Mathematical modeling of stability of mechanical system of discator

Abstract

The study is devoted to the construction of mathematical models of the stability of the mechanical system of the disc harrow for surface tillage. The objects of scientific research are selected disk working bodies on elastic racks and a support-rolling roller. The article presents the results of mathematical modeling of the stability of the mechanical system of the disc with the attachment of the working bodies on the elastic racks and the support-rolling roller. As a result of analytical researches the system of differential equations of oscillations of a frame and working bodies of the disc harrow during performance of technological process taking into account changes of physical and mechanical properties of soil is made. According to the developed algorithm in the Mathematica software package the expression in the form of regression equation for determining the degree of asymptotic stability at the angle of oscillation of the frame φ of the working bodies of the disc depending on its design and technological parameters, namely, the step of the spiral of the first and second rows aI aII, the distance between the elastic struts Δx, diameter d, angles of attack α and the inclination γ of the disk working body, the speed of its movement V when performing the process.

Determining the shape of a flexible thread in the field of horizontal and vertical forces

“…The movement of the tape along the inner surface of a stationary cylinder is considered in [8]. Paper [9] reports the construction of mathematical models of the stability of the functioning of a mechanical system under the condition of its fastening. The resulting models cannot be used for the case of a suspended state of the system.…”