Abstract
This paper proposes a lumped parameter model for the torsional vibration of a drill string, with a nonlinear friction torque representing the bit-rock interaction. This model is sufficient to analyze torsional instability (stick-slip oscillations). In the first part of the paper, field data with 50 Hz sample rate are used to fit the bit-rock interaction curve. With the identified bit-rock interaction model, the response of the proposed computational model is compared with the bit speed (field data), showing a good agreement. In the second part of the paper, the numerical model is used to construct a torsional stability map (rotational speed at the top vs. weight-on-bit). It should be remarked that the field data available in this paper is precious, due to its high frequency rate, and that the proposed model, although neglecting axial an lateral vibrations, can effectively tackle the problem of torsional stability.
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