考虑摩擦的多间隙直齿弯扭振动建模和分岔特性

采用集中质量法,建立了齿轮-转子-轴承系统的六自由度的多间隙弯扭耦合的非线性振动模型,模型中考虑了齿面摩擦、时变啮合刚度、齿侧间隙和支承间隙等因素.根据系统在转速、齿侧间隙、齿面摩擦以及啮合阻尼等参数下的全局分岔图和Poincare截面图,研究了各参数对系统分岔特性的影响.分析可知:在一定的齿侧间隙、啮合阻尼和低齿面摩擦因数下,随着转速的逐渐增加,系统通过拟周期分岔进入混沌.当齿面摩擦因数逐渐增加时,系统由良好润滑状态进入干摩擦,系统的混沌运动区域也因此在一临界点产生裂变,且通过激变的途径二次进入混沌;在一定的转速、啮合阻尼和齿面摩擦因数下,随着齿侧间隙的增加,系统通过激变进入混沌,同时可以发现,系统产生混沌和分岔主要发生在量纲一齿侧间隙小于3和大于7的区域,且最终通过倒分岔锁相为周期1运动;在一定的转速、啮合阻尼和齿侧间隙的条件下,随着齿面摩擦因数的增加,系统通过激变进入混沌.同时发现,随着啮合阻尼的增加,混沌区域逐渐裂变成2个、3个和4个混沌窗口,但最终都经由拟周期锁相为周期1运动.

Bifurcation characteristic and modeling of transverse-torsional spur gear vibration considering friction and multiple clearances

Using the mass centralized method, a six degree of freedom transverse-torsional coupled nonlinear gear-rotor-bearing vibration model with multiple clearances and tooth surface friction was established, while time-varying meshing stiffness, gear backlashes, bearing clearances were considered in the model as well. By studying Poincare maps and global bifurcation diagrams under above parameters, the bifurcation characteristics of the system were obtained. Under a certain gear backlash, meshing damp and low tooth surface meshing friction, the system enters into a chaos state by the way of quasi-periodic motion with the increase of the rotation rate. While the tooth surface meshing friction coefficient increases, namely system is changed from well lubricated state to dry lubrication, the window of the chaos motion is split into two pieces at a critical point, and the system motion enters into a chaos state again by the way of crisis; Under a certain rotation speed, meshing damp and tooth surface friction coefficient, the system enters into a chaos state by way of crisis with the increase of the gear backlash, and the bifurcation and chaos motion happens when dimensionless gear backlash is less than 3 or bigger than 7, and the system motion is locked into a period motion by channel of reverse bifurcation; Under a certain rotation rate, meshing damp and gear backlash, the system enters into a chaos state by the way of crisis with the increase of the tooth surface friction coefficient. Meanwhile, it could be observed that, with the increase of the meshing damp, the window of the chaotic motion is split into 2, 3 and 4 sub-windows subsequently. But at last, system always is locked into a period motion by channel of quasi-periodic motion.