SIST EN 14531-6:2009
(Main)Railway applications - Methods for calculation of stopping and slowing distances and immobilisation braking - Part 6: Step by step calculations for train sets or single vehicles
Railway applications - Methods for calculation of stopping and slowing distances and immobilisation braking - Part 6: Step by step calculations for train sets or single vehicles
This European Standard describes a general algorithm that may be used in all types of high speed and conventional vehicle applications, including self-propelling thermal or electric trains, thermal or electric traction units; passenger carriages, mobile railway infrastructure construction and maintenance equipment and freight wagons. This standard does not specify the performance requirements. It enables the calculation of the various aspects of the performance: stopping or slowing distances, dissipated energy, force calculations and immobilization braking. This standard enables the verification by calculation of the stopping, slowing and immobilization performance requirements for high speed and conventional trains operating on high speed and conventional infrastructure. Other calculation methods may be used providing that the order of accuracy achieved is in accordance with this European Standard. This standard presents: a) example of distance and other dynamic calculations, see Annex C; b) example of immobilisation calculations, see Annex D.
Bahnanwendungen - Verfahren zur Berechnung der Anhalte- und Verzögerungsbremswege und der Feststellbremsung - Teil 6: Schrittweise Berechnungen für Zugverbände oder Einzelfahrzeuge
In dieser Europäischen Norm wird ein grundlegender Algorithmus beschrieben, der verwendet werden kann für alle Betriebsarten der konventionellen und Hochgeschwindigkeitsfahrzeuge, einschließlich selbst fahrender Züge und Einheiten, die elektrisch oder durch Verbrennungskraft getrieben werden, Reisezugwagen, mobile Arbeits- und Wartungsfahrzeuge und Güterwagen. Die vorliegende Norm enthält keine Anforderungen an das Bremsvermögen. Es ermöglicht, die verschiedenen Kriterien des Bremsvermögens zu berechnen: Wege der Anhalte- oder Regulierbremsung, Energiedissipation, Kraftberechnungen und Stillstandsbremsung.
Die vorliegende Norm ermöglicht es, Anforderungen an Anhalte-, Verzögerungs- sowie Stillstandsbremsver-mögen für konventionelle und Hochgeschwindigkeitszüge, die auf konventionellen und Hochgeschwindigkeits¬strecken verkehren, mittels Berechnungen zu überprüfen.
Andere Berechnungsmethoden können genutzt werden, vorausgesetzt, dass die Genauigkeit in Überein-stimmung mit dieser Europäischen Norm erreicht wird.
Die vorliegende Norm enthält:
a) ein Beispiel der Weg- und anderer dynamischer Berechnungen, siehe Anhang C;
Berechnungsbeispiele einer Stillstandbremsung, siehe Anhang D.
Applications ferroviaires - Méthodes de calcul des distances d'arrêt, de ralentissement et d'immobilisation - Partie 6: Calculs pas à pas pour des compositions de trains ou véhicules isolés
La présente Norme européenne décrit l’algorithme général à utiliser pour les applications à tout type de
véhicule grande vitesse et conventionnel, y compris les trains automoteurs à traction thermique ou électrique,
les unités à traction thermique ou électrique, les voitures à voyageurs, les équipements mobiles de
construction et de maintenance d’infrastructure ferroviaire, et les wagons. La présente norme ne spécifie pas
les exigences de performances Elle permet de calculer les différents aspects des performances : distances
d’arrêt ou de ralentissement, énergie dissipée, calcul des efforts et freinage d’immobilisation.
La présente Norme européenne permet de vérifier au moyen de calcul, les exigences de performances
d’arrêt, de ralentissement et d’immobilisation des trains grande vitesse et conventionnels, circulant aussi bien
sur des infrastructures type « grande vitesse » que de type « rail conventionnel ».
D’autres méthodes de calcul peuvent être utilisées à condition que le niveau de précision atteint soit conforme
à la présente Norme européenne.
