Mathematical Modeling of the Resistance Force of the Profile of a Flat-Back Knife

Abstract

Based on the energy approach, the resistance force of a knife profile is presented as the deformational force of friction at the level of the macroscopic scale provided that the surface of the faces is smooth. Mathematical models have been developed for the dimensional and dimensionless resistance forces of the profile considering the normal contact pressures on the inclined faces. The dependence of the dimensional force on the sharpening angle and the thickness of the knife, the rheological properties of muscle tissue, and the cutting speed has been established. The dependence of the dimensionless force on the dimensionless cutting speed and the measure of the elasticity of the muscle tissue has been determined. Expressions for the upper and lower limits of the resistance forces of the profile achieved by varying the cutting speed and the sharpening half-angle have been obtained.