SIST EN 13103:2009+A2:2012
(Main)Railway applications - Wheelsets and bogies - Non powered axles - Design method
Railway applications - Wheelsets and bogies - Non powered axles - Design method
This standard: 1) defines the forces and moments to be taken into account with reference to masses and braking conditions; 2) gives the stress calculation method for axles with outside axle journals; 3) specifies the maximum permissible stresses to be assumed in calculations for steel grade EA1N defined in EN 13261; 4) describes the method for determination of the maximum permissible stresses for other steel grades; 5) determines the diameters for the various sections of the axle and recommends the preferred shapes and transitions to ensure adequate service performance. This standard is applicable to: 6) solid and hollow axles of railway rolling stock used for the transportation of passengers and freight; 7) axles defined in EN 13261; 8) all gauges. This standard is applicable to axles fitted to rolling stock intended to run under normal European conditions. Before using this standard, if there is any doubt as to whether the railway operating conditions are normal, it is necessary to determine whether an additional design factor has to be applied to the maximum permissible stresses. The calculation of wheelsets for special applications (e.g. tamping/lining/levelling machines) may be made according to this standard only for the load cases of free-running and running in train formation. This standard does not apply to workload cases. They are calculated separately. For light rail and tramway applications, other standards or documents agreed between the customer and supplier may be applied. Non-powered axles of motor bogies and locomotives are analysed according to the requirements of EN 13104.
Bahnanwendungen - Radsätze und Drehgestelle - Laufradsatzwellen - Konstruktions- und Berechnungsrichtlinie
Diese Europäische Norm:
1) gibt Kräfte und Momente an, die aufgrund der Massenwirkungen und Bremsbedingungen zu berücksichtigen sind;
2) gibt das Verfahren zur Spannungsberechnung außengelagerter Radsatzwellen an;
3) legt die höchstzulässigen Spannungen für den Stahl der Güte EA1N fest, die in die Berechnung einzusetzen sind nach EN 13261;
4) beschreibt die Vorgehensweise zur Ermittlung der höchstzulässigen Spannungen für andere Stähle;
5) bestimmt die Durchmesser der verschiedenen Wellenabschnitte. Die bevorzugten Formen und Übergänge werden definiert, um ein sicheres Betriebsverhalten zu erreichen.
Diese Norm gilt für:
6) Laufradsätze mit Voll- und Hohlwellen von rollendem Eisenbahnmaterial für Personen- und Güterverkehr;
7) Radsätze nach EN 13261;
8) alle Spurweiten. )
Diese Norm gilt für Radsatzwellen von Rollendem Material, das für den Einsatz unter üblichen in Europa herrschenden Betriebsbedingungen vorgesehen ist. Wenn Zweifel bestehen, ob normale Betriebsbedingun¬gen vorherrschen, ist es notwendig vor Anwendung dieser Norm zu entscheiden, ob ein zusätzlicher Konstruktionsfaktor für die maximal zulässigen Spannungen angewendet werden muss. Die Berechnung von Radsätzen für besondere Anwendungsfälle (z. B. Oberbauricht- und -stopfmaschinen) kann entsprechend der vorliegenden Norm ausschließlich für die Lastfälle Eigenfahrt und Fahrt im Zugverband durchgeführt werden. Diese Norm gilt nicht für Arbeitslastfälle. Solche werden separat berechnet.
Für Stadtbahnen und Straßenbahnen können andere zwischen Kunde und Lieferant vereinbarte Normen oder Dokumente zur Anwendung kommen.
Laufradsätze von Motordrehgestellen und Lokomotiven werden nach den Anforderungen von EN 13104 ausgelegt.
Applications ferroviaires - Essieux montés et bogies - Essieux-axes porteurs - Méthode de conception
La présente Norme:
1) définit les forces et moments à prendre en compte en fonction des masses et du freinage;
2) donne la méthode de calcul des contraintes dans les essieux-axes à fusées extérieures;
3) prescrit les contraintes maximales admissibles à prendre en compte dans les calculs pour la nuance d'acier EA1N définie dans l’EN 13261;
4) décrit la méthode de détermination des contraintes maximales admissibles pour les autres nuances d'acier;
5) permet de calculer les diamètres des différentes parties de l'essieu-axe et recommande les formes et raccordements les mieux adaptés pour garantir une bonne tenue mécanique en service.
