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Prediction of RCF and wear evolution of iron-ore locomotive wheels
Wear 338-339 (2015) 62–72
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Wear journal homepage: www.elsevier.com/locate/wear
Prediction of RCF and wear evolution of iron-ore locomotive wheels Saeed Hossein Nia n, Carlos Casanueva, Sebastian Stichel KTH Royal Institute of Technology, Stockholm, Sweden
art ic l e i nf o
a b s t r a c t
Article history: Received 13 February 2015 Received in revised form 26 May 2015 Accepted 28 May 2015 Available online 6 June 2015
Locomotives for the iron ore line in northern Sweden and Norway have a short wheel life. The average running distance between two consecutive wheel turnings is around 40,000 km which makes the total life of a wheel around 400,000 km. The main reason of the short wheel life is the severe rolling contact fatigue (RCF). The train operator (LKAB) has decided to change the wheel profiles to get a better match with the rail shapes in order to decrease the creep forces leading to RCF. Two wheel profiles optimised via a genetic algorithm were proposed. They have, however, not been analysed for long term wear development. There is a risk that the optimised profiles might wear in an unfavourable way and after a while cause even higher RCF or wear than the original one. This study predicts wheel profile evolution using the uniform wear prediction tool based on Archard’s wear law. RCF evolution on the surface of the wheel profiles is also investigated. The impact of wear on polishing the wheel surface and avoiding the RCF cracks to propagate is considered via introducing a correction factor to the calculated RCF index. Traction and braking are also considered in the dynamic simulation model, where a PID control system keeps the speed of the vehicle constant by applying a torque on the loco wheels. The locomotives are also equipped with a flange lubrication system, therefore the calculations are performed both for lubricated and non-lubricated wheels. The simulation results for the wheel profiles currently in use, which are performed to validate the model and the simulation procedure, show a good agreement with the measurements. It is also concluded that the lubrication system partly does not perform as expected. Comparison between the proposed optimised profiles for their long term behaviour suggests that one of them produces less RCF and wear compared to the other one. & 2015 Elsevier B.V. All rights reserved.
Keywords: RCF Wear Heavy haul Traction Braking Lubrication
1. Introduction The Swedish iron-ore company LKAB uses Bombardier locomotives with 30 t axle load to transport pellets from the mines in Kiruna and Malmberget to the ports in Luleå and Narvik. The average mileage interval between two consecutive wheel turnings for a wagon wheel is around 250,000 km while it is much lower for a loco wheel, around 40,000 km. The turning intervals lead to a total service life of the wagon wheels of 1,000,000 km and the locomotive wheels of 400,000 km. The difference between the numbers is mainly due to RCF on the loco wheels. LKAB uses three measurement stations on Malmbanan in order to detect high vertical impact forces, possibly due to wheel flats, where urgent maintenance actions are needed. Besides, regular inspections for wheels are carried out every 26,000 km for the locomotives and every 80,000 km for the wagons. These inspections are performed in the workshop located in Kiruna and they are mainly for detecting cracks on the wheels and possible needs n
Corresponding author. E-mail address: [email protected] (S. Hossein Nia).
http://dx.doi.org/10.1016/j.wear.2015.05.015 0043-1648/& 2015 Elsevier B.V. All rights reserved.
for re-profiling. Rails are checked by the Swedish infrastructure owner, Trafikverket, and are ground once a year. Each traction unit consists of two identical Co-Co locomotives permanently coupled back to back. There are 68 wagons connected to the locomotives and in the laden condition the total weight carried by the loco is more than 8000 t. The maximum speed of the locos on tangent track is 60 km/h for loaded and 70 km/h for unloaded trains. The simulation model of the loco is developed at Bombardier via SIMPACK [1] and is translated to GENSYS [2] for this study. To enhance the service life of the wheels, LKAB has decided to change the wheel profiles in to achieve a better curving performance for the loco and, consequently, a reduction of the generated creep forces. To optimise the wheel profiles a genetic algorithm [3] is used. For details of the optimisation process, see [4]. Two optimised wheel profiles (WPLX2 and WPLX4) are suggested as potential profiles for field testing. However, in order to study the long-term stability of the optimised profiles, monitoring the evolution of the profiles is inevitable. There is a risk that the new profiles might wear in an unfavourable way and after a while cause even higher RCF or wear than the original one: depending on the shape of the profile, the elements which determine the risk of RCF such as lateral and
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longitudinal creep forces would change. The evolution of the profile affects the conicity of the wheel and influences the curving performance and attack angle of the wheelset, which will eventually change the wheel–rail contact forces and modify the RCF risk. This paper studies the evolution of wear and RCF of the proposed wheel profiles as a function of running distance. The procedure is repeated for the current locomotive wheel profile (WPL9) and the results are compared with measurements in order to validate and tune the wear and RCF calculation model characteristics. 1.1. Wear From the tribological point of view wear is defined as any damage to a solid surface, involving progressive loss of material and relocation of material when two surfaces are interacting via a relative motion. How a material wears depends not only on the nature of the material but also on other elements of the tribosystem such as geometry of contacting pairs, surface topography, loading, lubrication and environment. The mechanisms causing such damages are usually complicated and most of the time it is not possible to distinguish one from another. In [5], approximately 60 terms describing wear behaviour and mechanisms are listed. Some of the most important wheel–rail related mechanisms are mentioned below.
Abrasive wear: wear caused by rough and hard surfaces sliding
on each other or wear caused by hard particles trapped between two surfaces like hard oxide debris. Adhesive wear: wear caused by shearing of junctions formed between two contacting surfaces, sometimes used as a synonym for dry sliding wear. Chemical wear (Corrosive wear): wear caused by formation of any oxide or other components on surfaces due to chemical reaction of the surfaces with the environment. Erosive wear: Wear due to relative motion of contact surfaces while a fluid containing solid particles is between the surfaces. Rolling contact fatigue (RCF): caused by cyclic stress variations leading to fatigue of the materials. Generally resulting in the formation of surface, sub-surface and deep-surface cracks, material pitting and spalling.
Kimura [6] studies adhesive wear and RCF and concludes that both phenomena have elemental processes in common. In this study the term “wear” is used for adhesive wear, otherwise the complete term of the damage mechanism is mentioned. Note that the term “mechanical wear” is also used for abrasion, erosion, adhesion and surface fatigue. Published research and studies on wear modelling usually have three approaches:
Field measurements, laboratory tests, and theoretical prediction models. Most of the field measurements have addressed the effect of lubrication on wear such as [7,,8]. Archard [9] took the idea of the adhesive wear definition and found that the volume of material removed by wear per sliding distance (W) is proportional to the quotient of the pressure (p) and the hardness (H) of the softer material. The proportionality factor is called the wear coefficient (k) which is expected to be a function of wheel and rail material. Two separate mild and severe wear regimes are suggested; therefore a constant K is added to maintain the relation in the severe regime.
Fig. 1. Wear map for wheel and rail steel; H is the hardness of the material.
W=
kp + K. H
(1)
The wear coefficient depends on the governing wear mechanisms. Archard validated his model by determining the wear rates for different material pairs by pin-on-disc tests. Lim and Ashby [10] performed large amounts of laboratory tests and introduced wear maps where the wear coefficient is plotted as a function of sliding velocity and the nominal pressure (normal load divided by the nominal contact area). The wear map corresponding to medium carbon steel, based largely on pin-on-disc data, is generally divided into two main regions of mechanical and chemical wear. Childs [11] suggested a wear map for the mechanical wear mechanism where the wear coefficient is a function of the asperities attack angle and the relative strength of the interfaces. The chemical part of the map, however, consists of two regions: mild and severe oxidational wear. Olofsson and Telliskivi [12] have investigated the evolution of the rail profiles of a commuter track within two years together with performing several laboratory tests with two different testing machines: a two-roller (disc on disc) and a pin-on-disc machine. The results of the tests were simplified into a wear map where wear coefficient depends on local sliding velocity and contact pressure, cf. Fig. 1. Several authors have investigated and developed wheel wear prediction tools. Important contributions can be found in studies from Kalker [13], Pearce and Sherratt [14], Ward [15] and Jendel [16]. Note that the studies mentioned here have all neglected the plastic deformation of the material and focused on uniform wear. Enblom [17] used the same methodology as Jendel. However, he included the elastic strain in the sliding velocity assessment. He also increased the simulation set with simulation of disc braking. In a different approach McEven and Harvey [18] used a fullscale wheel-on-rail-wear rig. They have proposed a linear relation between the wear rate and the dissipated energy per unit distance ¯ per unit area A, adjusted with a constant off-set term,K . rolled E, The energy dissipation per unit distance area is the creep forces times the creepages added to the moment times the spin in the contact patch. They also have predicted two wear regimes of mild (tread contact) and severe (flange contact) wear.
Wear rate per unit rolled distance = k where
E̅ A
E¯ + K, A
(2)
is sometimes called the wear number.
