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Proceedings of the 2009 ASME Joint Rail Conference
JRC2009
March 3-5, 2009 Pueblo, Colorado, USA
JRC2009-63055
Thermal Analysis of Railroad Bearings: Effect of Wheel Heating
Constantine M. Tarawneh, Ph.D.
Mechanical Engineering Department
The University of Texas-Pan American
1201 W. University Dr., Edinburg, TX 78539,
Tel: (956) 381-2607; Fax: (956) 381-3527,
email: tarawneh@utpa.edu
Arturo A. Fuentes, Ph.D.
Mechanical Engineering Department
The University of Texas-Pan American
1201 W. University Dr., Edinburg, TX 78539,
Tel: (956) 316-7099; Fax: (956) 381-3527,
email: aafuentes@utpa.edu
Brent M. Wilson, Ph.D.
Director of Research and Development
Amsted Rail
1700 Walnut St, Granite City, IL 62040,
Tel: (618) 791-4217; Fax: (618) 452-7155,
email: bwilson@amstedrail.com
Kevin D. Cole, Ph.D.
Mechanical Engineering Department
University of Nebraska-Lincoln
N104 WSEC, Lincoln, NE 68588,
Tel: (402) 472-5857; Fax: (402) 472-1465,
email: kcole1@unl.edu
Lariza Navarro
Mechanical Engineering Department
The University of Texas-Pan American
1201 W. University Dr., Edinburg, TX 78539,
Tel: (956) 283-4050; Fax: (956) 381-3527,
email: larizanaiz@yahoo.com
ABSTRACT
Catastrophic bearing failure is a major concern for the railroad
industry because it can lead to costly train stoppages and even
derailments. Excessive heat buildup within the bearing is one
of the main factors that can warn of impending failure. A
question is often raised regarding the transfer of heat from a
wheel during braking and whether this can lead to false set-
outs. Therefore, this work was motivated by the need to
understand and quantify the heat transfer paths to the tapered
roller bearing within the railroad wheel assembly when wheel
heating occurs. A series of experiments and finite element (FE)
analyses were conducted in order to identify the different heat
transfer mechanisms, with emphasis on radiation. The
experimental setup consisted of a train axle with two wheels
and bearings pressed onto their respective journals. One of the
wheels was heated using an electric tape placed around the
outside of the rim. A total of 32 thermocouples scattered
throughout the heated wheel, the axle, and the bearing
circumference measured the temperature distribution within the
assembly. In order to quantify the heat radiated to the bearing,
a second set of experiments was developed; these included, in
addition to the axle and the wheel pair, a parabolic reflector that
blocked body-to-body radiation to the bearing. The appropriate
boundary conditions including ambient temperature, emissivity,
and convection coefficient estimates were measured or
calculated from the aforementioned experiments. The FE
thermal analysis of the wheel assembly was performed using
the ALGORTM software. Experimental temperature data along
the radius of the heated wheel, the bearing circumference, and
at selected locations on the axle were compared to the results of
the FE model to verify its accuracy. The results indicate that
the effect of thermal radiation from a hot wheel on the cup
temperature of the adjacent bearing is minimal when the wheel
tread temperature is at 135°C (275°F), and does not exceed
17°C (31°F) when the wheel tread is at 315°C (600°F).
INTRODUCTION
A primary reason for early removal of a railroad tapered roller
bearing from service is by setting off a hot-box detector. A hot-
box detector is designed to identify those bearings which are
operating at temperatures greater than 105.5°C (190°F) above
ambient conditions. As a safety precaution, bearings which are
determined to be running hot are set-out for later removal,
disassembly, and examination. An extension of this practice is
the tracking of temperature data and comparing individual
bearings against the averages of the remainder along a train [1].
1 Copyright © 2009 by ASME
Thermal investigations of roller bearings have been carried out
for more than three decades now [2]. The main goals and
objectives of many researchers were to identify the various
sources of bearing heating, and to study the different effects
that may lead to above normal bearing operating temperatures
[3-8]. Over the past three years and in a series of five papers,
the authors of this paper have performed several detailed
laboratory experiments and theoretical studies focused on
understanding and quantifying the heat transfer paths within
railroad tapered roller bearings in an effort to identify the root
cause(s) of warm bearing temperature trending [9-13].
Yet in all of the efforts reported above, the thermal radiation
effects of a hot railroad wheel on the adjacent bearing have not
been investigated. With this motivation, the wheel set shown in
Fig. 1 was instrumented and utilized to perform a series of
laboratory tests aimed at exploring and quantifying the heat
transfer paths to the tapered roller bearing when wheel heating
occurs. A detailed description of these experiments and a
thorough analysis of the results acquired will be provided in the
sections to follow. In addition, the analyses performed using
the finite element (FE) method will be presented and discussed
along with a comparison between experiment and theory.
Figure 1. A picture of the wheel set assembly at The University
of Texas-Pan American used to conduct the wheel
heating experiments.
THERMAL EXPERIMENTAL TESTING
A total of five thermal experiments were conducted with the
purpose of identifying the effects of thermal radiation from a
hot railroad wheel on the neighboring tapered roller bearing.
