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EP1523597B1 - Voie ferree a courbe de raccordement et a rampe de surhaussement a forces minimales - Google Patents

Voie ferree a courbe de raccordement et a rampe de surhaussement a forces minimales Download PDF

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Publication number
EP1523597B1
EP1523597B1 EP03765068A EP03765068A EP1523597B1 EP 1523597 B1 EP1523597 B1 EP 1523597B1 EP 03765068 A EP03765068 A EP 03765068A EP 03765068 A EP03765068 A EP 03765068A EP 1523597 B1 EP1523597 B1 EP 1523597B1
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Prior art keywords
track
function
superelevation
curvature
centre line
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Expired - Lifetime
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EP03765068A
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German (de)
English (en)
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EP1523597A1 (fr
Inventor
Herbert L. Hasslinger
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Osterreichische Bundesbahnen
Wiener Linien & Co KG GmbH
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Osterreichische Bundesbahnen
Wiener Linien & Co KG GmbH
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Priority to SI200331396T priority Critical patent/SI1523597T1/sl
Publication of EP1523597A1 publication Critical patent/EP1523597A1/fr
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    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01B—PERMANENT WAY; PERMANENT-WAY TOOLS; MACHINES FOR MAKING RAILWAYS OF ALL KINDS
    • E01B2/00—General structure of permanent way

