JP2011201476A - Railroad vehicle, and method of suppressing vibration of vehicle body of the same - Google Patents

Railroad vehicle, and method of suppressing vibration of vehicle body of the same Download PDF

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JP2011201476A
JP2011201476A JP2010072564A JP2010072564A JP2011201476A JP 2011201476 A JP2011201476 A JP 2011201476A JP 2010072564 A JP2010072564 A JP 2010072564A JP 2010072564 A JP2010072564 A JP 2010072564A JP 2011201476 A JP2011201476 A JP 2011201476A
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vehicle body
vibration
damping
mass
ratio
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Takahiro Tomioka
隆弘 富岡
Tadao Takigami
唯夫 瀧上
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Railway Technical Research Institute
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Abstract

PROBLEM TO BE SOLVED: To provide a railroad vehicle and a method of suppressing the vibration of a vehicle body of the same capable of obtaining an excellent vibration suppressing effect without performing complicated adjustment.SOLUTION: A railroad vehicle 1 includes: the vehicle body 10; and a mass body fitted to the vehicle body through spring elements and damping elements so as to vibrate relative to the vehicle body. The natural frequency of the mass body is set lower than that of the vehicle body in elastic vibration, and a damping capacity of the mass body is set larger than that of the vehicle body in elastic vibration.

Description

本発明は、鉄道車両、及び、鉄道車両用車体の振動抑制方法に関し、特に、車体に対して弾性支持された付加系を用いて振動を抑制するものに関する。   The present invention relates to a railway vehicle and a method for suppressing vibration of a railway vehicle body, and more particularly to an apparatus for suppressing vibration using an additional system elastically supported with respect to the vehicle body.

旅客用の鉄道車両用車体は、屋根構、床構、側構、妻構からなるほぼ六面体状に形成され、軌道の進行方向に沿って長く伸びた形状となっていることが一般的である。このような車体は、走行時に台車からの上下加振力等によって、それ自体が一本のはりに類似した上下曲げ振動や、車体断面のせん断変形を伴う振動等の様々な振動モードを示すことが知られている。このような車体の弾性振動は、旅客が乗り心地の悪さとして感じることから、抑制することが要望されている。   Generally, a railway vehicle body for passengers is formed in a substantially hexahedron shape including a roof structure, a floor structure, a side structure, and a wife structure, and has a shape that extends long along the traveling direction of the track. . Such a car body exhibits various vibration modes such as vertical bending vibration that resembles a single beam or vibration that accompanies shear deformation of the car body cross section due to the vertical vibration force from the carriage during traveling. It has been known. Such elastic vibration of the vehicle body is perceived by passengers as being inferior in riding comfort, and is therefore required to be suppressed.

従来、弾性振動を抑制する技術として、制振対象となる振動体にばね要素及び減衰要素を介して質量を連結した動吸振器(ダイナミックダンパ)を用いることが知られている。
例えば、非特許文献1には、鉄道車両の床下機器をばねで吊り、チューニングを行うことによりダイナミックダンパとして作用させることが記載されている。
また、特許文献1には、走行中の鉄道車両に生じる曲げ振動を抑制する動吸振器として、鉄道車両の長手方向の中央部を含み、鉄道車両の床上又は床よりも上方の位置に、所定の質量を有するおもりを弾性体を介して取り付けることが記載されている。
Conventionally, as a technique for suppressing elastic vibration, it is known to use a dynamic vibration absorber (dynamic damper) in which a mass is connected to a vibration body to be controlled via a spring element and a damping element.
For example, Non-Patent Document 1 describes that an underfloor device of a railway vehicle is suspended by a spring and tuned to act as a dynamic damper.
Patent Document 1 discloses a dynamic vibration absorber that suppresses bending vibration generated in a running railway vehicle, including a central portion in the longitudinal direction of the railway vehicle, at a predetermined position on the floor of the railway vehicle or above the floor. It is described that a weight having a mass of 1 is attached via an elastic body.

「ダイナミックダンパによる車体曲げ振動の低減」石川龍太郎他著 日本機械学会第68期通常総会講演会講演論文集(Vol.C)1991年3月4日"Reducing body bending vibration by dynamic damper" Ryutaro Ishikawa et al. Proceedings of the 68th General Meeting of the Japan Society of Mechanical Engineers (Vol.C) March 4, 1991

特開2002−029420号公報JP 2002-029420 A

一般に、動吸振器の設計法として、2自由度系の定点理論が広く知られている。すなわち、動吸振器を取り付けた主系の応答曲線には2つの定点が存在することを利用し、応答曲線がその2つの定点で極大値をとり、かつ、その高さが等しくなるように設計する。あるいは、より簡便には、付加系の固有振動数が制振対象の固有振動数(ピーク振動数)と一致するように設定し、さらに減衰を調整して制振効果が最適となるようにする。いずれの場合も付加系の質量に応じてばね定数と減衰定数の細かい調整を必要とする。
しかし、鉄道車両の場合には、軌道高低不整などの入力が広範な周波数帯域に分布した特性を有し、また乗り心地に影響の大きい20Hz以下の周波数に限定してもその範囲に複数の固有振動数をもつ。このため、上述の定点理論に基づいて設計した同調型動吸振器によってピーク周波数近傍だけ周波数応答(FRF)の大きさが低下しても、それ以外の周波数で増大すると、結果として全体の振動低減にならない場合がある。また複数のモードが乗り心地に影響することがあるため、1つのモードだけを制振しても全体として乗り心地向上につながらないこともある。さらに、制振効果が最適となるように動吸振器の減衰を調整することは煩雑である。また、使用中に様々な原因で付加系の固有振動数や減衰が変化することが考えられるが、上述の動吸振器ではそれにより制振性能が大幅に悪化する。
上述した問題に鑑み、本発明の課題は、煩雑な調整を行うことなしに良好な振動抑制効果を得られる鉄道車両、及び、鉄道車両用車体の振動抑制方法を提供することである。
In general, a fixed point theory of a two-degree-of-freedom system is widely known as a design method for a dynamic vibration absorber. In other words, utilizing the fact that there are two fixed points in the response curve of the main system to which a dynamic vibration absorber is attached, the response curves are designed to have maximum values at the two fixed points and to have the same height. To do. Or, more simply, it is set so that the natural frequency of the additional system matches the natural frequency (peak frequency) of the damping target, and the damping is adjusted to optimize the damping effect. . In either case, fine adjustment of the spring constant and damping constant is required according to the mass of the additional system.
However, in the case of a railway vehicle, the input such as track height irregularities has characteristics distributed over a wide frequency band, and even if it is limited to a frequency of 20 Hz or less, which has a great influence on the ride comfort, there are a plurality of inherent characteristics within that range. Has a frequency. For this reason, even if the magnitude of the frequency response (FRF) is reduced only in the vicinity of the peak frequency by the tuned dynamic vibration absorber designed based on the above fixed point theory, if the frequency response is increased at other frequencies, the overall vibration is reduced. It may not be. In addition, since a plurality of modes may affect the ride comfort, even if only one mode is controlled, the overall ride comfort may not be improved. Furthermore, it is complicated to adjust the attenuation of the dynamic vibration absorber so that the vibration damping effect is optimized. Further, it is conceivable that the natural frequency and damping of the additional system change due to various causes during use. However, in the above-described dynamic vibration absorber, the vibration damping performance is greatly deteriorated.
In view of the above-described problems, an object of the present invention is to provide a railway vehicle and a vibration suppression method for a railway vehicle body that can obtain a good vibration suppression effect without complicated adjustment.

