Increase the transmission ratio to 30, take the gear ratio of 2:60, and design and calculate the gear parameters. The values of helix angle at the center point, tooth crest height coefficient and tooth height coefficient of the small wheel are the same as those of the aforementioned 3:60 hypoid gear. This time, the cone angle of the large wheel surface has reached 84.431 °, and the risk of interference between the large wheel surface cone and the cutter head is further increased.
The three-dimensional model of the completed large and small wheels is shown in Figures 1 and 2. From the figure, the shape of large and small gear teeth is intact, without undercutting and sharpening. Therefore, the scheme of hypoid gear 2-tooth small wheel transmission is also feasible.
Finally, it should be noted that the meshing backlash of gear teeth is not considered in the solid modeling of hypoid gear pinion and wheel, but it does not affect the judgment of gear tooth geometric topology, tooth tip sharpening and undercutting.
From the above models of 4, 3 and 2-tooth small wheels, with the increase of helix angle, the risk of undercutting of large and small wheels and sharpening of tooth top is not large. When the transmission ratio reaches 30, the face cone angle of the big wheel is close to the limiting condition of 85 degrees, which will increase the risk of interference between the disc milling cutter and the face cone of the big wheel in the processing of the big wheel. Therefore, when the transmission ratio is greater than 30, the design of hypoid gear needs special consideration.