-
1
The estimation method of wheel load and lateral force using the
axlebox acceleration
1H. Tanaka, 1A. Furukawa 1Railway Technical Research Institute,
Tokyo, Japan
Abstract
The track condition of Japanese high-speed railways, Shinkansen,
is maintained by properly correcting and/or improving track
irregularities. In general, interacting forces between wheel and
rail, namely wheel load and lateral force cant be easily measured.
On the other hand, it is very important to estimates wheel load and
lateral force especially some values more than and/or less than
prescribed thresholds and locations at which those values take
place, from the view points of running safety of vehicles and the
material deterioration of track components. There are some kinds of
technique for directly measuring wheel loads and lateral forces.
However, they are so costly and fragile, that it is difficult to
adopt them for frequent and regular measurement. This paper
describes the method of estimating the extraordinary values of
wheel loads and lateral force and their locations by using the
axlebox acceleration that can be easily measured.
1. Introduction
For the running safety of vehicles, track irregularity of
Shinkansen has been controlled with high accuracy since the
operation of Shinkansen started in 1964. The one of main track
maintenance works is that track irregularities measured with track
inspection cars must be rectified to keep them below the track
irregularity criteria which have been already decided for running
safety. In general, we judge that wheel load or lateral force
larger than the safety criteria will not occur when track
irregularity is lower than the criteria. However it is known that
very large wheel loads or lateral forces are caused by such short
wavelength track irregularity as can not be detected with the track
inspection car. Moreover these large wheel loads or lateral forces
will often occur when the operational speed of trains will increase
more than the current speed. Hence, focusing on the high speed of
train operation, it is necessary to make accuracy of the track
maintenance higher than that accepted for the present speed. In
addition, strictly speaking, when a different type vehicle runs on
the track of the same irregularity, occurring wheel load or lateral
force will be different. Therefore, it is very important to
identify the wheel load and lateral force which are actually
generated by vehicle running on even such a short wavelength.
Also, the current measuring device of wheel loads and lateral
forces adopted commonly in Japan has the function of measuring the
continuous waveform of them from DC to 100Hz [1]. Since the device
is very expensive and delicate, a track inspection car is not
equipped with it, which means the measurement of wheel loads and
lateral forces can not be carried out regularly. This device is
used only in the case of some special examinations such as checking
the function of newly developed vehicles and the running safety for
speed-up tests.
The purpose of this paper is to report the results of study on
how to estimate wheel loads and lateral forces with a method which
is cheaper and more robust than the current method adopted commonly
in Japan. There is vertical axlebox acceleration as an index often
used to evaluate the track irregularity whose wavelength is
relatively short, such as rail surface roughness and loose sleeper
[2]. Also, it has already been identified that the correlation
between the vertical axlebox acceleration and the wheel load is
high [3]. However, the relation between the lateral force and the
lateral axlebox acceleration has not been so clarified yet as with
the relation between the wheel load and the vertical axlebox
acceleration [4]. In this paper, the relation between the wheel
load and the vertical axlebox acceleration, and that between the
lateral force and the lateral axlebox acceleration through
measurement by the above-mentioned method were analyzed. In
addition, the management system of a large wheel load and a large
lateral force by the use of the axlebox acceleration was
examined.
2. Measurement and data processing of wheel load, lateral force
and axlebox acceleration
2.1 Measurement method Wheel loads and lateral forces are
measured by the technique called as "New continuous method" in
Japan [1]. This technique makes it possible to calculate a
continuous wheel load and
-
2
lateral force for the frequency band from DC to 100Hz, through
the measurement of the strain of the wheel with a lot of strain
gauges attached on the wheel,
The axlebox acceleration can be measured with the accelerometer
fixed to the axlebox that supports the wheel set of the vehicle. In
this paper, the acceleration in the vertical direction will be
called as "vertical axlebox acceleration" and the horizontal
acceleration as "lateral axlebox acceleration". Moreover, the
generic name of both will be called as "axlebox acceleration".
