The whirl phenomena in the bottom hole assembly (BHA) is believed to be formed by the imbalance of the rotational drill collar. Backward whirl is caused by the nonlinear contact between the BHA and the borehole, and can be extremely damaging to the down hole tools and borehole. In the previous studies, a two-degrees-of-freedom lumped parameter model is developed for representing the drill collar in lateral motions (whirl). Due to the bit-rock interaction, the stick slip torsional vibration is very common. In the current work, therefore, the torsional vibration causing fluctuation of rotary speed is taken into account. The simulation results indicate that the drill collar whirls forward at lower constant rotary speed. With increasing rotary speed, the backward whirl is activated by the contact between the drill collar and the borehole wall. The nonlinear contact forces obey the Hertzian contact law, which led to lateral bounce of the drill collar and impact borehole wall chaotically. The modified Karnopp friction model is adopted to simulate the stick slip rotary vibration of the BHA. The different characters of lateral vibrations are identified by a power spectrum density diagram with and without consideration of the stick slip vibration.

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