La présente Norme est applicable:
6) aux essieux-axes pleins et creux du matériel roulant ferroviaire destiné au transport des personnes et des marchandises;
7) aux essieux-axes définis par l’EN 13261;
8) à tous les écartements de voie ).
La présente Norme est applicable aux essieux-axes destinés aux matériels roulant dans des conditions d'exploitation normale européenne. Avant l’utilisation de cette Norme et en cas de doutes sur la normalité des conditions d’exploitation, il est impératif d’établir la nécessité d’appliquer un coefficient de sécurité supplémentaire aux contraintes admissibles maximales. Les calculs d’essieux pour des applications spéciales (par exemple: les bourreuses, niveleuses, dresseuses) peuvent être menés selon la présente Norme, uniquement pour les cas de charges véhicule isolé, hors séquence de travail et véhicule incorporé dans un train. Cette Norme ne s’applique pas aux cas de charges de travail. Ceux-ci sont calculés séparément.
Pour les véhicules légers et les tramways, d’autres normes ou documents acceptés entre client et fournisseur peuvent être utilisés.
Les essieux-axes porteurs des bogies moteurs et les essieux-axes porteurs des locomotives sont calculés suivant les prescriptions de l’EN 13104.
Železniške naprave - Kolesne dvojice in podstavni vozički - Proste osi - Konstrukcijska metoda
Ta standard: 1) določa sile in momente, ki jih je treba upoštevati v zvezi z masami in zavornimi pogoji; 2) navaja metodo za izračun napetosti za osi z zunanjim oselnikom; 3) določa največje dovoljene napetosti, ki se predpostavijo v izračunih za razred jekla EA1N iz standarda EN 13261; 4) opisuje metodo za določitev največjih dovoljenih napetosti za druge razrede jekla; 5) določa premere različnih delov osi ter priporoča najboljše oblike in prehode za zagotovitev ustrezne učinkovitosti storitev. Ta standard se uporablja za: 6) trdne in votle osi tirnih vozil za prevoz potnikov in tovora; 7) osi iz standarda EN 13261; 8) vse širine tira. Ta standard se uporablja za osi, pritrjene na tirna vozila, namenjena za uporabo pod običajnimi evropskimi pogoji. Če obstaja kakršen koli dvom v zvezi s tem, ali so pogoji delovanja železnice običajni, je treba pred uporabo tega standarda ugotoviti, ali je treba za največje dovoljene napetosti uporabiti dodaten konstrukcijski dejavnik. Izračun kolesnih dvojic za posebne uporabe (npr. stroji za gramoziranje/oblaganje/izenačevanje) se na podlagi tega standarda lahko izvede le za proste in vodene primere obremenitve pri sestavi vlaka. Ta standard se ne uporablja za primere delovne obremenitve. Ti se izračunajo ločeno. Za lahka železniška in tramvajska vozila je mogoče uporabiti druge standarde ali dokumente, o katerih sta se dogovorila stranka in dobavitelj. Proste osi motornih podstavnih vozičkov in lokomotiv se analizirajo v skladu z zahtevami iz standarda EN 13104.