Since the axlebox acceleration contains various information of the
track in a wide frequency band, it is often measured with a very
high sampling frequency. Fig.1 shows the schematic representation
of wheel load, lateral force and axlebox acceleration, and the
photo of accelerometers installed at an axlebox.
Fig.1 Schematic representation of wheel load, lateral force and
axlebox acceleration,
and the photo of accelerometers installed at an axlebox. 2.2
Processing procedure of measured data
The data set handled in this paper includes the wheel load and
the lateral force measured by the new continuous method, and the
vertical axlebox and lateral acceleration and the lateral axlebox
acceleration whose measured signals are obtained simultaneously on
the same measuring wheel set installed in a Shinkansen train. In
general, these data are obtained under the sampling frequency of
several thousand Hz. In this paper, the low-pass filter (LPF)
processing of 100Hz is adopted to all the measured data to examine
the relation between the wheel load and the lateral force and the
axlebox acceleration. Afterwards, the data of time sampling are
converted into the data of distance sampling at several cm
intervals by using the distance signals that were recorded
simultaneously together with these time sampling data. The distance
signals is generated by a tacho-generator at the rate of about 100
pulses per one wheel rotation which means the interval of one pulse
is several cm. Even if the running speed of vehicle changes, the
data of equal intervals can be obtained by using this distance
signals. During these data processings, it is necessary to take
careful consideration so as not to cause the aliasing. Fig.2 shows
the detailed procedure of data processing.
Accelerometer
-
3
Fig.2 The detailed procedure of data processing.
3. Frequency analysis
3.1 Frequency characteristics At first, focusing on the
influence of track alignment on the frequency characteristics of
wheel
loads, lateral forces and axlebox accelerations, the data
obtained by a vehicle running in a tangent track and a curved track
were analyzed by the FFT analysis. Fig.3 (a) shows a power spectrum
density (PSD) of the wheel load and the lateral force, Fig3 (b)
shows a PSD of axlebox acceleration. PSDs of wheel load are similar
to those of vertical axlebox acceleration in all bandwidths. On the
other hand, PSD of lateral force in long-wavelength side is larger
than that in short-wavelength side, and PSD of lateral axlebox
acceleration is strong in the bandwidth on the long-wavelength side
and the short wavelength side power. Investigating those PSD, the
influence on track alignment is not clearly identified.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0.0 0.5 1.0Spatial frequency [1/m]
PS
D [
kN2m
]
inner rail
tangentouter rail
Wheel load
Lateral force
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0.0 0.5 1.0Spatial frequency [1/m]
PS
D [
(m/s2
)2m
]
inner rail
tangent
outer rail
Vertical axlebox acceleration
Lateral axlebox acceleration
(a) Wheel load and lateral force (b) Axlebox acceleration
Fig.3 Power spectrum density.
Fig.4 shows the coherence between vertical axlebox acceleration
and wheel load, and that between lateral axlebox acceleration and
lateral force. Both of the frequency response functions in Fig.5
look similar to each other. These show only the case of a tangent
track because a remarkable change in PSD could not be observed due
to the difference of the alignment. The coherence between vertical
axlebox acceleration and wheel load is high in the spatial
frequency of 0.2-1.2 [1/m]. Almost no variation of amplitude gain
with spatial frequency can be identified through all bands. As for
the relation between vertical axlebox acceleration and wheel load,
the frequency component of this frequency band is significant and
the correlation of the two frequency response functions is high.
The coherence between lateral axlebox acceleration and lateral
force is higher in the spatial frequency of 0.2-0.4 [1/m] and
0.9-1.2 [1/m]. The amplitude gain is large in the range of low
spatial frequency (long-wavelength side). Accordingly as for the
relation between lateral axlebox acceleration and lateral force,
the frequency component of spatial frequency in 0.2-0.4 [1/m] is
significant and the correlation of the two coherence is high.
