JP2009113530A - Method for estimating strain of trolley wire from contact force of pantograph - Google Patents

Method for estimating strain of trolley wire from contact force of pantograph Download PDF

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JP2009113530A
JP2009113530A JP2007285686A JP2007285686A JP2009113530A JP 2009113530 A JP2009113530 A JP 2009113530A JP 2007285686 A JP2007285686 A JP 2007285686A JP 2007285686 A JP2007285686 A JP 2007285686A JP 2009113530 A JP2009113530 A JP 2009113530A
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trolley wire
pantograph
strain
contact force
trolley
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JP5184050B2 (en
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Mitsuo Amihoshi
光雄 網干
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Railway Technical Research Institute
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Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for estimating the strain of trolley wire from the contact force of a pantograph capable of accurately and continuously estimating the stress (strain) exerted on the trolley wire during passing of the pantograph, by using the actually measured contact force between a wire and the pantograph. <P>SOLUTION: The method relates to estimating of the stress (strain) of the trolley wire at a pantograph point. That is, from a characteristic equation (a) obtained from the wave equation of the trolley wire, λ<SP>4</SP>-(T-ρν<SP>2</SP>/EI)λ<SP>2</SP>-i(2ρνω/EI)λ-(ρω<SP>2</SP>/EI)=0 ... (A), where in these four characteristic roots of the formula (A), λ<SB>1</SB>is a complex number whose real part is positive, λ<SB>3</SB>is a complex number whose real part is negative, λ<SB>2</SB>is a positive pure imaginary number, and λ<SB>4</SB>is a negative pure imaginary number, the stress (strain) of the trolley wire at the pantograph point is estimated by multiplying a measured contact force by a conversion factor (b) into the strain of the trolley wire, (γ/EI)×[(λ<SB>1</SB>+λ<SB>2</SB>)/(λ<SB>1</SB>-λ<SB>3</SB>)(λ<SB>1</SB>-λ<SB>4</SB>)] ...(B). <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

本発明は、パンタグラフの接触力からトロリ線のひずみを推定する方法に関するものである。   The present invention relates to a method for estimating the distortion of a trolley wire from the contact force of a pantograph.

パンタグラフとトロリ線間の接触力によりトロリ線に曲げ応力(ひずみ)が発生し、この曲げ応力が繰り返し作用するとトロリ線が疲労破断(断線)する恐れがあるため、応力(ひずみ)の許容値が設定されている。特に、高速度運転する新幹線ではトロリ線に発生する曲げ応力は著大になる傾向があり、高速化の良否を判断する重要な指標の一つとなっている。   The bending force (strain) is generated in the trolley wire due to the contact force between the pantograph and the trolley wire. If this bending stress is repeatedly applied, the trolley wire may be subject to fatigue fracture (disconnection). Is set. In particular, in the Shinkansen operating at high speed, the bending stress generated on the trolley line tends to be significant, and this is one of the important indicators for judging whether the speed is high.

これまでは、トロリ線に直接ひずみゲージを貼り、パンタグラフ通過時の値を実測していたが、事実上測定箇所が限定される上に、必ずしもその測定箇所が応力(ひずみ)の最大値を発生する箇所とも限らないため、空間的に連続な測定が望まれていた。そこで、パンタグラフに作用する接触力を実測して、トロリ線の最大応力(ひずみ)を連続的に算出する方法が望まれていた。   Previously, a strain gauge was directly attached to the trolley wire to actually measure the value when passing through the pantograph. However, the measurement location was practically limited, and the measurement location necessarily generated the maximum value of stress (strain). Therefore, spatially continuous measurement has been desired. Therefore, a method for continuously calculating the maximum stress (strain) of the trolley wire by measuring the contact force acting on the pantograph has been desired.

