Dynamics of regular microrelief formation on internal cylindric surfaces

Abstract

An analysis of modern literature sources to search for mathematical models describing the dynamics of the process of forming a regular microrelief on the inner cylindrical surface of parts, gas transmission equipment operating in severe operating conditions, in order to increase their life. It is established that there are no mathematical models describing this process and the peculiarities of its implementation under the point action of the deforming element on the workpiece surface. The molding movements accompanying the process of forming a regular microrelief on the inner cylindrical surface of the workpiece are considered and the driving forces that accompany this process are analyzed. A mathematical model of dynamic process of regular microrelief formation on internal cylindric surface of the part has been developed. The process of formation is a unique one as it occurs due to the concentrated force whose point of application varies in radial and axial directions relative to the part. Thus, the action has been described by the mathematical model with discrete right-hand side. This action is proposed to be simulated by Dirac delta functions of linear and time variables using the method of regularization of the specific features under discussion. These peculiar features have been described by the conventional methods of integrating of correspondent nonlinear mathematical models of longitudinal and lateral vibrations of the part. The analytical dependencies describing these vibrations have been obtained based on the initial data. Using Maple software, 3D changes in the torsion angle depending on different output values are constructed. The conducted researches will allow to consider torsional fluctuations that is especially actual for long cylindrical details, such as sleeves of hydraulic cylinders, details of drilling mechanisms and others.