Cleaning process simulation of the dielectric sorting device

The article presents theoretical studies to substantiate some parameters of the dielectric sorting device of alfalfa seeds, in particular: the width of the outlet slot of the hopper, the step and depth of the metering groove, the length of the limiter and the angle of its installation. When developing a theoretical study to substantiate the parameters of the sorting device, the physical and mechanical properties of a heap of alfalfa seeds were taken into account. Substantiated parameters make it possible to improve the design and thereby improve the technological process of sorting and cleaning of alfalfa seeds of a dielectric sorting device.


Introduction
Considering that today "... more than 30 million hectares are sown with alfalfa all over the world" [1], then an important task is the development of energy-saving technologies and technical means aimed at reducing the irrecoverable loss of seeds during harvesting and improving the quality of processing seed heap. In this direction, the development of a constructive scheme and theoretical studies of a dielectric sorting device for alfalfa seeds is relevant. At present, for the conditions of Uzbekistan, the technology of harvesting alfalfa seed plants with the processing of the seed heap at a stationary point is recognized as the most rational [5]. In this case, the threshing of a heap is usually carried out by grain harvesters or a thresher-winnower MV-2.5A, which is associated with high costs and seed losses that exceed 10 ... 15%. Further, the primary cleaning of seeds is carried out using complex seed cleaning machines OVS-28, the principle of which is based on the difference in the physical and mechanical properties of alfalfa seeds and weeds (specific weight, windage, dimensions, etc.). After this operation, the yield of cleaned alfalfa seeds is about 80%. Final cleaning is carried out on an electromagnetic seed cleaning machine EMC-1, based on the ability of weed seeds (due to their surface roughness) to be enveloped with a special coal-metal powder, which is produced by the chemical industry and has a high cost [2]. In real economic conditions, in the presence of a large number of small farms and dekhkan farms in the republic, for effective preliminary cleaning of alfalfa seeds it is necessary to develop and use a mobile, small-sized grating machine, and for final cleaning -a simple and reliable device that provides sufficient productivity with minimal manual labor, high quality seed cleaning, environmental friendliness and low cost [3]. The carried out researches made it possible to determine the most rational technology for post-harvest processing of alfalfa seed heaps and purification of its seeds from weeds and quarantine inclusions.
The use of this technology does not provide for the use of traditionally used seed cleaning machines, due to their absence, physical wear and tear of the existing ones, as well as high metal and energy consumption and the significant cost of new ones. This leads to an increase in material costs, which is unprofitable for most small farms. The proposed technology differs from the existing simplicity and the number of machines used, their low cost and mobility. It provides for the use of the following set of machines: thresher MV 2.5A -for processing seed biomass; grating machine K-05M -for grinding seed pods and separating seeds, as well as a dielectric seed cleaning device -for sorting and final cleaning of seeds [4]. The purpose of the research is to increase the efficiency of the sorting device for cleaning alfalfa seeds by improving its design and optimizing technological and design parameters.

Materials and Methods
The theoretical prerequisites for substantiating the parameters of the dielectric device dispenser are fulfilled in accordance with the basic principles of mechanics and higher mathematics, taking into account the technological features of the process of dispensing alfalfa seeds, as well as its physical and mechanical properties. Differential equations were solved by numerical methods "Runge-Kutta-Felberg" with automatic step selection [5].

Results and Discussion
The feed hopper of the dielectric sorting device is a hopper with an outlet slot ( Figure 1).

