## 4 Results
### Simulations to Support the Formulated Hypothesis  
Optical measurements data of the rail surface are not available to verify this hypothesis, but some further investigations can be carried out to support it. MBD simulations can be used to study the interaction between wheel defects and rail corrugation, and some rail corrugation indicator signals are available to be compared with the results obtained.  
The MBD simulations are used to simulate different scenarios and investigate the mutual influence between the wheel defects (OOR and corrugation) and the rail corrugation (represented as sinusoidal signal). The simulations are performed on the 100 m section selected in the FFT analysis, using the same track layout and curve characteristics. First, the wheel corrugation is analysed considering six scenarios (three with wheel corrugation only, three with the same wheel corrugation and additional rail corrugation):  
1. wheel corrugation with a wavelength of 60 mm and an amplitude of 10 \(\upmu\)m;
2. wheel corrugation with a wavelength of 50 mm and an amplitude of 8 \(\upmu\)m;
3. wheel corrugation with a wavelength of 40 mm and an amplitude of 6 \(\upmu\)m;
4. rail corrugation with a wavelength of 61 mm and an amplitude of 5 \(\upmu\)m + wheel corrugation 1;
5. rail corrugation with a wavelength of 61 mm and an amplitude of 5 \(\upmu\)m + wheel corrugation 2;
6. rail corrugation with a wavelength of 61 mm and an amplitude of 5 \(\upmu\)m + wheel corrugation 3.  
Figure 11a shows the reference FFT of the axle box acceleration (Figure 6) with the ripple and slip waves wavelength range. Figure 11b shows the FFT of the axle box accelerations from three simulations. These three simulations are performed considering only wheel corrugation as in scenarios 1, 2 and 3. Figure 11c shows the results of wheel and rail corrugation for scenarios 4, 5 and 6.  
11. rail corrugation + OOR 5;
12. rail corrugation + OOR 6.  
In Figure 12 the reference from the measurements is shown again in (a), in (b) the scenarios considering only OOR (1, 2, 3, 4, 5, 6), are shown and in (c) the scenarios combining both OOR and rail corrugation are shown.  
As mentioned above, the wavelength range of the OOR is typically between 140 mm and the wheel circumference, which is greater than the peaks observed in the axle box acceleration measurements. The scenarios presented in Figure 12b prove that only the unusual very high order of the OOR (15 th-20 th) can be observed in the wavelength range of the rail corrugation. However, when rail corrugation with a wavelength of 61 mm is added (c), some OOR effects can be observed around the corrugation peak.  
Figure 11: Wheel corrugation analysis: (**a**) reference peaks FFT axle box acceleration measurements; (**b**) FFT axle box accelerations simulated with wheel corrugation; (**c**) FFT axle box accelerations simulated with wheel corrugation and rail corrugation.  
Figure 12: Wheel corrugation analysis: (**a**) reference peaks FFT axle box acceleration measurements; (**b**) FFT axle box accelerations simulated with OOR; (**c**) FFT axle box accelerations simulated with OOR and rail corrugation.  
These MBD simulation results support the hypothesis formulated in the spectrogram analysis: the peaks found in the axle box acceleration, which last only a few hundred metres, cannot be wheel corrugation due to their length and cannot be OOR if not combined with rail corrugation.