| Drillstring is the indispensable tool for drilling operations.Due to the influence of many complicated factors,multiple coupled nonlinear motions are often generated,and its motion trajectory is difficult to predict and control.At the same time,drillstring failure accidents occur and cause huge losses.In this paper,through the study of the dynamics of the drillstring system,the mechanism explanation of the drillstring vibration is given in essence,and the nonlinear vibration law of the drillstring is discussed,in order to take good measures to avoid harmful vibration and excite beneficial vibration,which provides scientific basis for engineering design and control.Firstly,based on Euler-Bernoulli beam theory,the vibration response of drillstring under the action of annulus fluid and the nonlinear force at stabilizer is established.The control equation is discretized by Galerkin method,and the transverse principal resonance,sub-harmonic resonance and super-harmonic resonance response formulas of drillstring are derived by multi-scale method.The response curves of drillstring vibration under two different working conditions are given.In order to more truly reflect the lateral dynamic motion law of drillstring,a 4-DOF nonlinear dynamic model of drillstring movement in horizontal or inclined sections is established by applying Lagrange's principle and taking into account the factors such as fluid damping,drillstring-wellbore rubbing and so on.Based on this model,the motion characteristics of drillstring at different deviation angles are analyzed.Secondly,taking the drillstring micro-element as the research object,the force acting on the drillstring under the action of internal and external flow is analyzed,including hydrodynamic force,pressure force,viscous friction force,etc.The motion equation of the drillstring immersing internal and external fluid is established,and the discrete form of the control equation is derived by using the differential quadrature method(DQM).By solving the generalized eigenvalues of the system,the stability of the system under different parameters is discriminated,and the corresponding stability chart is given.Furthermore,in order to observe the dynamic behavior of the drillstring from the overall perspective,the drillstring is simplified into several mass unit parts.The lumped mass dynamics model of the drillpipe-BHA-bit coupling in vertical-horizontal-torsional directions is established.The rubbing effect between drillstring and borehole wall is taken into account.At the same time,the interaction law between drill bit and rock formation is simplified by assuming the bottom hole morphology.With the help of the MATLAB program,the corresponding numerical simulation research is carried out,and the motion patterns of each part of the drillstring under specific working conditions are depicted,and the variation rules of the corresponding control parameters are given.The causes of stickslip vibration of the drillstring are explained theoretically,so as to provide reference for improvement of drilling engineering practice.Finally,in order to more realistically reflect the interaction between bit and rock,the time-delay dynamic differential equation of BHA is established based on the reduction of the aforementioned lumped mass model,meanwhile,introducing the regenerative cutting effect.The numerical simulation technology is applied to study the system,and the motion trajectory of BHA,time-delay effect,stick-slip and regenerative cutting are analyzed.Then,the nonlinear time-delay term of govern equation is linearized with constant time-delay,and the corresponding linear iteration scheme is derived by semi-discrete method.By solving the spectral radius of the transfer coefficient matrix,the stability of the system under different parameters is judged,and the corresponding stability chart is given. |
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