基于齿面摩擦的人字齿轮副动力学特性分析

Dynamic characteristics analysis of double helical gear pairs considering teeth surface sliding friction

建立了考虑齿面摩擦、时变啮合刚度、齿侧间隙和综合传递误差的16自由度人字齿轮副三维空间弯曲-扭转-轴向耦合的非线性动力学模型,应用牛顿第二运动定律,建立系统的振动微分方程。根据人字齿轮副的啮合特性,通过数值积分方法分析了轮齿的啮合力,时变摩擦力和摩擦力矩,并采用基于弹流润滑理论(EHL)的摩擦因数计算模型计算了齿面摩擦因数。为了分析齿面摩擦对人字齿轮副周期振动及分岔特性的影响规律,比较了有无考虑齿面摩擦时系统的周期振动时域响应、振动位移分岔图及最大lyapunov指数变化图。结果表明,齿面摩擦导致齿轮副垂直于啮合平面方向的振动位移加剧,且减弱了齿轮副沿啮合线方向的振动。同时,齿面摩擦的存在使得系统提前进入混沌,且抑制了系统的混沌运动。文章的研究成果有助于进一步认识齿面摩擦对人字齿轮传动周期振动及非线性振动特性的影响,为人字齿轮传动设计提供技术依据。

A three-dimensional nonlinear dynamic model of a double helical gear pair with 16-DOF was established taking teeth surface sliding friction,time-varying meshing stiffness,gear backlashes and gear mesh errors into account. The dynamic equations of the system were established with Newton Second Law.The tooth meshing force,tooth friction and friction torque were calculated with numerical integration according to the meshing characteristics of the double helical gear pair.The teeth surface friction coefficient was calculated with the model based on EHL.The effects of teeth surface friction on the dynamic behaviors of the system were analyzed.The results showed that the teeth surface sliding friction can lead to increase in vibration displacements in the direction perpendicular to the line of action and decrease in vibration along the line of action;the bifurcation of the system becomes blurred at higher meshing frequencies and the chaotic motion of the system appears earlier and infirmly due to the effect of teeth surface friction.The study was helpful for the further understanding the effect of teeth surface friction on periodic vibration and nonlinear vibration of double helical gear pairs.The results provided a technical basis for the design of double helical gear transmission.