## 2 Development of an Advanced SR-JOINT (SR-II)
### Optimal SR-Joint Shape Design  
#### 2.2.1 Optimal Shape Design Variables  
The new SR-joint shape (SR-II) was designed to prevent corrosion by placing a gap between the rubber and metal rings. The initial shape of SR-II designed using field experience was compared with the conventional SR-I shape through finite element analysis. The results of the SR-II initial shape analysis shown in Figure 6 indicate that the maximum load was 192.7 kN, which was a decrease in load by approximately 57% compared with that of the conventional SR-joint. The load was reduced by dispersing the stress concentrated in the adjacent part of the metal and rubber rings of the conventional shape; this implies that the maximum press load to be combined was small, rendering it easier to perform molding. The purpose of this study is obtaining an optimal design that minimizes the press load for light-weighting the pressure jig and improving the lifetime of the pressure jig. The optimal design variables were set as the curling length at the top of the joint, distance between the metal and rubber rings, and jig radius. The defect form and the constraints of the shape based on the range of the design variables are shown in Figure 7. When the SR-joint is pressed, the metal ring should not be inclined, and the inner pipe must be deformed horizontally such that it can be compressed. It was discovered through finite element analysis that the metal ring collapsed due to compression when the metal ring was inclined and the distance was less than 6 mm. Therefore, the distance between the metal and rubber rings was set in the range of 6-15 mm in consideration of the metal ring defects and pressure jig size. The jig radius was initially set to 4.7 mm based on field experience. However, the SR-joint may be dented if the jig radius is less than 4.7 mm. In addition, the inner pipe and SR-joint may not be in contact with each other, resulting in a short shot if the jig radius exceeds 5 mm. Therefore, the jig radius was set to 4.7-5.0 mm. When the curling length exceeded 5.7 mm, the metal ring was prevented from compressing the inner pipe because it was in contact with the pipe before the metal ring. If the length is less than 5.3 mm, then the curling length will be short, rendering it impossible to prevent external impurities from flowing into the metal ring. Therefore, the curling length range was specified as 5.3-5.7 mm. The optimum design constraint was a metal ring inclination of less than 10\({}^{\circ}\) to withstand vibration or deflection after molding, and the upper part of the SR-joint (the curling length part) and the lower  
Figure 6: Numerical load–stroke curves of the proposed SR-joint (SR-II). part of the rubber ring must be in contact with the inner pipe. This is to prevent foreign substances flowing from the upper part after connecting the SR-joint and to prevent water flowing from the lower part of the rubber ring, thereby causing corrosion. The load applied to the pressing jig was measured through finite element analysis. As for the load, the maximum load in the pressure jig was measured after finite element analysis; the load showed significant results for the design variables. Therefore, the objective function served to improve the lifetime of the pressure jig and minimize the load for light-weighting in this optimal design. The design variables, constraints, and objective functions for the optimal design are shown in Table 2, and the descriptions of the SR-joint (SR-II) analysis modeling and design variables are shown in Figure 8.  
The full parameter case comprised 200 cases (\(5\times 10\times 4\)): 5 curling lengths, 10 distances, and 4 jig radii depending on the design variables. Accordingly, a finite element analysis was performed by randomly selecting 100 datasets using the \"random\" function. The analysis results show that the upper part of the curling did not establish a contact with pipe when the curling length was 5.3 mm, and the jig radius was 5.0 mm.