These five tests are summarized in Table 1, along with the total
power input provided to heat the wheel, and the average
steady-state temperature of the wheel tread, bearing cup, axle,
and ambient.
Table 1. A brief description of the five laboratory experiments
conducted to study the effect of wheel heating on the
adjacent railroad bearing.
Te st
# Experiment Description
To ta l
Heat Input
[W]
Average
Steady-State
Temperatures
[ºC]
1
Wheel tread heated using
electric resistance heater.
Body-to-body radiation
from wheel to bearing
was allowed.
(48-hour test)
1789
Twheel = N/A
Tcup= 47.0
Taxle = N/A
Tamb = 29.6
2
Wheel tread heated using
electric resistance heater.
Body-to-body radiation
from wheel to bearing
was allowed.
(36-hour test)
1815
Twheel = 133.5
Tcup= 46.8
Taxle = 41.0
Tamb = 30.3
3
Wheel tread heated using
electric resistance heater.
Body-to-body radiation
from wheel to bearing
was blocked using a
parabolic reflector.
(36-hour test)
1774
Twheel = 136.1
Tcup= 43.3
Taxle = 41.3
Tamb = 31.2
4
Wheel tread heated using
electric resistance heater.
Body-to-body radiation
from wheel to bearing
was blocked using a
parabolic reflector.
(36-hour test)
1815
Twheel = 137.8
Tcup= 44.8
Taxle = 42.7
Tamb = 31.1
5
Wheel tread heated using
electric resistance heater.
Body-to-body radiation
from wheel to bearing
was allowed.
(36-hour test)
1834
Twheel = 132.8
Tcup= 47.0
Taxle = 43.0
Tamb = 31.7
In Table 1, it should be noted that Test 1 is missing the average
wheel tread temperature because the thermocouples attached to
the wheel perimeter were making contact with the electric
heating tape, which caused them to read much higher than
actual. However, Test 1 was crucial in determining the
required duration to achieve steady-state, and provided a good
guideline for the remaining tests. Apart from the wheel tread
temperature, the remaining data acquired from Test 1 was
accurate and repeatable as can be seen from Table 1. Based on
the results of Test 1, the experimental time for each of the
remaining tests was reduced from 48 hours to 36 hours, and
one thermocouple was added to measure the surface
temperature of the axle at a location 30.5 cm (1 ft) away from
2 Copyright © 2009 by ASME
the wheel. Furthermore, all of the thermocouples that
monitored and recorded the wheel temperature were welded to
the wheel to ensure good surface contact and accurate readings.
EXPERIMENTAL SETUP AND PROCEDURE
The wheel set assembly shown in Fig. 1 was used to carry out
all five tests described in this paper. A total of 32 K-type
thermocouples measured the temperatures throughout the
experimental setup as demonstrated in Figs. 2 and 3.
Thermocouples 1 through 10, placed 36° apart and situated
2.54 cm (1 in) away from the front rim face of the wheel,
monitored the wheel tread temperature; thermocouples 11
through 16 positioned 60° apart monitored the temperature of
the bearing cup circumference midway along its width;
thermocouples 17 through 28 monitored the temperature
distribution throughout the wheel radius; thermocouples 29 and
30 were placed 7 cm (2.75 in) apart and measured the surface
temperatures of the wheel hub and axle between the wheel and
the bearing, respectively; thermocouple 31 monitored the axle
surface temperature 30.5 cm (1 ft) away from the wheel; and
finally, thermocouple 32 measured the ambient temperature
approximately 1.5 m (~5 ft) away from the wheel.
Figure 2. A schematic diagram showing the thermocouple
locations on the wheel tread, bearing cup, and axle.
Figure 3. A schematic diagram showing the thermocouple
distribution along the wheel radius.
As mentioned earlier, all of the thermocouples assigned to the
wheel were welded to the surface, whereas, the remaining
thermocouples were fixed to their locations using hose clamps.
Two experimental setups were utilized in order to quantify the
heat transfer by thermal radiation from the wheel to the bearing
cup. The first setup, shown in Fig. 4, was used to conduct Tests
1, 2, and 5 in which radiation exchange between the wheel and
the bearing was allowed. The second setup, shown in Fig. 5,
was used for Tests 3 and 4 in which radiation exchange
between the wheel and bearing was blocked via a parabolic
reflector fabricated out of 0.4 mm (1/64 in) thick aluminum
sheet. The parabolic reflector was placed on the axle between
thermocouples 29 and 30, 8.26 cm (3.25 in) away from the
bearing. The diameter of the reflector at its largest end is 84
cm (33.1 in) which is big enough to shield the bearing entirely
from the wheel. Furthermore, the side of the reflector facing
the bearing was painted white to minimize heat emission to the
bearing cup.
Wheel heating was achieved through an Omega ultra high-
temperature heating tape (SWH351-080), 243.84 cm (96 in)
long and 8.26 cm (3.25 in) wide, rated at 2512 W and 120 V.
The tape was wrapped around the wheel tread on top of the
thermocouples, and held in place using two sets of hose
clamps. Unfortunately, the heating tape lengths available were
either shorter or longer than the circumference of the wheel.
