Wheel wear dynamics in sharp curves: Insights from T-gamma indicator study on heavy-haul railways

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A.P. Pacheco, M. V. Lopes, A. A. Santos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6172977/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The dynamic interaction between railway wheels and rails is critical for ensuring maintenance and safety in railway operations. Accurate assessment of wheel wear is essential, particularly in sharp curves where wear is more pronounced. This study focuses on using the T-gamma (Tγ) indicator to quantify wheel wear in sharp curves. Despite its usefulness, Tγ alone does not fully capture the complexities of material removal and contact dynamics, making it insufficient as a sole index for optimizing wheel profiles. This research evaluates a meter gauge heavy haul vehicle from a Brazilian railway. Comprehensive multibody simulations were conducted on various sharp curves to investigate the relationship between Tγ, the maximum penetration under varying speeds, and the non-compensated lateral accelerations (Anc). The findings indicate that using the total Tγ, which includes both the Tγ values from the tread and the flange, is more effective for analyzing wear depth than examining the Tγ values individually for the tread and flange. The results also show the high influence of Anc on flange wear depth. Besides, a strong relationship between tread wear depth and Anc was found, except for very sharp and very wide curves, which showed to have low influence of Anc. By focusing on sharp curves, the study aims to deepen the understanding of wheel-rail wear dynamics in such challenging conditions and to provide valuable insights for improving maintenance strategies. Wear number Wear volume Wear modeling Multibody dynamic simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 INTRODUCTION Increasing axle loads and speeds results in progressive wear between wheels and rails, altering the profiles of the original wheels and rails [ 1 ]. The performance of rail vehicles and the resulting maintenance costs are both affected by this type of wear [ 2 ]. The high acquisition and maintenance cost of wheels make them significative on overall maintenance costs [ 3 ]. Therefore, understanding the wear mechanisms of components in contact and predicting their useful lives are of great interest. In railway systems, curved track sections represent a critical aspect, particularly due to their significant impact on dynamic responses, which are often more degraded compared to straight track sections [ 4 ]. Railroads with sharp curves can lead to serious challenges to wear and train running safety. Frequently, sharp curves can cause severe wheel flange wear [ 5 ]. Due to the change in wheel-rail contact in sharp curves, the risk of severe or catastrophic wear increases, so the wagon derailment risk [ 6 ]. According to Pacheco et al [ 7 ], Brazilian heavy-haul freight wagons in sharp curves, as low as 300 m radius, exhibit a high level of wheel wear due to higher slip speeds on the flange. In a broader evaluation, Pacheco, Lopes and Santos [ 8 ] utilized multibody dynamic simulations to analyze a meter gauge wagon under various conditions such as different curves, speeds, and superelevations. Their findings suggest that the curvature radius significantly impacts both the wear area and depth on the wheels. As expected, larger curve radii result in reduced effects on wheel wear. Bai et al. [ 9 ] employed a wheel/rail rolling contact test rig to perform tests across a wide spectrum of operational conditions, spanning from mild to harsh environments. The focus was on assessing the wear resistance and the consequent failure mechanisms in rails. Their findings reveal that high axle loads and small curve radii significantly impact the deterioration of rail materials. As axle loads increase, the wear rate rises, while decreasing with larger curve radii. Ignesti et al. [ 10 ] present a model specifically developed to evaluate wheel and rail wear, as well as the evolution of wheel and rail profiles. The model consists of two mutually interacting components: a vehicle model for dynamic analysis and a wear estimation model. The results indicate that sharp curves increase wear in the flange region, which may reduce wheel lifespan. According to Zhang et al. [ 11 ], for every 1 mm of wear on the flange, up to 4.2 mm must be removed from the wheel diameter during reprofiling. Currently, the main research approach on wheel wear comprises using multibody dynamics simulation (MBS) with experimentally derived material loss functions (referred to as wear models), to estimate the loss of wheel material [ 12 , 13 , 14 ]. One of the most common strategies is to employ advanced wheel-rail contact models in multibody codes to analyze vehicle behavior and wheel-rail wear [ 6 ]. Meanwhile, the Archard wear equation, which posits that wear is directly proportional to normal force and sliding distance, and inversely proportional to material hardness, continue to be widely utilized in wear studies [ 3 , 7 , 15 , 16 ]. This study aims to get a deeper understanding of the prevalent wear issues occurring on sharp curves along the Brazilian rail network. It adopts the methodology outlined in References [ 7 , 8 ] applied to a metric-gauge heavy-haul railway in Brazil. The approach consists on using a computational tool based on multibody simulation to replicate the dynamic performance of railway vehicles and trace the evolution of wheel profile wear over the distance traveled. The correlation between curve radius and worn material is explored through short-term simulations using new wheel profiles. Section 2 provides an overview of the research methodology, detailing multibody simulations and wear calculations. Section 3 delves into the results, while Section 4 presents the conclusions drawn from this work. 2 METHODS The process of comparing curve radius and wear volume began with the development of multibody dynamic simulations with a wagon widely used on heavy haul railways, with Ride Control bogies and metric gauge. The simulation output is the wear depth. Multibody dynamics software is widely used to study vehicle/track interaction. Among commercial software, SIMPACK® is one of the most used due to its flexibility and scope and will be the one employed in this work. Dynamic simulations As mentioned before, the metric gauge GDE-Ride Control wagon was selected due to its widespread use, particularly in Brazilian railways. The simulation model and parameter values are referred to in previous works [ 7 , 8 , 17 , 18 , 19 ]. The Ride Control is a three-piece bogie. The axle load of the GDE is 27.5 tons. The wagon model is shown in Fig. 1 . The rails were designated as components in the inertial reference frame with a cant of 1:40. New rail and wheel profiles were used and are presented in Fig. 2 . The wheel-rail contact forces were calculated using the Semi-Hertzian SIMPACK® Discrete Elastic Contact method. It computes normal and tangential forces by considering the actual shape of the contact patch. The procedure for determining tangential forces resembles that of FASTSIM [ 7 , 20 ]. The primary suspension links the wheelset to the side frame pedestal via a rubber PAD adapter [ 21 ]. In the multibody model, this component was represented by three connecting elements with vertical, lateral, and longitudinal stiffness and damping. These three elements are laterally aligned, with the central one exhibiting non-linear characteristics in both longitudinal and lateral stiffness. Another notable aspect of this bogie is its secondary suspension. Apart from the spring system, it has a constant damping wedge. The simulation of dry friction between contacting surfaces involved the use of discrete contact elements. Furthermore, no constant contact roller side bearing is utilized in this bogie. A spring-based contact model was employed for the roller side bearing support. In all simulations, the wagon speed profile is kept essentially constant along the track. So, the draft gear was not modeled. Wear analysis The wear number ( Tγ ) is determined by calculating the energy dissipation within the contact patch [ 19 , 22 ]. We use the complete form of Tγ (Eq. 1 ), i.e., considering the spin part in our analysis. $$\:T\gamma\:=\left|{F}_{x}{v}_{x}\right|+\left|{F}_{y}{v}_{y}\right|+\left|{M}_{z}{\phi\:}_{z}\right|$$ 1 F x , F y , and M z represent the longitudinal, lateral, and rotational forces acting on the contact area, while v x , v y , and φ z denote the longitudinal, lateral, and rotational creepage, respectively. Typically, wheel wear simulation models comprise three main components: a vehicle dynamics simulation, a wear model that correlates the dynamics simulation outcomes with the material degradation of the wheel surface, and a strategy for updating the wheel profile [ 3 , 22 ]. The SIMPACK® simulation environment enables the calculation of wheel wear, providing access to both the depth and profile of the wear on the wheel [ 3 , 7 , 8 ]. Wear calculations were conducted using the Archard method, a widely adopted approach for this purpose [ 23 ]. This method relates the wear volume, denoted as V [m³], to the sliding distance, represented by Δs [m], and the normal force, designated as N [N], while inversely correlating it with the material hardness, denoted as H [Pa] (Eq. 2 ). $$\:V=\frac{N.