基于多项式的等高齿锥齿轮时变啮合刚度建模

针对某型雷达装置的等高齿锥齿轮在啮合时的时变啮合刚度,提出一种多项式函数展开的时变啮合刚度新模型。通过转速、负载扭矩、阻尼因子系数分析,构建了多项式函数展开的时变啮合刚度模型,建立了等高齿锥齿轮的非线性动力学方程。将本文建立的时变啮合刚度模型与传统的多阶简谐波叠加形式的时变啮合刚度模型以及综合刚度参考数据模型进行分析对比,发现在小阻尼、重载工况下这种多项式形式的时变啮合刚度模型能更贴近于时变啮合刚度的实际特性,该模型为齿轮传动的减振、降噪、平稳传动等方面的动力学研究打下基础。

一种改进的非线性接触齿廓修形直齿轮啮合刚度分析方法

时变啮合刚度是齿轮副的周期性内部激励,是齿轮传动系统振动和噪声问题的主要来源。针对齿廓修形的直齿轮啮合刚度计算问题,从能量等效思想出发,结合悬臂梁模型,考虑接触对间的非线性接触,提出了一种改进的非线性接触齿廓修形直齿轮啮合刚度解析模型。首先,在已有文献的基础上,将轮齿简化为齿根圆上的悬臂梁,三维的齿轮副传动模型转换为二维的平面齿廓,进行了接触分析,考虑齿对间的非线性接触,通过能量法构建了齿廓修形直齿轮单齿啮合刚度半解析模型;然后,补充了变形协调与力平衡方程,导出了齿廓修形直齿轮副综合啮合刚度模型;最后,将采用该方法所得结果与有限元计算结果进行了对比,完成了对该计算方法的验证,并分析了不同摩擦系数与齿轮参数对齿轮啮合刚度的影响规律。研究结果表明:相较于传统的有限元计算结果,采用该解析模型得到的计算误差在3%以内,计算速度提高150倍,在精度损失较小的情况下,能够实现对非线性接触齿廓修形圆柱齿轮啮合刚度的快速求解。

齿向修形直齿轮系统动力学特性分析

研究了直齿轮齿向修形对齿轮系统振动特性的影响。首先考虑直齿轮齿向修形偏差,将轮齿沿轴向离散成若干宽度相等的薄片,建立了齿轮副啮合刚度模型。然后以一对直齿轮副为例,分别使用有限元法和本文方法分析了齿轮副啮合刚度,结果表明所提方法能够快速准确求解齿向修形直齿轮副的啮合刚度。最后建立齿轮系统有限元模型,分析了齿向修形对系统固有特性、振动响应特性的影响。研究结果表明:齿向修形降低了齿轮副啮合刚度,考虑齿向修形后齿轮系统弯扭耦合固有频率减小,齿轮系统响应的共振峰出现了偏移。研究结果可为齿向修形齿轮的动态响应计算和结构设计提供理论依据。

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.