The problem of propagation of bending waves in rotating pipes prestressed by longitudinal force and torque is stated and solved. Such waves are shown to be spiral ones. It is established that four waves exist for every wavelength, two of which are right-handed spirals and the other two are left-handed. These waves propagate with different velocities in different directions Introduction. How the perturbation in a wave deflects from the propagation direction in a continuum is determined by polarization. If perturbation oscillates in one direction all the time, this is the elementary case of a linearly polarized wave. In media transmitting transverse waves, other, more complex types of polarization are possible. For example, if the extreme point of the perturbation vector describes a circle or an ellipse in the plane of oscillation, then the polarization is circular or elliptic. Perturbations with such polarization can be excited as displacements and velocities in elastic waves or intensity of electric and magnetic fields in electromagnetic waves [2,5]. If two harmonic transverse elastic waves of equal length propagate in perpendicular planes of an elastic rod with a phase shift of p/2, the resulting traveling wave will have the form of a spiral. However, the situation will be essentially different if the rod is prestressed by a torque. It will be shown below that no waves other than spiral ones are possible in such a rod. It will be established that for every wavelength there are four such waves, two of which are left-handed spirals, while the other two are right-handed spirals. A dispersion analysis of these waves shows that they are dispersing. The velocities of the right-and left-handed spiral waves are different, and the velocities of each of these waves in positive and negative directions of the rod axis are different too.These results can be used to analyze the dynamic behavior of drillstrings in the oil and gas industries. While rotating, drillstrings, usually several thousand meters long, are subject to torque and longitudinal force. Quite specific dynamic effects are caused by the inertial forces induced by the fluids moving inside them. Therefore, dynamic processes excited in such columns are very complex and are yet to be understood. Some issues of the dynamics of such systems are addressed in [8][9][10][11][12][13].1. Problem Formulation. Consider an infinite elastic pipe subjected to a longitudinal force T and a torque M z . The pipe spins with constant angular velocity r w. A fluid of density r fl moves with velocity V inside the pipe. Let us derive the
Fluoropolymers (FP) are materials with a combination of excellent physical and chemical properties which make them useful in various industries. Thin films of these almost insoluble polymers were deposited with decomposition-evaporation of bulk FP in a vacuum. The pretreatment of the evaporated FP, the pressure of the emitted gas, the activation with accelerated electrons, the additional radio frequency (RF) plasma and the external magnetic field had complex effects on the morphology and relief of polytetrafluoroethylene (PTFE) films. Thin PTFE films with a roughness from 2 to 100 nm were produced. A PTFE film grown in a magnetic filed had nanoworms on its surface. The hardness of PTFE films was increased using low power RF plasma during deposition. The hardness of polychlorothrifluoroethylene (PCTFE) thin film was significantly smaller, whilst the relief of PCTFE films was rougher than that of PTFE films. A conformal PTFE coating was deposited on a nanostructured plastic surface using PTFE evaporation with electron activation and low power RF plasma.
An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic (nonholonomic) models of mechanic interaction between the contacting uneven bodies. The bit is considered to be an absolutely rigid spherical or ellipsoidal body, the well bottom surface can be plane or spherical. It is assumed that the system coaxiality is disturbed through small initial curvature of the drill string, imperfections of the bit and bore-well geometry or the system mass debalance. Linearized equations of the bit whirling are deducted, the frequencies of periodic motions are calculated, and their modes are constructed for different geometric parameters of the spherical and ellipsoidal bits. It is demonstrated that, depending on the system properties, the bit motion can acquire the regimes of forward and backward whirlings or to transit to the state of stationary spinning relative to an immovable center of velocities. The most unfavorable and atypical whirling modes are characteristic for oblate ellipsoidal bits and curvilinear surfaces of the well bottom.
