中文摘要：

以一个两对斜齿轮耦合的三平行轴转子系统为研究对象，考虑静态传递误差、齿轮几何偏心的影响建立了全自由度通用齿轮啮合动力学模型，并考虑转子系统的影响，建立了平行轴系齿轮转子系统有限元模型，其中转子系统采用梁单元来模拟，齿轮之间的耦合作用通过啮合刚度矩阵和阻尼矩阵来模拟。通过修改啮合刚度矩阵研究了无耦合、单轴弯扭轴摆耦合、轴系弯弯耦合、轴系扭扭耦合、轴系弯扭耦合、轴系弯扭轴摆耦合的系统模态变化规律，采用模态应变能确定了系统各阶主导模态，研究结果可为齿轮及转子系统设计提供参考。

英文摘要：

Considering the static transmission error and geometric eccentricities of the gears, a general total degree of freedom dynamic model of a helical gear pair was established. Combining with the rotor systems, a finite element model of the multi-shaft helical gear rotor system was built. In the model, the rotor system was simulated by using beam element and the gear pair by using mesh stiffness matrix and damping matrix. By modifying mesh stiffness matrix, the mode change tendencies were studied under six kinds of conditions （no coupling, bending-torsional-axial-swing coupling of a single shaft, bending-bending coupling, torsional-torsional coupling, bending-torsional coupling and bending-torsional-axial-swing coupling）. Finally, modal strain energy was adopted to identify the dominant mode. The results are helpful to the structure design of gear and rotor system.