Gear is the most commonly used transmission component

and its most common failure mode is tooth surface pitting and tooth root fracture. In order to analyze its reliability quickly and accurately

an improved fourth moment method considering failure correlation was proposed. Firstly

according to the failure mechanism

the reliability models of tooth contact fatigue and tooth root bending fracture failure were established respectively. Secondly

in order to improve the accuracy of the traditional fourth order moment solution

the second order reliability index obtained by the improved first order second moment method was used to obtain the new fourth order reliability index

so as to improve the reliability solution accuracy of single failure mode. Then

the correlation between multiple failure modes and the overall failure probability considering failure correlation were calculated based on the conditional probability dimension reduction method. Finally

taking the transmission gear of a system a a example

the calculation results of the proposed method

mean value first order second moment (MVFOSM) method

advanced first order second moment (AFOSM) method and traditional high-order moment standardization technique (HOMST) method were compared. The results show that the accuracy and efficiency of the proposed method are greatly improved

and it also provides a theoretical method to analyze the reliability of multiple failure modes.