近年、弾性支床梁モデルを用いて、パンタグラフ点のトロリ線ひずみを算出する方法が提案されている。
久須美 俊一,福谷 隆宏,岩井中 篤史,「接触力によるトロリ線ひずみ推定の検討」,平成16年電気学会産業応用部門大会,2004年8月,3−27,pp.III −239〜242
In recent years, a method for calculating a trolley line strain of a pantograph point using an elastic floor beam model has been proposed.
Shunichi Kusumi, Takahiro Fukuya, Atsushi Iwainaka, “Examination of Trolley Line Strain Estimation by Contact Force”, 2004 Annual Meeting of the Institute of Electrical Engineers of Japan, August 2004, 3-27, pp. III -239-242

しかしながら、上記した方法は、定常状態における接触力とトロリ線応力との関係から導出された式を用いており、変動する接触力に対しては算出誤差が大きいという欠点があった。   However, the above-described method uses a formula derived from the relationship between the contact force and the trolley line stress in the steady state, and has a drawback that the calculation error is large for the varying contact force.

本発明は、上記状況に鑑みて、近年、パンタグラフに作用する接触力が精度良く測定できるようになり、また、パンタグラフ点のトロリ線応力が最大となる特性を利用して、パンタグラフ通過時にトロリ線に作用する応力(ひずみ)を、実測された架線・パンタグラフ間の接触力を用いて精度良く連続的に推定することができる、パンタグラフの接触力からのトロリ線のひずみ推定方法を提供することを目的とする。   In view of the above situation, the present invention has recently made it possible to accurately measure the contact force acting on a pantograph, and to take advantage of the characteristic that the trolley line stress at the pantograph point is maximized. To provide a method for estimating the strain of a trolley wire from the contact force of a pantograph, which can accurately and continuously estimate the stress (strain) acting on the pantograph using the measured contact force between the overhead line and the pantograph Objective.

本発明は、上記目的を達成するために、
〔1〕パンタグラフ点におけるトロリ線応力(ひずみ)を推定する方法であって、
トロリ線の波動方程式から得られる特性方程式、
(a)λ4 −(T−ρν2 /EI)λ2 −i(2ρνω/EI)λ−(ρω2 /EI)=0 …(A)
(ここで、ρはトロリ線の線密度、νは列車走行速度、iは虚数単位、Tはトロリ線の張力、EIはトロリ線の曲げ剛性、ωは振動角周波数)
上記式(A)の4つの特性根のうち、λ1 を実数部が正の複素数、λ3 を実数部が負の複素数、λ2 を正の純虚数、λ4 を負の純虚数とし、計測された接触力に対して、トロリ線ひずみへの変換係数
(b)(γ/EI)・〔(λ1 +λ2 )/(λ1 −λ3 )(λ1 −λ4 )〕
…(B)
(ここで、γはトロリ線の中立軸から表面までの距離であり、トロリ線の形状が円形の場合は半径に相当)
を乗じてパンタグラフ点におけるトロリ線応力(ひずみ)を推定することを特徴とする。
In order to achieve the above object, the present invention provides
[1] A method for estimating a trolley line stress (strain) at a pantograph point,
Characteristic equation obtained from wave equation of trolley wire,
(A) λ 4 − (T−ρν 2 / EI) λ 2 −i (2ρνω / EI) λ− (ρω 2 / EI) = 0 (A)
(Where ρ is the line density of the trolley wire, ν is the train traveling speed, i is the imaginary unit, T is the tension of the trolley wire, EI is the bending rigidity of the trolley wire, and ω is the vibration angular frequency)
Of the four characteristic roots of the above formula (A), λ 1 is a real complex number, λ 3 is a real complex negative number, λ 2 is a positive pure imaginary number, and λ 4 is a negative pure imaginary number. Conversion coefficient (b) (γ / EI) · [(λ 1 + λ 2 ) / (λ 1 −λ 3 ) (λ 1 −λ 4 )] for the measured contact force
... (B)
(Where γ is the distance from the neutral axis of the trolley wire to the surface, and corresponds to the radius when the shape of the trolley wire is circular)
The trolley line stress (strain) at the pantograph point is estimated by multiplying by.

〔2〕上記〔1〕記載のパンタグラフの接触力からのトロリ線のひずみ推定方法において、前記式(B)は周波数特性を示すので、予めインパルス応答関数を用意しておき、実測された時間軸の接触力波形に対して前記インパルス応答関数を重畳積分することにより、前記時間軸のパンタグラフ点におけるトロリ線応力(ひずみ)を推定することを特徴とする。   [2] In the trolley wire strain estimation method from the contact force of the pantograph described in [1] above, since the equation (B) indicates a frequency characteristic, an impulse response function is prepared in advance, and the measured time axis The trolley line stress (strain) at the pantograph point on the time axis is estimated by superimposing and integrating the impulse response function on the contact force waveform.