Since overlapping the heating tape creates a fire hazard, the
shorter tape was used which meant that about 43 cm (16.9 in)
of the bottom of the wheel circumference was not covered by
the heating tape, as shown in Fig. 6. To ensure that all of the
heat input went into heating the wheel and none escaped
outward, the heating tape was blanketed with two layers of
insulation sandwiched between two layers of fiber glass, as
shown in Fig. 7.
3 Copyright © 2009 by ASME
Figure 4. First experimental setup used to perform Tests 1, 2,
and 5 in which thermal radiation exchange between
the wheel and the bearing was allowed.
Figure 5. Second experimental setup utilized for Tests 3 and 4
in which thermal radiation exchange between the
wheel and the bearing was blocked via a parabolic
reflector which acts as a radiation shield.
Figure 6. A schematic diagram showing the layout of the
electric heating tape around the wheel tread. The
uncovered portion at the bottom of the wheel
circumference is approximately 43 cm (16.9 in)
long.
Figure 7. A picture of the insulation layers blanketing the
electric heating tape in order to prevent any heat
loss to the outside.
All data was acquired utilizing an Omega Engineering OMB-
ChartScan-1400 data acquisition system (DAQ) equipped with
two 16-channel temperature cards. The data acquisition system
allows the user to control all aspects of the data acquisition
process as well as display the real-time data on-screen and
record it in a spreadsheet for later analysis. In addition, the
data acquisition system has an added feature which allows for
automatic cold-junction temperature compensation for all
common thermocouple types. A ground wire was attached to
the wheel set assembly using hose clamps, and then connected
to the data acquisition system to eliminate any signal
interference.
Parabolic Reflector
Power was delivered to the electric heating tape, which
contains two separate resistance wires, through two variable
AC power supplies (Variacs). An isolation transformer was
4 Copyright © 2009 by ASME
used to filter out the noise from the AC power supplies and
eliminate the interference with the data acquisition system.
Separate CHY 20 multi-meters connected in series were used to
continuously monitor the current flowing through each of the
two resistance wires within the heating tape. The voltage input
to each resistance wire was measured using a separate Instek
GW Model GDM 8135 digital multi-meter connected in
parallel. The power input to each resistance wire is calculated
by multiplying the voltage and current. The voltage and
current were measured and recorded every hour. The total
power input to the heating tape is obtained by adding the power
input to each of the two resistance wires constituting the
heating tape. The value for the total heat input reported in
Table 1 for each of the five tests represents the average of all
the total power input values obtained during each experiment.
For consistency, the same experimental procedure was
implemented for all the tests conducted for this study. To begin
the experiment, the data acquisition system (DAQ) was turned
on, and the software program that controls its function was
provided with the appropriate input parameters. Before
supplying power to the resistance heaters, the data acquisition
software was initiated, and 120 seconds of data were acquired
and displayed on-screen to ensure that all thermocouples read
room temperature. Both Variacs were then adjusted, with the
aid of the digital multi-meters, to produce the maximum
possible power output without exceeding their operational
limits. The DAQ software was set to acquire 48 hours of
temperature data for Test 1 and 36 hours of data for the
remaining four tests, at a sampling rate of 64 Hz (i.e., 64
Samples/sec), while averaging every 30 seconds to produce
smoother temperature profiles. The software produced a
spreadsheet that consisted of 33 columns of data with the first
column containing the time stamp (30 second intervals), and
the remaining 32 columns containing the temperature data
(averaged over 30 second intervals) from the 32
thermocouples, respectively.
FINITE ELEMENT MODELING
Finite element (FE) modeling was used to analyze four
different wheel heating scenarios. The first two simulations
focused on replicating the two experimental setups described
earlier, where the wheel tread temperature reached
approximately 135°C (275°F). The purpose of the other two
heating scenarios was to predict the thermal behavior of the
two experimental setups at conditions when the wheel tread
temperature reaches 315°C (600°F). To this effect, a computer
solid model of the wheel-bearing assembly was created. Once
the model was completed, it was imported to ALGORTM 20.3
software and discretized into 5297 elements with a mesh size of
0.02515 m. A combination of bricks, wedges, pyramids and
tetrahedral elements were used to successfully mesh the model;
surface knitting was used in order to properly apply convection
loads. A picture of the meshed model is given in Fig. 8.
Figure 8. A picture of the meshed CAD model that was used to
perform all the FE simulations for this project.
Boundary Conditions: 135°C Heating Scenario
Materials and Conduction Loads
The materials used for the analysis were taken from the
ALGORTM material library. For the wheel steel, AISI 1080
with a thermal conductivity of 47.7 W/m·K was used; for the
axle steel, AISI 1060 with a thermal conductivity of 51.9
W/m·K was chosen; and for the bearing steel, AISI 8620 with a
thermal conductivity of 46.6 W/ m·K was selected.
