MEASUREMENT OF INTERACTION FORCES BETWEEN
WHEEL AND RAIL ON AN EXTREME TRAIN WHEELSET
R.A. Cláudio, J. Duarte Silva, A.J. Valido, P.J. Moita
Department of Mechanical Engineering
Escola Superior de Tecnologia de Setúbal
Instituto Politécnico de Setúbal
Campus do IPS, Estefanilha, 2910-761 Setúbal
[email protected]; [email protected]; [email protected]; [email protected]
ABSTRACT
This paper presents a methodology to measure directly and independently the lateral and vertical wheel/rail interaction forces
in both wheels of a wheelset of a train. The methodology is based on a hybrid technique that relates the strains measured with
strain gages bonded to the faces of the wheel to the corresponding values calculated by the Finite Element Method (FEM),
considering both lateral and vertical forces. Several Wheatstone full bridges were used to combine different signals obtained
from specific strain gages, whose locations were determined taking into consideration the results of the FEM analysis, in order
to obtain signals that are proportional only to the applied lateral or vertical forces. This methodology was validated statically in
a testing facility, simulating several combinations of forces and different contact points between wheel and rail. Measurements
in real running conditions tests were carried out on an extreme wheelset of a passenger’s train. Telemetry equipment was
used to transmit the strain gages signals, measured in the rotating wheels and axle, to the train car body, where a data logger
was installed. Some graphs are presented showing the forces measured in curve at different speeds and load conditions.
Introduction
The recent developments in software and hardware provided significant improvements in computational simulation, including
dynamic analysis. Particularly, in the study of railway vehicles, it is possible to have a quite accurate prediction of the vehicle
dynamic behaviour under real running conditions. Thus, it is possible to market new train technology in a shorter period of
time, reducing to a minimum the number of necessary prototypes and, consequently, the development costs. However, to
validate a new train technology, computational simulations are not enough, being necessary to conduct experimental tests in
real conditions, to ensure the vehicle safety and reliability.
The UIC 518 Code [1] covers all the provisions dealing with on-line running tests and the analysis of results for international
traffic acceptance of railway vehicles, from the point of view of dynamic behaviour in connection with safety, track fatigue and
running behaviour. The vehicle type, the track quality, the loading conditions, the atmospheric conditions and the quantities to
be measured are parameters that have to be considered in these tests. The code also defines the statistical treatment that
must be applied to the quantities calculated with the experimental values, in order to verify if they are inside safe limits. Two of
the most important variables to be measured are the lateral and vertical wheel/rail interaction forces on each wheel of a
wheelset, designated by Y and Q, respectively, in the code terminology. Joly [2] and Silva et al. [3] have presented different
methodologies to determine these forces, that can be classified as direct or indirect.
Using an indirect methodology, the interaction forces can be obtained by measuring the forces transmitted by the suspension
to the car body. Establishing the dynamic equilibrium of the suspension, it is possible to determine the vertical force on each
wheel and the sum of the lateral forces produced in both wheels of the same wheelset. However, this methodology does not
allow the determination of the lateral force in each wheel. It also depends on many characteristics of the suspension elements,
loosing some accuracy.
The direct methodology, measuring the forces using transducers on the wheels, provides a solution to these problems, but
involves the use of direct instrumentation to transmit signals obtained in rotating parts to the stationary car body. An alternative
solution is to replace the real wheelset by a specially designed and instrumented one, exclusively for the acceptance running
tests.
Traditionally, the direct methodology used slip rings and brushes, Figure 1 a), to transmit the signals and supply transducers
with energy, but it introduces too much noise and has reliability problems, due to abrasion,. Nowadays, the use of radio
telemetry and inductive systems, Figure 1 b), allow the signal transmission almost free of noise and the supply of energy to the
transducers without contact. The telemetry systems, including filter and amplifier, digitalize the signal close to the sensor,
reducing to a minimum the noise. Their transmission speeds are usually above 1000 samples/sec/channel, being able to
transmit several channels continuously.
a) Slip rings and brushes
b) Telemetry (KMT GmbH)
Figure 1. Shaft signal transmission.
