Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2022.35.0042 Acta Polytechnica CTU Proceedings 35:42–48, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague COMPARISON OF SELECTED PARAMETERS FOR EVALUATION OF RAIL SURFACE DAMAGE INTENSITY Jiří Šlapák∗, Tomáš Michálek University of Pardubice, Faculty of Transport Engineering, Department of Transport Means and Dignostics, Studentská 95, 532 10 Pardubice, Czech Republic ∗ corresponding author: jiri.slapak@upce.cz Abstract. This paper deals with the issue of evaluation of a rail surface damage (RSD) intensity. Some ways of calculating parameters that represent the RSD are described. In this context, a multi-body model of a railway vehicle was created and several simulations of this model on a curved track were performed. Furthermore, these simulations were evaluated and the RSD parameters were compared. Keywords: Wheel/rail interaction, rail surface damage, wear number, multi-body simulation. 1. Introduction In recent years, some railway infrastructure managers have started to use vehicle ratings based on damaging effects of vehicles on tracks. These damaging effects are directly related to maintenance requirements of tracks. One of the damaging effect is the rail surface damage (RSD), which occurs when wheels roll on rails. RSD primarily represents a wear of rails by abrasion and secondarily a relationship between the wear and a rolling contact fatigue (RCF ). This method of evaluation may motivate vehicle operators to use and purchase track-friendly vehicles. This paper is focused on several methods for evalu- ating RSD intensity and these methods are compared. These evaluation methods are described. The param- eters that represent RSD intensity are compared de- pending on selected vehicle parameters. By means of multi-body simulations of vehicle running, a quantifi- cation of the parameters representing RSD intensity and damaging effects can be performed. 2. Rail surface damage Rolling of wheels on rails is possible due to normal forces acting in wheel/rail contact areas and the exis- tence of adhesion in these contact areas. In general, when wheels rolls on rails, creepages and tangential (creepage) forces occur in the wheel/rail contact areas. The creepages occur in the longitudinal and lateral directions and also as a spin (rotation around the vertical axis). The longitudinal creepage is primarily related to traction and braking forces and also to the conditions of the wheelset/track interaction (specifi- cally on the delta-r function) in curves. The increase in the lateral creepage is caused by an increase in the angle of attack of the wheelset. The spin is related to the inclination of the wheel/rail contact area. Creepages and spin result in tangential (creepage) forces and spin moment that cause loading of the rail surface. Due to this loading, the rail surfaces are damaged. In more detail, the issue of creepage forces is described in [1]. The first damaging effect is the wear of the rails and wheels by abrasion. The amount of wear depends on some design parameters of a vehicle, some wheel/rail contact conditions (coefficient of friction/adhesion, materials) and some track parameters. The rolling contact fatigue (RCF ) is another dam- aging effect caused by wheels rolling on rails. RCF causes cracks on the rail surface. Under certain con- ditions, crack initiations can be removed by wear on the rail surface. Thus, the wear can be beneficial in terms of the rolling contact fatigue. 2.1. Wear number The parameter called the wear number Tγ [Nm/m] is the first option for evaluating and comparing the damaging effects of vehicles that result in RSD. This parameter is based on the physical assumption that the wear of the rails and wheels is caused by friction work performed in the wheel/rail contact. According this assumption, the wear number is defined as: Tγ = |Txγx| + |Ty γy | , (1) where T [N] is the tangential (creepage) force and γ [−] is the creepage in the wheel/rail contact. The letters x and y describe the longitudinal and lateral direction of these quantities. Equation 1 applies when spin and spin moment are neglected. Since these quantities (specifically creepages and lateral creepage force) cannot be measured on a real vehicle, it is necessary to determine the value of the wear number using multi-body simulations of vehicle running. The wear number presented in Equation 1 corre- sponds to the specific friction work performed in the wheel/rail contact. Furthermore, the wear number in this form is used in the methodologies of some railway infrastructure managers for setting track acess charges (e.g. methodology [2]). 