1.2. RCF As mentioned above, the rolling contact fatigue or RCF is also a type of surface deterioration and material loss which generally starts some millimetres below the material surface and propagates
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Fig. 2. Shakedown map.
through the surface. Surface initiated fatigue usually occurs when the response of a material to a cyclic load leads to ratchetting of the plastic deformation. In such a phase the plastic deformation will remain unstable and there will be an incremental strain growth at each load cycle. However, in the cyclic plasticity phase (plastic shakedown) the material could be subjected to surface initiated cracks in the low cycle fatigue process (LCF). Using the discussed regimes above, together with the perfectly elastic and elastic shakedown phase, Johnson, in 1989, proposed a theory for predicting rolling contact fatigue [19]. From the solid mechanics point of view he has the von Mises, maximum-distortion-energy, yielding criterion and developed the so called shakedown map. A simplified shakedown diagram is presented in Fig. 2. The location of the points in the shakedown diagram is a function of, firstly, the traction coefficient (T )
T=
FT = FZ
Fx2 + Fy2 Fz
,
(3)
where Fz is the normal contact force, Fx and Fy are longitudinal and lateral creep forces respectively. Secondly, it depends on the normalised vertical load (v ) which is the maximum contact pressure (p0 ) divided by the yield stress in shear (k ) of the softer material in contact:
v = p0 / k .
(4)
The boundary curve for surface plasticity (BC) is calculated as
BC =1/T .
(5)
If a working point passes the boundary curve above the friction level around 0.3 ratchetting occurs, while below this friction level, the material is subjected to low cycle fatigue or plastic shakedown. However, if a working point does not pass the boundary curve, depending on the normal load, the material is in either the perfectly elastic or the elastic shakedown regime. Note that for elastic shakedown which is considered as high cycle fatigue (HCF), the cracks may be initiated in subsurface of the material. Ekberg [20] used the idea of the shakedown map and developed an engineering approach to predict RCF in railway applications. He calculated the distance of the points from the boundary curve and called it surface fatigue index (FIsurface)
FIsurf = T − 1/v = T −
2π a . b . k 3Fz
(6)
where a and b are the semi-axes of the elliptic contact area in the Hertzian contact. RCF is likely to happen for positive values of FIsurface. The fatigue index approach is nowadays widely used in multibody simulation softwares. There is a debate on propagation of the cracks. Due to the direction of the longitudinal creep forces on wheels and rails low viscous fluids like oil lubricants or water could be trapped in the
Fig. 3. Three bands of RCF on an iron-ore locomotive wheel. Photo by Roger Deuce/ Copyright: Bombardier Inc.
cracks. Furthermore, the stresses force the fluid to the tip of the crack. As the fluid is incompressible there will be extremely high stresses around the trapped fluid. Finally, the stresses help the crack to develop further after the crack leaves the contact area [21]. Following a laboratory test on gears, Kimura [6] observed a similar behaviour with the fatigue life of the dedendum and the addendum. As the slip signs are in opposite directions above (addendum) and below (dedendum) the pitch circle (pure rolling) of a gear, cracks appeared always on the dedendum first. Later Kimura suggested that although this theory seems reasonable, there are facts which make it doubtful. Firstly, the phenomenon is supposed to be seen only in lubricated systems but similar behaviour is also seen in non-lubricated systems. Secondly, it is seen that cracks will also initiate and grow in the addendum in considerably high traction forces. In railway applications, for example on iron-ore lines, technicians reported a trend of RCF cracks in three bands on the locomotive wheels (Fig. 3). The first two bands, RCF1 and RCF3, are located at the field side (typically due to curving, on the inner rail) and the nominal rolling radius area (typically due to braking and traction) while the third band (RCF2) is usually located at the flange side (due to curving, on the outer rail). Fig. 3 shows a photo of an actual iron-ore wheel profile right before reprofiling, where the three bands of RCF can easily be seen. Many attempts have been made to combine wear and RCF effects in the prediction of wheel and rail damages. At a certain level of wear depth the initiated cracks could be polished away from the surface. In the UK a model has been proposed and calibrated on six intermediate-radius curves, where RCF on rails is observed, see [22]. In the mentioned work it is assumed that the wear depth is linearly proportional to the wear number. However, the spin effect is not included in the calculation of the energy dissipation. In the current paper we took the idea of the influence of energy dissipation on RCF and assumed that RCF is worn out for high energy dissipation values in the wheel–rail contact patch.
2. Calculation methodology In this section the calculation methodology is discussed. This includes the simulation of short term dynamic behaviour and long term damage mechanism.
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Fig. 4. Methodology of wheel wear prediction developed by Jendel [16].
Table 1 Details of track design geometries for each simulation case concluding a wear step R (m)
r350 350–400 400–450 450–600 600–800 800–1000 1000–1300 1300–1500 41500
Radius (m) Transition in and out (m)
Constant Length (%) Cant curve (m) (mm)
Gauge (mm)
305 368 409 547 648 934 1102 1395 1
270 210 140 227 210 200 210 190 500
1444 1443 1448 1447 1445 1444 1443 1440 1435
80 100 175 145 140 170 110 110 –
4.4 0.9 1.5 13.9 16.1 7.9 5.4 1.8 48.1
68 61 66 51 46 37 33 28 0
2.1. Wear prediction In the present work we have used the Jendel approach [16] to predict the wheel profile evolution. Jendel has used the Archard formula, Eq. (1), to develop his method. The methodology is based on a load collective concept, which determines a set of dynamic time-domain simulations. These simulations reflect the actual rail network for the vehicles in question. The Hertzian theory is used for the normal contact and the FASTSIM method is applied for the tangential contact problem. Fig. 4 shows Jendel’s wheel wear prediction flowchart. 2.2. Operational cases To reflect the actual rail network a set of time-domain simulation cases called load collective is prepared. Then, parametric studies are performed with running distance of 10,000 km for each case and the results are compared with the measurements data in order to tune the simulation parameters. The parameters for designing a load collective are:
track geometry and irregularities, rail profiles,
Table 2 Track quality distribution on iron-ore line according to UIC 518. Maximum speed of 80 km/h assumed R (m)
Radius (m)
QN1 (%)
QN2 (%)
QN3 (%)
4QN3 (%)
r 350 350–400 400–450 450–600 600–800 800–1000 1000–1300 1300–1500 4 1500
305 368 409 547 648 934 1102 1395 1
33 70 70 82 80 71 100 100 100
25 19 8 10 11 8 0 0 0
42 11 22 8 9 21 0 0 0
0 0 0 0 0 0 0 0 0
friction coefficient, lubrication, wear coefficent, vehicle speed, traction and braking. The precise prediction of wear profile evolution is very dependant on the accuracy of the inputs above cf . [21,,23,,27]. Based on the statistics of the measured track design geometry of the iron-ore railway line, nine track sections have been chosen. Details of each section are presented in Table 1. The process of choosing the track design geometries of the simulation cases is well described in [23]. The fifth column of Table 1 is the contribution of the length of each curve interval (R) to the total length of the line (LT ¼470 km). For example the number 1.5 at the fourth row of the fifth column means that the sum of the length of the curve sections with radii between 400 m and 450 m is only 1.5% of the total length of the iron-ore line and the average value of the corresponding curve radii is 409 m (second column of the same row). The calculated wear depths for each of these nine simulation cases are weighted with column 5 of Table 1 and summed up at the end. The track irregularities are also chosen based on measurement data. The details of the track geometry qualities are presented in Table 2. Note that for quantification of the irregularities the
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Table 3 Distribution of the rail profiles for present iron-ore line; the chosen rail profiles for the simulation cases are in bold. Curve radiir600 m
Norway Sweden
High rail MB1_assymetric MB1
Curve radii4600 m Low rail MB4 UIC60
High rail MB4 MB1
Straight track Low rail MB4 UIC60
High rail MB4 MB4 UIC60
Low rail MB4 MB4 UIC60
2.3. Lubrication
Fig. 5. Existing nominal rail profiles on the iron-ore line (rail inclination 1/30).
As the locomotives are equipped with a wheel flange lubrication system, the wheel–rail friction is different on the flange side compared to the field side. Therefore, in the simulations, the friction value for the flange side (starting from the flange root at 35 mm from the nominal rolling radius point) is 0.1 while for the field side of the wheel, it is 0.4. Note that there is a transition length between the two areas is around 10 mm where the friction value changes linearly between the two limits as shown in Fig. 6. A certain level of friction is required to achieve adequate adhesion conditions and better radial steering. However, high friction values lead to larger creep forces and will increase the risk of RCF. For more details on the effect of friction on RCF see [25]. Fig. 7(a) and (b) shows the calculated RCF indices, cf. Eq. (6), on the “outer” and “inner” wheel respectively. The figures compare the lubricated and the nonlubricated simulation cases with 305 m curve radius. As Fig. 7 (a) shows, the RCF index is considerably lower on the outer wheel, where the contact is at the lubricated flange side. As can be seen in Fig. 7(b), the differences between lubricated and non-lubricated wheel are much smaller compared to the outer wheel. Correspondingly, the wear coefficients shown in Fig. 1 are also modified. Comparing the calculated results with the measurement data, it is decided to reduce the wear coefficients on the wheel flange 500 times. 2.4. Traction and braking
Fig. 6. Variation of friction coefficient values along the wheel profile due to flange lubrication.
