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1 Bulletin of the JSME Mechanical Engineering Journal Vol.4, No.4, 2017 Study on modeling and numerical analysis for the prediction of wheel wear development Ariku YOSHIOKA*, Yoshiaki TERUMICHI**, Masahiro TSUJIE*** and Jun MATSUI**** * Department of Science and Technology, Graduate School of Sophia University 7-1 Kioicho, Chiyoda, Tokyo, , Japan ** Department of Engineering and Applied Sciences, Sophia University 7-1 Kioicho, Chiyoda, Tokyo, , Japan *** Railway Dynamics Division, Railway Technical Research Institute Kokubunji-shi, Tokyo, , Japan tsujie.masahiro.13@rtri.or.jp **** Dassault Systemes K.K Osaki, Shinagawa, Tokyo, , Japan Received: 27 February 2017; Revised: 24 May 2017; Accepted: 6 June 2017 Abstract The rights-of-way of urban railway systems contain many sharp curves. Since sharp curves can contribute to wheel and rail wear, the ability to predict the development of wheel wear is crucial to maintaining safe operation of such systems. Observation of wear development in practical railway systems is inefficient and time consuming. In order to efficiently predict wheel wear, numerical analysis using multi-body dynamics software, such as Simpack, is proposed. Contact pressure, slip ratio, and other necessary parameters are determined from Simpack s vehicle motion analysis. Wear depth is derived to create a worn wheel profile. The current wheel profile is updated using the wear profile, and is then adopted as the new wheel profile in Simpack. The rail vehicle modeled in our numerical analysis is based on a typical Japanese commuter rail vehicle. Wear depth is calculated based on the Archard wear theory. Wear development in the wheel/rail contact area is calculated, and nodes are replaced by calculated wear depth. Validity of the wear coefficient used in the simulation is discussed. The results of the numerical analysis are compared with experimental results to assess the amount of wear from the viewpoint of mechanical and tribological contact problems. Key words : Wheel, Profile prediction, Wear, MbD software, Rolling contact 1. Introduction In the dynamic behavior of railway vehicles, the contact condition between the wheel and the rail has a strong effect on the development of wheel wear, and this has become a topic of extensive investigation. It is generally known that the evolution of the profile shape of the wheel and rail due to wear strongly affects vehicle dynamics and running stability, leading to variations in performance in negotiating both curves and straight track, (Ignesti et al., 2012). In urban railway systems, which have numerous sharp curves, countermeasures for wear development are required in order to control wheel and rail wear. The ability to predict the development of wheel wear is crucial to maintaining safe operation of such systems. Since the observation of wear development in practical systems is inefficient and time consuming, various experimental and numerical approaches have been proposed (Pombo et al., 2010, Sun et al., 2011) as alternatives. For example, multi-body dynamics (MbD) software is a useful tool for analyzing vehicle dynamics that considers both car body motion and wheel/rail contact conditions. Numerical simulation software has been widely used in the analysis of running stability and body vibration (Gan et al., 2015), but a comparison of simulation predictions with real railway system results was not made (Tsujie et al., 2013). Paper No J-STAGE Advance Publication date: 16 June,

2 In the present study, a numerical analysis method is proposed for predicting wheel/rail wear profile by incorporating a wear calculation user routine into Simpack. As used in a previous study (Jina et al., 2011), Simpack is very efficient in its modeling and prediction of wear. The calculation flow of the proposed analysis is as follows: First, contact pressure and slip ratio are determined from vehicle motion analysis using Simpack. Next, using a program we developed independently, wear amount is calculated by substituting contact pressure and slip ratio into the user routine. The amount of wear calculated in this step is applied to the new wheel profiles, which are used as the new wheelset in Simpack This paper presents our numerical results. The amount of wear for the contact conditions is considered, and the validity of the proposed approach is discussed. The wear coefficient is experimentally investigated using wheel/rail rolling contact fatigue test equipment, and the mechanism of wear development is discussed from the viewpoint of mechanical and tribological contact problems. 