Contributions to the Process of Calibrating Corn Seeds Using a Calibrator with Cylindrical Sieves

Abstract

This paper presents theoretical and experimental research on the process of calibrating corn seeds using a specialized equipment with cylindrical sieves, studying the influence of process parameters and corn seed particularities on the quality of the calibration work. The research took into consideration corn seed characteristics, namely, their dimensions (length, width, and thickness) and weight, determining the influence of process parameters—the contact point between the seed and the cylindrical sieve, the influence of the length of the sieve, and the sieve’s revolution speed on the separation process. The experiments for determining the influence of these parameters on the calibration process were conducted on a calibrating equipment with cylindrical sieves using three different corn hybrids. It was noticed from the experiments that, overall, the revolution speed had the most important effect on the calibration process, with sieve length also affecting the process, but to a lesser degree. Seed calibration efficiency was best at the smallest revolution speed (33 rot/min) and decreased when the revolution speed increased up to 49 rot/min for all corn hybrids tested. The number of calibrated seeds decreased in the second part of the cylindrical sieve. Seed thickness influenced the process, in the respect that seeds smaller than 4.8 mm passed through the first third of the sieve and those with a thickness between 4.8 and 5 mm passed through the other two thirds of the sieve length.

1. Introduction

Corn, or maize (Zea mays L.), the name given by natives in Haiti, meaning “that what sustains life”, is a plant from the group of cereals (fam. Gramineae), cultivated mainly for its seeds that are used in human food, animal feed, and in numerous industrial sectors (corn flour, glucose, dextrose, spirit, glues, starch, biscuits, flakes, edible oil, medicines, etc.) [1,2,3].

Corn is widely cultivated due to its special phytotechnical and biological characteristics. It is a drought-resistant plant, affected by few diseases and pests, that can be cultivated on very different soils and in different climatic conditions; it supports monoculture, leaves the land clean of weeds, and is a good precursor for many plants, even for autumn wheat. It also makes very good use of organic and mineral fertilizers; reacts very strongly to irrigation; can be cultivated in successive crops either for seeds or for green fodder or silage; and has a very high reproduction coefficient due to its characteristics as a unisexual monoecious plant, allowing for the convenient obtaining of very productive hybrids. Corn seeds contain 10–12% protein substances, 68–70% non-nitrogen extractives, and 4.5% fat. Corn protein (zein) is low in lysine and tryptophan. Based on the Opaque 2 gene, however, hybrids rich in these two amino acids were created, making corn, in terms of nutritional value, a super cereal [4,5,6,7].

In Europe, corn was introduced first in Spain after the first expedition made by Christopher Columbus at the end of the 15th century from where it spread on the European continent and then further into Asia and Africa [2,5].

Corn seeds (kernels) consist of three main parts (Figure 1), namely, the pericarp (or hull, representing the harder outer layer of the seed offering protection), the endosperm (the starchy part storing reserve nutrients), and the embryo (that develops into a new plant after sowing) [8,9,10].

Following the threshing process of corn cobs, a mixture is obtained consisting of corn seeds; chaff; dust; and seeds from other crops, including weeds, mechanical impurities, etc. [11].

The preparation of seeds for sowing or consumption in order to answer the increasingly demanding modern technologies includes a complex of operations aiming at removing all impurities and unvaluable seeds [12,13,14].

In the purpose of achieving large and good quality yields, an important role is that of assuring a seed pool from hybrids with the highest genetic characteristics that are adequate for each pedo-climatic area [15,16,17,18].

The purpose of cleaning is to remove the impurities from the seed mass with the help of air currents, sieves, inclined planes, and cylinders. Through cleaning, inorganic impurities (dust, sand, stones) and organic impurities (plant residues, chaff, weed seeds, and broken seeds of the basic crop) are removed. It is a mandatory operation both for seeds intended for sowing (in which case, the purity must be very high) and for those for consumption, where seeds need to meet requirements that are even more strict. Seeds for consumption and industry must also be cleaned because impurities negatively influence further processing [19,20,21,22,23].

Sorting/calibration can be done separately or simultaneously with basic or additional cleaning. Sorted seeds (uniform in size) are sown with greater precision, germinate evenly, and produce more vigorous plants. Sorting is also of particular importance for seeds intended for industrial processing [21,22,24,25,26].

Taking into account these conditions, the cleaning and sorting operations must be performed on specific and high-performance equipment [27,28,29,30].

During cleaning, the corn seeds are separated from the rest of the initial mixture, and during sorting/calibration, they are separated into fractions that differ from each other according to one of the following criteria: size, specific weight, shape, etc. For the calibrated seeds, experience has proven two aspects, namely [11,22],

• technical aspects:

  -

  mature and well-developed seeds have a maximum germinative energy and biological value;

  -

  calibrated seeds ensure an increase in yield per hectare from 500 to 800 kg [22,24,25];

  -

  the maximum evenness of the seeds is an important factor in obtaining a field of plants of uniform size, with all the technological implications arising from this [26,29].

• commercial aspects:

  -

  for the same type of seed on the world market, a differentiated system of payments is practiced, depending on the calibration precision.

Equipment for cleaning and sorting corn seeds, depending on their destination (consumption, sowing, animal feed), use working bodies whose action results in the separation of seeds according to one or more criteria that characterize the physical–mechanical properties of corn seeds, aerodynamic properties, dimensions, specific weight, etc. [29].

Corn seed calibrators by size are of two types: with plane sieves and with cylindrical sieves. Those with plane sieves represent larger constructions due to the large sieve surface and face a series of problems caused by vibrations and sieve clogging. Calibrators with cylindrical sieve are smaller in size; orifice clearing is done during operation, and they are overall easier to use and more precise [30,31].