La présente norme présente :
a) un exemple de distance et autres calculs dynamiques, voir Annexe C ;
b) un exemple de calculs d’immobilisation, voir Annexe D.
Železniške naprave - Metode za izračun zavornih poti, poti za kontrolo hitrosti in zavarovanj stoječih vozil - 6. del: Izračun za vlakovne kompozicije ali posamezna vozila s postopkom "korak za korakom"
General Information
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Standards Content (Sample)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Bahnanwendungen - Verfahren zur Berechnung der Anhalte- und Verzögerungsbremswege und der Feststellbremsung - Teil 6: Schrittweise Berechnungen für Zugverbände oder EinzelfahrzeugeApplications ferroviaires - Méthodes de calcul des distances d'arrêt, de ralentissement et d'immobilisation - Partie 6: Calculs pas à pas pour des compositions de trains ou véhicules isolésRailway applications - Methods for calculation of stopping and slowing distances and immobilisation braking - Part 6: Step by step calculations for train sets or single vehicles45.020Železniška tehnika na splošnoRailway engineering in generalICS:Ta slovenski standard je istoveten z:EN 14531-6:2009SIST EN 14531-6:2009en01-september-2009SIST EN 14531-6:2009SLOVENSKI
STANDARD
SIST EN 14531-6:2009
EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN 14531-6May 2009ICS 45.060.01 English VersionRailway applications - Methods for calculation of stopping andslowing distances and immobilisation braking - Part 6: Step bystep calculations for train sets or single vehiclesApplications ferroviaires - Méthodes de calcul desdistances d'arrêt, de ralentissement et d'immobilisation -Partie 6: Calculs pas à pas pour des compositions de trainsou véhicules isolésBahnanwendungen - Verfahren zur Berechnung derAnhalte- und Verzögerungsbremswege und derFeststellbremsung - Teil 6: Schrittweise Berechnungen fürZugverbände oder EinzelfahrzeugeThis European Standard was approved by CEN on 23 April 2009.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the CEN Management Centre or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as theofficial versions.CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre:
Avenue Marnix 17,
B-1000 Brussels© 2009 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN 14531-6:2009: ESIST EN 14531-6:2009
EN 14531-6:2009 (E) 2 Contents Page Foreword . 4Introduction . 51Scope. 62Normative references . 63Definitions, symbols and abbreviations . 63.1Terms and definitions . 63.2Symbols and indices . 74General algorithms . 104.1General algorithm to calculate stopping and slowing distances . 104.2General algorithm to calculate immobilization brake . 105Stopping and slowing distances calculation . 105.1Accuracy of input values. 105.2General characteristics . 105.3Brake equipment characteristics . 125.4Initial and operating characteristics . 235.5Sharing, proportioning of the brake forces - achieved forces . 255.6Braking force per axle . 255.7Total force on train level. 255.8Time step integration loop . 265.9Other decelerations . 265.10Time . 275.11Distance calculations . 285.12Other calculations . 296Immobilization brake calculation . 316.1General . 316.2General characteristics . 326.3Characteristics of the immobilization brake equipment . 326.4Train and operating characteristics . 326.5Immobilization force provided by each equipment type . 336.6Immobilization force . 336.7External forces . 346.8Final results . 35Annex A (normative)
Workflow of kinetic and static calculations . 37Annex B (informative)
Example of time step integration loop . 40Annex C (informative)