\varDelta\:s}{H}.k$$ 2 The wear coefficient, denoted by k , varies based on the contact pressure and slip velocity and is usually determined from experimental maps [ 7 , 25 , 26 ]. The map adopted in this work is the same used by Pacheco et al. [ 7 ]. Design of experiments The model developed for the wagon was subjected to the same route at three different speeds, generating negative, neutral, and positive non-compensated accelerations (when possible), computed according to Eq. 3 . $$\:Anc=\frac{v²}{R}-\frac{H}{G}g\:\:\:\:\:\:\:\left[m/s²\right]$$ 3 ν: speed [m/s] R: curve radius [m] g: acceleration of gravity [m/s²] H: superelevation [m] G: gauge [m] Based on the ABNT 16810 standard [ 27 ], the non-compensated accelerations (Anc) were constrained, with the theoretical values presented in Table 1 . The minimum curve radius considered in this study is 200 m, which represents the narrowest curve in the Brazilian heavy-haul railway under study. Table 1 Description of the simulations, each simulation is composed of the combination of curve radius and superelevation for three different speeds (R-curve radius, H-superelevation, G – gauge, V- speed, Anc –non-compensated acceleration). Track R V max H ⁄ G V 1 A nc1 V 2 A nc2 V 3 A nc3 [m] [km/h] [mm/m] [km/h] [m/s²] [km/h] [m/s²] [km/h] [m/s²] 1 200 67 120 46 -0,36 55 -0,01 67 0,54 2 275 72 90 44 -0,35 56 0,00 72 0,55 3 350 75 70 40 -0,34 56 0,00 75 0,56 4 425 80 60 38 -0,33 57 0,00 80 0,57 5 500 83 50 33 -0,32 56 -0,01 83 0,57 6 200 55 60 26 -0,33 39 0,00 55 0,57 7 275 60 45 20 -0,32 39 -0,01 60 0,58 8 350 65 35 24 -0,22 39 -0,01 65 0,58 9 425 70 30 21 -0,22 40 0,00 70 0,58 10 500 73 25 20 -0,18 39 -0,01 73 0,58 11 200 39 0 20 0,15 30 0,35 39 0,59 12 275 46 0 20 0,11 32 0,29 46 0,59 13 350 52 0 20 0,09 35 0,27 52 0,60 14 425 57 0 20 0,07 38 0,26 57 0,59 15 500 62 0 20 0,06 41 0,26 62 0,59 The reference track is composed of a tangent section (100 m), an entry transition curve (160 m) defined as a linear clothoid equation, a complete left turn (200 m long), an exit curve transition (160 m), followed by the same sequence for the opposite side and a final tangent section (100 m). The differences between the tracks remain in the curve radius and superelevation. The wear depth is recorded for the right wheel of the first wheelset and totaled over the entire length of each curve. In this investigation, the wear depth is associated with the tread and flange regions, as defined by AAR M-107 [ 28 ]. The transition between the tread and the flange area starts at -23.7 mm from the tape line (Fig. 3 ). The tape line represents the measurement position from the inner face of the wheel, where the radius is determined; for this study, this value is 70 mm. 3 RESULTS AND DISCUSSIONS The results obtained from the methodology outlined in section 2 are presented in this section. Figure 4 illustrates the wear depth on the flange and tread for the simulated scenarios. A strong relationship can be observed between Tγ and wear with the curve radius. As the curve radius decreases the Tγ and wear depth increases. Additionally, it's noticeable that the increase in Tγ becomes more pronounced as the radius decreases. Between 500 and 425 meters, the variance is less than 50 N, whereas between 275 and 200 meters, the difference exceeds 700 N. The same behavior is observed for the wear depth in the tread and flange. For the tread (Fig. 4 a), there is a strong relationship between its wear depth and Anc, except for the sharpest and widest curves, which have low Anc influence. An increase in the Anc decreases the tread wear depth. For the flange (Fig. 4 b), except for the 500 and 475 m radius curves, the data seem to present a positive correlation between flange wear depth and Anc, i.e. an increase in the Anc increases the flange wear depth. Additionally, in Fig. 4 b, one specific point in the 200-meter radius curve exhibits significantly less wear than the others. This outcome is observed when 0 mm superelevation is adopted and the Anc approaches zero, indicating no contact with the outer wheel flange during the curve. For other curves where wear differences are also noted, the same happens when Anc is less than zero. As showed by Pacheco et al [ 7 ], positive Anc values indicate lateral displacement of the wheelset towards the field side. In sharp curves, this can lead to flange contact, increasing flange forces and, consequently, increasing flange wear. Figure 5 presents the wear depth results considering the Tγ values individually for the tread and flange. Tγ on the tread also demonstrates an inverse relationship with the curve radius, for curves ranging from 275 to 500 m, the Tγ values vary between 20 N and 60 N (Fig. 5 a). However, for the sharpest curve, there's an increase of about 100 N in the Tγ value. Furthermore, the Tγ on the tread presents a negative correlation with Anc, except for the 200 m curve, where a positive correlation is seen. A weak correlation exists between Tγ and tread wear depth; that is the reason to the presence of data points with the same Tγ value but with different depth values. The results of Tγ on tread for flange wear depth (Fig. 5 b) shows two inverse correlations for 200 and 275 m curves. The first correlation is positive, while the second is negative, i.e., for the 200 m radius curve, wear increases with Tγ, whereas for the 250 m radius curve, wear decreases with Tγ. There is no correlation observed for the other curves, indicating that Tγ on the tread is not a good parameter to evaluate flange wear depth. The results show that the wear depth on the tread decreases with an increase in Tγ on the flange for curves longer than 200 meters (Fig. 5 c). For the 200 m radius curve, no correlation is observed. For the flange wear depth (Fig. 5 b) a positive correlation with the Tγ on the flange is seen as expected. A similar observation can be made about the correlation between Tγ on the flange and Anc. The findings in Figs. 4 and 5 indicate that the total Tγ, which includes both the Tγ values from the tread and the flange, is more effective for analyzing wear depth compared to examining the Tγ values individually for the tread and flange. Figure 6 shows the wear depth on the tread and the flange results for the inner wheel. The correlation between Tγ and curve radius is positive, as expected. On the sharpest curves (Fig. 6 a), 200 and 275 m in radius, Tγ is negatively correlated with Anc, while on larger curves, this correlation is positive. Besides, the radius is negatively correlated with the wear depth on the tread. However, no correlation between the wear depth on the tread and the Tγ was observed. An analysis of the wear depth on the flange (Fig. 6 b) reveals a positive correlation with the Anc. Further, the correlation between Tγ and wear depth is negative for the sharpest curves (200 and 275 m radius). Since the inner wheel does not contact the flange, the outcomes for individual Tγ values on the tread exhibit identical behavior to the overall Tγ. 4 CONCLUSIONS This article explores how Tγ relates to maximum wear penetration on sharp curves. The study utilized multibody dynamic simulations across different sharp curves, varying speeds, and non-compensated lateral accelerations (Anc). The