The contact condition between the wheel and the rail is paramount to the lifespan, safety, and smooth operation of any rail network. The wheel/rail contact condition has been estimated, calculated, and simulated successfully for years, but accurate dynamic measurement has still not been achieved. Methods using pressure-sensitive films and controlled air flow have been employed, but both are limited. The work described in this paper has enabled, for the first time, the measurement of a dynamic wheel/rail contact patch using an array of 64 ultrasonic elements mounted in the rail. Previous work has successfully proved the effectiveness of ultrasonic reflectometry for static wheel/rail contact determination. The dynamic real-time measurement is based on previous work, but now each element of an array is individually pulsed in sequence to build up a linear measurement of the interface. These cross-sectional, line measurements are then processed and collated resulting in a two-dimensional contact patch. This approach is able to provide not only a contact patch, but more importantly, a detailed and relatively high-resolution pressure distribution plot of the contact. Predictions using finite element methods (FEM) have also been carried out for validation. Work is now underway to increase the speed of the measurement.

## Introduction

Contact conditions are vital to the life prediction, daily maintenance, profile design, and safety of rail tracks. Research and investigations have been undertaken for years to study the wheel/rail contact. Due to the complexity of the dynamic wheel/rail interface, no practical methods can truly reflect conditions near the contact area. Although controlled air flow [1] and pressure sensitive films [2] have been developed for contact characterization, these are, respectively, limited by resolution and because the technique affects the contact. Numerical methods have been proposed [3,4] for wheel/rail contact prediction following Kalker's work [5,6]. With the development of computing software, finite element methods (FEMs) have been more and more utilized to simulate static and dynamic wheel/rail contacts in various conditions [7,8]. However, the difficulties in simulating real surfaces with surface roughness and wear evolution put forward doubts as to whether FEM results are accurate. Numerical methods and, particularly, FEMs need good validation from an effective experimental approach.

Ultrasound reflectometry being a nondestructive measuring technique has been successfully applied on a variety of static machine-element contacts including bolted joints, ball bearings, press fits [9], as well as wheel and rail specimens [1012]. The technique involves pulsing an ultrasonic pressure wave toward the contact interface and deriving information from reflected signals. For a perfectly bonded contact pair, the proportion of reflected signal, known as the reflection coefficient R, is dependent on the acoustic impedance z of the materials and is determined by the following relationship:
$R=z1−z2z1+z2$
(1)
where z1 and z2 are the acoustic impedances of materials 1 and 2, respectively (a multiplication of density and speed of sound in the material). Hence, the acoustic impedance of air is far smaller than that of a solid. As the ultrasonic wave reaches the solid–air interface, almost all of it will be reflected. Through this, it is possible to characterize a contact using ultrasonic reflectometry.

For machine-elements no surface is smooth, asperities are present and roughness inherently exists. When two solids are pressed together, it is those asperities that are actually in contact with each other and thus air gaps are formed in between them at the interface. The ultrasonic wave incident at the interface is transmitted at points of contact and is reflected at the air gaps. The behavior of asperities is modeled with a quasi-static spring approach [13]. As the load is increased, the asperities deform more and are further pressed together, resulting in a greater amount of ultrasonic signal transmission due to an increase in the interfacial stiffness as analogized as springs under deformation, as shown in Fig. 1.

The reflection coefficient is not only dependent on acoustic impedance but also on the stiffness and properties of the ultrasonic waves. The full form of the reflection coefficient equation is given by
$R=z1−z2+iω(z1z2/K)z1+z2+iω(z1z2/K)$
(2)
where ω = 2πf is the angular frequency of the ultrasound wave and K is the stiffness of the interface. For the case of the same or similar materials being in contact，z1 = z2 and Eq. (2) can be rearranged into Eq. (3), where |R| is the modulus of the reflection coefficient and K can be calculated. K can be related to contact pressure with a series of calibration tests. This is carried out using two specimens of the same material and surface roughness of the test components. By applying a known load to a known contact, for instance with a flat-on-flat contact, a relationship between contact pressure and interfacial stiffness can be plotted:
$K=ωz2(1|R|2−1)$
(3)

Static wheel/rail contact patch characterization has been carried out using a focusing transducer, and a two-dimensional (2D) map has been achieved by moving the transducer in two directions of the scanning plane step-by-step [10]. This is limited only to static tests, although it results in a high-resolution image.