General Information
Relations
Standards Content (Sample)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Bahnanwendungen - Radsätze und Drehgestelle - Laufradsatzwellen - Konstruktions- und BerechnungsrichtlinieApplications ferroviaires - Essieux montés et bogies - Essieux-axes porteurs - Méthode de conceptionRailway applications - Wheelsets and bogies - Non powered axles - Design method45.040Materiali in deli za železniško tehnikoMaterials and components for railway engineeringICS:Ta slovenski standard je istoveten z:EN 13103:2009+A2:2012SIST EN 13103:2009+A2:2012en,fr,de01-oktober-2012SIST EN 13103:2009+A2:2012SLOVENSKI
STANDARD
SIST EN 13103:2009+A2:2012
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
EN 13103:2009+A2
July 2012 ICS 45.040 Supersedes EN 13103:2009+A1:2010English Version
Railway applications - Wheelsets and bogies - Non powered axles - Design method
Applications ferroviaires - Essieux montés et bogies - Essieux-axes porteurs - Méthode de conception
Bahnanwendungen - Radsätze und Drehgestelle - Laufradsatzwellen - Konstruktions- und Berechnungsrichtlinie This European Standard was approved by CEN on 26 December 2008 and includes Amendment 1 approved by CEN on 14 September 2010 and Amendment 2 approved by CEN on 3 June 2012.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC 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 translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre:
Avenue Marnix 17,
B-1000 Brussels © 2012 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN 13103:2009+A2:2012: ESIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 2 Contents Page Foreword .4 Introduction .5 1 Scope .6 2 Normative references .6 3 Symbols and abbreviations .7 4 General .8 5 Forces and moments to be taken into consideration .9 5.1 Types of forces .9 5.2 Effects due to masses in motion .9 5.3 Effects due to braking .13 5.4 Effects due to curving and wheel geometry .14 5.5 Calculation of the resultant moment .14 6 Determination of geometric characteristics of the various parts of the axle .19 6.1 Stresses in the various sections of the axle .19 6.2 Determination of the diameter of journals and axle bodies .23 6.3 Determination of the diameter of the various seats from the diameter of the axle body or from the journals .23 6.3.1 Collar bearing surface .23 6.3.2 Transition between collar bearing surface and wheel seat .25 6.3.3 Wheel seat in the absence of an adjacent seat .26 6.3.4 Case of two adjacent wheel seats .26 6.3.5 Configuration of the wheel seats .27 7 Maximum permissible stresses .27 7.1 General .27 7.2
Steel grade EA1N .27 7.3
Steel grades other than EA1N .28 Annex A (informative)
Model of axle calculation sheet .31 Annex B (informative)
Procedure for the calculation of the load coefficient for tilting vehicles .32 Annex C (informative)
Values of forces to take into consideration for wheelsets for reduced gauge track (metric or close to a metre) .34 Annex D (normative)
Method for determination of full-scale fatigue limits for new materials .35 D.1 Scope .35 D.2 General requirements for the test pieces .35 D.3 General requirements for test apparatus .35 D.4 Axle body fatigue limit ("F1") .36 D.4.1 Geometry .36 D.4.2 Verification of the applied stress .36 D.4.3 End of test criterion .37 D.4.4 Determination of the fatigue limit .37 D.5 Axle bore fatigue limit ("F2") .38 D.5.1 Geometry .38 D.5.2 Verification of the applied stress .38 D.5.3 End of test criterion .38 D.5.4 Determination of the fatigue limit .38 D.6 Wheel seat fatigue limit ("F3 and F4") .39 D.6.1 Geometry .39 SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 3 D.6.2 Verification of the applied stress . 40 D.6.3 End of test criterion . 40 D.6.4 Determination of the fatigue limit . 40 D.7 Content of the test report . 41 Annex ZA (informative)
!Relationship between this
European
Standard and the Essential Requirements
of EU Directive 2008/57/EC" . 42 Bibliography . 46
SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 4 Foreword This document (EN 13103:2009+A2:2012) 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 January 2013, and conflicting national standards shall be withdrawn at the latest by January 2013. 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 document comprises amendment 1 adopted by CEN on 2010-09-14 and amendment 2, adopted by CEN on 2012-06-03. This document supersedes #EN 13103:2009+A1:2010$. The start and end of the text added or modified by the amendment is indicated in the text by !" and #$. !This document has been prepared under a mandate given to CEN/CENELEC/ETSI 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, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 5
Introduction Railway axles were among the first train components to give rise to fatigue problems. Many years ago, specific methods were developed in order to design these axles. They were based on a feedback process from the service behaviour of axles combined with the examination of failures and on fatigue tests conducted in the laboratory, so as to characterize and optimize the design and materials used for axles. A European working group under the aegis of UIC1 started to harmonize these methods at the beginning of the 1970s. This led to an ORE2 document applicable to the design of trailer stock axles, subsequently incorpo-rated into national standards (French, German, Italian) and consequently converted into a UIC leaflet. The bibliography lists the relevant documents used for reference purposes. The method described therein is largely based on conventional loadings and applies the beam theory for the stress calculation. The shape and stress recommendations are derived from laboratory tests and the outcome is validated by many years of operations on the various railway systems. This standard is based largely on this method which has been improved and its scope enlarged.