Definitions

  • the invention relates to a track with transitional bow and krafteminimal Studentshöhungsrampe and on the track guidance of such a track.
  • the routing of the tracks of railways, subways and other track-guided vehicles is usually carried out as a succession of elements of constant curvature in plan, such as straight and circular arc, and elements with variable curvature.
  • the transition from a straight track to a straight track deviating from it at an angle is carried out either in two parts, that is to say with two adjoining vertex transition arcs, or the transition is made in three parts, to which a straight track is followed by a conventional transitional bend Connects circular arc, which is followed by another conventional transition arc, which then joins the second straight track.
  • a track distortion which is the excessive transition from one track to another, parallel track at a certain distance, is currently carried out either from two circular arcs or from a sequence of a transition arc, a circular arc, a turning transition arc, a circular arc and a transition arc.
  • the guide surface is rotated about the center line of the guide.
  • elevation In railroads, that angular travel, measured at the top of the arched rail relative to the top of the arched rail, about which the transverse direction of the track is twisted about the track centerline, is referred to as elevation. To set this elevation is usually prescribed a proportional to the curvature of the track center line elevation. This results in no elevation on straight stretches and for curved stretches an increasing with the curvature of the track centerline cant on the outside of the track.
  • the clothoid When traversing tracks, the most common element that has a variable curvature in plan is the clothoid. This is a curve in which the curvature changes linearly from one value to another.
  • the associated, proportional to the curvature elevation is a linearly changing elevation, the straight Studentshöhungsrampe. This results in kinks at the connection points to the neighboring elements with constant elevation. A unbalanced lateral acceleration is then obtained in the guide center line which changes linearly between the constant values in the neighboring elements.
  • the routing of the tracks should be such that the desired kinematic properties not along the guide center line, but for a particular vehicle point, such as the center of gravity of the vehicle to be respected.
  • a particular vehicle point such as the center of gravity of the vehicle to be respected.
  • the function outside the guide center line must be twice continuously differentiable.
  • From the AT 401 781 B is a track with a real surface strip with a steady curve of the curvature in the transition arc is known, in the routing of a fictitious surface strip is provided with a guideline along which a rated speed moving point has an unbalanced lateral acceleration of zero. From the guideline of the fictitious surface stripe, the guideline of the real surface stripe is created by shifting each individual guideline point along the stripe normal by a constant distance.
  • a track according to the preamble of claim 1 is known from DE-A-32 28553 known.
  • the first derivative (the angle) is minimal, and with it the track twist and the roll angular velocity, but all other derivatives are unlimited but at the edges.
  • the second derivatives In the case of the ramp composed of two square parabolas, the second derivatives have minimum values corresponding to the ramp curvature.
  • the roll angle accelerations are minimal in this embodiment, but the ramp is steeper in the middle and the other derivatives at the edges and in the middle do not exist and therefore not the roll angle. This is similar to the cubic polynomial and the cosine half wave.
  • the jerks at the edges also exist, but the first and second derivative show higher values than the other superelevation ramps.
  • the object of the invention is to avoid the above disadvantages and to provide a track that can be produced in reality and achieves a smooth course of the unbalanced lateral acceleration.
  • a further feature of the invention provides that the function can be differentiated at least four times in its entire course, including at the area borders, and also that the fourth derivatives of the function have finite values everywhere.
  • a further feature of the invention provides that in the determination of the curvature ( ⁇ H ) of the track center line in the floor plan, the route height zero is selected as the fixed route height.
  • Another feature of the invention provides that, as a normalized function, the function given below in equation (5) is used with a fifth-order polynomial in combination with only the sine, which normalizes Function is used for the course of the elevation angle and for the total, unbalanced lateral acceleration and from this the curvature ( ⁇ H ) of the track center line is determined in plan according to equation (1):
  • f s l + 15 15 - ⁇ 2 ⁇ + s l - 1 2 ⁇ ⁇ ⁇ sin ( 2 ⁇ ⁇ ⁇ s l ) - ⁇ 2 15 - ⁇ 2 ⁇ ( s l ⁇ ) 2 ⁇ ( + 6 ⁇ ( s l ⁇ ) 2 - 15 ⁇ s l + 10 ) With 0 ⁇ s l ⁇ 1.
  • a further feature of the invention provides that a raised element which connects a straight track to a straight track diverging at an angle thereto is designed in one piece.
  • a further feature of the invention is that a four times finite value differentiable function is used for a one-piece and cambered track element connecting a straight track to a straight track diverging at an angle therefrom.
  • Another feature of the invention is that a canted track-tie connecting a straight track to a straight track parallel thereto is laid out in one piece.
  • a further feature of the invention is that a four times finite value differentiable function is used for a one-piece, over-the-top rail distortion connecting a straight track to a parallel straight track.
  • the vehicle on its guide, the track, is considered taking into account its height, Fig. 1 .
  • the dimensioning height (h) is understood to be the height at which the unbalanced lateral acceleration is considered and evaluated.
  • Fig. 2 shows by way of example the normalized course function of a force minimum ramp according to the invention with its likewise normalized derivatives, starting from the formula (2).
  • the function itself as the 0 derivative corresponds to the overshoot profile.
  • Its 1st derivative is the ramp angle corresponding to the track distortion and the angular velocity of the vehicle about the longitudinal axis.
  • the second derivative is still smooth and proportional to the rail curvature in the elevation, to the angular acceleration about the longitudinal axis of the vehicle and to the bending moment in the rail (s) forming the ramps.
  • the 3rd derivative is still continuous and corresponds to the change of the rail curvature in the elevation, the angular pressure about the longitudinal axis of the vehicle and the lateral force in the rail (s) forming the ramps.
  • the 4th derivative still exists. It has discontinuities at the edges and is proportional to the rail (s) forming on the ramps over the Rail fasteners acting force distribution per unit length, which is required to hold the ramp (s) in this form.
  • the procedure is different here: the elevation ramp itself is already known. We are looking for a direct stakeout of the track in such a way that the desired kinematic behavior of the vehicle running on the track is achieved.
  • the unbalanced lateral acceleration is considered. If one attaches these outside the track level, the known term, which consists of the product curvature times the squared driving speed, adds another term to the rolling motion, namely the roll angular acceleration about the vehicle longitudinal axis multiplied by the distance from the track centerline. If the curvature in the floor plan is chosen so that one part of it just compensates for the last-mentioned term and the other term is proportional to the superelevation, then the unbalanced lateral acceleration also becomes proportional to the superelevation. The curvature in the floor plan accordingly consists of two parts, a conventional proportion corresponding to the course of the elevation and a proportion proportional to the second derivative of the course of the elevation.
  • Fig. 3 shows a corresponding normalized curvature as it arises with the use of equations (1) and (12).
  • the described method can generally be applied to paths in areas of variable curvature and elevation and not only transition curves.
  • the procedure is different here: Accordingly, starting from a grading function that is at least three times differentiable or for fulfilling the requirements of bending theory starting from a four times differentiable grading function, the elevation and the unbalanced lateral acceleration in the trassing height, taking account of the component caused by the rolling motion, must compensate for the unbalanced lateral acceleration follow function and from the curvature in the floor plan are determined.
  • an advantageous feature of the invention generally provides for a four times differentiability of the overshoot function. From equation (1) the corresponding curvature of the track center line is then calculated in plan.
  • the normalized function describes directly the course of the elevation ramp.
  • the differentiability can also be increased slightly.
  • an increase by 1 in the normalized function Equation (7) a special polynomial of ninth order, is shown: With this profile as overshoot function, the bedding distribution of the rail is not only limited but also continuous and the jerk distribution not only continuous, but also smooth , For the amplitudes are again slightly larger than in the course of equation (2).
  • the overshoot ramps are formed from equation (10).
  • Two differentiation according to the arc length along the track center line and insertion into the equation (1) adapted for transition curves in the following form provides the curvature ( ⁇ H ) of the track center line in plan:
  • the method according to the invention can be analogously applied for a one-piece, excessive transition from a straight track to a straight track diverging at an angle therefrom.
  • the choice of a corresponding function for the superelevation and the assumption of the total unbalanced lateral acceleration including the portion of the roll motion with the same function provides the curvature of the track in the floor plan.
  • For the elevation a function increasing from zero to a maximum value and then decreasing to zero is selected.
  • a function is selected which is also four times differentiable at the area edges.
  • the avoidance of an obstacle that is, a route that emanates from a straight track, escapes an obstacle to one side, then runs back to the imaginary extension of the straight track and this crosses, then continues on the other side and in ending in a single piece on a straight track continuing to this side.
  • the route courses and the requirements of the bendability of the rails can be designed with ramp shapes with perfect dynamic properties for all conceivable applications.

