Centrifugal separator impeller and method of sieving of bulk materials in the centrifugal separator

EP4770804A1Pending Publication Date: 2026-07-08POLITECHNA WROCLAWSKA +1

Patent Information

Authority / Receiving Office
EP · EP
Patent Type
Applications
Current Assignee / Owner
POLITECHNA WROCLAWSKA
Filing Date
2023-08-28
Publication Date
2026-07-08

AI Technical Summary

Technical Problem

Existing centrifugal separators face inefficiencies in sieving bulk materials due to rapid material flow along the axis of rotation, leading to unsieved material waste or the need for re-sieving, and require transfer media or external force fields for effective operation.

Method used

A centrifugal separator impeller with a rotating truncated cone perforated sheet equipped with a spiral channel that moves separated material along a spiral path, allowing controlled speed of material flow and efficient sieving without transfer media or external force fields, utilizing local elastic deformations induced by resonant vibrations for enhanced separation.

Benefits of technology

The solution significantly increases the efficiency of the sieving process by extending the spin time of material, reducing unsieved material waste, and allowing operation independent of external media or force fields, resulting in a more effective and cost-efficient separation of bulk materials.

✦ Generated by Eureka AI based on patent content.

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Abstract

A centrifugal separator impeller designed for sieving bulk materials, granulates of various density and gradation, such as minerals, sand, grains, capsules, pellets or others, made of a perforated sheet (1) in the shape of a truncated cone, on whose inner surface flows the separated material, is characterized by the fact that the perforated sheet (1) on the inner side is equipped with a spiral channel (2) which forces a spiral path of movement, consistent with its geometry, of the separated material flowing along the inner surface of the side face of the sheet (1). A method of sieving bulk materials in a centrifugal separator in which the bulk material is sieved on a vibrating impeller, which has the form of a truncated cone perforated sheet and whose inner side is equipped with a spiral channel forcing a spiral path of movement, consistent with its geometry, of the separated material, which flows over the inner surface of the side face of the sheet, is characterized by the fact that the material is sieved in the impeller, whose natural frequencies, when coinciding with the frequency of the force vibrating the impeller, i.e. when in resonance, introduce local elastic deformations of the impeller,
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Description

[0001] Centrifugal separator impeller and method of sieving of bulk materials in the centrifugal separator

[0002] The subject matter of the invention is a centrifugal separator impeller designed for sieving bulk materials, granular materials of various density and gradation such as minerals, sand, grains, capsules, pellets or others. The solution is designed for use in the chemical, food, and agricultural industries, in mining and rock processing, and space technologies, among others. The subject matter of the invention is also the method of sieving bulk materials in a centrifugal separator.

[0003] Polish patent no. PL179543 discloses a centrifugal separator for separating a mixture of materials into components of different specific weights, whose bowl consists of a flat bottom and a conical circumferential wall protruding upwards from the bottom. The inlet conduit reaches the bottom of the bowl. The conical part of the circumferential wall of the bowl is smooth, without holes. Above the upper edge of the conical part of the bowl are placed two axially spaced recesses, equipped with holes for water fluidizing the discharged material of a higher specific weight.

[0004] Polish patent no. PL183804 discloses a centrifugal separator comprising a centrifugal centrifuge with a central axis rotating in a given direction, having a chamber free of rotating bodies in an area located radially inside a circle, the center of which is on the said central axis and the radius is equal to the first distance, and also including an outlet member, consisting of an outlet conduit with an inlet opening leading hitherto, the outlet member being movable about a second axis parallel to the central axis a second distance from the central axis, the second distance being smaller than the first distance, and the outlet member being movable towards and away from the central axis.

[0005] European invention no. EP218657 IB 1 discloses a centrifugal separator with at least one housing forming a swirl chamber with at least one tangential inlet, with a lower discharge in the installation position for the heavy components deposited in the centrifugal field and with an upper, in relation to the installation position, discharge passing through the housing cover, which includes a dip tube extending to the housing, the dip tube being connected to the side of the housing cover facing the swirl chamber. In the invention, the dip tube is suspended from a support ring connected to the side of the housing cover facing away from the swirl chamber with the housing cover being interposed.

