Drilling dynamic dysfunction condition occurs when dynamic forces in the drillstring cause very high stresses and fatigue or physical damage to the string and thus reduced bit performance or caused wellbore damage. These forces may generate from vibrations, shocks, oscillations, and BHA dynamic buckling. Failure of drillstring components due to torsional stresses are caused by torsional vibrations. This work investigates the response of drillstring to torsional vibrations through analysis on an elemental stepped-shaft drillstring model in a vibration damping medium. The work directs its analysis on the stick-slip motion, which is the most common form of torsional vibrations of drillstring while drilling.

The interaction between the wellbore and the drill-bit is identified in this research as the source of excitation, that is, as the downhole vibratory source. Hence, the exciting torque is derived from the resolution of forces and reactions at wellbore-drill-bit contact. The response equations obtained from theories of mechanical vibrations and mathematical principles in this research are in two forms: the transient state and steady-state responses. This work is different from other similar works where only the steady-state response is presented. A computer program was developed and tested with suitable drilling data to solve the response equations. Extensive vibration analysis was carried out using the program to examine the responses of different forms of excitations. Beside this, the effectiveness of a torsional vibration absorber was discussed with regards to reduction of drillstring oscillations. The torque-rectification control (TRC) system was introduced and analyzed as regards its use for automatic vibration control during drilling. Simulation results from the computer program show the impacts of torsional vibration absorber and TRC system. In conclusion, recommendations are given based on practical solutions to the problems of drillstring vibrations and from the findings of this project.