simulations involved a meter gauge heavy haul vehicle used in a Brazilian railway. Comparative results obtained from the dynamic simulations simulation show that the curve's radius significantly impacts wear depth on both the tread and the flange. Sharper curve radii lead to more pronounced effects on wheel wear, as expected. This relationship is also evident in the correlation between curve radius and Tγ. The results for the outer wheel suggest that the combined Tγ, incorporating values from both the tread and flange, is more effective to assess the wear depth than separately examining tread and flange Tγ values. The findings highlight the significant Anc impact on flange wear depth. Additionally, a strong correlation between tread wear depth and Anc was found, except for the sharpest and widest curves, where Anc's influence is minimal. For the inner wheel no correlation between the wear depth on the tread and the Tγ is observed. However, the wear depth on the flange shows a positive correlation with the Anc. Additionally, there is a negative correlation between Tγ and wear depth for the sharpest curves (200 and 275 m radius). By focusing on sharp curves, this study contributed to deepening the understanding of wheel-rail wear dynamics in such challenging conditions and provide valuable insights for improving maintenance strategies and enhancing railway safety.. Declarations Author Contribution P.A.P.P.: Conceptualization, Methodology, Software, Writing - Original Draft, Investigation. M.V.L.: Conceptualization, Data curation, Visualization, Review & Editing. A.A.S.: Conceptualization, Writing - Review & Editing, Supervision. Acknowledgement The authors wish to express their acknowledgment to Vale S.A. for funding this study and providing technical support and to CNPq , which funded partially this project. References Lewis, R., Dwyer-Joyce, R. S., Olofsson, U., Pombo, J., Ambrósio, J., Pereira, M., Ariaudo, C., Kuka, N.: Mapping railway wheel material wear mechanisms and transitions. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 224 (2010), 125–137. DOI: https://doi.org/10.1243/09544097JRRT328 Almeida, L. P. F., Falqueto, L. E., Goldenstein, H., and Scandiana, A. C.: Study of Sliding Wear of the Wheel Flange-Rail Gauge Corner Contact Conditions: Comparative Between Cast and Forged Steel Wheel Materials. Wear, 432 (2019). DOI: https://doi.org/10.1016/j.wear.2019.05.009 Pacheco, P. A. d. P., Endlich, C. S., Vieira, K. L. S., Reis, T., Santos, G. F. M. d., and Júnior, A. A. d. S.: Optimization of Heavy Haul Railway Wheel Profile Based on Rolling Contact Fatigue and Wear Performance. Wear, 522 (2023). DOI: https://doi.org/10.1016/j.wear.2023.204704 Pan, L., Xu, L., Chen, X., and Zhu, Z.: Curved Ballasted Track–Vehicle Dynamic Interaction: Effects of Curve Radius and Track Structural Nonlinearity. J. Comput. Nonlinear Dynam., 16 (2021). DOI: https://doi.org/10.1115/1.4050953 Lai, J., Chen, Y., Liao, T., Zheng, Z., Xu, J., Chen, R., and Wang, P.: Study on Train Running Safety in Railway Switches and Sharp Curves Considering Wheel Wear Evolution. Vehicle System Dynamics (2024). DOI: 10.1080/00423114.2024.2319277 Salehi, S., Farrahi, G., and Sohrabpour, S.: Dynamic Behavior of Worn Wheels in a Track Containing Several Sharp Curves Based on Simulation. Scientia Iranica B, 26(2019), 2854–2864. DOI: 10.24200/sci.2018.50749.1849 Pacheco, P. A. P., Magelli, M., Lopes, M. V., Correa, P. A., Zampieri, N., Bosso, N., and Santos, A. A.: The Effectiveness of Different Wear Indicators in Quantifying Wear on Railway Wheels of Freight Wagons. Railway Engineering Science (2024). DOI: 10.1007/s40534-024-00334-8 Pacheco, P., Lopes, M., and Santos, A.: Influência da Aceleração Lateral Não Compensada no Desgaste de Rodas Ferroviárias. VII Simpósio de Engenharia Ferroviária (2024). DOI: 10.29327/vii- simposio-de-engenharia-ferroviaria-410736.807262 Bai, W., Zhou, L., Wang, P., Hu, Y., Wang, W., Ding, H., Han, Z., Xu, X., and Zhu, M.: Damage Behavior of Heavy-Haul Rail Steels Used from the Mild Conditions to Harsh Conditions. Wear, 496 (2022). DOI: https://doi.org/10.1016/j.wear.2022.204290 Ignesti, M., Marini, L., Meli, E., and Rindi, A.: Development of a Model for the Prediction of Wheel and Rail Wear in the Railway Field. J. Comput. Nonlinear Dynam., 7 (2012). DOI: https://doi.org/10.1115/1.4006732 Zhang, H., Wei, X., Guan, Q., and Zhang, W.: Joint Maintenance Strategy Optimization for Railway Bogie Wheelset. Applied Sciences, 12(2022). DOI: https://doi.org/10.3390/app12146934 Ye, Y., Sun, Y., Shi, D., Peng, B., and Hecht, M.: A Wheel Wear Prediction Model of Non-Hertzian Wheel-Rail Contact Considering Wheelset Yaw: Comparison Between Simulated and Field Test Results. Wear (2021). DOI: https://doi.org/10.1016/j.wear.2021.203715 Wu, Q., Bernal, E., Spiryagin, M., Krishna, V., Ding, H., Stichel, S., and Cole, C.: Heavy Haul Rail/Wheel Wear and RCF Assessments Using 3D Train Models and a New Wear Map. Wear, 538 (2024). DOI: https://doi.org/10.1016/j.wear.2023.205226 Vicente, F. S., and Guillamón, M.: Use of the Fatigue Index to Study Rolling Contact Wear. Wear, 436 (2019). DOI: https://doi.org/10.1016/j.wear.2019.203036 Hardwick, C., Lewis, R., and Eadie, D.: Wheel and Rail Wear—Understanding the Effects of Water and Grease. Wear, 314 (2014), pp. 198–204. DOI: https://doi.org/10.1016/j.wear.2013.11.020 Archard, J.: Contact and Rubbing of Flat Surfaces. J. Appl. Phys., 24 (1953), 981–988. DOI: https://doi.org/10.1063/1.1721448 Pacheco, P., Lopes, M., Correa, P., and Santos, A.: Influence of Primary Suspension Parameters on the Wear Behaviour of Heavy-Haul Railway Wheels Using Multibody Simulation. Proc. of the International Conference on Electrical, Computer, Communications and Mechatronics Engineering (2023), Tenerife. Pacheco, P., Reis, T., Ramos, P., Santos, G. d., and Santos, A.: Wear and Fatigue-Oriented Wheel Profile Optimized for Heavy Haul. VI Simpósio de Engenharia Ferroviária (2023), Campinas. DOI: 10.17648/sef-2023-165737 Ramos, P., Correa, P., Texeira, L., Kurka, P., and Santos, A.: Dynamic Effect of Hollow-Worn Wheels for Freight Rail Vehicles in a Consist. Proceedings of the Fifth International Conference on Railway Technology: Research, Development and Maintenance (2022), 22–25 August 2022. SIMPACK: About Rail-Wheel Pairs. Simpack User Assistance (2022), Dassault Systemes Simula Corp. Lima, E. A., Baruffaldi, L. B., Manetti, J. L. B., Martins, T. S., and Santos, A. A.: Effect of Truck Shear Pads on the Dynamic Behaviour of Heavy Haul Railway Cars. Vehicle System Dynamics, 60(2022), 1188–1208. DOI: https://doi.org/10.1080/00423114.2020.1858120 Rovira, A., Roda, M. B., Marshall, H., Brunskill, H., and Lewis, R.: Experimental and Numerical Modelling of Wheel–Rail Contact and Wear. Wear, 271 (2011), pp. 911–924. DOI: https://doi.org/10.1016/j.wear.2011.03.024 Luo, R., Liu, B., and Qu, S.: A Fast Simulation Algorithm for the Wheel Profile Wear of High-Speed Trains Considering Stochastic Parameters. Wear, 480–481 (2021). DOI: https://doi.org/10.1016/j.wear.2021.203942 Liu, B., Bruni, S., and Lewis, R.: Numerical Calculation of Wear in Rolling Contact Based on the Archard Equation: Effect of Contact Parameters and Consideration of Uncertainties. Wear, 490 (2022). DOI: https://doi.org/10.1016/j.wear.2021.204188 Jendel, T.: Prediction of Wheel Profile Wear—Comparisons with Field Measurements. Wear 253 (2002), pp. 89–99. DOI: https://doi.org/10.1016/S0043-1648(02)00087-X Lewis, R., and Olofsson, U.: Mapping Rail Wear Regimes and Transitions. Wear, 257 (2004), pp. 721–729. DOI: https://doi.org/10.1016/j.wear.2004.03.019 ABNT: NBR 16810: Via Férrea - Superelevação em Curvas. ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS (2019), Rio de Janeiro. AAR: WHEELS, CARBON STEEL Specification M-107/M-208. AAR Manual of Standards and Recommended Practices (2011). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6172977","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":435731171,"identity":"08aad398-a438-4f76-87ca-6c0a190304d6","order_by":0,"name":"P. A.P. Pacheco","email":"data:image/png;base64,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","orcid":"","institution":"Federal Institute of the Southeast of MG","correspondingAuthor":true,"prefix":"","firstName":"P.","middleName":"A.P.","lastName":"Pacheco","suffix":""},{"id":435731172,"identity":"3b863a92-5bdb-491a-9da3-31f0a2aabf91","order_by":1,"name":"M. V. Lopes","email":"","orcid":"","institution":"University of Campinas","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"V.","lastName":"Lopes","suffix":""},{"id":435731173,"identity":"381f5038-e730-4322-9cca-2e10b20b21fc","order_by":2,"name":"A. A. Santos","email":"","orcid":"","institution":"University of Campinas","correspondingAuthor":false,"prefix":"","firstName":"A.","middleName":"A.","lastName":"Santos","suffix":""}],"badges":[],"createdAt":"2025-03-06 18:53:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6172977/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6172977/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79834901,"identity":"2278d1fe-b6ce-4bc7-ba3a-3b8148863172","added_by":"auto","created_at":"2025-04-03 11:13:15","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":301813,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eGDE-Ride Control wagon modeled in SIMPACK® multibody simulation software, on the right the three-piece bogie is highlighted.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/3b3ace6584a89298290a6b59.png"},{"id":79834903,"identity":"949dfa33-04d9-4fbb-8a41-ceae94c632ff","added_by":"auto","created_at":"2025-04-03 11:13:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":562623,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eWheel and Rail profiles with the contact patch.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/9f381981beaf1ee931469387.png"},{"id":79834906,"identity":"95df47f2-ce2f-4845-8e7d-0d364359ff1c","added_by":"auto","created_at":"2025-04-03 11:13:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":720562,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eFlange and tread regions for the wheel profile [7].\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/d67965ba40beca1c82c63503.png"},{"id":79834904,"identity":"dd1d7e89-198b-470e-b3e2-61ad2445de34","added_by":"auto","created_at":"2025-04-03 11:13:15","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1244725,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eOuter wheel wear depth by wear number and Anc: (a) on the tread; (b) on the flange.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/ae8dd442b0ab28142173bdee.png"},{"id":79834907,"identity":"03563f4d-68d4-48fc-9c71-cfedf55246e8","added_by":"auto","created_at":"2025-04-03 11:13:15","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":2675415,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eOuter wheel results: (a) tread wear depth by Tγ on tread; (b) flange wear depth by Tγ on tread; (c) tread wear depth by Tγ on flange; (d) flange wear depth by Tγ on flange.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/1adfead5e2bc7e77774d3df4.png"},{"id":79834911,"identity":"9f18ca42-dfd4-4bcb-8143-3d6b513b170b","added_by":"auto","created_at":"2025-04-03 11:13:16","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":2638097,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eInner wheel results: (a) tread wear depth by Tγ; (b) flange wear depth by Tγ; (c) tread wear depth by Tγ on tread; (d) flange wear depth by Tγ on tread.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/d70fd0f130dcdf54d9dc429e.png"},{"id":86143830,"identity":"7042cb21-759b-4edd-b7b7-1d51440ab57c","added_by":"auto","created_at":"2025-07-07 08:47:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8653262,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6172977/v1/17894dea-a280-48e1-bdd0-6fc06abedfbe.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Wheel wear dynamics in sharp curves: Insights from T-gamma indicator study on heavy-haul railways","fulltext":[{"header":"1 INTRODUCTION","content":"\u003cp\u003eIncreasing axle loads and speeds results in progressive wear between wheels and rails, altering the profiles of the original wheels and rails [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The performance of rail vehicles and the resulting maintenance costs are both affected by this type of wear [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The high acquisition and maintenance cost of wheels make them significative on overall maintenance costs [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Therefore, understanding the wear mechanisms of components in contact and predicting their useful lives are of great interest.\u003c/p\u003e \u003cp\u003eIn railway systems, curved track sections represent a critical aspect, particularly due to their significant impact on dynamic responses, which are often more degraded compared to straight track sections [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Railroads with sharp curves can lead to serious challenges to wear and train running safety. Frequently, sharp curves can cause severe wheel flange wear [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Due to the change in wheel-rail contact in sharp curves, the risk of severe or catastrophic wear increases, so the wagon derailment risk [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAccording to Pacheco et al [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], Brazilian heavy-haul freight wagons in sharp curves, as low as 300 m radius, exhibit a high level of wheel wear due to higher slip speeds on the flange. In a broader evaluation, Pacheco, Lopes and Santos [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] utilized multibody dynamic simulations to analyze a meter gauge wagon under various conditions such as different curves, speeds, and superelevations. Their findings suggest that the curvature radius significantly impacts both the wear area and depth on the wheels. As expected, larger curve radii result in reduced effects on wheel wear. Bai et al. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] employed a wheel/rail rolling contact test rig to perform tests across a wide spectrum of operational conditions, spanning from mild to harsh environments. The focus was on assessing the wear resistance and the consequent failure mechanisms in rails. Their findings reveal that high axle loads and small curve radii significantly impact the deterioration of rail materials. As axle loads increase, the wear rate rises, while decreasing with larger curve radii. Ignesti et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] present a model specifically developed to evaluate wheel and rail wear, as well as the evolution of wheel and rail profiles. The model consists of two mutually interacting components: a vehicle model for dynamic analysis and a wear estimation model. The results indicate that sharp curves increase wear in the flange region, which may reduce wheel lifespan. According to Zhang et al. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], for every 1 mm of wear on the flange, up to 4.2 mm must be removed from the wheel diameter during reprofiling.\u003c/p\u003e \u003cp\u003eCurrently, the main research approach on wheel wear comprises using multibody dynamics simulation (MBS) with experimentally derived material loss functions (referred to as wear models), to estimate the loss of wheel material [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. One of the most common strategies is to employ advanced wheel-rail contact models in multibody codes to analyze vehicle behavior and wheel-rail wear [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Meanwhile, the Archard wear equation, which posits that wear is directly proportional to normal force and sliding distance, and inversely proportional to material hardness, continue to be widely utilized in wear studies [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis study aims to get a deeper understanding of the prevalent wear issues occurring on sharp curves along the Brazilian rail network. It adopts the methodology outlined in References [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] applied to a metric-gauge heavy-haul railway in Brazil. The approach consists on using a computational tool based on multibody simulation to replicate the dynamic performance of railway vehicles and trace the evolution of wheel profile wear over the distance traveled. The correlation between curve radius and worn material is explored through short-term simulations using new wheel profiles. Section 2 provides an overview of the research methodology, detailing multibody simulations and wear calculations. Section 3 delves into the results, while Section 4 presents the conclusions drawn from this work.