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Research Papers

State-Dependent Delay Influenced Drill-String Oscillations and Stability Analysis

[+] Author and Article Information
Xianbo Liu

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: liuxianbo@sjtu.edu.cn

Nicholas Vlajic

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: vlajic@umd.edu

Xinhua Long

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: xhlong@sjtu.edu.cn

Guang Meng

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: gmeng@sjtu.edu.cn

Balakumar Balachandran

Fellow ASME
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: balab@umd.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 10, 2013; final manuscript received June 27, 2014; published online July 25, 2014. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 136(5), 051008 (Jul 25, 2014) (9 pages) Paper No: VIB-13-1394; doi: 10.1115/1.4027958 History: Received November 10, 2013; Revised June 27, 2014

In this paper, the authors present a discrete system model to study the coupled axial–torsional dynamics of a drill string. The model is developed taking into account state-dependent time delay and nonlinearities due to dry friction and loss of contact. Simulations are carried out by using a 32-segment model with 128 states. Bit bounce is observed through time histories of axial vibrations, while stick-slip phenomenon is noted in the torsion response. The normal strain contours of this spatial–temporal system demonstrate the existence of strain wave propagation along the drill string. The shear strain wave exhibits features of wave nodes and wave loops along the drill string, which indicate that the torsional motion has the properties of a standing wave. When the penetration rate is varied, qualitative changes are observed in the system response. The observed behavior includes chaotic and hyperchaotic dynamics. Stability analysis reveals a stable region for the degenerate one-segment model. This stable region becomes infinitesimally small, as the resolution of spatial discretization is increased. This finding suggests that drill-string motions have a high likelihood of being self-exited in practical drilling operations.

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References

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Figures

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Fig. 1

Representative schematic of a drilling system and its components

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Fig. 2

Discretization and multisegment model

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Fig. 3

Drill bit-rock interaction and time-delay effects

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Fig. 4

The 64DOF system results for axial dynamics with ω0 = 10 and v0 = 2.5: (a) t∧ range of 0–200 and (b) expanded diagram for t∧ range of 196–200

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Fig. 5

The 64DOF system results for torsion dynamics with ω0 = 10 and v0 = 2.5: (a) t∧ range of 0–200 and (b) expanded diagram for t∧ range of 196–200 to show the stick-slip vibrations of the drill bit

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Fig. 6

Strain distribution for drill-string system: (a) normal strain due to axial vibrations and (b) shear strain due to torsional vibrations

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Fig. 7

Route from limit cycle to torus, chaos, and hyperchaos for quasi-static variation of the axial penetration rate when ω0 = 10: (a) periodic motion for v0 = 1.5, (b) quasi-periodic motion for v0 = 2.5, (c) chaotic motion for v0 = 2.7, and (d) hyperchaotic motion for v0 = 3.2

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Fig. 8

Stability boundary in the ω0v0 plane for the degenerate model (n = 1) [15], and numerical verification

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Fig. 9

Stability boundaries for different spatial discretization resolutions of drill string

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Fig. 10

Assembling of the global mass matrix

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