In this work it is presented a hybrid methodology to measure directly the Y (lateral) and Q (vertical) forces in each wheel of a
extreme wheelset of a trailer bogie. Results from the FEM analysis of a wheel are used to relate the strain measured by strain
gages bonded in specific positions of a wheel to the Y and Q forces applied to that wheel, thus allowing the independent
calculation of the Y and Q forces on each wheels.
Measurements obtained using a telemetry system during the operation of a passengers train under several conditions are
presented.
Methodology to measure interaction forces
The specific wheel under study has 18 holes for the installation of the breaking system (see Figure 4). Removal of the breaking
system permits the use of these holes to pass cables from one side of the wheel to the other, allowing the bonding of strain
gages in both the inner and outer face of the wheels. All the signals from the two faces of the two wheels from the same
wheelset can be connected to the same encoder, in order to be sent by a unique telemetry transmitter and received by the
data logger unit installed inside the train car body. This methodology is different from the one used before by Silva [3], where
only the inner side of the wheel was available to install strain gages.
Using classic beam theory, it is quite easy to measure the axial or transversal forces applied, without mutual influence. The
axial force is proportional to the sum of signals from opposite sides of the same section, Figure 2 a) and Eq. (1), and the
transversal force is proportional to the difference in signals measured in the same side of two away sections, Figure 2 b) and
Eq. (2).
L1
L2
Y
1
1
Q
3
2
a) axial force measurement
b) transveral force measurement
Figure 2. Measurement of axial and transversal forces in a beam
ε1 + ε2 =
Q×2
∝Q
EA
(1)
ε1 − ε3 =
(Y .(L1 + L2 )) .h − (Y .L2 ) .h = Y . L1.h ∝ Y
E.I
E.I
E.I
(2)
To understand the wheel behavior under different loading conditions and to define the best locations to bond the strain gages,
a finite element model was built. Due to symmetry of load and geometry only half of the wheel was modeled. The model was
generated using 11756 solid elements with 20 nodes per element, resulting in a total of 170052 degrees of freedom. Figure 3
shows the mesh and the strain distribution in a section (between holes) when a vertical or a lateral force is applied.
a) FE mesh
b) strain field for a vertical or a lateral force
Figure 3. FEM model of half of the wheel.
The analysis of the strain distribution shows that the behavior of the web of the wheel is similar to that of the cantilever beam
of Figure 2. Thus, it is expectable that the vertical force is proportional to the sum of the strains in positions 1 and 2 (located in
opposite sides of the wheel) and that the vertical force is proportional to the difference of the strains in positions 1 and 3 (taken
from the same side but at a different radius), Figure 4 and Eq.(3).
a) inner side
b) outer side
Figure 4. Strain gages location
Q = K1 ( ε1 + ε2 )
Y = K 2 ( ε1 − ε3 )
(3)
The wheel under study can be instrumented with strain gages in six sections between the holes, Figure 4. In total, to measure
experimentally the vertical and horizontal contact forces when each of these sections is in contact with the rail, a telemetry with
18 channels was required. To reduce the number of telemetry channels, full Wheatstone bridges were built by combining the
o
o
o
o
o
o
signals of opposite sections, i.e., measurements in sections at 0 and 180 , at 60 and 240 , at 120 and 300 , Figure 4. The
FEM analysis shows that when the contact forces are in line with one section with strain gages, the opposite section strain
gauges combinations, 4+ 5 and 4- 6, show very low values, also proportional to the applied forces, allowing the calculation
of the lateral and vertical forces in accordance to Eq. (4).
Q = K 3 ( ε1 + ε2 − ε4 − ε5 )
(4)
Y = K 4 ( ε1 − ε3 + ε4 − ε6 )
The values of the constants K3 and K4 are obtained using the FEM analysis of the wheel, applying a unitary load only in one
direction (Q=1[N] and Y=0[N]; Q=0[N] and Y=1[N]) in several contact points between wheel and rail. Some of these results are
8
8
presented in Tables 1 and 2. The mean values obtained for the case under study are K3 = -7.17x10 [N] and K4 = 5.97x10 [N],
with a maximum variation with contact point of 2.6% and 0.3%, respectively.
