Testing and modelling of transient adhesion phenomena in rolling–sliding contacts

: Transient adhesion effects in rolling–sliding contacts influence all aspects of train–track interaction. This is of high importance specifically when these effects result in critically low adhesion, which poses a risk to traction and braking of railway vehicles. This study presents a model that can replicate the transient changes of the coefficient of adhesion with tested water and solid particle mix. The experimental data for the model are measured using a commercial ball-on-disc tribometer. The experimental results showed a liquid reservoir in front of the contact area that slowly reduces in size. This observation was used in the modelling approach to divide the calculation into two stages where the reservoir is present and when it disappears. The model was able to reproduce the occurrence of low adhesion region seen in experimental results with different particle concentrations.


Introduction
For railway vehicles, the adhesion between wheel and rail is important to ensure safe braking distances and sufficient traction forces.Conditions that lead to loss of adhesion from environmental sources have been found in the autumn months as a result of leaf contamination [1].However, low adhesion events were also found under conditions where precipitation occurs and high humidity and water contamination affect the contact area [2].
Studies are published in which twin-disc/ball-ondisc machines are used to investigate the conditions that lead to a decrease in the coefficient of adhesion in water-contaminated contact, e.g., Refs.[3][4][5][6][7][8].Beagley and Pritchard [3] studied cases where water was applied to the rail steel specimen or the surface was coated with iron oxide paste, as seen in Fig. 1.The initial reduction in the coefficient of adhesion to a plateau after the first adhesion drop was followed by a second adhesion drop.After this, a valley with a low coefficient of adhesion values was visible before the recovery, where the coefficient of adhesion increased again when the specimen dried out.Similar behavior was reported with the use of water and talc powder with a coefficient of adhesion as low as 0.05 [6].The increase in the amount of talc in the composition prolonged the adhesion drop by up to a minute but did not affect the measured values in the valley drop.
The first drop to a plateau and the second drop to a valley were also observed with pure water under very low temperature conditions [9] as well as different applied amounts [7].However, with pure water, the low adhesion valley after the second drop occurs only for a few seconds.These results suggest that the presence of solid particles with drying water content yields low adhesion conditions for a prolonged period of time.The severity of adhesion drop appears to be related to the material of particles present, as seen with twin-disc experiments of powdered material added to water [4].
A considerably low coefficient of adhesion was also previously observed with water applied to oxidized surfaces [5,7,10].This can be explained by the presence of oxidized wear particles mixed with water that create a paste-like substance that causes low adhesion conditions [5].Based on the published results [5,8], a clear conclusion can be drawn, that lower amounts of water added to a particle-contaminated contact are far more dangerous in causing very low coefficient of adhesion.The driving factor for this behavior is the formation of a high viscosity paste that has the proper rheological properties to produce surface separation with low shear strength.A key parameter that defines the rheological properties is the concentration of solid particles suspended in water.For mineral particles of talc, the critical concentration that causes a coefficient of adhesion lower than 0.1 is 15% [6].For oxide particles, the critical concentration is higher, around 50% [5,11].
Due to the transient nature of this phenomenon at the microscopic level, it is difficult to use experimental methods for the evaluation of the interfacial layer properties, as well as the interaction between surfaces and the mix of water and particles.Several modelling approaches have been proposed to provide deeper insights into the transient behavior of the low adhesion problem.Measurements of both solid and fluid properties of iron oxide and water mix [12] indicated that a simple boundary lubrication theory cannot be sufficient.The presented rheological model predicts that the very low adhesion conditions occur at a very high particle concentration.The increase in viscosity and shear strength with increasing particle content causes a transition from fluid flow behavior to predominantly solid-to-solid interaction characteristics.At the stage where the water content is very low, a loss of adhesion can be expected.This is in line with later findings in the studies [5,8].An improved model that takes into account both the interaction of the rough wheel and rail surfaces and the effect of liquid substance [11,13] was used to investigate the transitioning behavior that causes low adhesion conditions.Using the experimental results from a high-pressure torsion device and previous results of Beagley [12], the model predicts low adhesion conditions with an iron oxide concentration of around 90%.
The current state of the research provides possible explanations for the conditions that lead to loss of adhesion with water contamination.The most important concept is that the concentration of particles suspended in water needs to be in a specific range to create a viscous paste.This viscous paste has such rheological properties that the surfaces are separated with a low shear strength film.The frictional effects observed in studies [3,6,7,9] can be explained by drying of the substance and a change in the concentration of particle content leading to low adhesion as described by published models [11,13].However, the experimental results do not provide information about the particle concentration evolution during the test.
The aim of this work is to propose a model that provides a link between the transient frictional behavior of experimental testing and the idea that the coefficient of adhesion changes with particle concentration.The key is to find a model description that changes the water and solid particle content in a way that fits the experimental changes in the coefficient of adhesion.