This paper presents both theoretical and experimental research on the process of calibrating corn seeds from three different corn hybrids using a calibrator with cylindrical sieves, taking into consideration seed particularities, seed movement in the cylindrical sieve, the revolution speed of the sieve, and the length of the sieve.

2. Materials and Methods

2.1. Properties Affecting the Separation/Calibration Process

In general, the separation of a mixture into its component parts is possible if they have properties (characteristics) that distinguish (differentiate) them.

In particular, seed cleaning and sorting are based on those properties that most differentiate the components of the seed mixture, and which are the basis of the appropriate separation methods. In order to specify the separation methods and the respective working bodies, the properties by which the components of a seed mixture differ the most must be specified. These characteristics are found among the physical–mechanical properties of the seeds that vary widely depending on crop, variety, moisture, etc.

The shape and dimensions of the seeds are characterized by the ratio between length, width, and thickness; by the number of planes of symmetry; and by the absolute value of the dimensions, which are of a great variety. Corn seeds are part of the flat-shaped seeds, but their shape is complicated by the presence of ribs, grooves, etc.

Physical purity—represents the percentage content of pure seed in relation to the total mass of the analyzed sample and by extension of the lot it represents.

Mass of 1000 seeds—gives indications on the size of the seeds and is of particular importance for agricultural practice because the mass of 1000 seeds is taken into account when calculating the amount of seeds per hectare. It varies from species to species and within the species from variety to variety or from hybrid to hybrid.

Hectoliter mass—represents the mass of one hectoliter of seeds. The hectoliter mass is influenced by the moisture content of the seeds, the content of impurities and their nature, and on the nature of the basic product characterized by:

-

the specific mass of the seeds;

-

seeds coating;

-

pericarp thickness (seeds coated with pericarp have smaller hectoliter mass due to a lower unit weight—for corn, the hectoliter mass is between 72 and 77 kg).

Unit weight—represents the weight of the unit volume of the seed material; it varies within wide limits and depends on the chemical composition and anatomical structure of the seeds, the degree of maturity, moisture, and the amount of air contained in the seed. The unit weight values of corn seeds are between 1.3 and 1.4 (gf/cm²) [32].

Seed moisture—for the purpose of good preservation, the seeds must have a water content below a critical level. Moisture is determined directly by oven drying and indirectly with the electronic moisture meter.

Porosity—represents the totality of the spaces occupied by air between the solid parts of the seed mass and is expressed by the percentage ratio between the volume of the inter-granular space and the total volume of the seed mass.

Flowability–natural slope angle—represents the ability of seeds and seed mass to flow when dropped on an inclined surface or in the open air. For corn seeds, the natural slope angle has values between 30 and 40 degrees, and the flow angle has values between 19 and 30 degrees [22,29].

Aerodynamic properties—take into account the different resistances to movement of the seeds in an air current. The aerodynamic properties can be characterized by the floating speed of the seeds. The floating speed depends on the weight, surface condition, and geometric shape of the particles that form the components of the seed mixture.

Elastic properties—seeds have the property of returning to their original shape after deformation, a property called elasticity. The elasticity is appreciated by the collision restitution coefficient (K) equal to the ratio of the speeds after the collision (V₂) and before the collision (V₁), in a centric collision.

$$K=\frac{V_2}{V_1}$$

(1)

This coefficient can be determined experimentally by letting the seeds fall (with no initial velocity) from a height H onto a hard surface and measuring the height h of lift after impact. If air resistance is neglected, the following relation applies:

$$K=\sqrt{\frac{h}{H}}$$

(2)

Self-sorting—is the ability of the seed mass to automatically separate into size categories, both during transport and during storage or handling in silos. Differentiation is made according to shape, size, density, surface condition, and floating speed. Size and unit weight are essential. The seeds with high unit weight (therefore heavier) occupy the area in the center and at the base. Those with reduced mass settle on the surface and on the periphery of the seed mass.

2.2. Choice of Corn Hybrids to Be Studied

Corn seeds are attached to the rachis of the cob, which differs from hybrid to hybrid; they have different masses, different colors of the seeds and rachis, different shapes of the seeds depending on the place they occupy on the rachis, etc. In order to conduct the experiments, three corn hybrids cultivated in Romania were used for experiments as follows:

SUM 96521, SAATEN UNION—Germany—the position of the cobs on the plant is medium to high with one or two cobs per plant. They ripen late and have a large production capacity. In normal non-irrigated crop conditions, the average seed production is between 8100 and 11,200 kg/ha, and between 12,200 and 13,850 kg/ha when irrigated. It is not resistant to drought. The cobs have dentiform seeds rich in protein, starch, and fat; they are large, have a red rachis and seeds, and are easy to detach from the rachis.

LIMAGRAIN GENETICS, LG 2244—France—The position of the cobs on the plant is medium, with single cob per plant. It has a medium vegetation period and a good production capacity. In normal crop conditions, the average seed production in non-irrigated conditions is between 6200 and 8700 kg/ha, and between 9200 and 11,300 kg/ha in irrigated conditions. It shows very good resistance to low temperatures in the first part of the vegetation period. It is not resistant to drought and heat. The cobs have indurata-type seeds, are medium in size, and have a white rachis; moreover, the seeds are easy to detach.