[0006] The American patent application no. US20160082478A1 discloses a centrifugal separator comprising a rotating conical or cylindrical screen, along whose inside face flows the separated material. The separation of the material in the rotating conical screen is possible due to the generated centrifugal forces acting on the surface of the rotating screen. The reaction along the axis of the rotating conical screen causes the material to flow downwards. If the rotating screen is cylindrical, the separation of the material is also possible due to the generated centrifugal force acting on the surface of the rotating screen, with the movement of the separated material along the axis of rotation of the screen being forced by an additional medium or an appropriate inclination of the rotating screen. Alternatively, in a cylindrical rotating screen, the separated material can be moved along its axis of rotation by a screw auger placed inside it, whose rotation is independent of the rotation of the screen.

[0007] When using a conical rotating screen, in order to increase the sieving force, it is necessary to increase the centrifugal force. The increase in centrifugal force, achieved by increasing the rotation speed of the screen, also increases the reaction force along the axis of the conical screen, resulting in a faster flow of the separated material along the cone axis. An increase in the rotation speed usually causes a decrease in the efficiency of sieving through the sieve and thus decreases the efficiency and effectiveness of the device. Therefore, due to the rapid flow of material along the axis of rotation of the screen, a large amount of material remains unsieved and is wasted or needs to be sieved again. The disadvantage of using a cylindrical rotating screen is the necessity to use a transfer medium, the need to accurately adjust the inclination of the cylindrical rotating screen in relation to the vector of gravity, or the requirement to use additional mechanical force to move the material lengthwise. Without the use of air or water, or the presence of a sufficiently high gravitational or other mechanical force, the separator with a cylindrical rotating screen will underperform. Including an installation of a transfer medium in the separator or placing an additional movable element inside the cylindrical rotating screen increases the complexity of the installation, increases the cost of its construction, and the demand for electricity. If a screw auger is placed inside the rotating screen, there is the additional problem of choosing the appropriate width for the gap between the rotating screen and the spiral. Namely, the gap on one side should be sufficiently small so that the spiral could scrape all of the unsieved material from the surface of the rotating screen. However, if the width of the gap is too small, the material will accumulate inside it causing friction between the rotating screen and the spiral and additional resistance of motion between the rotating cylinder and the spiral due to the fact that their speeds of rotation are different. The above mentioned phenomena may adversely affect the structure of the sieved material, namely the material collecting in the gap may, for example, crumble or crush. If the sieved material is abrasive, this will lead to a rapid wear of the screen surface and the spiral. Increasing the gap between the rotating screen surface and the spiral edge will reduce the negative effects described above, but will also decrease the efficiency of flow of the separated material along the rotating screen axis and thus the efficiency of the device.

[0008] The above US filing no. US20160082478A1 also discloses a structure consisting of multiple coaxially rotating conical surfaces. Such a design can separate several material fractions in one feed, namely the largest fractions settle on the first rotating surface, the smaller fractions flow further and settle on the next rotating surface with a smaller mesh / perforation than the surface of the first rotating screen, and so on for each subsequent rotating screen.

[0009] Commonly, separators with a conical impeller are equipped with an exciter that vibrates the impeller. Solutions known from the state of the art vibrate as a whole (global vibrations - rigid body modes), which directly reflects the externally excited vibrational motion by imbalance or a vibration generator.

[0010] The goal according to the present invention is to provide a solution that in a truncated cone impeller will improve the control of the speed of material flow along the axis of rotation.

[0011] The goal according to the present invention is to provide a solution that will allow the sieving / separation of bulk materials without the need to use transfer media, such as water or air, and without the need to use (without the presence of) an external force field, such as gravity.

[0012] The centrifugal separator impeller consisting of a rotating truncated cone perforated sheet, along whose inside wall the separated material is moved, according to the present invention, is characterized by the fact that the interior of the perforated sheet is equipped with a spiral channel to move the separated material along a spiral path, consistent with its geometry, along the inside surface of the side face of the sheet.

[0013] Preferably, the impeller has a design that, in the resonant frequencies determined at the design stage and dependent on its design, is characterized by local elastic deformations that help separate the material. Preferably, the spiral channel has the form of a spiral flange, whose outer spiral edge is attached to the perforated surface of the sheet.

[0014] Preferably, the spiral channel in the form of a flange together with the perforated surface of the sheet form a channel.

[0015] Preferably, the spiral channel has the form of a spiral embossed on the inside face of the sheet and convex on the outside of the sheet.

