Stick-Slip Whirl Interaction in Drillstring Dynamics
01 Apr 2002-Journal of Vibration and Acoustics (American Society of Mechanical Engineers)-Vol. 124, Iss: 2, pp 209-220
TL;DR: In this paper, a stick-slip whirl model is presented which is a simplification of an oilwell drillstring confined in a borehole with drilling fluid, and the disappearance of stickslip vibration when whirl vibration appears is explained by bifurcation theory.
Abstract: A Stick-slip Whirl Model is presented which is a simplification of an oilwell drillstring confined in a borehole with drilling fluid. The disappearance of stick-slip vibration when whirl vibration appears is explained by bifurcation theory. The numerical results are compared with the experimental data from a full-scale drilling rig.
Citations
More filters
Patent•
19 Sep 2008
TL;DR: In this article, a modified drilling path is created to the target location as selected based on the amount of deviation from the planned drilling path, and drilling rig control signals that steer the bottom hole assembly of the drilling system to a target location along the modified path are generated.
Abstract: Methods and systems for drilling to a target location include a control system that receives an input comprising a planned drilling path to a target location and determines a projected location of a bottom hole assembly of a drilling system. The projected location of the bottom hole assembly is compared to the planned drilling path to determine a deviation amount. A modified drilling path is created to the target location as selected based on the amount of deviation from the planned drilling path, and drilling rig control signals that steer the bottom hole assembly of the drilling system to the target location along the modified drilling path are generated.
209 citations
TL;DR: In this article, a dynamic model of the drillstring including the drillpipes and drillcollars is formulated and the equation of motion of the rotating drillstring is derived using Lagrangian approach in conjunction with the finite element method.
181 citations
TL;DR: A broad survey of the drillstring vibration modeling literature can be found in this paper, where the state-of-the-art models for predicting axial, torsional and bending vibrations (uncoupled and coupled), boundary condition assumptions, equation formulation methods, and applications to vibration mitigation are reviewed.
169 citations
TL;DR: In this article, the authors extended the analysis of the self-excited vibrations of a drilling structure presented in an earlier paper by basing the formulation of the model on a continuum representation of the drillstring rather than on a characterization of the drilling structure by a 2 degree of freedom system.
143 citations
TL;DR: In this paper, the authors give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems and present a small number of well-chosen examples of various kinds of nonsmooth systems.
Abstract: The aim of the paper is to give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems. A small number of well-chosen examples of various kinds of non-smooth systems will be presented, followed by a discussion of the bifurcation phenomena in hand and a brief introduction to the mathematical tools which have been developed to study these phenomena. The bifurcations of equilibria in two planar non-smooth continuous systems are analysed by using a generalised Jacobian matrix. A mechanical example of a non-autonomous Filippov system, belonging to the class of differential inclusions, is studied and shows a number of remarkable discontinuous bifurcations of periodic solutions. A generalisation of the Floquet theory is introduced which explains bifurcation phenomena in differential inclusions. Lastly, the dynamics of the Woodpecker Toy is analysed with a one-dimensional Poincare map method. The dynamics is greatly influenced by simultaneous impacts which cause discontinuous bifurcations.
129 citations
Cites methods from "Stick-Slip Whirl Interaction in Dri..."
...…of periodic solutions of Filippov systems are furthermore studied in previous works of the authors (Leine et al., 2000; Leine, 2000; Leine and Van Campen, 2002; Leine et al., 2002; Leine and Nijmeijer, 2004), in which non-conventional bifurcations are addressed as discontinuous bifurcations....
[...]
References
More filters
Book•
30 Sep 1988
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Abstract: Approach your problems from the right end It isn't that they can't see the solution It is and begin with the answers Then one day, that they can't see the problem perhaps you will find the final question G K Chesterton The Scandal of Father 'The Hermit Clad in Crane Feathers' in R Brown 'The point of a Pin' van Gulik's The Chinese Maze Murders Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes They draw upon widely different sections of mathematics
6,398 citations
Book•
01 Jan 1994
TL;DR: In this article, the Branching Behaviour of Nonlinear Equations of Boundary-value Problems Stability of Periodic Solutions Qualitative Instruments Chaos Chaos and Continuation of Continuation.
Abstract: Basic Nonlinear Phenomena Practical Problems Principles of Continuation Calculation of the Branching Behaviour of Nonlinear Equations Calculating Branching Behaviour of Boundary-value Problems Stability of Periodic Solutions Qualitative Instruments Chaos.
537 citations
TL;DR: In this article, a simple and efficient alternate friction model is presented to simulate stick-slip vibrations, which can be integrated with any standard ODE-solver and is shown to be more efficient from a computational point of view.
Abstract: In the present paper a simple and efficient alternate friction model is presented to simulate stick-slip vibrations. The alternate friction model consists of a set of ordinary non-stiff differential equations and has the advantage that the system can be integrated with any standard ODE-solver. Comparison with a smoothing method reveals that the alternate friction model is more efficient from a computational point of view. A shooting method for calculating limit cycles, based on the alternate friction model, is presented. Time-dependent static friction is studied as well as application in a system with 2-DOF.
337 citations
Journal Article•
324 citations
TL;DR: In this article, the authors show how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions, which can jump through the unit circle causing discontinuous bifurcations.
Abstract: This paper treats bifurcations of periodic solutions in discontinuous systems of the Filippov type. Furthermore, bifurcations of fixed points in non-smooth continuous systems are addressed. Filippov's theory for the definition of solutions of discontinuous systems is surveyed and jumps in fundamental solution matrices are discussed. It is shown how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions. The Floquet multipliers can jump through the unit circle causing discontinuous bifurcations. Numerical examples are treated which show various discontinuous bifurcations. Also infinitely unstable periodic solutions are addressed.
281 citations