The effect of top of rail lubricant composition on adhesion and rheological behaviour

The effect of top of rail lubricant composition on adhesion and rheological behaviour Daniel Kvarda a, ⇑ , Simon Skurka a , Radovan Galas a , Milan Omasta a , Lu-bing Shi b,c , Haohao Ding b , Wen-jian Wang b , Ivan Krupka a , Martin Hartl a a Faculty of Mechanical Engineering, Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic b Tribology Research Institute, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China c Zhengzhou Research Institute of Mechanical Engineering Co., Ltd., Zhengzhou 450001, China article info Article history: Received 5 August 2021 Revised 4 January 2022 Accepted 23 January 2022 Keywords: Coefficient of adhesion Top of rail lubrication Wheel-rail tribology Rheology Numerical model abstract The effect of top of rail lubricant composition on adhesion has been investigated using a laboratory ballon-disc tribometer. Rheological properties were analysed using viscosimeter and high pressure torsion device. As a base medium, a biodegradable ester oil with bentonite thickener was selected. Added particles for friction modification were aluminium oxide, zinc oxide, copper sulfide and solid lubricants molybdenum disulfide and graphite. The effect of these components in the base medium on adhesion was evaluated. It was found that the most dominant component was the solid particles for friction modification. Based on the results, top of rail lubricant substances were prepared and tested. The best performing substances provided the optimal level of adhesion. These substances also showed resilience to overdosing, which caused commercial products to provide very low adhesion conditions. The rheological investigation confirmed the very low adhesion is controlled by elastohydrodynamic regime while the stable values are a result of transition to boundary lubrication. Ó2022 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction Railway transportation runs into high demands in terms of energy efficiency, safety and reliability. A key role in train operation is played by the contact between wheel and rail where traction and braking forces are transferred. In recent decades, the application of top of rail (TOR) products to manage wheel-rail friction was thoroughly studied and employed by many train operators all over the world. The TOR products can be divided into three main categories: oil-based (TOR lubricants), water-based (friction modifiers) and solid stick. Their use and positive effects have been reported by several laboratory and field studies. The main idea is to reduce the coefficient of friction to an intermediate level (around 0.3) and provide a positive slope of frictional characteristic [1]. One of the main resulting benefits is the reduction of wear [2,3] as well as head checks [4] which can be completely eliminated. Field studies also demonstrated the benefits in reducing short pitch corrugation [5–7] and suppressing its evolution. If the application of TOR product is stopped, the corrugation starts to grow [6]. In city transportation systems, the impact of friction modification goes beyond the vehicle and track itself when noise emission in urban areas is an unpleasant problem. Stick-slip phenomena causing a noise generation can be minimized [8–10] by the positive slope of friction curve provided by TOR products. This has been supported by numerical works [11,12]. Other typical benefits can be achieved with respect to reducing lateral forces [13,14] and rolling contact fatigue [4]. However, TOR lubricant studies [1,2,15] suggest that it is important to correctly set the applied quantity. Overdosing the contact can lead to very low adhesion. This can also happen for friction modifiers [3] when the water base does not dry out. When these low adhesion conditions occur, the braking performance of the train can be significantly reduced [9]. The overdosing effect is more dominant for TOR lubricants [1], where lower values of coefficient of friction can arise. Study of commercial TOR lubricants [2] showed that different products can lead to varying frictional behaviour after application. Also, under fully flooded conditions the coefficient of adhesion dropped as low as 0.02 for one of the tested products. However, because the products are commercial with no detailed specification, it is not easy to draw conclusions about the influence of the composition. In experiments with wheel-rail products [16], the https://doi.org/10.1016/j.jestch.2022.101100 2215-0986/Ó2022 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). ⇑ Corresponding author. E-mail address: [email protected] (D. Kvarda). Peer review under responsibility of Karabuk University. Engineering Science and Technology, an International Journal 35 (2022) 101100 Contents lists available at ScienceDirect Engineering Science and Technology, an International Journal journal homepage: www.elsevier.com/locate/jestch TOR lubricant performed similarly to grease and gauge face lubricant and did not provide adhesion levels required for friction management as suggested by study [1]. As in the previous study, the composition of tested TOR lubricant is not known. Other frictional studies [9,15,17,18] suggest that TOR lubricants can achieve very low levels of coefficient of adhesion, especially after initial application or overapplication. The solution to prevent these low levels of adhesion is to optimize the application process either by changing the amount applied or by improving the application