In this article, friction-based damping principles and their suitability for dampening self-excited torsional oscillations in drill strings are investigated. Analytical and semi-analytical solutions based on a modally reduced model are derived by approximating the dynamic behavior with the Harmonic Balance method. The results are validated through time-domain simulations, and limitations of the method are shown. The method enables consideration of the damper position that determines the local amplitudes experienced by the damper. In analytical solutions, the damper location is represented by the local value of the mass-normalized mode shape. The analytical approach can be used to calculate and optimize an equivalent damping ratio for every torsional mode based on the parameters and placement of the friction damper. The provided damping can then be used to estimate the stability of critical torsional modes.

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Recent advances in downhole vibration monitoring have enabled detection of high-frequency torsional oscillations (HFTO) of drilling systems in the field. The general understanding of torsional behavior of drilling systems derived from elaborate efforts in the literature does not explain the mechanism responsible for HFTO. Even for the well-known and extensively studied stick/slip vibrations, the mechanism perpetuating the vibrations is not agreed upon by researchers. The paper discusses findings from experimental and analytical studies regarding the HFTO of bottomhole assemblies (BHAs). The phenomenon is investigated and reproduced in field tests, full-scale laboratory tests, and computer modeling. Drilling conditions are identified in which the drilling system is prone to exhibit the vibrations. Interaction of the bit and the drilling system, which can generate self-excited vibrations, is investigated using analytical methods. Cutter-rock interaction as a possible excitation source is studied using laboratory experiments to elucidate its interaction with the system. The integrated analysis investigating rock, cutter, bit, and BHA interaction identifies HFTO as a bit-induced BHA torsional resonance that can occur at vibration modes higher than the fundamental mode of the BHA. It is demonstrated that modes most susceptible to exhibiting HFTO can be identified and the dominant mode predicted. The understanding gained can be employed to mitigate torsional resonance and enhance drilling performance.

Drilling systems are subject to torsional vibrations that are excited by bit-rock or by drillstring formation interaction forces. These torsional oscillations can be distinguished by mode shape and frequency. Well-known stick/slip oscillations are characterized by low frequencies (usually below 1 Hz) and affect the entire drill-string. High-frequency torsional oscillations (HFTO), in contrast, name the excitation of a high-order natural mode (reaching 400 Hz). In case of HFTO, the bottom-hole assembly (BHA) is exposed to high dynamics loads. Torsional vibrations compromise drilling efficiency and tool reliability. To address these challenges, we are proposing a method for automated BHA optimization based on mechanical drill string models. Through extensive analysis of high-frequency (1400 Hz sampling frequency) data from field measurements, an analytical, verified, and easy to use criterion for the prediction of the excited torsional mode and the corresponding loads was derived. The criterion is based on the comparison of the resulting excitation from cutting forces at the bit and the damping of a torsional mode. The criterion is unique for every torsional mode and can be used to rank the susceptibility of torsional modes for HFTO or stick/slip. A software application (Torsional Oscillation Advisor, TOA) has been developed for user-friendly interpretation of the underlying analytical method towards practical issues. The use of the TOA provides valuable input for drilling optimization: For stick/slip, the influence of various drill pipe sizes and the length of the drill pipe section on torsional stick/slip mode are analyzed. It is shown that the limit for stable drilling in case of bit induced stick/slip can be extended by stiffer drill pipes whereas the influence of the length of the drill pipe section is marginal. The material of the bit and its mass distribution is shown to have a considerable influence on the excitation of HFTO. The software also enables automated BHA optimization in both new product development and tool operation phases. A numerical optimization approach is used to minimize the susceptibility of the bottom-hole assembly for stick/slip and HFTO for given constraints of the geometry and material parameters. Herein, a significant increase of stable drilling conditions regarding weight on bit and bit rotational speed with respect to torsional oscillations is achieved. Even small changes in the drilling system design have a visible impact on the torsional stability. The ability to identify and predict modes of stick/slip and HFTO that are most likely to be excited while drilling, an extension of the stable drilling zone and the estimation of loads before field deployment will result in higher drilling efficiency, more reliable tools and lower non-productive time.

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