In downhole drilling systems, self-excited torsional vibrations caused by the bit-rock interactions can affect the drilling process and lead to the premature failure of components. Especially self-excited oscillations of higher-order modes lead to critical dynamic loads. The slim drill string design and the naturally limited drilled borehole diameter limit the installation space, power supply and lead to numerous potentially critical self-excited torsional modes. Consequently, small and robust passive damping concepts are required. The variety of possible downhole boundary conditions and potential damper designs necessitates analytical solutions for effective damper design and optimization. In this paper, two nonlinear passive damper concepts are investigated regarding design and effectiveness to reduce self-excited high-frequency torsional oscillations in drill string dynamics. Based on a finite element model of a drill string, a suitable minimal model based on the identified critical mode is generated and solved analytically using the Multiple Scales Lindstedt-Poincaré (MSLP) method. The advantages of MSLP compared to conventional MS methods are shown for this example. On the basis of the analytical solution, parameter influences are determined, and design equations are derived. The analytical results are transferred to self-excited drill string vibrations and discussed using time domain simulations of the drill string model.

In this paper, a passive damper based on energy dissipation through shock and dry friction (shock‐friction damper) is investigated regarding its design and effectiveness for damping self‐excited torsional vibrations similar to those occurring in deep drilling. The results are compared to the results of conventional friction dampers. The effectiveness of the damper for different operational drilling parameters that change during the drilling process, such as the weight on the bit and the rotary speed of the bit, is analyzed. Two linear reduced order models of a drill string that are based on a complex finite element model are set up. One is reduced using the component mode synthesis and one is reduced to the identified critical mode. A lumped mass represents the inertia of a forcedly connected nonlinear damper. A combined reduced order model of the complex system and the inertia damper is introduced to investigate its dynamic motion and stability. Particular focus is on the energy flow within the dynamic system and on the change of the dissipation energy in the contact. A semi‐analytical solution is derived using the harmonic balance method that is used to investigate the damping effect for various designs and operational parameters. Herein, the modal properties as well as parameters of the damper are examined regarding the damping effect and the stability of the system. Finally, the capability of the mechanism to suppress the self‐excitation due to the bit–rock interaction in a drilling system is discussed, and recommendations are made with respect to the design parameters and placement of the damper.

Drilling a wellbore can result in several types of vibration that lead to inefficient drilling and premature failure of drill string components. These vibrations are subdivided based on their operating direction into lateral, torsional, and axial vibrations. Especially in hard and dense formations, high-frequency torsional oscillations are found in the bottom-hole assembly (BHA). These critical vibrations are induced by a self-excitation mechanism caused by the bit–rock interaction. Self-excitation mechanisms are regenerative effects, mode coupling, or a velocity-dependent torque characteristic at the drill bit. To increase drilling performance and reduce tool failure due to high-frequency torsional oscillations, the critical vibration amplitudes localized at the bottom-hole assembly need to be minimized. Increasing the damping of self-excited systems to affect the energy output during vibration is a common approach to mitigate self-excited vibrations. In drilling systems, the achievable damping is naturally limited by the small installation space due to the drilled borehole diameter. Therefore, alternative methods to influence vibrations are necessary. Applying parametric excitation in self-excited systems can result in a parametric anti-resonance and therefore in an energy transfer within different modes of the structure. This allows, among other benefits, improved utilization of the structural damping. In this article, the influence of additional stiffness–based parametric excitation on self-excited torsional vibration in downhole drilling systems is investigated. For this purpose, a finite element model of a drill string is reduced using the component mode synthesis and analyzed with the goal to mitigate torsional vibrations. The multiple degree of freedom drill string model is investigated regarding the additional energy transfer due to the parametric excitation. Robustness of various parameters, especially with regard to the positioning within the bottom-hole assembly, is analyzed and discussed. Additionally, the problem of multiple unstable self-excited modes due to the nonlinear velocity-dependent torque characteristic in drilling systems is addressed.

Dynamic analysis of three-dimensional structures is common practice in industry to optimize products and in research to gain insights on the influence of parameters. The complexity differs based on the linearity or nonlinearity of the underlying problem, the type of excitation, e.g., forced or self-excitation, and the number of degrees of freedom that need to be examined. Reduced order models and optimized numerical methods are used to optimize the time and computational power needed to gain a certain insight. This article focusses on a specific class of problems where the modes of the structure do not or do not significantly change through the (damping) device or force that is added to the structure. Herein, lumped mass models are commonly used for analysis of the dynamic response of the system. In the article, it is highlighted that lumped mass models can give quantitative insight but modally reduced models allow a direct optimization of the problems with respect to the physical degree of freedom that, for example, is subject to self-excitation or dampened. The benefit of modal minimal models and its limitations are shown and discussed for different linear and nonlinear dynamic problems.