International standard UIC518 is used [24]. According to the table, for tight curves track irregularities are randomly chosen in each wear step, among the three available track qualities; however, for wider curve sections, only QN1 track quality is used. Various types of rail profiles are installed on the iron-ore line depending on curve radius and on whether the track is located in Norway or Sweden. As around 75% of the tight curves (below 600 m radius) are located on the Norwegian side of the line we only used the Norwegian standard for the tight curve sections. Likewise, for 88% of the medium (600–800 m) and wide curves (above 800 m radius) it was reasonable to use the Swedish standard for the wide curve sections, cf. Table 3. All the nominal (nonworn) rail profiles of the iron-ore line are compared in Table 3 (Fig. 5). The speed of the locomotive is also chosen according to the sections’ curve radii, i.e. 50 km/h for the tight curves, 55 km/h for medium curves and for wide curves and straight track 60 km/h is chosen. Note that the locomotives are always carrying ballast and have an axle load of 30 t but the weight of the wagons changes between laden and tare. This means that the load pulled by the locomotives changes every 470 km of running distance. Finally, it is assumed that the inner and outer wheel wear symmetrically. Thus, the calculated wear depth on the inner and outer wheels is averaged in the end of each wear step.
It is important to consider the effects of traction and braking in a locomotive, as it has a big influence in the creepages and creep forces. To include their effects on loco wheel damage, the total running resistance force for each of the nine simulation cases are calculated. This force is applied at the end of the locomotive at the buffer height. The applied force would decrease the speed gradually until it stops the vehicle. In order to avoid this, the locomotive simulation model includes a PID controller to keep the speed of the vehicle constant by applying the required torque on the gear boxes. All axles of the locomotive are driven. The same procedure is applied for including the braking effects; however, this time the force will be in the direction of the vehicle speed and tends to push the vehicle further. This is the case in downhill sections on the Norwegian side of the line, where the train is fully loaded. Note that there is no limitation for the tractive forces in the simulation. However, as the drivers are told to not use braking forces above 500 kN (for both loco units) unless necessary, the limit of the simulated braking force is set to this value. It is assumed that the rest of the required braking force is taken care of by the pneumatic tread braking system of the wagons. The total running resistance (Dt) can be divided into four parts:
Mechanical resistance (Dm), which is rolling resistance and the
loss of energy in mechanical parts of the vehicle such as: axle bearings, springs, dampers, etc. Aerodynamic resistance (Da), which is proportional to the square of the vehicle speed, the air density and the cross sectional area of the vehicle.
S. Hossein Nia et al. / Wear 338-339 (2015) 62–72
Curve resistance (Dc), additional rolling resistance caused by
the friction forces in the wheel–rail contact in curves. It is proportional to the curvature (inverse of the curve radius) of the track section and the flexibility of the primary suspension. Gradient resistance (Dg), which is proportional to the train weight, gravitational acceleration and the track gradient.
For details of the calculation of the mentioned resistance forces see [26]. Generally, the most important part of the total drag force for a low speed heavy haul vehicle is the gradient resistance. According to the topography of the line (from Sweden to Norway) the RMS value of the line gradient on the Swedish side is 6.84(‰), while the mean value is 1.47(‰). However, these values on the Norwegian side are 13.61(‰) and 13.44(‰) respectively. This means the Swedish side is much more flat than the Norwegian but it also has more ups and downs. Therefore, it is decided that the gradient of the each section is randomly chosen between 0, 6.84 (‰) and þ6.84(‰) for the simulation cases located in the Swedish side. For the sections located on the Norwegian side, depending on whether the train is loaded or empty, the gradient is set to 13.61 (‰) and 13.61(‰) respectively. Table 4 shows an example of the estimated resistance forces for a curve section with 648 m radius in Sweden and a section with 409 m radius in Norway. Note that a negative total resistance force (Dt) means that the vehicle needs to accelerate while a positive value means that the vehicle needs to brake to keep the speed constant. The influence of the traction and braking forces on the wheel damage is quite complex. On straight tracks they definitely increase the risk of RCF and wear. This is due to the fact that the wheels are running mostly in centred position at the nominal rolling radius. Therefore, the rolling radius difference is almost zero and longitudinal creep forces are at their minimum. Thus, any increase in the absolute values of the longitudinal forces whether it is braking (negative) or traction (positive) leads to
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greater tangential stresses and higher risk of RCF, e.g. RCF3 in Fig. 3. Likewise, the sliding velocity between the wheel and the rail (the creepages) increases due to the braking and traction which increases the dissipated energy in the contact area and consequently the amount of wear. On curve sections, as the direction of longitudinal traction forces are in opposite directions on the inner (positive) and outer wheels (negative) the effect of traction and braking can be very different depending on the curve radius and the amount of longitudinal force applied on the wheelsets in braking and traction. As an example, regardless of the lateral creep forces, in a relatively tight curve where the steering force is already high on the wheels an extra negative longitudinal force (braking) will lead to even higher stresses on the outer wheel and less stresses on the inner wheel. Oppositely, an extra positive longitudinal force (traction) will make the inner wheel more vulnerable to crack initiation compared to the outer wheel. It is possible to make the same conclusion regarding the amount of wear in tight curves. Fig. 8 shows the calculated energy dissipation in one of the curve sections where the vehicle is using traction to overcome the resistance forces. The above statements could be different in the wide curve sections and for high traction or braking forces. As the steering forces are low there is a possibility that a high pure longitudinal force (braking or traction) could overcome the steering force and cause a high force in the other direction. 2.5. RCF prediction The methodology for calculating RCF damage is the same as described in Section 1.2. Fig. 9(a) shows the corresponding shakedown diagram for one of the simulation cases. Simulation points beyond the boundary line (BC) with positive values of fatigue index, cf. Equation (6), are subjected to RCF (Fig. 9, red points). In order to extend this methodology for the calculation of the long
Fig. 7. Calculated FIsurf index for the non-lubricated and lubricated simulations wheel (R ¼305 m): (a) outer wheel and (b) inner wheel.
Table 4 Distribution of the estimated resistance forces for various track and traffic conditions.
Sweden
Norway
Gradient
Dg (kN)
Dc (kN)
Da (kN)
Dm (kN)
Dt (kN)
6.84 0 6.84
Loaded 563 0 563
Empty 122 0 122
Loaded 92 92 92
Empty 20 20 20
Loaded 26 26 26
Empty 26 26 26
Loaded 7 7 7
Empty 7 7 7
Loaded 438 125 688
Empty 69 53 175
13.61 13.61
1120
244
154
34
24
24
6
6
936
308
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Fig. 8. Calculated energy dissipation per rolling distance on (a) outer wheel and (b) inner wheel; with and without tractive forces (R¼ 547 m).
Fig. 9. (a) Shakedown diagram for one simulation case and (b): the corresponding position of the simulation points with risk of RCF (R¼ 409 m). (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
Fig. 11. RCF correction factor according to the energy dissipation per metre rolling distance. Fig. 10. Number of RCF points for all nine simulation cases (first wear step).
term development of RCF and uniform wear, it is possible to find the position of the points subject to RCF on the wheel profile. The wheel profile is discretized into 5 mm intervals and the points are placed in each corresponding interval. The number of the located simulation points subjected to RCF regarding their positions on the wheel profile is shown in Fig. 9(b). It is obvious that the positions with higher numbers of simulation points subjected to RCF are more at risk regarding surface initiated cracks. As we have nine simulation cases (in each wear step), Fig. 9(b) is extended in order to show all RCF positions for all simulation cases, cf. Fig. 10. The number of RCF points for each simlation case is weighted according to the length of that section, cf. column five of Table 1. It is possible to consider the effect of wear when calculating the RCF locations on the wheel profile. It is reasonable to assume that
below a certain value of energy dissipation (E¯1) there is little wear. This allows the cracks to grow. As wear becomes dominating (above E¯2), the initiated cracks are polished from the surface before they can propagate. With this concept we introduce a factor to correct the RCF index shown in Fig. 10. The schematic figure of this correction factor is shown in Fig. 11. The energy dissipation limit values are chosen to achieve the best correlation between the simulation results and the actual observed RCF locations on iron-ore locomotive wheels. 100 J/m and 150 J/m are used for E¯1 and E¯2 respectively. The wheel is discretized as described above for RCF. This time the mean values of the energy dissipation for the corresponding wheel position interval have been used and the values are weighted according to the length of the simulation cases, as shown in Fig. 12(a). The RCF correction factor for a single wear step is calculated according to Fig. 11. The result is
S. Hossein Nia et al. / Wear 338-339 (2015) 62–72
Fig. 12. Calculated energy dissipation of one of the three contact points of the outer wheel for all nine simulation cases (a) and the corresponding RCF factor (b).
Fig. 13. Number of RCF points for all nine simulation cases after applying the RCF correction factor.
Fig. 14. Comparison between the measured and the simulated wheel profiles after 35,000 km of running distance for the original WPL9 wheel profile.
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shown in Fig. 12(b). Note that in Fig. 12 only the results of one of the possible three contact points of the outer wheel are shown. In fact, in the calculation process each contact point is considered separately and the results are summed up at the end. Now the factor can be applied on the RCF values. This simply means to multiply the values of Fig. 12(b) with the corresponding RCF values of the same contact point and repeating the procedure for all contact points. Finally, the corrected RCF values for all contact points of both the inner and the outer wheels have to be summed up to achieve the positions on the wheel that are subjected to surface initiated fatigue. Fig. 13 shows the modified RCF positions from Fig. 10 after considering the wear effect.
