Influence of main operating conditions on contact wire wear of rigid catenary lines

Tribology International 196 (2024) 109708 Available online 26 April 2024 0301-679X/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Influence of main operating conditions on contact wire wear of rigid catenary lines Montserrat Simarro a , S. Postigo a , * , Carlos Casanueva b , Luis Rodríguez-Tembleque c , Juan J. Castillo a a Escuela de Ingenierías Industriales, Universidad de M´ alaga, c/ Doctor Ortiz Ramos s/n. M´ alaga Department of Mechanical Engineering, Thermal and Fluid Mechanics, University of Malaga, Spain b Rail Vehicles unit, Engineering Mechanics Department, KTH Royal Institute of Technology, Stockholm, Sweden c Mec´ anica de Medios Continuos y Teoría de Estructuras, Escuela T´ ecnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain ARTICLE INFO Keywords: Wear Contact forces Overhead conductor rail (OCR) Pantograph ABSTRACT A validated overhead conductor rail and a well-known wear model have been programmed to perform closer-to- reality simulations. Reliable wear rate estimates for two configurations of overhead conductor rails and three models of pantographs at different speeds and supply currents have been obtained. Results show that wear decreases with increasing speed at high currents and when the distances between supports are uniform. In addition, the use of different types of pantographs in the same facility has a positive effect in terms of wear reduction. Consequently, an adequate selection of the operating conditions contributes to reducing the wear rate. 1. Introduction Rail transport of goods and people has undergone continuous progress since the beginning of the railway. This mode of transport has several advantages compared to road transport. Thus, rail transport is considered to be reliable, safe and efficient. Furthermore, it can deal with large volumes that can be shipped over great distances with a reduced transport cost. In addition, European policies seek to promote the use of railways thanks to their high energy efficiency and their contribution to mitigating the effects of climate change. A fundamental infrastructure in rail transport is the system necessary to provide energy to trains. Overhead railway power cables were introduced in 1879 by Siemens in Berlin [1]. Today, the most used method to supply energy to trains in railway systems is the well-known Overhead Contact System (OCS). This system allows feeding the locomotives even at high speeds. However, its installation is difficult in some cases, and it can present safety problems, in tunnels for example. Feeding systems based on rigid catenary allow coping with the shortcomings of flexible systems in these particular facilities. These systems are also referred to as Overhead Conductor Rail (OCR). Rigid catenary systems can be installed in infrastructures with a low gauge, providing high levels of safety and low maintenance costs. However, the installation costs are high and its performance at high driving speeds is still not satisfactory. Poor behavior at high speeds is mainly due to excessive variations in the contact forces that appear between the pantograph and the contact wire of the rigid catenary (especially in the area close to the expansion joints between sections). As speed increases, so do vibrations and oscillations of contact forces, leading to poor current transmission and premature wear problems. Flexible catenary has been extensively studied by multiple research teams, delving into the design of catenary infrastructures or improving the current ones [2,3]. In contrast, to the our knowledge, there are few research teams who have focused on the study of the rigid catenary and its interaction with the pantograph. Despite the studies carried out so far, there is still room for improvement to alleviate its defects and increase its virtues. Previous research groups have focused on different aspects of this type of facilities, such as OCR design, calculation methods, current collection, regulations, maintenance and cost (See Table 1). The study of the wear produced in the contact wire in OCR with the * Correspondence to: Departamento de Ingeniería Mec´ anica, T´ ermica y de Fluidos [Department of Mechanical Engineering, Thermal and Fluid Mechanics], Universidad de M´ alaga [University of Malaga], Escuela de Ingenierías Industriales [School of Industrial Engineering], C/ Doctor Ortiz Ramos S/N, Campus de Teatinos, 29071 M´ alaga, Spain. E-mail address: [email protected] (S. Postigo). Contents lists available at ScienceDirect Tribology International journal homepage: www.elsevier.com/locate/triboint https://doi.org/10.1016/j.triboint.2024.109708 Received 19 February 2024; Received in revised form 15 April 2024; Accepted 25 April 2024 Tribology International 196 (2024) 109708 2 objective to evaluate the influence of various operational factors and the estimation of its durability is of undoubted interest. This knowledge will make it possible to improve this type of facility, improving the design and quality of current collection, preventing stoppages or accidents in tunnels and reducing the consumption of natural resources by reducing the wear and tear of materials. Damages in the OCR-strip contact are mainly due to mechanical interactions and electric arcs. Contact force can be use to evaluate the interaction between the catenary and the pantograph. When the contact force is low, there is a higher likelihood of electric arcs occurring due to the separation between the two systems. High contact forces lead to excessive wear and higher possibility of breakage of the contact wire. The mean contact force depends on the initial preload with which the pantograph is set, the speed of the train and the characteristics of the catenary. An adequate design of these systems is one that attempts to reduce contact forces to cause less wear on the materials, while avoiding detachments between the pantograph and the catenary in all conditions. Therefore, better knowledge of the wear process in the pantographcatenary contact is of great interest not only to establish preventive maintenance plans but also to improve currently existing systems and to develop new catenary designs with a longer service life. Wear mechanism has been studied in depth for decades by numerous research groups. These works have allowed knowing the behavior of materials involved in this sliding contact, main wear mechanisms and factors with higher influence on the flexible catenary-pantograph interaction. Thus, the study of materials used in the conductor wire and pantograph strips has been extensively addressed in [20–30]. Regarding wear mechanisms with higher relevance in the pantograph-catenary sliding contact, previous works highlighted three main wear mechanisms: adhesive, abrasive and electrical [31–35]. In [36–42] the influence of certain operating parameters on the wear rate was studied, identifying speed, preload and current as factors with a main effect. In addition, several models were proposed to predict the wear rate of both the contact wire and the contact strips, most of them focused on OCS [43–47]. However, few studies have been focused on evaluating wear in rigid catenary. In [16], wear mechanism, wear analysis and wear calculation were studied focusing on a metro system. This way, authors proposed models that allowed calculating and predicting wear on the contact wire and pantograph strips. Among the general conclusions, the following stood out: the mean wear on the contact wire was much higher in the areas where the train accelerated compared to constant speeds or decelerations. Observing the results, the factor with the greatest influence on wear was the variation in current intensity, coinciding with the previous point. The highest power consumption occurred in acceleration zones, which led to greater wear on the contact wire; With regard to wear on the pantograph strips, they concluded that it was important to take the design of the superstructure of the rigid catenary and its zig-zag into account, since this could generate inhomogeneous wear on the strips. In addition, results also showed, in the higher stagger value, long sliding distance generated non-uniform and undesired wear of the contact wire. Finally, they also concluded that the presented models were reliable to calculate and predict the wear of materials in contact during the interaction. Nevertheless, they highlighted the complexity of the problem studied and the need for further research. Guiming [17] also described the main problems of premature wear of the materials in contact. The authors focused on studying the tribological performance of the interaction through laboratory experiments simulating different working conditions. The main conclusions included that wear of the pantograph strips was greater when current was applied. The range of abrasion became almost 18 times greater compared to a test without current. It was also shown that