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Information model for calculating power spiral screw inertial screening machine

Автор/Author: Rudakova E.V.

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Список литературы/References:

1. Bogdanov, V. S. Laboratory unit inertial rumble with helical sifting surface / V. S. Bogdanov, S. S. Latyshev, E. V. Rudakova // Innovative materials and technologies, proc. Intern. scientific. scient. Conf. ( Belgorod, 11-12 Oct. 2011) / Belgor. state Indus. Univ – Belgorod: Publishing house of BSTU, 2011. – pp. 71-73.

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3. Kalekin, VS Processes and devices of chemical technology: Mass transfer and mechanical processes: studies. allowance. At 2 pm. Part 2 / VS Kalekin. – Omsk: Publishing house of Omsk state technical University, 2007.– 200 P.

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Содержание статьи/Article:

The process of separating solid granular materials with different properties of the particles (pieces of grain) has been used by mankind since ancient times [6] and was named "material classification" [2, 3].

In the building materials industry, the most widespread classification of materials by size particles. With the help of technology to solve the following problem [2, 4, 5]:

selection of material particles whose size does not meet the specified requirements (greater than or less than the permissible);

separation of particulate material by size into several fractions.

Classification of materials by size implemented in ways of sorting, as a mechanical, hydraulic, air.

The most commonly used inertial screens have such advantages as high screening efficiency due to good separation of the material on the surface of the screening (85-90%); high performance; low power consumption.

The main indicators characterizing the operation screens are screening capacity, screening efficiency and productivity screen.

To solve the problem by studying the process of classification of fine loose building material and develop an information model for calculating capacity was studied design spiral screw inertial screen (Fig. 1). [1]


Fig. 1. General view of the circuit and spiral-helix inertial screen:

1 - duct; 2 - screening surface; 3 - spring; 4 - vibrator; 5 -zagruzochny hopper; 6 - drain connection


Materials and Methods

Power [image] Consumed screw roar can be represented as the sum of

,                                                                              (1)

where   [image] - The power consumed by a crash at idle (in the absence of additional weight added to the box screen to change the amplitude of the oscillations boxes, and the material in the box rumble in the classification process);   [image] - Additional power consumed by a crash due to the presence of attached to the body mass;   [image] - Additional power consumed by a crash to post the material movement in the classification process.

Additional power consumed by a crash due to the presence of attached to the body mass, is given by:


where   [image] - The power consumed due to the addition to the box additional weight; [image] - The power consumption due to the presence in the box screen material.

In turn, the power   [image] the sum of the power [image] Consumed for vertical movement of the material, and [image]   - To move the material along the sieve (horizontal):

.                                                                                  (3)

Power calculation   [image] and

Power   [image] Consumed a crash idling - without additional cost and classified material has been measured experimentally and was 0.21 kW.

Dependence of the power   [image] by weight of the additional load   [image] was also determined experimentally. This dependence is determined by the formula. Thus, when [image] = 3.5 kg, n = 50 Hz, A = 2 mm obtain


To calculate the power consumption   [image] necessary to determine the average amount of material in the box at any given time.

Material is removed from the case only through the discharge nozzles undersize, so that the calculation scheme material distribution along the length of the helical tube, for example, three equal (in length) sieve, it looks as shown in Figure 2 (according to what material is sieved while moving one situ, it does not matter because both oversize and undersize materials are in a box).

Fig. 2. The distribution of material along the length of the screw box


If the velocity of the material along the sieve is denoted by [image] , The distance   [image] material passes during [image] Calculated by the formula

.                                                                                    (5)

During this time, go through the feed opening amount of material whose mass can be determined by the performance of screening for the original product [image] . Namely, if   [image] measured in "kg / h", the quantity of material   [image] Passing through a screen in one second is equal to

,                                                                               (6)

but for the time [image] - [image] :


That is the amount of material and is located on the first sieve.

In the general case, let there   [image] sieves with lengths   [image] and the transmittance of the material through [image] -e sieve  , [image] . Coefficients [image] characterized by the ratio of undersize to oversize on - [image] th sieve, i.e. if the amount of material reaching the sieve mass [image] Mass undersize material after passing over the screen - [image] Then

,                                                                                     (8)

wherein [image] .

