# SIST-TS CEN/TS 13103-2:2020

(Main)## Railway applications - Wheelsets and bogies - Part 2: Design method for axles with internal journals

## Railway applications - Wheelsets and bogies - Part 2: Design method for axles with internal journals

This document:

- defines the forces and moments to be taken into account with reference to masses, traction and braking conditions;

- gives the stress calculation method for axles with inboard axle journals;

- specifies the maximum permissible stresses to be assumed in calculations for steel grade EA1N, EA1T and EA4T defined in EN 13261;

- describes the method for determination of the maximum permissible stresses for other steel grades;

- determines the diameters for the various sections of the axle and recommends the preferred shapes and transitions to ensure adequate service performance.

This document is applicable for axles defined in EN 13261. This document applies only for heavy rail vehicles.

The calculation of wheelsets for special applications (e.g. railbound construction and maintenance machines) can be made according to this document only for the load cases of free-rolling and rolling in train formation.

## Bahnanwendungen - Radsätze und Drehgestelle - Teil 2: Konstruktionsleitfaden für innengelagerte Radsatzwellen

Dieses Dokument:

- definiert die zu berücksichtigenden Kräfte und Momente in Bezug auf Masse, Traktions- und Bremsbedingungen;

- gibt die Spannungsberechnungsmethode für innengelagerte Radsatzwellen an;

- legt die maximal zulässigen Spannungen fest, die bei den Berechnungen für die in EN 13261 definierten Stahlsorten EA1N, EA1T und EA4T anzunehmen sind;

- beschreibt das Verfahren zur Bestimmung der höchstzulässigen Spannungen für andere Stahlgüten;

- bestimmt die Durchmesser für die verschiedenen Abschnitte der Radsatzwelle und empfiehlt die bevorzugten Formen und Übergänge, um eine angemessene Betriebsleistung sicherzustellen.

Dieses Dokument gilt für Radsatzwellen, die in EN 13261 definiert sind.

Dieses Dokument gilt nur für Vollbahnfahrzeuge.

Die Berechnung von Radsätzen für spezielle Anwendungen (z. B. schienengebundene Bau- und Wartungsmaschinen) kann nach diesem Dokument nur für die Lastfälle Freilaufen und Rollen im Zugverband erfolgen.

## Applications ferroviaires - Essieux montés et bogies - Partie 2: Méthode de conception pour les essieux-axes à fusées intérieures

Le présent document :

— définit les forces et moments à prendre en compte en fonction des masses, de la traction et du freinage ;

— donne la méthode de calcul des contraintes dans les essieux-axes à fusées intérieures ;

— prescrit les contraintes maximales admissibles à prendre en compte dans les calculs pour les nuances d'acier EA1N, EA1T et EA4T définies dans l'EN 13261 ;

— décrit la méthode de détermination des contraintes maximales admissibles pour les autres nuances d'acier ;

— permet de calculer les diamètres des différentes parties de l'essieu-axe et recommande les formes et raccordements préférentiels pour garantir une bonne tenue en service.

Le présent document est applicable aux essieux-axes définis dans l'EN 13261.

Le présent document s'applique exclusivement aux véhicules ferroviaires lourds.

Les calculs d'essieux pour des applications spéciales (par exemple, les machines de construction et de maintenance empruntant les voies ferrées) peuvent être menés selon le présent document, uniquement pour les cas de charges de véhicule isolé, hors séquence de travail et véhicule incorporé dans un train.

## Železniške naprave - Kolesne dvojice in podstavni vozički - 2. del: Metode za načrtovanje osi z notranjim uležajenjem

### General Information

### Standards Content (sample)

SLOVENSKI STANDARD

SIST-TS CEN/TS 13103-2:2020

01-september-2020

Železniške naprave - Kolesne dvojice in podstavni vozički - 2. del: Metode za

načrtovanje osi z notranjim uležajenjem

Railway applications - Wheelsets and bogies - Part 2: Design method for axles with

internal journalsBahnanwendungen - Radsätze und Drehgestelle - Teil 2: Konstruktionsleitfaden für

innengelagerte Radsatzwellen

Applications ferroviaires - Essieux montés et bogies - Partie 2: Méthode de conception

pour les essieux-axes à fusées intérieuresTa slovenski standard je istoveten z: CEN/TS 13103-2:2020

ICS:

45.040 Materiali in deli za železniško Materials and components

tehniko for railway engineering

SIST-TS CEN/TS 13103-2:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TS CEN/TS 13103-2:2020

CEN/TS 13103-2

TECHNICAL SPECIFICATION

SPÉCIFICATION TECHNIQUE

June 2020

TECHNISCHE SPEZIFIKATION

ICS 45.040

English Version

Railway applications - Wheelsets and bogies - Part 2:

Design method for axles with internal journals

Applications ferroviaires - Essieux montés et bogies - Bahnanwendungen - Radsätze und Drehgestelle - Teil

Partie 2: Méthode de conception pour les essieux-axes 2: Konstruktionsleitfaden für innengelagerte

à fusées intérieures RadsatzwellenThis Technical Specification (CEN/TS) was approved by CEN on 13 April 2020 for provisional application.

The period of validity of this CEN/TS is limited initially to three years. After two years the members of CEN will be requested to

submit their comments, particularly on the question whether the CEN/TS can be converted into a European Standard.