the vibration of the pantograph could affect wear of the pantograph and contact wire. A relationship between the fluctuation of contact forces and the fluctuation of current intensity was observed, which led to the appearance of electric arcs. Authors also confirmed that the temperature of the pantograph and the energy of the electric arc discharges increased as intensity increased. Finally, they concluded that a poor union between two parts of the pantograph strip could cause strands in the contact wire. The authors’ research group has conducted several studies related to the interaction between OCR and pantograph. First, a validation procedure was developed, employing evolutionary algorithms to determine the stiffness degrees of the supports for rigid overhead catenaries facilities. Next, virtual modal tests were conducted to assess the reliability and robustness of the proposed methodology. [9]. Next, contact forces between eleven pantograph models and two OCR sections were obtained at three different operating speeds [14]. Finally, the influence of parameters such as span length, speed and preload in the catenary-pantograph interaction were evaluated using validated catenary models [15]. The novelty of this work lies in being one of the first studies that specifically focuses in depth on the wear rate of the contact wire in overhead conductor rail collector systems, analysing some of the more relevant operational parameters, i.e. speed, current, facility and pantograph. To the best of the authors’ knowledge, this is the first time that the influence of these parameters on the wear of the contact wire in the overhead conductor rail and pantograph strip system contact has been studied numerically. To do so, a validated OCR finite element (FE) model has been used to evaluate the influence of train speed, current flow, type of facility and pantograph on contact wire wear. Three operational speeds: 70, 100 and 130 km/h, three current flows: 300, 500 and 1000 A, three types of pantographs and two types of facilities have been reproduced by means of simulations to obtain the wear rate. In addition, the contribution of mechanical, electrical and arc wear has been determined. This paper is divided into four main sections. Section 2 is devoted to describing the methodology followed to obtain the contact forces and the wire wear. Results and discussions are included in Section 3. Finally, the main conclusions are stated in Section 4. 2. Methodology This section is dedicated to describing the methodology followed to obtain, first of all, the forces in the pantograph-catenary contact. With these forces, and using a wear model, the depth of wear on the contact wire is calculated. Finally, the iterative process used to calculate this wear as a function of the number of pantograph passes is described. Thus, first, the OCR FE model and pantograph lumped-element models are presented. Next, the wear model is used to obtain the wear volume, and the parameters and variables are described. Finally, the algorithm used to obtain the wear is outlined. 2.1. Dynamical model for the pantograph-overhead conductor rail interaction The OCR reproduced in this paper consists of a structure made of extruded aluminum profile beams with profile type PAC 110 joined with Table 1 Previous research on OCR. Focus References Redesign of the rigid catenary configuration Oya et al.[4],Cophura vera et al.[5],Calleja et al.[6] Improvement of calculation alternatives Bautista et al.[7], J. D Sanz[8], Simarro et al.[9] Speed Increase - Evaluation of current harvesting performance Takemura et al.[10], Huang et al.[11], Chen et al.[12], Furrer & Frey[13], Simarro et al. [14,15] Premature wear of contact materials Wei et al.[16], Guiming et al.[17] Review of current regulations of the rigid catenary Carnevale et al.[18] Installation and maintenance costs Mak Man[19] M. Simarro et al. Tribology International 196 (2024) 109708 3 flanges [15]. A 150 mm 2 cross-section contact wire is attached to the beam by clamping (Fig. 1). Ceramic insulators are incorporated to the ends of the bars that support the beams. These bars are hitched to L-angle beams via threaded rods. The entire structure is rigidly fixed to the tunnel ceiling with supports. The beam presents a zig-zag configuration offset from the central axis of the track, referred to as stagger, thus ensuring consistent wear on the pantograph strips. Fig. 2 displays the 2-D FE model that replicates OCR behavior. The parameters of the