2. Wear Prediction Model 2.1 Structure The calculation procedure of the model is shown in Fig. 1. The vehicle and track model is created using Simpack, and wheel/rail contact conditions are calculated for each section of track. The wear depth of the wheel is calculated under the contact conditions, which are determined in the wear calculation user routine. A new rail profile for each section of track is generated based on the wear depth of the wheel and is used to update the vehicle and track model. The change in the wheel profile for each section is calculated by repeating this procedure. Since the vehicle and track model is included in the MbD software, the software can be used to examine the influences of various parameters, such as the vehicle and track specifications, wheel and rail profiles, tie plate angle, track irregularity and wheel load variation. Utilizing the described calculation procedure, the wheel wear depth is calculated using not only the vehicle model but also a model of the wheel/rail rolling contact fatigue test equipment. Simpack Construction of Railway Model Vehicle Dynamics Analysis Wear Calculation User Routine Wheel/Rail Contact Analysis Update of Profiles Wear Calculation Results of Numerical Analysis Creation of Worn Profile on Wheel/Rail Contact Point of Wheel Fig. 1 Wheel wear development is predicted using Simpack and a wear calculation user routine. Dynamics analysis is performed using constructed models, with the results incorporated into the user routine to create wheel and rail wear profiles. These profiles are then incorporated into the Simpack model. z y Wheel Contact Point (1) Monitoring Point Contact (1) Point (2) P (1) P ) max max (2 Contact Force Rail (2) P( i, P ( i max ) Contact area ( Distribution of Contact Force ( C( C( C( Y C( cos( C( C( cos( 2.2 Creation of Worn Wheel Profiles Our wheel model is constructed as follows: The wheel profile has a total of 400 nodes (data points that can be set through Simpack) arranged at intervals of 0.4 mm. The nodes of the wheel profile are arranged in the lateral direction with spline interpolation of adjacent points. The process for reproducing a worn wheel profile is shown in Fig. 2. For each node, the wear amount and wear depth are calculated based on the law of wear, which is discussed in Section 2.4. A total of 400 nodes are updated using the calculated wear depth, and spline interpolation is carried out again. To update the wheel profile in Simpack, vehicle analysis with the worn wheel profile can be performed in this manner. 2

3 Nodes Movement Wheel Wear Depth Initial Profile Worn Profile Nodes of Wheel (400Nodes) Rail Fig. 2 Wheel profile and updating of the worn profile. From the flange top to the wheel tread, a total of 400 nodes are arranged at intervals of 0.4 mm. Nodes of the initial profile (blue) are moved by the length of wear depth and the wheel is updated to the worn profile (red). 2.3 Distribution of Contact Force Contact position and width of the wheel/rail contact are calculated by vehicle dynamics analysis, but detailed distribution of contact pressure results are not derived from Simpack; the distribution of pressure on a contact surface is calculated using the contact radius of the cross-sectional direction calculated based on the contact theory of Hertz. More than one contact point is considered to exist between the wheel and the rail in the vehicle analysis involving wheel wear. The maximum number of contact points that can be considered in Simpack is 10. Therefore, we consider 10 points arranged in order, starting from the negative direction (top of the flange) of an axis. The 400 observation points are arranged similarly. In our model, an axis parallel to a contact surface is denoted as (, and contact force is an elliptical distribution force with maximum force at the contact point. The maximum pressure P ( [N/m 2 ] is expressed as N( [N] based on the contact force between the wheel and the rail. ( is the angle between the Y-axis and the ( -axis, which is parallel to the contact surface. Considering the Y- axis