Dynamic model of process of deformation of elastic rack of disk cultivator

Abstract

The article presents the results of theoretical studies of the dynamic model of the process of deformation of the elastic rack of a disk tool of arbitrary shape, a system of differential equations in general and developed the corresponding program code in Mathematica software package. Taking the form of an elastic discus disk for an Archimedean spiral, when the functions of its boundaries are given in polar coordinates, where the parameters of the geometric shape a (spiral pitch), b (spiral displacement along the radial coordinate), h (elastic column thickness) are determined by its equivalent physical a mathematical model in the form of a rigid mathematical pendulum of length l, to the load of which are attached two springs along the axes Ox and Oz with stiffness coefficients kx and kz, respectively, which deflect it by an angle φ. The dependences of the stiffness coefficients kx and kz, the length l and the angle φ of the equivalent physicomathematical model of the elastic stand of the disc with the parameters of the geometric shape a=0.8 m, b=0 m, h=0.01 m on the values of Fex and Fez, acting on the free end of the rack along the axes Ox and Oz.