Pilot studies have been carried out on quasi-static wheel/rail contact using an ultrasonic array. The wheel specimen was manually moved over the rail in which the array was mounted and measurements were taken [11,14]. The array consists of 64 elements and each element is pulsed individually, all the elements are arranged in a line. As one contact body moves over the other, the ultrasonic signals are partially transmitted (as with the static technique) resulting in a drop of received reflected signals. The resulting cross-sectional line measurements are then processed and translated into a two-dimensional contact patch map. In this paper, the technique was advanced to fully dynamic measurements on a full-scale wheel/rail contact rig. Finite element analysis was also carried out as a validation.

## Ultrasonic Measurements

### Full-Scale Wheel/Rail Rig.

The full-scale wheel–rail test rig (see Fig. 2) used to carry out the tests is hydraulically driven and can apply a vertical load up to 200 kN. This rig has recently been recommissioned. Previous work using the rig has involved friction and wear studies [15]. A wheel (5) is suspended on an axle that rotates in two journal bearings located in a loading frame (2) and can rotate freely. The vertical actuator (1) is used to simulate axle loads acting on the wheel. A rail section (6) is fitted and clamped at the bottom into a sliding bed with an inclination of 1 in 20. The rail is driven by hydraulic actuators (3) and can be pulled and pushed longitudinally, the wheel rotates due to friction as the rail moves.

### Test Conditions.

The wheel has a worn P8 profile at a diameter of 920 mm. A 1200 mm long UIC60A rail section is used. As described in Sec. 2.1, the wheel rolls over the rail as the rail is pulled. During one pass, the wheel rotates about 1/3 of a full revolution. For the experiments carried out here, a 200-mm long rolling path was used as the test zone. During the testing period, the wheel is lowered onto the rail by a vertical ram and loaded up, the rail is pulled forward in a longitudinal direction so that the wheel is able to roll over the rail in the opposite direction due to friction. After one pass, the rail is pushed backward and the wheel rolls in the reverse direction. In this way two measurements are taken, one in each direction, during a full test cycle. Since there is no constraint mechanism for wheel lateral movement, the contact position between the wheel and rail is not fixed, there is a 2 mm–3 mm lateral displacement throughout one pass. Therefore, the initial contact is a tread contact, but can extend to be near the flange area at the end of the test.

### Ultrasonic Equipment.

A 64-element ultrasonic scanning array was used for taking measurements. The ultrasonic pulsar receiver and data acquisition system is a FMS100 type ultrasonic computer manufactured by Tribosonics, Ltd. and has eight channels that can emit and receive ultrasonic signals simultaneously and each channel is responsible for pulsing 8 elements. The elements are arranged in a line, as shown in Fig. 3. The array is 42 mm long and the actual pulsing length is 40 mm.

A hole was machined on the test rail specimen to fit the array into. A holder was designed and manufactured to clamp the array in position while taking measurements. The hole is located about 1/3 of the way along the length from the start of the test cycle in the longitudinal direction, as shown in Fig. 4.

In terms of lateral position, since the array is smaller than the width of the railhead, it is impossible for the scanning area to cover the whole railhead. But with proper fitting, the array is enough to capture all the contact information, as shown in Fig. 5. For universal notation purposes and to avoid confusion, in this paper, the x-axis always refers to the lateral direction of the rail and the y-axis refers to the longitudinal (rolling) direction.

The array was fitted in such a way that ultrasonic signals were perpendicular to the contact region so as to get the best reflection information. When taking measurements, the elements pulse ultrasonic signals toward the railhead, which then bounce back, and the reflected signals are received by the array and processed. A limitation of the array is that only one channel (eight elements) can pulse simultaneously at any one time; therefore, a multiplexor is needed to switch channels. The switching cycle is shown in Fig. 6. As the array is fixed at one point in the rail and the wheel moves continually during the testing period, the multiplexor switching speed has to be fast enough so that the longitudinal offset from the measurements between channels in one switching cycle can be ignored. In that way, the array can be regarded as 64 elements pulsing and taking measurements at the same time.

