平行轴齿轮传动系统动力学建模的有限单元法

Dynamic modeling of parallel shaft gear transmissions using finite element method

为了能获取更为准确的轴承响应以预测齿轮箱体噪声,提出了适用于平行轴外啮合圆柱齿轮-轴-轴承-箱体系统动力学建模的有限单元法。该方法将连续分布的齿轮系统离散为轴段单元、啮合单元和轴承-基础单元,通过建立模块化的单元运动方程,根据单元连接关系生成矩阵组装规则,实现系统整体动力学模型的自动建立。模型中考虑了轴段剪切效应的影响,推导了齿轮副在不同旋向和转向时的弯-扭-轴-摆全自由度耦合振动方程,提出了箱体柔性对转子系统振动耦合作用的计入方法。以一对单级斜齿轮传动为例,通过与已有实验数据的对比验证了此方法的有效性。结果表明,采用有限元法计算齿轮副和轴承响应比常规集中质量法具有更高的求解精度。利用此方法编写了规范化程序,为工程中处理多级复杂平行轴齿轮系统的振动和噪声问题提供了有效手段。

In order to obtain more accurate bearing responses to predict the noise of gearbox, a comprehensive fully coupled dynamic model of a parallel-shaft external cylindrical gear-shaft-bearing-case system was proposed. The continuous gear system was divided into discrete shaft element, mesh element, and bearing-base element. The modularized equations of motion for each element were built, and the dynamic model of the system was automatically created according to the relationship between different elements. The shear deformation effect of the shaft element was considered in the model. The dynamic equations with all degrees of freedom coupled （ transverse-rotational-axialpendular） were given as well. The effect of different gear hand direction and rotating direction were considered. Then the coupling vibration between the gear rotor system and the case was also introduced in the analysis. A single-stage helical gear pair was taken as an example to validate the proposed method by comparing the predicted data with the experimental ones. The results show that the finite element method has higher precision than the common lumped mass method to predict the dynamic response for both gears and bearings. A standardized program for the proposed method has been created, which can provide an effective means to predict the vibration and noise of multi-stage complex parallel shaft gear transmissions in engineering practice.