As most of the locomotive wheels are reprofiled after around 40,000 km, the simulation of the wheel profile evolution is also limited to this distance. To compare the calculated worn wheel profile and the measured wheel profile one of the few available measured profiles is chosen. Unfortunately, the exact running distance of the measured worn profile is not known. It is possible to estimate it to around the reprofiling limit of 40,000 km. The closest simulated wheel profile to the mentioned profile has run for 35,000 km, cf.Fig. 14. The agreement between the simulated and the measured worn profile is very good. There are two differences between the results. One is at the flange side where the simulated wear is underestimated. This could be due to the flange lubrication system. The
transition between the greased and dry parts on the wheels is not known and it could be varying in each curve section. However, in the simulations it is assumed that in all curves lubrication is perfect and there is a fixed transition area between the lubricated and non-lubricated parts. The other observed difference is at the far end of the field side, where, contact usually occurs in switches and crossings. In the current study we neglected this effect. However, in [27] the problem is investigated and the possibilities of considering the effect of switches and crossings on the wheel profile evolution are shown. The simulations are repeated for the two new wheel profile candidates. The wear depth values for each of their first wheelset are compared with WPL9 wheel profiles in Fig. 15. As observed in the figure the profile WPLX2 produces the least amount of wear compared the other two profiles. It seems that the WPLX4, one of the field test candidates, produces even more flange wear than the current wheel profile. To see the evolution of RCF on the wheel profiles we need to first sum up the weighted RCF indices for the nine simulation cases of a wear step, as shown in Fig. 13. Secondly, the procedure needs to be repeated this for all consecutive wear steps until the desired travelling distance is achieved to get the accumulative RCF cracks locations on the wheel profiles. In Fig. 16 the accumulated risk for RCF is shown as function of the position on the wheel profile and of the rolling distance. The case with lubrication can be found in Fig. 16(a), while the results in Fig. 16(b) are without lubrication. Comparing the results with field observations, it is reasonable to conclude that the lubrication is partly not working properly. On one hand, with low friction
Fig. 15. Total calculated material removal of the leading axle after 35,000 km for all three investigated wheel profiles.
Fig. 17. Calculated accumulated RCF on WLP9 profiles without considering the wear effect.
3. Results and discussion
Fig. 16. Evolution of RCF on the first axle for the WPL9 wheel profile (a) lubricated and (b) non-lubricated. The darker the area the more severe the RCF.
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Fig. 18. Evolution of RCF on the lubricated WPLX2 (a) and WPLX4 wheel profiles (b); the darker the area the more severe the RCF.
coefficients, it is impossible to get RCF on the surface which is seen on the actual wheel profiles, cf.Figs. 3 and 16(b). On the other hand, without lubrication, RCF on the field side is overestimated in the simulation results while it is quite accurately estimated in the simulation results with lubricated wheels, cf. Fig. 16(a). This result matches well with the observations in Fig. 3 and other reports such as [28]. In case that the effect of wear would not have been taken into account, results would look as in Fig. 17, where the energy dissipation limits are removed from the RCF calculations. As seen the figure, the calculated RCF is much more pronounced in Fig. 17 than in Fig. 16(b). Finally, the results of the simulated RCF for the proposed new wheel profiles with flange lubrication are presented in Fig. 18. As seen in Fig. 18 when comparing with Fig. 16(a) both proposed wheel profiles are less at risk of RCF compared to the original one. However, the performance of the WPLX2 profile is even better than for the WPLX4 profile. It produces very low RCF on the tread side.
4. Conclusion The paper analyses the long term wheel damage evolution of the iron-ore locomotive running in northern Sweden and Norway. Existing RCF and uniform wear calculation methodologies have been combined and further developed in order to locate the position of the damage modes in the profile. As every axle of the locomotive is driven, the effect of traction and braking forces on both the dynamic behaviour of the loco and on the different wheel damage modes is considered. The locomotive is also equipped with a flange lubrication system, so both non-lubricated and lubricated conditions are investigated. The methodology is first validated by comparing the simulated and measured worn profiles for the actual wheel profiles. Comparing the simulated wear and RCF evolution of the current wheel profiles with measurement and observation data shows good agreement, where minor differences are mainly due to uncertainties in how the lubrication system is working and the wear at the corner of the field side due to switches and crossings. Comparison between the predicted and measured wheel flange wear suggests that the vehicle lubrication system is not always performing as expected, as shown by the cracks on the wheel flanges of both the actual and the simulation without flange lubrication. Both optimised wheel profiles (WPLX2 and WPLX4) are performing well compared to the current wheel profile. However, the WPLX2 profile performs better in long term, especially regarding the influence of wear on the probability of RCF.
Acknowledgement The authors gratefully thank HLRC (Hjalmar Lundbohm Research Centre) for funding this project and particularly Thomas Nordmark for all supports throughout the project. The authors also wish to thank Bombardier for the locomotive model in SIMPACK and MiW Rail Technology AB, especially Peter Hartwig, for providing the model in GENSYS. And finally, the authors acknowledge the comments and technical supports of Ingemar Persson from DEsolver for the help with technical issues and questions regarding GENSYS.
References [1] SIMPACK, Version 8903. [2] GENSYS 14.10 online manual www.gensys.se; AB Desolver, Östersund, 2013. [3] I. Persson, S.D. Iwnicki, Optimization of railway wheel profiles using a genetic algorithm, Vehicle System Dynamics, vol. 41, 2004, pp. 517–526 [4] P. Hartwig, Radprofiloptimierung an den Erzwaggons der Malmbanan/Ofotbanan, Tagungsband 13 Internationale Schienenfahrzeugtagung, Dresden, 2014, pp. 26 –28 [5] P.J. Blau (Ed.), Glossary of terms, Friction, Lubrication, and Wear Technology Metals Handbook, vol. 18, ASME International, Metals Park, OH, 1992. [6] Y. Kimura, et al., Wear and fatigue in rolling contact, Wear 252 (2002) 9–16. [7] R.K. Steele, Rail Lubrication: The Relation of Wear and Fatigue Transportation Research Record 1042 ,1985, pp. 24–32 [8] R. Nilsson, On wear in rolling sliding contacts. TRITA-MMK (Doctoral thesis), Department of Mechanical Design, KTH Royal Institute of Technology, Stockholm, 2005. [9] J.F. Archard, Contact and rubbing of flat surface, J. Appl. Phys. 24 (981) (1953). [10] S.C. Lim, M.F. Ashby, Wear mechanisms maps, Acta Metall. 35 (1987) 1–24. [11] T.H.C. Childs, The mapping of metallic sliding wear, in: Proc. Instn. Mech. Engrs. C 202, 1988, pp 379–395. [12] U. Olofsson, T. Telliskivi, Wear, plastic deformation and friction of two rail steels-a full-scale test and a laboratory study, Wear 254 (2003) 80–93. [13] J. Kalker, Simulation of the development of a railway wheel profile through wear, Wear 150 (1991) 355–365. [14] T.G. Pearce, N.D. Sherratt, Prediction of wheel profile wear, Wear 144 (1991) 343–351. [15] A. Ward, R. Lewis, R.S. Dwyer-Joyce, Incorporating a railway wheel/rail model into multi-body simulations of wheelset dynamics, in: Proceedings of the 29th Leeds-Lyon Symposium on Tribology, 2003. [16] T. Jendel, Prediction of wheel profile wear-comparisons with field measurements, Wear 253 (2002) 89–99. [17] R. Enblom, Simulation of wheel and rail profile evolution-wear modeling and validation, TRITA AVE 2004:19 (Licentiate Thesis), Department of Aeronautical and Vehicle Engineering 2004, Royal Institute of Technology (KTH), Stockholm [18] I.J. McEven, R.F. Harvey, Full-scale wheel-on-rail wear testing: comparisons with service wear and a developing theoretical predictive method, Lubr. Eng. J. Am. Soc. Lubr. Eng. 4 (1985) 80–88. [19] K.L. Johnson, The strength of surfaces in rolling contact, Proc. Inst. Mech. Eng. 203 (1989) 151–163. [20] A. Ekberg, E. Kabo, H. Andersson, An engineering model for prediction of rolling contact fatigue of railway wheels., Fatigue Fract. Eng. Mater. Struct. 25 (2002) 899–909. [21] B. Dirk, R. Enblom, Prediction model for wheel profile wear and rolling contact fatigue, Wear 271 (1–2) (2011) 210–217.
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[22] M.C. Burstow, Whole life rail model application and development for RSSB – Continued development of an RCF damage parameter, Rail safety and standards board 2004; Issue 2 Report EATR-S-2004-2880. [23] B.Dirks, Vehicle dynamics simulation of wheel wear for Swedish high-speed train X2000, Master thesis, TRITA AVE 2003:16, Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), Stockholm, 2003. [24] UIC: Testing and approval of railway vehicles from the point of view of their dynamic behaviour –safety –Track fatigue – Ride quality, Code 518 OR, 2nd ed., April 2003.
[25] S. Hossein Nia, P.-A. Jönsson, S. Stichel, Wheel damage on the Swedish ironore line investigated via multibody simulation, J. Rail Rapid Transit 228 (2014) 652–662. [26] E. Andersson, M. Berg, Spårtrafiksystem och spårfordon, Del 2: spårfordon. Stockholm, 2007. [27] C. Casanueva, et al., Influence of switches and crossings on wheel profile evolution in freight vehicles, Veh. Syst. Dyn. 52 (2014) 317–337. [28] A. Ekberg, et al., Identifying the root causes of damage on the wheels of heavy haul locomotives and its mitigation, J. Rail Rapid Transit 228 (2014) 663–672.