42 https://doi.org/10.14311/APP.2022.35.0042 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 35/2022 Comparison of Selected Parameters 2.1.1. RCF prediction method based on Tγ The wear number Tγ is also used in the RCF predic- tion method. The non-linear dependence of the wear number and the so-called RCF damage index is shown in Figure 1 and described in [3]. This index indicates whether the rails are damaged due to wear, RCF or a combination of both, which is more common option. According to Figure 1: • RCF damage index increases from 0 to 1 · 10−5 as the wear number values incease from 15 N to 65 N. When the wear number value is 65 N, the probability of RCF crack initiation is greatest. • Then the index value decreases to 0 as the wear number increases to 175 N. In this part, a wear begins to predominate over RCF. • For the wear number values greater than 175 N, the RCF damage index has negative value. This mean that only wear damage occurs. Figure 1. Dependence of the wear number Tγ and RCF damage index. [3] Figure 1 applies to R260 steel. For other steels, the position of the characteristic points differs. 2.2. Rail surface damage parameter according to EN 14363 In the standard EN 14363 [4], the current evaluation of rail load in lateral direction is performed using the quatistatic lateral guiding force Ya,qst. This force is also used as indirect evaluation parameter for the rail surface damage intensity especially the wear of rails, but sometimes it shows a very weak connection with RSD. Another parameter for the evaluating of the rail surface damage intensity is presented in Annex K of standard EN 14363 [4]. The standard proposes the parameter Tqst which is a combined quantity of lateral Yqst, longitudinal Tx,qst and vertical Qqst forces acting in the wheel/rail contact and represents the rail surface damage intensity. The parameter Tqst is defined as: Tqst = Qqst 10000 · ( 330 · f 2 − 62 · f + 4 ) , (2) where f = Yqst Qqst + 0, 62 · |Tx,qst| Qqst . (3) The constants in these equations are derived as regres- sion parameters from the dependence of Tqst and Tγ . The parameter f (Equation 3) is dimensionless then the unit of the parameter Tqst (Equation 2) is Newton [N]. This parameter has been defined in order to be able to measure the values of input parameters (forces) on a real vehicle without multi-body simulation. Compared to the guiding force Ya,qst, the parameter Tqst better includes the influence of friction conditions in the wheel/rail contact area. The parameter Tqst has only been defined for the guiding wheel of a vehicle. 3. Multi-body simulations The values of previously defined quantities were ob- tained from multi-body simulations of running vehi- cle. The model and multi-body simulations of railway vehicle running were performed using SIMPACK sim- ulation software. 3.1. Model of railway vehicle For the purposes of this study, the multi-body model of a conventional passenger car of an electric unit was used. The fundamental parameters of this model are listed in Table 1. Parameter Value Unit Nominal mass of the carbody 40000 kg Mass of the bogie frame 5200 kg Mass of the wheelset 2100 kg Bogie distance 19 m Nominal bogie wheelbase 2.4 m Vertical stiffness of the primary spring (per wheel) 1.6 kN/mm Vertical stiffness of the secondary spring (per side of bogie) 0.7 kN/mm Table 1. Fundamental parameters of the multi-body model of the railway vehicle. Setting the wheel/rail contact conditions is a very important part of the simulations. The wheel profile ORE S1002 and the rail profile 60E1 were used. The rail inclination of 1:40 was considered. The nominal friction coefficient value 0.4 was chosen. The FAST- SIM algorithm was chosen to calculate the tangential (creepage) forces. Figure 2. The vehicle model created in SIMPACK. 43 Jiří Šlapák, Tomáš Michálek Acta Polytechnica CTU Proceedings Figure 3. Basic comparison of the mentioned parameters used to evaluate RSD intensity depending on the curve radius R. Only for the guiding wheel on vehicle. 3.2. Track conditions The simulations were performed on several curved tracks with a radius from 250 m to 1200 m. The length of the curve was set to 600 m. The cant D and cant deficiency I values are constant for all simulations. • D = 150 mm • I = 130 mm According to these conditions, the vehicle speed was set in the range of values from 77 km/h to 169 km/h. In the order to consider a real model of the track, reference track irregularities were used and a model of elastic track foundation was created. 