-
4
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0Spatial frequency [1/m]
Cohere
nce
Lateral axlebox acceleration Lateral force
Vertical axleboxacceleration
Wheel load
1.E-02
1.E-01
1.E+00
1.E+01
0.0 0.5 1.0Spatial frequency [1/m]
Am
plit
ude
gai
n [
kN/(m
/s2
)]
Lateral axlebox acceleration Lateral force
Vertical axlebox acceleration Wheel load
Fig.4 Coherence. Fig.5 Frequency response function.
3.2 Extracted frequency component
The significant frequency range in which a high correlation
between wheel load, lateral force and axlebox acceleration were
recognized, and were obtained by the frequency analysis.
Considering such a fact, large wheels load and lateral forces can
be estimated from large axlebox accelerations, if that frequency
range is extracted and the relation between both parameters is
analyzed. Although some bandwidth of spatial frequency in which a
high correlation between both is obtained, it is easier to apply
LPF processing beforehand at the time sampling stage, taking into
consideration the running speed of the Shinkansen train and the
cut-off frequency of the output waveform of new continuous method.
That is, LPF process by 100Hz should be applied to wheel load and
vertical axlebox acceleration, and that by 30Hz to lateral force
and lateral axlebox acceleration.
The results obtained by LPF processing are shown in Fig.6. In
Fig.6 (a), 100Hz-LPF processing was adopted for wheel load and
vertical axlebox acceleration, and the processed waveform of wheel
load looks similar to that of vertical axlebox acceleration. Also,
the processed wheel load wave has the quasi static part
corresponding to the static wheel load, however vertical axlebox
acceleration wave has no such quasi static part. In addition,
100Hz-LPF processing and 30Hz-LPF processing were adopted for
lateral force and lateral axlebox acceleration shown in Fig.6 (b).
In this figure, the short-wavelength response is prominent in
acceleration wave, and the correlation between the lateral force
and lateral axlebox acceleration is not significantly identified in
the processing waveform of 100Hz-LPF. However, the correlation
between lateral axlebox acceleration and lateral force can be
recognized in the processing waveform of 30Hz-LPF. Further it can
be seen that, the processed lateral force waveforms of 100Hz-LPF
and that of 30Hz-LPF have no clear difference.
(a) Wheel load and vertical axlebox acceleration (100Hz-LPF)
Fig.6 Waveform obtained by LPF processing.
-
5
(b) Lateral force and lateral axlebox acceleration (30Hz-LPF and
100Hz-LPF)
Fig.6 Waveform obtained by LPF processing.
4. Lot statistic analysis
4.1 Elimination of quasi static forces The excessive centrifugal
force acts when not only Shinkansen vehicles but also other
vehicles
run at high speed in a curved track and the quasi static
component of wheel load and lateral force changes. The quasi static
component doesn't change when the vehicle runs in the curve at the
balancing speed. However, it has recently come to be very important
to take into account the effect of the excessive centrifugal force
on the quasi static component disregard the change in the quasi
static component in the case that, speed-up more than the design
speed of the line is achieved. With respect to the measurement of
axlebox acceleration, it is difficult to measure with high accuracy
both impact acceleration acting for very short time and quasi
static acceleration due to the excess centrifugal force with acting
almost constantly from the view point of the performance of the
accelerometer. In this paper, a strain gage type accelerometer
suitable for measuring impact acceleration is used because of
focusing on a large impact acceleration. In addition, quasi static
component has been eliminated by applying the high-pass filter
(HPF) processing to axlebox acceleration waveform in order to
eliminate the error by other factors such as the temperature
drifts.
Large values of wheel load and lateral force are generated
because impact forces interact between wheel and rail. Therefore,
it is considered that by eliminating the quasi static component of
wheel load and lateral force, the correlation between the axlebox
acceleration and wheel load / lateral force will become clear.
