## 3 Parameters Studies and Discussions
### Orthogonal Design Test  
#### 3.2.1 Analysis Factor and Observation Parameters  
In this Section, 13 system parameters influencing the dynamic vehicle-turnout properties are selected as the analysis factors for studying in order to evaluate the degree of influence of the different analysis factors on the dynamic vehicle-turnout interaction and select those analysis factors significantly influencing the rail surface initiated RCF. The selected 13 analysis factors and their three-level values are shown in Table 1. The turnouts are subject to track irregularity due to asymmetric structures, therefore the influence of geometric track irregularity on the dynamic response of the vehicle-turnout system is not considered in the factor analysis.  
In Table 1, besides the wheel profile, the levels of analysis factors can be realized through adjusting the parameters. For wheel profiles, in this paper the one corresponding to Level 1 is a Chinese standard LMA wheel tread, the one corresponding to Level 2 is a Chinese standard S1002 CN wheel tread, and the one corresponding to Level 3 is a Chinese standard XP55 wheel tread, see Figure 10 for the three-level wheel treads.  
After the analysis factors and their levels are obtained, the observation parameters related to the rail surface initiated RCF should be ascertained. The fatigue index in Equations (1) and (2) have been used as a marker for RCF probability, but always qualitatively. Therefore, this index will not be used directly as the observation parameter in factorial design. According to the discussion results in Section 2.3, the parameters influencing the rail surface initiated RCF of railway turnout are the normal and tangential contact stresses, where the normal wheel contact stress is mainly related to the normal wheel-rail force and contact patch area. Therefore, in this paper, the normal wheel-rail contact  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Analysis Factor**} & \multicolumn{3}{c}{**Analysis Factor Levels**} \\ \cline{3-5}  & & **Level 1** & **Level 2** & **Level 3** \\ \hline \(x_{1}\) & Train speed/(km/h) & 40 & 80 & 120 \\ \(x_{2}\) & Train axle load/(t) & 12 & 14 & 16 \\ \(x_{3}\) & Nominal wheel rolling radius/(mm) & 420 & 460 & 500 \\ \(x_{4}\) & Wheel profile & LMA & S1002 CN & XP55 \\ \(x_{5}\) & Lateral stiffness of primary suspension/(kN/mm) & 5.0 & 6.5 & 8.0 \\ \(x_{6}\) & Vertical stiffness of primary suspension/(kN/mm) & 1.0 & 1.2 & 1.4 \\ \(x_{7}\) & Lateral stiffness of secondary suspension/(kN/mm) & 0.10 & 0.15 & 0.20 \\ \(x_{8}\) & Vertical stiffness of secondary suspension/(kN/mm) & 0.15 & 0.18 & 0.21 \\ \(x_{9}\) & Rail gauge/(mm) & 1432 & 1435 & 1438 \\ \(x_{10}\) & Stock rail cart & 0 & 1/40 & 1/20 \\ \(x_{11}\) & Integral lateral track stiffness/(kN/mm) & 30 & 50 & 70 \\ \(x_{12}\) & Integral vertical track stiffness/(kN/mm) & 80 & 100 & 120 \\ \(x_{13}\) & Wheel-rail friction coefficient & 0.1 & 0.3 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Analysis factors of turnout rail surface initiated RCF and their levels.  
Figure 10: Three-level definition of wheel profile.  
force \(F_{z}\) and contact patch area \(A_{c}\) are selected for reflecting the normal wheel-rail contact stress level. Similarly, the tangential wheel-rail contact stress is mainly related to the tangential wheel-rail force and contact patch area. Therefore, in this paper the longitudinal wheel-rail creep force \(F_{x}\), lateral creep force \(F_{y}\) and contact patch area \(A_{c}\) are selected for reflecting the tangential wheel-rail contact stress level. In conclusion, \(F_{z}\), \(F_{x}\), \(F_{y}\) and \(A_{c}\) are adopted as the observation parameters in the factorial design. In fact, these parameters are not independent markers for surface initiated RCF. The main purpose of this is to find out what is missing in the factorial design as the single parameter \(FI_{surf}\) cannot be used.