Abstract
Based on a lumped parameter model with two degrees of freedom, the periodic response of the coupled axial-torsional nonlinear vibration of drill strings is studied by HB-AFT (harmonic balance and alternating frequency/time domain) method and numerical simulations. The amplitude-frequency characteristic curves of axial relative displacement and torsional relative angular velocity are given to reveal the mechanism of bit bounce and stick-slip motion. The stability of periodic response is analyzed by Floquet theory, and the boundary conditions of bifurcation of periodic response are given when parameters such as nominal drilling pressure, angular velocity of turntable, and formation stiffness are varied. The results show that the amplitude of the periodic response of the system precipitates a spontaneous jump and Hopf bifurcation may occur when the angular velocity of the turntable is varied. The variation of parameters may lead to the complex dynamic behavior of the system, such as period-doubling motion, quasiperiodic motion, and chaos. Bit bounce and stick-slip phenomenon can be effectively suppressed by varying the angular velocity of turntable and nominal drilling pressure.
Highlights
Rotary drilling systems using drag bits are widely used for the exploration and production of oil and gas. ey often suffer from severe vibrations which can be categorized as lateral, axial, and torsional vibrations. ese vibrations can lead to fatigue problems, reduction of bit life, unexpected changes in drilling direction, and even failure of the drill string
When the driving angular velocity of the turntable is at [16, 32], the drill string system makes a simple periodic motion, and the amplitude related to the decrease is greater than that related to the increase. ere is a jump phenomenon in the steady-state response of the axialtorsional coupling vibration of the drill string, and the jump occurs before the peak amplitude with the increase of the angular velocity of the turntable drive. ese results are consistent with the results of theoretical analysis
In this paper, considering the two states of bit contact and noncontact, the axial-torsional coupled nonlinear vibration of drill string is studied based on a two-degree-of-freedom lumped parameter model, by the HB-AFT method and numerical method, respectively
Summary
Rotary drilling systems using drag bits are widely used for the exploration and production of oil and gas. ey often suffer from severe vibrations which can be categorized as lateral, axial, and torsional vibrations. ese vibrations can lead to fatigue problems, reduction of bit life, unexpected changes in drilling direction, and even failure of the drill string. Considering the state-dependent time delay and nonlinear motion caused by dry friction and contact loss, Liu et al [14, 15] established a dynamic model of drill string system with two degrees of freedom and axial-torsional coupling. Gupta and Wahi [16] considered the drill bit bounce and stick-slip caused by the axial regeneration effect under variable cutting depth and used the parameter-concentrated drill string axial torsion model and linear cutting force model to study the overall dynamics of the system. E structure of this paper is as follows: In Section 2, the axial-torsional coupled two-degreeof-freedom nonlinear dynamic governing equation of the drill string based on the complex bit-formation interaction model is given.
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