Then, the quasi static component was eliminated by applying HPF
processing for waveforms of wheel load and lateral force, and only
the variable components of wheel load and lateral force were
examined. 4.2 Relation between the lot maximum values of wheel load
and vertical axlebox acceleration
The 50m each lot maximum value was obtained from 100Hz-LPF
processing waveform of wheel load and vertical axlebox acceleration
after eliminating quasi static component, and the relation of the
maximum values of both parameters was analyzed. Fig.7 shows the
relation of the maximum values of wheel load and vertical axlebox
acceleration. The relation can be expressed by linear equation
based on the result of regression analysis. The running speeds of a
vehicle dont have influence on the regression coefficient, but
vehicle types have influence on it. It shows that the relationship
between wheel load and vertical axlebox acceleration is simply the
relation between force and acceleration, and then it is dependent
on the spring-mass system of a bogie. Therefore, a large value of
wheel load processed with 100Hz-LPF can be estimated by a large
value of vertical axlebox acceleration processed with
100Hz-LPF.
-
6
Q100 = 0.47 JV100 = 0.90
0
20
40
60
80
100
0 50 100 150 200 250
Vertical axlebox acceleration 100Hz-LPF
JV100 [m/s2]
Wheel lo
ad
100H
z-LP
F, elim
inat
ed
quas
i st
atic
com
ponent
Q100 [kN
]
Fig.7 Relation between the lot maximum values of wheel load and
vertical axlebox acceleration.
4.3 Relation between the lot maximum values of lateral force and
lateral axlebox acceleration
The 50m each lot maximum value was obtained from processed
waveform of 30Hz-LPF of lateral force and lateral axlebox
acceleration after eliminating quasi static component, and the
relation of the maximum values of both parameters was analyzed in
the same way as the case of wheel load and vertical axlebox
acceleration discussed in the 4.2 section above. Fig.8 shows the
relation of the maximum values of lateral force and lateral axlebox
acceleration. The relation of the lot maximum values of both
parameters is divided into two groups obtained from the result of
regression analysis. When each lot is examined here, the group A in
the Fig.8 contains the data obtained in the tangent track and from
the inner rail side of curved track. The group B contains the data
obtained at discontinuous points of the rail such as a turnout and
an expansion joint, etc. and from the outer rail side of curved
track. Therefore, the data of the group A is thought to be caused
by the lateral movement of wheel set within the lateral gap between
wheel flange and rail gauge face which means wheel flange doesnt
contact with rail gauge face. On the other hand, the data of the
group B is thought to be caused by the lateral movement of wheel
set whose wheel flange making contact with rail gauge face, and the
relation of the lot maximum values is divided into two groups from
the result of regression analysis as mentioned above. The large
lateral force which needs to be focused on is measured only in the
case that the wheel flange makes contact with the rail gauge face.
The
Group A
Y30 = 0.79 JH30 = 0.37
Group B
Y30 = 2.22 JH30 = 0.84
0
5
10
15
20
25
0 2 4 6 8 10
Lateral axlebox acceleration 30Hz-LPF
JH30 [m/s2]
Lat
era
l fo
rce
30H
z-LP
F, elim
inat
ed
quas
i st
atic
com
ponente
) Y
30 [kN
]
Y100 = 1.20 Y30 = 0.95
0
5
10
15
20
25
0 5 10 15 20 25
Lateral force 30Hz-LPF,eliminated
quasi static componentY30 [kN]
Lar
era
l fo
rce
100H
z-LP
F, elim
inat
ed
quas
i st
atic
com
ponent
Y100 [kN
]
Fig.8 Relation between the lot maximum Fig.9 Relation between
the lot maximum values of lateral force and these of values of 100
Hz-LPF and these of lateral axlebox acceleration. 30 Hz-LPF
processing lateral force.
-
7
coefficient of this regression linear line in the case of group
B is specific to vehicle types as in well as the case of wheel
load.
Here, the maximum lateral force processed by 30Hz-LPF is not
expected to be actually estimated. What is expected to estimate is
the maximum lateral force of a processed waveform of 100Hz-LPF that
is equivalent of the output wave form of the new continuous method.
