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© Faculty of Mechanical Engineering, Belgrade. All rights reserved. FME Transactions (2003) 31, 15-20 15
Du{an Milutinovi}
Railway Transport Company Belgrade
Aleksandar Radosavljevi}
Traffic Institute CIP, Belgrade
Vojkan Lu~anin
Associate professor
University of Belgrade
Faculty of Mechanical Engineering
Temperature and Stress State of the
Block-Braked Solid Wheel in Operation
on Yugoslav Railways
Thermal load of the block-braked solid wheel railway vehicles is
dominant on the other types of loads. This load, which is mainly
consequence of long-term braking on downgrades for maintaining the
defined constant speed purpose, is the main cause of occurrence of cracks
on treads of wheel and finally fractures of wheel. The paper gives the
analysis calculation results of the thermal load of the railway vehicle
block-braked solid wheel on characteristic selected line on Yugoslav
Railways network. Thermal analysis was done using the finite elements
method, which was also used for obtaining wheel temperature and stress
states in the simulated operation conditions.
Keywords: railway, thermal load, residual stresses, block-brake, braking,
FEM, temperature and stress state.
1. INTRODUCTION
Occurrence of fractures on block-braked solid whe-
els railway vehicles, caused by thermal load, has been
researched in Europe for more than 15 years. Research-
ing is mostly performed in Rail Research Institute
(ERRI) [1-7] with the basic aim was to define new
design of solid wheel which is as little as possible
sensitive to thermal overloads [8].
Previous results confirmed dominant influence of
thermal loads in regard to mechanical loads [1,3,8, 9,10]
but in [11] and [12] regulated residual stresses measure-
ment appeared because of high thermal loads in block-
braked solid wheel. It means that the problem
prevention damages of solid wheels fractures are still
very actual [9]. It is necessary to emphasis that high
thermal loads, in other words overloads, of wheel very
often occur as a result of long-term braking for the
maintenance constant train speed on down-grade or
unwanted locking of wheels purposes.
The paper presents results of estimated analysis of
solid wheel thermal loads on selected characteristic line
part on the network of Yugoslav Railways (JŽ).
Calculations of temperature and stress states are made
by finite element method (FEM), and characteristic line
part is chosen as a line with maximum thermal loads of
braking on the basis of detailed analysis of all lines on
the JŽ network. Result of this analysis is thermal loads
collective of braking on chosen line Belgrade - Bar (port
on Adriatic coast), which is characterize by referent
slope of 25‰ in both directions of train running. Final
calculation results show changes of temperature in
chosen wheel points during train running and pictures of
stress states in periods of highest temperatures. On the
basis of obtained results we can confirm hypothesis that
thermal loads are the main cause of cracks occurrence
on wheel rim on the JŽ network.
2. CALCULATION OF BRAKING POWER
DISTRIBUTION
Numerous high up-grades and downgrades lead to
an increase of both train traction consumed energy and
thermal load as a result of intensive braking. All this
results in motive power cost increase. In addition to
increased consumed train traction energy to overcome
rolling resistance in curves and gradient forces, very
important costs are from frequent use of brakes for
stopping as well as for maintenance issued train speed
on down-grades. However, we are not asking a question
of increased operation costs but increased maintenance
costs is of great significance.
For calculation of power breaking distribution on
Belgrade (Resnik) - Podgorica line it was necessary to
simulate train traction in both directions. Train traction
simulation is performed for longitudinal rail profile
divided by train traction simulation software, which is
shown in [13].
Electric brake diagram of locomotive series JŽ 461
for determination power braking distribution to
maintenance-regulated speed on downgrades is used
[14]. On the diagram basis are determined: braking
effort, braking current and excitation current of traction
motor for every train (locomotive) speed value, and
finally braking power. Since train-running simulation is
executed in function of time as a result we obtain
dissipated train energy applying electric brake. In that
way by train, running simulation, for each concrete
case, is obtained brake energy distribution in function of
passed route and running time. Therefore, brake energy
Received: November 2002, accepted: April 2003.
