Mathematical simulation of effective resistance forces during cutting of chilled food products
DOI: 10.17586/1606‑4313‑2020‑19‑3-70-82
UDC 621.565:664.95
Aqeev O.V., Naumov V. A., Fatykhov J.A.
Keywords: effective resistance, cutting, force, sharpness, knife, edge, rheology, viscoelasticity.
UDC 621.565:664.95
Mathematical simulation of effective resistance forces during cutting of chilled food products
For citation: Ageev O. V., Naumov V. A., Fatykhov J. A. Mathematical simulation of effective resistance forces during cutting of chilled
food products. Vestnik Mezhdunarodnoi akademii kholoda. 2020. No 3. p. 70–82.
Abstract
The relevance of the research of the cutting process of chilled food products has been shown. The muscle tissue of the chilled raw material has been described by the Maxwell-Thomson rheological model. The formulation and solution of the problem of mathematical modeling of the effective resistances forces have been completed. The muscle filaments of the product during cutting are interpreted as viscoelastic beams. The bending and tensile strains of the filaments under the influence of the knifepoint have been considered. Expressions for the dimensional and dimensionless forces of effective resistance have been obtained. The dependences of the indicated forces on the cutting edge sharpness, the half angle of knife sharpening, the rheological parameters of the material, the design parameters of the cutting body,and the operating characteristics of the cutting process have been investigated. It is shown that the nature of the dependence of the effective resistance forces on the blade sharpness is determined by the rheological state of the chilled raw material due to a change in the type of fiber deformation upon destruction. With the values of dimensionless sharpness of the knife 0.2; dimensionless cutting speed 5; measures of elasticity 5; dimensionless immersion depth of the knife 1; dimensionless half the width of the deformable layer of 0.4; dimensionless layer thickness 0.01; half angle of knife sharpening 5º; 25º; 35º; 45º, the value of the dimensionless effective resistance force is 4.91; 4.49; 3.88; and 3.07, respectively. With the values of dimensionless sharpness of the knife 0.2; half angle of knife sharpening 20º; dimensionless cutting speed 5; dimensionless immersion depth of the knife 1; dimensionless half the width of the deformable layer of 0.4; dimensionless layer thickness 0.01; elasticity measures 3; 5; 8; 12, the dimensionless force value is 3.16; 4.70; 7.91; and 10.09, respectively.
Abstract
The relevance of the research of the cutting process of chilled food products has been shown. The muscle tissue of the chilled raw material has been described by the Maxwell-Thomson rheological model. The formulation and solution of the problem of mathematical modeling of the effective resistances forces have been completed. The muscle filaments of the product during cutting are interpreted as viscoelastic beams. The bending and tensile strains of the filaments under the influence of the knifepoint have been considered. Expressions for the dimensional and dimensionless forces of effective resistance have been obtained. The dependences of the indicated forces on the cutting edge sharpness, the half angle of knife sharpening, the rheological parameters of the material, the design parameters of the cutting body,and the operating characteristics of the cutting process have been investigated. It is shown that the nature of the dependence of the effective resistance forces on the blade sharpness is determined by the rheological state of the chilled raw material due to a change in the type of fiber deformation upon destruction. With the values of dimensionless sharpness of the knife 0.2; dimensionless cutting speed 5; measures of elasticity 5; dimensionless immersion depth of the knife 1; dimensionless half the width of the deformable layer of 0.4; dimensionless layer thickness 0.01; half angle of knife sharpening 5º; 25º; 35º; 45º, the value of the dimensionless effective resistance force is 4.91; 4.49; 3.88; and 3.07, respectively. With the values of dimensionless sharpness of the knife 0.2; half angle of knife sharpening 20º; dimensionless cutting speed 5; dimensionless immersion depth of the knife 1; dimensionless half the width of the deformable layer of 0.4; dimensionless layer thickness 0.01; elasticity measures 3; 5; 8; 12, the dimensionless force value is 3.16; 4.70; 7.91; and 10.09, respectively.
Keywords: effective resistance, cutting, force, sharpness, knife, edge, rheology, viscoelasticity.
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