4. Simulation results Time records of the quantities acting in the wheel/rail contact (lateral, longitudinal and vertical forces) and the parameter wear number Tγ were monitored and exported from the multi-body simulations. From these records, the mean values of the quantities in the fully curved part of the tracks were calculated. The ex- ported data from simulations were processed in MAT- LAB. Because the parameters Tqst and Ya,qst are defined for the guiding wheel of a vehicle, all comparisons and evaluations have been processed for the guiding wheel only. 4.1. Comparison of evaluation parameters For the first look at the comparison of the mentioned RSD intensity parameters (Tγ , Tqst, Ya,qst), the pa- rameter values depending on the curve radius are plotted in Figure 3. This figure only shows the situa- tion on the guiding wheel of vehicle for the nominal setting of the multi-body model and the simulation. According to Figure 3, all RSD intensity param- eters depending on the curve radius have the same trend and the shapes of the graph curves are similar. The values of the parameters progressively increase as the curve radius decreases. The figure further shows that the parameter Tqst values are smaller than the wear number Tγ values in curve radii greater than 700 m. Then for smaller values of the curve radii, the parameter Tqst values are greater then the values of the wear number Tγ . However, this only applies to the guiding wheel of the vehicle. Figure 3 further shows that the curve of the wear number Tγ has a convex character in the whole range of curve radii. This also applies to the parameter Tqst, except for the situation of the very small curve radius where the curve begins to be concave. 4.2. Influence of selected parameters According to the standard EN 14363 [4], the formula for the parameter Tqst (Equation 2) was defined for a wide range of selected operating conditons of a vehicle. Therefore, vehicle running simulations were performed with a focus on the influence of these parameters: • friction coefficient in the wheel/rail contact µ, • weight of vehicle body m, • bogie wheelbase 2a, • longitudinal stiffness of wheelset guiding kx per one wheel. For all these parameters, the dependences of Tqst and Tγ on the curve radius R are plotted in graphs. To compare of RSD intensity parameters, the difference between Tqst and Tγ is defined and calculated as: Tγ − Tqst [N ]. (4) Furthermore, the relative difference is defined and calculated as: (Tγ − Tqst) /Tγ · 100 [%]. (5) 4.2.1. Influence of friction coefficient In the first part, the influence of the friction coeffi- cient values in the wheel/rail contact was investigated. Friction coefficient values of 0.2, 0.4 and 0.6 were selected. Figure 4 shows comparison of the wear number Tγ and the parameter Tqst (calculated according to [4]) on the guiding wheel of the vehicle. For different 44 vol. 35/2022 Comparison of Selected Parameters values of the friction coefficient µ in the wheel/rail contact area, the individual curves are plotted as a function of the curve radius R. For all investigated values of the friction coefficient, this figure shows that the values of the parameter Tqst are very close in the range of the curve radius from 700 m to 1200 m. This behavior of the parametr Tqst is different from the wear number Tγ . Further, as the curve radius value decreases, the values of the parameter Tqst as well as the parameter Tγ values increase. Figure 4. Dependence of the Tqst and Tγ on the curve radius R in defined range of the friction coefficient values µ. Figure 4 shows that the friction coefficient value in the wheel/rail contact area has a great influence on the values of wear number Tγ and also shows that the parameter Tqst follows this trend. Figure 5. Dependence of the Ya,qst on the curve radius R in defined range of the friction coefficient values µ. In Figure 5, the influence of the friction coefficient µ on lateral guiding force Ya,qst is shown. As the friction coefficient values increase, the slope of the plotted curves increases. This behavior is the same as for the parameters in Figure 4. But the curves are shifted, which causes a large mismatch between the force Ya,qst and the parameters Tqst and Tγ . The next Figure 6 shows the difference and the relative difference between the values of the wear number Tγ and the parameter Tqst in defined range of friction coefficient values. In general, the best match of these parameters occurs for the smallest value of the friction coefficient. But for very small curve radii, the value of the relative difference for the friction coefficient of 0.6 is the smallest. This mean that in very small curve radii, Tqst corresponds better to the wear number Tγ with increasing value of the friction coefficient. On the other hand, for large curve radii, the parameter Tqst best corresponds to the wear number Tγ under the conditions of the smallest value of the friction coefficient. For a radius curve of 1200 m and a friction coefficient of 0.6, the value of the relative difference is 78%. Figure 6. The difference Tγ − Tqst depending on the curve radius R (above) and the relative differ- ence (Tγ − Tqst) /Tγ depending on the curve radius R (below) in the defined range of friction coefficient µ values. 4.2.2. Influence of vehicle weight In the next part, the influence of the vehicle weight was investigated. For this evaluation, the vehicle body mass m was set to 35, 40 and 45 tons. Figure 7 shows the values of the parameter Tqst and the wear number Tγ as a function of the curve radius R for the defined values of the vehicle body weight. According to this figure, the weight of vehicle has an effect on the wear number Tγ values. This effect is most evident for the small curve radii. On the other hand, the values of the parameter Tqst do not change when the vehicle weight changes. This applies in whole range of the curve radii expect the very small curve radii. 