Wear 261 (2006) 1253–1264

A mathematical model to predict railway wheel

profile evolution due to wear
F. Braghin a,∗ , R. Lewis b , R.S. Dwyer-Joyce b , S. Bruni a
aPolitecnico di Milano, Mechanical Engineering Department, Italy
b University of Sheffield, Department of Mechanical Engineering, UK
Received 20 April 2005; received in revised form 28 February 2006; accepted 10 March 2006
Available online 18 April 2006

Abstract
Wheel and rail wear is a fundamental problem in the railway field: the change of profile shape deeply affects the dynamic characteristics of
railway vehicles such as stability or passenger comfort and, in the worst cases, can cause derailment. It is therefore of great economic relevance to
develop a software able to predict the wheel profile evolution due to the wear process since it could be used to effectively evaluate maintenance
intervals, to optimise wheel and rail profiles with respect to wear and to optimise the railway vehicle’s suspensions with new and worn wheel
profiles.
A wheel wear prediction model is a rather complex mathematical tool since it couples several tasks: simulation of vehicle dynamics, local
wheel–rail contact model, local wear model, each one bearing its own uncertainties. Moreover, each single task may be solved by different
approaches that may be more or less accurate and, correspondingly, may require a higher or lower computational effort. This paper presents a
fast and reliable wear prediction model that has been validated through comparison with full-scale experimental tests carried out on a single
mounted wheelset under laboratory conditions. As described later in this paper, the wear prediction model can also be used to determine the
best re-profiling interval (to minimise total life cycle costs) and to determine those vehicle design parameters that determine less wheel (and rail)
wear.
© 2006 Elsevier B.V. All rights reserved.

Keywords: Railway wheel wear; Numerical model; Wear coefficients; Twin disc testing

1. Introduction the railway vehicle dynamics that is affected by the change of

wheel profile shape: both stability and passenger comfort depend
The life of railway wheels is usually limited by wear. The on wheel and rail wear.
wheel surface is subjected to high normal and tangential con- There are several advantages to be gained by the availability
tact stress. Contact forces change magnitude and orientation of a reliable predictive model of wheel wear. Primarily, it would
as the wheel travels over the rail curves, crossings, and local allow operators to effectively define maintenance schedules for
surface perturbations. This constantly changing contact patch wheel re-profiling. But it would also facilitate the design of vehi-
moves over the wheel tread and to a certain extent the flange. cles and wheelsets that cause reduced wear to both wheel and
The contact is nominally rolling but a small amount of local slid- rail surfaces.
ing takes place at the interface. The amount of sliding depends The requirements for modelling wheel profile evolution due
on the contact patch geometry, normal force, lateral force, and to wear are threefold. First, it is necessary to determine the
friction coefficient. variation of wheel contact forces as the wheelset passes over
The removal of material from the surface by wear is a function a pre-defined rail track route. Secondly, these forces must be
of the sliding and contact stresses. These quantities depend on related to the contact patch position and local traction and slip.
And finally, the local contact patch conditions must be related
to the material removal by wear. The calculation process is nec-
∗ Corresponding author. Tel.: +39 02 2399 8306; fax: +39 02 2399 8492. essarily iterative, because wheel profile changes will alter the
E-mail address: francesco.braghin@polimi.it (F. Braghin). dynamic behaviour of the wheelset and therefore the contact

0043-1648/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.wear.2006.03.025
1254 F. Braghin et al. / Wear 261 (2006) 1253–1264