Fig.9 shows the relation between the maximum lateral force of 100Hz
and that of 30Hz-LPF processing. The relation of the lot maximum
values of both waveforms can be expressed with one liner equation
based on the result of regression analysis. Therefore, a large
lateral force of processed waveform of 100Hz-LPF can be predicted
based on a large lateral axlebox acceleration of 30Hz-LPF
processing waveform. 4.4 Estimated equation of quasi static
component of wheel load and lateral force
After eliminating the quasi static component, relation between
the variable components of wheel load and lateral force, and
axlebox acceleration was obtained as described above. On the other
hand, it is necessary to predict the quasi static component as well
as in order to estimate large wheel load and lateral force from
large axlebox acceleration. Regarding the estimating formula of the
quasi static component [5], there is the one proposed for the sharp
curves of the narrow gauge lines. The estimating formula of wheel
load is a simple form in which the parameters used in the form are
only some of technical details of curved tracks and the running
speed of vehicle as shown in the formula (1) to (3). For the
estimation of quasi static component of lateral force, some
parameters related to the steering ability for curved tracks and
the twist of air suspension are needed in addition to the
parameters mentioned above. These additional parameters are
different according to the type of bogie and the shape of wheel
tread, and also are very influenced by depend on a curve radius. In
this paper, it was assumed that the influence of these additional
parameters on quasi static component of lateral force was small
when a vehicle ran in the curved track whose radius was large.
Accordingly, the formula was transformed to the one that was able
to be presumed only by a curve parameter and the running speed of
vehicle. The estimation formula of wheel load expressed by the
equations (1) to (3) doesn't change regardless of the
above-mentioned assumption because the formula is expressed only by
the excessive centrifugal force. On the other hand, the estimation
formula of lateral force is very simplified as follow. Equation (4)
is associated with lateral axle load. In addition, the lateral axle
load has a difference between lateral force at outer rail and that
of inner rail. If the axle load is assumed to be equally borne by
an inner rail and an outer rail, the quasi static lateral force at
the outer rail and that of the inner rail can be expressed by
formula (5) and (6).
*2 221 Go oHV C V CQ Q
gR G G gR G
= + ? -
(1)
*2 221 Gi iHV C V CQ Q
gR G G gR G
= + ? -
(2)
* 1.25G GH H= (3)
( )2 2
0 o io iV C V CY W Q Q Y YgR G gR G
D = - = + - = - (4)
20
2o
W V CYgR G
= - (5)
20
2i
W V CYgR G
= - - (6)
where, oQ quasi static wheel load at outer rail [kN] iQ quasi
static wheel load at inner rail
[kN] YD lateral axle load [kN] oY quasi static lateral force at
outer rail [kN] iY quasi static lateral force at inner rail [kN] oQ
static wheel load at outer rail [kN] iQ static wheel load at inner
rail [kN], oW axle load [kN]Vrunning velocity of vehicle
[km/h]ggravitational acceleration [m/s2]Rcurve radius [m]Cdesign
superelevation or cant [m]Gtrack gauge [m]HGeffective height of
gravitational center [m]HGheight of gravitational center [m].
-
8
Fig.10 shows the comparison between measured results and
estimated results of quasi static force of wheel load and lateral
force. Measured results were obtained from eliminating the variable
component from the measurement waveform by the LPF processing. It
is shown that the wheel load can be predicted with high accuracy
even if a vehicle runs at high-speed like Shinkansen. Similarly it
is shown that not only lateral axle load but also quasi static
lateral force at inner rail and outer rail can be presumed at high
accuracy, though the estimating formula of the lateral force is a
simple. In other words the excessive centrifugal force has a great
influence on the quasi static component of lateral force when a
Shinkansen train runs in the curved track whose radius of curve is
large.