本発明によれば、次のような効果を奏することができる。   According to the present invention, the following effects can be achieved.

(1)パンタグラフ通過時におけるトロリ線の最大応力(ひずみ)を空間連続的に推定することができ、走行安全性の確認や要注意箇所の抽出を容易に、かつ正確に行うことができる。   (1) The maximum stress (strain) of the trolley wire when passing through the pantograph can be estimated spatially continuously, and it is possible to easily and accurately check traveling safety and extract a point requiring attention.

(2)現車走行試験における測定の効率化が大幅に向上する。   (2) The measurement efficiency in the current vehicle running test is greatly improved.

(3)トロリ線断線等の事故の恐れが少なくなり、安全性が向上する。   (3) The risk of accidents such as trolley wire breakage is reduced and safety is improved.

本発明のパンタグラフの接触力からのトロリ線のひずみ推定方法は、パンタグラフ点におけるトロリ線応力(ひずみ)を推定する方法であって、
トロリ線の波動方程式から得られる特性方程式、
(a)λ4 −(T−ρν2 /EI)λ2 −i(2ρνω/EI)λ−(ρω2 /EI)=0 …(A)
(ここで、ρはトロリ線の線密度、νは列車走行速度、iは虚数単位、Tはトロリ線の張力、EIはトロリ線の曲げ剛性、ωは振動角周波数)
上記式(A)の4つの特性根のうち、λ1 を実数部が正の複素数、λ3 を実数部が負の複素数、λ2 を正の純虚数、λ4 を負の純虚数とし、計測された接触力に対して、トロリ線ひずみへの変換係数
(b)(γ/EI)・〔(λ1 +λ2 )/(λ1 −λ3 )(λ1 −λ4 )〕
…(B)
(ここで、γはトロリ線の中立軸から表面までの距離であり、トロリ線の形状が円形の場合は半径に相当)
を乗じてパンタグラフ点におけるトロリ線応力(ひずみ)を推定することを特徴とする。
The strain estimation method of the trolley line from the contact force of the pantograph of the present invention is a method of estimating the trolley line stress (strain) at the pantograph point,
Characteristic equation obtained from wave equation of trolley wire,
(A) λ 4 − (T−ρν 2 / EI) λ 2 −i (2ρνω / EI) λ− (ρω 2 / EI) = 0 (A)
(Where ρ is the line density of the trolley wire, ν is the train traveling speed, i is the imaginary unit, T is the tension of the trolley wire, EI is the bending rigidity of the trolley wire, and ω is the vibration angular frequency)
Of the four characteristic roots of the above formula (A), λ 1 is a real complex number, λ 3 is a real complex negative number, λ 2 is a positive pure imaginary number, and λ 4 is a negative pure imaginary number. Conversion coefficient (b) (γ / EI) · [(λ 1 + λ 2 ) / (λ 1 −λ 3 ) (λ 1 −λ 4 )] for the measured contact force
... (B)
(Where γ is the distance from the neutral axis of the trolley wire to the surface, and corresponds to the radius when the shape of the trolley wire is circular)
The trolley line stress (strain) at the pantograph point is estimated by multiplying by.

以下、本発明の実施の形態について詳細に説明する。   Hereinafter, embodiments of the present invention will be described in detail.

図1は本発明に係るパンタグラフの接触力からのトロリ線のひずみ推定装置のブロック図である。   FIG. 1 is a block diagram of an apparatus for estimating distortion of a trolley wire from the contact force of a pantograph according to the present invention.

図1において、1はデータ入力装置、2は推定装置、3はCPU(中央処理装置)、4はトロリ線に関する情報の記憶装置であり、ここでは、トロリ線の線密度ρ、トロリ線の張力T、トロリ線の曲げ剛性EI、列車走行速度ν、λ1 ,λ3 ,λ2 ,λ4 (後述)などが記憶される。5は入力インタフェース、6は出力インタフェース、7は出力装置である。 In FIG. 1, 1 is a data input device, 2 is an estimation device, 3 is a CPU (central processing unit), 4 is a storage device for information relating to the trolley wire, and here, the line density ρ of the trolley wire, the tension of the trolley wire T, bending rigidity EI of the trolley wire, train traveling speed ν, λ 1 , λ 3 , λ 2 , λ 4 (described later) are stored. Reference numeral 5 denotes an input interface, 6 denotes an output interface, and 7 denotes an output device.

