that had a significant impact on the optimization of the separation process were: the properties of the bulk vegetable mixture of nettle chopped to 4 mm (moisture 11.45%, particle average diameter 5.23 mm, density 47.2 kg/m³, specific mass 37.5 kg/m³, 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/dm². 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.

The separation process was found to be successful at amplitudes smaller than the particle size of the mixture. In addition, for all mixtures used and operating modes, the minimum time for complete separation was achieved when the angle of inclination of the sieve was approximately equal to the angle of repose of the mixture particles.

Fragments passing through the meshes depend on the size of the ratio of the meshes size to that of the fragments. The higher the ratio of the mesh size to the plant fragment size, the greater the amount of fragments passing simultaneously through the meshes [18,26]. The analysis of the distribution by size [27,36,43] of the plant mixture subjected to separation, which consists of separating into size classes on a sieve separator, is important in the process sorting, because it characterizes the size of the plant fragments.

The loading of a medicinal plant sorter sieve can range between 30 and 120 kg/m·h, with a height of the chopped plant material layer on the sieves of up to 20 mm. The sieve working regime is influenced by the rate and amount of sieve compartment feeding but also by the sorting time from the first discharge of the chopped material into the sorter hopper to the total separation of the fragments by dimensional sorts [44].

The sieve working capacity varies directly proportional to its width [38,45], and the ratio between the length and the width of the sieve should be between 1 and 3 [40].

The separation of bulk mixtures is an essential part of the separation process for both seeds and vegetable raw materials [1,11,46]. Thus, the problem of increasing the efficiency of separation and optimizing the methods of separation by the vibration of materials remains topical [6,11]. A mathematical model was presented in a study [14] to increase the speed of passage of bulk raw material through the sieve openings. The obtained results allow for improving the efficiency of the separation process, to regulate the processes, and to follow the influence of the physical and mechanical characteristics of the bulk raw materials on the efficiency and productivity of the separation process.

The morphological characteristics of the particles greatly influence the physical properties of granular/vegetable biomass materials. From Table 2, it can be seen that the order of distribution of plant fragments separated on the sieve classifier was as follows: Sort 2 ˃ Sort 3 ˃ Sort 4 ˃ Sort 1, so it is recommended for the whole nettle plant, chopped to 4 mm, to be used for the separation sieve with mesh sizes between 2.8 and 5.6 mm.

Data obtained experimentally regarding the efficiency of the separation of medicinal herbs chopped in bulk on oscillating plane sieves showed the optimization of the separation coefficient for nettle according to the specific flow rate (Figure 5 and Figure 6). It was observed that the variation in the Ce_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 (R² = 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].

The conducted studies revealed the influence of the vibration frequency and the tilt angle on the sorting efficiency. Thus, with the increase in the vibration frequency and vibration amplitude of the equipment, material separation and sorting speed increase. The number of throws of the material subjected to the sorting process is influenced by the transport, the time the material remains on the surface of the sieve, and the frequency of vibrations. It was found that, when the frequency of the vibrations of the separator and the angle of inclination of the sieve increase, the number of throws of the material on the sieve increases due to the increase in the forced vibrations of the whole equipment [47]. From Table 7, it can be seen that the Ce_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°.

Further research defined the mathematical models for the separation of plant mass taking into account the basic parameters. For a very long time, it is known that different types of statistical laws have been proposed and tested for the distribution of the separation intensity along the length of the sieve for the separation process, especially of cereal seeds [8,48,49]. Some authors [39,48,49,50,51] described the coefficients of the mathematical equations used to describe the process of seed separation along sieves with oscillating motion considering the factors that influence the process (both the characteristics of the seeds and their impurities, as well as the constructive and functional parameters of the separation block). A previous study [18] described a standard method of particle size distribution (PSD) analysis, with the separation being conducted with a standard sieve so that non-uniform particles are separated. An improved image processing method based on computer vision can be successfully applied to the analysis of particle morphology being considered as an alternative for the analysis of the sieve separation process [18,52].

