The paper presents the results of investigation of the axial beat loads' influence on the transverse rotating rods' oscillations and their stability. The perforator's long drills are considered as objects of investigation.The analysis of different author's papers that are studded the dynamics of oscillations of shafts and rotating rods is carried out. The relevance of the research topic is substantiated. The model of the considered dynamic system is described and equations of oscillations in space are given.The technique for investigation is presented. This technique is based on search for new bend forms of rotating rod by solving the equations of oscillations with using the Hubbolt 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.Diagrams with regions of stable and instable motion of the rods, that were found by different parameters and boundary conditions are shown. The analysis of the results is obtained and the conclusion about possibility of operating the equipment in certain frequency ranges is done. The space oscillating process of rotating rods is considered with account of the gyroscopic loads and geometric nonlinearity.

методику чисельного диференціювання складних форм вигину стрижнів значної довжини за допомогою поліноміальних функцій, яка разом із використанням методу інтегрування за часом застосовується для розв'язання задач динаміки коливального руху стрижнів, що обертаються, з урахуванням геометричної нелінійності та інших параметрів. В цій методиці моделювання коливань при обертанні з візуальним представленням результату в реальному часі здійснюється на основі багатократного (циклічного) розв'язку системи рівнянь коливального руху для кожної точки механічної системи з метою пошуку нових координат положення цих точок в кожний наступний момент часу t+t. Реалізація методики здійснена у комп'ютерній програмі з графічним інтерфейсом, що розроблена автором, яка дає змогу в реальному часі спостерігати за розвитком процесу коливального руху змодельованої системи шляхом обчислення і побудови у вікні програми поточних форм вигину стрижнів при коливанні. Наведені результати дослідження коливального руху стрижня, що моделює роботу бурильної колони при обертанні, у вигляді можливих форм вигину, у різні моменти часу, після виведення його зі стану рівноваги. Відмічено, що дія зосередженої на нижньому кінці вагомого стрижня сили, що стискує, призводить до збільшення амплітуди вигину стрижня в його нижній частині, внаслідок чого починає відбуватись закручування стрижня по спіралі. Такий ефект обумовлюється дією гіроскопічних моментів, які виникають саме внаслідок збільшення вигину стрижня в нижній частині, що призводе до збільшення кутів оберту перетину, швидкість зміни яких і є складовими гіроскопічного моменту. На наведеному прикладі дослідження показано, що розглянута методика та реалізоване на її основі програмне забезпечення дає змогу здійснювати дослідження динаміки руху об'єктів, які моделюються стрижнями значної довжини.

The results of numerical investigation of shafts transverse oscillations with account of gyroscopic inertia forces are presented. It is shown what the action and how the gyroscopic forces influence on the transverse oscillations of the shafts during rotation. 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 the system of differential equations of oscillations for every point of mechanical system in order to find the new coordinates of positions of these points in each next point of time t+Dt. 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. Defines the dynamic stability fields and draw the diagrams of found fields. Using this program, the dynamics of a range of objects which are modeled by long elastic rods have been studied. For some objects is shown that on special rotational speeds of shafts with different lengths, in the rotating with shaft coordinate system, the trajectories of center of the section have an ordered character in the form of n-pointed star in time interval from excitation to the start of established circular oscillation with amplitude that harmoniously changes in time. It is noted that such trajectories are fact of the action of gyroscopic inertia forces that arise in rotation.

The paper presents the investigation results of the transmission shaft dynamic behavior in transient modes of motion with change of the rotational speeds. Such modes occur during the transmission shaft transmits torque from engine to executive device. This process can be accompanied by vibration with change of frequency and amplitude of shaft oscillation. Therefore, the question of studying the dynamic behavior of such systems with identifying the impact of rotational speeds changing on them is relevant. In this regard, the study was done by developed software, in which a technique of computer simulation of the oscillating motion of considerable rotating rods under the action of inertia forces is implemented. Such software gives the possibility to model the oscillatory motion of rotating rods and determine the parameters by which the dynamic stability loss of the studying system can occur. Using this software, the diagrams of rod oscillating motion of the rotating shaft were drawn for definite parameters of the considered system. The process of oscillation is considered in space. The mathematical model of transverse oscillations is described by system of differential equations in rotating coordinate system that is tied to the shaft, but diagrams of oscillations is shown in inertial coordinate system. It is shown that when the speed of rotation changes, namely at the time interval of its increase, this process continues with growth of oscillation frequency during the acceleration time. Also shown that the amplitude of oscillations increases, too. After pass to next constant speed of rotation, the frequency of oscillations, as shown in diagrams, decreases back. Such increase of oscillation frequency during the acceleration can lead to undesirable consequences of destructive nature.

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.