The extrusion process of oil-containing raw materials using a twin-screw extruder is becoming increasingly common in food technology. The problem of high energy costs for the implementation of this process is solved by reducing the resistance of the process mass due to the preliminary grinding of raw materials. The classical theory of extrusion is based mainly on the use of theoretical solutions of mathematical models of processes, which are simplified and allow determining integral parameters using coefficients, the preparation of which for the calculation of the corresponding processes and equipment is a rather complicated and approximate procedure. Mathematical modelling of the movement of the technological medium at the individual stages of the processing of raw materials allows us to determine the analytical dependences for the power and energy parameters of the system and to carry out their effective technical and economic evaluation. Using the methods of mathematical analysis and data processing in the MathCAD software environment, graphical dependences of the power and energy parameters of the research technical system were obtained. By increasing the density of the oil-containing raw materials, which is extruded in the research extruder by 40.5% the pressure force increases by 41%, that is, there is an almost proportional relationship between the pressure force and the density of the processed raw material. With an increase in the angular velocity of the drive shaft ω more than 8 rad.s-1, the pressure force in the research process increases sharply. With an increase in the density of raw materials, it is grinded before extrusion by 40%, the power consumption for the grinding process increases by 2.8 times for the recommended operating mode. Energy losses for pressing completely grinded raw materials are reduced by 2.52 times.

The theory of extrusion was developed mainly for the case of processing synthetic materials, which throughout the volume have a relatively uniform molecular weight and are characterized by a high level of dissipation of mechanical energy (

The aim of this scientific work is a feasibility study of the implementation of the stage of preliminary grinding of oilcontaining raw materials in the extrusion process of oil by a twin-screw extruder based on a theoretical graphanalytical analysis of the power and energy parameters of the process. To achieve this aim it is necessary to solve the following tasks:

• determination and assessment of power and energy characteristics for the implementation of the mechanical extrusion of the liquid fraction of oilcontaining raw materials;

• obtaining graphical interdependencies of the research factors for the developed extruder circuit;

• substantiation of regime power and kinematic parameters of the executive bodies of the developed extruder.

Thus, the theoretical justification of the power and energy parameters during the implementation of individual stages of the extrusion process of oil-containing raw materials to reduce energy consumption and increase oil yield is quite an urgent task, which is solved in this scientific research.

Grinding of oil-containing raw materials before pressing and selection of the optimal operating mode of the extruder can increase the efficiency of its operation – increase the pressing force and oil yield and reduce energy consumption for the process.

When operating screw presses, from the beginning to the end of the pressing of seeds, it passes from one physical state to another until the oil and oil meal come out. To research these processes, they used the method of separation or decomposition, examining them in stages. Although the individual stages are interconnected, each of them in a complex system of processing of raw materials can occur simultaneously, parallel or sequentially, which happens inside the extruder's press path, where the operations of transportation, grinding, mixing, heating and extrusion of the raw material are carried out.

When conducting a theoretical analysis and justification of the power, torque and energy characteristics of the developed twin-screw apparatus for oil extrusion, methods of mathematical analysis and data processing in the MathCAD software environment were used to obtain the necessary graphical and analytical dependencies describing the main operating parameters of the system.

The statistical evaluation of the results was carried out by standard methods using statistical software Statgraphics Centurion XVII (StatPoint, USA) – multifactor analysis of variance (MANOVA), LSD test. Statistical processing was performed in Microsoft Excel 2016 in combination with XLSTAT. Values were estimated using mean and standard deviations.

In scientific works (

The design scheme of a twin-screw press extruder. Note: 1 – hopper, 2 – twin screw, 3 – heating chamber, 4 – grinding elements (nozzles), 5 – grain chamber, 6 – cone nozzle, 7 – matrix, 8 – electrical heating. Note: _{s}_{rm}_{oil}_{c}_{rf a}_{rda}

When describing the screw pressing mechanism, the principle of dividing it into sections is applied. In scientific works (

In accordance with the specified method of separation into sections or elementary screw mechanisms with conditionally constant parameters of the pressing process, the press path of the research twin-screw press extruder was divided into four conditional sections: І, ІІ, ІІІ, and ІV. Each section ends with a section of the mechanism on which the bore of the extrusion path of the press is reduced or increased within the same type of working bodies. In section

Assuming that in the research process grinding of seeds is realized in the radial direction to the center of the seeds, it is possible to determine the geometric parameters of the grinding unit of the extruder, which are presented in Figure

Scheme for determining the geometrical parameters of the seed grinding unit in triangular cam nozzles. Note: _{S}_{S}_{S}_{ge}_{ge}_{1}, О_{2}_{ge}_{s}

Using the calculated scheme of the interaction of the cams (Figure

Settlement scheme of interaction of grinding cams. Note: _{1}, О_{2}_{ge}_{3}_{s}

In the research system, three main forces can be noted: grinding force F_{P}; a force of pressure created in the screws of the screw F_{S}; friction force F_{f}. The direction of the grinding force is taken normal to the seed, which is crushed (Figure

Given the regularities of the mechanics of movement of the executive bodies and the geometric characteristics of the extruder presented above (Figure

Where: nS and w – respectively, the speed and angular velocity of the screw shaft; _{S}_{S}_{max} – the maximum pressure that develops the auger.