Example of distance and other dynamic calculations . 41C.1Input data . 41C.1.1Mass data . 41C.1.2Wheel data . 42C.1.3Train resistance . 42C.1.4Data for brake equipment types . 42C.1.5Characteristics and settings of the brake equipment . 44C.1.6Initial and final speed. 44C.1.7Gradient . 44C.2Calculation results . 45C.2.1Braking force of single equipments and train resistance . 45C.2.2Total braking force per equipment type and train resistance . 46C.2.3Distances . 46SIST EN 14531-6:2009
EN 14531-6:2009 (E) 3 C.2.4Stopping time . 47C.2.5Equivalent response time . 47C.2.6Equivalent deceleration . 47C.2.7Decelerations . 47C.2.8Required adhesion . 48Annex D (informative)
Example of immobilisation calculations . 50D.1Input data . 50D.1.1Mass data . 50D.1.2Wheel data . 51D.1.3Train resistance . 51D.1.4Wind force on the train . 51D.1.5Data for axle related disc brake equipment . 51D.1.6Gradient . 52D.1.7Available adhesion . 52D.1.8Brake equipment in use. 52D.2Calculation results of the immobilisation calculation . 52D.2.1Immobilisation force . 52D.2.2Immobilisation safety factor . 53D.2.3Required adhesion per axle . 53D.2.4Maximum achievable gradient . 53Annex ZA (informative)
Relationship between this
European
Standard and the Essential Requirements
of EC Directive 2008/27/EC . 54Bibliography . 57 SIST EN 14531-6:2009
EN 14531-6:2009 (E) 4 Foreword This document (EN 14531-6:2009) has been prepared by Technical Committee CEN/TC 256 “Railway applications”, the secretariat of which is held by DIN. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by November 2009, and conflicting national standards shall be withdrawn at the latest by November 2009. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights. This Standard1 is one in a series of six, under the generic title EN 14531, Railway applications — Methods for calculation of stopping distances, slowing distances and immobilization braking. The other five are:
Part 1: General algorithms; Part 2: Application to Single Freight Wagon (in preparation); Part 3: Application to mass transit (in preparation); Part 4: Single passenger coaches (in preparation); Part 5: Locomotives (in preparation). This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association, and supports essential requirements of EU Directive 2008/57/EC. For relationship with EU Directive 2008/57/EC, see informative Annex ZA, which is an integral part of this document. According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom.
1 Although it was originally intended to prepare a series of six parts for this Standard, the intention is now to rationalize and restructure the Standard so that it comprises fewer parts. SIST EN 14531-6:2009
EN 14531-6:2009 (E) 5 Introduction The objective of this European Standard is to enable the railway industries and operators to work with a common calculation method. It describes the adapted algorithms and step-by-step calculations for the design of brake equipment for all types of train sets, electrical multiple units, diesel multiple units and single vehicles. SIST EN 14531-6:2009
EN 14531-6:2009 (E) 6 1 Scope This European Standard describes a general algorithm that may be used in all types of high speed and conventional vehicle applications, including self-propelling thermal or electric trains, thermal or electric traction units; passenger carriages, mobile railway infrastructure construction and maintenance equipment and freight wagons. This standard does not specify the performance requirements. It enables the calculation of the various aspects of the performance: stopping or slowing distances, dissipated energy, force calculations and immobilization braking. This standard enables the verification by calculation of the stopping, slowing and immobilization performance requirements for high speed and conventional trains operating on high speed and conventional infrastructure.