1 UIC : Union Internationale des Chemins de fer. 2 ORE: Office de Recherches et d'Essais de l'UIC. SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 6
1 Scope This standard: 1) defines the forces and moments to be taken into account with reference to masses and braking conditions; 2) gives the stress calculation method for axles with outside axle journals; 3) specifies the maximum permissible stresses to be assumed in calculations for steel grade EA1N defined in
EN 13261; 4) describes the method for determination of the maximum permissible stresses for other steel grades; 5) determines the diameters for the various sections of the axle and recommends the preferred shapes and transitions to ensure adequate service performance.
This standard is applicable to: 6) solid and hollow axles of railway rolling stock used for the transportation of passengers and freight; 7) axles defined in EN 13261; 8) all gauges3. This standard is applicable to axles fitted to rolling stock intended to run under normal European conditions. Before using this standard, if there is any doubt as to whether the railway operating conditions are normal, it is necessary to determine whether an additional design factor has to be applied to the maximum permissible stresses. The calculation of wheelsets for special applications (e.g. tamping/lining/levelling machines) may be made according to this standard only for the load cases of free-running and running in train formation. This standard does not apply to workload cases. They are calculated separately. For light rail and tramway applications, other standards or documents agreed between the customer and supplier may be applied. Non-powered axles of motor bogies and locomotives are analysed according to the requirements of
EN 13104. 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 13260:2009, Railway applications — Wheelsets and bogies — Wheelsets — Product requirements EN 13261:2009, Railway applications — Wheelsets and bogies — Axles — Product requirements #EN 15313, Railway applications – In-service wheelset operation requirements – In-service and off-vehicle wheelset maintenance$
3 If the gauge is not standard, certain formulae need to be adapted. SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 7 3 Symbols and abbreviations For the purposes of this European Standard, the symbols and abbreviations in Table 1 apply: Table 1 Symbol Unit Description 1m kg Mass on journals (including bearings and axle boxes) 2m kg Wheelset mass and masses on the wheelset between running surfaces (brake disc, etc.) 21mm+ kg For the wheelset considered, proportion of the mass of the vehicle on the rails g m/s2 Acceleration due to gravity P N Half the vertical force per wheelset on the
rail 2)(21gmm+ 0P N Vertical static force per journal when the wheelset is loaded symmetrically 21gm 1P N Vertical force on the more heavily-loaded journal 2P N Vertical force on the less heavily-loaded journal 'P N Proportion of P braked by any mechanical braking system
1Y N Wheel/rail horizontal force perpendicular to the rail on the side of the more heavily-loaded journal 2Y N Wheel/rail horizontal force perpendicular to the rail on the side of the less heavily-loaded journal H N Force balancing the forces 1Y and 2Y 1Q N Vertical reaction on the wheel situated on the side of the more heavily-loaded journal 2Q N Vertical reaction on the wheel situated on the side of the less heavily-loaded journaliF N Forces exerted by the masses of the unsprung elements situated between the two wheels (brake disc(s) etc.) fF N Maximum force input of the brake shoes of the same shoeholder on one wheel or interface force of the pads on one disc xM Nmm Bending moment due to the masses in motion 'xM , 'zM Nmm
Bending moments due to braking 'yM Nmm
Torsional moment due to braking MX, MZ Nmm
Sum of bending moments MY Nmm
Sum of torsional moments MR Nmm
Resultant moment b2 mm Distance between vertical force input points on axle journals s2 mm Distance between wheel rolling circles SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 8 Table 1 (continued) Symbol Unit Description 1h mm Height above the axle centreline of vehicle centre of gravity of masses carried by the wheelset iy mm Distance between the rolling circle of one wheel and force iF y mm Abscissa for any section of the axle calculated from the section subject to force 1P Γ
Average friction coefficient between the wheel and the brake shoe or between the brake pads and the disc σ=N/mm2=πtress=calc×lated=in=one=section=K
Fatigue stress concentration factor R mm Nominal radius of the rolling circle of a wheel bR mm Brake radius d mm Diameter for one section of the axle 'd mm Bore diameter of a hollow axle D mm Diameter used for determining K r mm Radius of transition fillet or groove used to determine K S
Security coefficient G
Centre of gravity fLR N/mm2 Fatigue limit under rotating bending up to 107 cycles for smooth test pieces fER N/mm2 Fatigue limit under rotating bending up to 107 cycles for notched test pieces qa m/s2 Unbalanced transverse acceleration qf
Thrust factor 4 General The major phases for the design of an axle are: a) definition of the forces to be taken into account and calculation of the moments on the various sections of the axle; b) selection of the diameters of the axle body and journals and - on the basis of these diameters - calculation of the diameters for the other parts of the axle; c) the options taken are verified in the following manner: ⎯ stress calculation for each section; ⎯ comparison of these stresses with the maximum permissible stresses. The maximum permissible stresses are mainly defined by: ⎯ the steel grade; ⎯ whether the axle is solid or hollow. An example of a data sheet with all these phases is given in Annex A. SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 9 5 Forces and moments to be taken into consideration 5.1 Types of forces Two types of forces are to be taken into consideration as a function: 1) of the masses in motion; 2) of the braking system. 5.2 Effects due to masses in motion The forces generated by masses in motion are concentrated along the vertical symmetry plane (y, z) (see Figure 1) intersecting the axle centreline.
Figure 1 Unless otherwise defined by the customer, the masses )(21mm+ to be taken into account for the main types of rolling stock are defined in Table 2. For particular applications, e.g. suburban vehicles, other definitions for masses are necessary, in accordance with the specific operating requirements.
SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 10 Table 2 Type of rolling stock units Mass )(21mm+ Freight wagons For the axle considered, proportion of the wagon mass under maximum permissible loading in service Coaches including accommodation for passengers, luggage or post
Mass in service + 1,2 × payload,
1 – Main line vehiclesa "mass in service" is defined as: the vehicle mass without passengers, tanks full (of water, sand, fuel, etc.); "payload" is defined as the mass of a passenger estimated at 80 kg, including hand luggage; ⎯ 1 passenger per seat; ⎯ 2 passengers per m² in corridors and vestibules; ⎯ 2 passengers per attendant compartment; ⎯ 300 kg per m2 in luggage compartments.
2 – Suburban vehiclesa b Mass in service + 1,2 × payload, "mass in service" is defined as the vehicle mass without passengers, tanks full (of water, sand, fuel, etc.); "payload" is defined as the mass of a passenger, which is estimated at 70 kg (little or no luggage); ⎯ 1 passenger per seat; ⎯ 3 passengers per m² in corridor areas; ⎯ 4 or 5 passengers per m² in vestibule areas b; ⎯ 300 kg per m2 in luggage compartments. a The payloads to be taken into account to determine the mass of the mainline and suburban vehicles broadly reflect the normal operating conditions of the member railways of the International Union of Railways (UIC). If the operating conditions differ significantly, these masses may be modified, for example, by increasing or decreasing the number of passengers per m² in corridors and vestibules. b These vehicles are sometimes associated with classes of passenger travel, i.e. 1st or 2nd class. The bending moment xM in any section is calculated from forces 1P, 2P, 1Q, 2Q, 1Y, 2Y and iF as shown in Figure 2. It represents the most adverse condition for the axle, i.e.: 1) asymmetric distribution of forces; 2) the direction of the forces iF due to the masses of the unsprung components selected in such a manner that their effect on bending is added to that due to the vertical forces; 3) the value of the forces iFresults from multiplying the mass of each unsprung component by 1 g.
SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 11
Key G
centre of gravity of vehicle Figure 2 Table 3 shows the values of the forces calculated from 1m. The formulae coefficient values are applicable to standard gauge axles and classical suspension. For very
different gauges, metric gauge for example, or a new system of suspension, tilting system for example, other values shall be considered (see Annexes B and C). SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 12
Table 3 All axles except guiding axlea gmbhP111)/075,0625,0(+= gmbhP112)/075,0625,0(−= gmY1130,0= gmY1215,0= gmYYH12115,0=−= Guiding axlea gmbhP111)/0875,0625,0(+= gmbhP112)/0875,0625,0(−= gmY1135,0= gmY12175,0= gmYYH121175,0=−= For all axles
()()()()[]iiiysFRYYsbPsbPsQ−Σ−−+−−+=22121211
()()()[]iiiyFRYYsbPsbPsQΣ−−−−−+=2112221 a The guiding axle is the axle of the first (i.e. leading) bogie of a coach used at the head of a reversible trainset. If an axle can be used in both positions (guiding or non-guiding), it is to be considered as a guiding axle.
Table 4 shows the formulae to calculate xM for each zone of the axle and the general outline of xM variations along the axle. Table 4 Zone of the axle xMa
Between loading plane and running surface yPMx1=
Between running surfaces Mx = P1y – Q1 (y – b + s) + Y1R – ΣiFi (y – b + s – yi)
SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 13
iF: force(s) on the left of the section considered
General outline of xM
variations
a For a non-symmetric axle, the calculations shall be carried out after applying the load alternately to the two journals to determine the worst case.
5.3 Effects due to braking Braking generates moments that can be represented by three components:'xM,'yM,'zM (see Figure 3).
Figure 3 SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 14 1) the bending component 'xM is due to the vertical forces parallel to the z axis; 2) the bending component 'zM is due to the horizontal forces parallel to the x axis; 3) the torsional component 'yM is directed along the axle centreline (y axis); it is due to the forces applied tangentially to the wheels. The components 'xM , 'yM and 'zM are shown in Table 5 for each method of braking. If several methods of braking are superimposed, the values corresponding to each method shall be added. NOTE If other methods of braking are used, the forces and moments to be taken into account can be obtained on the basis of the same principles as those shown in Table 5. Special attention should be paid to the calculation of the 'xM component, which is to be added directly to the xM component representing masses in motion. 5.4 Effects due to curving and wheel geometry For an unbraked wheelset, the torsional moment 'yM is equal to 0,2 PR to account for possible differences in wheel diameters and the effect of passing through curves. For a braked wheelset, these effects are included in the effects due to braking. 5.5 Calculation of the resultant moment In every section, the maximum stresses are calculated from the resultant moment MR(see the following note), which is equal to: 222MZMYMXMR++= where MX, MYand MZare the sums of the various components due to masses in motion and braking: ∑+='xxMMMX ∑='yMMY ∑='zMMZ
NOTE At a point on the outer surface of a solid cylinder (also in the case of a hollow one) with d as diameter, the components MX, MYand MZgenerate: ⎯ a normal stress for MXand MZ; ⎯ a shear stress for MY. The normal stress has the following value (bending of beams with a circular section): 32232dMZMXnπσ+= The value of the shear stress is the following (torsion of beams with a circular section): SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 15 316dMYtπσ= As a result, the two principal stresses 1σ and 2σ are obtained as: 24221tnnσσσσ++=24222tnnσσσσ+−= Since the normal stress has a much higher absolute value (10 to 20 times) than the shear stress, the diameter of the largest Mohr's circle is selected (21σσ− in this case) as a check of the value assumed ford. 22232t2n21MYMZMXd324++π=σ+σ=σ−σ=σ As a result, the definition of a resultant moment is: 222MZMYMXMR++= SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 16 Table 5 Components M’x, M’z, M’y Method of braking used Friction brake blocks on both sides of each wheelFriction brake block on one side only of each wheel Between loading plane and running surface Between running surfaces Between loading plane and running surface Between running surfaces