KALISTA, ROMAN—VERNEUIL—France—following the tests carried out in the pedo-climatic conditions of Romania, the hybrid easily adapted to the soil and environmental conditions. It belongs to the category of semi-early hybrids with a single cob per plant. The position of the cob on the plant is low; the cobs have indurata-type seeds, are medium in size, and have a white rachis. Moreover, the seeds are easy to detach. It has good production capacity. Under normal growing conditions, the average seed production in non-irrigated conditions is between 7200 and 10,300 kg/ha, and between 10,200 and 12,700 kg/ha under irrigated conditions. It shows a very good resistance to low temperatures in the first part of the vegetation period, drought, and heat.

These hybrids were chosen because they represent the two types of corn varieties (dent and indurata type), and they are cultivated both for human consumption as well as for animal feed. The main characteristics of the hybrids studied are shown in

Table 1. The main characteristics of the hybrids analyzed.

No.	Hybrid/Sample	Total Mass (Seeds + Rachis) Mt (kg)	Total No. of Seeds/ Mass of Seeds Ms (kg)	η = Ms/Mt (%)	No. of Rows/No. of Seeds per Row	Seed Moisture/ Rachis Moisture (%)
1	SUM 96521/S1	0.290	601/0.262	90.34	14/44	8.46/8.31
2	SUM 96521/S2	0.343	722/0.311	90.67	16/46	8.31/8.45
3	SUM 96521/S3	0.284	509/0.268	91.54	12/43	8.78/8.22
4	SUM 96521/S4	0.252	531/0.260	92.06	12/45	8.74/8.17
5	SUM 96521/S5	0.322	668/0.232	90.05	16/42	8.25/8.16
6	LG 2244/S1	0.256	514/0.274	93.75	14/37	8.24/6.04
7	LG 2244/S2	0.200	439/0.240	94.45	12/37	3.78/5.83
8	LG 2244/S3	0.212	617/0.189	91.98	16/39	4.08/6.26
9	LG 2244/S4	0.204	618/0.195	93.62	16/39	7.20/6.00
10	LG 2244/S5	0.221	538/0.191	92.76	14/39	5.88/6.23
11	KALISTA/S1	0.226	527/0.211	93.36	14/38	6.01/5.39
12	KALISTA/S2	0.217	515/0.221	92.62	14/37	5.79/5.68
13	KALISTA/S3	0.236	618/0.221	93.64	16/39	6.17/5.33
14	KALISTA/S4	0.234	555/0.217	92.73	14/40	6.00/5.73
15	KALISTA/S5	0.236	634/0.217	91.74	16/40	6.29/5.85

.

2.3. Seed Sorting Using a Calibrator with Cylindrical Sieves

Seed sorting can be achieved using equipment with plane or cylindrical sieves. Plane sieves perform separation by width and sometimes thickness (if the orifices are elongated) and they rely on vibration and an inclination angle to perform the separation. Their main shortcomings are represented by large equipment dimension; maintenance problems caused by vibrations; orifice clogging; and the seeds tending to gather in the center of the sieves, causing deformations due to weight.

Cylindrical sieves present a series of advantages compared to plane sieves, including smaller gauge, simpler operation, lack of vibrations, more efficient separation in the sense that centrifugal force is added to the weight of the seeds, orifice unclogging systems of the seeds that could not pass through them that are much simpler and more efficient than the one from plane sieves, etc. The main shortcoming of these sieves is that the surface of the sieve is not fully used in the separation process.

In order to find the most effective solutions in order to increase their efficiency, it is necessary to study the kinematics of the cylindrical sieves and the process of separating the seeds through their orifices.

The tests regarding the calibration operation were performed on the CCM 2630 Modulated Cylindrical Calibrator (Figure 2), designed and manufactured at INMA Bucharest.

When establishing the technical–constructive solutions, the realization of high-performance equipment is characterized by processing capacity at the level of current requirements, specific consumption of energy and reduced materials, a high precision of the separation of seeds according to size (width and thickness), access to the active organs, maintenance, and easy operation.

A module of the cylindrical calibrator consists of the following main parts: frame, calibration cylinder, sieve, drive support, feeding inlet, feeding funnel, exhaust funnel, doors, covers, protective guards, etc. The main technical characteristics of the sorter are shown in

Table 2. Main technical characteristics of the plant sorter.

Characteristic	Unit	Value
Capacity (for one module)	t/h	1.5–2.5
Calibration precision	%	95
Calibration cylinder (sieve) diameter	mm	630
Calibration cylinder revolution speed	rot/min	30–50
Calibration sieve type	-	round or elongated
Orifice size	mm	Φ7, Φ8, Φ9, Φ10, 5 × 25, 5.6 × 26, 6.3 × 25
Max no of sieves per module	-	3
Active sieve surface	m2	1.18
Rotative cleaner type	-	with rubber pallets
Fixed cleaner type	-	with brushes
Overall dimensions
- length	mm	3535
- width	mm	1010
- height	mm	1730
Installed power	kW	2.2

.

Operation of the Cylindrical Calibrator

The corn seeds are fed through the feeding inlet and inserted into the feeding funnel. By means of the vane group that has the vanes mounted at an angle to ensure a good feeding of the sieves, the seeds are introduced on their surface. The calibration cylinder can be equipped, depending on the technological requirements, with the same type of cylindrical sieves or with cylindrical sieves with different orifice sizes, with those with smaller sizes being mounted towards the product supply. The sieves receive the rotation movement from the planetary gear motor. During the work process, the seeds that are smaller than the orifices will pass through them, and those that will remain as refuse will pass towards the second sieve (if the calibrator is equipped with cylindrical sieves of different sizes). Part of the remaining seeds will pass through the orifices of the second sieve if they have a size corresponding to the size at which the sorting is done (smaller than the orifices), and those that will remain as refuse will pass to the third sieve. On this sieve, the seeds that have the size corresponding to the size at which the sorting is done will pass through the orifices, and those that will remain as refuse will be evacuated through the evacuation funnel. In order to be able to calibrate the corn seeds according to the number of fractions requested (this also being conditioned by the results obtained from the dimensional analysis of the sample subjected to analysis from the product mass to be processed), several such calibrators are needed, which can work in cascade or of a single calibrator, changing the cylindrical sieves successively, as needed. The revolution speed of the cylindrical sieves is regulated by using double chain wheels, interchangeably, obtaining the optimal transmission ratio.