45 Jiří Šlapák, Tomáš Michálek Acta Polytechnica CTU Proceedings Figure 7. Dependence of the Tqst and Tγ on the curve radius R for defined values of the vehicle body mass m. Figure 8. Dependence of the Ya,qst on the curve radius R for defined values of the vehicle body mass m. Figure 8 shows that the weight of the vehicle body has an effect on the guiding force Ya,qst. The wear number Tγ (in Figure 7) has a similar effect. Further- more, the dependence of the force Ya,qst on the curve radius is concave in very small curve radii, as well as the dependence of the parameter Tqst on the curve radius. In Figure 9, the difference and the relative difference of the parameters Tqst and Tγ are shown in relation to Figure 7. In very small curve radii, the best match of the investigated parameters occurs at higher values of the vehicle weight. Then in the large curve radii, the best match of the parameters occurs for the lightest vehicle but the differences disappear in very large curve radii. In the value of the curve radius of 1200 m, the relative difference value is 72% and this value does not depend on the vehicle weight. Figure 9. The difference Tγ − Tqst depending on the curve radius R (above) and the relative difference (Tγ − Tqst) /Tγ depending on the curve radius R (be- low) for defined values of the vehicle body mass m. 4.2.3. Influence of bogie wheelbase In this part the influence of the bogie wheelbase 2a on the parameters Tqst and Tγ is analyzed. The value of the bogie wheelbase was set to 2.0, 2.4 and 2.8 meters. Figure 10. Dependence of the Tqst and Tγ on the curve radius R for defined values of the bogie wheel- base 2a. In Figure 10, the influence of the bogie wheelbase values is evident for both parameters of RSD intensity over the whole range of the curve radii. Again, the values of Tqst are smaller than the values of Tγ for large curve radii. Then, for small curve radii, the values of Tqst increase over the values of Tγ . 46 vol. 35/2022 Comparison of Selected Parameters Figure 11. Dependence of the Ya,qst on the curve radius R for defined values of the bogie wheelbase 2a. According to Figure 11, the influence of the bogie wheelbase 2a on the guiding force Ya,qst values and on the parameter Tqst is similar. For large and very small curve radii, it is difficult to predict and describe the values of the force Ya,qst . The dependence of the Tγ values on the curve ra- dius has the same trend for different values of bogie wheelbase. This does not apply to the parameter Tqst whose trends are changing in the very small curve radii. This is also shown in Figure 12 where the both differences increase (in terms of absolute values) in the very small curve radii under the condition of the bogie wheelbase of 2.0 m. But for the other values of the bogie wheelbase in the very small curve radii, the differences decrease with decreasing the curve radius. Figure 12. The difference Tγ − Tqst depending on the curve radius R (above) and the relative difference (Tγ − Tqst) /Tγ depending on the curve radius R (be- low) for defined values of the bogie wheelbase 2a. In general, Figure 12 shows that the best match between the Tqst and Tγ parameters occurs for the vehicle with the longest bogie wheelbase. According to the first graph in Figure 12 and for the curve radius of 250 m, the value of the difference is 150 N for the vehicle with bogie wheelbase of 2.0 m. It is the highest value of the absolute diference of the RSD intensity parameters. But from the point of view of the relative difference of these parameters, the value corresponds to the relative difference of 37%. A much larger relative difference occurs in curve radius of 950 m where the value is about 74% and it is the highest value of the relative difference of the parameters for this analysis. 4.2.4. Influence of longitudinal stiffness of wheelset guiding The influence of the longitudinal stiffness of the wheelset guiding kx per one wheel on the parame- ter Tqst and the wear number Tγ is the last analyzed part. The values of the longitudinal stiffness of the wheelset guiding per one wheel were set to 2.0 · 107, 3.5 · 107 and 5.0 · 107 N/m. Figure 13. Depencence of the Tqst and Tγ on the curve radius R in defined range of the longitudinal stiffness of wheelset guiding kx per one wheel. Figure 14. Depencence of the Ya,qst on the curve radius R in defined range of the longitudinal stiffness of wheelset guiding kx per one wheel. Figure 13 shows that the longitudinal stiffness of the wheelset guiding in defined range of values has 47 Jiří Šlapák, Tomáš Michálek Acta Polytechnica CTU Proceedings a small effect (in comparison with other investigated parameters) on the values of the parameter Tqst and the wear