Based on the modeling method of system level theory, the gear transmission system is divided into three subsystems: primary DSI planetary gear train C1, secondary bevel gear train C2 and tertiary bevel gear train C3. The estimated parameters of correlation coefficients of Gumbel cop ⁃ ula functions at all levels are shown in the table. According to the properties of Gumbel copula function, the correlation coefficient is unknown θ The smaller, the greater the correlation coefficient between the described variables. It can be seen from the table that the failure correlation of DSI planetary gear train is smaller than that of bevel gear train. From the perspective of the whole system, the failure correlation between parts changes from small to large with the direction of power transmission.
| C1 | C2 | C3 | |
| θ | 66.878 3 | 39.386 5 | 9.258 2 |
The variation law of reliability related to the failure of the whole gear system and subsystems at all levels is shown in Figure 10. The reliability of the first stage DSI planetary gear train running for 3000 h is 88 90%, the reliability of the two-stage bevel gear train running for 3000 h is 96 77%, and the reliability of three-stage bevel gear train running for 3000 h is 93 81%, and the reliability of the whole gear transmission system running for 3000 h is 84 01%。 Without considering the failure correlation, according to the principle of the weakest link of the system, the system reliability depends on the parts with the lowest reliability in the system, so the system reliability is 89 43%, which is 5.5% different from the reliability calculated by failure correlation 42%。
It can be seen that due to the failure coupling between subsystems, the reliability of the whole transmission system is obviously weakened. After 3000 hours of operation, the reliability of DSI planetary gear train is less than 90%, which can not meet the use requirements of flying vehicles. It is a weak link in the whole transmission system, and further structural improvement and optimization are needed in the future.