Convection Loads
Only free convection was assumed to be present since the
experimental setup was in a room with quiescent air. The latter
assumption is valid and simulates a worst case scenario where
the effects of cooling by forced convection are minimal. The
aforementioned free convection coefficients were calculated by
modeling the wheel as a flat vertical disk, and the bearing and
axle as horizontal cylinders of finite length. The assumptions
made were justifiable and will be discussed in the results
section of this paper. The following formulas were utilized to
calculate the average free convection coefficient values [14]:
Flat vertical plate correlations (for this case, L = D)
(
)
υα
β
3
LTTg
Ra s
L
∞
−
= (1)
()
[]
k
hLRa
Nu L
L=
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
+
+=
2
94
169
61
Pr492.01
387.0
825.0 (2)
Horizontal cylinder correlations
(
)
υα
β
3
DTTg
Ra s
D
∞
−
= (3)
()
[]
k
hDRa
Nu D
D=
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
+
+=
2
278
169
61
Pr559.01
387.0
6.0 (4)
5 Copyright © 2009 by ASME
The surface temperatures, Ts, used in the above correlations are
the steady-state average values reported in Table 1 for the
bearing cup and axle, and the average wheel surface
temperature calculated from the radial temperature distribution
data acquired for Tests 1 through 5. The ambient temperature,
Tamb, was measured to be 22°C (71.6°F) at the center of the
laboratory housing the experimental setup. The free convection
coefficients obtained and used in the FE model were the
following; for the wheel, 5.3 W/m2·K; for the axle, 4.2
W/m2·K; and for the bearing cup, 4.3 W/m2·K.
Radiation
For tests performed utilizing the first experimental setup, where
no parabolic reflector was included (i.e., Tests 1, 2, and 5), two
types of radiation loads were used, radiation to the ambient,
and body-to-body radiation exchange applied throughout the
whole model. To simulate the results of the tests conducted
with the second experimental setup, where the parabolic
reflector was used (i.e., Tests 3 and 4), the same two types of
radiation loads were applied with the only difference being that
body-to-body radiation exchange between the wheel and the
bearing was eliminated. The emissivity for all surfaces was
measured to be approximately 0.96.
Surface Heat Flux
In order to simulate the total power input provided by the
electric heating tape, a surface heat flux was applied to the area
of the wheel tread covered by the heating tape. For example, in
Test 4, the average total heat input supplied to the wheel was
1815 W; taking into account the dimensions of the heating tape,
the surface heat flux boundary condition applied to the wheel
tread was 9011 W/m2.
Boundary Conditions: 315°C Heating Scenario
The main objective of this study was to explore the effects of
thermal radiation of a hot wheel with a tread temperature of
315°C (600°F) on the bearing cup temperature. This
temperature was chosen based on conversations with railroad
personnel, and is not meant to signify or replicate a measured
wheel temperature. In service, excess heat in the wheel could
be generated from a train going down a long grade and the
brakes are applied, or in the case of a stuck handbrake, as
examples. In the laboratory, it is not practically feasible to get
the wheel tread temperature to the desired 315°C with
conventional heating tapes. Therefore, it was decided to carry
out the experimental testing by heating the wheel tread as much
as possible using the electric resistance tape described earlier,
and then put together the most accurate FE model that can
replicate the acquired experimental results. The constructed FE
model can then be utilized to quantify the thermal radiation
exchange between the hot wheel and the bearing, which will
help answer the question posed earlier regarding the transfer of
heat from a wheel during braking and whether this can lead to
false set-outs. Furthermore, the use of symmetry was possible
for this analysis; consequently, the meshed CAD model shown
in Fig. 8 was cut in half and a zero heat flux (insulated)
boundary condition was applied at the surface where the cut
was made. The aforementioned means that only one wheel,
one bearing, and half the axle were used in the FE model,
which greatly reduced the computational time.
The thermal conductivity constants and the radiation boundary
conditions used for this analysis are essentially the same as the
ones for the 135°C (275°F) heating scenario. The free
convection coefficients and the surface heat flux value had to
be modified due to their dependence on the surface
temperatures. First, the heat flux needed to heat the surface of
the wheel tread to the desired 315°C (600°F) temperature was
determined by trial and error using the constructed FE model.
The required surface heat flux was found to be about 17,410
W/m2. Second, in order to obtain the appropriate surface
temperatures, the analysis was run with the same free
convection coefficients as the ones used for the 135°C heating
scenario. The latest surface temperatures were then utilized to
calculate the new convection coefficient values using Eqs. (1-
4). Finally, the analysis was run again using the corrected
values to produce the most accurate predictions possible. The
free convection coefficients employed in the 315°C heating
scenario analysis are; for the wheel, 5.7 W/m2·K; for the axle,
5.2 W/m2·K; and for the bearing, 5.0 W/m2·K.
DISCUSSION OF RESULTS
In this section, a discussion of the results acquired from the
experimental testing and a comparison of these results with the
finite element (FE) model analysis will be provided. In
addition, the FE model predictions for the 315°C (600°F)
heating scenario will be explained in detail.
Experimental Results
To ensure accuracy and repeatability of the experimental
results, each test was performed twice, not counting the first
test, Test 1, which was carried out in order to devise the most
appropriate experimental procedure. From Table 1, it can be
seen that Test 3 was repeated in Test 4, and Test 2 was repeated
in Test 5. Therefore, only the results of Tests 4 and 5 will be
given in this section since they exhibit almost identical trends
to those observed in Tests 3 and 2, respectively.