process. Because only commercial products are used, studies do not focus on the effect of the TOR composition and its possible influence on overdosing the contact. Study [3] showed that using not only different solid lubricant, but also hard particles for friction modification, can improve the performance of friction modifier and prevent low adhesion conditions. However, this study is focused on friction modifiers, which are water-based substances. TOR lubricants work differently as described in [1], which means that a study on the composition of these oil-based substances can provide new information and possible ways to suppress the effect of overapplication. Due to the complexity of the problem and its use in railway systems, modelling approaches have been employed in many fields such as contact mechanics, dynamics and wear simulations. Modelling wheel-rail contact is an important approach to demonstrate or prove a tool and concept without additional costs of experiments and field testing. Significant contributions to exact and simplified models have been made by Kalker and can be found in his book [19]. Studies mainly build upon the simplified algorithm FASTIM. To accurately represent the experimental results for dry and contaminated contact calculation, the changes in traction curve, such as lower initial slope and decreasing coefficient of adhesion at high slips, had to be implemented. This has been done by introducing velocity/slip dependent frictional characteristics by different authors [20–24]. This was applied to contact contaminated with oil and leaves as well as friction enhancers [21]. With this approach, the authors worked backwards to identify the model parameter based on the twin-disc experimental data. This method does not use or provide information on the rheological properties of interfacial layer. Rheological elasto-plastic material characteristics measured by high pressure torsion [25] implemented in FASTSIM calculation model were demonstrated in dry, wet and sanded conditions. These models using FASTSIM algorithm do not account for elastohydrodynamic (EHL) effects where surface separation can cause a decrease in coefficient of friction, as was demonstrated in water-contaminated contact [26,27] with a constant coefficient of friction. Previous studies point to the right direction where the rheological properties of the interfacial layer can be used to improve wheel-rail contact models. Considering TOR lubricants, the pure boundary model is not satisfiable as the EHL regime can be present with oil based substances as suggested by study [2]. Additionally, the effect of frictional heating can be considered [28] to account for decrease in coefficient of adhesion at higher slips. However, a direct comparison between the rheological properties used for modelling and frictional response was not thoroughly investigated. Despite several improvements in the model predictions, an approach for both boundary and EHL friction of TOR lubricant has not been studied yet. To achieve this, the interfacial layer needs to be characterized by rheological properties for both the boundary and the EHL friction. In the boundary regime, the shear stresses arise from surface displacements while the EHL regime responds to the rate of displacement. The studies mentioned above are primarily focused on the use of commercial products. However, the composition of these products is crucial in terms of the desired behaviour after application. Commercial products do not list specific components, and thus it is not easy to assess the effect of different materials used. A study looking into water-based friction modifiers was already published [3]. However, a deeper analysis of TOR lubricant composition is still an unexplored area. Especially because of the sensitivity to application [1], which could be suppressed by changing the substance composition. This article aims to investigate the role of different components in TOR lubricant on adhesion behaviour. Selected compositions are then compared with commercial products. The boundary and EHL frictional properties are then compared with a numerical model to assess the lubrication regime and validate the model for complex TOR substances. 2. Materials and Methods 2.1. Adhesion tests In this study, a ball-on-disc tribometer Mini Traction Machine (MTM) from PCS Instruments was used for coefficient of adhesion evaluation. Scheme of the apparatus can be seen in Fig. 1. The normal force is measured by force transducer attached to the ball loading system. The frictional force is calculated from the measured torque by transducer attached to the disc shaft. Data acquisition software is provided by the device manufacturer. All sensor data are acquired with a sampling frequency of 1 Hz. However, this 1 Hz signal is a result of averaging a higher frequency input signal that the manufacturer does not specify. The measurement system uses a feedback loop to actively control the driving parameters. Ball and disc of diameters 19.05 mm and 46 mm respectively are loaded against each other and driven by individual servomotors, thus SRR (slide-to-roll ratio) can be controlled and determined by the following equation: Nomenclature CoA Coefficient of adhesion (-) DEllipticity parameter (-) F N Normal force (N) F T Frictional force (N) GDimensionless materials parameter (-) h c Central film thickness (m) pContact pressure (Pa) rRolling radius (m) r ball Radius of ball specimen (m) r disc Radius of disc specimen (m) SRR Slide to roll ratio (-) UDimensionless