Semi-Analytical Approach for Derivation of an Equivalent Modal Friction-Damping Ratio and its Application in a Self-Excited Drilling System

Abstract 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.