正交面齿轮传动系统分岔特性

Bifurcation charactristics of face-gear transmission system

为了研究面齿轮传动的非线性动力学分岔特性,建立了包含支承、齿侧间隙、时变啮合刚度、综合误差、阻尼和外激励等参数的系统弯-扭耦合动力学模型,并使用PNF(Poincaré-Newton-Floquet)方法对系统进行了求解.计算结果表明:当时变啮合刚度幅值系数从0.4增加到0.5时,系统会由倍周期分岔进入混沌;当啮合阻尼比由0.061 000 0减小到0.060 000 0时,系统会经过拟周期分岔进入混沌;当量纲一化综合传动误差幅值从0.120减小到0.112时,系统会发生边界激变后进入混沌.

To study the non-linear bifurcation characteristics of face-gear transmission system, a nonlinear dynamic model is presented. This model includes bearings, backlash, time-varying meshing stiffness, general transmission error, meshing damping, and external load, etc. The PNF（Poincare-Newton-Floquet） method is used to solve the dynamic differential equations. The calculation results show： when the amplitude coefficient of time-varying meshing stiffness increases from 0.4 to 0. 5, the system will go into chaos through period-doubling bifurcation; when the meshing damping ratio decreases from 0. 061 000 0 to 0. 060 000 0, the system will enter chaos through quasi-periodicity bifurcation; when non-dimension amplitude of general transmission error decreases from 0. 120 to 0. 112, the system will appear boundary cataclysm.