Other calculation methods may be used providing that the order of accuracy achieved is in accordance with this European Standard. This standard presents: a) example of distance and other dynamic calculations, see Annex C; b) example of immobilisation calculations, see Annex D. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 14478:2005, Railway applications — Braking — Generic vocabulary EN 14531-1:2005, Railway applications — Methods for calculation of stopping distances, slowing distances and immobilization braking — Part 1: General algorithms prEN 15328, Railway applications - Braking - Brake pads 2 ISO 80000-3:2006, Quantities and units — Part 3: Space and time ISO 80000-4:2006, Quantities and units — Part 4: Mechanics 3 Definitions, symbols and abbreviations 3.1 Terms and definitions For the purposes of this document, the definitions given in EN 14478:2005, EN 14531-1:2005,
ISO 80000-3:2006, ISO 80000-4:2006, and the following apply. 3.1.1 static mass per axle (1) mass, measured by weighing at the wheel-rail interface, or estimated from design evaluation of each axle in a stationary condition
2 At the time of publication, this Standard was in the process of being prepared. SIST EN 14531-6:2009
EN 14531-6:2009 (E) 7 (2) mass of the train divided by the quantity of axles in case where the static mass per axle is not known 3.1.2 static mass of the train summation of all the static mass per axle values, including all operating loads 3.1.3 brake equipment type group of equipment the purpose of which is to provide braking force 3.1.4 isolated brake equipment status of inoperable brakes on e.g. bogie (see EN 14478) 3.1.5 active brake equipment equipment considered during the calculation of a specific type of braking (in opposition with isolation) (see EN 14478) 3.1.6 step by step calculation numerical method with finite time steps NOTE Synonym for a numerical type of solving an integral. 3.2 Symbols and indices For the purposes of this document, the general symbols given in Table 1 and indices given in Table 2 apply. NOTE Specific symbols and indices are defined in the relevant clauses. SIST EN 14531-6:2009
EN 14531-6:2009 (E) 8 Table 1 — Symbols Symbol Definition Unit A area m2 As swept area of a friction surface m2 a deceleration m/s2 B braked weight t D wheel diameter m d diameter m F force N FB braking force N Fg downhill force on the train N f coefficient of friction - gn standard acceleration of free fall = 9,80665 m/s2 (refer to ISO 80000-3) m/s2 i gradient a
-
i C cylinder ratio
- i rig rigging ratio - i tra transmission ratio - m mass kg n quantity - P power W p pressure Pa R wheel radius m r radius m s distance m S safety factor - t time s τ coefficient of adhesion
- v speed m/s W energy J WS energy per square unit J/m2 λ brake percentage
- µ coefficient of friction (brake pad or blocks) - η efficiency - a Rising gradient is positive; e.g. for a gradient of 5 ‰i= 0,005. SIST EN 14531-6:2009
EN 14531-6:2009 (E) 9 Table 2 — General indices Symbol Term AMG attraction force for a magnetic track brake ax axle
a available B friction BEC braking force for an eddy current brake BED electro-dynamic braking force BFR fluid retarder braking force BMG braking force for a magnetic brake b block or pad bog bogie C cylinder cha characteristic Bd brake force demand disc disc dyn dynamic e or 2 final e equivalent ext
external H hand brake i brake equipment type im immobilization, parking, holding int internal inst instantaneous m average, mean max maximum min minimum mot motor m_unsp unsprung mass MG magnetic brake n normal direction r responsen Ra train resistance to motion req required rig rigging rot rotating R1 return spring R2 regulator S spring st static t tangential direction tot
total tra transmission wind wind 0 or 1 initial SIST EN 14531-6:2009
EN 14531-6:2009 (E) 10 4 General algorithms 4.1 General algorithm to calculate stopping and slowing distances This algorithm is presented in Figure A.1 This algorithm shall be used with instantaneous values which are calculated step by step. The numerical integration shall be time based (see 5.8). A rough estimation can be based on EN 14531-1. The rough estimation shall only be used to check the results of the numerical integration. The content of each algorithm, the corresponding definitions of input values and different phases of calculation are given in Clause 5. 4.2 General algorithm to calculate immobilization brake This algorithm is presented in Figure A.2. The content of each algorithm, the corresponding definitions of input values and different phases of calculation are given in Clause 6. 5 Stopping and slowing distances calculation 5.1 Accuracy of input values The accuracy of the calculation described here depends directly on the accuracy of the input data. All the input data shall have an appropriate order of accuracy and shall be justified by tests, further calculations or engineer's estimations, etc. Corresponding calculations or test reports (or extracts of these documents) should be attached with the performance calculation. 5.2 General characteristics 5.2.1 Train formation The parameters which shall be used to define train formation are: a) quantity of motor axles; b) quantity of trailer axles; c) quantity of braked axles for each adhesion dependent brake equipment type; d) quantity of non-adhesion dependent brake equipment type. According to the braking system design, the parameters can also be defined at the level of the bogies, or of the vehicles. Calculations shall be performed for each brake equipment type. In so doing, the brake force contributions from each of the brake equipment subtypes (e.g. disc brakes, tread brakes, electrodynamic brakes) shall be taken into consideration. All of the various types of brake equipment applied to one axle shall be identified and accounted for in the calculation. NOTE 1 When there are several brake equipment types, it is preferable to identify each type (for example by means of a number: type 1, type 2, etc.). SIST EN 14531-6:2009
EN 14531-6:2009 (E) 11 When brake equipment is used on one part of the train under certain conditions and used on another part under different conditions (for example with two different cylinder pressures for the same load level), two different brake equipment types shall be considered. In such cases, the two brake equipment types shall be identified and accounted for separately in the calculation. NOTE 2 The total quantity of axles is the result of the sum of the quantity of braked and unbraked axles.
