最佳当量齿数研究

Study on the Best Virtual Number of Teeth

应用最佳逼近理论 ,在当量齿轮齿廓曲面的两主曲率与对应齿轮的两主曲率分别相等或最接近的条件下 ,导出当量齿数。根据微分几何 ,这样得到的当量齿轮的齿廓与对应齿轮的齿廓最接近 ,相应的当量齿数称为最佳当量齿数。渐开线斜齿圆柱齿轮和直齿圆锥齿轮的最佳当量齿数分别为zv=z/cos3 βb,zv=z/cosδa。

In this paper, according to the theory of the best approximation, the virtual numbers of teeth are given when the principal curvatures of virtual gears and their corresponding gears are equal or best approximate. Therefore the tooth form of virtual gears is most approaching to its corresponding gears, based on differential geometry. And these tooth numbers are called the best virtual number of teeth. The best virtual number of teeth of involutes helical gear is z v=z / cos 3β b and that of spur bevel gear is z v=z/cosδ a.