相交轴渐开线变厚齿轮几何设计与啮合特性分析

Geometry Design and Tooth Contact Analysis of Intersected Beveloid Gears

根据空间齿轮啮合原理,建立相交轴渐开线变厚齿轮传动工作节圆锥模型,确定工作节锥角、齿线倾斜角及两齿轮安装距。提出空间点接触到线接触的转变控制条件,实现相交轴齿轮副的近似线接触;推导齿轮变位系数对节圆锥左右两侧有效齿宽的影响;基于相交轴变厚齿轮副参数关系,分析设计参数对啮合主方向角(FPD角)和齿轮副重合度的影响;根据线接触控制条件完成齿轮副参数设计并采用有限元法进行啮合特性分析,结果表明,考虑线接触条件的节圆锥设计得到的相交轴齿轮副在加载情况下,啮合状态呈现明显的线接触且啮合区域达到整个区域的50%左右,试验验证了理论分析的正确性。

According to the spatial gearing theory, the mathematical model for working pitch cone design of intersected beveloid gears is created in order to confirm the working cone angles and the helix angles as well as the mounting distance of the two meshing gears. The formulas to determine the transition from point contact to line contact are derived to achieve the approximate line contact. Besides, the formulas to determine the effective tooth width of the two sides of the working pitch circle are derived. Based on the relationship of the parameters of the beveloid gears using in intersected axis transmission, the analyses of the effects of key design parameters on the angle between the first principle directions（FPD） as well as on the contact ratio are conducted. The fundamental design parameters of one case for the proposed beveloid gear drive in line contact is derived and the loaded tooth contact analysis is performed using the finite element method. The conclusions indicted that the intersected heveloid gears engage with each other in line contact which is considered the geometry design approach assuming line contact. Also, the area of the contact pattern is approximately 50%. A practical tooth bearing test is conducted to demonstrate the proposed design procedure and the experimental results compared well with the simulation.