上述した課題を解決するため、本発明の鉄道車両は、車体と、前記車体に対してばね要素及び減衰要素を介して取り付けられ、前記車体に対して相対振動する質量体とを備える鉄道車両であって、前記質量体の固有振動数を前記車体の弾性振動における固有振動数に対して低くするとともに、前記質量体の減衰能を前記車体の弾性振動における減衰能に対して大きく設定したことを特徴とする。   In order to solve the above-described problems, a railway vehicle according to the present invention is a railway vehicle that includes a vehicle body and a mass body that is attached to the vehicle body via a spring element and a damping element and that vibrates relative to the vehicle body. The natural frequency of the mass body is set lower than the natural frequency of the elastic vibration of the vehicle body, and the damping capacity of the mass body is set to be larger than the damping capacity of the elastic vibration of the vehicle body. Features.

上述したように、通常の動吸振器の設計手法においては、周波数応答特性におけるピーク高さを低くすることはできるが、その両側に新たなピークが形成されて乗り心地が悪化するなど、鉄道車両への適用を考慮した場合には必ずしも最適な結果を得ることはできない場合があった。
また、付加系の固有振動数を制振対象の固有振動数と一致させた動吸振器においては、付加系の支持剛性や減衰特性によって制振効果が大きく変化するため、制振対象の特性に応じた剛性や減衰能の調整が必要であり、設計や製作が煩雑である。
これに対し、本発明によれば、付加系を構成する質量体の固有振動数を車体の弾性振動における固有振動数に対して低く設定するとともに、その減衰能(減衰比)を車体の弾性振動における減衰能(減衰比)に対して大きく設定したことによって、固有振動数以外の振動に対しても良好な制振効果を発揮することができ、さらに付加系の剛性や減衰能を厳密に調整しなくても最適な場合と大差ない制振効果を確保することができる。
As described above, in the usual dynamic vibration absorber design method, the peak height in the frequency response characteristics can be lowered, but a new peak is formed on both sides of the railway vehicle so that the ride comfort deteriorates. In some cases, it was not always possible to obtain optimum results when considering the application to the above.
In addition, in a dynamic vibration absorber with the natural frequency of the additional system matched to the natural frequency of the vibration suppression target, the vibration suppression effect varies greatly depending on the support rigidity and damping characteristics of the additional system. It is necessary to adjust the rigidity and damping capacity accordingly, and the design and production are complicated.
On the other hand, according to the present invention, the natural frequency of the mass body constituting the additional system is set lower than the natural frequency in the elastic vibration of the vehicle body, and the damping capacity (damping ratio) is set to the elastic vibration of the vehicle body. By setting a large value for the damping capacity (damping ratio), it is possible to achieve a good damping effect even for vibrations other than the natural frequency, and to adjust the rigidity and damping capacity of the additional system strictly. Even if it is not necessary, it is possible to ensure the vibration control effect which is not much different from the optimum case.

本発明において、複数の前記質量体を分散させて前記車体に取り付けた構成とすることができる。
これによれば、複数の振動モードを効果的に制振することができ、鉄道車両の乗り心地をより改善することができる。
In the present invention, a plurality of mass bodies can be dispersed and attached to the vehicle body.
According to this, a plurality of vibration modes can be effectively suppressed, and the riding comfort of the railway vehicle can be further improved.

また、本発明において、前記質量体は、前記車体の床下に吊り下げられる機器である構成とすることができる。
これによれば、動吸振器として専用の重りを追加する従来技術のように車両の重量を増加させることがなく、既存の機器の支持部におけるばね特性及び減衰特性を調節することによって本発明の制振効果を得ることができる。
Moreover, in this invention, the said mass body can be set as the structure which is an apparatus suspended under the floor of the said vehicle body.
According to this, the weight of the vehicle is not increased as in the prior art in which a dedicated weight is added as a dynamic vibration absorber, and the spring characteristics and the damping characteristics of the support portion of the existing equipment are adjusted by adjusting the spring characteristics and the damping characteristics of the present invention. A vibration control effect can be obtained.

また、本発明の鉄道車両用車体の振動抑制方法は、車体に対して相対振動可能な質量体をばね要素及び減衰要素を介して取り付けるとともに、前記質量体の固有振動数を前記車体の弾性振動における固有振動数に対して低くしかつ前記質量体の減衰能を前記車体の弾性振動における減衰能に対して大きく設定したことを特徴とする。
本発明において、複数の前記質量体を分散させて前記車体に取り付ける構成とすることができる。
また、本発明において、前記質量体は、前記車体の床下に吊り下げられる機器である構成とすることができる。
In addition, the method for suppressing vibration of a vehicle body for a railway vehicle according to the present invention attaches a mass body capable of relative vibration to the vehicle body via a spring element and a damping element, and sets the natural frequency of the mass body to elastic vibration of the vehicle body. And the damping capacity of the mass body is set to be larger than the damping capacity of the elastic vibration of the vehicle body.
In the present invention, a plurality of mass bodies can be dispersed and attached to the vehicle body.
Moreover, in this invention, the said mass body can be set as the structure which is an apparatus suspended under the floor of the said vehicle body.

