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 journals
Bahnanwendungen - 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 intérieures
Ta 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 Radsatzwellen
This 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
worldwide for CEN national Members.
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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
2
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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
Kingdom.
3
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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 maintenance
EN 15663, Railway applications - Definition of vehicle reference masses
4
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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 3.1
3.3
technical specification
document, describing specific parameters and/or product requirements as an addition to the
requirements of this standard
3.4
guiding axle
first axle (i.e. leading) of a train set
5
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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 abbreviations
Symbol Unit Description
kg Mass on journals (including bearings and axle boxes)
m
1
kg Wheelset mass and masses on the wheelset between rolling circles according to
m
2
EN 13262 (brake disc, gear wheel etc.)
kg For the wheelset considered, proportion of the mass of the vehicle on the rails
m + m
12
g
2
m/s Acceleration due to gravity
P
N
()m + m g
12
Half the vertical force per wheelset on the rail
2
N Vertical static force per journal when the wheelset is loaded symmetrically
P
0
m g
1
2
N Vertical force on the more heavily-loaded journal
P
1
N Vertical force on the less heavily-loaded journal
P
2
'
N Proportion of P braked by any mechanical braking system
P
N Wheel/rail horizontal force perpendicular to the rail on the side of the more
Y
1
heavily- loaded journal
N Wheel/rail horizontal force perpendicular to the rail on the side of the less
Y
2
heavily-loaded journal
H
N
Force balancing the forces Y and Y
1 2
N Vertical reaction on the wheel situated on the side of the more heavily-loaded
Q
1
journal
N Vertical reaction on the wheel situated on the side of the less heavily-loaded
Q
2
journal
N Forces exerted by the masses of the unsprung elements situated between the
F
i
two wheels (brake disc(s), pinion, etc.)
N Maximum force input of the brake shoes of the same shoeholder on one wheel
F
f
or interface force of the pads on one disc
N∙mm Bending moment due to the masses in motion
M
x
' '
N∙mm Bending moments due to braking
M , M
x z
'
N∙mm Torsional moment due to braking
M
y
'' ''
N∙mm Bending moments due to traction
,
M M
x z
6
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''
N∙mm Torsional moment due to traction
M
y
MX , MZ N∙mm Sum of bending moments
MY
N∙mm Sum of torsional moments
MR
N∙mm Resultant moment
2b
mm Distance between vertical force input points on axle journals
2s
mm Distance between wheel rolling circles
mm Height above the axle centreline of vehicle centre of gravity of masses carried by
h
1
the wheelset
mm
y Distance between the rolling circle of one wheel and force F
i i
y
mm Abscissa for any section of the axle calculated from the section subject to force
Q
1
Γ
Average friction coefficient between the wheel and the brake shoe or between
the brake pads and the disc
σ
2
N/mm Stress calculated in one section
K
Fatigue stress correction factor
R
mm Nominal wheel radius (Nominal wheel diameter / 2)
mm Brake radius
R
b
d mm Diameter for one section of the axle
'
mm Bore diameter of a hollow axle
d
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
2 7
N/mm Fatigue limit under rotating bending up to 10 cycles for unnotched test pieces
R
fL
2 7
N/mm Fatigue limit under rotating bending up to 10 cycles for notched test pieces
R
fE
2
m/s Unbalanced transverse acceleration
a
q
Thrust factor
f
q
7
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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
8
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The bending moment M is due to the vertical forces parallel to the Z axis.
x
Unless otherwise defined in the technical specification, the masses ()m + m to be taken into account for
12
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
12
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 i
in 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
i
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
i
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
design.
9
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Figure 2 — Forces for calculation of bending moment
Table 3 shows the values of the forces calculated from m .
1
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.
a
Table 3 — Formulae for calculation of forces for main line vehicles
Load case 1:
P = 08, m g
11
Straight track
P = 08, m g
2 1
Y = 0
1
Y = 0
2
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
11
Y = 0,21m g
21
H= Y− Y= 0,075m g
21 1
10
=
=
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For load cases 1 and 2
1
Q Ps+ b+ Ps−+b Y− Y R+ F y 2s− y
( ) ( ) ( ) ( )
1 1 2 21 ii i
∑
2s
i
1
Q Ps−+b Ps+ b− Y− Y R+ F y
( ) ( ) ( )
2 1 2 21 ∑ ii
2s
i
a
Valid for guiding and non-guiding axles.
