Krzysztof Marynowski

Stability of symmetrical rotor supported in flexibly mounted, self-acting gas journal bearings

This paper describes the results of numerical investigations of the stability problem of the rigid symmetrical rotor, supported in two self-acting gas journal bearings. Bushes of the bearings are mounted on a system of linear springs and viscous dampers. When the stiffness and damping coefficients of these springs and dampers are chosen correctly, it is possible to avoid the self-excited vibrations of the rotor. Such vibrations, which are caused by the phenomenon of a half-synchronic whirl, are the major obstacle to the widespread application of gas bearings.

Stability of rotors supported in gas bearings with bushes mounted in air rings

Abstract When during the operation of rotors supported in gas bearings their rotational velocity reaches a sufficiently high value, the loss of steady-state stability occurs. This instability is caused by the loss of damping properties of the gas film, which leads to self-excited vibrations. These vibrations are the basic obstacle to a widespread application of gas bearings. The phenomenon of self-excited vibrations can be avoided by introducing an elastic supporting structure between the bearing bushes and the casing, characterised by properly selected stiffness and damping coefficients. In practice such a structure can have the form of an externally pressurised gas ring. In this paper we demonstrate, on the basis of selected examples, which ranges of the values of stiffness and damping coefficients of the gas ring make it possible to retain steady-state stability at practically any rotational velocity of the rotor. We also show a design of the ring structure, especially of its feeding system, which ensures the required values of stiffness and damping coefficients (with regard to the stability). Our investigations have been carried out by means of a numerical simulation method with the use of a mathematical model of the gas bearing, verified already many times.

Instabilities of the elastically supported laval rotor subjected to a longitudinal force

Abstract In this paper an analysis of individual and coupling effects of various parameters on the stability of the Laval rotor subjected to a longitudinal force is presented. In the case of a rotor with a mass-point, only divergence instability of the rotor motion can be observed. The regions of flutter instability appear only for the rotor with a disk. In both cases the critical load of the rotor is dependent on the disk position, the support stiffness and the value of the angular velocity. It is shown that neglecting the non-conservative character of the load may lead to incorrect results.

Axially Moving Microscale Panel Model Based on Modified Couple Stress Theory

AbstractThe problem of the axially moving microscale panel based on the modified couple stress theory and the principle of minimum total potential energy is analyzed. The mathematical model of the considered system contains the internal material length parameter and can capture the size effect. The equation of equilibrium states of the axially moving panel tensioned with the constant longitudinal load is derived. As a direct application of the model, an axially moving microscale panel with two simply supported and two free longitudinal edges is solved. The effects of the transport speed, the length scale parameter, and the geometry of the microscale panel on the dynamic behavior of the axially moving system are presented. The investigation results show that the dynamic behavior of the panel in the overcritical range of transport speed is mostly affected by time histories of lowest frequencies of free flexural vibrations.

Stiffness and damping coefficients of air rings with a chamber feeding system

Abstract When, during the operation of rotors supported in gas bearings, their rotational velocity reaches a sufficiently high value, loss of steady state stability occurs. This instability is caused by the loss of damping properties of the gas film, which leads to self-excited vibrations. These vibrations are the basic obstacle to a widespread application of gas bearings. The phenomenon of self-excited vibrations can be avoided by introducing an elastic supporting structure between the bearing bushes and the casing, characterized by properly selected stiffness and damping coefficients. In practice, such a structure can have the form of an externally pressurized gas ring. In this paper, on the basis of selected examples, those ranges of the values of stiffness and damping coefficients of the gas ring that make it possible to retain steady state stability at practically any rotational velocity of the rotor are demonstrated. A design of the ring structure, especially of its feeding system, is also shown, which ensures the required values of stiffness and damping coefficients (with regard to the stability). These investigations have been carried out by means of a numerical simulation method with the use of a mathematical model of the gas bearing, which has already been verified many times.

Beam Model of the Moving Viscoelastic Web

The results of analysis of the axially moving web dynamics obtained with the nonlinear mathematical model developed in Chap. 3 have been presented in the previous chapters. The complexity of this model as regards a complicated nature of the mathematical description causes that it is not convenient in engineering applications. The level of complexity of the mathematical description and its size are especially important in calculations of this kind, where computation time plays a significant role. On the other hand, the results of analyses obtained so far indicate

State of Knowledge on Dynamics of Axially Moving Systems

One of the most important phenomena that are analyzed during investigations of the dynamic behavior of the system are vibrations and dynamic stability of the system motion. Due to high transport speeds that are attained by webs in various industrial applications, investigations of motion stability are crucial as they allow to avoid folding or even breaking of the web.

Dynamical Analysis of the Undamped Axially Moving Web System

Dynamics of the thin web moving axially with a constant velocity is considered in this chapter. The geometrical dimensions of the system under analysis along with the assumed system of coordinates are presented

Displacements of the Web in Equilibrium States of the Linearized System

A mathematical model of the axially moving orthotropic plate, derived in Sect. 4.2, describing a transverse motion of the web and a field of sectional forces is applied in this section. A static analysis involving determination of the non-trivial equilibrium positions existence is used in the investigations of stability of the web motion. Equations of equilibrium positions of the axially moving web performing uniform motion have been derived. Transverse displacements and wrinkling of the webs made of two kinds of papers and the three-layered corrugated board composed of these papers have been investigated.