Abstract
When constructing a mathematical model for the interaction of a free-rotating plane disk with soil, it is necessary to take into account that the magnitude of its kinematic parameter, equal to the ratio of its circumferential velocity to the speed of translational movement of the disk, is not a given quantity, but a definite quantity. With uniform rotation of the disk and its translational movement at a constant speed, the kinematic parameter is determined from the equilibrium equation of external forces, applied to the disk. The generalized mathematical model of disk-soil interaction, proposed earlier, was taken into account, but in view of relative complexity it was not widely used. The aim of the study is to construct a simpler, but adequate mathematical model for the interaction of a free-spinning disc with soil. The model is constructed under the assumptions of the constancy of the translational velocity of the disk, the permanence of its penetration and the possibility of replacing the pressure on the disc’s lateral surfaces with its mean value and replacing the force per unit length of the blade with its mean value. Since the distribution of the elementary forces of soil reactions is ultimately determined by the distribution of the absolute velocities of the points of the disk in contact with the soil, the resultant reactions of the soil and their total moment are functions of the kinematic parameter of the disk and its relative burial. These functions are given by integrals, that are not expressed in terms of elementary functions by a finite number of operations. However, the proximity of the kinematic parameter of the free-spinning disk to unity makes it possible, with the help of an estimate of these integrals, to obtain approximate expressions in terms of elementary functions for the resultant reactions of the soil and their total angular momentum. It is shown that the accuracy of the approximations obtained is sufficient for engineering practice.
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