弹性支承下弧齿锥齿轮系统的振动分析属于高维非线性动力学问题，其参数平面中的域界结构研究对实施振动抑制与控制具有重要意义。以某新型航空发动机的中心轴弧齿锥齿轮传动系统为研究对象，建立了7自由度非线性动力学模型。采用Adomian分解算法求解了振动方程的分级响应。基于胞映射和庞加莱截面的思想，在支承刚度与啮合频率、支承阻尼与啮合频率以及支承刚度与支承阻尼所构成的参数平面中，分析了弧齿锥齿轮非线性系统的不同周期振动之间以及周期振动和混沌振动之间的域界。借助平面域界图，研究了参数平面内系统振动分岔类型与分岔结构。研究结果为弧齿锥齿轮系统的支承参数设计与振动主动控制提供了依据，并可根据系统参数所处的范围对弹性支承下弧齿锥齿轮系统的振动形态进行预测。

The vibration analysis of a spiral bevel gear system with elastic support belongs to multidimensional nonlinear dynamics problem, its domain boundary structure in parameter plane is significative to restrain and control vibration. Based on the aviation spiral bevel gear, an seven degree freedom dynamic model is established. The vibration equations are solved by Adomian decomposition method. Based on cell mapping and Poincaré section,in the parameter planes of meshing frequency and bearing stiffness, meshing frequency and support damping, bearing stiffness and support damping, analysis on domain boundaries of different periodic domains and periodic domain with chaotic domain are obtained. In virtue of plots of domain boundary plane, vibration bifurcation types and structure in parameter planes are studied. The results are valuable in designing parameters and active controlling vibration, and prediction of the vibration form based on the range of system parameter.