The evacuation of the sieved material is done laterally for each circular sieve separately, and the refuse is evacuated axially on the right end, with the supply on the left. In the case of clogging of the orifices with corn seeds whose size is approximately equal to that of the orifices, unclogging is done by using the rotary cleaner and a fixed brush located inside the cylindrical sieve.

In order to follow as easily as possible and for the results to be as conclusive as possible, the corn seeds were dyed in different colors as follows:

-

SUM 96521 seeds—green;

-

LG 2244 seeds—red;

-

Kalista seeds—black.

By using all sprockets, 11 corresponding revolution speeds were obtained. For each speed, the seeds were separated for each type of hybrid separately. The fractions that passed through the sieve (sifted) were collected in special trays for each sieve segment (about 220 mm active length for each one).

All seeds that passed through the orifices of each segment of the sieve were evacuated through the funnels numbered from 1 to 9 (Figure 3a), starting from the first segment, and were then collected in the collection trays. The fraction that did not pass through the sieve (refuse) was collected separately in a tray at the opposite end from where the material was fed into the equipment. The tray corresponding to the funnel where the refuse was evacuated was numbered with the number 10 (Figure 3b). All seeds collected into each tray were numbered.

2.4. Theoretical Notions for Corn Seed Calibration on Cylindrical Sieves

For tests, the following notations were made: “a” seed length, “b” seed width, “c” seeds thickness, (Figure 4), “m” mass of one seed, “m_i” mass of seeds on one ring (one seed for each row), and “m_r” mass of seeds on one row, and then each seed on one row was measured for corn cobs of each hybrid analyzed. Corn seed samples were measured using eXpert 470150 electronic callipers manufactured by Facom—France with measuring range between 0 and 200 mm, 0.01 mm resolution, and 0.03 precision. Corn seed sample weighing was done using an analytical ATX224 type balance manufactured by Shimadzu—Japan with a measurement error of 10⁻⁴ g. For each cob, histograms and distribution curves by size classes for length, width, and thickness were drawn using Microsoft Excel 2021 software.

2.4.1. Kinematic Regimes of Cylindrical Sieves

A seed, or any material particle, placed on the inner surface of a horizontal cylinder, which rotates at a uniform speed, can acquire one of two types of movements, fundamentally distinct, depending on certain conditions.

The difference between these types of movements is determined by the absence or presence of the relative phase of repose of the particle in relation to the sieve in the general cycle of its movement on the inner surface of the cylinder.

For a better understanding of the phases of seed movement, it was agreed [22,29] to name the movements as such:

-

type 1 movement—seed movement without the phase of relative repose;

-

type 2 movement—seed movement with the phase of relative repose.

In order to understand the particularities of type 2 movement, which is characteristic for the calibration on cylindrical sieves, it is necessary to follow the movement of a seed on the compact and smooth surface of a cylinder in stable motion. In this case, the seed will pass through three variable phases:

• relative repose (on the surface of the cylinder);
• relative movement (sliding on the surface of the cylinder);
• free movement (detached from the surface of the cylinder).

2.4.2. Phase of Relative Repose

Considering this, at the initial moment, t = t₀ = 0, the seed is at point M₀ of the surface (Figure 5) and has the same movement as the surface; in other words, it is in the phase of relative repose. An analysis is conducted to see under which conditions the particle is at relative repose if the cylinder; after a certain time interval, it rotates with the angle α = ωt, and without the seed slipping, it moves with the surface from position M₀ to position M.

The seed will remain in relative repose if the forces acting of it will be in balance.

The following forces act on the seed:

• the force of gravity, G = mg, directed downwards;
• reaction N of the surface, normal in point M and directed towards the centre O;
• the friction force F = f_N, directed on the tangent in the direction of revolution;
• the inertial force in the transport movement mRω², directed in the direction of the radius outwards.

A mobile system of coordinate axes ξOη is chosen, with its center in O, rotating with the cylinder with the angular speed ω = const.

The forces mentioned above are projected on the coordinate axes. For the seed to be at relative repose, the sum of the projections on the coordinate axes must be equal to zero.

$$mR{\omega }^2-N+mgcos\omega t=0$$

(3)

$$F-mgsin\omega t=0$$

(4)

From relation (3), the normal is determined:

$$N=m\left(R{\omega }^2+g cos\omega t\right)=mg\left(\frac{R{\omega }^2}{g}+cos\omega t\right)$$

(5)

Relation (4) includes the friction force F, which can have any value that is not higher than the limit value F_lim = fN, where f is the friction coefficient that will be denoted by tgφ (φ being the friction angle). The maximum value of the friction force is limited by the friction coefficient and the normal force, which is equal to the weight of the seed.

