# Comparison of Fatigue Performances Based on Shape Change of Rail Fastening Spring
## 4 Conclusions  
This study evaluated the effects of various shape factors, namely, the fastening spring end height, spring arm height, and overall lateral width and diameter of the cross section of the fastening spring, on fatigue performance. The following conclusions were obtained from this work:  
1. The shape changes in the height of both the spring end and arm only slightly affected the mean stress and stress amplitude, which were the two main factors affecting the fatigue performance. This observation can be attributed to the similar internal forces (i.e., shear force and bending moment) that occurred in the critical sections with slight changes in the moment arm for each model. These two variables did not significantly change the safety margin ratio. In the case of the spring end height, the safety margin ratio was about the same (75%) when varied from 0% to 50%. In the case of the spring arm height, the safety margin ratio decreased from 75% to 73% when varied from \(-\)20% to 20%.
2. The overall lateral width of the fastening spring significantly affected the stress condition, particularly the stress amplitude. The mean stress and stress amplitude both decreased as the width increased. With increasing width, this curvature effect on the maximum principal stress was more significant than that of the increased internal force at the critical sections. When the width increased from \(-\)20% to 20%, the safety margin ration increased from 64% to 82%.
3. The variation in the maximum principal stress and the stress range according to the change in the cross-sectional diameter of the fastening spring were very remarkable.  
Figure 16: Stress variation with the spring diameter: (**a**) maximum principal stress; (**b**) maximum principal stress range.  
Figure 17: Comparison of the fatigue performance when varying the spring diameter: (**a**) fracture criteria; (**b**) margin of safety (%).  
The maximum principal stress decreased as the diameter increased. In contrast, the stress range increased. The fatigue performance in the case of the modified Goodman criterion increased. For example, when the diameter was 13 mm, the safety margin was 54%, whereas in the case of the 18 mm diameter, the safety margin was 81%. It is believed that the maximum principal stress at the initial fastening has a greater dominant effect on the fatigue performance than the stress amplitude.  
Both the lateral width and cross-sectional diameter of the fastening spring significantly influenced the fatigue performance. Moreover, the design that decreased the maximum principal stress can be more efficient than the one that reduced the stress range for the fatigue performance improvement. However, this study was based on the results of finite element and theoretical fatigue performance analyses; thus, the field environment, including constructability, should be separately considered. Future research may also include the fatigue testing of an optimized shape of the fastening spring based on the results of this work.  
Conceptualization, X.-J.F. and H.-B.S.; methodology, X.-J.F., Y.-C.P. and H.-B.S.; validation, J.-W.H. and Y.-C.P.; investigation, X.-J.F., [PERSON]-C.P. and H.-B.S.; resources, H.-B.S.; writing--original draft preparation, X.-J.F.; writing--review and editing, Y.-C.P., [PERSON]-W.H. and H.-B.S.; visualization, X.-J.F.; supervision, H.-B.S.; project administration, H.-B.S.; funding acquisition, Y.-C.P., J.-W.H. and H.-B.S. All authors have read and agreed to the published version of the manuscript.  
This work has been supported by the National Research Foundation of Korea (NRF). The grant has been funded by the Korean government (MSIT) (No. 2020R1A4A4079299). This work was also funded by the Incheon National University (International Cooperative) Research Grant (2018-0359).  
The authors declare no conflict of interest.