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  • Architecture (AREA)
  • Civil Engineering (AREA)
  • Structural Engineering (AREA)
  • Engineering & Computer Science (AREA)
  • Magnetic Bearings And Hydrostatic Bearings (AREA)
  • Train Traffic Observation, Control, And Security (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)
  • Control Of El Displays (AREA)
  • Surface Acoustic Wave Elements And Circuit Networks Thereof (AREA)
  • Transition And Organic Metals Composition Catalysts For Addition Polymerization (AREA)
  • Percussion Or Vibration Massage (AREA)
  • Soil Working Implements (AREA)
  • Control Of Velocity Or Acceleration (AREA)
  • Credit Cards Or The Like (AREA)
  • Lining And Supports For Tunnels (AREA)
  • Earth Drilling (AREA)
  • On-Site Construction Work That Accompanies The Preparation And Application Of Concrete (AREA)
  • Current-Collector Devices For Electrically Propelled Vehicles (AREA)

Claims (13)

  1. Voie ferrée ayant une ligne médiane de courbure ( κH ) variable en projection horizontale et un angle (ψ) de surhaussement variable, caractérisée en ce que la courbure (κH ) est déterminée à partir d'une fonction prise pour le surhaussement, de façon à ce que toute l'accélération latérale non compensée sur une hauteur (h) de tracé fixe et sélectionnée en tenant compte de la proportion, provoquée par le mouvement de roulis, de l'accélération latérale non compensée ait une courbe comme cette fonction et satisfasse à l'équation différentielle suivante : κ H s = κ c ψ c ⋅ ψ s - h ⋅ d 2 ⁢ ψ d ⁢ s 2
    Figure imgb0052
    dans laquelle
    κ H (S) signifie courbure de la ligne médiane de la voie ferrée en projection dans un plan horizontal
    S signifie longueur de l'arc le long de la ligne médiane de la voie ferrée
    κ c signifie courbure de référence constante (dans un arc de cercle)
    ψ C signifie angle de surhaussement de référence constant ( dans un arc de cercle)
    ψ(s) signifie angle de surhaussement
    h signifie hauteur de tracé
    d signifie opérateur différentiel
  2. Voie ferrée suivant la revendication 1, caractérisée en ce que la fonction dans toute sa courbe, également sur les bords, est différentiable au moins quatre fois, en sorte que même encore les quatrièmes dérivés de la fonction ont partout des valeurs finies.
  3. Voie ferrée suivant la revendication 1 ou 2, caractérisée en ce que, lors de la détermination de la courbure (κ H ) de la ligne médiane de la voie ferrée en vue en projection dans un plan horizontal, la hauteur du tracé est choisie égale à zéro en tant que hauteur (h) fixe de tracé.
  4. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'il est utilisé comme fonction normée le polynôme suivant du septième ordre : f s l = ( s l ⁢ ) 4 ⋅ 35 - 84 ⋅ s l + 70 ⋅ ( s l ⁢ ) 2 - 20 ⋅ ( s l ⁢ ) 3
    Figure imgb0053
    avec 0 ≤ s l ≤ 1 ,
    Figure imgb0054
    dans lequel
    s signifie la longueur de l'arc le long de la ligne médiane de la voie ferrée
    l signifie la longueur de la courbe de raccord et de la rampe de surhaussement,
    cette fonction normée étant utilisée pour la courbe de l'angle de surhaussement et pour toute l'accélération latérale non compensée et on en détermine la courbure (κH ) de la ligne médiane de la voie ferrée en vue en projection sur un plan horizontal suivant l'équation (1).
  5. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'il est utilisé comme fonction normée le polynôme suivant du troisième ordre en combinaison avec le sinus et le cosinus et une valeur (Z) constante : f s l = ( s l ⁢ ) 2 ⋅ - 2 ⋅ s l + 3 + 6 Z 2 ⋅ + 2 ⋅ s l - 1 + cos Z ⋅ s l - 2 Z ⋅ sin Z ⋅ s l
    Figure imgb0055
    avec tangente Z 2 = Z 2 ≈ 4 , 49340946
    Figure imgb0056
     et 0 ≤ s l ≤ 1 ,
    Figure imgb0057
    dans laquelle
    s signifie la longueur de l'arc le long de la ligne médiane de la voie ferrée
    l signifie la longueur de l'arc de raccord et de la rampe de surhaussement,
    cette fonction normée étant utilisée pour la courbe de l'angle de surhaussement et pour toute l'accélération latérale non compensée et il en est déterminé la courbure (κH ) de la ligne médiane de la voie ferrée en projection sur un plan horizontal suivant l'équation (1).
  6. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'il est utilisé comme fonction normée le polynôme suivant du troisième ordre en combinaison avec le sinus et le cosinus : f s l = + 1 π 2 - 9 ⋅ + π 2 ⋅ ( s l ⁢ ) 2 ⋅ ( - 2 ⋅ s l + 3 ) - 6 ⋅ + 1 - cos π ⋅ s l + 3 π 2 - 9 ⋅ ( + s l - 1 2 ⋅ π ⋅ sin 2 ⋅ π ⋅ s l )
