Torsional stick–slip vibrations easily occur when the drill bit encounters a hard or a hard-soft staggered formation during drilling process. Moreover, serious stick–slip vibrations of the drill string is the main factor leading to low drilling efficiency or even causing the downhole tools failure. Therefore, establishing the stick–slip theoretical model, which is more consistent with the actual field conditions, is the key point for new drilling technology. Based on this, a new torsional vibration tool is proposed in this paper, then the multidegree-of-freedom torsional vibrations model and nonlinear dynamic model of the drill string are established. Combined with the actual working conditions in the drilling process, the stick–slip reduction mechanism of the drill string is studied. The research results show that the higher rotational speed of the top drive, smaller viscous damping of the drill bit, and smaller WOB (weight on bit) will prevent the stick–slip vibration to happen. Moreover, the new torsional vibration tool has excellent stick–slip reduction effect. The research results and the model established in this paper can provide important references for reducing the stick–slip vibrations of the drill string and improving the rock-breaking efficiency.

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