Theoretical aspects of the working process of a press extruder with a variable step auger for preparation of concentrated feed

The article discusses the labor-intensive process of extruding soybeans. The parameters of production lines, methods and technical means intended for the implementation of the processes of preparing concentrated feeds based on insoluble soybean residue are theoretically substantiated. The results of theoretical studies to determine the optimal structural and technological parameters of a press extruder are presented: productivity, energy consumption, angular velocity, radius of the screw.


Introduction
For growing animals [1] at all stages of their development, a huge role is played by feed mixtures designed for both certain types of animals and their age characteristics, these mixtures contain nutrients that stimulate the growth and protective properties of the animal's body. In all feed mixtures [2], [3] should be predominantly freshly prepared, have a certain taste and not have sharp unpleasant odors. Soya is a key crop plant in the world in terms of ensuring a full-fledged diet for animal feeding. The process of pressing the hay-of straw materials are devoted to many researchers.
However, questions devoted to the pressing of concentrated feeds based on insoluble soya bean residue are not fully covered, since the designs of press-extruders made in the form of a body with a profiled inner surface containing mixing and barothermal processing zones were not considered .

Materials and methods
In the process of research, the technological scheme for preparing final feeds based on insoluble soybean residue (figure 1) was considered, it is more expedient to use the extrusion process, since it is possible to combine mixing and barothermic processing of the material [21,22].  Analysis of the studies showed that the mixing and barothermal process using the extruder of the proposed design has not been studied, therefore, there is no data on choosing a rational scheme for its use in production conditions, as well as optimal parameters in the mixing mode and barothermic processing of the mixture of grain feed and insoluble soy residue.
The working body [4] of the proposed extruder with annular outlet is a screw with a variable pitch (figure 2).  Figure 2. Press -extruder for the preparation of feed. a -extruder press; b -four feather knife; cknife. 1 -housing in the form of a hollow surface; 2 -inner surface with profiled guides; 3 -auger with variable pitch; 4 -four feather knife; 5 -molding cone; 6 -annular gap; 7 -regulating washer; 8knife; 9 -hopper -feeder.
For the parameter determining the position of point M, we can take the angle , formed by the x axis and the projection OP of the segment OM. The coordinates x and y of point M will be the same as that of point P. As for the vertical displacement Z, it grows in proportion to the angle of rotation , i.e. Z = C · t.
The rotation surface for a helical surface is a drawing.
It is known from surface theory that helical surfaces are superimposed on their surface of revolution. The surface of rotation for the considered screw surfaces has the form Where, d =  for the upper surface P 1; d = − for the lower surface of P 2. From equations (3) it follows that the surfaces of revolution is part of a circle located in the horizontal plane and bounded by circles of radius R 2 and R 1.
The rotation surface for L 1 is X ucos ; Y = usin ; Z (R -u)tg The helical surface P 1 is described by the equations The helical surface P 2 is described by the equations Thus, screw surfaces (6) and (7) as conical surfaces have, as follows from (4) and (5), conical surfaces. Since the screw surfaces (6) and (7) are superimposed on (4) and (5), respectively , and they, in turn, are linear surfaces developing on a plane, the considered screw surfaces are technological from the point of view of manufacturing.
Productivity is the main indicator characterizing the operation of a screw press. It can be defined as the sum of the screw cavity volume along the length of the screw filled with material per unit time.
The final expressions of performance for a screw press with a variable pitch and shaft diameter can be written It was noted above that the auger should be with different reduction stages, since the CKM moves along it. This follows from the fact that as this movement moves, the CMM becomes denser and closer to the condition of close ability to take the necessary shape in accordance with the requirements of the process. Let the OKM density at the time of loading be equal (established experimentally). We assume that in the auger, the OKM is a continuous continuous medium ( figure 5). Therefore, the OKM of volume dv has mass where , is the OKM density. By point A 1 we mean the point of intersection of the section Z with the surface P 1 at u = r = R From the third equation (6) it follows The cross section of the OKM at different levels of Z differs only in the area of the curved triangle A 1 B 1 (B 2 ) A 2 A 1 enclosed in the circuit A 1 B 1 (B 2 ) A 2 A 1 . We see that the area of the triangle increases with Z. The cross sectional area of OKM changes very little with increasing Z. About relations section for So / the S can be taken as a unit and then can be written as When C ( ) = C e -b , expression (12) takes the form We substitute the value b = bk, into expression (13), we obtain the final formula for determining  The required power on the motor shaft is determined by the formula: (15) Where, A is the work spent on moving the material along the axis of the screw, Nm;  --angular velocity of the screw, s -1;  -efficiency transmission from the motor shaft to the screw drive shaft.
The work involved in moving the material is determined by the expression Where, v -the speed of movement of the material, m / s ; тр F -friction force, H .
In expression (6) where , p-density OKM, kg / m 3 ; S -the cross-sectional area of the material, m 2.

Results and discussion
An analysis of the presented dependences (figure 6) shows that with an increase in the rotational speed of the screw n from 5 s -1 to 6 s -1, there is a continuous increase in productivity from 140 to 160 kg / h. The dependence built on the basis of theoretical research is in good agreement with the experimental one. The discrepancy between the results does not exceed 3.5 ... 6%. Figure 6. The influence of the angular speed of rotation of the screw ω, s -1 on the productivity Q of the press extruder: 1 -theoretical; 2experimental.