Time-dependent reliability analysis of planar mechanisms considering truncated random variables and joint clearances

• Published in: Probabilistic engineering mechanics 2024-01, Vol.75, p.103552, Article 103552
• Main Authors: Cheng, Yufan, Zhuang, Xinchen, Yu, Tianxiang
• Format: Article
• Language: English
• Subjects: Envelope function; Joint clearance; Motion accuracy; Time-dependent reliability; Truncated random variables
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2023.103552

The dimension variables and joint clearances are key factors affecting the motion accuracy of a mechanism. The existing time-dependent reliability analysis methods usually assume that the dimension variables follow ideal distribution, ignoring the truncation restrictions due to production and manufacturing. In addition, improper handling of the correlation between joint clearance variables leads to inaccurate calculation results. To address the above issues, this paper proposes a time-dependent kinematic reliability analysis method, in which the truncated random variables and joint clearances are comprehensively considered. Firstly, the complex correlation of clearance variables in the motion error function is processed by the dimension reduction method. Then, the truncated variables are converted into truncated standard normal variables. Furthermore, the envelope function method with expansion at the most probable point (MPP) is used to transform time-dependent reliability into time-independent reliability at multiple time points, greatly reducing computational complexity. On this basis, the saddlepoint method is used to fit the motion error cumulative distribution function at each time point, and the upper and lower bounds of failure probability are obtained through the Copula function and second-order narrow reliability bounds. The effectiveness of the proposed method is verified by a typical 4-bar linkage and a single crank double rocker mechanism.