# Comparison of Fatigue Performances Based on Shape Change of Rail Fastening Spring
## 1 Introduction  
A rail fastening system is critical to the running safety of a railway because it secures the rail to the sleeper or track substructure. Among the components of a rail fastening system, the fastening spring can generate a large initial tensile stress that exceeds the yield stress during the initial fastening in the assembly process. As a result of repeated stress caused by rail deflection while the train is running, the fastening spring may be vulnerable to fatigue failure. A thorough investigation on the fastening spring is required from safety perspectives. Existing studies on rail fastening systems focused solely on analyzing the interaction of the track system with each component [1, 2], dynamic behavior [3, 4], and overall mechanical behavior [5, 6]. Regarding cases of fatigue damage to the fastening spring, studies were conducted to analyze the stress conditions and fatigue performance in the train operation [7, 8, 9] and the initial fastening process of the fastening spring [10, 11]. Studies on the failure analysis of fatigue cracks in fastening springs [12, 13] and fatigue reliability analysis [14] were also conducted.  
The KR-type rail fastening system is an independently developed Korean rail fastening system and is used on some domestic railways. Figure 1a shows the assembly of the KR-type rail fastening system, while Figure 1b shows the geometry with the dimensions. The shape optimization analysis [15] and structural and fatigue performance analysis [16] for this new KR-type rail fastening system are being studied; however, these studies are stillinsufficient. In the shape optimization analysis studied by [PERSON] et al., they developed a fastening spring that could lower longitudinal resistance and accommodate the upward force generated by the bending angle [15]. They also conducted the shape optimization of the Vossloh fastening system [17]. Considering the resonance effect, [PERSON] et al. changed the natural frequency of the fastening spring [17]. However, the fatigue strength of metallic structures can be defined by the initial stress and stress range. A higher initial tensile stress or stress range reduces the fatigue strength of a structure [12; 18]. Past studies to identify main geometrical parameters affecting the stress condition and the fatigue performance of fastening springs have been very limited. Furthermore, a sensitivity analysis with various shape parameters to improve the fatigue performance of fastening springs has been also insufficient. As part of the method for improving the fatigue performance of the KR-type fastening spring, the effect of changing the shape of the fastening spring on fatigue performance is investigated in this study using the finite element analysis. The shape change variables include the heights of the fastening spring end and spring arm, overall lateral width, and the diameter of the cross section of the fastening spring. A sensitivity analysis of the factors is conducted. The initial stresses during the fastening process and the stress fluctuation (or amplitude) caused by vertical rail displacement owing to train use are first derived using finite element analysis. The fatigue performances of each shape change are then compared using the modified Goodman fatigue diagram [19].