水力发电机组轴系哈密顿建模与动力学特性分析

为研究水力发电机组轴系横向振动特性,以水力发电机组轴系为研究对象,首先将转子转轮形心定义为广义坐标,利用系统能量函数推求广义动量,组成系统一阶微分运动方程.将轴系外部作用力包括不平衡磁拉力与水力不平衡力作为输入控制项,建立了水力发电机组主轴系统广义哈密顿控制模型.通过算例求解得到了机组转速与阻尼系数变化时系统非线性动力学响应的分岔图、轴系轴心轨迹图和时、频域图.结果表明:在转速一定的情况下系统稳定性受到阻尼系数变化影响.当阻尼系数较小时系统运动不稳定,存在明显的倍周期现象,振动响应剧烈;当阻尼系数逐渐增大时,轴心振幅减小并稳定为周期运动.上述结果为水力发电机组轴系稳定运行提供了理论依据,同时也为进一步研究机组在不同外部输入激励下的振动控制提供了新的思路.

Hamiltonian modeling and dynamic analysis of shafting system in hydroturbine generating set

To study the lateral vibration characteristics of hydroturbine generating set shaft system, the rotor and runner of the hydroelectric generating set were taken as research object, then the first-order differential motion equation was established by defining the generalized coordinates and the generalized momentum first to construct energy function. Besides, the additional external force was used as the external input excitation to form the generalized Hamiltonian model. The nonlinear dynamic responses of rotor and runner with varying damping coefficient and speed under the combined action of unbalanced magnetic tensile force and hydraulic unbalanced force were analyzed by numerical analysis method, as well as the characteristics of the shaft center axis and time and frequency domain. The results show that damping coefficient is one of the important factors that affect the stability of the system. When the damping coefficient is small, the system motion has obvious double-cycle characteristics, and the lateral vibration amplitude is large; when the damping coefficient is increased, the axis amplitude decreases and the system is stabilized to periodic motion. The results provide a theoretical basis for the stable operation of hydroelectric generating set, and also provide new ideas for further research on the vibration control of the unit under different external input excitations.