以上のように、本発明によれば、煩雑な調整を行うことなしに良好な振動抑制効果を得られる鉄道車両、及び、鉄道車両用車体の振動抑制方法を提供することができる。   As described above, according to the present invention, it is possible to provide a railway vehicle and a vibration suppression method for a railway vehicle body that can obtain a good vibration suppression effect without complicated adjustments.

主系及び付加系をそれぞればねと粘性減衰で支持された単純質点とした場合のモデル図である。It is a model figure at the time of making a main system and an additional system into a simple mass point supported by a spring and viscous damping, respectively. 図1のモデルにおける質量比0.06、主系減衰比0.03、付加系と主系の固有振動数比0.6の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.06, the main system damping ratio is 0.03, and the natural frequency ratio of the additional system and the main system is 0.6 in the model of FIG. 図1のモデルにおける質量比0.06、主系減衰比0.03、付加系と主系の固有振動数比0.8の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.06, the main system damping ratio is 0.03, and the natural frequency ratio between the additional system and the main system is 0.8 in the model of FIG. 図1のモデルにおける質量比0.06、主系減衰比0.03、付加系と主系の固有振動数比1.0の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.06, the main system damping ratio is 0.03, and the natural frequency ratio of the additional system and the main system is 1.0 in the model of FIG. 図1のモデルにおける質量比0.06、主系減衰比0.03、付加系と主系の固有振動数比1.2の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.06, the main system damping ratio is 0.03, and the natural frequency ratio of the additional system and the main system is 1.2 in the model of FIG. 図1のモデルにおける質量比0.20、主系減衰比0.03、付加系と主系の固有振動数比0.6の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.20, the main system damping ratio is 0.03, and the natural frequency ratio between the additional system and the main system is 0.6 in the model of FIG. 図1のモデルにおける質量比0.20、主系減衰比0.03、付加系と主系の固有振動数比0.8の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.20, the main system damping ratio is 0.03, and the natural frequency ratio between the additional system and the main system is 0.8 in the model of FIG. 図1のモデルにおける質量比0.20、主系減衰比0.03、付加系と主系の固有振動数比1.0の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.20, the main system damping ratio is 0.03, and the natural frequency ratio of the additional system and the main system is 1.0 in the model of FIG. 図1のモデルにおける質量比0.20、主系減衰比0.03、付加系と主系の固有振動数比1.2の場合の周波数応答を示すグラフである。2 is a graph showing a frequency response when the mass ratio is 0.20, the main system damping ratio is 0.03, and the natural frequency ratio of the additional system and the main system is 1.2 in the model of FIG. 図1のモデルにおける主系の固有振動数に対する付加系の固有振動数、及び、主系の減衰比に対する付加系の減衰比をパラメータとした場合における周波数応答関数の面積比を示すコンター図であって、質量比0.06、主系減衰比0.03の場合のデータを示すものである。FIG. 2 is a contour diagram showing an area ratio of a frequency response function when the natural frequency of the additional system with respect to the natural frequency of the main system and the damping ratio of the additional system with respect to the damping ratio of the main system are used as parameters in the model of FIG. The data for a mass ratio of 0.06 and a main system damping ratio of 0.03 are shown. 図1のモデルにおける主系の固有振動数に対する付加系の固有振動数、及び、主系の減衰比に対する付加系の減衰比をパラメータとした場合における周波数応答関数の面積比を示すコンター図であって、質量比0.20、主系減衰比0.03の場合のデータを示すものである。FIG. 2 is a contour diagram showing an area ratio of a frequency response function when the natural frequency of the additional system with respect to the natural frequency of the main system and the damping ratio of the additional system with respect to the damping ratio of the main system are used as parameters in the model of FIG. The data for a mass ratio of 0.20 and a main system damping ratio of 0.03 are shown. 2軸の1位台車、2位台車を有するボギー車である鉄道車両の車両振動解析モデルを示す図である。It is a figure which shows the vehicle vibration analysis model of the railway vehicle which is a bogie car which has a 2-axis 1st trolley | bogie and a 2nd trolley | bogie. 図12のモデルにおける輪軸加振時の車体中央における加速度の周波数応答を示すグラフである。13 is a graph showing the frequency response of acceleration at the center of the vehicle body when the wheel shaft is vibrated in the model of FIG. 図12のモデルにおける輪軸加振時の台車直上における加速度の周波数応答を示すグラフである。It is a graph which shows the frequency response of the acceleration directly on the trolley | bogie at the time of wheel-axis vibration in the model of FIG.

以下、本発明を適用した鉄道車両、及び、鉄道車両用車体の弾性振動抑制方法について説明する。
先ず、本発明の発明者が行った動吸振器の基本特性に関する検討について説明する。
検討に用いた動吸振器のモデル図を図1に示す。
図1に示すように、このモデルは、制振対象となる主系、及び、動吸振器として機能する付加系からなる。主系は、質量mの質量体を、ばね定数kのばね要素、及び、減衰係数cの減衰要素によって支持したものである。付加系は、この主系に質量mの質量体を、ばね定数kのばね要素、及び、減衰係数cの減衰要素を介して取り付けたものである。
Hereinafter, a railway vehicle to which the present invention is applied and an elastic vibration suppressing method for a railway vehicle body will be described.
First, the study on the basic characteristics of the dynamic vibration absorber performed by the inventor of the present invention will be described.
A model diagram of the dynamic vibration absorber used for the study is shown in FIG.
As shown in FIG. 1, this model is composed of a main system to be controlled and an additional system that functions as a dynamic vibration absorber. The main system is a mass body having a mass m 0 supported by a spring element having a spring constant k 0 and a damping element having a damping coefficient c 0 . The additional system is obtained by attaching a mass body having a mass m 1 to the main system via a spring element having a spring constant k 1 and a damping element having a damping coefficient c 1 .