Contact
position
Table 2. Determination of K4
Inner side (ridge) -------------- outer side
0.0232
0.0000
-0.0240
-0.0375
Radius
-0.4274
-0.4250
-0.4238
-0.4227
Q [N]
1
1
1
1
Y [N]
0
0
0
ε1 [ε]
-7.87E-10
-6.63E-10
ε2 [ε]
-5.10E-10
ε3 [ε]
-7.58E-10
ε4 [ε]
Applied force
Applied force
Table 1. Determination of K3
Contact
position
Inner side (ridge) -------------- outer side
-0.0240
-0.0375
Radius
-0.4274
-0.4250
-0.4238
-0.4227
Q [N]
0
0
0
0
0
Y [N]
1
1
1
1
-5.19E-10
-4.33E-10
ε1 [ε]
-6.76E-10
-6.65E-10
-6.60E-10
-6.50E-10
-6.79E-10
-8.34E-10
-9.21E-10
-5.45E-10
-3.18E-10
-1.89E-10
1.30E-11
3.35E-11
5.53E-11
6.78E-11
ε5 [ε]
5.12E-11
2.65E-11
1.63E-12
-1.23E-11
ε6 [ε]
9.64E-11
3.22E-11
-3.35E-11
-7.01E-11
ε1+ε2-ε4-ε5 [ε]
-1.36E-09
-1.40E-09
-1.41E-09
-1.41E-09
ε1-ε3+ε4-ε6 [ε]
1.68E-09
1.68E-09
1.67E-09
1.67E-09
K3 [N]
-7.35E+8
-7.14E+8
-7.09E+8
-7.09E+8
K4 [N]
5.95E+08
5.95E+08
5.99E+08
5.99E+08
Strain calculated
0.0000
Strain calculated
0.0232
ε2 [ε]
6.57E-10
6.35E-10
6.26E-10
6.22E-10
ε3 [ε]
-3.30E-09
-3.28E-09
-3.26E-09
-3.25E-09
ε4 [ε]
2.86E-11
3.08E-11
3.22E-11
3.36E-11
ε5 [ε]
-1.57E-11
-1.82E-11
-1.95E-11
-2.06E-11
ε6 [ε]
9.73E-10
9.66E-10
9.63E-10
9.61E-10
The FEM analysis shows an unexpected interference of the vertical force in the calculation of the horizontal force and viceversa. In fact, when a unit load is applied vertically, a Y load (6.6% proportional to Q) is obtained applying Eq. (4). Similarly,
when a unit load is applied horizontally, a Q load (2.7% proportional to Y) is calculated. Due to these interferences, the Q and
Y values obtained by Eq. (4) must be corrected:
Qcorrected = Q − Y × 2.7%
Ycorrected = Y − Q × 6.6%
(5)
Applying Eq. (5), the maximum error in the determination of the vertical and horizontal forces is always bellow 1%, although
dependent on the position where load is applied. Even for combined loads the error remains at this level.
To validate this methodology, tests in laboratory were carried out on a wheelset, [4]. Several known vertical and lateral forces
were applied to the wheel, the strains being measured in points 1 to 6 (see Figure 4). It was concluded that the maximum error
in the determination of forces was 6.7% for the vertical force and 1.8% for the lateral force.
In real running conditions the load is measured 6 times per revolution, but this frequency of measurement does not fulfill the
conditions established in [1]. Joly [2] showed that, if the signals from eight sections and both sides of the wheel were added
together, the resulting signal was almost constant and proportional to the applied load. However, this concept could not be
applied directly to the wheel under study, because the holes do not allow for an arrangement similar to the one presented by
Joly.
Applying the same concept to the six sections where strain gages can be bonded, using the finite element analysis values and
adding the full bridges to measure the Y force in each section, results in a periodical and almost constant signal, as shown in
Figure 5 (Y0, Y60 and Y120 represent the bridges to measure the Y force at 0º and 180º, 60º and 240º, and 120º and 300º). If
the same procedure is used to calculate the vertical force, adding the absolute value of each full bridge, the resulting signal is
also periodical, but with a significant amplitude. These curves are used as calibration functions of the Y and Q contact forces.
