## 5 Deterioration Model for Wire Load-Bearing Strength
### Deterioration of the Wire Load-Bearing Strength  
According to the tensile finite element analysis results of the worn wire described in Section 5.3, the fitting method was used to establish the deterioration model of the wire's load-bearing strength. The life of the experimental steel wire was predicted. (1) Wire-saddle groove  
As shown in Figure 10, the quadratic function is used to fit the data points obtained by tensile simulation, and the goodness of fit is above 0.98. At a contact load of 60 N, the load-bearing strength of the fatigue wire changes little at the beginning with increasing fatigue cycles. As the frequency of fatigue continues to increase, the load-bearing strength of the wire begins to decrease continuously because of the increased damage to the wire. By comparing the curves under the different contact loads, it can be seen that, with an increase in contact load, the load-bearing strength of the wire under the same number of cycles decreases. This is because the increase in contact load can promote damage to the steel wire. The larger the contact load is, the larger the failure area of the wire is and the lower the bearing strength of the wire is. From Figure 10b, the larger the fatigue load is, the lower the load-bearing strength of the wire is. The reason for this is the same as that affected by the contact load. As shown in Table 6, the predicted life of the fatigue wire decreases from 4.02 \(\times\) 10\({}^{6}\) to 3.44 \(\times\) 10\({}^{6}\) times with increasing contact load. The predicted life of the wire decreases from 4.02 \(\times\) 10\({}^{6}\) to 3.16 \(\times\) 10\({}^{6}\) times with an increase in fatigue load. In conclusion, the larger the contact load and the larger the fatigue load peak, the lower the predicted life of the fatigue steel wire. (2) Parallel wire-wire  
As shown in Figure 11 and Table 7, the quadratic function is used to fit the data points obtained by the tensile simulation. The goodness of fit under different contact loads is \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & \multicolumn{2}{c}{**Fitting Equation**} & **Goodness of Fit (R2)** & **Predicted Life** \\ \hline \multirow{3}{*}{Contact load (N)} & 60 & y = \(-5.47\times 10^{-11}\)\(N^{2}-2.79\times 10^{-5}\)\(N+1650\) & 0.9875 & 4.02 \(\times\) 10\({}^{6}\) \\  & 80 & y = \(-5.87\times 10^{-11}\)\(N^{2}-3.16\times 10^{-5}\)\(N+1650\) & 0.9878 & 3.86 \(\times\) 10\({}^{6}\) \\  & 100 & y = \(-7.20\times 10^{-11}\)\(N^{2}-4.28\times 10^{-5}\)\(N+1650\) & 0.9974 & 3.44 \(\times\) 10\({}^{6}\) \\ \hline \multirow{3}{*}{Fatigue load peak (N)} & 1000 & y = \(-5.47\times 10^{-11}\)\(N^{2}-2.79\times 10^{-5}\)\(N+1650\) & 0.9875 & 4.02 \(\times\) 10\({}^{6}\) \\  & 1100 & y = \(-7.00\times 10^{-11}\)\(N^{2}-3.12\times 10^{-5}\)\(N+1650\) & 0.9890 & 3.43 \(\times\) 10\({}^{6}\) \\ \cline{1-1}  & 1200 & y = \(-7.52\times 10^{-11}\)\(N^{2}-3.75\times 10^{-5}\)\(N+1650\) & 0.9936 & 3.16 \(\times\) 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Fitting equation of worn wire (pair: groove) strength degradation. Figure 10: Strength degradation curves of worn wire (pair: groove) under different contact loads (**a**) and different fatigue loads (**b**). above 0.96, as compared to 0.97 under different fatigue loads. At a contact load of 60 N, the load-bearing strength of the fatigue wire decreases greatly at the initial stage, which is different from that between the wire and the saddle groove. This is attributed to the fact that the tribo-corrosion-fatigue test between the two wires has four wear marks, while the test between the wire and the groove has only two wear marks. The greater damage caused by the four wear marks decreases the load-bearing strength rapidly. As the fatigue frequency continues to increase, the load-bearing strength of the wire decreases further due to increasing damage to the wire. Under the same fatigue cycles, as the contact and fatigue loads increase, the load-bearing strength of the fatigue wire decreases.