Jixie qiangdu (Dec 2023)
PREDICTION OF FATIGUE LIFE BASED ON FUZZY MATHEMATICS AND GREY SYSTEM THEORY
Abstract
The traditional fatigue life prediction method Miner theory ignored the damage caused by stress below the fatigue limit to the component, resulting in a large error in fatigue life prediction. In order to calculate the damage caused by the stress below the fatigue limit to the component, according to the loading stress and its characteristics of the damage, the partial large membership function in the semi-trapezoidal and trapezoidal distribution is selected, and the degree of damage caused by the stress below the fatigue limit is characterized by its membership. The damage phenomenon reflected by this membership functionis regarded as a gray system, and an equally spaced GM(1,1) model of stress and membership is established. Then, it fitted its function expression and combined it with the membership function to calculate the damage caused by stress below the fatigue limit. Two sets of 41Cr4 multi-level loading experimental data were used to verify and evaluate the proposed new model, and the error between the estimated results and the experimental results was about 7.5%. Compared with Miner theory, the predicted fatigue life model of the equally spaced grey system, and the grey Verhulst predicted fatigue life model, this model improves the fatigue life prediction accuracy.
