Torsional and lateral vibrations in flexible rotor systems with friction

Self-sustained vibrations which can appear in mechanical systems often limit the performance of such systems or can even cause failure or damage to such systems. Moreover, different types of vibration can appear in dynamical systems. In order to gain an improved understanding and to predict different types of vibrations which appear in mechanical systems, it is important to understand the causes for such vibrations and the interaction between those vibrations. In this thesis, we address on the one hand friction-induced vibrations in flex- ible mechanical systems, and on the other hand lateral vibrations caused by mass- unbalance in rotor systems, and the interaction between those two types of vibrations. Although a lot of theoretical research has been done on vibrations in flexible rotor systems, a limited number of papers is available which include experimental results on the friction-induced vibrations and on the interaction between different types of vibrations. For this purpose, we have designed and constructed an experimental drill-string set-up which exhibits both types of vibration. The set-up consists of a DC-motor, two rotating (upper and lower) discs, a low-stiffness string, which connects the two discs, and an additional brake at the lower disc. The lower disc can rotate around its geometric center and is also free to move in lateral direction. The configuration of the experimental set-up is representative for many other mechanical systems, in which friction or unbalance can deteriorate the system performance by the appearance of vibrations. For example, when the lower disc is fixed in lateral direction (i.e. when the lower disc only rotates), the system forms a configuration of two masses, coupled by a flexibility, of which one is subject to friction and the other is driven by an actuator. In this context, one can think of set-ups such as printers, pick and place machines, industrial and domestic robots, braking mechanisms and many others. Moreover, when mass-unbalance is present at the lower disc and the disc can move in lateral direction, this configuration can be recognized in drilling systems which are used for exploration of oil and gas, in electrical shavers, in various turbines, pumps, fans and so on. The drill-string set-up is modelled and the parameters of the model are estimated. The comparison between responses of the experimental set-up and estimated model indicates a high accuracy of the obtained parameter estimates. The steady-state behaviour of the drill-string system has been analyzed when various constant input voltages are applied to the DC motor; first, when only torsional and no lateral vi- brations occur and, second, when both torsional and lateral vibrations appear in the system. When analyzing the friction-induced vibrations a discontinuous static friction model is used. We have chosen such a model and not a more complicated dynamical friction model since it accounts for the friction characteristics which are crucial for the global dynamics of the system but avoids unnecessary complexity. A discontin- uous friction model leads to a discontinuous model of the system dynamics which exhibits both friction-induced vibrations and the interaction between friction-induced vibrations and vibrations due to mass-unbalance. As a result of the analysis on a theoretical, numerical and experimental level the following conclusions are drawn. When analyzing the set-up with only friction-induced torsional vibrations and no lateral vibrations, the main conclusion is that a subtle interplay of negative damping characteristics at low velocities and viscous friction at higher velocities determines the occurrence and nature of friction-induced limit cycling. It also determines the range of parameters for which these limit cycles sustain. Furthermore, the level of posi- tive damping at very low velocities relative to the negative damping level at slightly higher velocities determines whether torsional vibrations with or without stick-slip can occur. Then, both model-based and experimental bifurcation analysis confirm that discontinuous bifurcations play a crucial role in the creation and disappearance of these limit cycles. Also, the way in which such friction characteristics are influ- enced by physical conditions such as temperature and normal forces on the frictional contact is experimentally studied. An important observation is that the normal force in the frictional contact influences the friction force in a rather complex way and can induce a higher negative damping level (for larger normal forces), which in turn can give rise to limit cycles of a larger amplitude for a larger range of constant input voltages to the DC motor. The analysis of the set-up, when both torsional and lateral vibrations are present, leads to the main conclusion that two types of torsional vibrations can appear. Firstly, friction-induced torsional vibrations and, secondly, torsional vibrations due to cou- pling between torsional and lateral dynamics may appear. Furthermore, if mass- unbalance is present at the lower disc, the amplitude of friction-induced vibrations and the region in which these vibrations occur, both decrease compared to the situ- ation without mass-unbalance. Moreover, it is shown that if the mass-unbalance is large enough then torsional vibrations can disappear entirely. Next, on a simulation level it is shown that torsional vibrations due to coupling between torsional and lateral modes appear for input voltages to the DC motor which are higher than the so-called critical voltage, which is related to the critical angular velocity inducing resonance in lateral direction. Due to limitations in the available DC motor, those vibrations are studied only at a simulation level. Finally, the knowledge obtained in this thesis provides a better understanding of the causes for torsional and lateral vibrations. Moreover, based on this knowledge, various control strategies may be designed and tested on the designed set-up in or- der to eliminate torsional and lateral vibrations. Furthermore, the results presented here can support the design of various braking mechanisms, pumps and fans in pre- venting the occurrence of or in decreasing the amplitude of friction-induced torsional vibrations and lateral vibrations due to mass-unbalance