Method
In order to achieve the set goal, experiments with water and talc mix of different concentrations were performed.These were then used to calibrate a model that uses the concentration and the amount of used contaminant as inputs to predict the coefficient of adhesion.

Apparatus and methodology
A rolling-sliding ball-on-disc tribometer Mini Traction Machine (MTM) from PCS Instrument, as seen in Fig. 2, was used to investigate the change in the coefficient of adhesion with water and particle mix.The measurements were conducted using a ball and a disc of diameters r ball = 19.05mm and r disc = 46 mm.The speeds of the specimens ω ball and ω disc are controlled by servomotors, allowing precise control of the slide-to-roll ratio (SRR).The normal and frictional force is measured by a force transducer mounted on the loading arm of the ball specimen.The coefficient of adhesion is evaluated as a ratio of frictional and normal force.The sensor data are outputted with a 1-Hz-frequency.
The ball and disc specimens were made of AISI 52100 bearing steel with a hardness of 800-920 HV and 720-780 HV, respectively.The initial roughnesses R a of these specimens are 0.01 μm for the ball and 0.02 μm for the disc.The specimen material used is not representative of real wheel and rail material.However, it gives more stable behavior in terms of changes in wear, roughness, and oxidation.All these aspects are important to ensure that the surface conditions do not drastically change during the experiments and that wear particles are not released from the surface and influence the frictional characteristics.Due to this, the same specimen material has previously been used in studies [6,7,14].
The experiments were carried out at a mean rolling speed of 300 mm/s and a 5% SRR.Based on the analysis of lubrication parameter lambda done in Ref. [14], the rolling speed set in the MTM experiments corresponds to about 18 km/h rolling speed for a wheel-rail contact.The lubrication parameter lambda for pure water is lower than 0.1, which puts the experimental conditions in a boundary lubrication regime.Using a higher mean speed would cause the applied waterparticle mix to be displaced by centrifugal force.The maximum Hertzian contact pressure was set to 750 MPa, which roughly corresponds to the contact pressures expected in light-rail systems.The applied normal load to achieve this pressure was set to 16 N.
Before each experiment, the specimen surfaces were cleaned with acetone and a surface run-in phase was conducted.This run-in ensured similar contact conditions for all experiments in terms of roughness and the initial dry value of the coefficient of adhesion.The roughness after run-in was between 0.2 and 0.3 μm for both specimen surfaces.The run-in phase for the cleaned specimen was stopped once the coefficient of adhesion reached and stabilized at dry values of around 0.5.At this point, the specified amount of tested volume was applied to the contact.