    Figure imgb0058
    avec 0 ≤ s l ≤ 1 ,
    Figure imgb0059
    dans laquelle
    s signifie la longueur de l'arc suivant la ligne médiane de la voie ferrée
    l signifie la longueur de l'arc de raccord et de la rampe de surhaussement,
    cette fonction normée étant utilisée pour la courbe de l'angle de surhaussement et pour toute l'accélération latérale non compensée et il en est déterminé la courbure (κH ) de la ligne médiane de la voie ferrée en projection sur un plan horizontal suivant l'équation (1).
  7. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'il est utilisé comme fonction normée le polynôme suivant du cinquième ordre en combinaison avec seulement le sinus : f s l = + 15 15 - π 2 ⋅ + s l - 1 2 ⋅ π ⋅ sin ( 2 ⋅ π ⋅ s l ) - π 2 15 - π 2 ⋅ ( s l ⁢ ) 2 ⋅ ( + 6 ⋅ ( s l ⁢ ) 2 - 15 ⋅ s l + 10 )
    Figure imgb0060
    avec 0 ≤ s l ≤ 1 ,
    Figure imgb0061
    dans laquelle
    s signifie la longueur de l'arc suivant la ligne médiane de la voie ferrée
    1 signifie la longueur de l'arc de raccord et de la rampe de surhaussement,
    cette fonction normée étant utilisée pour la courbe de l'angle de surhaussement et pour toute l'accélération latérale non compensée et il en est déterminé la courbure (κH ) de la ligne médiane de la voie ferrée en projection sur un plan horizontal suivant l'équation (1).
  8. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'il est utilisé comme fonction normée le polynôme suivant du cinquième ordre en combinaison avec seulement le cosinus : f s l = + 15 10 - π 2 ⋅ + 1 - cos π ⋅ s l - π 2 2 ⋅ ( 10 - π 2 ) ⋅ ( s l ⁢ ) 2 ⋅ ( + 2 ⋅ ( s l ⁢ ) 3 - 5 ⋅ s l 2 + 5 )
    Figure imgb0062
    avec 0 ≤ s l ≤ 1 ,
    Figure imgb0063
    dans laquelle
    s signifie la longueur de l'arc suivant la ligne médiane de la voie ferrée
    1 signifie la longueur de l'arc de raccord et de la rampe de surhaussement,
    cette fonction normée étant utilisée pour la courbe de l'angle de surhaussement et pour toute l'accélération latérale non compensée et il en est déterminé la courbure (κ H ) de la ligne médiane de la voie ferrée en projection sur un plan horizontal suivant l'équation (1).
  9. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'il est utilisé comme fonction normée le polynôme suivant du neuvième ordre : f s l = s l 5 ⋅ 126 - 420 ⋅ s l + 540 ⋅ s l 2 - 315 ⋅ s l 3 + 70 ⋅ s l 4
    Figure imgb0064
    avec 0 ≤ s l ≤ 1 ,
    Figure imgb0065
    dans laquelle
    s signifie la longueur de l'arc suivant la ligne médiane de la voie ferrée
    1 signifie la longueur de l'arc de raccord et de la rampe de surhaussement,
    cette fonction normée étant utilisée pour la courbe de l'angle de surhaussement et pour toute l'accélération latérale non compensée et il en est déterminé la courbure (κH ) de la ligne médiane de la voie ferrée en projection sur un plan horizontal suivant l'équation (1).
  10. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'un élément de tracé réalisé avec ou sans surhaussement et reliant une voie ferrée droite à une voie ferrée droite s'en écartant d'un angle est conçu par une fonction unipartie.
  11. Voie ferrée suivant la revendication 10, caractérisée en ce que la fonction unipartie, qui est à la base de l'élément de tracé réalisé avec ou sans surhaussement et reliant une voie ferrée rectiligne à une voie ferrée rectiligne s'en écartant d'un angle, est dérivable quatre fois en ayant des valeurs finies.
  12. Voie ferrée suivant l'une des revendications 1 à 3, caractérisée en ce qu'un tirage de voie réalisé avec ou sans surhaussement et reliant une voie droite à une voie droite qui lui est parallèle est conçu par une fonction unipartie.
  13. Voie ferrée suivant la revendication 12, caractérisée en ce que la fonction unipartie, qui est à la base du tirage de voie réalisé avec ou sans surhaussement et reliant une voie ferrée droite à une voie ferrée droite parallèle, est dérivable quatre fois en ayant des valeurs finies.
EP03765068A 2002-07-23 2003-07-22 Voie ferree a courbe de raccordement et a rampe de surhaussement a forces minimales Expired - Lifetime EP1523597B1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
SI200331396T SI1523597T1 (sl) 2002-07-23 2003-07-22 Tir s predhodnim lokom in nagibna rampa z minimalnimi silami