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Prediction of RCF and wear evolution of iron-ore locomotive wheels Saeed Hossein Nia n, Carlos Casanueva, Sebastian Stichel KTH Royal Institute of Technology, Stockholm, Sweden
art ic l e i nf o
a b s t r a c t
Article history: Received 13 February 2015 Received in revised form 26 May 2015 Accepted 28 May 2015 Available online 6 June 2015
Locomotives for the iron ore line in northern Sweden and Norway have a short wheel life. The average running distance between two consecutive wheel turnings is around 40,000 km which makes the total life of a wheel around 400,000 km. The main reason of the short wheel life is the severe rolling contact fatigue (RCF). The train operator (LKAB) has decided to change the wheel profiles to get a better match with the rail shapes in order to decrease the creep forces leading to RCF. Two wheel profiles optimised via a genetic algorithm were proposed. They have, however, not been analysed for long term wear development. There is a risk that the optimised profiles might wear in an unfavourable way and after a while cause even higher RCF or wear than the original one. This study predicts wheel profile evolution using the uniform wear prediction tool based on Archard’s wear law. RCF evolution on the surface of the wheel profiles is also investigated. The impact of wear on polishing the wheel surface and avoiding the RCF cracks to propagate is considered via introducing a correction factor to the calculated RCF index. Traction and braking are also considered in the dynamic simulation model, where a PID control system keeps the speed of the vehicle constant by applying a torque on the loco wheels. The locomotives are also equipped with a flange lubrication system, therefore the calculations are performed both for lubricated and non-lubricated wheels. The simulation results for the wheel profiles currently in use, which are performed to validate the model and the simulation procedure, show a good agreement with the measurements. It is also concluded that the lubrication system partly does not perform as expected. Comparison between the proposed optimised profiles for their long term behaviour suggests that one of them produces less RCF and wear compared to the other one. & 2015 Elsevier B.V. All rights reserved.
Keywords: RCF Wear Heavy haul Traction Braking Lubrication
1. Introduction The Swedish iron-ore company LKAB uses Bombardier locomotives with 30 t axle load to transport pellets from the mines in Kiruna and Malmberget to the ports in Luleå and Narvik. The average mileage interval between two consecutive wheel turnings for a wagon wheel is around 250,000 km while it is much lower for a loco wheel, around 40,000 km. The turning intervals lead to a total service life of the wagon wheels of 1,000,000 km and the locomotive wheels of 400,000 km. The difference between the numbers is mainly due to RCF on the loco wheels. LKAB uses three measurement stations on Malmbanan in order to detect high vertical impact forces, possibly due to wheel flats, where urgent maintenance actions are needed. Besides, regular inspections for wheels are carried out every 26,000 km for the locomotives and every 80,000 km for the wagons. These inspections are performed in the workshop located in Kiruna and they are mainly for detecting cracks on the wheels and possible needs n
Corresponding author. E-mail address: [email protected] (S. Hossein Nia).
http://dx.doi.org/10.1016/j.wear.2015.05.015 0043-1648/& 2015 Elsevier B.V. All rights reserved.
for re-profiling. Rails are checked by the Swedish infrastructure owner, Trafikverket, and are ground once a year. Each traction unit consists of two identical Co-Co locomotives permanently coupled back to back. There are 68 wagons connected to the locomotives and in the laden condition the total weight carried by the loco is more than 8000 t. The maximum speed of the locos on tangent track is 60 km/h for loaded and 70 km/h for unloaded trains. The simulation model of the loco is developed at Bombardier via SIMPACK [1] and is translated to GENSYS [2] for this study. To enhance the service life of the wheels, LKAB has decided to change the wheel profiles in to achieve a better curving performance for the loco and, consequently, a reduction of the generated creep forces. To optimise the wheel profiles a genetic algorithm [3] is used. For details of the optimisation process, see [4]. Two optimised wheel profiles (WPLX2 and WPLX4) are suggested as potential profiles for field testing. However, in order to study the long-term stability of the optimised profiles, monitoring the evolution of the profiles is inevitable. There is a risk that the new profiles might wear in an unfavourable way and after a while cause even higher RCF or wear than the original one: depending on the shape of the profile, the elements which determine the risk of RCF such as lateral and
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longitudinal creep forces would change. The evolution of the profile affects the conicity of the wheel and influences the curving performance and attack angle of the wheelset, which will eventually change the wheel–rail contact forces and modify the RCF risk. This paper studies the evolution of wear and RCF of the proposed wheel profiles as a function of running distance. The procedure is repeated for the current locomotive wheel profile (WPL9) and the results are compared with measurements in order to validate and tune the wear and RCF calculation model characteristics. 1.1. Wear From the tribological point of view wear is defined as any damage to a solid surface, involving progressive loss of material and relocation of material when two surfaces are interacting via a relative motion. How a material wears depends not only on the nature of the material but also on other elements of the tribosystem such as geometry of contacting pairs, surface topography, loading, lubrication and environment. The mechanisms causing such damages are usually complicated and most of the time it is not possible to distinguish one from another. In [5], approximately 60 terms describing wear behaviour and mechanisms are listed. Some of the most important wheel–rail related mechanisms are mentioned below.
Abrasive wear: wear caused by rough and hard surfaces sliding
on each other or wear caused by hard particles trapped between two surfaces like hard oxide debris. Adhesive wear: wear caused by shearing of junctions formed between two contacting surfaces, sometimes used as a synonym for dry sliding wear. Chemical wear (Corrosive wear): wear caused by formation of any oxide or other components on surfaces due to chemical reaction of the surfaces with the environment. Erosive wear: Wear due to relative motion of contact surfaces while a fluid containing solid particles is between the surfaces. Rolling contact fatigue (RCF): caused by cyclic stress variations leading to fatigue of the materials. Generally resulting in the formation of surface, sub-surface and deep-surface cracks, material pitting and spalling.
Kimura [6] studies adhesive wear and RCF and concludes that both phenomena have elemental processes in common. In this study the term “wear” is used for adhesive wear, otherwise the complete term of the damage mechanism is mentioned. Note that the term “mechanical wear” is also used for abrasion, erosion, adhesion and surface fatigue. Published research and studies on wear modelling usually have three approaches:
Field measurements, laboratory tests, and theoretical prediction models. Most of the field measurements have addressed the effect of lubrication on wear such as [7,,8]. Archard [9] took the idea of the adhesive wear definition and found that the volume of material removed by wear per sliding distance (W) is proportional to the quotient of the pressure (p) and the hardness (H) of the softer material. The proportionality factor is called the wear coefficient (k) which is expected to be a function of wheel and rail material. Two separate mild and severe wear regimes are suggested; therefore a constant K is added to maintain the relation in the severe regime.
Fig. 1. Wear map for wheel and rail steel; H is the hardness of the material.
W=
kp + K. H
(1)
The wear coefficient depends on the governing wear mechanisms. Archard validated his model by determining the wear rates for different material pairs by pin-on-disc tests. Lim and Ashby [10] performed large amounts of laboratory tests and introduced wear maps where the wear coefficient is plotted as a function of sliding velocity and the nominal pressure (normal load divided by the nominal contact area). The wear map corresponding to medium carbon steel, based largely on pin-on-disc data, is generally divided into two main regions of mechanical and chemical wear. Childs [11] suggested a wear map for the mechanical wear mechanism where the wear coefficient is a function of the asperities attack angle and the relative strength of the interfaces. The chemical part of the map, however, consists of two regions: mild and severe oxidational wear. Olofsson and Telliskivi [12] have investigated the evolution of the rail profiles of a commuter track within two years together with performing several laboratory tests with two different testing machines: a two-roller (disc on disc) and a pin-on-disc machine. The results of the tests were simplified into a wear map where wear coefficient depends on local sliding velocity and contact pressure, cf. Fig. 1. Several authors have investigated and developed wheel wear prediction tools. Important contributions can be found in studies from Kalker [13], Pearce and Sherratt [14], Ward [15] and Jendel [16]. Note that the studies mentioned here have all neglected the plastic deformation of the material and focused on uniform wear. Enblom [17] used the same methodology as Jendel. However, he included the elastic strain in the sliding velocity assessment. He also increased the simulation set with simulation of disc braking. In a different approach McEven and Harvey [18] used a fullscale wheel-on-rail-wear rig. They have proposed a linear relation between the wear rate and the dissipated energy per unit distance ¯ per unit area A, adjusted with a constant off-set term,K . rolled E, The energy dissipation per unit distance area is the creep forces times the creepages added to the moment times the spin in the contact patch. They also have predicted two wear regimes of mild (tread contact) and severe (flange contact) wear.
Wear rate per unit rolled distance = k where
E̅ A
E¯ + K, A
(2)
is sometimes called the wear number.
