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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

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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.

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(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.

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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.

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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].

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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

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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

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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).

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