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Whirl Interaction of a Drill Bit with the Bore-Hole Bottom 认领 引用 被引量：2
1
作者 Nabil W. Musa V. I. Gulyayev +1 位作者 L. V. Shevchuk Hasan Aldabas 《Modern Mechanical Engineering》 2015年第3期41-60,共20页
This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body... This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body with uneven surface. It is attached to the lower end of a rotating elastic drill string. In the perturbed state, the bit can roll without sliding on the bore-hole bottom, performing whirling vibrations (the model of dynamic equilibrium with pure rolling when maximum cohesive force does not exceed the ultimate Coulombic friction). To describe these motions, a nonholonomic dynamic model is proposed, constitutive partial differential equations are deduced. With their use, the whirling vibrations of oblong and oblate ellipsoidal bits are analyzed, the functions of cohesive (frictional) forces are calculated. It is shown that the system of elastic drill string and ellipsoidal bit can acquire stable or unstable whirl modes with approaching critical Eulerian values by the parameters of axial force, torque and angular velocity. The analogy of the found modes of motions with ones of the Celtic stones is established. It is shown that the ellipsoidal bits can stop their whirling vibrations and change directions of their circumferential motions in the same manner as the ellipsoidal Celtic stones do. As this takes place, the trajectories of the oblate ellipsoidal bits are characterized by more complicated paths and irregularities. 展开更多
关键词 Deep Drilling Ellipsoidal Bits Nonholonomic Dynamics Celtic Stones Instability Forward and Backward Whirling Motions
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Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes 认领 引用 被引量：1
2
作者 Nabil Musa Valery Gulyayev +1 位作者 Nataliya Shlyun Hasan Aldabas 《Journal of Mechanics Engineering and Automation》 2016年第1期25-38,共14页
Notwithstanding the fact that the problem of drill string buckling （Eulerian instability） inside the cylindrical cavity of an inclined bore-hole attracts attention of many specialists, it is far from completion. Thi... Notwithstanding the fact that the problem of drill string buckling （Eulerian instability） inside the cylindrical cavity of an inclined bore-hole attracts attention of many specialists, it is far from completion. This peculiarity can be explained by the complexity of its mathematic model which is described by singularly perturbed equations. Their solutions （eigen modes） have the shapes of boundary effects or buckles （harmonic wavelets） localized in zones of the bore-hole that are not specified in advance. Therefore, the problem should be stated in the domain of entire length of the drill string or in some separated part including an expected zone of its buckling. In the paper, a mathematic model for computer analysis of incipient buckling of a drill string in cylindrical channel of an inclined bore-hole is elaborated. The constitutive equation is deduced with allowance made for action of gravity, contact, and friction forces. Computer simulation of the drill string buckling is performed for different values of the bore-hole inclination angle, its length, friction coefficient, and clearance. The eigen values （critical loads） are found and modes of stability loss are constructed. The numerical results for the case when the inclination angle equals friction angle coincide with ones obtained analytically. 展开更多
关键词 Deep drilling inclined bore-holes drill strings stability singularly perturbed problem.
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