An anti stick–slip tool (ASST) is a mechanical device comprised of two parts connected to each other by a pre-loaded spring and a helical spline, which mathematically is a constraint. This constraint converts an excessive external torque to an axial displacement during operation of the tool, which shortens a drill-string and prevents a drill-bit to get stuck. In this study, a mathematical model of the ASST has been developed for the first time by considering internal friction on the helical spline and a pre-load of the internal spring, where we propose four distinct states of the coupled rotational and axial movements of this tool. The system is described by a non-smooth oscillator when the tool is activated, and by a kinematic relation when the tool is not activated. During operation, axial and rotational movements are applied at the top part of the ASST, and the axial force and torque acting at the bottom are prescribed as external excitations. Parametric studies are presented, and undertaken modelling and the obtained results are first steps to fully understand the mechanics of the ASST, where there is an interplay between the dry friction and the pre-load. This study should help to understand intricacies of the ASST operation, and it can be used to create a more realistic model by relaxing simplifying assumptions to describe the operation of the tool with more fidelity.
- Anti stick–slip tool
- Drill-string dynamics
- Dry friction
- Torsional and axial vibrations