# Measurement Repeatability of Rail Wheel Loads Caused by Rolling Surface Damages
## 5 Distribution of Values of Wheel Vertical Forces  
The authors propose to use the ratio of the total width of the two middle quartiles of the scattering field of the vertical force values to the median (indicator \(Q_{M}\), Formula (1)) to examine the impact of the wheel-rolling surface damage on the measurement repeatability of the vertical forces. Two wheel-rolling surface damage types were selected for this study. For each damage type (shape), the vertical forces caused by the wheel damage were measured in four dimensions. Four data sets were obtained: mean values of vertical forces of unloaded wagon and of loaded; values of maximal vertical forces of unloaded wagon and of loaded wagon. First, the test was performed with the damaged left wheel of the first wheelset. The wheel has two 20 \(\times\) 10 \(\times\) 4 mm and 15 \(\times\) 40 \(\times\) 3 mm cracks. Wheel damages provided in Figure 10.  
Box and whisker values of the maximal vertical forces of loaded goods wagon are shown Figure 11.  
Figure 8: Correlation of measured values of basic vertical forces according to measurement systems. Figure 9: Correlation of measured values of maximal vertical forces according to measurement systems. The values of the indicator \(Q_{M}\), calculated by the Formula (1) of maximal vertical forces of the loaded wagon are provided in Figure 12.  
The data in Figure 12 reveal that the influence of wagon wheel damage on the measurement of repeatability vertical forces is the highest at 30 km/h--lowest \(Q_{M}\) value, and the highest value is at a speed of 60 km/h. When wagon running speed increases, this impact on measurement repeatability decreases. It is inappropriate to perform tests at a speed of fewer than 30 km/h because, in this case, the amplitude of the carriage's oscillations may be lower than when driving at higher speeds, which would distort the adequacy of the results (equipment may not capture all damage). Since the tests are carried out on freight wagons, it is not appropriate to conduct them at speeds higher than 80 km/h. More test results were analyzed to better examine the dependences of wheel damage nature on  
Figure 11: Maximal force values of loaded wagon. Figure 10: Two cracks in the wagon’s first wheelset wheel. repeatability. The values of the maximal vertical forces are given in the form of a box and whisker graph in Figure 13 when the goods wagon is unloaded. The chart of Figure 13 shows that the maximal scatter of the force values is at a speed level of 70 km/h. The values of \(Q_{M}\), calculated according to Formula (1) for the maximal forces when the goods wagon is unloaded, are given in Figure 14.  
The data in Figure 14 reveal that the impact of wheel damage on the repeatability of measurement of vertical forces is the best (the lowest values of the indicator \(Q_{M}\)) at a speed of 40-60 km/h. More test results were analyzed to examine these dependencies better. The values of the mean vertical forces of loaded goods wagon are given in Figure 15.  
The chart of Figure 15 clearly disclose that as the wagon speed increases, the dispersion of the mean vertical forces increases. The values of \(Q_{M}\) with the loaded wagon are shown in Figure 16.  
The data in Figure 16 disclose that the impact of wheel damage on measurement repeatability of vertical forces is best at speeds of 40 and 60 km/h. No clear law is seen here. More test results were analyzed to examine the correlations with measurement repeatability better. The values of the mean forces of unloaded wagon are given in Figure 11.0  
The chart of Figure 17 shows that the force dissipation is lowest at a speed of 30 km/h. The values of \(Q_{\text{M}}\) when the wagon is unloaded are given in Figure 11.1  
The data of Figure 18 show that the impact of wheel damage nature on the measurement repeatability of the vertical forces is best at a speed of 30 km/h. Figure 11.2 Values of the indicator \(Q_{M}\), according to the mean vertical forces of loaded wagon. Figure 11.3 Vertical force mean values of unloaded wagon.