中文摘要：

针对航空发动机三支点柔性转子系统的支承不同心问题,充分考虑转子结构特征和载荷特征,首次将当量刚度引入多支点柔性转子不同心问题的动力学分析,定量描述转子系统各支承间不同心度带来的转子轴段刚度非线性,并提出了多跨度柔性转子系统支承不同心激励的数学描述,建立了不同心激励下多跨度柔性转子系统的力学模型。基于Lagrange能量法,给出了转子系统动力学方程的求解方法,研究得到了支承不同心转子系统的动力响应特征。结果表明：支承不同心不仅引起转子过渡轴的刚度非线性,产生2倍频激励,还会给转子系统带来附加不平衡激励;对于三支点柔性转子系统而言,2倍频分量同样是支承不同心下转子系统振动响应的典型特征之一。转子系统2倍频分量随不同心量的增加而迅速增加,而1倍频分量基本保持不变。同时转子振动响应呈现＂缓增速降＂趋势,且随非线性刚度、不平衡量的增大愈加明显。

英文摘要：

Equivalent stiffness is introduced for the first time into dynamics analysis of the problem of bearing misalignment of flexible rotor system with three supportings, based on comprehensive consideration of the characteristics of rotor structure and load. Nonlinear stiffness of the rotor shaft with bearing misalignment can then be described quantitatively. Mathematical descriptions of the misalignment excitation of multi-span flexible rotor are obtained, and the mechanical modeling for the flex- ible rotor with bearing misalignment is established. The solution method for the governing equations for the rotor system with bearing misalignment is established based on Lagrange energy method, and the vibration characteristics of the rotor system is studied. The results show that the bearing misalignment leads to nonlinearity of the coupling＇s stiffness, resulting in 2 times frequency excitation load and extra unbalanced load. The 2 times frequency component is one typical feature of the ro- tor system with bearing misalignment. The 2 times frequency component increases rapidly with the increase of bearing mis- alignment, and the 1 times frequency component remains the same. The vibration response of the rotor shows a trend of ＂in- creasing slowly first, and then reducing quickly with the increase of rotation frequency＂, and turns to be more obvious with the increase of the nonlinear stiffness and unbalance.