Comparing the values obtained for the efficiency of separation from this work—the index of the average separation coefficient of 0.922 (92.2% separation)—with those from the specialized literature—the values of the indices of 0.8 [17], or the percentages: 91.8% [12], 80% [13], 87.9–94.7% [14], and 76–85.8% [18]—it is estimated that the obtained efficiency is acceptable.

In our study, the maximum average deviation of the average separation coefficient was 5.5% for the polytropic function (Equation (15)), corresponding to the following parameter values: n = 900 rpm and α = 14.7°. The deviation obtained in this study, compared to that presented in study [14], in which the deviation is between 5.3 and 8.1%, can be considered acceptable.

High separation efficiency can also be achieved when the sieve, while vibrating in a non-uniform manner, has a self-cleaning ability over its entire surface and, thus, releases blocked particles. Increasing the frequency of oscillations at constant values of the sieve inclination angle relative to the horizontal increases the average velocity of the material movement on the sieve. In order to ensure a normal functioning of the sieve, the stagnation moments of the material are harmful [1]. In practice, the amplitude of the oscillatory motion is determined by the size of the sieve meshes, as sieves with large meshes require larger amplitudes to achieve a sufficiently large jump to pass the fragment from orifice to orifice [38].

Partial results of experimental research on the separation into size classes of lavender herbs [53], wild thyme [54], nettle [55], and chicory [56] are presented by the authors of this paper in the above-mentioned works.

It is known that medicinal plants are rich in bioactive compounds [57], which are beneficial not only for health. In this sense, the studied plant, nettle, from which plant extracts are obtained [58], has the highest amounts of phenolic compounds (especially 3-caffeoylquinic acid and rutin), in the leaves, as determined in study [59], and sterols and carotenoids in the aerial parts, respectively [33], so an efficient separation of nettle is very important.

The quality of the process of sorting medicinal plants into size classes discussed in this study allows the development of recommendations for optimizing the structural and technological parameters of the separators with the oscillating planar sieve, improving the working parameters of the sieve itself, which, in the future, will significantly increase the efficiency of the separators and natural resources from medicinal plants.

5. Conclusions

Depending on the type of plant, the existing equipment, and the finished product, the sorting of medicinal plants is performed mechanically, according to certain dimensional criteria depending on the intended purpose. Knowing the dimensions of the fragments of chopped medicinal plants is important for identifying the varieties from which the largest amount of bioactive substances can be obtained. Therefore, it is important to optimally adjust the parameters of the sorting stand to obtain the maximum extraction coefficient of the desired sort from each plant.

Using the experimental data obtained from sorting medicinal plants on plane sieves, a regression function of polytropic form was obtained. This function can be used to calculate the average separation coefficient for nettle for specific flows q = 4–10 kg/dm·h, sieve inclination angles α = 12.08–14.7°, and speeds of the drive mechanism n = 900–1000 rpm. The movement of the material on the sieve is upward and downward, more downward with detachment.

The evaluation of the separation process quality was made by calculating the average separation coefficient. The regression function allows for the average separation coefficient for nettle to be calculated with a deviation from the experimentally determined values of maximum 5.5%.

The average separation coefficient increased when the drive mechanism speed increased (kinematic index k increases) and when the sieve inclination angle decreased.

Nettle separation was of superior quality (Ce_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°.

For the separation on plane sieves of nettle, the following recommendations are made: drive mechanism speed n = 1000 rpm; sieve inclination angle α = 12.08°; material specific flow q = 4 kg/dm·h; sieve length L = 1.4 m.

Considering the current trend regarding the use of medicinal plants as phytotherapeutic remedies, the study of the separation process on other mechanical separation equipment but also for other species of medicinal plants, as well as the optimization of the separation process on flat sites of medicinal plants and obtaining an extraction coefficient maximum, using the mathematical relationships and the experimental results from this work can be useful to the designers of machines, the processors of medicinal plants, and implicitly the consumers of medicinal products.