Water-particle mix
The water-particle mix consisted of water and mineral particles of talc.The size of talc particles (D90) was 12.3 μm with a flake-like shape.Talc was selected based on previous experience in the study [6].In this study, talc mixed with water provided a very low adhesion drop and a clear dependence of the coefficient of adhesion on the amount of talc in the mix and the amount applied.Among others, talc can be present as a component in top-of-rail friction modifiers.The precise compositions of the tested water-particle mix substances were prepared using a laboratory balance and mixed with a laboratory shaft mixer prior to each experiment.To prevent any sedimentation of the prepared sample before application, the substance was applied no more than 30 seconds after mixing stopped.
The main experiments were conducted for three different applied amounts: 10, 20, and 40 μL.And four concentrations: 5%, 10%, 15%, and 20%.To obtain a complete relationship between concentration and coefficient of adhesion, additional tests with concentrations of 50%, 70%, and 80% were done with 1 mL applied.The higher applied amount was needed due to the high viscosity of the water-particle mix, which prevented the use of a micropipette, but instead, www.Springer.com/journal/40544| Friction a regular syringe was used.For a 100% concentration, 50 mg of talc powder was used.The 90% concentration was not feasible to test, due to a very low amount of water that makes it impossible to mix with the particles homogeneously and apply with a syringe.Each experiment was repeated 3 times to provide a statistical data set.
Data points of the coefficient of adhesion for the relationship between concentration and the coefficient of adhesion were taken from the main experiment set.A mean value of the coefficient of adhesion was calculated between 5 and 15 seconds for each experiment with a set concentration.This ensured that the mean value calculation avoided the first drop after application and enough data points were taken in the stable part of the measured curve.In total, 9 points for each concentration were taken from experiments with amounts of 10, 20, and 40 μL.Additionally, it was assumed that the stable coefficient of adhesion in this time window implies negligible changes in concentration.For the 100% concentration, a 10 s window after the coefficient of adhesion stabilized was used for the mean values.This was chosen due to the different behavior of dry powders compared to a liquid water-particle mix.

Mathematical model
The baseline experiment for 10 wt% talc and 20 μL applied, as seen in Fig. 3, showed three distinct regions of the coefficient of adhesion.After the application of the water-particle mix and the first drop, a plateau in the coefficient of adhesion around 0.3 appeared.This plateau was characterized by a visible reservoir in front of the contact area, as shown by the images (1), (2), and (3) in Fig. 3.The reservoir is commonly referred to as a meniscus.From the experimental results, it can be seen that the meniscus gets smaller as the water is removed and the particles are redistributed outside the contact path, thus reducing the volume of the water-particle mix.This behavior is described in Eq. (1).
This equation does not provide a change in concentration, as both the water medium and the solid particles are removed proportionally.As long as the meniscus is present, the reduction of water-particle mix volume V L is controlled by the water-particle mix removal rate k 1 .The presence of the meniscus is defined by the meniscus threshold volume k L .This separates the calculation into a first stage, where the volume of the water-particle mix is larger than the meniscus threshold volume and a second stage, where the volume of the water-particle mix is lower.
In the second stage after the meniscus vanishes, as seen in images (4), (5), and (6) in Fig. 3, a valley in the coefficient of adhesion appears, causing values lower than 0.1.At this point, the solid particles can no longer be redistributed outside the contact because the remaining volume of the water-particle mix directly interacts with the contact path.In our modelling  | https://mc03.manuscriptcentral.com/frictionapproach, this means that the volume of solid particles is kept constant in the second stage.However, the water content in the contact path is removed in both the first and second stages and changes the concentration of the water-particle mix.The changes in the volume of water are controlled by the water removal rate k 2 and defined by Eq. ( 2).
Here, it is important to mention that the removal of water can be caused by various factors such as evaporation, ejection due to centrifugal forces or sprayed out due to the running speed of the contact surfaces.Furthermore, simple considerations revealed that the energy input from the dissipated energy in the contact due to slip is negligible.This might change when it comes to full-scale wheel-rail contact conditions.
During the whole process in the first and second stage, the total volume of the water-particle mix has to be equal to the sum of solid particles and water content, as defined by Eq. ( 3).
The concentration of the water-particle mix is defined as a mass fraction of solid particles in the total mass of the water-particle mix.This is defined by Eq. ( 4), where ρ S is the density of solid particles and ρ W is the density of water.
To compare the results of the model with experimental data, the coefficient of adhesion is needed as a model output.Because the model only predicts the change in water-particle mix concentration, a dependency between the concentration and the coefficient of adhesion is required.This dependency is derived from the main measurement set.
The results of concentration to the coefficient of adhesion dependency are shown in Fig. 4.An initial concentration lower than 20% showed a higher standard deviation with coefficient of adhesion values corresponding to the plateau region.The increased scattering at low concentrations is a result of the initial plateau region not having the same stable value.This scattering did not show a significant correlation to the applied volume, as the data points for different volumes were scattered randomly.Once the concentration reached 20% and up to 80%, a low coefficient of adhesion below 0.1 was reached with a very low standard deviation.These values correspond well to the valley region, where the coefficient of adhesion is expected to be around 0.05 for talc mixed with water.The pure talc powder resulted in a mean coefficient of adhesion of 0.43.All these findings are in line with previous experiments with water and talc particles [6].
In the model, the predicted coefficient of adhesion  is a function of the particle concentration C(t).This function is based on linear interpolation using the mean of measured values of the coefficient of adhesion, as seen in Fig. 4.This interpolation gives the resulting predicted coefficient of adhesion based on the calculated concentration at each time step.For the purposes of concentration calculation, the density of water is set to 1 g/mL and talc powder to 2.7 g/mL.The initial conditions for the calculation are defined by the initial concentration C(t = 0) and the initial volume of water-particle mix V L (t = 0).
The last region observed in Fig. 3 showed a coefficient of adhesion recovery to values similar to dry contact conditions.The recovery occurs after the water content is removed and the viscous paste film is broken up.In this region, the solid particle breakage might play a role, as well as the interaction of the particles and their fragments with the rough wheel www.Springer.com/journal/40544| Friction and rail surfaces.This is not predicted by the model.To predict the coefficient of adhesion in this region, a new set of equations would be needed.This could be a topic of future research.