The temperature histories of the wheel tread and bearing cup
for Tests 5 and 4 are shown in Figs. 9 and 10, respectively. In
both Figs. 9 and 10, each curve is obtained by averaging the
profiles of all the thermocouples assigned to monitor each
object’s temperature, i.e.; the wheel tread temperature curve is
the arithmetic mean of thermocouples 1 through 10, and the
bearing cup temperature curve is the mean of thermocouples 11
through 16. The steady state temperature distribution along the
radius of the wheel is plotted in Figs. 11 and 12 for Tests 5 and
4, respectively, along with the steady state average wheel tread
and bearing cup temperatures.
6 Copyright © 2009 by ASME
0 3 6 9 12 15 18 21 24 27 30 33 36
20
30
40
50
60
70
80
90
100
110
120
130
140
Time [hrs]
Temp erature [° C]
Wheel Tread
Bearing Cup
Figure 9. A plot of the transient temperature profiles for the
wheel tread and bearing cup for Test 5, in which
body-to-body radiation between the wheel and the
bearing was allowed. [Total heat input = 1834 W].
0 3 6 9 12 15 18 21 24 27 30 33 36
20
30
40
50
60
70
80
90
100
110
120
130
140
Time [hrs]
Temp eratu re [°C ]
Wheel Tread
Bearing Cup
Figure 10. A plot of the transient temperature profiles for the
wheel tread and bearing cup for Test 4, in which
body-to-body radiation between the wheel and the
bearing was blocked via a parabolic reflector.
[Total heat input = 1815 W].
050 100 150 200 250 300 350 400 450 500
40
50
60
70
80
90
100
110
120
130
140
Pos ition [mm]
Temp eratu re [°C ]
T1 7
T1 9
T2 0
T21
T2 2
T2 3
T24
T25
T26
T2 7
T2 8
T29
T30 Bearing Cup Temperature (47.0°C)
T1 8
Wheel Tread Temperature (132.8°C)
Figure 11. A plot of the steady state temperature distribution
along the radius of the wheel for Test 5, in which
body-to-body radiation between the wheel and the
bearing was allowed. Also shown are the steady
state average wheel tread and bearing cup
temperatures. [Total heat input = 1834 W].
050 100 150 200 250 300 350 400 450 500
40
50
60
70
80
90
100
110
120
130
140
Pos ition [mm]
Temperature [°C]
T3 0
T25
T23
T28
T29
T2 6
T2 4
T2 2
T2 1
T2 0
T1 7
T1 8
T27
T19
Bearing Cup Temperature (44.8 °C)
Wheel Tread Temperature (137.8°C)
Figure 12. A plot of the steady state temperature distribution
along the radius of the wheel for Test 4, in which
body-to-body radiation between the wheel and the
bearing was blocked via a parabolic reflector.
Also shown are the steady state average wheel
tread and bearing cup temperatures. [Total heat
input = 1815 W].
7 Copyright © 2009 by ASME
By looking at both Figs. 9 and 10, it can be seen that, in both
tests, the wheel tread reaches steady state conditions much
faster than the bearing cup, which is to be expected since the
heat input is applied to the wheel tread which then in turn heats
up the bearing. Furthermore, the effect of radiation exchange
between the hot wheel and the bearing is minimal. The latter
can be more clearly noticed in Figs. 11 and 12 which provide
values for the steady state average temperature of the wheel
tread and bearing cup. The plots show only a 2.2°C (4°F) rise
in the bearing cup temperature when body-to-body radiation is
allowed. In fact, referring to Table 1, the maximum increase in
the bearing cup temperature caused by thermal radiation
exchange between the hot wheel and the bearing does not
exceed 3.7°C (6.7°F) in any of the tests conducted. Hence,
most of the bearing heating occurs by thermal conduction from
the wheel through the axle, which transpires over several hours.
The aforementioned is further validated by looking at the
temperature distribution along the wheel radius in both Figs. 11
and 12, where it can be observed that the temperature
systematically decreases from the wheel tread until it reaches
its lowest value at the surface of the axle just before the
bearing, T30 (refer to Fig. 2). Also, in both tests (Tests 4 and
5), the radial temperature distribution exhibits almost identical
trends, and the bearing cup temperature is lower than the
temperature at the surface of the axle just before the bearing,
T30; a clear indication that conduction heating is the major
contributor.
To asses the effectiveness of the parabolic reflector in blocking
the thermal radiation exchange between the wheel and the
bearing, its surface temperature was monitored and recorded on
an hourly basis. The data taken indicates that the surface
temperature of the parabolic reflector was no more than 2°C
(3.6°F) above room ambient temperature throughout Tests 3
and 4, which confirms that the reflector effectively shields
almost all thermal radiation incident on the bearing from the
hot wheel.
Comparison with FE Model: 135°C Heating Scenario
After the experimental testing was completed, the next step in
this study was to put together a finite element (FE) model that
can match the results acquired from the laboratory tests.
Implementing the boundary conditions mentioned earlier in this
paper, the FE model was used to simulate the conditions of
Tests 4 and 5 which were aimed at quantifying the effect of
body-to-body thermal radiation exchange between the wheel
and the bearing. The simulation results for Test 5, in which
thermal radiation exchange between the wheel and bearing was
allowed, are shown in Fig. 13. The simulation results for Test 4
were very similar to those shown in Fig. 13 since, as explained
earlier, the effect of thermal radiation exchange is minimal
when the wheel tread temperature is at about 135°C (275°F).