speed parameter (-) WDimensionless load parameter (-) zRoelands pressure-viscosity coefficient (Pa-1) a Barrus pressure-viscosity coefficient (Pa-1) g Viscosity at operating conditions (Pa∙s) g 0 Viscosity at room temperature and ambient pressure (Pa∙s) x ball Rotational velocity of ball specimen (rad∙s) x disc Rotational velocity of disc specimen (rad∙s) D. Kvarda, S. Skurka, R. Galas et al. Engineering Science and Technology, an International Journal 35 (2022) 101100 2 SRR ¼ x ball r ball  x disc r disc x ball r ball þ x disc r disc 200%ð1Þ Where x ball and x disc are angular velocities of ball and disc respectively, and r ball and r disc stands for specimen’s radii. The normal force F N and the friction force F T are measured simultaneously and the coefficient of adhesion (CoA) is evaluated using the following formula: CoA ¼F T F N ð2Þ The material of both specimens is AISI 52,100 bearing steel with Vickers macro-hardness of 800–920 HV (ball) and 720–780 HV (disc). Hardened bearing steel is not a typical rail material [29], and it was used to reduce excessive wear losses and changes in surface topography during the adhesion test. This ensures similar contact conditions for all tests, which is desirable for quantitative comparison of the tested substances and suppressing the effect of surface wear debris. A similar approach has been already used in studies [2,3,9,30]. The parameters for the tests were as follows: normal force of 18 N (800 MPa maximum Hertzian contact pressure), mean rolling speed of 1000 mm/s and 2 % SRR. The parameters for normal load were selected to represent the contact pressure of a lightrail tram system. The rolling speed was set based on analysis of a lambda lubrication parameter. The study [31] compares the lambda parameter of MTM conditions with a commuter train where the mean rolling speed 1 m/s of MTM corresponds to approximately 60 km/h for the train. The mean speed of MTM also has a limitation due to displacement of the applied composition by centrifugal force, which had to be taken into account. The SRR was set to represent realistic conditions of wheel and rail contact. Higher values would also promote wear that changes surface conditions during the experiment. The duration of each experiment was 20 min to provide enough time for the compositions to exceed the optimal levels of adhesion or show an overlubricating effect. Longer test times could also cause excessive wear of the contacting surfaces, resulting in a change of experimental conditions. There was also an initial runin phase before each experiment with a duration of 10 min, after which the roughness of both specimens was measured. The purpose of the run-in phase was to stabilize the roughness of the surface in 0.1–0.3 mm interval, so similar surface conditions and thus the lubrication regime could be maintained before each experiment. Both specimens were cleaned in acetone before each test. The amount of lubricant applied for the adhesion test was 4 ml. The solid particles in dry contact were applied by mixing with ethanol and drying out before the start of the experiment. The applied amount was 0.5 ml with particles representing 1/7 of the total weight. The results are reported in the form of a time chart of coefficient of adhesion or as a bar chart showing the mean value of coefficient of adhesion calculated as an average from the last 100 s of the experiment. For data interpretation, the optimal value of coefficient of adhesion is considered 0.15 – 0.25. This value is based on the lower SRR of 2 % and the lower measured coefficient of adhesion in dry conditions than suggested by study [1]. 2.2. Rheological tests To obtain information about the lubrication regime, a set of rheological tests were conducted. These tests were designed to identify the boundary and EHL properties of the tested substances. The measured parameters are used as input to the prediction model. The viscosity and pressure-viscosity coefficient of the base oil were measured using a custom-made high pressure viscosimeter. This viscosimeter allows to measure pressures up to 0.3 GPa. It is built on the principle of a falling cylinder element where the position of the falling element is measured by a linear variable differential transformer sensor. Based on the velocity of the falling element, the viscosity is calculated. For viscosity measurements, the oil separated from the base medium was used. Viscosity was measured at 50 MPa steps up to 300 MPa at an ambient temperature of 25 °C. Fig. 1. Scheme of MTM apparatus [3] with picture after experiment. Fig. 2. High pressure torsion rig. D. Kvarda, S. Skurka, R. Galas et al. Engineering Science and Technology, an International Journal 35 (2022) 101100 3 The boundary layer parameters were measured by a high pressure torsion (HPT) apparatus as seen in Fig. 2. The HPT apparatus provides information about the relationship between surface displacements and coefficient of friction. This is used in the boundary regime calculation to estimate the shear stresses by multiplying the local normal stress and the coefficient of friction for local surface displacement, as measured by HPT. This HPT device consists of a hydraulic cylinder that loads the lower specimen against the upper specimen by a set normal force. The maximum normal loading force capability is 100 kN. The normal force is measured using a pressure gauge. The torque is applied by a loading arm with a worm jack driven by a stepper motor. Between the loading arm and the worm jack, there is a 2 kN force