Dynamic Modeling And Analysis Of The Main Shaft System Of Francis Turbine-Generator Units

For a long time, the vibration phenomenon of Francis turbine-generator units strongly affects the safe work of the units and attracts the close attention of people. With the development of industrial science and technology and the leap of energy demand, the single-machine capacity of the Francis turbine-generator units is bulked and the monolithic construction is more giant and more complicated. Under the combination action of high head, high flow rate and strong electromagnetic field, the vibration law of Francis turbine-generator units hasn't been thoroughly discovered. In order to guarantee the safe and normal work of Francis turbine-generator units, researching the vibration problem and grasping the rules of vibration are very necessary.In this paper, the main shaft system of Francis turbine-generator units is the subject of research, the dynamic equations including structural parameters, electromagnetic parameters and fluid parameters are established by the finite element methods (FEM). A generator unit which regarding the transverse vibration and the torsional oscillation of the generator rotor as the nodal displacements are established. The air-gap field magnetic energy of non-uniform airspace of generator rotor and the nodal displacements of generator rotor are hung together by the Lagrange method. In the analysis of hydraulic driving unit, the element mass matrix is derived from the relationship between the kinetic energy and the nodal displacements of elastic shaft and the element stiffness matrix is derived from the relationship between the potential energy and the nodal displacements of elastic shaft. The dynamic response factor of oil film in guide bearings, the unbalanced mechanical force and the unbalanced hydraulic force in water seal gap are taken into account, the dynamic equations of main shaft system are established by the finite element methods (FEM), which can present the fluid state, the mechanical state and the electromagnetic state. The dynamic equations are the base of further study of the vibration law of Francis turbine-generator units.