-9
Strain [µεx10 ]
5
5.E-09
4
Y0 + Y60 + Y120
3
2
ABS (Q0) + ABS (Q60) + ABS (Q120)
1
0
0.E+00
0
60
120
180
240
300
360
Angle [º]
Figure 5. FEM full bridge strain combination at 0º, 60º e 120º.
Implementation in a passengers train wheelset
To calculate the contact forces in real running conditions, one extreme wheelset of a trailer bogie, with the breaking system
removed, was instrumented. The measurements were made using strain gages (HBM LY11 – 6/530) properly bonded to the
wheels and connected according to the methodology presented above. A telemetry equipment with16 channels (KMT – MT32)
was used to transmit the signals measured in the rotating wheels and axle to the car body, Figure 6. This equipment included
modules for signal conditioning, digitalization, encoding and decoding, as shown in Figure 6.
Figure 6. Wheel with isolated strain gages, conditioning modules and telemetry equipment
with emission and reception antennas.
The modules to condition the strain gage signals (KMT MT32-STG) included 4 Volts excitation, 1000x amplification, low pass
filter and 12 bit digitalization. They were installed as closest as possible to the strain gages. The enconder (KMT MT32ENC16) combines all the digital signals from each conditioner in a unique signal to be transmitted by the transmitter (KMT
MT32-Short) at a rate of 640 Kbits/s, equivalent to 40 kSamples/s for all channels. The reception antenna is close to the axle
and receives the signal to be decoded by the decoder unit (KMT MT32-DEC16).
Twelve full Wheatstone bridges were used to calculate the contact forces in a complete wheelset (2 wheels). In order to fulfil
all the requirements of UIC 518 code [1], 59 additional signals (acceleration, displacement, strain and temperature) were
measured and information regarding the track and testing conditions registered. All data was recorded by a data logger
(National Instruments PXI 1011), which included a computer (NI 8171, PIII 800MHz, 256MB, 20GB), an A/D board (NI 6070E,
1.25 MSamples/s, 12 bits, 8 channels) and several conditioning modules. A LabView application was developed to control the
acquisition, to show some of the acquired data and to record all the data into a binary file.
(Encoder)
MT32-Short
(Transmitter)
(Decoder)
16 Channel
output
+/- 5 volts
PXI 1011
MT32-ENC16
...
MT32
DEC16
Radio Frequency
Axle
Battery
Other
Transducers
Figure 7. Measurement chain.
Experimental measurements
Hundreds of kilometers were measured under several operation conditions, ranging from low to high speed, from low radius
curves to straight lines, in tare and overloaded (with full passengers load simulated with weights distributed on the floor).
Figures 8 to 11 show the Q and Y forces measured in some of these operating conditions. The total uncompensated
acceleration, referred to in the graphs as “a”, is the resultant of the centrifugal and gravity accelerations corrected with the
slope of the line track with respect to the horizontal plane (cant). The value of the uncompensated acceleration is zero when
total acceleration is perpendicular to the rails plan. Wheels 1 and 2 correspond to the right and left wheels, when the wheelset
is in the front. Y forces and accelerations are considered positive when directed from wheel 1 to wheel 2. All the graphs
present data measured in curves to the left with a radius lower than 400m.
Figure 8 shows the variation of Y force over 50 meters in curve and in overload condition, when the wheelset is in the front or
in the back of the vehicle. When the wheelset is in the front, forces are much higher because the bogie has to guide the
vehicle.
The influence of the uncompensated acceleration can be observed in Figure 9, taking into consideration that the mean vertical
force in both wheels is 57.8KN (measured with balances during the weighting of the overloaded vehicle). The difference
between the average values of the Q force in wheels 1 and 2 increases with the increase of the uncompensated acceleration.
As expected, wheel 1 is more loaded than wheel 2 when the uncompensated acceleration is positive. The sum of the average
2
2
values of the vertical forces for both wheels is 117.6KN (a=1.08m/s ) and 116.7KN (a=-0.37m/s ), representing a deviation of
1.7% and 1.0%, respectively, in relation to the vehicle weight transmitted to the front wheelset.
