Dynamics Research And Control For A Nonlinear Rotor-bear-sealing System

Rotor is considered to be one of the vital parts in some high speed rotating machineries,and the operation state of the rotor is normal or not is directly affect its movement status andpower transmission. As the rotor is influenced by various nonlinear factors when it is inworking condition, some types of irregular vibration will occur in the whole system, whichcan greatly affect the work efficiency. But when a fault occurs, the motion characteristics ofthe rotor system will become more complex, especially the impact of the nonlinear oil filmforce to be sustained by the bearing or nonlinear seal force on its property is significant,which can be observed in many systems such as rotor-bearing system studied by most of thescholars, rotor-seal system and so on, however, the mentioned research only consider theeffect of single factor on the rotor dynamics, therefore, we need to conduct more thoroughresearch need to be conduct to investigate the coupling faults of rotor system.In the21st century, with the rapid development of computer technology, the problemswhich can not be solved by the theoretical analysis can be easily solved by using the computernow. This allows domestic and foreign scholars to conduct a further study on the rotor system.The combination of the bifurcation diagram got by numerical simulation and Lyapunov indexis applied to analyze the dynamic behaviors of the system, and further analysis can beperformed by using Poincare mapping, the time corresponding diagram and phase diagram tomake the result be concretion and visualization, which benefit for the analysis and study.According to the research, the dynamic behavior and vibration status of the rotor system arenot only affected by the parameters such as rotate speed, damping, and stiffness and so on, butalso affected by the sealing force. However, as the analysis of sealing force is more complex,which brings great difficulty for the analysis of the motion characteristics of the system, sothe computer is becoming more and more important in the study of rotor dynamics analysis.Main jobs in this paper:1The significance of study and the study on the status at home and abroad, as well assome definitions, theorems, research method and judgment method of the rotor-bear-sealsystem are described briefly.2The analysis method of nonlinear system is introduced briefly, the method how tojudge the periodic, quasi periodic solution and chaotic solution is concisely proposed, whichallows us to recognize the difference and determination among bifurcation diagram,Lyapunov diagram, phase difference between the index and the Poincare map. Some controlmethods are also introduced.3The mathematical model of rotor-seal system is established, the balance point and thecharacteristic value are calculated, the Hopf bifurcation is judged and calculated with the R-Hstability criterion, then numerical simulation is used to test and verify the conclusion. 4The mathematical model of the rotor-bear--seal system is established, the coupling ofoil film force and sealing force instead of a single sealing force make the motioncharacteristics of the model more complex. Then the numerical simulation of therotor-bear-seal system is performed, and the dynamical behaviors of the system are studiedand analyzed by using the bifurcation diagram with Lyapunov index diagram, phase diagramand Poincare’ maps, time response diagram of the system with different parameters (such asspeed, damping c1, stiffness k1, eccentricity r, sealing pressure Pand so on) to obtain theoptimal value of the oil film force and the sealing force of the system.5The piecewise quadratic function control method and proportional differential controlmethod are respectively used to control the system, on the basis of which, the impact oncontrol results with different parameters (such as the control parameter K2, damping c1andso on) is also investigated.