model used in this study were derived from experimental validation already described in a previous study by this research group on a real OCR facility located in a tunnel of a commuter train in Malaga, Spain [14]. In this model, the aluminum profile and the contact wire are replicated as a unified body, having identical sections and mechanical properties mirroring those of the actual system. This way, 2-node beam elements with a length of 0.2 m were used, which are based on Timoshenko’s theory. Flanges were modeled with point elements that incorporate mass and rotary inertia, while the supports that connect the beam to the ceiling of the tunnel were modeled using uniaxial tension-compression elements with constant stiffness. Table A.III.2 in Appendix III presents the primary OCR model parameters that have been throughout this document. In Fig. 2, K s denotes the support stiffness (Appendix III - table A.III.1), d F is the distance between the supports and the flanges, and L S represents the span length [15]. This figure shows the interaction between the contact wire (CW) and pantograph strip (PS) and a schematic representation of the wear depth (gw) on the CW as a function of the wear angle (θw) and the wire radius (Rw). Appendix I, II and III present a graphical representation of the section and the location of the supports, along with the assigned values for each parameter. Contact forces that appear in the interaction between the pantograph and catenary were derived from simulations replicating a train passing beneath a catenary stretch. The simulated catenary stretch was divided into two sections. The first one, named initial section, aimed at eliminating transient effects at the onset of train movement. The second one, called reference section, was used to measure the contact forces (Appendix I). The length of the catenary stretch was 507.61 m (TL), with initial and reference sections measuring 120.65 m and 390.5 m, respectively. For comparison purposes, two test sections have been simulated. The first one, called ideal section, represents a perfectly installed facility with an uniform distance between supports of 8 m (Appendix II). The second one, called real section, replicates a real facility of a commuter train operating in the city of Malaga (Spain). In this real section, the length of the spans is not uniform due to installation inaccuracies (Appendix III). Pantograph displacements have been obtained using models with 3 or 2 degrees of freedom (DOF). In the first case, 9 mass-spring-damper lumped elements have been utilized (see Fig. 3.a). In the second case, 7 lumped element models and two force saturations were employed (see Fig. 3.b). Table 2 includes the masses, degrees of stiffness and dampings of the pantograph models. It has also been included the references in which these models were proposed. For the sake of clarity, the same nomenclature of pantograph models used in a previous reference of this research group has been used [14]. A preload of 100 N and a contact stiffness of 50.000 N/m between the pantograph strips and the contact wire were stablished. The model also incorporates the effect of the gravity and aerodynamic forces [50] [51,52]. Penalty method and numerical damping were used to obtain the contact forces, which were also smothered with a 20 Hz cut-off frequency filter. The time step was fixed at 0.0025 s. An Intel(R) Core i7–8700 K CPU, 3.7 GHz, 36 GB RAM computer with ANSYS® 2022 software were used to perform the simulations. 2.2. Wear model The wear model of the contact wire used in this work is the one presented by G. Bucca and A. Collina [45]. This wear model contemplates a mechanical contribution due to friction, an electrical component due to the current flow through the contact section and a component due to the energy dissipated during the formation of electric arcs. This wear model is heuristic and depends on numerous parameters associated with the materials and the interaction conditions. The parameters of the wear model presented in this reference were fitted using a test rig. Tests at different speeds, preloads and electrical currents were conducted. Load cells were used to measure the vertical and longitudinal components of the contact force. The contact wire wear rate was estimated by measuring the thickness after the test. The model was fitted for the Fig. 1. Profile Type Pac 110 and support. M. Simarro et al. Tribology International 196 (2024) 109708 4 interaction between a copper contact wire