Wirl vibrations of the drillstring bottom hole assembly

Gulyaev, V. I.; Khudolii, S. N.; Borshch, E. I.

doi:10.1007/s11223-010-9252-y

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…Taking into account rotation of the drill string, let us introduce a local coordinate system Ox y z ′ ′ ′ rotating along with the drill string [14,15]. The z′ -axis coincides with the direction of the axis of the rod.…”

Section: Derivation Of the Nonlinear Modelmentioning

confidence: 99%

Modeling of Nonlinear Dynamics of Drill Strings in a Supersonic Air Flow

Khajiyeva¹,

Kudaibergenov²

2015

Proceedings of the 5th International Symposium on Knowledge Acquisition and Modeling

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In this work we study nonlinear lateral vibrations of a drill string moving in a supersonic air flow. A nonlinear mathematical model of drill string vibrations is created on the basis of the nonlinear theory of elasticity making use of the Hamilton principle. Solution to the model is obtained by the Bubnov-Galerkin method in the first, second and third approximations. After reducing to a system of ordinary differential equations the numerical stiffness switching method is applied since the problem appears to be stiff. Comparative analysis of the nonlinear model and its geometrically linear analogue is carried out, and the significance of application of the governing equations taking into account geometric nonlinearity is shown. Drill strings with various parameters of length, operating frequency, axial force, and air flow pressure are investigated.

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Section: Derivation Of the Nonlinear Modelmentioning

confidence: 99%

Modeling of Nonlinear Dynamics of Drill Strings in a Supersonic Air Flow

Khajiyeva¹,

Kudaibergenov²

2015

Proceedings of the 5th International Symposium on Knowledge Acquisition and Modeling

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“…Thus, if the force of the bit thrust to the bottom is not large and adhesion between them is disrupted, then the typical frictional interaction described by the Coulomb friction law prevails. Analysis of the bit dynamics is performed with the use of such model in paper [8].…”

Section: Introductionmentioning

confidence: 99%

Whirl Interaction of a Drill Bit with the Bore-Hole Bottom

Musa¹,

Gulyayev²,

Shevchuk³

et al. 2015

MME

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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.

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“…Analysis of self-excited vibrations of this kind is carried out in another study. 19 In the second kind of motion, the rotating bit rolls without sliding on the bore-hole bottom surface, subjecting to the conditions of kinematic (nonholonomic) constraints. Self-excited vibration analysis of that system can be performed only with the use of nonholonomic mechanics methods.…”

Section: Introductionmentioning

confidence: 99%

Nonholonomic dynamics of drill string bit whirling in a deep bore-hole

Gulyayev

Shevchuk

2013

Proceedings of the Institution of Mechanical Engineers, Part K:

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This article studies the problem of wirl vibrations of a rotating drill string bit under conditions of its friction interaction with the bore-hole bottom surface at the wandering contact point. The mechanism of the bit spinning and rolling without sliding on the rigid surface has been analyzed. To study the wirl vibrations, the methods of nonholonomic mechanics are used. As an example, spherical bit whirling on spherical bore-hole bottom is considered. The kinematic inducement of the rotating bit motion without sliding is shown to be the main cause of its stability loss. The detailed study of the bit whirling revealed three types of its stable and unstable motions associated with direct and inverse rolling as well as pure spinning. It is found that the most detectable influence on dynamics of the system and its stability is exerted by the overall stiffness of the drill string tube, which depends on parameters of compressive axial force and torque and diminishes as their critical values are approached.

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Wirl vibrations of the drillstring bottom hole assembly

Cited by 5 publications

References 7 publications

Modeling of Nonlinear Dynamics of Drill Strings in a Supersonic Air Flow

Modeling of Nonlinear Dynamics of Drill Strings in a Supersonic Air Flow

Whirl Interaction of a Drill Bit with the Bore-Hole Bottom

Nonholonomic dynamics of drill string bit whirling in a deep bore-hole

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