[0016] Preferably, inside the sheet there is a truncated cone core which forms a transport gap between its side face and the perforated sheet.

[0017] The method of sieving bulk materials in a centrifugal separator, in which the bulk material is sieved by a vibrating impeller, which has the form of a truncated cone perforated sheet and whose interior is equipped with a spiral channel to move the separated material along a spiral path in accordance with its geometry over the inner surface of the side face, according to the present invention is characterized by the fact that the material is sieved inside an impeller whose selected natural frequencies, when coinciding with the frequency of the vibrations of the impeller, i.e. when resonating, induce local elastic deformations of the impeller.

[0018] In the solution according to the present invention, the rotating impeller generates a vector of centrifugal force. The tangential component of the centrifugal force vector, whose magnitude depends on the angle of inclination of the side face of the impeller a, acts along the side face of the impeller, which causes the material to move toward the larger diameter of the cone. The normal component moves the sieved material to the outside of the impeller, thereby sieving it through the side face of the perforated screen. The integrated with the impeller spiral channel, of any geometry and design, opposes the main outward movement of the material resulting from the action of the tangential component of the centrifugal force, in a controlled manner, depending on the angle of inclination of the spiral channel 0 which allows the speed of material flow along the axis of the impeller to be controlled, and thus makes the sieving process efficient by extending the spin time of the material. In the solution according to the present invention there is no need to use transfer media (water, air) or an external field of force or acceleration (gravity). The flow speed of the separated material in the solution according to the present invention depends on the angle of inclination of the spiral channel 0 and the angle of inclination of the conical side face of the impeller a. In the centrifugal separator with the impeller, according to the present invention, efficiency is significantly increased due to the fact that the grains are longer in contact with the sieve (perforated surface of the side face) and their path is the result of moving along the side face of the impeller, on the spiral channel located inside it, which produces more of the final sieved product with the desired gradation. In current solutions, the rapid movement of the material only along the axis of the conical impeller results in a significant amount of unsieved material that is wasted or requires re-sieving. In the solution according to the present invention, the movement of the material inside the impeller is controlled in all directions by adjusting the ratio of the angles of inclination of the impeller side face and the spiral channel and the speed of rotation (centrifugal force). As a result, the solution according to the present invention can be completely independent of media used to move the material, such as air or water, and an external force field. Solutions known from the state of the art vibrate as a whole (global vibrations - rigid body modes), which directly reflects the externally excited vibrational motion by an imbalance or a vibration generator. The impeller according to the present invention is designed in such a manner that its resonant frequency causes local elastic deformation of the impeller. In the solution according to the present invention, the resonating impeller undergoes local elastic deformations, which cause local agitation and detachment of the separated material from the side face and the spiral channel. This ensures easier separation of the material and prevents clogging of the impeller perforations. The impeller according to the present invention vibrates in resonance as its desired state. A characteristic feature of the local resonant vibrations of the impeller according to the present invention, in contrast to the known sieves that vibrate with forced vibrations of global rigid body modes, is that the direction of vibrations and local / resonant deformation modes results from the assumptions determined in the impeller design, and not only from the method of exciting the impeller vibrations (for example imbalance, exciter). This causes local agitation of the granular material and its local detachment from the side face and the spiral channel. The design of the impeller according to the present invention generates large enough forces, which result in sieving, so that the presence of a gravity field, the angle of the axis of rotation in the field of gravity or the absence of a gravity field is of secondary importance. Therefore, the position / inclination of the impeller can be arbitrary in relation to the vertical and the position of the impeller should be determined on the basis of the operating parameters of the device and the possible location of other auxiliary devices.

[0019] In the solution according to the present invention, the material flow and segregation parameters are determined by the angle of inclination of the impeller side face a, the angle of inclination of the spiral channel , the diameter of the conical impeller, the impeller height, the rotational speed of the impeller assembly with the spiral channel and the characteristics of the vibration spectrum of the impeller and the spiral channel assembly, with the last two parameters (rotational speed, vibration spectrum) being controlled in real time. These parameters, as well as the shape of the spiral channel and the size of the perforation holes of the side face, are also determined in relation to the characteristics of the dry material, such as density, granulometric composition, external friction coefficient and natural angle of repose.

