带非线性支撑的转子有限元模型求解方法

Solution method of rotor finite element model with nonlinear support

用数值方法研究了非线性支撑的柔性转子系统的动学行为,提出了一种将有限元与非线性支撑结合的模型和求解方法。利用有限元法(FEM)构建转轴和转盘部分的模型,通过矩阵进行组合;利用离散元方法对包含滚动轴承和挤压油膜阻尼器(SFD)的支撑部分进行建模,此部分包含4个单元,分别为轴承内圈、外圈、SFD内圈和支撑鼠笼。有限元部分和离散元部分通过轴端节点相连,仿真过程中轴端位移传递给非线性支撑部分,支撑部分通过位移计算得到的非线性力反过来作用于有限元转子轴端部分。为了耦合求解有限元转子和非线性支撑组成的数学模型,提出了一种综合的迭代求解方法,克服传统的有限元求解方法对轴端隐性非线性支撑的求解局限性。由于转轴部分采用了Timoshenko梁单元建模,对比与简单转子模型,可以考虑陀螺力矩和轴的柔性特征,更能体现非线性支撑对振动真实影响。在建立的20个轴单元的有限元转子模型中,非线性响应更多体现在靠近非线性支撑的节点1和节点21处,响应频谱中靠近轴端的节点能体现出滚动轴承的2倍和3倍变柔振动频率。

The dynamic behavior of a flexible rotor system with nonlinear support was studied by the numerical method of a model and the solution combining the finite element model with nonlinear supports.The finite element method(FEM)was used to build the model of the rotating shaft and the rotary table,and the matrix was used for combination;the discrete element method was used to model the support(including:rolling bearing and squeeze film damper(SFD)),which specifically consists of four elements:bearing inner ring,outer ring,SFD inner ring and supporting cage.The finite element part and the discrete element part were connected by the nodes at the shaft end,and the displacement at the shaft end was transmitted to the nonlinear support.The nonlinear force and the nonlinear support calculated by the displacement at the support acted on the finite element rotor part at the shaft end in turn.In order to solve the coupling problem of the finite element rotor and the nonlinear support,a comprehensive iterative method was proposed to overcome the limitation of the traditional finite element method for solving the implicit nonlinear support at the shaft end.Because the Timoshenko beam element was used to model the rotating shaft,the gyroscopic moment and the flexibility of the shaft can be considered,which can better reflect the real effect of nonlinear support on the vibration.In the 20 shaft finite elements rotor model,the nonlinear response was more reflected in the 1 and 21 nodes closed to the nonlinear supports,and the nodes near the shaft end in the response spectrum can reflect two times and three times the flexible vibration frequency of the rolling bearing.