Abstract: According to the rotor dynamical design requirements in aero engines，the critical speed prediction method for double spools system were put forward based on the finite element method and the vibration mode selection technique，and it was practical for solving engineering problems. The detailed solving process of the full method and the reduction method were discussed with a double spools example. It exhibited that the results obtained by both methods were exactly the same. However，the reduction method need less iterations and was more convenient to obtain the critical speed. The co-rotating double spools possessed five critical rotation speed，and the counter-rotating double spools had three more critical rotation speed in the same rotation speed range，whose modes were n=3，n=4 and n=5，respectively，caused by the anti-precession. The densification of the critical rotation speed would lead to the complexity in the rotor dynamical design in aero engines.

Key words: Rotor dynamics；Double spools；Critical rotation speed；Counter rotating；Selection by vibration modes

摘要： 针对航空发动机转子动力学设计需求，将有限元法与振型筛选法相结合，提出适于工程应用的临界转速求解方法，结合算例详细论述了完全法和缩减法的求解过程。研究结果表明:两种求解方法的结果完全一致，而缩减法求解过程迭代次数少，更为方便；某双转子系统，顺转时存在5阶临界转速，而反转时在相同的转速范围内将增加n=3，n=4和n=5的反进动临界转速，临界转速的密集性导致反转转子的动力学设计更为复杂。

关键词: 转子动力学；双转子系统；临界转速；反转；振型筛选