Derivation and experimental validation of an analytical criterion for the identification of self-excited modes in drilling systems

A Method for the Design and Optimization of Nonlinear Tuned Damping Concepts to Mitigate Self-Excited Drill String Vibrations Using Multiple Scales Lindstedt-Poincaré

“…In addition, the large but slim design of the drill string with little available installation space leads to low reactive effects of dampers on the torsional dynamics of the drill string. In [8,16,19], a The mass and stiffness matrix are determined from the design of the generic bottom hole assembly (BHA) using Young's modulus, density and geometry, while the damping matrix is unknown. Previous studies show that, in many cases, a critical mode dominates the system behavior [17,18].…”

“…Therefore, the damping matrix can be determined by the modal damping ratio of the modes. Using the predictive criterion derived in [8] and determining the S c,k value, the BHA can be reduced to a single modal degree of freedom representing the critical high frequency mode. This modal reduction of the torsional dynamic of a drill string is despite its complexity suitable, because when HFTO occur, mostly one critical mode dominates the entire torsional system dynamic of the BHA.…”

“…The bit rock interaction during drilling is a complex process with many uncertainties [6], which can be considered, in various ways, e.g., with hybrid uncertainties [7]. It has been shown that, for the torsional dynamic of the drill string, the energy input can be modeled using a nonlinear torque characteristic at the bit [8]. Due to improved and new measuring tools, high-frequency oscillations have been identified as the cause of numerous drill string failures and have been intensively investigated over the last years with studies [9,10], simulations [8,11] and experiments [12,13].…”

“…It has been shown that, for the torsional dynamic of the drill string, the energy input can be modeled using a nonlinear torque characteristic at the bit [8]. Due to improved and new measuring tools, high-frequency oscillations have been identified as the cause of numerous drill string failures and have been intensively investigated over the last years with studies [9,10], simulations [8,11] and experiments [12,13]. Especially drilling in hard and dense formations leads to highfrequency torsional oscillations (HFTO) with frequencies between 50 Hz and 500 Hz [14,15].…”

“…is derived [8], wherein represents the modal damping, , the natural angular frequency and the deflection of the mass normalized eigenvector of mode k. Additionally, a maximum amplitude at the bit (φ ) that depends on the revolutions per minute (RPM) in the operating point…”