Therefore, relation (4) will be written as

$$fN-mgsin\omega t\ge 0$$

(6)

The inequality states that the maximum force of friction, fN, must be greater than or equal to the component of the gravitational force acting tangentially to the circular path of the seed, mgsin(ωt), in order for the seed to remain in circular motion without slipping. This condition ensures that the object remains in contact with the surface and does not slide or slip. Coefficient f is calculated depending on the material of the sieve, the revolution speed, the inclination angle, and the characteristics of the seeds.

Or, taking note of relation (5), will be

$$tg\phi \left(r{\omega }^2+g cos \omega t\right)\ge g sin \omega t$$

(7)

After some simple transformations, the relation becomes

$$k sin \phi \ge sin \left(\omega t-\phi \right)$$

(8)

where $k=\frac{r{\omega }^2}{g}$ is the index characterizing the movement regime of the cylinder.

Relations (5) and (8) determine the conditions that ensure the phase of relative repose of the seed on the inner surface of the moving cylinder. For this, it is necessary that the reaction N of the surface be a positive quantity, namely,

$$N=mg (k+cos \omega t)>0$$

(9)

Only in these conditions will the seed be found on the surface of the cylinder. Relation (8) determines the condition for the seed, located on the surface of the sieve, not to slide off it, meaning that it has an identical movement to that of the sieve.

The same relation contains a variable quantity, namely, time t; the other quantities k, r and φ, for a given cylinder and seed, are constant. Under these conditions, the left side of relation (8) is constant and the right side increases with time; and at a given moment when t = t₁, both sides become equal.

For t > t₁, the condition imposed by this inequality is violated, in other words, the phase of relative repose ends and the phase of relative movement begins, translated in the sliding of the seed on the surface of the sieve.

Thus, the limit position of the seed in the phase of relative repose will be determined by relation (10) having the sign of equality.

$$sin\left({\alpha }_1-\phi \right)=k sin \phi$$

(10)

where ${\alpha }_1=\omega t_1$ is the angle where it is possible to move along with the cylinder surface without sliding.

The solution of relation (10) with real significance is

$${\alpha }_1=\phi +arc sin\left(k sin \phi \right)$$

(11)

In relation (10), sin (α₁ − φ) cannot have a value that surpasses the unit, namely, the right part of this relation

$$k sin \phi \le 1$$

(12)

Therefore, the limit value of index k will be

$$k_{lim}=\frac{1}{sin\phi }=\frac{\sqrt{1+t{g}^2\phi }}{tg\phi }=\frac{\sqrt{1+f^2}}{f}=\sqrt{1+\frac{1}{f^2}}$$

(13)

For the regime determined by the index k = k_lim, relation (10) becomes

$$sin\left({\alpha }_{1}lim-\phi \right)=1$$

(14)

from which the limit value of the angle results α₁:

$${\alpha }_{1lim}=\frac{\pi }{2}+\phi$$

(15)

Given that the friction angle φ is always smaller than $\frac{\pi }{2}$, it results that α_1lim < π.

In other words, for any regime, the particle will not remain in the relative repose phase at the end of the M₀M arc, equal to the semicircle, meaning that the seed will never be lifted without sliding to the highest point of the surface, which coincides with the upper end of the vertical diameter.

2.4.3. Phase of Free Movement

At the moment corresponding to the start of sliding, the seed will remain on the surface of the cylinder. Next, the movement of the seed is analyzed in the moments that follow the beginning of the slide (Figure 6).

The placement height of the point M where the particle detaches from the cylinder surface takes place, which is where, therefore, the particle’s free movement phase begins; in this case, the seed, having the linear velocity V₀ = Rω, directed the tangent to the circle of radius R, begins to move in a free movement, like a body thrown at an angle π/2 − θ to the horizontal.

At the end of the free movement phase, the particle hits the surface of the cylinder at point P, whose position is determined by the angle γ to the horizontal. To determine the coordinates of point P, the equation of the parabola and the circle are simultaneously solved.

The coordinates of the center of the circle in the XMY coordinate system are

$$x_c=R sin \theta$$

(16)

$$y_c=-R cos \theta$$

(17)

After calculations, the relations represent the coordinates of the contact point P, where the seed meets the surface of the cylinder at the end of the free movement, which are

$$X_p=4R sin\theta co{s}^2\theta$$

(18)

$$Y_p=-4R si{n}^2\theta cos\theta$$

(19)

The particle detached from the surface of the cylinder at a height corresponding to the angle at the center π/2 − θ reaches the surface of the cylinder again at the height determined by the value of the angle π − γ. The angle θ is the angle that the particle makes when detaching from the surface of the cylinder with the horizontal. The value of the angle π − γ is measured from the horizontal diameter in the opposite direction of the cylinder rotation. Given that the diameter of the cylindrical sieve is 630 mm, therefore R = 315 mm, and for values of θ between 45° and 65°, the entry data shown in

Table 3. The coordinates of the contact point for different values of the angle θ.

Crt. No	θ	Xp	Yp	Crt. No.	θ	Xp	Yp	Crt. No.	θ	Xp	Yp
1	45	0.445	−0.445	8	52	0.376	−0.482	15	59	0.286	−0.477
2	46	0.437	−0.452	9	53	0.364	−0.484	16	60	0.273	−0.473
3	47	0.428	−0.460	10	54	0.352	−0.485	17	61	0.259	−0.467
4	48	0.419	−0.466	11	55	0.339	−0.485	18	62	0.245	−0.461
5	48	0.409	−0.471	12	56	0.327	−0.484	19	63	0.232	−0.454
6	50	0.399	−0.475	13	57	0.313	−0.483	20	64	0.218	−0.446
7	51	0.388	−0.479	14	58	0.300	−0.480	21	65	0.204	−0.437

were obtained.

