DESCRIPTION AND PREDICTION OF CATASTROPHE OF VIBRATION STATE FOR FAULTY ROTORS

A sudden increase of vibration amplitude with no foreboding often results in an abrupt breakdown of a mechanical system.The catastrophe of vibration state of a faulty rotor is a typical nonlinear phenomenon,and very difficult to be described and predicted with linear vibration theory.On the basis of nonlinear vibration and catastrophe theory,fhe eatastrophe of the vibration amplitude of the faulty rotor is described;a way to predict its emergence is developed.

Nonlinear Vibration Induced by the Water-film Whirl and Whip in a Sliding Bearing Rotor System

Many industrial applications and experiments have shown that sliding bearings often experience fluid film whip due to nonlinear fluid film forces which can cause rotor-stator rub-impact failures. The oil-film whips have attracted many studies while the water-film whips in the water lubricated sliding bearing have been little researched with the mechanism still an open problem. The dynamic fluid film forces in a water sliding bearing are investigated numerically with rotational, whirling and squeezing motions of the journal using a nonlinear model to identify the relationships between the three motions. Rotor speed-up and slow-down experiments are then conducted with the rotor system supported by a water lubricated sliding bearing to induce the water-film whirl/whip and verify the relationship. The experimental results show that the vibrations of the journal alternated between increasing and decreasing rather than continuously increasing as the rotational speed increased to twice the first critical speed, which can be explained well by the nonlinear model. The radial growth rate of the whirl motion greatly affects the whirl frequency of the journal and is responsible for the frequency lock in the water-film whip. Further analysis shows that increasing the lubricating water flow rate changes the water-film whirl/whip characteristics, reduces the first critical speed, advances the time when significant water-film whirling motion occurs, and also increases the vibration amplitude at the bearing center which may lead to the rotor-stator rub-impact. The study gives the insight into the water-film whirl and whip in the water lubricated sliding bearing.

QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS

Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quantitative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point （DCP） of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP＇s kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare are determined.

A NUMERICAL METHOD ON ESTIMATION OF STABLE REGIONS OF ROTOR SYSTEMS SUPPORTED ON LUBRICATED BEARINGS

The stability degree of periodic solution of nonlinear nonautonomous system was defined by means of the Floquet theory. A method evaluating the stability degree of periodic solution based on transient response was presented by the aid of the concept of dynamic,systems or flows. The critical value of a system was determined by the condition, i.e., its stability degree equals zero. Stable regions of rotor systems with balanced and unbalanced disk supported on lubricated bearings were calculated. The study shows that stable region decreases with the increase of speed for a balanced rotor system and decreases with the increase of unbalance for an unbalanced rotor system. Stable regions of periodic solutions are less than that of equilibrium points under the same systematic conditions.

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.

Bifurcation analysis on full annular rub of a nonlinear rotor system

In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging method and constraint bifurcation theory to discuss the effects of system parameters on jump phenomena. Routh-Hurwitz criteria are employed to analyze the stability of synchronous full annular rub solution and determine the boundaries of static and Hopf bifurcations. Finally, the response and onset condition of reverse dry whip are investigated numerically, and at the same time, the influences of rotor parameters and rotation speed on the characteristics of the rotor response are investigated.