Abstract: Two methods named Direct method and Complete method were established based on the commercial finite element software， to resolve the critical speeds calculation problem of counter-rotating rotor system and satisfy the design requirement of rotor dynamics. The basic theory and calculation process of two methods were presented in detail with a typical two spools system， while the results were verified by Harmonic response analysis. Results exhibit that the Complete method based on the eigenvalues analysis of finite element software could distinguish curves of forward or backward procession easily without any information of vibration modes， which means the solving process could be simplified significantly. The Direct method was carried out on the matrices drawn from finite element software， and all the critical speeds could be acquired by only single eigenvalues calculation without iterations. The critical speeds of a typical two spools system obtained by Direct method， Complete method and Harmonic response are exactly the same. When two spools are counter-rotating， forward procession curves descend with the increased absolute rotational speed value of the rotor which is not the excitation source. Therefore， the critical speeds are totally different from those obtained from co-rotating spools， and the dynamic characteristics of counter-rotating spools must be designed carefully.

Key words: Rotor dynamics;Two spools system;Counter-rotating;Critical speed;Direct method;Complete method

摘要： 为解决对转双转子航空发动机临界转速求解的难题，满足转子动力学设计需求，结合商业有限元软件，给出直接法和完全法两种临界转速求解方法，并结合算例详细论述了方法的理论基础和求解过程，最终以谐响应分析结果加以验证。研究结果表明：基于商业有限元软件特征值分析的完全法不需要任何振型信息，就可对正反进动曲线进行区分，极大简化了对转双转子系统临界转速的求解过程，而由有限元软件生成矩阵后进行处理并计算的直接法不需迭代，可由一次特征值求解得到全部临界转速。双转子系统临界转速的计算结果表明，直接法、完全法和谐响应分析的结果完全一致。双转子对转时，正进动临界转速曲线随非激励源转子的转速绝对值增加而降低，使临界转速分布规律区别于同转转子，其动力特性需予以细致考虑。

关键词: 转子动力学;双转子系统;对转;临界转速;直接法;完全法