弹性支承下弧齿锥齿轮系统参数平面中的域界结构研究

Domain boundary structure in parameter plane of a spiral bevel gear system with elastic supports

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 supports belongs to multidimensional nonlinear dynamics problem,and its domain boundary structure in parameter plane is significative to restrain and control vibration.Based on certain novel aviation spiral bevel gear,an seven degrees of freedom dynamic model was established.The vibration equations were solved by Adomian decomposition method.Taking advantages of the cell mapping and Poincaré section,in the parameter planes of meshing frequency versus bearing stiffness,meshing frequency versus support damping and bearing stiffness versus support damping,domain boundaries between different periodic domains as well as between periodic domain and chaotic domain were obtained.In virtue of plots of domain boundary plane,vibration bifurcation types and its corresponding structure in parameter planes were studied.The results are valuable to support parameters design,active vibration control,and vibration form prediction based on the different ranges of system parameters.