Figure 13. A graphic of the simulation that was performed
utilizing the finite element model devised to match
the results of Test 5, in which body-to-body
radiation exchange between the hot wheel and the
bearing was allowed. The surface heat flux
applied to the area of the wheel tread covered by
the heating tape was approximately 9,106 W/m2.
Looking at Fig. 13, it can be seen that it is an accurate
depiction of the experimental test as shown by the fact that the
lower portion of the heated wheel is cooler than the rest of the
wheel because this represents the area of the wheel tread that
was not covered by the heating tape. Furthermore, the other
wheel is entirely cold since no heat was applied to its tread and
it lies relatively far from the heat source.
By comparing the results of the FE model to those of the
experimental testing, the temperature values corresponded very
well for all tests conducted, with the percent error being within
6%. Detailed comparison of the FE and experimental results
are given in Tables 2 and 3 for Tests 5 and 4, respectively. In
addition, a plot comparing the experimental temperature
distribution along the radius of the wheel to that produced by
the FE model is provided in Fig. 14 for Test 5.
8 Copyright © 2009 by ASME
Table 2. Detailed comparison of the temperature data acquired
from Test 5 to the results obtained from the finite
element model.
Position TTest5 [°C] TFEM [°C] % Error
Axle Surface 43.0 43.1 0.3
Bearing Cup 47.0 47.5 1.1
Wheel Tread 132.8 132.1 0.5
T17 131.4 130.9 0.4
T18 131.4 125.7 4.3
T19 125.5 119.3 5.0
T20 117.2 111.3 5.0
T21 108.7 105.0 3.5
T22 96.0 95.1 0.9
T23 86.0 84.0 2.4
T24 77.5 75.5 2.5
T25 68.2 69.3 1.6
T26 61.3 64.8 5.7
T27 59.6 62.2 4.3
T28 58.5 61.7 5.4
T29 58.7 59.5 1.4
Radial Distribution
T30 53.7 52.3 2.6
Table 3. Detailed comparison of the temperature data acquired
from Test 4 to the results obtained from the finite
element model.
Position TTest4 [°C] TFEM [°C] % Error
Axle Surface 42.7 42.7 0.0
Bearing Cup 44.8 44.9 0.4
Wheel Tread 137.8 135.6 1.6
T17 133.6 132.6 0.8
T18 133.8 131.5 1.7
T19 127.7 123.7 3.1
T20 119.4 117.0 2.0
T21 109.2 109.8 0.5
T22 99.9 99.6 0.3
T23 88.0 87.4 0.7
T24 79.5 78.2 1.6
T25 69.7 71.3 2.4
T26 62.1 65.3 5.2
T27 60.2 63.7 5.8
T28 59.2 62.5 5.6
T29 59.3 60.4 2.0
Radial Distribution
T30 51.6 50.7 1.8
050 100 150 200 250 300 350 400 450 500
40
50
60
70
80
90
100
110
120
130
140
Position [mm]
Temperature [°C]
Exp e ri m e ntal Re s u l ts
Finite Element Model
T20
T29
T30
T28
T27
T26
T25 T24
T23
T22
T21
T19
T18
T17
Figure 14. A plot comparing the temperature distribution along
the radius of the wheel obtained experimentally
from Test 5 to that produced by the FE model.
In Fig. 14, the radial temperature distribution obtained by the
FE model seems to correlate fairly well with the one acquired
experimentally. Examining Tables 2 and 3, one can notice the
remarkable agreement between the FE and experimental
temperature values for the axle surface, the bearing cup, and
the wheel tread. The small difference in the temperature of the
wheel tread results from applying the average heat input of
each test in the FE model. The slight differences between the
radial temperature distribution obtained experimentally and that
acquired from the FE model are attributed mainly to the
radiation boundary conditions implemented, in particular the
body-to-body radiation exchange boundary condition. Finally,
it should be noted that the excellent agreement between the FE
model results and the acquired experimental temperature data
provides validation for the developed FE model, and indicates
that the assumptions made during the development of the
model and the correlations used to calculate the free convection
coefficients were appropriate.
FE Model Predictions: 315°C Heating Scenario
In this section, the results acquired from the FE model that was
developed to quantify the thermal radiation exchange between
the wheel and the bearing when the temperature of the wheel
tread is at 315°C (600°F) will be presented and discussed.
By applying the specific boundary conditions associated with
this heating scenario, explained earlier in this paper, the FE
model was run for the two cases of interest, which are; first,
when body-to-body radiation exchange between the wheel and
the bearing is present, and second, when body-to-body
9 Copyright © 2009 by ASME
radiation exchange between the wheel and the bearing is
blocked emulating the use of the parabolic reflector which acts
as a radiation shield. The steady state results of the finite
element analysis are shown in Fig. 15 and summarized in detail
in Table 4.
Figure 15. A graphic from the simulation that was performed
utilizing the FE model to predict the thermal
radiation exchange between the wheel and the
bearing when the wheel tread temperature is at
315°C (600°F). The surface heat flux required to
achieve the 315°C temperature was found to be
approximately 17,410 W/m2.