5.2.2 Vehicle and train characteristics 5.2.2.1 Static mass per axle, Static mass
When there are different “static mass per axle”, see 3.1.1, the location in the train shall be indicated. 5.2.2.2 Equivalent rotating masses Rotating mass (as defined in EN 14478) shall be calculated using a theoretical approach or an approved test method when applicable. It shall be indicated the wheel size and the relevant static mass condition which is related to the mass inertias (e.g. new wheel and tare load condition). When there are different “rotating mass per axle”, the location in the train shall be indicated. 5.2.2.3 Wheel diameters The wheel diameter is measured on the nominated line of contact with the running surface of the rail. The wheel diameter used in the emergency brake calculation shall be that of a wheel which gives the lowest deceleration (e.g. in the case of disc brakes, this would normally be the maximum wheel diameter). For checking the adhesion required, τreq , the wheel diameter used shall be that which gives the maximum adhesion required (e.g. in the case of disc brakes, this would normally be the minimum wheel diameter). If the train is equipped with different sizes of wheels, each size of wheel shall be indicated to the train composition. 5.2.2.4 Train resistance
The value of train resistance may be by analogy to another existing vehicle, or based on a specific calculation. When the values are the results of tests, the test conditions shall be similar to the expected operating conditions.
The train resistance is represented by a formula which consists of: a) one term independent of vehicle speed; b) one term proportional to the speed, dealing with the mechanical components (train and track); c) a third term proportional to a power n of the speed (aerodynamic resistance).
According to this formula the mathematical formulae that shall be applied are the following:
To obtain the instantaneous train resistance as a function of the speed: SIST EN 14531-6:2009
EN 14531-6:2009 (E) 12 nRaFABvCv=+⋅+⋅
(1) where: FRa
is the instantaneous value of the train resistance
N
v
is the instantaneous speed of the vehicle
m/s
A
is the characteristic coefficient of the vehicle
N
B
is the characteristic coefficient of the vehicle.
N/(m/s)
C
is the characteristic coefficient of the vehicle.
N/(m/s)n
n
is the exponent to be defined exactly. In case there is no exact value available, n is estimated to be 2
For the application of more usual units, the coefficients of the formula shall be adapted. The above units shall be used for the calculations purpose, but the speed can be expressed usually in km/h and the train resistance in N or kN. In this case, A, B, C are expressed in N, N/(km/h), N/(km/h)n or kN, kN/(km/h), kN/(km/h)n.
NOTE 1 A, B, and C coefficients are function of various parameters, e.g. mass, train length. Values for A, B, and C may be obtained using the test method given in EN 14067-2. NOTE 2 For a first calculation, the average train resistance to motion as detailed in EN 14531-1 may be used. EXAMPLE In all these formulae, the train resistance FRa is given in N and the instantaneous speed v in m/s. A = 4 144,9 N; B = 100,8 N/(m/s); C = 7,53 N/(m/s²). For a speed of 300 km/h corresponding to 83,3 m/s, train resistance force is: FRa = 4 144,9 + 100,8 × 83,3 + 7,53 × 83,3²; FRa = 6 4791 N. NOTE Other examples of values are given in Annex C.
