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March 2019 (published: 29.03.2019)
Number 1(39)
Home > Issue > Mathematical simulation of knife profile resistance forces during fish cutting
Aqeev O.V., Naumov V. A., Fatykhov J.A.
The relevance of researching the process of fish cutting and modeling forces of harmful resistance has been shown. Muscular tissue of fish has been described by Maxwell-Thomson rheological model. The conditions of constrained compression in the direction of cuttingand perpendicular to direction of knife movement have been accepted. On the basis of the energy approach the knife profile resistance force has been interpreted as deformational friction force at the macroscopic scale level, provided that the surface of the faces is smooth.The mathematical models for dimensional and dimensionless profile resistance forces of the flat back and double-edged knives have been developed. The dependences of the dimensional and dimensionless forces on the knife geometry, blade immersion depth, cutting speed, and rheological properties of material have been established. The dependenciesof forces on the dimensionless cutting speed are monotonic, while by absence of constrained compression of the material in the direction of cutting, the corresponding dependences exhibit non-monotonicity and have pronounced maximums.A comparative analysis of the dimensionless profile resistance forces of flat back knife and double-edged knives has been carried out. Using double-edged knife without side edges is shown to provide a significant reduction in the force of harmful resistances and a reduction in the energy consumption during fish cutting.When the value of dimensionless immersion depth, dimensionless cutting speed, dimensionless sample material height, the measure of material elasticity, ratio of half sharpening angles tangent of double-edged knives, dimensionless height of knife with back sides, then the values of dimensionless profile resistance forces of flat back knife and double-edged knives are 57.89; 57.05; 56.34respectively, while dimensionless profile resistance force of flat back knife without constrained compression in the cut direction is 1.91.
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Keywords: pretreatment of raw materials; fish cutting; math modeling; resistance force; knife profile; rheology; viscoelasticity
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
UDC 664.9.022
Mathematical simulation of knife profile resistance forces during fish cutting
The relevance of researching the process of fish cutting and modeling forces of harmful resistance has been shown. Muscular tissue of fish has been described by Maxwell-Thomson rheological model. The conditions of constrained compression in the direction of cuttingand perpendicular to direction of knife movement have been accepted. On the basis of the energy approach the knife profile resistance force has been interpreted as deformational friction force at the macroscopic scale level, provided that the surface of the faces is smooth.The mathematical models for dimensional and dimensionless profile resistance forces of the flat back and double-edged knives have been developed. The dependences of the dimensional and dimensionless forces on the knife geometry, blade immersion depth, cutting speed, and rheological properties of material have been established. The dependenciesof forces on the dimensionless cutting speed are monotonic, while by absence of constrained compression of the material in the direction of cutting, the corresponding dependences exhibit non-monotonicity and have pronounced maximums.A comparative analysis of the dimensionless profile resistance forces of flat back knife and double-edged knives has been carried out. Using double-edged knife without side edges is shown to provide a significant reduction in the force of harmful resistances and a reduction in the energy consumption during fish cutting.When the value of dimensionless immersion depth, dimensionless cutting speed, dimensionless sample material height, the measure of material elasticity, ratio of half sharpening angles tangent of double-edged knives, dimensionless height of knife with back sides, then the values of dimensionless profile resistance forces of flat back knife and double-edged knives are 57.89; 57.05; 56.34respectively, while dimensionless profile resistance force of flat back knife without constrained compression in the cut direction is 1.91.
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Keywords: pretreatment of raw materials; fish cutting; math modeling; resistance force; knife profile; rheology; viscoelasticity
DOI 10.17586/2310-1164-2019-12-1-46-61
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License