Solving the Contact Problem of Elasticity Theory in Modelling an Operating Tool for Tillage

Viewing soil as a medium with linear elastoviscous deformation, a mathematical model is proposed, which makes it possible to develop a toothed tool with such a shape of the working surface that satisfies the agrotechnical, technological and economic indicators when soil tilling. The operating tool is made in the form of a block of teeth. The valley and the protrusion of the tooth in the horizontal plane are made along a logarithmic spiral, and the protrusions are made in the form of a fourth-degree parabola. The toothed tool equation is presented as a combination of rotation, displacement and compression matrices.