Strain results
Three full-bridge strain gauge channels were installed for measuring the pure shear strain at either end of a 220 mm long section of crossing between two bearers, and the bending strain at the midpoint. The bridge configurations compensate for temperature variations and are nominally insensitive to loading in directions other than vertical. The bridge configuration also improves the signal-to-noise ratio [5, 7]. The raw bending and shear strain data for trains travelling at 100 and 193 km/h are shown in Fig. 14.
The shear strains are only reaching 5–10 microstrain (με) which is approaching the lower limit of strain measurement. Some background noise of around 1με is visible on the signals. The shear strain goes negative (positive) as the first wheelset approaches in the reverse (normal) direction, then reverses sign as each wheelset crosses over the sensor. On the slower train (left) there is an impulsive disturbance around 13.3 s that also appears in the bending strain.
The bending strain is largely in one direction as the train wheels pass over the crossing with a small amount of reverse direction bending as the leading wheelset of a bogie (or of two closely spaced bogies) approaches. The bending strain is nearly three times higher for the higher speed train and about 10 times larger than the shear strain. Individual wheelsets are easily identifiable, much more so than from accelerometer data. This is because strain is more like displacement than acceleration in that the amplitude tends to decrease with increasing frequency.
Forces calculation (from shear strain difference)
The forces are estimated from two separate shear strain full-bridge channels by
$$F = 2\alpha \gamma_{{\text{A}}} - 2\beta \gamma_{{\text{B}}} ,$$
(1)
where γA and γB are the pure shear strain at A–A′ and B–B′ cross sections, respectively, as shown in Fig. 3; constants α and β depend on the material properties and the cross-sectional geometry:
$$\alpha = \frac{{I_{{\text{A}}} t_{{\text{A}}} G}}{{Q_{{\text{A}}} }},$$
(2)
$$\beta = \frac{{I_{{\text{B}}} t_{{\text{B}}} G}}{{Q_{{\text{B}}} }},$$
(3)
where IA and IB are, respectively, the moments of inertia at cross sections A–A′ and B–B′ computed about the neutral axis, G is the shear modulus of the crossing material, tA and tB are the width of the member cross-sectional area at the sensor locations, and QA and QB are the first moments of area at cross sections A–A′ and B–B′, respectively, with consideration of the area above the neutral axis.
Frequency analysis
To identify the required frequency range for bending strain and the forces, one-third octave band spectrum for three train datasets is shown in Fig. 15.
One-third octave spectra from the same train types but with different speeds and different train conditions are compared in Fig. 15. Figure 15a shows the results from the bending strain. The energy from lower speed is mostly below 20 Hz but from a high-speed train is mostly below 300 Hz. Figure 15b shows the spectrum for the force. Significant energy found above 2 kHz was traced to interference from the traction return current of electrically powered trains. In general, the peak forces from the higher speed trains are higher than those from lower speed ones.
The peak force is dominated by the higher frequency for higher speed trains and a lower frequency for lower speed trains. Ignoring the electrical interference, the force distribution from lower- and high-speed trains is below 2 kHz. The energy is mainly located at lower frequencies for the lower speed trains.
A similar pattern is found comparing the results from trains with and without wheelset problems, as shown in Fig. 15b. High forces can be found from 10 to 300 Hz and 500–2,000 Hz, which represents frequency range for the P2 force (low-frequency impact forces) and P1 force (transient high-frequency impact forces), for results from higher speeds, as shown in Fig. 15b. The first impact peak, P1, occurs when the wheel transfers from the wing rail to the crossing, a major contributor to the crossing surface degradation, and the second peak, P2, occurs following the first peak, the dominant cause of foundation degradation [26].
The bending strain amplitude from the normal and faulty train is similar but higher forces can be found from the faulty train at higher frequencies. Furthermore, the same peak can be found in the bending strain spectrum at lower frequencies, but no peaks can be found in the higher frequencies, as shown in Fig. 15a. In summary, to capture the bending strain and forces appropriately, 300 Hz and 2,000 Hz bandwidths are required, respectively. Furthermore, bending stain only captures low-frequency information such as P2 forces but cannot capture the high-frequency content such as P1.
Measured forces
Including frequencies up to 2,000 Hz is suggested for the force results at the crossing to capture P1 and P2 forces. The measured force should correlate with crossing damage such as cracks, rolling contact fatigue (RCF) and plastic deformation. A wheel load detector for measuring the wheel loads of passing trains has been commercially available and used in the UK to detect damaging trains and to get these trains removed from the track as soon as possible. However, consideration of dynamic loading is usually neglected and the actual impact force, which is one of the most crucial factors for material degradation, cannot be captured. Therefore, it is very important to try to measure dynamic forces, a conclusion reached in other works [26, 27]. The results from train speeds 53, 105 and 193 km/h in the trailing and facing directions are discussed first, and the average results from all trains are shown in the end to show the importance of consideration of the dynamic effect.
