## 3 Results and Discussion
### Contact Pressure and Gap Distance under Axial Compression  
Contact pressure is one of the most important variables for distinguishing the sealing capacity of a sealant. The distribution of the contact pressure along the outer area of a UMS was investigated. As shown in Figure 5, the contact-pressure distributions along the interface between the outer area of the UMS and the surrounding area were compared using line profile plots. In general, the contact pressure tended to increase as the TR increased. Figure 5a,c show symmetrical changes in contact pressure around the arc length at 0 mm, whereas Figure 5b shows asymmetric changes in contact pressure. Type 1 showed a narrow and sharp increase in contact pressure because of the geometrical effect of the open grooves (Figure 5a). In particular, the contact pressure increased to its highest value of 43.8 MPa at TR = 0.50. Type 3, with no open groove, showed a wide and slow increase in contact pressure at both ends of the UMS, with its highest value of 47.1 MPa at TR = 1.50 (Figure 5b). Type 2 showed the characteristics of both types 1 and 3. The leg with an open groove showed a sudden increase in contact pressure, with a maximum value of 43.5 MPa at TR = 0.25,  
Figure 5: Contact-pressure distributions along the interface between the outer area of the UMS and the surrounding area at 40% of the axial compression in assembly: (**a**) type 1; (**b**) type 2; and (**c**) type 3. SOP: symmetric open groove; ASOP: asymmetric open groove; SNO: symmetric no groove. whereas the leg with no groove showed a gradual increase, with its highest value of 32.5 MPa at TR = 1.50. Using the stress-strain curve suggested in the literature [25], the approximate stress of the 40%-deformed FKM material was experimentally reported to be about 1.5-2.0 MPa at constant volume assumption. Referring to the suggested equations in another literature [1], it was reported that when elastomeric seals were compressed by 40%, the contact pressure of the axially and radially restrained grooves would exponentially increase by about 20-25 times greater than those of the unrestrained geometry. Thus, taking these references together, one can estimate that contact pressure obtained in this study was likely to be about between 30.0 and 50.0 MPa for validity, which corresponded to the results shown in Figure 5. In addition, as shown in the literature, the exponential behavior of elastomeric materials under compressive condition was consistent with our findings. In Figure 5, particular intervals showing 0 MPa of contact pressure exist in the arc-length range from \(-22.5\) to \(22.5\) mm, which corresponds to the UMS body area. This implies that there was no contact pressure because the outer surface of the UMS was detached from the surrounding surface of the retainer. To examine the detachment characteristics in more detail, further analysis was conducted on the gap-distance profile, as shown in Figure 6.  
In the case of type 1, as shown in Figure 6a, a symmetric detachment region occurred in the arc-length section from \(-10.8\) to \(10.8\) mm at TR = 0.25, with a maximum gap of 0.12 mm. As the TR ratio increased to 0.5, the detachment region reduced from \(-6.2\) to \(6.2\) mm, with a decreased gap of 0.03 mm. In the case of type 2, as shown in Figure 6b, the gap was the largest of the three types. Figure 6: Gap-distance profile along the interface between the outer area of the UMS and the surrounding retainer at 40% of axial compression during assembly: (**a**) type 1, (**b**) type 2, and (**c**) type 3. SOP: symmetric open groove; ASOP: asymmetric open groove; SNO: symmetric no groove. Because of the asymmetric geometry of type 2, the detachment region was distributed asymmetrically. The detachment region and the gap were broad and large in the direction in which there was no open groove. On the other hand, they were narrow and small in the direction where there was an open groove.