Model calibration
To replicate the baseline results in Fig. 3, an optimization routine was applied to the prediction model to find the parameters k 1 , k 2 , and k L .The initial concentration was set C(t = 0) = 0.1 and the initial volume of waterparticle mix V L (t = 0) = 20 μL, according to the experiment.The optimization aimed to minimize the error between the experimental and simulation data.
The error E was defined as an RMS value between measurement and model, as defined by Eq. ( 5).

 
In this equation, corresponds to data from experimental measurements and  to the predicted values of the coefficient of adhesion.The value corresponds to the end time of the experimental measurement.The results of the optimization are shown in Fig. 5.The optimized parameters are: k 1,0 = 0.235 μL/s, k 2,0 = 0.07 μL/s and k L,0 = 1.1 μL.The predicted results show reasonable agreement with the experimental data in the regions of plateau, valley, and recovery.In the plateau region, the prediction shows a more stable coefficient of adhesion than the measurement.The difference in the observed trend could be explained by the high scattering of the coefficient of adhesion at low concentrations, as seen in Fig. 4. The predicted drop into the valley region precisely reflects the measurement.Furthermore, the vanishing of the meniscus occurs at a similar time to the camera observations in Fig. 3.The dashed line of the meniscus threshold volume represents a point where the volume of the water-particle mix reaches the value k L .In the recovery region, the measured data show a more gradual increasing trend compared to the rapid increase predicted by the model.Due to this, the point at which the coefficient of adhesion starts to increase is predicted a few seconds later.As mentioned previously, the model cannot describe the gradual recovery region.
From the concentration results in Fig. 5, it is evident that the gradient of concentration change increases until 100% concentration is reached.The rapid increase around 60 s is due to a very low amount of water, around 1 μL.At this point of the meniscus vanishing, the water removal coefficient k 2 in Eq. ( 2) becomes dominant.In this valley region, the volume of solid particles remains constant at 0.07 μL.