and a Kasperovski-type pantograph strip. Eqs. (1–5) show the employed model, as well as the parameters on which it depends. It is observed that, from the point of view of the operational aspects of the interaction, the model shows a dependence on parameters such as: sliding speed, electrical current and contact force. Hence, the wear model used has three main terms. Each of them takes into account one wear mechanism, total wear volume (NWR) being the sum of the three terms, as shown in Eq. (1). This way, the first term (NWR f ) is used to model wear due to friction power dissipation, which is obtained from Eq. (2). Next, the second term (NWR j ) models the wear contribution due to Joule effect, obtained from Eq. (3). Finally, Eq. (4) provides the wear due to electric arcs (NWR a ). NWR =NWRf+NWRj+NWRa(1) Where each term of Eq. 1 is obtained from: NWRf=k1•(1 2•(1+IC I0))− α •(Fm F0)β •Fm H(2) NWRj=k2•RC(Fm) • I2 C H•V• (1−u)(3) NWRa=k3•u•Va•IC V•Hm• ρ (4) Where, RC(Fm) = 0.013 +0.909 •e−Fm−14 11 (5) Table 3 shows the variables, parameters and units used in the contact wire wear model. According to Table 3, all model parameters are kept constant in all simulations. On the contrary, variables are, on one hand, set by the type of test conducted (nominal electrical current and sliding speed) and, on the other hand, obtained from the catenary and pantograph models (contact force mean value and strip and wire electrical contact resistance) for the selected operational conditions. 2.3. Computing scheme Fig. 4 shows the flowchart to calculate the wear proposed in this work. The process starts with the selection of the pantograph type and configuration of the catenary. In addition, the operational conditions, i. e. train speed and current, are set (a). Next, interaction is simulated and the instantaneous contact force between them is obtained (F m ). To do so, contact forces are calculated from the catenary FEM model and the pantograph lumped model (b). The next step (c) is devoted to obtaining strip and wire electrical contact resistance, which is obtained from Eq. (5). These variables are provided to the wear model to calculate the wear Fig. 2. OCR FE model and contact geometry. Fig. 3. Pantograph lumped-element models. Table 2 Pantograph models parameters. Pant. model m1 (kg) m2 (kg) m3 (kg) k1 (N/m) k2 (N/m) k3 (N/m) C1 (Ns/m) C2 (Ns/m) C3 (Ns/m) P01[48] 12.2 11,3 5,9 5156 22,736 165,6 29 0,03 50,3 P10[49] 7.12 6 5.8 9430 141,000 80 0 0 70 m1 (kg) m2 (kg) k1 (N/m) k2 (N/m) C1 (Ns/m) C2 (Ns/m) F1 (±N) F2 (±N) kF (N/m) kS (N/m) dS (m) P08[48] 6 19,7 5800 - - 63.5 4 3 1e6 1e6 0.053 M. Simarro et al. Tribology International 196 (2024) 109708 5 volume contribution of each wear mechanism (d). To do so, model parameters included in Table 3 and Eqs. (2) to (4) are used. The contributions of all wear mechanisms are aggregated to obtain the associated local wear volume in the contact wire (e) according to Eq. (1). The wear volume generated by the pantograph pass is increased by a factor of 100 (pantograph passes). Finally, the instantaneous wear depth at each point of the catenary is determined from geometric relationships, as shown in Fig. 2. With this update of the worn catenary profile, the interaction between the catenary and pantograph is newly simulated to calculate the updated contact force. An increment of 100 pantograph passes has been selected, equivalent to approximately one day of accumulated wear. It is assumed that contact wire wear has had a constant evolution during this period [45]. Section 5.1 presents the results of a comparison of the wear obtained by taking a factor of 1 versus a factor of 100 pantograph passes for the first 2000 iterations. 3. Numerical results and discussion The proposed methodology has been applied to the study of wear on the contact wire of a rigid catenary system. The OCR has been subjected to the repeated passage of the selected pantograph models, with three levels of current intensity (300, 500 and 1000 A), three operating speeds (70, 100 and 130 km/h) and with two rigid catenary configurations (ideal and real). Thus, the influence of power supply current, operating speed, catenary configuration and pantographs used on the wear rate has been evaluated. The results obtained in the different scenarios and a discussion are included next. 3.1. Selection of the pantograph pass factor As mentioned before, in order to reduce the computing time, the wear obtained in each iteration of the calculation process is assumed