Resonances and Synchronization in Two Coupled Oscillators with Stick-Slip Vibrations and Spring Pendulums

We study the dynamical behavior of a system of two coupled mechanical oscillators with spring pendulums and driven by a stick-slip induced vibrations. Each of the oscillator consists of the body placed onto a moving belt/foundation, mechanical coupling associated with the body load pressed the belt depending on the body movement as well as suspended spring pendulum. In addition, the influence of the presence of additional electric/electromagnetic forces acting on the pendulums are analyzed. Different kinds of resonance behavior can be found in the studied system, even if it is simplified to a single degree-of-freedom system. As a result, due to many degrees-of-freedom and strong nonlinearity and discontinuity of the considered system, novel nonlinear dynamical phenomena occur, both near and beyond to the resonance. The motion analysis for different cases is carried out by employing standard numerical methods dedicated for nonlinear systems, including both qualitative and quantitative methods, as well as original animations of the system dynamics created in Mathematica. Understanding the role of coupling, transition between fixed points and energy transition in the considered system can be potentially applied in other similar systems, especially in real electro-mechanical systems, power system or in structural engineering

Two-Speed Gearbox Dynamic Simulation Predictions and Test Validation

Dynamic simulations and experimental validation tests were performed on a two-stage, two-speed gearbox as part of the drive system research activities of the NASA Fundamental Aeronautics Subsonics Rotary Wing Project. The gearbox was driven by two electromagnetic motors and had two electromagnetic, multi-disk clutches to control output speed. A dynamic model of the system was created which included a direct current electric motor with proportional-integral-derivative (PID) speed control, a two-speed gearbox with dual electromagnetically actuated clutches, and an eddy current dynamometer. A six degree-of-freedom model of the gearbox accounted for the system torsional dynamics and included gear, clutch, shaft, and load inertias as well as shaft flexibilities and a dry clutch stick-slip friction model. Experimental validation tests were performed on the gearbox in the NASA Glenn gear noise test facility. Gearbox output speed and torque as well as drive motor speed and current were compared to those from the analytical predictions. The experiments correlate very well with the predictions, thus validating the dynamic simulation methodologies

Investigation on dynamics of drillstring systems from random viewpoint

Drillstrings are one of the critical components used for exploring and exploiting oil and gas reservoirs in the petroleum industry. As being very long and slender, the drillstring experiences various vibrations during the drilling operation, and these vibrations are random in essence. The first part of the thesis focuses on stochastic stick-slip dynamics of the drill bit by a finite element model and a single degree of freedom drillstring model in Chapters 3 and 4, respectively. In the single degree of freedom model, the path integration (PI) method is firstly used to obtain the probability density evolution of the dynamic response. Then Monte Carlo (MC) simulation is used for validating PI results and conducting the parametric study. The second step of my research is to study the stochastic dynamics of a vertical, multiple degrees of freedom drillstring system. The work of this part is presented in Chapter 5. The novelty of this work relies on the fact that it is the first time that the statistic linearization method is applied to a drillstring system in the bit-rock interaction to find an equivalent linear dynamic system which is then solved with the stochastic Newmark algorithm. After that, the stick-slip and bit-bounce phenomena are analyzed from random viewpoint. The third step of my research move on to directional drilling. A static study of directional drillstring from random viewpoint is presented in Chapter 6. The finite element method (FEM) based on the soft string model is employed and built. Then two strategies are taken to model the random component for hoisting drag calculation. The purpose of this work is to analyze the effects of the random component on hoisting drag calculation by the MC simulation method

Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations

We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate-strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics, and thus produce useful information about a variety of granular phenomena including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.Comment: 12 pages, 8 figure

Modeling and Control of a Flexible Structure Incorporating Inertial Slip-Stick Actuators

Shape and vibration control of a linear flexible structure by means of a new type of inertial slip-stick actuator are investigated. A nonlinear model representing the interaction between the structure and a six-degree-of-freedom Stewart platform system containing six actuators is derived, and closed-loop stability and performance of the controlled systems are investigated. A linearized model is also derived for design purposes. Quasistatic alignment of a payload attached to the platform is solved simply by using a proportional controller based on a linear kinematic model. The stability of this controller is examined using a dynamic model of the complete system and is validated experimentally by introducing random thermal elongations of several structural members. Vibration control is solved using an H∞ loop-shaping controller and, although its performance is found to be less satisfactory than desired, the nonlinear model gives good predictions of the performance and stability of the closed-loop system

Dynamics beyond dynamic jam; unfolding the Painlev\'e paradox singularity

This paper analyses in detail the dynamics in a neighbourhood of a G\'enot-Brogliato point, colloquially termed the G-spot, which physically represents so-called dynamic jam in rigid body mechanics with unilateral contact and Coulomb friction. Such singular points arise in planar rigid body problems with slipping point contacts at the intersection between the conditions for onset of lift-off and for the Painlev\'e paradox. The G-spot can be approached in finite time by an open set of initial conditions in a general class of problems. The key question addressed is what happens next. In principle trajectories could, at least instantaneously, lift off, continue in slip, or undergo a so-called impact without collision. Such impacts are non-local in momentum space and depend on properties evaluated away from the G-spot. The results are illustrated on a particular physical example, namely the a frictional impact oscillator first studied by Leine et al. The answer is obtained via an analysis that involves a consistent contact regularisation with a stiffness proportional to $1/\varepsilon^2$. Taking a singular limit as $\varepsilon \to 0$, one finds an inner and an outer asymptotic zone in the neighbourhood of the G-spot. Two distinct cases are found according to whether the contact force becomes infinite or remains finite as the G-spot is approached. In the former case it is argued that there can be no such canards and so an impact without collision must occur. In the latter case, the canard trajectory acts as a dividing surface between trajectories that momentarily lift off and those that do not before taking the impact. The orientation of the initial condition set leading to each eventuality is shown to change each time a certain positive parameter $\beta$ passes through an integer