Then the mass of material in each moment in the din [image] , Defined by the formula:


wherein, in accordance with formula (7)

,                                                                                  (10)

so that we obtain:

.                                           (11)

In order to use the formula (11), it is necessary to know the coefficients   [image] and the average velocity of the material on the sieve [image] . Coefficients   [image] determined experimentally during search experiments.

The average speed [image] movement  of material in a helical pipe can be calculated as follows. If the performance of screening for the original product   [image] measured in kg / h, the quantity of material   [image] Passing through a screen in one hour, will be equal to

,                                                                                      (12)

wherein [image] will have a dimension of "kg".

If this mass of material away from the screen size in [image] (Mesh width) [image]  (Average height of the layer of material on the sieve) and a length [image] , The length   [image] can be determined from the relationship

,                                                                              (13)

so that


"Ribbon" of material so long moved through a screen in one hour, therefore, the average speed is equal to


When using formula (15) should be borne in mind that, firstly,   [image] - The average height of the layer of material along the length of the screw boxes, which can be defined as


where [image] - Height of the bed material in the inlet duct;

[image] - Height of the bed material at the outlet of the duct.

Second, the bulk density of the material [image] also decreases along the length of the box, since each successive sieve are more and larger particles of material. Therefore, the average mass density of the material should be calculated by a formula similar to (16):


where [image] - Bulk density of the starting material;

[image] - The mass density of the material on the top sieve.

In view of (15) The above formula (11) can be written in the following final form:

.                                                (18)

Thus, for the following input parameters: , , ,  ,  ( ) [image] - Get

Further, when   ,   [image] obtain

Thus, the second term in the formula (1), with the formula (4), we obtain:

.                           (19)

In the resulting formula [image] has dimension "kg", and the product [image]

The pre-estimate theoretically possible maximum value [image] - [image] .

On the particles on the surface of the screen, in the vertical direction are two forces: the force of pressure from the septum   [image] and gravity [image] . While the particle is on the screen (fixed relative to it), its motion is determined by the movement of the screen:

,                                                                                    (20)

where [image] - Oscillation amplitude, [image] - Circular frequency sieve.



then the equation of motion of a particle can be written as


or, subject to (21)


This implies that at the time [image]  normal pressure force becomes equal to the force of gravity, the speed starts to decrease in the sieve according to (20), and also decreases the velocity of the particle, but only under the influence of gravity.

Thus, after separation from the sieve particle moves to the next encounter with him on a parabolic trajectory by law

,                                                       (24)

where   [image] determined by the first formula in  (21) [image] .

The collision with the screen is determined from the equation


Figures 3 - 5 presents the results of the calculation of the particle's trajectory and sieves for three different values ​​of the amplitudes of the oscillations of the screen.

[******* 879]

Fig. 3. The trajectories of particles (1) and sieves (2) at an amplitude [image] = 0.5 mm


During the free flight of the particles is: amplitude of 0.5 mm - 0.025 to 1.0 mm - 0.051 to 1.5 mm - 0.076 s.

Next, consider the part of the layer oversize material occupying the following scope: width equal to the width of the screen , [image] Height is the height of the layer   [image] and length - [image] . Weight   [image] this volume is equal to

,                                                                                    (26)

where [image] - The specific density of the material.

[******* 881]

Fig. 4. The trajectories of particles (1) and sieves (2) at an amplitude [image] = 1.0 mm


If this volume of material is thrown up at a rate of sieve [image] , By the same token he reported the kinetic energy   [image] As determined by the formula

.                                                                                (27)

Given the formulas (21) and (27) we find

,                                                                   (28)

or as

,                                                                                            (29)

where     [image] - Frequency of oscillation sieve, formula (28) can be written as


The kinetic energy that is transferred roar around the material on the sieve is determined by the formula

,                                                           (31)

where   [image] - The total length of the sieve (centerline) and specific density [image] and the height of the layer of material [image]  vary depending on its distance from the load (due to screening of the material).