Correspondence to: Vojkan Lu~anin,
Faculty of Mechanical Engineering,
27. marta 80, 11000 Belgrade, Serbia and Montenegro
E-mail: vlucanin@mas.bg.ac.yu
16 ▪ Vol. 31, No 1, 2003 FME Transactions
is calculated in this way, which is developed during
maintenance assigned constant speed on downgrades.
For simulation in direction Resnik - Podgorica,
freight train with the mass of Q=1000 t and brake
percentage of p=60%, is chosen hauled by electric
locomotive series JŽ 461. In opposite direction freight
train with the mass of Q=1060 t and brake percentage of
p=61% is chosen with the same locomotive.
Considering obtained power braking distribution
values, characteristic intervals with intensive braking
and average values of brake power, are established. All
of this is done to prepare input data for thermal load
calculation of block-braked solid wheel by finite
element method. Brake power diagram of freight train
in Resnik-Podgorica direction is shown in Fig. 1.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150 200 250 300 350 400 450 500 550
t [min]
P, Psr [kW]
P
Psr
Train standstill
Resnik
Podgorica
Bela Reka
Veliki Borak
Vreoci
Divci
Valjevo
Valjevski Gradac
Požega
Sevojno
Užice ter.
Sušica
Prijepolje ter.
Bijelo Polje
Figure 1. Brake power diagram (Resnik-Podgorica).
Average brake power value in Resnik-Podgorica direc-
tion on an energy maximum load point is 2.473 kW and
in opposite direction 2.031 kW.
3. CALCULATION OF TEMPERATURE AND STRESS
STATES CHANGES OF BLOCK-BRAKED SOLID
WHEEL ON BELGRADE - PODGORICA LINE
Influence of thermal load from block braking on
temperature and stress states of solid wheel is analysed
by finite element method. Inside this analysis calcula-
tions for chosen line part, in both directions, and freight
trains (train data are given in previous item) are
conducted. Two groups of calculations are carried out:
temperature states calculation of solid wheel during
train running and stress states calculation which is result
of temperature states, in other words thermal loads.
Calculations are repeated for load case with allowable
block-brake positions on the wheel tread during braking
when the block-brakes are moved in relation to wheel
tread for 10 mm. This case during operation is relatively
often. All thermal loads, as input data, are defined on
the basis of brake power diagram for chosen characte-
ristic line part, which is shown in Fig.1.
Performed calculation of temperature and stress
states of block-braked solid wheel presented simulation
of more consecutive long-term braking, which happen
on high down-grades for the maintenance constant train
speed purposes, with separate periods of train running in
traction regime and by coasting or time periods when
train stop in station and there was no braking. In this
cases wheels are exposed to process of cooling.
3.1. Models and loads
Wheel model created for calculation of temperature
and appropriate stress condition, in other words corres-
ponding finite element mesh, is shown in Fig. 2.
For calculation is used model of solid wheel, shown
in [10], which presents dominate influence of thermal
loads on stress condition and probability of occurrence
cracks on wheel rim. Marked numbers of nodes are
shown on presented net for which will be later given
temperature change in function of time. Model is taken
as axisymmetric because the processes of convection
and conduction on wheel surface, during high wheel
revolution, may be considered as uniform.
Figure 2. Solid wheel model (acc. FEM).
One of more significant phases of temperature states
calculation was determination of thermal wheel balance,
in other words determination wheel areas where thermal
energy exchange with environment is in positive and
negative direction. Input and output characteristics of
thermal energy are obtained on the basis results of
researches performed in ERRI reports [1,8] and shown
in Fig.3 and Table 1.
Figure 3. Wheel areas where thermal energy exchange is
performed.
In Table 1, characteristic heat transition on environ-
ment from wheel surfaces, marked S1-S4 (in other
words corresponding heat-transition coefficients), which
depends on temperature are shown. In that way, thermal
load change during braking is taken into consideration
and simulated nonstationary process. On the surface S5,
FME Transactions Vol. 31, No 1, 2003 ▪ 17
which is in firm contact with axle (pressed fit), thermal
energy transfer is defined like heat conduction with
constant thermal energy flux.
Table 1. Heat-transition coefficients [ W/mm2 ].
