High-Frequency Torsional Oscillations (HFTO) are bit induced self-excited vibrations which can cause downhole tool failures and reduce the reliability of downhole tools. It is essential to understand the interaction of HFTO with other vibrational phenomena to develop effective HFTO mitigation strategies. While coupling with axial vibrations and stick-slip have already been studied extensively, the interaction of HFTO with lateral vibrations has received less attention. This paper analyzes this interaction based on a bit rock interaction model that accounts for the superimposed movement of whirl and HFTO at the bit.

The excitation of HFTO can be attributed to a velocity-dependent characteristic of the cutting torque. A model that incorporates the superposition of lateral and torsional movement at the bit is used to calculate the velocity-dependent bit torque based on three components: the cutting velocity at each cutter, the normal force distribution along bit blades, and velocity-dependent forces between the bit and the rock. The velocity distribution is based on a kinematic model that superimposes the lateral motion of whirling and the rotational motion of HFTO. The normal force distribution is derived from the bit blade and cutter configuration, and the velocity-dependent force characteristics at each bit element is based on findings of laboratory tests with single cutting elements. A continuous multivariable function determines the nonlinear drilling torque characteristic depending on the amplitudes of HFTO and backward whirl.

Evaluation of the simulated drilling torque shows that HFTO cannot be excited in presence of bit backward whirl. Specifically, it was found that an increasing rate of bit backward whirl leads to a bit torque characteristic generating less energy input or even energy output to HFTO. This is caused by backwards cutters with negative cutting torques corresponding to high energy dissipation. Forward whirl, on the other hand, cannot suppress HFTO. Comparison with laboratory data confirms these results. Cutter geometry and normal force distribution do not appear to have a significant effect on the results in either case.

The new bit model provides a physics-based explanation of why bit backward whirl and torsional vibrations cannot be observed simultaneously. The influence of parameters, like the cutting-edge geometry, can be evaluated much faster than, for example, with particle or finite element models.

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