Parameter study
To understand the influence of the model parameters, a parameter study with the calibrated model was conducted.For each result set, only one parameter changes, and the others are fixed to values found in the previous section of model calibration.The parameters evaluated were: initial concentration, initial volume of water-particle mix, water-particle mix removal rate, water removal rate and meniscus threshold volume.
The influence of the initial concentration is shown in Fig. 6.With increasing initial concentration, the valley region is prolonged.This is the result of starting the simulation closer to concentration 0.2 where the valley occurs.Starting at 0.2 initial concentration or higher will result in a valley drop from the beginning of the simulation until the recovery region around concentration 0.8 is reached.The time to recovery does not change significantly, due to the same starting volume of 20 μL.The small changes in time to recovery are caused by different initial amounts of water in the water-particle mix.A higher initial concentration means  a lower water amount that is removed more quickly by k 2 , and thus a few seconds shorter time to the adhesion increase.The time when the meniscus vanishes is the same for all three cases at 62 s.This is evident, as the initial volume is the same and the removal rate parameters k 1 and k 2 , as well as the meniscus threshold k L are also the same for all three shown cases.
The effect of the initial volume of water-particle mix is shown in Fig. 7.The time to recovery increases with a higher initial water-particle mix volume and the meniscus threshold moves further into the valley region.The occurrence of the meniscus threshold deeper in the valley region for higher initial volume is explained by the k 2 parameter acting for a longer time in the plateau region compared to the other two cases.Thus, causing more substantial changes in concentration.The length of the valley is also prolonged with higher initial volume, as the meniscus threshold k L is already situated in the valley drop.For the lowest initial volume of 10 μL, after the meniscus threshold is reached, there is still around 4 s needed Fig. 7 Parameter study: the effect of applied volume.
to reach the low coefficient of adhesion below 0.1.However, the main influence of the initial volume of water-particle mix is on the total length to reach recovery and not necessarily on the shape of the curve.
The removal rate parameters k 1 and k 2 define the amount of volume removed per second.For k 1 , this affects the water-particle mix and for k 2 only the water content.These parameters will depend on the running and environmental conditions.The increase in the water-particle mix removal rate k 1 , as shown in Fig. 8, causes a shorter time to reach recovery, due to faster removal of the water-particle mix volume in the first stage.The time between the meniscus threshold and the time to recovery does not change, as the parameters k 2 and k L affecting this stage are the same for all three cases.The length of the valley drop increases with a lower water-particle mix removal rate.This is caused by the more dominant influence of k 2 compared to k 1 in the plateau region, causing a faster concentration change, and thus a faster transition to low values of the coefficient of adhesion.
The parameter for water removal rate k 2 causes changes in the water volume throughout the whole simulation.As seen in Fig. 9, the higher the value of k 2 , the shorter the time to reach recovery, and the valley region occurs sooner than the meniscus threshold is reached.Similarly to the Fig. 8, the larger k 2 is compared to k 1 , the sooner the valley drop will occur.Due to this, the valley is wider for lower water removal rates because it takes more time to remove the water content from the set meniscus threshold volume k L .The meniscus threshold volume parameter defines when the volume of the water-particle mix does not create a reservoir around the contact and only acts on the running path of the contacting surfaces.This means that the value will be mainly influenced by the geometry of contacting bodies.A larger contact area will require a larger volume of meniscus threshold to cover the running path of contacting surfaces.The effect of the meniscus threshold volume is shown in Fig. 10.The meniscus threshold volume k L changes the point at which the k 1 is no longer active.Thus, the larger parameter k L causes an earlier transition to the point where only water removal rate k 2 occurs.This will prolong the valley region, as more water needs to be removed to get to recovery.

Wider experimental validation
The comparison of the main experiments with model prediction is shown in Fig. 11.The model parameters were estimated using the same optimization routine The model prediction shows an overall reasonable agreement with the measurement results.The main effects can be reproduced by the model.However, for the experiments with an initial concentration of 15% deviations can be observed.These deviations could be explained by a rapid change in the coefficient of adhesion between 15% and 20% as seen in Fig. 4. The coefficient of adhesion to concentration dependency is linearly interpolated between data points, which might not represent real behavior.Additionally, variations in the concentration of the applied waterparticle mix for the conducted experiments can increase the uncertainty.This can be caused by factors such as sedimentation, evaporation of water before application or the accuracy of weighing the material during preparation.
For concentrations higher than 20%, the viscosity of the substance rapidly increases.This results in starvation effects, where the water-particle mix can no longer replenish the contact and is squeezed and kept out of contact.This was observed during the experiments and also explains the increasing time difference between the time to recovery predicted by the model and that obtained from the experiment in tests at 20% concentration.The same behavior was observed with an increase in the water-particle mix viscosity by a bentonite thickener [6].With increasing the applied amount of water-particle mix V L (t = 0), this effect becomes more influential, since more water-particle mix volume is affected by the starvation effect.
In the initial plateau region, a discrepancy in the progression of the coefficient of adhesion can be seen.After the application of the water-particle mix, the coefficient of adhesion decreases until stable values are reached.For some experiments, the plateau is flat with minimal changes until the valley drop occurs.But for other cases, an increasing trend can be seen as most visible in experiments with a 5% initial | https://mc03.manuscriptcentral.com/frictionconcentration and 20 μL of water-particle mix applied.A visible decreasing trend was observed throughout the plateau region for one experiment at 10% initial concentration and 20 μL of water-particle mix applied (blue data points).These variations can be seen in Fig. 4 for up to 15% initial concentration.