Figure 1. Technological diagram of a dielectric sorting device
To ensure a continuous flow of a heap of alfalfa seeds through the slot of the hopper, the width (a) of the outlet slot should be equal to or greater than the maximum value of the largest arch-forming dimensions of the outlet openings, i.e. а [6]. The maximum size of alfalfa seed bridging above the bunker slot can be determined by the formula [4]: where ч d is the diameter of alfalfa seeds, m; 0 А -coefficient of proportionality between vertical and horizontal forces acting along the length of the perimeter of the cross-section of the flow sliding surface; 3)  Coefficients а о and А at hydraulic flow of bulk materials (if б    ) are determined from the following formulas [7,8]: where б angle of inclination of the wall of the bottom of the bunker to the vertical, degree; angle of friction of particles against the wall of the bin, degrees. At normal expiration, if: where пр reduced angle of internal friction, degree. Then: The critical angle of inclination of the bunker wall, characterizing the transition of the hydraulic type of outflow of bulk material to normal, is the angle: Provided when we have the case of hydraulic, and under the condition when The numerical value of the stacking angle, the particle shape of which is close to an ellipsoid, is . 17  у  [9,10]. Formula (1) gives the smallest value of the width of the hopper slot, at which the roof does not form, which leads to a continuous flow of bulk material through the slot of the hopper. Substituting expression 0 A into formula (1), we obtain a more simplified expression for determining the maximum size of bridging: In order to ensure a continuous outflow of the seed heap, it is necessary that the width of the slot a of the hopper satisfies the following condition: On the surface of the metering drum, grooves are made along the entire length with a step i and a depth h. For uniform and single-layer feeding of the seed heap to the surface of the dielectric drum, it is necessary that the alfalfa seeds are placed in the grooves [11]. Suppose that the longitudinal section of alfalfa seeds is approximately an ellipse in shape with major semiaxes a c and b c .  For convenience, we denote that: where d is the diameter of the dosing drum, m. From the right-angled triangle ВЕО 1 , you can determine the leg О 1 Е: We denote by m the length of the CM segment and then: Let's introduce the notation: Therefore, the coordinates of the point ) ; 0 ( m b C с  , and the coordinates of the point , therefore, for the line BC to be tangent to the ellipse, it is necessary that the line and the ellipse have a single common point.
The equation of the tangent to the ellipse passing through points B and C has the following form: Substituting the value of x from formula (14) into formula (15), we obtain a quadratic equation: After transforming the quadratic equation (16), we get the following expression: Hence: Quadratic equation (18) has one unique solution when its discriminant is zero: For a quadratic equation to have at most one solution, it is necessary that its discriminant be nonpositive. Transformation of expression (19) will lead to the following form: Further transformation of formula (20) will lead to the form: The condition for placing alfalfa seeds in the groove is the following inequality: Given that h j m   , expression (22) will take the form: (24) Figure 4 shows that: We define the discriminant of the quadratic equation (24): (25) After transformations we get:  The discriminant of this equation (27) is positive; therefore, the corresponding quadratic equation has two solutions. Therefore, in order for alfalfa seeds to fit in the groove, the following conditions must be met: Considering that the groove depth cannot be a negative number, we have: Since j b с  , the final formula for determining the depth of the metering drum groove will be as follows: Substituting the known parameter values: 0, 033 j mm  into the formula (3.6.30), we find the depth of the groove of the dosing drum: At the outlet of the bunker there is a stop made of a metal plate (section BK), which, under the action of periodic impacts of the dosing drum, vibrates between the dosing drum and the casing (bottom of the bunker). Thus, the limiter either passes or stops the flow of the seed heap [10]. For even distribution of the seed heap in the grooves of the metering drum, the length and angle of the stopper are very important. Under the influence of the oscillating movement of the limiter, the alfalfa seeds try to take a more stable position in the grooves of the metering drum ( Figure 5).
where ωdosing drum angular speed, m / s; Angle 0  is determined from the tangent formula: where b-distance between the dosing drum and the hopper outlet, m Transformation of expression (32) will result in the following form: Assuming that the differential equation of the oscillatory motion of the limiter is similar to the differential equation of a mathematical pendulum, one can write [12]: Where k yproportionality coefficient characterizing the elasticity of the stopper material.
Since the vibrations of the limiter can be considered very small, the angle difference can be represented in the form sin( , then the differential equation will take the following form: The solution to the differential equation (35) are the functions: ) kt sin( Ak Comparing the obtained expressions (36), (37) and (38), we determine the relationship of the proportionality coefficient: By the sine theorem for the triangle AOK at the moment of impact t = t y have [11]: After transformation, expression (40) will take the following form: Assuming that at the moment of impact at ó t t  , the angles are also equal, i.e.
Hence, from expression (42), we find the time at the moment the drum hits the restrictive plate: (44) Then, the value of the initial phase is: Let us find the time derivative of expression (44) t : From formula (44), if Substituting expression (47) into formula (46), we obtain: Moment of time t , during which the impact occurs is determined from the expression: The angle of installation of the limiter should be chosen in such a way that the following inequalities are satisfied: