Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

Liu, Xianbo; Vlajic, Nicholas; Long, Xinhua; Meng, Guang; Balachandran, Balakumar

doi:10.1007/s11071-012-0690-x

Cited by 129 publications

(64 citation statements)

References 23 publications

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“…An initial periodic response is shown in Fig. 3, which corresponds to a cyclic stick-slip behavior of the drillstring model (8). In panel (b), we show the periodic response for the time window 10 ≤ t ≤ 25s.…”

Section: Numerical Investigation Of the Drill-string Modelmentioning

confidence: 95%

“…In this section, we will present a detailed numerical investigation of the dynamical response of the drillstring model (8). For this purpose, we will apply numerical continuation methods for non-smooth dynamical systems, implemented via the continuation platform COCO [25,26].…”

Section: Numerical Investigation Of the Drill-string Modelmentioning

confidence: 99%

“…A reduced-order model allowing for radial, bending, and torsion motions of a flexible drill-string and stickslip interactions between the drill-string and the outer shell was developed by Liao et al [7]. Later on, Liu et al [8] studied an eight degrees-of-freedom discrete model taking into account axial, torsional, and lateral dynamics of both the drill-pipes and the BHA. Nandakumar and Wiercigroch [9] considered a fully coupled two degrees-of-freedom model which assumed a state-dependent time delay and a viscous damping for both the axial and torsional motions.…”

Section: Introductionmentioning

confidence: 99%

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Numerical and experimental studies of stick–slip oscillations in drill-strings

Liu

Chávez

et al. 2017

Nonlinear Dyn

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The cyclic nature of the stick-slip phenomenon may cause catastrophic failures in drillstrings or at the very least could lead to the wear of expensive equipment. Therefore, it is important to study the drilling parameters which can lead to stickslip, in order to develop appropriate control methods for suppression. This paper studies the stick-slip oscillations encountered in drill-strings from both numerical and experimental points of view. The numerical part is carried out based on path-following methods for nonsmooth dynamical systems, with a special focus on the multistability in drill-strings. Our analysis shows that, under a certain parameter window, the multistability can be used to steer the response of the drill-strings from a sticking equilibrium or stick-slip oscillation to an equilibrium with constant drill-bit rotation. In addition, a small-scale downhole drilling rig was implemented to conduct a parametric study of the stick-slip phenomenon. The parametric study involves the use of two flexible shafts with varying mechanical properties to observe the effects that would have on stick-slip during operation. Our experimental results demonstrate that varying some of the mechanical properties of the drill-string could in fact control the nature of stick-slip oscillations.

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Section: Numerical Investigation Of the Drill-string Modelmentioning

confidence: 95%

Section: Numerical Investigation Of the Drill-string Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical and experimental studies of stick–slip oscillations in drill-strings

Liu

Chávez

et al. 2017

Nonlinear Dyn

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show abstract

“…There are vast of existing literatures using lumpedparameters model to study the drill-string dynamics, e.g. [5][6][7]. Balakumar [5] developed a lumped-parameter model to study the coupled axial, torsion, and lateral dynamics of a drill-string dynamics, including stick-slip and delay effect.…”

Section: Introductionmentioning

confidence: 99%

Proportional-Derivative Control of Stick-Slip Oscillations in Drill-Strings

Lin

Liu

2018

MATEC Web Conf.

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Abstract. Stick-slip oscillation in drill-string is a universal phenomenon in oil and gas drilling. It could lead to the wear of drill bit, even cause catastrophic failure of drill-strings and measurement equipment.Therefore, it is crucial to study drilling parameters and develop appropriate control method to suppress such oscillation. This paper studies a discrete model of the drill-string system taking into account torsional degreeof-freedom, drill-string damping, and highly nonlinear friction of rock-bit interaction. In order to suppress the stick-slip oscillation, a new proportional-derivative controller, which can maintain drill bit's rotation at a constant speed, is developed. Numerical results are given to demonstrate its efficacy and robustness.

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“…Examples include wheel-shimmy [37,41], delaycoupled networks [40], predictive control systems [30,16,31] and machine tool vibrations [36,11,27,32]. Differential equations involving state-dependent delays also often show up in different fields of science, such as classical electrodynamics [13], population models [26,35], market dynamics [6], and, again, machine tool vibrations [23,15,3,28,29]. In this paper, a model is presented for machining, which involves a combination of these two types of delays: a state-dependent distributed delay.…”

mentioning

confidence: 99%

State-dependent distributed-delay model of orthogonal cutting

2015

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In this paper we present a model of turning operations with state-dependent distributed time delay. We apply the theory of regenerative machine tool chatter and describe the dynamics of the tool-workpiece system during cutting by delay-differential equations. We model the cutting-force as the resultant of a force system distributed along the rake face of the tool, which results in a short distributed delay in the governing equation superimposed on the large regenerative delay. According to the literature on stress distribution along the rake face, the length of the chip-tool interface, where the distributed cutting-force system is acting, is function of the chip thickness, which depends on the vibrations of the tool-workpiece system due to the regenerative effect. Therefore, the additional short delay is state-dependent. It is shown that involving statedependent delay in the model does not affect linear stability properties, but does affect the nonlinear dynamics of the cutting process. Namely, the sense of the Hopf bifurcation along the stability boundaries may turn from sub-to supercritical at certain spindle speed regions.

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Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

Cited by 129 publications

References 23 publications

Numerical and experimental studies of stick–slip oscillations in drill-strings

Numerical and experimental studies of stick–slip oscillations in drill-strings

Proportional-Derivative Control of Stick-Slip Oscillations in Drill-Strings

State-dependent distributed-delay model of orthogonal cutting

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