用于柔性转子主动控制的等几何Timoshenko梁模型及其数值验证

为了克服采用标准有限元方法建立的转子模型自由度多不便直接用于控制器设计的问题,结合等几何分析方法的精度高、自由度少的特点,提出了把低阶等几何Timoshenko梁模型运用到柔性转子的主动控制中,并进行了数值验证。首先,给出了半离散等几何模型及在主动控制中作为转子控制输入信号的各类边界条件;其次,分别对比了高、低阶等几何模型的奇异值响应以及简支条件下的高、低阶模型的数值解与理论解;最后,在采用磁悬浮轴承支撑和给定分布不平衡力扰动的条件下,对转子进行了分散比例微分(PD)仿真控制。结果表明:所采用的低阶模型的奇异值响应在前6阶临界转速范围内与高阶模型基本一致;高阶模型的前10阶模态频率很好地吻合了理论解,低阶模型前4阶模态频率误差在0.2%以内;高、低阶等几何梁模型下的转子不平衡振动位移稳态响应的差别很小,该误差可看成工作转速下的同频小扰动。低阶等几何梁模型在低频范围的高精度验证了该方法所得低阶模型直接用于控制器设计的可行性。

Research on dynamic model of rotors with bearing misalignment

Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor system in aero-engines. The motion equations are derived through Lagrange method. The relationship between structural and mechanics characteristics parameters are built up. Finally, the dynamic influence of bearing misalignment on rotor system are divided into three kinds： additional rotor bending rigidity, additional bearing misalignment excitation force and additional imbalance. The equations suggest that additional imbalance excitation force activates the nonlinearity on rotor system and an additional 2x excitation force might appear.