计及摩擦影响的直齿轮时变啮合刚度计算方法

An analytical method for mesh stiffness calculation of spur gears influenced by friction

针对现有的齿轮时变啮合刚度计算模型不考虑时变摩擦影响的问题,以一种弹流润滑状态下的时变摩擦系数为基础,通过推导齿轮副的齿面速度、滚滑比、卷汲速度、赫兹应力,得到了弹流润滑状态下,考虑单双齿啮合情况下载荷变化的时变摩擦系数;并应用于势能法刚度计算模型,提出了计及齿面摩擦的时变啮合刚度计算方法。计算结果表明:齿面摩擦对时变啮合刚度有很大的影响;在节点位置,不存在相对滑动,刚度和不考虑摩擦情况一致;在单双齿啮合区的临界点,单齿刚度存在突变的现象;随着载荷的增大,时变啮合刚度减小。该方法同样适合于其它摩擦模型,从而为后续进行考虑摩擦影响的齿轮动力学分析提供新的时变啮合刚度理论基础。

In view of existed calculation method for time-varying mesh stiffness regardless of the presence of changing friction,an improved method is proposed based on traditional potential energy method which considering the influence of friction between the engaging tooth.The EHL-based time-varying friction coefficient for gear pairs is obtained based on a friction coefficient formula established by lots of ball-disk tests.The surface velocity,the roll-slide ratio,the entraining velocity and the Hertzian pressure are deduced according to the precise tooth profile equation.The calculation results reveal the great influence of friction force on time-varying mesh stiffness;the stiffness calculated by the presented method equals to that without considering of friction at the pitch position due to the absence of relative sliding at that moment;at the critical position of single-double contact,the stiffness exhibits remarkably sudden change;as the torque increases,the stiffness decreases.The presented method is suited to other friction coefficient model as well,which provides new theoretical basis for the nonlinear dynamic analysis of gear system influenced by friction in the future.