Analysis motion of borehole-expander - device for densifying subsurface walls of boreholes

Abstract

The paper introduces an algorithm for analyzing the following solids of rotation and their motion: a bearing roller and a borehole-expander - a device for densifying subsurface walls of boreholes. These devices are moving in the environment with rheological properties typical for the Kelvin model, with nonholonomic constraints that impose restrictions on the velocity of the disk points. The research presents both mathematical models of the standard viscoelastic hereditary-deformed cylinder and a weakly singular model proposed by A.R. Rzhanitsin, representing a nonautonomous system of differential equations in the form of Routh. The fact that this system is nonautonomous complicates its sustainability analysis. The presentation of a rheological force in a differential form does not lead to a system of equations in the form of Chaplygin. The solution was found by numerical integration. The solution is multivariant as one initial value of generalized coordinates and generalized accelerations corresponds to a series of initial generalized speeds. It is shown that the disk is not able to fall in the course of motion because its point of contact being in a radial vibration is still within the tension region of the cylinder wall.