计入结构柔性和边界条件的内齿圈面内振动分析

In-plane vibration analysis of ring gear with considerations for structural flexibility and boundary conditions

采用弹性力学方法推导内齿圈的运动微分方程,用摄动法求解无约束条件下内齿圈的固有频率和振型函数,并通过消除永年项获得了含约束条件下的内齿圈面内振动频率的解析表达式.以某汽车变速箱中的内齿圈为例,运用所获的解析式计算了该齿圈的面内振动频率,其结果与前人研究中的有限元仿真及模态实测数据吻合较好.表明所提理论模型具有较高的计算精度,能准确揭示内齿圈的振动特性.最后,依托所建理论模型,分析内齿圈结构柔性和内、外约束条件对其面内振动特性的影响.计算结果表明,内齿圈面内振动频率随外约束刚度的增大而增大,且当内齿圈所有外约束的刚度之和不变时,降低单个外约束的刚度也即增大外约束的数目可小幅度地降低齿圈的面内振动频率;相比于外约束,内约束数目和刚度对内齿圈面内振动频率影响较小,随着内约束数目和刚度的增加,同一节径数下的内齿圈面内振动频率呈缓慢增大趋势.啮合相位变化时,面内振动模式的固有频率变化较大.

The differential equation of motion for the ring gear is derived and solved,leading to an analytical expression for the natural frequency of in-plane vibration. The proposed model is then applied to a ring gear in an automobile transmission gearbox to formulate the in-plane vibration characteristics and validated by numerical and experimental results in previous research,indicating the present model can be applied for further parameter studies. The effects of structural flexibilities as well as boundary conditions on in-plane vibration properties are investigated with the purpose of providing some useful information for planetary gear train designers. The studies show that the rim thickness affects the vibration frequencies significantly and the external constrains have a ‘stronger＇influence on the vibration frequencies than the internal constrains. It is suggested that more attentions should be made on the installing of ring gear to achieve good dynamic performance.