\u003c/p\u003e"},{"header":"2 METHODS","content":"\u003cp\u003eThe process of comparing curve radius and wear volume began with the development of multibody dynamic simulations with a wagon widely used on heavy haul railways, with Ride Control bogies and metric gauge. The simulation output is the wear depth. Multibody dynamics software is widely used to study vehicle/track interaction. Among commercial software, SIMPACK\u0026reg; is one of the most used due to its flexibility and scope and will be the one employed in this work.\u003c/p\u003e\n\u003cp\u003eDynamic simulations\u003c/p\u003e\n\u003cp\u003eAs mentioned before, the metric gauge GDE-Ride Control wagon was selected due to its widespread use, particularly in Brazilian railways. The simulation model and parameter values are referred to in previous works [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. The Ride Control is a three-piece bogie. The axle load of the GDE is 27.5 tons. The wagon model is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe rails were designated as components in the inertial reference frame with a cant of 1:40. New rail and wheel profiles were used and are presented in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe wheel-rail contact forces were calculated using the Semi-Hertzian SIMPACK\u0026reg; Discrete Elastic Contact method. It computes normal and tangential forces by considering the actual shape of the contact patch. The procedure for determining tangential forces resembles that of FASTSIM [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eThe primary suspension links the wheelset to the side frame pedestal via a rubber PAD adapter [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. In the multibody model, this component was represented by three connecting elements with vertical, lateral, and longitudinal stiffness and damping. These three elements are laterally aligned, with the central one exhibiting non-linear characteristics in both longitudinal and lateral stiffness.\u003c/p\u003e\n\u003cp\u003eAnother notable aspect of this bogie is its secondary suspension. Apart from the spring system, it has a constant damping wedge. The simulation of dry friction between contacting surfaces involved the use of discrete contact elements.\u003c/p\u003e\n\u003cp\u003eFurthermore, no constant contact roller side bearing is utilized in this bogie. A spring-based contact model was employed for the roller side bearing support.\u003c/p\u003e\n\u003cp\u003eIn all simulations, the wagon speed profile is kept essentially constant along the track. So, the draft gear was not modeled.\u003c/p\u003e\n\u003cp\u003eWear analysis\u003c/p\u003e\n\u003cp\u003eThe wear number (\u003cem\u003eT\u0026gamma;\u003c/em\u003e) is determined by calculating the energy dissipation within the contact patch [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e]. We use the complete form of \u003cem\u003eT\u0026gamma;\u003c/em\u003e (Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), i.e., considering the spin part in our analysis.\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$$\\:T\\gamma\\:=\\left|{F}_{x}{v}_{x}\\right|+\\left|{F}_{y}{v}_{y}\\right|+\\left|{M}_{z}{\\phi\\:}_{z}\\right|$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cem\u003eF\u003c/em\u003e \u003csub\u003e \u003cem\u003ex\u003c/em\u003e \u003c/sub\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e represent the longitudinal, lateral, and rotational forces acting on the contact area, while \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003e\u0026phi;\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e denote the longitudinal, lateral, and rotational creepage, respectively.\u003c/p\u003e\n\u003cp\u003eTypically, wheel wear simulation models comprise three main components: a vehicle dynamics simulation, a wear model that correlates the dynamics simulation outcomes with the material degradation of the wheel surface, and a strategy for updating the wheel profile [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eThe SIMPACK\u0026reg; simulation environment enables the calculation of wheel wear, providing access to both the depth and profile of the wear on the wheel [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e]. Wear calculations were conducted using the Archard method, a widely adopted approach for this purpose [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. This method relates the wear volume, denoted as \u003cem\u003eV\u003c/em\u003e [m\u0026sup3;], to the sliding distance, represented by \u003cem\u003e\u0026Delta;s\u003c/em\u003e [m], and the normal force, designated as \u003cem\u003eN\u003c/em\u003e [N], while inversely correlating it with the material hardness, denoted as H [Pa] (Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$$\\:V=\\frac{N.\\varDelta\\:s}{H}.k$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe wear coefficient, denoted by \u003cem\u003ek\u003c/em\u003e, varies based on the contact pressure and slip velocity and is usually determined from experimental maps [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e]. The map adopted in this work is the same used by Pacheco et al. [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eDesign of experiments\u003c/p\u003e\n\u003cp\u003eThe model developed for the wagon was subjected to the same route at three different speeds, generating negative, neutral, and positive non-compensated accelerations (when possible), computed according to Eq.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$$\\:Anc=\\frac{v\u0026sup2;}{R}-\\frac{H}{G}g\\:\\:\\:\\:\\:\\:\\:\\left[m/s\u0026sup2;\\right]$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e\u0026nu;:\u0026nbsp;\u003c/em\u003e\u003c/strong\u003espeed [m/s]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eR:\u0026nbsp;\u003c/strong\u003ecurve radius [m]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eg:\u0026nbsp;\u003c/strong\u003eacceleration of gravity [m/s\u0026sup2;]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eH:\u0026nbsp;\u003c/strong\u003esuperelevation [m]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eG:\u0026nbsp;\u003c/strong\u003egauge [m]\u003c/p\u003e\n\u003cp\u003eBased on the ABNT 16810 standard [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e], the non-compensated accelerations (Anc) were constrained, with the theoretical values presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The minimum curve radius considered in this study is 200 m, which represents the narrowest curve in the Brazilian heavy-haul railway under study.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eDescription of the simulations, each simulation is composed of the combination of curve radius and superelevation for three different speeds (R-curve radius, H-superelevation, G \u0026ndash; gauge, V- speed, Anc \u0026ndash;non-compensated acceleration).\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eTrack\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eH\u003c/em\u003e\u0026nbsp;\u0026frasl;\u0026nbsp;\u003cem\u003eG\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003enc1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003enc2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003enc3\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[m]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[km/h]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[mm/m]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[km/h]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[m/s\u0026sup2;]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[km/h]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[m/s\u0026sup2;]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[km/h]\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e[m/s\u0026sup2;]\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e200\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e67\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e120\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,36\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e55\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,01\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