Stick-slip torsional vibration raising from bit-formation contact is a catastrophic dynamic phenomenon occurring in deep-water oil and gas drilling systems. The torsional vibrations can result in premature fatigue failure of drilling equipment and reduce drilling efficiency. Thus, studying the dynamics of the system is a vital key to identify the roots of the vibration and establish appropriate mitigation and remediation methods. In this paper, an efficient approach for finite element (FE) modeling of stick-slip vibrations of the full drill strings was proposed. The model was developed based on a rate-dependent formulation of bit-rock interaction, in which the cutting process was integrated through the frictional contact. The nonlinear effects of the large rotations and the geometrically nonlinear axial-torsional coupling were taken into account. The effect of energy dissipation due to the presence of drill mud along the drill pipes and drill collars was incorporated through Rayleigh viscous damping. Modal analysis was conducted to determine the natural frequencies and the mode shapes of the drill string. Furthermore, a five degree-of-freedom lumped parameter model was developed. The performance of the developed models was verified through comparisons with example stick-slip results from a field test. The study showed that the self-excited torsional vibrations may also occur at fundamental frequencies lower than the first natural torsional frequency of the drill string, depending on operational parameters. The conducted research work resulted in a robust and practical integrated FE model to simulate the entire drill string system dynamics under torsional vibrations.

由于钻头与钻头形成接触而产生的粘滑摩擦是在深水油气钻探系统中发生的灾难性动力学现象。扭转振动会导致钻井设备过早疲劳失效，并降低钻井效率。因此，研究系统动力学是确定振动根源并建立适当的缓解和修复方法的关键。本文提出了一种有效的全钻柱粘滑振动有限元（FE）建模方法。该模型是基于与速率相关的位-岩相互作用公式开发的，其中切削过程是通过摩擦接触进行整合的。考虑了大旋转的非线性效应和几何非线性的轴向扭转耦合。由于瑞利粘滞阻尼，沿钻杆和钻collar存在钻探泥浆，从而产生了能量耗散效应。进行模态分析以确定钻柱的固有频率和振型。此外，建立了一个五自由度集总参数模型。通过与来自现场测试的示例粘滑结果进行比较，验证了开发模型的性能。研究表明，根据运行参数，自激扭转振动也可能在低于钻柱的第一个自然扭转频率的基频上发生。进行的研究工作建立了一个强大而实用的集成有限元模型，可以模拟扭转振动下整个钻柱系统的动力学。