forces. Each of these tasks can be carried out using a different proportionality between material removed and work done at
approach with various degrees of accuracy and computational the wheel–rail interface (the proportionality constant was deter-
effort. As yet, there is no general consensus to the best approach. mined from full-scale experimental tests). Since simulation time
This paper covers all three aspects of the modelling proce- was excessive, wheel profiles were updated only twice over a
dure; a multi-body simulation package is used to predict contact mileage of 10,500 km. The use of the contact model proposed
forces, an advanced contact model is used to deduce local contact by Kik and Piotrokswi [6] was also investigated, showing that
conditions, and experimental data is used to relate these condi- this algorithm can be used as a valid alternative to CONTACT93
tions to wear rates. This procedure has been used to simulate to speed up simulations.
the performance of a full-scale axle roller test rig. The predicted A number of different techniques have been used for study-
wear rates are then compared with measurements from the tested ing wear rates of railway wheel steels to generate data for use
wheels. in wear modelling procedures. Field measurements have been
used in the past to study the causes of wear as in Dearden [7].
2. Background A large amount of data has also been gathered from simulated
field experiments carried out on specially built test tracks [8].
One of the first attempts to simulate wear of railway wheels Laboratory methods used range from full-scale laboratory exper-
was made by Pearce and Sherratt [1]. Their model is very sim- iments [9] and scaled-down tests [10] to bench tests using a twin
ple in order to achieve a reasonable simulation time: after the disc set-up [11–15]. The twin disc approach has been used more
calculation of the global contact forces and creepages acting than most because it offers greater control over experimental
on the contact patch the amount of material removed is calcu- variables as well as the ability to test a wide range of materials
lated through a wear index (later called the “Derby wear index”). at lower cost.
The considered track is made of a straight line plus an S curve. The Derby wear index used by Pearce and Sherratt [1] adopts
A maximum kilometres updating strategy is used. The optimal an energy approach in the analysis of the relationship between
route length for the updating is found to be equal to 1100 km. wear rate and contact conditions. It is assumed that wear rate
Zobory [2] used Hertz theory to solve the wheel–rail normal (␮g/m rolled/mm2 contact area) is related to work done at the
contact problem and FASTSIM to solve the tangential contact wheel–rail contact (wear rate = KTγ/A, where T is tractive force
problem. The multi-body vehicle model used is ELDACW. Dif- and γ slip at the wheel–rail interface, K a wear coefficient and A is
ferent wear modelling approaches are discussed, mainly based the contact area). Various researchers have reported wheel–rail
on the proportionality of wear with the energy dissipated at the wear results using twin disc test machines of varying geome-
contact. Due to the very different wear regimes on wheel tread tries as well as full-scale test results that support this approach
and wheel flange, Zobory introduced two proportionality con- [12,10,13,9,16]. While it has been found to break down at high
stants, one for the “mild” regime on the tread and one for the slip and contact stress conditions [12], it still provides the most
“severe” regime on the flange. The transition between the two suitable basis for a wear model and has a number of advan-
regimes depends on wheel and rail material properties. Simu- tages over the other models mentioned above. It was apparent,
lation results are compared with various on-line measurements however, that improvements could be made to this modelling
related to a vehicle running on the Gotthard line for a maxi- approach, especially with regard to the wear regime at higher
mum mileage of 27,000 km. Wheel profiles are updated every slips and contact stresses. Tread and flange wear fall with differ-
1000 km. To be able to compare experimental data and numeri- ent wear regimes and it may therefore be better to use different
cal results, a smoothing procedure (based on a smoothing spline) wear constants for each. An improved definition of the wear
was applied to the updated wheel profile. regimes was also required.
Jendel and Berg [3] developed a similar model using the In this work it was decided to adapt the Derby wear index
multi-body code Gensys for the dynamic railway vehicle simu- approach to take account of the point made above and to generate
lations. Again, the local contact analysis was solved by applying the wear coefficient using a series of twin disc tests varying T
Hertz theory and FASTSIM. The contact model used within the and γ, as will be explained in the next section.
multi-body simulation was able to find at most two contact points
at the same time on a given wheel–rail pair. For the wear predic- 3. Twin disc wear tests
tion, Archards wear model was applied locally. The wheel profile
was updated every time a maximum wear depth of 0.1 mm was In order to characterise the wear of the wheel material, wear
reached or a maximum distance of 1500 km was run. A cubic tests were carried out using a twin disc test machine. These were
spline was applied both on wear distribution and the updated designed to establish the wear mechanisms, identify the wear
wheel profile for smoothing purposes. The simulation results regimes of the wheel material and determine the wear constants
were compared with measurements of serviced wheels on the necessary for the wear index analysis to be carried out in the
commuter railway network in Stockholm. wear modelling procedure described later.
Braghin et al. [4] developed a wheel wear prediction model
based on a multi-body code for the railway dynamic simula- 3.1. Apparatus
tions, on CONTACT93 algorithm by Kalker [5] to solve both
the non-Hertzian normal contact problem as well as the tangen- The twin disc test machine was used to carry out the testing
tial problem and on a local wear model that assumes a direct (shown in Fig. 1). The original development of this machine, and
 F. Braghin et al. / Wear 261 (2006) 1253–1264 1255

Fig. 1. Schematic diagram of the twin disc test machine.

more recent work carried out to add a feedback control system,

have been described previously [17,18].
The test discs are hydraulically loaded together and driven at
controlled rotational speed by independent electric motors. Shaft
encoders monitor the speeds continuously. A torque transducer
is assembled on one of the drive shafts and a load cell is mounted
beneath the hydraulic jack. The slip ratio required is achieved
by adjustment of the rotational speeds. All data is acquired on a
PC which is also used for load and speed control. Repeatability
in wear and fatigue testing on the test rig has been shown to be
very good and wear results are consistently within ±0.1 ␮g [18].

3.2. Specimens

Discs to be used during the testing were cut from R8T wheel
rims and UIC60 900A rail sections and machined to a diameter
of 47 mm with a contact track width of 10 mm. Wheel specimens
were drawn from the wheel rim parallel and as close as possible
to the outer surface.
Fig. 2. Schematic diagram of the disc environment chamber.
3.3. Experimental procedure