11
=
=
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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 x
variations along the axle.
Table 4 — Formulae for calculation of bending moment
Zone of the axle
M
x
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
i
F : force(s) on the left of the section considered
i
General outline of M
x
variations
12
=
=
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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 z
Figure 3 — Moments due to braking
'
— the bending component M is due to the vertical forces parallel to the z axis;
x
'
— the bending component M is due to the horizontal forces parallel to the x-axis;
z
'
— the torsional component M is directed along the axle centreline (y-axis); it is due to the forces
y
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 x
masses in motion.
13
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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’
x
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
b)
a,b a,b b b
M’
z
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
f
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 )
i
b b b b
M’
x
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’
z
M’ M’ = 0,3 P’R M’ = 0,3 P’R
y y y
d,e d,e
15
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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
f
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’ =
x
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
M’
x
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’
z
M’ M’ = 0,3 P’R M’ = 0,3 P’R
y y y
d,e d,e
16
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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
x
- b)
(b + s - y) /
2b
b b b b
M’
x
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’
z
M’ M’ = 0,3 P’R M’ = 0,3 P’R
y y y
d,e d,e
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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;
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 .
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 0,3P . It includes the torsional
moment as specified in 6.3.
'
d
P is the proportion of P braked with the method of braking considered.
'
e
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.
f
When the disc is mounted on the wheel web, then y = 0
i
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
y
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 .
y
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.
18
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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 motion
Starting forces
P = 0,55m g
1 1
P = 0,55m g
21
Y = 0,10m g
11
Y = 0,05m g
2 1
H = 0,05mg
1
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:
'
1
MX M+∑ M
xx
'
1
MY=∑ M
y
'
1
MZ=∑ M
z
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 2
32 MX + MZ
σ =
n
3
π d
The value of the shear stress is the following (torsion of beams with a circular section):
16MY
σ =
t
3
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
1
The values, , may be replaced respectively by , and if the moments due to traction are greater than the moments
due to braking.
19
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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 2
d.
32
2 2 2 2 2
σσ=−=σ σ+ 4σ= MX+ MZ+ MY
1 2 nt
3
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
2
— for a solid axle (see Figure 4a): σ=
3
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
2
is a fatigue stress correction factor (i.e. it takes into account the geometry).
20
=
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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 journals
Bahnanwendungen - 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 intérieures
Ta 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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kSIST-TS FprCEN/TS 13103-2:2020
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 Radsatzwellen
This 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
worldwide for CEN national Members.
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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
2
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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.
3
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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 maintenance
EN 15663, Railway applications - Definition of vehicle reference masses
4
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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 3.1
3.3
technical specification
document, describing specific parameter and/or product requirements as an addition to the
requirements of this standard
3.4
guiding axle
first axle (i.e. leading) of a train set
5
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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 abbreviations
Symbol Unit Description
m kg Mass on journals (including bearings and axle boxes)
1
m kg Wheelset mass and masses on the wheelset between rolling circles according to
2
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 2
g
2
m/s Acceleration due to gravity
P
N (m+m )g
1 2
Half the vertical force per wheelset on the rail
2
P
N Vertical static force per journal when the wheelset is loaded symmetrically
0
mg
1
2
P
N Vertical force on the more heavily-loaded journal
1
P N Vertical force on the less heavily-loaded journal
2
'
N Proportion of P braked by any mechanical braking system
P
Y N Wheel/rail horizontal force perpendicular to the rail on the side of the more
1
heavily- loaded journal
Y
N Wheel/rail horizontal force perpendicular to the rail on the side of the less
2
heavily-loaded journal
H
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
1
journal
Q
N Vertical reaction on the wheel situated on the side of the less heavily-loaded
2
journal
F N Forces exerted by the masses of the unsprung elements situated between the
i
two wheels (brake disc(s), pinion, etc.)