CEN members are required to announce the existence of this CEN/TS in the same way as for an EN and to make the CEN/TS

available promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in

parallel to the CEN/TS) until the final decision about the possible conversion of the CEN/TS into an EN is reached.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2020 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TS 13103-2:2020 E

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Contents Page

European foreword ............................................................................................................................................. 3

1 Scope .......................................................................................................................................................... 4

2 Normative references .......................................................................................................................... 4

3 Terms and definitions ......................................................................................................................... 5

4 Symbols and abbreviations ............................................................................................................... 6

5 General ...................................................................................................................................................... 8

6 Forces and moments to be taken into consideration ............................................................... 8

6.1 Types of forces ....................................................................................................................................... 8

6.2 Influence of masses in motion .......................................................................................................... 8

6.3 Effects due to braking ........................................................................................................................13

6.4 Effects due to curving and wheel geometry ...............................................................................18

6.5 Effects due to traction ........................................................................................................................18

6.6 Calculation of the resultant moment ...........................................................................................19

7 Determination of geometric characteristics of the various parts of the axle ................20

7.1 Stresses in the various sections of the axle ................................................................................20

7.2 Determination of the diameter of journals and axle bodies ................................................23

7.3 Determination of the diameter of the various seats from the diameter of the axle

body or from the journals ................................................................................................................23

8 Maximum permissible stresses ......................................................................................................26

8.1 General ....................................................................................................................................................26

8.2 Steel grade EA1N and EA1T .............................................................................................................27

8.3 Steel grade other than EA1N or EA1T ..........................................................................................29

Annex A (informative) Model of axle calculation sheet ......................................................................35

Bibliography ........................................................................................................................................................36

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European foreword

This document (CEN/TS 13103-2:2020) has been prepared by Technical Committee CEN/TC 256

“Railway applications”, the secretariat of which is held by DIN.Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

According to the CEN/CENELEC Internal Regulations, the national standards organisations of the

following countries are bound to announce this Technical Specification: Austria, Belgium, Bulgaria,

Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United

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1 Scope

This document:

— defines the forces and moments to be taken into account with reference to masses, traction and

braking conditions;— gives the stress calculation method for axles with inboard axle journals;

— specifies the maximum permissible stresses to be assumed in calculations for steel grade EA1N, EA1T

and EA4T defined in EN 13261;— describes the method for determination of the maximum permissible stresses for other steel grades;

— determines the diameters for the various sections of the axle and recommends the preferred shapes

and transitions to ensure adequate service performance.This document is applicable for axles defined in EN 13261.

This document applies only for heavy rail vehicles.

The calculation of wheelsets for special applications (e.g. railbound construction and maintenance

machines) can be made according to this document only for the load cases of free-rolling and rolling in

train formation.2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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, Railway applications — Wheelsets and bogies — Wheelsets — Product requirements

EN 13261, Railway applications — Wheelsets and bogies — Axles — Product requirements

EN 15313, Railway applications - In-service wheelset operation requirements - In-service and off-vehicle

wheelset maintenanceEN 15663, Railway applications - Definition of vehicle reference masses

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3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— IEC Electropedia: available at http://www.electropedia.org/— ISO Online browsing platform: available at https://www.iso.org/obp

3.1

powered axle

vehicle axle that is driven by a vehicle’s engine. For the purpose of this standard, the following solid and

hollow axles are considered as “powered axles”:— powered axles for railway rolling stock;

— non-powered axles of motor bogies;

— non-powered axles of locomotives

3.2

non-powered axle

solid and hollow axle of railway rolling stock used for the transportation of passengers and freight that is

not considered as a powered axle as defined in 3.13.3

technical specification

document, describing specific parameters and/or product requirements as an addition to the

requirements of this standard3.4

guiding axle

first axle (i.e. leading) of a train set

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4 Symbols and abbreviations

For the purposes of this document, the symbols and abbreviations in Table 1 apply.

Table 1 — Symbols and abbreviationsSymbol Unit Description

kg Mass on journals (including bearings and axle boxes)

kg Wheelset mass and masses on the wheelset between rolling circles according to

EN 13262 (brake disc, gear wheel etc.)

kg For the wheelset considered, proportion of the mass of the vehicle on the rails

m + mm/s Acceleration due to gravity

()m + m g

Half the vertical force per wheelset on the rail

N Vertical static force per journal when the wheelset is loaded symmetrically

m g

N Vertical force on the more heavily-loaded journal

N Vertical force on the less heavily-loaded journal

N Proportion of P braked by any mechanical braking system

N Wheel/rail horizontal force perpendicular to the rail on the side of the more

heavily- loaded journal

N Wheel/rail horizontal force perpendicular to the rail on the side of the less

heavily-loaded journal

Force balancing the forces Y and Y

1 2

N Vertical reaction on the wheel situated on the side of the more heavily-loaded

journal

N Vertical reaction on the wheel situated on the side of the less heavily-loaded

journal

N Forces exerted by the masses of the unsprung elements situated between the

two wheels (brake disc(s), pinion, etc.)

N Maximum force input of the brake shoes of the same shoeholder on one wheel

or interface force of the pads on one disc

N∙mm Bending moment due to the masses in motion

' '

N∙mm Bending moments due to braking

M , M

x z

N∙mm Torsional moment due to braking

'' ''

N∙mm Bending moments due to traction

M M

x z

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N∙mm Torsional moment due to traction

MX , MZ N∙mm Sum of bending moments

N∙mm Sum of torsional moments

N∙mm Resultant moment

mm Distance between vertical force input points on axle journals

mm Distance between wheel rolling circles

mm Height above the axle centreline of vehicle centre of gravity of masses carried by

the wheelsety Distance between the rolling circle of one wheel and force F

i i

mm Abscissa for any section of the axle calculated from the section subject to force

Average friction coefficient between the wheel and the brake shoe or betweenthe brake pads and the disc

N/mm Stress calculated in one section

Fatigue stress correction factor

mm Nominal wheel radius (Nominal wheel diameter / 2)

mm Brake radius

d mm Diameter for one section of the axle

mm Bore diameter of a hollow axle

mm Diameter used for determining K

mm Radius of transition fillet or groove used to determine

Security coefficient

Centre of gravity

2 7

N/mm Fatigue limit under rotating bending up to 10 cycles for unnotched test pieces

2 7N/mm Fatigue limit under rotating bending up to 10 cycles for notched test pieces

m/s Unbalanced transverse accelerationThrust factor

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5 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;

— the type of transmission of motor power.