e67\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,54\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e275\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e72\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e90\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e44\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e72\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,55\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e350\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e75\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,34\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e75\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,56\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e425\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e38\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e57\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,57\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e500\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e83\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,32\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e56\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,01\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e83\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,57\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e200\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e55\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e26\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e55\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,57\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e275\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e45\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,32\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,01\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,58\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e350\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e24\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,01\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e65\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,58\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e425\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e21\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,00\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,58\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e500\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e73\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-0,01\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e73\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,58\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e200\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,59\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e12\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e275\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e32\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,29\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,59\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e350\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,09\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,27\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e52\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,60\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e425\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e57\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e38\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,26\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e57\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,59\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e500\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,06\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e41\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0,26\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e62\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0,59\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe reference track is composed of a tangent section (100 m), an entry transition curve (160 m) defined as a linear clothoid equation, a complete left turn (200 m long), an exit curve transition (160 m), followed by the same sequence for the opposite side and a final tangent section (100 m). The differences between the tracks remain in the curve radius and superelevation.\u003c/p\u003e\n\u003cp\u003eThe wear depth is recorded for the right wheel of the first wheelset and totaled over the entire length of each curve. In this investigation, the wear depth is associated with the tread and flange regions, as defined by AAR M-107 [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e]. The transition between the tread and the flange area starts at -23.7 mm from the tape line (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). The tape line represents the measurement position from the inner face of the wheel, where the radius is determined; for this study, this value is 70 mm.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"3 RESULTS AND DISCUSSIONS","content":"\u003cp\u003eThe results obtained from the methodology outlined in section 2 are presented in this section. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the wear depth on the flange and tread for the simulated scenarios. A strong relationship can be observed between Tγ and wear with the curve radius. As the curve radius decreases the Tγ and wear depth increases. Additionally, it's noticeable that the increase in Tγ becomes more pronounced as the radius decreases. Between 500 and 425 meters, the variance is less than 50 N, whereas between 275 and 200 meters, the difference exceeds 700 N. The same behavior is observed for the wear depth in the tread and flange.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the tread (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea), there is a strong relationship between its wear depth and Anc, except for the sharpest and widest curves, which have low Anc influence. An increase in the Anc decreases the tread wear depth. For the flange (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb), except for the 500 and 475 m radius curves, the data seem to present a positive correlation between flange wear depth and Anc, i.e. an increase in the Anc increases the flange wear depth.\u003c/p\u003e \u003cp\u003eAdditionally, in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb, one specific point in the 200-meter radius curve exhibits significantly less wear than the others. This outcome is observed when 0 mm superelevation is adopted and the Anc approaches zero, indicating no contact with the outer wheel flange during the curve. For other curves where wear differences are also noted, the same happens when Anc is less than zero. As showed by Pacheco et al [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], positive Anc values indicate lateral displacement of the wheelset towards the field side. In sharp curves, this can lead to flange contact, increasing flange forces and, consequently, increasing flange wear.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the wear depth results considering the Tγ values individually for the tread and flange. Tγ on the tread also demonstrates an inverse relationship with the curve radius, for curves ranging from 275 to 500 m, the Tγ values vary between 20 N and 60 N (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). However, for the sharpest curve, there's an increase of about 100 N in the Tγ value. Furthermore, the Tγ on the tread presents a negative correlation with Anc, except for the 200 m curve, where a positive correlation is seen. A weak correlation exists between Tγ and tread wear depth; that is the reason to the presence of data points with the same Tγ value but with different depth values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results of Tγ on tread for flange wear depth (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb) shows two inverse correlations for 200 and 275 m curves. The first correlation is positive, while the second is negative, i.e., for the 200 m radius curve, wear increases with Tγ, whereas for the 250 m radius curve, wear decreases with Tγ. There is no correlation observed for the other curves, indicating that Tγ on the tread is not a good parameter to evaluate flange wear depth.