Wear tests were carried out using the wheel disc as the driving velocities of the two disc specimens. Tests were performed at a
disc and rail disc as the braking disc, as shown in Fig. 2. All tests range of Tγ/A values achieved by varying both the load and the
were done in dry conditions without lubrication (resulting in a slip. Table 1 shows the test conditions and corresponding values
friction coefficient of 0.45–0.50). of Tγ/A. Typical wheel–rail Tγ/A values occur up to 10 N/mm2
A nominal disc rotational speed of 400 rpm was used in the for tread contacts and greater than 20 N/mm2 for flange contacts.
tests. An environment chamber enclosed the discs and air cooling
was provided to both. Suction was provided to remove wear Table 1
debris for analysis. Wear measurement was determined by mass Twin disc test conditions and values of the wear index Tγ/A
loss of the discs, measured before and after tests and at intervals Contact pressure (N/m2 ) Slip (%) Tγ/A (N/mm2 )
during initial tests to determine the number of cycles required
to reach steady state wear. Weighing scales with an accuracy of 1500 0.2 0.21
1500 0.3 0.64
±0.00001 g were used for the measurements. Contact stresses 1500 0.5 1.47
and slip were changed in order to vary the Tγ/A parameter for 1500 0.7 2.47
the wear index analysis (see Section 4.2), T being the contact 1200 1.0 3.58
force in the contact plane, A being the contact area and γ being 1500 1.0 4.12
the relative slip defined as 1800 1.0 4.81
1500 1.5 7.07
s v1 − v2 1500 2.0 10.37
γ= =2 (1) 1500 3.0 16.61
v v1 + v 2
1500 5.0 28.27
where v1 and v2 are the tangential velocities of the two disc 1500 7.5 40.64
specimen, v the reference speed equal to the mean value of 1500 10.0 53.01
1500 15.0 79.52
the tangential velocities of the two disc specimen and s is the 1500 20.0 117.81
(imposed) slip equal to the difference between the tangential
1256 F. Braghin et al. / Wear 261 (2006) 1253–1264

Fig. 3. R8T wheel material wear rates at: (a) low Tγ/A values and (b) over the full range of Tγ/A values.

A steady state wear rate is achieved after 20,000 cycles. Each

test lasted 30,000 cycles.
Tests were carried out under dry conditions so that results
of the modelling to be carried out could be compared realisti-
cally with those from the full-scale tests, which were also run
dry. Clearly in field conditions environmental conditions such as
rain and varying humidity and friction modifiers applied at some
curves will mean that the wheel–rail contact will be partially
lubricated at times. However, determining wear coefficients for
these conditions and then incorporating this into a wear mod-
elling procedure would be extremely complex, but would be the
next step in this type of work.

3.4. Wear test results

Fig. 3 shows the wear rate against the wear index Tγ/A. At
low values of Tγ/A, wear rate is proportional to Tγ/A. It can Fig. 4. Wheel rolling surface on the full-scale roller rig after 2000 km.
be seen that varying contact pressure to change Tγ/A still gives
results that fit on the same line of proportionality. (see Fig. 5a). Fig. 5b also shows the subsurface morphology
As Tγ/A was increased, however, the wear rate levelled and of the wheel disc. At the surface the oxide layer is just visible.
then increased again quite rapidly indicating that as the severity There is a very small amount of deformation just below the wear
of the contact is increased different wear regimes are apparent surface of the disc.
(see Fig. 3). As Tγ/A was increased, the wear mechanism altered. The
At low Tγ/A oxidative wear was seen to occur on both wheel wheel material appeared to wearing by a delamination process.
and rail discs. The disc surfaces turned a rusty brown colour. Closer examination of the wheel disc surfaces revealed that this
A similar effect has been observed on wheel treads in full-scale was the case (see Fig. 6a). Observation of the subsurface mor-
testing, as observed by McEwen and Harvey [9] and after tests on phologies revealed that a larger amount of plastic deformation
a full-scale roller-rig, as shown in Fig. 4. Closer examination of was occurring below the wheel disc wear surface and crack for-
the wear surface of the wheel disc revealed abrasive score marks mation just below the surface was visible which was leading
and evidence of the oxide layer breaking away from the surface to thin slivers of material breaking away from the surface (see

Fig. 5. R8T wheel material disc surface at low Tγ/A.

 F. Braghin et al. / Wear 261 (2006) 1253–1264 1257

Fig. 6. R8T wheel material disc surface at higher Tγ/A.

Table 2
Wear regimes and coefficients for R8T wheel and UIC60 900A rail materials
Regime Tγ/A (N/mm2 ) Wear rate (␮g/m/mm2 )

