大型水轮发电机组轴系扭振的分岔和稳定域分析

应用拉格朗日－麦克斯韦方程建立大型水轮发电机组数学模型，研究该系统平衡位置的稳定性和局部分岔，进一步证明轴承扭振不会发生Hopf分岔，利用构造李雅普诺夫函数对稳定域进行估计，并对三峡大型水轮发电机进行数值仿真。

Analysis of bifurcation and stable region for water turbine generator shaft torsional vibrations

Using Lagrange equations, a set of differential equations are established, to research the local stability and bifurcation at the equilibrium point of water turbine generators for shaft torsional vibrations. It is proved that there isn't Hopf bifurcation for normal parameters in the parameter space. The water tubine generator's stable region is estimated by the Lyapnuov function, and the stable bifurcations are testi-fied by Sanxia water turbine generator's simulation.