An example of a data sheet with all these phases is given in Annex A.

6 Forces and moments to be taken into consideration

6.1 Types of forces

Three types of forces are to be taken into consideration as a function of the:

— masses in motion;

— braking system;

— traction.

6.2 Influence of 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 — Definition of centrelines and of moments due to masses in motion

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The bending moment M is due to the vertical forces parallel to the Z axis.

Unless otherwise defined in the technical specification, the masses ()m + m to be taken into account for

the main types of rolling stock are defined in Table 2. For particular applications, other definitions for

masses are necessary, in accordance with the specific operating requirements.Table 2 — Masses to take into account for the main types of rolling stock

Type of rolling stock

Mass ()m + m

Freight wagons Design mass in working order + Normal design

payload (Maximum payload),

Traction units with no passenger accommodation,

Design mass in working order and Normal design

luggage areas and postal vans

payload are defined in EN 15663.

Coaches and traction units including Design mass in working order + 1,2 × Normal

accommodation for passengers, luggage or post design payload,

1 – High speed and long distance trains Design mass in working order is defined in

EN 15663.Normal design payload is defined in EN 15663 on

which the standing passengers shall be:

2 2

160 kg/m (2 passengers per m ) in standing and

catering areas.

2 – Passenger vehicles other than high speed and Design mass in working order is defined in

long distance trains EN 15663.Normal design payload is defined in EN 15663 on

which the standing passengers shall be:

2 2

— 210 kg/m (3 passengers per m ) in corridor

areas;

2 2

— 350 kg/m (5 passengers per m ) in vestibule

2 2

areas, 280 kg/m (4 passengers per m ) may be

used for specific services (e.g. 1st class area) as

described in the technical specification.

The bending moment M in any section is calculated from forces P , P , Q , Q , Y , Y and F as shown

x 1 2 1 2 1 2 iin Figure 2. It represents the force equilibrium for right hand curving, i.e.:

— asymmetric distribution of forces;

— the direction of the forces F due to the masses of the non-suspended components selected in such a

manner that their effect on bending is added to that due to the vertical forces;— the value of the forces F results from multiplying the mass of each non-suspended component by

3 g.Left hand curving force equilibrium shall be also considered and the formulae and the forces in Figure 2

adapted.Both cases, left-hand and right hand curving, shall be calculated to cover the worst case for the axle

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Figure 2 — Forces for calculation of bending moment

Table 3 shows the values of the forces calculated from m .

The formulae coefficient values are applicable to standard gauge axles and classical suspension. For

specific designs (different gauges, e.g. metric gauge, or a new system of suspension, e.g. tilting system),

other values shall be considered.NOTE These specific designs will be taken into account in a future version.

Table 3 — Formulae for calculation of forces for main line vehicles

Load case 1:

P = 08, m g

Straight track

P = 08, m g

2 1

Y = 0

Y = 0

H= 0

Load case 2:

P (,0 5625+ 0,0375h / bm) g

1 11

Curve

P (,0 5625− 0,0375h / bm) g

2 11

Y = 0,135m g

Y = 0,21m g

H= Y− Y= 0,075m g

21 1

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For load cases 1 and 2

Q Ps+ b+ Ps−+b Y− Y R+ F y 2s− y

( ) ( ) ( ) ( )

1 1 2 21 ii i

Q Ps−+b Ps+ b− Y− Y R+ F y

( ) ( ) ( )

2 1 2 21 ∑ ii

Valid for guiding and non-guiding axles.

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Table 4 shows the formulae to calculate M for each zone of the axle and the general outline of M

x xvariations along the axle.

Table 4 — Formulae for calculation of bending moment

Zone of the axle

Between rolling circle and

M Q y+ YR

x 11

loading plane

Between loading planes

M Q y+ YR− P y−+s b− F y− y

( ) ( )

( )

x 1 11 ∑ ii

F : force(s) on the left of the section considered

General outline of M

variations

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6.3 Effects due to braking

' ' '

Braking generates moments that can be represented by three components: M , M , M (see Figure 3).

x y zFigure 3 — Moments due to braking

— the bending component M is due to the vertical forces parallel to the z axis;

— the bending component M is due to the horizontal forces parallel to the x-axis;

— the torsional component M is directed along the axle centreline (y-axis); it is due to the forces

applied tangentially to the wheels.' ' '

The components M , M and M are shown in Table 5 for each method of braking.

x y z

If several methods of braking are superimposed, the values corresponding to each method shall be added.

For example, forces and moments due to electric braking or regenerative braking shall be added.

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 M component, which is to be added directly to the M component representing

x xmasses in motion.

