Statistical modelling of wire breakage progression and rope fatigue life considering tension history

• Bending-over-sheave fatigue testing of wire ropes under switching tension. • Modeling tension-dependent progression of wire breakage using Weibull distribution. • Calculating rope cross-sectional area loss for rope damage by wire breakage model. • Estimating rope fatigue life and damage progression considering tension history. Wire ropes are extensively utilised in mechanical systems such as cranes and elevators, where they are subjected to repeated bending stresses under varying tension levels. This cyclic loading leads to progressive wire breakage and, ultimately, rope failure. To enhance the prediction of rope damage and optimise discard timing, this study proposes a statistical damage model that incorporates tension history. The model quantifies rope damage by evaluating the loss of cross-sectional area resulting from wire breakage. The progression of wire breakage is characterised using a Weibull distribution with tension-dependent parameters. A hierarchical Bayesian framework is employed to robustly estimate the failure probability parameters across different wire types within the rope. The validity of the model was demonstrated through fatigue tests conducted under constant, two-step, and multistep tension conditions. Compared with Miner’s rule, the proposed approach offers superior prediction accuracy for fatigue life and effectively captures the nonlinear progression of wire rope damage. Furthermore, the model accurately predicts rope damage from its initial state to the point of discard. These findings highlight the capability of the proposed method to quantitatively evaluate rope damage under various tension histories, thereby contributing to safer and more effective maintenance strategies.