F
N Maximum force input of the brake shoes of the same shoeholder on one wheel
f
or interface force of the pads on one disc
M
N∙mm Bending moment due to the masses in motion
x
' '
N∙mm Bending moments due to braking
M , M
x z
'
M N∙mm Torsional moment due to braking
y
'' ''
N∙mm Bending moments due to traction
M , M
x z
''
N∙mm Torsional moment due to traction
M
y
MX , MZ N∙mm Sum of bending moments
6
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MY
N∙mm Sum of torsional moments
MR
N∙mm Resultant moment
2b
mm Distance between vertical force input points on axle journals
2s
mm Distance between wheel rolling circles
h mm Height above the axle centreline of vehicle centre of gravity of masses carried by
1
the wheelset
y Distance between the rolling circle of one wheel and force
mm F
i i
y
mm Abscissa for any section of the axle calculated from the section subject to force
Q
1
Γ
Average friction coefficient between the wheel and the brake shoe or between
the brake pads and the disc
σ 2
N/mm Stress calculated in one section
K
Fatigue stress correction factor
R
mm Nominal wheel radius (Nominal wheel diameter / 2)
mm Brake radius
R
b
d
mm Diameter for one section of the axle
'
mm Bore diameter of a hollow axle
d
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
2 7
N/mm Fatigue limit under rotating bending up to 10 cycles for unnotched test pieces
R
fL
2 7
N/mm Fatigue limit under rotating bending up to 10 cycles for notched test pieces
R
fE
2
a m/s Unbalanced transverse acceleration
q
f
Thrust factor
q
7
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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
8
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The bending moment is due to the vertical forces parallel to the Z axis.
M
x
Unless otherwise defined in the technical specification, the masses (m +m ) to be taken into account for
1 2
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 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 i
x
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
i
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.
i
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
design.
9
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Figure 2 – Forces for calculation of bending moment
Table 3 shows the values of the forces calculated fromm .
1
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
10
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a
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
1
Y = 0
2
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
2s
i
1
Q P s−+b P s+b− Y−Y R+ Fy
( ) ( ) ( )
2 1 2 21 ∑ ii
2s
i
a
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 x
variations along the axle.
11
=
=
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Table 4 – Formulae for calculation of bending moment
M
Zone of the axle
x
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
i
F : force(s) on the left of the section considered
i
General outline of M
x
variations
12
=
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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 z
Figure 3 – Moments due to braking
'
— the bending component M is due to the vertical forces parallel to the z axis;
x
'
— the bending component M is due to the horizontal forces parallel to the x-axis;
z
'
— the torsional component M is directed along the axle centreline (y-axis); it is due to the forces
y
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 x
masses in motion.
13
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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’
x
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’
z
M’ M’ = 0,3P’R M’ = 0,3P’R
y y y
c d c d
14
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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
f
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 )
i
b b b b
M’
x
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’
z
M’ M’ = 0,3 P’R M’ = 0,3 P’R
y y y
d, e d, e
15
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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
f
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’ =
x
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
M’
x
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’
z
M’ M’ = 0,3 P’R M’ = 0,3 P’R
y y y
d, e d, e
16
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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
y)
F Γ (y + s -
f i
M’ = 0
x
b)
(b + s - y) /
2b
b b b b
M’
x
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 b
M’
z
M’ M’ = 0,3 P’R M’ = 0,3 P’R
y y y
d, e d, e
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kSIST-TS FprCEN/TS 13103-2:2020
FprCEN/TS 13103-2:2019 (E)
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:
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
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 0,3P . It includes the torsional
moment as specified in 6.3.
'
d
P is the proportion of P braked with the method of braking considered.
e
'
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.
f
y = 0
i
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
y
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 y
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 .
y
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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kSIST-TS FprCEN/TS 13103-2:2020
FprCEN/TS 13103-2:2019 (E)
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
1
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:
'
1
MX= M +∑M
x x
'
1
MY=∑M
y
'
1
MZ=∑M
z
d
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 MZ
the 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 2
32 MX +MZ
σ =
n
3
πd
The value of the shear stress is the following (torsion of beams with a circular section):
16MY
σ =
t 3
πd
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
' ' ' '' '' ''
1
The valuesM , M y , M may be replaced respectively by M , M and M if the moments due to traction are
z
x x y z
greater 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 2
ford .
32
2 2 2 2 2
σ=σ −σ = σ + 4σ = MX + MZ + MY
1 2 n t
3
πd
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
2
— for a solid axle (see Figure 4a): σ=
3
πd
— 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
2
K is a fatigue stress correction factor (i.e. it takes into account the geometry).
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kSIST-TS FprCEN/TS 13103-2:2020
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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