number Tγ . From this point of view, the behavior of these parameters is the same. Thus, in general, changing the stiffness value causes the same reaction in the parameter Tqst as in the wear number Tγ . According to Figure 14, the behavior of the depen- dence of the guiding force Ya,qst on the curve radius is the same as the dependences on Figure 13. This means that the effect of the longitudinal stiffness of wheelset guiding kx in a defined range of values on the guiding force Ya,qst values is small. Figure 15. The difference Tγ − Tqst depending on the curve radius R (above) and the relative difference (Tγ − Tqst) /Tγ depending on the curve radius R (be- low) in the defined range of the longitudinal stiffness of wheelset guiding kx per one wheel. This fact is confirmed in Figure 15. This figure shows that the difference and the relative difference values are almost idential for the defined range of the longitudinal stiffness values. Some effect of the longitudinal stiffness to the difference and the relative differrence of RSD intensity parameters occurs in very small curve radii. 5. Conclusions It can be assumed that the wear number Tγ represents the wheel and rail abrasion wear and indirectly also represents the rolling contact fatigue effects. It is used by railway infrastructure managers as an indicator of damage and maintenance requirements of a curved track. Unfortunately, the wear number must be ob- tained from multi-body simulations and cannot be measured on a real vehicle. This fact means a risk that the results of the multi-body simulations can be affected by the model settings. The correctness of this settings cannot be experimentally verified. The lateral guiding force Ya,qst is a parameter that is used to evaluate the lateral load of the rails. This force exhibits similar behavior and trends as the wear number Tγ depending on the curve radius, but its values are different. For the reason, an alternative quantity, the parameter Tqst is defined in the standard EN 14363. Based on multi-body simulations of running a con- ventional passenger four-axle railway vehicle, it was found that the parameter Tqst shows the same trends as the wear number Tγ on the outer guiding wheel of a vehicle. However, there are differences between the values of these parameters, which vary depend- ing on the curve radius. The parameter Tqst values are smaller than the wear number values in the large curve radii. Conversely, the parameter Tqst values are higher than the wear number in the very small curve radii. The best match of these parameters occurs in curve radii from 400 to 600 meters. The worst match occurs in the very large curve radii where the relative difference between the parameter Tqst and the wear number Tγ has a value higher than 70 percent. This mean that this approximation of the parameter Tqst is bad for very large curve radii. The friction coefficient value in the wheel/rail con- tact area has the greates influence on the RSD in- tensity parameters. Further, the vehicle body weight affects the wear number values, but has almost no effect on the parameter Tqst value. The values of the longitudinal stiffness of wheelset guiding have the same effect on both RSD intensity parameter. The defined parameter Tqst for evaluation of RSD intensity follows the trend of the wear number. But between these parameters, there is bad match in the large curve radii and the parametr Tqst does not re- spond to the vehicle weight change. The parameter Tqst can represent the wear number, but the accuracy of this parameter could be improved. Acknowledgements This work was supported by the scientific research project of the University of Pardubice No. SGS_2021_010. References [1] Voltr, P.: Calculation of locomotive traction force in transient rolling contact. In: Applied and Computational Mechanics, 11, 69-80, 2017. [2] Feredal Office of Transport. Base Price Wear in the train-path pricing system 2017 – Instruction for determining vehicle prices. Bern, 2017. [3] Iwnicki, D. S.: The Effect of Profiles on Wheel and Rail Damage. In: International Journal of Vehicle Structures & Systems,1(4), 99-104, 2009. [4] EN 14363:2016+A1:2018. Railway applications – Testing and Simulation for the acceptance of running characteristics of railway vehicles – Running behaviour and stationary tests. Brusel: European Committee for Standardization, 2018. 48 Acta Polytechnica CTU Proceedings 35:42–48, 2022 1 Introduction 2 Rail surface damage 2.1 Wear number 2.1.1 RCF prediction method based on T 2.2 Rail surface damage parameter according to EN 14363 3 Multi-body simulations 3.1 Model of railway vehicle 3.2 Track conditions 4 Simulation results 4.1 Comparison of evaluation parameters 4.2 Influence of selected parameters 4.2.1 Influence of friction coefficient 4.2.2 Influence of vehicle weight 4.2.3 Influence of bogie wheelbase 4.2.4 Influence of longitudinal stiffness of wheelset guiding 5 Conclusions Acknowledgements References