This paper deals with investigatson of the process of drill bit whirling on the rough plane of the well bottom. Nonholonomic kinematic models of the mechanical interaction of contacting bodies with defects at the initial stage of system self-excitation are applied. On the basis of the results of experimental studies, it is believed that one of the main factors influencing on the whirlings vibrations is the geometry of the bit. The bit is considered to be an absolutely rigid ellipsoidal body, the well bottom surface is supposed to be a plane. The resulting oscillations are associated with spontaneous bending deformations of the drill string, which are accompanied by continuous contact of the bit and the rock. The equations of motion of the bit in the linear approximation are obtained. The analysis of the solution of the linearized equations is carried out, and the frequencies of the arising periodic motions are found. The forms of oscillations under different geometrical parameters of an ellipsoidal bit are analyzed. It is shown that the bit can rotate in backward direction, moving at angular velocities that exceed the angular frequency of the drill string. The research results can be used in the development of new types of drilling rigs.
In the paper an initial stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of nonholonomic kinematic models of mechanic interaction between the contacting uneven bodies. It is assumed that the drill bit is an absolutely rigid spherical body, the well bottom surface is spherical too. It is supposed that the system coaxiality is disturbed through small initial curvature of the drill string, defects of the bit and bore-well geometry or the debalance of the system mass. Linearized equations of the drill bit movement are derived, the frequencies of periodic motions are calculated, and their types are constructed for different geometric parameters of the spherical bits. It is shown that, depending on the system properties, the drill bit motion can to transit to the state of stationary spinning relative to an immovable center of velocities or acquire the regimes of forward and backward whirlings.
Поставлена задача про коливання кружляння бурового долота, що обертається, в умовах його контактної взаємодії із шорсткуватим дном свердловини. Оскільки такий тип вібрацій зустрічається в 40% випадків буріння глибоких свердловин, проблема їх вивчення представляє як науковий, так і прикладний інтерес.Встановлено, що ефект самозбурення таких коливань пов'язаний зі збільшенням сили контактного тиску між долотом та свердловиною і її наближенням до критичного значення Ейлера. У цих умовах згинна жорсткість бурильної колони зменшується й вона може випучувати. При цьому вісь долота нахиляється й починає прецесувати. В результаті долото втрачає здатність ковзати по дну й починає котитися по його поверхні, відстаючи або випереджаючи обертання бурильної колони. При такому русі точка контакту долота із зазначеною поверхнею (миттєвий центр швидкостей) може описувати надзвичайно складні траєкторії у вигляді петель і точок загострення й змінювати напрямок руху. В якості прикладу розглянуті коливання кружляння доліт сферичної форми.Ключові слова: глибоке буріння, долото, неголономна динаміка, прямі та зворотні кружляння.Поставлена задача о колебаниях кружения вращающегося бурового долота в условиях его контактного взаимодействия с шероховатым дном скважины. Поскольку такой тип вибраций встречается в 40% случаев бурения глубоких скважин, проблема их изучения представляет как научный, так и прикладной интерес. Установлено, что эффект самовозбуждения таких колебаний связан с увеличением силы контактного давления между долотом и скважиной и ее приближением к критическому значению Эйлера. В этих условиях изгибная жесткость бурильной колонны уменьшается и она может выпучивать. При этом ось долота наклоняется и начинает прецессировать. В результате долото теряет способность скользить по дну и начинает катиться по его поверхности, отставая или опережая вращение бурильной колонны. При таком движении точка контакта долота с указанной поверхностью (мгновенный центр скоростей) может описывать чрезвычайно сложные траектории в виде петель и точек заострения и изменять направление движения. В качестве примера рассмотрены колебания кружения долот сферической формы.Ключевые слова: глубокое бурение, долото, неголономная динамика, прямое и обратное кружение.This paper studies the problem of whirl vibrations of rotating drill string bit under conditions of its contact interaction with the borehole bottom surface. The destructive effects of whirl vibrations of drill bits and drill strings have long been recognized. The backward whirling is believed to randomly happen to some degree in 40 % of all wells.It is shown that the situation is essentially associated with enlargement of the compressive thrust force and its approaching to the Eulerian critical value. Then, the bending stiffness of the drill string reduces, it hogs and the diamond impregnations existing in the bit surface penetrate into the rock medium. As this takes place, the bit axis tilts and nutates. It should be particularly emphasized that at this stage, the bit is under action of the ...
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