図2から図9は、図1のモデルを用いて主系に力加振を与え、主系の質量mで付加系の質量mを除した質量比(m/m)、主系の固有振動数で付加系の固有振動数を除した振動数比kf、及び、主系の減衰比で付加系の減衰比を除した減衰能比kzをパラメータとして変化させた場合における無次元振動数に対する周波数応答関数(FRF)ゲインを示すグラフである。
各図において、横軸は主系の固有振動数で正規化した無次元振動数を示し、縦軸は主系の応答倍率(FRFゲイン)を示している。この応答倍率とは、主系の変位Xを主系単体の静変位Xst=F/kで除したものである。ここで、Fは主系に作用する加振力である。
2 to 9 show a mass ratio (m 1 / m 0 ) obtained by applying force excitation to the main system using the model of FIG. 1, and dividing the mass m 1 of the additional system by the mass m 0 of the main system, Dimensionless when the frequency ratio kf obtained by dividing the natural frequency of the additional system by the natural frequency of the system and the damping capacity ratio kz obtained by dividing the damping ratio of the additional system by the damping ratio of the main system are changed as parameters. It is a graph which shows the frequency response function (FRF) gain with respect to a frequency.
In each figure, the horizontal axis indicates the dimensionless frequency normalized by the natural frequency of the main system, and the vertical axis indicates the response magnification (FRF gain) of the main system. The response magnification is obtained by dividing the displacement X of the main system by the static displacement Xst = F / k 0 of the main system alone. Here, F is an excitation force acting on the main system.

図2から図9の各図においては、付加系なしの場合、減衰能比kzが1,2,4,8,10の場合の周波数応答をそれぞれ異なった線種により図示している。
図2から図5は、主系に対する付加系の質量比が0.06、主系の減衰比が0.03である場合を示しており、それぞれ付加系の固有振動数の主系の固有振動数に対する振動数比kfを0.6,0.8,1.0,1.2とした場合のFRFゲインを示している。
図6から図9は、主系に対する付加系の質量比が0.20、主系の減衰比が0.03である場合を示しており、それぞれ付加系の固有振動数の主系の固有振動数に対する振動数比kfを0.6,0.8,1.0,1.2とした場合のFRFゲインを示している。
In each of FIGS. 2 to 9, the frequency response when the damping capacity ratio kz is 1, 2, 4, 8, and 10 when there is no additional system is shown by different line types.
2 to 5 show cases where the mass ratio of the additional system to the main system is 0.06 and the damping ratio of the main system is 0.03, and the natural frequency of the main system has the natural frequency of the additional system. The FRF gain when the frequency ratio kf to the number is 0.6, 0.8, 1.0, 1.2 is shown.
6 to 9 show cases where the mass ratio of the additional system to the main system is 0.20 and the damping ratio of the main system is 0.03. The FRF gain when the frequency ratio kf to the number is 0.6, 0.8, 1.0, 1.2 is shown.

図4及び図8に示すように、付加系の固有振動数を主系の固有振動数と一致させた場合(振動数比=1)の場合には、主系の固有振動数(無次元振動数=1)におけるピーク高さは低くなるが、その両側に振動が増幅される周波数領域があることがわかる。
また、制振効果の付加系の減衰比に対する依存度が大きく、減衰比が最適値から乖離すると振動低減効果は悪化するため、減衰の調整を行うことが必要となる。
また、図5及び図8に示すように、付加系の固有振動数を主系の固有振動数に対して高くした場合にも、振動低減効果が悪化する場合が見られる。
As shown in FIGS. 4 and 8, when the natural frequency of the additional system is matched with the natural frequency of the main system (frequency ratio = 1), the natural frequency of the main system (non-dimensional vibration) It can be seen that the peak height in number = 1) is low, but there are frequency regions on both sides of which the vibration is amplified.
In addition, since the dependence of the damping effect on the damping ratio of the additional system is large, and the damping ratio deviates from the optimum value, the vibration reducing effect is deteriorated, so that it is necessary to adjust the damping.
Further, as shown in FIGS. 5 and 8, even when the natural frequency of the additional system is made higher than the natural frequency of the main system, the vibration reduction effect may be deteriorated.

これに対し、付加系の固有振動数を主系の固有振動数に対して低くした場合、とりわけ図2、図6に示すように、振動数比kfを0.6程度まで小さくした場合には、主系の固有振動数を含む広範な周波数帯域において制振効果を発揮することができ、ピーク周波数の両側に新たなピークが形成されるといった弊害もほとんど生じないことがわかる。また、この場合には、付加系の剛性や減衰比を変化させた場合であっても制振効果に及ぼす影響が軽微であることから、厳密な剛性や減衰比の調整が必要ないことがわかる。   On the other hand, when the natural frequency of the additional system is made lower than the natural frequency of the main system, especially when the frequency ratio kf is reduced to about 0.6, as shown in FIGS. It can be seen that the damping effect can be exerted in a wide frequency band including the natural frequency of the main system, and there is almost no adverse effect such that new peaks are formed on both sides of the peak frequency. In this case, even when the rigidity and damping ratio of the additional system are changed, the influence on the vibration damping effect is negligible, so that it is not necessary to adjust the rigidity and damping ratio strictly. .

図10及び図11は、図1のモデルにおける付加系非適用時のFRFゲイン線図面積に対する付加系適用時のFRFゲイン線図面積の面積比を示すコンター図である。この面積を算出する根拠となる面積は、図2乃至図9における無次元振動数が0から3までの範囲における面積である。
図10及び図11において、横軸は主系の固有振動数に対する付加系の固有振動数の比である振動数比kfを示し、縦軸は主系の減衰比に対する付加系の減衰比の比である減衰能比kzを示している。また、図10は主系の質量に対する付加系の質量の比である質量比が0.06の場合を示し、図11は質量比が0.20の場合を示している。
10 and 11 are contour diagrams showing the area ratio of the FRF gain diagram area when the additional system is applied to the FRF gain diagram area when the additional system is not applied in the model of FIG. The area that is the basis for calculating this area is the area in the range from 0 to 3 in the dimensionless frequency in FIGS.
10 and 11, the horizontal axis represents the frequency ratio kf, which is the ratio of the natural frequency of the additional system to the natural frequency of the main system, and the vertical axis represents the ratio of the damping ratio of the additional system to the damping ratio of the main system. The damping capacity ratio kz is shown. FIG. 10 shows the case where the mass ratio, which is the ratio of the mass of the additional system to the mass of the main system, is 0.06, and FIG. 11 shows the case where the mass ratio is 0.20.