M’x = 0,3Ff Γ y M’x = 0,3Ff Γ (b – s) M’x = Ff Γ y M’x = Ff Γ (b – s)
a b
a b b b M’x
M’z = Ff (0,3 + Γ )y M’z = Ff (0,3 + Γ )(b – s)M’z = Ff (1 + Γ )y M’z = Ff (1 + Γ )(b – s)
a a
M’z
M’y
M’y = 0
M’y = 0,3P’R c d
M’y = 0
M’y = 0,3P’R c d
SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 17 Table 5 (continued) Components M’x, M’z, M’y Method of braking used
Two brake discs mounted on the axle Two brake discs attached to the wheel hubf Between loading plane and running surface Between running surfaces and disc Between discsBetween loading plane and running surface Between running surfaces
M’x = Ff Γ y M’x = Ff Γ (b – s + yi) M’x = Ff Γ y M’x = Ff Γ (b – s + yi)
b b b b M’x
M’z = Ff ΓyRRb M’z = Ff Γ RRb (b – s) M’z = Ff ΓyRRb M’z = Ff Γ (b – s) RRb
b b b b M’z
M’y M’y = 0 RPMy''3,0= d e
M’y = 0,3 P’R M’y = 0 M’y = 0,3 P’R
d, e
d, e SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 18 Table 5 (continued) Components M’x, M’z, M’y Method of braking used One brake disc mounted on the axle One brake disc attached to the wheel hubf Between first loading plane and disc Between disc and second loading plane Between first loading plane and disc Between disc and second loading plane
M’x = Ff Γ ()ybysbi2−+
M’x = Ff Γ ()()ybbysbi−+−22M’x = b21Ff Γ y (b+s-yi) M’x = Ff Γ()()ybbysbi−+−22 b B b b M’x
Between loading planes and running surface Between running surfaces
M’z = 21Ff ΓyRRb M’z =21Ff ΓRRb(b – s)M’z = 21Ff ΓyRRb M’z = 21Ff Γ (b – s) RRbM’z
Between loading planes and running surface Between running surfaces
M’y M’y = 0 M’y = 0,3 P’R M’y = 0 M’y = 0,3 P’R
d, e
d, e SIST EN 13103:2009+A2:2012
EN 13103:2009+A2:2012 (E) 19 Table 5 (continued) a The coefficient 0,3 results from experiments which established the possible differences between the applied forces of two blocks on each wheel. b Unless other values are justified: − for brake blocks: - Γ = 0,1 for cast iron blocks; - Γ = 0,1 7 for all blocks with low-friction coefficient excluding cast iron; - Γ = 0,25 for all blocks with high-friction coefficient excluding cast iron. − for brake pads: - Γ = 0,35. c This value was obtained from experimental tests and corresponds to a braking force difference between the two wheels producing a force difference tangential to the wheels and equates to '3,0P. It includes the torsional moment as specified in 5.3. d 'P is the proportion of P braked with the method of braking considered. e By convention, the torsional moment between running surfaces is selected at the value of RP'3,0. It includes the torsional moment due to braking and the torsional moment as specified in 5.4. f When the disc is mounted on the wheel web, then 0=iy 6 Determination of geometric characteristics of the various parts of the axle 6.1 Stresses in the various sections of the axle On any section of the axle with d as diameter, the stress4 to be taken into account is the following: ⎯ for a solid axle (see Figure 4a): 332dMRKπσ××= 5) ⎯ for a hollow axle (see Figure 4b): ⎯ on the outer surface:
)(324'4dddMRK−×××=πσ ⎯ in the bore:
)(324'4'dddMRK−×××=πσ
4 In the case of a conical wheel seat, the stress is calculated for the section where the resultant moment is the highest and the diameter of this section is taken to be equal to the lower diameter of the wheel seat. 5 Kis a fatigue stres
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