coordinate, the width of the contact area is obtained as Eq. (1), and the maximum contact pressure is obtained as Eqs. (2) and (3) when the number of points is denoted as Q. max C( cos ( y( i, C( cos ( (ⅰ)i Q P Max 3N( ( 2 (ⅱ )i Q ( 0 P Max (1) (2) (3) where b ( [m] is the minor axis of the contact ellipse and C( is the Y-axis coordinate of the center of the contact point calculated by Simpack. Wheel Contact Point (1) Data Point Contact (1) Point (2) P (1) max P max (2) Contact Force Rail (2) Contact Point Between the Wheel and the Rail P( i, P ( i max ) Distribution of pressure on a contact surface Contact Area ( ( C( C( C( Y C( cos( C( C( cos( Fig. 3 Contact points between the wheel and the rail, and distribution of the contact forces. This figure shows that the wheel is in contact with the rail at two points. At each point, the distribution of the contact force is calculated based on the contact theory of Hertz. In this model, an axis parallel to a contact surface is denoted as, and a contact force is an elliptical distribution force that the maximum force at the contact point. 23

4 If y( i, is not in the range of Eq. (1), then the contact force is P( i, 0. The force distribution in the width direction of the contact area is determined by Eq. (4). P( i, P( Max 2 y( i, C( 1 ( ) b i 1 2 (4) 2.4 Law of Wear Adhesive wear is a wear mode caused by wheel/rail contact (Athukorala et al., 2015). A number of studies that have reproduced adhesive wear based on the law of wear have been performed under various conditions (Elkins and Eickhoff, 2011), (Kalousek, 1978). The wear prediction equation of Archard (Archard, 1953) and Ward (Ward, 2003) is a typical prediction equation applied to adhesive wear. The law of wear used in this model, which is based on the equation of Archard and Ward, is: k P( i, ( W ( i, H (5) where W( [m 3 ] and P( [N/m 2 ] are the wear depth and contact pressure, respectively, at each observation point, H [N/m 2 ] is the Vickers hardness of wheel material, k is the wear coefficient determined in Section 3, and ( [m] is the sliding distance per unit length grasped by the longitudinal slip rate and the lateral slip rate grasped through the Simpack analysis: 2 2 ( ( x ( y (6) Since the wear model considered in the present study considers macroscopic wear between the wheel and rail, the sliding/adherence area of the contact surface was not identified. 3. Wear Test Machine In this section, we describe the indoor wear test. This test was performed in order to determine the wear coefficient to be used in the numerical analysis to predict initial wear development of wheel. The wheel profile is compared to results derived from the numerical analysis described in Section Outline of the Wear Test Machine and Model Wear testing and prediction of wear development were performed using the wheel/rail rolling contact fatigue test equipment and model shown in Fig. 4. In these figures, the left-hand side is an overview of the test machine while the right-hand side is the Simpack model. The features of the test machine are as follows: The wheel and rail roller units can rotate independently and can generate slip between the wheel and rail. The diameter of wheel is 500 mm and its profile is flat. The profile of the rail roller is the JIS50kgN profile, which is that of a full-scale rail commonly used in Japan. In order to avoid the influence of gravity at the contact point, the wheel and rail units are set parallel to the ground. The numerical model is as follows: A virtual wear test machine model having the same profile and properties as the physical test machine is created in Simpack. The wear depth calculation explained in Section 2 is integrated into this model. As in the physical wear test machine, the profile of the wheel in the model is flat, and the profile of the rail is JIS50kgN. In order to reproduce a contact pressure of 800 MPa, a load of 5.4 kn, which is calculated using Hertzian theory, is applied at the wheel/rail contact point. As in the physical test machine, the acceleration of gravity acts in the longitudinal direction of the contact plane. 24

