Dynamics of relative torsional vibrations in the formation of a regular microrelief on internal cylindrical surfaces

The article presents the results of analysis modern literature sources in search mathematical models describing dynamics process forming regular microrelief on inner cylindrical surfaces parts operating difficult conditions, order to increase their life cycle. absence this and peculiarities its implementation with point action deforming element surface body part are established. movements tool during a considered driving forces that follow analyzed. Based analysis, model dynamic was developed. peculiarity is formed by concentrated force, application which constantly changing radial axial directions relative part. Therefore, describes will have discrete right-hand side. It proposed such an using Dirac delta functions linear temporal variables, method regularization these features, particular, existing methods integrating corresponding nonlinear torsional vibrations Analytical relations obtained. Using Maple software 3D changes torsion angle depending different values source data constructed. conducted research allow consider oscillations crucial for long details, as sleeves hydraulic cylinders, drilling mechanisms others.