張力のかかった無限長梁モデルを用いて、加振力Fが速度νで移動している場合、トロリ線の波動方程式は以下の式(1)で表される。なお、ここでは、トロリ線の減衰は無視する。
〔ρ(∂2 y/∂t2 )〕−〔T(∂2 y/∂x2 )〕+〔EI(∂4 y/∂x4 )〕=F・δ(x−νt) …(1)
これを移動座標系ξ=x−νtに変換すると
〔ρ(∂2 y/∂t2 )〕−〔2ρνT(∂2 y/∂t∂ξ)〕−(T−ρν2 )(∂2 y/∂ξ2 )+〔EI(∂4 y/∂ξ4 )〕=F・δ(ξ)
…(2)
となる。
When the exciting force F is moving at a speed ν using an infinitely long beam model to which tension is applied, the wave equation of the trolley wire is expressed by the following equation (1). Here, the attenuation of the trolley wire is ignored.
[Ρ (∂ 2 y / ∂t 2 ) ] - [T (∂ 2 y / ∂x 2 ) ] + [EI (∂ 4 y / ∂x 4 ) ] = F · δ (x-νt ) ... (1 )
When this is converted into the moving coordinate system ξ = x−νt, [ρ (∂ 2 y / ∂t 2 )] − [2ρνT (∂ 2 y / ∂t∂ξ)] − (T−ρν 2 ) (∂ 2 y / ∂ξ 2 ) + [EI (∂ 4 y / ∂ξ 4 )] = F · δ (ξ)
... (2)
It becomes.

ここで、加振力Fを
F=f・exp(iωt) …(3)
ここでiは虚数単位とし、解の形を
y=A・exp(λξ)・exp(iωt) …(4)
と仮定して、上記式(2)に代入すると、次の特性方程式を得ることができる。
λ4 −(T−ρν2 /EI)λ2 −i(2ρνω/EI)λ−(ρω2 /EI)=0 …(5)
この式(5)の4つの特性根のうち、λ1 を実数部が正の複素数、λ3 を実数部が負の複素数、λ2 を正の純虚数、λ4 を負の純虚数とする。
Here, the excitation force F is expressed as F = f · exp (iωt) (3)
Here, i is an imaginary unit, and the form of the solution is y = A · exp (λξ) · exp (iωt) (4)
Assuming that the above equation (2) is substituted, the following characteristic equation can be obtained.
λ 4 − (T−ρν 2 / EI) λ 2 −i (2ρνω / EI) λ− (ρω 2 / EI) = 0 (5)
Of the four characteristic roots of Equation (5), λ 1 is a real complex number with a real part, λ 3 is a complex number with a negative real part, λ 2 is a positive pure imaginary number, and λ 4 is a negative pure imaginary number. .

移動加振力がトロリ線に作用した場合と、波動がパンタグラフに入射した場合とでは、接触力とパンタグラフ点におけるトロリ線応力(ひずみ)との比を表す式は厳密には異なる。しかし実際の架線・パンタグラフの特性を用いて約50Hz程度以下に限定すれば、概ね両者が一致する特性を有する。   The expression of the ratio between the contact force and the trolley line stress (strain) at the pantograph point is strictly different when the moving excitation force acts on the trolley line and when the wave enters the pantograph. However, if it is limited to about 50 Hz or less using the characteristics of the actual overhead line / pantograph, the characteristics are almost the same.

そこで、ひずみ/接触力比を以下の式(6)で表すと、
(ε/F)=(γ/EI)・〔(λ1 +λ2 )/(λ1 −λ3 )(λ1 −λ4 )〕 …(6)
となる。
Therefore, when the strain / contact force ratio is expressed by the following equation (6),
(Ε / F) = (γ / EI) · [(λ 1 + λ 2 ) / (λ 1 −λ 3 ) (λ 1 −λ 4 )] (6)
It becomes.