5.3 Brake equipment characteristics 5.3.1 General The final result of this part is the braking force generated by each brake equipment related to the top of the rail. This clause considers the braking force generated by each brake equipment type by reference to the most common brake equipment i.e. tread and disc braking. If this equipment is not applicable, other suitable methods of brake force calculation should be adopted. SIST EN 14531-6:2009
EN 14531-6:2009 (E) 13 5.3.2 Friction brake equipment forces 5.3.2.1 Tread brake unit
The brake equipment of a tread brake unit acts on one shoe arrangement per cylinder as shown in Figures 1 and 2.
Figure 1 — Pressure applied tread brake unit
Figure 2 — Spring applied tread brake unit The braking force characteristic of a tread brake unit can be expressed by: Output cylinder force η=⋅⋅⋅+cccccs,cFpAiF (2) Application force on the shoe
ncrigrig,dyns,rigFFiFη=⋅⋅+
(3) Braking force per unit B,CnFFµ=⋅
(4) where: pC
is the brake cylinder pressure
Pa
AC
is the brake cylinder piston area
m2
ηC
is the cylinder efficiency
-
iC
is the cylinder ratio
NOTE 1
For pressure applied brake equipment:
positive value; for spring applied brake equipment: negative value.
-
FS,C
is the cylinder spring force NOTE 2 For braking force: positive value; for releasing force: negative value.
N
SIST EN 14531-6:2009
EN 14531-6:2009 (E) 14 ηrig,dyn
is the rigging efficiency in dynamic condition
-
irig
is the rigging ratio
-
FS,rig
is the rigging spring force NOTE 3 For braking force: positive value; for releasing force: negative value.
N
µ
is the friction coefficient
-
Ab
is the area of the shoe (appear only in the Figures 1 and 2, not in the above formulae)
m2
5.3.2.2 Clasp brake If clasp brakes are utilized, then their relevant and specific brake characteristics shall be applied in accordance with EN 14531-1. 5.3.2.3 Disc brake unit A disc brake unit typically acts on one caliper per cylinder as shown in Figures 3 and 4.
Figure 3 — Pressure applied disc brake unit Figure 4 — Spring applied disc brake unit The braking force characteristic of a disc brake unit can be expressed by: Output cylinder force η=⋅⋅⋅+CCCCCS,CFpAiF (5) Clamp force on the pad ()nCrigrig,dynb,C/FFinη=⋅⋅
(6) Tangential force on the disc tnb,CFFnµ=⋅⋅
(7) SIST EN 14531-6:2009
EN 14531-6:2009 (E) 15 Braking force per unit straB,Cttra/2riFFDη=⋅⋅
(8) where: pC
is the brake cylinder pressure
Pa
AC
is the brake cylinder piston area
m2
ηC
is the cylinder efficiency
-
iC
is the cylinder ratio NOTE 1 For pressure applied brake equipment:
positive value; for spring applied brake equipment: negative value.
-
FS,C
is the cylinder spring force NOTE 2 For braking force: positive value; for releasing force: negative value.
N
ηrig,dyn
is the rigging efficiency in dynamic condition
-
irig
is the rigging ratio
-
µ
is the friction coefficient
-
ηtra
is the transmission efficiency
-
itra
is the transmission ratio
-
Ab
is the type and area of the pad per face of disc (appear only in the Figures 3 and 4, not in the above formulae)
m2
rs
is the mean swept radius
m
D
is the diameter of the wheel
m As
is the swept area (2 faces) of the disc (appear only in the Figures 3 and 4 , not in the above formulae)
m2
nb,C
is the quantity of pads per cylinder
-
5.3.2.4 Coefficient of friction The nominal static and dynamic values of the coefficient of friction shall
...
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