K1 Tγ/A < 10.4 5.3Tγ/A

K2 10.4 < Tγ/A < 77.2 55.0
K3 77.2 < Tγ/A 61.9Tγ/A

Clearly, with the lack of data generated in the third regime

there is a possibility of less accurate wear predictions for con-
tacts at these conditions. It would be anticipated, however, that
wheel–rail contact is in K1 and K2 regions most if not all of
the time and only reaches K3 region in the most severe curves.
Fig. 7. Wear rate for different values of the wear index Tγ/A. Work carried out to compare wear regimes with predicted tread-
rail head and flange-gauge corner contacts has shown this to be
the case [19].
Fig. 6b). As Tγ/A was increased further these cracks were seen to
alter direction from running parallel to the wear surface and turn- 4. Wheel profile wear prediction model
ing up to turning down into the material causing larger chunks
of material to break away. The wear features and mechanisms A schematic representation of the wheel wear prediction
are discussed in greater detail in Lewis and Dwyer-Joyce [15]. model ProfCon (Profile Control) is shown in Fig. 8, and is made
With wear testing such as the twin disc methodology used up of four main tasks:
here, there is always an issue of scaling the results to the full-
scale application. The Tγ/A approach used here provided the 1. multi-body simulation of railway vehicle dynamics;
best way to accomplish this. Comparisons of wheel and rail 2. local analysis of wheel–rail contact;
material wear rates determined during small scale testing have 3. wear calculation;
been compared with those from full-scale tests for given values 4. smoothing and updating of the wheel profile.
of Tγ/A and have been shown to compare well [9,19,15].
In order to provide wear coefficients for use in the wheel Starting from the vehicle characteristics and initial wheel and
wear modelling procedure the wear rate data was split into three rail profiles, a sequence of service conditions (e.g. tangent track
regions (see Fig. 7). A wear coefficient was defined for each of running at different speeds, curve negotiation at specified cant
these regions (see Table 2). deficiencies, etc.) called the vehicle “mission track” is simulated

Fig. 8. Scheme of the wheel wear prediction model ProfCon.

1258 F. Braghin et al. / Wear 261 (2006) 1253–1264

using a multi-body vehicle model (task 1). At each integration fied lumped parameter scheme. The equations of motion of the
step of the multi-body simulation, global contact parameters vehicle are linearised (only with respect to kinematic non-linear
(position and dimensions of the various active contacts, resulting effects) assuming the motion of the vehicle to be a small per-
contact forces and creepages) are downloaded and used to per- turbation around that of a moving reference travelling along the
form the local contact analysis which provides as an output the track centreline with constant speed and having longitudinal axis
distribution of slip and tractions over the contact patch (task 2). tangent to the track centreline.
Then, the wear model described in Section 3.4 is used to cal- The inputs of the multi-body code are the vehicle parame-
culate the distribution of removed material in each contact patch ters and speed, the wheel and rail profiles, the track flexibility,
and the wear caused by a single mission track is determined the ideal geometry of the line (in particular, for curved tracks,
(task 3). Since the variation of wheel profiles produced by one the curve radius, the cant and the length of transition curves)
single mission track is so small that it produces negligible vari- and wheel and rail irregularities. Wheel and rail profiles are
ations on the results of the multi-body dynamic simulations and described by discrete points making it possible to update the
of the local contact analysis, in order to speed up the wheel pro- profile by the procedure described above.
file wear prediction, the amount of wear is multiplied by n. The The procedure adopted to compute wheel–rail contact forces
integer n is chosen in order to obtain a total wear amount below takes into account that contact between a single wheel and rail
a prescribed threshold. This threshold has to be small enough in may occur simultaneously at more than one location (multiple
order to produce small variations on the results of the dynamic contact condition). Due to the fact that the two contacting bodies
simulation and of the local contact analysis. Then, wheel pro- have the same elastic properties (Young’s modulus and Poisson’s
files are updated and eventually smoothed and the corresponding ratio) the problem of finding the normal contact force component
distance run, equal to n times the length of the mission track, (normal problem) can be considered de-coupled from that of
is added to the total vehicle mileage (task 4). The worn pro- determining the tangential contact force component (tangential
files obtained by this procedure are fed back into the multi-body problem). Therefore, these two problems are solved separately
model of the railway vehicle. and sequentially.
The described procedure is repeated several times until the In order to solve the normal contact problem, a multi-Hertzian
whole wear life of the profiles (i.e. the mileage after which re- approach is applied. This approach allows to approximate the
profiling is necessary) is reached. At the end of each iteration, generally non-Hertzian contact area through multiple ellipses.
the worn wheel profiles are stored together with wear control The number of considered ellipses directly influences the accu-
parameters Qr , Sh and Sd used for maintenance purposes (see racy of the methodology: by increasing this number, the approx-
Section 5.2). Another output of the model is the amount of wear imate solution converges to the exact one. Thus, a best compro-
at each iteration associated with the three wear regions identified mise between accuracy and computational cost can be found.
through twin disc tests (mild, intermediate and severe wear) as The tangential contact problem, a function of the normal force
described in Section 3.4. and of the creepage components, is then solved through the
Besides the modelling problems associated with the above heuristic formulae by Shen at al. [22]. More details on the
described tasks, the choice of the mission track is critical with wheel–rail contact model used in the multi-body simulations
respect to the comparison between numerical results and exper- can be found in Braghin et al. [23]. It should be pointed out
imental wear data. In principle, the set of running conditions that the Hertzian approach is used to solve the normal contact
to be simulated should include all the different conditions the problem both inside the multi-body code and in the local contact
wheelset will encounter during its lifetime. At the same time analysis. The formulae used to solve the tangential contact prob-
these running conditions should be kept as small as possible in lem, instead, are very fast and reliable, but do not provide the
order to reduce the computational effort. distribution of stresses and slippages inside the contact patch.
Also the criterion adopted for wheel profile updating is criti- Thus, the local contact analysis is necessary.
cal: increasing n leads to a smaller computational effort but the
accuracy of the results will be poorer. If n is too big, the wheel 4.2. Local contact analysis
profile wear prediction algorithm may also diverge.
The local contact analysis is carried out to compute slip-
4.1. Multi-body model of the railway vehicle page and traction distributions inside the contact patch once
the “global” contact quantities, i.e. the contact area dimensions
Vehicle dynamic simulations of the specified mission track (semi-axes of the elliptical patch), the normal contact force, the
are performed using a mathematical model of train–track inter- longitudinal and lateral creepages, the friction coefficient and the
action previously developed at the Mechanical Engineering speed of the train, are given. To this end, different algorithms
Department of Politecnico di Milano [20,21]. Carbodies and are available, like the approximate solution for elliptic contact
bogies are schematised through rigid bodies while the wheelsets patches called FASTSIM by Kalker [5,24], the approximate
are represented as flexible bodies by means of the modal super- solution for non-Hertzian contact patches by Kik and Piotrokswi
position approach. Primary and secondary suspensions are rep- [6] or the “exact” solution (within the elastic half-space approxi-
resented through linear and non-linear viscoelastic elements, mation for the contacting bodies) implemented in CONTACT93
while track deformability may be accounted for either by means algorithm by Kalker [5]. In the present work a simplified ver-
of a detailed finite element model or by means of a simpli- sion of FASTSIM algorithm neglecting the effect of spin was
 F. Braghin et al. / Wear 261 (2006) 1253–1264 1259

