中文摘要：

推导了双圆环面包络环面蜗杆磨齿啮合界线方程及其与相配蜗轮啮合的啮合界线方程。阐明双圆环面二次包络副的二次包络啮合界线与一次包络啮合界线共轭线重合，是二次包络新接触线族的包络线，与二次包络原接触线族相交，将蜗杆螺线面划分为单线接触区与双线接触区，从而诠释了双圆环面包络环面蜗杆螺旋面的结构。同时指明，可以通过合理搭配参数，调整二次包络啮合界线沿蜗杆轴向的位置，增加瞬时接触线的总长，提高传动副承载能力。

英文摘要：

The equations of the meshing limit line in the first and second enveloping of the dual-torus double-enveloping toroidal worm drive are presented in this paper. It is illustrated that the meshing limit line of the worm pair in the second enveloping is the reappearance of the conjugate curve of the meshing limit line in the first enveloping as well as the envelope curve of the new contact lines which intersects the former contact lines and divides the worm helicoids into two sections, slngle-line and double-line contact zones. Consequently, the configuration of the worm helicoids is shown. Meanwhile, it is pointed out that by reasonably arranging the parameters and adjusting the axial position of the meshing limit line in the second enveloping along the worm axis, the total length of the instantaneous contact lines will be increased which is very propitious to enhance the carrying capacity of the worm set.