# Measurement Repeatability of Rail Wheel Loads Caused by Rolling Surface Damages
## 3 Research Methodology  
At first, the study compares the results of measuring vertical forces by different systems. In the same graph, the force values obtained from the ATLAS LG system are plotted on one axis and the special designed measurement system IC VEIP on the other. The view of both used measurement systems is presented in Figure 6.  
The measuring range consists of 14 sleeper reaction measuring points (R-points) and 12 axle load measuring points (T-points). The last T-point is used for identifying wheelsets. Vertical impact on rail and static axle load of wheels is measured by strain gauges mounted on the rail neck. The main particularities are: ATLAS-LG system measures directly the vertical force, while the IC-VEIP system measures the rail acceleration and then converts it into a force value.  
The best result is when the readings of both systems coincide. This result would indicate that both systems are equally suitable for studies on the influence of wagon wheelset damage on the nature of vertical forces. If all values are in a straight line and the line is formed at a different angle with the axes, it would mean that there is a systematic error in at least one of the systems. If the values are not in a straight line (scattered in the plane), then the measurement results are not related to different systems, and at least one system is unsuitable for the test. Another important issue is estimating the scattering field for the measured force values. The box and whisker principle is used in the study [39].  
The box and whisker graph is convenient in that it shows where the median of the values is (see Figure 7). It also shows where the 50% of values closest to the median (upper quartile and lower quartile) are distributed, the range of the remaining values (upper extreme and lower extreme). In addition, this type of graph can show individual values  
Figure 5: Wheelset oscillation of on the track.  
Figure 6: Used measurement systems: (**a**) regular system ATLAS-LG; (**b**) specially designed system IC VEIP.  
that stand out from the whole (outlier). A median value is used, taking into account the specific algorithm of the box and whisker method. This type of graph is very suitable for evaluating the repeatability of experimental results. Understandably, the better the repeatability of the results, the smaller the scatter fields of the values. An example of the application of the box and whisker principle is shown in Figure 7.  
In the middle of the diagram in Figure 7, there are two middle quartiles. They are the limits between which half of all measurement values are distributed (twice 25%--two quartiles). In the middle of these quartiles, there is a median-mean value. The remaining values are outside these limits, and the authors did not analyze these values.  
The ratio of the total width of the two middle quartiles to the median in estimating the wagon wheel damage magnitudes is calculated as:  
\[Q_{M}=\frac{Q_{U}-Q_{L}}{M}\to min \tag{1}\]  
where \(Q_{U}\)--upper quartile; \(Q_{L}\)--lower quartile; \(M\)--median (Figure 6).  
For simplicity, this indicator name is sometimes abbreviated to indicator \(Q_{M}\). This methodology estimates the ratio of the wheel-to-rail scattering field to the median \(Q_{M}\). Such an indicator is important in proving that the size of the scatter field of impact values is less significant at high force values. Therefore, the lower value of the indicator \(Q_{M}\) shows better repeatability of the measured vertical force. The value of \(Q_{M}\) is calculated under different operating conditions of the rolling stock (in this case--different speeds). Comparing the \(Q_{M}\) values in different cases determined the states that are best suited to relate the magnitude of the damage to its vertical impact on the rail.