transducer that is used for calculation of the applied torque. The transducer has a sensitivity error of 0.25%. The maximum allowable torque is limited by the nominal rated force of the transducer to 400 Nm. The coefficient of friction is calculated as the measured torque divided by the loading force and the effective radius of contact area. The rotational displacement of the upper specimen is measured by a rotary encoder. The displacement resolution at the effective radius of the specimen is 20 nm. The acquisition of data from all sensors was done by a measurement card with sampling frequency of 100 Hz. All HPT tests were carried out at 750 MPa normal pressure and displacement speed 1 mm/s. The specimens were made from DIN 100CrMn6 which is similar to the specimen used in MTM tests. The contact surface is an annulus with an inner radius of 3 mm and an outer radius of 6 mm. These contact dimensions result in an effective radius of 4.66 mm. Each substance was applied to the contact surface by a micropipette. The amount applied was 8ml to ensure that the entire contact surface was covered. To simulate a small amount of slip distance, as in the ball-on-disc tribometer, a preliminary run-in was done. This consisted of a shear displacement of 60 mm at a pressure of 500 MPa. After this phase, the pressure was increased to 750 MPa for the main test. The maximum shear displacement was set to 0.1 mm where all tested substances reached saturation in coefficient of friction. 2.3. Tested components and substances The focus of this study is on oil-based TOR lubricants. They dominantly consist of oil-based medium, friction modifier particles and solid lubricants. No other additives were used in this study. A grease based on synthetic ester oil with bentonite thickener was used as a base medium. Alumina particles of two different sizes, zinc oxide and copper sulfide were used as friction modifier particles. Graphite and molybdenum disulfide were used as solid lubricant. For more details, see Table 1. All components were weighted using an analytical laboratory balance and then mixed by a shaft mixer for two hours before each test to ensure homogeneity of the composition. For comparison, two commercial oil-based TOR lubricants were selected. These lubricants are referred to as TOR A and TOR B. Both are biodegradable high pressure resistance lubricants that are water repulsive. The main benefits of using these lubricants are reducing wear and elimination of squeal noise in curves. 2.4. Numerical model The motivation for the use of a numerical model is to validate a tool to predict the adhesion behaviour of TOR lubricants. Such a tool is helpful when assessing a variety of running conditions without the need for excessive experimental effort. The numerical results can be further built upon with the use of dynamic simulations focusing on vehicle-track interaction. Another utilization is to predict the consumption of the applied product and its redistribution by assessing the time for reapplication and the amount of lubricant needed. The idea behind the model is to use the rheological properties of the interfacial layer. This provides a clear and direct algorithm without any ambiguous parameters. Another motivation is to understand the functioning of TOR lubricants. These substances are more complex than TOR FMs due to the contribution of the EHL lubrication regime. The frictional model, which is closely described in [32], is composed of two main calculation algorithms: boundary friction and EHL friction. The mixed lubrication regime using the asperity contact model is not used due to the starvation effect and complicated interaction with solid particles in contact. This is due to the oilbase content being slowly consumed by the contact resulting in an increase of coefficient of adhesion due to starvation which promotes the boundary lubrication effect. As such, the prediction would need to include a time-dependent starvation model in combination with mixed lubrication to accurately estimate the transition between EHL and the boundary regime during the rollingsliding test. This is a complex problem that is considered for future work and development of the model. The boundary friction model is based on Kalker’s FASTIM [33] routine to calculate surface displacements. Based on the calculated displacements and elasto-plastic shear behaviour from HPT tests, the coefficient of friction in the boundary lubrication regime is determined. The model is used to provide information on the frictional properties of the TOR lubricant in different regimes. Validation of the model with experimental data can help with future transfer of the results to real wheel-rail contact. Its use can bring benefits to dynamic models, wear estimation and design of TOR products. The inputs are geometry, material properties, loading, kinematics and rheological properties. The contact area is divided into a discrete grid, where at each point the calculation is realized. The EHL calculation uses viscosity and pressure-viscosity coefficient together with analytically determined film thickness to calculate the EHL shear stress. The boundary calculation uses the FASTSIM algorithm to determine surface displacements. Based on the calculated surface displacements and friction-displacement relationship from HPT test the boundary shear stresses in contact area can be determined. Using the calculated shear stress and normal stress from Hertz theory, the coefficient of adhesion is determined as a ratio between shear and normal