1.2. RCF As mentioned above, the rolling contact fatigue or RCF is also a type of surface deterioration and material loss which generally starts some millimetres below the material surface and propagates
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Fig. 2. Shakedown map.
through the surface. Surface initiated fatigue usually occurs when the response of a material to a cyclic load leads to ratchetting of the plastic deformation. In such a phase the plastic deformation will remain unstable and there will be an incremental strain growth at each load cycle. However, in the cyclic plasticity phase (plastic shakedown) the material could be subjected to surface initiated cracks in the low cycle fatigue process (LCF). Using the discussed regimes above, together with the perfectly elastic and elastic shakedown phase, Johnson, in 1989, proposed a theory for predicting rolling contact fatigue [19]. From the solid mechanics point of view he has the von Mises, maximum-distortion-energy, yielding criterion and developed the so called shakedown map. A simplified shakedown diagram is presented in Fig. 2. The location of the points in the shakedown diagram is a function of, firstly, the traction coefficient (T )
T=
FT = FZ
Fx2 + Fy2 Fz
,
(3)
where Fz is the normal contact force, Fx and Fy are longitudinal and lateral creep forces respectively. Secondly, it depends on the normalised vertical load (v ) which is the maximum contact pressure (p0 ) divided by the yield stress in shear (k ) of the softer material in contact:
v = p0 / k .
(4)
The boundary curve for surface plasticity (BC) is calculated as
BC =1/T .
(5)
If a working point passes the boundary curve above the friction level around 0.3 ratchetting occurs, while below this friction level, the material is subjected to low cycle fatigue or plastic shakedown. However, if a working point does not pass the boundary curve, depending on the normal load, the material is in either the perfectly elastic or the elastic shakedown regime. Note that for elastic shakedown which is considered as high cycle fatigue (HCF), the cracks may be initiated in subsurface of the material. Ekberg [20] used the idea of the shakedown map and developed an engineering approach to predict RCF in railway applications. He calculated the distance of the points from the boundary curve and called it surface fatigue index (FIsurface)
FIsurf = T − 1/v = T −
2π a . b . k 3Fz
(6)
where a and b are the semi-axes of the elliptic contact area in the Hertzian contact. RCF is likely to happen for positive values of FIsurface. The fatigue index approach is nowadays widely used in multibody simulation softwares. There is a debate on propagation of the cracks. Due to the direction of the longitudinal creep forces on wheels and rails low viscous fluids like oil lubricants or water could be trapped in the
Fig. 3. Three bands of RCF on an iron-ore locomotive wheel. Photo by Roger Deuce/ Copyright: Bombardier Inc.
cracks. Furthermore, the stresses force the fluid to the tip of the crack. As the fluid is incompressible there will be extremely high stresses around the trapped fluid. Finally, the stresses help the crack to develop further after the crack leaves the contact area [21]. Following a laboratory test on gears, Kimura [6] observed a similar behaviour with the fatigue life of the dedendum and the addendum. As the slip signs are in opposite directions above (addendum) and below (dedendum) the pitch circle (pure rolling) of a gear, cracks appeared always on the dedendum first. Later Kimura suggested that although this theory seems reasonable, there are facts which make it doubtful. Firstly, the phenomenon is supposed to be seen only in lubricated systems but similar behaviour is also seen in non-lubricated systems. Secondly, it is seen that cracks will also initiate and grow in the addendum in considerably high traction forces. In railway applications, for example on iron-ore lines, technicians reported a trend of RCF cracks in three bands on the locomotive wheels (Fig. 3). The first two bands, RCF1 and RCF3, are located at the field side (typically due to curving, on the inner rail) and the nominal rolling radius area (typically due to braking and traction) while the third band (RCF2) is usually located at the flange side (due to curving, on the outer rail). Fig. 3 shows a photo of an actual iron-ore wheel profile right before reprofiling, where the three bands of RCF can easily be seen. Many attempts have been made to combine wear and RCF effects in the prediction of wheel and rail damages. At a certain level of wear depth the initiated cracks could be polished away from the surface. In the UK a model has been proposed and calibrated on six intermediate-radius curves, where RCF on rails is observed, see [22]. In the mentioned work it is assumed that the wear depth is linearly proportional to the wear number. However, the spin effect is not included in the calculation of the energy dissipation. In the current paper we took the idea of the influence of energy dissipation on RCF and assumed that RCF is worn out for high energy dissipation values in the wheel–rail contact patch.
2. Calculation methodology In this section the calculation methodology is discussed. This includes the simulation of short term dynamic behaviour and long term damage mechanism.
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Fig. 4. Methodology of wheel wear prediction developed by Jendel [16].
Table 1 Details of track design geometries for each simulation case concluding a wear step R (m)
r350 350–400 400–450 450–600 600–800 800–1000 1000–1300 1300–1500 41500
Radius (m) Transition in and out (m)
Constant Length (%) Cant curve (m) (mm)
Gauge (mm)
305 368 409 547 648 934 1102 1395 1
270 210 140 227 210 200 210 190 500
1444 1443 1448 1447 1445 1444 1443 1440 1435
80 100 175 145 140 170 110 110 –
4.4 0.9 1.5 13.9 16.1 7.9 5.4 1.8 48.1
68 61 66 51 46 37 33 28 0
2.1. Wear prediction In the present work we have used the Jendel approach [16] to predict the wheel profile evolution. Jendel has used the Archard formula, Eq. (1), to develop his method. The methodology is based on a load collective concept, which determines a set of dynamic time-domain simulations. These simulations reflect the actual rail network for the vehicles in question. The Hertzian theory is used for the normal contact and the FASTSIM method is applied for the tangential contact problem. Fig. 4 shows Jendel’s wheel wear prediction flowchart. 2.2. Operational cases To reflect the actual rail network a set of time-domain simulation cases called load collective is prepared. Then, parametric studies are performed with running distance of 10,000 km for each case and the results are compared with the measurements data in order to tune the simulation parameters. The parameters for designing a load collective are:
track geometry and irregularities, rail profiles,
Table 2 Track quality distribution on iron-ore line according to UIC 518. Maximum speed of 80 km/h assumed R (m)
Radius (m)
QN1 (%)
QN2 (%)
QN3 (%)
4QN3 (%)
r 350 350–400 400–450 450–600 600–800 800–1000 1000–1300 1300–1500 4 1500
305 368 409 547 648 934 1102 1395 1
33 70 70 82 80 71 100 100 100
25 19 8 10 11 8 0 0 0
42 11 22 8 9 21 0 0 0
0 0 0 0 0 0 0 0 0
friction coefficient, lubrication, wear coefficent, vehicle speed, traction and braking. The precise prediction of wear profile evolution is very dependant on the accuracy of the inputs above cf . [21,,23,,27]. Based on the statistics of the measured track design geometry of the iron-ore railway line, nine track sections have been chosen. Details of each section are presented in Table 1. The process of choosing the track design geometries of the simulation cases is well described in [23]. The fifth column of Table 1 is the contribution of the length of each curve interval (R) to the total length of the line (LT ¼470 km). For example the number 1.5 at the fourth row of the fifth column means that the sum of the length of the curve sections with radii between 400 m and 450 m is only 1.5% of the total length of the iron-ore line and the average value of the corresponding curve radii is 409 m (second column of the same row). The calculated wear depths for each of these nine simulation cases are weighted with column 5 of Table 1 and summed up at the end. The track irregularities are also chosen based on measurement data. The details of the track geometry qualities are presented in Table 2. Note that for quantification of the irregularities the
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Table 3 Distribution of the rail profiles for present iron-ore line; the chosen rail profiles for the simulation cases are in bold. Curve radiir600 m
Norway Sweden
High rail MB1_assymetric MB1
Curve radii4600 m Low rail MB4 UIC60
High rail MB4 MB1
Straight track Low rail MB4 UIC60
High rail MB4 MB4 UIC60
Low rail MB4 MB4 UIC60
2.3. Lubrication
Fig. 5. Existing nominal rail profiles on the iron-ore line (rail inclination 1/30).
As the locomotives are equipped with a wheel flange lubrication system, the wheel–rail friction is different on the flange side compared to the field side. Therefore, in the simulations, the friction value for the flange side (starting from the flange root at 35 mm from the nominal rolling radius point) is 0.1 while for the field side of the wheel, it is 0.4. Note that there is a transition length between the two areas is around 10 mm where the friction value changes linearly between the two limits as shown in Fig. 6. A certain level of friction is required to achieve adequate adhesion conditions and better radial steering. However, high friction values lead to larger creep forces and will increase the risk of RCF. For more details on the effect of friction on RCF see [25]. Fig. 7(a) and (b) shows the calculated RCF indices, cf. Eq. (6), on the “outer” and “inner” wheel respectively. The figures compare the lubricated and the nonlubricated simulation cases with 305 m curve radius. As Fig. 7 (a) shows, the RCF index is considerably lower on the outer wheel, where the contact is at the lubricated flange side. As can be seen in Fig. 7(b), the differences between lubricated and non-lubricated wheel are much smaller compared to the outer wheel. Correspondingly, the wear coefficients shown in Fig. 1 are also modified. Comparing the calculated results with the measurement data, it is decided to reduce the wear coefficients on the wheel flange 500 times. 2.4. Traction and braking
Fig. 6. Variation of friction coefficient values along the wheel profile due to flange lubrication.