30
40
50
60
70
80
150 200 250 300 350
Running speed V [km/h]
Wheel lo
ad Q
[kN
]Wheel load of outer rail
Wheel load of innerr rail
(a) Wheel load
-10
-5
0
5
10
15
20
150 200 250 300 350
Running speed V [km/h]
Lat
era
l fo
rce Y
[kN
]
Lateral force of inner rail
Lateral axle load
Lateral force of outer rail
(b) Lateral force
Fig.10 Estimated result of quasi static component (for R=4000m,
C=155mm)
5. Example of estimating large wheel load and lateral force
A large wheel load and a large lateral force can be predicted as
the sum of the impact element estimated from the axlebox
acceleration and the excessive centrifugal force obtained from
geometrical details as shown in formula (7) based on the
above-discussions. The correction coefficient of wheel load is a
slope of the regression line of Fig.7. The correction coefficient
of lateral force is a product of the slope of the regression line
of group B in Fig.8 and in Fig.9. These correction coefficients are
specific to the vehicle type that depends on the primary suspension
and stiffness of the steering of the bogie as described above.
(Large value) = (impact component) + (quasi static component)
(7)
The comparison of estimation from axlebox acceleration by the
above-mentioned technique with measured wheel loads and lateral
forces are shown in Fig.11. The axlebox acceleration, wheel load
and lateral force were measured for the same vehicle running at
different speeds in different track. The correlation of estimated
and measured wheel load is high and estimation accuracy may be
high. Because the estimation of lateral force is divided into two
groups as shown in Fig.8, the estimation accuracy seems bad.
However, it is considered that lateral axlebox acceleration that
exceeds threshold corresponding to the criteria of control of a
large lateral force is generated only in the case
-
9
of group B where the wheel flange has come in contact with the
rail, and lateral axlebox acceleration that exceeds threshold is
not observed in the case of group A where wheel flange doesnt make
contact with gauge face. Therefore, if only lateral axlebox
acceleration exceeding threshold is measured, it is possible to
estimate occurrence points of a large lateral force and its
value.
Q100,M = 0.98 Q100,E = 0.94
0
50
100
150
200
0 50 100 150 200Estimated wheel load Q100,E [kN]
Meas
ure
d w
heel lo
ad Q
100,M
[kN
]
0
5
10
15
20
25
30
0 5 10 15 20 25 30Estimated lateral force Y100,E [kN]
Meas
ure
d la
tera
l fo
rce Y
100,M
[kN
]
Group B
GroupA
Y100,M = 0.95Y100,E = 0.93
(a) Wheel load (b) Lateral force
Fig.11 Comparison between measurement and estimation of the lot
maximum value
6. Monitoring method of large wheel load and lateral force by
using axlebox acceleration
According to the above discussions, it is possible to identify
the location, where a large wheel load and lateral force take place
and to estimate the magnitude of the parameters by measuring the
axlebox acceleration. Fig.12 shows the outline of the monitoring
system of large values of the wheel load and lateral force by the
use of axlebox acceleration. The locations of large force are
specified by the system and the magnitude of large force is roughly
estimated, by the accelerometer installed to the axlebox of
vehicle. As a result, the weak points of the track can be
maintained in the areas where large values that exceeded threshold
have been generated. Or by using the track irregularities measured
with the track inspection cars in addition, the track
irregularities causing large forces can be adjusted. In order to
simplify the on-board measuring system, it is preferable to adopt
the sub system of off-line data processing.
Fig.12 Outline of monitoring system
-
10
If a railway operator once examines the relationship between
wheel load or lateral force and axlebox acceleration and decides a
threshold, only the axlebox accelerations should be measured
afterwards. With respect to the data set required in order to
analyze these relations, it is efficient to measure them in
on-track tests of a new car development or in speed-up tests. In
addition, since only an accelerometer is used for this method, this
method is easier and cheaper than the direct measurement method of
wheel load and lateral force which needs expensive equipment.