Summary and discussion
The results from laboratory experiments show three distinct regions of coefficient of adhesion during the rolling-sliding test with a water-particle mix: plateau, valley, and recovery.Similar findings have been previously reported in other studies [3,6] with different types of water-particle mix and surface conditions.In other studies, these three phases are observed with pure water applied [7,9].In the presented study, observation of the contact area with a camera during a baseline experiment showed a meniscus reservoir in front of the contact area that slowly decreases in size until it is completely removed.Based on this finding, a mathematical model was built to replicate the coefficient of adhesion results.
The presented model uses the occurrence of the meniscus to divide the calculation into the first and second stages.The dividing condition is when the volume of the water-particle mix decreases below the meniscus threshold volume k L .In the first stage, the volume of the entire water-particle mix is removed by means of the water-particle mix removal rate k 1 .This is supported by the observation that the water content is removed from the meniscus area, and simultaneously the solid particles stick to the surfaces outside of contact where water is no longer present.The water removal rate k 2 , which affects the water content in the running path, is also active in the first stage.The second stage occurs when there is no meniscus reservoir and the remaining water-particle mix acts directly in the contact area.At this stage, the solid particles cannot be carried outside contact by www.Springer.com/journal/40544| Friction the water.Thus, the volume of solid particles is kept constant and only the water content is removed by the water removal rate k 2 .Interestingly, the effect of temperature on the model parameters was not found to be influential.However, at large scales, this could play a major role as an additional parameter for water removal.
The three above-mentioned parameters control changes in the volume of water, solid particles and consequently the total volume of water-particle mix.The calculated volumes and known densities of the water-particle mix components give the concentration of solid particles, defined by the weight percentage.The empirically derived dependency of the coefficient of adhesion on the concentration is then used to find the time evolution of the coefficient of adhesion.This dependency can be found experimentally, as shown in this study and others [5,6,11,12].Furthermore, recent studies [11,13] used a modelling approach to find out how the concentration of solid particles affects the coefficient of adhesion.
A further topic of future research is to gain a better understanding of how the shape, size and material parameters of the solid particles affect the results.Especially the recovery of the adhesion after the low adhesion region (adhesion valley) is thought to be influenced by effects from particle-particle interaction including particle breakage, but also the influence of these quantities on the suspension viscosity might be of interest.An advanced model that would describe the variations in the viscosity of the water-particle mixture and resulting surface separation could provide a fundamental understanding of the underlying mechanisms of low adhesion.The final goal is to apply the model to wheel-rail contact and predict the possible events of low adhesion that pose a danger in terms of braking and traction.A precautionary measure can then be taken to minimize the risk of accidents and delays.

Conclusions
The presented work uses a combination of experimental and simulation approaches to predict transient changes in the coefficient of adhesion with solid particles suspended in water.The effect of model parameters on the progression of the coefficient of adhesion has been shown.Finally, the model was validated on experimental data consisting of different initial applied amounts and concentrations.The main findings of this study can be summarized by the following highlights:  A three-parameter model, defined by the two removal parameters and the meniscus threshold parameter, with concentration/coefficient of adhesion dependency was able to reproduce measurements of the coefficient of adhesion with water-particle mix substances.
 The presence of the meniscus in front of the contact area is closely related to the changes in concentration and subsequent drop in the coefficient of adhesion. The time to recovery is mainly controlled by the total volume of liquid, while the progression of the coefficient of adhesion depends on the initial concentration of solid particles.

Fig. 4
Fig.4 Relationship between particle concentration and coefficient of adhesion.

Fig. 5
Fig.5 Simulation of baseline experiment with 10% talc and 20 µL of water-particle mix applied.

Fig. 8 Fig. 9
Fig.8Parameter study: the effect of water-particle mix removal rate k 1 .

Fig. 10
Fig. 10 Parameter study: the effect of meniscus threshold volume k L .

Fig. 11
Fig. 11 Comparison of all measurements with model prediction.