When drilling ultra-deep wells with polycrystalline diamond compact (PDC) bits, the drillstring suffered from severe vibrations that were responsible for the premature failure of drillstring components and the inefficient drilling process. In this paper, a field experiment was conducted in an ultra-deep well to measure the downhole tri-axial accelerations of the drillstring. The analyses of the acceleration data in the time and frequency domains show that the drillstring is subjected mainly to violent stick–slip and whirling vibrations. Comparisons between two adjacent sets of tri-axial acceleration data suggest that the occurrence of stick–slip oscillations intensifies the downhole drillstring whirling vibrations. To numerically study the measured stick–slip and whirling vibrations, a fully coupled finite element model for the axial, torsional and lateral vibrations of the drillstring is developed. The bit–rock interaction, which is responsible for the stick–slip oscillations, is modeled by a non-regularized dry friction law, the key parameters of which are fitted by the experimental results. Hertzian contact theory is used to model the nonlinear contacts between the drillstring and the wellbore wall. The downhole angular velocity fluctuations that are due to the stick–slip oscillations are also considered, and they lead to the coupling between the stick–slip and the whirling vibrations. The satisfactory agreement between the numerical and experimental results supports the fidelity of the proposed finite element model. The experimentally observed intensifying effects of the stick–slip oscillations on the whirling vibrations are verified via comparisons between simulation results with and without consideration of the coupling effects. On this basis, parametric studies are conducted to analyze the influence of the drilling parameters on the stick–slip oscillations and the whirling behaviors.

在使用多晶金刚石复合片（PDC）钻头钻超深井时，钻柱会遭受剧烈的振动，这是导致钻柱组件过早失效以及钻进过程效率低下的原因。在本文中，在超深井中进行了现场试验，以测量钻柱的井下三轴加速度。在时域和频域上对加速度数据的分析表明，钻柱主要受到剧烈的粘滑和旋转振动的影响。两组相邻的三轴加速度数据之间的比较表明，粘滑振动的发生加剧了井下钻柱回旋振动。为了对测得的粘滑和回旋振动进行数值研究，采用了轴向耦合的全耦合有限元模型，产生了钻柱的扭转和横向振动。由非规则的干摩擦定律对负责粘滑滑动的钻头-岩石相互作用进行建模，其关键参数与实验结果相符。赫兹接触理论用于模拟钻柱和井眼壁之间的非线性接触。还考虑了由于粘滑振荡引起的井下角速度波动，它们导致粘滑和回旋振动之间的耦合。数值和实验结果之间令人满意的一致性支持了所提出的有限元模型的保真度。在不考虑耦合效应的情况下，通过模拟结果之间的比较，可以验证实验观察到的粘滑振动对回旋振动的增强作用。在此基础上，进行了参数研究，以分析钻削参数对粘滑振动和回旋行为的影响。