Results from the trailing direction
Figure 16 shows the shear strain results at the A–A′ and B–B′ cross sections for four axles from a 53 km/h train travelling in the trailing direction. The force within the measuring region between A and B based on known cross section and material data and shear difference is shown in the second graph. The full-bandwidth vertical acceleration on one side of the crossing between A and B is shown in the third graph. The difference between left and right crossing vertical acceleration, which tends to have high potential for detecting the load transfer location, is shown at the bottom, low pass filtered to 500 Hz.
Shear strain results from the A–A′ cross section are similar to those from cross section B–B′ but with a temporal shift equal to the time taken for a wheelset to travel from A to B, at least for the first two wheelsets indicated at ‘1’ and ‘2’.
Based on the vertical acceleration and the difference between left and right accelerations, the load transfers for the second pair of wheelsets occur at positions marked ‘7’ and ‘8’, around 440 mm after the wheelset passes over A–B. A similarly positioned load transfer for the leading wheelsets is indicated by ‘5’ and ‘6’. Considering the results are from the trailing direction, the loads transfer from the crossing nose to the wing rail. As shown in Fig. 16, the first wheelsets tend to transfer the load after the measure section, and the second wheelsets tend to transfer the load to the wing rail before the measured section. Therefore, forces cannot be measured for the second wheelsets because the load is applied at the wing rail instead of the crossing nose where the strain gauge is installed.
Figure 17 shows similar data for a 105 km/h train moving over the crossing in the trailing direction. In this case, the shear strains are similar to those from the 53 km/h freight train and only one oscillatory force appears with a reasonable value. Again, the load transfer, as indicated by ‘5’–‘8’ in the crossing rotation disturbance at the bottom of the figure, happens outside of the load measuring region. This time, the load transfer occurs about 200 mm closer to the crossing nose than the instrumented section. The acceleration signal is notable for being significantly more variable than from the freight train with an odd excitation marked as ‘9’ in the figure. The wheelsets of the train may be somewhat rough and potentially there is a wheel flat at the peak acceleration. Acceleration does not show much at the time of load transfer but the rotation signal low pass filtered at 500 Hz shows the load transfer well and with some consistency.
Results from the facing direction
Figure 18 shows the acceleration and shear strain data for two wheelsets on a 105 km/h train travelling in the facing direction. The shear strains are the opposite way up because of the direction of train travel. The marks ‘1’ and ‘2’ show where two wheelsets on one bogie pass over the instrumented section. The load transfer location can be observed from the forces (marks ‘3’ and ‘4’), vertical accelerations (marks ‘5’ and ‘6’), and the difference between left and right vertical acceleration (marks ‘7’ and ‘8’). For the force results, a higher peak (P1 force) occurs first when the load transfer happens and a second peak (P2 force), which is lower and wider than the first peak, occurs following the first peak.
Figure 19 shows the acceleration and shear strain data for two wheelsets on a 193 km/h train travelling in the facing direction. Similar strain results (1 and 2) are obtained compared to the lower speed results, but an extra upward peak appears in the shear strains, marked with ‘3’ around 13.8 s between the two wheelsets. This may be due to the torsion effect. However, this effect cancels after subtracting the two results for calculating the forces. The force shows some general positive change but mainly oscillation. The peak values appear to be reasonable for the vehicle type, but it is evidently affected by vibration in the measuring section that makes the interpretation as load suspect. The difference between left and right vertical acceleration (5 and 6) shows some evidence of load transfer. Based on additional wheelsets and the results from other similar speed trains, the load transfer is sometimes clear but often messy around 193 km/h. The accelerations show some spikes that could correspond to load transfer positions but there is also an additional acceleration burst marked with ‘4’.
Average results from all trains
Figure 20 shows the average of the maximum forces from each train after low-pass filtering with cut-off frequencies of 100 Hz, 1 and 2 kHz. The UK wheel load limit for plain track [28] is also indicated with imposed speed limits. Based on UK standards, a speed restriction needs to be applied when the measured force is within the warning range. As shown, without consideration of dynamic effects, the forces are underestimated and only results with 100 Hz low-pass filter are within the allowable region. Much higher dynamic forces are obtained at the crossing compared to the results measured at the plain track where the wheel load is typically measured. These measurements are generally measured with bending strain rather than shear strain and naturally show lower frequency behaviour, as seen in the third-octave results above.
This may be the reason why crossing service life is often shorter than the design service life—it suffers significantly higher impact forces than the forces measured on plain track and the dynamic effect is usually ignored. Furthermore, the crossing degrades significantly faster after a fault develops. For example, a degraded crossing with 24 mrad crossing dip angle causes around three times larger impact forces than a crossing with zero dip angle [29]. Therefore, consideration of dynamic forces is very important and the bandwidth over which the force is measured is critical.