In the simulation provided in Fig. 15, the wheel tread
temperature was maintained at approximately 315°C (600°F)
by applying a 17,410 W/m2 heat flux boundary condition all
around its surface, and body-to-body radiation exchange
between the hot wheel and the bearing was allowed. Detailed
temperature values for the latter simulation are given in Table 4
in the column with the heading “Without Reflector”, which
indicates that the thermal radiation exchange was not blocked.
A similar simulation was carried out for the case where body-
to-body radiation exchange between the wheel and bearing was
suppressed, and the acquired temperature values are given in
Table 4 under the heading “With Reflector”. Also listed in
Table 4 is the temperature difference between the two cases
analyzed, which can be used to quantify the effect of thermal
radiation from a hot wheel on its adjacent bearing.
Table 4. A summary of the results predicted by the FE model
developed to quantify the thermal radiation exchange
between the hot wheel and the bearing when the
wheel tread temperature is at 315°C (600°F).
Temperature [°C]
Position Without
Reflector
With
Reflector Difference
Axle Surface 135.2 134.6 0.6
Bearing Cup 111.4 94.5 16.9
Wheel Tread 316.0 316.0 0.0
T17 311.4 309.1 2.3
T18 305.2 302.7 2.5
T19 298.1 297.2 0.9
T20 285.1 285.9 0.8
T21 272.6 271.1 1.5
T22 250.2 248.3 1.9
T23 225.1 221.9 3.2
T24 205.4 201.6 3.8
T25 191.1 186.8 4.3
T26 179.6 177.9 1.7
T27 175.5 170.8 4.7
T28 169.2 164.0 5.2
T29 164.5 158.8 5.7
Radial Distribution
T30 149.7 148.4 1.3
By examining the results of Table 4, it can be noticed that the
temperature values of both cases analyzed, with and without
radiation shield, are very close and fall within 6°C (11°F) of
each other, except the bearing cup temperature which exhibits a
16.9°C (30°F) difference in this ambient condition. The latter
implies that the thermal radiation exchange between the hot
wheel and the bearing accounts for the 16.9°C temperature
increase observed in the bearing cup. The majority of the heat
is transferred to the bearing from the hot wheel by thermal
conduction through the axle, which occurs over an extended
period of time (more than five hours). The aforementioned is
validated by the radial temperature distribution which decreases
steadily from the wheel tread inward along the radius toward
the wheel hub and the axle surface between the wheel and the
bearing, T30. The fact that the axle surface temperature T30 is
much larger than the bearing cup surface temperature is
explained by the path the heat has to travel to reach the bearing
cup. Thermal conduction has to pass through the inner cones
and then through the rollers which are surrounded by a thin
layer of grease, and have limited surface contact with the
bearing cup. The axle surface temperature at the other side of
the wheel is also relatively high because the FE model assumes
symmetry, i.e., it simulates the case where both wheels are
10 Copyright © 2009 by ASME
simultaneously heating up, which is what happens in real
service when brakes are applied. Hence, heat will transfer to
the axle by conduction from both wheels, which justifies the
temperature value listed in Table 4.
From the discussion above, it is believed that the results
predicted by the FE model present a logical and accurate
depiction of the heating scenario that takes place when the
wheel tread temperature is at 315°C (600°F). The main sources
of error come from the assumed boundary conditions and the
associated conduction, convection, and emissivity coefficients
used in the analyses, and from the trial and error method which
was utilized to determine the applied surface heat flux value.
MODEL SENSITIVITY
A comment is in order regarding the finite element (FE) model
sensitivity. Since there were several assumptions made while
developing the FE model, it was vital to verify the sensitivity of
the various boundary conditions used, including convection
coefficients and emissivity. To this effect, the values of each of
the three free convection coefficients were modified by ±1, and
the emissivity was reduced to 0.9 instead of the measured value
of 0.96. Using the bearing cup temperature as our reference
point, the latter modifications altered the original results by less
than 5%, with the emissivity having the least effect changing
the results by only 1.5%.
CONCLUSIONS
In service, the temperature of the wheel tread can reach 315°C
(600°F) when a train travels down a long grade and the brakes
are applied. The effect of such elevated temperatures on the
bearing cup, which is the part of the assembly that is scanned
by the wayside infrared detectors, has not been thoroughly
investigated or documented in the literature. With this
motivation, carefully planned experiments were conducted and
finite element (FE) models were developed with the purpose of
exploring and quantifying the effect of thermal radiation
exchange between a hot wheel and the adjacent bearing.
Since it was not feasible to achieve a 315°C wheel tread
temperature in the laboratory, the experimental testing was
performed with a wheel tread temperature of 135°C (275°C),
which was the maximum attainable temperature, and an FE
model that can accurately replicate the experimental results was
developed so that it could be used to simulate the 315°C
heating scenario. The experimental testing concluded that
thermal radiation exchange between the wheel and the bearing
when the wheel tread temperature is at 135°C is minimal and
does not exceed 3.7°C (6.7°F) in any of the tests conducted.
Therefore, most of the bearing heating takes place by thermal
conduction from the hot wheel through the axle, which occurs
over several hours.