Temperature [oC]
Area label
0 200 400 600
S1 17e-6 27e-6 43e-6 68e-6
S2 17e-6 27e-6 43e-6 78e-6
S3 37e-6 50e-6 70e-6 95e-6
S4 31e-6 43e-6 62e-6 84e-6
S5 Heat conduction Q5 = - 6.6e-3 W/mm2
Generation of thermal energy dependence on load
step and heat-transition with coefficients:
S6
28e-6 39e-6 57e-6 77e-6
Surface S6, representing a part of tread wheel upon
which slide the friction parts of the block-brake, has
been somewhat more complicated problem for
modelling the heat exchange. Because of the adopted
axisymmetric model, at that surface it was necessary to
simulate the simultaneous heat inflow from friction (a
part of heat transferred to the wheel rim) and heat
outflow due to cooling at the segments of the surface,
which are not in contact with block-brakes. The
problem of simultaneous heat inflow and outflow is
solved by introducing into the model at the surface S6
special surface elements serving solely for heat genera-
tion. Simultaneously, the heat-transition coefficients at
the surface S6 are reduced compared with the
corresponding coefficients at the surface S4 for the ratio
of areas of block-brake contact surface and S6 shoe
sliding surface. The reason is simulation of reduced heat
removal surface caused by permanently present block-
brake at the surface (defined axisymmetric model
assumes heat removal from the complete surface S6).
The computation included using the wheel material
characteristics dependent upon temperature [1] shown in
Fig. 4, so the nonlinearity of the process was included.
0
5
10
15
20
25
0 200 400 600 800
Temp erature
[
o
C]
E 10^10
ALPHA 10^-6
Cp 10^-1
Se 10^2
Figure 4. Dependence of the material characteristics upon
temperature: modulus of elasticity E [N/mm2], extension
coefficient ALPHA [1/°C], specific heat Cp [kJ/kgK] and
yield stress Se [N/mm2].
Presented dependencies, especially the dependence of
material yield stress upon temperature, were used for
explaining the obtained results of computation that
follows.
Variable thermal load of the wheel, occurring as the
result of braking with shoes during the train running at
the given line, was simulated in the form of the so-
called load steps. Each of the load steps represents a
constant thermal load with respect to input data for the
temperature state computation. That means that charac-
teristics of heat inflow and outflow through defined
outer surfaces of the wheel are constant for each load
step, i.e.: dependencies of heat-transition coefficients on
temperature, dependencies of material characteristics on
temperature and quantity of heat flux generated during
the simulated long-lasting braking are constant for each
load step.
The load steps are defined on the basis of braking
power distribution diagrams, at which have been clearly
marked the segments of the line with braking of the
train with the aim of keeping the constant speed of
motion when going downhill. In order to speed up the
computation realisation, and with no significant
influence upon the accuracy of the results, several
consecutive brakings have been unified and defined are
the mean braking powers for chosen periods of downhill
braking. In that manner, determined are the load steps
shown in Fig. 1 (thicker dashed lines marked with Psr),
which simulate long lasting downhill braking and load
steps without thermal load from braking (periods when
the train is in traction regime, coasting or standing at the
station).
For computation of the change of temperature state
in the braked wheel of the train, performed in table,
used are the data on time of start and duration of load
and data on heat input for each load step. With the aim
of analysing critical load cases, data on heat input are
defined also for the case of wheel with irregularly
placed shoes at the tread wheel, when the width of the
contact surface is reduced from 80 to 70 mm. It should
be mentioned that the quantities of the heat input
obtained on the basis of braking powers reduced by the
part of heat transferred onto the shoe during the braking
process (about 30% according to ERRI data [1]). On the
other hand, these data were, when simulating the
braking with irregularly placed shoes, increased
proportionally to reduction of contact surface with aim
of keeping the same braking energy in both cases.
Mean braking power per wheel, computed based
upon data on the mean train braking power, indicates
that the largest mean power of 24.72 kW lasting 51.54
min is realised at line Belgrade-Podgorica (line part
Kos-Podgorica). At that line part the largest braking
energy per wheel of 76.44 MJ is realised, so it is
realistic to expect largest values of temperature and
strain load of the wheel at that section.
In direction towards Belgrade, the largest mean
braking power per wheel is 15.82 kW lasting 36.36 min,
so the total braking energy per wheel is 34.52 MJ.
