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.