ここで、γはトロリ線の中立軸から表面までの距離である。   Here, γ is the distance from the neutral axis of the trolley line to the surface.

実測された接触力に対して、適用すれば算出誤差も概ね10%以内に収めることができる。   If applied to the actually measured contact force, the calculation error can be kept within 10%.

上記式(6)は周波数特性であるので、予めインパルス応答関数を用意しておき、実測された時間軸の接触力波形に対して、このインパルス応答関数を重畳積分すれば、時間軸のパンタグラフ点におけるトロリ線応力(ひずみ)を推定することができる。   Since the above equation (6) is a frequency characteristic, if an impulse response function is prepared in advance and this impulse response function is superimposed and integrated with the actually measured contact force waveform on the time axis, the pantograph points on the time axis are obtained. The trolley line stress (strain) in can be estimated.

トロリ線の応力(ひずみ)は、パンタグラフ点が最大となるので、この方法を用いれば、トロリ線の最大応力(ひずみ)を空間連続的に推定することができる。   Since the pantograph point has the maximum trolley wire stress (strain), the maximum stress (strain) of the trolley wire can be spatially estimated using this method.

本発明によれば、パンタグラフ通過時におけるトロリ線の最大応力(ひずみ)を空間連続的に推定することができ、走行安全性の確認や要注意箇所の抽出を容易に、かつ正確に行うことができる。   According to the present invention, the maximum stress (strain) of the trolley wire when passing through the pantograph can be continuously estimated, and it is possible to easily and accurately check traveling safety and extract a point requiring attention. it can.

また、現車走行試験における測定の効率化が大幅に向上する。   In addition, the efficiency of measurement in the current vehicle running test is greatly improved.

さらに、トロリ線断線等の事故の恐れが少なくなり、安全性が向上する。   Furthermore, the risk of accidents such as trolley wire disconnection is reduced, and safety is improved.

このように、上記式(6)に基づき、接触力とトロリ線ひずみについて試算する。   Thus, based on the above formula (6), the contact force and the trolley wire strain are estimated.

図2に、本発明に係るコンピュータシミュレーション手法を用いてパンタグラフの接触力とその点のトロリ線ひずみを計算した例を示す。これを真値と仮定した場合、図示の点では、497μの値となっている。これに対して、従来の方法である弾性支床梁モデルを用いる方法では、685μと誤差が大きいが、本発明の手法を用いれば、517μとほぼ正確に推定できることが分かる。   FIG. 2 shows an example in which the contact force of the pantograph and the trolley line distortion at that point are calculated using the computer simulation method according to the present invention. Assuming that this is a true value, the value shown in the figure is 497 μ. On the other hand, the conventional method using an elastic floor beam model has a large error of 685 μm, but it can be understood that the method of the present invention can be estimated almost accurately as 517 μm.

なお、本発明は上記実施例に限定されるものではなく、本発明の趣旨に基づき種々の変形が可能であり、これらを本発明の範囲から排除するものではない。   In addition, this invention is not limited to the said Example, Based on the meaning of this invention, a various deformation | transformation is possible and these are not excluded from the scope of the present invention.

本発明のパンタグラフの接触力からのトロリ線のひずみ推定方法は、パンタグラフ通過時におけるトロリ線の最大応力(ひずみ)を空間連続的に推定することができ、走行安全性の確認や要注意箇所の抽出を容易に、かつ正確に行うことのできるトロリ線のひずみ推定方法として利用可能である。   The strain estimation method of the trolley wire from the contact force of the pantograph according to the present invention can continuously estimate the maximum stress (strain) of the trolley wire when passing through the pantograph, confirming driving safety and The present invention can be used as a trolley wire distortion estimation method that can be easily and accurately extracted.

本発明に係るパンタグラフの接触力からのトロリ線のひずみ推定装置のブロック図である。It is a block diagram of the distortion estimation apparatus of the trolley line from the contact force of the pantograph which concerns on this invention. 本発明に係るコンピュータシミュレーション手法を用いてパンタグラフの接触力とその点のトロリ線ひずみを計算した例を示す図である。It is a figure which shows the example which calculated the contact force of the pantograph and the trolley line distortion of the point using the computer simulation method which concerns on this invention.