5 Top view Wheel Motor Wheel (Flat Profile) Rail Roller (JIS50kgN Profile) Rail Motor Simpack Model Fig. 4 Overview of the wear test machine and analytical model created in Simpack and composed of a wheel and rail roller. To avoid the influence of gravity at the contact point, the wheel and rail units are set parallel to the ground. The profile of the wheel, which has a 500 mm diameter, is flat. The rail, which has a 500 mm diameter roller, has the JIS50kgN profile. 3.2 Experimental Conditions of the Wear Test Only the longitudinal slip rate was used to derive the wear coefficient; the attack angle was not given in order to avoid the effect of lateral slip. The longitudinal slip rate was set to 0.5%, and the contact load was 800 MPa. The test was terminated after 200,000 rotations of the wheel, which is equal to a wheel travel distance of 200 km. The conditions of the wear test are shown in Table 1. Table 1 Radius Shape Velocity Contact Pressure Attack Angle Wheel 500 [mm] Flat 80 [kg/h] Rail 350 [mm] JIS50kgN [km/h] Wear Test Conditions 800 MPa Results of the Wear Test 1.0E E E E E Before -4.0E After -5.0E Wheel Profile [mm] 1.0E E E E E E E Wheel Profile [mm] Fig. 5 Experimental wheel profile and wear depth. On the left-hand side of this figure, the wheel profile before the test is indicated by the solid line, and that after the test is indicated by the dashed line. The right-hand side shows the wear depth. The maximum wear depth is approximately m, and the contact width is approximately m. The wear depth was determined by calculating the difference in the wheel profile before and after the test. The lefthand side of Fig. 5 shows the wheel profile before (dashed line) and after (solid line) the test. The calculated wear depth is shown on the right-hand side of Fig. 5. The wear depth reaches approximately m. The contact width is considered to be approximately m. The results of the wear test are input to the Archard wear prediction equation. 25

6 The wear coefficient k is calculated as follows: First, the wear area is calculated based on the results for the wear depth shown in Fig. 5. Next, the circumference of the test wheel is multiplied by the wear area to calculate the wear volume. The Vickers hardness of the wheel material (H [N/m 2 ]) is measured at the surface after this test, which is necessary to calculate the wear coefficient. The wear amount is determined by the calculated wear volume. The wear coefficient is then calculated by inputting 4 the wear amount into the Archard equation, which gives k In this study, the wheel rotates only 200,000 times (equivalent to 200 km of travel), producing only an initial wear state. Therefore, the derived wear coefficient represents the initial development of wheel wear. 4. Numerical Analysis Using the Wear Test Machine Model 4.1 Outline of the Model Analysis In order to examine the validity of the wear coefficient and the wear prediction model, experimental results are compared to the results derived from the wear model incorporated into Simpack. A virtual wear test machine model, with the same properties as the physical wear test machine, was constructed in Simpack. In our numerical analysis, the wheel was rotated 200,000 times, as was done in the physical experiment. The wheel was rotated 10,000 times for each iteration of the numerical analysis. The numerical analysis was repeated 20 times, and the profile was reproduced after 200,000 rotations. In order to compare the results of the experiment and the numerical analysis, the validity of the wear coefficient was examined. The results are presented below. 4.2 Outline of the Model Analysis 4 iterations 8 iterations 12 iterations 16 iterations 20 iterations Experimental 1.0E E E E E E E E Fig. 6 Results of wear development on wheel. Y=0 corresponds to the center of wheel. The dashed line indicates experimental result, and the solid line indicates analytical result. These results are indicated after four iterations, eight iterations, 12 iterations, 16 iterations, and 20 iterations. Wear depth [mm] The experimental and analytical results are shown in Fig. 6. In this section, we primarily discuss the wear depth. As shown in the figure, wheel profiles were determined and the wear depth was calculated after four, eight, 12, 16, and 20 iterations. The figure also shows the experimental results for the wheel profile after 200,000 rotations. The figure indicates that wear depth increases as the wheel profile is updated. Moreover, even if the rail profile is updated, no tendency for the contact point to move significantly is observed. The experimental and analytical results for the wear width are approximately the same, although the experimental wear depth is smaller. Based on these results in the range of initial wear (before 200,000 rotations), predictions of our numerical analysis are very close to the actual measured values. Further numerical analysis was performed to investigate how much the wear coefficient changed to derive results close to actual measurement values. 26

