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中文摘要：
根据不平衡磁拉力与转子偏心的非线性关系,把气隙磁导展开为傅里叶级数,推导出不平衡磁拉力的解析式,建立了水轮发电机组轴系非线性电磁振动的动力学模型和微分方程,并采用数值方法分析了不平衡磁拉力下转子系统的非线性动力学响应.仿真结果表明：发电机转子和水轮机转子随激磁电流变化存在周期1运动、周期7运动及复杂的拟周期运动等,其特征频率除主要在1倍频处外,还分别在1.2～1.5倍频和0.2～0.8倍频处存在大量的谐波分量;随着转子质量偏心的增大,转子系统的固有频率降低,发电机转子高频分量不断减小,水轮机转子低频谐波却不断增大.
英文摘要：
Electromagnetic vibration in hydropower unit was endowed with strong nonlinear characteristic due to the coupling of mechanical and electromagnetic reasons. According to nonlinear relation of unbalanced magnetic pull （UMP） and mass eccentricity of the rotor,the air-gap permeance was expressed as a Fourier series. Then the analytical expression of UMP was derived and the kinetic equation was set up to describe electromagnetic vibration of the shaft system. Numerical method was adopted to analyze the nonlinear dynamic response of the rotor system with exciting current and mass eccentricity as a control parameter,respectively. Simulation results display that the influence of exciting current on vibration of the rotor system is obvious and various nonlinear phenomena compressing periodic,period-seven and complicated quasi-periodic motion is investigated. There are many harmonics with large amplitude at the 1.2～1.5 frequency component for generator rotor and at the 0.2～0.8 frequency components for hydraulic turbine rotor. When the mass eccentricity increases,the natural frequency of the rotor system will decrease and the vibration characteristics change continuously.
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