[0020] The subject matter of the present invention is shown in the drawings in which fig. 1 is the schematic diagram of the solution, fig. 2 is the side view of a first embodiment of the centrifugal separator impeller, fig. 3 is the top view of a first embodiment of the centrifugal separator impeller, fig. 4 is a diagram of the cross-section of the centrifugal separator impeller along the A-A line in fig. 2. fig. 5 is detail "B" in fig. 4, fig. 6 is an example of the centrifugal separator with the impeller from the first embodiment according to the present invention (side view and cross-section of the separators), fig. 7 is the top view of a second embodiment of the centrifugal separator impeller, fig. 8 is the side view of a second embodiment of the centrifugal separator impeller, fig. 9 is a diagram of the cross-section of the centrifugal separator impeller along the C-C line in fig. 8, fig. 10 is detail "D" in fig. 9, fig. 11 is a top view of a third embodiment of the centrifugal separator impeller, fig. 12 is the side view of a third embodiment of the centrifugal separator impeller, fig. 13 is a diagram of the cross-section of the centrifugal separator impeller along the E-E line in fig. 12, fig. 14 is detail "G" in fig. 13, fig. 15 is detail "F" in fig. 12, fig. 16 is the axonometric projection of a fourth embodiment of the centrifugal separator impeller, fig. 17 is a diagram of the longitudinal section of a fourth embodiment of the centrifugal separator impeller, fig. 18 is a bottom view of three concentrically nested impellers in the third embodiment, fig. 19 is the side view of impellers in fig. 18, fig. 20 is a diagram of the cross-section of the centrifugal separator impellers along the H-H line in fig. 19, fig. 21 is detail "I" in fig. 20, and fig. 22 is the schematic diagram of the separator according to the present invention excited to resonant vibrations.

[0021] The impeller of the centrifugal separator in the first embodiment according to the present invention is made of a perforated sheet 1 in the shape of a truncated cone, along whose interior side face flows the separated material. The perforation of the sheet 1 in the figure is marked la. The sheet 1 on the inner side is equipped with a spiral channel 2 whose geometry causes the separated material to move along a spiral path on the inner

[0022] SUBSTITUTE SHEET (RULE 26) surface of the side face 1 due to the influence of the tangential component of the centrifugal force acting on it. The spiral channel 2 has the form of a spiral flange 2a with its outer spiral edge attached to the side face of the sheet 1 and its second, inner, spiral edge connected to a wall 2b extending upwards from it. The flange 2a together with the perforated surface of screen 1 and the wall 2b form a channel. The spiral channel 2 spans the entire height of the sheet 1. Of course, in another embodiment, the spiral channel 2 can span only a part of the sheet 1. The impeller can be made of perforated sheet metal or a mesh. The spiral channel 2 is made of sheet metal and is fixed to the side of the sheet 1 by welding. For example, the impeller side face (sheet 1) can be made of a mesh with a hole diameter of 3 mm. The angle of inclination of the impeller side face acan be in the rangeD 65 75°, the angle of inclination of the spiral channel 0 in the range of 2 3°, the diameter of the impeller base is 1700 1900mm and the impeller height is 1600mm. The width of the flange 2a can be 100mm, and of the wall 2b extending from it - 50mm. This allows for sieving of bulk materials such as sand, gravel and separating a fraction smaller than 3mm from fractions exceeding this grain size. The impeller according to the present invention has a design that in the resonant frequencies determined at the design stage and dependent on its design, is characterized by local elastic deformations that help to separate the material. The design of the impeller aimed at ensuring its operation in resonance as the desirable and beneficial state, as opposed to the typical avoidance of this phenomenon, can be attained by commonly known analytical and numerical methods. In the described invention, however, such an approach to designing is aimed at obtaining a controlled resonance in order to intentionally introduce the additional energy of local elastic vibrations into the structure without destroying it. In such designing methods, having defined the impeller operating parameters, i.e. the rotational speed, the sieved material (batch size, granulation), or the external excitation frequency of the exciter, or imbalance (if such is present), by using commonly known analytical and numerical methods, the structural stiffness of the impeller is chosen (based on the stiffness of its structure resulting from its shape and by selecting the material that has appropriate stiffness / elasticity). This allows for determining the form and resonant frequency of the impeller that is safe for its structure and at the same time beneficial for the sieving / separation process. The impeller with such a design can be made using commonly known methods and the choice of the method of manufacturing it mainly depends on the degree of complexity of its geometry and the construction material (for example, welding from components, 3D printing, casting, etc.). As depicted in fig. 6 the above mentioned impeller inside the centrifugal separator can be placed in the housing 3 containing outlets 4, 5 for separated fractions. The material to be separated is fed through the inlet 6 and then travels along the inner surface of the impeller side face on the spiral channel 2. Material with a gradation corresponding to the size of the perforations la of the impeller side face exits the impeller and is then discharged through the outlet 4. Material with a gradation greater than the perforation size la of the impeller side face flows along the axis of rotation of the impeller, towards its larger diameter, and then is discharged through outlet 5. The impeller is rotated by means of an electric motor 7, which, in addition, through imbalance or the use of an exciter in the electric motor assembly 7, vibrates the impeller. The operation of the separator can be supported in a controlled manner by vibrations of a given frequency, which helps to increase the efficiency of transfer and sieving of the material and prevents clogging of the perforations la in the impeller side face. The controlled vibrations can be used to produce resonance in the transferred material, the individual steps of the machine (natural vibrations of the separator components) as well as in the entire separator, which further increases the energy of sieving supplied to the material.