7 Additional numerical analyses were performed in which 80% and 90% of the value of the wear coefficient (k = ) are considered. The results are shown in Fig. 7. The results for 90% of the wear coefficient are closest to the experimental results. In other words, compared to the experimental results, the prediction model differs by less than 10%. Experimental k:100% k:90% k:80% 1.0E E E E E E E E Wear depth [mm] Fig. 7 Results of wheel wear development with 80 90% change in wear coefficient. The dashed line indicates experimental result, and the solid line indicates analytical result. Results of wear depth when wear coefficient is 90% (green) is the closest to actual measurement values. are indicated after four iterations, eight iterations, 12 iterations, 16 iterations, and 20 iterations Contact Force[N] k:100% k:90% k:80% Number of Iterations Fig. 8 Contact forces calculated by the model. This figure shows contact force fluctuation when the wear coefficients change from 100% (blue) to 90% (red) and 80% (black). It can say that even if wear coefficient change, contact force is approximately constant and the wear coefficient is dominant at these analysis. In order to compare results, the contact force for each analysis condition is shown in Fig. 8. Equation (5) shows that wear depth is linearly related to wear coefficient and contact force when slip rate is considered to be constant. Fig. 8 shows that contact force is approximately constant. In other words, contact force does not change with wheel profile. In this situation, the wear coefficient is dominant. The reason analytical results for the wear coefficient and wear depth are smaller than the corresponding experimental results is discussed in Section Discussion The analytical and experimental results for wear depth differ for the following reasons: The numerical analysis assumes perfectly dry conditions, whereas humidity is present in the experiment. The effects of wear debris at the contact point are not taken into consideration by the numerical analysis. The wear state shifts more quickly to mild-wear as a result of wear debris being deposited on the contact surface (Kikuchi et al. 1998). In our physical test machine, the wheel unit is worn repeatedly, so wear debris easily accumulates. The resultant shift to a mild-wear state causes an experimental wear depth that is smaller than the analytical wear depth. Since initial wear is the focus of this study, this difference does not significantly affect the validity of our analytical result. 27

8 5. Results Derived Using the Railway Model 5.1 Vehicle and Track Model In this section, a simple analysis is conducted using the model we constructed to predict initial wear of wheel profile. The results are presented below: Travel direction Direction Body Body Coordinates System (B1) Bogie Frame X (W1) Y y x z Z (W2) Wheelset Car Body (W3) (W4) Fig. 9 Analytical model of the vehicle in Simpack. This multi-body dynamics model consist of 1 car body (C), 2 bogie frames (B1, 2) and 4 wheelsets (W1 4). Each body is rigid and 6 degrees of freedom. This vehicle model simulates standard vehicles used in a Japanese commuter line. (C) (B2) Table 3 Properties of the Vehicle Length Table 2 Properties of the Vehicle Mass Wheelset 26,000 Distance of Two Bogies 12 Wheelbase 1.9 Mass [kg] Bogies 900 Car Body 1,296 Length [m] Car Body Length Car Body Width Car Body Height Curvature [m] Table 4 Cant [mm] Sharp Curve Moderate Curve Properties of the Track Gauge Widening [mm] Curve Length [m] Number of Wheel Rotations ,000 A simple analysis of initial wear development was conducted using the vehicle and track model shown above. A model simulating a typical Japanese commuter rail line vehicle was created using the parameters shown in Table 2 and Table 3. The vehicle travels at 54 km/h in the analysis. As shown in Table 4, the track model includes two different curves: a sharp curve (R = 300 m) and a moderate curve (R = 900 m). A modified arc wheel profile is adopted as the initial profile. The rail has a JIS50kgN profile; rail wear is not taken into consideration. R = 300 m is chosen to represent a sharp curve because, according to previous research, the wear coefficient changes significantly at that curvature, (Nishitani et al., 2015). 28

