NUMERICAL DIFFERENTIATION OF COMPLEX BEND FORMS OF LONG ROTATING RODS

Abstract

The technique of numerical differentiation of the complex bend forms of long rotating rods is presented. This technique is based on search for new bend forms of the rotating rod by solving the equations of oscillations with using the Houbolt time integration method and the polynomial functions (splines) that are described the current bend form. In it, the spline functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points. Described technique was realized in a computer program with graphic user interface that is developed by author. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation. The results of investigation of the oscillations of long rotating rod are shown. This rod is modeling the drill string operation. Results are shown by possible bend forms at different moments of time after system had been out of equilibrium. It is noted that the action of an axial compressive force that is pointed to the lower end of the vertical heavy rod leads to the effect of twisting to a spiral of its lower part. This effect arises via action of gyroscopic moments, which begin to appear when the lower part of the rod starts to bend and this bending have been growing. It happens because the growth of bending leads to increase the angles of rod cross-sections’ turn, the velocity of change of which is part of the gyroscopic moment. The displayed instance shows, that the considered technique and developed on its basis software allows to investigate the dynamics of the objects which are modeled by heavy long rods.