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Table 5 — Formulae for calculation of moments due to braking

Components Method of braking used

M’ , M’ , M’

x z y

Friction brake blocks on both sides Friction brake block on one side only

of each wheel of each wheel

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

M’ = 0,3F Γ y M’ = 0,3F Γ (s – b) M’ = F Γ y M’ = F Γ (s – b)

x f x f x f x f

a,b a,b b b

M’ = F (0,3 + Γ)y M’ = F (0,3 + Γ)(s – M’ = F (1 + Γ)y M’ = F (1 + Γ)(s – b)

z f z f z f z f

a,b a,b b b

M’ M’ = 0,3P’R M’ = 0,3P’R

y y y

c,d c,d

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Components Method of braking used

M’ , M’ , M’

x z y

Two brake discs mounted on the axle Two brake discs attached inboard to the

wheel hub

Between Between Between Between rolling Between loading

rolling circle loading plane discs circle and loading planes

and loading and disc plane

plane

M’ = 0 M’ = M’ = M’ = F Γ (y – y) M’ = F Γ (b – s + y )

x x x x f i x f i

F Γ (b – s + y) F Γ (b – s +

f f

y )

b b b b

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

R R R R

b b b b

M’ = F Γ y M’ = F Γ (s – b) M’ = F Γ y M’ = F Γ (s – b)

z f z f z f z f

R R R R

b b b b

M’ M’ = 0,3 P’R M’ = 0,3 P’R

y y y

d,e d,e

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Components Method of braking used

M’ , M’ , M’

x z y

One brake disc mounted on the axle One brake disc attached inboard to the

wheel hub

Between Between first Between Between Between Between

rolling circle loading plane disc and rolling loading planes second

and loading and disc second circle and loading

plane loading first plane and

plane loading rolling

plane circle

M’ = 0 M’ = M’ = M’ =

x x x x

M’ =

F Γ (b + s - F Γ (b - s + F Γ (y – y)

f f f i

M’ = 0

F Γ (b - s + y )

y ) y ) x

f i

i i

(b + s - y) / 2b

(b – s + y) / (b + s - y) /

2b 2b

b b b b

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

R R R R

b b b b

M’ = F Γ y M’ = F Γ (s – b) M’ = F Γ y M’ = F Γ (s – b)

z f z f z f z f

2R 2R 2R 2R

M’ M’ = 0,3 P’R M’ = 0,3 P’R

y y y

d,e d,e

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Components Method of braking used

M’ , M’ , M’

x z y

One brake disc attached outboard to the Two brake discs attached outboard to the

f f

wheel hub wheel hub

Between rolling Between Between Between rolling Between loading

circle and first loading second circle and loading planes

loading plane planes loading plane

plane and

rolling

circle

M’ = F Γ (y + y) M’ = M’ = F Γ (y + y) M’ = F Γ (y + s - b)

x f i x x f i x f i

F Γ (y + s

f i

M’ = 0

- b)

(b + s - y) /

b b b b

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

R R R R

b b b b

M’ = F Γ y M’ = F Γ (s – b) M’ = F Γ y M’ = F Γ (s – b)

z f z f z f z f

2R 2R R R

b b b b

M’ M’ = 0,3 P’R M’ = 0,3 P’R

y y y

d,e d,e

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The coefficient 0,3 results from experiments which established the possible differences between the applied

forces of two blocks on each wheel.Unless other values are justified:

for brake blocks:

Γ = 0,1 for cast iron blocks;

for all blocks with low-friction coefficient excluding cast iron;

Γ = 0,17

Γ = 0,25 for all blocks with high-friction coefficient excluding cast iron.

for brake pads:

Γ = 0,35 .

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 0,3P . It includes the torsional

moment as specified in 6.3.P is the proportion of P braked with the method of braking considered.

By convention, the torsional moment between rolling circles is selected at the value of 0,3PR . It includes the

torsional moment due to braking and the torsional moment as specified in 6.4.When the disc is mounted on the wheel web, then y = 0

6.4 Effects due to curving and wheel geometry

For an unbraked wheelset, the torsional moment M 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.

6.5 Effects due to traction

The forces generated in the axle from the transmission of the driving torque under constant adhesion

conditions can normally be neglected. Calculation and experience have shown that the bending moments

'' '' ''M and M , and torsional moment M , are smaller than those generated by braking.

x z y

Traction and braking moments do not occur simultaneously.

The axle design should also take into account the instantaneous loss of traction, e.g. short-circuit

overload. Short-circuit torque shall be considered as a static load.Where traction control systems adopt a technique to maintain the tractive effort at the limit of adhesion,

any resultant controlled oscillations about the mean driving torque shall be considered in determining

the magnitude of the torsional moment M .For some applications, when driving torque is very high in starting conditions, and when they occur very

often, the calculation shall be done as follows:a) with the usual conditions described as above in 6.2, 6.3 and 6.4;

b) with the following starting conditions:

1) effects due to masses in motion given by Table 6;

2) effects due to starting driving torque.

The effect of the conditions defined in b 1) and b 2) shall be combined.

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The most severe conditions between a) and b) shall be used to calculate the axle.

Table 6 — Formulae for calculation of effects due to masses in motionStarting forces

P = 0,55m g

1 1

P = 0,55m g

Y = 0,10m g

Y = 0,05m g

2 1

H = 0,05mg

6.6 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:2 2 2

MR MX+ MY+ MZ

where MX , MY and MZ are the sums of the various components due to masses in motion and braking:

MX M+∑ MMY=∑ M

MZ=∑ M

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, MY and MZ generate:— a direct stress for MX and MZ;

— a shear stress for MY.