符号の説明Explanation of symbols

1 データ入力装置
2 推定装置
3 CPU(中央処理装置)
4 トロリ線に関する情報の記憶装置
5 入力インタフェース
6 出力インタフェース
7 出力装置
1 data input device 2 estimation device 3 CPU (central processing unit)
4 Storage device for trolley wire information 5 Input interface 6 Output interface 7 Output device

Claims (2)

パンタグラフ点におけるトロリ線応力(ひずみ)を推定する方法であって、
トロリ線の波動方程式から得られる特性方程式、
(a)λ4 −(T−ρν2 /EI)λ2 −i(2ρνω/EI)λ−(ρω2 /EI)=0 …(A)
(ここで、ρはトロリ線の線密度、νは列車走行速度、iは虚数単位、Tはトロリ線の張力、EIはトロリ線の曲げ剛性、ωは振動角周波数)
上記式(A)の4つの特性根のうち、λ1 を実数部が正の複素数、λ3 を実数部が負の複素数、λ2 を正の純虚数、λ4 を負の純虚数とし、計測された接触力に対して、トロリ線ひずみへの変換計数
(b)(γ/EI)・〔(λ1 +λ2 )/(λ1 −λ3 )(λ1 −λ4 )〕
…(B)
(ここで、γはトロリ線の中立軸から表面までの距離であり、トロリ線の形状が円形の場合は半径に相当)
を乗じてパンタグラフ点におけるトロリ線応力(ひずみ)を推定することを特徴とするパンタグラフの接触力からのトロリ線のひずみ推定方法。
A method of estimating trolley line stress (strain) at a pantograph point,
Characteristic equation obtained from wave equation of trolley wire,
(A) λ 4 − (T−ρν 2 / EI) λ 2 −i (2ρνω / EI) λ− (ρω 2 / EI) = 0 (A)
(Where ρ is the line density of the trolley wire, ν is the train traveling speed, i is the imaginary unit, T is the tension of the trolley wire, EI is the bending rigidity of the trolley wire, and ω is the vibration angular frequency)
Of the four characteristic roots of the above formula (A), λ 1 is a real complex number, λ 3 is a real complex negative number, λ 2 is a positive pure imaginary number, and λ 4 is a negative pure imaginary number. Conversion coefficient to trolley wire strain for measured contact force (b) (γ / EI) · [(λ 1 + λ 2 ) / (λ 1 −λ 3 ) (λ 1 −λ 4 )]
... (B)
(Where γ is the distance from the neutral axis of the trolley wire to the surface, and corresponds to the radius when the shape of the trolley wire is circular)
Is used to estimate the trolley line stress (strain) at the pantograph point, and the trolley line strain estimation method from the contact force of the pantograph.
請求項1記載のパンタグラフの接触力からのトロリ線のひずみ推定方法において、前記式(B)は周波数特性を示すので、予めインパルス応答関数を用意しておき、実測された時間軸の接触力波形に対して前記インパルス応答関数を重畳積分することにより、前記時間軸のパンタグラフ点におけるトロリ線応力(ひずみ)を推定することを特徴とするパンタグラフの接触力からのトロリ線のひずみ推定方法。   2. A method for estimating distortion of a trolley wire from a contact force of a pantograph according to claim 1, wherein the equation (B) indicates a frequency characteristic, so that an impulse response function is prepared in advance, and an actually measured contact force waveform on a time axis. A trolley wire strain estimation method based on a contact force of a pantograph, wherein the trolley wire stress (strain) at the pantograph point on the time axis is estimated by superimposing and integrating the impulse response function with respect to.
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JP2015102522A (en) * 2013-11-28 2015-06-04 公益財団法人鉄道総合技術研究所 Travel simulation device of overhead wire/pantograph system

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JPH0664116U (en) * 1993-02-12 1994-09-09 財団法人鉄道総合技術研究所 Automatic recorder for dynamic characteristics of overhead lines
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JP2015102522A (en) * 2013-11-28 2015-06-04 公益財団法人鉄道総合技術研究所 Travel simulation device of overhead wire/pantograph system

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