Динаміка відносних крутильних коливань при формуванні регулярного мікрорельєфу на внутрішніх циліндричних поверхнях

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. On the basis of the conducted analysis the mathematical model of dynamic process of formation of a regular microrelief on an internal cylindrical surface of a detail is developed. The peculiarity of this process is that the process of microrelief formation occurs by a concentrated force, the point of application of which in relation to the part is constantly changing in radial and axial directions, and then the mathematical model describing this process will be with a discrete right. It is proposed to model such an action using Dirac delta functions with linear and temporal variables, using the method of regularization of these features, in particular, existing methods of integrating the corresponding nonlinear mathematical models of torsional oscillations of a part. Analytical dependences are obtained, which describe these oscillations in the process of formation of a regular microrelief. 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.