| Generator, as a machine converting other forms of energy into electrical energy, has been playing a key role in the national economy. And it is crucial that generators operate safely. As the main factor affecting the plant operation and dynamoelectric performance, vibration, especially the one caused by unbalanced magnetic pull, has been attracting widespread concern of. researchers. In this thesis, based on the previous results about single-disk rotor subjected to unbalanced magnetic pull, finite element method (FEM) is used to simulate rotor's vibration response under unbalanced magnetic pull, the eccentric force and gyroscopic force simultaneously.According to electromagnetic theory, the Maxwell stress on the rotor surface is: where B=Λ(α,t)F (α,t) is the air-gap flux density,Λ(α,t) and F (α,t) are air-gap permeance and the fundamental MMF of the air-gap, respectively, andμ0 is the air permeance. The air-gap permeance can be expressed as a Fourier series: where the expansion coefficient is:The fundamental MMF of the air-gap in a three-phase generator under no-load can be written as: where Fj is the amplitude of the fundamental MMF. Therefore, unbalanced magnetic pull FxUMP and FyUMP can be obtained by calculating integral of Maxwell stress on the surface. When the number of pole-pairs of the generator is more than 3, and 3-order items are kept for the Taylor expansion, the unbalanced magnetic pull is given by: whereUnder the action of the unbalanced magnetic pull, eccentric force and gyroscopic forces, FEM equation of the system's vibration is as follows: MX+(C+G)X+KX=PXL+UMP (7) where M represents mass matrix, C represents damping matrix, G represents gyroscope matrix, K represents the stiffness matrix, PXL is the mass eccentric force, UMP is the unbalanced magnetic pull and X is displacement vector.Equation (7) is a system of second-order nonlinear differential equations in X; we use Newmark method to solve them. During the course, we solve the system by utilizing the direct iteration.Steps to solve equations (7) of motion with the Newmark method can be summarized as follows:1, Initialization:(1) Giving X0, X0, and calculating X0;(2) Setting time step At and parameterβand y, and calculating integration constant: (3) Forming the valid stiffness matrix: K=K+c0M+c1C(4) Triangular decomposition K= LDLT.2, for each time step:(1)Calculating the load at t+△t: where the displacement of UMP(Xt+△t)is obtained from the previous time step.(2)Solving the displacement at t+△t by applying iteration method to(3) Calculating the acceleration and velocity at t+△t: Xt+△t=c0(Xt+△t-Xt)-c2Xt-c3Xt Xt+△t=Xt+c6Xt+c7Xt+△tThen the next time step can start. The response at each time step can be obtained as the previous steps.ANSYS is utilized to obtain nodes data, discrete element data, the total stiffness matrix, the total mass matrix and gyroscopic and damping matrices. And then we handle the data with several FORTRAN programs. In this paper, a simple rotor model and a complex rotor are used to simulate transient dynamic response of hydro generator'system, which is electromechanical coupled. Dynamic response to hydro generator's system under unbalanced magnetic pull and mass eccentric force is also investigated. We get rotor's responses with different amplitudes of the fundamental MMF.From the results of simulation, we may conclude:1,Compared with steady-state response track under no magnetic pull, the radius of steady-state response track subjected to unbalanced magnetic pull is larger, and it enlarges when the fundamental MMF increases.2,The maximum displacement in transient response is inclined to be larger than the orbital radius of the steady-state response, so we should sufficiently consider this problem during the actual design.
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