The two phases of movement and the contact point of seeds with the cylindrical sieve surface present a significant importance in determining the revolution speed needed to be achieved for the cylindrical sieve and affect the calibration process in terms of duration and quality of calibration. The seed layer is in a mobile equilibrium; its central part is fixed, and the rest performs a complex movement around the central axis. This movement occurs due to the friction that arises between the seed layer and the surface with orifices of the sieve. The linear speed of the sieve’s surface exceeds the speed of the first row of seeds in the layer that is in direct contact with the surface with orifices; the orifices pass under the layer and capture the short seeds. The seeds that have entered in the orifices are carried by them, being removed from the layer. The long and short seeds left in the layer will continue to move. Therefore, the short seeds, which have reached the orifices, go into a state of relative repose, and the other seeds, which remain in the layer, maintain their movement. As the layer moves along the cylindrical sieve, the seeds mix, come in the bottom row in direct contact with the surface with the orifices, and create the possibility to settle in the orifices.

2.5. Main Objectives of the Experiments

The methodology for determining the quality indices of the calibration process is as follows:

-

defining the quality indices;

-

experimental setup (setting the controlled experiments using the cylindrical calibrator described above, setting the number of experiments—3 repetitions for each hybrid used);

-

data collection (data were collected for various parameters during experiments);

-

Data analysis and calculation (the data obtained were analyzed, and calculations were made in order to obtain the results);

-

Results analysis (results were analyzed and interpreted).

Experiments conducted for the three corn hybrids aimed at the following:

-

determining the contact point of the seeds with the cylindrical sieve—using a cylindrical sieve with a diameter of 630 mm; the angle of inclination of the inclined plane was varied so that θ took values between 45 and 60 degrees when the difference between the tangential and peripheral speed was as large as possible.

-

the influence of the length of the calibration cylinder as a function of speed—11 distinct revolutions were tested, obtained by using several spare chain wheels, and the seeds were introduced into the calibration cylinder and separated using the cylindrical sieve with 5 mm × 25 mm elongated orifices. The fractions that passed through the sieve were evacuated through the 9 funnels (fitted on the calibrating equipment only for experiments; in the case of use in production, three funnels were joined and collected the material from one segment of the sieve each) numbered from 1 to 9 and collected in special trays for each sieve segment of approximately 220 mm active length. The discharge funnel at the end of the calibration cylinder was marked with no. 10, and it collected the refusal from the calibration process. The results were recorded and processed for each individual hybrid.

-

the influence of speed on the separation process—in the same working conditions with 11 revolution speeds, the seeds evacuated through the 10 funnels were collected in trays; the seeds in each tray were counted, for each rotation separately, and the results obtained were recorded.

To determine the specific distribution curves, for each individual hybrid, we determined the following:

-

number of classes, n [-];

-

class interval, λ, [-];

-

T_s, the total number of seeds of a sample (the sum of the seeds of all cobs of a hybrid) [-];

-

the average size of a dimension, M_c = S_nl/T_s, [mm], where S_nl is the sum of all dimensions;

-

root mean square deviation for thickness σ_c, [-].

3. Results

The seeds of all hybrids (by summing the number of seeds of all cobs in a hybrid) were divided into size classes with a class interval of 0.1 mm, and the number of seeds in each thickness class was determined, obtaining the frequency of repetitions for each class. The results are presented in

Table 4. The distribution by thickness of the seeds for the analyzed hybrids.

Crt. No.	Seed Thickness	SUM 96521	LG 2244	KALISTA	Seed Thickness	SUM 96521	LG 2244	KALISTA
		No. of Seeds				No. of Seeds
01	3.3	-	-	-	6.1	14	91	48
02	3.4	-	-	-	6.2	38	91	63
03	3.5	4	-	-	6.3	-	65	35
04	3.6	-	-	-	6.4	-	39	29
05	3.7	42	-	-	6.5	28	38	38
06	3.8	14	-	-	6.6	14	24	25
07	3.9	28	6	-	6.7	35	22	29
08	4	98	13	-	6.8	32	48	18
09	4.1	116	-	-	6.9	28	26	26
10	4.2	158	17	9	7	14	24	-
11	4.3	224	52	21	7.1	34	22	17
12	4.4	182	65	44	7.2	-	-	21
13	4.5	196	91	87	7.3	32	23	18
14	4.6	420	99	126	7.4	29	42	-
15	4.7	308	208	246	7.5	22	-	15
16	4.8	336	299	601	7.6	14	22	2
17	4.9	210	287	402	7.7	-	13	-
18	5	218	298	303	7.8	8	-	-
19	5.1	205	186	230	7.9	-	-	-
20	5.2	126	195	219	8	-	-	-
21	5.3	130	143	151	8.1	-	11	-
22	5.4	112	117	127	8.2	-	-	-
23	5.5	84	130	78	8.3	-	-	-
24	5.6	28	78	74	8.4	-	-	-
25	5.7	42	82	66	8.5	-	-	-
26	5.8	14	89	73	8.6	-	-	-
27	5.9	28	65	71	8.7	-	3	-
28	6	39	91	65

.

The values of the parameters for determining the variation curves for each individual hybrid are presented in

Table 5. Parameter values necessary for variation curves.

Parameter	Corn Hybrid
	SUM 96521	LG 2244	KALISTA
λ	0.1	0.1	0.1
m	44	49	35
N	3668	3324	3377
Mc	5.076	5.017	4.948
σc	0.8351	0.8189	0.7945

.

