考虑啮合刚度随机扰动的斜齿轮系统分岔特性研究

Research of the Bifurcation Characteristic of Helical Gear System with Considering Random Perturbation of Mesh Stiffness

为了研究时变啮合刚度的随机扰动对斜齿轮传动系统动力学的影响,基于牛顿定律,建立单对6自由度斜齿轮传动系统的随机动力学模型并进行无量纲化处理。结合系统的分岔图、庞加莱映射图、李雅普诺夫指数图、相图和时间历程曲线图,对考虑啮合刚度随机扰动的斜齿轮传动系统的分岔特性进行分析。数值仿真分析结果表明,斜齿轮的时变啮合刚度在不断增大时,斜齿轮传动系统逐渐从周期运动通过倍化分岔变为混沌运动;随机扰动的增大使系统分岔特性发生变化,提前分岔进入混沌,对系统产生本质影响,故在设计时需选择合理参数,保证系统稳定性。

In order to study the influence of the random perturbation of time-varying mesh stiffness on the dynamics of the helical gearing system, based on Newton's law, a stochastic dynamics model of a six-degree-offreedom helical gear system is established and dimensionless processing is carried out. Combining the bifurcation diagram, Poincaré map, Lyapunov exponent diagram, phase diagram, and time history diagram of system, the bifurcation characteristics of the helical gear system with considering the random perturbation of mesh stiffness are analyzed. Numerical simulation analysis results show, when the time-varying mesh stiffness of helical gears increases, the helical gear transmission system gradually shifts from periodic motion to chaotic motion by doubling bifurcation. The increase of random disturbance makes the system’s bifurcation characteristics change, and enters chaos in advance, the dynamics characteristics of the system have an essential influence. Therefore, reasonable parameters should be selected during design to ensure system stability.