stress for both the boundary and the EHL regime. The shear stresses generated by the EHL film are the result of lubricant viscosity and shear rate. The change in viscosity with pressure is described by Barus [34] and Roelands [35] equations as described by Eq. (3) and Eq. (4). Eq. (3) is used to determine the pressure-viscosity coefficient a that is important in determining the surface separation. The Eq. (4) is more precise for high pressures and is used in the main calculation of shear stress by Newton’s law of viscosity. This means that no changes in viscosity with shear rate is considered. Table 1 Components for TOR lubricant. Category Name Particle size (mm) Mohs hardness (–) Oil-base medium Synthetic ester with bentonite thickener –– Friction modifier particles Aluminium oxide 10, 44 (D99) 9 Zinc oxide 5 (D99) 4.5 Copper(I) sulfide 5 2.5 Solid lubricants Graphite 7 (D90) 1–2 Molybdenum disulfide 4.2 (D50) 1–1.5 D. Kvarda, S. Skurka, R. Galas et al. Engineering Science and Technology, an International Journal 35 (2022) 101100 4 g ¼ g 0 e a p ð3Þ g ¼ g 0 e ln g 0 þ9:67½1þ5:110 9 p ðÞ z 1  ð4Þ The model is altered to be suitable for piezo-viscous liquids where the central film thickness is calculated by Eq. (5). Parameters G,Wand Urepresent the nondimensional material, load and speed respectively. Parameter Dis equal to 1 for circular contacts and ris equal to the rolling radius for the ball-on-disc apparatus. h c ¼2:69U 0:67 G 0:53 W 0:067 ð10:61e 0:73D Þrð5Þ 3. Results and discussion 3.1. Adhesion tests The first set of experimental results in Fig. 3 show the adhesion behaviour of separate components in dry conditions and mixed in base medium. The particles in the base medium were represented by 10 wt% for graphite and MoS 2 , 30 wt% for Cu 2 S and 15 wt% for oxides. The coefficient of adhesion for dry contact at run-in phase was measured 0.39. We can clearly see that the particles of alumina and zinc oxide are very close to dry contact. Solid lubricant MoS 2 and graphite can achieve a coefficient of adhesion equal to or lower than 0.1. The particles of Cu 2 S achieved a coefficient of adhesion 0.24 which is closer to dry conditions. The results of zinc oxide are in line with a previous study [3]. Similarly, the fact that larger particles provide a slightly lower coefficient of adhesion and larger deviations correspond with study [36]. With larger particles, we can expect higher resulting surface roughness and abrasive wear as a result of a more significant crushing process [37]. When mixed with the oil-base medium, only the aluminium oxides can provide an increased coefficient of adhesion. The increase is greater compared to the study [38], which might be due to the different particle size. Similarly, a lower coefficient of adhesion for zinc oxide compared to aluminium oxide under wet conditions was found in study [39]. Compared to the coefficient of adhesion of the base medium in Fig. 4, the particles of ZnO and Cu 2 S provided some increases in adhesion, but the increments are not significant enough to be considered for optimal level of adhesion between 0.15 and 0.25. These results show that for the particle sizes used, only aluminium oxide is a suitable material for friction modification particles. The effect of the weight content of the alumina particles is shown in Fig. 4. There is an increasing trend with higher amounts of particles. Only a slight inconsistency is shown for 15 wt% of Al 2 O 3 , which could be caused by the particles not entering the contact sufficiently. This is indicated by the initial increase being similar to 20 wt% but suddenly deviating around coefficient of adhesion 0.23. This fact means that the initial crushing and stabilization process plays an important role for the substance of base oil and particles for friction modification. Above 20 wt%, the results indicate close to dry levels of adhesion. For all tested contents, the time tests show significant time variability, especially at lower Al 2 O 3 contents. This suggests a complex interaction between the particles and the base surface. The saturation point of 20 wt% can be correlated to a similar study [36], where increasing the feed rate of alumina particles increased the coefficient of adhesion until a plateau is reached. Similar results are achieved with sand particles in water [37]. The coefficient of adhesion inconsistency with time might be result of the high ball and disc hardness. When a real wheel/rail specimen and continuous application are used [37,38], much smoother results are acquired. To further increase the complexity of the substance, a solid lubricant was added in the form of molybdenum disulfide and graphite particles. The base composition consists of the base medium and 10 wt% of Al 2 O 3 (10 mm). The results of these compositions are shown in Fig. 5. Increasing the amount of solid lubricant in the composition does not result in a steep coefficient of adhesion reduction. However, one would expect a much larger adhesion drop, as suggested by the use of a solid lubricant without Al 2 O 3 in Fig. 3. Both lubricants are able to reduce the coefficient of adhesion to values between 0.2 and 0.3 with the presence of Al 2 O 3 . Substances with 5, 10 and 30 wt% of MoS 2 give an average coefficient Fig. 3. Solid particles in dry conditions and mixed with oil-base medium. Fig. 4. Effect of aluminium oxide (10 mm) content in oil-base medium. Fig. 5. Effect of solid lubricant in oil-base with 10 wt% Al 2 O 3 (10 mm). D. Kvarda, S. Skurka, R. Galas et al. Engineering