The direct stress has the following value (bending of beams with a circular section):

2 232 MX + MZ

σ =

π d

The value of the shear stress is the following (torsion of beams with a circular section):

16MYσ =

π d

σ σ

As a result, the two principal stresses and are obtained as:

1 2

2 2 2 2

σ ++σσ4 σ −+σσ4

n nt n nt

σ = σ =

1 2

2 2

The values, , may be replaced respectively by , and if the moments due to traction are greater than the moments

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Since the direct 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 (σσ− in this case) as a check of the value assumed for

1 22 2 2 2 2

σσ=−=σ σ+ 4σ= MX+ MZ+ MY

1 2 nt

π d

As a result, the definition of a resultant moment is:

2 2 2

MR MX+ MY+ MZ

7 Determination of geometric characteristics of the various parts of the axle

7.1 Stresses in the various sections of the axle

On any section of the axle with d as diameter, the stress to be taken into account is the following:

K××32 MR— for a solid axle (see Figure 4a): σ=

π d

— for a hollow axle (see Figure 4b):

K××32 MR× d

— on the outer surface: σ=

4 ' 4

π()d − d

K××32 MR× d

— in the bore: σ=

4 ' 4

π()d − d

Figure 4a Figure 4b

Figure 4 — Geometrical parameters of the axle

is a fatigue stress correction factor (i.e. it takes into account the geometry).

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In a cylindrical part located on the surface of a solid or hollow axle and in the bore of a hollow axle, the

stress correction factor K is equal to 1. However, each change in section produces a stress increment, the

maximum value of which can be found:— at the bottom of a transition between two adjacent cylindrical parts with different diameters;

— at the groove bottom;— at the intersection of the transition radii when the transition length is short (see 7.3.3 Note 2).

The stress correction factor K to calculate this increment is shown in the nomograms in Figure 5

**...**

SLOVENSKI STANDARD

kSIST-TS FprCEN/TS 13103-2:2020

01-februar-2020

Železniške naprave - Kolesne dvojice in podstavni vozički - 2. del: Metode za

načrtovanje osi z notranjim uležajenjem

Railway applications - Wheelsets and bogies - Part 2: Design method for axles with

internal journalsBahnanwendungen - Radsätze und Drehgestelle - Teil 2: Konstruktionsleitfaden für

innengelagerte Radsatzwellen

Applications ferroviaires - Essieux montés et bogies - Partie 2: Méthode de conception

pour les essieux-axes à fusées intérieuresTa slovenski standard je istoveten z: FprCEN/TS 13103-2

ICS:

45.040 Materiali in deli za železniško Materials and components

tehniko for railway engineering

kSIST-TS FprCEN/TS 13103-2:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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FINAL DRAFT

TECHNICAL SPECIFICATION

FprCEN/TS 13103-2

SPÉCIFICATION TECHNIQUE

TECHNISCHE SPEZIFIKATION

December 2019

ICS

English Version

Railway applications - Wheelsets and bogies - Part 2:

Design method for axles with internal journals

Applications ferroviaires - Essieux montés et bogies - Bahnanwendungen - Radsätze und Drehgestelle - Teil

Partie 2: Méthode de conception pour les essieux-axes 2: Konstruktionsleitfaden für innengelagerte

à fusées intérieures RadsatzwellenThis draft Technical Specification is submitted to CEN members for Vote. It has been drawn up by the Technical Committee

CEN/TC 256.CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are

aware and to provide supporting documentation.Warning : This document is not a Technical Specification. It is distributed for review and comments. It is subject to change

without notice and shall not be referred to as a Technical Specification.EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. FprCEN/TS 13103-2:2019 E

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Contents Page

European foreword ............................................................................................................................................. 3

1 Scope .......................................................................................................................................................... 4

2 Normative references .......................................................................................................................... 4

3 Terms and definitions ......................................................................................................................... 5

4 Symbols and abbreviations ............................................................................................................... 6

5 General ...................................................................................................................................................... 8

6 Forces and moments to be taken into consideration ............................................................... 8

6.1 Types of forces ....................................................................................................................................... 8

6.2 Influence of masses in motion .......................................................................................................... 8

6.3 Effects due to braking ........................................................................................................................13

6.4 Effects due to curving and wheel geometry ...............................................................................18

6.5 Effects due to traction ........................................................................................................................18

6.6 Calculation of the resultant moment ...........................................................................................19

7 Determination of geometric characteristics of the various parts of the axle ................20

7.1 Stresses in the various sections of the axle ................................................................................20

7.2 Determination of the diameter of journals and axle bodies ................................................23

7.3 Determination of the diameter of the various seats from the diameter of the axle

body or from the journals ................................................................................................................23

7.3.1 Wheel hub and bearing overhang requirements ....................................................................23

7.3.2 Transition between collar surface and wheel seat .................................................................23

7.3.3 Seat in the absence of an adjacent seat .......................................................................................24

7.3.4 Case of two adjacent seats ................................................................................................................24

7.3.5 Case of two non-adjacent seats ......................................................................................................25

8 Maximum permissible stresses ......................................................................................................25

8.1 General ....................................................................................................................................................25

8.2 Steel grade EA1N and EA1T .............................................................................................................26

8.3 Steel grade other than EA1N or EA1T ..........................................................................................29

8.3.1 General ....................................................................................................................................................29

8.3.2 Steel grade EA4T ..................................................................................................................................30

8.3.3 Other steel grades ...............................................................................................................................33

Annex A (informative) Model of axle calculation sheet ......................................................................34

Bibliography ........................................................................................................................................................35

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European foreword

This document (FprCEN/TS 13103-2:2019) has been prepared by Technical Committee CEN/TC 256

“Railway applications”, the secretariat of which is held by DIN.This document is currently submitted to the vote on TS.

