| Summary: | This thesis has been motivated by the need to construct reliable, experimentally callibrated models of the drill-string assembly, that capture important phenomena associated with the drilling process, such as torsional oscillations, stick-slip and whirling. This can be achieved using a continuous finite element model, as well as low-dimensional torsional pendulum models in limited cases. The importance of this work lies in the fact, that the experimental rig utilizes real industrial drillbits and rock samples, which after careful identification of TOB speed curves, allows to use an equivalent friction model to accommodate for both frictional and cutting components of the bit-rock interactions. As a first step, a preliminary calibration of the FE model for a straight configuration of the drill-string is carried out, that allows to utilize the low-dimensional model to replicate behaviour of the system. In both of these cases, the agreement between experiments and modelling is achieved. Based on these preliminary studies, it is possible to verify the model in a prebuckled drill-string configuration, for which case a qualitative as well as quantitative agreement with the experiment is obtained. This allows to identify regions where the most dangerous phenomenon of stick-slip is present in parameter space of WOB and top angular speed. Next, the analysis is focused on the whirling phenomenon and calibration of the reduced order rotor model to replicate the motion of the BHA in the bore-hole. A qualitative agreement with the experiments is obtained. An interesting phenomenon of co-existing forward and backward periodic whirling solutions are observed both experimentally and numerically. The influence of the initial conditions and the friction between the BHA and the borehole are investigated, what revealed that there is a threshold value of friction coefficient for which the whirling direction changes from forward to backward.
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