人字齿轮齿向修形优化设计

Optimal design of longitudinal correction of double helical gear

摘要:

考虑到安装误差、轴弯曲变形及扭转变形对齿面载荷分布的影响,根据人字齿轮传动的特点,提出小轮轴向浮动安装的齿面修形优化设计方法；通过3次B样条将齿向修形曲线拟合为三维修形曲面,并与理论齿面叠加构造修形齿面,建立轴向串动的齿面接触分析(TCA)模型,结合承载接触分析(LTCA)模型对有轴向串动的人字齿轮传动进行仿真,轴向串动保证了两端齿面各承担一半的扭矩,人字齿轮的修形可认为是一个斜齿轮的修形,即只考虑一端修形,另一端修形则与之对称；以齿面载荷密度最小为优化目标,应用遗传算法确定最佳修形齿面. 算例表明：轴向串动是左右齿面间隙相互补偿的过程,串动后两边齿面载荷分布基本相同,修形后两端齿面载荷达到均匀；人字齿轮齿向修形与轴向串动相互补充,保证了齿面载荷整体上均匀.

Abstract:

Considering the effect of installation error, bending deflection and torsional deformation on load distribution, as well as drive feature of the gears, an approach based on the load sharing of modified double helical gears with the pinion axial float was proposed in which the modified tooth surfaces were represented by a sum of two vector functions that determine the theoretical tooth surface and the deviations surface fitted by 3 B-spline based on tooth surface mesh data from the longitudinal curves, and a TCA model including axial displacement and LTCA model was built. Besides, axial move process showed that the left and right tooth surface bore the same torques, so the modification was thought as a helical gear modification, and only one side tooth was considered and the other side was the same. In addition, minimum load density was used to evaluate load sharing, and genetic algorithm was used to optimize the parameter of curve. The results show that the axial motion process is about the tooth gap mutual compensation process which makes both of the tooth load distribution same and uniform, in short, when considering modification and axial motion, the loads tend to be uniform totally.