\u003c/p\u003e \u003cp\u003eThe results show that the wear depth on the tread decreases with an increase in Tγ on the flange for curves longer than 200 meters (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec). For the 200 m radius curve, no correlation is observed. For the flange wear depth (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb) a positive correlation with the Tγ on the flange is seen as expected. A similar observation can be made about the correlation between Tγ on the flange and Anc.\u003c/p\u003e \u003cp\u003eThe findings in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e indicate that the total Tγ, which includes both the Tγ values from the tread and the flange, is more effective for analyzing wear depth compared to examining the Tγ values individually for the tread and flange.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the wear depth on the tread and the flange results for the inner wheel. The correlation between Tγ and curve radius is positive, as expected. On the sharpest curves (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea), 200 and 275 m in radius, Tγ is negatively correlated with Anc, while on larger curves, this correlation is positive. Besides, the radius is negatively correlated with the wear depth on the tread. However, no correlation between the wear depth on the tread and the Tγ was observed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAn analysis of the wear depth on the flange (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb) reveals a positive correlation with the Anc. Further, the correlation between Tγ and wear depth is negative for the sharpest curves (200 and 275 m radius). Since the inner wheel does not contact the flange, the outcomes for individual Tγ values on the tread exhibit identical behavior to the overall Tγ.\u003c/p\u003e"},{"header":"4 CONCLUSIONS","content":"\u003cp\u003eThis article explores how Tγ relates to maximum wear penetration on sharp curves. The study utilized multibody dynamic simulations across different sharp curves, varying speeds, and non-compensated lateral accelerations (Anc). The simulations involved a meter gauge heavy haul vehicle used in a Brazilian railway.\u003c/p\u003e \u003cp\u003eComparative results obtained from the dynamic simulations simulation show that the curve's radius significantly impacts wear depth on both the tread and the flange. Sharper curve radii lead to more pronounced effects on wheel wear, as expected. This relationship is also evident in the correlation between curve radius and Tγ.\u003c/p\u003e \u003cp\u003eThe results for the outer wheel suggest that the combined Tγ, incorporating values from both the tread and flange, is more effective to assess the wear depth than separately examining tread and flange Tγ values. The findings highlight the significant Anc impact on flange wear depth. Additionally, a strong correlation between tread wear depth and Anc was found, except for the sharpest and widest curves, where Anc's influence is minimal.\u003c/p\u003e \u003cp\u003eFor the inner wheel no correlation between the wear depth on the tread and the Tγ is observed. However, the wear depth on the flange shows a positive correlation with the Anc. Additionally, there is a negative correlation between Tγ and wear depth for the sharpest curves (200 and 275 m radius).\u003c/p\u003e \u003cp\u003eBy focusing on sharp curves, this study contributed to deepening the understanding of wheel-rail wear dynamics in such challenging conditions and provide valuable insights for improving maintenance strategies and enhancing railway safety..\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eP.A.P.P.: Conceptualization, Methodology, Software, Writing - Original Draft, Investigation. M.V.L.: Conceptualization, Data curation, Visualization, Review \u0026amp; Editing. A.A.S.: Conceptualization, Writing - Review \u0026amp; Editing, Supervision.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors wish to express their acknowledgment to Vale S.A. for funding this study and providing technical support and to CNPq , which funded partially this project.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLewis, R., Dwyer-Joyce, R. S., Olofsson, U., Pombo, J., Ambr\u0026oacute;sio, J., Pereira, M., Ariaudo, C., Kuka, N.: Mapping railway wheel material wear mechanisms and transitions. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 224 (2010), 125\u0026ndash;137. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1243/09544097JRRT328\u003c/span\u003e\u003cspan address=\"10.1243/09544097JRRT328\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlmeida, L. P. F., Falqueto, L. E., Goldenstein, H., and Scandiana, A. C.: Study of Sliding Wear of the Wheel Flange-Rail Gauge Corner Contact Conditions: Comparative Between Cast and Forged Steel Wheel Materials. Wear, 432 (2019). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2019.05.009\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2019.05.009\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePacheco, P. A. d. P., Endlich, C. S., Vieira, K. L. S., Reis, T., Santos, G. F. M. d., and J\u0026uacute;nior, A. A. d. S.: Optimization of Heavy Haul Railway Wheel Profile Based on Rolling Contact Fatigue and Wear Performance. Wear, 522 (2023). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2023.204704\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2023.204704\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePan, L., Xu, L., Chen, X., and Zhu, Z.: Curved Ballasted Track\u0026ndash;Vehicle Dynamic Interaction: Effects of Curve Radius and Track Structural Nonlinearity. J. Comput. Nonlinear Dynam., 16 (2021). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1115/1.4050953\u003c/span\u003e\u003cspan address=\"10.1115/1.4050953\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLai, J., Chen, Y., Liao, T., Zheng, Z., Xu, J., Chen, R., and Wang, P.: Study on Train Running Safety in Railway Switches and Sharp Curves Considering Wheel Wear Evolution. Vehicle System Dynamics (2024). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1080/00423114.2024.2319277\u003c/span\u003e\u003cspan address=\"10.1080/00423114.2024.2319277\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSalehi, S., Farrahi, G., and Sohrabpour, S.: Dynamic Behavior of Worn Wheels in a Track Containing Several Sharp Curves Based on Simulation. Scientia Iranica B, 26(2019), 2854\u0026ndash;2864. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.24200/sci.2018.50749.1849\u003c/span\u003e\u003cspan address=\"10.24200/sci.2018.50749.1849\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePacheco, P. A. P., Magelli, M., Lopes, M. V., Correa, P. A., Zampieri, N., Bosso, N., and Santos, A. A.: The Effectiveness of Different Wear Indicators in Quantifying Wear on Railway Wheels of Freight Wagons. Railway Engineering Science (2024). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s40534-024-00334-8\u003c/span\u003e\u003cspan address=\"10.1007/s40534-024-00334-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePacheco, P., Lopes, M., and Santos, A.: Influ\u0026ecirc;ncia da Acelera\u0026ccedil;\u0026atilde;o Lateral N\u0026atilde;o Compensada no Desgaste de Rodas Ferrovi\u0026aacute;rias. VII Simp\u0026oacute;sio de Engenharia Ferrovi\u0026aacute;ria (2024). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.29327/vii-\u003c/span\u003e\u003cspan address=\"10.29327/vii-\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003esimposio-de-engenharia-ferroviaria-410736.807262\u003c/span\u003e\u003cspan address=\"http://simposio-de-engenharia-ferroviaria-410736.807262\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBai, W., Zhou, L., Wang, P., Hu, Y., Wang, W., Ding, H., Han, Z., Xu, X., and Zhu, M.: Damage Behavior of Heavy-Haul Rail Steels Used from the Mild Conditions to Harsh Conditions. Wear, 496 (2022). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2022.204290\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2022.204290\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIgnesti, M., Marini, L., Meli, E., and Rindi, A.: Development of a Model for the Prediction of Wheel and Rail Wear in the Railway Field. J. Comput. Nonlinear Dynam., 7 (2012). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1115/1.4006732\u003c/span\u003e\u003cspan address=\"10.1115/1.4006732\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang, H., Wei, X., Guan, Q., and Zhang, W.: Joint Maintenance Strategy Optimization for Railway Bogie Wheelset. Applied Sciences, 12(2022). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/app12146934\u003c/span\u003e\u003cspan address=\"10.3390/app12146934\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYe, Y., Sun, Y., Shi, D., Peng, B., and Hecht, M.: A Wheel Wear Prediction Model of Non-Hertzian Wheel-Rail Contact Considering Wheelset Yaw: Comparison Between Simulated and Field Test Results. Wear (2021). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2021.203715\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2021.203715\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu, Q., Bernal, E., Spiryagin, M., Krishna, V., Ding, H., Stichel, S., and Cole, C.: Heavy Haul Rail/Wheel Wear and RCF Assessments Using 3D Train Models and a New Wear Map. Wear, 538 (2024). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2023.205226\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2023.205226\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVicente, F. S., and Guillam\u0026oacute;n, M.: Use of the Fatigue Index to Study Rolling Contact Wear. Wear, 436 (2019). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2019.203036\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2019.203036\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHardwick, C., Lewis, R., and Eadie, D.: Wheel and Rail Wear\u0026mdash;Understanding the Effects of Water and Grease. Wear, 314 (2014), pp. 198\u0026ndash;204. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2013.11.020\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2013.11.020\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArchard, J.: Contact and Rubbing of Flat Surfaces. J. Appl. Phys., 24 (1953), 981\u0026ndash;988. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.1721448\u003c/span\u003e\u003cspan address=\"10.1063/1.1721448\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePacheco, P., Lopes, M., Correa, P., and Santos, A.: Influence of Primary Suspension Parameters on the Wear Behaviour of Heavy-Haul Railway Wheels Using Multibody Simulation. Proc. of the International Conference on Electrical, Computer, Communications and Mechatronics Engineering (2023), Tenerife.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePacheco, P., Reis, T., Ramos, P., Santos, G. d., and Santos, A.: Wear and Fatigue-Oriented Wheel Profile Optimized for Heavy Haul. VI Simp\u0026oacute;sio de Engenharia Ferrovi\u0026aacute;ria (2023), Campinas. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.17648/sef-2023-165737\u003c/span\u003e\u003cspan address=\"10.17648/sef-2023-165737\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRamos, P., Correa, P., Texeira, L., Kurka, P., and Santos, A.: Dynamic Effect of Hollow-Worn Wheels for Freight Rail Vehicles in a Consist. Proceedings of the Fifth International Conference on Railway Technology: Research, Development and Maintenance (2022), 22\u0026ndash;25 August 2022.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSIMPACK: About Rail-Wheel Pairs. Simpack User Assistance (2022), Dassault Systemes Simula Corp.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLima, E. A., Baruffaldi, L. B., Manetti, J. L. B., Martins, T. S., and Santos, A. A.: Effect of Truck Shear Pads on the Dynamic Behaviour of Heavy Haul Railway Cars. Vehicle System Dynamics, 60(2022), 1188\u0026ndash;1208. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/00423114.2020.1858120\u003c/span\u003e\u003cspan address=\"10.1080/00423114.2020.1858120\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRovira, A., Roda, M. B., Marshall, H., Brunskill, H., and Lewis, R.: Experimental and Numerical Modelling of Wheel\u0026ndash;Rail Contact and Wear. Wear, 271 (2011), pp. 911\u0026ndash;924. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2011.03.024\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2011.03.024\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLuo, R., Liu, B., and Qu, S.: A Fast Simulation Algorithm for the Wheel Profile Wear of High-Speed Trains Considering Stochastic Parameters. Wear, 480\u0026ndash;481 (2021). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2021.203942\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2021.203942\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu, B., Bruni, S., and Lewis, R.: Numerical Calculation of Wear in Rolling Contact Based on the Archard Equation: Effect of Contact Parameters and Consideration of Uncertainties. Wear, 490 (2022). DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2021.204188\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2021.204188\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJendel, T.: Prediction of Wheel Profile Wear\u0026mdash;Comparisons with Field Measurements. Wear 253 (2002), pp. 89\u0026ndash;99. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/S0043-1648(02)00087-X\u003c/span\u003e\u003cspan address=\"10.1016/S0043-1648(02)00087-X\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLewis, R., and Olofsson, U.: Mapping Rail Wear Regimes and Transitions. Wear, 257 (2004), pp. 721\u0026ndash;729. DOI: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.wear.2004.03.019\u003c/span\u003e\u003cspan address=\"10.1016/j.wear.2004.03.019\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eABNT: NBR 16810: Via F\u0026eacute;rrea - Supereleva\u0026ccedil;\u0026atilde;o em Curvas. ASSOCIA\u0026Ccedil;\u0026Atilde;O BRASILEIRA DE NORMAS T\u0026Eacute;CNICAS (2019), Rio de Janeiro.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAAR: WHEELS, CARBON STEEL Specification M-107/M-208. AAR Manual of Standards and Recommended Practices (2011).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Wear number, Wear volume, Wear modeling, Multibody dynamic simulation","lastPublishedDoi":"10.21203/rs.3.rs-6172977/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6172977/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe dynamic interaction between railway wheels and rails is critical for ensuring maintenance and safety in railway operations. Accurate assessment of wheel wear is essential, particularly in sharp curves where wear is more pronounced. This study focuses on using the T-gamma (Tγ) indicator to quantify wheel wear in sharp curves. Despite its usefulness, Tγ alone does not fully capture the complexities of material removal and contact dynamics, making it insufficient as a sole index for optimizing wheel profiles. This research evaluates a meter gauge heavy haul vehicle from a Brazilian railway. Comprehensive multibody simulations were conducted on various sharp curves to investigate the relationship between Tγ, the maximum penetration under varying speeds, and the non-compensated lateral accelerations (Anc). The findings indicate that using the total Tγ, which includes both the Tγ values from the tread and the flange, is more effective for analyzing wear depth than examining the Tγ values individually for the tread and flange. The results also show the high influence of Anc on flange wear depth. Besides, a strong relationship between tread wear depth and Anc was found, except for very sharp and very wide curves, which showed to have low influence of Anc. By focusing on sharp curves, the study aims to deepen the understanding of wheel-rail wear dynamics in such challenging conditions and to provide valuable insights for improving maintenance strategies.\u003c/p\u003e","manuscriptTitle":"Wheel wear dynamics in sharp curves: Insights from T-gamma indicator study on heavy-haul railways","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-03 11:13:11","doi":"10.21203/rs.3.rs-6172977/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"09ce39bf-a649-4a3c-9f03-0126e691ef50","owner":[],"postedDate":"April 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-07T08:39:08+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-03 11:13:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6172977","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6172977","identity":"rs-6172977","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}