図10及び図11のいずれにおいても、主系の固有振動数よりも付加系の固有振動数を低くしたほうが、面積比が所定値以下(例えば0.85以下、0.9以下等)となる範囲が広いことがわかる。
さらに、図10及び図11のいずれにおいても、付加系の減衰比を大きくしたほうが、面積比が所定値以下の範囲が広いことがわかる。
これらのことから、広い振動数範囲にわたって良好な制振効果を得るためには、制振対象よりも低い固有振動数をもつ高減衰能の振動体を動吸振器として付加することが有効であることがわかる。
10 and 11, the area ratio is less than a predetermined value (for example, 0.85 or less, 0.9 or less, etc.) when the natural frequency of the additional system is set lower than the natural frequency of the main system. It can be seen that the range is wide.
Further, in both FIG. 10 and FIG. 11, it can be seen that the area ratio is wider than the predetermined value when the attenuation ratio of the additional system is increased.
Therefore, in order to obtain a good damping effect over a wide frequency range, it is effective to add a vibration body with a high damping capacity having a natural frequency lower than that of the object to be damped as a dynamic vibration absorber. I understand that.

次に、制振対象に対して固有振動数が低く高減衰能である付加系(動吸振器)の鉄道車両への適用について説明する。
図12は、2軸の1位台車、2位台車を有するボギー車である鉄道車両の車両振動解析モデルを示す図である。
図12に示すように、このモデルにおける鉄道車両1は、車体10、1位台車20、2位台車30等を備えて構成されている。
Next, application of an additional system (dynamic vibration absorber) having a low natural frequency and a high damping capacity to a vibration suppression target will be described.
FIG. 12 is a diagram showing a vehicle vibration analysis model of a railway vehicle that is a bogie car having a two-axis first-position carriage and a second-position carriage.
As shown in FIG. 12, the railway vehicle 1 in this model includes a vehicle body 10, a first cart 20, a second cart 30, and the like.

車体10は、上下方向(図のy軸方向)の弾性変形および上下・前後方向の剛体変位を考慮した長さLの一様なはりとしてモデル化されている。
1位台車20及び2位台車30は、車両1の進行方向に沿って配置された2軸の台車である。
1位台車20は、台車枠21、第1輪軸22、第2輪軸23等を備えて構成されている。
The vehicle body 10 is modeled as a uniform beam having a length L in consideration of elastic deformation in the vertical direction (y-axis direction in the drawing) and rigid body displacement in the vertical and front-rear directions.
The first and second carts 20 and 30 are two-axis carts arranged along the traveling direction of the vehicle 1.
The first cart 20 includes a cart frame 21, a first wheel shaft 22, a second wheel shaft 23, and the like.

台車枠21は、第1輪軸22及び第2輪軸23が軸箱支持装置を介して取り付けられる枠状の構造体である。
第1輪軸22及び第2輪軸23は、車軸の両端部に車輪を固定したものであって、進行方向前方側から順次配列されている。第1輪軸22及び第2輪軸23の両端部には、軸受及び潤滑装置等を有する軸箱が設けられている。
The bogie frame 21 is a frame-like structure to which the first wheel shaft 22 and the second wheel shaft 23 are attached via a shaft box support device.
The first wheel shaft 22 and the second wheel shaft 23 have wheels fixed to both ends of the axle, and are sequentially arranged from the front side in the traveling direction. At both ends of the first wheel shaft 22 and the second wheel shaft 23, shaft boxes having bearings, a lubricating device, and the like are provided.

第1輪軸22の軸箱と台車枠21との間、及び、第2輪軸23の軸箱と台車枠21との間には、軸ばね24及び軸ダンパ25からなる1次ばね系が設けられている。
軸ばね24は、第1輪軸22及び第2輪軸23の台車枠21に対する上下方向(軌道面と直交方向)の相対変位に応じてばね反力を発生する。
軸ダンパ25は、 第1輪軸22及び第2輪軸23の台車枠21に対する上下方向の相対速度に応じて減衰力を発生する。
A primary spring system including a shaft spring 24 and a shaft damper 25 is provided between the axle box of the first wheel shaft 22 and the carriage frame 21 and between the axle box of the second wheel shaft 23 and the carriage frame 21. ing.
The shaft spring 24 generates a spring reaction force according to the relative displacement of the first wheel shaft 22 and the second wheel shaft 23 in the vertical direction (direction orthogonal to the raceway surface) with respect to the carriage frame 21.
The shaft damper 25 generates a damping force according to the vertical relative speed of the first wheel shaft 22 and the second wheel shaft 23 with respect to the carriage frame 21.

台車枠21と車体10の床構との間には、2次ばね系を構成する枕ばねである空気ばね26が設けられている。
空気ばね26は、台車枠21の車体10に対する上下方向の相対変位に応じてばね反力を発生する。また、空気ばね26は、台車枠21の車体10に対する上下方向の相対速度に応じて減衰力を発生する。このため、空気ばね26は、図12に示すモデルにおいては、並列に配置されたばね要素及び減衰要素として表現することができる。
An air spring 26 that is a pillow spring constituting a secondary spring system is provided between the carriage frame 21 and the floor structure of the vehicle body 10.
The air spring 26 generates a spring reaction force according to the relative displacement of the carriage frame 21 relative to the vehicle body 10 in the vertical direction. The air spring 26 generates a damping force according to the relative speed in the vertical direction of the carriage frame 21 with respect to the vehicle body 10. Therefore, the air spring 26 can be expressed as a spring element and a damping element arranged in parallel in the model shown in FIG.

さらに、台車枠21と車体10との間には、牽引装置27及びヨーダンパ28が設けられている。
牽引装置27は、台車枠21と車体10との間で前後力を伝達するリンク装置を備え、このリンクの両端部には、防振のため所定の粘弾性特性を有する緩衝ゴムが設けられている。
ヨーダンパ28は、実車においては、車体10に対する台車枠21のヨーイング(鉛直軸回りの揺動)を抑制するものである。本車両モデルでは台車と車体のヨーイングは考慮していないため、車体と台車の前後方向の相対速度に応じた減衰力を発生するものとしてモデル化している。また、ヨーダンパ28の両端部には、防振のため所定の粘弾性特性を有する緩衝ゴムが設けられている。
Further, a traction device 27 and a yaw damper 28 are provided between the carriage frame 21 and the vehicle body 10.
The traction device 27 includes a link device that transmits a longitudinal force between the carriage frame 21 and the vehicle body 10, and buffer rubber having a predetermined viscoelastic property is provided at both ends of the link for vibration isolation. Yes.
In an actual vehicle, the yaw damper 28 suppresses yawing (oscillation around the vertical axis) of the carriage frame 21 with respect to the vehicle body 10. Since this vehicle model does not consider yawing of the bogie and the vehicle body, it is modeled as generating a damping force according to the relative speed of the vehicle body and the bogie in the longitudinal direction. Further, buffer rubber having predetermined viscoelastic characteristics is provided at both ends of the yaw damper 28 for vibration isolation.

