Štěpán Dyk

Rigid Jeffcott Rotor Bifurcation Behaviour Using Different Models of Hydrodynamic Bearings

The paper studies dynamical behaviour of Jeffcott rotor supported by a hydrodynamic bearings. It uses different analytical formulations for hydrodynamic bearing forces acting on Jeffcott rotor. The model is nonlinear due to the presence of hydrodynamic bearings and can show different subharmonic behaviour like oil whip and oil whirl. Such a system is subjected to dynamical analysis using numerical continuation aimed at detection of nonlinear phenomena like bifurcations and unstable behaviours with respect to basic system parameters.

Steady-State Behaviour of the Rigid Jeffcott Rotor Comparing Various Analytical Approaches to the Solution of the Reynolds Equation for Plain Journal Bearing

A planar 2 DOF model of an unbalanced rigid disc on a massless rigid shaft (rigid Jeffcott rotor) is extended considering nonlinear forces in plain journal bearings. To express the fluid-film forces in the journal bearings, several approximate analytical solutions of the Reynolds equation are used, including widely used approximations for infinitely long and infinitely short journal bearing and a method using correction polynomial functions to extend the area of aspect ratios. The differences in steady-state response of such a rotor are studied. The influence of the approximate solution type, eccentricity ratio and aspect ratio is analysed. The aim is to find out the more effective approach to journal bearing description which could be further used in detailed dynamical analyses of both stable and unstable dynamic behaviour along with nonlinear phenomena like bifurcations and transitions to chaotic motions.

Nonlinear Vibration of Nuclear Fuel Rods

From mechanical point of view, nuclear fuel rod (FR) is a complex system consisting of two subsystems—fuel rod cladding (thin walled zirconium tube) and a fuel pellets stack placed inside the cladding placed with a small radial clearance. Both subsystems are beam-type continua that possibly impact-interact during the vibration caused by fuel assembly support plates motion. The FR is supported at eight levels by prestressed spacer grid cells. The paper focuses on complex mathematical modelling of such a system including all the nonlinearities given by possible impacts between cladding and fuel pellets stack and possible loose of contact between cladding and spacer grid cells due to low prestress. In all the contact points, friction-vibration interactions respect three possible phases—stick, slip and separation—depending on the slip velocity and normal contact force. The model is used for estimation of a fretting wear of the cladding in contact with spacer grids.

Nonlinear Dynamics of the Car Driving System with a Sequential Manual Transmission

Sequential manual transmissions are the most common sources of various contacts and impacts especially in rally cars. Dynamics of such systems can be very interesting and can influence the overall dynamic performance of a whole car. Therefore, it is necessary to have proper tools for dynamical modelling of gearboxes. This paper deals with the modelling and dynamic analysis of a driving system of a real car with a sequential manual transmission. A complex computational model of the sequential gearbox was created and after verification it allows to study nonlinear behaviour of the whole driving system. Parametric studies can be performed in order to investigate various qualitative effects of chosen design elements, etc.

Bifurcations in Mathematical Model of Nonlinear Vibration of the Nuclear Fuel Rod

The paper deals with nonlinear phenomena that occurs during vibration of nuclear fuel rod (FR). The FR is considered as a system consisting of two impact-interacting subsystems FR cladding (zircalloy tube) and fuel pellets stack placed inside FR cladding. Between both subsystems, there is a small radial clearance. The FR is bottom-end-fixed, and at eight equidistant levels, the FR cladding is supported by spacer grids (SG). Both subsystems are modelled by means of finite element method for one-dimensional Euler-Bernoulli continua. During fuel assembly (FA) motion caused by pressure pulsations of the coolant, the FR vibrates and impacts can possibly occur between FR cladding and fuel pellets stack. The paper focuses on qualitative change of vibration with change of bifurcation parameters clearance between FR cladding and fuel pellets stack and stiffness of spacer grids cells. The change of vibration quality is shown by extremes of relative radial displacements of both continua in discretization nodes and by phase trajectories. Dependence of impact motion on modal properties of both subsystems is shown.

Dynamic analysis of vibro-impact gear drive system

The mechanical systems with impact motion introduce a large class of mechanical devices. Impact oscillations are usually perceived as undesirable and harmful dynamic phenomena. However, the impact motions can have positive e ects (impact forming machines, drop hammers, impact presses, etc.). The contribution presents a methodology of modelling of mechanical systems with contacts which include normal forces. Such systems are described by non-smooth mathematical models, and specific numerical strategies have to be employed to solve them (smoothing method, switch method, event driven method). The methodology will be tested on a simplified model of test single-stage transmission. Abstrakt