基于LTCA的直齿轮啮合刚度的计算与分析

采用Matlab软件,运用三维有限元法获得了直齿轮齿面的柔度矩阵,对比分析了三种柔度矩阵的计算方法;建立了直齿轮啮合副的线接触和面接触两种轮齿承载接触分析模型,获得了齿轮副的啮合刚度,并分析了齿轮轮缘厚度、腹板厚度、施加载荷以及不同接触模型对啮合刚度的影响。研究结果表明:两种接触模型情况下获得的啮合刚度误差较小。轮缘厚度较小时,对啮合刚度影响较大;而腹板的厚度对啮合刚度的影响较小。在算例给定的参数下,当轮缘厚度与模数的比值大于3. 5左右时,轮缘厚度对啮合刚度的影响趋于平缓。

Calculation and Analysis of Mesh Stiffness of Spur Gear based on LTCA

Using Matlab software and three-dimensional finite element method, the flexibility matrix of spur gear tooth surface is obtained, and three calculation methods of matrix are compared and analyzed. The mesh stiffness of spur gear pair is obtained by establishing two kinds of loaded tooth contact analysis (LTCA) models, including line-contact and face-contact model. The effects of wheel flange thickness, web thickness,applied load and different contact models on mesh stiffness are analyzed.The results show that the mesh stiffness difference obtained by two kinds of contact model is small. When the flange thickness is small, the meshing stiffness is greatly affected while the web thickness has little effect on the mesh stiffness. In the given example, the influence of flange thickness on meshing stiffness tends to be gentle when the ratio of flange thickness to modulus is more than 3.5.