3.2 Results of computation of temperature and
stress states of the wheel
Results of computation of temperature are presented
in the form of diagrams of time dependence of
temperature in the critical point at the tread of wheel
and in the form of distribution of temperatures in the
cross section of the wheel in the moment of its maximal
thermal load, while the results of calculation stress
states are given in the form of stress distributions at the
wheel cross section at the moment of occurrence of
18 ▪ Vol. 31, No 1, 2003 FME Transactions
maximal thermal load. Computations were performed
for both directions of train running and for two shoe
positions at the tread of wheel when braking - for the
regular allowable position and for the unallowable
(irregular) position. Presentation of temperature change
in time is given only for the more critical case of the
unallowable shoe position, because for the allowable
shoe position curves of the same character of change are
obtained; however with somewhat lower general
temperature level.
Computational results of temperature change are by
its character very similar to the results obtained by
measuring during investigations performed at the same
railroad section in both directions [15]. Namely,
comparison of curves obtained by computation and
curves obtained by measurements shows that the
computational curves represent approximately the
curves of mean values around which dissipate the values
measured in exploitation. That and comparison with
results of computation and measurements, realised
within the investigations performed by ERRI [1,8],
confirm the satisfactory accuracy of the results of own
computations.
Figure 5. Wheel temperature change with the unallowable
placement of block-brakes.
In Fig. 5 we have the computationally obtained
diagram of temperature change depending upon the time
of train running for the line part from Belgrade to
Podgorica with unallowable placement of shoes at the
tread of wheel. Numbers by which the curves in the
picture are marked are the numbers of model nodes for
computation by the finite element method.
It can be seen from the given diagram, that the
maximum temperatures on wheel are attained
immediately before arrival of the train to Podgorica at
the downhill Kos-Podgorica part of line.
For the time moment with the highest temperatures
in the wheel (circled maximum of the curve in Fig. 5) in
Fig. 6 and 7 are shown temperature and stress states in
cross section of the wheel for the allowable and the
unallowable position of block-brake at the tread of
wheel.
Figure 6. Wheel temperature and stress states with the
allowable position of block-brake at maximum thermal
load.
Figure 7. Wheel temperature and stress states with the
unallowable position of block-brake at maximum thermal
load.
From the display of the temperature state of the wheel
for maximum thermal load at the Belgrade-Podgorica
line it can be seen that computation has yielded
maximum temperature of 288°C in the case with the
unallowable position of block-brake (Fig. 7), i.e. 268°C
in the case with the allowable position of block-brake.
So, with the unallowable position of block-brake the
maximum temperature was increased for about 20°C
and logical shift of the place of maximum temperature
to the edge of tread wheel (marks MX in Fig. 6 and 7).
The reviews of stress states, which are formed
because of the calculated temperature states under the
maximal thermal load conditions, show slightly lower
maximal stresses in case of unallowable brake blocks
FME Transactions Vol. 31, No 1, 2003 ▪ 19
position (690 MPa in case of unallowable and 720 MPa
in case of allowable brake blocks position). The
maximal stresses are formed on the middle curve of the
wheel disc and they are higher than the wheel material
yield stress. However, in order to explain the
appearance of the wheel rim cracks which are formed as
a consequence of the wheel thermal loads we have to
watch the more interesting appearance of the wheel rim
region with stresses above 250 MPa in the case of the
unallowable brake blocks position (Fig. 7). In this
region of maximal temperatures, thermal cracks appear
during usage. The explanation of the causes that make
cracks to appear in this region and not in the region of
maximal stresses lies in the fact that material yield
stress is significantly lower in the region of maximal
temperatures (Fig. 4).
When it comes to the opposite direction, the
maximal temperature on the first downgrade at the
beginning of the Podgorica-Belgrade line is not higher
than 180oC.
The maximal stress of 390 MPa is formed on the
wheel disc central curve and this is the same thing that
happened during running in the Belgrade-Podgorica
direction. The stresses in the region where thermal
cracks appear are also significantly lower (slightly
higher than 150 MPa).