The devised FE model produced results that matched the
experimental findings to within 6%. The main sources of error
come from the simplifying assumptions made in determining
the FE model boundary conditions. The FE model predictions
for the 315°C heating scenario suggest that thermal radiation
exchange is more significant than observed at the lower
temperature. The simulations conducted with and without the
body-to-body radiation exchange between the hot wheel and
the bearing show that radiation accounts for a 17°C (31°F)
increase in the bearing cup temperature with this assumed
ambient condition (room temperature). It is important to note;
however, that this temperature estimate represents a maximum
increase; in real service, the bearing cup is partially shielded by
the adapter plate and the side frame which will reduce the
amount of thermal radiation incident on the bearing cup.
Furthermore, the analysis was intentionally performed using
free convection coefficients assuming quiescent air in order to
give a worst case scenario. In actual operation, the bearing cup
will be more effectively cooled by forced convection caused by
the fast air streams flowing around the bearing. The latter is a
current topic of study by the authors along with some other
possible heating scenarios which will be shared in a future
publication.
Finally, the significance of the research presented in this paper
lies in the fact that it establishes measures to quantify the effect
of thermal radiation exchange between a hot wheel and the
adjacent bearing.
ACKNOWLEDGMENTS
Special thanks to Amsted Rail’s bearing division, Brenco, for
giving us the opportunity to work on this very exciting and
fulfilling project, and providing the funding needed to
successfully achieve the goals of this project. The technical
assistance of Mr. Martin Reed of Brenco and Dr. Todd Snyder
of the Union Pacific Railroad are greatly appreciated.
REFERENCES
1. Karunakaran, S., and Snyder, T. W., 2007, “Bearing
Temperature Performance in Freight Cars,” Proceedings of
the Bearing Research Symposium sponsored by the AAR
Research Program in conjunction with the ASME RTD
2007 Fall Technical Conference, Chicago, Illinois,
September 11-12.
2. Farnfield, N. E., 1972, “Thermal Investigations of Roller
Bearings,” Tribology, Vol. 5, No. 3, p. 104.
3. Dunnuck, D. L., 1992, “Steady-State Temperature and
Stack-Up Force Distributions in a Railroad Roller Bearing
Assembly,” M.S. thesis, University of Illinois at Urbana-
Champaign, Urbana, Illinois.
4. Wang, S., Cusano, C., and Conry, T. F., 1993, “A Dynamic
Model of the Torque and Heat Generation Rate in Tapered
Roller Bearings under Excessive Sliding Conditions,”
Tribology Transactions, Vol. 36, No. 4, pp. 513-524.
5. Wang, H., 1996, “Axle Burn-Off and Stack-Up Force
Analyses of a Railroad Roller Bearing Using the Finite
11 Copyright © 2009 by ASME
12 Copyright © 2009 by ASME
Element Method,” Ph.D. dissertation, University of Illinois
at Urbana-Champaign, Urbana, Illinois.
6. Hoeprich, M. R., 1996, “Rolling-element bearing internal
temperatures,” Tribology Transactions, Vol. 39, No. 4, pp.
855-858.
7. Kletzli, D. B., Cusano, C., and Conry, T. F., 1999,
“Thermally Induced Failures in Railroad Tapered Roller
Bearings,” Tribology Transactions, Vol. 424, pp. 824-832.
8. Li, X. K., Davies, A. R., Phillips, T.N., 2000, “A transient
thermal analysis for dynamically loaded bearings,”
Computers & Fluids, Vol. 29, pp. 749-790.
9. Tarawneh, C., Cole, K., Wilson, B., and Freisen, K., 2007,
“A Lumped Capacitance Model for the Transient Heating
of Railroad Tapered Roller Bearings,” Proceeding of the
2007 ASEE-GSW Annual conference, March 28-30.
10. Tarawneh, C., Cole, K., Wilson, B., and Alnaimat, F.,
2008, “Experiments and Models for the Thermal Response
of Railroad Tapered Roller Bearings,” Int. J. Heat Mass
Transfer, Vol. 51, pp. 5794-5803.
11. Cole, K. D., Tarawneh, C., and Wilson, B., 2009,
“Analysis of Flux-base Fins for Estimation of Heat
Transfer Coefficient,” Int. J. Heat Mass Transfer, Vol. 52,
pp. 92-99.
12. Tarawneh, C., Cole, K., Wilson, B., and Reed, M., 2008,
“A Metallurgical and Experimental Investigation into
Sources of Warm Bearing Trending,” Proceedings of the
2008 IEEE/ASME Joint Rail Conference, Wilmington,
Delaware, April 22-24.
13. Tarawneh, C., Wilson, B. M., Cole, K. D., Fuentes, A. A.,
and Cardenas, J. M., 2008, “Dynamic bearing testing
aimed at identifying the root cause of warm bearing
temperature trending,” Proceedings of the 2008 ASME
RTD Fall Technical Conference, RTDF2008-74036,
Chicago, Illinois, September 24-26.
14. Incropera, F. P., DeWitt, D. P., Bergman, T. L., Lavine, A.
S., 2007, “Introduction to Heat Transfer,” fifth Ed., Wiley,
New York.