applied to each Hertzian ellipse forming the multi-Hertzian con- Otherwise, slippage occurs and p is equal to
tact patch. The choice was driven by the fact that, among all pA (x, y)
other possible choices, this method requires the smallest com- pS (x, y) = pL (x, y) and
|pA (x, y)|
putational effort but, despite its simplicity, provides results of
acceptable accuracy when compared to the “reference” method Lv
sS (x, y) = [p (x, y) − pA (x, y)] (7)
CONTACT93. On the other hand, the direct use of CONTACT93 x S
algorithm for performing the local contact analysis has been Wear occurs only in the slip region of the contact patch and, as
proven to be too slow in a previous work [4]. In any event, shown in Section 3, it is a function of the non-dimensional slip
CONTACT93 algorithm has been used as a “reference” model γ that is equal to
to check, for some particular cases, the approximations intro-
duced by FASTSIM. sS (x, y) L
γ(x, y) = = [p (x, y) − pA (x, y)] (8)
FASTSIM algorithm is based on the hypothesis that the local v x S
tangential surface deformations u are linearly related to the tan- Thus, the wear index Tγ/A for the considered cell is equal to the
gential surface tractions p by a constant coefficient L called scalar product of the traction times the non-dimensional slip:
flexibility:
Tγ
= p(x, y) · γ(x, y) (9)
u(x, y) = Lp(x, y) (2) A
x being the longitudinal direction and y being the transversal The wear index, together with the information concerning the
direction in the contact plane. For more details on the propor- position of the contact point along the wheel profile, represents
tionality constant L see Kalker [24]. the input of the wear model.
The elliptical contact patch is discretised using a rectangular
grid having cell dimensions x and y. It should be noted that, 4.3. Wear model
while y is constant over the whole elliptical contact path, x
is a function of the width of the contact ellipse in longitudinal The wear model is based on the wear tests described in
direction (a strip). This non-uniformity in longitudinal direction Section 3. For each cell in the contact patch, the material loss pro-
is due to the fact that the width of the contact ellipse along duced by wear is determined according to the wear law depicted
this direction is always divided into an equal number of cells. in Fig. 7. Since the model is intended to simulate only the forma-
The result of this approach is that, with a minimum increase in tion of “regular wear” (i.e. the variation of the transverse profile
computational time, much more accurate results are achieved if and not the formation of wear patterns along the circumferen-
compared to a fully uniform grid in both x- and y-directions. tial direction), the wear that occurs at a given time instant and
The slip s that occurs in each cell is a function of the tangential at a particular wheel transversal position may be spread over
surface deformations u and of the rigid slip w that is equal to the whole circumference of the wheel according to the ratio
the creepage vector (w = {ξ, η}T ): between the real travelled distance vt and the length of the
circumference 2πR, t being the time interval between subse-
x quent integration steps and R the rolling radius of the wheel that
s(x, y) = u(x, y) − u(x − x, y) + wx (3)
v corresponds to the considered contact patch. Accordingly, the
where x − x is the position of the preceding cell (at a given wear depth δ for each cell is equal to
lateral position y) and v the speed of the train. Substituting Eq.  
Tγ vt vt
(2) into Eq. (3) we obtain δ(x, y) = K (10)
A ρ 2πR
x
s(x, y) = Lp(x, y) − Lp(x − x, y) + wx (4) K being the wear rate, a function of the wear index (Fig. 7 and
v Table 2) and ρ being the density of the wheel material. The wear
Let us assume that the considered cell is inside the adhesion depth values δ are then summed over the longitudinal direction
region of the contact patch. In this case the slip s is equal to zero and added to the cumulative wear depth vector.
and
x 4.4. Smoothing and updating of the wheel profile
pA (x, y) = p(x − x, y) − w and sA (x, y) = 0 (5)
L
The updating strategy is a key point of the profile wear pre-
To verify the assumed adhesion, the obtained pA value has to diction model. Its purpose is to determine the mileage after
be compared with the traction bound pL that is equal, apply- which wheel profiles should be updated and a new calculation
ing Hertz theory to determine the normal pressure value and of contact forces, tractions and slips should be performed. A too
Coulombs friction law locally, to “conservative” strategy, requiring too frequent profile updates,
  x 2  y 2 could result in unnecessary computational effort. On the other
3 Q
pL (x, y) = μ 1− − (6) hand, increasing the mileage between two calculations too much
2 πab a b may lead to inaccuracies in the final worn wheel profile (or even
where μ is the (static) friction coefficient and Q the applied divergence in the numerical procedure) due to the non-updated
normal load. If |pA | is smaller than pL value, adhesion occurs. wheel profiles in the multi-body code.
1260 F. Braghin et al. / Wear 261 (2006) 1253–1264

