# Mathematical simulation of profile resistance force for double-edged knife during chilled fish cutting

**DOI: 10.17586/1606-4313-2019-18-2-62-71**

**UDC 621.565:664.95**

## Mathematical simulation of profile resistance force for double-edged knife during chilled fish cutting

**Aqeev O.V., Naumov V. A., Fatykhov J.A.**

**For citation:**Ageev O.V., Naumov V.A., Fatykhov J.A. Mathematical simulation of profile resistance force for double-edged knife during chilled fish cutting. Vestnik Mezhdunarodnoi akademii kholoda. 2019. No 2. p.62-71

**Abstract**

The rheological properties of fish muscular tissue are described by Maxwell-Thomson model. On the basis of the energy approach the profile resistance force of double-edged knife has been interpreted as deformational force of friction at the macroscopic scale level provided that the surfaces of the faces are smooth. Using the normal contact pressures on the inclined faces, mathematical models for dimensional and dimensionless profile resistance forces of the double-edged knife has been developed. The dependence of the dimensional force on the rheological properties of chilled fish has been established. It has been shown, that the use of double-edged knife provides a significant reduction of the harmful resistances forces and a reduction of the energy consumption during fish cutting at low temperatures with the monotony changes of the muscle tissue rheological characteristics. The dependence of the force on the cutting speed is non-monotonic with a pronounced maximum. The dimensionless force has been defined as a component of the dimensional force, which characterizes the highly-elastic component of the relative deformation. The dependence of the dimensionless force on the dimensionless cutting speed and measure of the muscle tissue elasticity has been shown. With side edge lengths of 34; 103; 171; and 240 mm force maximums are 0.464; 0.551; 0.583; and 0.601 N, respectively. When the values of instantaneous modulus of elasticity are 1.5·105; 2·105; 2.5·105; and 3·105 N/m2 the maximums of the specified force are0.538; 0.719; 0.899; and 1.080 N, respectively. With dimensionless knife lengths of 1.5; 3; 5; and 8 maximum dimensionless force is 0.931; 1.124; 1.218; and 1.280, respectively. With the values of elasticity measure of 2; 4; 8; and 15 dimensionless force maximums are 1.124; 1.902; 3.458; and 6.176, respectively.

**Keywords:**fish, cutting, force, resistance, profile, knife, edge, rheology, viscoelasticity.

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