The stability of rotating rods under the action of vibro-impact load

The paper presents the investigation results of the vibro-impact loads’ influence on the stability of vibro-drilling machine’ drill-rod in the process of well in hard rock. The drilling process of such wells is significantly facilitated in case of vibro-impact action. The destroying of the rocks during the vibro-rotary drilling occurs via the complex effect of the vibration impulses and rotational motion. In this way, the task of such drill-rod study stability has actuality. In this case, the various modes of vibration and stability loss are possible. In this regard, the study was done by developed software, in which a technique of computer simulation of the oscillating motion of considerable length rotating rods under the action of axial periodic loads is implemented. Such software gives the possibility to model the oscillatory motion of rotating rods and determine the parameters by witch the dynamic stability loss of the studied system can occur. Using this software the diagrams with regions of stable and unstable motion of the rotating rod were drawn for different parameters of the considered system. The process of oscillation is considered in space with account of inertia forces and geometric nonlinearity of the rod. It is shown, that on certain rotational speeds and frequencies of vibro-impact load there are ranges of unstable motion where the run of equipment can inevitably lead to destruction. The obtained results have been analyzed. The conclusion about the possibility of running the equipment in certain frequency ranges is made.

THE PARAMETRIC OSCILLATIONS OF ROTATING ELASTIC RODS UNDER THE ACTION OF THE PERIODIC AXIAL FORCES

The paper presents the results of numerical investigation of the periodic axial forces’ influence on the transverse oscillations of long rotating rods. The gyroscopic inertia forces are taken to account and space oscillating process of rotating rods is considered with account of geometric nonlinearity. The study has been done with computer program with a graphical interface that is developed by authors. The process of numerical solution of the differential equations of oscillations of rotating rods using the method of numerical differentiation of rod’s bend forms by polynomial spline-functions and the Houbolt time integration method is described. A general block diagram of the algorithm is shown. This algorithm describes the process of repeated (cyclical) solving of the system of differential equations of oscillations for every point of mechanical system in order to find the new coordinates of the positions of these points in each next point of time t+∆t. The computer program in which the shown algorithm is realized allows to monitor for the behavior of moving computer model, which demonstrates the process of oscillatory motion in rotation. Moreover, the program draws the graphics of oscillations and changes of angular speeds and accelerations in different coordinate systems. Using this program, the dynamics of a range of objects which are modeled by long elastic rods have been studied. For investigated objects is shown that on various rotational speeds and beat frequencies the oscillatory motion of the rods occurs with different character of behavior. On certain speeds with different frequencies of axial load the oscillations have definite periodicity and occur with beats of amplitude which are the result of the periodic axial force action.

Buckling of rotating rods under the action of axial compressive forces taking into account their own weight

The article is devoted to the conclusion of resolving equations for solving the tasks of bulging rotating rods subject to the action of compressive co-centric forces taking into account uniformly distributed load along the axis. In this mode, for example, fast-moving shafts operate. The purpose of this article is to provide an engineer with a method for calculating drill pipes, tested diagrams and justification of conditions in rotary drilling. The new mathematical models describing stability of rods taking into account own weight and new software are proposed. Numerical simulation of load intensity distributions in the rod along the axis was carried out, at the same time different types of boundary conditions of rod fixation are used. Mathematical models and software for numerical simulation of stability of rotating rods under action of axial compressive forces have been improved. Note that the effect of torsion moment in the present case may not be considered as insignificant in comparison with the above loads. A new method of calculating stability of rotating rods, allowing to take into account any boundary conditions and taking into account own weight, has been developed and scientifically justified. There are proposed mathematical expressions convenient for practical use, which give very accurate results. Obtained results can be used in evaluation and diagnostics of state of samples of structural materials, in process of experimental investigations and in investigation of fast-flowing rotating processes in rod structures of variable stiffness, made of anisotropic composite materials in machine-building, shipbuilding, aircraft engineering, instrument-making, power engineering, etc.

Study of Vortex Noise of Rotating Blades

The paper gives a brief overview of propeller noise generation mechanisms. The vortex component of the propeller noise is considered in detail. The results of the study of the vortex noise of rotating rods in open areas are presented. The spectral, integral and spatial characteristics of the acoustic field of the rotating rods are obtained. We established that the audibility of rotating rods considered is determined by radiation in the frequency range 250--1250 Hz. We summarized the results of the studies regarding the effect of the flow around the blade profile, characterized by the Reynolds number, on the vortex noise intensity. Findings of research show that the exponent of the dependence of the vortex sound intensity on the characteristic velocity around the blade profile in various ranges of the Reynolds number can vary significantly. When changing the value of lg Re in the range from 1.8 to 5, the final dependence of growth rate exponent first falls from 6 to 3, remains equal to 3 in the range of lg Re from 2.65 to 3.2, and then again increases to 6 for lg Re in the range from 3.4 to 3.7, and with an even larger increase, the exponent increases from 7 to 8 and above (to 11) to lg Re = 4.5. At higher Reynolds numbers, (over 106) corresponding to self-similar modes of flow around the blades of light propeller aircraft, the exponent is 5. Based on the study, we recommend using one of the well-known trailing edge noise models for calculating the vortex noise of propellers at the sketch design stage. The paper also introduces the main methods formulated for reducing the intensity of the vortex sound of rotating blades