2位台車30は、1位台車20に対して進行方向後方側に配置されている。
2位台車30は、1位台車20の台車枠21、第1輪軸22、第3輪軸23、軸ばね24、軸ダンパ25、空気ばね26、牽引装置27、ヨーダンパ28と実質的に同様の台車枠31、第3輪軸32、第4輪軸33、軸ばね34、軸ダンパ35、空気ばね36、牽引装置37、ヨーダンパ38等を備えて構成されている。
The second cart 30 is arranged on the rear side in the traveling direction with respect to the first cart 20.
The second carriage 30 is substantially the same as the carriage frame 21, first wheel shaft 22, third wheel shaft 23, shaft spring 24, shaft damper 25, air spring 26, traction device 27, and yaw damper 28 of the first truck 20. A frame 31, a third wheel shaft 32, a fourth wheel shaft 33, a shaft spring 34, a shaft damper 35, an air spring 36, a traction device 37, a yaw damper 38, and the like are provided.

また、図12における符号の意味は以下の通りである。
〜z:第1輪軸〜第4輪軸への加振入力(軌道上下不整)
w1〜uw4:第1輪軸〜第4輪軸の軌道方向(進行方向)応答変位
t1,ut2:1位台車の台車枠、2位台車の台車枠の軌道方向応答変位
t1,wt2:1位台車の台車枠、2位台車の台車枠の上下方向応答変位
θt1,θt2:1位台車の台車枠、2位台車の台車枠のピッチング角度
:車体の軌道方向応答変位
(x,t):車体のx軸(軌道方向)上の所定の位置における時相tにおける上下方向応答変位
Moreover, the meanings of the symbols in FIG. 12 are as follows.
z 1 to z 4 : Excitation input to the first wheel shaft to the fourth wheel shaft (trajectory up and down irregularity)
u w1 to u w4 : Track direction (traveling direction) response displacement of the first wheel shaft to the fourth wheel shaft u t1 , u t2 : Track frame response displacement of the bogie frame of the first cart and the cart frame of the second cart w t1 , w t2: bogie frame 1 of the bogie, the vertical displacement response theta t1 of the bogie frame 2 of the bogie, theta t2: bogie frame 1 of the bogie, the pitching angle of the bogie frame 2 of the bogie u c: vehicle track direction response Displacement w c (x, t): vertical response displacement at time phase t at a predetermined position on the x-axis (trajectory direction) of the vehicle body

図13及び図14は、図12のモデルにおいて、全輪軸に同時に同じ大きさの変位加振(4軸同相加振)を与えたときの加振変位に対する車体加速度の周波数応答を示すグラフである。図13は車体中央のデータを示し、図14は台車直上のデータを示している。図13及び図14において、横軸は周波数を示し、縦軸は周波数応答関数ゲインを示している。
なお、このような4軸同相加振は、実際の走行とは異なるが、車体曲げ振動のピークが明確になるため採用した。
ここで、車体10の質量は25.4トン、図12に示すような1次の曲げ振動の固有振動数は10Hzとした。
FIGS. 13 and 14 are graphs showing the frequency response of the vehicle body acceleration to the vibration displacement when the displacement vibration of the same magnitude (4-axis in-phase vibration) is simultaneously applied to all the wheel shafts in the model of FIG. is there. FIG. 13 shows data at the center of the vehicle body, and FIG. 14 shows data immediately above the carriage. 13 and 14, the horizontal axis indicates the frequency, and the vertical axis indicates the frequency response function gain.
Such 4-axis in-phase excitation is different from the actual running, but was adopted because the peak of the vehicle body bending vibration becomes clear.
Here, the mass of the vehicle body 10 was 25.4 tons, and the natural frequency of the primary bending vibration as shown in FIG. 12 was 10 Hz.

また、図13及び図14において、各線種はそれぞれ以下のデータを表している。
実線 :付加質量なし
点線 :付加質量の固有振動数10Hz、減衰比0.3
一点鎖線:付加質量の固有振動数10Hz、減衰比0.5
二点鎖線:付加質量の固有振動数6Hz、減衰比0.3
三点鎖線:付加質量の固有振動数6Hz、減衰比0.5
なお、付加質量はいずれも車体中央部の床構下面部にばね要素及び粘性減衰要素を介して支持された900kgのものである。
このような付加質量として、鉄道車両の運行に必要な各種機器等を用いることができる。これによれば、動吸振器を構成するために新たな重りを搭載する必要がなく、車両の重量を増加させることなく制振効果を得ることができる。
このような機器として、例えば、各種制御機器、電気機器、空圧機器、油圧機器、空調装置、その他の機器を用いることができる。
Moreover, in FIG.13 and FIG.14, each line type represents the following data, respectively.
Solid line: No additional mass Dotted line: Natural frequency of additional mass 10 Hz, damping ratio 0.3
Dash-dot line: natural frequency of additional mass 10 Hz, damping ratio 0.5
Two-dot chain line: natural mass of added mass 6 Hz, damping ratio 0.3
Three-dot chain line: natural mass of added mass 6 Hz, damping ratio 0.5
The additional mass is 900 kg supported on the bottom surface of the floor structure at the center of the vehicle body via a spring element and a viscous damping element.
As such additional mass, various devices necessary for the operation of the railway vehicle can be used. According to this, it is not necessary to mount a new weight to configure the dynamic vibration absorber, and a vibration damping effect can be obtained without increasing the weight of the vehicle.
As such devices, for example, various control devices, electrical devices, pneumatic devices, hydraulic devices, air conditioners, and other devices can be used.

