## 4 Results and Discussion
### The Relationship between ABA and Wheel/Rail Force  
Time-course changes of variation of dynamic wheel/rail force \(F_{\text{dyn}}\) (the difference between the wheel/rail force and the static wheel load) of the three rail welds in Figure 10a are presented in Figure 13. When the wheel passed over the rail welds, \(F_{\text{dyn}}\) initially increased to a peak and then decayed gradually to complete the impact; the amplitude of \(F_{\text{dyn}}\) fluctuation was small once leaving the rail weld. By comparing to Figure 10a, it is easy to discover that the rail weld can excite only one impact of the wheel/rail force, but it can induce continuous fluctuations of ABA. The phenomena can be explained by the wheel/rail force that is determined mainly by local geometry irregularity. Thus, no obvious impact action will appear upon passing through the weld. Moreover, continuous fluctuations arise since ABA belongs to the structural vibration with energy that is difficult to dissipate quickly by primary suspension. The maximum of \(F_{\text{dyn}}\) will decrease in turn along with the wavelength increase, consistent with the change trend of \(\text{ABA}_{\text{F}}\).  
Figure 11: The influence of wavelength on (**a**) ABA and (**b**) variation of amplitude at\(f_{1}\) and \(f_{2}\).  
Figure 12: The influence of wave depth on ABA in (**a**) frequency and (**b**) time domains.  
As mentioned above, the first wave crest of ABA at rail welds represents the wheel/rail impact. Eighteen rail welds (including wave depths of 0.1, 0.2, and 0.3 mm that correspond to six wavelengths from 0.05 to 0.5m in Figure 11) were selected for calculation. The relationship between ABA\({}_{\text{F}}\) and maximum of \(F_{\text{dyn}}\) (\(F_{\text{dyn,max}}\)) has been established, as shown in Figure 14. Discrete points in the figure are the calculation results and the corresponding fitted curve is also shown in the figure; please see Equation (6),  
\[F_{\text{dyn,max}}=0.41\cdot\text{ABA}_{\text{F}} \tag{6}\]  
Obviously, a linear relationship is presented between ABA\({}_{\text{F}}\) and \(F_{\text{dyn,max}}\). The measured data in Figure 4 shows that the ABA excited by rail weld irregularities fluctuated within the range of \(\pm 50\) m/s\({}^{2}\) at a vehicle speed of 300 km/h. Thus, the ABA excited by rail welds of long wavelengths or shallow wave depths is submerged, as RW2 in Figure 4. However, a low ABA can mean a small dynamic effect. For instance, the ABA of 50 m/s\({}^{2}\) corresponds merely to the \(F_{\text{dyn}}\) of 20 kN--far less than the safety threshold--as shown in Figure 14. According to maintenance regulations on Chinese high-speed railways, the \(F_{\text{dyn,max}}\) shall be no more than 90 kN; we can find the corresponding threshold value of ABA\({}_{\text{F}}\) to be 220 m/s\({}^{2}\). High ABA is easily identified from the measured data, as shown in Figure 4,  
Figure 14: The relationship between ABA\({}_{\text{F}}\) and \(F_{\text{dyn,max}}\).  
Figure 13: The response of wheel–track force under excitation of welds with different wavelengths.  
so that ABA is a good measure for monitoring the health conditions of rail welds. Hence, 17 groups of welds in Figure 6 met the safety threshold. However, a portion of these were within an inch of the danger threshold of 220 m/s\({}^{2}\), indicating the need for maintenance as soon as possible.