to be constant during 100 pantograph passes (i.e. pantograph pass factor equal to 100). For verification purposes, Fig. 5 shows the contact forces and contact wire wear for pantograph P08 at a speed of 130 km/h with a preload of 100 N. Results show the contact force and wear values obtained after 100, 500 and 2000 iterations when wire wear is updated after each pantograph pass and when wire wear is updated after every 100 pantograph passes. It is observed that, for the first 2000 pantograph passes, forces and wear obtained with the pass factor selected in this work are equivalent to those obtained by updating the wear on the contact wire after each pantograph pass (i.e., pass factor equal to 1). Furthermore, Fig. 6 includes a zoom of the forces obtained in a small region of the test Table 3 Wear model variables and parameters of the contact wire. Meaning Symbol Cu- ETP Model parameters Mechanical contribution weight k 1 22.4 Electrical contribution weight k 2 10.3 Contribution due to electrical arcs weight k 3 0.4 Electrical current reference value [A] I 0 500 Mechanical contribution on the electrical current α 4.5 Non-linear dependence of mechanical contribution on the contact force mean value β 1.8 Contact force reference value [N] F 0 90 Hardness of material [N/mm 2 ] H 700 Reference value of sliding speed [m/s] V 0 44.4 Decimal fraction value of percentage of contact loss u - Electrical arc voltage [V] V a 50 Density of copper [kg/m 3 ] ρ 8940 Copper latent heat of fusion [kJ/kg] H m 205 Model variables Contact force mean value [N] F m – Nominal electrical current [A] I c – Strip and wire electrical contact resistance (Eq. 5) [Ω] R c – Sliding speed [m/s] V – Fig. 4. Procedure for contact wire wear calculation. M. Simarro et al. Tribology International 196 (2024) 109708 6 section. As it can be seen, the forces obtained in both cases are quite similar. In addition, Fig. 7 shows the root mean square error of contact forces and wear between employing a pass factor of 1 vs 100. It can be seen how the errors are less than 1 N in forces and less than 0.4 µm in wear after 2000 passes. Assuming a trend like that for the wear, i.e., an increase in wear of 0.2 µm per 1000 pantograph passes, the error after 18,000 pantograph passes will be below 3.6 µm. Therefore, selecting a pass factor of 100 is considered appropriate for these simulations. 3.2. Influence of the pantograph passing speed Train speed is one of the main parameters on which the wear of the contact wire on the rigid catenary depends. Fig. 8, Fig. 9 and Fig. 10 (left) show the evolution of the mean catenary wire wear depth for the three selected speeds and for the three selected current intensities respectively. Similarly, Fig. 8, Fig. 9 and Fig. 10 (right) also shows a bar chart with the mean, maximum and minimum wear values of the cases analysed for the 18,000 pantograph pass simulation. On one side, results suggest that, for low intensities, wear increases slightly with increasing speed. However, a large dispersion of the wear values along the wire is observed, as shown in the bar diagram. Thus, it can be seen that the maximum and minimum wear values differ considerably from their mean value. On the other hand, for high values of intensity, wear decreases with increasing speed, showing a greater uniformity in wire wear in this case. For intermediate values of current intensity, speed does not seem to be a factor that influences contact wire wear. The influence of train speed, at low and high current intensities, does not affect wear distribution in the same way. While at low current intensities, the difference between the highest and lowest wear is 88 µm, at high intensities, the difference is reduced to 6 µm. As indicated, speed has a moderate effect on wear. A change in the trend is seen between 70 and 130 km/h, the speed at which a smaller increase in wear is observed with increasing intensity due to the effect of Fig. 5. Comparison between pass factors. Fig. 6. Comparison of contact forces between pass factor x1 and x100. M. Simarro et al. Tribology International 196 (2024) 109708 7 current lubrication, as mentioned in the references. The dispersion of wear values is more important at 300 A than at higher intensities. This fact could indicate that areas with low current demand, such as specific train acceleration and braking zones, medium and low constant speed zones, and areas with slight slopes, may suffer from wear with significant irregularities. 