### Data Acquisition and Postprocessing.

Once the full-scale rig and the scanning array has been setup, a measurement can be carried out. The ultrasound incident signals and reflected signals are displayed in a group of eight (one channel) on the oscilloscope with respect to time latency. The reflected signals from the contact region are zoomed-in on and highlighted, the peak-to-peak value of each signal was recorded continually as the test proceeded (Fig. 7).

Each channel can pulse and take measurements twice during one switching cycle. Recorded data for each channel is then averaged and arranged in a way synchronized to match the physical arrangement of transducers in the array. After that, a row of data which has been measured outside the contact region is chosen as a reference, reflection coefficients can then be acquired by dividing all the data with the corresponding reference, a map of reflection coefficients is then plotted as shown in Fig. 8 (the x- and y-axes have been rescaled to distance).

As mentioned in Sec. 1, for two bodies of similar or the same materials in contact with each other, the contact stiffness K can be determined by Eq. (3), |R| can be obtained by dividing the amplitude of reflected signals by that of incident signals.

A series of calibration tests were carried out by Marshall et al. [10] with different pairs of wheel and rail surface roughness: unused, worn tread, worn flange, and sand damaged. A calibration curve was plotted and a linear relationship between contact stiffness and contact pressure was obtained for each case, respectively. For the worn tread case that applies here, the relationship between contact pressure p is
$p=123K$
(4)

Contact pressure maps can thus be plotted as in Fig. 9. The x-axis and y-axis refer to 64 elements and time, respectively. The resolution of the x-axis is limited to the physical arrangement of the elements and so is fixed at 64. The resolution of the y-axis is related to the switching speed of the multiplexor and the rolling speed of the wheel, the higher the switching speed or the lower the rolling speed is, the better the resolution that can be achieved. The switching speed in tests here was 10 Hz.

It should be noted that although the array is kept still measuring one area of railhead, the whole test can be regarded as the array swiping over the entire test length with the wheel rolling over a static rail at the point where the array is actually located. Therefore, the x- and y-axis in the contact pressure map can be translated to an actual longitudinal and lateral test length. Hence, the contact pressure distribution can be displayed in a more straightforward way.

### Results and Discussion.

A series of measurements were taken under different loads and rolling speeds. The tests started with a load of 40 kN at a rolling speed of 1 mm/s, and then the load was increased 20 kN steps up to 120 kN (mass of the wheel was taken into account). Figure 10 shows a pair of full scans at 40 kN and 1 mm/s, the contact can be seen 1/3 of the way along the test length as would be expected. The maximum contact pressure is 678 MPa and 739 MPa respectively, and for all the loads, maximum contact pressure taken from forward and backward tests differ no more than 10% and is found to be of the order of 5%.

Figure 11 show a series of contacts under the speed of 1 mm/s with increasing loads applied. The contacts are cut from the whole scan shown in Fig. 10 and interpolated for better visual effects. From the results, it can be seen that the contact area, as well as contact pressure, grows with increasing load. The contact patch grows from one side to the other and the main contact area splits into two as the load increases.

Results from the same load but inverse rolling direction match with each other very well in terms of contact area as well as pressure distribution. This indicates that the array is capable of producing consistent, repeatable measurements.

Tests at a rolling speed of 5 mm/s were carried out with the same loads applied. The array was moved approximately 3 mm in the lateral direction compared with the first tests due to the changing contact position.

Figure 12 show a series of contacts at a speed of 5 mm/s with increasing loads applied. Compared with pressure maps of 1 mm/s tests, more “defective” cells are observed in the 5 mm/s results. This is because less information was recorded at the same time as the rolling speed increased, which led to insufficient data for averaging. However, results from 5 mm/s still have enough information for each contact; generally, contact patches are nearly identical as the corresponding ones in 1 mm/s tests; contact pressure distributions also match quite well. Maximum contact pressure and contact area are plotted against load for tests at the two speeds, as shown in Fig. 14. Since the difference between results from forward and backward tests is acceptable, only data from the forward tests are plotted.

