Hopf Bifurcation Of A Jeffcott Rigid Rotor With Oil-Film Forces And Steam Forces

Large-scale rotary machinery is one of the most important equipments in the modern industrialized society, in the plenty of nonlinear stimulations that affects stabilities of the rotor system, nonlinear oil film force is the key factor of rotor machine's instability. The steam-excited vibration of rotors is the main problem of the instability of the turbine rotor, especially for the supercritical and ultra-supercritical steam turbines.Now, there are more studies on the modeling of airflow exciting-vibration force (Alford force) than on the mechanism of the steam-excited vibration, and the problem of instability as a result of the effect of both Alford force and nonlinear oil-film force have not been studied insufficiently up to now. Hence the stability of a rigid balanced Jeffcott rotor supported by two short journal bearings was discussed in the paper, in order to analyze the nonlinear aspects of the rotor under the nonlinear oil-film force and Alford force. The main parts included in the thesis are as follow:1. The state of the art of the nonlinear dynamics of rotor at broad and homes is summarized, especially of the effect of nonlinear oil-film force and Alford force;2. The non-dimensional motion differential equation of the rigid Jeffcott (with mass balance) system is set up.3. The critical instability rotary speed is calculated by analyzing the eigenvalue problem of the disturbed equation of the rotor. The results show that the critical instability speed is brought forward when the relative velocity of the airflow (V) increases.4. The bifurcation diagrams of the system in different parameter regions, the phase portraits, Poincarémaps of the system at some parameter points are obtained by numerical method. The results of calculations show that, in the case under both the oil-film force and the steam of forces, the responses of the system are very complex. For intensive comprehension of the effects of Alford force on the rotor system with oil film bearings, the bifurcation diagrams with the bifurcating parameter, V, are given in the thesis. The results show that the quasi-periodic movements occurred abruptly after the periodic motion with increasing V when fixing the rotary angular speed of the rotor, and the vibrating amplitude of the rotor center was enhanced with increasing V.From the results of this paper, the mechanism of instabilities of the rotor with Alford force and the nonlinear oil-film force on the rotor system, can be realized deeply. The study could help us to diagnose and control the instability of the rotor.