3.3. Influence of electrical current Current intensity is another main parameter to evaluate wear of the contact wire in a rigid catenary. Fig. 11, Fig. 12 and Fig. 13 (left) show the evolution of the mean wear depth in the catenary wire for the three elected current intensities and for the three chosen speeds respectively. Similarly, Fig. 11, Fig. 12 and Fig. 13 (right) also show bar diagrams with mean, maximum and minimum wear of the cases analysed for Fig. 7. RMS error of contact force (left) and wear (right) for a pass factor of 100. Fig. 8. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 08 – 300 A. Fig. 9. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 08 – 500 A. M. Simarro et al. Tribology International 196 (2024) 109708 8 18,000 pantograph passes. As shown in the previous subsection, it is observed that wear increases with operating speed for current intensities of 300 and 500 A. However, wear decreases with the increase in speed when the intensity is 1000 A. Additionally, it is observed that, smaller differences are obtained between the maximum and minimum wear for cases with greater intensity for the three speeds analysed. Similar results have been obtained with the simulations carried out with two other pantographs (see Fig. 14 and Fig. 15). This conclusion can be assigned by the so-called “current lubrication”, previously described in [26] [42], [44], [45], [53]. This factor was taken into account in Eq. (1). As indicated in the previous section, the wear rate is not strongly influenced by speed. On the contrary, the change in intensity is a more influential factor. From the results, it can be seen that, in order to evaluate the wear in a real installation, it is necessary to take into Fig. 10. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 08 – 1000 A. Fig. 11. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 08 – 70 km/h. Fig. 12. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 08 – 100 km/h. M. Simarro et al. Tribology International 196 (2024) 109708 9 account the current required by the units to properly evaluate the wear in the contact wire. Therefore, it is advisable to pay more attention to areas with medium-low demanded intensities, where the average wear is higher and there is a great difference between the maximum and minimum wear values. This wear behavior, over time and with the contribution of speed, could generate areas of non-homogeneous wear, which negatively feedback to the system and accelerates the whole deterioration process, as will be seen in the following section. 3.4. Influence of the rigid catenary configuration The geometric characteristics of the rigid catenary are the third parameter with a substantial influence on the wear of the contact wire, as they have a relevant impact on the contact forces during the Fig. 13. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 08 – 130 km/h. Fig. 14. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 01 – 130 km/h. Fig. 15. Wear depth vs pant. passes (left) and wear histogram (right) – Pant. 10 – 130 km/h. M. Simarro et al. Tribology International 196 (2024) 109708 16 Table A.III (continued) Support Stiffness (N/m) Support Stiffness (N/m) Support Stiffness (N/m) Support Stiffness (N/m) 10 375,512.20 23 378,076.02 36 381,563.66 49 382,073.23 11 373,381.74 24 377,678.35 37 380,444.30 50 381,406.29 12 374,483.94 25 374,483.94 38 378,305.76 51 381,780.16 13 375,512.20 26 374,051.93 39 378,885.84 52 38,0829.20 Table A.III 2. Parameters of the OCR FE model in the real section. Value Units General Number of spans 51 Span length 8 ±15 % [21 S] m Aluminum profile and contact wire Equivalent section area 2365 ×10 −6 m 2 Equivalent inertia flexural property 4.24678 ×10 −6 m 4 Equivalent density 3012.7 kg/m 3 Young modulus 6.9 ×10 10 N/m 2 Flange Weight 2.98 kg Moment of inertia 2.35 ×10 −3 kg m 2 Support Support stiffness Table A.III.1 References [1] Patent nº FR2185838: “Ligne d ′ alimentation ´ electrique rigide, notamment pour l ′ alimentation en courant de v´ ehicules ´ electriques sur rails (Rigid Overhead Current Conductor for ElectricRailways, in English)”, Delachaux, 1972. [2] Bruni Stefano, Bucca Giuseppe, Carnevale Marco, Collina Andrea, Facchinetti Alan. Pantograph–catenary interaction: recent achievements and future research challenges. Int J Rail Transp 2017;6(2017). https://doi.org/10.1080/ 23248378.2017.1400156. [3] Zhang W, Zou D, Tan M, et al. Review of pantograph and catenary interaction. 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