Wheel temperature and the corresponding stress
states in case of the allowable brake block position and
the maximal thermal load are slightly lower for this
direction. Calculated maximal temperature is 165oC and
the maximal stress at the centre of the disc central curve
is 410 MPa (the rim stresses are lower than 150 MPa).
Considering the complete results of the block-braked
wheel temperature and stress state analysis for the
Belgrade - Podgorica and Podgorica - Belgrade
directions we can conclude that the conditions which
cause thermal cracks to appear (which can lead to wheel
fracture) are present during this usage. These conditions
appear on the Kos - Podgorica down-grade in the
direction towards Podgorica in the cases of both
unallowable and allowable brake blocks position. 11
wheel fractures formed because of thermal overloads in
current usage on this line can be explained by this fact.
4. CONCLUSION
The JŽ network is versatile considering both the
allowable axle load and quality and the cross-section
and the longitudinal section characteristics. This
network is rich in slopes, and therefore causes
significant thermal loads of the railway vehicle wheels.
Performed analyses showed that (considering the wheel
thermal load during down-grade running) on the JŽ
network key line-part was Belgrade-Podgorica and for
this line part, the calculation of the time dependence of
wheel temperature and stress state was carried using the
finite elements method. The significance of the carried
calculation of the thermal load of the solid wheel being
braked by brake blocks on the JŽ increases if we
consider the fact that JŽ has almost 17.000 wagons and
over 4.000 coaches with brake blocks [16].
The calculation results both for allowable and
unallowable brake block positions on the wheel tread
during braking showed that high thermal loads appeared
on the biggest down-grade of the Belgrade-Podgorica
line (Kos-Podgorica line part). On that line part, the
calculated wheel rim maximal temperature was 288oC
for unallowable and 268oC for allowable brake-block
position. The calculation of stress states, as consequence
of thermal loads, shows that maximal stresses appeare
in the middle of the wheel disc central curve, and that
they are 720 MPa in the case of allowable and 690 MPa
in the case of unallowable brake blocks position. The
obtained stress values are higher than material yield
stress, therefore obtained conditions for the plastic
deformations, and initial cracks can lead to wheel
fracture.
In order to prevent fracture of the solid wheels
being braked by the brake-blocks caused by the thermal
overloading we have to take some measures during
usage. These measures consist of consistent wheel
monitoring process and examination of the residual
stresses in the wheel rim in order to prevent fracture of
solid wheel with high tensile residual stresses. As a part
of wheel monitoring, we have to carry out the following
processes:
- to determine paint burns and therefore to choose the
paint sensitive to high temperatures (burning is the
consequence of high thermal loads),
- to determine the increase of distance of the internal
side surfaces of the wheels,
- to determinate the brake-blocks positions on the tread
and
- to note and additionally make the slots those were
formed because of the tightening on the lathe for
wheel profile making.
All mentioned measures, providing they are carried
out consistently, could significantly decrease the
probability of appearing of cracks caused by the thermal
loads. These measures can also help these cracks to be
discovered on time.
Analysing the amount of energy obtained during
braking on the whole Belgrade-Bar line and comparing
it with the spent electrical energy for train traction we
can conclude that this line is ideal for the regenerative
brakes to be applied. However, the existing electric
locomotives on the JŽ network do not have regenerative
brakes and, what's more, the electrodynamics rheostat
brakes are out of order. Only 30% of the leading
electro-locomotives series JŽ 441 have the electric
brakes, which have many technical flaws, and therefore
their appliance is insecure. The same thing goes for the
locomotives from the JŽ 461 series. Although all these
locomotives have electric brakes, only few are in
function. This approach on electric braking significantly
increases the probability of cracking caused by the
railway vehicle wheel thermal loads.
The last and probably the most important measure
for preventing the solid wheel fractures to appear which
was prescribed by the newest changes of the UIC
leaflets 510-2 and 812-3 is the test of the residual
stresses in the wheel rim made of R2, R3, R8 and R9
materials in order to determine the possible exceed of
the allowable level. This measure (supported by the
large researches) represents the final part of the process
20 ▪ Vol. 31, No 1, 2003 FME Transactions
of solving problems concerning the solid wheel fracture
because of thermal loads.
REFERENCES
[1] ORE B 169/RP1 Limites thermiques des roues et
des sabots, Choix des paramètres pour l`étude des
limites thermiques des roues et des sabots, Utrecht,
1987.
