## 6 Conclusions  
1. The cross-sectional failure area of the fatigue wire increases with increasing contact load and fatigue load;
2. The fitting equations with a goodness of fit above 0.99 for the damage degree, \(D\), of the worn wire were established. The wire's \(D\) shows a good quadratic function relationship with the fatigue cycles;
3. The damage degree of the worn wire increases with increasing fatigue cycles. Under the same fatigue cycle, the greater the contact and fatigue load, the greater the \(D\) of the worn wire. The influence of contact load on wire damage degree is greater than that of fatigue load;
4. The finite element simulation model of the wire was established, and the stress-strain curve and residual load-bearing strength of the wire under various working  
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{1}{c}{**Parameters**} & \multicolumn{2}{c}{**Fitting Equation**} & \multicolumn{1}{c}{**Goodness of Fit (R\({}^{2}\))**} & \multicolumn{1}{c}{**Predicted Life**} \\ \hline \multirow{3}{*}{Contact load (N)} & 60 & y = \(-5.34\times 10^{-11}\)\(N^{2}-1.36\times 10^{-5}\)\(N+1650\) & 0.9835 & 4.20 \(\times\)\(10^{6}\) \\  & 80 & y = \(-6.29\times 10^{-11}\)\(N^{2}-2.96\times 10^{-5}\)\(N+1650\) & 0.9882 & 3.76 \(\times\)\(10^{6}\) \\  & 100 & y = \(-8.42\times 10^{-11}\)\(N^{2}-4.26\times 10^{-5}\)\(N+1650\) & 0.9617 & 3.20 \(\times\)\(10^{6}\) \\ \hline \multirow{3}{*}{Fatigue load peak (N)} & 1000 & y = \(-5.34\times 10^{-11}\)\(N^{2}-1.36\times 10^{-5}\)\(N+1650\) & 0.9835 & 4.02 \(\times\)\(10^{6}\) \\  & 1100 & y = \(-5.84\times 10^{-11}\)\(N^{2}-4.11\times 10^{-5}\)\(N+1650\) & 0.9751 & 3.66 \(\times\)\(10^{6}\) \\ \cline{1-1}  & 1200 & y = \(-10.37\times 10^{-11}\)\(N^{2}-4.25\times 10^{-5}\)\(N+1650\) & 0.9879 & 2.70 \(\times\)\(10^{6}\) \\ \hline \end{tabular}
\end{table}
Table 7: Fitting equation of worn wire (pair: wire) strength degradation.  
Figure 11: Strength degradation curves of the worn wire (pair: wire) under different contact loads (**a**) and different fatigue loads (**b**).  
conditions were obtained. Increasing contact load and fatigue load decreases the load-bearing strength of the wire;
* The fitting equations between the load-bearing strength and fatigue cycles of the worn wire were established, and the life of the wire was predicted.  
Conceptualization, X.S.; Methodology, H.C., D.W., B.W. and X.S.; Validation, M.A.W.; Resources, D.W.; Data curation, H.C. and B.W.; Writing--original draft, H.C., B.W. and X.S.; Writing--review & editing, B.W.; Supervision, D.W. and M.A.W.; Project administration, D.W.; Funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript.  
The research was supported by the National Nature Science Foundation of China (Grant No.51875565) and the Chinese Postdoctoral Science Foundation (Grant Nos. 2019M652001 and 2020T130659). The authors also wish to thank the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (TAPP) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).  
Not applicable.  
The authors declare no conflict of interest.