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.

The principle energy exchange of a brake system occurs in the tribological boundary layer between the pad and the disc. The associated phenomena are primarily responsible for the dynamics of brake systems. The wear debris forms flat contact structures, or “patches,” which carry the majority of the normal load in the system and are highly influential on the friction behavior of the system. A new simulation tool is presented, which is capable of rapidly performing simulations of the contact between an entire brake pad and disc. The “Abstract Cellular Automaton” simulations accurately model the patch coverage state of a brake pad surface based on the system’s load history. This can be used to simulate the complex dissipation phenomena within the tribological contact of the entire pad, including time-dependent local friction coefficients, wear and wear debris transport, and vibrational effects on highly differing scales.

Starved lubrication is an important strategy for minimizing the amount of lubricant needed, and also inevitably occurs during idling and fail-safe lubrication. In this regime, however, the flow of the lubricant and the related friction coefficients are yet to be fully understood. This research aims to make fundamental contributions to the understanding of contact mechanics of partially lubricated contacts. Recent experiments with a pin-on-disk tribometer examined the microscopic behavior of partially filled gaps. Using a new experimental setup on a macroscale, new insights into partially filled gaps with rough surfaces were gained. This work presents the systematic analyses of the lubricant flow, friction coefficients, and other variables over a wide range of friction parameters. Distinct friction behaviors were observed, and similar effects occur on both the micro and macroscale. The experimental results show that a typical Stribeck characteristic is visible regarding not only the relative velocity, but also regarding the lubricant filling level in the gap. The fluid exhibits a variety of flow patterns for various velocities and viscosities. The patterns relate to different friction regimes, such as dry friction and mixed lubrication. It is concluded that the filling level is a valid parameter for regulating the transition from dry friction to hydrodynamic lubrication. These findings are quantified regarding the filling level and it is shown that for the identification of the friction regimes the filling level is an independent parameter in addition to the established parameters like speed, viscosity and pressure.

Hot bands and hot spots are thermoelastic phenomena appearing in frictional systems with high energy dissipation like brake systems or clutches. These thermoelastic instabilities are driven by the interaction of friction-induced heat in the sliding plane and thermal expansion of the materials. Systems exposed to thermoelastic instabilities show a characteristic temperature pattern that can lead to local material damage and vibrations like judder or brake torque fluctuations. While hot bands are observable by a cut through the system normal to the direction of sliding, hot spots are described by a cut parallel to the direction of sliding. When an angle parameter is introduced in a model-based description, both types of thermoelastic instabilities can be described by one single model. Such a model is presented that comprises of layers corresponding to different mechanical parts (e.g. pad, disk, homogenized cooling channels). Every layer is described by field equations for thermoelastic behavior and heat conduction. All layers basically include the same set of solutions which can analytically be found by separation of complex variables. These solutions are scaled to satisfy the boundary conditions at the contact areas between the layers. No symmetry conditions are required, but if present, they can simplify the model. The stability of one thermoelastic phenomenon under investigation is determined by evaluating the characteristic equation of the system. The appearance of hot spots or bands, their spatial distribution and movement are discussed in terms of sliding velocity and other system parameters.