An apparatus and method for detecting a tool

The apparatus is adapted to detect a tool based on a 3D image obtained by a 3D ultrasound imaging system. The apparatus comprises an image processing unit, which includes a tool detection module configured to perform a tool detection procedure. The tool detection procedure involves identifying a shadow of the tool in the 3D image and calculating the position of a "tool plane section" of the 3D image in which the entire length of the tool is represented

Observer designs for experimental non-smooth and discontinuous systems

This brief presents the design and implementation of observer design strategies for experimental non-smooth continuous and discontinuous systems. First, a piece-wise linear observer is implemented for an experimental setup consisting of a harmonically excited flexible steel beam with a one-sided support which can be considered as a benchmark for a class of flexible mechanical systems with one-sided restoring characteristics. Second, an observer is developed for an experimental setup that describes a dynamic rotor system which is a benchmark for motion systems with friction and flexibility. In both cases, the implemented observers guarantee global asymptotic stability of the estimation error dynamic in theory. Simulation and experimental results are presented to demonstrate the performance of the observers in practice. These results support the use of (switched) observers to achieve state reconstruction for such non-smooth and discontinuous mechanical systems

Free energy barrier for melittin reorientation from a membrane-bound state to a transmembrane state

An important step in a phospholipid membrane pore formation by melittin antimicrobial peptide is a reorientation of the peptide from a surface into a transmembrane conformation. In this work we perform umbrella sampling simulations to calculate the potential of mean force (PMF) for the reorientation of melittin from a surface-bound state to a transmembrane state and provide a molecular level insight into understanding peptide and lipid properties that influence the existence of the free energy barrier. The PMFs were calculated for a peptide to lipid (P/L) ratio of 1/128 and 4/128. We observe that the free energy barrier is reduced when the P/L ratio increased. In addition, we study the cooperative effect; specifically we investigate if the barrier is smaller for a second melittin reorientation, given that another neighboring melittin was already in the transmembrane state. We observe that indeed the barrier of the PMF curve is reduced in this case, thus confirming the presence of a cooperative effect

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Drillstring-borehole interaction: backward whirl instabilities and axial loading

A major concern within the oil drilling industry remains the interaction between the drillstring and borehole. The interaction between the drillstring and borehole wall involves nonlinearities in the form of friction and contact. The drillstring borehole interaction induces whirling behaviour of the drillstring causing forward whirl, backward whirl or intermittent bouncing behaviour depending on the system parameters. The purpose of this study is to analyse the steady backward whirl behaviour within the system which reduces the fatigue life of the drillstring. Initially a two discs model was developed to analyse the behaviour of the system. The theoretical model was tuned by altering the phase of the eccentric mass. This excites each lateral modes of the system in isolation. The effects of impact, friction and mass unbalance are included in the model. For the tuned system the backward whirl behaviour was analysed by carrying out a rotor speed sweep spanning the lateral natural frequencies. The influence of rotor speed on the system dynamics is explored using a run up and run down and is analysed using a waterfall plot. The waterfall plot indicated the frequency of maximum response corresponding to each rotor speed. Depending on the whirling behaviour the dominant frequency was observed at the lateral natural frequency, the rotational speed or the backward whirl frequency. The influence of variation in whirling behaviour due to altering of the axial load was analysed for a multiple disc case consisting of five discs. A transition in behaviour along the length of the drillstring was observed due to the axial load and bending moment interactions. Depending on the mode excited impact and sustained contact initiation with the borehole varied across the different stabilizer locations

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets.

yesTraditional rotor dynamics mainly focuses on the steady- state behavior of the rotor and shafting. However, for systems such as hydro turbine generating sets (HTGS) where the control and regulation is frequently applied, the shafting safety and stabilization in transient state is then a key factor. The shafting transient state inevitably involves multiparameter domain, multifield coupling, and coupling dynamics. In this paper, the relative value form of the Lagrange function and its equations have been established by defining the base value system of the shafting. Takingthe rotation angle and the angular speed of the shafting as a link, the shafting lateral vibration and generator equations are integrated into the framework of generalized Hamiltonian system. The generalized Hamiltonian control model is thus established. To make the model more general, additional forces of the shafting are taken as the input excitation in proposed model. The control system of the HTGS can be easily connected with the shafting model to form the whole simulation system of the HTGS. It is expected that this study will build a foundation for the coupling dynamics theory using the generalized Hamiltonian theory to investigate coupling dynamic mechanism among the shafting vibration, transient of hydro turbine generating sets, and additional forces of the shafting.National Natural Science Foundation of China under Grant Nos. 51179079 and 5083900