Unveiling complexity of drill–string vibrations: Experiments and modelling

•Novel experimental rig capable of mimicking all major drill–string vibrations•Nonlinear dynamics of the drill–string modelled using FEM and verified experimentally.•An excellent agreement between the FEM and reduced order models.

We investigate complex drill–string dynamics on a novel experimental rig [1], capable of reproducing all major types of drill–string vibrations. One of the most important features of this versatile experimental rig is the fact that commercial drill–bits and rock-samples are used. The rig allows for different configurations, which enables the experimental study of various phenomena, such as stick–slip oscillations, whirling, drill–bit bounce and helical buckling of the drill–string. Special attention is given to the estimation of the physical parameters of the flexible shaft, which is the element used to mimic the characteristics of the drill–string and plays a crucial role in the creation of undesired vibrations. Furthermore, a low-dimensional model of the drilling assembly based on a torsional pendulum is developed and calibrated by means of the experimental measurements. In addition, a detail high-dimensional model of the drilling rig is developed using a Finite Elements Analysis approach. The experimental and numerical results demonstrate the predictive capabilities of our mathematical models, in particular when stick–slip oscillations occur.