中文摘要：

根据转子动力学和齿轮啮合的基本原理，建立了考虑陀螺力矩的齿轮转子系统的动力学模型，以此求得齿轮转子啮合刚度矩阵和阻尼矩阵。探讨了啮合刚度、支承刚度对系统固有频率以及系统稳定性的影响。结果表明齿轮的啮合刚度对弯曲振动以及弯扭耦合振动固有频率的影响不大，而当啮合刚度介于2×10^5～2×10^8之间时。对弯扭耦合振动的相对稳定性却有较大的影响；另增大支承刚度，固有频率相应提高；减小跨距可以提高系统的稳定性。分析结果对工程应用具有重要的意义。

英文摘要：

The dynamics model of a gear rotor system considering gyroscopic moment is established according to the basic principles of rotor dynamics and gear meshing. Following the model, its mesh stiffness matrix and damp matrix are obtained. Then the paper discusses whether its mesh stiffness and support stiffncss have influence on its natural frequency and stability. The discussion results show that its mesh stiffness has little influence on the natural frequency of bending vibration and bending and torsional coupled vibration. But when its mesh stiffness is between 2×10^5～2×^8 ,it has great influence on the stability of the bending and torsional coupled vibration. Besides, increasing its support stiffness and decreasing the span of bearings can improve the natural frequency and stability. The results are significant for engineering applications.