The friction force of raw materials on the inner surface of the extruder body can be described by the formula:

Where: k_{f} – the coefficient of friction of the raw material on the inner surface of the housing; F_{d} – a force of deformation of raw materials: F_{d} = F_{х}; F_{ad} – adhesive force, which takes into account the adhesion of the product with the parts of the press is determined by the adhesive experimentally.

The projections of the momentum of the elements of the system under study along the coordinate axes are:

Where: _{1}

It is obvious that _{1} υ_{y}

The axial velocity of the raw material along the auger channel can be determined by the formula

The time of promotion of products to the section with grinding cams is _{max} = _{S}_{max} = _{ge}

Using the presented equations, the projections of the mass forces of a mechanical system on the coordinate axis can be represented as:

Where:

Where:

Obviously a component _{y}

Based on the developed calculation scheme of the grinding unit, efforts were found to grind the raw materials from the equation of conservation of the amount of its movement.

Then the grinding force can be found by the equation:

or

Based on the obtained equations and using the MathCAD software environment, graphical dependences for the force and power characteristics of the research process were obtained (Figure ^{-1}, the pressure force on the raw material increases sharply, which justifies the recommended angular speed of rotation of the extruder shaft in the range ω = 4 – 7 rad.s^{-1}. The authors of the following scientific works (^{-1}, but rational is the speed not exceeding 7 rad.s^{-1}. For the recommended regime of rotational movement of the extruder's executive bodies, the force of grinding products by working rolls Fр increases 3 times (Figure

Dependences of the force of grinding of raw materials by working cams _{P}^{-3}); 2 – rapeseed (^{-3}); 3 – soybeans (^{-3}).

With an increase in the density of raw materials, it is grinded before being extruded by 40%, the power consumption for the grinding process increases by 2.8 times and amounts to 0.7 – 2 kW for the recommended operating mode (Figure

To evaluate the effectiveness of preliminary grinding of seeds in the process of oil extrusion, the following calculation procedure was used (

For whole seeds ^{-3}, _{0}^{-3}·_{0}^{6.66}, and for grinded seeds ^{-32}, _{1}=3.3·10^{-32}·ρ_{1}^{11,84}

Where: _{0}_{0}^{-3}; _{1}_{1}^{-3}.

The ratio of the power consumption for pressing whole seeds N_{0} and grinded N_{1} is:

When the energy efficiency coefficient kN was introduced to evaluate the research process, it was found that the coefficient c is inaccurate for the grinded material. After clarification for the grinded raw materials с = 3.86×10^{-30}.

That is, the energy loss for pressing the grinded material for the research process of oil extrusion is reduced by 2.52 times. The rational design and technological parameters of the modernized press extruder were determined based on the experimental researches, which were: the temperature of the first and second heating zones of the buildings 115 – 130 °C, the gap in the matrix 0.0042 – 0.005 m, the angular speed of the screw shaft 4 – 7 rad.s^{-1}, the time of technological influence on the oilcontaining material in the tract of the press is 45 – 75 s.

Application of new working bodies allows to increase the productivity of the machine and to reduce energy consumption for the process of oil extraction. The theoretical compression ratio of a press extruder with a set of new working bodies for the processing of sunflower, rapeseed and soybean seeds is 4.69; 3.36 and 2.55. This ensured the intermediate compaction of the oil-containing raw material, the intensification of its crushing, and the increase of oil yield to 3%.

1. Based on mathematical analysis of the movement of raw materials at separate stages of the extrusion process of oil in the developed twin-screw extruder determined the power and energy parameters of the research process and proved that the energy losses under the conditions of pre-grinding of seeds and, accordingly, reduction of technological resistance of the dispersed medium during oil extrusion are reduced by 2.52 times.

2. The graphical dependencies obtained in the MathCAD computer software environment showed that with an increase in the density of raw materials, it is grinded before being extruded by 40%, the power consumption for the extrusion process increases by 2.8 times and amounts to 0.7 – 2 kW for the recommended operating mode of the extruder.

3. For the recommended angular velocity of the extruder actuators (ω = 4 – 7 rad.s^{-1}), the grinding force of the raw materials by the work rolls F_{p} increases by 3 times.