9 5.2 Analytical Results In Fig. 9, the wear depth on the outer wheel of the wheelset closest to the front of the vehicle (in terms of travel direction) is denoted as W1. To determine the wear profile for a curved track section, wear calculation was performed for a vehicle running over a continuously curved section of track. During each analysis, the wheel rotates 5,000 times over a continuously curved section, with a total per wheel weight per pass of approximately 0.02 megatons. The numerical analysis is repeated 10 times; the wheel profile is updated after each pass. The number of wheel rotations is 50,000. The total weight for all passes is 0.2 megatons per wheel, which we consider to be within the range of initial wear Results of Wheel Wear Depth Flange Top Center of the Wheel Wheel Tread 0.0E+000 Contact Points 5.0E E R=900m -5.0E E E E R=300m R900_Outside Moderate Curve R300_Outside Shape Curve E-02 Wheel Profile E E E E E E E Wear Depth [mm] Wheel Profile [mm] Fig. 10 Contact points and wear depth for the sharp and moderate curves. The black line in this figure shows the wheel profile. At the sharp curve (blue), the contact point of the wheel is closer to the flange top as compared to the moderate curve (red), and the wear depth is greater. The results of wear depth after 20 iterations are shown in Fig. 10. This figure shows that the contact point of the outer wheel is closer to the flange top for the sharp curve (R=300 m) as compared to the moderate curve (R=900 m). The wear depth for R=300 m is greater than that for R=900 m because the slip rate increases if the contact point is closer to the flange top Results of Wheel Wear Growth Wear depths for 10,000 rotation increments are shown in Fig. 11. For each increment, the wear width increases when the wheel profile is updated, while the width expansion for the moderate curve is larger than that for the sharp curve. For R=900 m, the wear depth increases gradually. For R=300 m, the width expansion is not so large and the wear depth growth is approximately constant. The relationship between the number of profile updates and the increase in wear depth is nonlinear. A graph of worn area of the wheel vs. number of wheel rotations for track curvatures of R=300 m and R=900 m is shown in Fig. 12. The worn area is calculated based on the wear depth and contact width shown in Fig. 11. As shown in Fig. 12, the worn area for R=300 m is larger than that for R=900 m, with the worn area increasing linearly for both curvatures. For R=900 m, the slower increase in the wear depth is considered to be caused by the increase in the wear width. 29

10 0.00E+00 0 R=300m R=900m 0.00E E-05 Wear Depth [mm] E E E-05 R=900m_10000 R=300m_10000 R=900m_20000 R=300m_ E E R=900m_30000 R=300m_30000 R=900m_40000 R=300m_40000 R=900m_50000 R=300m_ E E Wheel Profile E E E E E E Fig. 11 Numerical results for wear depth and wear development. This is an enlarged view of a part of Fig. 10. The black line is the wheel profile, and the solid and dashed colored lines are sharp curve and moderate curve results, respectively. The relationship between the number of profile updates and the increase in the wear depth is nonlinear Wheel Profile [mm] Worn Area [mm 2 ] R=300m R=900m Number of Wheel Rotations Fig. 12 Numerical results for worn area. The worn area means the total area of the changing profile in Fig. 11, which is calculated based on the wear depth and the contact width. The worn area for R=300 m (blue) is larger than that for R=900 m (red) and increases linearly. 5.3 Discussion Our proposed model can predict wear depth and wear-induced change in wheel profile based on wheel/rail contact. These worn wheel profiles are then incorporated into the Simpack simulation model. The wear depth and wear profile are obtained by calculating the wheel/rail contact conditions using the worn wheel profiles. As shown in Fig. 11, the relationship between the number of wheel profile updates and the wear depth is nonlinear, and the worn area changes depending on the curvature of the curved section of track. Thus, the advantage of the proposed model, which uses updated wheel profiles, is verified. 6. Conclusion We constructed an initial-wear wheel profile prediction model by incorporating a wear calculation program into Simpack. A physical test machine was used to determine validity of the model s wear coefficient at the initial wear state. By comparing the predictions of our analytical model with experimental results, wheel wear development prediction by 10 2