Different wheel profile updating strategies were compared conditions (such as rail profiles, track gauge, operating speed
[25] and it was found that the most efficient one is based on the and loads and friction conditions) are precisely measured and
maximum wear depth, i.e. the profile is updated when a given kept under control (tests were carried out at ambient temper-
threshold of the maximum value of cumulative wear depth is ature, i.e. at 23 ◦ C, and at relative humidity of approximately
reached. A sensitivity analysis showed that a threshold of 0.1 mm 45%). Service data, as the one used by Jendel and Berg [3],
is low enough to guarantee a good accuracy and at the same time instead, are generally affected by a high dispersion of work-
does not lead to excessive computational effort. ing conditions and test variables. Therefore, the evaluation of
The worn wheel profile is then smoothed in order to avoid the accuracy of the wear prediction model may be, in this case,
short wavelength concavities along the wheel profiles that have affected by unknown contact loads, vehicle speed, rail profiles,
no physical meaning. In fact, due to the continuous variation temperature, humidity and friction coefficient values encoun-
of the worn wheel profile that occurs in reality, wheel–rail con- tered by the wheelset during service. It could be questioned that
tact is not stationary in position even if the running conditions laboratory tests are not fully representative of real working con-
of the wheel are maintained constant thus leading to a smooth ditions. However, the test stand used is specifically designed to
profile. For computational reasons, the wheel profile is updated reproduce as close as possible the real behaviour of the wheelset
at discrete steps. Therefore, the smoothing process is necessary in a wide variety of operating conditions. Therefore, collected
and allows to better approximating the continuous wear process wear data are closely representative of real service conditions.
with a discrete sequence of profile updates.
Different smoothing strategies were compared [25] in terms 5.1. Full-scale wear tests
of computational cost and stability and accuracy of the results.
The best smoothing strategy was found to be a combination of a Wear tests were carried out on the BU300 roller rig, owned
moving average applied to the cumulative wear depth before pro- by Lucchini Sidermeccanica and schematically shown in Fig. 9.
file update and a cubic smoothing spline applied to the updated The rig is composed by two discs driven by a DC motor and
profiles before starting a new iteration of the wear prediction bearing rail profiled steel rings. The wheelset is placed on these
model. discs and is connected, by the primary suspension, to a transverse
beam representing the half-bogie. Two hydraulic actuators are
5. Validation of the wheel profile wear prediction model placed vertically over the transversal beam, one for each side,
and are used to apply different vertical loads on each wheel, thus
The profile wear prediction model described in Section 4 was reproducing the vertical load acting on the wheelset as well as the
validated by means of comparison with experimental data. The load transfer from one wheel to the other occurring during curve
validation work was performed using the results of wear tests negotiation. A third hydraulic actuator applies a lateral force
performed on a full-scale roller rig for mounted wheelsets. The on the transversal beam to reproduce the lateral force acting
use of data coming from these laboratory tests allows to precisely on the wheelset in different service conditions such as curve
evaluate the model’s accuracy since test variables and working negotiation. At each side of the transversal beam two electric

Fig. 9. Schematic diagram of the BU300 full-scale roller rig for mounted wheelsets.
 F. Braghin et al. / Wear 261 (2006) 1253–1264 1261

