Tooth surface 6σ robust optimization desgin under installation error of spiral bevel gear

Due to the installation error in the transmission of aviation spiral bevel gears，its uncertainty had a great impact on the noise and robustness of the gear transmission.Monte Carlo simulation was used to describe the sampling method and the multi-island genetic algorithm for spiral bevel gears.The design of the second-order contact parameters was combined with the local synthesis method and the $\mathrm{6}\sigma$ analysis method to form a robust optimization design method.And a robust optimization design not sensitive to installation errors was developed.The results showed that，under a given working condition， the robustness of the uncertainty of installation error in gear transmission can be improved to more than 99.9% by reasonably presetting the value and tolerance of second-order contact parameters，the sensitivity of contact mark and transmission error can be effectively reduced by more than 30%，and the contact performance of spiral bevel gear transmission can thus be improved.The feasibility of the robust design method for spiral bevel gears based on the $\mathrm{6}\sigma$ robust optimization design technique in the article was verified.