International standard UIC518 is used [24]. According to the table, for tight curves track irregularities are randomly chosen in each wear step, among the three available track qualities; however, for wider curve sections, only QN1 track quality is used. Various types of rail profiles are installed on the iron-ore line depending on curve radius and on whether the track is located in Norway or Sweden. As around 75% of the tight curves (below 600 m radius) are located on the Norwegian side of the line we only used the Norwegian standard for the tight curve sections. Likewise, for 88% of the medium (600–800 m) and wide curves (above 800 m radius) it was reasonable to use the Swedish standard for the wide curve sections, cf. Table 3. All the nominal (nonworn) rail profiles of the iron-ore line are compared in Table 3 (Fig. 5). The speed of the locomotive is also chosen according to the sections’ curve radii, i.e. 50 km/h for the tight curves, 55 km/h for medium curves and for wide curves and straight track 60 km/h is chosen. Note that the locomotives are always carrying ballast and have an axle load of 30 t but the weight of the wagons changes between laden and tare. This means that the load pulled by the locomotives changes every 470 km of running distance. Finally, it is assumed that the inner and outer wheel wear symmetrically. Thus, the calculated wear depth on the inner and outer wheels is averaged in the end of each wear step.
It is important to consider the effects of traction and braking in a locomotive, as it has a big influence in the creepages and creep forces. To include their effects on loco wheel damage, the total running resistance force for each of the nine simulation cases are calculated. This force is applied at the end of the locomotive at the buffer height. The applied force would decrease the speed gradually until it stops the vehicle. In order to avoid this, the locomotive simulation model includes a PID controller to keep the speed of the vehicle constant by applying the required torque on the gear boxes. All axles of the locomotive are driven. The same procedure is applied for including the braking effects; however, this time the force will be in the direction of the vehicle speed and tends to push the vehicle further. This is the case in downhill sections on the Norwegian side of the line, where the train is fully loaded. Note that there is no limitation for the tractive forces in the simulation. However, as the drivers are told to not use braking forces above 500 kN (for both loco units) unless necessary, the limit of the simulated braking force is set to this value. It is assumed that the rest of the required braking force is taken care of by the pneumatic tread braking system of the wagons. The total running resistance (Dt) can be divided into four parts:
Mechanical resistance (Dm), which is rolling resistance and the
loss of energy in mechanical parts of the vehicle such as: axle bearings, springs, dampers, etc. Aerodynamic resistance (Da), which is proportional to the square of the vehicle speed, the air density and the cross sectional area of the vehicle.
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Curve resistance (Dc), additional rolling resistance caused by
the friction forces in the wheel–rail contact in curves. It is proportional to the curvature (inverse of the curve radius) of the track section and the flexibility of the primary suspension. Gradient resistance (Dg), which is proportional to the train weight, gravitational acceleration and the track gradient.
For details of the calculation of the mentioned resistance forces see [26]. Generally, the most important part of the total drag force for a low speed heavy haul vehicle is the gradient resistance. According to the topography of the line (from Sweden to Norway) the RMS value of the line gradient on the Swedish side is 6.84(‰), while the mean value is 1.47(‰). However, these values on the Norwegian side are 13.61(‰) and 13.44(‰) respectively. This means the Swedish side is much more flat than the Norwegian but it also has more ups and downs. Therefore, it is decided that the gradient of the each section is randomly chosen between 0, 6.84 (‰) and þ6.84(‰) for the simulation cases located in the Swedish side. For the sections located on the Norwegian side, depending on whether the train is loaded or empty, the gradient is set to 13.61 (‰) and 13.61(‰) respectively. Table 4 shows an example of the estimated resistance forces for a curve section with 648 m radius in Sweden and a section with 409 m radius in Norway. Note that a negative total resistance force (Dt) means that the vehicle needs to accelerate while a positive value means that the vehicle needs to brake to keep the speed constant. The influence of the traction and braking forces on the wheel damage is quite complex. On straight tracks they definitely increase the risk of RCF and wear. This is due to the fact that the wheels are running mostly in centred position at the nominal rolling radius. Therefore, the rolling radius difference is almost zero and longitudinal creep forces are at their minimum. Thus, any increase in the absolute values of the longitudinal forces whether it is braking (negative) or traction (positive) leads to
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greater tangential stresses and higher risk of RCF, e.g. RCF3 in Fig. 3. Likewise, the sliding velocity between the wheel and the rail (the creepages) increases due to the braking and traction which increases the dissipated energy in the contact area and consequently the amount of wear. On curve sections, as the direction of longitudinal traction forces are in opposite directions on the inner (positive) and outer wheels (negative) the effect of traction and braking can be very different depending on the curve radius and the amount of longitudinal force applied on the wheelsets in braking and traction. As an example, regardless of the lateral creep forces, in a relatively tight curve where the steering force is already high on the wheels an extra negative longitudinal force (braking) will lead to even higher stresses on the outer wheel and less stresses on the inner wheel. Oppositely, an extra positive longitudinal force (traction) will make the inner wheel more vulnerable to crack initiation compared to the outer wheel. It is possible to make the same conclusion regarding the amount of wear in tight curves. Fig. 8 shows the calculated energy dissipation in one of the curve sections where the vehicle is using traction to overcome the resistance forces. The above statements could be different in the wide curve sections and for high traction or braking forces. As the steering forces are low there is a possibility that a high pure longitudinal force (braking or traction) could overcome the steering force and cause a high force in the other direction. 2.5. RCF prediction The methodology for calculating RCF damage is the same as described in Section 1.2. Fig. 9(a) shows the corresponding shakedown diagram for one of the simulation cases. Simulation points beyond the boundary line (BC) with positive values of fatigue index, cf. Equation (6), are subjected to RCF (Fig. 9, red points). In order to extend this methodology for the calculation of the long
Fig. 7. Calculated FIsurf index for the non-lubricated and lubricated simulations wheel (R ¼305 m): (a) outer wheel and (b) inner wheel.
Table 4 Distribution of the estimated resistance forces for various track and traffic conditions.
Sweden
Norway
Gradient
Dg (kN)
Dc (kN)
Da (kN)
Dm (kN)
Dt (kN)
6.84 0 6.84
Loaded 563 0 563
Empty 122 0 122
Loaded 92 92 92
Empty 20 20 20
Loaded 26 26 26
Empty 26 26 26
Loaded 7 7 7
Empty 7 7 7
Loaded 438 125 688
Empty 69 53 175
13.61 13.61
1120
244
154
34
24
24
6
6
936
308
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Fig. 8. Calculated energy dissipation per rolling distance on (a) outer wheel and (b) inner wheel; with and without tractive forces (R¼ 547 m).
Fig. 9. (a) Shakedown diagram for one simulation case and (b): the corresponding position of the simulation points with risk of RCF (R¼ 409 m). (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)
Fig. 11. RCF correction factor according to the energy dissipation per metre rolling distance. Fig. 10. Number of RCF points for all nine simulation cases (first wear step).
term development of RCF and uniform wear, it is possible to find the position of the points subject to RCF on the wheel profile. The wheel profile is discretized into 5 mm intervals and the points are placed in each corresponding interval. The number of the located simulation points subjected to RCF regarding their positions on the wheel profile is shown in Fig. 9(b). It is obvious that the positions with higher numbers of simulation points subjected to RCF are more at risk regarding surface initiated cracks. As we have nine simulation cases (in each wear step), Fig. 9(b) is extended in order to show all RCF positions for all simulation cases, cf. Fig. 10. The number of RCF points for each simlation case is weighted according to the length of that section, cf. column five of Table 1. It is possible to consider the effect of wear when calculating the RCF locations on the wheel profile. It is reasonable to assume that
below a certain value of energy dissipation (E¯1) there is little wear. This allows the cracks to grow. As wear becomes dominating (above E¯2), the initiated cracks are polished from the surface before they can propagate. With this concept we introduce a factor to correct the RCF index shown in Fig. 10. The schematic figure of this correction factor is shown in Fig. 11. The energy dissipation limit values are chosen to achieve the best correlation between the simulation results and the actual observed RCF locations on iron-ore locomotive wheels. 100 J/m and 150 J/m are used for E¯1 and E¯2 respectively. The wheel is discretized as described above for RCF. This time the mean values of the energy dissipation for the corresponding wheel position interval have been used and the values are weighted according to the length of the simulation cases, as shown in Fig. 12(a). The RCF correction factor for a single wear step is calculated according to Fig. 11. The result is
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Fig. 12. Calculated energy dissipation of one of the three contact points of the outer wheel for all nine simulation cases (a) and the corresponding RCF factor (b).
Fig. 13. Number of RCF points for all nine simulation cases after applying the RCF correction factor.
Fig. 14. Comparison between the measured and the simulated wheel profiles after 35,000 km of running distance for the original WPL9 wheel profile.
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shown in Fig. 12(b). Note that in Fig. 12 only the results of one of the possible three contact points of the outer wheel are shown. In fact, in the calculation process each contact point is considered separately and the results are summed up at the end. Now the factor can be applied on the RCF values. This simply means to multiply the values of Fig. 12(b) with the corresponding RCF values of the same contact point and repeating the procedure for all contact points. Finally, the corrected RCF values for all contact points of both the inner and the outer wheels have to be summed up to achieve the positions on the wheel that are subjected to surface initiated fatigue. Fig. 13 shows the modified RCF positions from Fig. 10 after considering the wear effect.