[2] ORE B 169/RP 2 Limites thermiques des roues et
des sabots, Effet du cumul des freinages sur le
champ des contraintes résiduelles dans la jante des
roues,Utrecht,1989.
[3] ORE B 169/RP 3 Limites thermiques des roues et
des sabots, Recherche du seuil de rupture, Utrecht,
1991.
[4] ERRI B 169/RP 4 Standardization of coach
wheelsets, Standardization of a block-braked solid
wheel (rim diameter 920 mm) for coaches with a
maximum speed of 160 km/h, Standard wheelsets
for block brakes, Utrecht, 1993.
[5] ERRI B 169/RP 5 Standardisation des essieux,
Méthodes de surveillance des roues monoblocs
(mesures immédiates contre les ruptures des
roues), Utrecht, 1993.
[6] ERRI B 169/RP 6 Standardisation des essieux,
Méthodes de surveillance des roues monoblocs en
service, Méthode aux ultrasons pour la
détermination non destructive des contraintes
résiduelles dans les jantes de roues monobloc,
Utrecht, 1995.
[7] ERRI B 169/RP 8 Standardisation des essieux,
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critère d`acceptation, Utrecht, 1995.
[8] ORE B 106/RP 12 Standardization of coaches,
Standardization of a block-braked solid wheel
(tread diameter 920 mm) for coaches with a top
speed of 160 km/h, Basic calculations, Utrecht
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[9] Jovanović R., Milutinović D., Modern Ways for
Preventing the Domages Caused by the Railway
Vehicle Solid Wheel Fractures (in Serbian), VI
International Scientific Conference of Railway
Experts - JUŽEL, Vrnjačka Banja 1999.
[10] Milutinović D., Tasić M., Jovanović R., Thermal
Load as a Primary Cause for the Fracture of the
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br. 11-12, Belgrade 1999.
[11] UIC 510-2 Matériel remorqué, Roues et essieux
montés, Conditions concernant l`utilisation des
roues de différents diamètres, 3e édition, 1.1.1998.
[12] UIC 812-3 Technical specification for the supply of
solid (monobloc) wheels in rolled non-alloy steel
for tractive and trailing stock, 5th edition,
1.1.1984.
[13] Radosavljević A. et al., Consumption
rationalization and decrease of electric energy
costs during railway train traction – optimization
of the electric locomotive 441 series control (in
Serbian), Institute of transportation CIP, Belgrade,
1992.
[14] Radosavljević A., Milutinović D, Bečejac Lj.,
Simulation of Electric Locomotives Running for
the Driving Energy Savings Purposes, Fourth
International Conference "Drives and Supply
Systems for Modern Electric Traction in Integrated
XXIst Century Europe", Warsaw, Poland, 23-25
September 1999.
[15] Milovanović M., (PhD thesis), Addition to the
research of the maximal railway vehicle braking
possibilities (in Serbian), Faculty of Mechanical
Engineering, Belgrade, 1991.
[16] Milutinović D. et al., Study of the feasability of the
researches and development of the sinter brake
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TEMPERATURNO I NAPONSKO STAWE
MONOBLOK TO^KA KO^ENOG PAPU^AMA U
EKSPLOATACIJI NA JUGOSLOVENSKIM
PRUGAMA
D. Milutinovi}, A. Radosavqevi}, V. Lu~anin
Termi~ko optere}ewe monoblok to~ka `ele-
zni~kog vozila ko~enog papu~ama je dominantno
u odnosu na ostale vrste optere}ewa. To optere-
}ewe, koje je uglavnom posledica dugotrajnog
ko~ewa na padovima u ciqu odr`avawa brzine,
je osnovni uzrok pojave pukotina na povr{ini
kotrqawa to~ka i, kao krajwa posledica, loma
to~ka. U radu su dati rezultati prora~unske
analize termi~kog optere}ewa monoblok to~ka
na odabranoj karakteristi~noj deonici pruge
Jugoslovenskih `eleznica. Prora~uni tempera-
turnih i naponskih stawa to~ka ra|eni su
pomo}u metode kona~nih elemenata.
