本文采用模态综合法研究了齿轮传动转子系统的动力学特性，主要研究内容和结论如下： 首先利用当量齿形法建立了齿轮轮齿变形和啮合刚度计算模型，同时采用当量齿形法和有限元法对某型齿轮进行了计算和比较。然后建立了转子系统的有限元模型、推导了运动方程，研究了临界转速和不平衡响应的求解方法。基于转子系统的有限元法的研究，从理论上分析了齿轮传动转子系统的模态综合法的建模和求解的具体步骤。 以某齿轮传动转子系统为研究对象，采用模态综合法分析了其临界转速及相应的模态。数值结果表明转子系统在弹性支承时的临界转速值比刚性支承时的临界转速值小；耦合系统的临界转速包括与单转子非常接近的临界转速和耦合形成的新临界转速，而模态除了单转子模态和以某一单转子为主的耦合模态，还派生出新的耦合模态。 最后，研究了某齿轮传动转子系统的不平衡响应，分析了支承条件、耦合和不平衡分布对转子系统不平衡响应的影响。结果表明弹性支承时系统各结点的不平衡响应的幅值较刚性支承时大；在一定条件下，耦合有时会抑制系统的不平衡响应，也可能会加剧系统的不平衡响应；转子的转速越高，所引起的不平衡响应就越大，因此要特别注意提高高速转子上的动平衡精度，以提高系统的动态品质。 应用模态综合法分析齿轮传动转子系统的动力学特性，结果表明模态综合法能有效地降低系统的自由度，提高计算速度，对于复杂的多转子-轴承系统的动力学研究具有广泛的应用前景。

The study of dynamic behavior of geared rotor system was done by modal synthesis method in this dissertation. The main contributions and conclusions of the thesis were summarized as follows: Firstly, the models of gear tooth deformation and meshing stiffness were built by equivalent tooth profile method, and the results were compared with FEM. Then the modeling of rotor system using FEM, derivation of the equations of motion, solution of its critical speed and unbalance response were sutdied. Based on the study, the modeling of geared rotor system and the application of modal synthesis method for rotor system were discussed. Secondly, the critical speeds and corresponding modes of some geared rotor system were analyzed with the method proposed. The results indicated that, the critical speeds of the rotor system supported on elastic bearing were smaller than those on rigid bearing, and the critical speeds of geared rotor system included the ones that their value were near to single rotor and some new derived ones. Some new coupling modes were produced except single rotor modes and coupling modes being similar to single rotor. Finally, unbalance response of some geared rotor system was studied. The influence of bearing conditions, coupling and unbalance distribution of rotor system was analyzed. Numerical result showed that the node amplitude of unbalance response of the rotor system supported on elastic bearing was larger than that on rigid bearing. In some conditions, unbalance response of system would decrease or increase because of the coupling. The speed of rotor was higher, the vibration response was larger. In order to improve the dynamic quality of the whole system, the dynamic balance precision of the high speed rotor should be improved. Dynamic behavior of geared rotor system was analyzed using modal synthesis method, the result proved using modal synthesis method could reduce DOFs and improve the speed of the calculation of geared rotor system, and it had extensive application foreground for dynamic study of multi-rotor-bearing system.