[0023] The impeller of the centrifugal separator in the second embodiment according to the present invention is constructed similarly to the first embodiment, except that the spiral channel 2 has the form of a spiral embossed in the side face of the sheet 1 and convex on the outside of the sheet 1. The coils of the spiral channel 2 are located directly one below the other - their edges touch. The spiral channel 2 is formed across the entire height of the side face and its entire surface is perforated. The pitch of the spiral channel 2 and the shape and size of the perforations depend on the type of material to be separated. The solution according to this embodiment is structurally simpler than the impeller in the first embodiment, and therefore cheaper to produce. In this embodiment, the impeller side face (sheet 1) is made of perforated sheet metal with a mesh size of 5 mm and the radius of the channel is 160 mm. The angle of inclination of the impeller side face a is 75°, the angle of inclination of the spiral channel 0 is 1 2°, the diameter of the base of the cone is 1500 -^ 1 6 00mm and the height of the truncated cone is 1500mm. This allows for sifting of granules or pellets and separating fractions smaller than 5mm from fractions exceeding this grain size.

[0024] The impeller of the centrifugal separator in the third embodiment according to the present invention is built similarly to the second embodiment, except that the successive coils of the spiral channel 2 are not adjacent. The spiral channel 2 on the side face of the sheet 1 is formed so that the coils of the spiral channel 2 are separated by the wall of the side face, the coils run at a distance from each other. The spiral channel 2 is formed across the entire height of the side face and its entire surface is perforated. The side face of the sheet 1 in the area without embossments is also perforated. The impeller according to this embodiment in relation to the impeller in the second embodiment allows for a higher speed of material flow but at the expense of separation accuracy. In this embodiment, the cone side face is made of a mesh with a hole diameter of 0.5mm, the radius of the spiral channel 2 embossed on the side face of the sheet 1 is 25 mm, and its width is 15mm. The angle of inclination of the impeller side face ais 75 80°, the angle of inclination of the spiral channel 0 is 2.50 3.0°, the diameter of the base of the cone is 1400 1500mm and the height of the truncated cone is 1500mm. This allows the sieving of powders and separating fractions smaller than 0.5 mm from fractions exceeding this grain size.

[0025] The impeller of the centrifugal separator in the fourth embodiment according to the present invention is constructed similarly to the first embodiment, except that the spiral channel 2 consists of a flange formed of a profiled flat bar, the sheet 1 is adjacent to covers 8, 9 that close its interior, with an inlet 10 in one of them and an outlet 11 in the other for the flowing material, and inside the sheet 1 is placed a core 12, which has the shape of a conical frustum with its bases closed with covers. The placement of the core 12 inside the sheet 1 creates a transfer gap between the side face of the core 12 and the side face of the sheet 1. The transfer gap reduces the chaotic flow of the sieved material, especially in reduced gravity conditions, which improves the efficiency of the process. On the outer surface of the side face of the core 12 there is a spiral channel 13 in the form of a spiral flange formed from a profiled flat bar. The purpose of the above mentioned spiral channel 13 is to further increase the possibility of controlling the speed of the material inside the separator together with the existing spiral channel 2 on the side face of the sheet 1. In this embodiment, the ratio of the angle of inclination of the sheet side face 1 and the core 12 to the pitch of the spiral channels 2, 13 formed on them regulates the speed of the material flowing along the surface of the sheet 1, which allows the efficiency and effectiveness of sieving to be adjusted and the operation of the separator with the impeller according to the present invention to be adjusted to the type of material being separated. The core 12 can be stationary, in which case it performs the function of limiting the speed of material flow inside the sheet 1, in the axial direction, or it can rotate at a different or the same speed as the sheet 1. This allows for better regulation and optimization of the sieving process by accelerating, slowing down or reversing the material flow inside the sheet 1.