The results on the distribution of separated seeds on the cylindrical sieve with 5 mm × 25 mm elongated orifices at different speeds are presented in

Table 6. Distribution of separated seeds on the 5.5 mm × 25 mm cylindrical sieve.

Hybrid	Total No of Seeds	n = 33		n = 35		n = 36		n = 38		n = 41		n = 43
		T	R	T	R	T	R	T	R	T	R	T	R
SUM 96521	2355	2087	268	279	276	2071	284	2066	289	2061	294	2059	296
LG 2244	1757	1711	46	1703	54	1698	59	1693	64	1683	74	1678	77
KALISTA	2190	2011	179	2003	187	1996	194	1988	203	1981	209	1976	214
Hybrid	Total No of Seeds	n = 44		n = 46		n = 47		n = 48		n = 49
		T	R	T	R	T	T	T	R	T	R
SUM 96521	2355	2058	297	2053	302	2052	2041	2048	307	2041	314
LG 2244	1757	1676	79	1673	82	1672	1661	1668	87	1661	94
KALISTA	2190	1974	216	1969	221	1966	1954	1960	230	1954	236

n—revolution speed, [rot/min]; T—seeds passed through the sieve (sieved), [-]; R—seeds retained by the sieve (refuse), [-].

and Figure 7.

From Figure 7, it can be seen that the number of seeds that passed through the cylindrical sieve with 5 mm × 25 mm orifices had a linear tendency to decrease when increasing the revolution speed of the sieve, translating into a larger number of seeds that exited at the end of the equipment, without being fit into one of the calibration classes.

Using the data in Table 4, the distribution curves of the distribution by thickness of the seeds of all hybrids were drawn up, as shown in Figure 8.

From the analysis of the thickness distribution curves in Figure 8, it can be seen that for SUM 96521 and LG 224 corn varieties, the values were not uniform, but for Kalista, the values were uniform.

The other characteristics determined were as follows:

-

the participation of class i in the sample; p_i = (n_i/T_s) × 100;

-

average i class size; c_i = c_min + λ(2i − 1)/2;

-

the distribution curve of the seeds y, which is given by the relation

$$y=\frac{1}{{\sigma }_d\sqrt{2\pi }}{e}^{-\frac{\left(b-M_d\right)}{2{\sigma }_d^2}}$$

(20)

-

α_i, deviation from the average size, (α_i = l − M_d), presented synthetically in

Table 7. The values of the size characteristics of the distribution curve for the SUM 96521 hybrid.

Crt. No.	b	αi	ci	pi	y
01	3.5	−1.576	3.55	0.01	0.080
02	3.6	−1.476	3.65	0	0.099
03	3.7	−1.376	3.75	1.14	0.122
04	3.8	−1.276	3.85	0.38	0.148
05	3.9	−1.176	3.95	0.76	0.177
……	……	……	……	…….	…….
40	7.4	2.324	7.45	0.79	0.009
41	7.5	2.424	7.55	0.60	0.007
42	7.6	2.524	7.65	0.38	0.005
43	7.7	2.624	7.75	0	0.003
44	7.8	2.724	7.85	0.21	0.002

,

Table 8. The values of the size characteristics of the distribution curve for the LG 2244 hybrid.

Crt. No.	b	α1	c1	p1	y
01	3.9	−1.117	3.95	0.18	0.192
02	4.0	−1.017	4.05	0.39	0.225
03	4.1	−0.917	4.15	0	0.260
04	4.2	−0.817	4.25	0.51	0.296
05	4.3	−0.717	4.35	1.56	0.331
……	…….	……	……	……	…….
45	8.3	3.283	8.35	0	0.00015
46	8.4	3.383	8.45	0	0.0001
47	8.5	3.483	8.55	0	0.000058
48	8.6	3.583	8.65	0	0.000034
49	8.7	3.683	8.75	0.09	0.000020

and

Table 9. The values of the size characteristics of the distribution curve for the Kalista hybrid.

Crt. No.	b	αi	ci	pi	y
01	4.2	−0.748	4.25	0.26	0.322
02	4.3	−0.648	4.35	0.62	0.359
03	4.4	−0.548	4.45	1.30	0.396
04	4.5	−0.448	4.55	2.57	0.427
05	4.6	−0.348	4.65	3.73	0.456
……	……	……	……	……	……
31	7.2	2.252	7.25	0.62	0.009
32	7.3	2.352	7.35	0.53	0.006
33	7.4	2.452	7.45	-	0.004
34	7.5	2.552	7.55	0.44	0.002
35	7.6	2.652	7.65	0.059	0.0018

(b represents the width of the seeds).

The data obtained, entered in the relation of y, gave us the specific distribution curves for each type of hybrid, being represented in Figure 9, Figure 10 and Figure 11.

Analyzing the specific distribution curves, we observed that the hybrid whose specific distribution curve by thicknesses was closest to the normal distribution curve was SUM 96521.

The graphs in Figure 9, Figure 10 and Figure 11 help to determine the participation of fractions in the mass of hybrids, namely,

-

seed size fractions c ∈ [M_c − σ_c, M_c + σ_c];

-

seed size fractions c ∈ [M_c − 2σ_c, M_c + 2σ_c];

-

seed size fractions c ∈ [M_c − 3σ_c, M_c + 3σ_c].

The values obtained are shown in

Table 10. Participation of fractions in hybrids: SUM 96521, LG 2244, and Kalista.

Hybrid	(Mc − σ, Mc + σ) [%]	(Mc − 2σ, Mc + 2σ) [%]	(Mc − 3σ, Mc + 3σ) [%]
SUM 96521	77.29	95.17	99.61
LG 2244	74.12	92.08	98.76
Kalista	79.83	93.81	97.83

.

