# Integrated Design of Hydraulic Coupling Bolts for Large Shaft Systems
## 4 Design of Oil Passage Shape
### FE Analysis of Untightening Process  
In the FE analysis of the untightening process, we used the results of the tightening process conducted in the previous section. As shown in Figure 12, the untightening hydraulic pressure was applied to the oil passage on both the bolt surface and inner surface of the sleeve after tightening. The analysis of the untightening process consists of two steps. Step 1 involves the release of the originally applied tensile force on the bolt, and in Step 2, hydraulic pressure is applied to the oil passage. The untightening hydraulic pressure in the second step was set to be the same as the operating pressure of the tensioner applied to the second tightening process. Throughout the analysis, a boundary condition was imposed by constraining the displacement in the direction perpendicular to the longitudinal plane using the symmetry condition for the quarter model. In the case of the coupling, directions other than the radial direction were also constrained. As in the tightening process, nonlinear analysis was performed due to contact nonlinearity between the bolt and the sleeve and between the sleeve and the coupling. Because the separation between the bolt and the sleeve leads to the divergence of the solution in static analysis, the sub-step function was used, and simulation results at the beginning of the separation were analyzed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Simulation No.** & **Pitch [mm]** & **Oil Passage Length [mm]** \\ \hline
1 & 9 & 154 \\
2 & 9 & 158 \\
3 & 9 & 162 \\
4 & 10 & 154 \\
5 & 10 & 158 \\
6 & 10 & 162 \\
7 & 11 & 154 \\
8 & 11 & 158 \\
9 & 11 & 162 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Two-way table for FE analysis of oil passage shape.  
Figure 12: Application of untightening hydraulic pressure to oil passage: (**a**) on bolt surface and (**b**) on sleeve inner surface.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Level 1** & **Level 2** & **Level 3** \\ \hline Pitch [mm] & 9 & 10 & 11 \\ Oil passage length & 154 & 158 & 162 \\
[mm] & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Values of design variables for oil passage at each level.  
Figure 13a shows the variation in the maximum von-Mises stress on the sleeve in relation to the design variables during the untightening process. It should be noted that the allowable stress limit of 490 MPa was determined using a lower _SF_ of 1.43 compared to the tightening process because the load is locally applied only to the oil passage during the untightening process. For the identical oil passage length, reducing the pitch leads to a decrease in the stress applied to the sleeve. Similarly, when the pitch remains constant, increasing the oil passage length ensures structural integrity, although the pitch has a relatively greater effect than the oil passage length. Consequently, decreasing the pitch and increasing the length of the oil passage result in a larger total passage area, which allows the untightening process to be performed at a lower hydraulic pressure and more smoothly. Based on the analysis results, a pitch of 10 mm and an oil passage length of 158 mm were chosen as the optimal design conditions for the oil passage, which can enhance workability without exceeding the allowable stress level. Figure 13b,c show the von-Mises stress distribution on the bolt and sleeve, respectively, under the selected design conditions. It is evident that the structural integrity of the designed hydraulic coupling bolt is secured during the untightening process by comparing the von-Mises stress distribution with the allowable stress limit.  
Figure 13: FE analysis results for the untightening process: (**a**) maximum von-Mises stress variation of the sleeve according to oil passage length and pitch; von-Mises stress distribution (**b**) on the bolt and (**c**) on the sleeve for the selected oil passage shape.