Drill-string stability and stress localization: Influence of complex delay effects and dry friction

With the aim of enhancing the understanding of the complex dynamics of deep drilling, an integrated model with complex time delays and Stribeck friction is presented for studies on the axial-torsional dynamics of a drill string. Various aspects of the drill string are considered, including spatial distribution, structural and external damping, dry friction-induced damping, boundary conditions, and complex bit-rock interactions. The drill-string structure is spatially discretized by using the finite element method. With the resulting discretized complex delay system, stability analysis is conducted following the semi-discretization procedure. Through parametric studies, the effects of drilling parameters, dry friction, boundary conditions, and rock-strength properties on the drilling stability are obtained. Subsequently, an optimally tuned boundary condition with compliance is deployed at the top drive to expand the stable region and mitigate self-excited vibrations in the operational parameter space of drilling. To find the distribution of stress along the drill string, numerical simulations are conducted. The dynamical stress caused by self-excited vibrations is illustrated in the spatial- temporal plane. Strain and stress analysis reveal wave propagation along the drill string, including traveling and standing waves. The dynamic effective stress along the drill string is studied, and the von Mises effective stress is determined by combining the axial stress and torsional stress. On the basis of this information, the locations of the vulnerable points along the drill string are found in terms of structural strength. Finally, the tuned boundary condition at the top is deployed in the numerical simulations to show vibration control effectiveness. The results point to two possible vibration-cancellation approaches that can benefit from a tuned top boundary. The findings of this work can serve as a basis for identifying the locations of vulnerable points and alleviating the levels of axial-torsional vibrations in drilling applications.