Science and Technology, an International Journal 35 (2022) 101100 5 of adhesion below 0.25. The same applies for the substance with 15 wt% graphite. The main finding is that a higher solid lubricant content creates a paste-like substance. At such a state, it is not feasible to add more particles while maintaining a homogeneous mixture. This was achieved at 20 wt% of graphite and 35 wt% of MoS 2 . This thick state of the composition is also not suitable, as it creates difficulties with application and promotes starvation of the contact. Similar pastelike forming and related problems with application were found in studies [3,40]. These results suggest that the increased content of MoS 2 and graphite does not help reduce the coefficient of adhesion. The key to achieving intermediate adhesion seems to be mainly in using the correct amount of friction modification particles. The total amount of solid particles can be altered to result in a suitable viscosity of the substance with respect to the application and adherence to the surface. Based on these results, several substances were prepared and tested to assess the adhesion performance. The two main evaluated parameters were the time after application where very low adhesion conditions occur (<0.1) and the effective time between the optimal coefficient of adhesion of 0.15 – 0.25. Some of the substances show good performance in terms of optimal adhesion but with a substantial and prolonged drop in adhesion after application. Only three of the best performing substances are further compared. The composition of the selected substances is described in Table 2. Adhesion tests for the selected compositions are shown in Fig. 6. The lower and upper bound of the optimal level of adhesion is represented by dashed lines. It is evident that the application can be divided into two areas: (I) drop after application with a steep slope of the coefficient of adhesion, (II) effective part of the adhesion curve with a slow gradual increase in the coefficient of adhesion. This initial drop and then a slow increase in the coefficient of adhesion can also be found in previous studies [2,3,9,41]. It is beneficial to shorten the length or even eliminate these initial low adhesion conditions to prevent their negative impact, such as increased braking distance [9]. The substance N, which is characterized by a lower amount of particle portion, overshoots the initial increase in coefficient of adhesion. This was observed in a similar fashion with all repeated tests of substance N, but not by the other two substances. However, all three substances exhibit very similar behaviour in the initial drop of adhesion and its time length. Around 400 s, all three substances followed a similar trend, and around 1000 s the upper limit of optimal adhesion is reached. The selected compositions were also tested with different applied amounts together with commercial TOR lubricants for comparison. The applied amounts were 2, 4 and 6 ml based on previous experiments with TOR lubricants. The results are shown in Fig. 7. It is evident that an increased amount of TOR lubricant applied extends the effective time of the substance. For the 2 ml applied, all compositions exhibited a similar behaviour. After application, a coefficient of adhesion below 0.1 is reached and then increases towards dry conditions. The commercial substance TOR A has the longest part of optimal adhesion at this applied amount. However, increasing the amount to 4 ml causes TOR A to overlubricate the contact. Throughout the 800 s measured, the coefficient of adhesion is constantly between 0.05 and 0.1, which could be unacceptable for railway application. The other commercial product TOR B performs well at 4 ml with short duration below the coefficient of adhesion of 0.1. The duration before reaching the upper limit of optimal adhesion is around 300 s. The prepared substances provide a longer lasting effect. Substance N exceeds the optimal level after the initial rising of coefficient of adhesion. The other two substances, AO and AZ, provide around 600 s long-lasting effect and the initial drop of adhesion after application is the shortest of all tested substances. Especially the substance AZ shows a desirable trend of slowly increasing adhesion. For 6 ml applied, both commercial TOR lubricants overlubricate the contact. Substance N seems to be very unstable even though it satisfies the optimal adhesion. Substances AO and AZ provide very good behaviour for TOR lubricant. Comparing with commercial TOR products, the overdosing effect was not observed with the prepared substances. Based on the adhesion curves, we can assume that commercial products use different types and amounts of friction modifier particles. The measured curves for commercial TOR lubricants are very smooth with minimal instability. Nevertheless, this might be the reason why very low adhesion conditions were measured with a higher applied amount of TOR lubricant. Based on the SEM photographs of commercial products [2], we can assume that they are composed of smaller and more flake-like metal particles. These particles may be less prone to being crushed or cause abrasion that would transfer forces compared to rounder Al 2 O 3 particles in the prepared substances. This high sensitivity to the applied quantity was also observed for commercial TOR products in other studies [2,9,15]. It should be noted that this high sensitivity might be a result of the used scaled tribometer. For real wheel-rail, contact a less sensitive behaviour might be expected. 