It can be seen that the tooth surface shape of pure roll contact long epicycloid bevel gear can be controlled by the blade curve. Similar to pure rolling contact equiangular spiral bevel gear and pure rolling contact equidistant spiral bevel gear, the blade curve can be taken as double circular arc, as shown in Figure 1. Setting the blade curve as double arc has the following advantages:
- Double segment arc can easily control the theoretical contact point on the pitch line;
- The concave arc can increase the thickness of the tooth root, so as to reduce the bending stress;
- For the large and small wheels of long epicyclic bevel gear, the blade shape is consistent. Therefore, the large and small wheels of long epicyclic bevel gear can be processed by one tool.
The tooth surfaces of pinion and big gear can be obtained. Here, set a set of design parameters as an example. First set R1 = 10mm and R2 = 12mm, and then the large and small tooth surfaces of long epicycloid bevel gear can be obtained from the formula. After the tooth surface is arrayed and trimmed, figure 2 shows the final three-dimensional solid model of the pure roll contact long epicycloid bevel gear. Figure 3 shows the profile wheel and pinion model.