scholarly journals Theoretical and Numerical Analysis of Coupled Axial-Torsional Nonlinear Vibration of Drill Strings

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xinye Li ◽  
Tao Yu ◽  
Lijuan Zhang ◽  
Hao Zeng ◽  
Congcong Duan
Keyword(s):  
Angular Velocity ◽  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Period Doubling ◽  
Relative Displacement ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Periodic Response ◽  
Variation Of Parameters ◽  
Theoretical And Numerical Analysis

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.

scholarly journals State Feedback and Torque Feed Forward Combined Control System for Suppressing Drill-Strings Stick-Slip Vibration

2019 ◽  
Vol 37 (2) ◽  
pp. 291-298
Author(s):  
Meng Fu ◽  
Jianghong Li ◽  
Yafeng Wu ◽  
Shubiao Song ◽  
Aiqi Zhao ◽  
...  
Keyword(s):  
Control System ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Dynamic Performance ◽  
Experimental Tests ◽  
State Observer ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Feed Forward ◽  
Reference Governor

In drilling field, drill-strings stick-slip vibration is a common phenomenon and may lead to a series of drilling accidents. In order to improve drilling efficiency, this paper commits to study a new control system to suppress the undesired stick-slip vibration. In this work, a two degrees of freedom lumped parameter model is established to imitate the drill-strings. A state observer is proposed to estimate the unknown drill-strings states. A reference governor is put forward to optimize drilling parameters. In addition, in order to enhance the anti-interference ability of the closed-loop system, a torque feed forward is introduced into the control system. Based on the state observer and the reference governor, a state feedback and torque feed forward combined controller is designed. The simulation results indicate preliminarily that the designed state feedback and torque feed forward controller, compared with the drilling industry PI controller, has better dynamic performance and stronger ability to eliminate the drill-strings stick-slip vibration. Finally, the control system is applied in the drilling field. The experimental tests demonstrate that the designed controller can effectively suppress the drill-strings stick-slip vibration.

scholarly journals Fractional-order controllers for stick-slip vibration mitigation in oil well drill-strings

2021 ◽  
pp. 146134842098404
Author(s):  
Massinissa Derbal ◽  
Mohamed Gharib ◽  
Shady S Refaat ◽  
Alan Palazzolo ◽  
Sadok Sassi
Keyword(s):  
Fractional Order ◽  
Degrees Of Freedom ◽  
Lumped Parameter Model ◽  
Oil Well ◽  
Proportional Integral Derivative ◽  
Stick Slip ◽  
Proportional Integral ◽  
Drilling Performance ◽  
Weight On Bit ◽  
Rotary Speed

Drillstring–borehole interaction can produce severely damaging vibrations. An example is stick–slip vibration, which negatively affects drilling performance, tool integrity and completion time, and costs. Attempts to mitigate stick–slip vibration typically use passive means and/or change the operation parameters, such as weight on bit and rotational speed. Automating the latter approach, by means of feedback control, holds the promise of quicker and more effective mitigation. The present work presents three separate fractional-order controllers for mitigating drillstring slip–stick vibrations. For the sake of illustration, the drillstring is represented by a torsional vibration lumped parameter model with four degrees of freedom, including parameter uncertainty. The robustness of these fractional-order controllers is compared with traditional proportional-integral-derivative controllers under variation of the weight on bit and the drill bit’s desired rotary speed. The results confirm the proposed controllers effectiveness and feasibility, with rapid time response and less overshoot than conventional proportional-integral-derivative controllers.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

Study of stick–slip suppression and robustness to parametric uncertainty in drill strings containing torsional vibration tool using sliding-mode control

2021 ◽  
pp. 146441932110452
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Siqi Zhou ◽  
Yinglin Yang ◽  
Liming Dai
Keyword(s):  
Torsional Vibration ◽  
Complex Dynamics ◽  
Sliding Mode ◽  
Parametric Uncertainty ◽  
Drill String ◽  
Lumped Parameter Model ◽  
Drilling Process ◽  
Drill Bit ◽  
Stick Slip ◽  
Drilling Operations

Excessive stick–slip vibration of drill strings can cause inefficiency and unsafety of drilling operations. To suppress the stick–slip vibration that occurred during the downhole drilling process, a drill string torsional vibration system considering the torsional vibration tool has been proposed on the basis of the 4-degree of freedom lumped-parameter model. In the design of the model, the tool is approximated by a simple torsional pendulum that brings impact torque to the drill bit. Furthermore, two sliding mode controllers, U1 and U2, are used to suppress stick–slip vibrations while enabling the drill bit to track the desired angular velocity. Aiming at parameter uncertainty and system instability in the drilling operations, a parameter adaptation law is added to the sliding mode controller U2. Finally, the suppression effects of stick–slip and robustness of parametric uncertainty about the two proposed controllers are demonstrated and compared by simulation and field test results. This paper provides a reference for the suppression of stick–slip vibration and the further study of the complex dynamics of the drill string.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

Experimental Exploration of Schallamach Waves and Self-Excitation in a Belt-Drive System

2018 ◽  
Author(s):  
Yingdan Wu ◽  
Michael Varenberg ◽  
Michael J. Leamy
Keyword(s):  
Angular Velocity ◽  
Dynamic Behavior ◽  
Oscillation Amplitude ◽  
Operating Conditions ◽  
Drive System ◽  
Belt Drive ◽  
Stick Slip ◽  
Stick Slip Motion ◽  
System Inertia ◽  
Slip Motion

We study the dynamic behavior of a belt-drive system to explore the effect of operating conditions and system moment of inertia on the generation of waves of detachment (i.e., Schallamach waves) at the belt-pulley interface. A self-excitation phenomenon is reported in which frictional fluctuations serve as harmonic forcing of the pulley, leading to angular velocity oscillations which grow in time. This behavior depends strongly on operating conditions (torque transmitted and pulley speed) and system inertia, and differs between the driver and driven pulleys. A larger net torque applied to the pulley generally yields more remarkable stick-slip oscillations with higher amplitude and lower frequency. Higher driving speeds accelerate the occurrence of stick-slip motion, but have little influence on the oscillation amplitude. Contrary to our expectations, the introduction of flywheels to increase system inertia amplified the frictional disturbances, and hence the pulley oscillations. This does, however, suggest a way of facilitating their study, which may be useful in follow-on research.

ASYMPTOTIC NUMERICAL METHOD FOR THE DYNAMIC STUDY OF NONLINEAR VIBRATION ABSORBERS

2014 ◽  
Vol 06 (05) ◽  
pp. 1450053 ◽  
Author(s):  
FATHI DJEMAL ◽  
FAKHER CHAARI ◽  
JEAN LUC DION ◽  
FRANCK RENAUD ◽  
IMAD TAWFIQ ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Vibration Control ◽  
Numerical Method ◽  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Equation Of Motion ◽  
Vibration Absorbers ◽  
Asymptotic Numerical Method ◽  
Dynamic Absorber ◽  
Newton Raphson

Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. One of the most common methods of vibration control is the use of the dynamic absorber. The paper is interested in the study of a nonlinear two degrees of freedom (DOF) model. To solve nonlinear equation of motion a high order implicit algorithm is proposed. It is based on the introduction of a homotopy, an implicit scheme of Newmark and the use of techniques of Asymptotic Numerical method (ANM). We propose also a regularization of the contact force to overcome the difficulty of the singularity in this model. A comparison will be presented between the results obtained by the proposed algorithm and those using the classical Newton–Raphson and Newmark time scheme.

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