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Dynamic Fatigue Reliability Analysis of Transmission Gear Considering Failure Dependence

Yonghua Li1,*, Xiaoning Bai2, Shanshan Shi1, Shenxuan Wang1
1 College of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian, 116028, China
2 School of Mechanical Engineering, Dalian Jiaotong University, Dalian, 116028, China
* Corresponding Author: Yonghua Li. Email:
(This article belongs to this Special Issue: Computer-Aided Structural Integrity and Safety Assessment)

Computer Modeling in Engineering & Sciences 2022, 130(2), 1077-1092.

Received 05 July 2021; Accepted 20 August 2021; Issue published 13 December 2021


Multiple failure modes and strength degradation are usually inherent in the gear transmission system, which brings new challenges for conducting fatigue reliability analysis and design. This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of the Copula function and Gamma process. Firstly, the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history. The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model. The marginal distribution functions of tooth contact fatigue and dedendum bending fatigue are calculated respectively based on the dynamic interference model. Finally, the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence, and so the dynamic fatigue reliability considering failure dependence can be estimated. The effectiveness of the proposed method is illustrated with examples. The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.


Gear transmission system; failure dependence; dynamic fatigue reliability; the Gamma process; the Copula function

Cite This Article

Li, Y., Bai, X., Shi, S., Wang, S. (2022). Dynamic Fatigue Reliability Analysis of Transmission Gear Considering Failure Dependence. CMES-Computer Modeling in Engineering & Sciences, 130(2), 1077–1092.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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