[0026] In this embodiment, the diameter of the base of the cone is 600^-650 mm, the height of the conical frustum is 520^-560 mm, the angle of the side face of the sheet 1 is in the range of a=83^-84°, the pitch angle of the spiral channels 2,13 is 0=4.5-Hj.5°. The side face of the core 12 is parallel to the side face of the sheet 1, with a transfer gap of e=55^-65 mm between them. The width of the spiral channel 2 on the impeller 1 can be 12-H7 mm. The width of the spiral channel 13 on the core 12 can be 10 -H5 mm.

[0027] The impeller, in particular according to the second or third embodiment, can also be used in a centrifugal separator containing several concentrically nested impellers. Such a design can separate several material fractions in one feed, namely the largest fractions settle on the first interior perforated surface, the smaller fractions flow further and settle on the subsequent middle perforated surface with a smaller mesh / perforation size than the surface of the first sheet, and so on for each subsequent rotating sheet. The pitch of the embossed spiral and the shape and size of the perforations can vary for each impeller and can depend on the type of material to be separated, its mass, and its angle of repose. This solution allows for better control of the transported and separated material than in the case of solutions in embodiments 1 to 3, but it is characterized by a much greater weight and structural complexity. The advantage of combining a series of cones is the possibility of obtaining several fractions of the separated material from a single feedstock.

[0028] The method of sieving bulk materials in a centrifugal separator, in the embodiment according to the present invention, consists in the fact that the bulk material is separated on a vibrating impeller, which has the form of a perforated sheet 1 in the shape of a truncated cone and which on the inner side is equipped with a spiral channel 2 forcing a spiral path of movement, in accordance with its geometry, of the separated material which flows along the inner surface of the side face of the sheet 1. The material is sieved in the impeller, whose determined natural frequencies, when coinciding with the frequency of the force vibrating the impeller, i.e. when resonating, introduce local elastic deformations of the impeller (fig. 22). The method according to the above embodiment can be carried out in the separator presented in fig. 6, and the impeller is constructed as described in the first embodiment.

Claims

Patent claims1. The impeller of the centrifugal separator consisting of a truncated cone perforated sheet, on whose inner surface flows the separated material, characterized by the fact that the perforated sheet (1) on the inner side is equipped with a spiral channel (2) which forces a spiral path of movement of the separated material flowing along the inner surface of the side face of the sheet (1).

2. The impeller according to claim 1 , characterized by the fact that its design at resonant frequency is characterized by local elastic deformations.

3. The impeller according to claim 1, characterized by the fact that the spiral channel (2) has the form of a spirally shaped flange (2a), whose outer spiral edge is attached to the perforated surface of the sheet (1).

4. The impeller according to claim 3, characterized by the fact that the spiral channel (2) in the form of a flange (2a) together with the perforated surface of the sheet (1) form a conduit.

5. The impeller according to claim 1, characterized by the fact that the spiral channel (2) has the form of a spiral embossed in the side face of the sheet, and convex on the outside of the sheet (1).

6. The impeller according to claim 1, characterized by the fact that inside the sheet (1) there is a core (12) which has the shape of a truncated cone and which between its side face and the perforated sheet (1) forms a transfer gap.

7. A method of sieving bulk materials in a centrifugal separator in which the bulk material is sieved on a vibrating impeller, which has the form of truncated cone perforated screen and whose inner side is equipped with a spiral channel which forces a spiral path of movement, consistent with its geometry, of the separated material, which flows along the inner surface of the side face of the sheet, characterized by the fact that the material is sieved in the impeller whose natural frequencies, when coinciding with the frequency of the force vibrating the impeller, that is, when in resonance, introduce local elastic deformations of the impeller.