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Research Papers

Drill String Bit Whirl Simulation With the Use of Frictional and Nonholonomic Models

[+] Author and Article Information
V. I. Gulyayev

Department of Mathematics,
National Transport University,
Suvorov Street, 1,
Kiev 01010, Ukraine
e-mail: valery@gulyayev.com.ua

L. V. Shevchuk

Department of Mathematics,
National Transport University,
Suvorov Street, 1,
Kiev 01010, Ukraine

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 29, 2014; final manuscript received October 6, 2015; published online December 8, 2015. Assoc. Editor: Carole Mei.

J. Vib. Acoust 138(1), 011021 (Dec 08, 2015) (9 pages) Paper No: VIB-14-1362; doi: 10.1115/1.4031985 History: Received September 29, 2014; Revised October 06, 2015

The problem about computer simulation of whirl vibrations of a drill bit is considered. The dynamic process is assumed to be in an incipient stage when the bit rolls on the borehole bottom without reaching the well wall. Mathematic models of the bit moving based on assumptions of frictional (rolling with sliding) and kinematic (pure rolling) contact between the bit and borehole bottom surfaces are elaborated. The influence of the drill string (DS) bending flexibility and the bit shape on the whirl process is discussed. The most typical whirl phenomena are grounded due to computer simulation.

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Topics: Whirls , Vibration
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References

Figures

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Fig. 1

Frictional (a) and nonholonomic (b) models of a body movement on uneven surface

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Fig. 2

Structural (a) and calculation (b) schemes of drill bit whirling

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Fig. 3

Schematic of forces and moments acting on separated bit in the inclination plane

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Fig. 4

Top view of positions of points C and G and trace of the inclination plane σ

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Fig. 5

Diagram of friction force change in the regimes of bit rolling and sliding

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Fig. 6

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.1m, b=0.3m, T=−1×104N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

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Fig. 7

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.1m, b=0.3m, T=−1×105N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

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Fig. 8

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.3m, b=0.1m, T=−1×104N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

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Fig. 9

The trajectories of the oblong bit center C moving in the fixed reference frame (a=0.3m, b=0.1m, T=−1×105N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=1.0; d−μ=10; e−μ=30; f− nonholonomic model

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Fig. 10

Modes of bit vibrations in the fixed coordinate system (a=0.3m, b=0.1m, T=−1×105N, Mz=−1×104N m, ω=5rad/s): a−μ=0.2; b−μ=0.5; c−μ=30; d− nonholonomic model

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Fig. 11

The trajectory of the oblong bit center C moving in the fixed reference frame (a=0.3m, b=0.1m, T=−1×104N, Mz=−1×104N m, ω=10rad/s, μ=1, 0≤t≤20s)

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Fig. 12

Functions of angular velocities of the bit whirling (ωb) and the DS rotation (ω)

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