As most of the locomotive wheels are reprofiled after around 40,000 km, the simulation of the wheel profile evolution is also limited to this distance. To compare the calculated worn wheel profile and the measured wheel profile one of the few available measured profiles is chosen. Unfortunately, the exact running distance of the measured worn profile is not known. It is possible to estimate it to around the reprofiling limit of 40,000 km. The closest simulated wheel profile to the mentioned profile has run for 35,000 km, cf.Fig. 14. The agreement between the simulated and the measured worn profile is very good. There are two differences between the results. One is at the flange side where the simulated wear is underestimated. This could be due to the flange lubrication system. The
transition between the greased and dry parts on the wheels is not known and it could be varying in each curve section. However, in the simulations it is assumed that in all curves lubrication is perfect and there is a fixed transition area between the lubricated and non-lubricated parts. The other observed difference is at the far end of the field side, where, contact usually occurs in switches and crossings. In the current study we neglected this effect. However, in [27] the problem is investigated and the possibilities of considering the effect of switches and crossings on the wheel profile evolution are shown. The simulations are repeated for the two new wheel profile candidates. The wear depth values for each of their first wheelset are compared with WPL9 wheel profiles in Fig. 15. As observed in the figure the profile WPLX2 produces the least amount of wear compared the other two profiles. It seems that the WPLX4, one of the field test candidates, produces even more flange wear than the current wheel profile. To see the evolution of RCF on the wheel profiles we need to first sum up the weighted RCF indices for the nine simulation cases of a wear step, as shown in Fig. 13. Secondly, the procedure needs to be repeated this for all consecutive wear steps until the desired travelling distance is achieved to get the accumulative RCF cracks locations on the wheel profiles. In Fig. 16 the accumulated risk for RCF is shown as function of the position on the wheel profile and of the rolling distance. The case with lubrication can be found in Fig. 16(a), while the results in Fig. 16(b) are without lubrication. Comparing the results with field observations, it is reasonable to conclude that the lubrication is partly not working properly. On one hand, with low friction
Fig. 15. Total calculated material removal of the leading axle after 35,000 km for all three investigated wheel profiles.
Fig. 17. Calculated accumulated RCF on WLP9 profiles without considering the wear effect.
3. Results and discussion
Fig. 16. Evolution of RCF on the first axle for the WPL9 wheel profile (a) lubricated and (b) non-lubricated. The darker the area the more severe the RCF.
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Fig. 18. Evolution of RCF on the lubricated WPLX2 (a) and WPLX4 wheel profiles (b); the darker the area the more severe the RCF.
coefficients, it is impossible to get RCF on the surface which is seen on the actual wheel profiles, cf.Figs. 3 and 16(b). On the other hand, without lubrication, RCF on the field side is overestimated in the simulation results while it is quite accurately estimated in the simulation results with lubricated wheels, cf. Fig. 16(a). This result matches well with the observations in Fig. 3 and other reports such as [28]. In case that the effect of wear would not have been taken into account, results would look as in Fig. 17, where the energy dissipation limits are removed from the RCF calculations. As seen the figure, the calculated RCF is much more pronounced in Fig. 17 than in Fig. 16(b). Finally, the results of the simulated RCF for the proposed new wheel profiles with flange lubrication are presented in Fig. 18. As seen in Fig. 18 when comparing with Fig. 16(a) both proposed wheel profiles are less at risk of RCF compared to the original one. However, the performance of the WPLX2 profile is even better than for the WPLX4 profile. It produces very low RCF on the tread side.
4. Conclusion The paper analyses the long term wheel damage evolution of the iron-ore locomotive running in northern Sweden and Norway. Existing RCF and uniform wear calculation methodologies have been combined and further developed in order to locate the position of the damage modes in the profile. As every axle of the locomotive is driven, the effect of traction and braking forces on both the dynamic behaviour of the loco and on the different wheel damage modes is considered. The locomotive is also equipped with a flange lubrication system, so both non-lubricated and lubricated conditions are investigated. The methodology is first validated by comparing the simulated and measured worn profiles for the actual wheel profiles. Comparing the simulated wear and RCF evolution of the current wheel profiles with measurement and observation data shows good agreement, where minor differences are mainly due to uncertainties in how the lubrication system is working and the wear at the corner of the field side due to switches and crossings. Comparison between the predicted and measured wheel flange wear suggests that the vehicle lubrication system is not always performing as expected, as shown by the cracks on the wheel flanges of both the actual and the simulation without flange lubrication. Both optimised wheel profiles (WPLX2 and WPLX4) are performing well compared to the current wheel profile. However, the WPLX2 profile performs better in long term, especially regarding the influence of wear on the probability of RCF.
Acknowledgement The authors gratefully thank HLRC (Hjalmar Lundbohm Research Centre) for funding this project and particularly Thomas Nordmark for all supports throughout the project. The authors also wish to thank Bombardier for the locomotive model in SIMPACK and MiW Rail Technology AB, especially Peter Hartwig, for providing the model in GENSYS. And finally, the authors acknowledge the comments and technical supports of Ingemar Persson from DEsolver for the help with technical issues and questions regarding GENSYS.
References [1] SIMPACK, Version 8903. [2] GENSYS 14.10 online manual www.gensys.se; AB Desolver, Östersund, 2013. [3] I. Persson, S.D. Iwnicki, Optimization of railway wheel profiles using a genetic algorithm, Vehicle System Dynamics, vol. 41, 2004, pp. 517–526 [4] P. Hartwig, Radprofiloptimierung an den Erzwaggons der Malmbanan/Ofotbanan, Tagungsband 13 Internationale Schienenfahrzeugtagung, Dresden, 2014, pp. 26 –28 [5] P.J. Blau (Ed.), Glossary of terms, Friction, Lubrication, and Wear Technology Metals Handbook, vol. 18, ASME International, Metals Park, OH, 1992. [6] Y. Kimura, et al., Wear and fatigue in rolling contact, Wear 252 (2002) 9–16. [7] R.K. Steele, Rail Lubrication: The Relation of Wear and Fatigue Transportation Research Record 1042 ,1985, pp. 24–32 [8] R. Nilsson, On wear in rolling sliding contacts. TRITA-MMK (Doctoral thesis), Department of Mechanical Design, KTH Royal Institute of Technology, Stockholm, 2005. [9] J.F. Archard, Contact and rubbing of flat surface, J. Appl. Phys. 24 (981) (1953). [10] S.C. Lim, M.F. Ashby, Wear mechanisms maps, Acta Metall. 35 (1987) 1–24. [11] T.H.C. Childs, The mapping of metallic sliding wear, in: Proc. Instn. Mech. Engrs. C 202, 1988, pp 379–395. [12] U. Olofsson, T. Telliskivi, Wear, plastic deformation and friction of two rail steels-a full-scale test and a laboratory study, Wear 254 (2003) 80–93. [13] J. Kalker, Simulation of the development of a railway wheel profile through wear, Wear 150 (1991) 355–365. [14] T.G. Pearce, N.D. Sherratt, Prediction of wheel profile wear, Wear 144 (1991) 343–351. [15] A. Ward, R. Lewis, R.S. Dwyer-Joyce, Incorporating a railway wheel/rail model into multi-body simulations of wheelset dynamics, in: Proceedings of the 29th Leeds-Lyon Symposium on Tribology, 2003. [16] T. Jendel, Prediction of wheel profile wear-comparisons with field measurements, Wear 253 (2002) 89–99. [17] R. Enblom, Simulation of wheel and rail profile evolution-wear modeling and validation, TRITA AVE 2004:19 (Licentiate Thesis), Department of Aeronautical and Vehicle Engineering 2004, Royal Institute of Technology (KTH), Stockholm [18] I.J. McEven, R.F. Harvey, Full-scale wheel-on-rail wear testing: comparisons with service wear and a developing theoretical predictive method, Lubr. Eng. J. Am. Soc. Lubr. Eng. 4 (1985) 80–88. [19] K.L. Johnson, The strength of surfaces in rolling contact, Proc. Inst. Mech. Eng. 203 (1989) 151–163. [20] A. Ekberg, E. Kabo, H. Andersson, An engineering model for prediction of rolling contact fatigue of railway wheels., Fatigue Fract. Eng. Mater. Struct. 25 (2002) 899–909. [21] B. Dirk, R. Enblom, Prediction model for wheel profile wear and rolling contact fatigue, Wear 271 (1–2) (2011) 210–217.
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S. Hossein Nia et al. / Wear 338-339 (2015) 62–72
[22] M.C. Burstow, Whole life rail model application and development for RSSB – Continued development of an RCF damage parameter, Rail safety and standards board 2004; Issue 2 Report EATR-S-2004-2880. [23] B.Dirks, Vehicle dynamics simulation of wheel wear for Swedish high-speed train X2000, Master thesis, TRITA AVE 2003:16, Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), Stockholm, 2003. [24] UIC: Testing and approval of railway vehicles from the point of view of their dynamic behaviour –safety –Track fatigue – Ride quality, Code 518 OR, 2nd ed., April 2003.
[25] S. Hossein Nia, P.-A. Jönsson, S. Stichel, Wheel damage on the Swedish ironore line investigated via multibody simulation, J. Rail Rapid Transit 228 (2014) 652–662. [26] E. Andersson, M. Berg, Spårtrafiksystem och spårfordon, Del 2: spårfordon. Stockholm, 2007. [27] C. Casanueva, et al., Influence of switches and crossings on wheel profile evolution in freight vehicles, Veh. Syst. Dyn. 52 (2014) 317–337. [28] A. Ekberg, et al., Identifying the root causes of damage on the wheels of heavy haul locomotives and its mitigation, J. Rail Rapid Transit 228 (2014) 663–672.