基于状态依赖时滞的钻柱动力学稳定性分析

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (22) : 233-240.

论文

基于状态依赖时滞的钻柱动力学稳定性分析

张鹤1，狄勤丰1,2，王文昌1,2，陈锋3，段浩宇1

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Numerical stability analysis of the rotary drilling system on the basis of state-dependent delay

ZHANG He1,DI Qinfeng1,2,WANG Wenchang1,2,CHEN Feng3,DUAN Haoyu1

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摘要

在石油深井钻探中，钻头与岩石相互作用诱发钻柱系统的自激振动，严重时导致钻头磨损和钻柱疲劳失效，影响钻井效率。钻柱动力系统不稳定的主要原因是钻头与岩石的相互作用引起钻柱动力系统中出现了状态依赖时滞变量，本文考虑钻井液阻尼的影响，给出了控制钻头轴向和扭转运动的状态依赖时滞微分方程，引入钻头运动轨迹函数对状态依赖时滞变量进行描述，将状态依赖时滞微分方程转化为非线性耦合的偏微分和常微分方程，并利用谱方法和伽辽金方法分析了上述耦合方程的线性稳定性，给出了钻柱动力学系统随钻井参数变化的稳定性图谱，对多自由度钻柱动力学系统的稳定性进行了分析。最后，与相关文献中的结果及数值模拟结果进行对比，验证了本文稳定性数值分析方法的准确性，并研究了阻尼对钻柱动力学系统稳定性的影响。通过基于状态依赖时滞的钻柱动力学稳定性分析，有助于控制或避免钻柱的自激振动，进而延长钻头使用寿命，提高机械钻速。
关键词：钻头-岩石相互作用；状态依赖时滞；稳定性分析；粘滑振动；钻柱

Abstract

The bit-rock interaction introduces state-dependent delays in the rotary drilling systems, which cause the instability of the system and thus the self-excited vibrations of the drill string. These vibrations lead to the wear of drill bit as well as fatigue failure of the drill string and hence decrease the drilling efficiency. Therefore, stability analysis of the rotary drilling system helps to optimize the drilling parameters and bit design so as to reduce or eliminate the undesirable self-excited vibrations. In this paper, the state-dependent delay differential equations (SDDDEs) are derived with considering the torsional damping of drilling mud. The delay-related variable is reformulated via the introduction of the bit trajectory function, which transforms the SDDDEs into a system of nonlinear coupled partial differential equation (PDE) and ordinary differential equations (ODEs). The combination of spectral method and Galerkin method is utilized to analyze the linear stability of the coupled PDE-ODEs, which obtains the stability map of the system in the plane of drilling parameters. The fidelity of the proposed method is confirmed in comparison with the published results and the numerical simulation results. Finally, the effects of damping on the stability of the system are studied. The proposed numerical method in this paper could be extended to analyze the stability for a more generic lumped-parameter model with multiple degrees-of-freedom.
Key words bit-rock interaction; state-dependent delay; stability analysis; stick-slip oscillation; drillstring

导出引用

张鹤1，狄勤丰1,2，王文昌1,2，陈锋3，段浩宇1. 基于状态依赖时滞的钻柱动力学稳定性分析[J]. 振动与冲击, 2022, 41(22): 233-240

ZHANG He1,DI Qinfeng1,2,WANG Wenchang1,2,CHEN Feng3,DUAN Haoyu1. Numerical stability analysis of the rotary drilling system on the basis of state-dependent delay[J]. Journal of Vibration and Shock, 2022, 41(22): 233-240

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