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1 Scope

This document:

— defines the forces and moments to be taken into account with reference to masses, traction and

braking conditions;— gives the stress calculation method for axles with inboard axle journals;

— specifies the maximum permissible stresses to be assumed in calculations for steel grade EA1N, EA1T

and EA4T defined in EN 13261;— describes the method for determination of the maximum permissible stresses for other steel grades;

— determines the diameters for the various sections of the axle and recommends the preferred shapes

and transitions to ensure adequate service performance.This document is applicable for axles defined in EN 13261.

This document applies only for heavy rail vehicles.

The calculation of wheelsets for special applications (e.g. railbound construction and maintenance

machines) can be made according to this document only for the load cases of free-rolling and rolling in

train formation.2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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, Railway applications — Wheelsets and bogies — Wheelsets — Product requirements

EN 13261, Railway applications — Wheelsets and bogies — Axles — Product requirements

EN 15313, Railway applications - In-service wheelset operation requirements - In-service and off-vehicle

wheelset maintenanceEN 15663, Railway applications - Definition of vehicle reference masses

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3 Terms and definitions

For the purposes of this document, the following terms and definitions apply

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— IEC Electropedia: available at http://www.electropedia.org/— ISO Online browsing platform: available at http://www.iso.org/obp

3.1

powered axle

vehicle axle that is driven by a vehicle’s engine. For the purpose of this standard, the following solid and

hollow axles are considered as “powered axles”:— powered axles for railway rolling stock;

— non-powered axles of motor bogies;

— non-powered axles of locomotives

3.2

non-powered axle

solid and hollow axle of railway rolling stock used for the transportation of passengers and freight that is

not considered as a powered-axle as defined in 3.13.3

technical specification

document, describing specific parameter and/or product requirements as an addition to the

requirements of this standard3.4

guiding axle

first axle (i.e. leading) of a train set

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4 Symbols and abbreviations

For the purposes of this document, the symbols and abbreviations in Table 1 apply.

Table 1 – Symbols and abbreviationsSymbol Unit Description

m kg Mass on journals (including bearings and axle boxes)

m kg Wheelset mass and masses on the wheelset between rolling circles according to

EN 13262 (brake disc, gear wheel etc.)m +m

kg For the wheelset considered, proportion of the mass of the vehicle on the rails

1 2m/s Acceleration due to gravity

N (m+m )g

1 2

Half the vertical force per wheelset on the rail

N Vertical static force per journal when the wheelset is loaded symmetrically

N Vertical force on the more heavily-loaded journal

P N Vertical force on the less heavily-loaded journal

N Proportion of P braked by any mechanical braking system

Y N Wheel/rail horizontal force perpendicular to the rail on the side of the more

heavily- loaded journalN Wheel/rail horizontal force perpendicular to the rail on the side of the less

heavily-loaded journal

N Force balancing the forces Y and Y

1 2

Q N Vertical reaction on the wheel situated on the side of the more heavily-loaded

journalN Vertical reaction on the wheel situated on the side of the less heavily-loaded

journal

F N Forces exerted by the masses of the unsprung elements situated between the

two wheels (brake disc(s), pinion, etc.)

N Maximum force input of the brake shoes of the same shoeholder on one wheel

or interface force of the pads on one disc

N∙mm Bending moment due to the masses in motion

' '

N∙mm Bending moments due to braking

M , M

x z

M N∙mm Torsional moment due to braking

'' ''

N∙mm Bending moments due to traction

M , M

x z

N∙mm Torsional moment due to traction

MX , MZ N∙mm Sum of bending moments

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N∙mm Sum of torsional moments

N∙mm Resultant moment

mm Distance between vertical force input points on axle journals

mm Distance between wheel rolling circles

h mm Height above the axle centreline of vehicle centre of gravity of masses carried by

the wheelsety Distance between the rolling circle of one wheel and force

mm F

i i

mm Abscissa for any section of the axle calculated from the section subject to force

Average friction coefficient between the wheel and the brake shoe or betweenthe brake pads and the disc

σ 2

N/mm Stress calculated in one section

Fatigue stress correction factor

mm Nominal wheel radius (Nominal wheel diameter / 2)

mm Brake radius

mm Diameter for one section of the axle

mm Bore diameter of a hollow axle

mm Diameter used for determining K

mm Radius of transition fillet or groove used to determine K

Security coefficient

Centre of gravity

2 7

N/mm Fatigue limit under rotating bending up to 10 cycles for unnotched test pieces

2 7N/mm Fatigue limit under rotating bending up to 10 cycles for notched test pieces

a m/s Unbalanced transverse accelerationThrust factor

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5 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;

— the type of transmission of motor power.

An example of a data sheet with all these phases is given in Annex A.

6 Forces and moments to be taken into consideration

6.1 Types of forces

Three types of forces are to be taken into consideration as a function of the:

— masses in motion;

— braking system;

— traction.

6.2 Influence of 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 – Definition of centrelines and of moments due to masses in motion

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The bending moment is due to the vertical forces parallel to the Z axis.

Unless otherwise defined in the technical specification, the masses (m +m ) to be taken into account for

1 2the main types of rolling stock are defined in Table 2. For particular applications, other definitions for

masses are necessary, in accordance with the specific operating requirements.Table 2 – Masses to take into account according the main types of rolling stock

Type of rolling stock units Mass (m +m )

1 2

Freight wagons Design mass in working order + Normal design

payload (Maximum payload),

Traction units with no passenger accommodation,

Design mass in working order and Normal design

luggage areas and postal vans

payload are defined in EN 15663.