Comparison of peaks in dynamic force and vertical rail acceleration
Attaching an accelerometer to the rail or crossing is a more attractive proposition than using strain gauges. However, unlike force, which can correlate with crossing degradation, it is difficult to use acceleration as an indicator of S&C degradation. Peak rail vertical accelerations and impact forces at the crossing load transfer point are compared and assessed. Results from four trains are discussed, shown in Figs. 21–24. Based on the conclusions from Sect. 4.2, a 2 kHz low-pass filter is applied to accelerations. On the other hand, although 2 kHz has shown capability for capturing dynamic characteristics for the impact forces, at least 10 kHz is required for the rail accelerations to identify a faulty train [22]. Therefore, low-pass filters with upper cut-off frequencies of 2 kHz and 10 kHz are both used for rail accelerations to see which has the higher correlation with estimated dynamic force.
Figure 21 shows the results from a 100 km/h passenger train. The force exceeds 200 kN about 8 times. The most severe peak forces are associated with a small subset of all the wheelsets. There appears to be no reason for the spread of dynamic load results across different wheelsets other than the stochastic nature seen previously in the forces from different wheelsets. Meanwhile, only one strong peak is seen in the rail vertical accelerations even with a 10 kHz low-pass filter and it happens outside of the sensor location. After filtering at 2 kHz, the acceleration does not show any particularly strong peaks. The correlation between the force and acceleration is poor. This agrees with the previous comparisons over a few wheelsets.
Figure 22 shows the results from a passenger train travelling at 193 km/h. In this example, the force peaks of some magnitude are found for every wheelset, accompanied by strong acceleration peaks. Larger dynamic forces align with higher accelerations and the same trend is found for results after 2 and 10 kHz low-pass filtering. Unlike the results from the lower-speed train, where only positive impact forces are seen, negative impact forces are seen with almost the same magnitude as the positive impact forces. This suggests that the dynamic force is associated with vibration in the structure of the crossing rather than simply dynamic load from the wheelset above.
Figure 23 shows the results from the same train type as in Fig. 22 and the same train speed but perhaps with more worn wheelsets. Higher accelerations are obtained compared to the results from a normal passenger train and some strong peaks can be found in the accelerations due to defective wheelset(s). However, although clear peaks can still be found for both data, the acceleration results no longer follow the impact force trend. Some high-impact forces do not have corresponding high accelerations. The rail accelerations are interspersed with a number of unexpected impacts probably linked to the defective wheelset(s) and make it difficult to obtain useful conclusions for monitoring the crossing. Although a low-pass filter can remove these impacts, the remaining data loses potentially important impacts and so is not able to capture the most significant dynamic forces.
Figure 24 shows the results for a freight train travelling at 55 km/h. Similar phenomena are found compared to the lower speed passenger train, as shown in Fig. 21. However, although the maximum accelerations for both cases are similar, around 200 m/s2, the force results are significantly different. The forces for the lower speed passenger train are around 200 kN but the results from the freight train exceed 400 kN. Therefore, correlation between rail accelerations and the forces seems to be poor—the load may indicate more damage from the freight train than a similar-speed passenger train, whereas the acceleration does not distinguish between them.
Proposed condition monitoring for crossing degradation
A possible index for monitoring crossing degradation can be obtained by considering the shake-down map [30] with normalized vertical forces determined from the estimated the forces and the adhesion utilization, as shown in Fig. 25. RCF cracks start to initiate when the value is within the ‘ratchetting’ area. Therefore, the proposed index can be directly correlated to low-cycle fatigue failure.
Figure 25 shows how the estimated load data are mapped onto a shakedown diagram. Note that only the load applies between the instrumented section, which can happen when the load transfers from wing rail to crossing for the facing direction or when the load before transferring to the wing rail in the trailing direction, is considered. The vertical axis shows the normalized forces that are obtained from the estimated forces and the geometry of the wheel and the crossing nose at the measured location. The horizontal axis shows the adhesion utilization, the magnitude of the sum of tangential forces relative to the normal force. It is bound by the friction coefficient. The measured data are mapped considering a friction coefficient of 0.3 (typical for dry rails) and assuming that the slip ratio is randomly distributed between 70% and 100%. This assumption is motivated considering the fact that, in the crossing region, high tangential forces are needed to guide the wheelset through, thus high slip ratios are expected.
As shown in Fig. 25, most working points for the instrumented crossing falls within the ratcheting area of the shakedown map indicating a high risk of fatigue failure. In fact, defect on the crossing was found from a site inspection, as shown in Fig. 26. A 3D scan was carried out and the crossing dip angle was found to be around 24 mrad, which is considered to be a poor condition and causes three times higher impact forces compared to the nominal crossing geometry [29].
The proposed condition monitoring approach uses the estimated forces, which are ideally the actual forces applied to the crossing, to predict the crack initiation. There is no need to identifying the train because the approach takes into account a variety of impact forces induced by different train speeds and different train types with different wheel conditions. The index can directly correlate to crossing crack initiation and can apply to all crossings irrespective of angle with the known material properties and cross section parameter [see Eqs. (1–3)]. Indication of crack initiation can be identified and used for predictive maintenance. Furthermore, the crossing condition can be identified directly with the same warning baseline (threshold) for different support conditions.
Unfortunately, the load measured from the shear strain gauge arrangement is limited to load applied between the measurement positions, is a small value, is subject to errors in gauge position and cannot be applied too close to bearers. This makes the method practically difficult.