# Study on Gage Widening Methods for Small-Radius Curves
## 3 Status of Gage Widening Standards
to the characteristics of the maximum line gap of 5 m and the maximum difference of the radius of the concentric circle curve of 5 m, the archiving radius under the new standard was an integer multiple of 5 m, which avoided the possibility of different widening values for the same archiving radius. The minimum radius to be widened was 295 m, and the maximum widening value was 15 mm, divided into four levels [22; 23]. Under the conditions of four widening values, the minimum curve radius to ensure that electric, internal combustion, and steam locomotives pass through with normal forced inscribing was less than the corresponding curve radii specified in Table 14. The rail widening values given in Table 15 ensure that various types of locomotives pass through the curve with normal forced inscribing. This standard was formally implemented in 2014. Our analyses on gaze widening standards reveals that the minimum curve radius that would require widening is in the range of 220-350 mm, whereas some countries adopt 600 m as this radius. The maximum gage widening range is 15-20 mm, and only a few countries adopt values exceeding 30 mm. China's gage widening standard is equivalent to the widening standard commonly used abroad. [PERSON] et al. [24] proposed three methods for improving running performance on curves using existing types of wheels and rails and analyzed the effects of the three methods by numerical simulations. According to analytical results, 'expansion of gage widening' and 'larger rail inclination angle of inner rail installation' or 'asymmetrically inclined grinding of inner rail head' can obtain sufficient rolling radius difference and effectively improve running performance on curved tracks. [PERSON] et al. [25] performed a curve negotiation analysis of the three-axle bogie of locomotive type JZ 461. This locomotive has a large distance between the first and the middle, i.e., the middle and the last axle, leading to increased lateral forces during curve negotiation. The final result was the widening of the track gage in curves with a small radius. This paper points out that the infrastructure manager must consider vehicle performance and type of track when defining track gage in curves. [PERSON] et al. [26] studied the track gage widening rules of a small turnout and comprehensively considered the curve geometry, type of blade, gage at the entry of turnout, gage at the toe of blade, gage in diverging track, etc. Analyses of the reason for structure widening in switch panels were made, and the calculation methods for structure widening, in any case, were put forward. [PERSON] et al. [27] investigated determining maximum dangerous railway track gages with reinforced concrete sleepers and fastenings of the terminal-bolted track type, considering simultaneous actions of lateral forces and track \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Curve Radius R(m)** & **Wheelset Width \(\mathbf{q_{max}}\) (mm)** & **Outer Vector Distance \(\mathbf{f_{0}}\) (mm)** & **Gage s (mm)** & **Gage Widening Amount (mm)** \\ \hline
350 & 1422 & 10.4 & 1432.4 & \(-\)2.6 \\
300 & 1422 & 12.2 & 1434.2 & \(-\)0.8 \\
250 & 1422 & 14.6 & 1436.6 & 1.6 \\
200 & 1422 & 18.2 & 1440.2 & 5.2 \\
150 & 1422 & 24.3 & 1446.3 & 11.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Geometrically free-inscribed gage widening values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Gage Widening Amount (mm)** & **Electric Locomotive** & **Diesel Locomotive** & **Steam Locomotive** \\ \hline
0 & 93.5 & 101.7 & 126.5 \\
5 & 90.9 & 99.2 & 122.1 \\
10 & 88.4 & 96.9 & 118.1 \\
15 & 86.0 & 94.7 & 114.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Minimum curve radii (m) that a locomotive can pass through with normal forced inscribing. \begin{table}
\begin{tabular}{c c c c} \hline \hline Curve Radius (m) & R \(\geq\) 295 & 295 \(>\) R \(\geq\) 245 & 245 \(>\) R \(\geq\) 195 & R \(<\) 195 \\ \hline Widening Value (mm) & 0 & 5 & 10 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Current gage widening values (mm).