図13及び図14を見ると、一般的な動吸振器の設計で行われるように、付加質量の固有振動数を制振対象ピークと同調する10Hzに設定した場合(点線及び一点鎖線)には、ピーク高さの低減量は大きいが、付加質量を取り付けない場合に比べ、ピーク周波数の両側に振動増大する周波数領域がある。また、振動低減量が最大となる減衰比が存在し、減衰比がその値と異なると振動低減効果は悪化するため、減衰の調整が必要となる。
例えば、図13及び図14の例においては、0.2〜0.3の間に最適な減衰比が存在し、減衰比0.3(点線)に比べて減衰比0.5(一点鎖線)のピーク高さが増大している。
また、図13及び図14では図示していないが、0.2よりも小さい減衰比の場合には、制振対象ピークである10Hzの両側に2つのピークが生じ、減衰比が小さくなるほどそのピークが高くなるため、やはり振動低減効果は小さくなる。
As shown in FIGS. 13 and 14, when the natural frequency of the additional mass is set to 10 Hz that synchronizes with the vibration control target peak (dotted line and alternate long and short dash line), as in the design of a general dynamic vibration absorber. Although the reduction amount of the peak height is large, there is a frequency region in which vibration increases on both sides of the peak frequency as compared with the case where no additional mass is attached. In addition, there is a damping ratio that maximizes the amount of vibration reduction, and if the damping ratio is different from the value, the vibration reduction effect is deteriorated, so that it is necessary to adjust the damping.
For example, in the example of FIG. 13 and FIG. 14, there is an optimum attenuation ratio between 0.2 and 0.3, and the attenuation ratio is 0.5 (dashed line) compared to the attenuation ratio of 0.3 (dotted line). The peak height has increased.
Although not shown in FIGS. 13 and 14, in the case of an attenuation ratio smaller than 0.2, two peaks are generated on both sides of 10 Hz that is a vibration target peak, and the peak decreases as the attenuation ratio decreases. Therefore, the vibration reduction effect is also reduced.

これに対し、付加質量の固有振動数を制振対象ピーク周波数(10Hz)に対して小さい6Hzに設定した場合(二点鎖線及び三点鎖線:本発明の実施形態)には、減衰比を大きくするとピーク高さは低下するが、ピーク周波数の両側の周波数領域に目立った振動増大は見られない。また、図13及び図14では図示していないが、減衰比が0.7程度までの範囲では、減衰比の増大とともにピーク高さはほぼ単調に低下し、減衰比が0.4程度ではピーク高さの変化は小さくなる。したがってある程度(例えば0.4以上など)減衰比を大きくしておけば、特に減衰比を調整しなくても最適な場合と大差ない振動低減効果が期待できる。   On the other hand, when the natural frequency of the additional mass is set to 6 Hz which is smaller than the peak frequency to be controlled (10 Hz) (two-dot chain line and three-dot chain line: embodiments of the present invention), the damping ratio is increased. As a result, the peak height decreases, but no noticeable increase in vibration is observed in the frequency regions on both sides of the peak frequency. Although not shown in FIGS. 13 and 14, in the range up to about 0.7, the peak height decreases almost monotonously with the increase of the attenuation ratio, and peaks when the attenuation ratio is about 0.4. The change in height is small. Therefore, if the damping ratio is increased to some extent (for example, 0.4 or more), a vibration reduction effect that is not much different from the optimum case can be expected without adjusting the damping ratio.

鉄道車両の走行時に対応する加振条件では、例えば軌道高低不整などの入力が周波数特性を持つため、ピーク周波数の近傍だけ周波数応答関数ゲインが低下しても、それ以外の周波数で増大すると、結果として全体としての振動低減にならず、乗り心地が悪化する場合がある。周波数応答関数のゲインは入力に対する車体の応答しやすさを表すが、特に新幹線においては10から20Hzの周波数領域において軌道からの入力が大きくなる場合があるため、その周波数領域における振動の増大は好ましくない。
この点、本発明のように制振対象である車体に対して固有振動数が低くかつ高減衰の付加系を用いると、制振対象ピーク付近の狭い周波数領域における制振効果は通常の同調型動吸振器より劣るものの、広い周波数帯域にわたって良好な制振効果を発揮し、全体としての振動低減効果を向上することができる。
また、付加系にある程度以上の減衰比を持たせておけば、特に剛性や減衰を調整しなくても最適な場合と大差のない制振効果を得ることができる。
In the excitation condition corresponding to the running of the railway vehicle, for example, the input such as the irregularity of the track height has frequency characteristics, so even if the frequency response function gain decreases only in the vicinity of the peak frequency, it will increase at other frequencies. As a result, vibration as a whole may not be reduced, and riding comfort may deteriorate. The gain of the frequency response function expresses the ease of response of the vehicle body to the input, but especially on the Shinkansen, the input from the track may be large in the frequency range of 10 to 20 Hz, and therefore an increase in vibration in that frequency range is preferable. Absent.
In this regard, when an additional system having a low natural frequency and high attenuation is used for a vehicle body to be controlled as in the present invention, the damping effect in a narrow frequency region near the peak to be controlled is a normal tuning type. Although inferior to a dynamic vibration absorber, a good vibration damping effect can be exhibited over a wide frequency band, and the vibration reduction effect as a whole can be improved.
Further, if the additional system has a damping ratio of a certain level or more, it is possible to obtain a damping effect which is not much different from the optimum case without particularly adjusting the rigidity and damping.

(他の実施形態)
なお、本発明は上記した実施形態のみに限定されるものではなく、種々の応用や変形が考えられる。
例えば、上述した実施形態においては、動吸振器として機能する付加系を、車体中央に一箇所のみ設けているが、複数の付加系を分散させて設けてもよい。これによれば、複数の振動モードの制振が可能となる。その場合も本発明によれば個々の付加系の剛性や減衰を特に調整せずに複数モードの制振効果を得ることができる。
また、付加系を取り付ける位置も床構下部に限定されず、床構上部や屋根構、側構、妻構などに取り付けてもよい。
(Other embodiments)
In addition, this invention is not limited only to above-described embodiment, Various application and deformation | transformation can be considered.
For example, in the embodiment described above, only one additional system that functions as a dynamic vibration absorber is provided at the center of the vehicle body, but a plurality of additional systems may be provided in a distributed manner. According to this, vibration control in a plurality of vibration modes is possible. Even in such a case, according to the present invention, it is possible to obtain a multi-mode damping effect without particularly adjusting the rigidity and damping of each additional system.
Further, the position where the additional system is attached is not limited to the lower part of the floor structure, and may be attached to the upper part of the floor structure, the roof structure, the side structure, the wife structure, or the like.

