Research on Reliability Modelling for Heavy CNC Machine Tools under Uncertain Variables Based on Universal Generating Function

Due to the lack of historical data, the inability to carry out a large number of reliability tests on the machine tool, the lack of reliability information collected, and the change of the working environment of the machine tool, there are a lot of uncertainties in the machine tool. In the existing research, only unilateral uncertainty factors are usually considered, while in practical problems, random uncertainty and cognitive uncertainty exist at the same time. Therefore, in this study, the random uncertainty and cognitive uncertainty in the system are characterized by random variables, fuzzy variables, probability box variables, and interval variables. For the structural function with more variables, the dimension is reduced first, and then the reliability model of the universal generating function (UGF) is established. Taking the heavy CNC machine tool as an example, the structural reliability analysis model of the fatigue strength of the milling shaft based on the UGF is constructed. The local sensitivity analysis and global sensitivity analysis of the variables affecting the fatigue strength of the milling shaft are carried out, and the factors that have the greatest impact on the fatigue strength of the milling shaft are obtained. The case study shows the effectiveness of the method proposed in this study.