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2020 (published: 29.09.2020)
Number 3(45)
Home > Issue > Influence of counter-rotation elements on the law of pressure change inside the extruder screw
Pelenko V.V., Khlynovsky A.M., Usmanov I.I., Xia Chenguang
The equation for the law of pressure change in the screw along the length of the screw line is derived on the basis of physical and mathematical modeling of material moving along the surface of the screw channel of the screw under conditions of constrained compression, the presence of friction forces, and the influence of crumpling forces from the anti-skid elements on the inner cylindrical surface of the extruder body. The resulting equation allows to determine the length of the extruder body, which provides the required pressure in the extrusion zone. In terms of evaluating the efficiency of extruders and grinders, the law of distribution of raw material pressure along the screw channel is a determining factor, since it determines not only the nominal value of the required pressure in the extrusion zone through the grid holes, but also the total cost of mechanical energy for material deformation, movement, and undesirable product backflow. The need to understand the degree of influence of friction and crumpling forces from the counter-rotation elements on the longitudinal profile of the pressure distribution law is due to the requirement to minimize the backflow of material when it is injected into the extrusion zone, since the "sluicing" effect reduces productivity and increases energy consumption of the equipment. In this paper, the problem of determining the law of distribution of intra-screw pressure depending on the friction forces and mechanical resistance forces from special counter-rotation ribs on the inner surface of the extruder body is formulated and solved. The problem of correct modeling of the law of pressure distribution along the length of the screw body under the conditions of forces acting on the product from the counter-rotation collars is seen as the key one in this case. The differential equation of the equilibrium of forces acting on an elementary plate with a cross-section of the screw channel is taken as a mathematical model of the displacement process. The constancy of the ratio between the friction surface area of the elementary plate and the value of the corresponding contact perimeter in the direction of the feed along the curved surface of the screw is taken into account. On the basis of the analysis of a significant number of models of grinders, extruders, and tops, the limits of possible changes in their design parameters are determined. It is shown that the dimensions and material consumption of screw equipment can be significantly reduced by reducing the length of its body. The feasibility of the proposed mathematical modeling allows to expand the design capabilities of this type of equipment, and indicates the advantage of manufacturing screw extruders, grinders, and tops along the ratios obtained. Based on the derived analytical expression, the length of the top body and its other design parameters can be optimized according to the criteria of material consumption and energy efficiency.
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Keywords: mathematical modeling; pressure change; differential equation; law; extruder; friction; grinding
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
UDC 519.68:532.7:541.182.41
Influence of counter-rotation elements on the law of pressure change inside the extruder screw
The equation for the law of pressure change in the screw along the length of the screw line is derived on the basis of physical and mathematical modeling of material moving along the surface of the screw channel of the screw under conditions of constrained compression, the presence of friction forces, and the influence of crumpling forces from the anti-skid elements on the inner cylindrical surface of the extruder body. The resulting equation allows to determine the length of the extruder body, which provides the required pressure in the extrusion zone. In terms of evaluating the efficiency of extruders and grinders, the law of distribution of raw material pressure along the screw channel is a determining factor, since it determines not only the nominal value of the required pressure in the extrusion zone through the grid holes, but also the total cost of mechanical energy for material deformation, movement, and undesirable product backflow. The need to understand the degree of influence of friction and crumpling forces from the counter-rotation elements on the longitudinal profile of the pressure distribution law is due to the requirement to minimize the backflow of material when it is injected into the extrusion zone, since the "sluicing" effect reduces productivity and increases energy consumption of the equipment. In this paper, the problem of determining the law of distribution of intra-screw pressure depending on the friction forces and mechanical resistance forces from special counter-rotation ribs on the inner surface of the extruder body is formulated and solved. The problem of correct modeling of the law of pressure distribution along the length of the screw body under the conditions of forces acting on the product from the counter-rotation collars is seen as the key one in this case. The differential equation of the equilibrium of forces acting on an elementary plate with a cross-section of the screw channel is taken as a mathematical model of the displacement process. The constancy of the ratio between the friction surface area of the elementary plate and the value of the corresponding contact perimeter in the direction of the feed along the curved surface of the screw is taken into account. On the basis of the analysis of a significant number of models of grinders, extruders, and tops, the limits of possible changes in their design parameters are determined. It is shown that the dimensions and material consumption of screw equipment can be significantly reduced by reducing the length of its body. The feasibility of the proposed mathematical modeling allows to expand the design capabilities of this type of equipment, and indicates the advantage of manufacturing screw extruders, grinders, and tops along the ratios obtained. Based on the derived analytical expression, the length of the top body and its other design parameters can be optimized according to the criteria of material consumption and energy efficiency.
Read the full article
Keywords: mathematical modeling; pressure change; differential equation; law; extruder; friction; grinding
DOI 10.17586/2310-1164-2020-10-3-46-53
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License