servomotors are placed longitudinally at two different heights. contact parameters (contact dimensions and locations, resulting
These actuators are used to control the yaw movement of the forces and creepages) correspond to the tests performed on the
transversal beam and therefore the wheelset’s angle of attack. roller rig.
The test rig has been interfaced with a multi-body model of In Fig. 10 the wear depths measured on the right wheel for
the railway vehicle so that the reference signals for the actuators different mileages are compared to the results of numerical simu-
can be derived from the results of the simulation of a particular lation performed using the wheel profile wear prediction model.
service condition taking into account the effect of railway vehicle It can be observed in Fig. 10a that, at approximately 7500 km,
parameters (static loads, geometry, properties of the primary wear occurred at a lateral position of about −45 mm. This
and secondary suspensions), track layout and irregularities, train localised damage, not visible in the numerical model results,
speed, etc. More details on the test rig and on the generation of is due to a failure in the control system and not to regular wear.
the references for the actuators can be found in Bruni et al. [26]. Fortunately, this localised damage is located outside the region
For the experimental investigation of railway wheel wear a where contact normally takes place and therefore does not affect
new wheelset equipped with R8T wheels of an ETR500 Italian the numerical–experimental validation.
high speed train with ORES 1002 profiles was used. The rails, Two separate wear regions are visible in Fig. 10a, one on
instead, are UIC60 900A. The wear track, that was repeated sev- the wheel flange (from −40 to −30 mm) and one on the wheel
eral times in order to achieve a total mileage of 10,500 km, is tread (from 0 to 30 mm). Flange wear occurs when the wheel is
made up of a mix of tangent track running and curve nego- pushed against the rail by the lateral actuator, reproducing the
tiations. Since the percentage of curves in the wear track is condition of flanging contact typical of the outer wheel of the
much higher than in reality, the wear phenomenon is signifi- leading wheelset during curve negotiation. Tread wear instead
cantly accelerated. Thus, the obtained wear amount corresponds is mainly due to the longitudinal creep forces that are generated
to a mileage of approximately 50,000–80,000 km of normal ser- when the opposite wheel is flanging. Fig. 10a also shows that
vice. Traction and braking conditions were not included in the flange wear mainly occurred during the initial 2500 km. During
wear track. Profile changes due to wear are measured after every the following part of the wear test, the flange wear rate of growth
2000 km using a MiniProf device. The procedure followed to was smaller. This is due to the fact that, for a new profile, smaller
define the wear track and the results obtained in the tests are flange contact patches with higher values of local pressures,
described in Braghin et al. [4]. In this work, the same results and therefore of frictional work, take place. Tread wear instead
will be used to validate the wheel profile wear prediction model evolves more uniformly with mileage.
described in Section 4. The results of the numerical simulations performed using the
wheel profile wear prediction model (Fig. 10b) are in very good
5.2. Experimental–numerical comparison agreement with the measurements: the model is able to correctly
reproduce the position as well as the amount of flange and tread
Wear tests were simulated by the wheel profile wear predic- wear regions. In fact, the estimated total tread wear amount after
tion model. To this end, a mathematical model of the test rig a mileage of 10,500 km is 5% smaller than the experimental
was used in order to correctly take into account the dynamic one that is indeed a very good result considering that the wear
behaviour of the wheelset on the roller rig. The test rig model is indexes used in the wheel wear prediction model come from
described in Bruni et al. [26] and includes the same wheel–rail twin disc wear tests and no adjustment nor calibration of either
contact model as the one used by the vehicle’s multi-body component of the wheel wear prediction model was done. Con-
model described in Section 4.1 as well as the models of the cerning flange wear, the wheel wear prediction model is able
hydraulic and electric actuators together with their control log- to correctly foresee that about 60% of the total wear occurs in
ics. This model replaces the multi-body vehicle model in Prof- the first 2500 km. However, comparing the experimental and the
Con algorithm (see Fig. 8). Therefore, the calculated global numerical total flange wear amount, an overestimation of about

Fig. 10. Comparison between (a) experimental and (b) numerical transversal profile wear depths at different milages (the X-axis reference corresponds to the rolling
circle in Fig. 11).
1262 F. Braghin et al. / Wear 261 (2006) 1253–1264

In railway maintenance practice three indexes, called wear

control parameters and denoted by the symbols Sd , Sh and Qr ,
are used to quantify the degree or severity of profile wear. The
Sd index measures the flange thickness, the Sh index the flange
height and the Qr index the flange steepness (Fig. 11).
Fig. 12 shows the experimental and numerical evolution of Sd
index with mileage. Experimental and numerical results are well
overlapped. In particular, the initial flange thickness decrease
of 0.6–0.7 mm (occurring in the first 2000 km) is clearly vis-
ible. This thickness remains almost constant in the following
6000 km (both experimentally and numerically) and then starts
Fig. 11. Definition of Sd , Sh and Qr wear control parameters. to decrease again but of a lower rate than in the early running.
As discussed in Section 6, this behaviour is related to the occur-
rence of different wear regimes (mild, intermediate and severe
30% is obtained by the prediction model. Several reasons can be wear) that took place during the tests.
found for this error: the Hertzian approximation of flange con-
tact (where contact patches are non-elliptic), the neglecting of
6. Prediction of wheel wear in standard service
the spin creepage (that is particularly significant for the flange
contact) and the use of a single friction coefficient value for
In this section the wheel wear profile prediction model is
both tread and flange contacts (the friction coefficient value was
applied to predict the evolution of the wheel profile during stan-
measured on the wheel tread on BU300 test rig but no measure-
dard service thus allowing to set-up an optimised maintenance
ment facility was available to determine the friction coefficient
(re-profiling) strategy and/or to design a railway vehicle that is
value on the flange). Also the inaccuracy of the profilometer
less aggressive from a wheel wear point of view. To this end, an
used to measure the wheel transversal profile should be taken
ETR500 Italian high speed passenger vehicle initially equipped
into account: the declared accuracy is equal to ±0.1 mm but, due
with ORES 1002 wheel profiles is taken as reference. The vehi-
to the size factor of the tracer, higher errors could occur in case
cle is designed to be continuously operated on a high speed line.
of steep profile changes like those of a worn flange.
In order to define a wear track (see Section 5.1), the geome-
try of the high speed “Direttissima” line, connecting Rome with

Fig. 13. Numerical evolution of flange thickness control parameter Sd with

Fig. 12. Comparison between experimental and numerical evolution of flange mileage (lower) and amount of abraded material for each wear regime with
thickness control parameter Sd with mileage. mileage (upper).