Therefore, this method can be practically used as a constant
monitoring system of the wheel load and lateral force of operating
trains. Further, when several vehicle types run on the same track,
it is desirable to measure the parameters for the vehicle running
at the highest speed in the railway line, because larger wheel load
or lateral force are commonly generated by the fastest vehicle.
7. Conclusions
We analyzed the relation between wheel loads and vertical
axlebox acceleration, and that between lateral forces and lateral
axlebox acceleration of the Shinkansen train. The main results
obtained in this study are as follows:
(1) The relation between vertical axlebox acceleration and wheel
load has high correlation in
spatial frequency 0.2-1.2 [1/m], and the relation between
lateral axlebox acceleration and lateral force has high correlation
in space frequency 0.2-0.4 [1/m].
(2) The relation between lot maximum values of 100Hz-LPF
processing waveforms of vertical axlebox acceleration and wheel
load after eliminating quasi static component, can be expressed
with one linear equation. The occurrence point and the impact
component of a large wheel load can be presumed according to a
large value of the vertical axlebox acceleration.
(3) The relation between the lot maximum values of 30Hz-LPF
processing waveforms of lateral axlebox acceleration and lateral
force after eliminating quasi static component, can be expressed
with two liner equation. This division to two linear equations
depends on the state of contact between the wheel flange and the
rail. The large lateral force which needs to be maintained occurre
only in the state where the wheel flange contacts with side surface
of rail, and the occurrence point and the impact component of a
large lateral force can be presumed according to a large value of
the lateral axlebox acceleration.
(4) The quasi static component of wheel load and lateral force
in the curve section can be presumed only from the running speed of
vehicle and a curve parameter.
Summering up the above discussion, the location of a large wheel
load and lateral force and their
large values can be estimated from the measuring data of axlebox
acceleration, running speed of vehicle and a curve parameter.
References
[1] H. ISHIDA, K. UEKI, K. FUKAZAWA, K. TEZUKA, M. MATSUO. A New
Continuous Measuring Method of Wheel/Rail Contact Forces, QR of
RTRI, Vol.35, No.2, pp.105-111, (1994).
[2] F. COUDERT, Y. SUNAGA, K. TAKEGAMI. Use of Axle Box
Acceleration to Detect Track and Rail Irregularities, WCRR97,
pp.1-7, (1999).
[3] Y. SUNAGA, I. SANO, T. IDE. A Practical Use of Axlebox
Acceleration to Control the Short Wave Track Irregularities,
WCRR97, pp.1-7, (1997).
[4] M. YOSHIDA, S. SHINOWAKI, Y. SUNAGA. A Study on Lateral
Axlebox Acceleration for Detecting Irregularities of Rail Joints on
Sharp Curves, J-Rail 2004, pp.91-94, (2004).
[5] H. TAKAI, M. UCHIDA, H. MURAMATSU, H. ISHIDA. Derailment
Safety Evaluation by Analytic Equations, QR of RTRI, Vol.43, No.3,
pp.119-124, (2002).
/ColorImageDict > /JPEG2000ColorACSImageDict >
/JPEG2000ColorImageDict > /AntiAliasGrayImages false
/CropGrayImages true /GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic /GrayImageResolution 300
/GrayImageDepth -1 /GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true
/GrayImageFilter /DCTEncode /AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict >
/GrayImageDict > /JPEG2000GrayACSImageDict >
/JPEG2000GrayImageDict > /AntiAliasMonoImages false
/CropMonoImages true /MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic /MonoImageResolution 1200
/MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000
/EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode
/MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None
] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000
0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ]
/PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier ()
/PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped
/False
/Description > /Namespace [ (Adobe) (Common) (1.0) ]
/OtherNamespaces [ > /FormElements false /GenerateStructure true
/IncludeBookmarks false /IncludeHyperlinks false
/IncludeInteractive false /IncludeLayers false /IncludeProfiles
true /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe)
(CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /NA
/PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged /UseDocumentBleed false
>> ]>> setdistillerparams> setpagedevice