3.2. Rheological properties Based on available information, both commercial TOR lubricants use ester oil as a base medium with thickener. Because of this, the results for viscosity measurements are used for all tested products with similar base oil. The measured viscosity of the base oil at ambient conditions was g 0 = 0.09 Pa∙s. Based on the model fit to the viscosity measurements at higher pressures we get a = 13.5 GPa 1 and z= 0.468. The calculated film thickness (Eq. (5)) for experimental conditions is 360 nm. This value is slightly above the range of surface roughness 0.1 – 0.3 mm which the adhesion tests were conducted in. Accounting for the effect of hard particles in the contact, we can assume that the lubrication is in the range of mixed to boundary regime. The resulting EHL coefficient of adheTable 2 Composition of selected substances. Name Friction modification particles Solid lubricant N 3 wt% Al 2 O 3 (10 mm) 7 wt% Cu 2 S 1 wt% MoS 2 AO 10 wt% Al 2 O 3 (10 mm) 30 wt% MoS 2 AZ 10 wt% Al 2 O 3 (10 mm) 15 wt% Graphite Fig. 6. Effect of aluminium oxide (10 mm) content in oil-base medium. D. Kvarda, S. Skurka, R. Galas et al. Engineering Science and Technology, an International Journal 35 (2022) 101100 6 sion predicted by the model for base oil and the parameters used in the adhesion tests is 0.027. If we consider a temperature influence and shear-thinning properties on lubricant, this value could be even lower as suggested by study [42]. The boundary friction properties of the tested substances are shown in Fig. 8. The TOR A substance showed the lowest coefficient of friction after reaching plastic deformation shearing. The initial elastic region represents a situation where the surfaces with the applied substance between asperities are in locked state with no macroscopic slip with an increase of shear load. After the shear stress exceeds the ability of the surfaces and interfacial substance to carry the shearing load, a relative movement between surfaces occurs resulting in a plastic deformation. Surprisingly, all three prepared substances have a similar trend in the initial elastic and plastic parts of the curve. The maximum coefficient of friction occurs at the displacement distance 0.01 mm. After reaching the maximum, it slightly falls and reaches stable values around 0.2 for all three substances. The values for the commercial TOR product correspond to previous measurements by HPT rig with a larger contact surface [43]. The initial elastic part shows a slightly uneven increasing trend with a lower slope compared to the results in [43]. 3.3. Numerical model results The results were parametrized based on the hardening model as suggested by [32]. This hardening model describes the pseudoelasto-plastic behaviour seen in the HPT experiments using four parameters. This parametric model smoothly fits any data and provides a faster calculation time. Using these results as input to the boundary calculation predicted a too low coefficient of adhesion around 0.03 for the substance AZ. This is a result of the calculation predicting too low displacements in the ideal small point contact area in combination with the measured elastic part having an uneven slope. For the ideal contact geometry, the maximum calculated contact displacement is 4 l m while the average is about 1.7 l m. In reality, wear of the contact surfaces would change the true contact area and geometry of the specimen, resulting in different contact conditions and increase in surface displacements. The fact that the FASTIM algorithm was mainly used for larger contacts also introduces an error to the calculation. Using the results of HPT device for this boundary model is not reliable for such a small point contact compared to the HPT contact area and would need further investigation. Based on the previous MTM results of commercial TOR products [2], we can see that under the experimental conditions of the adhesion tests the boundary layer displacement is close to the frictional peak (as seen in Fig. 8). Based on this, the value for coefficient of adhesion is taken from the end of the elastic part of the measured curve. The results of the model are coefficient of adhesion values for the EHL regime of the base oil and coefficient of adhesion values for the boundary regime of the selected complete substances. The substance AZ is used for comparison with the commercial TOR product as it provides the most stable coefficient of adhesion from the three selected substances N, AO and AZ. The experimental results for TOR A and the substance AZ with an applied amount of 6 l l (from Fig. 7c) were selected for comparison with the model that predicts EHL and boundary coefficient of adhesion. This quantity shows a stable behaviour, which is the most representative of the HPT results. As seen in Fig. 9, the coefficient of adhesion of TOR A is between the predicted values of both the boundary and EHL regime. Since the predicted values are close together, it is evident that unless starvation occurs the substance should result in coeffiFig. 