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2021 (published: 17.12.2021)
Number 4(50)
Home > Issue > Theoretical simulation of resistance forces during food material cutting by circular knife
Aqeev O.V., Samojlova N.V., Naumov V. A., Fatykhov Yu. A., Zubkov Oleg A.
The relevance of mathematical modeling for the processes of food materials cutting by a circular knife has beenshown. The muscle tissue of the raw material has beendescribed by the Maxwell-Thomson viscoelastic rheological model. The process of product cutting by a circular knife has beeninvestigated. The formulation and solution of the problem ofmathematical modeling for the resistance forces during the movement of the circular knife in the material have beencarried out. A differential equation for the line of immersion of an elementary knife into the material in polar coordinates has beenproposed and solved. An expression for the actual cutting angle of the circular knife has beenobtained. The scalar fields of variation of the actual cutting angle, as well as the sliding coefficient of an elementary knife, depending on its angular coordinate has beeninvestigated. On the basis of expressions for determining the lines of immersion for an elementary knife into the material, mathematical models have been developed for calculating the harmful resistance forces on the circular knife, as well as their moments relative to the axis of rotation of the knife. Diagrams of the vertical and horizontal components of the dimensionless resistance force of the elementary circular knife form, as well as diagram of the resulting resistance force for the elementary circular knife form its moment have been constructed. The ranges of the most energetically favorable cutting angles, which are essential for resource saving in the design of cutting devices for processing machines, have been determined. With the values of the measure of elasticity of the material 3; 10; 20; 30, the values of the maxima of the specified dimensionless force are 9.55; 10.28; 11.37; 12.45, and the values of the maxima of the dimensionless moment are 5.66; 5.97; 6.42; 6.88, respectively. With the values of the ratio of the tangent of the angle of the knife sharpening to its thickness 0.01; 0.3; 0.7; 1.0, the values of the maxima of the resulting dimensionless force of the circular knife resistance are 9.28; 10.54; 12.27; 13.55, and the values of the maxima of the dimensionless moment are 5.55; 6.07; 6.81; 7.37, respectively.
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Keywords: pretreatment of raw materials; cutting food material; muscle tissue; math modeling; circular knife; resistance forces; rheology; viscoelasticity
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
UDC 664.9.022
Theoretical simulation of resistance forces during food material cutting by circular knife
The relevance of mathematical modeling for the processes of food materials cutting by a circular knife has beenshown. The muscle tissue of the raw material has beendescribed by the Maxwell-Thomson viscoelastic rheological model. The process of product cutting by a circular knife has beeninvestigated. The formulation and solution of the problem ofmathematical modeling for the resistance forces during the movement of the circular knife in the material have beencarried out. A differential equation for the line of immersion of an elementary knife into the material in polar coordinates has beenproposed and solved. An expression for the actual cutting angle of the circular knife has beenobtained. The scalar fields of variation of the actual cutting angle, as well as the sliding coefficient of an elementary knife, depending on its angular coordinate has beeninvestigated. On the basis of expressions for determining the lines of immersion for an elementary knife into the material, mathematical models have been developed for calculating the harmful resistance forces on the circular knife, as well as their moments relative to the axis of rotation of the knife. Diagrams of the vertical and horizontal components of the dimensionless resistance force of the elementary circular knife form, as well as diagram of the resulting resistance force for the elementary circular knife form its moment have been constructed. The ranges of the most energetically favorable cutting angles, which are essential for resource saving in the design of cutting devices for processing machines, have been determined. With the values of the measure of elasticity of the material 3; 10; 20; 30, the values of the maxima of the specified dimensionless force are 9.55; 10.28; 11.37; 12.45, and the values of the maxima of the dimensionless moment are 5.66; 5.97; 6.42; 6.88, respectively. With the values of the ratio of the tangent of the angle of the knife sharpening to its thickness 0.01; 0.3; 0.7; 1.0, the values of the maxima of the resulting dimensionless force of the circular knife resistance are 9.28; 10.54; 12.27; 13.55, and the values of the maxima of the dimensionless moment are 5.55; 6.07; 6.81; 7.37, respectively.
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Keywords: pretreatment of raw materials; cutting food material; muscle tissue; math modeling; circular knife; resistance forces; rheology; viscoelasticity
DOI 10.17586/2310-1164-2021-14-4-46-58
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License