The lateral and vertical forces are presented in Figures 10 and 11, when the train is in tare and overloaded for similar values of
uncompensated acceleration. The effect of the vehicle weight is much more significant on wheel 1 than in wheel 2, when the
lateral force is considered (Figure 10). Its effect in the vertical force is similar on both wheels (Figure 11). Knowing that the
vehicle in tare weights 89.5 KN in the front axle, the sum of the two vertical forces measured for this loading condition presents
a 5.2% deviation.
80
Wheel 1; Front; a=1.08 m/s2
40
70
30
60
20
50
10
2
Wheel 1; Back; a=1.05 m/s
0
-10
Wheel 2; Back; a=1.05 m/s2
-20
Wheel 2; Front; a=1.08 m/s2
-30
0
10
20
30
Distance [m]
40
50
Figure 8. Wheelset at front and back. Train overloaded at
96 Km/h, in curve to the left.
Q [KN]
Y [KN]
50
Wheel 1; a=1.08 m/s2 (Qaverage=71,5KN)
Wheel 2; a=1.08 m/s2 (Qaverage=46,1KN)
40
Wheel 1; a=-0,37 m/s
(Qaverage=56,7KN)
30
2
Wheel 2; a=-0,37 m/s2
(Qaverage=59,9KN)
20
10
0
0
10
20
30
40
50
Distance [m]
Figure 9. Vertical force measured in two curves with different
uncompensated accelerations. Wheelset on front with train
overloaded.
50
40
70
30
60
Wheel 1; Tare; a=1.04 m/s2
10
2
Wheel 1; Overloaded; a=1.08 m/s ; Qaverage=71,5KN
2
Wheel 1; Tare; a=1.04 m/s ; Qaverage=52,3KN
50
Q [KN]
20
Y [KN]
80
Wheel 1; Overloaded; a=1.08 m/s2
Wheel 2; Overloaded; a=1.08 m/s2 ; Qaverage=46,1KN
40
30
0
Wheel 2; Tare; a=1.04 m/s2 ; Qaverage=32,5KN
20
-10
Wheel 2; Tare; a=1.04 m/s2
-20
Wheel 2; Overloaded; a=1.08 m/s2
-30
0
10
20
30
Distance [m]
40
10
0
0
50
Figure 10. Lateral force measured in curve, wheelset at front.
Tare vs overloaded at 100 Km/h.
10
20
30
Distance [m]
40
50
Figure 11. Vertical force measured in curve, wheelset at front.
Tare vs overloaded at 100 Km/h.
Conclusions
A new hybrid methodology to measure directly and continuously the interaction forces between wheel (with holes) and rail in
running conditions was developed, implemented and validated. This methodology uses FEM strain solutions to determine
calibration curves to calculate vertical and lateral forces from strain measurements on the faces of the wheels.
This methodology was successfully implemented in a passengers train in running conditions, using a telemetry equipment to
transmit strain signals in rotating parts to the car body.
The influence of uncompensated acceleration, load and wheelset position on the values of lateral and vertical forces can be
clearly identified using the data presented.
Acknowledgments
We are grateful to Eng. Lamy Figueiras, Aristides Chaves and António Pereira for their support and collaboration in this work.
References
1.
2.
3.
4.
International Union of Railways, “Testing and acceptance of railway vehicles from the point of view of dynamic behaviour,
safety, track fatigue and running behaviour”, UIC code 518, 2nd Edition, (1999).
Joly, Roland, “Essais de Dynamique Ferroviaire”, Extrait de la revue générale dês chemins de fer, Juillet-Août, (1975).
Silva, J.M., Silva, J.D., Figueiras, L., Marques, J.D., Pereira, A., “Desenvolvimento de técnicas de medição das forças de
contacto roda e carril em veículos ferroviários, em condições reais de funcionamento“ Mecânica Experimental, No. 6, pág.
99-108, (2001).
Cláudio, R., “Ensaio laboratorial do rodado de um veículo ferroviário“, Proceedings of the 2as Jornadas Politécnicas de
Engenharia Mecânica, Automóvel, Organização e Gestão Industrial, Energia e Ambiente, Escola Superior de Tecnologia
de Setúbal, (2002).