Table 3
Wear track geometry used to simulate vehicle service on the “Direttissima” line
Curve radius (m) Cant (mm) Length of full curve (m) Length of transitions (m) % of occurrence Non-compensated acceleration (m/s2 )

2900 125 720 230 33 0.85

3000 125 620 230 28 0.79
3700 105 1086 260 16 0.62
4000 105 856 260 17 0.52
5800 80 570 155 6 0.31
 F. Braghin et al. / Wear 261 (2006) 1253–1264 1263

Fig. 14. Numerical evolution of flange thickness control parameter Sd with mileage in the case of reduced bogie wheelbase (a) and of increased primary suspension
longitudinal stiffness (b).

Florence, was considered. Fot this line, curves fall into three The results of the simulation suggest that a different main-
main groups that have mean curve radius of about 3000, 4000 tenance strategy could lead to a longer wheel life. In fact, re-
and 5800 m. Thus, in order to correctly represent the curve dis- profiling the wheel after about 200,000 km would reduce the
tribution along the “Direttissima” line, five typical curves were thickness of the removed material layer to less than a half, thus
selected as representative of the whole line. Their length was leading to a doubling of the wheel service life. However, the
determined taking into account the total length of similar curves number of re-profilings would be greater with higher associ-
and then re-scaled in order to maintain the correct percentage ated tooling costs. In any event, this application shows how the
of occurrence. For each of these curves, cant, gauge and length ProfCon algorithm could be used, together with an estimation
of the cubic transitions were determined as the average values of the costs associated with production and maintenance of the
of these parameters for the curves with equal curve radii along wheelset, to define an optimal re-profiling strategy and thus min-
the line. Also the vehicle speed (i.e. the non-compensated lateral imising total life cycle costs.
acceleration) was chosen as the mean value of the nominal pre-
scribed speeds along the corresponding curves. The wear track 6.2. Optimisation of railway vehicle’s design parameters
used for wheel wear prediction is summarised in Table 3. As in from a wear point of view
the validation process, the effect of braking was not taken into
account. It should be observed that this does not mean that the Another possible application of the wheel wear prediction
wheel wear prediction model cannot reproduce braking condi- model is the determination of the effects of a railway vehicle’s
tions. If enough precise data about the braking transients were design parameters on wheel wear. As an example, Fig. 14a shows
available, also braking manoeuvres could be included in the wear the evolution of Sd wear control parameter for the reference
track. ETR500 vehicle. The two cases show a vehicle having the same
parameters except that the bogie wheelbase is equal to 2.7 m
6.1. Optimisation of wheel re-profiling strategy instead of 3 m. Fig. 14b shows a similar result but for the cases
where the longitudinal stiffness of the primary suspension is
Based on the wear track described in Table 3, the service life increased by 50% with respect to the nominal value. In the case
of a wheelset was simulated. Fig. 13 shows, in the upper part, the of the decrease of the bogie wheelbase service life before re-
amount of abraded material (in grams) on the whole wheel pro- profiling is increased by about 20,000 km. While in the case
file that corresponds to the three identified wear regimes (mild, of the increase in the primary suspension stiffness service life
intermediate and severe wear) for every 25,000 km of mileage before re-profiling is decreased by about 50,000 km.
and, in the lower part, the continuous evolution of the flange Of course, the choice of these design parameters also affects
thickness parameter Sd with mileage. As already observed, the other critical issues such as vehicle stability and safety. There-
rate of material removal is rather high in the first 25,000 km fore, the advantage/disadvantage of modifying the values of
of service (significant intermediate wear occurs) leading to a these parameters should be judged considering all involved prob-
rather steep decrease of the flange thickness. From 50,000 to lems. Nevertheless, these examples show the potentialities of the
125,000 km the wear rate is much lower and the flange thick- wheel wear prediction model that can be used as a design tool
ness remains almost unchanged. In the final part of the service as well as for the optimisation of the maintenance process.
life, the wear rate increases again and severe wear is observed.
For a mileage higher than 200,000 km the wear rate becomes 7. Conclusions
very high, thus leading again to a steep decrease of the flange
thickness. After 310,000 km the minimum allowed value of Sd In this paper a fast and reliable wheel wear prediction model
wear control parameter is reached and the wheel has to be has been described. The model is based on a vehicle’s multi-
re-profiled. body code, a local contact analysis model and a local wear
1264 F. Braghin et al. / Wear 261 (2006) 1253–1264

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