Coaches and traction units including Design mass in working order + 1,2 × Normal

accommodation for passengers, luggage or post design payload,

1 – High speed and long distance trains Design mass in working order is defined in

EN 15663.Normal design payload is defined in EN 15663 on

which the standing passengers shall be:

2 2

160 kg/m (2 passengers per m ) in standing and

catering areas.

2 – Passenger vehicles other than high speed and Design mass in working order is defined in

long distance trains EN 15663.Normal design payload is defined in EN 15663 on

which the standing passengers shall be:

2 2

— 210 kg/m (3 passengers per m ) in corridor

areas;

2 2

— 350 kg/m (5 passengers per m ) in vestibule

2 2

areas, 280 kg/m (4 passengers per m ) may be

used for specific services (e.g. 1st class area) as

described in the technical specification.

The bending moment M in any section is calculated from forcesP ,P , Q , Q , Y , Y and F as shown in

1 2 1 2 1 2 iFigure 2. It represents the force equilibrium for right hand curving, i.e.:

— asymmetric distribution of forces;

— the direction of the forces F due to the masses of the non-suspended components selected in such a

manner that their effect on bending is added to that due to the vertical forces;— the value of the forces F results from multiplying the mass of each non-suspended component by 3 g.

Left hand curving force equilibrium shall be also considered and the formulae and the forces in Figure 2

adapted.Both cases, left-hand and right hand curving, shall be calculated to cover the worst case for the axle

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Figure 2 – Forces for calculation of bending moment

Table 3 shows the values of the forces calculated fromm .

The formulae coefficient values are applicable to standard gauge axles and classical suspension. For

specific designs (different gauges, e.g. metric gauge, or a new system of suspension, e.g. tilting system),

other values shall be considered.NOTE These specific designs will be taken into account in a future version

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Table 3 – Formulae for calculation of forces for main line vehicles

P= 0,8m g

Load case 1:

1 1

Straight track

P = 0,8m g

2 1

Y = 0

Y = 0

H= 0

Load case 2: P= (0,5625+ 0,0375h /b)m g

1 1 1

Curve

P = (0,5625− 0,0375h /b)m g

2 1 1

Y = 0,135m g

1 1

Y = 0,21m g

2 1

H=Y −Y = 0,075m g

2 1 1

For load cases 1 and 2

1

Q P s+b+P s−+b Y−Y R+ Fy 2s−y

( ) ( ) ( ) ( )

1 1 2 21 ∑ ii i

i

1

Q P s−+b P s+b− Y−Y R+ Fy

( ) ( ) ( )

2 1 2 21 ∑ ii

i

Valid for guiding and non-guiding axles.

Table 4 shows the formulae to calculate M for each zone of the axle and the general outline of M

x xvariations along the axle.

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Table 4 – Formulae for calculation of bending moment

Zone of the axle

Between rolling circle and

M = Q y+Y R

x 1 1

loading plane

Between loading planes

M Q y+ YR− P y−s+b− F y− y

( ) ( )

( )

x 11 1 ∑ ii

F : force(s) on the left of the section considered

General outline of M

variations

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6.3 Effects due to braking

' ' '

Braking generates moments that can be represented by three components:M ,M ,M (see Figure 3).

x y zFigure 3 – Moments due to braking

— the bending component M is due to the vertical forces parallel to the z axis;

— the bending component M is due to the horizontal forces parallel to the x-axis;

— the torsional component M is directed along the axle centreline (y-axis); it is due to the forces

applied tangentially to the wheels.' ' '

The components M , M and M are shown in Table 5 for each method of braking.

x y z

If several methods of braking are superimposed, the values corresponding to each method shall be added.

For example, forces and moments due to electric braking or regenerative braking shall be added.

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 M component, which is to be added directly to the M component representing

x xmasses in motion.

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Table 5 – Formulae for calculation of moments due to braking

Components Method of braking used

M’ , M’ , M’

x z y

Friction brake blocks on both sides Friction brake block on one side only

of each wheel of each wheel

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

M’ = 0,3F Γ y M’ = 0,3F Γ (s – b) M’ = F Γ y M’ = F Γ (s – b)

x f x f x f x f

a b a b b b

M’ = F (0,3 + Γ)y M’ = F (0,3 + Γ)(s – M’ = F (1 + Γ)y M’ = F (1 + Γ)(s –

z f z f z f z f

b) b)

a b a b b b

M’ M’ = 0,3P’R M’ = 0,3P’R

y y y

c d c d

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Components Method of braking used

M’ , M’ , M’

x z y

Two brake discs mounted on the axle Two brake discs attached inboard to the

wheel hub

Between Between Between Between rolling Between loading

rolling circle loading plane discs circle and loading planes

and loading and disc plane

plane

M’ = 0 M’ = M’ = M’ = F Γ (y – y) M’ = F Γ (b – s + y )

x x x x f i x f i

F Γ (b – s + y) F Γ (b – s +

f f

y )

b b b b

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

R R R R

b b b b

M’ = F Γ y M’ = F Γ (s – M’ = F Γ y M’ = F Γ (s –

z f z f z f z f

R R R R

b) b)

b b b b

M’ M’ = 0,3 P’R M’ = 0,3 P’R

y y y

d, e d, e

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Components Method of braking used