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
AT0111602A AT412975B (de) 2002-07-23 2002-07-23 Gleis mit übergangsbogen und kräfteminimaler überhöhungsrampe
AT11162002 2002-07-23
PCT/EP2003/007936 WO2004009906A1 (fr) 2002-07-23 2003-07-22 Voies ferree a courbe de raccordement et a rampe de surhaussement a forces minimales

Publications (2)

Publication Number Publication Date
EP1523597A1 EP1523597A1 (fr) 2005-04-20
EP1523597B1 true EP1523597B1 (fr) 2008-07-16

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EP03765068A Expired - Lifetime EP1523597B1 (fr) 2002-07-23 2003-07-22 Voie ferree a courbe de raccordement et a rampe de surhaussement a forces minimales

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EP (1) EP1523597B1 (fr)
AT (2) AT412975B (fr)
AU (1) AU2003251430A1 (fr)
DE (1) DE50310165D1 (fr)
DK (1) DK1523597T3 (fr)
ES (1) ES2310671T3 (fr)
ME (1) MEP15108A (fr)
PT (1) PT1523597E (fr)
RS (1) RS51441B (fr)
SI (1) SI1523597T1 (fr)
WO (1) WO2004009906A1 (fr)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2022178612A1 (fr) 2021-02-23 2022-09-01 Геннадий Викторович Величко Section transitoire de courbure de voies de chemin de fer

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107059501B (zh) * 2017-01-24 2024-01-16 北京交通大学 基于装配式技术的跨座式单轨交通钢轨道梁
CN107620229B (zh) * 2017-10-31 2023-09-26 中铁第四勘察设计院集团有限公司 一种高过岔速度的换梁型道岔梁

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AT184601B (de) * 1952-10-08 1956-02-10 Alweg Forschung Gmbh Anordnung des Tragkörpers einer Bahnlinie für spurgebundene Fahrzeuge in Kurven
AT370657B (de) * 1981-09-17 1983-04-25 Voest Alpine Ag Stranggiessanlage

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2022178612A1 (fr) 2021-02-23 2022-09-01 Геннадий Викторович Величко Section transitoire de courbure de voies de chemin de fer

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AU2003251430A1 (en) 2004-02-09
MEP15108A (en) 2010-06-10
SI1523597T1 (sl) 2008-12-31
AU2003251430A8 (en) 2004-02-09
AT412975B (de) 2005-09-26
ATE401455T1 (de) 2008-08-15
ATA11162002A (de) 2005-02-15
RS20050056A (sr) 2007-08-03
DE50310165D1 (de) 2008-08-28
ES2310671T3 (es) 2009-01-16
DK1523597T3 (da) 2008-11-17
EP1523597A1 (fr) 2005-04-20
RS51441B (sr) 2011-04-30
WO2004009906A1 (fr) 2004-01-29
PT1523597E (pt) 2008-10-23

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