Mathematical modeling of the deformation of a cylindrical ring under the influence of an external load distributed along the generatrix

Abstract

The article is devoted to the mathematical modeling of the deformation of a cylindrical ring under the influence of an external load applied to it by pressing parallel plates. It is shown that at the last stage of oil field operation, the main method of artificial lift is the use of sucker rod pumping units (SRPU), on whose failure-free operation the profitability of oil production largely depends. It is also shown that the technical condition of the SRPU is controlled by the dynamometry method, which is the dependence of the rod string force on the suspension on the stroke of the polished rod. In this case, the main source of information is the force transducer. In the article, we propose using a hollow thick-walled cylinder, which is compressed between traverses consisting of parallel flat plates, as the primary sensitive element of the force transducer. The question of refinement and determination of the non-Hertzian contact deformation during compression of a thick-walled hollow cylinder by two parallel flat plates within the elasticity range is considered. It is shown that the well-known formula for the convergence of the axes of the cylinders being compressed according to the Hertzian method does not take into account the real deformation and convergence of the points of the cylinder due to compression and contact deformation between the generatrices of the cylinders. By solving the differential equation, formulas are derived to determine the value of the elastic deformation of a cylinder depending on its geometric dimensions under the influence of an external load applied to it by pressing plates. An example of calculating elastic deformation for different values of cylinder thicknesses depending on the load is given and its graph is plotted.