Using the data in Table 3 for coordinates X_p and Y_p, the diagram for the contact point of seeds with the cylindrical sieve was obtained, as shown in Figure 12.

The diagram obtained in X_p and Y_p coordinates represents an arc of a circle inscribed in quadrant 4. From Figure 12 and analyzing the data in Table 3, it can be observed that as the angle θ took values between 50 and 60 degrees, X_p and Y_p decreased, with the contact point approaching the inferior point of the cylindrical sieve, the point of relative repose, with these points being the best points for the seeds to pass through the orifices of the cylindrical sieve.

Figure 13 shows the influence of the revolution speed on the calibration of corn seeds on the sieve with 5 mm × 25 mm orifices.

From Figure 14, it can be seen that the number of separated seeds was the highest for the smallest revolution speed (33 rot/min) and decreased when increasing the revolution speed up to 49 rot/min; the only exception was observed for the LG2244 hybrid, with this being explained by the distribution curve for this hybrid where it can be seen that the number of these seeds was equal for various classes of sizes. Also from Figure 14, it can be observed that when the revolution speed was higher than 40 rot/min, the decrease in seed separation was lower.

The speed of the cylindrical sieve with constant speed can be increased (therefore in terms of its productivity) without the appearance of relative rest, by using special devices: internal cylindrical screens, internal inclined planes, internal cylindrical screens with brushes, etc. Using such solutions, the speed can be increased 2–3 times compared to the speed of the simple cylindrical sieve, increasing its productivity accordingly.

During operation, the seed mixture is not distributed uniformly over its entire inner surface, but in a layer of uneven thickness having in the cross-section approximately the shape of a biconvex lens, which extends over an angle to the center of about 90–100°, so the contact of the seeds with the sieve is made on a small surface of it (about ¼). The working surface can be increased by using the same devices presented above.

Figure 14 and Figure 15 show the influence of sieve length on the calibration process for the lowest and highest revolution speeds.

From Figure 14 and Figure 15, it can be seen that for both revolution speeds, the highest part of separated seeds was found on the first third of the cylindrical sieve length. In the remaining two thirds, with small fluctuations, the separation was uniform. Measurements showed that in the first third of the sieve’s length, the seeds were separated that had a thickness up to 4.8 mm, and in the other two thirds of the sieve’s length, the seeds with thicknesses between 4.8 and 5 mm were separated.

4. Discussion

Following the measurements made on the seeds from the hybrids subjected to dimensional analysis, the following dimensions were obtained:

- for SUM 96521:	a = 8.1–14.8 mm; b = 6.7–11.8 mm; c = 3.5–7.8 mm;
- for LG 2244:	a = 5.5–13.1 mm; b = 6.2–10.3 mm; c = 3.9–8.7 mm;
- for Kalista:	a = 6.2–11.8 mm; b = 5.1–10.1 mm; c = 4.2–7.6 mm.

The hybrid with the largest mass was SUM 96521, having the average mass of 0.304 kg.

All analyzed hybrids had yields (M_s/M_t) over 90%, the highest being in the hybrid LG 2244 of 94.45%. The hybrid with the most uniform seed sizes was Kalista.

For the dent-type corn hybrid, the variation between the maximum and minimum sizes of the seeds was greater compared to those of the indurata-type corn hybrids.

Considering the advantages that the cylindrical sieve with uniform rotation has over the plane sieves with rectilinear–alternative oscillatory motion (higher compactness of the separation system, smaller gauge, easier balancing of inertial forces, simpler transmissions, simpler and more effective unclogging of orifices, more favorable conditions for seeds to pass through the orifices, the possibility of increasing the efficiency of seed separation) as well as the fact that the productivity of the cylindrical sieve can be increased by using special devices mounted inside the sieve, it is justified that this sieve be used more in the construction of cleaning and calibration equipment, in the construction of combines, or as a stand-alone machine.

The longer the length of the calibration cylinder, the easier the seeds whose thickness is close to the nominal size of the oblong hole can be separated.

When determining the point of contact of the seeds with the cylindrical sieve, the following were found: the seed detached from the surface of the cylinder, at a height corresponding to the angle at the center π/2 − θ, reached the surface of the cylinder again, at the height determined by the value of the angle π − γ.

Following the measurements, it was observed that for revolution speeds close in value, the number of separated seeds was approximately the same. Analyzing the influence, it can be seen that the best results were obtained for the lowest revolution speed (33 rot/min); good values were obtained for intermediate speeds; but when exceeding 38–40 rot/min, the number of separated seeds decreased and became uniform up to the highest revolution speed (49 rot/min), meaning that increased revolution speeds were not recommended.

The results obtained were consistent with other studies in the field, showing that seed shape and the three dimensions, namely, length, width, and thickness, greatly influenced the process, but this also highlights the necessity to have a good calibration process and to obtain a uniform mass of seed and, subsequently, a good germination or further processing [30,33,34].

5. Conclusions

The present study showed that there are a series of theoretical and experimental challenges in the process of calibrating corn seeds, given by the characteristics of the seeds and by the need to obtain a uniform seed mass. Although the process was investigated by many studies, new corn hybrids that have different characteristics are released constantly, and therefore these aspects need to be considered, as well as new requirements in terms of seed mass uniformity. Considering that the current trend for establishing crops is precision sowing and that farmers are constantly trying to improve production, the present work can help corn seed suppliers and farmers achieve a greater level of seed uniformity on various classes, leading to a better germination and crop uniformity and therefore to better yields and quality of corn.