7. Adhesion tests with different applied amounts. Fig. 8. High pressure torsion tests of selected substances. D. Kvarda, S. Skurka, R. Galas et al. Engineering Science and Technology, an International Journal 35 (2022) 101100 7 cient of adhesion between 0.02 and 0.05. This starvation effect was most evident at the applied amount of 2 l l as seen in Fig. 7a. The coefficient of adhesion of the substance AZ initially drops to 0.05, suggesting that the hard particles of Al 2 O 3 are not able to interact between the contact surfaces. Assuming the film thickness of 360 nm, the roughness is about 200 nm and the particle size in order of micrometres, it might be the case that only small and fragmented particles are able to enter the contact. This is in contradiction with study [44], but the high hardness of contact surfaces could promote particle fragmentation and prevent the larger particles to be embedded to the surface. The oil starvation causes an increase in coefficient of adhesion and the smooth curve transitions to a rough progression caused by particle interaction. A stable value was reached around the coefficient of adhesion 0.2 and running the test for longer time would cause the particles to be depleted and coefficient of adhesion to increase back to dry conditions. The boundary prediction for substance AZ shows that the saturation occurs at the same values as the HPT results. The transitioning behaviour of starvation and subsequent rise to dry conditions is hard to predict by the used numerical model due to the complex interaction between particles and contacting surfaces. The surface conditions also play a key role in determining the lubrication regime. Studying the influence of surface parameters and the interaction between solid particles in the contact area is the next step in understanding the TOR substances. Developing a model to explain the starvation behaviour that leads to dry contact conditions would also help with determining the correct application dosages. 4. Conclusions A laboratory experimental device was used to study the properties and composition of oil-based top of rail lubricants. Adhesion tests were conducted to evaluate the effect of different solid particles in TOR composition. It was found that the friction modification particles have a dominant effect on the adhesion behaviour in base medium. The hardness of the particles seems to be the key factor in increasing the coefficient of adhesion. Particles of aluminium oxide were the only ones that could increase the coefficient of adhesion above 0.1 in combination with oil-based medium. Zinc oxide and copper sulfide with less than half of the hardness of Al 2 O 3 were unable to have a significant effect. The addition of solid lubricant managed to decrease the coefficient of adhesion by 30 % at maximum. Increasing the amount of solid lubricant did not yield any more reduction. Moreover, there is a limit to how much solid lubricant can be homogenously dispersed in the oil-based medium. Increasing the amount also changes the consistency to more paste-like, which can be of importance in the application of the substance. The tested custom substances showed resilience against overdosing which caused very low adhesion conditions in commercial TOR lubricants. This can prevent problems with traction and braking of a railway vehicle. However, such a behaviour might not be expected in real wheel/rail contact, where the contact geometry differs from the used laboratory device. For further validation, an experimental device with a larger contact area should be used. Moreover, in laboratory experiments the contact always runs on the same path every rotation of the specimen. The high sensitivity to the applied amount of commercial product can also be the result of making the substance cost effective in terms of its consumption. The results suggest that the developed compositions could be suitable for use in the field with added benefits of overdosing resilience and stable frictional behaviour at doses that would cause very low adhesion conditions for a commercial product. However, before application to the field, an investigation on the wear properties should be conducted. Higher doses can cause unwanted surface damage due to hard particles. Especially the initiation of rolling contact fatigue, which could be accelerated by the oil entrapment in cracks causing them to grow. Lastly, compatibility with application units should be confirmed. The particle content could cause abrasion of key parts of the application units. Such a scenario is unsuitable for long term use. An analysis of the lubrication regime based on the base oil properties and the substance shear behaviour measured by high pressure torsion was carried out. At the maximum application amount of 6 l l, the commercial TOR lubricant behaved in an interval between the predicted boundary and EHL regime. The prepared substance AZ appeared to have more EHL tendency after application. However, after about 400 s the coefficient of adhesion increased to the values predicted by boundary lubrication HPT tests. This suggests a more complex interaction where starvation of the oil promotes more solid particles and asperity interaction. Future studies will focus on the time-dependance of coefficient of adhesion that is caused by the product consumption from starvation of the base oil. The use of HPT results for such small point contacts does not seem to be reliable and a more thorough investigation needs to be carried out. This will involve using both a larger scale rolling-sliding contact and a smaller HPT contact area. This will provide understanding of the transfer of experimental data between various scales of laboratory devices and real wheel and rail contact. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The work was supported by the project LTACH19001 with financial support from the Ministry of Education, Youth and Sports of the Czech Republic. 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