[******* 3]

Fig. 5. The trajectories of particles (1) and sieves (2) at an amplitude [image] = 1.5 mm


Thus, the power consumed by the movement of the material vertically - [image] Can be calculated by the formula


where   [image] - A time interval during which the kinetic energy is transferred to the material [image] .

Above was obtained by equation (25) to determine the time of the motion of individual particles clear of the screen until the collision with him, which is dependent on the amplitude of the oscillations   [image] sieve. In practice, the particles on the sieve surface, after separation from it immediately encounters particles located above it, which in turn collide with the particles positioned above them, and so forth.

Since all particle collisions are inelastic, in each collision there is a loss of kinetic energy.

Thus, the kinetic energy is dissipated during one period of oscillation [image] Which is defined by the formula

,                                                                                           (33)

so that   [image] formula (33) finally takes the following form:


We find the average rating of the kinetic energy [image] , Assuming that the value of the specific density   [image] and the height of the layer of material [image] constant and equal to their average values ​​in the place of loading. In this case, the formula (31) can be written as follows:


Thus, the average power consumed by the movement of the material vertically - [image]  Can be calculated by the formula


To estimate the order of magnitude   [image] calculate its average values ​​for the parameters in the formula: [image] [image]

[image] Substituting in the formula, we find


Calculate the second component of the power consumption [image] - [image] required to move the material along the surface of the screw and the sieve box.

Just as before, we consider the part of the layer of material with dimensions oversize [image] ,   [image] and [image] . To move it away [image]  Must overcome the frictional force   [image] Module, which is determined by the formula


where   [image] - Coefficient of sliding friction,

  [image] - The force of normal pressure.

In screens with flat sieve material in which the particles move in a plane, the normal pressure value of the force is determined only by the weight of the volume in the material.

In this case, the amount of material moving along a helical line, resulting in a force of inertia   [image] Which presses the material to the outside of the pipe, which are arranged in sieve. The magnitude of this force is determined by the formula


where [image] - Speed ​​of movement of the material along the helical tube;

  [image] - The curvature of the path, in this case, the distance from the axis of the helix to the middle (width) sieve.

In the first case, the force of normal pressure equal to the weight of the volume in the material:


in the second -


Thus, the work that must be expended to move material along the duct, defined by the formula


where     [image] - The coefficients of friction of the material on the screen surface and the surface of the pipe respectively;

  [image] - Move the volume of material.

Then the power needed to carry out the work on the movement of said volume defined by the formula


and the total power needed to move the material across the entire pipe - of formula


In view of formula (26), the last expression can be written as follows:


As previously for [image] , For the same values ​​of the input parameters, we find the average rating [image] . The formula for determining it as follows:


In view of (15) expression can also be written as


For the case when [image] , The other parameters are the same as in the calculation of [image]  And [image]   (Sieve friction greater than the surface friction on the spiral tube), we obtain:



Thus, the final formula for calculating power consumption screw roar as follows:


where   [image] kW / kg, symbols other parameters apparent from vysheissleduemogo material.


Based on the analysis of technical and patent literature, the problem is identified the need to improve the existing equipment and technology screening of small granular materials. Developed and tested design spiral screw inertial screen. A method of calculating the power consumption of the drive, which takes into account structural and technological parameters of the spiral screw inertial screener


In accordance with the results of mathematical modeling and experimental studies of the technique of engineering calculation of spiral-helix inertial screen.

Given the experience of the industrial implementation of spiral-helix inertial rumble, rumble recommended body with a cross section in the form of a rectangle, making maximum use of the space around the axis of the helix, which will provide a more rigid structure. It is mandatory to create a hard question space frame, which will reduce the amount of axial strain the body during its vibratory motion.

Screening efficiency and the power consumption of the vibrator driven through the selected screen modes in first approximation can be determined using the expressions:



where n- the frequency of the driving force, A - amplitude oscillation mm, Qисх- on the performance of the initial product screening.

Ключевые слова/Tags1: Screening, spiral crashing, screening efficiency, rational modes, power, oversize, undersize and material particles.