1 鉄道車両 10 車体
20 1位台車 21 台車枠
22 第1輪軸 23 第2輪軸
24 軸ばね 25 軸ダンパ
26 空気ばね 27 牽引装置
28 ヨーダンパ
30 2位台車 31 台車枠
32 第3輪軸 33 第4輪軸
34 軸ばね 35 軸ダンパ
36 空気ばね 37 牽引装置
38 ヨーダンパ
DESCRIPTION OF SYMBOLS 1 Railcar 10 Car body 20 1st place bogie 21 Bogie frame 22 1st wheel shaft 23 2nd wheel shaft 24 Shaft spring 25 Shaft damper 26 Air spring 27 Pulling device 28 Yaw damper 30 2nd bogie 31 Bogie frame 32 3rd wheel shaft 33 4th wheel shaft 34 Shaft spring 35 Shaft damper 36 Air spring 37 Traction device 38 Yaw damper

Claims (6)

車体と、
前記車体に対してばね要素及び減衰要素を介して取り付けられ、前記車体に対して相対振動する質量体と
を備える鉄道車両であって、
前記質量体の固有振動数を前記車体の弾性振動における固有振動数に対して低くするとともに、前記質量体の減衰能を前記車体の弾性振動における減衰能に対して大きく設定したこと
を特徴とする鉄道車両。
The car body,
A rail vehicle that is attached to the vehicle body via a spring element and a damping element and that vibrates relative to the vehicle body,
The natural frequency of the mass body is made lower than the natural frequency in the elastic vibration of the vehicle body, and the damping capacity of the mass body is set to be larger than the damping capacity in the elastic vibration of the vehicle body. Railway vehicle.
複数の前記質量体を分散させて前記車体に取り付けたこと
を特徴とする請求項1に記載の鉄道車両。
The railway vehicle according to claim 1, wherein a plurality of the mass bodies are dispersed and attached to the vehicle body.
前記質量体は、前記車体の床下に吊り下げられる機器であること
を特徴とする請求項1又は請求項2に記載の鉄道車両。
The railway vehicle according to claim 1 or 2, wherein the mass body is a device that is suspended under the floor of the vehicle body.
車体に対して相対振動可能な質量体をばね要素及び減衰要素を介して取り付けるとともに、前記質量体の固有振動数を前記車体の弾性振動における固有振動数に対して低くしかつ前記質量体の減衰能を前記車体の弾性振動における減衰能に対して大きく設定したこと
を特徴とする鉄道車両用車体の振動抑制方法。
A mass body capable of relative vibration with respect to the vehicle body is attached via a spring element and a damping element, the natural frequency of the mass body is made lower than the natural frequency in the elastic vibration of the vehicle body, and the mass body is attenuated. The vibration suppression method for a railway vehicle body is characterized in that the performance is set to be greater than the damping capacity in the elastic vibration of the vehicle body.
複数の前記質量体を分散させて前記車体に取り付けること
を特徴とする請求項4に記載の鉄道車両用車体の振動抑制方法。
The vibration suppression method for a railway vehicle body according to claim 4, wherein a plurality of mass bodies are dispersed and attached to the vehicle body.
前記質量体は、前記車体の床下に吊り下げられる機器であること
を特徴とする請求項4又は請求項5に記載の鉄道車両用車体の振動抑制方法。
The vibration suppression method for a railway vehicle body according to claim 4 or 5, wherein the mass body is a device that is suspended below the floor of the vehicle body.
JP2010072564A 2010-03-26 2010-03-26 Railroad vehicle, and method of suppressing vibration of vehicle body of the same Pending JP2011201476A (en)

Priority Applications (1)

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Application Number Priority Date Filing Date Title
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2017110747A (en) * 2015-12-17 2017-06-22 三菱自動車工業株式会社 Design method of vibration-proof structure

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH03204369A (en) * 1990-01-08 1991-09-05 Sumitomo Metal Ind Ltd Body bending vibration preventing device and installation method thereof
JPH09119477A (en) * 1995-10-27 1997-05-06 Kazuto Sedo Dynamic vibration absorber
JPH10147241A (en) * 1996-11-20 1998-06-02 Hitachi Ltd Body bending vibration reducer for rolling stock
JP2000142396A (en) * 1998-11-18 2000-05-23 Hitachi Ltd Rolling stock
JP2002029420A (en) * 2000-07-14 2002-01-29 Tokyu Car Corp Fitting method for dynamic vibration reducer and rolling stock
JP2004001686A (en) * 2002-03-29 2004-01-08 Railway Technical Res Inst Vibration reducing method for railroad vehicle, and the railroad vehicle
JP2006077812A (en) * 2004-09-07 2006-03-23 Tokkyokiki Corp Multiple dynamic vibration absorber designing method
JP2008180321A (en) * 2007-01-25 2008-08-07 Tokai Rubber Ind Ltd Fluid-sealed damping device

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH03204369A (en) * 1990-01-08 1991-09-05 Sumitomo Metal Ind Ltd Body bending vibration preventing device and installation method thereof
JPH09119477A (en) * 1995-10-27 1997-05-06 Kazuto Sedo Dynamic vibration absorber
JPH10147241A (en) * 1996-11-20 1998-06-02 Hitachi Ltd Body bending vibration reducer for rolling stock
JP2000142396A (en) * 1998-11-18 2000-05-23 Hitachi Ltd Rolling stock
JP2002029420A (en) * 2000-07-14 2002-01-29 Tokyu Car Corp Fitting method for dynamic vibration reducer and rolling stock
JP2004001686A (en) * 2002-03-29 2004-01-08 Railway Technical Res Inst Vibration reducing method for railroad vehicle, and the railroad vehicle
JP2006077812A (en) * 2004-09-07 2006-03-23 Tokkyokiki Corp Multiple dynamic vibration absorber designing method
JP2008180321A (en) * 2007-01-25 2008-08-07 Tokai Rubber Ind Ltd Fluid-sealed damping device

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2017110747A (en) * 2015-12-17 2017-06-22 三菱自動車工業株式会社 Design method of vibration-proof structure

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