Simulation of an elementary knife immersion depth into a material at cutting of fish
Existing mathematical models of fish cutting with a blade have been analyzed, their advantages and disadvantages having been revealed. The tail cutting of fish by disk knife has been investigated. A mathematical model of an elementary knife immersion into а material in the form of differential equation of the immersion line has been formulated in polar coordinates. The equation in polar coordinates has been solved by a numerical method that allowed constructing the lines of elementary knife immersion into the material for different knife circumferential speeds. The dependence of the actual cutting angle on the knife circumferential speed, which has pronounced maxima at different circumferential speeds, has been investigated. It is shown that, with increasing circumferential speed, the depth of elementary knife immersion into the material increases, and the immersion line tends to be near the disk knife edge, which results in a decrease in elementary knife efficiency. This results from the increase in the length of the force line along which the knife frictional forces act on the material being cut and, therefore, more energy is expended to overcome frictional forces. As the angle of rotation of the disk knife increases, the actual cutting angle increases also, and the elementary knife efficiency falls, meaning a kinematic blunting of the elementary knife. At rotation angles of from 65º and more, elementary knife is cinematically transformed and again sharpened, that allows to recommend cutting with a knife not only in the range of angles of from 0 to 45º, but also in the range of from 70 to 90º. It is recommended to increase the efficiency of fish cutting by increasing the circumferential speed of the disk knife. It is also recommended to cut еру the material at the minimum actual cutting angle while setting the material thickness and the relative position of the knife against the material.