In order to analyze the influence of variable tooth line radius on the contact stress of circular tooth line cylindrical gear, eight groups of gear pairs with different tooth line radius are selected for contact stress analysis, and the other parameters are listed in Table 1. The pinion is applied with a torque of T=200 N.m, and the analysis setting is consistent with the above. The eight groups of contact stress nephogram are shown in Figure 1.
| Parameters | Value |
| Number of teeth z1/z2 | 20/30 |
| Modulus m/mm | 4 |
| Tooth width b/mm | 40 |
| Tooth line radius Rt/mm | 100 |
Figure 1 (a)~(h) respectively correspond to the contact stress of 8 groups of circular tooth line cylindrical gear pairs with different tooth line radii under torque T=200 N.m. The contact stress values are listed in Table 2. The curve obtained by fitting the contact stress values of different tooth line radii is shown in Figure 2.
| Gear pair number | Tooth width/mm | Contact stress value/MPa |
| a | 30 | 278.67 |
| b | 40 | 222.87 |
| c | 50 | 236.90 |
| d | 60 | 210.23 |
| e | 70 | 222.57 |
| f | 80 | 178.98 |
| g | 90 | 224.59 |
| h | 100 | 218.12 |
As can be seen from Figure 2, the tooth number z, module m, tooth line b, and pressure angle of circular arc tooth line cylindrical gear α When the other parameters are fixed, the contact stress of the gear decreases first and then increases with the increase of the tooth line radius, and the figure is similar to a parabola. Through the analysis of the results, it can be seen that the load carrying capacity of the circular arc tooth line cylindrical gear is closely related to its tooth line radius, but the smaller the tooth line radius is, the better or the larger the tooth line radius is, but under the condition that other parameters are determined, the tooth line radius is within a certain range, the circular arc tooth line cylindrical gear has the best load carrying capacity and the minimum contact stress value. It can be seen from 10 that when 1.5b ≤ R ≤ 2.5b, the load carrying capacity of circular tooth profile cylindrical gear is the best.