In a two-dimensional plot, the “visible” contact patches (for example, as shown in Fig. 12) are larger than the actual nominal contact areas. This is because the ultrasonic array is working by taking averages of all data in the region it is interrogating, and this region cannot be infinitely small, the boundary between the contact area and noncontact area is not a clear line, but a transmission area, which is noted as the “blurring” effect. Another reason is that some of the elements are scanning around areas close to the rail sides where the profile is much more curved. As the load increases, the rail will deform, any tiny deformation around the rail sides will result in a large amplitude drop of reflected signals, and this effect is also captured in the 2D plots. To determine the area, a decision must be taken on where, in terms of contact pressure, to filter out data around the contact zone. As shown in Fig. 14, for wheel–rail contact under all loads, the contact area drops continuously with the lower bound pressure going up. The contact pressure is calculated from the reflected coefficient, therefore to choose a proper bottom pressure limit, a confidence interval of reflection coefficients must be decided to distinguish the contact area and noncontact area. From Eqs. (3) and (4), the bottom pressure limit Pbtm is calculated as
$Pbtm=123×ωz21|Rtop|2−1$
(5)

Figure 13 shows the distribution of reflection coefficients in a lateral direction under 40 kN load. As a contact patch measured from the ultrasonic approach is normally larger than the actual nominal region of contact, a cutoff reflection coefficient is necessary for contact area calculation. With a set of validation experiments carried out by applying casting blue paint to the test wheel, and comparing ultrasonic measurements with the paint pressed on the railhead after the test, the cutoff reflection coefficient Rtop can be selected as 0.9, through Eq. (5)Pbtm is determined as 77.62 MPa, from Fig. 14 the contact area under each load is 285, 354, 389, 415, and 418 mm2 for a rolling speed of 1 mm/s.

Contact area for rolling speed of 5 mm/s can be calculated in the same way. As shown in Fig. 15, the contact areas and maximum contact pressures under all loads are compared with each other, data from forward tests are used.

The current software limits the highest measurable rolling speed at 5 mm/s. By reconfiguring the software timing, it should be possible to measure rolling speeds of 100 mm/s and faster.

## Finite Element Analysis

### Modeling Approach.

To enable validation of the ultrasonic measurements, a three-dimensional (3D) finite element model of the contact patch between the wheel and the rail in the test rig was built using the commercial software abaqus.

One whole wheel with a profile measured in the test rig for the ultrasonic measurements was modeled and a 1.6 m part of the rail with a standard UIC60 E1 profile (the rail profile in the rig has not been measured). The wheel radius was 0.46 m. The two profiles are shown in Fig. 16 with their initial lateral positions. There is no inclination of the rail. Also, no angle of attack of the wheel is modeled. Details about the model are given in Ref. [16]. Since the shape and position are very sensitive to small deflections of the wheel and rail, their whole geometry was modeled. In the contact region, the mesh was refined (characteristic element length was less than 1.5 mm). A convergence study was conducted. For both wheel and rail, elastic steel properties are used with Young's modulus of 210 GPa and a Poisson's ratio of 0.3, respectively. To extend the work in the future, especially to study contact evolution with time, an elastic/plastic approach could be used to take account of work hardening behavior in the contact. The aim here though was a quick comparison, so the extra complexity was omitted. The vertical loads were chosen according to the ultrasonic measurements (40 kN to 120 kN in 20 kN steps). For the lateral loads (not applied in the measurements, but necessary in the model for defining a certain lateral position), a value of 5 kN is chosen. Friction coefficient was set to 0.5, which is a typical value of a dry wheel/rail contact.

The rail was modeled with and without the slot that contains the ultrasonic transducer. This slot is worked into the lower part railhead, as illustrated and dimensioned in Fig. 17.

The main influence of the slot is due to the changed stiffness and bending stiffness of the rail in the region of the slot. For high lateral loads, it is thus possible that the slot considerably changes the contact pressure distribution compared with a full rail. The vertical and lateral displacements for the two cases are shown in Fig. 18. The maximum displacements in the rail with the slot are higher than in the rail without a slot due to the mentioned change in the bending stiffness. The difference, however, is only small and does not change the contact pressure distribution.

### Finite Element Results.

Figure 19 shows contact pressure results for the highest load (120 kN vertical and 5 kN lateral load) in the model without and with a cavity worked into the rail. The pressure is evaluated when the wheel is situated directly above the slot. The maximum contact pressures are indicated for the two cases and are with 1445 MPa and 1442 MPa very similar. Also, the contact pressure distribution is very similar in the two models. It can be assumed that for lower vertical loads the difference is even smaller.

