The provided helical gear parameters are substituted into the algorithm in this paper. The comparison of calculation results is shown in Figure 1. The calculation results (left figure) are basically consistent with the screenshot (right figure) of the results in this article, which preliminarily verifies the correctness of the algorithm.
Taking an external meshing helical gear pair in a certain type of gearbox as an example, its basic structural parameters are shown in Table 1:
| z1 | z2 | Mn (mm) | αn (°) | b (mm) |
| 31 | 102 | 4.5 | 20 | 90 |
In order to study the general law, the formula is dimensionless, and the equation is written as:
The helical angle of the helical gear is infinitely close to 0, that is, it can be considered as a spur gear. The time-varying contact line changes as shown in Figure 2. The coincidence degree of the spur gear is between 1 and 2, and the tooth width is B. the total length of the contact line is 2B when the double teeth are engaged, and the total length of the contact line is B when the single tooth is engaged. It accords with the change law of spur gear contact line, and also proves that the algorithm in this paper is correct. It can calculate the contact line length of spur gears, and it is universal for helical gears and spur gears, which is not available.
Select 10 °, 15 °, 20 °, 25 ° and 30 ° in the common range of helix angle from 10 ° to 30 ° and calculate the change of total length of contact line with algorithm, as shown in Figure 3. Use CAD geometric drawing to measure the length of contact line with different helix angle, divide the end tooth pitch into 10 equal points, the number of meshing start point is 0, and the number of meshing end point is 10. Measure the total length of contact line corresponding to these 11 points, and the results are shown in Figure 4:
Table 2 shows the maximum, minimum and average values of the contact line length measured by the program and geometry:
| β (°) | Max Lmax text result / measurement result | Min Lmin text result / measurement result | Mean value Lm paper result / measurement result |
| 10 | 1.64/1.64 | 1.61/1.61 | 1.63/1.63 |
| 15 | 1.77/1.75 | 1.48/1.49 | 1.61/1.61 |
| 20 | 1.59/1.59 | 1.57/1.57 | 1.58/1.58 |
| 25 | 1.63/1.63 | 1.45/1.45 | 1.54/1.53 |
| 30 | 1.49/1.49 | 1.47/1.48 | 1.48/1.49 |
It can be seen from table 2 that the program calculation results are in good agreement with the measurement results, and the algorithm is verified to be correct again.
The calculation formula for the mean length of helical gear contact line in China aviation industry standard hb/z84.2-1984 is used to compare with the calculation results in this article, as shown in Table 3. The results show that the error between the average value of contact wire length calculated in this paper and the average value of standard calculation is less than 5%.
| β (°) | This paper calculates the mean value | Hb/z84.2-1984 calculated mean value | Error value |
| 10 | 1.63 | 1.71 | 4.67% |
| 15 | 1.62 | 1.59 | 1.85% |
| 20 | 1.58 | 1.52 | 3.79% |
| 25 | 1.48 | 1.45 | 2.03% |
| 30 | 1.54 | 1.48 | 3.89% |