Vibration Mechanism For Hydroelectric Genertating Unit Based On Nonlinear Rotor Dynamics

Hydroelectric system is a complex nonlinear dynamic hydro-mechanical-electrical system. As the system is running, there are a number of uncertain factors in the generation and development of vibration fault of hydropower generating unit, which are difficult to describe accurately using mathematical models. And, with the proportion of energy in the power structure, and the rapid increase of the single unit capacity and head of the hydropower generating units, vibration problems have become increasingly prominent, which serious threaten to the safe and reliable operation of the hydroelectric plant, even power grid. Once a failure for generating units occurs, it may cause the plant to non-planned shutdown or reduce capacity, even serious heavy casualties and serious damage to the system. Therefore, to further improve our design and operation of hydroelectric generating units and provide important theoretical and technical support, we must study on mechanism of different vibration faults and interaction between them and reveal influence of fault factors to the unit vibration stability and instability law. In this paper, based on nonlinear rotor dynamics theory and methods, many approaches such as bifurcation diagram, Poincare map, axis orbit, time domain waveform and amplitude spectrum diagram are employed to analyze the vibration characteristics on shaft system which including dynamic behavior of the rotor system with rotor rub-impact and bearing loose coupling faults, the dynamic response of generator rotor and turbine runner with comprehensive misalignment, nonlinear electromagnetic vibration characteristics of unit shaft and the analysis of turbine vibration and stability of the turbine seal system with considering the vibration of universal operation of the unit. The main contents of the paper as follows:(1) With considering the crack depth to shaft stiffness and continuous of switching function of crack, an improved switching crack model in a beam is presented. Dynamic characteristics of a rotor-bearing system with rub-impact and transverse crack are attempted. Due to the presence of coupling faults, the system becomes highly nonlinear. The stiffness of stator, crack depth, crack angle effects on the response of a rotor are investigated using numerical method. Various nonlinear phenomena compressing periodic, quasi-periodic and chaotic motions with rotating speed as a control parameter in the rotor system are analyzed. The research results show that as the increase of the stiffness, rub forces increase and gradually come to be the dominant factor, leading responses of the rotor evolving from chaos to periodic motions. In the cases of different cracks depth and crack angular, the responses of the rotor system present different bifurcation trajectory. Within the subcritical speed range responses of the rotor evolves from complex chaotic motion to four-periodic motion and within supercritical speed range mainly are quasi-periodic motions.(2) In order to solve the fault problems of the bearing looseness and rotor local rubbing caused by some nonlinear factors, considering the rigidity and damping between the stator and foundation, a dynamic model for the hydroelectric generating unit with coupling faults of bearing looseness and rub-impact is established. The nonlinear dynamic behaviors of the shaft system are analyzed, as ratio of rotation frequency, mass eccentricity of rotor and friction coefficient varied. The focus is mainly on the process of the stator-rotor rub-impact. The results show that the stiffness is unrelated to the range of rub occurring, and various non-linear phenomena compressing periodic, three-period and quasi-periodic motions occurs at different speed and there are some low frequencies with large amplitude in the amplitude spectrum Moreover, the speed range of rotor rub-impact enlarges constantly and dynamic responses of the system are complex as the increasing of mass eccentricity of the rotor.(3) Based on movement mechanism of rigid coupling with misalignment, a dynamic model for the shaft system with coupling faults of misalignment and rub-impact is established. The dynamic behaviors of the generator rotor and turbine runner are investigated, as rotating speed, parallel misalignment and angular misalignmen varied. Various nonlinear phenomena compressing periodic, three-periodic and quasi-periodic motions in the system are observed. The results reveal that when response is quasi-periodic motion, there are some low frequencies with large amplitude, especially at the 0.3-0.4X-ratational speed. While the speed goes up, their responses are periodic motion and the amplitudes are constantly changing and the responses will evolve from periodic motion to quasi-periodic motion as the increase of the speed.(4) According to nonlinear relation of unbalanced magnetic pull (UMP) and mass eccentricity of the rotor, the air-gap permeance is expressed as a Fourier series. Then the analytical expression of UMP is derived and the kinetic equation is set up to describe electromagnetic vibration of the shaft system. Numerical method is adopted to analyze the nonlinear dynamic response of the rotor and runner with rotation speed, exciting current and mass eccentricity of the rotor as a control parameter, respectively. Simulation results display that There are many harmonics with large amplitude at the 1～1.5X and 0.5～1X for generator rotor and at the 0.5～1X for turbine runner as the speed increasing. As the increase of exciting current and mass eccentricity, various nonlinear phenomena compressing periodic and complicated quasi-periodic motions in the system are observed, and the amplitude at the 1X increases and high frequency components decrease for the generator rotor, but it is opposite for the turbine runner.(5) As the structural parameters of hydroelectric generating units shaft increase, the flow induced force imposed on the hydraulic turbine runner will significantly increase, which easily causes abnormal vibration of the unit. According to the problem, the Muszynska's model of the nonlinear seal force is applied to building the dynamic equation of the shaft system with flow induced force. The vibration characteristics of the guide bearings at different mass eccentricity and dynamic stability of the hydraulic turbine rotor is analyzed. The results show that the vibration amplitude of three guide bearings is constantly changing with the increase of mass eccentricity. There is occurrence of Hopf bifurcation after threshold speed is exceeded and rich nonlinear motions such as periodic and quasi-periods, for hydraulic turbine runner. The main parameters of the sealed structure have important impaction the stability of the rotor system.