Comparing the peak pressure result in Fig. 19 with the peak pressure of 120 kN load from ultrasound measurements, it can be seen that the results are very close to each other. Multiple contact patches are also observed in FE results. The wheel and rail profiles used for FE analysis are new ones compared with worn wheel and rail in ultrasound tests, which is why there are some differences in contact shapes.

A picture of the tested wheel and rail was taken to show the approximate contact position as shown in Fig. 20. From the picture, it can be clearly seen that the contact position is located in the wheel tread–railhead contact zone. The white line (within the highlighted box) marks the contact “trace” as the wheel rolls over the rail, which gives a reasonable guide to where the contact is.

One contact pressure result was plotted on a 200 mm long 3D UIC60A model according to the position of the array (Fig. 21). Compared with the real picture (Fig. 20), the position of the main contact looks roughly the same.

## Conclusions

A method has been developed to characterize rolling contacts using a bespoke low-cost ultrasonic array system. This was successfully applied to a simple rolling ball on the flat arrangement. A rail mounted sensor was trialed in a static measurement, and the results were positive with minimal displacement of the railhead due to the hole.

A full-size wheel/rail rig was used to create a loaded wheel/rail interface for inspection. A rail mounted ultrasonic sensor was successfully used to measure the dynamic contact patch evolution. It is also possible to measure the contact pressure distribution with the aid of a calibration procedure. The current system is too slow for full speed rail, but with a commercial phased array system, the measurements would be possible at full speed.

Finite element analysis was carried out, dynamic wheel–rail contacts were simulated, and contact patch and pressure distribution were obtained. The influence of a hole cut in the rail has been analyzed.

The new ultrasonic measuring technique has been tested to successfully characterize dynamic contact and take real-time measurements using an ultrasonic scanning array. No significant difference was seen between forward and backward measurements under the same load, which proves the stability of this method. Obvious changes in the contact area and contact pressure were observed with increasing loads. With the current measuring equipment, the effect of speed change on measurement has been characterized; however, results from two speeds both display contact information clearly, which proves the capability of the technique at relatively higher speeds.

According to FE simulations, the influence of a hole cut in the rail is very limited to the contact pressure results and the vertical deformation under loads. The peak pressure from FE simulations and ultrasound measurements matches with each other well, which indicates the ultrasonic technique can be used as a good contact characterizing and validating method other than FE analysis.

## Proposed Future Work

Currently, due to the limitation of the channel switching speed, the technique can only provide sufficient contact information of wheel–rail contacts at relatively low speeds (wheel rolling speeds no higher than 50 mm/s). In future work, with software and hardware upgraded, this technique can be capable of much higher speed. What is more important, more new arrays and mounting ways of the array will be developed to avoid channel switching, and eventually, the ultrasound reflectometry technique is able to real-time characterize dynamic wheel–rail contact in actual field railway systems [17]. To apply this method to measure the rail network, the ultrasonic pulsing hardware would have to be faster. By using a phased array ultrasonic system, it would be possible to increase measurement speed and resolution, but it would dramatically increase the associated costs and complications in postprocessing. Figure 22 shows the possible number of measurements as the wheel rolls over the rail at various speeds and various pulse repetition frequencies.

Cutting a hole in the rail section is not an ideal solution and would not be permitted in a live rail network. It would be possible to mount the sensors at an angle on the outside of the railhead in pitch-catch configuration and achieve a similar result, although with lower resolution. It would also be possible to mount a series of sensors on the wheel but this would require the use of slip-rings or radio transmission.

Contact conditions are more severe during curving as the wheel/rail geometry becomes less conformal and contact occurs at the wheel flange. These conditions result in an increased slip and resultant wear due to deformation and rolling contact fatigue [18]. Too much lateral load will result in excessive flange contact and wheel climb that can lead to derailment. So investigation of flange contacts is of greater importance than normal contacts.

By monitoring the position of the wheel on the rail during railroad vehicle movement, it would be possible to optimize speed with a safety feedback loop system thus preventing too much flange contact. By mounting sensors on the outside of the wheel, it would be possible to create a flange contact detection monitoring system. The transducers would have to be positioned in such a way that the signals could be reflected off the interface at precise locations. To do so might require some removal of wheel material or the use of a wedge to get the correct angle of attack as shown in Fig. 23. A more in-depth feasibility study can be seen in Ref. [19].

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