11 our analytical model was shown to be valid. Changes in wheel profile were compared for two sections of curved track having different radii of curvature, with the following results: A wear test was conducted using wheel/rail rolling contact fatigue test equipment under conditions simulating the contact condition between the wheel and the rail. We applied the wear test results to the Archard wear prediction equation and determined the initial wear coefficient to be A wear profile prediction model was constructed using Simpack, a typical MbD software package. We constructed a user routine to predict worn wheel profiles, and then incorporated these worn wheel profiles into Simpack. Validity of the model s wear coefficient was determined by comparison with experimental results. The wear depth was found to be smaller in the experimental results because of the influence of wear debris, but the predicted wear coefficient value was close to the experimentally determined value. Simple analyses were conducted using the wear profile prediction model developed in the present study. The results obtained through these analyses suggest that worn wheel profiles change with the radius of curvature of the track. The relationship between the number of wheel profile updates and wear depth is nonlinear. In addition, the worn area changes with the curvature of the track. Thus, the advantage of the proposed model, which uses updated wheel profiles, is verified. References Archard, J.F., Contact and rubbing of flat surfaces, J. Applied Science, Vol. 24 (1953), pp Athukorala, C. A., Wickramasinghe, I. U. and De Pellegrin, V. D., Effect of Different Surface Profile on Wear of Rail Steel (AS1085.1) used in Australian heavy-haul railways, International Journal of Materials Engineering Innovation (2015), Vol. 6 Issue 4, DOI : /IJMATEI Elkins, J.A. and Eickhoff, B.M., Advances in non-linear wheel-rail force prediction methods and their validation, Wear 271 (2011), pp Gan, F., Dai, H., Gao, H. and Chi, M., Wheel-rail wear progression of high speed train with type S1002CN wheel treads, Wear (2015), pp Ignesti, M., Malvezzi, M., Marini, L., Meli, E. and Rindi, A., Development of a wear model for the prediction of wheel and rail profile evolution in railway systems, Wear (2012), pp Innocenti, A., Marini, L., Meli, E., Pallini, G. and Rindi, A., A new wear model for the analysis of wheel and rail profile evolution on complex railway networks, Railways (2014), Paper 257. Jina, Y., Ishida, M. and Namura A., Experimental simulation and prediction of wear of wheel flange and rail gauge corner, Wear 271 (2011), pp Kalousek, J. and Bethune, A.E., Rail wear under heavy traffic conditions, STP644 (1978), pp Kikuchi, K., Kamiya, O., Saito, Y., and Kumagai, K., Running-in behavior of repeated dry wear on metals, Journal of the society of materials engineering for resources of Japan, Vol. 11, No. 2 (1998), pp Nishitani, K., Terumichi, Y., Mori, H., Sato, Y., Takahashi, K. and Oka, Y., Experimental research on rail/wheel wear, Proceeding of the international symposium on speed-up and sustainable technology for railway and maglev systems (2015), Pombo, J., Ambrosio, J., Pereira, M., Lewis, R., Dwyer-Joyce, R.S., Ariaudo, C. and Kuka, N., A railway wheel wear prediction tool based on a multibody software, Journal of Theoretical and Applied Mechanics, Vol. 48 (2010), pp Tsujie, M., Mitoma, M. and Terumichi, Y., A Study on the Developing of a Model for Predicting Worn Profile of Rail by Use of Multi-Body Dynamics Software, Journal of the Japan Society of Mechanical Engineers, Vol.79, No.806 (2013), pp (in Japanese). Ward, A., Lewis, R. and Dwyer-Joyce, R.S., Incorporating a railway wheel wear model into multibody simulation of wheelset dynamics, Proceedings of the 29 th Leeds-Lyon symposium on tribology (2003), Vol. 41, pp