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莫帅, 黄祖瑞, 刘翊恒, 张伟. 航空非正交偏置面齿轮分汇流系统非线性动力学. 力学学报, 2024, 56(3): 2646-2658. DOI: 10.6052/0459-1879-23-232
引用本文: 莫帅, 黄祖瑞, 刘翊恒, 张伟. 航空非正交偏置面齿轮分汇流系统非线性动力学. 力学学报, 2024, 56(3): 2646-2658. DOI: 10.6052/0459-1879-23-232
Mo Shuai, Huang Zurui, Liu Yiheng, Zhang Wei. Non-linear dynamics of aeronautical non-orthogonal offset gear split flow system. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 2646-2658. DOI: 10.6052/0459-1879-23-232
Citation: Mo Shuai, Huang Zurui, Liu Yiheng, Zhang Wei. Non-linear dynamics of aeronautical non-orthogonal offset gear split flow system. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 2646-2658. DOI: 10.6052/0459-1879-23-232

航空非正交偏置面齿轮分汇流系统非线性动力学

NON-LINEAR DYNAMICS OF AERONAUTICAL NON-ORTHOGONAL OFFSET GEAR SPLIT FLOW SYSTEM

  • 摘要: 在面齿轮传动系统研究领域, 研究对象多为单级面齿轮副, 针对面齿轮分汇流传动系统动态特性的研究内容相对较少. 聚焦航空非正交偏置面齿轮分汇流系统的非线性动力学特性, 建立轴承滚动体变形、齿侧间隙以及综合传递误差的数学模型, 推导出包含轴承在内的非正交偏置面齿轮传动多自由度耦合弯扭组合动力学模型. 利用数值方法求解航空非正交偏置面齿轮分汇流系统的振动微分方程, 结合时域图、频域图、相图、Poincaré映射、李雅普诺夫指数以及分岔图研究复杂系统非线性动态特性. 研究了激励频率和啮合阻尼比变化对分流级与汇流级齿轮副之间啮合线位移的影响, 结果表明: 系统分流级与汇流级在特定参数下表现出不同的非线性特性, 随激励频率增大, 分流级出现单周期、多周期以及混沌现象, 而汇流级无混沌现象产生; 随啮合阻尼比增大, 分流级状态变化近似于逆倍周期分岔过程, 而汇流级在较小的阻尼比也可能保持周期运动状态; 合理的激励频率和啮合阻尼比能使得系统跳出混沌并保持稳定.

     

    Abstract: In the research field of face gear transmission system, most of the research objects are single-stage face gear pairs, and there are relatively few research contents on the dynamic characteristics of face gear split-confluence transmission system. Focusing on the nonlinear dynamic characteristics of the aviation non-orthogonal offset face gear shunt system, the mathematical models of bearing rolling element deformation, tooth side clearance and comprehensive transmission error are established, and the multi-degree-of-freedom coupling bending-torsion combination dynamic model of non-orthogonal offset face gear transmission including bearing is derived. The vibration differential equation of the non-orthogonal offset face gear flow separation and confluence system is solved by numerical method. The nonlinear dynamic characteristics of the complex system are studied by combining the time domain diagram, frequency domain diagram, phase diagram, Poincaré map, Lyapunov exponent and bifurcation diagram. The influence of excitation frequency and meshing damping ratio on the displacement of the meshing line between the shunt stage and the confluence stage gear pair is studied. The results show that the shunt stage and the confluence stage of the system show different nonlinear characteristics under specific parameters. With the increase of excitation frequency, the shunt stage appears single-period, multi-period and chaotic phenomena, while the confluence stage does not have chaotic phenomena. With the increase of meshing damping ratio, the state change of the shunt stage is similar to the inverse period doubling bifurcation process, while the confluence stage may also maintain a periodic motion state at a smaller damping ratio. Therefore, reasonable excitation frequency and meshing damping ratio can make the system jump out of chaos and remain stable, which provides a theoretical basis for fault prevention and fault diagnosis of face gear split-confluence transmission system. At the same time, it provides a reference for the design of face gear split-confluence transmission system and the selection of lubrication conditions.

     

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