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2021 (published: 17.12.2021)
Number 4(50)
Home > Issue > Analytical determination of the optimal ratio of the knife thickness and the outlet grate of the auger grinder with a parabolic pressure change along its radius
Pelenko V.V., Korotkova Tatiana Yu., Zlobin Vladimir G., Barinov Grigory V., Shahov S. V.
Difficulties arising in the mathematical description of the extrusion processes of solid materials in screw grinders are aggravated by the unknown nature of the change in the force effect on the cutting unit. The uneven distribution of the raw material pressure forces along the radius of the screw grinder outlet lattice is due not only to the complex helical nature of the material movement, but also due to the presence of an annular gap between the inner cylindrical surface of the grinder body and the outer surface of the projections of the screw last turn. Indeed, under certain technological conditions, a pressure isformed at the outlet of the grinder, the excess of which causes the phenomenon of "sluicing", that is, the reverse flow of solid material through the above-mentioned annular gap. The solution to the problem of optimizing the thickness of the knife blade under a load uniformly or linearly distributed over the radius of the output grinding grate is known. However, as thepreliminary results of our experimental studies show, the pressure distribution on the cutting unit is more complex. Therefore, in this study, the development of a mathematical model for the bending process of the output grinding grate as a circularperforated plate under the action of a load parabolically decreasing along the radius was carried out. In this case, the deflection of the knife blade under the action of a parabolic load is also analytically determined. Based on the analysis of the features of the physical model for the process of contact interaction between the elements of the cutting unit, the condition forminimizing the concentration of mutual frictional forces between the knife blade and the grate, which ensures a decrease in the rate of their wear, is formulated. Based on the condition of compatibility of deformations, an analytical dependence of the required thickness of the knife blade on the thickness of the output grinding grate is established to reduce the wear rate byensuring the equidistance of elastic lines of their bending under the action of a load parabolically decreasing along the radius.
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Keywords: mathematical modeling; differential equation of bending; variable pressure; wear rate; optimization; cutting pair; knife blade thickness
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
UDC 519.68:532.7:541.8:541.182.41
Analytical determination of the optimal ratio of the knife thickness and the outlet grate of the auger grinder with a parabolic pressure change along its radius
Difficulties arising in the mathematical description of the extrusion processes of solid materials in screw grinders are aggravated by the unknown nature of the change in the force effect on the cutting unit. The uneven distribution of the raw material pressure forces along the radius of the screw grinder outlet lattice is due not only to the complex helical nature of the material movement, but also due to the presence of an annular gap between the inner cylindrical surface of the grinder body and the outer surface of the projections of the screw last turn. Indeed, under certain technological conditions, a pressure isformed at the outlet of the grinder, the excess of which causes the phenomenon of "sluicing", that is, the reverse flow of solid material through the above-mentioned annular gap. The solution to the problem of optimizing the thickness of the knife blade under a load uniformly or linearly distributed over the radius of the output grinding grate is known. However, as thepreliminary results of our experimental studies show, the pressure distribution on the cutting unit is more complex. Therefore, in this study, the development of a mathematical model for the bending process of the output grinding grate as a circularperforated plate under the action of a load parabolically decreasing along the radius was carried out. In this case, the deflection of the knife blade under the action of a parabolic load is also analytically determined. Based on the analysis of the features of the physical model for the process of contact interaction between the elements of the cutting unit, the condition forminimizing the concentration of mutual frictional forces between the knife blade and the grate, which ensures a decrease in the rate of their wear, is formulated. Based on the condition of compatibility of deformations, an analytical dependence of the required thickness of the knife blade on the thickness of the output grinding grate is established to reduce the wear rate byensuring the equidistance of elastic lines of their bending under the action of a load parabolically decreasing along the radius.
Read the full article
Keywords: mathematical modeling; differential equation of bending; variable pressure; wear rate; optimization; cutting pair; knife blade thickness
DOI 10.17586/2310-1164-2021-14-4-20-36
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License