M’ , M’ , M’

x z y

One brake disc mounted on the axle One brake disc attached inboard to the

wheel hub

Between Between first Between Between Between Between

rolling circle loading plane disc and rolling loading planes second

and loading and disc second circle and loading

plane loading first plane and

plane loading rolling

plane circle

M’ = 0 M’ = M’ = M’ =

x x x x

M’ =

F Γ (b + s - F Γ (b - s + F Γ (y – y)

f f f i

M’ = 0

F Γ (b - s + y )

y ) y ) x

f i

i i

(b + s - y) / 2b

(b – s + y) / (b + s - y) /

2b 2b

b b b b

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

R R R R

b b b b

M’ = F Γ y M’ = F Γ (s – b) M’ = F Γ y M’ = F Γ (s – b)

z f z f z f z f

2R 2R 2R 2R

M’ M’ = 0,3 P’R M’ = 0,3 P’R

y y y

d, e d, e

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Components Method of braking used

M’ , M’ , M’

x z y

One brake disc attached outboard to the Two brake discs attached outboard to the

f f

wheel hub wheel hub

Between Between Between Between rolling Between loading

rolling circle loading second circle and loading planes

and first planes loading plane

loading plane plane and

rolling

circle

M’ = F Γ (y + M’ = M’ = F Γ (y + y) M’ = F Γ (y + s - b)

x f i x x f i x f i

F Γ (y + s -

f i

M’ = 0

(b + s - y) /

b b b b

Between rolling Between loading Between rolling Between loading

circle and loading planes circle and loading planes

plane plane

R R

R R

b b

b b

M’ = F Γ y M’ = F Γ (s – b)

M’ = F Γ y M’ = F Γ (s –

z f z f

z f z f

2R 2R

R R

b b b b

M’ M’ = 0,3 P’R M’ = 0,3 P’R

y y y

d, e d, e

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The coefficient 0,3 results from experiments which established the possible differences between the applied

forces of two blocks on each wheel.Unless other values are justified:

r brake blocks:

Γ= 0,1 for cast iron blocks;

Γ= 0,17 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

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 0,3P . It includes the torsional

moment as specified in 6.3.P is the proportion of P braked with the method of braking considered.

By convention, the torsional moment between rolling circles is selected at the value of 0,3P R . It includes the

torsional moment due to braking and the torsional moment as specified in 6.4.y = 0

When the disc is mounted on the wheel web, then

6.4 Effects due to curving and wheel geometry

For an unbraked wheelset, the torsional moment M 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.

6.5 Effects due to traction

The forces generated in the axle from the transmission of the driving torque under constant adhesion

conditions can normally be neglected. Calculation and experience have shown that the bending moments

'' '' ''M and M , and torsional moment M , are smaller than those generated by braking. Traction and

x z ybraking moments do not occur simultaneously.

The axle design should also take into account the instantaneous loss of traction, e.g. short-circuit

overload. Short-circuit torque shall be considered as a static load.Where traction control systems adopt a technique to maintain the tractive effort at the limit of adhesion,

any resultant controlled oscillations about the mean driving torque shall be considered in determining

the magnitude of the torsional moment M .For some applications, when driving torque is very high in starting conditions, and when they occur very

often, the calculation shall be done as follows:a) with the usual conditions described as above in 6.2, 6.3 and 6.4;

b) with the following starting conditions:

1) effects due to masses in motion given by Table 6;

2) effects due to starting driving torque.

The effect of the conditions defined in b 1) and b 2) shall be combined.

The most severe conditions between a) and b) shall be used to calculate the axle.

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Table 6 — Formulae for calculation of effects due to masses in motion

P= 0,55m g

Starting forces

1 1

P = 0,55m g

2 1

Y = 0,10m g

1 1

Y = 0,05m g

2 1

H = 0,05m g

6.6 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:2 2 2

MR= MX +MY +MZ

where MX , MY and MZ are the sums of the various components due to masses in motion and braking:

MX= M +∑Mx x

MY=∑M

MZ=∑M

NOTE At a point on the outer surface of a solid cylinder (also in the case of a hollow one) with as diameter,

MX MY MZthe components , and generate:

— a direct stress for MX and MZ ;

— a shear stress for MY .

The direct stress has the following value (bending of beams with a circular section):

2 232 MX +MZ

σ =

The value of the shear stress is the following (torsion of beams with a circular section):

16MYσ =

t 3

and are obtained as:

As a result, the two principal stresses σ σ

1 2

2 2 2 2

σ + σ + 4σ σ − σ + 4σ

n n t n n t

σ = σ =

1 2

2 2

' ' ' '' '' ''

The valuesM , M y , M may be replaced respectively by M , M and M if the moments due to traction are

x x y zgreater than the moments due to braking.

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kSIST-TS FprCEN/TS 13103-2:2020

FprCEN/TS 13103-2:2019 (E)

Since the direct 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 (σ −σ in this case) as a check of the value assumed

1 2ford .

2 2 2 2 2

σ=σ −σ = σ + 4σ = MX + MZ + MY

1 2 n t

As a result, the definition of a resultant moment is:

2 2 2

MR= MX +MY +MZ

7 Determination of geometric characteristics of the various parts of the axle

7.1 Stresses in the various sections of the axle

On any section of the axle with d as diameter, the stress to be taken into account is the following:

K× 32×MR— for a solid axle (see Figure 4a): σ=

— for a hollow axle (see Figure 4b):

K×32×MR×d

— on the outer surface: σ=

4 '4

π (d −d )

K×32×MR×d

— in the bore: σ=

4 '4

π (d −d )

a b

Figure 4 – Geometrical parameters of the axle

K is a fatigue stress correction factor (i.e. it takes into account the geometry).

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FprCEN/TS 13103-2:2019 (E)

In a cylindrical part located on the surface of a solid or hollow axle and in the bore of a hollow axle, the

stress**...**

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