## 5 Engineering Application Examples
### Design Scheme 2  
The high-and-then-low load after the first sequence adopts the same analysis theory, and the formulas used for the calculation results are not identical; relevant data can be seen in Tables 4 and 5. According to the calculated data in the above tables,  
1. When using the Miner model to design, the stress ratio is greater than 0.9, and the design results of fatigue life are independent of the loading sequence, which is consistent with [PERSON]'s theory. 2. When using the M-H model to design, the design results of fatigue life are closely related to loading sequence, and the more the load levels are, the more obvious the influence. For the third-level load, when the loading sequence is from high to low, the stress ratio is 1.2863, which is higher than the design for the linear Miner model. However, when the loading sequence changed from low to high, the stress ratio is 0.8467, which is lower than the design results of the linear Miner model. For the fourth-level load, the change of stress ratio is more obvious when the loading sequence changes. When the loading sequence is from high to low, the stress ratio is 1.3271, which is higher than the design for the linear Miner model. However, when the loading sequence changes from low to high, the stress ratio is 0.7616, which is lower than the design results of the linear Miner model. 3. When using the modified M-H model to design, the design results of fatigue life are closely related to the loading sequence. The more the load levels are, the more obvious the influence on the stress ratio. According to the results, the modified model can avoid the insufficient accuracy of prediction caused by simply considering the loading sequence effects to a certain extent, which is a modification of its analysis results to ensure the effectiveness of analysis and design. 4. According to different design theories, the results of design parameters for the stress ratio are obviously different, which can be chosen according to different working conditions and its design theory to design. For the multistage load actions, the design model based on the M-H model can take the loading sequence effects into account well, while the modified M-H model can consider loading sequence effects and load interactions at the same time, giving more reliable analysis results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Level \(i\)** & \(\sigma_{i}\)/**Mpa** & \(n_{i}\)/\(\times\)**10\({}^{7}\)** & \(N_{i}\)/\(\times\)**10\({}^{7}\)** & \(D_{i}\)(M) & \((\mathbf{u_{i-1}}\sigma_{i-1}^{m}\)/C)\({}^{\mathbf{\alpha}_{i}}\) & \((\mathbf{u_{i-1}}\sigma_{i-1}^{m}\)/C)\({}^{\mathbf{\alpha}_{i}^{*}}\) \\ \hline
1 & 0.55 & 0.4 & 3.27326 & 0.0612 & 0.0219 & 0.0212 \\
2 & 0.70 & 0.3 & 0.65687 & 0.1986 & 0.0594 & 0.0637 \\
3 & 0.85 & 0.3 & 0.51429 & 0.4512 & 0.1236 & 0.1214 \\ Total & - & 1.0 & - & 0.4512 & 0.1236 & 0.1214 \\ Miner model & \(\Delta\sigma_{\text{ref}}=0.6237\) MPa & \(\Delta\sigma_{\text{eq}}=0.6026\) MPa & \(s=0.9661\) \\ M–H model & \(\Delta\sigma_{\text{ref}}=0.6237\) MPa & \(\Delta\sigma_{\text{eq}}=0.5281\) MPa & \(s=0.8467\) \\ Modified M–H model & \(\Delta\sigma_{\text{ref}}=0.6237\) MPa & \(\Delta\sigma_{\text{eq}}=0.5410\) MPa & \(s=0.8674\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Three-level loads designed in the low-and-then-high loading sequence.